LMFDB - Embedded newform 690.2.m.g.541.3

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			541.3
Character	$\chi$	$=$	690.541
Dual form			690.2.m.g.301.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.841254 - 0.540641i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(0.415415 + 0.909632i) q^{6} +(1.76004 + 2.03119i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(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} +(1.76004 + 2.03119i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(-0.654861 + 0.755750i) q^{10} +(1.98022 + 1.27261i) q^{11} +(0.841254 + 0.540641i) q^{12} +(-1.36158 + 1.57134i) q^{13} +(2.57879 + 0.757200i) q^{14} +(-0.142315 - 0.989821i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(1.96729 + 4.30776i) q^{17} +(-0.959493 + 0.281733i) q^{18} +(1.47474 - 3.22923i) q^{19} +(-0.142315 + 0.989821i) q^{20} +(-2.26100 + 1.45306i) q^{21} +2.35390 q^{22} +(-0.956931 + 4.69939i) q^{23} +1.00000 q^{24} +(0.841254 - 0.540641i) q^{25} +(-0.295899 + 2.05802i) q^{26} +(0.415415 - 0.909632i) q^{27} +(2.57879 - 0.757200i) q^{28} +(2.69293 + 5.89669i) q^{29} +(-0.654861 - 0.755750i) q^{30} +(-0.280522 - 1.95108i) q^{31} +(-0.959493 - 0.281733i) q^{32} +(-1.54147 + 1.77896i) q^{33} +(3.98394 + 2.56032i) q^{34} +(-2.26100 - 1.45306i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(7.79797 + 2.28969i) q^{37} +(-0.505223 - 3.51390i) q^{38} +(-1.36158 - 1.57134i) q^{39} +(0.415415 + 0.909632i) q^{40} +(-0.914376 + 0.268485i) q^{41} +(-1.11649 + 2.44478i) q^{42} +(0.512153 - 3.56210i) q^{43} +(1.98022 - 1.27261i) q^{44} +1.00000 q^{45} +(1.73566 + 4.47074i) q^{46} -1.28736 q^{47} +(0.841254 - 0.540641i) q^{48} +(-0.0318055 + 0.221212i) q^{49} +(0.415415 - 0.909632i) q^{50} +(-4.54389 + 1.33421i) q^{51} +(0.863725 + 1.89129i) q^{52} +(-2.57228 - 2.96856i) q^{53} +(-0.142315 - 0.989821i) q^{54} +(-2.25855 - 0.663169i) q^{55} +(1.76004 - 2.03119i) q^{56} +(2.98648 + 1.91930i) q^{57} +(5.45343 + 3.50470i) q^{58} +(-0.927486 + 1.07038i) q^{59} +(-0.959493 - 0.281733i) q^{60} +(-0.359602 - 2.50109i) q^{61} +(-1.29082 - 1.48969i) q^{62} +(-1.11649 - 2.44478i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(0.863725 - 1.89129i) q^{65} +(-0.334994 + 2.32994i) q^{66} +(-4.29809 + 2.76221i) q^{67} +4.73572 q^{68} +(-4.51537 - 1.61598i) q^{69} -2.68765 q^{70} +(0.461255 - 0.296431i) q^{71} +(-0.142315 + 0.989821i) q^{72} +(3.91085 - 8.56356i) q^{73} +(7.79797 - 2.28969i) q^{74} +(0.415415 + 0.909632i) q^{75} +(-2.32478 - 2.68294i) q^{76} +(0.900349 + 6.26206i) q^{77} +(-1.99496 - 0.585774i) q^{78} +(0.555315 - 0.640868i) q^{79} +(0.841254 + 0.540641i) q^{80} +(0.841254 + 0.540641i) q^{81} +(-0.624068 + 0.720213i) q^{82} +(-6.18083 - 1.81486i) q^{83} +(0.382493 + 2.66030i) q^{84} +(-3.10124 - 3.57902i) q^{85} +(-1.49497 - 3.27352i) q^{86} +(-6.21991 + 1.82633i) q^{87} +(0.977844 - 2.14118i) q^{88} +(1.65288 - 11.4960i) q^{89} +(0.841254 - 0.540641i) q^{90} -5.58813 q^{91} +(3.87719 + 2.82265i) q^{92} +1.97114 q^{93} +(-1.08299 + 0.695998i) q^{94} +(-0.505223 + 3.51390i) q^{95} +(0.415415 - 0.909632i) q^{96} +(2.77124 - 0.813708i) q^{97} +(0.0928397 + 0.203291i) q^{98} +(-1.54147 - 1.77896i) 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	\( 30 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} - 3 q^{9} - 3 q^{10} + 8 q^{11} - 3 q^{12} - 5 q^{13} - 8 q^{14} - 3 q^{15} - 3 q^{16} + 4 q^{17} - 3 q^{18} + 6 q^{19} - 3 q^{20} + 3 q^{21} + 8 q^{22} + q^{23} + 30 q^{24} - 3 q^{25} - 5 q^{26} - 3 q^{27} - 8 q^{28} - 10 q^{29} - 3 q^{30} - 10 q^{31} - 3 q^{32} - 14 q^{33} - 7 q^{34} + 3 q^{35} - 3 q^{36} - 12 q^{37} - 5 q^{38} - 5 q^{39} - 3 q^{40} + 5 q^{41} + 3 q^{42} + 2 q^{43} + 8 q^{44} + 30 q^{45} - 21 q^{46} + 96 q^{47} - 3 q^{48} - 43 q^{49} - 3 q^{50} + 15 q^{51} - 16 q^{52} + 12 q^{53} - 3 q^{54} + 8 q^{55} - 8 q^{56} + 17 q^{57} + q^{58} - 9 q^{59} - 3 q^{60} + q^{61} - 32 q^{62} + 3 q^{63} - 3 q^{64} - 16 q^{65} - 3 q^{66} - 28 q^{67} + 4 q^{68} + 23 q^{69} + 14 q^{70} + 3 q^{71} - 3 q^{72} - 27 q^{73} - 12 q^{74} - 3 q^{75} - 16 q^{76} + 47 q^{77} + 6 q^{78} + 2 q^{79} - 3 q^{80} - 3 q^{81} + 27 q^{82} + 11 q^{83} + 3 q^{84} - 7 q^{85} + 2 q^{86} - 32 q^{87} - 3 q^{88} + 25 q^{89} - 3 q^{90} - 90 q^{91} - 10 q^{92} + 56 q^{93} - 25 q^{94} - 5 q^{95} - 3 q^{96} - 7 q^{97} - 32 q^{98} - 14 q^{99}+O(q^{100}) \) 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 + 8 * q^11 - 3 * q^12 - 5 * q^13 - 8 * q^14 - 3 * q^15 - 3 * q^16 + 4 * q^17 - 3 * q^18 + 6 * q^19 - 3 * q^20 + 3 * q^21 + 8 * q^22 + q^23 + 30 * q^24 - 3 * q^25 - 5 * q^26 - 3 * q^27 - 8 * q^28 - 10 * q^29 - 3 * q^30 - 10 * q^31 - 3 * q^32 - 14 * q^33 - 7 * q^34 + 3 * q^35 - 3 * q^36 - 12 * q^37 - 5 * q^38 - 5 * q^39 - 3 * q^40 + 5 * q^41 + 3 * q^42 + 2 * q^43 + 8 * q^44 + 30 * q^45 - 21 * q^46 + 96 * q^47 - 3 * q^48 - 43 * q^49 - 3 * q^50 + 15 * q^51 - 16 * q^52 + 12 * q^53 - 3 * q^54 + 8 * q^55 - 8 * q^56 + 17 * q^57 + q^58 - 9 * q^59 - 3 * q^60 + q^61 - 32 * q^62 + 3 * q^63 - 3 * q^64 - 16 * q^65 - 3 * q^66 - 28 * q^67 + 4 * q^68 + 23 * q^69 + 14 * q^70 + 3 * q^71 - 3 * q^72 - 27 * q^73 - 12 * q^74 - 3 * q^75 - 16 * q^76 + 47 * q^77 + 6 * q^78 + 2 * q^79 - 3 * q^80 - 3 * q^81 + 27 * q^82 + 11 * q^83 + 3 * q^84 - 7 * q^85 + 2 * q^86 - 32 * q^87 - 3 * q^88 + 25 * q^89 - 3 * q^90 - 90 * q^91 - 10 * q^92 + 56 * q^93 - 25 * q^94 - 5 * q^95 - 3 * q^96 - 7 * q^97 - 32 * q^98 - 14 * 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
$7$	1.76004	+	2.03119i	0.665232	+	0.767719i	0.983623	−	0.180241i	$-0.0576877\pi$
$7$	1.76004	+	2.03119i	0.665232	+	0.767719i	−0.318390	+	0.947960i	$0.603142\pi$
$8$	−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
$11$	1.98022	+	1.27261i	0.597060	+	0.383707i	0.803985	−	0.594650i	$-0.202709\pi$
$11$	1.98022	+	1.27261i	0.597060	+	0.383707i	−0.206925	+	0.978357i	$0.566346\pi$
$12$	0.841254	+	0.540641i	0.242849	+	0.156070i
$13$	−1.36158	+	1.57134i	−0.377633	+	0.435812i	−0.912470	−	0.409143i	$-0.865828\pi$
$13$	−1.36158	+	1.57134i	−0.377633	+	0.435812i	0.534837	+	0.844955i	$0.320373\pi$
$14$	2.57879	+	0.757200i	0.689209	+	0.202370i
$15$	−0.142315	−	0.989821i	−0.0367455	−	0.255571i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	1.96729	+	4.30776i	0.477138	+	1.04479i	0.983241	+	0.182313i	$0.0583584\pi$
