LMFDB - Embedded newform 231.2.y.a.25.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(4,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 6]))

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

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

chi := DirichletCharacter("231.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.y (of order $15$, degree $8$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			25.2
Character	$\chi$	$=$	231.25
Dual form			231.2.y.a.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70284 - 0.758153i) q^{2} +(0.978148 + 0.207912i) q^{3} +(0.986607 + 1.09574i) q^{4} +(0.363031 - 3.45401i) q^{5} +(-1.50800 - 1.09563i) q^{6} +(2.64131 - 0.153270i) q^{7} +(0.302713 + 0.931655i) q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})$	\(q+(-1.70284 - 0.758153i) q^{2} +(0.978148 + 0.207912i) q^{3} +(0.986607 + 1.09574i) q^{4} +(0.363031 - 3.45401i) q^{5} +(-1.50800 - 1.09563i) q^{6} +(2.64131 - 0.153270i) q^{7} +(0.302713 + 0.931655i) q^{8} +(0.913545 + 0.406737i) q^{9} +(-3.23685 + 5.60640i) q^{10} +(-3.06979 - 1.25554i) q^{11} +(0.737230 + 1.27692i) q^{12} +(-1.79406 + 1.30346i) q^{13} +(-4.61393 - 1.74152i) q^{14} +(1.07323 - 3.30305i) q^{15} +(0.499112 - 4.74873i) q^{16} +(4.58519 - 2.04146i) q^{17} +(-1.24725 - 1.38521i) q^{18} +(0.701537 - 0.779136i) q^{19} +(4.14286 - 3.00996i) q^{20} +(2.61546 + 0.399238i) q^{21} +(4.27547 + 4.46535i) q^{22} +(-3.39430 - 5.87909i) q^{23} +(0.102396 + 0.974234i) q^{24} +(-6.90766 - 1.46827i) q^{25} +(4.04322 - 0.859412i) q^{26} +(0.809017 + 0.587785i) q^{27} +(2.77388 + 2.74296i) q^{28} +(-0.131329 + 0.404189i) q^{29} +(-4.33176 + 4.81090i) q^{30} +(-0.0899183 - 0.855515i) q^{31} +(-3.47057 + 6.01121i) q^{32} +(-2.74167 - 1.86635i) q^{33} -9.35558 q^{34} +(0.429479 - 9.17875i) q^{35} +(0.455633 + 1.40230i) q^{36} +(-1.00565 + 0.213757i) q^{37} +(-1.78531 + 0.794871i) q^{38} +(-2.02586 + 0.901970i) q^{39} +(3.32784 - 0.707355i) q^{40} +(2.02483 + 6.23179i) q^{41} +(-4.15102 - 2.66275i) q^{42} +3.02146 q^{43} +(-1.65294 - 4.60241i) q^{44} +(1.73652 - 3.00774i) q^{45} +(1.32269 + 12.5846i) q^{46} +(-2.18640 + 2.42824i) q^{47} +(1.47552 - 4.54119i) q^{48} +(6.95302 - 0.809669i) q^{49} +(10.6495 + 7.73730i) q^{50} +(4.90943 - 1.04353i) q^{51} +(-3.19828 - 0.679816i) q^{52} +(1.28047 + 12.1829i) q^{53} +(-0.931995 - 1.61426i) q^{54} +(-5.45107 + 10.1473i) q^{55} +(0.942354 + 2.41439i) q^{56} +(0.848199 - 0.616252i) q^{57} +(0.530070 - 0.588702i) q^{58} +(-0.713615 - 0.792550i) q^{59} +(4.67814 - 2.08284i) q^{60} +(-0.755430 + 7.18744i) q^{61} +(-0.495495 + 1.52498i) q^{62} +(2.47530 + 0.934297i) q^{63} +(2.74132 - 1.99168i) q^{64} +(3.85087 + 6.66989i) q^{65} +(3.25365 + 5.25670i) q^{66} +(6.86264 - 11.8864i) q^{67} +(6.76068 + 3.01005i) q^{68} +(-2.09779 - 6.45633i) q^{69} +(-7.69023 + 15.3043i) q^{70} +(13.1390 + 9.54608i) q^{71} +(-0.102396 + 0.974234i) q^{72} +(3.40851 + 3.78553i) q^{73} +(1.87451 + 0.398440i) q^{74} +(-6.45144 - 2.87237i) q^{75} +1.54587 q^{76} +(-8.30070 - 2.84576i) q^{77} +4.13354 q^{78} +(5.25211 + 2.33839i) q^{79} +(-16.2210 - 3.44787i) q^{80} +(0.669131 + 0.743145i) q^{81} +(1.27669 - 12.1469i) q^{82} +(-11.1912 - 8.13092i) q^{83} +(2.14297 + 3.25974i) q^{84} +(-5.38665 - 16.5784i) q^{85} +(-5.14506 - 2.29073i) q^{86} +(-0.212495 + 0.368052i) q^{87} +(0.240463 - 3.24006i) q^{88} +(1.78299 + 3.08823i) q^{89} +(-5.23734 + 3.80515i) q^{90} +(-4.53888 + 3.71781i) q^{91} +(3.09311 - 9.51961i) q^{92} +(0.0899183 - 0.855515i) q^{93} +(5.56406 - 2.47728i) q^{94} +(-2.43647 - 2.70597i) q^{95} +(-4.64453 + 5.15828i) q^{96} +(14.7992 - 10.7522i) q^{97} +(-12.4537 - 3.89272i) q^{98} +(-2.29372 - 2.39559i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{3} + 10 q^{4} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 64 * q - 8 * q^3 + 10 * q^4 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q - 8 q^{3} + 10 q^{4} - q^{7} + 8 q^{8} + 8 q^{9} - 22 q^{10} - 13 q^{11} + 30 q^{12} - 8 q^{13} - 26 q^{14} + 4 q^{17} - 5 q^{18} + 10 q^{19} + 24 q^{20} + 2 q^{21} - 38 q^{22} - 8 q^{23} + 14 q^{24} - 2 q^{25} + 4 q^{26} + 16 q^{27} - 67 q^{28} + 2 q^{29} - 3 q^{30} + 25 q^{31} + 72 q^{32} - 12 q^{33} - 56 q^{34} + 19 q^{35} - 20 q^{36} - 12 q^{37} - 37 q^{38} - 4 q^{39} - 9 q^{40} + 20 q^{41} + 9 q^{42} - 100 q^{43} - 5 q^{44} - 33 q^{46} - 18 q^{47} + 10 q^{48} + 29 q^{49} - 46 q^{50} + 6 q^{51} + 26 q^{52} - 49 q^{53} - 10 q^{54} - 24 q^{55} - 48 q^{56} + 20 q^{57} - 40 q^{58} + q^{59} + 12 q^{60} + 3 q^{61} + 4 q^{62} - 7 q^{63} - 24 q^{64} + 82 q^{65} + 11 q^{66} + 76 q^{67} - 39 q^{68} - 16 q^{69} + 59 q^{70} + 70 q^{71} - 14 q^{72} - 3 q^{73} + 32 q^{74} - 28 q^{75} + 104 q^{76} + 38 q^{77} - 12 q^{78} - 15 q^{79} - 83 q^{80} + 8 q^{81} + 42 q^{82} + 68 q^{83} + 27 q^{84} + 62 q^{85} - 47 q^{86} - 54 q^{87} - 64 q^{88} + 82 q^{89} - 16 q^{90} - 10 q^{91} + 190 q^{92} - 25 q^{93} - 6 q^{94} - 53 q^{95} + 8 q^{96} - 32 q^{97} - 152 q^{98} + 16 q^{99}+O(q^{100}) \) 64 * q - 8 * q^3 + 10 * q^4 - q^7 + 8 * q^8 + 8 * q^9 - 22 * q^10 - 13 * q^11 + 30 * q^12 - 8 * q^13 - 26 * q^14 + 4 * q^17 - 5 * q^18 + 10 * q^19 + 24 * q^20 + 2 * q^21 - 38 * q^22 - 8 * q^23 + 14 * q^24 - 2 * q^25 + 4 * q^26 + 16 * q^27 - 67 * q^28 + 2 * q^29 - 3 * q^30 + 25 * q^31 + 72 * q^32 - 12 * q^33 - 56 * q^34 + 19 * q^35 - 20 * q^36 - 12 * q^37 - 37 * q^38 - 4 * q^39 - 9 * q^40 + 20 * q^41 + 9 * q^42 - 100 * q^43 - 5 * q^44 - 33 * q^46 - 18 * q^47 + 10 * q^48 + 29 * q^49 - 46 * q^50 + 6 * q^51 + 26 * q^52 - 49 * q^53 - 10 * q^54 - 24 * q^55 - 48 * q^56 + 20 * q^57 - 40 * q^58 + q^59 + 12 * q^60 + 3 * q^61 + 4 * q^62 - 7 * q^63 - 24 * q^64 + 82 * q^65 + 11 * q^66 + 76 * q^67 - 39 * q^68 - 16 * q^69 + 59 * q^70 + 70 * q^71 - 14 * q^72 - 3 * q^73 + 32 * q^74 - 28 * q^75 + 104 * q^76 + 38 * q^77 - 12 * q^78 - 15 * q^79 - 83 * q^80 + 8 * q^81 + 42 * q^82 + 68 * q^83 + 27 * q^84 + 62 * q^85 - 47 * q^86 - 54 * q^87 - 64 * q^88 + 82 * q^89 - 16 * q^90 - 10 * q^91 + 190 * q^92 - 25 * q^93 - 6 * q^94 - 53 * q^95 + 8 * q^96 - 32 * q^97 - 152 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−1.70284	−	0.758153i	−1.20409	−	0.536095i	−0.296128	−	0.955148i	$-0.595695\pi$
$2$	−1.70284	−	0.758153i	−1.20409	−	0.536095i	−0.907962	+	0.419053i	$0.862362\pi$
$3$	0.978148	+	0.207912i	0.564734	+	0.120038i
$3$	0.978148	+	0.207912i	0.564734	+	0.120038i
$4$	0.986607	+	1.09574i	0.493303	+	0.547869i
$5$	0.363031	−	3.45401i	0.162352	−	1.54468i	−0.545373	−	0.838193i	$-0.683612\pi$
$5$	0.363031	−	3.45401i	0.162352	−	1.54468i	0.707726	−	0.706487i	$-0.249721\pi$
$6$	−1.50800	−	1.09563i	−0.615638	−	0.447288i
$7$	2.64131	−	0.153270i	0.998321	−	0.0579308i
$7$	2.64131	−	0.153270i	0.998321	−	0.0579308i
$8$	0.302713	+	0.931655i	0.107025	+	0.329390i
$9$	0.913545	+	0.406737i	0.304515	+	0.135579i
$10$	−3.23685	+	5.60640i	−1.02358	+	1.77290i
$11$	−3.06979	−	1.25554i	−0.925577	−	0.378559i
$11$	−3.06979	−	1.25554i	−0.925577	−	0.378559i
$12$	0.737230	+	1.27692i	0.212820	+	0.368615i
$13$	−1.79406	+	1.30346i	−0.497582	+	0.361515i	−0.808093	−	0.589055i	$-0.799500\pi$
$13$	−1.79406	+	1.30346i	−0.497582	+	0.361515i	0.310510	+	0.950570i	$0.399500\pi$
$14$	−4.61393	−	1.74152i	−1.23312	−	0.465441i
$15$	1.07323	−	3.30305i	0.277106	−	0.852845i
$16$	0.499112	−	4.74873i	0.124778	−	1.18718i
$17$	4.58519	−	2.04146i	1.11207	−	0.495126i	0.233317	−	0.972401i	$-0.425042\pi$
$17$	4.58519	−	2.04146i	1.11207	−	0.495126i	0.878754	+	0.477275i	$0.158375\pi$
$18$	−1.24725	−	1.38521i	−0.293980	−	0.326498i
$19$	0.701537	−	0.779136i	0.160944	−	0.178746i	−0.657279	−	0.753647i	$-0.728293\pi$
$19$	0.701537	−	0.779136i	0.160944	−	0.178746i	0.818223	+	0.574901i	$0.194959\pi$
$20$	4.14286	−	3.00996i	0.926372	−	0.673048i
$21$	2.61546	+	0.399238i	0.570739	+	0.0871208i
$22$	4.27547	+	4.46535i	0.911534	+	0.952017i
$23$	−3.39430	−	5.87909i	−0.707760	−	1.22588i	−0.965686	−	0.259711i	$-0.916373\pi$
$23$	−3.39430	−	5.87909i	−0.707760	−	1.22588i	0.257927	−	0.966164i	$-0.416961\pi$
$24$	0.102396	+	0.974234i	0.0209015	+	0.198865i
$25$	−6.90766	−	1.46827i	−1.38153	−	0.293654i
$26$	4.04322	−	0.859412i	0.792940	−	0.168545i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	2.77388	+	2.74296i	0.524213	+	0.518371i
$29$	−0.131329	+	0.404189i	−0.0243872	+	0.0750561i	−0.962509	−	0.271248i	$-0.912564\pi$
$29$	−0.131329	+	0.404189i	−0.0243872	+	0.0750561i	0.938122	+	0.346304i	$0.112564\pi$
$30$	−4.33176	+	4.81090i	−0.790867	+	0.878347i
$31$	−0.0899183	−	0.855515i	−0.0161498	−	0.153655i	0.983475	−	0.181044i	$-0.0579475\pi$
$31$	−0.0899183	−	0.855515i	−0.0161498	−	0.153655i	−0.999625	+	0.0273885i	$0.991281\pi$
$32$	−3.47057	+	6.01121i	−0.613516	+	1.06264i
$33$	−2.74167	−	1.86635i	−0.477263	−	0.324889i
$34$	−9.35558			−1.60447
$35$	0.429479	−	9.17875i	0.0725953	−	1.55149i
$36$	0.455633	+	1.40230i	0.0759389	+	0.233716i
$37$	−1.00565	+	0.213757i	−0.165327	+	0.0351414i	−0.289831	−	0.957078i	$-0.593599\pi$
$37$	−1.00565	+	0.213757i	−0.165327	+	0.0351414i	0.124504	+	0.992219i	$0.460266\pi$
$38$	−1.78531	+	0.794871i	−0.289616	+	0.128945i
$39$	−2.02586	+	0.901970i	−0.324397	+	0.144431i
$40$	3.32784	−	0.707355i	0.526178	−	0.111843i
$41$	2.02483	+	6.23179i	0.316225	+	0.973242i	0.975247	+	0.221118i	$0.0709706\pi$
$41$	2.02483	+	6.23179i	0.316225	+	0.973242i	−0.659022	+	0.752124i	$0.729029\pi$
$42$	−4.15102	−	2.66275i	−0.640516	−	0.410872i
$43$	3.02146			0.460768			0.230384	−	0.973100i	$-0.426002\pi$
$43$	3.02146			0.460768			0.230384	+	0.973100i	$0.426002\pi$
$44$	−1.65294	−	4.60241i	−0.249190	−	0.693839i
$45$	1.73652	−	3.00774i	0.258865	−	0.448367i
$46$	1.32269	+	12.5846i	0.195020	+	1.85549i
$47$	−2.18640	+	2.42824i	−0.318919	+	0.354195i	−0.881194	−	0.472755i	$-0.843260\pi$
$47$	−2.18640	+	2.42824i	−0.318919	+	0.354195i	0.562275	+	0.826950i	$0.309926\pi$
$48$	1.47552	−	4.54119i	0.212973	−	0.655464i
$49$	6.95302	−	0.809669i	0.993288	−	0.115667i
