LMFDB - Embedded newform 690.2.m.h.541.2

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:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			541.2
Character	$\chi$	$=$	690.541
Dual form			690.2.m.h.301.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.841254 + 0.540641i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(0.959493 - 0.281733i) q^{5} +(-0.415415 - 0.909632i) q^{6} +(1.32702 + 1.53147i) q^{7} +(0.142315 + 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(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} +(1.32702 + 1.53147i) q^{7} +(0.142315 + 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(-0.654861 + 0.755750i) q^{10} +(-4.19881 - 2.69841i) q^{11} +(0.841254 + 0.540641i) q^{12} +(-3.70160 + 4.27187i) q^{13} +(-1.94434 - 0.570909i) q^{14} +(0.142315 + 0.989821i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(1.34898 + 2.95386i) q^{17} +(0.959493 - 0.281733i) q^{18} +(-1.34230 + 2.93924i) q^{19} +(0.142315 - 0.989821i) q^{20} +(-1.70473 + 1.09557i) q^{21} +4.99113 q^{22} +(4.79000 - 0.236515i) q^{23} -1.00000 q^{24} +(0.841254 - 0.540641i) q^{25} +(0.804434 - 5.59496i) q^{26} +(0.415415 - 0.909632i) q^{27} +(1.94434 - 0.570909i) q^{28} +(0.365316 + 0.799930i) q^{29} +(-0.654861 - 0.755750i) q^{30} +(1.55225 + 10.7962i) q^{31} +(0.959493 + 0.281733i) q^{32} +(3.26850 - 3.77205i) q^{33} +(-2.73182 - 1.75563i) q^{34} +(1.70473 + 1.09557i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(-6.98543 - 2.05111i) q^{37} +(-0.459853 - 3.19835i) q^{38} +(-3.70160 - 4.27187i) q^{39} +(0.415415 + 0.909632i) q^{40} +(-6.34228 + 1.86226i) q^{41} +(0.841806 - 1.84330i) q^{42} +(-1.16662 + 8.11402i) q^{43} +(-4.19881 + 2.69841i) q^{44} -1.00000 q^{45} +(-3.90173 + 2.78864i) q^{46} +3.29081 q^{47} +(0.841254 - 0.540641i) q^{48} +(0.411804 - 2.86416i) q^{49} +(-0.415415 + 0.909632i) q^{50} +(-3.11578 + 0.914875i) q^{51} +(2.34813 + 5.14169i) q^{52} +(-2.45743 - 2.83603i) q^{53} +(0.142315 + 0.989821i) q^{54} +(-4.78896 - 1.40616i) q^{55} +(-1.32702 + 1.53147i) q^{56} +(-2.71829 - 1.74694i) q^{57} +(-0.739798 - 0.475439i) q^{58} +(4.20982 - 4.85839i) q^{59} +(0.959493 + 0.281733i) q^{60} +(1.21583 + 8.45629i) q^{61} +(-7.14268 - 8.24310i) q^{62} +(-0.841806 - 1.84330i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(-2.34813 + 5.14169i) q^{65} +(-0.710312 + 4.94033i) q^{66} +(-8.99025 + 5.77768i) q^{67} +3.24732 q^{68} +(-0.447580 + 4.77490i) q^{69} -2.02642 q^{70} +(-9.47230 + 6.08748i) q^{71} +(0.142315 - 0.989821i) q^{72} +(6.92168 - 15.1564i) q^{73} +(6.98543 - 2.05111i) q^{74} +(0.415415 + 0.909632i) q^{75} +(2.11601 + 2.44200i) q^{76} +(-1.43939 - 10.0112i) q^{77} +(5.42353 + 1.59249i) q^{78} +(-1.28615 + 1.48429i) q^{79} +(-0.841254 - 0.540641i) q^{80} +(0.841254 + 0.540641i) q^{81} +(4.32865 - 4.99553i) q^{82} +(-5.00279 - 1.46895i) q^{83} +(0.288390 + 2.00580i) q^{84} +(2.12654 + 2.45416i) q^{85} +(-3.40535 - 7.45667i) q^{86} +(-0.843777 + 0.247755i) q^{87} +(2.07339 - 4.54009i) q^{88} +(2.22029 - 15.4424i) q^{89} +(0.841254 - 0.540641i) q^{90} -11.4543 q^{91} +(1.77469 - 4.45539i) q^{92} -10.9072 q^{93} +(-2.76840 + 1.77914i) q^{94} +(-0.459853 + 3.19835i) q^{95} +(-0.415415 + 0.909632i) q^{96} +(17.2633 - 5.06896i) q^{97} +(1.20205 + 2.63213i) q^{98} +(3.26850 + 3.77205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9} - 3 q^{10} - 18 q^{11} - 3 q^{12} + 13 q^{13} - 8 q^{14} + 3 q^{15} - 3 q^{16} - 6 q^{17} + 3 q^{18} + 4 q^{19} + 3 q^{20} - 3 q^{21} - 4 q^{22} - 23 q^{23} - 30 q^{24} - 3 q^{25} + 9 q^{26} - 3 q^{27} + 8 q^{28} + 18 q^{29} - 3 q^{30} - 8 q^{31} + 3 q^{32} + 4 q^{33} - 5 q^{34} + 3 q^{35} - 3 q^{36} - 32 q^{37} - 15 q^{38} + 13 q^{39} - 3 q^{40} + 35 q^{41} + 3 q^{42} + 48 q^{43} - 18 q^{44} - 30 q^{45} + q^{46} + 8 q^{47} - 3 q^{48} - 11 q^{49} + 3 q^{50} + 27 q^{51} + 2 q^{52} + 26 q^{53} + 3 q^{54} - 4 q^{55} - 8 q^{56} - 29 q^{57} - 7 q^{58} + 55 q^{59} + 3 q^{60} + 21 q^{61} + 8 q^{62} - 3 q^{63} - 3 q^{64} - 2 q^{65} + 7 q^{66} + 4 q^{67} - 28 q^{68} - 45 q^{69} - 14 q^{70} - 41 q^{71} + 3 q^{72} - 39 q^{73} + 32 q^{74} - 3 q^{75} + 4 q^{76} - 33 q^{77} - 2 q^{78} + 18 q^{79} + 3 q^{80} - 3 q^{81} + 31 q^{82} - 85 q^{83} - 3 q^{84} - 5 q^{85} + 40 q^{86} + 18 q^{87} - 15 q^{88} + 43 q^{89} - 3 q^{90} + 38 q^{91} + 10 q^{92} + 36 q^{93} - 19 q^{94} - 15 q^{95} + 3 q^{96} + 43 q^{97} + 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9 - 3 * q^10 - 18 * q^11 - 3 * q^12 + 13 * q^13 - 8 * q^14 + 3 * q^15 - 3 * q^16 - 6 * q^17 + 3 * q^18 + 4 * q^19 + 3 * q^20 - 3 * q^21 - 4 * q^22 - 23 * q^23 - 30 * q^24 - 3 * q^25 + 9 * q^26 - 3 * q^27 + 8 * q^28 + 18 * q^29 - 3 * q^30 - 8 * q^31 + 3 * q^32 + 4 * q^33 - 5 * q^34 + 3 * q^35 - 3 * q^36 - 32 * q^37 - 15 * q^38 + 13 * q^39 - 3 * q^40 + 35 * q^41 + 3 * q^42 + 48 * q^43 - 18 * q^44 - 30 * q^45 + q^46 + 8 * q^47 - 3 * q^48 - 11 * q^49 + 3 * q^50 + 27 * q^51 + 2 * q^52 + 26 * q^53 + 3 * q^54 - 4 * q^55 - 8 * q^56 - 29 * q^57 - 7 * q^58 + 55 * q^59 + 3 * q^60 + 21 * q^61 + 8 * q^62 - 3 * q^63 - 3 * q^64 - 2 * q^65 + 7 * q^66 + 4 * q^67 - 28 * q^68 - 45 * q^69 - 14 * q^70 - 41 * q^71 + 3 * q^72 - 39 * q^73 + 32 * q^74 - 3 * q^75 + 4 * q^76 - 33 * q^77 - 2 * q^78 + 18 * q^79 + 3 * q^80 - 3 * q^81 + 31 * q^82 - 85 * q^83 - 3 * q^84 - 5 * q^85 + 40 * q^86 + 18 * q^87 - 15 * q^88 + 43 * q^89 - 3 * q^90 + 38 * q^91 + 10 * q^92 + 36 * q^93 - 19 * q^94 - 15 * q^95 + 3 * q^96 + 43 * q^97 + 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
$7$	1.32702	+	1.53147i	0.501568	+	0.578840i	0.948920	−	0.315518i	$-0.102178\pi$
$7$	1.32702	+	1.53147i	0.501568	+	0.578840i	−0.447352	+	0.894358i	$0.647633\pi$
$8$	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
$11$	−4.19881	−	2.69841i	−1.26599	−	0.813601i	−0.276896	−	0.960900i	$-0.589306\pi$
$11$	−4.19881	−	2.69841i	−1.26599	−	0.813601i	−0.989092	+	0.147298i	$0.952942\pi$
$12$	0.841254	+	0.540641i	0.242849	+	0.156070i
$13$	−3.70160	+	4.27187i	−1.02664	+	1.18480i	−0.0440464	+	0.999029i	$0.514025\pi$
$13$	−3.70160	+	4.27187i	−1.02664	+	1.18480i	−0.982592	+	0.185775i	$0.940521\pi$
$14$	−1.94434	−	0.570909i	−0.519646	−	0.152582i
$15$	0.142315	+	0.989821i	0.0367455	+	0.255571i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	1.34898	+	2.95386i	0.327177	+	0.716417i	0.999721	−	0.0236403i	$-0.00752564\pi$
$17$	1.34898	+	2.95386i	0.327177	+	0.716417i	−0.672544	+	0.740057i	$0.734798\pi$
$18$	0.959493	−	0.281733i	0.226155	−	0.0664050i
$19$	−1.34230	+	2.93924i	−0.307946	+	0.674307i	−0.998815	−	0.0486730i	$-0.984501\pi$
$19$	−1.34230	+	2.93924i	−0.307946	+	0.674307i	0.690869	+	0.722980i	$0.257228\pi$
$20$	0.142315	−	0.989821i	0.0318226	−	0.221331i
$21$	−1.70473	+	1.09557i	−0.372004	+	0.239072i
$22$	4.99113			1.06411
$23$	4.79000	−	0.236515i	0.998783	−	0.0493168i
$23$	4.79000	−	0.236515i	0.998783	−	0.0493168i
$24$	−1.00000			−0.204124
$25$	0.841254	−	0.540641i	0.168251	−	0.108128i
$26$	0.804434	−	5.59496i	0.157763	−	1.09726i
$27$	0.415415	−	0.909632i	0.0799467	−	0.175059i
$28$	1.94434	−	0.570909i	0.367445	−	0.107892i
$29$	0.365316	+	0.799930i	0.0678374	+	0.148543i	0.940513	−	0.339756i	$-0.110345\pi$
$29$	0.365316	+	0.799930i	0.0678374	+	0.148543i	−0.872676	+	0.488300i	$0.837617\pi$
$30$	−0.654861	−	0.755750i	−0.119561	−	0.137980i
$31$	1.55225	+	10.7962i	0.278793	+	1.93905i	0.338821	+	0.940851i	$0.389972\pi$
$31$	1.55225	+	10.7962i	0.278793	+	1.93905i	−0.0600283	+	0.998197i	$0.519119\pi$
$32$	0.959493	+	0.281733i	0.169616	+	0.0498038i
$33$	3.26850	−	3.77205i	0.568972	−	0.656629i
$34$	−2.73182	−	1.75563i	−0.468503	−	0.301088i
$35$	1.70473	+	1.09557i	0.288153	+	0.185184i
$36$	−0.654861	+	0.755750i	−0.109143	+	0.125958i
$37$	−6.98543	−	2.05111i	−1.14840	−	0.337200i	−0.348484	−	0.937315i	$-0.613303\pi$
$37$	−6.98543	−	2.05111i	−1.14840	−	0.337200i	−0.799914	+	0.600115i	$0.795121\pi$
$38$	−0.459853	−	3.19835i	−0.0745980	−	0.518840i
$39$	−3.70160	−	4.27187i	−0.592730	−	0.684047i
$40$	0.415415	+	0.909632i	0.0656829	+	0.143825i
$41$	−6.34228	+	1.86226i	−0.990498	+	0.290837i	−0.736551	−	0.676382i	$-0.763547\pi$
$41$	−6.34228	+	1.86226i	−0.990498	+	0.290837i	−0.253947	+	0.967218i	$0.581729\pi$
$42$	0.841806	−	1.84330i	0.129893	−	0.284427i
$43$	−1.16662	+	8.11402i	−0.177908	+	1.23738i	0.683685	+	0.729777i	$0.260376\pi$
$43$	−1.16662	+	8.11402i	−0.177908	+	1.23738i	−0.861593	+	0.507599i	$0.830533\pi$
$44$	−4.19881	+	2.69841i	−0.632994	+	0.406801i
$45$	−1.00000			−0.149071
$46$	−3.90173	+	2.78864i	−0.575279	+	0.411162i
$47$	3.29081			0.480013			0.240007	−	0.970771i	$-0.422850\pi$
$47$	3.29081			0.480013			0.240007	+	0.970771i	$0.422850\pi$
$48$	0.841254	−	0.540641i	0.121424	−	0.0780348i
$49$	0.411804	−	2.86416i	0.0588292	−	0.409166i
$50$	−0.415415	+	0.909632i	−0.0587486	+	0.128641i
$51$	−3.11578	+	0.914875i	−0.436296	+	0.128108i
$52$	2.34813	+	5.14169i	0.325627	+	0.713024i
$53$	−2.45743	−	2.83603i	−0.337554	−	0.389558i	0.561441	−	0.827517i	$-0.310247\pi$
$53$	−2.45743	−	2.83603i	−0.337554	−	0.389558i	−0.898995	+	0.437959i	$0.855702\pi$
$54$	0.142315	+	0.989821i	0.0193666	+	0.134698i
$55$	−4.78896	−	1.40616i	−0.645743	−	0.189607i
$56$	−1.32702	+	1.53147i	−0.177331	+	0.204651i
$57$	−2.71829	−	1.74694i	−0.360046	−	0.231388i
$58$	−0.739798	−	0.475439i	−0.0971402	−	0.0624282i
$59$	4.20982	−	4.85839i	0.548072	−	0.632508i	−0.412361	−	0.911020i	$-0.635296\pi$
$59$	4.20982	−	4.85839i	0.548072	−	0.632508i	0.960433	+	0.278512i	$0.0898412\pi$
$60$	0.959493	+	0.281733i	0.123870	+	0.0363715i
$61$	1.21583	+	8.45629i	0.155671	+	1.08272i	0.906496	+	0.422215i	$0.138747\pi$