$17$	1.96729	+	4.30776i	0.477138	+	1.04479i	−0.506103	+	0.862473i	$0.668914\pi$
$18$	−0.959493	+	0.281733i	−0.226155	+	0.0664050i
$19$	1.47474	−	3.22923i	0.338328	−	0.740836i	−0.661631	−	0.749829i	$-0.730136\pi$
$19$	1.47474	−	3.22923i	0.338328	−	0.740836i	0.999960	+	0.00899360i	$0.00286279\pi$
$20$	−0.142315	+	0.989821i	−0.0318226	+	0.221331i
$21$	−2.26100	+	1.45306i	−0.493390	+	0.317083i
$22$	2.35390			0.501852
$23$	−0.956931	+	4.69939i	−0.199534	+	0.979891i
$23$	−0.956931	+	4.69939i	−0.199534	+	0.979891i
$24$	1.00000			0.204124
$25$	0.841254	−	0.540641i	0.168251	−	0.108128i
$26$	−0.295899	+	2.05802i	−0.0580305	+	0.403611i
$27$	0.415415	−	0.909632i	0.0799467	−	0.175059i
$28$	2.57879	−	0.757200i	0.487345	−	0.143097i
$29$	2.69293	+	5.89669i	0.500064	+	1.09499i	0.976449	+	0.215751i	$0.0692198\pi$
$29$	2.69293	+	5.89669i	0.500064	+	1.09499i	−0.476384	+	0.879237i	$0.658053\pi$
$30$	−0.654861	−	0.755750i	−0.119561	−	0.137980i
$31$	−0.280522	−	1.95108i	−0.0503833	−	0.350424i	−0.999382	−	0.0351444i	$-0.988811\pi$
$31$	−0.280522	−	1.95108i	−0.0503833	−	0.350424i	0.948999	−	0.315279i	$-0.102098\pi$
$32$	−0.959493	−	0.281733i	−0.169616	−	0.0498038i
$33$	−1.54147	+	1.77896i	−0.268336	+	0.309676i
$34$	3.98394	+	2.56032i	0.683241	+	0.439092i
$35$	−2.26100	−	1.45306i	−0.382179	−	0.245611i
$36$	−0.654861	+	0.755750i	−0.109143	+	0.125958i
$37$	7.79797	+	2.28969i	1.28198	+	0.376423i	0.850631	−	0.525764i	$-0.176220\pi$
$37$	7.79797	+	2.28969i	1.28198	+	0.376423i	0.431347	+	0.902186i	$0.358039\pi$
$38$	−0.505223	−	3.51390i	−0.0819580	−	0.570031i
$39$	−1.36158	−	1.57134i	−0.218027	−	0.251616i
$40$	0.415415	+	0.909632i	0.0656829	+	0.143825i
$41$	−0.914376	+	0.268485i	−0.142802	+	0.0419303i	−0.352352	−	0.935867i	$-0.614618\pi$
$41$	−0.914376	+	0.268485i	−0.142802	+	0.0419303i	0.209551	+	0.977798i	$0.432800\pi$
$42$	−1.11649	+	2.44478i	−0.172278	+	0.377237i
$43$	0.512153	−	3.56210i	0.0781026	−	0.543216i	−0.912776	−	0.408460i	$-0.866066\pi$
$43$	0.512153	−	3.56210i	0.0781026	−	0.543216i	0.990879	−	0.134756i	$-0.0430250\pi$
$44$	1.98022	−	1.27261i	0.298530	−	0.191854i
$45$	1.00000			0.149071
$46$	1.73566	+	4.47074i	0.255909	+	0.659174i
$47$	−1.28736			−0.187780			−0.0938902	−	0.995583i	$-0.529930\pi$
$47$	−1.28736			−0.187780			−0.0938902	+	0.995583i	$0.529930\pi$
$48$	0.841254	−	0.540641i	0.121424	−	0.0780348i
$49$	−0.0318055	+	0.221212i	−0.00454364	+	0.0316017i
$50$	0.415415	−	0.909632i	0.0587486	−	0.128641i
$51$	−4.54389	+	1.33421i	−0.636272	+	0.186826i
$52$	0.863725	+	1.89129i	0.119777	+	0.262275i
$53$	−2.57228	−	2.96856i	−0.353329	−	0.407764i	0.551065	−	0.834463i	$-0.314222\pi$
$53$	−2.57228	−	2.96856i	−0.353329	−	0.407764i	−0.904394	+	0.426699i	$0.859676\pi$
$54$	−0.142315	−	0.989821i	−0.0193666	−	0.134698i
$55$	−2.25855	−	0.663169i	−0.304542	−	0.0894217i
$56$	1.76004	−	2.03119i	0.235195	−	0.271430i
$57$	2.98648	+	1.91930i	0.395569	+	0.254217i
$58$	5.45343	+	3.50470i	0.716070	+	0.460190i
$59$	−0.927486	+	1.07038i	−0.120748	+	0.139351i	−0.812905	−	0.582396i	$-0.802115\pi$
$59$	−0.927486	+	1.07038i	−0.120748	+	0.139351i	0.692157	+	0.721747i	$0.256661\pi$
$60$	−0.959493	−	0.281733i	−0.123870	−	0.0363715i
$61$	−0.359602	−	2.50109i	−0.0460423	−	0.320231i	−0.999806	−	0.0196751i	$-0.993737\pi$
$61$	−0.359602	−	2.50109i	−0.0460423	−	0.320231i	0.953764	−	0.300556i	$-0.0971723\pi$
$62$	−1.29082	−	1.48969i	−0.163935	−	0.189191i
$63$	−1.11649	−	2.44478i	−0.140665	−	0.308013i
$64$	−0.959493	+	0.281733i	−0.119937	+	0.0352166i
$65$	0.863725	−	1.89129i	0.107132	−	0.234586i
$66$	−0.334994	+	2.32994i	−0.0412349	+	0.286795i
$67$	−4.29809	+	2.76221i	−0.525095	+	0.337458i	−0.776184	−	0.630506i	$-0.782847\pi$
$67$	−4.29809	+	2.76221i	−0.525095	+	0.337458i	0.251090	+	0.967964i	$0.419211\pi$
$68$	4.73572			0.574291
$69$	−4.51537	−	1.61598i	−0.543587	−	0.194542i
$70$	−2.68765			−0.321236
$71$	0.461255	−	0.296431i	0.0547409	−	0.0351798i	−0.512984	−	0.858398i	$-0.671460\pi$
$71$	0.461255	−	0.296431i	0.0547409	−	0.0351798i	0.567725	+	0.823218i	$0.307824\pi$
$72$	−0.142315	+	0.989821i	−0.0167720	+	0.116652i
$73$	3.91085	−	8.56356i	0.457730	−	1.00229i	−0.530269	−	0.847829i	$-0.677909\pi$
$73$	3.91085	−	8.56356i	0.457730	−	1.00229i	0.987999	−	0.154459i	$-0.0493636\pi$
$74$	7.79797	−	2.28969i	0.906495	−	0.266171i
$75$	0.415415	+	0.909632i	0.0479680	+	0.105035i
$76$	−2.32478	−	2.68294i	−0.266671	−	0.307754i
$77$	0.900349	+	6.26206i	0.102604	+	0.713628i
$78$	−1.99496	−	0.585774i	−0.225885	−	0.0663259i
$79$	0.555315	−	0.640868i	0.0624778	−	0.0721033i	−0.723650	−	0.690167i	$-0.757537\pi$
$79$	0.555315	−	0.640868i	0.0624778	−	0.0721033i	0.786128	+	0.618064i	$0.212083\pi$
$80$	0.841254	+	0.540641i	0.0940550	+	0.0604455i
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$	−0.624068	+	0.720213i	−0.0689168	+	0.0795342i
$83$	−6.18083	−	1.81486i	−0.678434	−	0.199206i	−0.0756788	−	0.997132i	$-0.524112\pi$
$83$	−6.18083	−	1.81486i	−0.678434	−	0.199206i	−0.602755	+	0.797926i	$0.705931\pi$
$84$	0.382493	+	2.66030i	0.0417334	+	0.290262i
$85$	−3.10124	−	3.57902i	−0.336377	−	0.388199i
$86$	−1.49497	−	3.27352i	−0.161207	−	0.352993i
$87$	−6.21991	+	1.82633i	−0.666845	+	0.195803i
$88$	0.977844	−	2.14118i	0.104238	−	0.228250i
$89$	1.65288	−	11.4960i	0.175205	−	1.21858i	−0.692470	−	0.721447i	$-0.743477\pi$
$89$	1.65288	−	11.4960i	0.175205	−	1.21858i	0.867675	−	0.497132i	$-0.165614\pi$
$90$	0.841254	−	0.540641i	0.0886759	−	0.0569885i
$91$	−5.58813			−0.585795
$92$	3.87719	+	2.82265i	0.404225	+	0.294282i
$93$	1.97114			0.204398
$94$	−1.08299	+	0.695998i	−0.111702	+	0.0717867i
$95$	−0.505223	+	3.51390i	−0.0518348	+	0.360519i
$96$	0.415415	−	0.909632i	0.0423981	−	0.0928389i
$97$	2.77124	−	0.813708i	0.281376	−	0.0826195i	−0.137999	−	0.990432i	$-0.544067\pi$
$97$	2.77124	−	0.813708i	0.281376	−	0.0826195i	0.419376	+	0.907813i	$0.362249\pi$
$98$	0.0928397	+	0.203291i	0.00937823	+	0.0205355i
$99$	−1.54147	−	1.77896i	−0.154924	−	0.178792i
$100$	−0.142315	−	0.989821i	−0.0142315	−	0.0989821i
$101$	−6.51123	−	1.91187i	−0.647892	−	0.190238i	−0.0587562	−	0.998272i	$-0.518713\pi$
$101$	−6.51123	−	1.91187i	−0.647892	−	0.190238i	−0.589136	+	0.808034i	$0.700532\pi$