$50$	10.6495	+	7.73730i	1.50606	+	1.09422i
$51$	4.90943	−	1.04353i	0.687458	−	0.146124i
$52$	−3.19828	−	0.679816i	−0.443522	−	0.0942735i
$53$	1.28047	+	12.1829i	0.175887	+	1.67345i	0.625499	+	0.780225i	$0.284895\pi$
$53$	1.28047	+	12.1829i	0.175887	+	1.67345i	−0.449613	+	0.893224i	$0.648438\pi$
$54$	−0.931995	−	1.61426i	−0.126828	−	0.219673i
$55$	−5.45107	+	10.1473i	−0.735023	+	1.36826i
$56$	0.942354	+	2.41439i	0.125927	+	0.322637i
$57$	0.848199	−	0.616252i	0.112347	−	0.0816246i
$58$	0.530070	−	0.588702i	0.0696016	−	0.0773004i
$59$	−0.713615	−	0.792550i	−0.0929048	−	0.103181i	0.694900	−	0.719107i	$-0.255449\pi$
$59$	−0.713615	−	0.792550i	−0.0929048	−	0.103181i	−0.787804	+	0.615926i	$0.788782\pi$
$60$	4.67814	−	2.08284i	0.603945	−	0.268894i
$61$	−0.755430	+	7.18744i	−0.0967230	+	0.920257i	0.833316	+	0.552797i	$0.186439\pi$
$61$	−0.755430	+	7.18744i	−0.0967230	+	0.920257i	−0.930039	+	0.367461i	$0.880227\pi$
$62$	−0.495495	+	1.52498i	−0.0629280	+	0.193672i
$63$	2.47530	+	0.934297i	0.311858	+	0.117710i
$64$	2.74132	−	1.99168i	0.342664	−	0.248960i
$65$	3.85087	+	6.66989i	0.477641	+	0.827299i
$66$	3.25365	+	5.25670i	0.400496	+	0.647055i
$67$	6.86264	−	11.8864i	0.838405	−	1.45216i	−0.0528226	−	0.998604i	$-0.516822\pi$
$67$	6.86264	−	11.8864i	0.838405	−	1.45216i	0.891228	−	0.453556i	$-0.149845\pi$
$68$	6.76068	+	3.01005i	0.819853	+	0.365022i
$69$	−2.09779	−	6.45633i	−0.252544	−	0.777251i
$70$	−7.69023	+	15.3043i	−0.919159	+	1.82922i
$71$	13.1390	+	9.54608i	1.55932	+	1.13291i	0.936566	+	0.350492i	$0.113986\pi$
$71$	13.1390	+	9.54608i	1.55932	+	1.13291i	0.622753	+	0.782419i	$0.286014\pi$
$72$	−0.102396	+	0.974234i	−0.0120675	+	0.114815i
$73$	3.40851	+	3.78553i	0.398936	+	0.443063i	0.908825	−	0.417177i	$-0.136980\pi$
$73$	3.40851	+	3.78553i	0.398936	+	0.443063i	−0.509889	+	0.860240i	$0.670314\pi$
$74$	1.87451	+	0.398440i	0.217908	+	0.0463177i
$75$	−6.45144	−	2.87237i	−0.744949	−	0.331673i
$76$	1.54587			0.177324
$77$	−8.30070	−	2.84576i	−0.945953	−	0.324304i
$78$	4.13354			0.468032
$79$	5.25211	+	2.33839i	0.590908	+	0.263089i	0.680332	−	0.732904i	$-0.261836\pi$
$79$	5.25211	+	2.33839i	0.590908	+	0.263089i	−0.0894234	+	0.995994i	$0.528502\pi$
$80$	−16.2210	−	3.44787i	−1.81356	−	0.385484i
$81$	0.669131	+	0.743145i	0.0743478	+	0.0825716i
$82$	1.27669	−	12.1469i	0.140987	−	1.34140i
$83$	−11.1912	−	8.13092i	−1.22840	−	0.892484i	−0.231630	−	0.972804i	$-0.574406\pi$
$83$	−11.1912	−	8.13092i	−1.22840	−	0.892484i	−0.996769	+	0.0803198i	$0.974406\pi$
$84$	2.14297	+	3.25974i	0.233817	+	0.355667i
$85$	−5.38665	−	16.5784i	−0.584264	−	1.79818i
$86$	−5.14506	−	2.29073i	−0.554806	−	0.247016i
$87$	−0.212495	+	0.368052i	−0.0227818	+	0.0394593i
$88$	0.240463	−	3.24006i	0.0256334	−	0.345391i
$89$	1.78299	+	3.08823i	0.188997	+	0.327352i	0.944916	−	0.327313i	$-0.106143\pi$
$89$	1.78299	+	3.08823i	0.188997	+	0.327352i	−0.755919	+	0.654665i	$0.772810\pi$
$90$	−5.23734	+	3.80515i	−0.552064	+	0.401098i
$91$	−4.53888	+	3.71781i	−0.475804	+	0.389733i
$92$	3.09311	−	9.51961i	0.322479	−	0.992488i
$93$	0.0899183	−	0.855515i	0.00932409	−	0.0887128i
$94$	5.56406	−	2.47728i	0.573889	−	0.255512i
$95$	−2.43647	−	2.70597i	−0.249976	−	0.277627i
$96$	−4.64453	+	5.15828i	−0.474031	+	0.526464i
$97$	14.7992	−	10.7522i	1.50263	−	1.09172i	0.533309	−	0.845921i	$-0.320948\pi$
$97$	14.7992	−	10.7522i	1.50263	−	1.09172i	0.969320	−	0.245803i	$-0.0790515\pi$
$98$	−12.4537	−	3.89272i	−1.25802	−	0.393224i
$99$	−2.29372	−	2.39559i	−0.230528	−	0.240766i
$100$	−5.20631	−	9.01759i	−0.520631	−	0.901759i
$101$	1.68182	+	16.0014i	0.167347	+	1.59220i	0.679741	+	0.733452i	$0.262092\pi$
$101$	1.68182	+	16.0014i	0.167347	+	1.59220i	−0.512393	+	0.858751i	$0.671241\pi$
$102$	−9.15114	−	1.94513i	−0.906097	−	0.192597i
$103$	−12.2139	+	2.59614i	−1.20347	+	0.255805i	−0.765650	−	0.643258i	$-0.777582\pi$
$103$	−12.2139	+	2.59614i	−1.20347	+	0.255805i	−0.437819	+	0.899063i	$0.644249\pi$
$104$	−1.75746	−	1.27687i	−0.172333	−	0.125207i
$105$	2.32846	−	8.88888i	0.227235	−	0.867466i
$106$	7.05606	−	21.7163i	0.685345	−	2.10927i
$107$	−10.9405	+	12.1506i	−1.05766	+	1.17465i	−0.0735078	+	0.997295i	$0.523419\pi$
$107$	−10.9405	+	12.1506i	−1.05766	+	1.17465i	−0.984148	+	0.177351i	$0.943247\pi$
$108$	0.154123	+	1.46638i	0.0148305	+	0.141103i
$109$	−1.11126	+	1.92477i	−0.106440	+	0.184359i	−0.914326	−	0.404980i	$-0.867278\pi$
$109$	−1.11126	+	1.92477i	−0.106440	+	0.184359i	0.807886	+	0.589339i	$0.200612\pi$
$110$	16.9755	−	13.1465i	1.61855	−	1.25347i
$111$	−1.02811			−0.0975841
$112$	0.590467	−	12.6194i	0.0557939	−	1.19242i
$113$	−0.572048	−	1.76058i	−0.0538137	−	0.165622i	0.920538	−	0.390654i	$-0.127751\pi$
$113$	−0.572048	−	1.76058i	−0.0538137	−	0.165622i	−0.974351	+	0.225033i	$0.927751\pi$
$114$	−1.91156	+	0.406315i	−0.179034	+	0.0380549i
$115$	−21.5387	+	9.58964i	−2.00849	+	0.894239i
$116$	−0.572456	+	0.254874i	−0.0531512	+	0.0236644i
$117$	−2.16912	+	0.461060i	−0.200535	+	0.0426251i
$118$	0.614298	+	1.89062i	0.0565507	+	0.174045i
$119$	11.7980	−	6.09489i	1.08152	−	0.558718i
$120$	3.40219			0.310576
$121$	7.84725	+	7.70848i	0.713386	+	0.700771i
$122$	6.73556	−	11.6663i	0.609809	−	1.05622i
$123$	0.684922	+	6.51660i	0.0617573	+	0.587582i
$124$	0.848707	−	0.942584i	0.0762161	−	0.0846466i
$125$	−2.21298	+	6.81085i	−0.197935	+	0.609181i
$126$	−3.50669	−	3.46761i	−0.312401	−	0.308919i
$127$	−8.85144	−	6.43095i	−0.785438	−	0.570654i	0.121168	−	0.992632i	$-0.461336\pi$
$127$	−8.85144	−	6.43095i	−0.785438	−	0.570654i	−0.906606	+	0.421978i	$0.861336\pi$
$128$	7.40090	−	1.57311i	0.654154	−	0.139045i
$129$	2.95543	+	0.628197i	0.260211	+	0.0553096i
$130$	−1.50061	−	14.2773i	−0.131612	−	1.25220i
$131$	7.51089	+	13.0092i	0.656230	+	1.13662i	0.981584	+	0.191031i	$0.0611830\pi$
$131$	7.51089	+	13.0092i	0.656230	+	1.13662i	−0.325355	+	0.945592i	$0.605484\pi$
$132$	−0.659921	−	4.84550i	−0.0574388	−	0.421747i
$133$	1.73356	−	2.16546i	0.150319	−	0.187770i
$134$	−20.6977	+	15.0378i	−1.78801	+	1.29907i
$135$	2.32392	−	2.58097i	0.200011	−	0.222134i
$136$	3.28993	+	3.65384i	0.282109	+	0.313314i
$137$	18.6358	−	8.29721i	1.59217	−	0.708878i	0.596565	−	0.802565i	$-0.296532\pi$
$137$	18.6358	−	8.29721i	1.59217	−	0.708878i	0.995602	+	0.0936866i	$0.0298652\pi$
$138$	−1.32269	+	12.5846i	−0.112595	+	1.07127i
$139$	−2.75479	+	8.47836i	−0.233658	+	0.719125i	0.763639	+	0.645644i	$0.223411\pi$
$139$	−2.75479	+	8.47836i	−0.233658	+	0.719125i	−0.997297	+	0.0734814i	$0.976589\pi$
$140$	10.4812	−	8.58522i	0.885826	−	0.725584i
$141$	−2.64348	+	1.92060i	−0.222621	+	0.161744i
$142$	−15.1363	−	26.2169i	−1.27021	−	2.20007i
$143$	7.14393	−	1.74884i	0.597405	−	0.146245i
$144$	2.38744	−	4.13517i	0.198954	−	0.344598i
$145$	1.34840	+	0.600345i	0.111978	+	0.0498560i
$146$	−2.93413	−	9.03033i	−0.242831	−	0.747356i
$147$	6.96942	+	0.653638i	0.574828	+	0.0539111i
$148$	−1.22640	−	0.891030i	−0.100809	−	0.0732422i
$149$	2.42117	−	23.0359i	0.198350	−	1.88717i	−0.215021	−	0.976609i	$-0.568982\pi$
$149$	2.42117	−	23.0359i	0.198350	−	1.88717i	0.413371	−	0.910563i	$-0.364351\pi$
$150$	8.80808	+	9.78237i	0.719177	+	0.798727i
$151$	−3.61498	−	0.768387i	−0.294183	−	0.0625305i	0.0584561	−	0.998290i	$-0.481382\pi$
$151$	−3.61498	−	0.768387i	−0.294183	−	0.0625305i	−0.352639	+	0.935760i	$0.614716\pi$
$152$	0.938251	+	0.417736i	0.0761022	+	0.0338829i
$153$	5.01911			0.405771
$154$	11.9773	+	11.1391i	0.965154	+	0.897612i
$155$	−2.98760			−0.239970
$156$	−2.98705	−	1.32992i	−0.239155	−	0.106479i
$157$	−8.21877	−	1.74695i	−0.655929	−	0.139422i	−0.132088	−	0.991238i	$-0.542168\pi$
$157$	−8.21877	−	1.74695i	−0.655929	−	0.139422i	−0.523841	+	0.851816i	$0.675502\pi$
$158$	−7.17064	−	7.96380i	−0.570466	−	0.633566i
$159$	−1.28047	+	12.1829i	−0.101548	+	0.966166i
$160$	19.5029	+	14.1697i	1.54184	+	1.12021i
$161$	−9.86647	−	15.0082i	−0.777587	−	1.18282i
$162$	−0.576005	−	1.77276i	−0.0452552	−	0.139281i
$163$	0.0843397	+	0.0375504i	0.00660599	+	0.00294118i	0.410037	−	0.912069i	$-0.365516\pi$
$163$	0.0843397	+	0.0375504i	0.00660599	+	0.00294118i	−0.403431	+	0.915010i	$0.632182\pi$
$164$	−4.83070	+	8.36701i	−0.377214	+	0.653354i
$165$	−7.44170	+	8.79221i	−0.579335	+	0.684473i
$166$	12.8924	+	22.3303i	1.00065	+	1.73317i
$167$	−6.71124	+	4.87600i	−0.519331	+	0.377316i	−0.816352	−	0.577555i	$-0.804007\pi$
$167$	−6.71124	+	4.87600i	−0.519331	+	0.377316i	0.297021	+	0.954871i	$0.404007\pi$
$168$	0.419781	+	2.55756i	0.0323868	+	0.197320i
$169$	−2.49758	+	7.68677i	−0.192122	+	0.591290i
$170$	−3.39637	+	32.3143i	−0.260489	+	2.47839i
$171$	0.957790	−	0.426435i	0.0732440	−	0.0326103i
$172$	2.98099	+	3.31073i	0.227299	+	0.252441i
$173$	2.45890	−	2.73088i	0.186946	−	0.207625i	−0.642385	−	0.766382i	$-0.722055\pi$
$173$	2.45890	−	2.73088i	0.186946	−	0.207625i	0.829331	+	0.558757i	$0.188722\pi$
$174$	0.640885	−	0.465630i	0.0485853	−	0.0352993i
$175$	−18.4703	−	2.81941i	−1.39622	−	0.213127i
$176$	−7.49438	+	13.9510i	−0.564910	+	1.05159i
$177$	−0.533241	−	0.923600i	−0.0400808	−	0.0694220i
$178$	−0.694796	−	6.61054i	−0.0520772	−	0.495481i
$179$	17.6680	+	3.75545i	1.32057	+	0.280695i	0.813678	−	0.581316i	$-0.197462\pi$
$179$	17.6680	+	3.75545i	1.32057	+	0.280695i	0.506890	+	0.862011i	$0.330795\pi$
$180$	5.00895	−	1.06469i	0.373345	−	0.0793570i
$181$	−2.17999	−	1.58386i	−0.162038	−	0.117727i	0.503812	−	0.863814i	$-0.331931\pi$
$181$	−2.17999	−	1.58386i	−0.162038	−	0.117727i	−0.665849	+	0.746086i	$0.731931\pi$
$182$	10.5477	−	2.88968i	0.781844	−	0.214197i
$183$	−2.23328	+	6.87331i	−0.165088	+	0.508090i
$184$	4.44979	−	4.94199i	0.328043	−	0.364328i
$185$	0.373237	+	3.55111i	0.0274409	+	0.261083i
$186$	−0.801728	+	1.38863i	−0.0587856	+	0.101820i
$187$	−16.6387	+	0.509969i	−1.21674	+	0.0372926i
$188$	−4.81783			−0.351376
$189$	2.22695	+	1.42852i	0.161987	+	0.103910i
$190$	2.09737	+	6.45505i	0.152159	+	0.468298i
$191$	−11.1623	+	2.37263i	−0.807678	+	0.171677i	−0.593204	−	0.805052i	$-0.702137\pi$
