LMFDB - Embedded newform 690.2.m.e.541.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (of order $11$, degree $10$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6 x^{19} + 21 x^{18} - 47 x^{17} + 44 x^{16} + 232 x^{15} - 1084 x^{14} + 1484 x^{13} + \cdots + 1849 $ x^20 - 6x^19 + 21x^18 - 47x^17 + 44x^16 + 232x^15 - 1084x^14 + 1484x^13 + 2670x^12 - 12826x^11 + 18393x^10 - 2728x^9 - 12654x^8 - 6818x^7 + 39054x^6 + 33738x^5 + 67716x^4 + 45635x^3 + 32892x^2 + 9761*x + 1849
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			541.1
Root			$2.29563 - 0.674057i$ of defining polynomial
Character	$\chi$	$=$	690.541
Dual form			690.2.m.e.301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.841254 + 0.540641i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(0.415415 + 0.909632i) q^{6} +(-1.56737 - 1.80884i) q^{7} +(0.142315 + 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(-0.841254 + 0.540641i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(0.415415 + 0.909632i) q^{6} +(-1.56737 - 1.80884i) q^{7} +(0.142315 + 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(0.654861 - 0.755750i) q^{10} +(-1.37163 - 0.881496i) q^{11} +(-0.841254 - 0.540641i) q^{12} +(-3.58307 + 4.13508i) q^{13} +(2.29649 + 0.674311i) q^{14} +(0.142315 + 0.989821i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(2.92093 + 6.39594i) q^{17} +(0.959493 - 0.281733i) q^{18} +(0.0124061 - 0.0271656i) q^{19} +(-0.142315 + 0.989821i) q^{20} +(-2.01349 + 1.29399i) q^{21} +1.63047 q^{22} +(3.70628 + 3.04360i) q^{23} +1.00000 q^{24} +(0.841254 - 0.540641i) q^{25} +(0.778675 - 5.41580i) q^{26} +(-0.415415 + 0.909632i) q^{27} +(-2.29649 + 0.674311i) q^{28} +(3.03551 + 6.64685i) q^{29} +(-0.654861 - 0.755750i) q^{30} +(-0.805005 - 5.59894i) q^{31} +(0.959493 + 0.281733i) q^{32} +(-1.06773 + 1.23222i) q^{33} +(-5.91515 - 3.80143i) q^{34} +(2.01349 + 1.29399i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(0.313038 + 0.0919164i) q^{37} +(0.00425014 + 0.0295604i) q^{38} +(3.58307 + 4.13508i) q^{39} +(-0.415415 - 0.909632i) q^{40} +(-6.45169 + 1.89439i) q^{41} +(0.994273 - 2.17715i) q^{42} +(-0.892008 + 6.20405i) q^{43} +(-1.37163 + 0.881496i) q^{44} +1.00000 q^{45} +(-4.76341 - 0.556676i) q^{46} +3.56788 q^{47} +(-0.841254 + 0.540641i) q^{48} +(0.180943 - 1.25848i) q^{49} +(-0.415415 + 0.909632i) q^{50} +(6.74653 - 1.98096i) q^{51} +(2.27294 + 4.97705i) q^{52} +(3.19497 + 3.68719i) q^{53} +(-0.142315 - 0.989821i) q^{54} +(1.56442 + 0.459355i) q^{55} +(1.56737 - 1.80884i) q^{56} +(-0.0251235 - 0.0161459i) q^{57} +(-6.14719 - 3.95056i) q^{58} +(-8.58579 + 9.90853i) q^{59} +(0.959493 + 0.281733i) q^{60} +(-0.408849 - 2.84360i) q^{61} +(3.70423 + 4.27491i) q^{62} +(0.994273 + 2.17715i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(2.27294 - 4.97705i) q^{65} +(0.232039 - 1.61387i) q^{66} +(-5.04507 + 3.24227i) q^{67} +7.03135 q^{68} +(3.54008 - 3.23540i) q^{69} -2.39344 q^{70} +(7.56127 - 4.85933i) q^{71} +(0.142315 - 0.989821i) q^{72} +(-5.80891 + 12.7197i) q^{73} +(-0.313038 + 0.0919164i) q^{74} +(-0.415415 - 0.909632i) q^{75} +(-0.0195570 - 0.0225700i) q^{76} +(0.555373 + 3.86271i) q^{77} +(-5.24986 - 1.54150i) q^{78} +(-3.29370 + 3.80113i) q^{79} +(0.841254 + 0.540641i) q^{80} +(0.841254 + 0.540641i) q^{81} +(4.40332 - 5.08171i) q^{82} +(-13.8778 - 4.07489i) q^{83} +(0.340623 + 2.36908i) q^{84} +(-4.60455 - 5.31394i) q^{85} +(-2.60376 - 5.70144i) q^{86} +(7.01119 - 2.05867i) q^{87} +(0.677320 - 1.48312i) q^{88} +(0.0865524 - 0.601985i) q^{89} +(-0.841254 + 0.540641i) q^{90} +13.0957 q^{91} +(4.30820 - 2.10699i) q^{92} -5.65651 q^{93} +(-3.00149 + 1.92894i) q^{94} +(-0.00425014 + 0.0295604i) q^{95} +(0.415415 - 0.909632i) q^{96} +(-8.03139 + 2.35823i) q^{97} +(0.528169 + 1.15653i) q^{98} +(1.06773 + 1.23222i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} + 2 q^{10} - 4 q^{11} + 2 q^{12} - 13 q^{13} + 2 q^{14} + 2 q^{15} - 2 q^{16} + 6 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} + 2 q^{21} + 26 q^{22} + 24 q^{23} + 20 q^{24} - 2 q^{25} + 13 q^{26} + 2 q^{27} - 2 q^{28} + 2 q^{29} - 2 q^{30} + 6 q^{31} + 2 q^{32} + 4 q^{33} + 5 q^{34} - 2 q^{35} - 2 q^{36} - 20 q^{37} + 4 q^{38} + 13 q^{39} + 2 q^{40} - 11 q^{41} - 13 q^{42} + 4 q^{43} - 4 q^{44} + 20 q^{45} - 2 q^{46} + 18 q^{47} + 2 q^{48} - 6 q^{49} + 2 q^{50} + 27 q^{51} - 2 q^{52} - 18 q^{53} - 2 q^{54} + 18 q^{55} + 2 q^{56} - 7 q^{57} + 9 q^{58} - 52 q^{59} + 2 q^{60} - 7 q^{61} + 16 q^{62} - 13 q^{63} - 2 q^{64} - 2 q^{65} + 7 q^{66} - 10 q^{67} + 28 q^{68} + 20 q^{69} - 20 q^{70} + 7 q^{71} + 2 q^{72} - 37 q^{73} + 20 q^{74} + 2 q^{75} - 4 q^{76} - 70 q^{77} + 9 q^{78} + 20 q^{79} - 2 q^{80} - 2 q^{81} - 11 q^{82} - 19 q^{83} - 9 q^{84} + 17 q^{85} - 26 q^{86} - 2 q^{87} + 4 q^{88} + 33 q^{89} + 2 q^{90} - 42 q^{91} - 9 q^{92} + 16 q^{93} - 7 q^{94} - 4 q^{95} - 2 q^{96} + 9 q^{97} + 6 q^{98} - 4 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 + 2 * q^10 - 4 * q^11 + 2 * q^12 - 13 * q^13 + 2 * q^14 + 2 * q^15 - 2 * q^16 + 6 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 + 2 * q^21 + 26 * q^22 + 24 * q^23 + 20 * q^24 - 2 * q^25 + 13 * q^26 + 2 * q^27 - 2 * q^28 + 2 * q^29 - 2 * q^30 + 6 * q^31 + 2 * q^32 + 4 * q^33 + 5 * q^34 - 2 * q^35 - 2 * q^36 - 20 * q^37 + 4 * q^38 + 13 * q^39 + 2 * q^40 - 11 * q^41 - 13 * q^42 + 4 * q^43 - 4 * q^44 + 20 * q^45 - 2 * q^46 + 18 * q^47 + 2 * q^48 - 6 * q^49 + 2 * q^50 + 27 * q^51 - 2 * q^52 - 18 * q^53 - 2 * q^54 + 18 * q^55 + 2 * q^56 - 7 * q^57 + 9 * q^58 - 52 * q^59 + 2 * q^60 - 7 * q^61 + 16 * q^62 - 13 * q^63 - 2 * q^64 - 2 * q^65 + 7 * q^66 - 10 * q^67 + 28 * q^68 + 20 * q^69 - 20 * q^70 + 7 * q^71 + 2 * q^72 - 37 * q^73 + 20 * q^74 + 2 * q^75 - 4 * q^76 - 70 * q^77 + 9 * q^78 + 20 * q^79 - 2 * q^80 - 2 * q^81 - 11 * q^82 - 19 * q^83 - 9 * q^84 + 17 * q^85 - 26 * q^86 - 2 * q^87 + 4 * q^88 + 33 * q^89 + 2 * q^90 - 42 * q^91 - 9 * q^92 + 16 * q^93 - 7 * q^94 - 4 * q^95 - 2 * q^96 + 9 * q^97 + 6 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{10}{11}\right)$

Coefficient data

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

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

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

$2$	−0.841254	+	0.540641i	−0.594856	+	0.382291i
$2$	−0.841254	+	0.540641i	−0.594856	+	0.382291i
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i
$4$	0.415415	−	0.909632i	0.207708	−	0.454816i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$6$	0.415415	+	0.909632i	0.169592	+	0.371356i
$7$	−1.56737	−	1.80884i	−0.592411	−	0.683679i	0.377815	−	0.925881i	$-0.376676\pi$
$7$	−1.56737	−	1.80884i	−0.592411	−	0.683679i	−0.970226	+	0.242202i	$0.922130\pi$
$8$	0.142315	+	0.989821i	0.0503159	+	0.349955i
$9$	−0.959493	−	0.281733i	−0.319831	−	0.0939109i
$10$	0.654861	−	0.755750i	0.207085	−	0.238989i
$11$	−1.37163	−	0.881496i	−0.413563	−	0.265781i	0.317272	−	0.948334i	$-0.397233\pi$
$11$	−1.37163	−	0.881496i	−0.413563	−	0.265781i	−0.730836	+	0.682553i	$0.760869\pi$
$12$	−0.841254	−	0.540641i	−0.242849	−	0.156070i
$13$	−3.58307	+	4.13508i	−0.993764	+	1.14687i	−0.00460923	+	0.999989i	$0.501467\pi$
$13$	−3.58307	+	4.13508i	−0.993764	+	1.14687i	−0.989155	+	0.146876i	$0.953078\pi$
$14$	2.29649	+	0.674311i	0.613763	+	0.180217i
$15$	0.142315	+	0.989821i	0.0367455	+	0.255571i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	2.92093	+	6.39594i	0.708429	+	1.55124i	0.829442	+	0.558592i	$0.188658\pi$
$17$	2.92093	+	6.39594i	0.708429	+	1.55124i	−0.121014	+	0.992651i	$0.538614\pi$
$18$	0.959493	−	0.281733i	0.226155	−	0.0664050i
$19$	0.0124061	−	0.0271656i	0.00284615	−	0.00623221i	−0.908204	−	0.418529i	$-0.862546\pi$
$19$	0.0124061	−	0.0271656i	0.00284615	−	0.00623221i	0.911050	+	0.412296i	$0.135273\pi$
$20$	−0.142315	+	0.989821i	−0.0318226	+	0.221331i
$21$	−2.01349	+	1.29399i	−0.439380	+	0.282373i
$22$	1.63047			0.347616
$23$	3.70628	+	3.04360i	0.772812	+	0.634635i
$23$	3.70628	+	3.04360i	0.772812	+	0.634635i
$24$	1.00000			0.204124
$25$	0.841254	−	0.540641i	0.168251	−	0.108128i
$26$	0.778675	−	5.41580i	0.152711	−	1.06213i
$27$	−0.415415	+	0.909632i	−0.0799467	+	0.175059i
$28$	−2.29649	+	0.674311i	−0.433996	+	0.127433i
$29$	3.03551	+	6.64685i	0.563681	+	1.23429i	0.950094	+	0.311963i	$0.100986\pi$
$29$	3.03551	+	6.64685i	0.563681	+	1.23429i	−0.386414	+	0.922326i	$0.626286\pi$
$30$	−0.654861	−	0.755750i	−0.119561	−	0.137980i
$31$	−0.805005	−	5.59894i	−0.144583	−	1.00560i	−0.924899	−	0.380213i	$-0.875851\pi$
$31$	−0.805005	−	5.59894i	−0.144583	−	1.00560i	0.780316	−	0.625386i	$-0.215058\pi$
$32$	0.959493	+	0.281733i	0.169616	+	0.0498038i
$33$	−1.06773	+	1.23222i	−0.185868	+	0.214503i
$34$	−5.91515	−	3.80143i	−1.01444	−	0.651940i
$35$	2.01349	+	1.29399i	0.340342	+	0.218725i
$36$	−0.654861	+	0.755750i	−0.109143	+	0.125958i
$37$	0.313038	+	0.0919164i	0.0514632	+	0.0151110i	0.307363	−	0.951592i	$-0.400553\pi$
$37$	0.313038	+	0.0919164i	0.0514632	+	0.0151110i	−0.255900	+	0.966703i	$0.582372\pi$
$38$	0.00425014	+	0.0295604i	0.000689464	+	0.00479533i
$39$	3.58307	+	4.13508i	0.573750	+	0.662143i
$40$	−0.415415	−	0.909632i	−0.0656829	−	0.143825i
$41$	−6.45169	+	1.89439i	−1.00758	+	0.295854i	−0.743565	−	0.668664i	$-0.766867\pi$
$41$	−6.45169	+	1.89439i	−1.00758	+	0.295854i	−0.264020	+	0.964517i	$0.585048\pi$
$42$	0.994273	−	2.17715i	0.153420	−	0.335942i
$43$	−0.892008	+	6.20405i	−0.136030	+	0.946109i	0.801448	+	0.598065i	$0.204063\pi$
$43$	−0.892008	+	6.20405i	−0.136030	+	0.946109i	−0.937478	+	0.348045i	$0.886846\pi$
$44$	−1.37163	+	0.881496i	−0.206782	+	0.132891i
$45$	1.00000			0.149071
$46$	−4.76341	−	0.556676i	−0.702327	−	0.0820774i
$47$	3.56788			0.520428			0.260214	−	0.965551i	$-0.416207\pi$
$47$	3.56788			0.520428			0.260214	+	0.965551i	$0.416207\pi$