$102$	−3.10124	+	3.57902i	−0.307068	+	0.354376i
$103$	−4.53844	−	2.91668i	−0.447185	−	0.287389i	0.297602	−	0.954690i	$-0.403813\pi$
$103$	−4.53844	−	2.91668i	−0.447185	−	0.287389i	−0.744788	+	0.667301i	$0.767449\pi$
$104$	1.74912	+	1.12409i	0.171515	+	0.110226i
$105$	1.76004	−	2.03119i	0.171762	−	0.198224i
$106$	−3.76886	−	1.10664i	−0.366064	−	0.107486i
$107$	−0.512436	−	3.56407i	−0.0495390	−	0.344552i	−0.999484	−	0.0321331i	$-0.989770\pi$
$107$	−0.512436	−	3.56407i	−0.0495390	−	0.344552i	0.949945	−	0.312419i	$-0.101139\pi$
$108$	−0.654861	−	0.755750i	−0.0630140	−	0.0727220i
$109$	−6.79994	−	14.8898i	−0.651316	−	1.42618i	−0.890397	−	0.455184i	$-0.849573\pi$
$109$	−6.79994	−	14.8898i	−0.651316	−	1.42618i	0.239081	−	0.971000i	$-0.423154\pi$
$110$	−2.25855	+	0.663169i	−0.215344	+	0.0632307i
$111$	−3.37615	+	7.39274i	−0.320450	+	0.701688i
$112$	0.382493	−	2.66030i	0.0361422	−	0.251375i
$113$	−6.54469	+	4.20602i	−0.615673	+	0.395669i	−0.810981	−	0.585073i	$-0.801066\pi$
$113$	−6.54469	+	4.20602i	−0.615673	+	0.395669i	0.195308	+	0.980742i	$0.437429\pi$
$114$	3.55004			0.332492
$115$	−0.405803	−	4.77863i	−0.0378413	−	0.445610i
$116$	6.48250			0.601885
$117$	1.74912	−	1.12409i	0.161706	−	0.103922i
$118$	−0.201562	+	1.40189i	−0.0185553	+	0.129055i
$119$	−5.28740	+	11.5778i	−0.484695	+	1.06133i
$120$	−0.959493	+	0.281733i	−0.0875893	+	0.0257185i
$121$	−2.26782	−	4.96584i	−0.206166	−	0.451440i
$122$	−1.65471	−	1.90963i	−0.149810	−	0.172890i
$123$	−0.135623	−	0.943278i	−0.0122287	−	0.0850525i
$124$	−1.89130	−	0.555334i	−0.169843	−	0.0498705i
$125$	−0.654861	+	0.755750i	−0.0585725	+	0.0675963i
$126$	−2.26100	−	1.45306i	−0.201426	−	0.129448i
$127$	16.2375	+	10.4352i	1.44085	+	0.925976i	0.999591	+	0.0285942i	$0.00910305\pi$
$127$	16.2375	+	10.4352i	1.44085	+	0.925976i	0.441255	+	0.897382i	$0.354533\pi$
$128$	−0.654861	+	0.755750i	−0.0578821	+	0.0667995i
$129$	3.45296	+	1.01388i	0.304016	+	0.0892672i
$130$	−0.295899	−	2.05802i	−0.0259520	−	0.180500i
$131$	−10.6837	−	12.3297i	−0.933442	−	1.07725i	−0.996854	−	0.0792619i	$-0.974744\pi$
$131$	−10.6837	−	12.3297i	−0.933442	−	1.07725i	0.0634120	−	0.997987i	$-0.479802\pi$
$132$	0.977844	+	2.14118i	0.0851104	+	0.186366i
$133$	9.15479	−	2.68809i	0.793821	−	0.233087i
$134$	−2.12242	+	4.64744i	−0.183349	+	0.401478i
$135$	−0.142315	+	0.989821i	−0.0122485	+	0.0851903i
$136$	3.98394	−	2.56032i	0.341620	−	0.219546i
$137$	4.23295			0.361646			0.180823	−	0.983516i	$-0.442124\pi$
$137$	4.23295			0.361646			0.180823	+	0.983516i	$0.442124\pi$
$138$	−4.67224	+	1.08174i	−0.397728	+	0.0920841i
$139$	−9.06927			−0.769246			−0.384623	−	0.923074i	$-0.625669\pi$
$139$	−9.06927			−0.769246			−0.384623	+	0.923074i	$0.625669\pi$
$140$	−2.26100	+	1.45306i	−0.191089	+	0.122806i
$141$	0.183210	−	1.27425i	0.0154291	−	0.107312i
$142$	0.227770	−	0.498747i	0.0191140	−	0.0418539i
$143$	−4.69594	+	1.37885i	−0.392694	+	0.115305i
$144$	0.415415	+	0.909632i	0.0346179	+	0.0758027i
$145$	−4.24513	−	4.89915i	−0.352539	−	0.406852i
$146$	−1.33980	−	9.31849i	−0.110882	−	0.771203i
$147$	−0.214434	−	0.0629635i	−0.0176862	−	0.00519314i
$148$	5.32217	−	6.14211i	0.437479	−	0.504878i
$149$	10.5252	+	6.76416i	0.862261	+	0.554142i	0.895376	−	0.445310i	$-0.146907\pi$
$149$	10.5252	+	6.76416i	0.862261	+	0.554142i	−0.0331153	+	0.999452i	$0.510543\pi$
$150$	0.841254	+	0.540641i	0.0686881	+	0.0441431i
$151$	−0.221834	+	0.256010i	−0.0180526	+	0.0208338i	−0.764704	−	0.644382i	$-0.777115\pi$
$151$	−0.221834	+	0.256010i	−0.0180526	+	0.0208338i	0.746651	+	0.665215i	$0.231660\pi$
$152$	−3.40624	−	1.00016i	−0.276282	−	0.0811238i
$153$	−0.673963	−	4.68752i	−0.0544867	−	0.378963i
$154$	4.14295	+	4.78122i	0.333848	+	0.385282i
$155$	0.818841	+	1.79301i	0.0657709	+	0.144018i
$156$	−1.99496	+	0.585774i	−0.159725	+	0.0468995i
$157$	8.45407	−	18.5118i	0.674708	−	1.47740i	−0.193447	−	0.981111i	$-0.561967\pi$
$157$	8.45407	−	18.5118i	0.674708	−	1.47740i	0.868155	−	0.496294i	$-0.165306\pi$
$158$	0.120682	−	0.839358i	0.00960091	−	0.0667758i
$159$	3.30442	−	2.12362i	0.262058	−	0.168414i
$160$	1.00000			0.0790569
$161$	−11.2296	+	6.32740i	−0.885017	+	0.498669i
$162$	1.00000			0.0785674
$163$	16.9082	−	10.8663i	1.32435	−	0.851111i	0.328718	−	0.944428i	$-0.393383\pi$
$163$	16.9082	−	10.8663i	1.32435	−	0.851111i	0.995636	+	0.0933170i	$0.0297470\pi$
$164$	−0.135623	+	0.943278i	−0.0105904	+	0.0736577i
$165$	0.977844	−	2.14118i	0.0761250	−	0.166691i
$166$	−6.18083	+	1.81486i	−0.479725	+	0.140860i
$167$	8.16532	+	17.8796i	0.631851	+	1.38356i	0.906578	+	0.422039i	$0.138685\pi$
$167$	8.16532	+	17.8796i	0.631851	+	1.38356i	−0.274726	+	0.961522i	$0.588587\pi$
$168$	1.76004	+	2.03119i	0.135790	+	0.156710i
$169$	1.23486	+	8.58867i	0.0949896	+	0.660667i
$170$	−4.54389	−	1.33421i	−0.348501	−	0.102329i
$171$	−2.32478	+	2.68294i	−0.177780	+	0.205170i
$172$	−3.02745	−	1.94562i	−0.230841	−	0.148352i
$173$	−2.42124	−	1.55604i	−0.184084	−	0.118303i	0.445353	−	0.895355i	$-0.353078\pi$
$173$	−2.42124	−	1.55604i	−0.184084	−	0.118303i	−0.629437	+	0.777052i	$0.716714\pi$
$174$	−4.24513	+	4.89915i	−0.321823	+	0.371403i
$175$	2.57879	+	0.757200i	0.194938	+	0.0572389i
$176$	−0.334994	−	2.32994i	−0.0252511	−	0.175626i
$177$	−0.927486	−	1.07038i	−0.0697141	−	0.0804543i
$178$	−4.82474	−	10.5647i	−0.361630	−	0.791858i
$179$	−8.31816	+	2.44243i	−0.621728	+	0.182556i	−0.577400	−	0.816461i	$-0.695933\pi$
$179$	−8.31816	+	2.44243i	−0.621728	+	0.182556i	−0.0443279	+	0.999017i	$0.514115\pi$
$180$	0.415415	−	0.909632i	0.0309632	−	0.0678000i
$181$	1.94605	−	13.5351i	0.144649	−	1.00606i	−0.780148	−	0.625595i	$-0.784856\pi$
$181$	1.94605	−	13.5351i	0.144649	−	1.00606i	0.924797	−	0.380461i	$-0.124235\pi$
$182$	−4.70103	+	3.02117i	−0.348464	+	0.223944i
$183$	2.52681			0.186787
$184$	4.78774	+	0.278397i	0.352957	+	0.0205237i
$185$	−8.12717			−0.597522
$186$	1.65823	−	1.06568i	0.121587	−	0.0781394i
$187$	−1.58644	+	11.0339i	−0.116012	+	0.806881i
$188$	−0.534788	+	1.17102i	−0.0390034	+	0.0854055i
$189$	2.57879	−	0.757200i	0.187579	−	0.0550782i
$190$	1.47474	+	3.22923i	0.106989	+	0.234273i
$191$	−7.54546	−	8.70792i	−0.545970	−	0.630083i	0.413969	−	0.910291i	$-0.364142\pi$
$191$	−7.54546	−	8.70792i	−0.545970	−	0.630083i	−0.959939	+	0.280208i	$0.909597\pi$