$191$	−11.1623	+	2.37263i	−0.807678	+	0.171677i	−0.214474	+	0.976730i	$0.568804\pi$
$192$	3.09551	−	1.37821i	0.223399	−	0.0994636i
$193$	4.44983	−	1.98119i	0.320306	−	0.142609i	−0.240285	−	0.970702i	$-0.577241\pi$
$193$	4.44983	−	1.98119i	0.320306	−	0.142609i	0.560591	+	0.828093i	$0.310574\pi$
$194$	−33.3525	+	7.08929i	−2.39457	+	0.508981i
$195$	2.37997	+	7.32478i	0.170433	+	0.524538i
$196$	7.74708	+	6.81986i	0.553363	+	0.487133i
$197$	−4.10130			−0.292206			−0.146103	−	0.989269i	$-0.546673\pi$
$197$	−4.10130			−0.292206			−0.146103	+	0.989269i	$0.546673\pi$
$198$	2.08962	+	5.81830i	0.148503	+	0.413488i
$199$	−0.829726	+	1.43713i	−0.0588177	+	0.101875i	−0.893935	−	0.448197i	$-0.852066\pi$
$199$	−0.829726	+	1.43713i	−0.0588177	+	0.101875i	0.835117	+	0.550072i	$0.185400\pi$
$200$	−0.723120	−	6.88002i	−0.0511323	−	0.486491i
$201$	9.18401	−	10.1999i	0.647790	−	0.719444i
$202$	9.26768	−	28.5230i	0.652072	−	2.00687i
$203$	−0.284930	+	1.08772i	−0.0199982	+	0.0763428i
$204$	5.98712	+	4.34990i	0.419182	+	0.304554i
$205$	22.2597	−	4.73145i	1.55469	−	0.330459i
$206$	22.7665	+	4.83918i	1.58622	+	0.337162i
$207$	−0.709601	−	6.75140i	−0.0493207	−	0.469255i
$208$	5.29434	+	9.17007i	0.367097	+	0.635830i
$209$	−3.13181	+	1.51098i	−0.216632	+	0.104517i
$210$	−10.7041	+	13.3710i	−0.738655	+	0.922687i
$211$	10.1590	−	7.38097i	0.699376	−	0.508127i	−0.180353	−	0.983602i	$-0.557724\pi$
$211$	10.1590	−	7.38097i	0.699376	−	0.508127i	0.879729	+	0.475475i	$0.157724\pi$
$212$	−12.0859	+	13.4228i	−0.830065	+	0.921881i
$213$	10.8672	+	12.0692i	0.744608	+	0.826970i
$214$	27.8419	−	12.3960i	1.90323	−	0.847374i
$215$	1.09688	−	10.4362i	0.0748069	−	0.711740i
$216$	−0.302713	+	0.931655i	−0.0205970	+	0.0633911i
$217$	−0.368627	−	2.24590i	−0.0250240	−	0.152461i
$218$	3.35157	−	2.43506i	0.226997	−	0.164923i
$219$	2.54697	+	4.41148i	0.172108	+	0.298100i
$220$	−16.4968	+	4.03844i	−1.11222	+	0.272272i
$221$	−5.56514	+	9.63910i	−0.374352	+	0.648396i
$222$	1.75071	+	0.779467i	0.117500	+	0.0523144i
$223$	7.26071	+	22.3462i	0.486213	+	1.49641i	0.830216	+	0.557442i	$0.188217\pi$
$223$	7.26071	+	22.3462i	0.486213	+	1.49641i	−0.344002	+	0.938969i	$0.611783\pi$
$224$	−8.24551	+	16.4094i	−0.550926	+	1.09640i
$225$	−5.71327	−	4.15093i	−0.380884	−	0.276729i
$226$	−0.360685	+	3.43169i	−0.0239924	+	0.228273i
$227$	−15.1289	−	16.8023i	−1.00414	−	1.11521i	−0.993334	−	0.115268i	$-0.963227\pi$
$227$	−15.1289	−	16.8023i	−1.00414	−	1.11521i	−0.0108052	−	0.999942i	$-0.503439\pi$
$228$	1.51209	+	0.321405i	0.100141	+	0.0212855i
$229$	−13.5151	−	6.01731i	−0.893103	−	0.397635i	−0.0917187	−	0.995785i	$-0.529236\pi$
$229$	−13.5151	−	6.01731i	−0.893103	−	0.397635i	−0.801384	+	0.598150i	$0.795903\pi$
$230$	43.9474			2.89780
$231$	−7.52765	−	4.50938i	−0.495283	−	0.296696i
$232$	−0.416320			−0.0273327
$233$	−2.82346	−	1.25708i	−0.184971	−	0.0823544i	0.312161	−	0.950029i	$-0.398947\pi$
$233$	−2.82346	−	1.25708i	−0.184971	−	0.0823544i	−0.497132	+	0.867675i	$0.665614\pi$
$234$	4.04322	+	0.859412i	0.264313	+	0.0561815i
$235$	7.59344	+	8.43337i	0.495341	+	0.550132i
$236$	0.164369	−	1.56387i	0.0106995	−	0.101799i
$237$	4.65116	+	3.37926i	0.302125	+	0.219507i
$238$	−24.7110	+	1.43393i	−1.60177	+	0.0929481i
$239$	−6.89040	−	21.2065i	−0.445703	−	1.37173i	−0.881711	−	0.471790i	$-0.843608\pi$
$239$	−6.89040	−	21.2065i	−0.445703	−	1.37173i	0.436008	−	0.899943i	$-0.356392\pi$
$240$	−15.1497	−	6.74506i	−0.977906	−	0.435392i
$241$	−2.66332	+	4.61301i	−0.171560	+	0.297150i	−0.938965	−	0.344012i	$-0.888214\pi$
$241$	−2.66332	+	4.61301i	−0.171560	+	0.297150i	0.767406	+	0.641162i	$0.221547\pi$
$242$	−7.51839	−	19.0757i	−0.483301	−	1.22623i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−8.62086	+	6.26342i	−0.551894	+	0.400975i
$245$	−0.272444	−	24.3097i	−0.0174058	−	1.55309i
$246$	3.77427	−	11.6160i	0.240638	−	0.740609i
$247$	−0.243026	+	2.31224i	−0.0154634	+	0.147124i
$248$	0.769826	−	0.342749i	0.0488840	−	0.0217646i
$249$	−9.25618	−	10.2800i	−0.586587	−	0.651470i
$250$	8.93202	−	9.92001i	0.564910	−	0.627397i
$251$	−17.0453	+	12.3842i	−1.07589	+	0.781682i	−0.976962	−	0.213412i	$-0.931542\pi$
$251$	−17.0453	+	12.3842i	−1.07589	+	0.781682i	−0.0989307	+	0.995094i	$0.531542\pi$
$252$	1.41840	+	3.63406i	0.0893507	+	0.228924i
$253$	3.03835	+	22.3093i	0.191020	+	1.40257i
$254$	10.1969	+	17.6616i	0.639813	+	1.10819i
$255$	−1.82209	−	17.3361i	−0.114104	−	1.08563i
$256$	−20.4240	−	4.34126i	−1.27650	−	0.271329i
$257$	4.35945	−	0.926629i	0.271935	−	0.0578015i	−0.0699258	−	0.997552i	$-0.522276\pi$
$257$	4.35945	−	0.926629i	0.271935	−	0.0578015i	0.341861	+	0.939751i	$0.388943\pi$
$258$	−4.55636	−	3.31039i	−0.283667	−	0.206096i
$259$	−2.62346	+	0.718733i	−0.163014	+	0.0446599i
$260$	−3.50917	+	10.8001i	−0.217629	+	0.669794i
$261$	−0.284374	+	0.315829i	−0.0176023	+	0.0195493i
$262$	−2.92684	−	27.8471i	−0.180821	−	1.72040i
$263$	7.47232	−	12.9424i	0.460763	−	0.798064i	−0.538236	−	0.842794i	$-0.680909\pi$
$263$	7.47232	−	12.9424i	0.460763	−	0.798064i	0.998999	+	0.0447295i	$0.0142426\pi$
$264$	0.908853	−	3.11926i	0.0559361	−	0.191977i
$265$	42.5447			2.61350
$266$	−4.59372	+	2.37314i	−0.281659	+	0.145506i
$267$	1.10195	+	3.39145i	0.0674382	+	0.207553i
$268$	19.7952	−	4.20759i	1.20918	−	0.257019i
$269$	−13.6087	+	6.05899i	−0.829738	+	0.369423i	−0.777245	−	0.629198i	$-0.783383\pi$
$269$	−13.6087	+	6.05899i	−0.829738	+	0.369423i	−0.0524931	+	0.998621i	$0.516717\pi$
$270$	−5.91403	+	2.63309i	−0.359916	+	0.160245i
$271$	−22.1640	+	4.71110i	−1.34637	+	0.286179i	−0.824023	−	0.566556i	$-0.808275\pi$
$271$	−22.1640	+	4.71110i	−1.34637	+	0.286179i	−0.522344	+	0.852735i	$0.674942\pi$
$272$	−7.40581	−	22.7927i	−0.449043	−	1.38201i
$273$	−5.21267	+	2.69289i	−0.315485	+	0.162981i
$274$	−38.0244			−2.29714
$275$	19.3616	+	13.1801i	1.16755	+	0.794791i
$276$	5.00476	−	8.66849i	0.301251	−	0.521782i
$277$	1.51752	+	14.4382i	0.0911789	+	0.867509i	0.940537	+	0.339692i	$0.110323\pi$
$277$	1.51752	+	14.4382i	0.0911789	+	0.867509i	−0.849358	+	0.527817i	$0.823011\pi$
$278$	11.1189	−	12.3487i	0.666865	−	0.740628i
$279$	0.265825	−	0.818125i	0.0159145	−	0.0489799i
$280$	8.68144	−	2.37840i	0.518815	−	0.142137i
$281$	−1.22012	−	0.886467i	−0.0727861	−	0.0528822i	0.550797	−	0.834639i	$-0.314324\pi$
$281$	−1.22012	−	0.886467i	−0.0727861	−	0.0528822i	−0.623583	+	0.781757i	$0.714324\pi$
$282$	5.95753	−	1.26631i	0.354766	−	0.0754078i
$283$	−13.4276	−	2.85413i	−0.798190	−	0.169661i	−0.209277	−	0.977856i	$-0.567111\pi$
$283$	−13.4276	−	2.85413i	−0.798190	−	0.169661i	−0.588914	+	0.808196i	$0.700444\pi$
$284$	2.50308	+	23.8152i	0.148530	+	1.41317i
$285$	−1.82062	−	3.15341i	−0.107844	−	0.186792i
$286$	−13.4909	−	2.43820i	−0.797731	−	0.144174i
$287$	6.30335	+	16.1497i	0.372075	+	0.953288i
$288$	−5.61550	+	4.07990i	−0.330897	+	0.240411i
$289$	5.48118	−	6.08746i	0.322422	−	0.358086i
$290$	−1.84095	−	2.04458i	−0.108104	−	0.120062i
$291$	16.7113	−	7.44035i	0.979633	−	0.436161i
$292$	−0.785094	+	7.46967i	−0.0459441	+	0.437129i
$293$	−0.716316	+	2.20459i	−0.0418476	+	0.128794i	−0.969798	−	0.243911i	$-0.921570\pi$
$293$	−0.716316	+	2.20459i	−0.0418476	+	0.128794i	0.927950	+	0.372705i	$0.121570\pi$
$294$	−11.3722	−	6.39693i	−0.663243	−	0.373076i
$295$	−2.99654	+	2.17711i	−0.174465	+	0.126757i
$296$	−0.503570	−	0.872208i	−0.0292694	−	0.0506961i
$297$	−1.74553	−	2.82013i	−0.101286	−	0.163641i
$298$	−21.5876	+	37.3908i	−1.25054	+	2.16599i
$299$	13.7527	+	6.12311i	0.795341	+	0.354108i
$300$	−3.21768	−	9.90299i	−0.185773	−	0.571749i
$301$	7.98060	−	0.463100i	0.459994	−	0.0266927i
$302$	5.57317	+	4.04915i	0.320700	+	0.233002i
$303$	−1.68182	+	16.0014i	−0.0966180	+	0.919259i
$304$	−3.34976	−	3.72029i	−0.192122	−	0.213373i
$305$	24.5513	+	5.21853i	1.40580	+	0.298812i
$306$	−8.54675	−	3.80526i	−0.488585	−	0.217532i
$307$	−19.8671			−1.13387			−0.566937	−	0.823761i	$-0.691872\pi$
$307$	−19.8671			−1.13387			−0.566937	+	0.823761i	$0.691872\pi$
$308$	−5.07133	−	11.9030i	−0.288966	−	0.678238i
$309$	−12.4867			−0.710346
$310$	5.08741	+	2.26506i	0.288945	+	0.128647i
$311$	11.8356	+	2.51573i	0.671134	+	0.142654i	0.530861	−	0.847459i	$-0.321869\pi$
$311$	11.8356	+	2.51573i	0.671134	+	0.142654i	0.140273	+	0.990113i	$0.455202\pi$
$312$	−1.45358	−	1.61436i	−0.0822927	−	0.0913953i
$313$	0.645568	−	6.14217i	0.0364896	−	0.347176i	−0.961011	−	0.276512i	$-0.910822\pi$
$313$	0.645568	−	6.14217i	0.0364896	−	0.347176i	0.997500	−	0.0706640i	$-0.0225118\pi$
$314$	12.6708	+	9.20587i	0.715054	+	0.519517i
$315$	4.12568	−	8.21052i	0.232456	−	0.462610i
$316$	2.61950	+	8.06200i	0.147359	+	0.453523i
$317$	0.601957	+	0.268008i	0.0338092	+	0.0150528i	0.423572	−	0.905863i	$-0.360776\pi$
$317$	0.601957	+	0.268008i	0.0338092	+	0.0150528i	−0.389762	+	0.920915i	$0.627443\pi$
$318$	11.4169	−	19.7747i	0.640230	−	1.10891i
$319$	0.910628	−	1.07589i	0.0509854	−	0.0602382i
$320$	−5.88411	−	10.1916i	−0.328932	−	0.569727i
$321$	−13.2277	+	9.61045i	−0.738296	+	0.536403i
$322$	5.42247	+	33.0369i	0.302182	+	1.84108i
$323$	1.62611	−	5.00464i	0.0904790	−	0.278466i
$324$	−0.154123	+	1.46638i	−0.00856240	+	0.0814658i
$325$	14.3066	−	6.36970i	0.793586	−	0.353327i
$326$	−0.115148	−	0.127885i	−0.00637746	−	0.00708288i
$327$	−1.48716	+	1.65166i	−0.0822402	+	0.0913370i
$328$	−5.19293	+	3.77289i	−0.286732	+	0.208323i
$329$	−5.40277	+	6.74884i	−0.297864	+	0.372076i
$330$	19.3379	−	9.32978i	1.06451	−	0.513588i
$331$	−3.91416	−	6.77953i	−0.215142	−	0.372637i	0.738175	−	0.674610i	$-0.235688\pi$
$331$	−3.91416	−	6.77953i	−0.215142	−	0.372637i	−0.953316	+	0.301973i	$0.902355\pi$
$332$	−2.13201	−	20.2847i	−0.117009	−	1.11327i
$333$	−1.00565	−	0.213757i	−0.0551090	−	0.0117138i
$334$	15.1249	−	3.21490i	0.827599	−	0.175912i
$335$	−38.5646	−	28.0188i	−2.10701	−	1.53083i
$336$	3.20128	−	12.2208i	0.174644	−	0.666701i
$337$	−2.51962	+	7.75460i	−0.137253	+	0.422420i	−0.995934	−	0.0900903i	$-0.971284\pi$
