LMFDB - Embedded newform 930.2.i.h.211.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(211,930)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("930.211");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	930.211
Dual form			930.2.i.h.811.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(1.50000 + 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(1.50000 + 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-2.50000 + 4.33013i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-3.00000 + 5.19615i) q^{13} +(1.50000 + 2.59808i) q^{14} +1.00000 q^{15} +1.00000 q^{16} +(-4.00000 - 6.92820i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(2.00000 + 3.46410i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-1.50000 + 2.59808i) q^{21} +(-2.50000 + 4.33013i) q^{22} +8.00000 q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-3.00000 + 5.19615i) q^{26} -1.00000 q^{27} +(1.50000 + 2.59808i) q^{28} -1.00000 q^{29} +1.00000 q^{30} +(3.50000 - 4.33013i) q^{31} +1.00000 q^{32} -5.00000 q^{33} +(-4.00000 - 6.92820i) q^{34} +3.00000 q^{35} +(-0.500000 + 0.866025i) q^{36} +(1.00000 + 1.73205i) q^{37} +(2.00000 + 3.46410i) q^{38} -6.00000 q^{39} +(0.500000 - 0.866025i) q^{40} +(3.00000 - 5.19615i) q^{41} +(-1.50000 + 2.59808i) q^{42} +(-4.00000 - 6.92820i) q^{43} +(-2.50000 + 4.33013i) q^{44} +(0.500000 + 0.866025i) q^{45} +8.00000 q^{46} +12.0000 q^{47} +(0.500000 + 0.866025i) q^{48} +(-1.00000 + 1.73205i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(4.00000 - 6.92820i) q^{51} +(-3.00000 + 5.19615i) q^{52} +(-2.50000 + 4.33013i) q^{53} -1.00000 q^{54} +(2.50000 + 4.33013i) q^{55} +(1.50000 + 2.59808i) q^{56} +(-2.00000 + 3.46410i) q^{57} -1.00000 q^{58} +(-5.50000 - 9.52628i) q^{59} +1.00000 q^{60} +12.0000 q^{61} +(3.50000 - 4.33013i) q^{62} -3.00000 q^{63} +1.00000 q^{64} +(3.00000 + 5.19615i) q^{65} -5.00000 q^{66} +(-5.00000 + 8.66025i) q^{67} +(-4.00000 - 6.92820i) q^{68} +(4.00000 + 6.92820i) q^{69} +3.00000 q^{70} +(-0.500000 + 0.866025i) q^{72} +(-3.00000 + 5.19615i) q^{73} +(1.00000 + 1.73205i) q^{74} +(0.500000 - 0.866025i) q^{75} +(2.00000 + 3.46410i) q^{76} -15.0000 q^{77} -6.00000 q^{78} +(-4.00000 - 6.92820i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.00000 - 5.19615i) q^{82} +(-1.50000 + 2.59808i) q^{83} +(-1.50000 + 2.59808i) q^{84} -8.00000 q^{85} +(-4.00000 - 6.92820i) q^{86} +(-0.500000 - 0.866025i) q^{87} +(-2.50000 + 4.33013i) q^{88} +(0.500000 + 0.866025i) q^{90} -18.0000 q^{91} +8.00000 q^{92} +(5.50000 + 0.866025i) q^{93} +12.0000 q^{94} +4.00000 q^{95} +(0.500000 + 0.866025i) q^{96} +13.0000 q^{97} +(-1.00000 + 1.73205i) q^{98} +(-2.50000 - 4.33013i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + q^{3} + 2 q^{4} + q^{5} + q^{6} + 3 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + q^3 + 2 * q^4 + q^5 + q^6 + 3 * q^7 + 2 * q^8 - q^9	\( 2 q + 2 q^{2} + q^{3} + 2 q^{4} + q^{5} + q^{6} + 3 q^{7} + 2 q^{8} - q^{9} + q^{10} - 5 q^{11} + q^{12} - 6 q^{13} + 3 q^{14} + 2 q^{15} + 2 q^{16} - 8 q^{17} - q^{18} + 4 q^{19} + q^{20} - 3 q^{21} - 5 q^{22} + 16 q^{23} + q^{24} - q^{25} - 6 q^{26} - 2 q^{27} + 3 q^{28} - 2 q^{29} + 2 q^{30} + 7 q^{31} + 2 q^{32} - 10 q^{33} - 8 q^{34} + 6 q^{35} - q^{36} + 2 q^{37} + 4 q^{38} - 12 q^{39} + q^{40} + 6 q^{41} - 3 q^{42} - 8 q^{43} - 5 q^{44} + q^{45} + 16 q^{46} + 24 q^{47} + q^{48} - 2 q^{49} - q^{50} + 8 q^{51} - 6 q^{52} - 5 q^{53} - 2 q^{54} + 5 q^{55} + 3 q^{56} - 4 q^{57} - 2 q^{58} - 11 q^{59} + 2 q^{60} + 24 q^{61} + 7 q^{62} - 6 q^{63} + 2 q^{64} + 6 q^{65} - 10 q^{66} - 10 q^{67} - 8 q^{68} + 8 q^{69} + 6 q^{70} - q^{72} - 6 q^{73} + 2 q^{74} + q^{75} + 4 q^{76} - 30 q^{77} - 12 q^{78} - 8 q^{79} + q^{80} - q^{81} + 6 q^{82} - 3 q^{83} - 3 q^{84} - 16 q^{85} - 8 q^{86} - q^{87} - 5 q^{88} + q^{90} - 36 q^{91} + 16 q^{92} + 11 q^{93} + 24 q^{94} + 8 q^{95} + q^{96} + 26 q^{97} - 2 q^{98} - 5 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + q^3 + 2 * q^4 + q^5 + q^6 + 3 * q^7 + 2 * q^8 - q^9 + q^10 - 5 * q^11 + q^12 - 6 * q^13 + 3 * q^14 + 2 * q^15 + 2 * q^16 - 8 * q^17 - q^18 + 4 * q^19 + q^20 - 3 * q^21 - 5 * q^22 + 16 * q^23 + q^24 - q^25 - 6 * q^26 - 2 * q^27 + 3 * q^28 - 2 * q^29 + 2 * q^30 + 7 * q^31 + 2 * q^32 - 10 * q^33 - 8 * q^34 + 6 * q^35 - q^36 + 2 * q^37 + 4 * q^38 - 12 * q^39 + q^40 + 6 * q^41 - 3 * q^42 - 8 * q^43 - 5 * q^44 + q^45 + 16 * q^46 + 24 * q^47 + q^48 - 2 * q^49 - q^50 + 8 * q^51 - 6 * q^52 - 5 * q^53 - 2 * q^54 + 5 * q^55 + 3 * q^56 - 4 * q^57 - 2 * q^58 - 11 * q^59 + 2 * q^60 + 24 * q^61 + 7 * q^62 - 6 * q^63 + 2 * q^64 + 6 * q^65 - 10 * q^66 - 10 * q^67 - 8 * q^68 + 8 * q^69 + 6 * q^70 - q^72 - 6 * q^73 + 2 * q^74 + q^75 + 4 * q^76 - 30 * q^77 - 12 * q^78 - 8 * q^79 + q^80 - q^81 + 6 * q^82 - 3 * q^83 - 3 * q^84 - 16 * q^85 - 8 * q^86 - q^87 - 5 * q^88 + q^90 - 36 * q^91 + 16 * q^92 + 11 * q^93 + 24 * q^94 + 8 * q^95 + q^96 + 26 * q^97 - 2 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	1.00000			0.500000
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	1.50000	+	2.59808i	0.566947	+	0.981981i	0.996866	+	0.0791130i	$0.0252088\pi$
$7$	1.50000	+	2.59808i	0.566947	+	0.981981i	−0.429919	+	0.902867i	$0.641458\pi$
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	−2.50000	+	4.33013i	−0.753778	+	1.30558i	0.192201	+	0.981356i	$0.438437\pi$
$11$	−2.50000	+	4.33013i	−0.753778	+	1.30558i	−0.945979	+	0.324227i	$0.894896\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−3.00000	+	5.19615i	−0.832050	+	1.44115i	0.0643593	+	0.997927i	$0.479500\pi$
$13$	−3.00000	+	5.19615i	−0.832050	+	1.44115i	−0.896410	+	0.443227i	$0.853834\pi$
$14$	1.50000	+	2.59808i	0.400892	+	0.694365i
$15$	1.00000			0.258199
$16$	1.00000			0.250000
$17$	−4.00000	−	6.92820i	−0.970143	−	1.68034i	−0.695113	−	0.718900i	$-0.744646\pi$
$17$	−4.00000	−	6.92820i	−0.970143	−	1.68034i	−0.275029	−	0.961436i	$-0.588688\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	0.998899	−	0.0469020i	$-0.0149348\pi$
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	−0.540068	+	0.841621i	$0.681602\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	−1.50000	+	2.59808i	−0.327327	+	0.566947i
$22$	−2.50000	+	4.33013i	−0.533002	+	0.923186i
$23$	8.00000			1.66812			0.834058	−	0.551677i	$-0.186012\pi$
$23$	8.00000			1.66812			0.834058	+	0.551677i	$0.186012\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−3.00000	+	5.19615i	−0.588348	+	1.01905i
$27$	−1.00000			−0.192450
$28$	1.50000	+	2.59808i	0.283473	+	0.490990i
$29$	−1.00000			−0.185695			−0.0928477	−	0.995680i	$-0.529597\pi$
$29$	−1.00000			−0.185695			−0.0928477	+	0.995680i	$0.529597\pi$
$30$	1.00000			0.182574
$31$	3.50000	−	4.33013i	0.628619	−	0.777714i
$31$	3.50000	−	4.33013i	0.628619	−	0.777714i
$32$	1.00000			0.176777
$33$	−5.00000			−0.870388
$34$	−4.00000	−	6.92820i	−0.685994	−	1.18818i
$35$	3.00000			0.507093
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	0.936442	−	0.350823i	$-0.114098\pi$
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	−0.772043	+	0.635571i	$0.780765\pi$
$38$	2.00000	+	3.46410i	0.324443	+	0.561951i
$39$	−6.00000			−0.960769
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	3.00000	−	5.19615i	0.468521	−	0.811503i	−0.530831	−	0.847477i	$-0.678120\pi$
$41$	3.00000	−	5.19615i	0.468521	−	0.811503i	0.999353	+	0.0359748i	$0.0114536\pi$
$42$	−1.50000	+	2.59808i	−0.231455	+	0.400892i
$43$	−4.00000	−	6.92820i	−0.609994	−	1.05654i	−0.991241	−	0.132068i	$-0.957838\pi$
$43$	−4.00000	−	6.92820i	−0.609994	−	1.05654i	0.381246	−	0.924473i	$-0.375495\pi$
$44$	−2.50000	+	4.33013i	−0.376889	+	0.652791i
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$	8.00000			1.17954
$47$	12.0000			1.75038			0.875190	−	0.483779i	$-0.160736\pi$
$47$	12.0000			1.75038			0.875190	+	0.483779i	$0.160736\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	−1.00000	+	1.73205i	−0.142857	+	0.247436i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	4.00000	−	6.92820i	0.560112	−	0.970143i
$52$	−3.00000	+	5.19615i	−0.416025	+	0.720577i
$53$	−2.50000	+	4.33013i	−0.343401	+	0.594789i	−0.985062	−	0.172200i	$-0.944912\pi$
$53$	−2.50000	+	4.33013i	−0.343401	+	0.594789i	0.641661	+	0.766989i	$0.278246\pi$
$54$	−1.00000			−0.136083
$55$	2.50000	+	4.33013i	0.337100	+	0.583874i
$56$	1.50000	+	2.59808i	0.200446	+	0.347183i
$57$	−2.00000	+	3.46410i	−0.264906	+	0.458831i
$58$	−1.00000			−0.131306
$59$	−5.50000	−	9.52628i	−0.716039	−	1.24022i	−0.962557	−	0.271078i	$-0.912620\pi$