$192$	−0.142315	−	0.989821i	−0.0102707	−	0.0714342i
$193$	2.47376	+	0.726362i	0.178065	+	0.0522847i	0.369550	−	0.929211i	$-0.379512\pi$
$193$	2.47376	+	0.726362i	0.178065	+	0.0522847i	−0.191484	+	0.981496i	$0.561330\pi$
$194$	1.89139	−	2.18278i	0.135794	−	0.156714i
$195$	1.74912	+	1.12409i	0.125257	+	0.0804979i
$196$	0.188009	+	0.120826i	0.0134292	+	0.00863043i
$197$	12.6829	−	14.6369i	0.903620	−	1.04283i	−0.0952572	−	0.995453i	$-0.530367\pi$
$197$	12.6829	−	14.6369i	0.903620	−	1.04283i	0.998877	−	0.0473801i	$-0.0150872\pi$
$198$	−2.25855	−	0.663169i	−0.160508	−	0.0471294i
$199$	2.35611	+	16.3871i	0.167020	+	1.16165i	0.885002	+	0.465588i	$0.154157\pi$
$199$	2.35611	+	16.3871i	0.167020	+	1.16165i	−0.717982	+	0.696062i	$0.754934\pi$
$200$	−0.654861	−	0.755750i	−0.0463056	−	0.0534396i
$201$	−2.12242	−	4.64744i	−0.149704	−	0.327805i
$202$	−6.51123	+	1.91187i	−0.458129	+	0.134519i
$203$	−7.23766	+	15.8483i	−0.507984	+	1.11233i
$204$	−0.673963	+	4.68752i	−0.0471869	+	0.328192i
$205$	0.801696	−	0.515219i	0.0559929	−	0.0359844i
$206$	−5.39485			−0.375877
$207$	2.24214	−	4.23943i	0.155840	−	0.294661i
$208$	2.07919			0.144166
$209$	7.02987	−	4.51782i	0.486266	−	0.312504i
$210$	0.382493	−	2.66030i	0.0263945	−	0.183578i
$211$	−8.95250	+	19.6033i	−0.616316	+	1.34954i	0.301853	+	0.953354i	$0.402395\pi$
$211$	−8.95250	+	19.6033i	−0.616316	+	1.34954i	−0.918169	+	0.396189i	$0.870332\pi$
$212$	−3.76886	+	1.10664i	−0.258847	+	0.0760042i
$213$	0.227770	+	0.498747i	0.0156065	+	0.0341736i
$214$	−2.35797	−	2.72124i	−0.161187	−	0.186020i
$215$	0.512153	+	3.56210i	0.0349286	+	0.242933i
$216$	−0.959493	−	0.281733i	−0.0652852	−	0.0191695i
$217$	3.46928	−	4.00377i	0.235510	−	0.271793i
$218$	−13.7705	−	8.84977i	−0.932656	−	0.599382i
$219$	7.91982	+	5.08976i	0.535172	+	0.343934i
$220$	−1.54147	+	1.77896i	−0.103926	+	0.119937i
$221$	−9.44759	−	2.77406i	−0.635514	−	0.186604i
$222$	1.15662	+	8.04445i	0.0776271	+	0.539908i
$223$	−7.31262	−	8.43922i	−0.489689	−	0.565132i	0.456093	−	0.889932i	$-0.349248\pi$
$223$	−7.31262	−	8.43922i	−0.489689	−	0.565132i	−0.945783	+	0.324800i	$0.894703\pi$
$224$	−1.11649	−	2.44478i	−0.0745988	−	0.163349i
$225$	−0.959493	+	0.281733i	−0.0639662	+	0.0187822i
$226$	−3.23180	+	7.07666i	−0.214976	+	0.470732i
$227$	3.60425	−	25.0681i	0.239223	−	1.66383i	−0.416732	−	0.909029i	$-0.636825\pi$
$227$	3.60425	−	25.0681i	0.239223	−	1.66383i	0.655955	−	0.754800i	$-0.272266\pi$
$228$	2.98648	−	1.91930i	0.197785	−	0.127108i
$229$	−22.8309			−1.50871			−0.754355	−	0.656466i	$-0.772050\pi$
$229$	−22.8309			−1.50871			−0.754355	+	0.656466i	$0.772050\pi$
$230$	−2.92491	−	3.80065i	−0.192863	−	0.250607i
$231$	−6.32646			−0.416250
$232$	5.45343	−	3.50470i	0.358035	−	0.230095i
$233$	−3.29520	+	22.9186i	−0.215876	+	1.50145i	0.537165	+	0.843477i	$0.319495\pi$
$233$	−3.29520	+	22.9186i	−0.215876	+	1.50145i	−0.753041	+	0.657973i	$0.771414\pi$
$234$	0.863725	−	1.89129i	0.0564634	−	0.123638i
$235$	1.23521	−	0.362690i	0.0805762	−	0.0236593i
$236$	0.588356	+	1.28832i	0.0382987	+	0.0838625i
$237$	0.555315	+	0.640868i	0.0360716	+	0.0416288i
$238$	1.81138	+	12.5984i	0.117414	+	0.816635i
$239$	−0.403465	−	0.118468i	−0.0260980	−	0.00766305i	0.268658	−	0.963236i	$-0.413420\pi$
$239$	−0.403465	−	0.118468i	−0.0260980	−	0.00766305i	−0.294755	+	0.955573i	$0.595238\pi$
$240$	−0.654861	+	0.755750i	−0.0422711	+	0.0487834i
$241$	0.857095	+	0.550822i	0.0552104	+	0.0354815i	0.567955	−	0.823060i	$-0.307735\pi$
$241$	0.857095	+	0.550822i	0.0552104	+	0.0354815i	−0.512744	+	0.858541i	$0.671371\pi$
$242$	−4.59255	−	2.95145i	−0.295220	−	0.189727i
$243$	−0.654861	+	0.755750i	−0.0420093	+	0.0484814i
$244$	−2.42445	−	0.711883i	−0.155210	−	0.0455737i
$245$	−0.0318055	−	0.221212i	−0.00203198	−	0.0141327i
$246$	−0.624068	−	0.720213i	−0.0397891	−	0.0459191i
$247$	3.06626	+	6.71416i	0.195101	+	0.427212i
$248$	−1.89130	+	0.555334i	−0.120097	+	0.0352638i
$249$	2.67601	−	5.85964i	0.169585	−	0.371339i
$250$	−0.142315	+	0.989821i	−0.00900078	+	0.0626018i
$251$	−9.65828	+	6.20700i	−0.609625	+	0.391782i	−0.808717	−	0.588199i	$-0.799837\pi$
$251$	−9.65828	+	6.20700i	−0.609625	+	0.391782i	0.199091	+	0.979981i	$0.436201\pi$
$252$	−2.68765			−0.169306
$253$	−7.87544	+	8.08804i	−0.495125	+	0.508491i
$254$	19.3016			1.21109
$255$	3.98394	−	2.56032i	0.249484	−	0.160334i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	−3.15200	+	6.90192i	−0.196616	+	0.430530i	−0.982102	−	0.188350i	$-0.939686\pi$
$257$	−3.15200	+	6.90192i	−0.196616	+	0.430530i	0.785486	+	0.618880i	$0.212413\pi$
$258$	3.45296	−	1.01388i	0.214972	−	0.0631214i
$259$	9.07392	+	19.8691i	0.563826	+	1.23461i
$260$	−1.36158	−	1.57134i	−0.0844414	−	0.0974506i
$261$	−0.922556	−	6.41652i	−0.0571048	−	0.397172i
$262$	−15.6537	−	4.59633i	−0.967086	−	0.283962i
$263$	−18.8393	+	21.7417i	−1.16168	+	1.34065i	−0.231814	+	0.972760i	$0.574466\pi$
$263$	−18.8393	+	21.7417i	−1.16168	+	1.34065i	−0.929868	+	0.367893i	$0.880079\pi$
$264$	1.98022	+	1.27261i	0.121874	+	0.0783239i
$265$	3.30442	+	2.12362i	0.202989	+	0.130453i
$266$	6.24821	−	7.21082i	0.383102	−	0.442123i
$267$	11.1438	+	3.27212i	0.681990	+	0.200250i
$268$	0.727107	+	5.05714i	0.0444151	+	0.308914i
$269$	1.88048	+	2.17019i	0.114655	+	0.132319i	0.810176	−	0.586187i	$-0.199372\pi$
$269$	1.88048	+	2.17019i	0.114655	+	0.132319i	−0.695521	+	0.718506i	$0.744826\pi$
$270$	0.415415	+	0.909632i	0.0252814	+	0.0553584i
$271$	17.7987	−	5.22617i	1.08119	−	0.317467i	0.307838	−	0.951439i	$-0.400395\pi$
$271$	17.7987	−	5.22617i	1.08119	−	0.317467i	0.773356	+	0.633972i	$0.218576\pi$
$272$	1.96729	−	4.30776i	0.119284	−	0.261197i
$273$	0.795274	−	5.53125i	0.0481322	−	0.334767i
$274$	3.56099	−	2.28851i	0.215127	−	0.138254i
$275$	2.35390			0.141945
$276$	−3.34570	+	3.43602i	−0.201388	+	0.206824i
$277$	32.7117			1.96546			0.982728	−	0.185056i	$-0.0592468\pi$
$277$	32.7117			1.96546			0.982728	+	0.185056i	$0.0592468\pi$
$278$	−7.62956	+	4.90322i	−0.457591	+	0.294076i
$279$	−0.280522	+	1.95108i	−0.0167944	+	0.116808i
$280$	−1.11649	+	2.44478i	−0.0667232	+	0.146103i
$281$	27.2795	−	8.00997i	1.62736	−	0.477835i	0.664374	−	0.747401i	$-0.268698\pi$
$281$	27.2795	−	8.00997i	1.62736	−	0.477835i	0.962982	+	0.269566i	$0.0868802\pi$