$337$	−2.51962	+	7.75460i	−0.137253	+	0.422420i	0.858681	+	0.512511i	$0.171284\pi$
$338$	10.0807	−	11.1958i	0.548320	−	0.608971i
$339$	−0.193502	−	1.84104i	−0.0105096	−	0.0999918i
$340$	12.8511	−	22.2587i	0.696948	−	1.20715i
$341$	−0.798102	+	2.73915i	−0.0432197	+	0.148333i
$342$	−1.95427			−0.105675
$343$	18.2410	−	3.20428i	0.984919	−	0.173015i
$344$	0.914635	+	2.81496i	0.0493138	+	0.151772i
$345$	−23.0618	+	4.90194i	−1.24161	+	0.263912i
$346$	−6.25753	+	2.78603i	−0.336407	+	0.149778i
$347$	−13.0544	+	5.81217i	−0.700794	+	0.312014i	−0.726025	−	0.687668i	$-0.758635\pi$
$347$	−13.0544	+	5.81217i	−0.700794	+	0.312014i	0.0252311	+	0.999682i	$0.491968\pi$
$348$	−0.612937	+	0.130284i	−0.0328569	+	0.00698395i
$349$	8.55755	+	26.3374i	0.458075	+	1.40981i	0.867486	+	0.497461i	$0.165734\pi$
$349$	8.55755	+	26.3374i	0.458075	+	1.40981i	−0.409411	+	0.912350i	$0.634266\pi$
$350$	29.3144	+	18.8043i	1.56692	+	1.00513i
$351$	−2.21758			−0.118366
$352$	18.2012	−	14.0957i	0.970129	−	0.751304i
$353$	6.73552	−	11.6663i	0.358495	−	0.620932i	−0.629214	−	0.777232i	$-0.716623\pi$
$353$	6.73552	−	11.6663i	0.358495	−	0.620932i	0.987710	+	0.156300i	$0.0499565\pi$
$354$	0.207793	+	1.97702i	0.0110441	+	0.105077i
$355$	37.7421	−	41.9169i	2.00315	−	2.22472i
$356$	−1.62478	+	5.00056i	−0.0861132	+	0.265029i
$357$	12.8074	−	3.50876i	0.677839	−	0.185703i
$358$	−27.2386	−	19.7900i	−1.43960	−	1.04593i
$359$	12.8074	−	2.72229i	0.675948	−	0.143677i	0.142868	−	0.989742i	$-0.454368\pi$
$359$	12.8074	−	2.72229i	0.675948	−	0.143677i	0.533080	+	0.846065i	$0.321034\pi$
$360$	3.32784	+	0.707355i	0.175393	+	0.0372809i
$361$	1.87114	+	17.8027i	0.0984812	+	0.936986i
$362$	2.51137	+	4.34983i	0.131995	+	0.228622i
$363$	6.07308	+	9.17157i	0.318754	+	0.481383i
$364$	−8.55184	−	1.30540i	−0.448238	−	0.0684216i
$365$	14.3127	−	10.3988i	0.749160	−	0.544296i
$366$	9.01394	−	10.0110i	0.471166	−	0.523283i
$367$	−13.1108	−	14.5610i	−0.684379	−	0.760080i	0.296429	−	0.955055i	$-0.404204\pi$
$367$	−13.1108	−	14.5610i	−0.684379	−	0.760080i	−0.980808	+	0.194975i	$0.937538\pi$
$368$	−29.6124	+	13.1843i	−1.54365	+	0.687278i
$369$	−0.684922	+	6.51660i	−0.0356556	+	0.339240i
$370$	2.05672	−	6.32995i	0.106924	−	0.329078i
$371$	5.24940	+	31.9825i	0.272535	+	1.66045i
$372$	1.02613	−	0.745530i	0.0532026	−	0.0386540i
$373$	−7.57666	−	13.1232i	−0.392304	−	0.679491i	0.600449	−	0.799663i	$-0.294989\pi$
$373$	−7.57666	−	13.1232i	−0.392304	−	0.679491i	−0.992753	+	0.120172i	$0.961655\pi$
$374$	28.7197	+	11.7463i	1.48506	+	0.607386i
$375$	−3.58068	+	6.20191i	−0.184905	+	0.320265i
$376$	−2.92413	−	1.30191i	−0.150801	−	0.0671408i
$377$	−0.291232	−	0.896321i	−0.0149992	−	0.0461629i
$378$	−2.70911	−	4.12092i	−0.139341	−	0.211957i
$379$	−9.29592	−	6.75388i	−0.477499	−	0.346924i	0.322857	−	0.946448i	$-0.395357\pi$
$379$	−9.29592	−	6.75388i	−0.477499	−	0.346924i	−0.800357	+	0.599524i	$0.795357\pi$
$380$	0.561199	−	5.33945i	0.0287889	−	0.273908i
$381$	−7.32095	−	8.13074i	−0.375063	−	0.416550i
$382$	20.8065	+	4.42255i	1.06455	+	0.226278i
$383$	−2.86361	−	1.27496i	−0.146324	−	0.0651476i	0.332268	−	0.943185i	$-0.392186\pi$
$383$	−2.86361	−	1.27496i	−0.146324	−	0.0651476i	−0.478592	+	0.878037i	$0.658853\pi$
$384$	7.56624			0.386113
$385$	−12.8427	+	27.6376i	−0.654524	+	1.40854i
$386$	−9.07940			−0.462130
$387$	2.76024	+	1.22894i	0.140311	+	0.0624704i
$388$	26.3826	+	5.60779i	1.33937	+	0.284693i
$389$	−14.7877	−	16.4234i	−0.749766	−	0.832700i	0.240679	−	0.970605i	$-0.422630\pi$
$389$	−14.7877	−	16.4234i	−0.749766	−	0.832700i	−0.990445	+	0.137905i	$0.955963\pi$
$390$	1.50061	−	14.2773i	0.0759861	−	0.722960i
$391$	−27.5654	−	20.0274i	−1.39404	−	1.01283i
$392$	2.85910	+	6.23272i	0.144406	+	0.314800i
$393$	4.64199	+	14.2866i	0.234157	+	0.720662i
$394$	6.98386	+	3.10942i	0.351842	+	0.156650i
$395$	9.98350	−	17.2919i	0.502324	−	0.870051i
$396$	0.361936	−	4.87682i	0.0181880	−	0.245069i
$397$	−13.1278	−	22.7381i	−0.658867	−	1.14119i	−0.980909	−	0.194466i	$-0.937703\pi$
$397$	−13.1278	−	22.7381i	−0.658867	−	1.14119i	0.322043	−	0.946725i	$-0.395631\pi$
$398$	2.50245	−	1.81814i	0.125437	−	0.0911351i
$399$	2.14590	−	1.75772i	0.107429	−	0.0879959i
$400$	−10.4201	+	32.0698i	−0.521005	+	1.60349i
$401$	−2.25072	+	21.4142i	−0.112396	+	1.06937i	0.782362	+	0.622824i	$0.214015\pi$
$401$	−2.25072	+	21.4142i	−0.112396	+	1.06937i	−0.894758	+	0.446551i	$0.852652\pi$
$402$	−23.3720	+	10.4059i	−1.16569	+	0.518998i
$403$	1.27645	+	1.41764i	0.0635844	+	0.0706177i
$404$	−15.8741	+	17.6300i	−0.789766	+	0.877124i
$405$	2.80975	−	2.04140i	0.139617	−	0.101438i
$406$	1.30985	−	1.63619i	0.0650066	−	0.0812026i
$407$	3.35550	+	0.606439i	0.166326	+	0.0300600i
$408$	2.45836	+	4.25801i	0.121707	+	0.210803i
$409$	1.17164	+	11.1474i	0.0579336	+	0.551202i	0.984539	+	0.175166i	$0.0560463\pi$
$409$	1.17164	+	11.1474i	0.0579336	+	0.551202i	−0.926605	+	0.376035i	$0.877287\pi$
$410$	−41.4920	−	8.81939i	−2.04914	−	0.435558i
$411$	19.9537	−	4.24129i	0.984243	−	0.209207i
$412$	−14.8950	−	10.8218i	−0.733823	−	0.533154i
$413$	−2.00635	−	1.98399i	−0.0987261	−	0.0976259i
$414$	−3.91026	+	12.0345i	−0.192179	+	0.591466i
$415$	−32.1471	+	35.7029i	−1.57804	+	1.75259i
$416$	−1.60896	−	15.3082i	−0.0788856	−	0.750547i
$417$	−4.45734	+	7.72034i	−0.218277	+	0.378067i
$418$	6.47852	−	0.198564i	0.316875	−	0.00971208i
$419$	22.4366			1.09610			0.548050	−	0.836445i	$-0.315370\pi$
$419$	22.4366			1.09610			0.548050	+	0.836445i	$0.315370\pi$
$420$	12.0372	−	6.21844i	0.587353	−	0.303429i
$421$	−3.89935	−	12.0010i	−0.190043	−	0.584891i	0.809956	−	0.586490i	$-0.199491\pi$
$421$	−3.89935	−	12.0010i	−0.190043	−	0.584891i	−0.999999	+	0.00159963i	$0.999491\pi$
$422$	−22.8951	+	4.86651i	−1.11452	+	0.236898i
$423$	−2.98503	+	1.32902i	−0.145137	+	0.0646192i
$424$	−10.9626	+	4.88088i	−0.532393	+	0.237036i
$425$	−34.6703	+	7.36941i	−1.68176	+	0.357469i
$426$	−9.35475	−	28.7910i	−0.453239	−	1.39493i
$427$	−0.893702	+	19.1000i	−0.0432493	+	0.924315i
$428$	−24.1078			−1.16530
$429$	7.35142	−	0.225318i	0.354930	−	0.0108785i
$430$	−9.78002	+	16.9395i	−0.471635	+	0.816895i
$431$	−3.92667	−	37.3598i	−0.189141	−	1.79956i	−0.518211	−	0.855253i	$-0.673402\pi$
$431$	−3.92667	−	37.3598i	−0.189141	−	1.79956i	0.329069	−	0.944306i	$-0.393265\pi$
$432$	3.19502	−	3.54843i	0.153721	−	0.170724i
$433$	7.40552	−	22.7918i	0.355886	−	1.09531i	−0.599607	−	0.800294i	$-0.704677\pi$
$433$	7.40552	−	22.7918i	0.355886	−	1.09531i	0.955494	−	0.295011i	$-0.0953234\pi$
$434$	−1.07502	+	4.10388i	−0.0516027	+	0.196993i
$435$	1.19411	+	0.867574i	0.0572533	+	0.0415970i
$436$	−3.20542	+	0.681333i	−0.153512	+	0.0326299i
$437$	−6.96184	−	1.47978i	−0.333030	−	0.0707877i
$438$	−0.992503	−	9.44304i	−0.0474236	−	0.451206i
$439$	−0.208627	−	0.361352i	−0.00995721	−	0.0172464i	0.861004	−	0.508598i	$-0.169836\pi$
$439$	−0.208627	−	0.361352i	−0.00995721	−	0.0172464i	−0.870961	+	0.491352i	$0.836503\pi$
$440$	−11.1039	−	2.00680i	−0.529357	−	0.0956705i
$441$	6.68122	+	2.08838i	0.318153	+	0.0994465i
$442$	16.7845	−	12.1946i	0.798355	−	0.580039i
$443$	6.29720	−	6.99375i	0.299189	−	0.332283i	−0.574741	−	0.818336i	$-0.694897\pi$
$443$	6.29720	−	6.99375i	0.299189	−	0.332283i	0.873929	+	0.486053i	$0.161564\pi$
$444$	−1.01434	−	1.12654i	−0.0481386	−	0.0534633i
$445$	11.3141	−	5.03734i	0.536338	−	0.238793i
$446$	4.57799	−	43.5567i	0.216774	−	2.06247i
$447$	7.15769	−	22.0291i	0.338547	−	1.04194i
$448$	6.93539	−	5.68081i	0.327667	−	0.268393i
$449$	14.4666	−	10.5106i	0.682720	−	0.496025i	−0.191539	−	0.981485i	$-0.561348\pi$
$449$	14.4666	−	10.5106i	0.682720	−	0.496025i	0.874259	+	0.485460i	$0.161348\pi$
$450$	6.58174	+	11.3999i	0.310266	+	0.537397i
$451$	1.60844	−	21.6725i	0.0757385	−	1.02052i
$452$	1.36475	−	2.36382i	0.0641925	−	0.111185i
$453$	−3.37623	−	1.50319i	−0.158629	−	0.0706261i
$454$	13.0233	+	40.0817i	0.611215	+	1.88113i
$455$	11.1936	+	17.0270i	0.524765	+	0.798239i
$456$	0.830895	+	0.603681i	0.0389102	+	0.0282699i
$457$	−2.89683	+	27.5615i	−0.135508	+	1.28927i	0.689556	+	0.724232i	$0.257806\pi$
$457$	−2.89683	+	27.5615i	−0.135508	+	1.28927i	−0.825064	+	0.565039i	$0.808861\pi$
$458$	18.4520	+	20.4930i	0.862206	+	0.957577i
$459$	4.90943	+	1.04353i	0.229153	+	0.0487079i
$460$	−31.7579	−	14.1395i	−1.48072	−	0.659260i
$461$	31.1388			1.45028			0.725140	−	0.688602i	$-0.241775\pi$
$461$	31.1388			1.45028			0.725140	+	0.688602i	$0.241775\pi$
$462$	9.39958	+	13.3859i	0.437308	+	0.622767i
$463$	14.7614			0.686020			0.343010	−	0.939332i	$-0.388554\pi$
$463$	14.7614			0.686020			0.343010	+	0.939332i	$0.388554\pi$
$464$	1.85384	+	0.825382i	0.0860623	+	0.0383174i
$465$	−2.92232	−	0.621158i	−0.135519	−	0.0288055i
$466$	3.85484	+	4.28123i	0.178572	+	0.198324i
$467$	−2.44687	+	23.2804i	−0.113228	+	1.07729i	0.779410	+	0.626515i	$0.215519\pi$
$467$	−2.44687	+	23.2804i	−0.113228	+	1.07729i	−0.892637	+	0.450776i	$0.851147\pi$
$468$	−2.64527	−	1.92190i	−0.122278	−	0.0888399i
$469$	16.3045	−	32.4476i	0.752872	−	1.49829i
$470$	−6.53663	−	20.1177i	−0.301512	−	0.927959i
$471$	−7.67596	−	3.41756i	−0.353690	−	0.157473i
$472$	0.522363	−	0.904759i	0.0240437	−	0.0416449i
$473$	−9.27525	−	3.79356i	−0.426477	−	0.174428i
$474$	−5.35818	−	9.28064i	−0.246109	−	0.426274i
$475$	−5.98997	+	4.35197i	−0.274839	+	0.199682i
$476$	18.3184	+	6.91425i	0.839622	+	0.316914i
$477$	−3.78546	+	11.6504i	−0.173324	+	0.533437i
$478$	−4.34450	+	41.3352i	−0.198713	+	1.89063i
$479$	7.97255	−	3.54961i	0.364275	−	0.162186i	−0.216433	−	0.976297i	$-0.569442\pi$
$479$	7.97255	−	3.54961i	0.364275	−	0.162186i	0.580708	+	0.814112i	$0.302776\pi$
$480$	16.1306	+	17.9149i	0.736259	+	0.817699i
$481$	1.52556	−	1.69431i	0.0695597	−	0.0772539i
$482$	8.03259	−	5.83602i	0.365874	−	0.265823i
$483$	−6.53047	−	16.7316i	−0.297147	−	0.761316i
$484$	−0.704332	+	16.2038i	−0.0320151	+	0.736535i
$485$	−31.7658	−	55.0199i	−1.44241	−	2.49833i
$486$	−0.194840	−	1.85378i	−0.00883812	−	0.0840891i