$48$	−0.841254	+	0.540641i	−0.121424	+	0.0780348i
$49$	0.180943	−	1.25848i	0.0258490	−	0.179784i
$50$	−0.415415	+	0.909632i	−0.0587486	+	0.128641i
$51$	6.74653	−	1.98096i	0.944703	−	0.277390i
$52$	2.27294	+	4.97705i	0.315200	+	0.690192i
$53$	3.19497	+	3.68719i	0.438863	+	0.506474i	0.931491	−	0.363766i	$-0.118509\pi$
$53$	3.19497	+	3.68719i	0.438863	+	0.506474i	−0.492628	+	0.870240i	$0.663964\pi$
$54$	−0.142315	−	0.989821i	−0.0193666	−	0.134698i
$55$	1.56442	+	0.459355i	0.210946	+	0.0619394i
$56$	1.56737	−	1.80884i	0.209449	−	0.241717i
$57$	−0.0251235	−	0.0161459i	−0.00332769	−	0.00213858i
$58$	−6.14719	−	3.95056i	−0.807166	−	0.518734i
$59$	−8.58579	+	9.90853i	−1.11777	+	1.28998i	−0.165003	+	0.986293i	$0.552764\pi$
$59$	−8.58579	+	9.90853i	−1.11777	+	1.28998i	−0.952772	+	0.303688i	$0.901782\pi$
$60$	0.959493	+	0.281733i	0.123870	+	0.0363715i
$61$	−0.408849	−	2.84360i	−0.0523477	−	0.364086i	−0.999111	−	0.0421559i	$-0.986577\pi$
$61$	−0.408849	−	2.84360i	−0.0523477	−	0.364086i	0.946763	−	0.321930i	$-0.104332\pi$
$62$	3.70423	+	4.27491i	0.470437	+	0.542913i
$63$	0.994273	+	2.17715i	0.125267	+	0.274296i
$64$	−0.959493	+	0.281733i	−0.119937	+	0.0352166i
$65$	2.27294	−	4.97705i	0.281924	−	0.617327i
$66$	0.232039	−	1.61387i	0.0285621	−	0.198654i
$67$	−5.04507	+	3.24227i	−0.616353	+	0.396106i	−0.811235	−	0.584721i	$-0.801204\pi$
$67$	−5.04507	+	3.24227i	−0.616353	+	0.396106i	0.194882	+	0.980827i	$0.437568\pi$
$68$	7.03135			0.852676
$69$	3.54008	−	3.23540i	0.426176	−	0.389497i
$70$	−2.39344			−0.286071
$71$	7.56127	−	4.85933i	0.897358	−	0.576697i	−0.00864769	−	0.999963i	$-0.502753\pi$
$71$	7.56127	−	4.85933i	0.897358	−	0.576697i	0.906006	+	0.423266i	$0.139116\pi$
$72$	0.142315	−	0.989821i	0.0167720	−	0.116652i
$73$	−5.80891	+	12.7197i	−0.679882	+	1.48873i	0.182886	+	0.983134i	$0.441456\pi$
$73$	−5.80891	+	12.7197i	−0.679882	+	1.48873i	−0.862768	+	0.505600i	$0.831271\pi$
$74$	−0.313038	+	0.0919164i	−0.0363900	+	0.0106851i
$75$	−0.415415	−	0.909632i	−0.0479680	−	0.105035i
$76$	−0.0195570	−	0.0225700i	−0.00224334	−	0.00258895i
$77$	0.555373	+	3.86271i	0.0632907	+	0.440196i
$78$	−5.24986	−	1.54150i	−0.594430	−	0.174540i
$79$	−3.29370	+	3.80113i	−0.370570	+	0.427661i	−0.910153	−	0.414271i	$-0.864036\pi$
$79$	−3.29370	+	3.80113i	−0.370570	+	0.427661i	0.539583	+	0.841932i	$0.318582\pi$
$80$	0.841254	+	0.540641i	0.0940550	+	0.0604455i
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$	4.40332	−	5.08171i	0.486266	−	0.561181i
$83$	−13.8778	−	4.07489i	−1.52328	−	0.447277i	−0.590297	−	0.807186i	$-0.700990\pi$
$83$	−13.8778	−	4.07489i	−1.52328	−	0.447277i	−0.932987	+	0.359909i	$0.882808\pi$
$84$	0.340623	+	2.36908i	0.0371650	+	0.258488i
$85$	−4.60455	−	5.31394i	−0.499434	−	0.576377i
$86$	−2.60376	−	5.70144i	−0.280771	−	0.614802i
$87$	7.01119	−	2.05867i	0.751679	−	0.220713i
$88$	0.677320	−	1.48312i	0.0722025	−	0.158102i
$89$	0.0865524	−	0.601985i	0.00917454	−	0.0638103i	−0.984720	−	0.174146i	$-0.944284\pi$
$89$	0.0865524	−	0.601985i	0.00917454	−	0.0638103i	0.993894	+	0.110336i	$0.0351926\pi$
$90$	−0.841254	+	0.540641i	−0.0886759	+	0.0569885i
$91$	13.0957			1.37280
$92$	4.30820	−	2.10699i	0.449161	−	0.219669i
$93$	−5.65651			−0.586553
$94$	−3.00149	+	1.92894i	−0.309580	+	0.198955i
$95$	−0.00425014	+	0.0295604i	−0.000436055	+	0.00303283i
$96$	0.415415	−	0.909632i	0.0423981	−	0.0928389i
$97$	−8.03139	+	2.35823i	−0.815464	+	0.239442i	−0.662762	−	0.748830i	$-0.730616\pi$
$97$	−8.03139	+	2.35823i	−0.815464	+	0.239442i	−0.152702	+	0.988272i	$0.548798\pi$
$98$	0.528169	+	1.15653i	0.0533532	+	0.116827i
$99$	1.06773	+	1.23222i	0.107311	+	0.123843i
$100$	−0.142315	−	0.989821i	−0.0142315	−	0.0989821i
$101$	−6.11955	−	1.79686i	−0.608918	−	0.178795i	−0.0372862	−	0.999305i	$-0.511871\pi$
$101$	−6.11955	−	1.79686i	−0.608918	−	0.178795i	−0.571632	+	0.820510i	$0.693690\pi$
$102$	−4.60455	+	5.31394i	−0.455919	+	0.526158i
$103$	−7.83932	−	5.03802i	−0.772431	−	0.496411i	0.0940829	−	0.995564i	$-0.470008\pi$
$103$	−7.83932	−	5.03802i	−0.772431	−	0.496411i	−0.866514	+	0.499153i	$0.833644\pi$
$104$	−4.60292	−	2.95811i	−0.451353	−	0.290067i
$105$	1.56737	−	1.80884i	0.152960	−	0.176525i
$106$	−4.68122	−	1.37453i	−0.454681	−	0.133506i
$107$	0.497618	+	3.46101i	0.0481066	+	0.334588i	0.999635	+	0.0270268i	$0.00860394\pi$
$107$	0.497618	+	3.46101i	0.0481066	+	0.334588i	−0.951528	+	0.307562i	$0.900487\pi$
$108$	0.654861	+	0.755750i	0.0630140	+	0.0727220i
$109$	0.389643	+	0.853199i	0.0373210	+	0.0817216i	0.927374	−	0.374135i	$-0.122060\pi$
$109$	0.389643	+	0.853199i	0.0373210	+	0.0817216i	−0.890053	+	0.455856i	$0.849333\pi$
$110$	−1.56442	+	0.459355i	−0.149162	+	0.0437978i
$111$	0.135531	−	0.296771i	0.0128640	−	0.0281683i
$112$	−0.340623	+	2.36908i	−0.0321858	+	0.223857i
$113$	0.172094	−	0.110598i	0.0161892	−	0.0104042i	−0.532521	−	0.846417i	$-0.678755\pi$
$113$	0.172094	−	0.110598i	0.0161892	−	0.0104042i	0.548710	+	0.836012i	$0.315119\pi$
$114$	0.0298644			0.00279705
$115$	−4.41363	−	1.87614i	−0.411573	−	0.174951i
$116$	7.30718			0.678455
$117$	4.60292	−	2.95811i	0.425540	−	0.273478i
$118$	1.86587	−	12.9774i	0.171767	−	1.19467i
$119$	6.99108	−	15.3083i	0.640871	−	1.40331i
$120$	−0.959493	+	0.281733i	−0.0875893	+	0.0257185i
$121$	−3.46522	−	7.58777i	−0.315020	−	0.689797i
$122$	1.88131	+	2.17115i	0.170326	+	0.196567i
$123$	0.956934	+	6.65562i	0.0862838	+	0.600117i
$124$	−5.42738	−	1.59362i	−0.487393	−	0.143112i
$125$	−0.654861	+	0.755750i	−0.0585725	+	0.0675963i
$126$	−2.01349	−	1.29399i	−0.179376	−	0.115278i
$127$	3.92354	+	2.52150i	0.348158	+	0.223747i	0.703018	−	0.711172i	$-0.251835\pi$
$127$	3.92354	+	2.52150i	0.348158	+	0.223747i	−0.354860	+	0.934919i	$0.615472\pi$
$128$	0.654861	−	0.755750i	0.0578821	−	0.0667995i
$129$	6.01396	+	1.76586i	0.529500	+	0.155475i
$130$	0.778675	+	5.41580i	0.0682943	+	0.474997i
$131$	6.91214	+	7.97704i	0.603917	+	0.696957i	0.972570	−	0.232610i	$-0.0747265\pi$
$131$	6.91214	+	7.97704i	0.603917	+	0.696957i	−0.368653	+	0.929567i	$0.620181\pi$
$132$	0.677320	+	1.48312i	0.0589531	+	0.129089i
$133$	−0.0685833	+	0.0201379i	−0.00594692	+	0.00174617i
$134$	2.49128	−	5.45514i	0.215214	−	0.471252i
$135$	0.142315	−	0.989821i	0.0122485	−	0.0851903i
$136$	−5.91515	+	3.80143i	−0.507220	+	0.325970i
$137$	−14.3695			−1.22767			−0.613836	−	0.789434i	$-0.710374\pi$
$137$	−14.3695			−1.22767			−0.613836	+	0.789434i	$0.710374\pi$
$138$	−1.22891	+	4.63571i	−0.104612	+	0.394617i
$139$	2.91930			0.247612			0.123806	−	0.992306i	$-0.460490\pi$
$139$	2.91930			0.247612			0.123806	+	0.992306i	$0.460490\pi$
$140$	2.01349	−	1.29399i	0.170171	−	0.109362i
$141$	0.507762	−	3.53156i	0.0427612	−	0.297411i
$142$	−3.73379	+	8.17586i	−0.313333	+	0.686103i
$143$	8.55972	−	2.51336i	0.715800	−	0.210178i
$144$	0.415415	+	0.909632i	0.0346179	+	0.0758027i
$145$	−4.78519	−	5.52240i	−0.397388	−	0.458610i
$146$	−1.99005	−	13.8411i	−0.164697	−	1.14549i
$147$	−1.21992	−	0.358202i	−0.100618	−	0.0295440i
$148$	0.213651	−	0.246566i	0.0175620	−	0.0202676i
$149$	3.32180	+	2.13479i	0.272133	+	0.174889i	0.669589	−	0.742732i	$-0.266470\pi$
$149$	3.32180	+	2.13479i	0.272133	+	0.174889i	−0.397456	+	0.917621i	$0.630107\pi$
$150$	0.841254	+	0.540641i	0.0686881	+	0.0441431i
$151$	13.0840	−	15.0998i	1.06476	−	1.22880i	0.0923049	−	0.995731i	$-0.470577\pi$
$151$	13.0840	−	15.0998i	1.06476	−	1.22880i	0.972459	−	0.233073i	$-0.0748780\pi$
$152$	0.0286546	+	0.00841376i	0.00232420	+	0.000682446i
$153$	−1.00067	−	6.95978i	−0.0808990	−	0.562665i
$154$	−2.55555	−	2.94926i	−0.205932	−	0.237658i
$155$	2.34980	+	5.14534i	0.188740	+	0.413284i
$156$	5.24986	−	1.54150i	0.420325	−	0.123419i
$157$	4.18065	−	9.15434i	0.333652	−	0.730596i	−0.666233	−	0.745743i	$-0.732095\pi$
$157$	4.18065	−	9.15434i	0.333652	−	0.730596i	0.999885	+	0.0151475i	$0.00482179\pi$
$158$	0.715790	−	4.97843i	0.0569452	−	0.396062i
$159$	4.10435	−	2.63771i	0.325496	−	0.209184i
$160$	−1.00000			−0.0790569
$161$	−0.303715	−	11.4745i	−0.0239361	−	0.904320i
$162$	−1.00000			−0.0785674
$163$	9.71145	−	6.24117i	0.760659	−	0.488846i	−0.101904	−	0.994794i	$-0.532494\pi$
$163$	9.71145	−	6.24117i	0.760659	−	0.488846i	0.862564	+	0.505948i	$0.168857\pi$
$164$	−0.956934	+	6.65562i	−0.0747240	+	0.519717i
$165$	0.677320	−	1.48312i	0.0527293	−	0.115461i
$166$	13.8778	−	4.07489i	1.07713	−	0.316272i
$167$	−4.59471	−	10.0610i	−0.355549	−	0.778544i	−0.999905	−	0.0138178i	$-0.995602\pi$
$167$	−4.59471	−	10.0610i	−0.355549	−	0.778544i	0.644355	−	0.764726i	$-0.277126\pi$
$168$	−1.56737	−	1.80884i	−0.120925	−	0.139555i
$169$	−2.41042	−	16.7649i	−0.185417	−	1.28961i
$170$	6.74653	+	1.98096i	0.517435	+	0.151933i
$171$	−0.0195570	+	0.0225700i	−0.00149556	+	0.00172597i
$172$	5.27285	+	3.38866i	0.402051	+	0.258383i
$173$	17.8347	+	11.4616i	1.35594	+	0.871412i	0.998054	−	0.0623516i	$-0.0198600\pi$
$173$	17.8347	+	11.4616i	1.35594	+	0.871412i	0.357890	+	0.933764i	$0.383496\pi$
$174$	−4.78519	+	5.52240i	−0.362764	+	0.418652i
$175$	−2.29649	−	0.674311i	−0.173599	−	0.0509731i
$176$	0.232039	+	1.61387i	0.0174906	+	0.121650i
$177$	8.58579	+	9.90853i	0.645348	+	0.744771i
$178$	0.252645	+	0.553216i	0.0189366	+	0.0414653i
$179$	−6.49754	+	1.90785i	−0.485649	+	0.142599i	−0.515386	−	0.856958i	$-0.672351\pi$
$179$	−6.49754	+	1.90785i	−0.485649	+	0.142599i	0.0297368	+	0.999558i	$0.490533\pi$
$180$	0.415415	−	0.909632i	0.0309632	−	0.0678000i
$181$	3.37257	−	23.4567i	0.250681	−	1.74352i	−0.343463	−	0.939166i	$-0.611600\pi$
$181$	3.37257	−	23.4567i	0.250681	−	1.74352i	0.594144	−	0.804359i	$-0.297491\pi$
$182$	−11.0168	+	7.08008i	−0.816621	+	0.524810i
$183$	−2.87285			−0.212367
$184$	−2.48516	+	4.10170i	−0.183209	+	0.302381i
$185$	−0.326254			−0.0239867
$186$	4.75856	−	3.05814i	0.348914	−	0.224234i
$187$	1.63155	−	11.3477i	0.119311	−	0.829824i
$188$	1.48215	−	3.24545i	0.108097	−	0.236699i