$282$	−0.534788	−	1.17102i	−0.0318461	−	0.0697333i
$283$	−9.84225	−	11.3586i	−0.585061	−	0.675196i	0.383624	−	0.923489i	$-0.374676\pi$
$283$	−9.84225	−	11.3586i	−0.585061	−	0.675196i	−0.968685	+	0.248293i	$0.920130\pi$
$284$	−0.0780305	−	0.542714i	−0.00463026	−	0.0322042i
$285$	−3.40624	−	1.00016i	−0.201768	−	0.0592445i
$286$	−3.20501	+	3.69878i	−0.189516	+	0.218713i
$287$	−2.15468	−	1.38473i	−0.127187	−	0.0817380i
$288$	0.841254	+	0.540641i	0.0495713	+	0.0318576i
$289$	−3.55397	+	4.10150i	−0.209057	+	0.241265i
$290$	−6.21991	−	1.82633i	−0.365246	−	0.107246i
$291$	0.411038	+	2.85883i	0.0240955	+	0.167588i
$292$	−6.16506	−	7.11486i	−0.360783	−	0.416366i
$293$	9.69107	+	21.2205i	0.566158	+	1.23971i	0.948818	+	0.315824i	$0.102281\pi$
$293$	9.69107	+	21.2205i	0.566158	+	1.23971i	−0.382660	+	0.923889i	$0.624992\pi$
$294$	−0.214434	+	0.0629635i	−0.0125060	+	0.00367210i
$295$	0.588356	−	1.28832i	0.0342554	−	0.0750089i
$296$	1.15662	−	8.04445i	0.0672270	−	0.467574i
$297$	1.98022	−	1.27261i	0.114904	−	0.0738444i
$298$	12.5114			0.724765
$299$	−6.08142	−	7.90225i	−0.351698	−	0.456999i
$300$	1.00000			0.0577350
$301$	8.13673	−	5.22916i	0.468994	−	0.301404i
$302$	−0.0482091	+	0.335301i	−0.00277412	+	0.0192944i
$303$	2.81906	−	6.17287i	0.161951	−	0.354622i
$304$	−3.40624	+	1.00016i	−0.195361	+	0.0573632i
$305$	1.04967	+	2.29846i	0.0601041	+	0.131610i
$306$	−3.10124	−	3.57902i	−0.177286	−	0.204599i
$307$	0.594658	+	4.13594i	0.0339389	+	0.236050i	0.999729	−	0.0232744i	$-0.00740913\pi$
$307$	0.594658	+	4.13594i	0.0339389	+	0.236050i	−0.965790	+	0.259325i	$0.916500\pi$
$308$	6.07019	+	1.78237i	0.345881	+	0.101560i
$309$	3.53288	−	4.07716i	0.200978	−	0.231941i
$310$	1.65823	+	1.06568i	0.0941811	+	0.0605265i
$311$	8.59246	+	5.52204i	0.487234	+	0.313126i	0.761092	−	0.648644i	$-0.224664\pi$
$311$	8.59246	+	5.52204i	0.487234	+	0.313126i	−0.273858	+	0.961770i	$0.588300\pi$
$312$	−1.36158	+	1.57134i	−0.0770841	+	0.0889598i
$313$	13.1539	+	3.86234i	0.743504	+	0.218313i	0.631479	−	0.775393i	$-0.282448\pi$
$313$	13.1539	+	3.86234i	0.743504	+	0.218313i	0.112025	+	0.993705i	$0.464266\pi$
$314$	−2.89623	−	20.1438i	−0.163444	−	1.13678i
$315$	1.76004	+	2.03119i	0.0991670	+	0.114445i
$316$	−0.352268	−	0.771358i	−0.0198166	−	0.0433923i
$317$	20.6197	−	6.05449i	1.15812	−	0.340054i	0.354417	−	0.935088i	$-0.384679\pi$
$317$	20.6197	−	6.05449i	1.15812	−	0.340054i	0.803701	+	0.595034i	$0.202861\pi$
$318$	1.63174	−	3.57301i	0.0915034	−	0.200364i
$319$	−2.17160	+	15.1038i	−0.121586	+	0.845651i
$320$	0.841254	−	0.540641i	0.0470275	−	0.0302227i
$321$	3.60072			0.200973
$322$	−6.02610	+	11.3941i	−0.335821	+	0.634970i
$323$	16.8120			0.935444
$324$	0.841254	−	0.540641i	0.0467363	−	0.0300356i
$325$	−0.295899	+	2.05802i	−0.0164135	+	0.114159i
$326$	8.34936	−	18.2826i	0.462429	−	1.01258i
$327$	15.7060	−	4.61169i	0.868542	−	0.255027i
$328$	0.395881	+	0.866859i	0.0218589	+	0.0478643i
$329$	−2.26580	−	2.61487i	−0.124918	−	0.144163i
$330$	−0.334994	−	2.32994i	−0.0184408	−	0.128259i
$331$	−9.80666	−	2.87950i	−0.539023	−	0.158271i	0.000878555	−	1.00000i	$-0.499720\pi$
$331$	−9.80666	−	2.87950i	−0.539023	−	0.158271i	−0.539902	+	0.841728i	$0.681539\pi$
$332$	−4.21846	+	4.86836i	−0.231518	+	0.267186i
$333$	−6.83701	−	4.39388i	−0.374666	−	0.240783i
$334$	16.5355	+	10.6267i	0.904783	+	0.581469i
$335$	3.34578	−	3.86123i	0.182799	−	0.210962i
$336$	2.57879	+	0.757200i	0.140684	+	0.0413086i
$337$	−0.308025	−	2.14236i	−0.0167792	−	0.116702i	0.979710	−	0.200418i	$-0.0642301\pi$
$337$	−0.308025	−	2.14236i	−0.0167792	−	0.116702i	−0.996490	+	0.0837164i	$0.973321\pi$
$338$	5.68222	+	6.55763i	0.309072	+	0.356688i
$339$	−3.23180	−	7.07666i	−0.175527	−	0.384351i
$340$	−4.54389	+	1.33421i	−0.246427	+	0.0723575i
$341$	1.92747	−	4.22056i	0.104378	−	0.228556i
$342$	−0.505223	+	3.51390i	−0.0273193	+	0.190010i
$343$	15.3217	−	9.84665i	0.827293	−	0.531669i
$344$	−3.59873			−0.194031
$345$	4.78774	+	0.278397i	0.257763	+	0.0149884i
$346$	−2.87814			−0.154730
$347$	19.7375	−	12.6845i	1.05957	−	0.680942i	0.109817	−	0.993952i	$-0.464974\pi$
$347$	19.7375	−	12.6845i	1.05957	−	0.680942i	0.949750	+	0.313010i	$0.101337\pi$
$348$	−0.922556	+	6.41652i	−0.0494542	+	0.343961i
$349$	−2.17455	+	4.76160i	−0.116401	+	0.254882i	−0.958861	−	0.283877i	$-0.908379\pi$
$349$	−2.17455	+	4.76160i	−0.116401	+	0.254882i	0.842460	+	0.538759i	$0.181107\pi$
$350$	2.57879	−	0.757200i	0.137842	−	0.0404740i
$351$	0.863725	+	1.89129i	0.0461022	+	0.100950i
$352$	−1.54147	−	1.77896i	−0.0821608	−	0.0948187i
$353$	3.86812	+	26.9033i	0.205879	+	1.43192i	0.786422	+	0.617690i	$0.211931\pi$
$353$	3.86812	+	26.9033i	0.205879	+	1.43192i	−0.580543	+	0.814230i	$0.697160\pi$
$354$	−1.35894	−	0.399021i	−0.0722268	−	0.0212077i
$355$	−0.359057	+	0.414374i	−0.0190568	+	0.0219927i
$356$	−9.77054	−	6.27915i	−0.517838	−	0.332794i
$357$	−10.7075	−	6.88127i	−0.566699	−	0.364195i
$358$	−5.67720	+	6.55184i	−0.300049	+	0.346275i
$359$	−27.1950	−	7.98518i	−1.43530	−	0.421442i	−0.530647	−	0.847593i	$-0.678051\pi$
$359$	−27.1950	−	7.98518i	−1.43530	−	0.421442i	−0.904652	+	0.426151i	$0.859869\pi$
$360$	−0.142315	−	0.989821i	−0.00750065	−	0.0521682i
$361$	4.18929	+	4.83470i	0.220489	+	0.254458i
$362$	−5.68050	−	12.4386i	−0.298561	−	0.653756i
$363$	5.23804	−	1.53803i	0.274926	−	0.0807255i
$364$	−2.32139	+	5.08314i	−0.121674	+	0.266429i
$365$	−1.33980	+	9.31849i	−0.0701281	+	0.487752i
$366$	2.12568	−	1.36609i	0.111111	−	0.0714069i
$367$	−21.1984			−1.10655			−0.553274	−	0.832999i	$-0.686622\pi$
$367$	−21.1984			−1.10655			−0.553274	+	0.832999i	$0.686622\pi$
$368$	4.17822	−	2.35425i	0.217805	−	0.122724i
$369$	0.952978			0.0496101
$370$	−6.83701	+	4.39388i	−0.355439	+	0.228427i
$371$	1.50242	−	10.4496i	0.0780019	−	0.542515i
$372$	0.818841	−	1.79301i	0.0424549	−	0.0929634i
$373$	10.9647	−	3.21951i	0.567728	−	0.166700i	0.0147433	−	0.999891i	$-0.495307\pi$
$373$	10.9647	−	3.21951i	0.567728	−	0.166700i	0.552985	+	0.833191i	$0.313489\pi$
$374$	4.63080	+	10.1400i	0.239453	+	0.524328i
$375$	−0.654861	−	0.755750i	−0.0338169	−	0.0390267i
$376$	0.183210	+	1.27425i	0.00944834	+	0.0657146i
$377$	−12.9324	−	3.79728i	−0.666050	−	0.195570i
$378$	1.76004	−	2.03119i	0.0905267	−	0.104473i