$61$	1.21583	+	8.45629i	0.155671	+	1.08272i	−0.750825	+	0.660502i	$0.770344\pi$
$62$	−7.14268	−	8.24310i	−0.907122	−	1.04687i
$63$	−0.841806	−	1.84330i	−0.106058	−	0.232234i
$64$	−0.959493	+	0.281733i	−0.119937	+	0.0352166i
$65$	−2.34813	+	5.14169i	−0.291250	+	0.637748i
$66$	−0.710312	+	4.94033i	−0.0874334	+	0.608113i
$67$	−8.99025	+	5.77768i	−1.09833	+	0.705856i	−0.958721	−	0.284350i	$-0.908222\pi$
$67$	−8.99025	+	5.77768i	−1.09833	+	0.705856i	−0.139613	+	0.990206i	$0.544586\pi$
$68$	3.24732			0.393795
$69$	−0.447580	+	4.77490i	−0.0538823	+	0.574830i
$70$	−2.02642			−0.242204
$71$	−9.47230	+	6.08748i	−1.12415	+	0.722450i	−0.964332	−	0.264695i	$-0.914729\pi$
$71$	−9.47230	+	6.08748i	−1.12415	+	0.722450i	−0.159823	+	0.987146i	$0.551092\pi$
$72$	0.142315	−	0.989821i	0.0167720	−	0.116652i
$73$	6.92168	−	15.1564i	0.810121	−	1.77392i	0.203234	−	0.979130i	$-0.434855\pi$
$73$	6.92168	−	15.1564i	0.810121	−	1.77392i	0.606887	−	0.794788i	$-0.292418\pi$
$74$	6.98543	−	2.05111i	0.812040	−	0.238436i
$75$	0.415415	+	0.909632i	0.0479680	+	0.105035i
$76$	2.11601	+	2.44200i	0.242723	+	0.280117i
$77$	−1.43939	−	10.0112i	−0.164034	−	1.14088i
$78$	5.42353	+	1.59249i	0.614094	+	0.180314i
$79$	−1.28615	+	1.48429i	−0.144703	+	0.166996i	−0.823474	−	0.567354i	$-0.807967\pi$
$79$	−1.28615	+	1.48429i	−0.144703	+	0.166996i	0.678771	+	0.734350i	$0.262513\pi$
$80$	−0.841254	−	0.540641i	−0.0940550	−	0.0604455i
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$	4.32865	−	4.99553i	0.478020	−	0.551664i
$83$	−5.00279	−	1.46895i	−0.549128	−	0.161238i	−0.00461233	−	0.999989i	$-0.501468\pi$
$83$	−5.00279	−	1.46895i	−0.549128	−	0.161238i	−0.544515	+	0.838751i	$0.683286\pi$
$84$	0.288390	+	2.00580i	0.0314659	+	0.218850i
$85$	2.12654	+	2.45416i	0.230656	+	0.266191i
$86$	−3.40535	−	7.45667i	−0.367208	−	0.804073i
$87$	−0.843777	+	0.247755i	−0.0904624	+	0.0265622i
$88$	2.07339	−	4.54009i	0.221024	−	0.483976i
$89$	2.22029	−	15.4424i	0.235350	−	1.63690i	−0.439003	−	0.898486i	$-0.644668\pi$
$89$	2.22029	−	15.4424i	0.235350	−	1.63690i	0.674353	−	0.738409i	$-0.264423\pi$
$90$	0.841254	−	0.540641i	0.0886759	−	0.0569885i
$91$	−11.4543			−1.20074
$92$	1.77469	−	4.45539i	0.185025	−	0.464506i
$93$	−10.9072			−1.13102
$94$	−2.76840	+	1.77914i	−0.285539	+	0.183505i
$95$	−0.459853	+	3.19835i	−0.0471799	+	0.328143i
$96$	−0.415415	+	0.909632i	−0.0423981	+	0.0928389i
$97$	17.2633	−	5.06896i	1.75282	−	0.514675i	0.761734	−	0.647890i	$-0.224348\pi$
$97$	17.2633	−	5.06896i	1.75282	−	0.514675i	0.991087	+	0.133215i	$0.0425301\pi$
$98$	1.20205	+	2.63213i	0.121426	+	0.265885i
$99$	3.26850	+	3.77205i	0.328496	+	0.379105i
$100$	−0.142315	−	0.989821i	−0.0142315	−	0.0989821i
$101$	−4.52223	−	1.32785i	−0.449978	−	0.132126i	0.0488884	−	0.998804i	$-0.484432\pi$
$101$	−4.52223	−	1.32785i	−0.449978	−	0.132126i	−0.498867	+	0.866679i	$0.666250\pi$
$102$	2.12654	−	2.45416i	0.210559	−	0.242998i
$103$	11.6474	+	7.48536i	1.14766	+	0.737555i	0.969171	−	0.246388i	$-0.0792437\pi$
$103$	11.6474	+	7.48536i	1.14766	+	0.737555i	0.178486	+	0.983942i	$0.442880\pi$
$104$	−4.75518	−	3.05597i	−0.466284	−	0.299663i
$105$	−1.32702	+	1.53147i	−0.129504	+	0.149456i
$106$	3.60059	+	1.05723i	0.349720	+	0.102687i
$107$	2.50898	+	17.4504i	0.242553	+	1.68699i	0.639217	+	0.769026i	$0.279258\pi$
$107$	2.50898	+	17.4504i	0.242553	+	1.68699i	−0.396665	+	0.917964i	$0.629832\pi$
$108$	−0.654861	−	0.755750i	−0.0630140	−	0.0727220i
$109$	−0.278428	−	0.609673i	−0.0266686	−	0.0583961i	0.895829	−	0.444399i	$-0.146583\pi$
$109$	−0.278428	−	0.609673i	−0.0266686	−	0.0583961i	−0.922498	+	0.386003i	$0.873855\pi$
$110$	4.78896	−	1.40616i	0.456609	−	0.134073i
$111$	3.02436	−	6.62242i	0.287060	−	0.628573i
$112$	0.288390	−	2.00580i	0.0272503	−	0.189530i
$113$	−1.66037	+	1.06706i	−0.156195	+	0.100380i	−0.616403	−	0.787430i	$-0.711411\pi$
$113$	−1.66037	+	1.06706i	−0.156195	+	0.100380i	0.460209	+	0.887811i	$0.347775\pi$
$114$	3.23124			0.302633
$115$	4.52933	−	1.57643i	0.422363	−	0.147003i
$116$	0.879399			0.0816502
$117$	4.75518	−	3.05597i	0.439617	−	0.282525i
$118$	−0.914881	+	6.36314i	−0.0842216	+	0.585774i
$119$	−2.73361	+	5.98577i	−0.250590	+	0.548715i
$120$	−0.959493	+	0.281733i	−0.0875893	+	0.0257185i
$121$	5.77901	+	12.6543i	0.525365	+	1.15039i
$122$	−5.59463	−	6.45655i	−0.506514	−	0.584549i
$123$	−0.940706	−	6.54276i	−0.0848206	−	0.589940i
$124$	10.4654	+	3.07291i	0.939817	+	0.275955i
$125$	0.654861	−	0.755750i	0.0585725	−	0.0675963i
$126$	1.70473	+	1.09557i	0.151870	+	0.0976008i
$127$	12.5524	+	8.06693i	1.11384	+	0.715825i	0.962128	−	0.272599i	$-0.0878833\pi$
$127$	12.5524	+	8.06693i	1.11384	+	0.715825i	0.151717	+	0.988424i	$0.451520\pi$
$128$	0.654861	−	0.755750i	0.0578821	−	0.0667995i
$129$	−7.86540	−	2.30949i	−0.692510	−	0.203339i
$130$	−0.804434	−	5.59496i	−0.0705536	−	0.490711i
$131$	−3.52684	−	4.07019i	−0.308141	−	0.355614i	0.580465	−	0.814286i	$-0.302871\pi$
$131$	−3.52684	−	4.07019i	−0.308141	−	0.355614i	−0.888606	+	0.458671i	$0.848326\pi$
$132$	−2.07339	−	4.54009i	−0.180466	−	0.395165i
$133$	−6.28261	+	1.84474i	−0.544772	+	0.159959i
$134$	4.43943	−	9.72099i	0.383508	−	0.839766i
$135$	0.142315	−	0.989821i	0.0122485	−	0.0851903i
$136$	−2.73182	+	1.75563i	−0.234251	+	0.150544i
$137$	5.51860			0.471486			0.235743	−	0.971815i	$-0.424248\pi$
$137$	5.51860			0.471486			0.235743	+	0.971815i	$0.424248\pi$
$138$	−2.20498	−	4.25888i	−0.187700	−	0.362540i
$139$	3.37373			0.286156			0.143078	−	0.989711i	$-0.454300\pi$
$139$	3.37373			0.286156			0.143078	+	0.989711i	$0.454300\pi$
$140$	1.70473	−	1.09557i	0.144076	−	0.0925922i
$141$	−0.468330	+	3.25731i	−0.0394405	+	0.274315i
$142$	4.67747	−	10.2422i	0.392524	−	0.859508i
$143$	27.0696	−	7.94834i	2.26367	−	0.664674i
$144$	0.415415	+	0.909632i	0.0346179	+	0.0758027i
$145$	0.575884	+	0.664606i	0.0478246	+	0.0551925i
$146$	2.37126	+	16.4925i	0.196247	+	1.36493i
$147$	2.77640	+	0.815226i	0.228994	+	0.0672387i
$148$	−4.76760	+	5.50211i	−0.391895	+	0.452271i
$149$	3.73910	+	2.40297i	0.306319	+	0.196859i	0.684765	−	0.728764i	$-0.259905\pi$
$149$	3.73910	+	2.40297i	0.306319	+	0.196859i	−0.378446	+	0.925623i	$0.623541\pi$
$150$	−0.841254	−	0.540641i	−0.0686881	−	0.0441431i
$151$	−8.87098	+	10.2377i	−0.721910	+	0.833129i	−0.991535	−	0.129837i	$-0.958555\pi$
$151$	−8.87098	+	10.2377i	−0.721910	+	0.833129i	0.269625	+	0.962965i	$0.413100\pi$
$152$	−3.10035	−	0.910344i	−0.251471	−	0.0738387i
$153$	−0.462141	−	3.21426i	−0.0373619	−	0.259858i
$154$	6.62335	+	7.64376i	0.533725	+	0.615952i
$155$	4.53101	+	9.92152i	0.363939	+	0.796916i
$156$	−5.42353	+	1.59249i	−0.434230	+	0.127501i
$157$	−2.28282	+	4.99868i	−0.182189	+	0.398938i	−0.978587	−	0.205835i	$-0.934009\pi$
$157$	−2.28282	+	4.99868i	−0.182189	+	0.398938i	0.796398	+	0.604773i	$0.206736\pi$
$158$	0.279507	−	1.94401i	0.0222364	−	0.154657i
$159$	3.15689	−	2.02881i	0.250357	−	0.160895i
$160$	1.00000			0.0790569
$161$	6.71865	+	7.02186i	0.529504	+	0.553400i
$162$	−1.00000			−0.0785674
$163$	17.3409	−	11.1443i	1.35825	−	0.872892i	0.360050	−	0.932933i	$-0.382760\pi$
$163$	17.3409	−	11.1443i	1.35825	−	0.872892i	0.998196	+	0.0600411i	$0.0191232\pi$
$164$	−0.940706	+	6.54276i	−0.0734568	+	0.510903i
$165$	2.07339	−	4.54009i	0.161413	−	0.353446i
$166$	5.00279	−	1.46895i	0.388292	−	0.114013i
$167$	−4.17122	−	9.13371i	−0.322779	−	0.706788i	0.676789	−	0.736177i	$-0.263371\pi$
$167$	−4.17122	−	9.13371i	−0.322779	−	0.706788i	−0.999568	+	0.0293895i	$0.990644\pi$
$168$	−1.32702	−	1.53147i	−0.102382	−	0.118155i
$169$	−2.69697	−	18.7578i	−0.207459	−	1.44291i
$170$	−3.11578	−	0.914875i	−0.238969	−	0.0701677i
$171$	2.11601	−	2.44200i	0.161815	−	0.186745i
$172$	6.89614	+	4.43188i	0.525826	+	0.337928i
$173$	6.25978	+	4.02292i	0.475922	+	0.305857i	0.756522	−	0.653968i	$-0.226897\pi$
$173$	6.25978	+	4.02292i	0.475922	+	0.305857i	−0.280600	+	0.959825i	$0.590533\pi$
$174$	0.575884	−	0.664606i	0.0436577	−	0.0503836i
$175$	1.94434	+	0.570909i	0.146978	+	0.0431567i
$176$	0.710312	+	4.94033i	0.0535418	+	0.372391i
$177$	4.20982	+	4.85839i	0.316429	+	0.365179i
$178$	6.48099	+	14.1914i	0.485771	+	1.06369i
$179$	18.1397	−	5.32629i	1.35582	−	0.398106i	0.478535	−	0.878068i	$-0.341168\pi$
$179$	18.1397	−	5.32629i	1.35582	−	0.398106i	0.877289	+	0.479963i	$0.159350\pi$
$180$	−0.415415	+	0.909632i	−0.0309632	+	0.0678000i
$181$	2.49209	−	17.3329i	0.185236	−	1.28834i	−0.658907	−	0.752225i	$-0.728981\pi$
$181$	2.49209	−	17.3329i	0.185236	−	1.28834i	0.844143	−	0.536119i	$-0.180110\pi$
$182$	9.63601	−	6.19269i	0.714268	−	0.459032i
$183$	−8.54324			−0.631535
$184$	0.915795	+	4.70758i	0.0675133	+	0.347047i
$185$	−7.28033			−0.535261
$186$	9.17570	−	5.89687i	0.672795	−	0.432379i
$187$	2.30661	−	16.0428i	0.168676	−	1.17317i
$188$	1.36705	−	2.99342i	0.0997024	−	0.218318i
$189$	1.94434	−	0.570909i	0.141430	−	0.0415275i
$190$	−1.34230	−	2.93924i	−0.0973809	−	0.213235i
$191$	−1.41112	−	1.62852i	−0.102105	−	0.117836i	0.702397	−	0.711786i	$-0.252113\pi$
$191$	−1.41112	−	1.62852i	−0.102105	−	0.117836i	−0.804502	+	0.593950i	$0.797568\pi$
$192$	−0.142315	−	0.989821i	−0.0102707	−	0.0714342i
$193$	−22.9921	−	6.75108i	−1.65500	−	0.485953i	−0.684899	−	0.728638i	$-0.740154\pi$
$193$	−22.9921	−	6.75108i	−1.65500	−	0.485953i	−0.970105	+	0.242685i	$0.921972\pi$
$194$	−11.7823	+	13.5975i	−0.845921	+	0.976245i
$195$	−4.75518	−	3.05597i	−0.340526	−	0.218843i
$196$	−2.43426	−	1.56441i	−0.173876	−	0.111743i
$197$	13.5476	−	15.6347i	0.965226	−	1.11393i	−0.0282175	−	0.999602i	$-0.508983\pi$
$197$	13.5476	−	15.6347i	0.965226	−	1.11393i	0.993443	−	0.114328i	$-0.0364714\pi$