$59$	−5.50000	−	9.52628i	−0.716039	−	1.24022i	0.246518	−	0.969138i	$-0.420713\pi$
$60$	1.00000			0.129099
$61$	12.0000			1.53644			0.768221	−	0.640184i	$-0.221142\pi$
$61$	12.0000			1.53644			0.768221	+	0.640184i	$0.221142\pi$
$62$	3.50000	−	4.33013i	0.444500	−	0.549927i
$63$	−3.00000			−0.377964
$64$	1.00000			0.125000
$65$	3.00000	+	5.19615i	0.372104	+	0.644503i
$66$	−5.00000			−0.615457
$67$	−5.00000	+	8.66025i	−0.610847	+	1.05802i	0.380251	+	0.924883i	$0.375838\pi$
$67$	−5.00000	+	8.66025i	−0.610847	+	1.05802i	−0.991098	+	0.133135i	$0.957496\pi$
$68$	−4.00000	−	6.92820i	−0.485071	−	0.840168i
$69$	4.00000	+	6.92820i	0.481543	+	0.834058i
$70$	3.00000			0.358569
$71$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$71$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	−3.00000	+	5.19615i	−0.351123	+	0.608164i	−0.986447	−	0.164083i	$-0.947534\pi$
$73$	−3.00000	+	5.19615i	−0.351123	+	0.608164i	0.635323	+	0.772246i	$0.280867\pi$
$74$	1.00000	+	1.73205i	0.116248	+	0.201347i
$75$	0.500000	−	0.866025i	0.0577350	−	0.100000i
$76$	2.00000	+	3.46410i	0.229416	+	0.397360i
$77$	−15.0000			−1.70941
$78$	−6.00000			−0.679366
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	0.548352	−	0.836247i	$-0.315255\pi$
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	−0.998388	+	0.0567635i	$0.981922\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	3.00000	−	5.19615i	0.331295	−	0.573819i
$83$	−1.50000	+	2.59808i	−0.164646	+	0.285176i	−0.936530	−	0.350588i	$-0.885982\pi$
$83$	−1.50000	+	2.59808i	−0.164646	+	0.285176i	0.771883	+	0.635764i	$0.219315\pi$
$84$	−1.50000	+	2.59808i	−0.163663	+	0.283473i
$85$	−8.00000			−0.867722
$86$	−4.00000	−	6.92820i	−0.431331	−	0.747087i
$87$	−0.500000	−	0.866025i	−0.0536056	−	0.0928477i
$88$	−2.50000	+	4.33013i	−0.266501	+	0.461593i
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$	0.500000	+	0.866025i	0.0527046	+	0.0912871i
$91$	−18.0000			−1.88691
$92$	8.00000			0.834058
$93$	5.50000	+	0.866025i	0.570323	+	0.0898027i
$94$	12.0000			1.23771
$95$	4.00000			0.410391
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	13.0000			1.31995			0.659975	−	0.751288i	$-0.270567\pi$
$97$	13.0000			1.31995			0.659975	+	0.751288i	$0.270567\pi$
$98$	−1.00000	+	1.73205i	−0.101015	+	0.174964i
$99$	−2.50000	−	4.33013i	−0.251259	−	0.435194i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−1.00000			−0.0995037			−0.0497519	−	0.998762i	$-0.515843\pi$
$101$	−1.00000			−0.0995037			−0.0497519	+	0.998762i	$0.515843\pi$
$102$	4.00000	−	6.92820i	0.396059	−	0.685994i
$103$	3.50000	−	6.06218i	0.344865	−	0.597324i	−0.640464	−	0.767988i	$-0.721258\pi$
$103$	3.50000	−	6.06218i	0.344865	−	0.597324i	0.985329	+	0.170664i	$0.0545913\pi$
$104$	−3.00000	+	5.19615i	−0.294174	+	0.509525i
$105$	1.50000	+	2.59808i	0.146385	+	0.253546i
$106$	−2.50000	+	4.33013i	−0.242821	+	0.420579i
$107$	2.50000	+	4.33013i	0.241684	+	0.418609i	0.961194	−	0.275873i	$-0.0889669\pi$
$107$	2.50000	+	4.33013i	0.241684	+	0.418609i	−0.719510	+	0.694482i	$0.755634\pi$
$108$	−1.00000			−0.0962250
$109$	−12.0000			−1.14939			−0.574696	−	0.818367i	$-0.694880\pi$
$109$	−12.0000			−1.14939			−0.574696	+	0.818367i	$0.694880\pi$
$110$	2.50000	+	4.33013i	0.238366	+	0.412861i
$111$	−1.00000	+	1.73205i	−0.0949158	+	0.164399i
$112$	1.50000	+	2.59808i	0.141737	+	0.245495i
$113$	5.00000	−	8.66025i	0.470360	−	0.814688i	−0.529065	−	0.848581i	$-0.677457\pi$
$113$	5.00000	−	8.66025i	0.470360	−	0.814688i	0.999425	+	0.0338931i	$0.0107906\pi$
$114$	−2.00000	+	3.46410i	−0.187317	+	0.324443i
$115$	4.00000	−	6.92820i	0.373002	−	0.646058i
$116$	−1.00000			−0.0928477
$117$	−3.00000	−	5.19615i	−0.277350	−	0.480384i
$118$	−5.50000	−	9.52628i	−0.506316	−	0.876965i
$119$	12.0000	−	20.7846i	1.10004	−	1.90532i
$120$	1.00000			0.0912871
$121$	−7.00000	−	12.1244i	−0.636364	−	1.10221i
$122$	12.0000			1.08643
$123$	6.00000			0.541002
$124$	3.50000	−	4.33013i	0.314309	−	0.388857i
$125$	−1.00000			−0.0894427
$126$	−3.00000			−0.267261
$127$	−3.50000	−	6.06218i	−0.310575	−	0.537931i	0.667912	−	0.744240i	$-0.267188\pi$
$127$	−3.50000	−	6.06218i	−0.310575	−	0.537931i	−0.978487	+	0.206309i	$0.933855\pi$
$128$	1.00000			0.0883883
$129$	4.00000	−	6.92820i	0.352180	−	0.609994i
$130$	3.00000	+	5.19615i	0.263117	+	0.455733i
$131$	8.00000	+	13.8564i	0.698963	+	1.21064i	0.968826	+	0.247741i	$0.0796882\pi$
$131$	8.00000	+	13.8564i	0.698963	+	1.21064i	−0.269863	+	0.962899i	$0.586978\pi$
$132$	−5.00000			−0.435194
$133$	−6.00000	+	10.3923i	−0.520266	+	0.901127i
$134$	−5.00000	+	8.66025i	−0.431934	+	0.748132i
$135$	−0.500000	+	0.866025i	−0.0430331	+	0.0745356i
$136$	−4.00000	−	6.92820i	−0.342997	−	0.594089i
$137$	3.00000	−	5.19615i	0.256307	−	0.443937i	−0.708942	−	0.705266i	$-0.750827\pi$
$137$	3.00000	−	5.19615i	0.256307	−	0.443937i	0.965250	+	0.261329i	$0.0841608\pi$
$138$	4.00000	+	6.92820i	0.340503	+	0.589768i
$139$	−10.0000			−0.848189			−0.424094	−	0.905618i	$-0.639408\pi$
$139$	−10.0000			−0.848189			−0.424094	+	0.905618i	$0.639408\pi$
$140$	3.00000			0.253546
$141$	6.00000	+	10.3923i	0.505291	+	0.875190i
$142$		0			0
$143$	−15.0000	−	25.9808i	−1.25436	−	2.17262i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−0.500000	+	0.866025i	−0.0415227	+	0.0719195i
$146$	−3.00000	+	5.19615i	−0.248282	+	0.430037i
$147$	−2.00000			−0.164957
$148$	1.00000	+	1.73205i	0.0821995	+	0.142374i
$149$	−6.50000	−	11.2583i	−0.532501	−	0.922318i	−0.999280	−	0.0379444i	$-0.987919\pi$
$149$	−6.50000	−	11.2583i	−0.532501	−	0.922318i	0.466779	−	0.884374i	$-0.345414\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	−5.00000			−0.406894			−0.203447	−	0.979086i	$-0.565214\pi$
$151$	−5.00000			−0.406894			−0.203447	+	0.979086i	$0.565214\pi$
$152$	2.00000	+	3.46410i	0.162221	+	0.280976i
$153$	8.00000			0.646762
$154$	−15.0000			−1.20873
$155$	−2.00000	−	5.19615i	−0.160644	−	0.417365i
$156$	−6.00000			−0.480384
$157$		0			0			−	1.00000i	$-0.5\pi$
$157$		0			0				1.00000i	$0.5\pi$
$158$	−4.00000	−	6.92820i	−0.318223	−	0.551178i
$159$	−5.00000			−0.396526
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	12.0000	+	20.7846i	0.945732	+	1.63806i
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$		0			0			−	1.00000i	$-0.5\pi$
$163$		0			0				1.00000i	$0.5\pi$
$164$	3.00000	−	5.19615i	0.234261	−	0.405751i
$165$	−2.50000	+	4.33013i	−0.194625	+	0.337100i
$166$	−1.50000	+	2.59808i	−0.116423	+	0.201650i
$167$	9.00000	+	15.5885i	0.696441	+	1.20627i	0.969693	+	0.244328i	$0.0785675\pi$
$167$	9.00000	+	15.5885i	0.696441	+	1.20627i	−0.273252	+	0.961943i	$0.588099\pi$
$168$	−1.50000	+	2.59808i	−0.115728	+	0.200446i
$169$	−11.5000	−	19.9186i	−0.884615	−	1.53220i
$170$	−8.00000			−0.613572
$171$	−4.00000			−0.305888
$172$	−4.00000	−	6.92820i	−0.304997	−	0.528271i
$173$	2.50000	−	4.33013i	0.190071	−	0.329213i	−0.755202	−	0.655492i	$-0.772461\pi$
$173$	2.50000	−	4.33013i	0.190071	−	0.329213i	0.945274	+	0.326278i	$0.105795\pi$
$174$	−0.500000	−	0.866025i	−0.0379049	−	0.0656532i
$175$	1.50000	−	2.59808i	0.113389	−	0.196396i
$176$	−2.50000	+	4.33013i	−0.188445	+	0.326396i
$177$	5.50000	−	9.52628i	0.413405	−	0.716039i
$178$		0			0
$179$	−5.50000	−	9.52628i	−0.411089	−	0.712028i	0.583920	−	0.811811i	$-0.301518\pi$
$179$	−5.50000	−	9.52628i	−0.411089	−	0.712028i	−0.995009	+	0.0997838i	$0.968185\pi$
$180$	0.500000	+	0.866025i	0.0372678	+	0.0645497i
$181$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$181$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$182$	−18.0000			−1.33425
$183$	6.00000	+	10.3923i	0.443533	+	0.768221i
$184$	8.00000			0.589768
$185$	2.00000			0.147043
$186$	5.50000	+	0.866025i	0.403280	+	0.0635001i
$187$	40.0000			2.92509
$188$	12.0000			0.875190
$189$	−1.50000	−	2.59808i	−0.109109	−	0.188982i
$190$	4.00000			0.290191
$191$	13.0000	−	22.5167i	0.940647	−	1.62925i	0.176406	−	0.984317i	$-0.443553\pi$
$191$	13.0000	−	22.5167i	0.940647	−	1.62925i	0.764241	−	0.644931i	$-0.223114\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	6.50000	+	11.2583i	0.467880	+	0.810392i	0.999326	−	0.0366998i	$-0.0116845\pi$
$193$	6.50000	+	11.2583i	0.467880	+	0.810392i	−0.531446	+	0.847092i	$0.678351\pi$
$194$	13.0000			0.933346
$195$	−3.00000	+	5.19615i	−0.214834	+	0.372104i
$196$	−1.00000	+	1.73205i	−0.0714286	+	0.123718i
$197$	5.00000	−	8.66025i	0.356235	−	0.617018i	−0.631093	−	0.775707i	$-0.717394\pi$
$197$	5.00000	−	8.66025i	0.356235	−	0.617018i	0.987329	+	0.158689i	$0.0507268\pi$
$198$	−2.50000	−	4.33013i	−0.177667	−	0.307729i