$379$	−2.04762	−	1.31593i	−0.105179	−	0.0675946i	0.486994	−	0.873405i	$-0.338093\pi$
$379$	−2.04762	−	1.31593i	−0.105179	−	0.0675946i	−0.592173	+	0.805811i	$0.701730\pi$
$380$	2.98648	+	1.91930i	0.153203	+	0.0984578i
$381$	−12.6398	+	14.5872i	−0.647559	+	0.747323i
$382$	−11.0555	−	3.24619i	−0.565648	−	0.166089i
$383$	−2.56757	−	17.8579i	−0.131197	−	0.912495i	−0.943998	−	0.329953i	$-0.892967\pi$
$383$	−2.56757	−	17.8579i	−0.131197	−	0.912495i	0.812801	−	0.582542i	$-0.197942\pi$
$384$	−0.654861	−	0.755750i	−0.0334182	−	0.0385667i
$385$	−2.62811	−	5.75475i	−0.133941	−	0.293289i
$386$	2.47376	−	0.726362i	0.125911	−	0.0369709i
$387$	−1.49497	+	3.27352i	−0.0759935	+	0.166403i
$388$	0.411038	−	2.85883i	0.0208673	−	0.145135i
$389$	27.0069	−	17.3563i	1.36930	−	0.879997i	0.370496	−	0.928834i	$-0.379188\pi$
$389$	27.0069	−	17.3563i	1.36930	−	0.879997i	0.998807	+	0.0488366i	$0.0155514\pi$
$390$	2.07919			0.105284
$391$	−22.1264	+	5.12283i	−1.11898	+	0.259073i
$392$	0.223487			0.0112878
$393$	13.7246	−	8.82029i	0.692316	−	0.444925i
$394$	2.75626	−	19.1702i	0.138858	−	0.965781i
$395$	−0.352268	+	0.771358i	−0.0177245	+	0.0388113i
$396$	−2.25855	+	0.663169i	−0.113496	+	0.0333255i
$397$	5.01974	+	10.9917i	0.251933	+	0.551657i	0.992771	−	0.120027i	$-0.0382983\pi$
$397$	5.01974	+	10.9917i	0.251933	+	0.551657i	−0.740837	+	0.671685i	$0.765571\pi$
$398$	10.8416	+	12.5119i	0.543441	+	0.627164i
$399$	1.35787	+	9.44416i	0.0679783	+	0.472799i
$400$	−0.959493	−	0.281733i	−0.0479746	−	0.0140866i
$401$	6.77221	−	7.81555i	0.338188	−	0.390290i	−0.561026	−	0.827798i	$-0.689593\pi$
$401$	6.77221	−	7.81555i	0.338188	−	0.390290i	0.899215	+	0.437508i	$0.144139\pi$
$402$	−4.29809	−	2.76221i	−0.214369	−	0.137767i
$403$	3.44776	+	2.21574i	0.171745	+	0.110374i
$404$	−4.44396	+	5.12861i	−0.221095	+	0.255158i
$405$	−0.959493	−	0.281733i	−0.0476776	−	0.0139994i
$406$	2.47951	+	17.2454i	0.123056	+	0.855874i
$407$	12.5278	+	14.4579i	0.620981	+	0.716651i
$408$	1.96729	+	4.30776i	0.0973954	+	0.213266i
$409$	−18.7252	+	5.49822i	−0.925903	+	0.271870i	−0.709721	−	0.704483i	$-0.751179\pi$
$409$	−18.7252	+	5.49822i	−0.925903	+	0.271870i	−0.216182	+	0.976353i	$0.569361\pi$
$410$	0.395881	−	0.866859i	0.0195512	−	0.0428111i
$411$	−0.602412	+	4.18987i	−0.0297148	+	0.206671i
$412$	−4.53844	+	2.91668i	−0.223593	+	0.143694i
$413$	−3.80655			−0.187308
$414$	−0.405803	−	4.77863i	−0.0199441	−	0.234857i
$415$	6.44177			0.316214
$416$	1.74912	−	1.12409i	0.0857577	−	0.0551132i
$417$	1.29069	−	8.97696i	0.0632055	−	0.439604i
$418$	3.47138	−	7.60127i	0.169791	−	0.371790i
$419$	10.2472	−	3.00886i	0.500610	−	0.146993i	−0.0216718	−	0.999765i	$-0.506899\pi$
$419$	10.2472	−	3.00886i	0.500610	−	0.146993i	0.522282	+	0.852773i	$0.325081\pi$
$420$	−1.11649	−	2.44478i	−0.0544792	−	0.119293i
$421$	−25.0605	−	28.9214i	−1.22138	−	1.40954i	−0.883551	−	0.468335i	$-0.844854\pi$
$421$	−25.0605	−	28.9214i	−1.22138	−	1.40954i	−0.337825	−	0.941209i	$-0.609691\pi$
$422$	3.06699	+	21.3314i	0.149299	+	1.03840i
$423$	1.23521	+	0.362690i	0.0600580	+	0.0176346i
$424$	−2.57228	+	2.96856i	−0.124921	+	0.144166i
$425$	3.98394	+	2.56032i	0.193250	+	0.124194i
$426$	0.461255	+	0.296431i	0.0223479	+	0.0143621i
$427$	4.44728	−	5.13243i	0.215219	−	0.248376i
$428$	−3.45487	−	1.01444i	−0.166997	−	0.0490348i
$429$	−0.696515	−	4.84437i	−0.0336281	−	0.233888i
$430$	2.35667	+	2.71974i	0.113649	+	0.131158i
$431$	15.5837	+	34.1234i	0.750638	+	1.64367i	0.765215	+	0.643774i	$0.222632\pi$
$431$	15.5837	+	34.1234i	0.750638	+	1.64367i	−0.0145772	+	0.999894i	$0.504640\pi$
$432$	−0.959493	+	0.281733i	−0.0461636	+	0.0135549i
$433$	0.213500	−	0.467501i	0.0102602	−	0.0224667i	−0.904433	−	0.426617i	$-0.859705\pi$
$433$	0.213500	−	0.467501i	0.0102602	−	0.0224667i	0.914693	+	0.404150i	$0.132433\pi$
$434$	0.753948	−	5.24382i	0.0361906	−	0.251711i
$435$	5.45343	−	3.50470i	0.261472	−	0.168038i
$436$	−16.3690			−0.783934
$437$	13.7642	+	10.0205i	0.658430	+	0.479347i
$438$	9.41431			0.449833
$439$	19.9994	−	12.8528i	0.954519	−	0.613432i	0.0320432	−	0.999486i	$-0.489799\pi$
$439$	19.9994	−	12.8528i	0.954519	−	0.613432i	0.922476	+	0.386054i	$0.126162\pi$
$440$	−0.334994	+	2.32994i	−0.0159702	+	0.111075i
$441$	0.0928397	−	0.203291i	0.00442094	−	0.00968051i
$442$	−9.44759	+	2.77406i	−0.449376	+	0.131949i
$443$	2.26387	+	4.95719i	0.107560	+	0.235523i	0.955757	−	0.294157i	$-0.0950390\pi$
$443$	2.26387	+	4.95719i	0.107560	+	0.235523i	−0.848197	+	0.529681i	$0.822312\pi$
$444$	5.32217	+	6.14211i	0.252579	+	0.291492i
$445$	1.65288	+	11.4960i	0.0783541	+	0.544965i
$446$	−10.7144	−	3.14602i	−0.507339	−	0.148968i
$447$	−8.19321	+	9.45547i	−0.387525	+	0.447228i
$448$	−2.26100	−	1.45306i	−0.106822	−	0.0686504i
$449$	0.422475	+	0.271508i	0.0199378	+	0.0128133i	0.550572	−	0.834788i	$-0.314410\pi$
$449$	0.422475	+	0.271508i	0.0199378	+	0.0128133i	−0.530634	+	0.847601i	$0.678046\pi$
$450$	−0.654861	+	0.755750i	−0.0308704	+	0.0356264i
$451$	−2.15235	−	0.631986i	−0.101350	−	0.0297590i
$452$	1.10717	+	7.70051i	0.0520767	+	0.362201i
$453$	−0.221834	−	0.256010i	−0.0104227	−	0.0120284i
$454$	−10.5208	−	23.0372i	−0.493764	−	1.08119i
$455$	5.36177	−	1.57436i	0.251364	−	0.0738071i
$456$	1.47474	−	3.22923i	0.0690610	−	0.151222i
$457$	0.234487	−	1.63089i	0.0109688	−	0.0762899i	−0.983602	−	0.180354i	$-0.942276\pi$
$457$	0.234487	−	1.63089i	0.0109688	−	0.0762899i	0.994571	+	0.104064i	$0.0331847\pi$
$458$	−19.2066	+	12.3433i	−0.897466	+	0.576766i
$459$	4.73572			0.221045
$460$	−4.51537	−	1.61598i	−0.210530	−	0.0753456i
$461$	37.4639			1.74487			0.872435	−	0.488730i	$-0.162540\pi$
$461$	37.4639			1.74487			0.872435	+	0.488730i	$0.162540\pi$
$462$	−5.32216	+	3.42034i	−0.247609	+	0.159129i
$463$	−2.02814	+	14.1061i	−0.0942559	+	0.655564i	0.886845	+	0.462067i	$0.152892\pi$
$463$	−2.02814	+	14.1061i	−0.0942559	+	0.655564i	−0.981101	+	0.193497i	$0.938017\pi$
$464$	2.69293	−	5.89669i	0.125016	−	0.273747i
$465$	−1.89130	+	0.555334i	−0.0877067	+	0.0257530i
$466$	9.61865	+	21.0619i	0.445576	+	0.975674i
$467$	−13.5572	−	15.6459i	−0.627354	−	0.724005i	0.349732	−	0.936850i	$-0.386273\pi$
$467$	−13.5572	−	15.6459i	−0.627354	−	0.724005i	−0.977086	+	0.212845i	$0.931727\pi$
$468$	−0.295899	−	2.05802i	−0.0136779	−	0.0951321i
$469$	−13.1754	−	3.86864i	−0.608383	−	0.178637i