$189$	2.29649	−	0.674311i	0.167045	−	0.0490489i
$190$	−0.0124061	−	0.0271656i	−0.000900033	−	0.00197080i
$191$	−8.19425	−	9.45667i	−0.592915	−	0.684261i	0.377415	−	0.926044i	$-0.376813\pi$
$191$	−8.19425	−	9.45667i	−0.592915	−	0.684261i	−0.970330	+	0.241784i	$0.922268\pi$
$192$	0.142315	+	0.989821i	0.0102707	+	0.0714342i
$193$	14.3451	+	4.21209i	1.03258	+	0.303193i	0.753760	−	0.657150i	$-0.228238\pi$
$193$	14.3451	+	4.21209i	1.03258	+	0.303193i	0.278821	+	0.960343i	$0.410056\pi$
$194$	5.48148	−	6.32597i	0.393547	−	0.454178i
$195$	−4.60292	−	2.95811i	−0.329622	−	0.211835i
$196$	−1.06959	−	0.687385i	−0.0763994	−	0.0490989i
$197$	−18.2963	+	21.1151i	−1.30356	+	1.50439i	−0.578558	+	0.815641i	$0.696384\pi$
$197$	−18.2963	+	21.1151i	−1.30356	+	1.50439i	−0.725002	+	0.688747i	$0.758161\pi$
$198$	−1.56442	−	0.459355i	−0.111179	−	0.0326450i
$199$	3.49557	+	24.3122i	0.247794	+	1.72345i	0.610908	+	0.791702i	$0.290805\pi$
$199$	3.49557	+	24.3122i	0.247794	+	1.72345i	−0.363113	+	0.931745i	$0.618286\pi$
$200$	0.654861	+	0.755750i	0.0463056	+	0.0534396i
$201$	2.49128	+	5.45514i	0.175721	+	0.384776i
$202$	6.11955	−	1.79686i	0.430570	−	0.126427i
$203$	7.26533	−	15.9089i	0.509926	−	1.11658i
$204$	1.00067	−	6.95978i	0.0700606	−	0.487282i
$205$	5.65664	−	3.63530i	0.395077	−	0.253901i
$206$	9.31861			0.649259
$207$	−2.69867	−	3.96449i	−0.187570	−	0.275551i
$208$	5.47150			0.379380
$209$	−0.0409630	+	0.0263253i	−0.00283347	+	0.00182096i
$210$	−0.340623	+	2.36908i	−0.0235052	+	0.163482i
$211$	−6.29472	+	13.7835i	−0.433347	+	0.948897i	0.559425	+	0.828881i	$0.311022\pi$
$211$	−6.29472	+	13.7835i	−0.433347	+	0.948897i	−0.992772	+	0.120016i	$0.961705\pi$
$212$	4.68122	−	1.37453i	0.321508	−	0.0944032i
$213$	−3.73379	−	8.17586i	−0.255835	−	0.560201i
$214$	−2.28979	−	2.64255i	−0.156527	−	0.180641i
$215$	−0.892008	−	6.20405i	−0.0608345	−	0.423113i
$216$	−0.959493	−	0.281733i	−0.0652852	−	0.0191695i
$217$	−8.86586	+	10.2317i	−0.601854	+	0.694576i
$218$	−0.789062	−	0.507100i	−0.0534420	−	0.0343451i
$219$	11.7636	+	7.56000i	0.794909	+	0.510857i
$220$	1.06773	−	1.23222i	0.0719862	−	0.0830765i
$221$	−36.9136	−	10.8388i	−2.48308	−	0.729097i
$222$	0.0464308	+	0.322933i	0.00311623	+	0.0216739i
$223$	12.4850	+	14.4085i	0.836057	+	0.964861i	0.999766	−	0.0216474i	$-0.00689112\pi$
$223$	12.4850	+	14.4085i	0.836057	+	0.964861i	−0.163709	+	0.986509i	$0.552346\pi$
$224$	−0.994273	−	2.17715i	−0.0664326	−	0.145467i
$225$	−0.959493	+	0.281733i	−0.0639662	+	0.0187822i
$226$	−0.0849807	+	0.186082i	−0.00565283	+	0.0123780i
$227$	3.61959	−	25.1748i	0.240241	−	1.67091i	−0.410690	−	0.911775i	$-0.634712\pi$
$227$	3.61959	−	25.1748i	0.240241	−	1.67091i	0.650931	−	0.759137i	$-0.274379\pi$
$228$	−0.0251235	+	0.0161459i	−0.00166384	+	0.00106929i
$229$	0.789165			0.0521495			0.0260747	−	0.999660i	$-0.491699\pi$
$229$	0.789165			0.0521495			0.0260747	+	0.999660i	$0.491699\pi$
$230$	4.72730	−	0.807882i	0.311709	−	0.0532702i
$231$	3.90243			0.256761
$232$	−6.14719	+	3.95056i	−0.403583	+	0.259367i
$233$	−0.720675	+	5.01240i	−0.0472130	+	0.328373i	0.952503	+	0.304530i	$0.0984994\pi$
$233$	−0.720675	+	5.01240i	−0.0472130	+	0.328373i	−0.999716	+	0.0238434i	$0.992410\pi$
$234$	−2.27294	+	4.97705i	−0.148587	+	0.325360i
$235$	−3.42335	+	1.00519i	−0.223315	+	0.0655711i
$236$	5.44645	+	11.9261i	0.354534	+	0.776321i
$237$	3.29370	+	3.80113i	0.213949	+	0.246910i
$238$	2.39504	+	16.6578i	0.155247	+	1.07977i
$239$	22.1674	+	6.50894i	1.43389	+	0.421028i	0.904180	−	0.427151i	$-0.140483\pi$
$239$	22.1674	+	6.50894i	1.43389	+	0.421028i	0.529709	+	0.848179i	$0.322301\pi$
$240$	0.654861	−	0.755750i	0.0422711	−	0.0487834i
$241$	1.62086	+	1.04167i	0.104409	+	0.0670996i	0.591803	−	0.806082i	$-0.298416\pi$
$241$	1.62086	+	1.04167i	0.104409	+	0.0670996i	−0.487394	+	0.873182i	$0.662053\pi$
$242$	7.01739	+	4.50980i	0.451095	+	0.289901i
$243$	0.654861	−	0.755750i	0.0420093	−	0.0484814i
$244$	−2.75648	−	0.809374i	−0.176465	−	0.0518149i
$245$	0.180943	+	1.25848i	0.0115600	+	0.0804016i
$246$	−4.40332	−	5.08171i	−0.280746	−	0.323998i
$247$	0.0678799	+	0.148636i	0.00431910	+	0.00945750i
$248$	5.42738	−	1.59362i	0.344639	−	0.101195i
$249$	−6.00842	+	13.1566i	−0.380768	+	0.833767i
$250$	0.142315	−	0.989821i	0.00900078	−	0.0626018i
$251$	6.01691	−	3.86683i	0.379784	−	0.244072i	−0.336795	−	0.941578i	$-0.609343\pi$
$251$	6.01691	−	3.86683i	0.379784	−	0.244072i	0.716579	+	0.697505i	$0.245707\pi$
$252$	2.39344			0.150773
$253$	−2.40074	−	7.44178i	−0.150933	−	0.467861i
$254$	−4.66392			−0.292640
$255$	−5.91515	+	3.80143i	−0.370421	+	0.238055i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	8.34663	−	18.2766i	0.520648	−	1.14006i	−0.448545	−	0.893760i	$-0.648058\pi$
$257$	8.34663	−	18.2766i	0.520648	−	1.14006i	0.969193	−	0.246301i	$-0.0792151\pi$
$258$	−6.01396	+	1.76586i	−0.374413	+	0.109937i
$259$	−0.324385	−	0.710305i	−0.0201563	−	0.0441362i
$260$	−3.58307	−	4.13508i	−0.222212	−	0.256447i
$261$	−1.03992	−	7.23281i	−0.0643695	−	0.447699i
$262$	−10.1276	−	2.97372i	−0.625684	−	0.183717i
$263$	−1.74370	+	2.01233i	−0.107521	+	0.124086i	−0.806959	−	0.590607i	$-0.798888\pi$
$263$	−1.74370	+	2.01233i	−0.107521	+	0.124086i	0.699438	+	0.714693i	$0.253434\pi$
$264$	−1.37163	−	0.881496i	−0.0844183	−	0.0542523i
$265$	−4.10435	−	2.63771i	−0.252128	−	0.162033i
$266$	0.0468086	−	0.0540200i	0.00287002	−	0.00331218i
$267$	−0.583540	−	0.171343i	−0.0357121	−	0.0104860i
$268$	0.853474	+	5.93604i	0.0521342	+	0.362601i
$269$	10.5744	+	12.2035i	0.644732	+	0.744060i	0.980204	−	0.197990i	$-0.0634413\pi$
$269$	10.5744	+	12.2035i	0.644732	+	0.744060i	−0.335472	+	0.942050i	$0.608896\pi$
$270$	0.415415	+	0.909632i	0.0252814	+	0.0553584i
$271$	−14.9962	+	4.40327i	−0.910952	+	0.267480i	−0.703441	−	0.710753i	$-0.748354\pi$
$271$	−14.9962	+	4.40327i	−0.910952	+	0.267480i	−0.207510	+	0.978233i	$0.566536\pi$
$272$	2.92093	−	6.39594i	0.177107	−	0.387811i
$273$	1.86372	−	12.9624i	0.112797	−	0.784522i
$274$	12.0884	−	7.76876i	0.730288	−	0.469328i
$275$	−1.63047			−0.0983208
$276$	−1.47242	−	4.56421i	−0.0886295	−	0.274733i
$277$	−11.6808			−0.701829			−0.350915	−	0.936407i	$-0.614129\pi$
$277$	−11.6808			−0.701829			−0.350915	+	0.936407i	$0.614129\pi$
$278$	−2.45587	+	1.57829i	−0.147293	+	0.0946596i
$279$	−0.805005	+	5.59894i	−0.0481944	+	0.335199i
$280$	−0.994273	+	2.17715i	−0.0594192	+	0.130110i
$281$	−30.6606	+	9.00276i	−1.82906	+	0.537060i	−0.999763	−	0.0217537i	$-0.993075\pi$
$281$	−30.6606	+	9.00276i	−1.82906	+	0.537060i	−0.829294	+	0.558813i	$0.811257\pi$
$282$	1.48215	+	3.24545i	0.0882607	+	0.193264i
$283$	−4.39448	−	5.07150i	−0.261224	−	0.301469i	0.609953	−	0.792438i	$-0.291188\pi$
$283$	−4.39448	−	5.07150i	−0.261224	−	0.301469i	−0.871177	+	0.490969i	$0.836643\pi$
$284$	−1.27914	−	8.89662i	−0.0759030	−	0.527917i
$285$	0.0286546	+	0.00841376i	0.00169735	+	0.000498388i
$286$	−5.84207	+	6.74211i	−0.345449	+	0.398669i
$287$	13.5389	+	8.70089i	0.799173	+	0.513598i
$288$	−0.841254	−	0.540641i	−0.0495713	−	0.0318576i
$289$	−21.2436	+	24.5164i	−1.24962	+	1.44214i
$290$	7.01119	+	2.05867i	0.411711	+	0.120889i
$291$	1.19124	+	8.28525i	0.0698317	+	0.485690i
$292$	9.15718	+	10.5679i	0.535883	+	0.618442i
$293$	−6.76831	−	14.8205i	−0.395409	−	0.865824i	−0.997715	−	0.0675594i	$-0.978479\pi$
$293$	−6.76831	−	14.8205i	−0.395409	−	0.865824i	0.602307	−	0.798265i	$-0.294248\pi$
$294$	1.21992	−	0.358202i	0.0711474	−	0.0208908i
$295$	5.44645	−	11.9261i	0.317105	−	0.694362i
$296$	−0.0464308	+	0.322933i	−0.00269873	+	0.0187701i
$297$	1.37163	−	0.881496i	0.0795903	−	0.0511496i
$298$	−3.94863			−0.228738
$299$	−25.8654	+	4.42032i	−1.49583	+	0.255634i
$300$	−1.00000			−0.0577350
$301$	12.6203	−	8.11056i	0.727421	−	0.467485i
$302$	−2.84343	+	19.7765i	−0.163621	+	1.13801i
$303$	−2.64948	+	5.80154i	−0.152208	+	0.333290i
$304$	−0.0286546	+	0.00841376i	−0.00164346	+	0.000482562i
$305$	1.19342	+	2.61323i	0.0683352	+	0.149633i
$306$	4.60455	+	5.31394i	0.263225	+	0.303778i
$307$	4.13712	+	28.7743i	0.236118	+	1.64224i	0.670789	+	0.741648i	$0.265956\pi$
$307$	4.13712	+	28.7743i	0.236118	+	1.64224i	−0.434671	+	0.900590i	$0.643135\pi$
$308$	3.74435	+	1.09944i	0.213354	+	0.0626465i
$309$	−6.10239	+	7.04254i	−0.347153	+	0.400636i
$310$	−4.75856	−	3.05814i	−0.270268	−	0.173691i
$311$	−17.6523	−	11.3444i	−1.00097	−	0.643284i	−0.0659288	−	0.997824i	$-0.521001\pi$
$311$	−17.6523	−	11.3444i	−1.00097	−	0.643284i	−0.935041	+	0.354540i	$0.884637\pi$
$312$	−3.58307	+	4.13508i	−0.202851	+	0.234103i
$313$	−17.9491	−	5.27032i	−1.01454	−	0.297896i	−0.268131	−	0.963383i	$-0.586406\pi$
$313$	−17.9491	−	5.27032i	−1.01454	−	0.297896i	−0.746410	+	0.665487i	$0.768224\pi$
$314$	1.43223	+	9.96135i	0.0808252	+	0.562151i
$315$	−1.56737	−	1.80884i	−0.0883114	−	0.101917i
$316$	2.08938	+	4.57511i	0.117537	+	0.257370i
$317$	−17.8680	+	5.24652i	−1.00357	+	0.294674i	−0.741919	−	0.670490i	$-0.766084\pi$
$317$	−17.8680	+	5.24652i	−1.00357	+	0.294674i	−0.261648	+	0.965163i	$0.584266\pi$
$318$	−2.02675	+	4.43796i	−0.113654	+	0.248868i
$319$	1.69555	−	11.7928i	0.0949328	−	0.660272i
$320$	0.841254	−	0.540641i	0.0470275	−	0.0302227i
$321$	3.49660			0.195161
$322$	6.45910	+	9.48879i	0.359952	+	0.528790i
$323$	0.209987			0.0116840
$324$	0.841254	−	0.540641i	0.0467363	−	0.0300356i
$325$	−0.778675	+	5.41580i	−0.0431931	+	0.300415i
$326$	−4.79556	+	10.5008i	−0.265602	+	0.581586i
$327$	0.899966	−	0.264254i	0.0497682	−	0.0146133i
$328$	−2.79328	−	6.11642i	−0.154233	−	0.337723i
$329$	−5.59219	−	6.45373i	−0.308307	−	0.355806i
$330$	0.232039	+	1.61387i	0.0127734	+	0.0888406i
$331$	31.5383	+	9.26047i	1.73350	+	0.509002i	0.987591	−	0.157047i	$-0.0501973\pi$
$331$	31.5383	+	9.26047i	1.73350	+	0.509002i	0.745909	+	0.666048i	$0.232015\pi$
$332$	−9.47169	+	10.9309i	−0.519826	+	0.599912i