$199$	−9.50000	+	16.4545i	−0.673437	+	1.16643i	0.303486	+	0.952836i	$0.401849\pi$
$199$	−9.50000	+	16.4545i	−0.673437	+	1.16643i	−0.976923	+	0.213591i	$0.931484\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	−10.0000			−0.705346
$202$	−1.00000			−0.0703598
$203$	−1.50000	−	2.59808i	−0.105279	−	0.182349i
$204$	4.00000	−	6.92820i	0.280056	−	0.485071i
$205$	−3.00000	−	5.19615i	−0.209529	−	0.362915i
$206$	3.50000	−	6.06218i	0.243857	−	0.422372i
$207$	−4.00000	+	6.92820i	−0.278019	+	0.481543i
$208$	−3.00000	+	5.19615i	−0.208013	+	0.360288i
$209$	−20.0000			−1.38343
$210$	1.50000	+	2.59808i	0.103510	+	0.179284i
$211$	8.00000	+	13.8564i	0.550743	+	0.953914i	0.998221	+	0.0596196i	$0.0189888\pi$
$211$	8.00000	+	13.8564i	0.550743	+	0.953914i	−0.447478	+	0.894295i	$0.647678\pi$
$212$	−2.50000	+	4.33013i	−0.171701	+	0.297394i
$213$		0			0
$214$	2.50000	+	4.33013i	0.170896	+	0.296001i
$215$	−8.00000			−0.545595
$216$	−1.00000			−0.0680414
$217$	16.5000	+	2.59808i	1.12009	+	0.176369i
$218$	−12.0000			−0.812743
$219$	−6.00000			−0.405442
$220$	2.50000	+	4.33013i	0.168550	+	0.291937i
$221$	48.0000			3.22883
$222$	−1.00000	+	1.73205i	−0.0671156	+	0.116248i
$223$	−0.500000	−	0.866025i	−0.0334825	−	0.0579934i	0.848799	−	0.528716i	$-0.177326\pi$
$223$	−0.500000	−	0.866025i	−0.0334825	−	0.0579934i	−0.882281	+	0.470723i	$0.843993\pi$
$224$	1.50000	+	2.59808i	0.100223	+	0.173591i
$225$	1.00000			0.0666667
$226$	5.00000	−	8.66025i	0.332595	−	0.576072i
$227$	12.5000	−	21.6506i	0.829654	−	1.43700i	−0.0686556	−	0.997640i	$-0.521871\pi$
$227$	12.5000	−	21.6506i	0.829654	−	1.43700i	0.898310	−	0.439363i	$-0.144796\pi$
$228$	−2.00000	+	3.46410i	−0.132453	+	0.229416i
$229$	1.00000	+	1.73205i	0.0660819	+	0.114457i	0.897173	−	0.441679i	$-0.145617\pi$
$229$	1.00000	+	1.73205i	0.0660819	+	0.114457i	−0.831092	+	0.556136i	$0.812283\pi$
$230$	4.00000	−	6.92820i	0.263752	−	0.456832i
$231$	−7.50000	−	12.9904i	−0.493464	−	0.854704i
$232$	−1.00000			−0.0656532
$233$	−14.0000			−0.917170			−0.458585	−	0.888650i	$-0.651644\pi$
$233$	−14.0000			−0.917170			−0.458585	+	0.888650i	$0.651644\pi$
$234$	−3.00000	−	5.19615i	−0.196116	−	0.339683i
$235$	6.00000	−	10.3923i	0.391397	−	0.677919i
$236$	−5.50000	−	9.52628i	−0.358020	−	0.620108i
$237$	4.00000	−	6.92820i	0.259828	−	0.450035i
$238$	12.0000	−	20.7846i	0.777844	−	1.34727i
$239$	−3.00000	+	5.19615i	−0.194054	+	0.336111i	−0.946590	−	0.322440i	$-0.895497\pi$
$239$	−3.00000	+	5.19615i	−0.194054	+	0.336111i	0.752536	+	0.658551i	$0.228830\pi$
$240$	1.00000			0.0645497
$241$	2.50000	+	4.33013i	0.161039	+	0.278928i	0.935242	−	0.354010i	$-0.115182\pi$
$241$	2.50000	+	4.33013i	0.161039	+	0.278928i	−0.774202	+	0.632938i	$0.781849\pi$
$242$	−7.00000	−	12.1244i	−0.449977	−	0.779383i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	12.0000			0.768221
$245$	1.00000	+	1.73205i	0.0638877	+	0.110657i
$246$	6.00000			0.382546
$247$	−24.0000			−1.52708
$248$	3.50000	−	4.33013i	0.222250	−	0.274963i
$249$	−3.00000			−0.190117
$250$	−1.00000			−0.0632456
$251$	−10.0000	−	17.3205i	−0.631194	−	1.09326i	−0.987308	−	0.158818i	$-0.949232\pi$
$251$	−10.0000	−	17.3205i	−0.631194	−	1.09326i	0.356113	−	0.934443i	$-0.384102\pi$
$252$	−3.00000			−0.188982
$253$	−20.0000	+	34.6410i	−1.25739	+	2.17786i
$254$	−3.50000	−	6.06218i	−0.219610	−	0.380375i
$255$	−4.00000	−	6.92820i	−0.250490	−	0.433861i
$256$	1.00000			0.0625000
$257$	−8.00000	+	13.8564i	−0.499026	+	0.864339i	−0.999999	−	0.00112398i	$-0.999642\pi$
$257$	−8.00000	+	13.8564i	−0.499026	+	0.864339i	0.500973	+	0.865463i	$0.332976\pi$
$258$	4.00000	−	6.92820i	0.249029	−	0.431331i
$259$	−3.00000	+	5.19615i	−0.186411	+	0.322873i
$260$	3.00000	+	5.19615i	0.186052	+	0.322252i
$261$	0.500000	−	0.866025i	0.0309492	−	0.0536056i
$262$	8.00000	+	13.8564i	0.494242	+	0.856052i
$263$	−6.00000			−0.369976			−0.184988	−	0.982741i	$-0.559225\pi$
$263$	−6.00000			−0.369976			−0.184988	+	0.982741i	$0.559225\pi$
$264$	−5.00000			−0.307729
$265$	2.50000	+	4.33013i	0.153574	+	0.265998i
$266$	−6.00000	+	10.3923i	−0.367884	+	0.637193i
$267$		0			0
$268$	−5.00000	+	8.66025i	−0.305424	+	0.529009i
$269$	9.00000	−	15.5885i	0.548740	−	0.950445i	−0.449622	−	0.893219i	$-0.648441\pi$
$269$	9.00000	−	15.5885i	0.548740	−	0.950445i	0.998361	−	0.0572259i	$-0.0182255\pi$
$270$	−0.500000	+	0.866025i	−0.0304290	+	0.0527046i
$271$	−17.0000			−1.03268			−0.516338	−	0.856385i	$-0.672705\pi$
$271$	−17.0000			−1.03268			−0.516338	+	0.856385i	$0.672705\pi$
$272$	−4.00000	−	6.92820i	−0.242536	−	0.420084i
$273$	−9.00000	−	15.5885i	−0.544705	−	0.943456i
$274$	3.00000	−	5.19615i	0.181237	−	0.313911i
$275$	5.00000			0.301511
$276$	4.00000	+	6.92820i	0.240772	+	0.417029i
$277$	−24.0000			−1.44202			−0.721010	−	0.692925i	$-0.756322\pi$
$277$	−24.0000			−1.44202			−0.721010	+	0.692925i	$0.756322\pi$
$278$	−10.0000			−0.599760
$279$	2.00000	+	5.19615i	0.119737	+	0.311086i
$280$	3.00000			0.179284
$281$	−8.00000			−0.477240			−0.238620	−	0.971113i	$-0.576695\pi$
$281$	−8.00000			−0.477240			−0.238620	+	0.971113i	$0.576695\pi$
$282$	6.00000	+	10.3923i	0.357295	+	0.618853i
$283$	−6.00000			−0.356663			−0.178331	−	0.983970i	$-0.557070\pi$
$283$	−6.00000			−0.356663			−0.178331	+	0.983970i	$0.557070\pi$
$284$		0			0
$285$	2.00000	+	3.46410i	0.118470	+	0.205196i
$286$	−15.0000	−	25.9808i	−0.886969	−	1.53627i
$287$	18.0000			1.06251
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	−23.5000	+	40.7032i	−1.38235	+	2.39431i
$290$	−0.500000	+	0.866025i	−0.0293610	+	0.0508548i
$291$	6.50000	+	11.2583i	0.381037	+	0.659975i
$292$	−3.00000	+	5.19615i	−0.175562	+	0.304082i
$293$	−4.50000	−	7.79423i	−0.262893	−	0.455344i	0.704117	−	0.710084i	$-0.251343\pi$
$293$	−4.50000	−	7.79423i	−0.262893	−	0.455344i	−0.967009	+	0.254741i	$0.918010\pi$
$294$	−2.00000			−0.116642
$295$	−11.0000			−0.640445
$296$	1.00000	+	1.73205i	0.0581238	+	0.100673i
$297$	2.50000	−	4.33013i	0.145065	−	0.251259i
$298$	−6.50000	−	11.2583i	−0.376535	−	0.652178i
$299$	−24.0000	+	41.5692i	−1.38796	+	2.40401i
$300$	0.500000	−	0.866025i	0.0288675	−	0.0500000i
$301$	12.0000	−	20.7846i	0.691669	−	1.19800i
$302$	−5.00000			−0.287718
$303$	−0.500000	−	0.866025i	−0.0287242	−	0.0497519i
$304$	2.00000	+	3.46410i	0.114708	+	0.198680i
$305$	6.00000	−	10.3923i	0.343559	−	0.595062i
$306$	8.00000			0.457330
$307$	−1.00000	−	1.73205i	−0.0570730	−	0.0988534i	0.836077	−	0.548612i	$-0.184843\pi$
$307$	−1.00000	−	1.73205i	−0.0570730	−	0.0988534i	−0.893150	+	0.449758i	$0.851510\pi$
$308$	−15.0000			−0.854704
$309$	7.00000			0.398216
$310$	−2.00000	−	5.19615i	−0.113592	−	0.295122i
$311$	−22.0000			−1.24751			−0.623753	−	0.781622i	$-0.714393\pi$
$311$	−22.0000			−1.24751			−0.623753	+	0.781622i	$0.714393\pi$
$312$	−6.00000			−0.339683
$313$	0.500000	+	0.866025i	0.0282617	+	0.0489506i	0.879810	−	0.475325i	$-0.157669\pi$
$313$	0.500000	+	0.866025i	0.0282617	+	0.0489506i	−0.851549	+	0.524276i	$0.824336\pi$
$314$		0			0
$315$	−1.50000	+	2.59808i	−0.0845154	+	0.146385i
$316$	−4.00000	−	6.92820i	−0.225018	−	0.389742i
$317$	15.5000	+	26.8468i	0.870567	+	1.50787i	0.861411	+	0.507908i	$0.169581\pi$
$317$	15.5000	+	26.8468i	0.870567	+	1.50787i	0.00915525	+	0.999958i	$0.497086\pi$
$318$	−5.00000			−0.280386
$319$	2.50000	−	4.33013i	0.139973	−	0.242441i
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	−2.50000	+	4.33013i	−0.139536	+	0.241684i
$322$	12.0000	+	20.7846i	0.668734	+	1.15828i
$323$	16.0000	−	27.7128i	0.890264	−	1.54198i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	6.00000			0.332820
$326$		0			0
$327$	−6.00000	−	10.3923i	−0.331801	−	0.574696i
$328$	3.00000	−	5.19615i	0.165647	−	0.286910i
$329$	18.0000	+	31.1769i	0.992372	+	1.71884i
$330$	−2.50000	+	4.33013i	−0.137620	+	0.238366i
$331$	6.00000	−	10.3923i	0.329790	−	0.571213i	−0.652680	−	0.757634i	$-0.726355\pi$
$331$	6.00000	−	10.3923i	0.329790	−	0.571213i	0.982470	+	0.186421i	$0.0596888\pi$
$332$	−1.50000	+	2.59808i	−0.0823232	+	0.142588i
$333$	−2.00000			−0.109599
$334$	9.00000	+	15.5885i	0.492458	+	0.852962i
$335$	5.00000	+	8.66025i	0.273179	+	0.473160i
$336$	−1.50000	+	2.59808i	−0.0818317	+	0.141737i
$337$	23.0000			1.25289			0.626445	−	0.779466i	$-0.284509\pi$
$337$	23.0000			1.25289			0.626445	+	0.779466i	$0.284509\pi$
$338$	−11.5000	−	19.9186i	−0.625518	−	1.08343i
$339$	10.0000			0.543125
$340$	−8.00000			−0.433861
$341$	10.0000	+	25.9808i	0.541530	+	1.40694i
$342$	−4.00000			−0.216295
$343$	15.0000			0.809924
$344$	−4.00000	−	6.92820i	−0.215666	−	0.373544i