$470$	0.843040	−	0.972920i	0.0388865	−	0.0448774i
$471$	17.1203	+	11.0025i	0.788860	+	0.506970i
$472$	1.19148	+	0.765715i	0.0548421	+	0.0352449i
$473$	5.54735	−	6.40199i	0.255068	−	0.294364i
$474$	0.813640	+	0.238906i	0.0373717	+	0.0109733i
$475$	−0.505223	−	3.51390i	−0.0231812	−	0.161229i
$476$	8.33506	+	9.61917i	0.382037	+	0.440894i
$477$	1.63174	+	3.57301i	0.0747122	+	0.163597i
$478$	−0.403465	+	0.118468i	−0.0184541	+	0.00541860i
$479$	−7.34461	+	16.0825i	−0.335584	+	0.734826i	−0.999921	−	0.0126071i	$-0.995987\pi$
$479$	−7.34461	+	16.0825i	−0.335584	+	0.734826i	0.664337	+	0.747434i	$0.268714\pi$
$480$	−0.142315	+	0.989821i	−0.00649575	+	0.0451790i
$481$	−14.2154	+	9.13569i	−0.648167	+	0.416552i
$482$	1.01883			0.0464065
$483$	−4.66486	−	12.0158i	−0.212258	−	0.546738i
$484$	−5.45917			−0.248144
$485$	−2.42973	+	1.56149i	−0.110328	+	0.0709038i
$486$	−0.142315	+	0.989821i	−0.00645553	+	0.0448992i
$487$	−16.1640	+	35.3942i	−0.732461	+	1.60387i	0.0631104	+	0.998007i	$0.479898\pi$
$487$	−16.1640	+	35.3942i	−0.732461	+	1.60387i	−0.795572	+	0.605860i	$0.792829\pi$
$488$	−2.42445	+	0.711883i	−0.109750	+	0.0322254i
$489$	8.34936	+	18.2826i	0.377571	+	0.826766i
$490$	−0.146353	−	0.168900i	−0.00661154	−	0.00763012i
$491$	0.192064	+	1.33583i	0.00866772	+	0.0602853i	0.993696	−	0.112106i	$-0.0357597\pi$
$491$	0.192064	+	1.33583i	0.00866772	+	0.0602853i	−0.985029	+	0.172391i	$0.944851\pi$
$492$	−0.914376	−	0.268485i	−0.0412232	−	0.0121042i
$493$	−20.1038	+	23.2010i	−0.905429	+	1.04492i
$494$	6.20945	+	3.99057i	0.279376	+	0.179544i
$495$	1.98022	+	1.27261i	0.0890044	+	0.0571997i
$496$	−1.29082	+	1.48969i	−0.0579596	+	0.0668890i
$497$	1.41394	+	0.415169i	0.0634237	+	0.0186229i
$498$	−0.916759	−	6.37620i	−0.0410810	−	0.285724i
$499$	5.40724	+	6.24029i	0.242061	+	0.279354i	0.863761	−	0.503902i	$-0.168103\pi$
$499$	5.40724	+	6.24029i	0.242061	+	0.279354i	−0.621699	+	0.783256i	$0.713557\pi$
$500$	0.415415	+	0.909632i	0.0185779	+	0.0406800i
$501$	−18.8596	+	5.53768i	−0.842585	+	0.247405i
$502$	−4.76930	+	10.4433i	−0.212864	+	0.466108i
$503$	−1.60458	+	11.1601i	−0.0715447	+	0.497604i	0.922269	+	0.386548i	$0.126333\pi$
$503$	−1.60458	+	11.1601i	−0.0715447	+	0.497604i	−0.993814	+	0.111056i	$0.964577\pi$
$504$	−2.26100	+	1.45306i	−0.100713	+	0.0647242i
$505$	6.78612			0.301978
$506$	−2.25252	+	11.0619i	−0.100137	+	0.491761i
$507$	−8.67699			−0.385359
$508$	16.2375	−	10.4352i	0.720423	−	0.462988i
$509$	4.65199	−	32.3553i	0.206196	−	1.43412i	−0.579228	−	0.815166i	$-0.696646\pi$
$509$	4.65199	−	32.3553i	0.206196	−	1.43412i	0.785424	−	0.618959i	$-0.212445\pi$
$510$	1.96729	−	4.30776i	0.0871131	−	0.190751i
$511$	24.2775	−	7.12851i	1.07397	−	0.315347i
$512$	0.415415	+	0.909632i	0.0183589	+	0.0402004i
$513$	−2.32478	−	2.68294i	−0.102642	−	0.118455i
$514$	1.07983	+	7.51037i	0.0476291	+	0.331268i
$515$	5.17632	+	1.51991i	0.228096	+	0.0669750i
$516$	2.35667	−	2.71974i	0.103747	−	0.119730i
$517$	−2.54925	−	1.63831i	−0.112116	−	0.0720526i
$518$	18.3755	+	11.8092i	0.807374	+	0.518868i
$519$	1.88478	−	2.17515i	0.0827326	−	0.0954785i
$520$	−1.99496	−	0.585774i	−0.0874849	−	0.0256879i
$521$	−2.99098	−	20.8027i	−0.131037	−	0.911383i	−0.944206	−	0.329356i	$-0.893169\pi$
$521$	−2.99098	−	20.8027i	−0.131037	−	0.911383i	0.813169	−	0.582028i	$-0.197741\pi$
$522$	−4.24513	−	4.89915i	−0.185804	−	0.214430i
$523$	7.38640	+	16.1740i	0.322985	+	0.707238i	0.999576	−	0.0291208i	$-0.00927074\pi$
$523$	7.38640	+	16.1740i	0.322985	+	0.707238i	−0.676591	+	0.736359i	$0.736543\pi$
$524$	−15.6537	+	4.59633i	−0.683833	+	0.200792i
$525$	−1.11649	+	2.44478i	−0.0487277	+	0.106699i
$526$	−4.09418	+	28.4756i	−0.178515	+	1.24160i
$527$	7.85291	−	5.04676i	0.342078	−	0.219840i
$528$	2.35390			0.102440
$529$	−21.1686	−	8.99399i	−0.920372	−	0.391043i
$530$	3.92797			0.170620
$531$	1.19148	−	0.765715i	0.0517056	−	0.0332292i
$532$	1.35787	−	9.44416i	0.0588709	−	0.409456i
$533$	0.823111	−	1.80236i	0.0356529	−	0.0780689i
$534$	11.1438	−	3.27212i	0.482240	−	0.141598i
$535$	1.49579	+	3.27533i	0.0646688	+	0.141605i
$536$	3.34578	+	3.86123i	0.144516	+	0.166780i
$537$	−1.23377	−	8.58109i	−0.0532413	−	0.370301i
$538$	2.75525	+	0.809014i	0.118787	+	0.0348791i
$539$	−0.344499	+	0.397573i	−0.0148386	+	0.0171247i
$540$	0.841254	+	0.540641i	0.0362018	+	0.0232655i
$541$	−25.6931	−	16.5120i	−1.10463	−	0.709905i	−0.144517	−	0.989502i	$-0.546163\pi$
$541$	−25.6931	−	16.5120i	−1.10463	−	0.709905i	−0.960117	+	0.279597i	$0.909799\pi$
$542$	12.1477	−	14.0192i	0.521790	−	0.602178i
$543$	13.1204	+	3.85249i	0.563049	+	0.165326i
$544$	−0.673963	−	4.68752i	−0.0288959	−	0.200976i
$545$	10.7194	+	12.3709i	0.459170	+	0.529911i
$546$	−2.32139	−	5.08314i	−0.0993465	−	0.217538i
$547$	−32.9897	+	9.68664i	−1.41054	+	0.414171i	−0.896289	−	0.443471i	$-0.853747\pi$
$547$	−32.9897	+	9.68664i	−1.41054	+	0.414171i	−0.514247	+	0.857642i	$0.671929\pi$
$548$	1.75843	−	3.85043i	0.0751165	−	0.164482i
$549$	−0.359602	+	2.50109i	−0.0153474	+	0.106744i
$550$	1.98022	−	1.27261i	0.0844370	−	0.0542644i
$551$	23.0131			0.980392
$552$	−0.956931	+	4.69939i	−0.0407297	+	0.200019i
$553$	2.27910			0.0969173
$554$	27.5188	−	17.6853i	1.16916	−	0.751376i
$555$	1.15662	−	8.04445i	0.0490957	−	0.341468i
$556$	−3.76751	+	8.24970i	−0.159778	+	0.349865i
$557$	−5.72534	+	1.68111i	−0.242591	+	0.0712310i	−0.400768	−	0.916180i	$-0.631257\pi$
$557$	−5.72534	+	1.68111i	−0.242591	+	0.0712310i	0.158177	+	0.987411i	$0.449438\pi$
$558$	0.818841	+	1.79301i	0.0346643	+	0.0759043i
$559$	4.89995	+	5.65485i	0.207246	+	0.239175i
$560$	0.382493	+	2.66030i	0.0161633	+	0.112418i
$561$	−10.6958	−	3.14058i	−0.451579	−	0.132596i
$562$	18.6184	−	21.4868i	0.785371	−	0.906366i
$563$	−37.6931	−	24.2239i	−1.58857	−	1.02091i	−0.972405	−	0.233301i	$-0.925047\pi$
$563$	−37.6931	−	24.2239i	−1.58857	−	1.02091i	−0.616170	−	0.787613i	$-0.711316\pi$
$564$	−1.08299	−	0.695998i	−0.0456023	−	0.0293068i
$565$	5.09461	−	5.87950i	0.214332	−	0.247352i
$566$	−14.4207	−	4.23431i	−0.606148	−	0.177981i
$567$	0.382493	+	2.66030i	0.0160632	+	0.111722i
$568$	−0.359057	−	0.414374i	−0.0150657	−	0.0173867i
$569$	2.73560	+	5.99014i	0.114683	+	0.251120i	0.958266	−	0.285879i	$-0.0922854\pi$
$569$	2.73560	+	5.99014i	0.114683	+	0.251120i	−0.843583	+	0.536998i	$0.819558\pi$