$333$	−0.274462	−	0.176386i	−0.0150404	−	0.00966590i
$334$	9.30470	+	5.97977i	0.509131	+	0.327198i
$335$	3.92725	−	4.53229i	0.214569	−	0.247626i
$336$	2.29649	+	0.674311i	0.125284	+	0.0367867i
$337$	−2.18171	−	15.1741i	−0.118845	−	0.826587i	−0.958831	−	0.283978i	$-0.908346\pi$
$337$	−2.18171	−	15.1741i	−0.118845	−	0.826587i	0.839986	−	0.542609i	$-0.182563\pi$
$338$	11.0916	+	12.8003i	0.603301	+	0.696246i
$339$	−0.0849807	−	0.186082i	−0.00461552	−	0.0101066i
$340$	−6.74653	+	1.98096i	−0.365882	+	0.107433i
$341$	−3.83127	+	8.38930i	−0.207475	+	0.454306i
$342$	0.00425014	−	0.0295604i	0.000229821	−	0.00159844i
$343$	−16.6545	+	10.7032i	−0.899256	+	0.577917i
$344$	−6.26785			−0.337940
$345$	−2.48516	+	4.10170i	−0.133797	+	0.220828i
$346$	−21.2001			−1.13972
$347$	−22.2528	+	14.3010i	−1.19459	+	0.767718i	−0.978012	−	0.208547i	$-0.933127\pi$
$347$	−22.2528	+	14.3010i	−1.19459	+	0.767718i	−0.216580	+	0.976265i	$0.569490\pi$
$348$	1.03992	−	7.23281i	0.0557456	−	0.387719i
$349$	9.47835	−	20.7547i	0.507365	−	1.11097i	−0.466640	−	0.884447i	$-0.654536\pi$
$349$	9.47835	−	20.7547i	0.507365	−	1.11097i	0.974005	−	0.226526i	$-0.0727369\pi$
$350$	2.29649	−	0.674311i	0.122753	−	0.0360434i
$351$	−2.27294	−	4.97705i	−0.121321	−	0.265655i
$352$	−1.06773	−	1.23222i	−0.0569101	−	0.0656777i
$353$	4.04594	+	28.1401i	0.215344	+	1.49775i	0.754923	+	0.655814i	$0.227674\pi$
$353$	4.04594	+	28.1401i	0.215344	+	1.49775i	−0.539579	+	0.841935i	$0.681417\pi$
$354$	−12.5798	−	3.69376i	−0.668608	−	0.196321i
$355$	−5.88595	+	6.79275i	−0.312394	+	0.360522i
$356$	−0.511630	−	0.328805i	−0.0271163	−	0.0174266i
$357$	−14.1576	−	9.09852i	−0.749298	−	0.481545i
$358$	4.43461	−	5.11782i	0.234377	−	0.270485i
$359$	21.6478	+	6.35638i	1.14253	+	0.335477i	0.797620	−	0.603160i	$-0.206092\pi$
$359$	21.6478	+	6.35638i	1.14253	+	0.335477i	0.344908	+	0.938636i	$0.387910\pi$
$360$	0.142315	+	0.989821i	0.00750065	+	0.0521682i
$361$	12.4418	+	14.3586i	0.654830	+	0.755714i
$362$	9.84448	+	21.5564i	0.517414	+	1.13298i
$363$	−8.00369	+	2.35010i	−0.420085	+	0.123348i
$364$	5.44016	−	11.9123i	0.285142	−	0.624373i
$365$	1.99005	−	13.8411i	0.104164	−	0.724475i
$366$	2.41679	−	1.55318i	0.126328	−	0.0811859i
$367$	14.9682			0.781333			0.390667	−	0.920532i	$-0.372245\pi$
$367$	14.9682			0.781333			0.390667	+	0.920532i	$0.372245\pi$
$368$	−0.126895	−	4.79415i	−0.00661484	−	0.249912i
$369$	6.72406			0.350041
$370$	0.274462	−	0.176386i	0.0142686	−	0.00916988i
$371$	1.66185	−	11.5584i	0.0862788	−	0.600082i
$372$	−2.34980	+	5.14534i	−0.121831	+	0.266774i
$373$	13.4377	−	3.94567i	0.695779	−	0.204299i	0.0853275	−	0.996353i	$-0.472806\pi$
$373$	13.4377	−	3.94567i	0.695779	−	0.204299i	0.610451	+	0.792054i	$0.290988\pi$
$374$	4.76247	+	10.4284i	0.246262	+	0.539238i
$375$	0.654861	+	0.755750i	0.0338169	+	0.0390267i
$376$	0.507762	+	3.53156i	0.0261858	+	0.182126i
$377$	−38.3617	−	11.2640i	−1.97573	−	0.580126i
$378$	−1.56737	+	1.80884i	−0.0806169	+	0.0930369i
$379$	−8.50073	−	5.46308i	−0.436653	−	0.280620i	0.303790	−	0.952739i	$-0.401748\pi$
$379$	−8.50073	−	5.46308i	−0.436653	−	0.280620i	−0.740443	+	0.672119i	$0.765384\pi$
$380$	0.0251235	+	0.0161459i	0.00128881	+	0.000828267i
$381$	3.05422	−	3.52475i	0.156472	−	0.180579i
$382$	12.0061	+	3.52531i	0.614286	+	0.180371i
$383$	1.28743	+	8.95428i	0.0657847	+	0.457542i	0.995914	+	0.0903097i	$0.0287857\pi$
$383$	1.28743	+	8.95428i	0.0657847	+	0.457542i	−0.930129	+	0.367233i	$0.880305\pi$
$384$	−0.654861	−	0.755750i	−0.0334182	−	0.0385667i
$385$	−1.62113	−	3.54977i	−0.0826203	−	0.180913i
$386$	−14.3451	+	4.21209i	−0.730145	+	0.214390i
$387$	2.60376	−	5.70144i	0.132357	−	0.289820i
$388$	−1.19124	+	8.28525i	−0.0604760	+	0.420620i
$389$	−15.3183	+	9.84446i	−0.776668	+	0.499134i	−0.867926	−	0.496693i	$-0.834547\pi$
$389$	−15.3183	+	9.84446i	−0.776668	+	0.499134i	0.0912583	+	0.995827i	$0.470911\pi$
$390$	5.47150			0.277060
$391$	−8.64092	+	32.5953i	−0.436990	+	1.64841i
$392$	1.27143			0.0642167
$393$	8.87954	−	5.70654i	0.447914	−	0.287857i
$394$	3.97617	−	27.6549i	0.200317	−	1.39323i
$395$	2.08938	−	4.57511i	0.105128	−	0.230199i
$396$	1.56442	−	0.459355i	0.0786151	−	0.0230835i
$397$	10.9878	+	24.0600i	0.551464	+	1.20754i	0.956095	+	0.293057i	$0.0946726\pi$
$397$	10.9878	+	24.0600i	0.551464	+	1.20754i	−0.404631	+	0.914480i	$0.632600\pi$
$398$	−16.0848	−	18.5629i	−0.806260	−	0.930473i
$399$	0.0101725	+	0.0707511i	0.000509261	+	0.00354199i
$400$	−0.959493	−	0.281733i	−0.0479746	−	0.0140866i
$401$	10.1629	−	11.7286i	0.507513	−	0.585701i	−0.442947	−	0.896548i	$-0.646067\pi$
$401$	10.1629	−	11.7286i	0.507513	−	0.585701i	0.950460	+	0.310847i	$0.100613\pi$
$402$	−5.04507	−	3.24227i	−0.251625	−	0.161710i
$403$	26.0364	+	16.7326i	1.29697	+	0.833510i
$404$	−4.17664	+	4.82010i	−0.207796	+	0.239809i
$405$	−0.959493	−	0.281733i	−0.0476776	−	0.0139994i
$406$	2.48899	+	17.3113i	0.123527	+	0.859146i
$407$	−0.348350	−	0.402018i	−0.0172671	−	0.0199273i
$408$	2.92093	+	6.39594i	0.144607	+	0.316646i
$409$	−4.20410	+	1.23444i	−0.207879	+	0.0610389i	−0.384014	−	0.923327i	$-0.625459\pi$
$409$	−4.20410	+	1.23444i	−0.207879	+	0.0610389i	0.176135	+	0.984366i	$0.443640\pi$
$410$	−2.79328	+	6.11642i	−0.137950	+	0.302069i
$411$	−2.04500	+	14.2233i	−0.100872	+	0.701582i
$412$	−7.83932	+	5.03802i	−0.386215	+	0.248206i
$413$	31.3801			1.54412
$414$	4.41363	+	1.87614i	0.216918	+	0.0922070i
$415$	14.4637			0.709993
$416$	−4.60292	+	2.95811i	−0.225676	+	0.145033i
$417$	0.415459	−	2.88958i	0.0203451	−	0.141503i
$418$	0.0202277	−	0.0442925i	0.000989370	−	0.00216642i
$419$	20.0776	−	5.89531i	0.980854	−	0.288005i	0.248277	−	0.968689i	$-0.420136\pi$
$419$	20.0776	−	5.89531i	0.980854	−	0.288005i	0.732577	+	0.680685i	$0.238318\pi$
$420$	−0.994273	−	2.17715i	−0.0485155	−	0.106234i
$421$	15.7661	+	18.1951i	0.768393	+	0.886773i	0.996214	−	0.0869298i	$-0.0277056\pi$
$421$	15.7661	+	18.1951i	0.768393	+	0.886773i	−0.227821	+	0.973703i	$0.573160\pi$
$422$	−2.15648	−	14.9986i	−0.104976	−	0.730121i
$423$	−3.42335	−	1.00519i	−0.166449	−	0.0488738i
$424$	−3.19497	+	3.68719i	−0.155161	+	0.179066i
$425$	5.91515	+	3.80143i	0.286927	+	0.184397i
$426$	7.56127	+	4.85933i	0.366345	+	0.235436i
$427$	−4.50282	+	5.19653i	−0.217907	+	0.251478i
$428$	3.35496	+	0.985106i	0.162168	+	0.0476169i
$429$	−1.26960	−	8.83028i	−0.0612970	−	0.426330i
$430$	4.10457	+	4.73693i	0.197940	+	0.228435i
$431$	1.04507	+	2.28838i	0.0503392	+	0.110227i	0.933130	−	0.359538i	$-0.117066\pi$
$431$	1.04507	+	2.28838i	0.0503392	+	0.110227i	−0.882791	+	0.469766i	$0.844338\pi$
$432$	0.959493	−	0.281733i	0.0461636	−	0.0135549i
$433$	11.8379	−	25.9214i	0.568893	−	1.24570i	−0.378492	−	0.925605i	$-0.623557\pi$
$433$	11.8379	−	25.9214i	0.568893	−	1.24570i	0.947385	−	0.320097i	$-0.103716\pi$
$434$	1.92674	−	13.4007i	0.0924862	−	0.643256i
$435$	−6.14719	+	3.95056i	−0.294735	+	0.189415i
$436$	0.937960			0.0449201
$437$	0.128662	−	0.0629239i	0.00615472	−	0.00301006i
$438$	−13.9834			−0.668153
$439$	−0.413833	+	0.265954i	−0.0197512	+	0.0126933i	−0.550479	−	0.834849i	$-0.685555\pi$
$439$	−0.413833	+	0.265954i	−0.0197512	+	0.0126933i	0.530728	+	0.847542i	$0.321919\pi$
$440$	−0.232039	+	1.61387i	−0.0110620	+	0.0769382i
$441$	−0.528169	+	1.15653i	−0.0251509	+	0.0550728i
$442$	36.9136	−	10.8388i	1.75580	−	0.515550i
$443$	2.19627	+	4.80917i	0.104348	+	0.228490i	0.954603	−	0.297880i	$-0.0962796\pi$
$443$	2.19627	+	4.80917i	0.104348	+	0.228490i	−0.850255	+	0.526371i	$0.823552\pi$
$444$	−0.213651	−	0.246566i	−0.0101394	−	0.0117015i
$445$	0.0865524	+	0.601985i	0.00410298	+	0.0285368i
$446$	−18.2928	−	5.37126i	−0.866191	−	0.254337i
$447$	2.58580	−	2.98418i	0.122304	−	0.141147i
$448$	2.01349	+	1.29399i	0.0951286	+	0.0611354i
$449$	−10.6402	−	6.83804i	−0.502142	−	0.322707i	0.264930	−	0.964268i	$-0.414651\pi$
$449$	−10.6402	−	6.83804i	−0.502142	−	0.322707i	−0.767073	+	0.641560i	$0.778287\pi$
$450$	0.654861	−	0.755750i	0.0308704	−	0.0356264i
$451$	10.5193	+	3.08873i	0.495333	+	0.145443i
$452$	−0.0291131	−	0.202486i	−0.00136937	−	0.00952414i
$453$	−13.0840	−	15.0998i	−0.614742	−	0.709450i
$454$	10.5655	+	23.1353i	0.495866	+	1.08579i
$455$	−12.5653	+	3.68949i	−0.589068	+	0.172966i
$456$	0.0124061	−	0.0271656i	0.000580969	−	0.00127214i
$457$	3.27950	−	22.8094i	0.153409	−	1.06698i	−0.757043	−	0.653365i	$-0.773357\pi$
$457$	3.27950	−	22.8094i	0.153409	−	1.06698i	0.910452	−	0.413616i	$-0.135734\pi$
$458$	−0.663888	+	0.426655i	−0.0310214	+	0.0199363i
$459$	−7.03135			−0.328195
$460$	−3.54008	+	3.23540i	−0.165057	+	0.150851i
$461$	−36.3465			−1.69283			−0.846413	−	0.532527i	$-0.821242\pi$
$461$	−36.3465			−1.69283			−0.846413	+	0.532527i	$0.821242\pi$
$462$	−3.28293	+	2.10981i	−0.152736	+	0.0981573i
$463$	4.25917	−	29.6231i	0.197940	−	1.37670i	−0.612309	−	0.790619i	$-0.709759\pi$
$463$	4.25917	−	29.6231i	0.197940	−	1.37670i	0.810249	−	0.586086i	$-0.199332\pi$
$464$	3.03551	−	6.64685i	0.140920	−	0.308572i
$465$	5.42738	−	1.59362i	0.251689	−	0.0739025i
$466$	−2.10364	−	4.60633i	−0.0974492	−	0.213384i
$467$	0.690571	+	0.796962i	0.0319558	+	0.0368790i	0.771503	−	0.636226i	$-0.219506\pi$
$467$	0.690571	+	0.796962i	0.0319558	+	0.0368790i	−0.739547	+	0.673105i	$0.764960\pi$
$468$	−0.778675	−	5.41580i	−0.0359943	−	0.250346i
$469$	13.7723	+	4.04390i	0.635944	+	0.186730i
$470$	2.33646	−	2.69642i	0.107773	−	0.124377i
$471$	−8.46619	−	5.44089i	−0.390102	−	0.250703i
$472$	−11.0296	−	7.08827i	−0.507677	−	0.326264i
$473$	6.69236	−	7.72339i	0.307715	−	0.355122i
$474$	−4.82589	−	1.41701i	−0.221660	−	0.0650853i
$475$	−0.00425014	−	0.0295604i	−0.000195010	−	0.00135632i
$476$	−11.0207	−	12.7186i	−0.505135	−	0.582957i
$477$	−2.02675	−	4.43796i	−0.0927984	−	0.203200i
$478$	−22.1674	+	6.50894i	−1.01391	+	0.297712i
$479$	9.95466	−	21.7977i	0.454840	−	0.995960i	−0.533794	−	0.845615i	$-0.679234\pi$