$345$	8.00000			0.430706
$346$	2.50000	−	4.33013i	0.134401	−	0.232789i
$347$	−2.50000	−	4.33013i	−0.134207	−	0.232453i	0.791087	−	0.611703i	$-0.209515\pi$
$347$	−2.50000	−	4.33013i	−0.134207	−	0.232453i	−0.925294	+	0.379250i	$0.876182\pi$
$348$	−0.500000	−	0.866025i	−0.0268028	−	0.0464238i
$349$	−20.0000			−1.07058			−0.535288	−	0.844670i	$-0.679797\pi$
$349$	−20.0000			−1.07058			−0.535288	+	0.844670i	$0.679797\pi$
$350$	1.50000	−	2.59808i	0.0801784	−	0.138873i
$351$	3.00000	−	5.19615i	0.160128	−	0.277350i
$352$	−2.50000	+	4.33013i	−0.133250	+	0.230797i
$353$	9.00000	+	15.5885i	0.479022	+	0.829690i	0.999711	−	0.0240566i	$-0.00765819\pi$
$353$	9.00000	+	15.5885i	0.479022	+	0.829690i	−0.520689	+	0.853746i	$0.674325\pi$
$354$	5.50000	−	9.52628i	0.292322	−	0.506316i
$355$		0			0
$356$		0			0
$357$	24.0000			1.27021
$358$	−5.50000	−	9.52628i	−0.290684	−	0.503480i
$359$	−2.00000	+	3.46410i	−0.105556	+	0.182828i	−0.913965	−	0.405793i	$-0.866996\pi$
$359$	−2.00000	+	3.46410i	−0.105556	+	0.182828i	0.808409	+	0.588621i	$0.200329\pi$
$360$	0.500000	+	0.866025i	0.0263523	+	0.0456435i
$361$	1.50000	−	2.59808i	0.0789474	−	0.136741i
$362$		0			0
$363$	7.00000	−	12.1244i	0.367405	−	0.636364i
$364$	−18.0000			−0.943456
$365$	3.00000	+	5.19615i	0.157027	+	0.271979i
$366$	6.00000	+	10.3923i	0.313625	+	0.543214i
$367$	−2.00000	+	3.46410i	−0.104399	+	0.180825i	−0.913493	−	0.406855i	$-0.866625\pi$
$367$	−2.00000	+	3.46410i	−0.104399	+	0.180825i	0.809093	+	0.587680i	$0.199959\pi$
$368$	8.00000			0.417029
$369$	3.00000	+	5.19615i	0.156174	+	0.270501i
$370$	2.00000			0.103975
$371$	−15.0000			−0.778761
$372$	5.50000	+	0.866025i	0.285162	+	0.0449013i
$373$	4.00000			0.207112			0.103556	−	0.994624i	$-0.466978\pi$
$373$	4.00000			0.207112			0.103556	+	0.994624i	$0.466978\pi$
$374$	40.0000			2.06835
$375$	−0.500000	−	0.866025i	−0.0258199	−	0.0447214i
$376$	12.0000			0.618853
$377$	3.00000	−	5.19615i	0.154508	−	0.267615i
$378$	−1.50000	−	2.59808i	−0.0771517	−	0.133631i
$379$	−14.0000	−	24.2487i	−0.719132	−	1.24557i	−0.961344	−	0.275349i	$-0.911206\pi$
$379$	−14.0000	−	24.2487i	−0.719132	−	1.24557i	0.242213	−	0.970223i	$-0.422127\pi$
$380$	4.00000			0.205196
$381$	3.50000	−	6.06218i	0.179310	−	0.310575i
$382$	13.0000	−	22.5167i	0.665138	−	1.15205i
$383$	−11.0000	+	19.0526i	−0.562074	+	0.973540i	0.435242	+	0.900314i	$0.356663\pi$
$383$	−11.0000	+	19.0526i	−0.562074	+	0.973540i	−0.997315	+	0.0732266i	$0.976670\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	−7.50000	+	12.9904i	−0.382235	+	0.662051i
$386$	6.50000	+	11.2583i	0.330841	+	0.573034i
$387$	8.00000			0.406663
$388$	13.0000			0.659975
$389$	−15.0000	−	25.9808i	−0.760530	−	1.31728i	−0.942578	−	0.333987i	$-0.891606\pi$
$389$	−15.0000	−	25.9808i	−0.760530	−	1.31728i	0.182047	−	0.983290i	$-0.441728\pi$
$390$	−3.00000	+	5.19615i	−0.151911	+	0.263117i
$391$	−32.0000	−	55.4256i	−1.61831	−	2.80299i
$392$	−1.00000	+	1.73205i	−0.0505076	+	0.0874818i
$393$	−8.00000	+	13.8564i	−0.403547	+	0.698963i
$394$	5.00000	−	8.66025i	0.251896	−	0.436297i
$395$	−8.00000			−0.402524
$396$	−2.50000	−	4.33013i	−0.125630	−	0.217597i
$397$	10.0000	+	17.3205i	0.501886	+	0.869291i	0.999998	+	0.00217869i	$0.000693499\pi$
$397$	10.0000	+	17.3205i	0.501886	+	0.869291i	−0.498112	+	0.867113i	$0.665973\pi$
$398$	−9.50000	+	16.4545i	−0.476192	+	0.824789i
$399$	−12.0000			−0.600751
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	2.00000			0.0998752			0.0499376	−	0.998752i	$-0.484098\pi$
$401$	2.00000			0.0998752			0.0499376	+	0.998752i	$0.484098\pi$
$402$	−10.0000			−0.498755
$403$	12.0000	+	31.1769i	0.597763	+	1.55303i
$404$	−1.00000			−0.0497519
$405$	−1.00000			−0.0496904
$406$	−1.50000	−	2.59808i	−0.0744438	−	0.128940i
$407$	−10.0000			−0.495682
$408$	4.00000	−	6.92820i	0.198030	−	0.342997i
$409$	4.50000	+	7.79423i	0.222511	+	0.385400i	0.955570	−	0.294765i	$-0.0952414\pi$
$409$	4.50000	+	7.79423i	0.222511	+	0.385400i	−0.733059	+	0.680165i	$0.761908\pi$
$410$	−3.00000	−	5.19615i	−0.148159	−	0.256620i
$411$	6.00000			0.295958
$412$	3.50000	−	6.06218i	0.172433	−	0.298662i
$413$	16.5000	−	28.5788i	0.811912	−	1.40627i
$414$	−4.00000	+	6.92820i	−0.196589	+	0.340503i
$415$	1.50000	+	2.59808i	0.0736321	+	0.127535i
$416$	−3.00000	+	5.19615i	−0.147087	+	0.254762i
$417$	−5.00000	−	8.66025i	−0.244851	−	0.424094i
$418$	−20.0000			−0.978232
$419$	−27.0000			−1.31904			−0.659518	−	0.751689i	$-0.729240\pi$
$419$	−27.0000			−1.31904			−0.659518	+	0.751689i	$0.729240\pi$
$420$	1.50000	+	2.59808i	0.0731925	+	0.126773i
$421$	−16.0000	+	27.7128i	−0.779792	+	1.35064i	0.152269	+	0.988339i	$0.451342\pi$
$421$	−16.0000	+	27.7128i	−0.779792	+	1.35064i	−0.932061	+	0.362301i	$0.881991\pi$
$422$	8.00000	+	13.8564i	0.389434	+	0.674519i
$423$	−6.00000	+	10.3923i	−0.291730	+	0.505291i
$424$	−2.50000	+	4.33013i	−0.121411	+	0.210290i
$425$	−4.00000	+	6.92820i	−0.194029	+	0.336067i
$426$		0			0
$427$	18.0000	+	31.1769i	0.871081	+	1.50876i
$428$	2.50000	+	4.33013i	0.120842	+	0.209305i
$429$	15.0000	−	25.9808i	0.724207	−	1.25436i
$430$	−8.00000			−0.385794
$431$	15.0000	+	25.9808i	0.722525	+	1.25145i	0.959985	+	0.280052i	$0.0903517\pi$
$431$	15.0000	+	25.9808i	0.722525	+	1.25145i	−0.237460	+	0.971397i	$0.576315\pi$
$432$	−1.00000			−0.0481125
$433$	14.0000			0.672797			0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000			0.672797			0.336399	+	0.941720i	$0.390791\pi$
$434$	16.5000	+	2.59808i	0.792025	+	0.124712i
$435$	−1.00000			−0.0479463
$436$	−12.0000			−0.574696
$437$	16.0000	+	27.7128i	0.765384	+	1.32568i
$438$	−6.00000			−0.286691
$439$	2.50000	−	4.33013i	0.119318	−	0.206666i	−0.800179	−	0.599761i	$-0.795262\pi$
$439$	2.50000	−	4.33013i	0.119318	−	0.206666i	0.919498	+	0.393095i	$0.128596\pi$
$440$	2.50000	+	4.33013i	0.119183	+	0.206431i
$441$	−1.00000	−	1.73205i	−0.0476190	−	0.0824786i
$442$	48.0000			2.28313
$443$	8.00000	−	13.8564i	0.380091	−	0.658338i	−0.610984	−	0.791643i	$-0.709226\pi$
$443$	8.00000	−	13.8564i	0.380091	−	0.658338i	0.991075	+	0.133306i	$0.0425592\pi$
$444$	−1.00000	+	1.73205i	−0.0474579	+	0.0821995i
$445$		0			0
$446$	−0.500000	−	0.866025i	−0.0236757	−	0.0410075i
$447$	6.50000	−	11.2583i	0.307439	−	0.532501i
$448$	1.50000	+	2.59808i	0.0708683	+	0.122748i
$449$	−24.0000			−1.13263			−0.566315	−	0.824189i	$-0.691631\pi$
$449$	−24.0000			−1.13263			−0.566315	+	0.824189i	$0.691631\pi$
$450$	1.00000			0.0471405
$451$	15.0000	+	25.9808i	0.706322	+	1.22339i
$452$	5.00000	−	8.66025i	0.235180	−	0.407344i
$453$	−2.50000	−	4.33013i	−0.117460	−	0.203447i
$454$	12.5000	−	21.6506i	0.586654	−	1.01611i
$455$	−9.00000	+	15.5885i	−0.421927	+	0.730798i
$456$	−2.00000	+	3.46410i	−0.0936586	+	0.162221i
$457$	−22.0000			−1.02912			−0.514558	−	0.857455i	$-0.672044\pi$
$457$	−22.0000			−1.02912			−0.514558	+	0.857455i	$0.672044\pi$
$458$	1.00000	+	1.73205i	0.0467269	+	0.0809334i
$459$	4.00000	+	6.92820i	0.186704	+	0.323381i
$460$	4.00000	−	6.92820i	0.186501	−	0.323029i
$461$	1.00000			0.0465746			0.0232873	−	0.999729i	$-0.492587\pi$
$461$	1.00000			0.0465746			0.0232873	+	0.999729i	$0.492587\pi$
$462$	−7.50000	−	12.9904i	−0.348932	−	0.604367i
$463$	27.0000			1.25480			0.627398	−	0.778699i	$-0.284120\pi$
$463$	27.0000			1.25480			0.627398	+	0.778699i	$0.284120\pi$
$464$	−1.00000			−0.0464238
$465$	3.50000	−	4.33013i	0.162309	−	0.200805i
$466$	−14.0000			−0.648537
$467$	23.0000			1.06431			0.532157	−	0.846646i	$-0.321382\pi$
$467$	23.0000			1.06431			0.532157	+	0.846646i	$0.321382\pi$
$468$	−3.00000	−	5.19615i	−0.138675	−	0.240192i
$469$	−30.0000			−1.38527
$470$	6.00000	−	10.3923i	0.276759	−	0.479361i
$471$		0			0
$472$	−5.50000	−	9.52628i	−0.253158	−	0.438483i
$473$	40.0000			1.83920
$474$	4.00000	−	6.92820i	0.183726	−	0.318223i
$475$	2.00000	−	3.46410i	0.0917663	−	0.158944i
$476$	12.0000	−	20.7846i	0.550019	−	0.952661i
$477$	−2.50000	−	4.33013i	−0.114467	−	0.198263i
$478$	−3.00000	+	5.19615i	−0.137217	+	0.237666i
$479$	−6.00000	−	10.3923i	−0.274147	−	0.474837i	0.695773	−	0.718262i	$-0.255062\pi$
$479$	−6.00000	−	10.3923i	−0.274147	−	0.474837i	−0.969920	+	0.243426i	$0.921729\pi$
$480$	1.00000			0.0456435
$481$	−12.0000			−0.547153
$482$	2.50000	+	4.33013i	0.113872	+	0.197232i
$483$	−12.0000	+	20.7846i	−0.546019	+	0.945732i
$484$	−7.00000	−	12.1244i	−0.318182	−	0.551107i
$485$	6.50000	−	11.2583i	0.295150	−	0.511214i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	−8.50000	+	14.7224i	−0.385172	+	0.667137i	−0.991793	−	0.127854i	$-0.959191\pi$