$487$	−3.13742	−	0.666879i	−0.142170	−	0.0302192i	0.136277	−	0.990671i	$-0.456486\pi$
$487$	−3.13742	−	0.666879i	−0.142170	−	0.0302192i	−0.278447	+	0.960452i	$0.589820\pi$
$488$	−6.92489	+	1.47193i	−0.313475	+	0.0666312i
$489$	0.0746895	+	0.0542651i	0.00337757	+	0.00245395i
$490$	−17.9666	+	41.6021i	−0.811647	+	1.87939i
$491$	−1.37204	+	4.22269i	−0.0619191	+	0.190567i	−0.977231	−	0.212179i	$-0.931944\pi$
$491$	−1.37204	+	4.22269i	−0.0619191	+	0.190567i	0.915312	+	0.402746i	$0.131944\pi$
$492$	−6.46473	+	7.17981i	−0.291453	+	0.323691i
$493$	0.222967	+	2.12139i	0.0100419	+	0.0955424i
$494$	2.16687	−	3.75313i	0.0974920	−	0.168861i
$495$	−9.10708	+	7.05286i	−0.409333	+	0.317003i
$496$	−4.10749			−0.184432
$497$	36.1674	+	23.2003i	1.62233	+	1.04068i
$498$	7.96796	+	24.5228i	0.357053	+	1.09890i
$499$	6.31787	−	1.34291i	0.282827	−	0.0601167i	−0.0643140	−	0.997930i	$-0.520486\pi$
$499$	6.31787	−	1.34291i	0.282827	−	0.0601167i	0.347141	+	0.937813i	$0.387153\pi$
$500$	−9.64625	+	4.29479i	−0.431393	+	0.192069i
$501$	−7.57836	+	3.37410i	−0.338576	+	0.150744i
$502$	38.4146	−	8.16528i	1.71453	−	0.364434i
$503$	−5.77237	−	17.7655i	−0.257377	−	0.792126i	−0.993352	−	0.115117i	$-0.963276\pi$
$503$	−5.77237	−	17.7655i	−0.257377	−	0.792126i	0.735975	−	0.677009i	$-0.236724\pi$
$504$	−0.121138	+	2.58895i	−0.00539593	+	0.115321i
$505$	55.8797			2.48662
$506$	11.7400	−	40.2926i	0.521907	−	1.79123i
$507$	−4.04117	+	6.99952i	−0.179475	+	0.310860i
$508$	−1.68626	−	16.0437i	−0.0748156	−	0.711823i
$509$	−27.3709	+	30.3984i	−1.21319	+	1.34739i	−0.292907	+	0.956141i	$0.594623\pi$
$509$	−27.3709	+	30.3984i	−1.21319	+	1.34739i	−0.920286	+	0.391246i	$0.872044\pi$
$510$	−10.0407	+	30.9020i	−0.444608	+	1.36836i
$511$	9.58314	+	9.47634i	0.423933	+	0.419209i
$512$	19.2451	+	13.9824i	0.850520	+	0.617939i
$513$	1.02552	−	0.217981i	0.0452778	−	0.00962410i
$514$	−8.12597	−	1.72723i	−0.358421	−	0.0761847i
$515$	4.53308	+	43.1293i	0.199751	+	1.90051i
$516$	2.22751	+	3.85816i	0.0980607	+	0.169846i
$517$	9.76053	−	4.70909i	0.429268	−	0.207105i
$518$	5.01224	+	0.765096i	0.220225	+	0.0336164i
$519$	2.97295	−	2.15997i	0.130498	−	0.0948122i
$520$	−5.04833	+	5.60674i	−0.221384	+	0.245872i
$521$	−1.36786	−	1.51916i	−0.0599271	−	0.0665558i	0.712436	−	0.701737i	$-0.247592\pi$
$521$	−1.36786	−	1.51916i	−0.0599271	−	0.0665558i	−0.772363	+	0.635182i	$0.780925\pi$
$522$	0.723690	−	0.322207i	0.0316750	−	0.0141026i
$523$	0.653387	−	6.21656i	0.0285706	−	0.271831i	−0.970905	−	0.239463i	$-0.923029\pi$
$523$	0.653387	−	6.21656i	0.0285706	−	0.271831i	0.999476	−	0.0323679i	$-0.0103048\pi$
$524$	−6.84443	+	21.0650i	−0.299000	+	0.920228i
$525$	−17.4805	−	6.59799i	−0.762912	−	0.287960i
$526$	−22.5365	+	16.3737i	−0.982638	+	0.713929i
$527$	−2.15879	−	3.73913i	−0.0940384	−	0.162879i
$528$	−10.2312	+	12.0879i	−0.445255	+	0.526059i
$529$	−11.5425	+	19.9922i	−0.501847	+	0.869225i
$530$	−72.4468	−	32.2554i	−3.14689	−	1.40108i
$531$	−0.329561	−	1.01428i	−0.0143017	−	0.0440162i
$532$	4.08312	−	0.236936i	0.177026	−	0.0102725i
$533$	−11.7556	−	8.54091i	−0.509189	−	0.369948i
$534$	0.694796	−	6.61054i	0.0300668	−	0.286066i
$535$	37.9967	+	42.1996i	1.64274	+	1.82445i
$536$	13.1515	+	2.79543i	0.568057	+	0.120744i
$537$	16.5011	+	7.34676i	0.712075	+	0.317036i
$538$	27.7671			1.19713
$539$	−22.3609	−	6.24426i	−0.963151	−	0.268959i
$540$	5.12086			0.220367
$541$	−4.45048	−	1.98148i	−0.191341	−	0.0851906i	0.308830	−	0.951117i	$-0.400063\pi$
$541$	−4.45048	−	1.98148i	−0.191341	−	0.0851906i	−0.500171	+	0.865927i	$0.666729\pi$
$542$	41.3135	+	8.78145i	1.77457	+	0.377196i
$543$	−1.80305	−	2.00249i	−0.0773764	−	0.0859352i
$544$	−3.64160	+	34.6475i	−0.156132	+	1.48550i
$545$	6.24474	+	4.53707i	0.267495	+	0.194347i
$546$	10.9180	−	0.633550i	0.467246	−	0.0271135i
$547$	−5.37326	−	16.5372i	−0.229744	−	0.707080i	−0.997775	−	0.0666674i	$-0.978763\pi$
$547$	−5.37326	−	16.5372i	−0.229744	−	0.707080i	0.768031	−	0.640413i	$-0.221237\pi$
$548$	27.4778	+	12.2339i	1.17379	+	0.522607i
$549$	−3.61352	+	6.25879i	−0.154221	+	0.267119i
$550$	−22.9772	−	37.1227i	−0.979751	−	1.58292i
$551$	0.222786	+	0.385877i	0.00949101	+	0.0164389i
$552$	5.38005	−	3.90883i	0.228990	−	0.166371i
$553$	14.2308	+	5.37141i	0.605157	+	0.228416i
$554$	8.36230	−	25.7365i	0.355280	−	1.09344i
$555$	−0.373237	+	3.55111i	−0.0158430	+	0.150736i
$556$	−12.0080	+	5.34629i	−0.509251	+	0.226733i
$557$	11.5002	+	12.7723i	0.487280	+	0.541180i	0.935771	−	0.352608i	$-0.114705\pi$
$557$	11.5002	+	12.7723i	0.487280	+	0.541180i	−0.448491	+	0.893787i	$0.648038\pi$
$558$	−1.07292	+	1.19160i	−0.0454204	+	0.0504445i
$559$	−5.42067	+	3.93835i	−0.229270	+	0.166574i
$560$	−43.3730	−	6.62070i	−1.83285	−	0.279776i
$561$	−16.3811	−	2.96056i	−0.691612	−	0.124995i
$562$	1.40559	+	2.43455i	0.0592911	+	0.102695i
$563$	3.37852	+	32.1444i	0.142387	+	1.35473i	0.799378	+	0.600828i	$0.205162\pi$
$563$	3.37852	+	32.1444i	0.142387	+	1.35473i	−0.656991	+	0.753898i	$0.728171\pi$
$564$	−4.71255	−	1.00168i	−0.198434	−	0.0421785i
$565$	−6.28874	+	1.33671i	−0.264569	+	0.0562359i
$566$	20.7013	+	15.0403i	0.870139	+	0.632193i
$567$	1.88128	+	1.86032i	0.0790064	+	0.0781259i
$568$	−4.91629	+	15.1308i	−0.206283	+	0.634874i
$569$	13.7003	−	15.2157i	0.574346	−	0.637876i	−0.384052	−	0.923311i	$-0.625472\pi$
$569$	13.7003	−	15.2157i	0.574346	−	0.637876i	0.958398	+	0.285436i	$0.0921383\pi$
$570$	0.709459	+	6.75006i	0.0297160	+	0.282729i
$571$	4.54476	−	7.87175i	0.190192	−	0.329422i	−0.755122	−	0.655585i	$-0.772422\pi$
$571$	4.54476	−	7.87175i	0.190192	−	0.329422i	0.945314	+	0.326162i	$0.105756\pi$
$572$	8.96452	+	6.10246i	0.374825	+	0.255157i
$573$	−11.4117			−0.476731
$574$	1.51037	−	32.2793i	0.0630416	−	1.34731i
$575$	14.8146	+	45.5945i	0.617810	+	1.90142i
$576$	3.31441	−	0.704499i	0.138100	−	0.0293541i
$577$	25.5828	−	11.3902i	1.06502	−	0.474179i	0.202023	−	0.979381i	$-0.435248\pi$
$577$	25.5828	−	11.3902i	1.06502	−	0.474179i	0.863002	+	0.505201i	$0.168582\pi$
$578$	−13.9488	+	6.21040i	−0.580193	+	0.258319i
$579$	4.76451	−	1.01273i	0.198006	−	0.0420875i
$580$	0.672517	+	2.06980i	0.0279248	+	0.0859436i
$581$	−30.8058	−	19.7610i	−1.27804	−	0.819823i
$582$	−34.0976			−1.41339
$583$	11.3653	−	39.0066i	0.470703	−	1.61549i
$584$	−2.49501	+	4.32149i	−0.103244	+	0.178824i
$585$	0.805050	+	7.65954i	0.0332847	+	0.316683i
$586$	2.89119	−	3.21099i	0.119434	−	0.132645i
$587$	4.77233	−	14.6877i	0.196975	−	0.606227i	−0.802973	−	0.596016i	$-0.796750\pi$
$587$	4.77233	−	14.6877i	0.196975	−	0.606227i	0.999948	−	0.0102110i	$-0.00325033\pi$
$588$	6.15986	+	8.28154i	0.254028	+	0.341525i
$589$	−0.729644	−	0.530117i	−0.0300645	−	0.0218431i
$590$	6.75322	−	1.43544i	0.278026	−	0.0590962i
$591$	−4.01168	−	0.852709i	−0.165018	−	0.0350757i
$592$	0.513143	+	4.88223i	0.0210900	+	0.200658i
$593$	11.9567	+	20.7096i	0.491002	+	0.850440i	0.999946	−	0.0103595i	$-0.00329760\pi$
$593$	11.9567	+	20.7096i	0.491002	+	0.850440i	−0.508945	+	0.860799i	$0.669964\pi$
$594$	0.834262	+	6.12561i	0.0342302	+	0.251337i
$595$	−16.7688	−	42.9630i	−0.687453	−	1.76131i
$596$	27.6300	−	20.0744i	1.13177	−	0.822279i
$597$	−1.11039	+	1.23321i	−0.0454453	+	0.0504721i
$598$	−18.7764	−	20.8533i	−0.767826	−	0.852757i
$599$	2.01754	−	0.898265i	0.0824343	−	0.0367021i	−0.365105	−	0.930966i	$-0.618967\pi$
$599$	2.01754	−	0.898265i	0.0824343	−	0.0367021i	0.447540	+	0.894264i	$0.352300\pi$
$600$	0.723120	−	6.88002i	0.0295212	−	0.280876i
$601$	−9.84703	+	30.3061i	−0.401669	+	1.23621i	0.521976	+	0.852960i	$0.325195\pi$
$601$	−9.84703	+	30.3061i	−0.401669	+	1.23621i	−0.923645	+	0.383249i	$0.874805\pi$
$602$	−13.9408	−	5.26194i	−0.568184	−	0.214460i
$603$	11.1040	−	8.06752i	0.452189	−	0.328535i
$604$	−2.72461	−	4.71917i	−0.110863	−	0.192020i
$605$	29.4740	−	24.3061i	1.19829	−	0.988182i
$606$	14.9954	−	25.9728i	0.609147	−	1.05507i
$607$	−11.2519	−	5.00967i	−0.456700	−	0.203336i	0.165475	−	0.986214i	$-0.447084\pi$
$607$	−11.2519	−	5.00967i	−0.456700	−	0.203336i	−0.622175	+	0.782878i	$0.713751\pi$
$608$	2.24881	+	6.92113i	0.0912014	+	0.280689i
$609$	−0.504853	+	1.00471i	−0.0204577	+	0.0407128i
$610$	−37.8504	−	27.4999i	−1.53252	−	1.11344i
$611$	0.757411	−	7.20628i	0.0306416	−	0.291535i
$612$	4.95189	+	5.49963i	0.200168	+	0.222309i
$613$	−15.2341	−	3.23812i	−0.615301	−	0.130786i	−0.110291	−	0.993899i	$-0.535178\pi$
$613$	−15.2341	−	3.23812i	−0.615301	−	0.130786i	−0.505011	+	0.863113i	$0.668511\pi$
$614$	33.8305	+	15.0623i	1.36529	+	0.607865i
$615$	22.7570			0.917652
$616$	0.138531	−	8.59484i	0.00558157	−	0.346296i
$617$	−30.3050			−1.22003			−0.610016	−	0.792389i	$-0.708837\pi$
$617$	−30.3050			−1.22003			−0.610016	+	0.792389i	$0.708837\pi$
$618$	21.2629	+	9.46686i	0.855320	+	0.380813i
$619$	−25.8966	−	5.50450i	−1.04087	−	0.221244i	−0.344397	−	0.938824i	$-0.611917\pi$
$619$	−25.8966	−	5.50450i	−1.04087	−	0.221244i	−0.696476	+	0.717580i	$0.745250\pi$
$620$	−2.94759	−	3.27363i	−0.118378	−	0.131472i
$621$	0.709601	−	6.75140i	0.0284753	−	0.270924i
$622$	−18.2468	−	13.2571i	−0.731629	−	0.531560i
$623$	5.18276	+	7.88369i	0.207643	+	0.315853i
$624$	3.27208	+	10.0704i	0.130988	+	0.403140i
$625$	−9.53585	−	4.24563i	−0.381434	−	0.169825i
$626$	−5.75600	+	9.96969i	−0.230056	+	0.398469i
$627$	−3.37752	+	0.826821i	−0.134885	+	0.0330200i
$628$	−6.19449	−	10.7292i	−0.247187	−	0.428141i
$629$	−4.17470	+	3.03310i	−0.166456	+	0.120937i
$630$	−13.2502	+	10.8533i	−0.527901	+	0.432406i
$631$	0.304170	−	0.936140i	0.0121088	−	0.0372672i	−0.944820	−	0.327591i	$-0.893763\pi$
$631$	0.304170	−	0.936140i	0.0121088	−	0.0372672i	0.956928	+	0.290324i	$0.0937631\pi$
$632$	−0.588690	+	5.60101i	−0.0234168	+	0.222796i
$633$	11.4716	−	5.10749i	0.455956	−	0.203005i
$634$	−0.821844	−	0.912751i	−0.0326396	−	0.0362500i
$635$	−25.4259	+	28.2383i	−1.00900	+	1.12060i
$636$	−14.6126	+	10.6167i	−0.579426	+	0.420978i
$637$	−11.4187	+	10.5156i	−0.452427	+	0.416642i