$479$	9.95466	−	21.7977i	0.454840	−	0.995960i	0.988633	−	0.150346i	$-0.0480387\pi$
$480$	−0.142315	+	0.989821i	−0.00649575	+	0.0451790i
$481$	−1.50172	+	0.965096i	−0.0684725	+	0.0440046i
$482$	−1.92673			−0.0877599
$483$	−11.4010	−	1.33237i	−0.518762	−	0.0606251i
$484$	−8.34158			−0.379163
$485$	7.04167	−	4.52541i	0.319746	−	0.205488i
$486$	−0.142315	+	0.989821i	−0.00645553	+	0.0448992i
$487$	9.00390	−	19.7158i	0.408005	−	0.893407i	−0.588390	−	0.808577i	$-0.700238\pi$
$487$	9.00390	−	19.7158i	0.408005	−	0.893407i	0.996395	−	0.0848301i	$-0.0270347\pi$
$488$	2.75648	−	0.809374i	0.124780	−	0.0366387i
$489$	−4.79556	−	10.5008i	−0.216863	−	0.474863i
$490$	−0.832607	−	0.960880i	−0.0376133	−	0.0434081i
$491$	1.61413	+	11.2265i	0.0728445	+	0.506645i	0.993279	+	0.115747i	$0.0369263\pi$
$491$	1.61413	+	11.2265i	0.0728445	+	0.506645i	−0.920434	+	0.390898i	$0.872165\pi$
$492$	6.45169	+	1.89439i	0.290865	+	0.0854056i
$493$	−33.6463	+	38.8299i	−1.51535	+	1.74881i
$494$	−0.137463	−	0.0883422i	−0.00618476	−	0.00397470i
$495$	−1.37163	−	0.881496i	−0.0616504	−	0.0396203i
$496$	−3.70423	+	4.27491i	−0.166325	+	0.191949i
$497$	−20.6411	−	6.06078i	−0.925880	−	0.271863i
$498$	−2.05839	−	14.3164i	−0.0922389	−	0.641535i
$499$	9.45183	+	10.9080i	0.423122	+	0.488309i	0.926785	−	0.375591i	$-0.122560\pi$
$499$	9.45183	+	10.9080i	0.423122	+	0.488309i	−0.503664	+	0.863900i	$0.668015\pi$
$500$	0.415415	+	0.909632i	0.0185779	+	0.0406800i
$501$	−10.6125	+	3.11611i	−0.474131	+	0.139218i
$502$	−2.97118	+	6.50597i	−0.132610	+	0.290376i
$503$	−1.21901	+	8.47837i	−0.0543528	+	0.378032i	0.944430	+	0.328712i	$0.106614\pi$
$503$	−1.21901	+	8.47837i	−0.0543528	+	0.378032i	−0.998783	+	0.0493199i	$0.984295\pi$
$504$	−2.01349	+	1.29399i	−0.0896881	+	0.0576391i
$505$	6.37790			0.283813
$506$	6.04296	+	4.96249i	0.268642	+	0.220609i
$507$	−16.9373			−0.752210
$508$	3.92354	−	2.52150i	0.174079	−	0.111874i
$509$	−5.03799	+	35.0400i	−0.223305	+	1.55312i	0.502107	+	0.864805i	$0.332558\pi$
$509$	−5.03799	+	35.0400i	−0.223305	+	1.55312i	−0.725412	+	0.688315i	$0.758351\pi$
$510$	2.92093	−	6.39594i	0.129341	−	0.283217i
$511$	32.1128	−	9.42916i	1.42059	−	0.417122i
$512$	−0.415415	−	0.909632i	−0.0183589	−	0.0402004i
$513$	0.0195570	+	0.0225700i	0.000863462	+	0.000996489i
$514$	2.85943	+	19.8878i	0.126124	+	0.877211i
$515$	8.94114	+	2.62536i	0.393994	+	0.115687i
$516$	4.10457	−	4.73693i	0.180694	−	0.208532i
$517$	−4.89382	−	3.14507i	−0.215230	−	0.138320i
$518$	0.656910	+	0.422171i	0.0288630	+	0.0185491i
$519$	13.8831	−	16.0220i	0.609401	−	0.703286i
$520$	5.24986	+	1.54150i	0.230222	+	0.0675992i
$521$	5.71491	+	39.7481i	0.250375	+	1.74139i	0.595967	+	0.803009i	$0.296769\pi$
$521$	5.71491	+	39.7481i	0.250375	+	1.74139i	−0.345592	+	0.938385i	$0.612322\pi$
$522$	4.78519	+	5.52240i	0.209442	+	0.241709i
$523$	−9.55195	−	20.9158i	−0.417677	−	0.914586i	−0.995168	−	0.0981886i	$-0.968695\pi$
$523$	−9.55195	−	20.9158i	−0.417677	−	0.914586i	0.577490	−	0.816398i	$-0.304032\pi$
$524$	10.1276	−	2.97372i	0.442425	−	0.129908i
$525$	−0.994273	+	2.17715i	−0.0433936	+	0.0950188i
$526$	0.378941	−	2.63560i	0.0165226	−	0.114917i
$527$	33.4591	−	21.5028i	1.45750	−	0.936679i
$528$	1.63047			0.0709569
$529$	4.47298	+	22.5609i	0.194477	+	0.980907i
$530$	4.87885			0.211924
$531$	11.0296	−	7.08827i	0.478642	−	0.307605i
$532$	−0.0101725	+	0.0707511i	−0.000441033	+	0.00306745i
$533$	15.2834	−	33.4660i	0.661998	−	1.44957i
$534$	0.583540	−	0.171343i	0.0252523	−	0.00741473i
$535$	−1.45254	−	3.18062i	−0.0627988	−	0.137510i
$536$	−3.92725	−	4.53229i	−0.169632	−	0.195765i
$537$	0.963734	+	6.70292i	0.0415882	+	0.289252i
$538$	−15.4935	−	4.54929i	−0.667970	−	0.196134i
$539$	−1.35754	+	1.56668i	−0.0584732	+	0.0674817i
$540$	−0.841254	−	0.540641i	−0.0362018	−	0.0232655i
$541$	11.6538	+	7.48942i	0.501034	+	0.321995i	0.766630	−	0.642089i	$-0.221932\pi$
$541$	11.6538	+	7.48942i	0.501034	+	0.321995i	−0.265596	+	0.964085i	$0.585569\pi$
$542$	10.2350	−	11.8118i	0.439630	−	0.507360i
$543$	−22.7380	−	6.67648i	−0.975781	−	0.286515i
$544$	1.00067	+	6.95978i	0.0429032	+	0.298398i
$545$	−0.614233	−	0.708863i	−0.0263109	−	0.0303644i
$546$	5.44016	+	11.9123i	0.232817	+	0.509799i
$547$	7.46937	−	2.19321i	0.319367	−	0.0937747i	−0.118120	−	0.992999i	$-0.537687\pi$
$547$	7.46937	−	2.19321i	0.319367	−	0.0937747i	0.437487	+	0.899225i	$0.355869\pi$
$548$	−5.96932	+	13.0710i	−0.254997	+	0.558365i
$549$	−0.408849	+	2.84360i	−0.0174492	+	0.121362i
$550$	1.37163	−	0.881496i	0.0584867	−	0.0375871i
$551$	0.218224			0.00929667
$552$	3.70628	+	3.04360i	0.157750	+	0.129544i
$553$	12.0381			0.511913
$554$	9.82649	−	6.31510i	0.417487	−	0.268303i
$555$	−0.0464308	+	0.322933i	−0.00197088	+	0.0137077i
$556$	1.21272	−	2.65549i	0.0514308	−	0.112618i
$557$	33.3542	−	9.79367i	1.41326	−	0.414971i	0.516045	−	0.856562i	$-0.327404\pi$
$557$	33.3542	−	9.79367i	1.41326	−	0.414971i	0.897217	+	0.441591i	$0.145586\pi$
$558$	−2.34980	−	5.14534i	−0.0994749	−	0.217820i
$559$	−22.4581	−	25.9181i	−0.949878	−	1.09622i
$560$	−0.340623	−	2.36908i	−0.0143939	−	0.100112i
$561$	−11.0000	−	3.22989i	−0.464420	−	0.136366i
$562$	20.9261	−	24.1500i	0.882713	−	1.01870i
$563$	25.5360	+	16.4110i	1.07622	+	0.691642i	0.953680	−	0.300822i	$-0.0972611\pi$
$563$	25.5360	+	16.4110i	1.07622	+	0.691642i	0.122535	+	0.992464i	$0.460898\pi$
$564$	−3.00149	−	1.92894i	−0.126385	−	0.0812230i
$565$	−0.133964	+	0.154602i	−0.00563590	+	0.00650417i
$566$	6.43873	+	1.89058i	0.270640	+	0.0794670i
$567$	−0.340623	−	2.36908i	−0.0143048	−	0.0994921i
$568$	5.88595	+	6.79275i	0.246969	+	0.285018i
$569$	−2.35648	−	5.15997i	−0.0987887	−	0.216317i	0.853785	−	0.520627i	$-0.174302\pi$
$569$	−2.35648	−	5.15997i	−0.0987887	−	0.216317i	−0.952573	+	0.304309i	$0.901574\pi$
$570$	−0.0286546	+	0.00841376i	−0.00120021	+	0.000352414i
$571$	−1.90600	+	4.17356i	−0.0797637	+	0.174658i	−0.945312	−	0.326167i	$-0.894243\pi$
$571$	−1.90600	+	4.17356i	−0.0797637	+	0.174658i	0.865548	+	0.500825i	$0.166970\pi$
$572$	1.26960	−	8.83028i	0.0530848	−	0.369213i
$573$	−10.5266	+	6.76502i	−0.439754	+	0.282613i
$574$	−16.0937			−0.671737
$575$	4.76341	+	0.556676i	0.198648	+	0.0232150i
$576$	1.00000			0.0416667
$577$	9.34229	−	6.00392i	0.388924	−	0.249947i	−0.331536	−	0.943443i	$-0.607567\pi$
$577$	9.34229	−	6.00392i	0.388924	−	0.249947i	0.720460	+	0.693496i	$0.243930\pi$
$578$	4.61667	−	32.1097i	0.192028	−	1.33559i
$579$	6.21074	−	13.5996i	0.258109	−	0.565181i
$580$	−7.01119	+	2.05867i	−0.291124	+	0.0854817i
$581$	14.3808	+	31.4896i	0.596617	+	1.30641i
$582$	−5.48148	−	6.32597i	−0.227215	−	0.262220i
$583$	−1.13209	−	7.87383i	−0.0468862	−	0.326101i
$584$	−13.4170	−	3.93958i	−0.555198	−	0.163021i
$585$	−3.58307	+	4.13508i	−0.148142	+	0.170965i
$586$	13.7064	+	8.80860i	0.566208	+	0.363880i
$587$	−17.1480	−	11.0203i	−0.707773	−	0.454858i	0.136591	−	0.990627i	$-0.456385\pi$
$587$	−17.1480	−	11.0203i	−0.707773	−	0.454858i	−0.844364	+	0.535769i	$0.820022\pi$
$588$	−0.832607	+	0.960880i	−0.0343361	+	0.0396260i
$589$	−0.162085	−	0.0475925i	−0.00667861	−	0.00196102i
$590$	1.86587	+	12.9774i	0.0768167	+	0.534272i
$591$	18.2963	+	21.1151i	0.752611	+	0.868559i
$592$	−0.135531	−	0.296771i	−0.00557028	−	0.0121972i
$593$	−15.5458	+	4.56466i	−0.638390	+	0.187448i	−0.584881	−	0.811119i	$-0.698859\pi$
$593$	−15.5458	+	4.56466i	−0.638390	+	0.187448i	−0.0535091	+	0.998567i	$0.517041\pi$
$594$	−0.677320	+	1.48312i	−0.0277908	+	0.0608533i
$595$	−2.39504	+	16.6578i	−0.0981869	+	0.682905i
$596$	3.32180	−	2.13479i	0.136066	−	0.0874445i
$597$	24.5622			1.00526
$598$	19.3695	−	17.7025i	0.792079	−	0.723909i
$599$	3.53322			0.144364			0.0721818	−	0.997391i	$-0.477004\pi$
$599$	3.53322			0.144364			0.0721818	+	0.997391i	$0.477004\pi$
$600$	0.841254	−	0.540641i	0.0343440	−	0.0220716i
$601$	3.57165	−	24.8414i	0.145691	−	1.01330i	−0.777479	−	0.628909i	$-0.783502\pi$
$601$	3.57165	−	24.8414i	0.145691	−	1.01330i	0.923170	−	0.384393i	$-0.125589\pi$
$602$	−6.23195	+	13.6461i	−0.253995	+	0.556172i
$603$	5.75416	−	1.68957i	0.234327	−	0.0688047i
$604$	−8.29994	−	18.1743i	−0.337720	−	0.739504i
$605$	5.46257	+	6.30415i	0.222085	+	0.256300i
$606$	−0.907670	−	6.31299i	−0.0368716	−	0.256447i
$607$	−17.3896	−	5.10605i	−0.705823	−	0.207248i	−0.0909279	−	0.995857i	$-0.528983\pi$
$607$	−17.3896	−	5.10605i	−0.705823	−	0.207248i	−0.614895	+	0.788609i	$0.710801\pi$
$608$	0.0195570	−	0.0225700i	0.000793141	−	0.000915333i
$609$	−14.7130	−	9.45545i	−0.596199	−	0.383154i
$610$	−2.41679	−	1.55318i	−0.0978530	−	0.0628863i
$611$	−12.7839	+	14.7535i	−0.517183	+	0.596861i
$612$	−6.74653	−	1.98096i	−0.272712	−	0.0800755i
$613$	−2.45466	−	17.0725i	−0.0991426	−	0.689552i	−0.977405	−	0.211374i	$-0.932206\pi$
$613$	−2.45466	−	17.0725i	−0.0991426	−	0.689552i	0.878263	−	0.478178i	$-0.158703\pi$
$614$	−19.0370	−	21.9698i	−0.768269	−	0.886629i
$615$	−2.79328	−	6.11642i	−0.112636	−	0.246638i
$616$	−3.74435	+	1.09944i	−0.150864	+	0.0442977i
$617$	9.22878	−	20.2082i	0.371537	−	0.813552i	−0.627843	−	0.778340i	$-0.716062\pi$
$617$	9.22878	−	20.2082i	0.371537	−	0.813552i	0.999380	−	0.0352121i	$-0.0112107\pi$
$618$	1.32618	−	9.22376i	0.0533467	−	0.371034i
$619$	−34.1388	+	21.9397i	−1.37215	+	0.881830i	−0.998945	−	0.0459176i	$-0.985379\pi$
$619$	−34.1388	+	21.9397i	−1.37215	+	0.881830i	−0.373209	+	0.927747i	$0.621742\pi$
$620$	5.65651			0.227171
$621$	−4.30820	+	2.10699i	−0.172882	+	0.0845506i
$622$	20.9833			0.841354
$623$	−1.22456	+	0.786975i	−0.0490609	+	0.0315295i
$624$	0.778675	−	5.41580i	0.0311719	−	0.216806i
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$	17.9491	−	5.27032i	0.717388	−	0.210644i
$627$	0.0202277	+	0.0442925i	0.000807817	+	0.00176887i
$628$	−6.59038	−	7.60570i	−0.262985	−	0.303500i
$629$	0.326471	+	2.27066i	0.0130172	+	0.0905370i
$630$	2.29649	+	0.674311i	0.0914945	+	0.0268652i