$198$	−4.78896	−	1.40616i	−0.340336	−	0.0999318i
$199$	−1.66350	−	11.5699i	−0.117923	−	0.820170i	−0.959837	−	0.280559i	$-0.909480\pi$
$199$	−1.66350	−	11.5699i	−0.117923	−	0.820170i	0.841914	−	0.539611i	$-0.181429\pi$
$200$	0.654861	+	0.755750i	0.0463056	+	0.0534396i
$201$	−4.43943	−	9.72099i	−0.313133	−	0.685666i
$202$	4.52223	−	1.32785i	0.318183	−	0.0934269i
$203$	−0.740284	+	1.62099i	−0.0519577	+	0.113772i
$204$	−0.462141	+	3.21426i	−0.0323564	+	0.225043i
$205$	−5.56072	+	3.57366i	−0.388377	+	0.249595i
$206$	−13.8453			−0.964651
$207$	−4.66260	−	1.12256i	−0.324073	−	0.0780235i
$208$	5.65250			0.391930
$209$	13.5673	−	8.71920i	0.938473	−	0.603120i
$210$	0.288390	−	2.00580i	0.0199008	−	0.138413i
$211$	2.47374	−	5.41675i	0.170300	−	0.372904i	−0.805168	−	0.593047i	$-0.797925\pi$
$211$	2.47374	−	5.41675i	0.170300	−	0.372904i	0.975468	+	0.220143i	$0.0706522\pi$
$212$	−3.60059	+	1.05723i	−0.247290	+	0.0726108i
$213$	−4.67747	−	10.2422i	−0.320495	−	0.701785i
$214$	−11.5451	−	13.3237i	−0.789204	−	0.910790i
$215$	1.16662	+	8.11402i	0.0795628	+	0.553372i
$216$	0.959493	+	0.281733i	0.0652852	+	0.0191695i
$217$	−14.4741	+	16.7040i	−0.982565	+	1.13394i
$218$	0.563843	+	0.362360i	0.0381883	+	0.0245421i
$219$	14.0170	+	9.00820i	0.947183	+	0.608718i
$220$	−3.26850	+	3.77205i	−0.220362	+	0.254311i
$221$	−17.6119	−	5.17133i	−1.18471	−	0.347861i
$222$	1.03610	+	7.20623i	0.0695384	+	0.483650i
$223$	8.81423	+	10.1722i	0.590244	+	0.681178i	0.969775	−	0.244001i	$-0.0784600\pi$
$223$	8.81423	+	10.1722i	0.590244	+	0.681178i	−0.379531	+	0.925179i	$0.623915\pi$
$224$	0.841806	+	1.84330i	0.0562455	+	0.123161i
$225$	−0.959493	+	0.281733i	−0.0639662	+	0.0187822i
$226$	0.819900	−	1.79533i	0.0545390	−	0.119424i
$227$	−0.672959	+	4.68053i	−0.0446658	+	0.310658i	0.955225	+	0.295880i	$0.0956130\pi$
$227$	−0.672959	+	4.68053i	−0.0446658	+	0.310658i	−0.999891	+	0.0147773i	$0.995296\pi$
$228$	−2.71829	+	1.74694i	−0.180023	+	0.115694i
$229$	16.4662			1.08812			0.544060	−	0.839046i	$-0.316886\pi$
$229$	16.4662			1.08812			0.544060	+	0.839046i	$0.316886\pi$
$230$	−2.95803	+	3.77492i	−0.195047	+	0.248911i
$231$	10.1141			0.665462
$232$	−0.739798	+	0.475439i	−0.0485701	+	0.0312141i
$233$	−2.62942	+	18.2880i	−0.172259	+	1.19809i	0.701837	+	0.712337i	$0.252363\pi$
$233$	−2.62942	+	18.2880i	−0.172259	+	1.19809i	−0.874097	+	0.485752i	$0.838546\pi$
$234$	−2.34813	+	5.14169i	−0.153502	+	0.336123i
$235$	3.15750	−	0.927127i	0.205973	−	0.0604791i
$236$	−2.67052	−	5.84763i	−0.173836	−	0.380648i
$237$	−1.28615	−	1.48429i	−0.0835443	−	0.0964153i
$238$	−0.936493	−	6.51345i	−0.0607038	−	0.422204i
$239$	16.0033	+	4.69901i	1.03517	+	0.303953i	0.754811	−	0.655942i	$-0.227728\pi$
$239$	16.0033	+	4.69901i	1.03517	+	0.303953i	0.280359	+	0.959895i	$0.409547\pi$
$240$	0.654861	−	0.755750i	0.0422711	−	0.0487834i
$241$	9.19139	+	5.90695i	0.592070	+	0.380500i	0.802095	−	0.597196i	$-0.203718\pi$
$241$	9.19139	+	5.90695i	0.592070	+	0.380500i	−0.210026	+	0.977696i	$0.567355\pi$
$242$	−11.7030	−	7.52108i	−0.752299	−	0.483473i
$243$	−0.654861	+	0.755750i	−0.0420093	+	0.0484814i
$244$	8.19718	+	2.40691i	0.524771	+	0.154087i
$245$	−0.411804	−	2.86416i	−0.0263092	−	0.182985i
$246$	4.32865	+	4.99553i	0.275985	+	0.318504i
$247$	−7.58737	−	16.6140i	−0.482773	−	1.05712i
$248$	−10.4654	+	3.07291i	−0.664551	+	0.195130i
$249$	2.16597	−	4.74282i	0.137263	−	0.300564i
$250$	−0.142315	+	0.989821i	−0.00900078	+	0.0626018i
$251$	−10.3474	+	6.64990i	−0.653125	+	0.419738i	−0.824807	−	0.565414i	$-0.808716\pi$
$251$	−10.3474	+	6.64990i	−0.653125	+	0.419738i	0.171682	+	0.985152i	$0.445080\pi$
$252$	−2.02642			−0.127653
$253$	−20.7505	−	11.9323i	−1.30457	−	0.750177i
$254$	−14.9211			−0.936231
$255$	−2.73182	+	1.75563i	−0.171073	+	0.109942i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	−6.32432	+	13.8483i	−0.394500	+	0.863836i	0.603298	+	0.797516i	$0.293853\pi$
$257$	−6.32432	+	13.8483i	−0.394500	+	0.863836i	−0.997798	+	0.0663196i	$0.978874\pi$
$258$	7.86540	−	2.30949i	0.489679	−	0.143783i
$259$	−6.12863	−	13.4198i	−0.380814	−	0.833867i
$260$	3.70160	+	4.27187i	0.229563	+	0.264930i
$261$	−0.125152	−	0.870448i	−0.00774669	−	0.0538794i
$262$	5.16748	+	1.51731i	0.319248	+	0.0937396i
$263$	0.498902	−	0.575763i	0.0307636	−	0.0355031i	−0.740159	−	0.672432i	$-0.765250\pi$
$263$	0.498902	−	0.575763i	0.0307636	−	0.0355031i	0.770923	+	0.636929i	$0.219795\pi$
$264$	4.19881	+	2.69841i	0.258419	+	0.166076i
$265$	−3.15689	−	2.02881i	−0.193926	−	0.124629i
$266$	4.28793	−	4.94853i	0.262910	−	0.303414i
$267$	14.9693	+	4.39538i	0.916105	+	0.268993i
$268$	1.52088	+	10.5780i	0.0929026	+	0.646152i
$269$	2.94135	+	3.39450i	0.179337	+	0.206966i	0.838300	−	0.545210i	$-0.183550\pi$
$269$	2.94135	+	3.39450i	0.179337	+	0.206966i	−0.658963	+	0.752176i	$0.729004\pi$
$270$	0.415415	+	0.909632i	0.0252814	+	0.0553584i
$271$	−7.52232	+	2.20875i	−0.456948	+	0.134172i	−0.502103	−	0.864808i	$-0.667440\pi$
$271$	−7.52232	+	2.20875i	−0.456948	+	0.134172i	0.0451546	+	0.998980i	$0.485622\pi$
$272$	1.34898	−	2.95386i	0.0817942	−	0.179104i
$273$	1.63012	−	11.3378i	0.0986595	−	0.686192i
$274$	−4.64254	+	2.98358i	−0.280466	+	0.180245i
$275$	−4.99113			−0.300977
$276$	4.15747	+	2.39070i	0.250250	+	0.143903i
$277$	−8.56030			−0.514338			−0.257169	−	0.966366i	$-0.582790\pi$
$277$	−8.56030			−0.514338			−0.257169	+	0.966366i	$0.582790\pi$
$278$	−2.83816	+	1.82398i	−0.170222	+	0.109395i
$279$	1.55225	−	10.7962i	0.0929310	−	0.646349i
$280$	−0.841806	+	1.84330i	−0.0503075	+	0.110158i
$281$	8.76365	−	2.57324i	0.522796	−	0.153507i	−0.00967817	−	0.999953i	$-0.503081\pi$
$281$	8.76365	−	2.57324i	0.522796	−	0.153507i	0.532474	+	0.846447i	$0.321263\pi$
$282$	−1.36705	−	2.99342i	−0.0814066	−	0.178256i
$283$	20.0925	+	23.1880i	1.19438	+	1.37839i	0.907303	+	0.420477i	$0.138137\pi$
$283$	20.0925	+	23.1880i	1.19438	+	1.37839i	0.287074	+	0.957908i	$0.407317\pi$
$284$	1.60243	+	11.1451i	0.0950866	+	0.661342i
$285$	−3.10035	−	0.910344i	−0.183649	−	0.0539241i
$286$	−18.4752	+	21.3215i	−1.09246	+	1.26077i
$287$	−11.2684	−	7.24173i	−0.665150	−	0.427466i
$288$	−0.841254	−	0.540641i	−0.0495713	−	0.0318576i
$289$	4.22708	−	4.87832i	0.248652	−	0.286960i
$290$	−0.843777	−	0.247755i	−0.0495483	−	0.0145487i
$291$	2.56054	+	17.8090i	0.150102	+	1.04398i
$292$	−10.9113	−	12.5924i	−0.638538	−	0.736912i
$293$	7.14627	+	15.6481i	0.417489	+	0.914174i	0.995194	+	0.0979280i	$0.0312215\pi$
$293$	7.14627	+	15.6481i	0.417489	+	0.914174i	−0.577704	+	0.816246i	$0.696051\pi$
$294$	−2.77640	+	0.815226i	−0.161923	+	0.0475449i
$295$	2.67052	−	5.84763i	0.155484	−	0.340462i
$296$	1.03610	−	7.20623i	0.0602221	−	0.418854i
$297$	−4.19881	+	2.69841i	−0.243640	+	0.156578i
$298$	−4.44467			−0.257473
$299$	−16.7203	+	21.3377i	−0.966959	+	1.23399i
$300$	1.00000			0.0577350
$301$	−13.9745	+	8.98086i	−0.805476	+	0.517648i
$302$	1.92785	−	13.4085i	0.110935	−	0.771571i
$303$	1.95791	−	4.28723i	0.112479	−	0.246295i
$304$	3.10035	−	0.910344i	0.177817	−	0.0522118i
$305$	3.54899	+	7.77121i	0.203215	+	0.444978i
$306$	2.12654	+	2.45416i	0.121566	+	0.140295i
$307$	−1.71335	−	11.9166i	−0.0977862	−	0.680118i	−0.978466	−	0.206407i	$-0.933823\pi$
$307$	−1.71335	−	11.9166i	−0.0977862	−	0.680118i	0.880680	−	0.473712i	$-0.157086\pi$
$308$	−9.70445	−	2.84948i	−0.552962	−	0.162364i
$309$	−9.06678	+	10.4636i	−0.515791	+	0.595254i
$310$	−9.17570	−	5.89687i	−0.521145	−	0.334919i
$311$	10.1992	+	6.55461i	0.578342	+	0.371678i	0.796868	−	0.604153i	$-0.206488\pi$
$311$	10.1992	+	6.55461i	0.578342	+	0.371678i	−0.218526	+	0.975831i	$0.570125\pi$
$312$	3.70160	−	4.27187i	0.209562	−	0.241847i
$313$	−26.4284	−	7.76009i	−1.49382	−	0.438626i	−0.570064	−	0.821600i	$-0.693082\pi$
$313$	−26.4284	−	7.76009i	−1.49382	−	0.438626i	−0.923759	+	0.382974i	$0.874900\pi$
$314$	−0.782060	−	5.43934i	−0.0441342	−	0.306960i
$315$	−1.32702	−	1.53147i	−0.0747693	−	0.0862884i
$316$	0.815877	+	1.78652i	0.0458966	+	0.100500i
$317$	2.77748	−	0.815541i	0.155999	−	0.0458054i	−0.202801	−	0.979220i	$-0.565004\pi$
$317$	2.77748	−	0.815541i	0.155999	−	0.0458054i	0.358799	+	0.933415i	$0.383186\pi$
$318$	−1.55889	+	3.41348i	−0.0874180	+	0.191419i
$319$	0.624648	−	4.34452i	0.0349736	−	0.243247i
$320$	−0.841254	+	0.540641i	−0.0470275	+	0.0302227i
$321$	−17.6298			−0.984000
$322$	−9.44840	−	2.27479i	−0.526539	−	0.126769i
$323$	−10.4928			−0.583837
$324$	0.841254	−	0.540641i	0.0467363	−	0.0300356i
$325$	−0.804434	+	5.59496i	−0.0446220	+	0.310353i
$326$	−8.56303	+	18.7504i	−0.474262	+	1.03849i
$327$	0.643092	−	0.188829i	0.0355631	−	0.0104423i
$328$	−2.74591	−	6.01270i	−0.151617	−	0.331996i
$329$	4.36698	+	5.03976i	0.240759	+	0.277851i
$330$	0.710312	+	4.94033i	0.0391014	+	0.271956i
$331$	−0.751242	−	0.220585i	−0.0412920	−	0.0121244i	0.261021	−	0.965333i	$-0.415941\pi$
$331$	−0.751242	−	0.220585i	−0.0412920	−	0.0121244i	−0.302313	+	0.953209i	$0.597759\pi$
$332$	−3.41444	+	3.94047i	−0.187392	+	0.216262i
$333$	6.12461	+	3.93605i	0.335626	+	0.215694i
$334$	8.44711	+	5.42863i	0.462205	+	0.297041i
$335$	−6.99832	+	8.07649i	−0.382359	+	0.441266i
$336$	1.94434	+	0.570909i	0.106072	+	0.0311456i
$337$	0.456063	+	3.17199i	0.0248433	+	0.172789i	0.998466	−	0.0553771i	$-0.0176361\pi$
$337$	0.456063	+	3.17199i	0.0248433	+	0.172789i	−0.973622	+	0.228166i	$0.926727\pi$
$338$	12.4101	+	14.3220i	0.675020	+	0.779014i
$339$	−0.819900	−	1.79533i	−0.0445309	−	0.0975090i
$340$	3.11578	−	0.914875i	0.168977	−	0.0496160i
$341$	22.6149	−	49.5196i	1.22466	−	2.68164i
$342$	−0.459853	+	3.19835i	−0.0248660	+	0.172947i
$343$	16.8660	−	10.8391i	0.910678	−	0.585257i
$344$	−8.19746			−0.441977