$638$	−2.36634	+	1.14167i	−0.0936844	+	0.0451992i
$639$	8.12038	+	14.0649i	0.321237	+	0.556399i
$640$	−2.74678	−	26.1339i	−0.108576	−	1.03303i
$641$	−7.09002	−	1.50703i	−0.280039	−	0.0595241i	0.0657510	−	0.997836i	$-0.479056\pi$
$641$	−7.09002	−	1.50703i	−0.280039	−	0.0595241i	−0.345790	+	0.938312i	$0.612389\pi$
$642$	29.8108	−	6.33648i	1.17654	−	0.250081i
$643$	8.05300	+	5.85085i	0.317579	+	0.230735i	0.735142	−	0.677913i	$-0.237116\pi$
$643$	8.05300	+	5.85085i	0.317579	+	0.230735i	−0.417563	+	0.908648i	$0.637116\pi$
$644$	6.71078	−	25.6183i	0.264442	−	1.00950i
$645$	3.24271	−	9.98004i	0.127682	−	0.392964i
$646$	−6.56329	+	7.28927i	−0.258229	+	0.286792i
$647$	0.491298	+	4.67438i	0.0193149	+	0.183769i	0.999926	−	0.0121969i	$-0.00388248\pi$
$647$	0.491298	+	4.67438i	0.0193149	+	0.183769i	−0.980611	+	0.195966i	$0.937216\pi$
$648$	−0.489800	+	0.848359i	−0.0192412	+	0.0333267i
$649$	1.19557	+	3.32894i	0.0469304	+	0.130672i
$650$	−29.1910			−1.14497
$651$	0.106377	−	2.27346i	0.00416923	−	0.0891040i
$652$	0.0420647	+	0.129462i	0.00164738	+	0.00507011i
$653$	−8.45668	+	1.79752i	−0.330935	+	0.0703425i	−0.370383	−	0.928879i	$-0.620774\pi$
$653$	−8.45668	+	1.79752i	−0.330935	+	0.0703425i	0.0394476	+	0.999222i	$0.487440\pi$
$654$	3.78461	−	1.68502i	0.147990	−	0.0658894i
$655$	47.6608	−	21.2199i	1.86226	−	0.829132i
$656$	30.6037	−	6.50502i	1.19487	−	0.253978i
$657$	1.57411	+	4.84462i	0.0614120	+	0.189007i
$658$	14.3167	−	7.39607i	0.558123	−	0.288329i
$659$	−4.04586			−0.157604			−0.0788022	−	0.996890i	$-0.525110\pi$
$659$	−4.04586			−0.157604			−0.0788022	+	0.996890i	$0.525110\pi$
$660$	−16.9760	+	0.520307i	−0.660789	+	0.0202529i
$661$	8.32331	−	14.4164i	0.323739	−	0.560732i	−0.657517	−	0.753439i	$-0.728393\pi$
$661$	8.32331	−	14.4164i	0.323739	−	0.560732i	0.981256	+	0.192707i	$0.0617267\pi$
$662$	1.52527	+	14.5120i	0.0592813	+	0.564024i
$663$	−7.44761	+	8.27141i	−0.289241	+	0.321235i
$664$	4.18747	−	12.8877i	0.162505	−	0.500140i
$665$	−6.85020	−	6.77386i	−0.265639	−	0.262679i
$666$	1.55039	+	1.12643i	0.0600765	+	0.0436482i
$667$	2.82204	−	0.599842i	0.109270	−	0.0232260i
$668$	−11.9642	−	2.54306i	−0.462908	−	0.0983940i
$669$	2.45602	+	23.3675i	0.0949552	+	0.903438i
$670$	44.4267	+	76.9494i	1.71635	+	2.97281i
$671$	11.3431	−	21.1155i	0.437896	−	0.815154i
$672$	−11.4770	+	14.3365i	−0.442736	+	0.553041i
$673$	−3.01328	+	2.18928i	−0.116154	+	0.0843905i	−0.644346	−	0.764734i	$-0.722870\pi$
$673$	−3.01328	+	2.18928i	−0.116154	+	0.0843905i	0.528192	+	0.849125i	$0.322870\pi$
$674$	10.1697	−	11.2946i	0.391722	−	0.435051i
$675$	−4.72539	−	5.24808i	−0.181880	−	0.201999i
$676$	−10.8868	+	4.84712i	−0.418724	+	0.186428i
$677$	−2.55180	+	24.2787i	−0.0980735	+	0.933107i	0.829258	+	0.558866i	$0.188763\pi$
$677$	−2.55180	+	24.2787i	−0.0980735	+	0.933107i	−0.927332	+	0.374241i	$0.877903\pi$
$678$	−1.06629	+	3.28171i	−0.0409507	+	0.126033i
$679$	37.4412	−	30.6682i	1.43686	−	1.17694i
$680$	13.8147	−	10.0370i	0.529771	−	0.384901i
$681$	−11.3049	−	19.5806i	−0.433204	−	0.750332i
$682$	3.43574	−	4.05925i	0.131561	−	0.155437i
$683$	6.37357	−	11.0394i	0.243878	−	0.422409i	−0.717938	−	0.696108i	$-0.754914\pi$
$683$	6.37357	−	11.0394i	0.243878	−	0.422409i	0.961816	+	0.273698i	$0.0882470\pi$
$684$	1.41222	+	0.628762i	0.0539977	+	0.0240413i
$685$	−21.8933	−	67.3805i	−0.836498	−	2.57448i
$686$	−33.4908	−	8.37307i	−1.27868	−	0.319685i
$687$	−11.9687	−	8.69576i	−0.456634	−	0.331764i
$688$	1.50805	−	14.3481i	0.0574937	−	0.547016i
$689$	−18.1771	−	20.1878i	−0.692494	−	0.769093i
$690$	42.9870	+	9.13717i	1.63649	+	0.347846i
$691$	15.2649	+	6.79637i	0.580704	+	0.258546i	0.675998	−	0.736903i	$-0.263713\pi$
$691$	15.2649	+	6.79637i	0.580704	+	0.258546i	−0.0952945	+	0.995449i	$0.530379\pi$
$692$	5.41829			0.205973
$693$	−6.42560	−	5.97593i	−0.244088	−	0.227007i
$694$	26.6360			1.01109
$695$	28.2843	+	12.5930i	1.07288	+	0.477679i
$696$	−0.407222	−	0.0865578i	−0.0154357	−	0.00328096i
$697$	22.0062	+	24.4403i	0.833543	+	0.925743i
$698$	5.39567	−	51.3364i	0.204229	−	1.94311i
$699$	−2.50040	−	1.81664i	−0.0945737	−	0.0687118i
$700$	−15.1336	−	23.0203i	−0.571996	−	0.870084i
$701$	−7.93645	−	24.4259i	−0.299756	−	0.922553i	−0.981582	−	0.191039i	$-0.938814\pi$
$701$	−7.93645	−	24.4259i	−0.299756	−	0.922553i	0.681827	−	0.731514i	$-0.261186\pi$
$702$	3.77618	+	1.68126i	0.142523	+	0.0634552i
$703$	−0.538953	+	0.933493i	−0.0203270	+	0.0352074i
$704$	−10.9159	+	2.67222i	−0.411409	+	0.100713i
$705$	5.67411	+	9.82784i	0.213699	+	0.370138i
$706$	−20.3143	+	14.7592i	−0.764540	+	0.555470i
$707$	6.89475	+	42.0070i	0.259304	+	1.57983i
$708$	0.485925	−	1.49552i	0.0182622	−	0.0562052i
$709$	4.50551	−	42.8670i	0.169208	−	1.60991i	−0.499455	−	0.866340i	$-0.666466\pi$
$709$	4.50551	−	42.8670i	0.169208	−	1.60991i	0.668663	−	0.743566i	$-0.266867\pi$
$710$	−96.0483	+	42.7634i	−3.60463	+	1.60488i
$711$	3.84693	+	4.27245i	0.144271	+	0.160229i
$712$	−2.33743	+	2.59598i	−0.0875989	+	0.0972884i
$713$	−4.72444	+	3.43251i	−0.176932	+	0.128549i
$714$	−24.4691	−	3.73510i	−0.915733	−	0.139783i
$715$	−3.44705	−	25.3101i	−0.128912	−	0.946544i
$716$	13.3164	+	23.0646i	0.497656	+	0.861966i
$717$	−2.33075	−	22.1756i	−0.0870436	−	0.828165i
$718$	−23.8728	−	5.07433i	−0.890927	−	0.189372i
$719$	30.3331	−	6.44750i	1.13123	−	0.240451i	0.395990	−	0.918255i	$-0.370401\pi$
$719$	30.3331	−	6.44750i	1.13123	−	0.240451i	0.735243	+	0.677803i	$0.237068\pi$
$720$	−13.4162	−	9.74745i	−0.499993	−	0.363266i
$721$	−31.8627	+	8.72923i	−1.18663	+	0.325093i
$722$	10.3109	−	31.7338i	0.383734	−	1.18101i
$723$	−3.56422	+	3.95847i	−0.132555	+	0.147217i
$724$	−0.415303	−	3.95135i	−0.0154346	−	0.146851i
$725$	1.50064	−	2.59918i	0.0557322	−	0.0965310i
$726$	−3.38803	−	20.2220i	−0.125742	−	0.750510i
$727$	3.36801			0.124913			0.0624563	−	0.998048i	$-0.480107\pi$
$727$	3.36801			0.124913			0.0624563	+	0.998048i	$0.480107\pi$
$728$	−4.83770	−	3.10324i	−0.179297	−	0.115014i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−32.2561	+	6.85624i	−1.19385	+	0.253761i
$731$	13.8540	−	6.16818i	0.512407	−	0.228138i
$732$	−9.73472	+	4.33417i	−0.359805	+	0.160196i
$733$	9.98167	−	2.12167i	0.368682	−	0.0783657i	−0.0198454	−	0.999803i	$-0.506317\pi$
$733$	9.98167	−	2.12167i	0.368682	−	0.0783657i	0.388527	+	0.921437i	$0.372984\pi$
$734$	11.2861	+	34.7351i	0.416579	+	1.28210i
$735$	4.78779	−	23.8352i	0.176600	−	0.879173i
$736$	47.1206			1.73689
$737$	−35.9908	+	27.8726i	−1.32574	+	1.02670i
$738$	6.10689	−	10.5774i	0.224798	−	0.389361i
$739$	−2.36039	−	22.4576i	−0.0868284	−	0.826117i	−0.948100	−	0.317972i	$-0.896998\pi$
$739$	−2.36039	−	22.4576i	−0.0868284	−	0.826117i	0.861272	−	0.508145i	$-0.169669\pi$
$740$	−3.52285	+	3.91252i	−0.129503	+	0.143827i
$741$	−0.718458	+	2.21119i	−0.0263932	+	0.0812299i
$742$	15.3087	−	58.4409i	0.562002	−	2.14543i
$743$	−20.2308	−	14.6985i	−0.742194	−	0.539236i	0.151203	−	0.988503i	$-0.451685\pi$
$743$	−20.2308	−	14.6985i	−0.742194	−	0.539236i	−0.893398	+	0.449267i	$0.851685\pi$
$744$	0.824265	−	0.175203i	0.0302190	−	0.00642325i
$745$	−78.6872	−	16.7255i	−2.88288	−	0.612774i
$746$	2.95247	+	28.0909i	0.108098	+	1.02848i
$747$	−6.91657	−	11.9799i	−0.253064	−	0.438320i
$748$	−16.9746	−	17.7285i	−0.620655	−	0.648219i
$749$	−27.0348	+	33.7704i	−0.987831	+	1.23394i
$750$	10.7993	−	7.84616i	0.394335	−	0.286501i
$751$	−14.8345	+	16.4754i	−0.541319	+	0.601196i	−0.950296	−	0.311349i	$-0.899219\pi$
$751$	−14.8345	+	16.4754i	−0.541319	+	0.601196i	0.408977	+	0.912545i	$0.365886\pi$
$752$	10.4398	+	11.5946i	0.380700	+	0.422811i
$753$	−19.2477	+	8.56962i	−0.701424	+	0.312294i
$754$	−0.183627	+	1.74709i	−0.00668729	+	0.0636253i
$755$	−3.96637	+	12.2072i	−0.144351	+	0.444266i
$756$	0.631840	+	3.84955i	0.0229798	+	0.140007i
$757$	34.0443	−	24.7347i	1.23736	−	0.898996i	0.239943	−	0.970787i	$-0.422871\pi$
$757$	34.0443	−	24.7347i	1.23736	−	0.898996i	0.997420	+	0.0717908i	$0.0228714\pi$
$758$	10.7090	+	18.5485i	0.388968	+	0.673712i
$759$	−1.66640	+	22.4535i	−0.0604864	+	0.815009i
$760$	1.78348	−	3.08908i	0.0646936	−	0.112053i
$761$	−37.3293	−	16.6201i	−1.35319	−	0.602477i	−0.403299	−	0.915068i	$-0.632136\pi$
$761$	−37.3293	−	16.6201i	−1.35319	−	0.602477i	−0.949888	+	0.312591i	$0.898803\pi$
$762$	6.30206	+	19.3957i	0.228300	+	0.702634i
$763$	−2.64018	+	5.25422i	−0.0955810	+	0.190216i
$764$	−13.6126	−	9.89014i	−0.492487	−	0.357813i
$765$	1.82209	−	17.3361i	0.0658780	−	0.626787i
$766$	3.90966	+	4.34212i	0.141262	+	0.156887i
$767$	2.31332	+	0.491712i	0.0835293	+	0.0177547i
$768$	−19.0751	−	8.49279i	−0.688314	−	0.306457i
$769$	−3.87395			−0.139698			−0.0698490	−	0.997558i	$-0.522252\pi$
$769$	−3.87395			−0.139698			−0.0698490	+	0.997558i	$0.522252\pi$
$770$	42.8226	−	37.3257i	1.54322	−	1.34513i
$771$	4.45684			0.160509
$772$	6.56111	+	2.92119i	0.236139	+	0.105136i
$773$	12.2684	+	2.60773i	0.441264	+	0.0937935i	0.423185	−	0.906043i	$-0.360912\pi$
$773$	12.2684	+	2.60773i	0.441264	+	0.0937935i	0.0180782	+	0.999837i	$0.494245\pi$
$774$	−3.76852	−	4.18537i	−0.135457	−	0.150440i
$775$	−0.635002	+	6.04164i	−0.0228099	+	0.217022i
$776$	14.4973	+	10.5329i	0.520422	+	0.378109i
$777$	−2.71556	+	0.157579i	−0.0974202	+	0.00565312i
$778$	12.7296	+	39.1778i	0.456379	+	1.40459i
$779$	6.27591	+	2.79421i	0.224858	+	0.100113i
$780$	−5.67795	+	9.83450i	−0.203303	+	0.352132i
$781$	−28.3487	−	45.8011i	−1.01440	−	1.63889i
$782$	31.7556	+	55.0023i	1.13558	+	1.96688i
$783$	−0.343824	+	0.249803i	−0.0122873	+	0.00892722i
$784$	−0.374568	−	33.4221i	−0.0133774	−	1.19365i
$785$	−9.01767	+	27.7535i	−0.321854	+	0.990566i
$786$	2.92684	−	27.8471i	0.104397	−	0.993272i
$787$	11.5493	−	5.14207i	0.411687	−	0.183295i	−0.190434	−	0.981700i	$-0.560989\pi$
$787$	11.5493	−	5.14207i	0.411687	−	0.183295i	0.602120	+	0.798405i	$0.294323\pi$
$788$	−4.04637	−	4.49395i	−0.144146	−	0.160090i
$789$	9.99991	−	11.1060i	0.356006	−	0.395385i
$790$	−30.1102	+	21.8764i	−1.07127	+	0.778326i