$631$	19.8378	−	22.8940i	0.789729	−	0.911396i	−0.208042	−	0.978120i	$-0.566709\pi$
$631$	19.8378	−	22.8940i	0.789729	−	0.911396i	0.997771	+	0.0667239i	$0.0212547\pi$
$632$	−4.23119	−	2.71922i	−0.168308	−	0.108165i
$633$	12.7474	+	8.19225i	0.506663	+	0.325613i
$634$	12.1950	−	14.0738i	0.484327	−	0.558943i
$635$	−4.47500	−	1.31398i	−0.177585	−	0.0521436i
$636$	−0.694333	−	4.82919i	−0.0275321	−	0.191490i
$637$	4.55561	+	5.25745i	0.180500	+	0.208308i
$638$	4.94930	+	10.8375i	0.195945	+	0.429059i
$639$	−8.62402	+	2.53224i	−0.341161	+	0.100174i
$640$	−0.415415	+	0.909632i	−0.0164207	+	0.0359564i
$641$	−1.25122	+	8.70241i	−0.0494201	+	0.343724i	0.950077	+	0.312015i	$0.101004\pi$
$641$	−1.25122	+	8.70241i	−0.0494201	+	0.343724i	−0.999497	+	0.0317090i	$0.989905\pi$
$642$	−2.94153	+	1.89040i	−0.116093	+	0.0746083i
$643$	−42.9535			−1.69392			−0.846960	−	0.531657i	$-0.821570\pi$
$643$	−42.9535			−1.69392			−0.846960	+	0.531657i	$0.821570\pi$
$644$	−10.5638	−	4.49043i	−0.416271	−	0.176948i
$645$	−6.26785			−0.246796
$646$	−0.176652	+	0.113527i	−0.00695028	+	0.00446667i
$647$	3.42603	−	23.8286i	0.134691	−	0.936797i	−0.804635	−	0.593770i	$-0.797639\pi$
$647$	3.42603	−	23.8286i	0.134691	−	0.936797i	0.939326	−	0.343027i	$-0.111452\pi$
$648$	−0.415415	+	0.909632i	−0.0163190	+	0.0357337i
$649$	20.5109	−	6.02255i	0.805123	−	0.236406i
$650$	−2.27294	−	4.97705i	−0.0891521	−	0.195216i
$651$	8.86586	+	10.2317i	0.347480	+	0.401014i
$652$	−1.64289	−	11.4265i	−0.0643404	−	0.447497i
$653$	18.1084	+	5.31712i	0.708638	+	0.208075i	0.616139	−	0.787638i	$-0.288696\pi$
$653$	18.1084	+	5.31712i	0.708638	+	0.208075i	0.0924996	+	0.995713i	$0.470514\pi$
$654$	−0.614233	+	0.708863i	−0.0240184	+	0.0277187i
$655$	−8.87954	−	5.70654i	−0.346952	−	0.222973i
$656$	5.65664	+	3.63530i	0.220855	+	0.141935i
$657$	9.15718	−	10.5679i	0.357256	−	0.412295i
$658$	8.19360	+	2.40586i	0.319420	+	0.0937901i
$659$	2.78037	+	19.3379i	0.108308	+	0.753296i	0.969513	+	0.245039i	$0.0788009\pi$
$659$	2.78037	+	19.3379i	0.108308	+	0.753296i	−0.861205	+	0.508257i	$0.830290\pi$
$660$	−1.06773	−	1.23222i	−0.0415612	−	0.0479642i
$661$	−9.41808	−	20.6227i	−0.366321	−	0.802131i	−0.999602	−	0.0282091i	$-0.991020\pi$
$661$	−9.41808	−	20.6227i	−0.366321	−	0.802131i	0.633281	−	0.773922i	$-0.281708\pi$
$662$	−31.5383	+	9.26047i	−1.22577	+	0.359918i
$663$	−15.9818	+	34.9954i	−0.620683	+	1.35911i
$664$	2.05839	−	14.3164i	0.0798812	−	0.555586i
$665$	0.0601317	−	0.0386443i	0.00233181	−	0.00149856i
$666$	0.326254			0.0126421
$667$	−8.97990	+	33.8740i	−0.347703	+	1.31160i
$668$	−11.0605			−0.427944
$669$	16.0386	−	10.3074i	0.620088	−	0.398506i
$670$	−0.853474	+	5.93604i	−0.0329726	+	0.229329i
$671$	−1.94584	+	4.26079i	−0.0751182	+	0.164486i
$672$	−2.29649	+	0.674311i	−0.0885891	+	0.0260121i
$673$	15.4582	+	33.8487i	0.595868	+	1.30477i	0.931830	+	0.362894i	$0.118211\pi$
$673$	15.4582	+	33.8487i	0.595868	+	1.30477i	−0.335962	+	0.941876i	$0.609061\pi$
$674$	10.0391	+	11.5858i	0.386692	+	0.446267i
$675$	0.142315	+	0.989821i	0.00547770	+	0.0380982i
$676$	−16.2512	−	4.77178i	−0.625046	−	0.183530i
$677$	9.34249	−	10.7818i	0.359061	−	0.414379i	−0.547264	−	0.836960i	$-0.684331\pi$
$677$	9.34249	−	10.7818i	0.359061	−	0.414379i	0.906325	+	0.422582i	$0.138876\pi$
$678$	0.172094	+	0.110598i	0.00660922	+	0.00424749i
$679$	16.8538	+	10.8313i	0.646791	+	0.415668i
$680$	4.60455	−	5.31394i	0.176577	−	0.203780i
$681$	−24.4035	−	7.16550i	−0.935143	−	0.274583i
$682$	−1.31253	−	9.12887i	−0.0502595	−	0.349563i
$683$	−0.176746	−	0.203976i	−0.00676301	−	0.00780493i	0.752358	−	0.658754i	$-0.228916\pi$
$683$	−0.176746	−	0.203976i	−0.00676301	−	0.00780493i	−0.759121	+	0.650950i	$0.774371\pi$
$684$	0.0124061	+	0.0271656i	0.000474359	+	0.00103870i
$685$	13.7875	−	4.04836i	0.526792	−	0.154680i
$686$	8.22405	−	18.0082i	0.313996	−	0.687555i
$687$	0.112310	−	0.781132i	0.00428489	−	0.0298021i
$688$	5.27285	−	3.38866i	0.201026	−	0.129191i
$689$	−26.6946			−1.01698
$690$	−0.126895	−	4.79415i	−0.00483079	−	0.182510i
$691$	4.35336			0.165610			0.0828049	−	0.996566i	$-0.473612\pi$
$691$	4.35336			0.165610			0.0828049	+	0.996566i	$0.473612\pi$
$692$	17.8347	−	11.4616i	0.677972	−	0.435706i
$693$	0.555373	−	3.86271i	0.0210969	−	0.146732i
$694$	10.9885	−	24.0615i	0.417119	−	0.913363i
$695$	−2.80104	+	0.822461i	−0.106250	+	0.0311977i
$696$	3.03551	+	6.64685i	0.115061	+	0.251948i
$697$	−30.9613	−	35.7313i	−1.17274	−	1.35342i
$698$	3.24714	+	22.5843i	0.122906	+	0.854830i
$699$	4.85882	+	1.42668i	0.183778	+	0.0539619i
$700$	−1.56737	+	1.80884i	−0.0592411	+	0.0683679i
$701$	−4.68916	−	3.01354i	−0.177107	−	0.113820i	0.449084	−	0.893490i	$-0.351751\pi$
$701$	−4.68916	−	3.01354i	−0.177107	−	0.113820i	−0.626191	+	0.779670i	$0.715387\pi$
$702$	4.60292	+	2.95811i	0.173726	+	0.111647i
$703$	0.00638055	−	0.00736354i	0.000240647	−	0.000277721i
$704$	1.56442	+	0.459355i	0.0589613	+	0.0173126i
$705$	0.507762	+	3.53156i	0.0191234	+	0.133006i
$706$	−18.6174	−	21.4856i	−0.700674	−	0.808621i
$707$	6.34137	+	13.8857i	0.238492	+	0.522224i
$708$	12.5798	−	3.69376i	0.472777	−	0.138820i
$709$	−3.67061	+	8.03752i	−0.137853	+	0.301855i	−0.965950	−	0.258729i	$-0.916696\pi$
$709$	−3.67061	+	8.03752i	−0.137853	+	0.301855i	0.828097	+	0.560585i	$0.189424\pi$
$710$	1.27914	−	8.89662i	0.0480053	−	0.333884i
$711$	4.23119	−	2.71922i	0.158682	−	0.101979i
$712$	0.608176			0.0227923
$713$	14.0574	−	23.2013i	0.526452	−	0.868896i
$714$	16.8291			0.629815
$715$	−7.50489	+	4.82310i	−0.280667	+	0.180374i
$716$	−0.963734	+	6.70292i	−0.0360164	+	0.250500i
$717$	9.59743	−	21.0154i	0.358423	−	0.784836i
$718$	−21.6478	+	6.35638i	−0.807890	+	0.237218i
$719$	1.53886	+	3.36963i	0.0573897	+	0.125666i	0.936154	−	0.351590i	$-0.114359\pi$
$719$	1.53886	+	3.36963i	0.0573897	+	0.125666i	−0.878764	+	0.477256i	$0.841632\pi$
$720$	−0.654861	−	0.755750i	−0.0244052	−	0.0281651i
$721$	3.17413	+	22.0766i	0.118211	+	0.822174i
$722$	−18.2295	−	5.35267i	−0.678432	−	0.199206i
$723$	1.26174	−	1.45612i	0.0469245	−	0.0541538i
$724$	−19.9360	−	12.8121i	−0.740915	−	0.476157i
$725$	6.14719	+	3.95056i	0.228301	+	0.146720i
$726$	5.46257	−	6.30415i	0.202735	−	0.233969i
$727$	−19.6536	−	5.77080i	−0.728910	−	0.214027i	−0.103838	−	0.994594i	$-0.533112\pi$
$727$	−19.6536	−	5.77080i	−0.728910	−	0.214027i	−0.625072	+	0.780567i	$0.714930\pi$
$728$	1.86372	+	12.9624i	0.0690739	+	0.480419i
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$	5.80891	+	12.7197i	0.214998	+	0.470779i
$731$	−42.2862	+	12.4164i	−1.56401	+	0.459236i
$732$	−1.19342	+	2.61323i	−0.0441102	+	0.0965879i
$733$	−0.00909127	+	0.0632312i	−0.000335794	+	0.00233550i	−0.989989	−	0.141147i	$-0.954921\pi$
$733$	−0.00909127	+	0.0632312i	−0.000335794	+	0.00233550i	0.989653	+	0.143482i	$0.0458301\pi$
$734$	−12.5920	+	8.09241i	−0.464781	+	0.298696i
$735$	1.27143			0.0468972
$736$	2.69867	+	3.96449i	0.0994741	+	0.146133i
$737$	9.77804			0.360179
$738$	−5.65664	+	3.63530i	−0.208224	+	0.133817i
$739$	3.55423	−	24.7202i	0.130745	−	0.909348i	−0.813842	−	0.581086i	$-0.802628\pi$
$739$	3.55423	−	24.7202i	0.130745	−	0.909348i	0.944587	−	0.328262i	$-0.106463\pi$
$740$	−0.135531	+	0.296771i	−0.00498221	+	0.0109095i
$741$	0.156784	−	0.0460359i	0.00575959	−	0.00169117i
$742$	4.85091	+	10.6220i	0.178082	+	0.389946i
$743$	−28.8356	−	33.2781i	−1.05788	−	1.22085i	−0.974512	−	0.224335i	$-0.927979\pi$
$743$	−28.8356	−	33.2781i	−1.05788	−	1.22085i	−0.0833642	−	0.996519i	$-0.526566\pi$
$744$	−0.805005	−	5.59894i	−0.0295129	−	0.205267i
$745$	−3.78869	−	1.11246i	−0.138807	−	0.0407573i
$746$	−9.17134	+	10.5843i	−0.335787	+	0.387518i
$747$	12.1676	+	7.81965i	0.445190	+	0.286106i
$748$	−9.64444	−	6.19811i	−0.352636	−	0.226625i
$749$	5.48047	−	6.32480i	0.200252	−	0.231103i
$750$	−0.959493	−	0.281733i	−0.0350357	−	0.0102874i
$751$	1.71835	+	11.9514i	0.0627034	+	0.436112i	0.996856	+	0.0792374i	$0.0252485\pi$
$751$	1.71835	+	11.9514i	0.0627034	+	0.436112i	−0.934152	+	0.356874i	$0.883842\pi$
$752$	−2.33646	−	2.69642i	−0.0852020	−	0.0983283i
$753$	−2.97118	−	6.50597i	−0.108276	−	0.237091i
$754$	38.3617	−	11.2640i	1.39705	−	0.410211i
$755$	−8.29994	+	18.1743i	−0.302066	+	0.661432i
$756$	0.340623	−	2.36908i	0.0123883	−	0.0861627i
$757$	−17.4136	+	11.1910i	−0.632908	+	0.406746i	−0.817385	−	0.576091i	$-0.804577\pi$
$757$	−17.4136	+	11.1910i	−0.632908	+	0.406746i	0.184477	+	0.982837i	$0.440941\pi$
$758$	10.1048			0.367024
$759$	−7.70769	+	1.31722i	−0.279772	+	0.0478122i
$760$	−0.0298644			−0.00108329
$761$	28.3546	−	18.2224i	1.02785	−	0.660562i	0.0859008	−	0.996304i	$-0.472623\pi$
$761$	28.3546	−	18.2224i	1.02785	−	0.660562i	0.941954	+	0.335741i	$0.108987\pi$
$762$	−0.663745	+	4.61645i	−0.0240449	+	0.167236i
$763$	0.932588	−	2.04208i	0.0337620	−	0.0739284i
$764$	−12.0061	+	3.52531i	−0.434366	+	0.127541i
$765$	2.92093	+	6.39594i	0.105606	+	0.231246i
$766$	−5.92411	−	6.83678i	−0.214047	−	0.247023i
$767$	−10.2091	−	71.0059i	−0.368629	−	2.56387i
$768$	0.959493	+	0.281733i	0.0346227	+	0.0101661i
$769$	2.66451	−	3.07501i	0.0960847	−	0.110888i	−0.705671	−	0.708540i	$-0.749354\pi$
$769$	2.66451	−	3.07501i	0.0960847	−	0.110888i	0.801755	+	0.597652i	$0.203900\pi$
$770$	3.28293	+	2.10981i	0.118309	+	0.0760323i
$771$	−16.9027	−	10.8627i	−0.608735	−	0.391210i
$772$	9.79061	−	11.2990i	0.352372	−	0.406659i
$773$	43.5842	+	12.7975i	1.56761	+	0.460293i	0.946306	−	0.323273i	$-0.104783\pi$
$773$	43.5842	+	12.7975i	1.56761	+	0.460293i	0.621309	+	0.783566i	$0.286601\pi$
$774$	0.892008	+	6.20405i	0.0320626	+	0.223000i
$775$	−3.70423	−	4.27491i	−0.133060	−	0.153559i
$776$	−3.47721	−	7.61403i	−0.124825	−	0.273328i
$777$	−0.749240	+	0.219997i	−0.0268788	+	0.00789234i
$778$	7.56424	−	16.5634i	0.271191	−	0.593826i
$779$	−0.0285782	+	0.198766i	−0.00102392	+	0.00712153i