$345$	0.915795	+	4.70758i	0.0493048	+	0.253448i
$346$	−7.44102			−0.400032
$347$	11.9399	−	7.67330i	0.640967	−	0.411924i	−0.179389	−	0.983778i	$-0.557412\pi$
$347$	11.9399	−	7.67330i	0.640967	−	0.411924i	0.820355	+	0.571854i	$0.193776\pi$
$348$	−0.125152	+	0.870448i	−0.00670883	+	0.0466609i
$349$	9.52333	−	20.8532i	0.509772	−	1.11625i	−0.463396	−	0.886151i	$-0.653369\pi$
$349$	9.52333	−	20.8532i	0.509772	−	1.11625i	0.973168	−	0.230094i	$-0.0739034\pi$
$350$	−1.94434	+	0.570909i	−0.103929	+	0.0305164i
$351$	2.34813	+	5.14169i	0.125334	+	0.274443i
$352$	−3.26850	−	3.77205i	−0.174211	−	0.201051i
$353$	0.513368	+	3.57056i	0.0273238	+	0.190041i	0.998912	−	0.0466368i	$-0.0148503\pi$
$353$	0.513368	+	3.57056i	0.0273238	+	0.190041i	−0.971588	+	0.236678i	$0.923941\pi$
$354$	−6.16817	−	1.81114i	−0.327834	−	0.0962609i
$355$	−7.37356	+	8.50954i	−0.391348	+	0.451640i
$356$	−13.1246	−	8.43467i	−0.695602	−	0.447036i
$357$	−5.53581	−	3.55765i	−0.292986	−	0.188291i
$358$	−12.3805	+	14.2878i	−0.654328	+	0.755135i
$359$	−31.5443	−	9.26223i	−1.66484	−	0.488842i	−0.692308	−	0.721602i	$-0.743406\pi$
$359$	−31.5443	−	9.26223i	−1.66484	−	0.488842i	−0.972534	+	0.232760i	$0.925224\pi$
$360$	−0.142315	−	0.989821i	−0.00750065	−	0.0521682i
$361$	5.60503	+	6.46855i	0.295002	+	0.340450i
$362$	7.27438	+	15.9287i	0.382333	+	0.837193i
$363$	−13.3479	+	3.91930i	−0.700583	+	0.205710i
$364$	−4.75831	+	10.4192i	−0.249403	+	0.546116i
$365$	2.37126	−	16.4925i	0.124117	−	0.863256i
$366$	7.18703	−	4.61883i	0.375672	−	0.241430i
$367$	9.17838			0.479108			0.239554	−	0.970883i	$-0.422999\pi$
$367$	9.17838			0.479108			0.239554	+	0.970883i	$0.422999\pi$
$368$	−3.31553	−	3.46515i	−0.172834	−	0.180634i
$369$	6.61004			0.344105
$370$	6.12461	−	3.93605i	0.318403	−	0.204625i
$371$	1.08221	−	7.52695i	0.0561856	−	0.390780i
$372$	−4.53101	+	9.92152i	−0.234922	+	0.514407i
$373$	−12.9018	+	3.78832i	−0.668032	+	0.196152i	−0.598126	−	0.801402i	$-0.704088\pi$
$373$	−12.9018	+	3.78832i	−0.668032	+	0.196152i	−0.0699053	+	0.997554i	$0.522270\pi$
$374$	6.73296	+	14.7431i	0.348153	+	0.762349i
$375$	0.654861	+	0.755750i	0.0338169	+	0.0390267i
$376$	0.468330	+	3.25731i	0.0241523	+	0.167983i
$377$	−4.76945	−	1.40044i	−0.245639	−	0.0721262i
$378$	−1.32702	+	1.53147i	−0.0682547	+	0.0787702i
$379$	−4.12614	−	2.65171i	−0.211945	−	0.136209i	0.430361	−	0.902657i	$-0.358386\pi$
$379$	−4.12614	−	2.65171i	−0.211945	−	0.136209i	−0.642307	+	0.766448i	$0.722023\pi$
$380$	2.71829	+	1.74694i	0.139445	+	0.0896160i
$381$	−9.77122	+	11.2766i	−0.500595	+	0.577717i
$382$	2.06756	+	0.607090i	0.105785	+	0.0310614i
$383$	3.12932	+	21.7649i	0.159901	+	1.11213i	0.898813	+	0.438332i	$0.144430\pi$
$383$	3.12932	+	21.7649i	0.159901	+	1.11213i	−0.738913	+	0.673801i	$0.764660\pi$
$384$	0.654861	+	0.755750i	0.0334182	+	0.0385667i
$385$	−4.20157	−	9.20015i	−0.214132	−	0.468883i
$386$	22.9921	−	6.75108i	1.17026	−	0.343621i
$387$	3.40535	−	7.45667i	0.173104	−	0.379044i
$388$	2.56054	−	17.8090i	0.129992	−	0.904113i
$389$	−0.111952	+	0.0719469i	−0.00567617	+	0.00364785i	−0.543476	−	0.839425i	$-0.682892\pi$
$389$	−0.111952	+	0.0719469i	−0.00567617	+	0.00364785i	0.537800	+	0.843073i	$0.319256\pi$
$390$	5.65250			0.286225
$391$	7.16026	+	13.8299i	0.362110	+	0.699410i
$392$	2.89362			0.146150
$393$	4.53068	−	2.91169i	0.228543	−	0.146876i
$394$	−2.94417	+	20.4772i	−0.148325	+	1.03162i
$395$	−0.815877	+	1.78652i	−0.0410512	+	0.0898896i
$396$	4.78896	−	1.40616i	0.240654	−	0.0706624i
$397$	11.2195	+	24.5672i	0.563088	+	1.23299i	0.950397	+	0.311041i	$0.100678\pi$
$397$	11.2195	+	24.5672i	0.563088	+	1.23299i	−0.387308	+	0.921950i	$0.626595\pi$
$398$	7.65460	+	8.83388i	0.383690	+	0.442802i
$399$	−0.931856	−	6.48120i	−0.0466511	−	0.324466i
$400$	−0.959493	−	0.281733i	−0.0479746	−	0.0140866i
$401$	−3.65393	+	4.21686i	−0.182468	+	0.210580i	−0.839613	−	0.543184i	$-0.817218\pi$
$401$	−3.65393	+	4.21686i	−0.182468	+	0.210580i	0.657145	+	0.753764i	$0.271764\pi$
$402$	8.99025	+	5.77768i	0.448393	+	0.288165i
$403$	−51.8656	−	33.3320i	−2.58361	−	1.66039i
$404$	−3.08645	+	3.56196i	−0.153557	+	0.177214i
$405$	0.959493	+	0.281733i	0.0476776	+	0.0139994i
$406$	−0.253610	−	1.76390i	−0.0125864	−	0.0875406i
$407$	23.7958	+	27.4618i	1.17951	+	1.36123i
$408$	−1.34898	−	2.95386i	−0.0667847	−	0.146238i
$409$	−34.8569	+	10.2349i	−1.72356	+	0.506084i	−0.985649	−	0.168810i	$-0.946008\pi$
$409$	−34.8569	+	10.2349i	−1.72356	+	0.506084i	−0.737915	+	0.674894i	$0.764189\pi$
$410$	2.74591	−	6.01270i	0.135611	−	0.296946i
$411$	−0.785378	+	5.46243i	−0.0387398	+	0.269442i
$412$	11.6474	−	7.48536i	0.573829	−	0.368777i
$413$	13.0270			0.641016
$414$	4.52933	−	1.57643i	0.222605	−	0.0774774i
$415$	−5.21399			−0.255945
$416$	−4.75518	+	3.05597i	−0.233142	+	0.149831i
$417$	−0.480132	+	3.33939i	−0.0235122	+	0.163531i
$418$	−6.69962	+	14.6701i	−0.327689	+	0.717539i
$419$	−28.0599	+	8.23913i	−1.37082	+	0.402508i	−0.882563	−	0.470194i	$-0.844184\pi$
$419$	−28.0599	+	8.23913i	−1.37082	+	0.402508i	−0.488253	+	0.872702i	$0.662366\pi$
$420$	0.841806	+	1.84330i	0.0410759	+	0.0899437i
$421$	−7.47322	−	8.62455i	−0.364222	−	0.420335i	0.543828	−	0.839197i	$-0.316975\pi$
$421$	−7.47322	−	8.62455i	−0.364222	−	0.420335i	−0.908050	+	0.418862i	$0.862429\pi$
$422$	0.847467	+	5.89426i	0.0412541	+	0.286928i
$423$	−3.15750	−	0.927127i	−0.153523	−	0.0450785i
$424$	2.45743	−	2.83603i	0.119343	−	0.137730i
$425$	2.73182	+	1.75563i	0.132513	+	0.0851606i
$426$	9.47230	+	6.08748i	0.458934	+	0.294939i
$427$	−11.3371	+	13.0837i	−0.548640	+	0.633164i
$428$	16.9157	+	4.96689i	0.817650	+	0.240084i
$429$	4.01504	+	27.9252i	0.193848	+	1.34824i
$430$	−5.36819	−	6.19523i	−0.258877	−	0.298760i
$431$	−7.69876	−	16.8579i	−0.370836	−	0.812018i	−0.999413	−	0.0342702i	$-0.989089\pi$
$431$	−7.69876	−	16.8579i	−0.370836	−	0.812018i	0.628576	−	0.777748i	$-0.283638\pi$
$432$	−0.959493	+	0.281733i	−0.0461636	+	0.0135549i
$433$	2.88546	−	6.31828i	0.138667	−	0.303637i	−0.827540	−	0.561407i	$-0.810260\pi$
$433$	2.88546	−	6.31828i	0.138667	−	0.303637i	0.966206	+	0.257770i	$0.0829875\pi$
$434$	3.14552	−	21.8776i	0.150990	−	1.05016i
$435$	−0.739798	+	0.475439i	−0.0354706	+	0.0227956i
$436$	−0.670242			−0.0320988
$437$	−5.73446	+	14.3964i	−0.274316	+	0.688673i
$438$	−16.6621			−0.796145
$439$	17.7163	−	11.3856i	0.845552	−	0.543403i	−0.0446328	−	0.999003i	$-0.514212\pi$
$439$	17.7163	−	11.3856i	0.845552	−	0.543403i	0.890184	+	0.455600i	$0.150575\pi$
$440$	0.710312	−	4.94033i	0.0338628	−	0.235521i
$441$	−1.20205	+	2.63213i	−0.0572405	+	0.125339i
$442$	17.6119	−	5.17133i	0.837714	−	0.245975i
$443$	16.1987	+	35.4703i	0.769625	+	1.68524i	0.727477	+	0.686132i	$0.240693\pi$
$443$	16.1987	+	35.4703i	0.769625	+	1.68524i	0.0421474	+	0.999111i	$0.486580\pi$
$444$	−4.76760	−	5.50211i	−0.226260	−	0.261119i
$445$	−2.22029	−	15.4424i	−0.105252	−	0.732042i
$446$	−12.9145	−	3.79203i	−0.611518	−	0.179558i
$447$	−2.91064	+	3.35906i	−0.137669	+	0.158878i
$448$	−1.70473	−	1.09557i	−0.0805411	−	0.0517606i
$449$	−17.7966	−	11.4372i	−0.839874	−	0.539754i	0.0485272	−	0.998822i	$-0.484547\pi$
$449$	−17.7966	−	11.4372i	−0.839874	−	0.539754i	−0.888401	+	0.459067i	$0.848184\pi$
$450$	0.654861	−	0.755750i	0.0308704	−	0.0356264i
$451$	31.6552	+	9.29480i	1.49058	+	0.437675i
$452$	0.280885	+	1.95360i	0.0132117	+	0.0918896i
$453$	−8.87098	−	10.2377i	−0.416795	−	0.481007i
$454$	−1.96436	−	4.30134i	−0.0921919	−	0.201872i
$455$	−10.9904	+	3.22706i	−0.515236	+	0.151287i
$456$	1.34230	−	2.93924i	0.0628591	−	0.137642i
$457$	−3.87594	+	26.9578i	−0.181309	+	1.26103i	0.672363	+	0.740221i	$0.265279\pi$
$457$	−3.87594	+	26.9578i	−0.181309	+	1.26103i	−0.853672	+	0.520811i	$0.825630\pi$
$458$	−13.8523	+	8.90232i	−0.647275	+	0.415978i
$459$	3.24732			0.151572
$460$	0.447580	−	4.77490i	0.0208685	−	0.222631i
$461$	−2.25820			−0.105175			−0.0525873	−	0.998616i	$-0.516747\pi$
$461$	−2.25820			−0.105175			−0.0525873	+	0.998616i	$0.516747\pi$
$462$	−8.50856	+	5.46812i	−0.395854	+	0.254400i
$463$	3.98746	−	27.7334i	0.185313	−	1.28888i	−0.658638	−	0.752460i	$-0.728867\pi$
$463$	3.98746	−	27.7334i	0.185313	−	1.28888i	0.843951	−	0.536420i	$-0.180224\pi$
$464$	0.365316	−	0.799930i	0.0169594	−	0.0371358i
$465$	−10.4654	+	3.07291i	−0.485320	+	0.142503i
$466$	−7.67525	−	16.8065i	−0.355549	−	0.778544i
$467$	−25.6135	−	29.5596i	−1.18525	−	1.36785i	−0.914187	−	0.405294i	$-0.867169\pi$
$467$	−25.6135	−	29.5596i	−1.18525	−	1.36785i	−0.271066	−	0.962561i	$-0.587376\pi$
$468$	−0.804434	−	5.59496i	−0.0371850	−	0.258627i
$469$	−20.7786	−	6.10115i	−0.959467	−	0.281725i
$470$	−2.15502	+	2.48702i	−0.0994036	+	0.114718i
$471$	−4.62292	−	2.97097i	−0.213013	−	0.136895i
$472$	5.40806	+	3.47555i	0.248926	+	0.159975i
$473$	26.7934	−	30.9212i	1.23196	−	1.42176i
$474$	1.88445	+	0.553324i	0.0865555	+	0.0254150i
$475$	0.459853	+	3.19835i	0.0210995	+	0.146750i
$476$	4.30927	+	4.97316i	0.197515	+	0.227944i
$477$	1.55889	+	3.41348i	0.0713765	+	0.156293i
$478$	−16.0033	+	4.69901i	−0.731976	+	0.214927i
$479$	0.771941	−	1.69032i	0.0352709	−	0.0772325i	−0.891176	−	0.453657i	$-0.850119\pi$
$479$	0.771941	−	1.69032i	0.0352709	−	0.0772325i	0.926447	+	0.376424i	$0.122846\pi$
$480$	−0.142315	+	0.989821i	−0.00649575	+	0.0451790i
$481$	34.6193	−	22.2485i	1.57851	−	1.01444i
$482$	−10.9258			−0.497658
$483$	−7.90655	+	5.65095i	−0.359761	+	0.257127i
$484$	13.9114			0.632337
$485$	15.1359	−	9.72726i	0.687286	−	0.441692i
$486$	0.142315	−	0.989821i	0.00645553	−	0.0448992i
$487$	7.73160	−	16.9298i	0.350352	−	0.767164i	−0.649624	−	0.760256i	$-0.725074\pi$