$487$	−8.50000	+	14.7224i	−0.385172	+	0.667137i	0.606621	+	0.794991i	$0.292524\pi$
$488$	12.0000			0.543214
$489$		0			0
$490$	1.00000	+	1.73205i	0.0451754	+	0.0782461i
$491$	3.50000	−	6.06218i	0.157953	−	0.273582i	−0.776178	−	0.630514i	$-0.782844\pi$
$491$	3.50000	−	6.06218i	0.157953	−	0.273582i	0.934130	+	0.356932i	$0.116177\pi$
$492$	6.00000			0.270501
$493$	4.00000	+	6.92820i	0.180151	+	0.312031i
$494$	−24.0000			−1.07981
$495$	−5.00000			−0.224733
$496$	3.50000	−	4.33013i	0.157155	−	0.194428i
$497$		0			0
$498$	−3.00000			−0.134433
$499$	19.0000	+	32.9090i	0.850557	+	1.47321i	0.880707	+	0.473662i	$0.157068\pi$
$499$	19.0000	+	32.9090i	0.850557	+	1.47321i	−0.0301498	+	0.999545i	$0.509598\pi$
$500$	−1.00000			−0.0447214
$501$	−9.00000	+	15.5885i	−0.402090	+	0.696441i
$502$	−10.0000	−	17.3205i	−0.446322	−	0.773052i
$503$	−7.00000	−	12.1244i	−0.312115	−	0.540598i	0.666705	−	0.745321i	$-0.267704\pi$
$503$	−7.00000	−	12.1244i	−0.312115	−	0.540598i	−0.978820	+	0.204723i	$0.934371\pi$
$504$	−3.00000			−0.133631
$505$	−0.500000	+	0.866025i	−0.0222497	+	0.0385376i
$506$	−20.0000	+	34.6410i	−0.889108	+	1.53998i
$507$	11.5000	−	19.9186i	0.510733	−	0.884615i
$508$	−3.50000	−	6.06218i	−0.155287	−	0.268966i
$509$	10.5000	−	18.1865i	0.465404	−	0.806104i	−0.533815	−	0.845601i	$-0.679242\pi$
$509$	10.5000	−	18.1865i	0.465404	−	0.806104i	0.999220	+	0.0394971i	$0.0125756\pi$
$510$	−4.00000	−	6.92820i	−0.177123	−	0.306786i
$511$	−18.0000			−0.796273
$512$	1.00000			0.0441942
$513$	−2.00000	−	3.46410i	−0.0883022	−	0.152944i
$514$	−8.00000	+	13.8564i	−0.352865	+	0.611180i
$515$	−3.50000	−	6.06218i	−0.154228	−	0.267131i
$516$	4.00000	−	6.92820i	0.176090	−	0.304997i
$517$	−30.0000	+	51.9615i	−1.31940	+	2.28527i
$518$	−3.00000	+	5.19615i	−0.131812	+	0.228306i
$519$	5.00000			0.219476
$520$	3.00000	+	5.19615i	0.131559	+	0.227866i
$521$	1.00000	+	1.73205i	0.0438108	+	0.0758825i	0.887099	−	0.461579i	$-0.152717\pi$
$521$	1.00000	+	1.73205i	0.0438108	+	0.0758825i	−0.843288	+	0.537461i	$0.819383\pi$
$522$	0.500000	−	0.866025i	0.0218844	−	0.0379049i
$523$	20.0000			0.874539			0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000			0.874539			0.437269	+	0.899331i	$0.355946\pi$
$524$	8.00000	+	13.8564i	0.349482	+	0.605320i
$525$	3.00000			0.130931
$526$	−6.00000			−0.261612
$527$	−44.0000	−	6.92820i	−1.91667	−	0.301797i
$528$	−5.00000			−0.217597
$529$	41.0000			1.78261
$530$	2.50000	+	4.33013i	0.108593	+	0.188089i
$531$	11.0000			0.477359
$532$	−6.00000	+	10.3923i	−0.260133	+	0.450564i
$533$	18.0000	+	31.1769i	0.779667	+	1.35042i
$534$		0			0
$535$	5.00000			0.216169
$536$	−5.00000	+	8.66025i	−0.215967	+	0.374066i
$537$	5.50000	−	9.52628i	0.237343	−	0.411089i
$538$	9.00000	−	15.5885i	0.388018	−	0.672066i
$539$	−5.00000	−	8.66025i	−0.215365	−	0.373024i
$540$	−0.500000	+	0.866025i	−0.0215166	+	0.0372678i
$541$	−4.00000	−	6.92820i	−0.171973	−	0.297867i	0.767136	−	0.641484i	$-0.221681\pi$
$541$	−4.00000	−	6.92820i	−0.171973	−	0.297867i	−0.939110	+	0.343617i	$0.888348\pi$
$542$	−17.0000			−0.730213
$543$		0			0
$544$	−4.00000	−	6.92820i	−0.171499	−	0.297044i
$545$	−6.00000	+	10.3923i	−0.257012	+	0.445157i
$546$	−9.00000	−	15.5885i	−0.385164	−	0.667124i
$547$	16.0000	−	27.7128i	0.684111	−	1.18491i	−0.289605	−	0.957146i	$-0.593524\pi$
$547$	16.0000	−	27.7128i	0.684111	−	1.18491i	0.973715	−	0.227768i	$-0.0731428\pi$
$548$	3.00000	−	5.19615i	0.128154	−	0.221969i
$549$	−6.00000	+	10.3923i	−0.256074	+	0.443533i
$550$	5.00000			0.213201
$551$	−2.00000	−	3.46410i	−0.0852029	−	0.147576i
$552$	4.00000	+	6.92820i	0.170251	+	0.294884i
$553$	12.0000	−	20.7846i	0.510292	−	0.883852i
$554$	−24.0000			−1.01966
$555$	1.00000	+	1.73205i	0.0424476	+	0.0735215i
$556$	−10.0000			−0.424094
$557$	−21.0000			−0.889799			−0.444899	−	0.895581i	$-0.646761\pi$
$557$	−21.0000			−0.889799			−0.444899	+	0.895581i	$0.646761\pi$
$558$	2.00000	+	5.19615i	0.0846668	+	0.219971i
$559$	48.0000			2.03018
$560$	3.00000			0.126773
$561$	20.0000	+	34.6410i	0.844401	+	1.46254i
$562$	−8.00000			−0.337460
$563$	−22.5000	+	38.9711i	−0.948262	+	1.64244i	−0.199177	+	0.979963i	$0.563827\pi$
$563$	−22.5000	+	38.9711i	−0.948262	+	1.64244i	−0.749085	+	0.662474i	$0.769506\pi$
$564$	6.00000	+	10.3923i	0.252646	+	0.437595i
$565$	−5.00000	−	8.66025i	−0.210352	−	0.364340i
$566$	−6.00000			−0.252199
$567$	1.50000	−	2.59808i	0.0629941	−	0.109109i
$568$		0			0
$569$	−21.0000	+	36.3731i	−0.880366	+	1.52484i	−0.0294311	+	0.999567i	$0.509370\pi$
$569$	−21.0000	+	36.3731i	−0.880366	+	1.52484i	−0.850935	+	0.525271i	$0.823964\pi$
$570$	2.00000	+	3.46410i	0.0837708	+	0.145095i
$571$	22.0000	−	38.1051i	0.920671	−	1.59465i	0.122292	−	0.992494i	$-0.460975\pi$
$571$	22.0000	−	38.1051i	0.920671	−	1.59465i	0.798379	−	0.602155i	$-0.205691\pi$
$572$	−15.0000	−	25.9808i	−0.627182	−	1.08631i
$573$	26.0000			1.08617
$574$	18.0000			0.751305
$575$	−4.00000	−	6.92820i	−0.166812	−	0.288926i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	15.0000	+	25.9808i	0.624458	+	1.08159i	0.988645	+	0.150268i	$0.0480135\pi$
$577$	15.0000	+	25.9808i	0.624458	+	1.08159i	−0.364187	+	0.931326i	$0.618653\pi$
$578$	−23.5000	+	40.7032i	−0.977471	+	1.69303i
$579$	−6.50000	+	11.2583i	−0.270131	+	0.467880i
$580$	−0.500000	+	0.866025i	−0.0207614	+	0.0359597i
$581$	−9.00000			−0.373383
$582$	6.50000	+	11.2583i	0.269434	+	0.466673i
$583$	−12.5000	−	21.6506i	−0.517697	−	0.896678i
$584$	−3.00000	+	5.19615i	−0.124141	+	0.215018i
$585$	−6.00000			−0.248069
$586$	−4.50000	−	7.79423i	−0.185893	−	0.321977i
$587$	37.0000			1.52715			0.763577	−	0.645717i	$-0.223441\pi$
$587$	37.0000			1.52715			0.763577	+	0.645717i	$0.223441\pi$
$588$	−2.00000			−0.0824786
$589$	22.0000	+	3.46410i	0.906494	+	0.142736i
$590$	−11.0000			−0.452863
$591$	10.0000			0.411345
$592$	1.00000	+	1.73205i	0.0410997	+	0.0711868i
$593$	−34.0000			−1.39621			−0.698106	−	0.715994i	$-0.745974\pi$
$593$	−34.0000			−1.39621			−0.698106	+	0.715994i	$0.745974\pi$
$594$	2.50000	−	4.33013i	0.102576	−	0.177667i
$595$	−12.0000	−	20.7846i	−0.491952	−	0.852086i
$596$	−6.50000	−	11.2583i	−0.266250	−	0.461159i
$597$	−19.0000			−0.777618
$598$	−24.0000	+	41.5692i	−0.981433	+	1.69989i
$599$	8.00000	−	13.8564i	0.326871	−	0.566157i	−0.655018	−	0.755613i	$-0.727339\pi$
$599$	8.00000	−	13.8564i	0.326871	−	0.566157i	0.981889	+	0.189456i	$0.0606724\pi$
$600$	0.500000	−	0.866025i	0.0204124	−	0.0353553i
$601$	−11.0000	−	19.0526i	−0.448699	−	0.777170i	0.549602	−	0.835426i	$-0.314779\pi$
$601$	−11.0000	−	19.0526i	−0.448699	−	0.777170i	−0.998302	+	0.0582563i	$0.981446\pi$
$602$	12.0000	−	20.7846i	0.489083	−	0.847117i
$603$	−5.00000	−	8.66025i	−0.203616	−	0.352673i
$604$	−5.00000			−0.203447
$605$	−14.0000			−0.569181
$606$	−0.500000	−	0.866025i	−0.0203111	−	0.0351799i
$607$	12.0000	−	20.7846i	0.487065	−	0.843621i	−0.512824	−	0.858494i	$-0.671401\pi$
$607$	12.0000	−	20.7846i	0.487065	−	0.843621i	0.999889	+	0.0148722i	$0.00473415\pi$
$608$	2.00000	+	3.46410i	0.0811107	+	0.140488i
$609$	1.50000	−	2.59808i	0.0607831	−	0.105279i
$610$	6.00000	−	10.3923i	0.242933	−	0.420772i
$611$	−36.0000	+	62.3538i	−1.45640	+	2.52257i
$612$	8.00000			0.323381
$613$	−8.00000	−	13.8564i	−0.323117	−	0.559655i	0.658012	−	0.753007i	$-0.271397\pi$
$613$	−8.00000	−	13.8564i	−0.323117	−	0.559655i	−0.981129	+	0.193352i	$0.938064\pi$
$614$	−1.00000	−	1.73205i	−0.0403567	−	0.0698999i
$615$	3.00000	−	5.19615i	0.120972	−	0.209529i
$616$	−15.0000			−0.604367
$617$	16.0000	+	27.7128i	0.644136	+	1.11568i	0.984500	+	0.175382i	$0.0561162\pi$
$617$	16.0000	+	27.7128i	0.644136	+	1.11568i	−0.340365	+	0.940294i	$0.610551\pi$
$618$	7.00000			0.281581
$619$	−4.00000			−0.160774			−0.0803868	−	0.996764i	$-0.525616\pi$
$619$	−4.00000			−0.160774			−0.0803868	+	0.996764i	$0.525616\pi$
$620$	−2.00000	−	5.19615i	−0.0803219	−	0.208683i
$621$	−8.00000			−0.321029
$622$	−22.0000			−0.882120
$623$		0			0
$624$	−6.00000			−0.240192
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	0.500000	+	0.866025i	0.0199840	+	0.0346133i
$627$	−10.0000	−	17.3205i	−0.399362	−	0.691714i
$628$		0			0
$629$	8.00000	−	13.8564i	0.318981	−	0.552491i
$630$	−1.50000	+	2.59808i	−0.0597614	+	0.103510i
$631$	18.5000	−	32.0429i	0.736473	−	1.27561i	−0.217601	−	0.976038i	$-0.569823\pi$
$631$	18.5000	−	32.0429i	0.736473	−	1.27561i	0.954074	−	0.299571i	$-0.0968437\pi$
$632$	−4.00000	−	6.92820i	−0.159111	−	0.275589i
$633$	−8.00000	+	13.8564i	−0.317971	+	0.550743i
$634$	15.5000	+	26.8468i	0.615584	+	1.06622i
$635$	−7.00000			−0.277787