$780$	−4.60292	+	2.95811i	−0.164811	+	0.105917i
$781$	−14.6548			−0.524390
$782$	−10.3531	−	32.0925i	−0.370227	−	1.14763i
$783$	−7.30718			−0.261137
$784$	−1.06959	+	0.687385i	−0.0381997	+	0.0245495i
$785$	−1.43223	+	9.96135i	−0.0511183	+	0.355536i
$786$	−4.38476	+	9.60129i	−0.156399	+	0.342467i
$787$	−13.7963	+	4.05096i	−0.491785	+	0.144401i	−0.518217	−	0.855249i	$-0.673404\pi$
$787$	−13.7963	+	4.05096i	−0.491785	+	0.144401i	0.0264313	+	0.999651i	$0.491586\pi$
$788$	11.6064	+	25.4145i	0.413461	+	0.905353i
$789$	1.74370	+	2.01233i	0.0620772	+	0.0716409i
$790$	0.715790	+	4.97843i	0.0254667	+	0.177125i
$791$	−0.469790	−	0.137943i	−0.0167038	−	0.00490468i
$792$	−1.06773	+	1.23222i	−0.0379401	+	0.0437852i
$793$	13.2235	+	8.49821i	0.469579	+	0.301780i
$794$	−22.2514	−	14.3001i	−0.789672	−	0.507491i
$795$	−3.19497	+	3.68719i	−0.113314	+	0.130771i
$796$	23.5673	+	6.91998i	0.835320	+	0.245272i
$797$	7.96651	+	55.4083i	0.282188	+	1.96266i	0.270461	+	0.962731i	$0.412824\pi$
$797$	7.96651	+	55.4083i	0.282188	+	1.96266i	0.0117273	+	0.999931i	$0.496267\pi$
$798$	−0.0468086	−	0.0540200i	−0.00165701	−	0.00191229i
$799$	10.4215	+	22.8199i	0.368686	+	0.807310i
$800$	0.959493	−	0.281733i	0.0339232	−	0.00996075i
$801$	−0.252645	+	0.553216i	−0.00892678	+	0.0195469i
$802$	−2.20862	+	15.3613i	−0.0779889	+	0.542425i
$803$	19.1801	−	12.3263i	0.676852	−	0.434986i
$804$	5.99708			0.211501
$805$	3.52416	+	10.9242i	0.124210	+	0.385026i
$806$	−30.9496			−1.09015
$807$	13.5842	−	8.73002i	0.478186	−	0.307311i
$808$	0.907670	−	6.31299i	0.0319317	−	0.222090i
$809$	4.98778	−	10.9217i	0.175361	−	0.383987i	−0.801459	−	0.598050i	$-0.795942\pi$
$809$	4.98778	−	10.9217i	0.175361	−	0.383987i	0.976820	+	0.214063i	$0.0686697\pi$
$810$	0.959493	−	0.281733i	0.0337131	−	0.00989907i
$811$	5.10734	+	11.1835i	0.179343	+	0.392706i	0.977858	−	0.209268i	$-0.0671082\pi$
$811$	5.10734	+	11.1835i	0.179343	+	0.392706i	−0.798515	+	0.601974i	$0.794381\pi$
$812$	−11.4531	−	13.2176i	−0.401924	−	0.463845i
$813$	2.22427	+	15.4702i	0.0780087	+	0.542562i
$814$	0.510398	+	0.149866i	0.0178895	+	0.00525282i
$815$	−7.55973	+	8.72439i	−0.264806	+	0.305602i
$816$	−5.91515	−	3.80143i	−0.207072	−	0.133077i
$817$	0.157470	+	0.101200i	0.00550919	+	0.00354054i
$818$	2.86933	−	3.31138i	0.100324	−	0.115780i
$819$	−12.5653	−	3.68949i	−0.439065	−	0.128921i
$820$	−0.956934	−	6.65562i	−0.0334176	−	0.232424i
$821$	2.44751	+	2.82457i	0.0854186	+	0.0985783i	0.796850	−	0.604177i	$-0.206498\pi$
$821$	2.44751	+	2.82457i	0.0854186	+	0.0985783i	−0.711431	+	0.702756i	$0.751953\pi$
$822$	−5.96932	−	13.0710i	−0.208204	−	0.455903i
$823$	5.40039	−	1.58570i	0.188246	−	0.0552739i	−0.186251	−	0.982502i	$-0.559634\pi$
$823$	5.40039	−	1.58570i	0.188246	−	0.0552739i	0.374497	+	0.927228i	$0.377816\pi$
$824$	3.87109	−	8.47651i	0.134856	−	0.295293i
$825$	−0.232039	+	1.61387i	−0.00807858	+	0.0561877i
$826$	−26.3986	+	16.9654i	−0.918526	+	0.590301i
$827$	−9.59775			−0.333746			−0.166873	−	0.985978i	$-0.553367\pi$
$827$	−9.59775			−0.333746			−0.166873	+	0.985978i	$0.553367\pi$
$828$	−4.72730	+	0.807882i	−0.164285	+	0.0280758i
$829$	9.91900			0.344501			0.172251	−	0.985053i	$-0.444896\pi$
$829$	9.91900			0.344501			0.172251	+	0.985053i	$0.444896\pi$
$830$	−12.1676	+	7.81965i	−0.422344	+	0.271424i
$831$	−1.66235	+	11.5619i	−0.0576662	+	0.401077i
$832$	2.27294	−	4.97705i	0.0788001	−	0.172548i
$833$	8.57771	−	2.51864i	0.297200	−	0.0872658i
$834$	1.21272	+	2.65549i	0.0419931	+	0.0919520i
$835$	7.24310	+	8.35899i	0.250658	+	0.289275i
$836$	0.00692971	+	0.0481972i	0.000239669	+	0.00166693i
$837$	5.42738	+	1.59362i	0.187598	+	0.0550837i
$838$	−13.7031	+	15.8142i	−0.473365	+	0.546293i
$839$	−45.8711	−	29.4796i	−1.58365	−	1.01775i	−0.974415	−	0.224755i	$-0.927842\pi$
$839$	−45.8711	−	29.4796i	−1.58365	−	1.01775i	−0.609231	−	0.792993i	$-0.708522\pi$
$840$	2.01349	+	1.29399i	0.0694721	+	0.0446470i
$841$	−15.9753	+	18.4364i	−0.550872	+	0.635740i
$842$	−23.1003	−	6.78286i	−0.796089	−	0.233753i
$843$	4.54767	+	31.6297i	0.156630	+	1.08939i
$844$	9.92301	+	11.4518i	0.341564	+	0.394186i
$845$	7.03599	+	15.4067i	0.242046	+	0.530006i
$846$	3.42335	−	1.00519i	0.117697	−	0.0345590i
$847$	−8.29381	+	18.1609i	−0.284979	+	0.624016i
$848$	0.694333	−	4.82919i	0.0238435	−	0.165835i
$849$	−5.64527	+	3.62800i	−0.193745	+	0.124513i
$850$	−7.03135			−0.241173
$851$	0.880450	+	1.29343i	0.0301814	+	0.0443383i
$852$	−8.98810			−0.307927
$853$	−11.8340	+	7.60526i	−0.405189	+	0.260399i	−0.727323	−	0.686295i	$-0.759236\pi$
$853$	−11.8340	+	7.60526i	−0.405189	+	0.260399i	0.322135	+	0.946694i	$0.395600\pi$
$854$	0.978556	−	6.80601i	0.0334855	−	0.232897i
$855$	0.0124061	−	0.0271656i	0.000424280	−	0.000929043i
$856$	−3.35496	+	0.985106i	−0.114670	+	0.0336702i
$857$	2.57007	+	5.62767i	0.0877920	+	0.192238i	0.948435	−	0.316970i	$-0.102666\pi$
$857$	2.57007	+	5.62767i	0.0877920	+	0.192238i	−0.860643	+	0.509208i	$0.829938\pi$
$858$	5.84207	+	6.74211i	0.199445	+	0.230172i
$859$	0.306030	+	2.12848i	0.0104416	+	0.0726229i	0.994376	−	0.105908i	$-0.0337748\pi$
$859$	0.306030	+	2.12848i	0.0104416	+	0.0726229i	−0.983934	+	0.178530i	$0.942866\pi$
$860$	−6.01396	−	1.76586i	−0.205074	−	0.0602152i
$861$	10.5391	−	12.1628i	0.359172	−	0.414507i
$862$	−2.11636	−	1.36010i	−0.0720835	−	0.0463252i
$863$	44.0981	+	28.3402i	1.50112	+	0.964710i	0.994744	+	0.102396i	$0.0326509\pi$
$863$	44.0981	+	28.3402i	1.50112	+	0.964710i	0.506374	+	0.862314i	$0.330985\pi$
$864$	−0.654861	+	0.755750i	−0.0222788	+	0.0257111i
$865$	−20.3413	−	5.97276i	−0.691627	−	0.203080i
$866$	4.05548	+	28.2065i	0.137811	+	0.958496i
$867$	21.2436	+	24.5164i	0.721470	+	0.832621i
$868$	5.62411	+	12.3151i	0.190895	+	0.418001i
$869$	7.86844	−	2.31038i	0.266919	−	0.0783744i
$870$	3.03551	−	6.64685i	0.102914	−	0.225349i
$871$	4.66978	−	32.4790i	0.158229	−	1.10051i
$872$	−0.789062	+	0.507100i	−0.0267210	+	0.0171726i
$873$	8.37045			0.283297
$874$	−0.0742178	+	0.122495i	−0.00251046	+	0.00414344i
$875$	2.39344			0.0809132
$876$	11.7636	−	7.56000i	0.397455	−	0.255429i
$877$	−3.45051	+	23.9988i	−0.116516	+	0.810383i	0.844829	+	0.535036i	$0.179702\pi$
$877$	−3.45051	+	23.9988i	−0.116516	+	0.810383i	−0.961345	+	0.275347i	$0.911207\pi$
$878$	0.204353	−	0.447470i	0.00689657	−	0.0151014i
$879$	−15.6329	+	4.59023i	−0.527285	+	0.154825i
$880$	−0.677320	−	1.48312i	−0.0228324	−	0.0499961i
$881$	8.94603	+	10.3243i	0.301399	+	0.347833i	0.886166	−	0.463368i	$-0.153359\pi$
$881$	8.94603	+	10.3243i	0.301399	+	0.347833i	−0.584766	+	0.811202i	$0.698814\pi$
$882$	−0.180943	−	1.25848i	−0.00609266	−	0.0423754i
$883$	−24.0837	−	7.07161i	−0.810481	−	0.237979i	−0.149869	−	0.988706i	$-0.547885\pi$
$883$	−24.0837	−	7.07161i	−0.810481	−	0.237979i	−0.660612	+	0.750727i	$0.729703\pi$
$884$	−25.1938	+	29.0752i	−0.847359	+	0.977904i
$885$	−11.0296	−	7.08827i	−0.370755	−	0.238270i
$886$	−4.44766	−	2.85833i	−0.149422	−	0.0960276i
$887$	2.11500	−	2.44084i	0.0710147	−	0.0819553i	−0.719131	−	0.694875i	$-0.755460\pi$
$887$	2.11500	−	2.44084i	0.0710147	−	0.0819553i	0.790145	+	0.612920i	$0.210005\pi$
$888$	0.313038	+	0.0919164i	0.0105049	+	0.00308451i
$889$	−1.58864	−	11.0492i	−0.0532811	−	0.370578i
$890$	−0.398270	−	0.459628i	−0.0133501	−	0.0154068i
$891$	−0.677320	−	1.48312i	−0.0226911	−	0.0496865i
$892$	18.2928	−	5.37126i	0.612490	−	0.179843i
$893$	0.0442634	−	0.0969234i	0.00148122	−	0.00324342i
$894$	−0.561949	+	3.90844i	−0.0187944	+	0.130718i
$895$	5.69684	−	3.66114i	0.190424	−	0.122378i
$896$	−2.39344			−0.0799594
$897$	0.694303	+	26.2312i	0.0231821	+	0.875834i
$898$	12.6480			0.422070
$899$	34.7717	−	22.3464i	1.15970	−	0.745294i
$900$	−0.142315	+	0.989821i	−0.00474383	+	0.0329940i
$901$	−14.2508	+	31.2048i	−0.474762	+	1.03958i
$902$	−10.5193	+	3.08873i	−0.350253	+	0.102844i
$903$	−6.23195	−	13.6461i	−0.207386	−	0.454113i
$904$	0.133964	+	0.154602i	0.00445557	+	0.00514200i
$905$	3.37257	+	23.4567i	0.112108	+	0.779728i
$906$	19.1706	+	5.62898i	0.636899	+	0.187010i
$907$	22.5370	−	26.0091i	0.748328	−	0.863617i	−0.246077	−	0.969250i	$-0.579142\pi$
$907$	22.5370	−	26.0091i	0.748328	−	0.863617i	0.994405	+	0.105633i	$0.0336870\pi$
$908$	−21.3962	−	13.7505i	−0.710058	−	0.456326i
$909$	5.36543	+	3.44815i	0.177960	+	0.114368i
$910$	8.57587	−	9.89708i	0.284287	−	0.328085i
$911$	46.6978	+	13.7117i	1.54717	+	0.454289i	0.940252	−	0.340479i	$-0.110589\pi$
$911$	46.6978	+	13.7117i	1.54717	+	0.454289i	0.606914	+	0.794768i	$0.292407\pi$
$912$	0.00425014	+	0.0295604i	0.000140736	+	0.000978842i
$913$	15.4433	+	17.8225i	0.511097	+	0.589838i
$914$	9.57282	+	20.9616i	0.316641	+	0.693347i
$915$	2.75648	−	0.809374i	0.0911263	−	0.0267571i
$916$	0.327831	−	0.717849i	0.0108318	−	0.0237184i
$917$	3.59532	−	25.0060i	0.118728	−	0.825770i
$918$	5.91515	−	3.80143i	0.195229	−	0.125466i
$919$	16.6549			0.549393			0.274697	−	0.961531i	$-0.411423\pi$
$919$	16.6549			0.549393			0.274697	+	0.961531i	$0.411423\pi$
$920$	1.22891	−	4.63571i	0.0405161	−	0.152835i
$921$	29.0702			0.957897
$922$	30.5766	−	19.6504i	1.00699	−	0.647152i
$923$	−6.99881	+	48.6778i	−0.230369	+	1.60225i
$924$	1.62113	−	3.54977i	0.0533312	−	0.116779i
$925$	0.313038	−	0.0919164i	0.0102926	−	0.00302219i
$926$	12.4324	+	27.2233i	0.408555	+	0.894612i
$927$	6.10239	+	7.04254i	0.200429	+	0.231307i
$928$	1.03992	+	7.23281i	0.0341371	+	0.237428i
$929$	−25.1545	−	7.38604i	−0.825294	−	0.242328i	−0.158300	−	0.987391i	$-0.550601\pi$
$929$	−25.1545	−	7.38604i	−0.825294	−	0.242328i	−0.666994	+	0.745063i	$0.732419\pi$
$930$	−3.70423	+	4.27491i	−0.121466	+	0.140180i
$931$	−0.0319427	−	0.0205283i	−0.00104688	−	0.000672788i
$932$	4.26006	+	2.73778i	0.139543	+	0.0896788i
$933$	−13.7412	+	15.8581i	−0.449865	+	0.519172i
$934$	−1.01182	−	0.297096i	−0.0331076	−	0.00972128i
$935$	1.63155	+	11.3477i	0.0533574	+	0.371109i