$487$	7.73160	−	16.9298i	0.350352	−	0.767164i	0.999976	−	0.00690864i	$-0.00219910\pi$
$488$	−8.19718	+	2.40691i	−0.371069	+	0.108956i
$489$	8.56303	+	18.7504i	0.387234	+	0.847924i
$490$	1.89492	+	2.18685i	0.0856035	+	0.0987918i
$491$	−1.12976	−	7.85767i	−0.0509855	−	0.354612i	−0.999304	−	0.0372930i	$-0.988127\pi$
$491$	−1.12976	−	7.85767i	−0.0509855	−	0.354612i	0.948319	−	0.317319i	$-0.102783\pi$
$492$	−6.34228	−	1.86226i	−0.285932	−	0.0839573i
$493$	−1.87008	+	2.15818i	−0.0842241	+	0.0971997i
$494$	15.3651	+	9.87456i	0.691309	+	0.444278i
$495$	4.19881	+	2.69841i	0.188722	+	0.121285i
$496$	7.14268	−	8.24310i	0.320716	−	0.370126i
$497$	−21.8927	−	6.42829i	−0.982023	−	0.288348i
$498$	0.742029	+	5.16092i	0.0332511	+	0.231266i
$499$	10.7788	+	12.4394i	0.482527	+	0.556866i	0.943853	−	0.330365i	$-0.107172\pi$
$499$	10.7788	+	12.4394i	0.482527	+	0.556866i	−0.461326	+	0.887231i	$0.652626\pi$
$500$	−0.415415	−	0.909632i	−0.0185779	−	0.0406800i
$501$	9.63437	−	2.82891i	0.430432	−	0.126386i
$502$	5.10962	−	11.1885i	0.228053	−	0.499367i
$503$	−2.11374	+	14.7014i	−0.0942469	+	0.655502i	0.886860	+	0.462037i	$0.152881\pi$
$503$	−2.11374	+	14.7014i	−0.0942469	+	0.655502i	−0.981107	+	0.193464i	$0.938028\pi$
$504$	1.70473	−	1.09557i	0.0759349	−	0.0488004i
$505$	−4.71314			−0.209732
$506$	23.9075	−	1.18048i	1.06282	−	0.0524787i
$507$	18.9507			0.841631
$508$	12.5524	−	8.06693i	0.556922	−	0.357912i
$509$	1.06818	−	7.42934i	0.0473462	−	0.329300i	−0.952358	−	0.304982i	$-0.901350\pi$
$509$	1.06818	−	7.42934i	0.0473462	−	0.329300i	0.999704	−	0.0243178i	$-0.00774136\pi$
$510$	1.34898	−	2.95386i	0.0597340	−	0.130799i
$511$	32.3967	−	9.51253i	1.43315	−	0.420810i
$512$	−0.415415	−	0.909632i	−0.0183589	−	0.0402004i
$513$	2.11601	+	2.44200i	0.0934241	+	0.107817i
$514$	−2.16662	−	15.0691i	−0.0955654	−	0.664672i
$515$	13.2845	+	3.90069i	0.585386	+	0.171885i
$516$	−5.36819	+	6.19523i	−0.236322	+	0.272730i
$517$	−13.8175	−	8.87994i	−0.607691	−	0.390539i
$518$	12.4110	+	7.97609i	0.545310	+	0.350449i
$519$	−4.87283	+	5.62354i	−0.213893	+	0.246846i
$520$	−5.42353	−	1.59249i	−0.237838	−	0.0698354i
$521$	−1.03340	−	7.18744i	−0.0452740	−	0.314887i	−0.999856	−	0.0169407i	$-0.994607\pi$
$521$	−1.03340	−	7.18744i	−0.0452740	−	0.314887i	0.954583	−	0.297947i	$-0.0963018\pi$
$522$	0.575884	+	0.664606i	0.0252058	+	0.0290890i
$523$	4.69832	+	10.2879i	0.205443	+	0.449858i	0.984105	−	0.177585i	$-0.0568286\pi$
$523$	4.69832	+	10.2879i	0.205443	+	0.449858i	−0.778662	+	0.627444i	$0.784101\pi$
$524$	−5.16748	+	1.51731i	−0.225742	+	0.0662839i
$525$	−0.841806	+	1.84330i	−0.0367394	+	0.0804481i
$526$	−0.108422	+	0.754089i	−0.00472741	+	0.0328799i
$527$	−29.7964	+	19.1490i	−1.29795	+	0.834143i
$528$	−4.99113			−0.217211
$529$	22.8881	−	2.26581i	0.995136	−	0.0985136i
$530$	3.75260			0.163003
$531$	−5.40806	+	3.47555i	−0.234690	+	0.150826i
$532$	−0.931856	+	6.48120i	−0.0404011	+	0.280996i
$533$	15.5212	−	33.9868i	0.672300	−	1.47213i
$534$	−14.9693	+	4.39538i	−0.647784	+	0.190207i
$535$	7.32368	+	16.0366i	0.316631	+	0.693324i
$536$	−6.99832	−	8.07649i	−0.302281	−	0.348851i
$537$	2.69053	+	18.7131i	0.116105	+	0.807528i
$538$	−4.30962	−	1.26542i	−0.185801	−	0.0545561i
$539$	−9.45777	+	10.9149i	−0.407375	+	0.470136i
$540$	−0.841254	−	0.540641i	−0.0362018	−	0.0232655i
$541$	31.5281	+	20.2619i	1.35550	+	0.871127i	0.998026	−	0.0627963i	$-0.0200018\pi$
$541$	31.5281	+	20.2619i	1.35550	+	0.871127i	0.357474	+	0.933923i	$0.383638\pi$
$542$	5.13404	−	5.92499i	0.220526	−	0.254500i
$543$	16.8018	+	4.93345i	0.721034	+	0.211715i
$544$	0.462141	+	3.21426i	0.0198141	+	0.137810i
$545$	−0.438915	−	0.506535i	−0.0188011	−	0.0216976i
$546$	4.75831	+	10.4192i	0.203637	+	0.445902i
$547$	−20.3098	+	5.96348i	−0.868382	+	0.254980i	−0.685427	−	0.728141i	$-0.740384\pi$
$547$	−20.3098	+	5.96348i	−0.868382	+	0.254980i	−0.182955	+	0.983121i	$0.558566\pi$
$548$	2.29251	−	5.01989i	0.0979311	−	0.214439i
$549$	1.21583	−	8.45629i	0.0518904	−	0.360905i
$550$	4.19881	−	2.69841i	0.179038	−	0.115061i
$551$	−2.84155			−0.121054
$552$	−4.79000	+	0.236515i	−0.203876	+	0.0100668i
$553$	−3.97990			−0.169243
$554$	7.20138	−	4.62805i	0.305957	−	0.196627i
$555$	1.03610	−	7.20623i	0.0439800	−	0.305887i
$556$	1.40150	−	3.06885i	0.0594368	−	0.130148i
$557$	15.4809	−	4.54560i	0.655947	−	0.192603i	0.0632109	−	0.998000i	$-0.479866\pi$
$557$	15.4809	−	4.54560i	0.655947	−	0.192603i	0.592736	+	0.805397i	$0.298048\pi$
$558$	4.53101	+	9.92152i	0.191813	+	0.420011i
$559$	−30.3437	−	35.0185i	−1.28340	−	1.48112i
$560$	−0.288390	−	2.00580i	−0.0121867	−	0.0847603i
$561$	15.5513	+	4.56626i	0.656575	+	0.192788i
$562$	−5.98125	+	6.90273i	−0.252304	+	0.291174i
$563$	−14.6542	−	9.41765i	−0.617599	−	0.396907i	0.194101	−	0.980982i	$-0.437821\pi$
$563$	−14.6542	−	9.41765i	−0.617599	−	0.396907i	−0.811700	+	0.584075i	$0.801457\pi$
$564$	2.76840	+	1.77914i	0.116571	+	0.0749155i
$565$	−1.29249	+	1.49162i	−0.0543756	+	0.0627527i
$566$	−29.4393	−	8.64416i	−1.23743	−	0.363341i
$567$	0.288390	+	2.00580i	0.0121112	+	0.0842355i
$568$	−7.37356	−	8.50954i	−0.309388	−	0.357053i
$569$	3.74676	+	8.20425i	0.157072	+	0.343940i	0.971764	−	0.235954i	$-0.0758213\pi$
$569$	3.74676	+	8.20425i	0.157072	+	0.343940i	−0.814692	+	0.579894i	$0.803094\pi$
$570$	3.10035	−	0.910344i	0.129859	−	0.0381301i
$571$	7.29548	−	15.9749i	0.305306	−	0.668527i	−0.693336	−	0.720614i	$-0.743860\pi$
$571$	7.29548	−	15.9749i	0.305306	−	0.668527i	0.998643	+	0.0520867i	$0.0165872\pi$
$572$	4.01504	−	27.9252i	0.167877	−	1.16761i
$573$	1.81277	−	1.16500i	0.0757296	−	0.0486684i
$574$	13.3947			0.559085
$575$	3.90173	−	2.78864i	0.162713	−	0.116294i
$576$	1.00000			0.0416667
$577$	7.89740	−	5.07535i	0.328773	−	0.211289i	−0.365832	−	0.930681i	$-0.619216\pi$
$577$	7.89740	−	5.07535i	0.328773	−	0.211289i	0.694605	+	0.719391i	$0.255579\pi$
$578$	−0.918633	+	6.38923i	−0.0382101	+	0.265757i
$579$	9.95447	−	21.7972i	0.413694	−	0.905863i
$580$	0.843777	−	0.247755i	0.0350359	−	0.0102875i
$581$	−4.38917	−	9.61094i	−0.182093	−	0.398729i
$582$	−11.7823	−	13.5975i	−0.488393	−	0.563635i
$583$	2.66552	+	18.5391i	0.110394	+	0.767810i
$584$	15.9871	+	4.69425i	0.661553	+	0.194249i
$585$	3.70160	−	4.27187i	0.153042	−	0.176620i
$586$	−14.4718	−	9.30049i	−0.597826	−	0.384200i
$587$	30.5223	+	19.6155i	1.25979	+	0.809619i	0.988256	−	0.152809i	$-0.0488321\pi$
$587$	30.5223	+	19.6155i	1.25979	+	0.809619i	0.271536	+	0.962428i	$0.412468\pi$
$588$	1.89492	−	2.18685i	0.0781450	−	0.0901841i
$589$	−33.8160	−	9.92929i	−1.39337	−	0.409129i
$590$	0.914881	+	6.36314i	0.0376651	+	0.261966i
$591$	13.5476	+	15.6347i	0.557273	+	0.643128i
$592$	3.02436	+	6.62242i	0.124300	+	0.272180i
$593$	−14.0235	+	4.11766i	−0.575874	+	0.169092i	−0.556685	−	0.830724i	$-0.687927\pi$
$593$	−14.0235	+	4.11766i	−0.575874	+	0.169092i	−0.0191897	+	0.999816i	$0.506109\pi$
$594$	2.07339	−	4.54009i	0.0850723	−	0.186282i
$595$	−0.936493	+	6.51345i	−0.0383925	+	0.267026i
$596$	3.73910	−	2.40297i	0.153159	−	0.0984295i
$597$	11.6889			0.478395
$598$	2.52994	−	26.9901i	0.103457	−	1.10371i
$599$	29.3143			1.19775			0.598876	−	0.800842i	$-0.295614\pi$
$599$	29.3143			1.19775			0.598876	+	0.800842i	$0.295614\pi$
$600$	−0.841254	+	0.540641i	−0.0343440	+	0.0220716i
$601$	1.54936	−	10.7760i	0.0631995	−	0.439562i	−0.933513	−	0.358544i	$-0.883273\pi$
$601$	1.54936	−	10.7760i	0.0631995	−	0.439562i	0.996713	−	0.0810190i	$-0.0258174\pi$
$602$	6.90067	−	15.1104i	0.281250	−	0.615852i
$603$	10.2538	−	3.01080i	0.417569	−	0.122609i
$604$	5.62736	+	12.3222i	0.228974	+	0.501383i
$605$	9.11004	+	10.5135i	0.370376	+	0.427436i
$606$	0.670750	+	4.66517i	0.0272474	+	0.189510i
$607$	10.7425	+	3.15429i	0.436025	+	0.128029i	0.492376	−	0.870382i	$-0.336128\pi$
$607$	10.7425	+	3.15429i	0.436025	+	0.128029i	−0.0563509	+	0.998411i	$0.517947\pi$
$608$	−2.11601	+	2.44200i	−0.0858155	+	0.0990364i
$609$	−1.49914	−	0.963440i	−0.0607483	−	0.0390406i
$610$	−7.18703	−	4.61883i	−0.290994	−	0.187011i
$611$	−12.1812	+	14.0579i	−0.492800	+	0.568722i
$612$	−3.11578	−	0.914875i	−0.125948	−	0.0369816i
$613$	−2.71341	−	18.8722i	−0.109594	−	0.762241i	−0.968303	−	0.249778i	$-0.919642\pi$
$613$	−2.71341	−	18.8722i	−0.109594	−	0.762241i	0.858709	−	0.512463i	$-0.171267\pi$
$614$	7.88398	+	9.09860i	0.318172	+	0.367190i
$615$	−2.74591	−	6.01270i	−0.110726	−	0.242455i
$616$	9.70445	−	2.84948i	0.391003	−	0.114809i
$617$	−15.7523	+	34.4927i	−0.634162	+	1.38862i	0.270594	+	0.962693i	$0.412780\pi$
$617$	−15.7523	+	34.4927i	−0.634162	+	1.38862i	−0.904757	+	0.425929i	$0.859947\pi$
$618$	1.97040	−	13.7044i	0.0792611	−	0.551273i
$619$	−12.9085	+	8.29577i	−0.518835	+	0.333435i	−0.773711	−	0.633539i	$-0.781602\pi$
$619$	−12.9085	+	8.29577i	−0.518835	+	0.333435i	0.254876	+	0.966974i	$0.417965\pi$
$620$	10.9072			0.438043
$621$	1.77469	−	4.45539i	0.0712160	−	0.178788i
$622$	−12.1238			−0.486120
$623$	26.5960	−	17.0922i	1.06554	−	0.684784i
$624$	−0.804434	+	5.59496i	−0.0322031	+	0.223978i
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$	26.4284	−	7.76009i	1.05629	−	0.310155i
$627$	6.69962	+	14.6701i	0.267557	+	0.585868i
$628$	3.59864	+	4.15305i	0.143601	+	0.165725i
$629$	−3.36454	−	23.4009i	−0.134153	−	0.933055i
$630$	1.94434	+	0.570909i	0.0774643	+	0.0227456i
$631$	10.8682	−	12.5426i	0.432656	−	0.499312i	−0.496995	−	0.867754i	$-0.665563\pi$
$631$	10.8682	−	12.5426i	0.432656	−	0.499312i	0.929651	+	0.368442i	$0.120109\pi$
$632$	−1.65222	−	1.06182i	−0.0657220	−	0.0422369i
$633$	5.00956	+	3.21945i	0.199112	+	0.127962i
$634$	−1.89565	+	2.18770i	−0.0752858	+	0.0868845i
$635$	14.3167	+	4.20375i	0.568139	+	0.166821i