$791$	−1.78080	−	4.56256i	−0.0633179	−	0.162226i
$792$	1.53752	−	2.86213i	0.0546335	−	0.101701i
$793$	−8.01325	−	13.8794i	−0.284559	−	0.492871i
$794$	5.11565	+	48.6722i	0.181548	+	1.72731i
$795$	41.6150	+	8.84554i	1.47593	+	0.313719i
$796$	−2.39333	+	0.508718i	−0.0848293	+	0.0180310i
$797$	−25.3544	−	18.4211i	−0.898100	−	0.652508i	0.0398776	−	0.999205i	$-0.487303\pi$
$797$	−25.3544	−	18.4211i	−0.898100	−	0.652508i	−0.937977	+	0.346697i	$0.887303\pi$
$798$	−4.98674	+	1.36619i	−0.176529	+	0.0483625i
$799$	−5.06789	+	15.5974i	−0.179289	+	0.551795i
$800$	32.7996	−	36.4277i	1.15964	−	1.28791i
$801$	0.372746	+	3.54645i	0.0131703	+	0.125307i
$802$	20.0679	−	34.7586i	0.708622	−	1.22737i
$803$	−5.71053	−	15.9003i	−0.201520	−	0.561110i
$804$	20.2374			0.713718
$805$	−55.4205	+	28.6304i	−1.95332	+	1.00909i
$806$	−1.09880	−	3.38176i	−0.0387036	−	0.119117i
$807$	−14.5711	+	3.09718i	−0.512926	+	0.109026i
$808$	−14.3987	+	6.41072i	−0.506545	+	0.225528i
$809$	28.2303	−	12.5689i	0.992524	−	0.441900i	0.154772	−	0.987950i	$-0.450536\pi$
$809$	28.2303	−	12.5689i	0.992524	−	0.441900i	0.837753	+	0.546050i	$0.183869\pi$
$810$	−6.33224	+	1.34596i	−0.222492	+	0.0472922i
$811$	15.6393	+	48.1327i	0.549169	+	1.69017i	0.710867	+	0.703327i	$0.248303\pi$
$811$	15.6393	+	48.1327i	0.549169	+	1.69017i	−0.161698	+	0.986840i	$0.551697\pi$
$812$	−1.47297	+	0.760940i	−0.0516910	+	0.0267038i
$813$	−22.6592			−0.794691
$814$	−5.25411	−	3.57665i	−0.184156	−	0.125362i
$815$	0.160318	−	0.277678i	0.00561568	−	0.00972664i
$816$	−2.50510	−	23.8344i	−0.0876959	−	0.834371i
$817$	2.11967	−	2.35413i	0.0741577	−	0.0823605i
$818$	6.45630	−	19.8705i	0.225739	−	0.694754i
$819$	−5.65864	+	1.55026i	−0.197729	+	0.0541706i
$820$	27.1461	+	19.7228i	0.947981	+	0.688749i
$821$	−21.4230	+	4.55360i	−0.747668	+	0.158922i	−0.565962	−	0.824431i	$-0.691495\pi$
$821$	−21.4230	+	4.55360i	−0.747668	+	0.158922i	−0.181706	+	0.983353i	$0.558162\pi$
$822$	−37.1935	−	7.90572i	−1.29727	−	0.275744i
$823$	4.08271	+	38.8444i	0.142314	+	1.35403i	0.799665	+	0.600446i	$0.205010\pi$
$823$	4.08271	+	38.8444i	0.142314	+	1.35403i	−0.657351	+	0.753585i	$0.728323\pi$
$824$	−6.11600	−	10.5932i	−0.213061	−	0.369033i
$825$	16.1982	+	16.9176i	0.563950	+	0.588996i
$826$	1.91233	+	4.89954i	0.0665384	+	0.170477i
$827$	12.3679	−	8.98580i	0.430074	−	0.312467i	−0.351605	−	0.936149i	$-0.614364\pi$
$827$	12.3679	−	8.98580i	0.430074	−	0.312467i	0.781678	+	0.623682i	$0.214364\pi$
$828$	6.69767	−	7.43852i	0.232760	−	0.258506i
$829$	17.6389	+	19.5899i	0.612623	+	0.680387i	0.967018	−	0.254709i	$-0.0819798\pi$
$829$	17.6389	+	19.5899i	0.612623	+	0.680387i	−0.354395	+	0.935096i	$0.615313\pi$
$830$	81.8096	−	36.4240i	2.83965	−	1.26429i
$831$	−1.51752	+	14.4382i	−0.0526422	+	0.500857i
$832$	−2.32200	+	7.14639i	−0.0805010	+	0.247756i
$833$	30.2280	−	17.9068i	1.04734	−	0.620433i
$834$	13.4433	−	9.76715i	0.465505	−	0.338209i
$835$	14.4054	+	24.9508i	0.498518	+	0.863459i
$836$	−4.74550	−	1.94090i	−0.164127	−	0.0671274i
$837$	0.430114	−	0.744979i	0.0148669	−	0.0257502i
$838$	−38.2060	−	17.0104i	−1.31980	−	0.587614i
$839$	3.06478	+	9.43243i	0.105808	+	0.325644i	0.989919	−	0.141633i	$-0.0452352\pi$
$839$	3.06478	+	9.43243i	0.105808	+	0.325644i	−0.884111	+	0.467277i	$0.845235\pi$
$840$	8.98622	−	0.521455i	0.310054	−	0.0179919i
$841$	23.3154	+	16.9396i	0.803978	+	0.584124i
$842$	−2.45860	+	23.3920i	−0.0847289	+	0.806142i
$843$	−1.00915	−	1.12077i	−0.0347569	−	0.0386015i
$844$	18.1106	+	3.84952i	0.623392	+	0.132506i
$845$	25.6435	+	11.4172i	0.882163	+	0.392764i
$846$	6.09062			0.209400
$847$	21.9085	+	19.1577i	0.752784	+	0.658267i
$848$	58.4923			2.00864
$849$	−12.5408	−	5.58353i	−0.430399	−	0.191626i
$850$	64.6252	+	13.7365i	2.21663	+	0.471158i
$851$	4.67015	+	5.18673i	0.160091	+	0.177799i
$852$	−2.50308	+	23.8152i	−0.0857540	+	0.815895i
$853$	21.1701	+	15.3810i	0.724850	+	0.526635i	0.887930	−	0.459978i	$-0.152143\pi$
$853$	21.1701	+	15.3810i	0.724850	+	0.526635i	−0.163080	+	0.986613i	$0.552143\pi$
$854$	16.0026	−	31.8467i	0.547597	−	1.08977i
$855$	−1.12521	−	3.46303i	−0.0384812	−	0.118433i
$856$	−14.6320	−	6.51459i	−0.500112	−	0.222664i
$857$	−21.7863	+	37.7349i	−0.744204	+	1.28900i	0.206361	+	0.978476i	$0.433838\pi$
$857$	−21.7863	+	37.7349i	−0.744204	+	1.28900i	−0.950566	+	0.310524i	$0.899496\pi$
$858$	−12.6891	−	5.18982i	−0.433200	−	0.177178i
$859$	−10.1360	−	17.5560i	−0.345834	−	0.599002i	0.639671	−	0.768649i	$-0.279071\pi$
$859$	−10.1360	−	17.5560i	−0.345834	−	0.599002i	−0.985505	+	0.169647i	$0.945737\pi$
$860$	12.5175	−	9.09448i	0.426843	−	0.310119i
$861$	2.80789	+	17.1074i	0.0956927	+	0.583017i
$862$	−21.6380	+	66.5948i	−0.736992	+	2.26823i
$863$	−1.73494	+	16.5068i	−0.0590579	+	0.561898i	0.924484	+	0.381220i	$0.124496\pi$
$863$	−1.73494	+	16.5068i	−0.0590579	+	0.561898i	−0.983542	+	0.180678i	$0.942171\pi$
$864$	−6.34105	+	2.82322i	−0.215727	+	0.0960478i
$865$	−8.53984	−	9.48445i	−0.290363	−	0.322481i
$866$	−29.8901	+	33.1963i	−1.01571	+	1.12806i
$867$	6.62705	−	4.81484i	0.225067	−	0.163520i
$868$	2.09723	−	2.61974i	0.0711845	−	0.0889197i
$869$	−13.1869	−	13.7726i	−0.447336	−	0.467203i
$870$	−1.37563	−	2.38266i	−0.0466382	−	0.0807798i
$871$	3.18152	+	30.2702i	0.107802	+	1.02566i
$872$	−2.12961	−	0.452663i	−0.0721178	−	0.0153291i
$873$	17.8930	−	3.80328i	0.605588	−	0.128722i
$874$	10.7330	+	7.79798i	0.363049	+	0.263771i
$875$	−4.80126	+	18.3287i	−0.162312	+	0.619624i
$876$	−2.32097	+	7.14321i	−0.0784183	+	0.241347i
$877$	−20.9141	+	23.2274i	−0.706218	+	0.784334i	−0.984353	−	0.176208i	$-0.943617\pi$
$877$	−20.9141	+	23.2274i	−0.706218	+	0.784334i	0.278135	+	0.960542i	$0.410284\pi$
$878$	0.0812977	+	0.773496i	0.00274366	+	0.0261042i
$879$	−1.15902	+	2.00749i	−0.0390929	+	0.0677109i
$880$	45.4661	+	30.9503i	1.53266	+	1.04333i
$881$	−12.5333			−0.422257			−0.211129	−	0.977458i	$-0.567714\pi$
$881$	−12.5333			−0.422257			−0.211129	+	0.977458i	$0.567714\pi$
$882$	−9.79374	−	8.62156i	−0.329772	−	0.290303i
$883$	−6.28545	−	19.3446i	−0.211522	−	0.650999i	−0.999382	−	0.0351443i	$-0.988811\pi$
$883$	−6.28545	−	19.3446i	−0.211522	−	0.650999i	0.787860	−	0.615854i	$-0.211189\pi$
$884$	−16.0525	+	3.41207i	−0.539905	+	0.114760i
$885$	−3.38371	+	1.50652i	−0.113742	+	0.0506412i
$886$	−16.0255	+	7.13499i	−0.538386	+	0.239705i
$887$	41.2805	−	8.77445i	1.38606	−	0.294617i	0.546310	−	0.837583i	$-0.316032\pi$
$887$	41.2805	−	8.77445i	1.38606	−	0.294617i	0.839755	+	0.542966i	$0.182699\pi$
$888$	−0.311223	−	0.957846i	−0.0104440	−	0.0321432i
$889$	−24.3651	−	15.6295i	−0.817178	−	0.524195i
$890$	−23.0851			−0.773815
$891$	−1.12104	−	3.12142i	−0.0375564	−	0.104571i
$892$	−17.3221	+	30.0027i	−0.579986	+	1.00457i
$893$	0.358090	+	3.40700i	0.0119830	+	0.114011i
$894$	−28.8898	+	32.0854i	−0.966220	+	1.07310i
$895$	19.3854	−	59.6621i	0.647982	−	1.99428i
$896$	19.3070	−	5.28941i	0.645000	−	0.176707i
$897$	12.1791	+	8.84866i	0.406649	+	0.295448i
$898$	−32.6029	+	6.92996i	−1.08797	+	0.231256i
$899$	0.357599	+	0.0760100i	0.0119266	+	0.00253508i
$900$	−1.08842	−	10.3556i	−0.0362805	−	0.345186i
$901$	30.7420	+	53.2468i	1.02417	+	1.77391i
$902$	−19.1700	+	35.6854i	−0.638292	+	1.18820i
$903$	7.90249	+	1.20628i	0.262979	+	0.0401425i
$904$	1.46709	−	1.06590i	0.0487946	−	0.0354514i
$905$	−6.26207	+	6.95473i	−0.208158	+	0.231183i
$906$	4.60952	+	5.11939i	0.153141	+	0.170080i
$907$	−1.40283	+	0.624579i	−0.0465801	+	0.0207388i	−0.429894	−	0.902879i	$-0.641449\pi$
$907$	−1.40283	+	0.624579i	−0.0465801	+	0.0207388i	0.383314	+	0.923618i	$0.374783\pi$
$908$	3.48469	−	33.1546i	0.115643	−	1.10027i
$909$	−4.97196	+	15.3021i	−0.164909	+	0.507539i
$910$	−6.15185	−	37.4808i	−0.203932	−	1.24248i
$911$	−21.1533	+	15.3688i	−0.700839	+	0.509190i	−0.880205	−	0.474593i	$-0.842595\pi$
$911$	−21.1533	+	15.3688i	−0.700839	+	0.509190i	0.179366	+	0.983782i	$0.442595\pi$
$912$	−2.50307	−	4.33544i	−0.0828849	−	0.143561i
$913$	24.1461	+	39.0113i	0.799120	+	1.29108i
$914$	25.8287	−	44.7365i	0.854336	−	1.47975i
$915$	22.9298	+	10.2090i	0.758034	+	0.337499i
$916$	−6.74069	−	20.7457i	−0.222719	−	0.685458i
$917$	21.8325	+	33.2102i	0.720973	+	1.09670i
$918$	−7.56882	−	5.49907i	−0.249808	−	0.181496i
$919$	−3.72780	+	35.4677i	−0.122969	+	1.16997i	0.742796	+	0.669518i	$0.233499\pi$
$919$	−3.72780	+	35.4677i	−0.122969	+	1.16997i	−0.865764	+	0.500452i	$0.833167\pi$
$920$	−15.4543	−	17.1637i	−0.509513	−	0.565871i
$921$	−19.4329	−	4.13060i	−0.640337	−	0.136108i
$922$	−53.0244	−	23.6080i	−1.74627	−	0.777488i
$923$	−36.0152			−1.18545
$924$	−2.48573	−	12.6973i	−0.0817744	−	0.417711i
$925$	7.26051			0.238724
$926$	−25.1363	−	11.1914i	−0.826030	−	0.367772i
$927$	−12.2139	−	2.59614i	−0.401156	−	0.0852684i
$928$	−1.97388	−	2.19221i	−0.0647957	−	0.0719629i
$929$	−5.18530	+	49.3348i	−0.170124	+	1.61862i	0.492943	+	0.870062i	$0.335921\pi$
$929$	−5.18530	+	49.3348i	−0.170124	+	1.61862i	−0.663067	+	0.748560i	$0.730745\pi$
$930$	4.50531	+	3.27330i	0.147735	+	0.107336i
$931$	4.24696	−	5.98536i	0.139188	−	0.196162i
$932$	−1.40821	−	4.33402i	−0.0461274	−	0.141966i
$933$	11.0539	+	4.92151i	0.361888	+	0.161123i
$934$	21.8168	−	37.7878i	0.713867	−	1.23645i
$935$	−4.27893	+	57.6554i	−0.139936	+	1.88553i
$936$	−1.08617	−	1.88130i	−0.0355026	−	0.0614923i
$937$	38.6661	−	28.0926i	1.26317	−	0.917744i	0.264258	−	0.964452i	$-0.414873\pi$
$937$	38.6661	−	28.0926i	1.26317	−	0.917744i	0.998909	+	0.0467082i	$0.0148731\pi$
$938$	−52.3642	+	42.8918i	−1.70975	+	1.40047i
$939$	1.90849	−	5.87372i	0.0622812	−	0.191682i
$940$	−1.74902	+	16.6408i	−0.0570468	+	0.542764i
$941$	−4.69172	+	2.08889i	−0.152946	+	0.0680959i	−0.481782	−	0.876291i	$-0.660010\pi$
$941$	−4.69172	+	2.08889i	−0.152946	+	0.0680959i	0.328836	+	0.944387i	$0.393344\pi$
$942$	10.4799	+	11.6391i	0.341454	+	0.379223i
$943$	29.7644	−	33.0567i	0.969262	−	1.07647i
$944$	−4.11978	+	2.99320i	−0.134087	+	0.0974202i
$945$	5.74259	−	7.17332i	0.186806	−	0.233348i