$936$	3.58307	+	4.13508i	0.117116	+	0.135159i
$937$	−15.4647	−	33.8629i	−0.505209	−	1.10625i	−0.974741	−	0.223338i	$-0.928305\pi$
$937$	−15.4647	−	33.8629i	−0.505209	−	1.10625i	0.469532	−	0.882915i	$-0.344422\pi$
$938$	−13.7723	+	4.04390i	−0.449680	+	0.132038i
$939$	−7.77109	+	17.0163i	−0.253600	+	0.555306i
$940$	−0.507762	+	3.53156i	−0.0165614	+	0.115187i
$941$	3.72643	−	2.39483i	0.121478	−	0.0780692i	−0.478491	−	0.878093i	$-0.658816\pi$
$941$	3.72643	−	2.39483i	0.121478	−	0.0780692i	0.599969	+	0.800023i	$0.295180\pi$
$942$	10.0638			0.327896
$943$	−29.6775	−	12.6153i	−0.966433	−	0.410809i
$944$	13.1109			0.426722
$945$	−2.01349	+	1.29399i	−0.0654989	+	0.0420936i
$946$	−1.45439	+	10.1155i	−0.0472863	+	0.328883i
$947$	5.18100	−	11.3448i	0.168360	−	0.368657i	−0.806580	−	0.591125i	$-0.798684\pi$
$947$	5.18100	−	11.3448i	0.168360	−	0.368657i	0.974940	+	0.222468i	$0.0714113\pi$
$948$	4.82589	−	1.41701i	0.156738	−	0.0460223i
$949$	−31.7834	−	69.5960i	−1.03173	−	2.25918i
$950$	0.0195570	+	0.0225700i	0.000634513	+	0.000732267i
$951$	2.65023	+	18.4328i	0.0859397	+	0.597724i
$952$	16.1474	+	4.74132i	0.523341	+	0.153667i
$953$	−16.7063	+	19.2801i	−0.541170	+	0.624544i	−0.958803	−	0.284072i	$-0.908315\pi$
$953$	−16.7063	+	19.2801i	−0.541170	+	0.624544i	0.417632	+	0.908616i	$0.362860\pi$
$954$	4.10435	+	2.63771i	0.132883	+	0.0853989i
$955$	10.5266	+	6.76502i	0.340632	+	0.218911i
$956$	15.1294	−	17.4603i	0.489320	−	0.564705i
$957$	−11.4315	−	3.35659i	−0.369528	−	0.108503i
$958$	3.41031	+	23.7193i	0.110182	+	0.766334i
$959$	22.5224	+	25.9922i	0.727286	+	0.839333i
$960$	−0.415415	−	0.909632i	−0.0134075	−	0.0293582i
$961$	−0.955757	+	0.280636i	−0.0308309	+	0.00905276i
$962$	0.741556	−	1.62378i	0.0239087	−	0.0523528i
$963$	0.497618	−	3.46101i	0.0160355	−	0.111529i
$964$	1.62086	−	1.04167i	0.0522045	−	0.0335498i
$965$	−14.9507			−0.481279
$966$	10.3114	−	5.04296i	0.331765	−	0.162255i
$967$	30.2799			0.973736			0.486868	−	0.873476i	$-0.338139\pi$
$967$	30.2799			0.973736			0.486868	+	0.873476i	$0.338139\pi$
$968$	7.01739	−	4.50980i	0.225547	−	0.144950i
$969$	0.0298842	−	0.207849i	0.000960019	−	0.00667708i
$970$	−3.47721	+	7.61403i	−0.111647	+	0.244472i
$971$	5.34613	−	1.56977i	0.171566	−	0.0503762i	−0.194822	−	0.980839i	$-0.562413\pi$
$971$	5.34613	−	1.56977i	0.171566	−	0.0503762i	0.366387	+	0.930463i	$0.380595\pi$
$972$	−0.415415	−	0.909632i	−0.0133244	−	0.0291765i
$973$	−4.57563	−	5.28055i	−0.146688	−	0.169287i
$974$	3.08460	+	21.4538i	0.0988369	+	0.687426i
$975$	5.24986	+	1.54150i	0.168130	+	0.0493675i
$976$	−1.88131	+	2.17115i	−0.0602194	+	0.0694969i
$977$	41.9909	+	26.9859i	1.34341	+	0.863355i	0.997198	−	0.0748026i	$-0.0238327\pi$
$977$	41.9909	+	26.9859i	1.34341	+	0.863355i	0.346208	+	0.938158i	$0.387469\pi$
$978$	9.71145	+	6.24117i	0.310538	+	0.199571i
$979$	−0.649366	+	0.749408i	−0.0207538	+	0.0239512i
$980$	1.21992	+	0.358202i	0.0389690	+	0.0114423i
$981$	−0.133486	−	0.928413i	−0.00426187	−	0.0296419i
$982$	−7.42740	−	8.57167i	−0.237018	−	0.273533i
$983$	−15.0427	−	32.9389i	−0.479787	−	1.05059i	−0.982522	−	0.186147i	$-0.940400\pi$
$983$	−15.0427	−	32.9389i	−0.479787	−	1.05059i	0.502735	−	0.864441i	$-0.332327\pi$
$984$	−6.45169	+	1.89439i	−0.205672	+	0.0603909i
$985$	11.6064	−	25.4145i	0.369810	−	0.809772i
$986$	7.31204	−	50.8564i	0.232863	−	1.61960i
$987$	−7.18389	+	4.61681i	−0.228666	+	0.146955i
$988$	0.163403			0.00519853
$989$	−22.1887	+	20.2790i	−0.705560	+	0.644835i
$990$	1.63047			0.0518196
$991$	6.87237	−	4.41660i	0.218308	−	0.140298i	−0.426917	−	0.904291i	$-0.640400\pi$
$991$	6.87237	−	4.41660i	0.218308	−	0.140298i	0.645224	+	0.763993i	$0.276764\pi$
$992$	0.805005	−	5.59894i	0.0255589	−	0.177766i
$993$	13.6546	−	29.8994i	0.433315	−	0.948827i
$994$	20.6411	−	6.06078i	0.654696	−	0.192236i
$995$	−10.2035	−	22.3426i	−0.323473	−	0.708307i
$996$	9.47169	+	10.9309i	0.300122	+	0.346359i
$997$	4.39324	+	30.5557i	0.139135	+	0.967708i	0.933067	+	0.359701i	$0.117121\pi$
$997$	4.39324	+	30.5557i	0.139135	+	0.967708i	−0.793932	+	0.608007i	$0.791969\pi$
$998$	−13.8487	−	4.06634i	−0.438372	−	0.128718i
$999$	−0.213651	+	0.246566i	−0.00675962	+	0.00780101i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.e.541.1	yes	20
23.2	even	11	inner	690.2.m.e.301.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.e.301.1	✓	20	23.2	even	11	inner
690.2.m.e.541.1	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.841254 + 0.540641i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(0.415415 + 0.909632i) q^{6} +(-1.56737 - 1.80884i) q^{7} +(0.142315 + 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(-0.841254 + 0.540641i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(0.415415 + 0.909632i) q^{6} +(-1.56737 - 1.80884i) q^{7} +(0.142315 + 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(0.654861 - 0.755750i) q^{10} +(-1.37163 - 0.881496i) q^{11} +(-0.841254 - 0.540641i) q^{12} +(-3.58307 + 4.13508i) q^{13} +(2.29649 + 0.674311i) q^{14} +(0.142315 + 0.989821i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(2.92093 + 6.39594i) q^{17} +(0.959493 - 0.281733i) q^{18} +(0.0124061 - 0.0271656i) q^{19} +(-0.142315 + 0.989821i) q^{20} +(-2.01349 + 1.29399i) q^{21} +1.63047 q^{22} +(3.70628 + 3.04360i) q^{23} +1.00000 q^{24} +(0.841254 - 0.540641i) q^{25} +(0.778675 - 5.41580i) q^{26} +(-0.415415 + 0.909632i) q^{27} +(-2.29649 + 0.674311i) q^{28} +(3.03551 + 6.64685i) q^{29} +(-0.654861 - 0.755750i) q^{30} +(-0.805005 - 5.59894i) q^{31} +(0.959493 + 0.281733i) q^{32} +(-1.06773 + 1.23222i) q^{33} +(-5.91515 - 3.80143i) q^{34} +(2.01349 + 1.29399i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(0.313038 + 0.0919164i) q^{37} +(0.00425014 + 0.0295604i) q^{38} +(3.58307 + 4.13508i) q^{39} +(-0.415415 - 0.909632i) q^{40} +(-6.45169 + 1.89439i) q^{41} +(0.994273 - 2.17715i) q^{42} +(-0.892008 + 6.20405i) q^{43} +(-1.37163 + 0.881496i) q^{44} +1.00000 q^{45} +(-4.76341 - 0.556676i) q^{46} +3.56788 q^{47} +(-0.841254 + 0.540641i) q^{48} +(0.180943 - 1.25848i) q^{49} +(-0.415415 + 0.909632i) q^{50} +(6.74653 - 1.98096i) q^{51} +(2.27294 + 4.97705i) q^{52} +(3.19497 + 3.68719i) q^{53} +(-0.142315 - 0.989821i) q^{54} +(1.56442 + 0.459355i) q^{55} +(1.56737 - 1.80884i) q^{56} +(-0.0251235 - 0.0161459i) q^{57} +(-6.14719 - 3.95056i) q^{58} +(-8.58579 + 9.90853i) q^{59} +(0.959493 + 0.281733i) q^{60} +(-0.408849 - 2.84360i) q^{61} +(3.70423 + 4.27491i) q^{62} +(0.994273 + 2.17715i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(2.27294 - 4.97705i) q^{65} +(0.232039 - 1.61387i) q^{66} +(-5.04507 + 3.24227i) q^{67} +7.03135 q^{68} +(3.54008 - 3.23540i) q^{69} -2.39344 q^{70} +(7.56127 - 4.85933i) q^{71} +(0.142315 - 0.989821i) q^{72} +(-5.80891 + 12.7197i) q^{73} +(-0.313038 + 0.0919164i) q^{74} +(-0.415415 - 0.909632i) q^{75} +(-0.0195570 - 0.0225700i) q^{76} +(0.555373 + 3.86271i) q^{77} +(-5.24986 - 1.54150i) q^{78} +(-3.29370 + 3.80113i) q^{79} +(0.841254 + 0.540641i) q^{80} +(0.841254 + 0.540641i) q^{81} +(4.40332 - 5.08171i) q^{82} +(-13.8778 - 4.07489i) q^{83} +(0.340623 + 2.36908i) q^{84} +(-4.60455 - 5.31394i) q^{85} +(-2.60376 - 5.70144i) q^{86} +(7.01119 - 2.05867i) q^{87} +(0.677320 - 1.48312i) q^{88} +(0.0865524 - 0.601985i) q^{89} +(-0.841254 + 0.540641i) q^{90} +13.0957 q^{91} +(4.30820 - 2.10699i) q^{92} -5.65651 q^{93} +(-3.00149 + 1.92894i) q^{94} +(-0.00425014 + 0.0295604i) q^{95} +(0.415415 - 0.909632i) q^{96} +(-8.03139 + 2.35823i) q^{97} +(0.528169 + 1.15653i) q^{98} +(1.06773 + 1.23222i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} + 2 q^{10} - 4 q^{11} + 2 q^{12} - 13 q^{13} + 2 q^{14} + 2 q^{15} - 2 q^{16} + 6 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} + 2 q^{21} + 26 q^{22} + 24 q^{23} + 20 q^{24} - 2 q^{25} + 13 q^{26} + 2 q^{27} - 2 q^{28} + 2 q^{29} - 2 q^{30} + 6 q^{31} + 2 q^{32} + 4 q^{33} + 5 q^{34} - 2 q^{35} - 2 q^{36} - 20 q^{37} + 4 q^{38} + 13 q^{39} + 2 q^{40} - 11 q^{41} - 13 q^{42} + 4 q^{43} - 4 q^{44} + 20 q^{45} - 2 q^{46} + 18 q^{47} + 2 q^{48} - 6 q^{49} + 2 q^{50} + 27 q^{51} - 2 q^{52} - 18 q^{53} - 2 q^{54} + 18 q^{55} + 2 q^{56} - 7 q^{57} + 9 q^{58} - 52 q^{59} + 2 q^{60} - 7 q^{61} + 16 q^{62} - 13 q^{63} - 2 q^{64} - 2 q^{65} + 7 q^{66} - 10 q^{67} + 28 q^{68} + 20 q^{69} - 20 q^{70} + 7 q^{71} + 2 q^{72} - 37 q^{73} + 20 q^{74} + 2 q^{75} - 4 q^{76} - 70 q^{77} + 9 q^{78} + 20 q^{79} - 2 q^{80} - 2 q^{81} - 11 q^{82} - 19 q^{83} - 9 q^{84} + 17 q^{85} - 26 q^{86} - 2 q^{87} + 4 q^{88} + 33 q^{89} + 2 q^{90} - 42 q^{91} - 9 q^{92} + 16 q^{93} - 7 q^{94} - 4 q^{95} - 2 q^{96} + 9 q^{97} + 6 q^{98} - 4 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 + 2 * q^10 - 4 * q^11 + 2 * q^12 - 13 * q^13 + 2 * q^14 + 2 * q^15 - 2 * q^16 + 6 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 + 2 * q^21 + 26 * q^22 + 24 * q^23 + 20 * q^24 - 2 * q^25 + 13 * q^26 + 2 * q^27 - 2 * q^28 + 2 * q^29 - 2 * q^30 + 6 * q^31 + 2 * q^32 + 4 * q^33 + 5 * q^34 - 2 * q^35 - 2 * q^36 - 20 * q^37 + 4 * q^38 + 13 * q^39 + 2 * q^40 - 11 * q^41 - 13 * q^42 + 4 * q^43 - 4 * q^44 + 20 * q^45 - 2 * q^46 + 18 * q^47 + 2 * q^48 - 6 * q^49 + 2 * q^50 + 27 * q^51 - 2 * q^52 - 18 * q^53 - 2 * q^54 + 18 * q^55 + 2 * q^56 - 7 * q^57 + 9 * q^58 - 52 * q^59 + 2 * q^60 - 7 * q^61 + 16 * q^62 - 13 * q^63 - 2 * q^64 - 2 * q^65 + 7 * q^66 - 10 * q^67 + 28 * q^68 + 20 * q^69 - 20 * q^70 + 7 * q^71 + 2 * q^72 - 37 * q^73 + 20 * q^74 + 2 * q^75 - 4 * q^76 - 70 * q^77 + 9 * q^78 + 20 * q^79 - 2 * q^80 - 2 * q^81 - 11 * q^82 - 19 * q^83 - 9 * q^84 + 17 * q^85 - 26 * q^86 - 2 * q^87 + 4 * q^88 + 33 * q^89 + 2 * q^90 - 42 * q^91 - 9 * q^92 + 16 * q^93 - 7 * q^94 - 4 * q^95 - 2 * q^96 + 9 * q^97 + 6 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

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