$636$	−0.534051	−	3.71440i	−0.0211765	−	0.147286i
$637$	10.7110	+	12.3612i	0.424385	+	0.489767i
$638$	1.82334	+	3.99256i	0.0721867	+	0.158067i
$639$	10.8036	−	3.17224i	0.427385	−	0.125492i
$640$	0.415415	−	0.909632i	0.0164207	−	0.0359564i
$641$	−3.76507	+	26.1867i	−0.148712	+	1.03431i	0.769621	+	0.638501i	$0.220445\pi$
$641$	−3.76507	+	26.1867i	−0.148712	+	1.03431i	−0.918332	+	0.395810i	$0.870464\pi$
$642$	14.8311	−	9.53139i	0.585338	−	0.376174i
$643$	−17.3348			−0.683617			−0.341808	−	0.939770i	$-0.611039\pi$
$643$	−17.3348			−0.683617			−0.341808	+	0.939770i	$0.611039\pi$
$644$	9.17834	−	3.19452i	0.361677	−	0.125882i
$645$	−8.19746			−0.322775
$646$	8.82714	−	5.67286i	0.347299	−	0.223196i
$647$	5.08621	−	35.3753i	0.199959	−	1.39075i	−0.604436	−	0.796654i	$-0.706601\pi$
$647$	5.08621	−	35.3753i	0.199959	−	1.39075i	0.804395	−	0.594095i	$-0.202490\pi$
$648$	−0.415415	+	0.909632i	−0.0163190	+	0.0357337i
$649$	−30.7861	+	9.03963i	−1.20846	+	0.354836i
$650$	−2.34813	−	5.14169i	−0.0921013	−	0.201674i
$651$	−14.4741	−	16.7040i	−0.567284	−	0.654681i
$652$	−2.93356	−	20.4034i	−0.114887	−	0.799058i
$653$	2.53449	+	0.744194i	0.0991824	+	0.0291226i	0.330947	−	0.943649i	$-0.392632\pi$
$653$	2.53449	+	0.744194i	0.0991824	+	0.0291226i	−0.231765	+	0.972772i	$0.574450\pi$
$654$	−0.438915	+	0.506535i	−0.0171629	+	0.0198071i
$655$	−4.53068	−	2.91169i	−0.177028	−	0.113769i
$656$	5.56072	+	3.57366i	0.217110	+	0.139528i
$657$	−10.9113	+	12.5924i	−0.425692	+	0.491275i
$658$	−6.39844	−	1.87875i	−0.249437	−	0.0732413i
$659$	−2.41690	−	16.8099i	−0.0941489	−	0.654820i	−0.981178	−	0.193106i	$-0.938144\pi$
$659$	−2.41690	−	16.8099i	−0.0941489	−	0.654820i	0.887029	−	0.461714i	$-0.152765\pi$
$660$	−3.26850	−	3.77205i	−0.127226	−	0.146827i
$661$	0.846476	+	1.85352i	0.0329241	+	0.0720938i	0.925380	−	0.379042i	$-0.123746\pi$
$661$	0.846476	+	1.85352i	0.0329241	+	0.0720938i	−0.892455	+	0.451136i	$0.851019\pi$
$662$	0.751242	−	0.220585i	0.0291979	−	0.00857326i
$663$	7.62513	−	16.6967i	0.296135	−	0.648446i
$664$	0.742029	−	5.16092i	0.0287963	−	0.200283i
$665$	−5.50840	+	3.54003i	−0.213607	+	0.137277i
$666$	−7.28033			−0.282107
$667$	1.93906	+	3.74526i	0.0750805	+	0.145017i
$668$	−10.0411			−0.388502
$669$	−11.3230	+	7.27686i	−0.437773	+	0.281340i
$670$	1.52088	−	10.5780i	0.0587567	−	0.408662i
$671$	17.7135	−	38.7871i	0.683822	−	1.49736i
$672$	−1.94434	+	0.570909i	−0.0750044	+	0.0220233i
$673$	19.9384	+	43.6591i	0.768570	+	1.68293i	0.729776	+	0.683687i	$0.239625\pi$
$673$	19.9384	+	43.6591i	0.768570	+	1.68293i	0.0387946	+	0.999247i	$0.487648\pi$
$674$	−2.09857	−	2.42188i	−0.0808340	−	0.0932874i
$675$	−0.142315	−	0.989821i	−0.00547770	−	0.0380982i
$676$	−18.1831	−	5.33904i	−0.699350	−	0.205348i
$677$	−8.18562	+	9.44671i	−0.314599	+	0.363067i	−0.890923	−	0.454155i	$-0.849941\pi$
$677$	−8.18562	+	9.44671i	−0.314599	+	0.363067i	0.576324	+	0.817221i	$0.304487\pi$
$678$	1.66037	+	1.06706i	0.0637663	+	0.0409801i
$679$	30.6717	+	19.7115i	1.17707	+	0.756459i
$680$	−2.12654	+	2.45416i	−0.0815491	+	0.0941127i
$681$	−4.53712	−	1.33222i	−0.173863	−	0.0510507i
$682$	7.74750	+	53.8851i	0.296667	+	2.06337i
$683$	10.3315	+	11.9232i	0.395324	+	0.456228i	0.918163	−	0.396203i	$-0.129673\pi$
$683$	10.3315	+	11.9232i	0.395324	+	0.456228i	−0.522839	+	0.852432i	$0.675127\pi$
$684$	−1.34230	−	2.93924i	−0.0513243	−	0.112384i
$685$	5.29505	−	1.55477i	0.202314	−	0.0594046i
$686$	−8.32850	+	18.2369i	−0.317984	+	0.696287i
$687$	−2.34339	+	16.2986i	−0.0894059	+	0.621832i
$688$	6.89614	−	4.43188i	0.262913	−	0.168964i
$689$	21.2116			0.808096
$690$	−3.31553	−	3.46515i	−0.126220	−	0.131916i
$691$	−30.4189			−1.15719			−0.578595	−	0.815615i	$-0.696399\pi$
$691$	−30.4189			−1.15719			−0.578595	+	0.815615i	$0.696399\pi$
$692$	6.25978	−	4.02292i	0.237961	−	0.152928i
$693$	−1.43939	+	10.0112i	−0.0546780	+	0.380294i
$694$	−5.89597	+	12.9104i	−0.223808	+	0.490071i
$695$	3.23707	−	0.950490i	0.122789	−	0.0360541i
$696$	−0.365316	−	0.799930i	−0.0138473	−	0.0303213i
$697$	−14.0565	−	16.2221i	−0.532428	−	0.614455i
$698$	3.26255	+	22.6915i	0.123489	+	0.858886i
$699$	−17.7277	−	5.20532i	−0.670523	−	0.196883i
$700$	1.32702	−	1.53147i	0.0501568	−	0.0578840i
$701$	−26.6760	−	17.1436i	−1.00754	−	0.647505i	−0.0707829	−	0.997492i	$-0.522550\pi$
$701$	−26.6760	−	17.1436i	−1.00754	−	0.647505i	−0.936755	+	0.349987i	$0.886186\pi$
$702$	−4.75518	−	3.05597i	−0.179473	−	0.115340i
$703$	15.4053	−	17.7786i	0.581020	−	0.670533i
$704$	4.78896	+	1.40616i	0.180491	+	0.0529968i
$705$	0.468330	+	3.25731i	0.0176383	+	0.122677i
$706$	−2.36226	−	2.72619i	−0.0889049	−	0.102602i
$707$	−3.96755	−	8.68773i	−0.149215	−	0.326736i
$708$	6.16817	−	1.81114i	0.231814	−	0.0680667i
$709$	−1.11627	+	2.44429i	−0.0419223	+	0.0917971i	−0.929434	−	0.368987i	$-0.879705\pi$
$709$	−1.11627	+	2.44429i	−0.0419223	+	0.0917971i	0.887512	+	0.460784i	$0.152432\pi$
$710$	1.60243	−	11.1451i	0.0601381	−	0.418269i
$711$	1.65222	−	1.06182i	0.0619633	−	0.0398214i
$712$	15.6012			0.584681
$713$	9.98874	+	51.3464i	0.374081	+	1.92294i
$714$	6.58043			0.246266
$715$	23.7338	−	15.2528i	0.887592	−	0.570421i
$716$	2.69053	−	18.7131i	0.100550	−	0.699340i
$717$	−6.92869	+	15.1717i	−0.258757	+	0.566598i
$718$	31.5443	−	9.26223i	1.17722	−	0.345663i
$719$	−0.274768	−	0.601659i	−0.0102471	−	0.0224381i	0.904439	−	0.426602i	$-0.140290\pi$
$719$	−0.274768	−	0.601659i	−0.0102471	−	0.0224381i	−0.914686	+	0.404164i	$0.867562\pi$
$720$	0.654861	+	0.755750i	0.0244052	+	0.0281651i
$721$	3.99286	+	27.7709i	0.148702	+	1.03424i
$722$	−8.21241	−	2.41138i	−0.305634	−	0.0897423i
$723$	−7.15490	+	8.25719i	−0.266093	+	0.307088i
$724$	−14.7313	−	9.46723i	−0.547484	−	0.351847i
$725$	0.739798	+	0.475439i	0.0274754	+	0.0176574i
$726$	9.11004	−	10.5135i	0.338105	−	0.390194i
$727$	−18.1201	−	5.32054i	−0.672037	−	0.197328i	−0.0721270	−	0.997395i	$-0.522979\pi$
$727$	−18.1201	−	5.32054i	−0.672037	−	0.197328i	−0.599910	+	0.800068i	$0.704797\pi$
$728$	−1.63012	−	11.3378i	−0.0604164	−	0.420205i
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$	6.92168	+	15.1564i	0.256183	+	0.560962i
$731$	−25.5415	+	7.49965i	−0.944685	+	0.277384i
$732$	−3.54899	+	7.77121i	−0.131174	+	0.287232i
$733$	−1.09330	+	7.60404i	−0.0403818	+	0.280862i	−1.00000		0.000444380i	$-0.999859\pi$
$733$	−1.09330	+	7.60404i	−0.0403818	+	0.280862i	0.959618	+	0.281306i	$0.0907676\pi$
$734$	−7.72135	+	4.96221i	−0.285000	+	0.183158i
$735$	2.89362			0.106733
$736$	4.66260	+	1.12256i	0.171866	+	0.0413782i
$737$	53.3389			1.96476
$738$	−5.56072	+	3.57366i	−0.204693	+	0.131548i
$739$	−1.80775	+	12.5732i	−0.0664990	+	0.462511i	0.929178	+	0.369632i	$0.120516\pi$
$739$	−1.80775	+	12.5732i	−0.0664990	+	0.462511i	−0.995677	+	0.0928792i	$0.970393\pi$
$740$	−3.02436	+	6.62242i	−0.111178	+	0.243445i
$741$	17.5247	−	5.14572i	0.643786	−	0.189033i
$742$	3.15896	+	6.91716i	0.115969	+	0.253937i
$743$	11.0599	+	12.7638i	0.405747	+	0.468257i	0.921442	−	0.388515i	$-0.127012\pi$
$743$	11.0599	+	12.7638i	0.405747	+	0.468257i	−0.515695	+	0.856772i	$0.672466\pi$
$744$	−1.55225	−	10.7962i	−0.0569084	−	0.395806i
$745$	4.26463	+	1.25221i	0.156244	+	0.0458774i
$746$	8.80559	−	10.1622i	0.322396	−	0.372064i
$747$	4.38629	+	2.81890i	0.160486	+	0.103138i
$748$	−13.6349	−	8.76259i	−0.498540	−	0.320392i
$749$	−23.3952	+	26.9995i	−0.854841	+	0.986539i
$750$	−0.959493	−	0.281733i	−0.0350357	−	0.0102874i
$751$	6.01273	+	41.8195i	0.219408	+	1.52601i	0.740233	+	0.672351i	$0.234715\pi$
$751$	6.01273	+	41.8195i	0.219408	+	1.52601i	−0.520825	+	0.853664i	$0.674376\pi$
$752$	−2.15502	−	2.48702i	−0.0785855	−	0.0906925i
$753$	−5.10962	−	11.1885i	−0.186205	−	0.407732i
$754$	4.76945	−	1.40044i	0.173693	−	0.0510009i
$755$	−5.62736	+	12.3222i	−0.204801	+	0.448451i
$756$	0.288390	−	2.00580i	0.0104886	−	0.0729501i
$757$	−11.0715	+	7.11524i	−0.402401	+	0.258608i	−0.726151	−	0.687535i	$-0.758693\pi$
$757$	−11.0715	+	7.11524i	−0.402401	+	0.258608i	0.323750	+	0.946143i	$0.395056\pi$
$758$	4.90475			0.178149
$759$	14.7639	−	18.8411i	0.535897	−	0.683890i
$760$	−3.23124			−0.117209
$761$	17.9374	−	11.5276i	0.650229	−	0.417877i	−0.173521	−	0.984830i	$-0.555514\pi$
$761$	17.9374	−	11.5276i	0.650229	−	0.417877i	0.823750	+	0.566954i	$0.191878\pi$
$762$	2.12349	−	14.7692i	0.0769259	−	0.535031i
$763$	0.564214	−	1.23546i	0.0204259	−	0.0447265i
$764$	−2.06756	+	0.607090i	−0.0748016	+	0.0219637i
$765$	−1.34898	−	2.95386i	−0.0487726	−	0.106797i
$766$	−14.3995	−	16.6179i	−0.520276	−	0.600430i
$767$	5.17136	+	35.9676i	0.186727	+	1.29872i
$768$	−0.959493	−	0.281733i	−0.0346227	−	0.0101661i
$769$	20.6944	−	23.8827i	0.746261	−	0.861231i	−0.247940	−	0.968775i	$-0.579753\pi$
$769$	20.6944	−	23.8827i	0.746261	−	0.861231i	0.994200	+	0.107545i	$0.0342989\pi$
$770$	8.50856	+	5.46812i	0.306627	+	0.197057i
$771$	−12.8073	−	8.23077i	−0.461245	−	0.296424i
$772$	−15.6922	+	18.1098i	−0.564776	+	0.651786i
$773$	−45.1631	−	13.2611i	−1.62440	−	0.476967i	−0.662205	−	0.749323i	$-0.730379\pi$
$773$	−45.1631	−	13.2611i	−1.62440	−	0.476967i	−0.962197	+	0.272355i	$0.912197\pi$
$774$	1.16662	+	8.11402i	0.0419333	+	0.291652i
$775$	7.14268	+	8.24310i	0.256573	+	0.296101i
$776$	7.47419	+	16.3662i	0.268308	+	0.587512i
$777$	14.1554	−	4.15641i	0.507823	−	0.149110i
$778$	0.0552822	−	0.121051i	0.00198196	−	0.00433990i
$779$	3.03964	−	21.1412i	0.108907	−	0.757462i
$780$	−4.75518	+	3.05597i	−0.170263	+	0.109421i
$781$	56.1989			2.01095
$782$	−13.5006	−	7.76335i	−0.482781	−	0.277617i
$783$	0.879399			0.0314272
$784$	−2.43426	+	1.56441i	−0.0869380	+	0.0558717i
$785$	−0.782060	+	5.43934i	−0.0279129	+	0.194139i