$636$	−5.00000			−0.198263
$637$	−6.00000	−	10.3923i	−0.237729	−	0.411758i
$638$	2.50000	−	4.33013i	0.0989759	−	0.171431i
$639$		0			0
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	6.00000	−	10.3923i	0.236986	−	0.410471i	−0.722862	−	0.690992i	$-0.757174\pi$
$641$	6.00000	−	10.3923i	0.236986	−	0.410471i	0.959848	+	0.280521i	$0.0905072\pi$
$642$	−2.50000	+	4.33013i	−0.0986671	+	0.170896i
$643$	40.0000			1.57745			0.788723	−	0.614749i	$-0.210743\pi$
$643$	40.0000			1.57745			0.788723	+	0.614749i	$0.210743\pi$
$644$	12.0000	+	20.7846i	0.472866	+	0.819028i
$645$	−4.00000	−	6.92820i	−0.157500	−	0.272798i
$646$	16.0000	−	27.7128i	0.629512	−	1.09035i
$647$	−12.0000			−0.471769			−0.235884	−	0.971781i	$-0.575799\pi$
$647$	−12.0000			−0.471769			−0.235884	+	0.971781i	$0.575799\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	55.0000			2.15894
$650$	6.00000			0.235339
$651$	6.00000	+	15.5885i	0.235159	+	0.610960i
$652$		0			0
$653$	−9.00000			−0.352197			−0.176099	−	0.984373i	$-0.556348\pi$
$653$	−9.00000			−0.352197			−0.176099	+	0.984373i	$0.556348\pi$
$654$	−6.00000	−	10.3923i	−0.234619	−	0.406371i
$655$	16.0000			0.625172
$656$	3.00000	−	5.19615i	0.117130	−	0.202876i
$657$	−3.00000	−	5.19615i	−0.117041	−	0.202721i
$658$	18.0000	+	31.1769i	0.701713	+	1.21540i
$659$	15.0000			0.584317			0.292159	−	0.956370i	$-0.405627\pi$
$659$	15.0000			0.584317			0.292159	+	0.956370i	$0.405627\pi$
$660$	−2.50000	+	4.33013i	−0.0973124	+	0.168550i
$661$	−4.00000	+	6.92820i	−0.155582	+	0.269476i	−0.933271	−	0.359174i	$-0.883059\pi$
$661$	−4.00000	+	6.92820i	−0.155582	+	0.269476i	0.777689	+	0.628649i	$0.216392\pi$
$662$	6.00000	−	10.3923i	0.233197	−	0.403908i
$663$	24.0000	+	41.5692i	0.932083	+	1.61441i
$664$	−1.50000	+	2.59808i	−0.0582113	+	0.100825i
$665$	6.00000	+	10.3923i	0.232670	+	0.402996i
$666$	−2.00000			−0.0774984
$667$	−8.00000			−0.309761
$668$	9.00000	+	15.5885i	0.348220	+	0.603136i
$669$	0.500000	−	0.866025i	0.0193311	−	0.0334825i
$670$	5.00000	+	8.66025i	0.193167	+	0.334575i
$671$	−30.0000	+	51.9615i	−1.15814	+	2.00595i
$672$	−1.50000	+	2.59808i	−0.0578638	+	0.100223i
$673$	2.50000	−	4.33013i	0.0963679	−	0.166914i	−0.813811	−	0.581130i	$-0.802611\pi$
$673$	2.50000	−	4.33013i	0.0963679	−	0.166914i	0.910179	+	0.414216i	$0.135944\pi$
$674$	23.0000			0.885927
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$	−11.5000	−	19.9186i	−0.442308	−	0.766099i
$677$	−19.5000	+	33.7750i	−0.749446	+	1.29808i	0.198643	+	0.980072i	$0.436347\pi$
$677$	−19.5000	+	33.7750i	−0.749446	+	1.29808i	−0.948089	+	0.318006i	$0.896987\pi$
$678$	10.0000			0.384048
$679$	19.5000	+	33.7750i	0.748341	+	1.29617i
$680$	−8.00000			−0.306786
$681$	25.0000			0.958002
$682$	10.0000	+	25.9808i	0.382920	+	0.994855i
$683$	9.00000			0.344375			0.172188	−	0.985064i	$-0.444916\pi$
$683$	9.00000			0.344375			0.172188	+	0.985064i	$0.444916\pi$
$684$	−4.00000			−0.152944
$685$	−3.00000	−	5.19615i	−0.114624	−	0.198535i
$686$	15.0000			0.572703
$687$	−1.00000	+	1.73205i	−0.0381524	+	0.0660819i
$688$	−4.00000	−	6.92820i	−0.152499	−	0.264135i
$689$	−15.0000	−	25.9808i	−0.571454	−	0.989788i
$690$	8.00000			0.304555
$691$	−5.00000	+	8.66025i	−0.190209	+	0.329452i	−0.945319	−	0.326146i	$-0.894250\pi$
$691$	−5.00000	+	8.66025i	−0.190209	+	0.329452i	0.755110	+	0.655598i	$0.227583\pi$
$692$	2.50000	−	4.33013i	0.0950357	−	0.164607i
$693$	7.50000	−	12.9904i	0.284901	−	0.493464i
$694$	−2.50000	−	4.33013i	−0.0948987	−	0.164369i
$695$	−5.00000	+	8.66025i	−0.189661	+	0.328502i
$696$	−0.500000	−	0.866025i	−0.0189525	−	0.0328266i
$697$	−48.0000			−1.81813
$698$	−20.0000			−0.757011
$699$	−7.00000	−	12.1244i	−0.264764	−	0.458585i
$700$	1.50000	−	2.59808i	0.0566947	−	0.0981981i
$701$	−15.5000	−	26.8468i	−0.585427	−	1.01399i	−0.994822	−	0.101632i	$-0.967594\pi$
$701$	−15.5000	−	26.8468i	−0.585427	−	1.01399i	0.409395	−	0.912357i	$-0.365740\pi$
$702$	3.00000	−	5.19615i	0.113228	−	0.196116i
$703$	−4.00000	+	6.92820i	−0.150863	+	0.261302i
$704$	−2.50000	+	4.33013i	−0.0942223	+	0.163198i
$705$	12.0000			0.451946
$706$	9.00000	+	15.5885i	0.338719	+	0.586679i
$707$	−1.50000	−	2.59808i	−0.0564133	−	0.0977107i
$708$	5.50000	−	9.52628i	0.206703	−	0.358020i
$709$	−22.0000			−0.826227			−0.413114	−	0.910679i	$-0.635559\pi$
$709$	−22.0000			−0.826227			−0.413114	+	0.910679i	$0.635559\pi$
$710$		0			0
$711$	8.00000			0.300023
$712$		0			0
$713$	28.0000	−	34.6410i	1.04861	−	1.29732i
$714$	24.0000			0.898177
$715$	−30.0000			−1.12194
$716$	−5.50000	−	9.52628i	−0.205545	−	0.356014i
$717$	−6.00000			−0.224074
$718$	−2.00000	+	3.46410i	−0.0746393	+	0.129279i
$719$	3.00000	+	5.19615i	0.111881	+	0.193784i	0.916529	−	0.399969i	$-0.130979\pi$
$719$	3.00000	+	5.19615i	0.111881	+	0.193784i	−0.804648	+	0.593753i	$0.797646\pi$
$720$	0.500000	+	0.866025i	0.0186339	+	0.0322749i
$721$	21.0000			0.782081
$722$	1.50000	−	2.59808i	0.0558242	−	0.0966904i
$723$	−2.50000	+	4.33013i	−0.0929760	+	0.161039i
$724$		0			0
$725$	0.500000	+	0.866025i	0.0185695	+	0.0321634i
$726$	7.00000	−	12.1244i	0.259794	−	0.449977i
$727$	−9.50000	−	16.4545i	−0.352335	−	0.610263i	0.634323	−	0.773068i	$-0.281279\pi$
$727$	−9.50000	−	16.4545i	−0.352335	−	0.610263i	−0.986658	+	0.162805i	$0.947946\pi$
$728$	−18.0000			−0.667124
$729$	1.00000			0.0370370
$730$	3.00000	+	5.19615i	0.111035	+	0.192318i
$731$	−32.0000	+	55.4256i	−1.18356	+	2.04999i
$732$	6.00000	+	10.3923i	0.221766	+	0.384111i
$733$	23.0000	−	39.8372i	0.849524	−	1.47142i	−0.0321090	−	0.999484i	$-0.510222\pi$
$733$	23.0000	−	39.8372i	0.849524	−	1.47142i	0.881633	−	0.471935i	$-0.156444\pi$
$734$	−2.00000	+	3.46410i	−0.0738213	+	0.127862i
$735$	−1.00000	+	1.73205i	−0.0368856	+	0.0638877i
$736$	8.00000			0.294884
$737$	−25.0000	−	43.3013i	−0.920887	−	1.59502i
$738$	3.00000	+	5.19615i	0.110432	+	0.191273i
$739$	5.00000	−	8.66025i	0.183928	−	0.318573i	−0.759287	−	0.650756i	$-0.774452\pi$
$739$	5.00000	−	8.66025i	0.183928	−	0.318573i	0.943215	+	0.332184i	$0.107785\pi$
$740$	2.00000			0.0735215
$741$	−12.0000	−	20.7846i	−0.440831	−	0.763542i
$742$	−15.0000			−0.550667
$743$	−24.0000			−0.880475			−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000			−0.880475			−0.440237	+	0.897881i	$0.645106\pi$
$744$	5.50000	+	0.866025i	0.201640	+	0.0317500i
$745$	−13.0000			−0.476283
$746$	4.00000			0.146450
$747$	−1.50000	−	2.59808i	−0.0548821	−	0.0950586i
$748$	40.0000			1.46254
$749$	−7.50000	+	12.9904i	−0.274044	+	0.474658i
$750$	−0.500000	−	0.866025i	−0.0182574	−	0.0316228i
$751$	−7.50000	−	12.9904i	−0.273679	−	0.474026i	0.696122	−	0.717923i	$-0.254907\pi$
$751$	−7.50000	−	12.9904i	−0.273679	−	0.474026i	−0.969801	+	0.243898i	$0.921574\pi$
$752$	12.0000			0.437595
$753$	10.0000	−	17.3205i	0.364420	−	0.631194i
$754$	3.00000	−	5.19615i	0.109254	−	0.189233i
$755$	−2.50000	+	4.33013i	−0.0909843	+	0.157589i
$756$	−1.50000	−	2.59808i	−0.0545545	−	0.0944911i
$757$	−18.0000	+	31.1769i	−0.654221	+	1.13314i	0.327867	+	0.944724i	$0.393670\pi$
$757$	−18.0000	+	31.1769i	−0.654221	+	1.13314i	−0.982088	+	0.188420i	$0.939663\pi$
$758$	−14.0000	−	24.2487i	−0.508503	−	0.880753i
$759$	−40.0000			−1.45191
$760$	4.00000			0.145095
$761$	7.00000	+	12.1244i	0.253750	+	0.439508i	0.964555	−	0.263881i	$-0.0850027\pi$
$761$	7.00000	+	12.1244i	0.253750	+	0.439508i	−0.710805	+	0.703389i	$0.751669\pi$
$762$	3.50000	−	6.06218i	0.126792	−	0.219610i
$763$	−18.0000	−	31.1769i	−0.651644	−	1.12868i
$764$	13.0000	−	22.5167i	0.470323	−	0.814624i
$765$	4.00000	−	6.92820i	0.144620	−	0.250490i
$766$	−11.0000	+	19.0526i	−0.397446	+	0.688397i
$767$	66.0000			2.38312
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	11.5000	+	19.9186i	0.414701	+	0.718283i	0.995397	−	0.0958377i	$-0.0305530\pi$
$769$	11.5000	+	19.9186i	0.414701	+	0.718283i	−0.580696	+	0.814120i	$0.697220\pi$
$770$	−7.50000	+	12.9904i	−0.270281	+	0.468141i
$771$	−16.0000			−0.576226
$772$	6.50000	+	11.2583i	0.233940	+	0.405196i
$773$	14.0000			0.503545			0.251773	−	0.967786i	$-0.418987\pi$
$773$	14.0000			0.503545			0.251773	+	0.967786i	$0.418987\pi$
$774$	8.00000			0.287554
$775$	−5.50000	−	0.866025i	−0.197566	−	0.0311086i
$776$	13.0000			0.466673
$777$	−6.00000			−0.215249
$778$	−15.0000	−	25.9808i	−0.537776	−	0.931455i
$779$	24.0000			0.859889
$780$	−3.00000	+	5.19615i	−0.107417	+	0.186052i
$781$		0			0
$782$	−32.0000	−	55.4256i	−1.14432	−	1.98202i
$783$	1.00000			0.0357371
$784$	−1.00000	+	1.73205i	−0.0357143	+	0.0618590i
$785$		0			0
$786$	−8.00000	+	13.8564i	−0.285351	+	0.494242i