$946$	12.9182	+	13.4919i	0.420006	+	0.438659i
$947$	−20.0586	−	34.7425i	−0.651816	−	1.12898i	−0.982682	−	0.185301i	$-0.940674\pi$
$947$	−20.0586	−	34.7425i	−0.651816	−	1.12898i	0.330866	−	0.943678i	$-0.392659\pi$
$948$	0.886076	+	8.43045i	0.0287784	+	0.273808i
$949$	−11.0494	−	2.34861i	−0.358677	−	0.0762392i
$950$	13.4994	−	2.86939i	0.437979	−	0.0930953i
$951$	0.533080	+	0.387306i	0.0172863	+	0.0125592i
$952$	9.24974	+	9.14666i	0.299786	+	0.296445i
$953$	−8.91613	+	27.4410i	−0.288822	+	0.888902i	0.696405	+	0.717649i	$0.254782\pi$
$953$	−8.91613	+	27.4410i	−0.288822	+	0.888902i	−0.985227	+	0.171253i	$0.945218\pi$
$954$	15.2788	−	16.9689i	0.494671	−	0.549388i
$955$	4.14281	+	39.4162i	0.134058	+	1.27548i
$956$	16.4386	−	28.4725i	0.531663	−	0.920867i
$957$	1.11442	−	0.863047i	0.0360240	−	0.0278984i
$958$	−16.2671			−0.525567
$959$	47.9513	−	24.7718i	1.54843	−	0.799923i
$960$	−3.63658	−	11.1922i	−0.117370	−	0.361228i
$961$	29.5988	−	6.29141i	0.954799	−	0.202949i
$962$	−3.88234	+	1.72853i	−0.125172	+	0.0557300i
$963$	−14.9367	+	6.65026i	−0.481329	+	0.214302i
$964$	−7.68231	+	1.63293i	−0.247430	+	0.0525930i
$965$	−5.22764	−	16.0890i	−0.168284	−	0.517924i
$966$	−1.56479	+	33.4424i	−0.0503463	+	1.07599i
$967$	−35.8128			−1.15166			−0.575831	−	0.817569i	$-0.695321\pi$
$967$	−35.8128			−1.15166			−0.575831	+	0.817569i	$0.695321\pi$
$968$	−4.80618	+	9.64439i	−0.154477	+	0.309982i
$969$	2.63110	−	4.55719i	0.0845230	−	0.146398i
$970$	12.3785	+	117.773i	0.397449	+	3.78148i
$971$	25.0233	−	27.7912i	0.803036	−	0.891862i	−0.192964	−	0.981206i	$-0.561810\pi$
$971$	25.0233	−	27.7912i	0.803036	−	0.891862i	0.996001	+	0.0893435i	$0.0284769\pi$
$972$	−0.455633	+	1.40230i	−0.0146144	+	0.0449787i
$973$	−5.97676	+	22.8162i	−0.191606	+	0.731454i
$974$	4.83693	+	3.51423i	0.154985	+	0.112603i
$975$	15.3183	−	3.25600i	0.490578	−	0.104276i
$976$	33.7542	+	7.17467i	1.08044	+	0.229656i
$977$	−2.76014	−	26.2609i	−0.0883046	−	0.840162i	−0.945599	−	0.325335i	$-0.894523\pi$
$977$	−2.76014	−	26.2609i	−0.0883046	−	0.840162i	0.857294	−	0.514827i	$-0.172144\pi$
$978$	−0.0860430	−	0.149031i	−0.00275135	−	0.00476548i
$979$	−1.59602	−	11.7188i	−0.0510090	−	0.374536i
$980$	26.3683	−	24.2827i	0.842304	−	0.775682i
$981$	−1.79806	+	1.30637i	−0.0574077	+	0.0417092i
$982$	5.53780	−	6.15035i	0.176718	−	0.196266i
$983$	−29.7004	−	32.9856i	−0.947294	−	1.05208i	−0.998574	−	0.0533923i	$-0.982997\pi$
$983$	−29.7004	−	32.9856i	−0.947294	−	1.05208i	0.0512795	−	0.998684i	$-0.483670\pi$
$984$	−5.86388	+	2.61077i	−0.186934	+	0.0832283i
$985$	−1.48890	+	14.1659i	−0.0474403	+	0.451365i
$986$	1.22866	−	3.78142i	0.0391285	−	0.120425i
$987$	−6.68787	+	5.47806i	−0.212877	+	0.174369i
$988$	−2.77338	+	2.01498i	−0.0882330	+	0.0641051i
$989$	−10.2557	−	17.7634i	−0.326113	−	0.564844i
$990$	20.8551	−	5.10534i	0.662817	−	0.162258i
$991$	−9.41079	+	16.3000i	−0.298944	+	0.517786i	−0.975895	−	0.218243i	$-0.929968\pi$
$991$	−9.41079	+	16.3000i	−0.298944	+	0.517786i	0.676951	+	0.736028i	$0.263301\pi$
$992$	5.45475	+	2.42861i	0.173188	+	0.0771085i
$993$	−2.41909	−	7.44518i	−0.0767673	−	0.236266i
$994$	−43.9979	−	66.9269i	−1.39553	−	2.12279i
$995$	4.66264	+	3.38761i	0.147816	+	0.107394i
$996$	2.13201	−	20.2847i	0.0675552	−	0.642745i
$997$	3.49172	+	3.87794i	0.110584	+	0.122816i	0.795895	−	0.605434i	$-0.207001\pi$
$997$	3.49172	+	3.87794i	0.110584	+	0.122816i	−0.685311	+	0.728250i	$0.740334\pi$
$998$	−11.7765	−	2.50316i	−0.372777	−	0.0792362i
$999$	−0.939227	−	0.418171i	−0.0297158	−	0.0132303i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.y.a.25.2	yes	64
3.2	odd	2		693.2.by.d.487.7		64
7.2	even	3	inner	231.2.y.a.58.7	yes	64
11.4	even	5	inner	231.2.y.a.4.7	✓	64
21.2	odd	6		693.2.by.d.289.2		64
33.26	odd	10		693.2.by.d.235.2		64
77.37	even	15	inner	231.2.y.a.37.2	yes	64
231.191	odd	30		693.2.by.d.37.7		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.y.a.4.7	✓	64	11.4	even	5	inner
231.2.y.a.25.2	yes	64	1.1	even	1	trivial
231.2.y.a.37.2	yes	64	77.37	even	15	inner
231.2.y.a.58.7	yes	64	7.2	even	3	inner
693.2.by.d.37.7		64	231.191	odd	30
693.2.by.d.235.2		64	33.26	odd	10
693.2.by.d.289.2		64	21.2	odd	6
693.2.by.d.487.7		64	3.2	odd	2

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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.70284 - 0.758153i) q^{2} +(0.978148 + 0.207912i) q^{3} +(0.986607 + 1.09574i) q^{4} +(0.363031 - 3.45401i) q^{5} +(-1.50800 - 1.09563i) q^{6} +(2.64131 - 0.153270i) q^{7} +(0.302713 + 0.931655i) q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})\)	\(q+(-1.70284 - 0.758153i) q^{2} +(0.978148 + 0.207912i) q^{3} +(0.986607 + 1.09574i) q^{4} +(0.363031 - 3.45401i) q^{5} +(-1.50800 - 1.09563i) q^{6} +(2.64131 - 0.153270i) q^{7} +(0.302713 + 0.931655i) q^{8} +(0.913545 + 0.406737i) q^{9} +(-3.23685 + 5.60640i) q^{10} +(-3.06979 - 1.25554i) q^{11} +(0.737230 + 1.27692i) q^{12} +(-1.79406 + 1.30346i) q^{13} +(-4.61393 - 1.74152i) q^{14} +(1.07323 - 3.30305i) q^{15} +(0.499112 - 4.74873i) q^{16} +(4.58519 - 2.04146i) q^{17} +(-1.24725 - 1.38521i) q^{18} +(0.701537 - 0.779136i) q^{19} +(4.14286 - 3.00996i) q^{20} +(2.61546 + 0.399238i) q^{21} +(4.27547 + 4.46535i) q^{22} +(-3.39430 - 5.87909i) q^{23} +(0.102396 + 0.974234i) q^{24} +(-6.90766 - 1.46827i) q^{25} +(4.04322 - 0.859412i) q^{26} +(0.809017 + 0.587785i) q^{27} +(2.77388 + 2.74296i) q^{28} +(-0.131329 + 0.404189i) q^{29} +(-4.33176 + 4.81090i) q^{30} +(-0.0899183 - 0.855515i) q^{31} +(-3.47057 + 6.01121i) q^{32} +(-2.74167 - 1.86635i) q^{33} -9.35558 q^{34} +(0.429479 - 9.17875i) q^{35} +(0.455633 + 1.40230i) q^{36} +(-1.00565 + 0.213757i) q^{37} +(-1.78531 + 0.794871i) q^{38} +(-2.02586 + 0.901970i) q^{39} +(3.32784 - 0.707355i) q^{40} +(2.02483 + 6.23179i) q^{41} +(-4.15102 - 2.66275i) q^{42} +3.02146 q^{43} +(-1.65294 - 4.60241i) q^{44} +(1.73652 - 3.00774i) q^{45} +(1.32269 + 12.5846i) q^{46} +(-2.18640 + 2.42824i) q^{47} +(1.47552 - 4.54119i) q^{48} +(6.95302 - 0.809669i) q^{49} +(10.6495 + 7.73730i) q^{50} +(4.90943 - 1.04353i) q^{51} +(-3.19828 - 0.679816i) q^{52} +(1.28047 + 12.1829i) q^{53} +(-0.931995 - 1.61426i) q^{54} +(-5.45107 + 10.1473i) q^{55} +(0.942354 + 2.41439i) q^{56} +(0.848199 - 0.616252i) q^{57} +(0.530070 - 0.588702i) q^{58} +(-0.713615 - 0.792550i) q^{59} +(4.67814 - 2.08284i) q^{60} +(-0.755430 + 7.18744i) q^{61} +(-0.495495 + 1.52498i) q^{62} +(2.47530 + 0.934297i) q^{63} +(2.74132 - 1.99168i) q^{64} +(3.85087 + 6.66989i) q^{65} +(3.25365 + 5.25670i) q^{66} +(6.86264 - 11.8864i) q^{67} +(6.76068 + 3.01005i) q^{68} +(-2.09779 - 6.45633i) q^{69} +(-7.69023 + 15.3043i) q^{70} +(13.1390 + 9.54608i) q^{71} +(-0.102396 + 0.974234i) q^{72} +(3.40851 + 3.78553i) q^{73} +(1.87451 + 0.398440i) q^{74} +(-6.45144 - 2.87237i) q^{75} +1.54587 q^{76} +(-8.30070 - 2.84576i) q^{77} +4.13354 q^{78} +(5.25211 + 2.33839i) q^{79} +(-16.2210 - 3.44787i) q^{80} +(0.669131 + 0.743145i) q^{81} +(1.27669 - 12.1469i) q^{82} +(-11.1912 - 8.13092i) q^{83} +(2.14297 + 3.25974i) q^{84} +(-5.38665 - 16.5784i) q^{85} +(-5.14506 - 2.29073i) q^{86} +(-0.212495 + 0.368052i) q^{87} +(0.240463 - 3.24006i) q^{88} +(1.78299 + 3.08823i) q^{89} +(-5.23734 + 3.80515i) q^{90} +(-4.53888 + 3.71781i) q^{91} +(3.09311 - 9.51961i) q^{92} +(0.0899183 - 0.855515i) q^{93} +(5.56406 - 2.47728i) q^{94} +(-2.43647 - 2.70597i) q^{95} +(-4.64453 + 5.15828i) q^{96} +(14.7992 - 10.7522i) q^{97} +(-12.4537 - 3.89272i) q^{98} +(-2.29372 - 2.39559i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{3} + 10 q^{4} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 64 * q - 8 * q^3 + 10 * q^4 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q - 8 q^{3} + 10 q^{4} - q^{7} + 8 q^{8} + 8 q^{9} - 22 q^{10} - 13 q^{11} + 30 q^{12} - 8 q^{13} - 26 q^{14} + 4 q^{17} - 5 q^{18} + 10 q^{19} + 24 q^{20} + 2 q^{21} - 38 q^{22} - 8 q^{23} + 14 q^{24} - 2 q^{25} + 4 q^{26} + 16 q^{27} - 67 q^{28} + 2 q^{29} - 3 q^{30} + 25 q^{31} + 72 q^{32} - 12 q^{33} - 56 q^{34} + 19 q^{35} - 20 q^{36} - 12 q^{37} - 37 q^{38} - 4 q^{39} - 9 q^{40} + 20 q^{41} + 9 q^{42} - 100 q^{43} - 5 q^{44} - 33 q^{46} - 18 q^{47} + 10 q^{48} + 29 q^{49} - 46 q^{50} + 6 q^{51} + 26 q^{52} - 49 q^{53} - 10 q^{54} - 24 q^{55} - 48 q^{56} + 20 q^{57} - 40 q^{58} + q^{59} + 12 q^{60} + 3 q^{61} + 4 q^{62} - 7 q^{63} - 24 q^{64} + 82 q^{65} + 11 q^{66} + 76 q^{67} - 39 q^{68} - 16 q^{69} + 59 q^{70} + 70 q^{71} - 14 q^{72} - 3 q^{73} + 32 q^{74} - 28 q^{75} + 104 q^{76} + 38 q^{77} - 12 q^{78} - 15 q^{79} - 83 q^{80} + 8 q^{81} + 42 q^{82} + 68 q^{83} + 27 q^{84} + 62 q^{85} - 47 q^{86} - 54 q^{87} - 64 q^{88} + 82 q^{89} - 16 q^{90} - 10 q^{91} + 190 q^{92} - 25 q^{93} - 6 q^{94} - 53 q^{95} + 8 q^{96} - 32 q^{97} - 152 q^{98} + 16 q^{99}+O(q^{100}) \) 64 * q - 8 * q^3 + 10 * q^4 - q^7 + 8 * q^8 + 8 * q^9 - 22 * q^10 - 13 * q^11 + 30 * q^12 - 8 * q^13 - 26 * q^14 + 4 * q^17 - 5 * q^18 + 10 * q^19 + 24 * q^20 + 2 * q^21 - 38 * q^22 - 8 * q^23 + 14 * q^24 - 2 * q^25 + 4 * q^26 + 16 * q^27 - 67 * q^28 + 2 * q^29 - 3 * q^30 + 25 * q^31 + 72 * q^32 - 12 * q^33 - 56 * q^34 + 19 * q^35 - 20 * q^36 - 12 * q^37 - 37 * q^38 - 4 * q^39 - 9 * q^40 + 20 * q^41 + 9 * q^42 - 100 * q^43 - 5 * q^44 - 33 * q^46 - 18 * q^47 + 10 * q^48 + 29 * q^49 - 46 * q^50 + 6 * q^51 + 26 * q^52 - 49 * q^53 - 10 * q^54 - 24 * q^55 - 48 * q^56 + 20 * q^57 - 40 * q^58 + q^59 + 12 * q^60 + 3 * q^61 + 4 * q^62 - 7 * q^63 - 24 * q^64 + 82 * q^65 + 11 * q^66 + 76 * q^67 - 39 * q^68 - 16 * q^69 + 59 * q^70 + 70 * q^71 - 14 * q^72 - 3 * q^73 + 32 * q^74 - 28 * q^75 + 104 * q^76 + 38 * q^77 - 12 * q^78 - 15 * q^79 - 83 * q^80 + 8 * q^81 + 42 * q^82 + 68 * q^83 + 27 * q^84 + 62 * q^85 - 47 * q^86 - 54 * q^87 - 64 * q^88 + 82 * q^89 - 16 * q^90 - 10 * q^91 + 190 * q^92 - 25 * q^93 - 6 * q^94 - 53 * q^95 + 8 * q^96 - 32 * q^97 - 152 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more