$786$	−2.23727	+	4.89895i	−0.0798009	+	0.174740i
$787$	−6.84920	+	2.01111i	−0.244147	+	0.0716882i	−0.401517	−	0.915852i	$-0.631517\pi$
$787$	−6.84920	+	2.01111i	−0.244147	+	0.0716882i	0.157369	+	0.987540i	$0.449699\pi$
$788$	−8.59400	−	18.8182i	−0.306148	−	0.670372i
$789$	0.498902	+	0.575763i	0.0177614	+	0.0204977i
$790$	−0.279507	−	1.94401i	−0.00994441	−	0.0691649i
$791$	−3.83752	−	1.12680i	−0.136446	−	0.0400643i
$792$	−3.26850	+	3.77205i	−0.116141	+	0.134034i
$793$	−40.6247	−	26.1079i	−1.44263	−	0.927119i
$794$	−22.7204	−	14.6015i	−0.806318	−	0.518189i
$795$	2.45743	−	2.83603i	0.0871561	−	0.100583i
$796$	−11.2154	−	3.29314i	−0.397520	−	0.116722i
$797$	−5.95912	−	41.4466i	−0.211083	−	1.46811i	−0.769550	−	0.638586i	$-0.779520\pi$
$797$	−5.95912	−	41.4466i	−0.211083	−	1.46811i	0.558467	−	0.829526i	$-0.311390\pi$
$798$	4.28793	+	4.94853i	0.151791	+	0.175176i
$799$	4.43924	+	9.72059i	0.157049	+	0.343890i
$800$	0.959493	−	0.281733i	0.0339232	−	0.00996075i
$801$	−6.48099	+	14.1914i	−0.228994	+	0.501428i
$802$	0.794074	−	5.52291i	0.0280397	−	0.195021i
$803$	−69.9609	+	44.9611i	−2.46887	+	1.58664i
$804$	−10.6867			−0.376892
$805$	8.42479	+	4.84456i	0.296935	+	0.170748i
$806$	61.6528			2.17163
$807$	−3.77854	+	2.42832i	−0.133011	+	0.0854810i
$808$	0.670750	−	4.66517i	0.0235969	−	0.164120i
$809$	−7.53841	+	16.5068i	−0.265036	+	0.580349i	−0.994626	−	0.103537i	$-0.966984\pi$
$809$	−7.53841	+	16.5068i	−0.265036	+	0.580349i	0.729589	+	0.683886i	$0.239711\pi$
$810$	−0.959493	+	0.281733i	−0.0337131	+	0.00989907i
$811$	−13.7576	−	30.1250i	−0.483095	−	1.05783i	−0.981601	−	0.190945i	$-0.938845\pi$
$811$	−13.7576	−	30.1250i	−0.483095	−	1.05783i	0.498506	−	0.866886i	$-0.333882\pi$
$812$	1.16698	+	1.34677i	0.0409531	+	0.0472624i
$813$	−1.11573	−	7.76009i	−0.0391305	−	0.272158i
$814$	−34.8652	−	10.2373i	−1.22202	−	0.358819i
$815$	13.4988	−	15.5784i	0.472841	−	0.545688i
$816$	2.73182	+	1.75563i	0.0956327	+	0.0614594i
$817$	−22.2831	−	14.3204i	−0.779585	−	0.501009i
$818$	23.7901	−	27.4552i	0.831801	−	0.959950i
$819$	10.9904	+	3.22706i	0.384034	+	0.112763i
$820$	0.940706	+	6.54276i	0.0328509	+	0.228483i
$821$	1.82271	+	2.10351i	0.0636128	+	0.0734131i	0.786664	−	0.617381i	$-0.211806\pi$
$821$	1.82271	+	2.10351i	0.0636128	+	0.0734131i	−0.723051	+	0.690794i	$0.757261\pi$
$822$	−2.29251	−	5.01989i	−0.0799604	−	0.175089i
$823$	−12.7020	+	3.72965i	−0.442765	+	0.130008i	−0.495513	−	0.868600i	$-0.665020\pi$
$823$	−12.7020	+	3.72965i	−0.442765	+	0.130008i	0.0527483	+	0.998608i	$0.483202\pi$
$824$	−5.75157	+	12.5942i	−0.200365	+	0.438739i
$825$	0.710312	−	4.94033i	0.0247299	−	0.172000i
$826$	−10.9590	+	7.04292i	−0.381313	+	0.245055i
$827$	−37.1978			−1.29349			−0.646747	−	0.762705i	$-0.723871\pi$
$827$	−37.1978			−1.29349			−0.646747	+	0.762705i	$0.723871\pi$
$828$	−2.95803	+	3.77492i	−0.102799	+	0.131188i
$829$	−18.6095			−0.646334			−0.323167	−	0.946342i	$-0.604748\pi$
$829$	−18.6095			−0.646334			−0.323167	+	0.946342i	$0.604748\pi$
$830$	4.38629	−	2.81890i	0.152250	−	0.0978454i
$831$	1.21826	−	8.47316i	0.0422609	−	0.293931i
$832$	2.34813	−	5.14169i	0.0814068	−	0.178256i
$833$	9.01586	−	2.64730i	0.312381	−	0.0917234i
$834$	−1.40150	−	3.06885i	−0.0485299	−	0.106266i
$835$	−6.57552	−	7.58856i	−0.227555	−	0.262613i
$836$	−2.29519	−	15.9634i	−0.0793807	−	0.552105i
$837$	10.4654	+	3.07291i	0.361736	+	0.106215i
$838$	19.1511	−	22.1015i	0.661563	−	0.763485i
$839$	18.3103	+	11.7673i	0.632142	+	0.406253i	0.817102	−	0.576493i	$-0.195579\pi$
$839$	18.3103	+	11.7673i	0.632142	+	0.406253i	−0.184960	+	0.982746i	$0.559216\pi$
$840$	−1.70473	−	1.09557i	−0.0588189	−	0.0378006i
$841$	18.4845	−	21.3323i	0.637398	−	0.735596i
$842$	10.9497	+	3.21511i	0.377350	+	0.110800i
$843$	1.29985	+	9.04066i	0.0447692	+	0.311377i
$844$	−3.89961	−	4.50039i	−0.134230	−	0.154910i
$845$	−7.87242	−	17.2382i	−0.270819	−	0.593012i
$846$	3.15750	−	0.927127i	0.108557	−	0.0318753i
$847$	−11.7107	+	25.6429i	−0.402385	+	0.881100i
$848$	−0.534051	+	3.71440i	−0.0183394	+	0.127553i
$849$	−25.8115	+	16.5880i	−0.885848	+	0.569300i
$850$	−3.24732			−0.111382
$851$	−33.9453	−	8.17263i	−1.16363	−	0.280154i
$852$	−11.2597			−0.385752
$853$	24.1279	−	15.5060i	0.826122	−	0.530917i	−0.0579213	−	0.998321i	$-0.518447\pi$
$853$	24.1279	−	15.5060i	0.826122	−	0.530917i	0.884044	+	0.467405i	$0.154811\pi$
$854$	2.46378	−	17.1360i	0.0843090	−	0.586382i
$855$	1.34230	−	2.93924i	0.0459058	−	0.100520i
$856$	−16.9157	+	4.96689i	−0.578166	+	0.169765i
$857$	−19.2159	−	42.0768i	−0.656401	−	1.43732i	−0.885838	−	0.463994i	$-0.846416\pi$
$857$	−19.2159	−	42.0768i	−0.656401	−	1.43732i	0.229437	−	0.973323i	$-0.426311\pi$
$858$	−18.4752	−	21.3215i	−0.630732	−	0.727904i
$859$	6.74193	+	46.8912i	0.230032	+	1.59991i	0.697958	+	0.716139i	$0.254092\pi$
$859$	6.74193	+	46.8912i	0.230032	+	1.59991i	−0.467926	+	0.883768i	$0.654999\pi$
$860$	7.86540	+	2.30949i	0.268208	+	0.0787530i
$861$	8.77168	−	10.1231i	0.298938	−	0.344993i
$862$	15.5907	+	10.0195i	0.531021	+	0.341267i
$863$	8.23823	+	5.29439i	0.280433	+	0.180223i	0.673295	−	0.739374i	$-0.264879\pi$
$863$	8.23823	+	5.29439i	0.280433	+	0.180223i	−0.392862	+	0.919597i	$0.628515\pi$
$864$	0.654861	−	0.755750i	0.0222788	−	0.0257111i
$865$	7.13960	+	2.09638i	0.242754	+	0.0712789i
$866$	0.988516	+	6.87528i	0.0335911	+	0.233631i
$867$	4.22708	+	4.87832i	0.143559	+	0.165676i
$868$	9.18173	+	20.1052i	0.311648	+	0.682414i
$869$	9.40553	−	2.76171i	0.319061	−	0.0936847i
$870$	0.365316	−	0.799930i	0.0123854	−	0.0271202i
$871$	8.59677	−	59.7919i	0.291291	−	2.02597i
$872$	0.563843	−	0.362360i	0.0190941	−	0.0122711i
$873$	−17.9921			−0.608940
$874$	−2.95915	−	15.2113i	−0.100095	−	0.514530i
$875$	2.02642			0.0685056
$876$	14.0170	−	9.00820i	0.473592	−	0.304359i
$877$	−4.12687	+	28.7030i	−0.139354	+	0.969231i	0.793395	+	0.608707i	$0.208311\pi$
$877$	−4.12687	+	28.7030i	−0.139354	+	0.969231i	−0.932750	+	0.360524i	$0.882598\pi$
$878$	−8.74838	+	19.1563i	−0.295244	+	0.646493i
$879$	−16.5059	+	4.84657i	−0.556730	+	0.163471i
$880$	2.07339	+	4.54009i	0.0698940	+	0.153047i
$881$	−22.3415	−	25.7835i	−0.752705	−	0.868668i	0.242122	−	0.970246i	$-0.422157\pi$
$881$	−22.3415	−	25.7835i	−0.752705	−	0.868668i	−0.994828	+	0.101577i	$0.967611\pi$
$882$	−0.411804	−	2.86416i	−0.0138662	−	0.0964414i
$883$	39.7770	+	11.6796i	1.33860	+	0.393049i	0.871171	−	0.490979i	$-0.163361\pi$
$883$	39.7770	+	11.6796i	1.33860	+	0.393049i	0.467432	+	0.884029i	$0.345179\pi$
$884$	−12.0203	+	13.8721i	−0.404285	+	0.466570i
$885$	5.40806	+	3.47555i	0.181790	+	0.116829i
$886$	−32.8039	−	21.0818i	−1.10207	−	0.708257i
$887$	−14.4668	+	16.6956i	−0.485749	+	0.560584i	−0.944725	−	0.327865i	$-0.893671\pi$
$887$	−14.4668	+	16.6956i	−0.485749	+	0.560584i	0.458976	+	0.888449i	$0.348216\pi$
$888$	6.98543	+	2.05111i	0.234416	+	0.0688306i
$889$	4.30308	+	29.9286i	0.144321	+	1.00377i
$890$	10.2166	+	11.7906i	0.342462	+	0.395223i
$891$	−2.07339	−	4.54009i	−0.0694612	−	0.152099i
$892$	12.9145	−	3.79203i	0.432409	−	0.126967i
$893$	−4.41726	+	9.67245i	−0.147818	+	0.323676i
$894$	0.632543	−	4.39943i	0.0211554	−	0.147139i
$895$	15.9043	−	10.2211i	0.531623	−	0.341653i
$896$	2.02642			0.0676980
$897$	−18.7410	−	19.5868i	−0.625744	−	0.653983i
$898$	21.1549			0.705947
$899$	−8.06911	+	5.18570i	−0.269120	+	0.172953i
$900$	−0.142315	+	0.989821i	−0.00474383	+	0.0329940i
$901$	5.06220	−	11.0847i	0.168646	−	0.369284i
$902$	−31.6552	+	9.29480i	−1.05400	+	0.309483i
$903$	−6.90067	−	15.1104i	−0.229640	−	0.502841i
$904$	−1.29249	−	1.49162i	−0.0429876	−	0.0496104i
$905$	−2.49209	−	17.3329i	−0.0828400	−	0.576165i
$906$	12.9976	+	3.81645i	0.431818	+	0.126793i
$907$	−19.8380	+	22.8943i	−0.658712	+	0.760194i	−0.982566	−	0.185913i	$-0.940476\pi$
$907$	−19.8380	+	22.8943i	−0.658712	+	0.760194i	0.323855	+	0.946107i	$0.395021\pi$
$908$	3.97800	+	2.55651i	0.132015	+	0.0848407i
$909$	3.96495	+	2.54812i	0.131509	+	0.0845157i
$910$	7.50100	−	8.65661i	0.248656	−	0.286964i
$911$	−56.3685	−	16.5513i	−1.86757	−	0.548368i	−0.998564	−	0.0535689i	$-0.982940\pi$
$911$	−56.3685	−	16.5513i	−1.86757	−	0.548368i	−0.869007	−	0.494799i	$-0.835242\pi$
$912$	0.459853	+	3.19835i	0.0152272	+	0.105908i
$913$	17.0419	+	19.6674i	0.564005	+	0.650897i
$914$	−11.3138	−	24.7738i	−0.374228	−	0.819445i
$915$	−8.19718	+	2.40691i	−0.270990	+	0.0795700i
$916$	6.84033	−	14.9782i	0.226011	−	0.494894i
$917$	1.55316	−	10.8025i	0.0512899	−	0.356729i
$918$	−2.73182	+	1.75563i	−0.0901634	+	0.0579445i
$919$	26.3477			0.869132			0.434566	−	0.900640i	$-0.356902\pi$
$919$	26.3477			0.869132			0.434566	+	0.900640i	$0.356902\pi$
$920$	2.20498	+	4.25888i	0.0726960	+	0.140411i
$921$	12.0392			0.396704
$922$	1.89971	−	1.22087i	0.0625638	−	0.0402073i
$923$	9.05772	−	62.9978i	0.298139	−	2.07360i
$924$	4.20157	−	9.20015i	0.138221	−	0.302663i
$925$	−6.98543	+	2.05111i	−0.229679	+	0.0674400i
$926$	11.6393	+	25.4866i	0.382492	+	0.837541i
$927$	−9.06678	−	10.4636i	−0.297792	−	0.343670i
$928$	0.125152	+	0.870448i	0.00410830	+	0.0285739i
$929$	14.6318	+	4.29628i	0.480053	+	0.140956i	0.512801	−	0.858507i	$-0.328608\pi$
$929$	14.6318	+	4.29628i	0.480053	+	0.140956i	−0.0327480	+	0.999464i	$0.510426\pi$
$930$	7.14268	−	8.24310i	0.234218	−	0.270302i
$931$	7.86568	+	5.05497i	0.257787	+	0.165670i
$932$	15.5431	+	9.98893i	0.509131	+	0.327198i
$933$	−7.93939	+	9.16255i	−0.259924	+	0.299968i
$934$	37.5286	+	11.0194i	1.22797	+	0.360565i
$935$	−2.30661	−	16.0428i	−0.0754342	−	0.524656i
$936$	3.70160	+	4.27187i	0.120991	+	0.139631i
$937$	3.02019	+	6.61328i	0.0986652	+	0.216047i	0.952528	−	0.304452i	$-0.0984734\pi$