$787$	−2.00000	−	3.46410i	−0.0712923	−	0.123482i	0.828176	−	0.560469i	$-0.189379\pi$
$787$	−2.00000	−	3.46410i	−0.0712923	−	0.123482i	−0.899468	+	0.436987i	$0.856046\pi$
$788$	5.00000	−	8.66025i	0.178118	−	0.308509i
$789$	−3.00000	−	5.19615i	−0.106803	−	0.184988i
$790$	−8.00000			−0.284627
$791$	30.0000			1.06668
$792$	−2.50000	−	4.33013i	−0.0888336	−	0.153864i
$793$	−36.0000	+	62.3538i	−1.27840	+	2.21425i
$794$	10.0000	+	17.3205i	0.354887	+	0.614682i
$795$	−2.50000	+	4.33013i	−0.0886659	+	0.153574i
$796$	−9.50000	+	16.4545i	−0.336719	+	0.583214i
$797$	4.50000	−	7.79423i	0.159398	−	0.276086i	−0.775254	−	0.631650i	$-0.782378\pi$
$797$	4.50000	−	7.79423i	0.159398	−	0.276086i	0.934652	+	0.355564i	$0.115711\pi$
$798$	−12.0000			−0.424795
$799$	−48.0000	−	83.1384i	−1.69812	−	2.94123i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$		0			0
$802$	2.00000			0.0706225
$803$	−15.0000	−	25.9808i	−0.529339	−	0.916841i
$804$	−10.0000			−0.352673
$805$	24.0000			0.845889
$806$	12.0000	+	31.1769i	0.422682	+	1.09816i
$807$	18.0000			0.633630
$808$	−1.00000			−0.0351799
$809$	−22.0000	−	38.1051i	−0.773479	−	1.33970i	−0.935645	−	0.352941i	$-0.885182\pi$
$809$	−22.0000	−	38.1051i	−0.773479	−	1.33970i	0.162167	−	0.986763i	$-0.448152\pi$
$810$	−1.00000			−0.0351364
$811$	3.00000	−	5.19615i	0.105344	−	0.182462i	−0.808535	−	0.588449i	$-0.799739\pi$
$811$	3.00000	−	5.19615i	0.105344	−	0.182462i	0.913879	+	0.405987i	$0.133072\pi$
$812$	−1.50000	−	2.59808i	−0.0526397	−	0.0911746i
$813$	−8.50000	−	14.7224i	−0.298108	−	0.516338i
$814$	−10.0000			−0.350500
$815$		0			0
$816$	4.00000	−	6.92820i	0.140028	−	0.242536i
$817$	16.0000	−	27.7128i	0.559769	−	0.969549i
$818$	4.50000	+	7.79423i	0.157339	+	0.272519i
$819$	9.00000	−	15.5885i	0.314485	−	0.544705i
$820$	−3.00000	−	5.19615i	−0.104765	−	0.181458i
$821$	−25.0000			−0.872506			−0.436253	−	0.899824i	$-0.643695\pi$
$821$	−25.0000			−0.872506			−0.436253	+	0.899824i	$0.643695\pi$
$822$	6.00000			0.209274
$823$	−15.5000	−	26.8468i	−0.540296	−	0.935820i	−0.998887	−	0.0471726i	$-0.984979\pi$
$823$	−15.5000	−	26.8468i	−0.540296	−	0.935820i	0.458591	−	0.888648i	$-0.348354\pi$
$824$	3.50000	−	6.06218i	0.121928	−	0.211186i
$825$	2.50000	+	4.33013i	0.0870388	+	0.150756i
$826$	16.5000	−	28.5788i	0.574108	−	0.994385i
$827$	−14.0000	+	24.2487i	−0.486828	+	0.843210i	−0.999885	−	0.0151439i	$-0.995179\pi$
$827$	−14.0000	+	24.2487i	−0.486828	+	0.843210i	0.513058	+	0.858354i	$0.328513\pi$
$828$	−4.00000	+	6.92820i	−0.139010	+	0.240772i
$829$	32.0000			1.11141			0.555703	−	0.831381i	$-0.312449\pi$
$829$	32.0000			1.11141			0.555703	+	0.831381i	$0.312449\pi$
$830$	1.50000	+	2.59808i	0.0520658	+	0.0901805i
$831$	−12.0000	−	20.7846i	−0.416275	−	0.721010i
$832$	−3.00000	+	5.19615i	−0.104006	+	0.180144i
$833$	16.0000			0.554367
$834$	−5.00000	−	8.66025i	−0.173136	−	0.299880i
$835$	18.0000			0.622916
$836$	−20.0000			−0.691714
$837$	−3.50000	+	4.33013i	−0.120978	+	0.149671i
$838$	−27.0000			−0.932700
$839$	28.0000			0.966667			0.483334	−	0.875436i	$-0.339426\pi$
$839$	28.0000			0.966667			0.483334	+	0.875436i	$0.339426\pi$
$840$	1.50000	+	2.59808i	0.0517549	+	0.0896421i
$841$	−28.0000			−0.965517
$842$	−16.0000	+	27.7128i	−0.551396	+	0.955047i
$843$	−4.00000	−	6.92820i	−0.137767	−	0.238620i
$844$	8.00000	+	13.8564i	0.275371	+	0.476957i
$845$	−23.0000			−0.791224
$846$	−6.00000	+	10.3923i	−0.206284	+	0.357295i
$847$	21.0000	−	36.3731i	0.721569	−	1.24979i
$848$	−2.50000	+	4.33013i	−0.0858504	+	0.148697i
$849$	−3.00000	−	5.19615i	−0.102960	−	0.178331i
$850$	−4.00000	+	6.92820i	−0.137199	+	0.237635i
$851$	8.00000	+	13.8564i	0.274236	+	0.474991i
$852$		0			0
$853$	40.0000			1.36957			0.684787	−	0.728743i	$-0.259895\pi$
$853$	40.0000			1.36957			0.684787	+	0.728743i	$0.259895\pi$
$854$	18.0000	+	31.1769i	0.615947	+	1.06685i
$855$	−2.00000	+	3.46410i	−0.0683986	+	0.118470i
$856$	2.50000	+	4.33013i	0.0854482	+	0.148001i
$857$	12.0000	−	20.7846i	0.409912	−	0.709989i	−0.584967	−	0.811057i	$-0.698893\pi$
$857$	12.0000	−	20.7846i	0.409912	−	0.709989i	0.994880	+	0.101068i	$0.0322260\pi$
$858$	15.0000	−	25.9808i	0.512092	−	0.886969i
$859$	−21.0000	+	36.3731i	−0.716511	+	1.24103i	0.245863	+	0.969305i	$0.420929\pi$
$859$	−21.0000	+	36.3731i	−0.716511	+	1.24103i	−0.962374	+	0.271728i	$0.912405\pi$
$860$	−8.00000			−0.272798
$861$	9.00000	+	15.5885i	0.306719	+	0.531253i
$862$	15.0000	+	25.9808i	0.510902	+	0.884908i
$863$	−24.0000	+	41.5692i	−0.816970	+	1.41503i	0.0909355	+	0.995857i	$0.471014\pi$
$863$	−24.0000	+	41.5692i	−0.816970	+	1.41503i	−0.907905	+	0.419176i	$0.862319\pi$
$864$	−1.00000			−0.0340207
$865$	−2.50000	−	4.33013i	−0.0850026	−	0.147229i
$866$	14.0000			0.475739
$867$	−47.0000			−1.59620
$868$	16.5000	+	2.59808i	0.560046	+	0.0881845i
$869$	40.0000			1.35691
$870$	−1.00000			−0.0339032
$871$	−30.0000	−	51.9615i	−1.01651	−	1.76065i
$872$	−12.0000			−0.406371
$873$	−6.50000	+	11.2583i	−0.219992	+	0.381037i
$874$	16.0000	+	27.7128i	0.541208	+	0.937400i
$875$	−1.50000	−	2.59808i	−0.0507093	−	0.0878310i
$876$	−6.00000			−0.202721
$877$	4.00000	−	6.92820i	0.135070	−	0.233949i	−0.790554	−	0.612392i	$-0.790207\pi$
$877$	4.00000	−	6.92820i	0.135070	−	0.233949i	0.925624	+	0.378444i	$0.123541\pi$
$878$	2.50000	−	4.33013i	0.0843709	−	0.146135i
$879$	4.50000	−	7.79423i	0.151781	−	0.262893i
$880$	2.50000	+	4.33013i	0.0842750	+	0.145969i
$881$	−9.00000	+	15.5885i	−0.303218	+	0.525188i	−0.976863	−	0.213866i	$-0.931394\pi$
$881$	−9.00000	+	15.5885i	−0.303218	+	0.525188i	0.673645	+	0.739055i	$0.264728\pi$
$882$	−1.00000	−	1.73205i	−0.0336718	−	0.0583212i
$883$	−2.00000			−0.0673054			−0.0336527	−	0.999434i	$-0.510714\pi$
$883$	−2.00000			−0.0673054			−0.0336527	+	0.999434i	$0.510714\pi$
$884$	48.0000			1.61441
$885$	−5.50000	−	9.52628i	−0.184880	−	0.320222i
$886$	8.00000	−	13.8564i	0.268765	−	0.465515i
$887$	−18.0000	−	31.1769i	−0.604381	−	1.04682i	−0.992149	−	0.125061i	$-0.960087\pi$
$887$	−18.0000	−	31.1769i	−0.604381	−	1.04682i	0.387768	−	0.921757i	$-0.373246\pi$
$888$	−1.00000	+	1.73205i	−0.0335578	+	0.0581238i
$889$	10.5000	−	18.1865i	0.352159	−	0.609957i
$890$		0			0
$891$	5.00000			0.167506
$892$	−0.500000	−	0.866025i	−0.0167412	−	0.0289967i
$893$	24.0000	+	41.5692i	0.803129	+	1.39106i
$894$	6.50000	−	11.2583i	0.217393	−	0.376535i
$895$	−11.0000			−0.367689
$896$	1.50000	+	2.59808i	0.0501115	+	0.0867956i
$897$	−48.0000			−1.60267
$898$	−24.0000			−0.800890
$899$	−3.50000	+	4.33013i	−0.116732	+	0.144418i
$900$	1.00000			0.0333333
$901$	40.0000			1.33259
$902$	15.0000	+	25.9808i	0.499445	+	0.865065i
$903$	24.0000			0.798670
$904$	5.00000	−	8.66025i	0.166298	−	0.288036i
$905$		0			0
$906$	−2.50000	−	4.33013i	−0.0830569	−	0.143859i
$907$	−26.0000			−0.863316			−0.431658	−	0.902037i	$-0.642071\pi$
$907$	−26.0000			−0.863316			−0.431658	+	0.902037i	$0.642071\pi$
$908$	12.5000	−	21.6506i	0.414827	−	0.718502i
$909$	0.500000	−	0.866025i	0.0165840	−	0.0287242i
$910$	−9.00000	+	15.5885i	−0.298347	+	0.516752i
$911$	−15.0000	−	25.9808i	−0.496972	−	0.860781i	0.503022	−	0.864274i	$-0.332222\pi$
$911$	−15.0000	−	25.9808i	−0.496972	−	0.860781i	−0.999994	+	0.00349271i	$0.998888\pi$
$912$	−2.00000	+	3.46410i	−0.0662266	+	0.114708i
$913$	−7.50000	−	12.9904i	−0.248214	−	0.429919i
$914$	−22.0000			−0.727695
$915$	12.0000			0.396708
$916$	1.00000	+	1.73205i	0.0330409	+	0.0572286i
$917$	−24.0000	+	41.5692i	−0.792550	+	1.37274i
$918$	4.00000	+	6.92820i	0.132020	+	0.228665i
$919$	11.5000	−	19.9186i	0.379350	−	0.657053i	−0.611618	−	0.791153i	$-0.709481\pi$
$919$	11.5000	−	19.9186i	0.379350	−	0.657053i	0.990968	+	0.134100i	$0.0428143\pi$
$920$	4.00000	−	6.92820i	0.131876	−	0.228416i
$921$	1.00000	−	1.73205i	0.0329511	−	0.0570730i
$922$	1.00000			0.0329332
$923$		0			0
$924$	−7.50000	−	12.9904i	−0.246732	−	0.427352i
$925$	1.00000	−	1.73205i	0.0328798	−	0.0569495i
$926$	27.0000			0.887275
$927$	3.50000	+	6.06218i	0.114955	+	0.199108i
$928$	−1.00000			−0.0328266
$929$	12.0000			0.393707			0.196854	−	0.980433i	$-0.436928\pi$
$929$	12.0000			0.393707			0.196854	+	0.980433i	$0.436928\pi$
$930$	3.50000	−	4.33013i	0.114770	−	0.141990i
$931$	−8.00000			−0.262189
$932$	−14.0000			−0.458585
$933$	−11.0000	−	19.0526i	−0.360124	−	0.623753i
$934$	23.0000			0.752583
$935$	20.0000	−	34.6410i	0.654070	−	1.13288i
$936$	−3.00000	−	5.19615i	−0.0980581	−	0.169842i
$937$	19.0000	+	32.9090i	0.620703	+	1.07509i	0.989355	+	0.145522i	$0.0464860\pi$
$937$	19.0000	+	32.9090i	0.620703	+	1.07509i	−0.368652	+	0.929567i	$0.620181\pi$