$937$	3.02019	+	6.61328i	0.0986652	+	0.216047i	−0.853862	+	0.520499i	$0.825746\pi$
$938$	20.7786	−	6.10115i	0.678446	−	0.199210i
$939$	11.4423	−	25.0550i	0.373404	−	0.817641i
$940$	0.468330	−	3.25731i	0.0152753	−	0.106242i
$941$	20.0005	−	12.8535i	0.651997	−	0.419013i	−0.172398	−	0.985027i	$-0.555152\pi$
$941$	20.0005	−	12.8535i	0.651997	−	0.419013i	0.824395	+	0.566014i	$0.191515\pi$
$942$	5.49528			0.179046
$943$	−29.9391	+	10.4203i	−0.974950	+	0.339331i
$944$	−6.42857			−0.209232
$945$	1.70473	−	1.09557i	0.0554550	−	0.0356388i
$946$	−5.82276	+	40.4982i	−0.189314	+	1.31671i
$947$	−1.82418	+	3.99439i	−0.0592778	+	0.129800i	−0.936953	−	0.349456i	$-0.886366\pi$
$947$	−1.82418	+	3.99439i	−0.0592778	+	0.129800i	0.877675	+	0.479256i	$0.159094\pi$
$948$	−1.88445	+	0.553324i	−0.0612040	+	0.0179711i
$949$	39.1248	+	85.6713i	1.27004	+	2.78101i
$950$	−2.11601	−	2.44200i	−0.0686524	−	0.0792291i
$951$	0.411964	+	2.86527i	0.0133588	+	0.0929128i
$952$	−6.31388	−	1.85392i	−0.204634	−	0.0600860i
$953$	26.3668	−	30.4289i	0.854105	−	0.985690i	−0.145888	−	0.989301i	$-0.546604\pi$
$953$	26.3668	−	30.4289i	0.854105	−	0.985690i	0.999993	+	0.00361092i	$0.00114939\pi$
$954$	−3.15689	−	2.02881i	−0.102208	−	0.0656851i
$955$	−1.81277	−	1.16500i	−0.0586599	−	0.0376984i
$956$	10.9224	−	12.6051i	0.353255	−	0.407679i
$957$	4.21141	+	1.23658i	0.136135	+	0.0399730i
$958$	0.264455	+	1.83933i	0.00854416	+	0.0594260i
$959$	7.32331	+	8.45155i	0.236482	+	0.272915i
$960$	−0.415415	−	0.909632i	−0.0134075	−	0.0293582i
$961$	−84.4033	+	24.7830i	−2.72269	+	0.799453i
$962$	−17.0952	+	37.4332i	−0.551171	+	1.20690i
$963$	2.50898	−	17.4504i	0.0808508	−	0.562330i
$964$	9.19139	−	5.90695i	0.296035	−	0.190250i
$965$	−23.9627			−0.771387
$966$	3.59628	−	9.02849i	0.115708	−	0.290487i
$967$	−13.4231			−0.431657			−0.215829	−	0.976431i	$-0.569245\pi$
$967$	−13.4231			−0.431657			−0.215829	+	0.976431i	$0.569245\pi$
$968$	−11.7030	+	7.52108i	−0.376149	+	0.241737i
$969$	1.49329	−	10.3860i	0.0479713	−	0.333648i
$970$	−7.47419	+	16.3662i	−0.239982	+	0.525487i
$971$	−57.0616	+	16.7548i	−1.83120	+	0.537687i	−0.999837	−	0.0180496i	$-0.994254\pi$
$971$	−57.0616	+	16.7548i	−1.83120	+	0.537687i	−0.831358	+	0.555737i	$0.812436\pi$
$972$	0.415415	+	0.909632i	0.0133244	+	0.0291765i
$973$	4.47702	+	5.16676i	0.143527	+	0.165639i
$974$	2.64873	+	18.4223i	0.0848707	+	0.590289i
$975$	−5.42353	−	1.59249i	−0.173692	−	0.0510006i
$976$	5.59463	−	6.45655i	0.179080	−	0.206669i
$977$	10.5050	+	6.75117i	0.336085	+	0.215989i	0.697788	−	0.716305i	$-0.254168\pi$
$977$	10.5050	+	6.75117i	0.336085	+	0.215989i	−0.361702	+	0.932294i	$0.617804\pi$
$978$	−17.3409	−	11.1443i	−0.554502	−	0.356357i
$979$	−50.9926	+	58.8486i	−1.62973	+	1.88081i
$980$	−2.77640	−	0.815226i	−0.0886890	−	0.0260414i
$981$	0.0953853	+	0.663420i	0.00304542	+	0.0211814i
$982$	5.19860	+	5.99950i	0.165894	+	0.191452i
$983$	20.0883	+	43.9873i	0.640719	+	1.40298i	0.899448	+	0.437028i	$0.143969\pi$
$983$	20.0883	+	43.9873i	0.640719	+	1.40298i	−0.258729	+	0.965950i	$0.583304\pi$
$984$	6.34228	−	1.86226i	0.202185	−	0.0593668i
$985$	8.59400	−	18.8182i	0.273827	−	0.599599i
$986$	0.406407	−	2.82662i	0.0129426	−	0.0900179i
$987$	−5.60995	+	3.60529i	−0.178567	+	0.114758i
$988$	−18.2646			−0.581073
$989$	−3.66902	+	39.1420i	−0.116668	+	1.24464i
$990$	−4.99113			−0.158629
$991$	2.71940	−	1.74765i	0.0863846	−	0.0555160i	−0.496735	−	0.867902i	$-0.665468\pi$
$991$	2.71940	−	1.74765i	0.0863846	−	0.0555160i	0.583120	+	0.812386i	$0.301832\pi$
$992$	−1.55225	+	10.7962i	−0.0492841	+	0.342778i
$993$	0.325252	−	0.712203i	0.0103216	−	0.0226011i
$994$	21.8927	−	6.42829i	0.694395	−	0.203893i
$995$	−4.85574	−	10.6326i	−0.153937	−	0.337076i
$996$	−3.41444	−	3.94047i	−0.108191	−	0.124859i
$997$	4.13133	+	28.7341i	0.130841	+	0.910017i	0.944462	+	0.328621i	$0.106584\pi$
$997$	4.13133	+	28.7341i	0.130841	+	0.910017i	−0.813621	+	0.581396i	$0.802507\pi$
$998$	−15.7930	−	4.63724i	−0.499919	−	0.146789i
$999$	−4.76760	+	5.50211i	−0.150840	+	0.174079i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.h.541.2	yes	30
23.2	even	11	inner	690.2.m.h.301.2	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.h.301.2	✓	30	23.2	even	11	inner
690.2.m.h.541.2	yes	30	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)

\(f(q)\)	\(=\)	\(q+(-0.841254 + 0.540641i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(0.959493 - 0.281733i) q^{5} +(-0.415415 - 0.909632i) q^{6} +(1.32702 + 1.53147i) q^{7} +(0.142315 + 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(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} +(1.32702 + 1.53147i) q^{7} +(0.142315 + 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(-0.654861 + 0.755750i) q^{10} +(-4.19881 - 2.69841i) q^{11} +(0.841254 + 0.540641i) q^{12} +(-3.70160 + 4.27187i) q^{13} +(-1.94434 - 0.570909i) q^{14} +(0.142315 + 0.989821i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(1.34898 + 2.95386i) q^{17} +(0.959493 - 0.281733i) q^{18} +(-1.34230 + 2.93924i) q^{19} +(0.142315 - 0.989821i) q^{20} +(-1.70473 + 1.09557i) q^{21} +4.99113 q^{22} +(4.79000 - 0.236515i) q^{23} -1.00000 q^{24} +(0.841254 - 0.540641i) q^{25} +(0.804434 - 5.59496i) q^{26} +(0.415415 - 0.909632i) q^{27} +(1.94434 - 0.570909i) q^{28} +(0.365316 + 0.799930i) q^{29} +(-0.654861 - 0.755750i) q^{30} +(1.55225 + 10.7962i) q^{31} +(0.959493 + 0.281733i) q^{32} +(3.26850 - 3.77205i) q^{33} +(-2.73182 - 1.75563i) q^{34} +(1.70473 + 1.09557i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(-6.98543 - 2.05111i) q^{37} +(-0.459853 - 3.19835i) q^{38} +(-3.70160 - 4.27187i) q^{39} +(0.415415 + 0.909632i) q^{40} +(-6.34228 + 1.86226i) q^{41} +(0.841806 - 1.84330i) q^{42} +(-1.16662 + 8.11402i) q^{43} +(-4.19881 + 2.69841i) q^{44} -1.00000 q^{45} +(-3.90173 + 2.78864i) q^{46} +3.29081 q^{47} +(0.841254 - 0.540641i) q^{48} +(0.411804 - 2.86416i) q^{49} +(-0.415415 + 0.909632i) q^{50} +(-3.11578 + 0.914875i) q^{51} +(2.34813 + 5.14169i) q^{52} +(-2.45743 - 2.83603i) q^{53} +(0.142315 + 0.989821i) q^{54} +(-4.78896 - 1.40616i) q^{55} +(-1.32702 + 1.53147i) q^{56} +(-2.71829 - 1.74694i) q^{57} +(-0.739798 - 0.475439i) q^{58} +(4.20982 - 4.85839i) q^{59} +(0.959493 + 0.281733i) q^{60} +(1.21583 + 8.45629i) q^{61} +(-7.14268 - 8.24310i) q^{62} +(-0.841806 - 1.84330i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(-2.34813 + 5.14169i) q^{65} +(-0.710312 + 4.94033i) q^{66} +(-8.99025 + 5.77768i) q^{67} +3.24732 q^{68} +(-0.447580 + 4.77490i) q^{69} -2.02642 q^{70} +(-9.47230 + 6.08748i) q^{71} +(0.142315 - 0.989821i) q^{72} +(6.92168 - 15.1564i) q^{73} +(6.98543 - 2.05111i) q^{74} +(0.415415 + 0.909632i) q^{75} +(2.11601 + 2.44200i) q^{76} +(-1.43939 - 10.0112i) q^{77} +(5.42353 + 1.59249i) q^{78} +(-1.28615 + 1.48429i) q^{79} +(-0.841254 - 0.540641i) q^{80} +(0.841254 + 0.540641i) q^{81} +(4.32865 - 4.99553i) q^{82} +(-5.00279 - 1.46895i) q^{83} +(0.288390 + 2.00580i) q^{84} +(2.12654 + 2.45416i) q^{85} +(-3.40535 - 7.45667i) q^{86} +(-0.843777 + 0.247755i) q^{87} +(2.07339 - 4.54009i) q^{88} +(2.22029 - 15.4424i) q^{89} +(0.841254 - 0.540641i) q^{90} -11.4543 q^{91} +(1.77469 - 4.45539i) q^{92} -10.9072 q^{93} +(-2.76840 + 1.77914i) q^{94} +(-0.459853 + 3.19835i) q^{95} +(-0.415415 + 0.909632i) q^{96} +(17.2633 - 5.06896i) q^{97} +(1.20205 + 2.63213i) q^{98} +(3.26850 + 3.77205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9} - 3 q^{10} - 18 q^{11} - 3 q^{12} + 13 q^{13} - 8 q^{14} + 3 q^{15} - 3 q^{16} - 6 q^{17} + 3 q^{18} + 4 q^{19} + 3 q^{20} - 3 q^{21} - 4 q^{22} - 23 q^{23} - 30 q^{24} - 3 q^{25} + 9 q^{26} - 3 q^{27} + 8 q^{28} + 18 q^{29} - 3 q^{30} - 8 q^{31} + 3 q^{32} + 4 q^{33} - 5 q^{34} + 3 q^{35} - 3 q^{36} - 32 q^{37} - 15 q^{38} + 13 q^{39} - 3 q^{40} + 35 q^{41} + 3 q^{42} + 48 q^{43} - 18 q^{44} - 30 q^{45} + q^{46} + 8 q^{47} - 3 q^{48} - 11 q^{49} + 3 q^{50} + 27 q^{51} + 2 q^{52} + 26 q^{53} + 3 q^{54} - 4 q^{55} - 8 q^{56} - 29 q^{57} - 7 q^{58} + 55 q^{59} + 3 q^{60} + 21 q^{61} + 8 q^{62} - 3 q^{63} - 3 q^{64} - 2 q^{65} + 7 q^{66} + 4 q^{67} - 28 q^{68} - 45 q^{69} - 14 q^{70} - 41 q^{71} + 3 q^{72} - 39 q^{73} + 32 q^{74} - 3 q^{75} + 4 q^{76} - 33 q^{77} - 2 q^{78} + 18 q^{79} + 3 q^{80} - 3 q^{81} + 31 q^{82} - 85 q^{83} - 3 q^{84} - 5 q^{85} + 40 q^{86} + 18 q^{87} - 15 q^{88} + 43 q^{89} - 3 q^{90} + 38 q^{91} + 10 q^{92} + 36 q^{93} - 19 q^{94} - 15 q^{95} + 3 q^{96} + 43 q^{97} + 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9 - 3 * q^10 - 18 * q^11 - 3 * q^12 + 13 * q^13 - 8 * q^14 + 3 * q^15 - 3 * q^16 - 6 * q^17 + 3 * q^18 + 4 * q^19 + 3 * q^20 - 3 * q^21 - 4 * q^22 - 23 * q^23 - 30 * q^24 - 3 * q^25 + 9 * q^26 - 3 * q^27 + 8 * q^28 + 18 * q^29 - 3 * q^30 - 8 * q^31 + 3 * q^32 + 4 * q^33 - 5 * q^34 + 3 * q^35 - 3 * q^36 - 32 * q^37 - 15 * q^38 + 13 * q^39 - 3 * q^40 + 35 * q^41 + 3 * q^42 + 48 * q^43 - 18 * q^44 - 30 * q^45 + q^46 + 8 * q^47 - 3 * q^48 - 11 * q^49 + 3 * q^50 + 27 * q^51 + 2 * q^52 + 26 * q^53 + 3 * q^54 - 4 * q^55 - 8 * q^56 - 29 * q^57 - 7 * q^58 + 55 * q^59 + 3 * q^60 + 21 * q^61 + 8 * q^62 - 3 * q^63 - 3 * q^64 - 2 * q^65 + 7 * q^66 + 4 * q^67 - 28 * q^68 - 45 * q^69 - 14 * q^70 - 41 * q^71 + 3 * q^72 - 39 * q^73 + 32 * q^74 - 3 * q^75 + 4 * q^76 - 33 * q^77 - 2 * q^78 + 18 * q^79 + 3 * q^80 - 3 * q^81 + 31 * q^82 - 85 * q^83 - 3 * q^84 - 5 * q^85 + 40 * q^86 + 18 * q^87 - 15 * q^88 + 43 * q^89 - 3 * q^90 + 38 * q^91 + 10 * q^92 + 36 * q^93 - 19 * q^94 - 15 * q^95 + 3 * q^96 + 43 * q^97 + 4 * q^99

Introduction

L-functions

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