$938$	−30.0000			−0.979535
$939$	−0.500000	+	0.866025i	−0.0163169	+	0.0282617i
$940$	6.00000	−	10.3923i	0.195698	−	0.338960i
$941$	7.50000	−	12.9904i	0.244493	−	0.423474i	−0.717496	−	0.696563i	$-0.754712\pi$
$941$	7.50000	−	12.9904i	0.244493	−	0.423474i	0.961989	+	0.273088i	$0.0880451\pi$
$942$		0			0
$943$	24.0000	−	41.5692i	0.781548	−	1.35368i
$944$	−5.50000	−	9.52628i	−0.179010	−	0.310054i
$945$	−3.00000			−0.0975900
$946$	40.0000			1.30051
$947$	−26.0000	−	45.0333i	−0.844886	−	1.46339i	−0.885720	−	0.464220i	$-0.846335\pi$
$947$	−26.0000	−	45.0333i	−0.844886	−	1.46339i	0.0408333	−	0.999166i	$-0.486999\pi$
$948$	4.00000	−	6.92820i	0.129914	−	0.225018i
$949$	−18.0000	−	31.1769i	−0.584305	−	1.01205i
$950$	2.00000	−	3.46410i	0.0648886	−	0.112390i
$951$	−15.5000	+	26.8468i	−0.502622	+	0.870567i
$952$	12.0000	−	20.7846i	0.388922	−	0.673633i
$953$	−24.0000			−0.777436			−0.388718	−	0.921357i	$-0.627082\pi$
$953$	−24.0000			−0.777436			−0.388718	+	0.921357i	$0.627082\pi$
$954$	−2.50000	−	4.33013i	−0.0809405	−	0.140193i
$955$	−13.0000	−	22.5167i	−0.420670	−	0.728622i
$956$	−3.00000	+	5.19615i	−0.0970269	+	0.168056i
$957$	5.00000			0.161627
$958$	−6.00000	−	10.3923i	−0.193851	−	0.335760i
$959$	18.0000			0.581250
$960$	1.00000			0.0322749
$961$	−6.50000	−	30.3109i	−0.209677	−	0.977771i
$962$	−12.0000			−0.386896
$963$	−5.00000			−0.161123
$964$	2.50000	+	4.33013i	0.0805196	+	0.139464i
$965$	13.0000			0.418485
$966$	−12.0000	+	20.7846i	−0.386094	+	0.668734i
$967$	−8.00000	−	13.8564i	−0.257263	−	0.445592i	0.708245	−	0.705967i	$-0.249487\pi$
$967$	−8.00000	−	13.8564i	−0.257263	−	0.445592i	−0.965508	+	0.260375i	$0.916154\pi$
$968$	−7.00000	−	12.1244i	−0.224989	−	0.389692i
$969$	32.0000			1.02799
$970$	6.50000	−	11.2583i	0.208702	−	0.361483i
$971$	16.5000	−	28.5788i	0.529510	−	0.917139i	−0.469897	−	0.882721i	$-0.655709\pi$
$971$	16.5000	−	28.5788i	0.529510	−	0.917139i	0.999408	−	0.0344175i	$-0.0109576\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	−15.0000	−	25.9808i	−0.480878	−	0.832905i
$974$	−8.50000	+	14.7224i	−0.272358	+	0.471737i
$975$	3.00000	+	5.19615i	0.0960769	+	0.166410i
$976$	12.0000			0.384111
$977$	−56.0000			−1.79160			−0.895799	−	0.444459i	$-0.853396\pi$
$977$	−56.0000			−1.79160			−0.895799	+	0.444459i	$0.853396\pi$
$978$		0			0
$979$		0			0
$980$	1.00000	+	1.73205i	0.0319438	+	0.0553283i
$981$	6.00000	−	10.3923i	0.191565	−	0.331801i
$982$	3.50000	−	6.06218i	0.111689	−	0.193452i
$983$	14.0000	−	24.2487i	0.446531	−	0.773414i	−0.551627	−	0.834091i	$-0.685993\pi$
$983$	14.0000	−	24.2487i	0.446531	−	0.773414i	0.998157	+	0.0606773i	$0.0193260\pi$
$984$	6.00000			0.191273
$985$	−5.00000	−	8.66025i	−0.159313	−	0.275939i
$986$	4.00000	+	6.92820i	0.127386	+	0.220639i
$987$	−18.0000	+	31.1769i	−0.572946	+	0.992372i
$988$	−24.0000			−0.763542
$989$	−32.0000	−	55.4256i	−1.01754	−	1.76243i
$990$	−5.00000			−0.158910
$991$	8.00000			0.254128			0.127064	−	0.991894i	$-0.459445\pi$
$991$	8.00000			0.254128			0.127064	+	0.991894i	$0.459445\pi$
$992$	3.50000	−	4.33013i	0.111125	−	0.137482i
$993$	12.0000			0.380808
$994$		0			0
$995$	9.50000	+	16.4545i	0.301170	+	0.521642i
$996$	−3.00000			−0.0950586
$997$	5.00000	−	8.66025i	0.158352	−	0.274273i	−0.775923	−	0.630828i	$-0.782715\pi$
$997$	5.00000	−	8.66025i	0.158352	−	0.274273i	0.934274	+	0.356555i	$0.116049\pi$
$998$	19.0000	+	32.9090i	0.601434	+	1.04172i
$999$	−1.00000	−	1.73205i	−0.0316386	−	0.0547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.i.h.211.1	✓	2
31.5	even	3	inner	930.2.i.h.811.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.i.h.211.1	✓	2	1.1	even	1	trivial
930.2.i.h.811.1	yes	2	31.5	even	3	inner

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(1.50000 + 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(1.50000 + 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-2.50000 + 4.33013i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-3.00000 + 5.19615i) q^{13} +(1.50000 + 2.59808i) q^{14} +1.00000 q^{15} +1.00000 q^{16} +(-4.00000 - 6.92820i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(2.00000 + 3.46410i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-1.50000 + 2.59808i) q^{21} +(-2.50000 + 4.33013i) q^{22} +8.00000 q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-3.00000 + 5.19615i) q^{26} -1.00000 q^{27} +(1.50000 + 2.59808i) q^{28} -1.00000 q^{29} +1.00000 q^{30} +(3.50000 - 4.33013i) q^{31} +1.00000 q^{32} -5.00000 q^{33} +(-4.00000 - 6.92820i) q^{34} +3.00000 q^{35} +(-0.500000 + 0.866025i) q^{36} +(1.00000 + 1.73205i) q^{37} +(2.00000 + 3.46410i) q^{38} -6.00000 q^{39} +(0.500000 - 0.866025i) q^{40} +(3.00000 - 5.19615i) q^{41} +(-1.50000 + 2.59808i) q^{42} +(-4.00000 - 6.92820i) q^{43} +(-2.50000 + 4.33013i) q^{44} +(0.500000 + 0.866025i) q^{45} +8.00000 q^{46} +12.0000 q^{47} +(0.500000 + 0.866025i) q^{48} +(-1.00000 + 1.73205i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(4.00000 - 6.92820i) q^{51} +(-3.00000 + 5.19615i) q^{52} +(-2.50000 + 4.33013i) q^{53} -1.00000 q^{54} +(2.50000 + 4.33013i) q^{55} +(1.50000 + 2.59808i) q^{56} +(-2.00000 + 3.46410i) q^{57} -1.00000 q^{58} +(-5.50000 - 9.52628i) q^{59} +1.00000 q^{60} +12.0000 q^{61} +(3.50000 - 4.33013i) q^{62} -3.00000 q^{63} +1.00000 q^{64} +(3.00000 + 5.19615i) q^{65} -5.00000 q^{66} +(-5.00000 + 8.66025i) q^{67} +(-4.00000 - 6.92820i) q^{68} +(4.00000 + 6.92820i) q^{69} +3.00000 q^{70} +(-0.500000 + 0.866025i) q^{72} +(-3.00000 + 5.19615i) q^{73} +(1.00000 + 1.73205i) q^{74} +(0.500000 - 0.866025i) q^{75} +(2.00000 + 3.46410i) q^{76} -15.0000 q^{77} -6.00000 q^{78} +(-4.00000 - 6.92820i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.00000 - 5.19615i) q^{82} +(-1.50000 + 2.59808i) q^{83} +(-1.50000 + 2.59808i) q^{84} -8.00000 q^{85} +(-4.00000 - 6.92820i) q^{86} +(-0.500000 - 0.866025i) q^{87} +(-2.50000 + 4.33013i) q^{88} +(0.500000 + 0.866025i) q^{90} -18.0000 q^{91} +8.00000 q^{92} +(5.50000 + 0.866025i) q^{93} +12.0000 q^{94} +4.00000 q^{95} +(0.500000 + 0.866025i) q^{96} +13.0000 q^{97} +(-1.00000 + 1.73205i) q^{98} +(-2.50000 - 4.33013i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + q^{3} + 2 q^{4} + q^{5} + q^{6} + 3 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + q^3 + 2 * q^4 + q^5 + q^6 + 3 * q^7 + 2 * q^8 - q^9	\( 2 q + 2 q^{2} + q^{3} + 2 q^{4} + q^{5} + q^{6} + 3 q^{7} + 2 q^{8} - q^{9} + q^{10} - 5 q^{11} + q^{12} - 6 q^{13} + 3 q^{14} + 2 q^{15} + 2 q^{16} - 8 q^{17} - q^{18} + 4 q^{19} + q^{20} - 3 q^{21} - 5 q^{22} + 16 q^{23} + q^{24} - q^{25} - 6 q^{26} - 2 q^{27} + 3 q^{28} - 2 q^{29} + 2 q^{30} + 7 q^{31} + 2 q^{32} - 10 q^{33} - 8 q^{34} + 6 q^{35} - q^{36} + 2 q^{37} + 4 q^{38} - 12 q^{39} + q^{40} + 6 q^{41} - 3 q^{42} - 8 q^{43} - 5 q^{44} + q^{45} + 16 q^{46} + 24 q^{47} + q^{48} - 2 q^{49} - q^{50} + 8 q^{51} - 6 q^{52} - 5 q^{53} - 2 q^{54} + 5 q^{55} + 3 q^{56} - 4 q^{57} - 2 q^{58} - 11 q^{59} + 2 q^{60} + 24 q^{61} + 7 q^{62} - 6 q^{63} + 2 q^{64} + 6 q^{65} - 10 q^{66} - 10 q^{67} - 8 q^{68} + 8 q^{69} + 6 q^{70} - q^{72} - 6 q^{73} + 2 q^{74} + q^{75} + 4 q^{76} - 30 q^{77} - 12 q^{78} - 8 q^{79} + q^{80} - q^{81} + 6 q^{82} - 3 q^{83} - 3 q^{84} - 16 q^{85} - 8 q^{86} - q^{87} - 5 q^{88} + q^{90} - 36 q^{91} + 16 q^{92} + 11 q^{93} + 24 q^{94} + 8 q^{95} + q^{96} + 26 q^{97} - 2 q^{98} - 5 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + q^3 + 2 * q^4 + q^5 + q^6 + 3 * q^7 + 2 * q^8 - q^9 + q^10 - 5 * q^11 + q^12 - 6 * q^13 + 3 * q^14 + 2 * q^15 + 2 * q^16 - 8 * q^17 - q^18 + 4 * q^19 + q^20 - 3 * q^21 - 5 * q^22 + 16 * q^23 + q^24 - q^25 - 6 * q^26 - 2 * q^27 + 3 * q^28 - 2 * q^29 + 2 * q^30 + 7 * q^31 + 2 * q^32 - 10 * q^33 - 8 * q^34 + 6 * q^35 - q^36 + 2 * q^37 + 4 * q^38 - 12 * q^39 + q^40 + 6 * q^41 - 3 * q^42 - 8 * q^43 - 5 * q^44 + q^45 + 16 * q^46 + 24 * q^47 + q^48 - 2 * q^49 - q^50 + 8 * q^51 - 6 * q^52 - 5 * q^53 - 2 * q^54 + 5 * q^55 + 3 * q^56 - 4 * q^57 - 2 * q^58 - 11 * q^59 + 2 * q^60 + 24 * q^61 + 7 * q^62 - 6 * q^63 + 2 * q^64 + 6 * q^65 - 10 * q^66 - 10 * q^67 - 8 * q^68 + 8 * q^69 + 6 * q^70 - q^72 - 6 * q^73 + 2 * q^74 + q^75 + 4 * q^76 - 30 * q^77 - 12 * q^78 - 8 * q^79 + q^80 - q^81 + 6 * q^82 - 3 * q^83 - 3 * q^84 - 16 * q^85 - 8 * q^86 - q^87 - 5 * q^88 + q^90 - 36 * q^91 + 16 * q^92 + 11 * q^93 + 24 * q^94 + 8 * q^95 + q^96 + 26 * q^97 - 2 * q^98 - 5 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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