$570$	−3.40624	+	1.00016i	−0.142672	+	0.0418922i
$571$	3.63538	−	7.96036i	0.152136	−	0.333131i	−0.818184	−	0.574957i	$-0.805019\pi$
$571$	3.63538	−	7.96036i	0.152136	−	0.333131i	0.970320	+	0.241826i	$0.0777462\pi$
$572$	−0.696515	+	4.84437i	−0.0291228	+	0.202553i
$573$	9.69312	−	6.22939i	0.404936	−	0.260236i
$574$	−2.56128			−0.106906
$575$	1.73566	+	4.47074i	0.0723821	+	0.186443i
$576$	1.00000			0.0416667
$577$	−29.2735	+	18.8129i	−1.21867	+	0.783192i	−0.982089	−	0.188419i	$-0.939664\pi$
$577$	−29.2735	+	18.8129i	−1.21867	+	0.783192i	−0.236582	+	0.971611i	$0.576027\pi$
$578$	−0.772351	+	5.37182i	−0.0321256	+	0.223438i
$579$	−1.07102	+	2.34521i	−0.0445102	+	0.0974636i
$580$	−6.21991	+	1.82633i	−0.258268	+	0.0758343i
$581$	−7.19218	−	15.7487i	−0.298382	−	0.653365i
$582$	1.89139	+	2.18278i	0.0784005	+	0.0904790i
$583$	−1.31585	−	9.15193i	−0.0544969	−	0.379034i
$584$	−9.03296	−	2.65232i	−0.373787	−	0.109754i
$585$	−1.36158	+	1.57134i	−0.0562943	+	0.0649670i
$586$	19.6253	+	12.6124i	0.810714	+	0.521014i
$587$	−34.7489	−	22.3318i	−1.43424	−	0.921730i	−0.999779	−	0.0210402i	$-0.993302\pi$
$587$	−34.7489	−	22.3318i	−1.43424	−	0.921730i	−0.434462	−	0.900690i	$-0.643061\pi$
$588$	−0.146353	+	0.168900i	−0.00603548	+	0.00696532i
$589$	−6.71417	−	1.97146i	−0.276653	−	0.0812325i
$590$	−0.201562	−	1.40189i	−0.00829817	−	0.0577151i
$591$	12.6829	+	14.6369i	0.521705	+	0.602080i
$592$	−3.37615	−	7.39274i	−0.138759	−	0.303840i
$593$	−35.8502	+	10.5266i	−1.47219	+	0.432274i	−0.916811	−	0.399322i	$-0.869246\pi$
$593$	−35.8502	+	10.5266i	−1.47219	+	0.432274i	−0.555381	+	0.831596i	$0.687427\pi$
$594$	0.977844	−	2.14118i	0.0401214	−	0.0878536i
$595$	1.81138	−	12.5984i	0.0742594	−	0.516485i
$596$	10.5252	−	6.76416i	0.431131	−	0.277071i
$597$	−16.5556			−0.677576
$598$	−9.38830	−	3.35993i	−0.383916	−	0.137398i
$599$	−36.4366			−1.48876			−0.744379	−	0.667757i	$-0.767254\pi$
$599$	−36.4366			−1.48876			−0.744379	+	0.667757i	$0.767254\pi$
$600$	0.841254	−	0.540641i	0.0343440	−	0.0220716i
$601$	1.44474	−	10.0484i	0.0589323	−	0.409883i	−0.938906	−	0.344173i	$-0.888159\pi$
$601$	1.44474	−	10.0484i	0.0589323	−	0.409883i	0.997839	−	0.0657106i	$-0.0209314\pi$
$602$	4.01796	−	8.79810i	0.163760	−	0.358584i
$603$	4.90219	−	1.43941i	0.199633	−	0.0586174i
$604$	0.140722	+	0.308137i	0.00572588	+	0.0125379i
$605$	3.57500	+	4.12577i	0.145344	+	0.167736i
$606$	−0.965765	−	6.71705i	−0.0392315	−	0.272861i
$607$	−19.8573	−	5.83062i	−0.805982	−	0.236658i	−0.147313	−	0.989090i	$-0.547062\pi$
$607$	−19.8573	−	5.83062i	−0.805982	−	0.236658i	−0.658670	+	0.752432i	$0.728881\pi$
$608$	−2.32478	+	2.68294i	−0.0942823	+	0.108808i
$609$	−14.6569	−	9.41943i	−0.593929	−	0.381695i
$610$	2.12568	+	1.36609i	0.0860664	+	0.0553115i
$611$	1.75284	−	2.02288i	0.0709121	−	0.0818370i
$612$	−4.54389	−	1.33421i	−0.183676	−	0.0539321i
$613$	6.37438	+	44.3348i	0.257459	+	1.79067i	0.550778	+	0.834652i	$0.314331\pi$
$613$	6.37438	+	44.3348i	0.257459	+	1.79067i	−0.293319	+	0.956015i	$0.594760\pi$
$614$	2.73631	+	3.15787i	0.110429	+	0.127441i
$615$	0.395881	+	0.866859i	0.0159635	+	0.0349551i
$616$	6.07019	−	1.78237i	0.244575	−	0.0718137i
$617$	11.4115	−	24.9877i	0.459409	−	1.00597i	−0.528213	−	0.849112i	$-0.677138\pi$
$617$	11.4115	−	24.9877i	0.459409	−	1.00597i	0.987622	−	0.156854i	$-0.0501351\pi$
$618$	0.767767	−	5.33994i	0.0308841	−	0.214804i
$619$	−30.7795	+	19.7808i	−1.23713	+	0.795057i	−0.984986	−	0.172632i	$-0.944773\pi$
$619$	−30.7795	+	19.7808i	−1.23713	+	0.795057i	−0.252146	+	0.967689i	$0.581136\pi$
$620$	1.97114			0.0791629
$621$	3.87719	+	2.82265i	0.155586	+	0.113269i
$622$	10.2139			0.409539
$623$	26.2598	−	16.8762i	1.05208	−	0.676130i
$624$	−0.295899	+	2.05802i	−0.0118454	+	0.0823868i
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$	13.1539	−	3.86234i	0.525737	−	0.154370i
$627$	3.47138	+	7.60127i	0.138634	+	0.303565i
$628$	−13.3270	−	15.3802i	−0.531805	−	0.613736i
$629$	5.47742	+	38.0963i	0.218399	+	1.51900i
$630$	2.57879	+	0.757200i	0.102741	+	0.0301676i
$631$	2.87255	−	3.31510i	0.114354	−	0.131972i	−0.695686	−	0.718346i	$-0.744900\pi$
$631$	2.87255	−	3.31510i	0.114354	−	0.131972i	0.810041	+	0.586374i	$0.199445\pi$
$632$	−0.713374	−	0.458458i	−0.0283765	−	0.0182365i
$633$	−18.1296	−	11.6512i	−0.720589	−	0.463094i
$634$	14.0731	−	16.2412i	0.558914	−	0.645021i
$635$	−18.5197	−	5.43788i	−0.734933	−	0.215796i
$636$	−0.559009	−	3.88799i	−0.0221661	−	0.154169i
$637$	−0.304294	−	0.351174i	−0.0120566	−	0.0139140i
$638$	6.33887	+	13.8802i	0.250958	+	0.549522i
$639$	−0.526085	+	0.154473i	−0.0208116	+	0.00611084i
$640$	0.415415	−	0.909632i	0.0164207	−	0.0359564i
$641$	2.96320	−	20.6095i	0.117039	−	0.814027i	−0.843748	−	0.536740i	$-0.819656\pi$
$641$	2.96320	−	20.6095i	0.117039	−	0.814027i	0.960787	−	0.277287i	$-0.0894354\pi$
$642$	3.02912	−	1.94670i	0.119550	−	0.0768300i
$643$	−28.5121			−1.12441			−0.562203	−	0.826999i	$-0.690046\pi$
$643$	−28.5121			−1.12441			−0.562203	+	0.826999i	$0.690046\pi$
$644$	1.09066	+	12.8433i	0.0429780	+	0.506097i
$645$	−3.59873			−0.141700
$646$	14.1431	−	9.08925i	0.556455	−	0.357612i
$647$	−2.15994	+	15.0227i	−0.0849160	+	0.590603i	0.902287	+	0.431136i	$0.141887\pi$
$647$	−2.15994	+	15.0227i	−0.0849160	+	0.590603i	−0.987203	+	0.159468i	$0.949022\pi$
$648$	0.415415	−	0.909632i	0.0163190	−	0.0357337i
$649$	−3.19880	+	0.939253i	−0.125564	+	0.0368689i
$650$	0.863725	+	1.89129i	0.0338781	+	0.0741826i
$651$	3.46928	+	4.00377i	0.135972	+	0.156920i
$652$	−2.86036	−	19.8943i	−0.112021	−	0.779120i
$653$	−38.2461	−	11.2301i	−1.49668	−	0.439466i	−0.572017	−	0.820242i	$-0.693839\pi$
$653$	−38.2461	−	11.2301i	−1.49668	−	0.439466i	−0.924667	+	0.380776i	$0.875657\pi$
$654$	10.7194	−	12.3709i	0.419163	−	0.483740i
$655$	13.7246	+	8.82029i	0.536266	+	0.344637i
$656$	0.801696	+	0.515219i	0.0313010	+	0.0201159i
$657$	−6.16506	+	7.11486i	−0.240522	+	0.277577i
$658$	−3.31982	−	0.974787i	−0.129420	−	0.0380011i
$659$	−5.89947	−	41.0317i	−0.229811	−	1.59837i	−0.698901	−	0.715218i	$-0.746327\pi$
$659$	−5.89947	−	41.0317i	−0.229811	−	1.59837i	0.469091	−	0.883150i	$-0.344582\pi$
$660$	−1.54147	−	1.77896i	−0.0600018	−	0.0692458i
$661$	10.5912	+	23.1915i	0.411950	+	0.902045i	0.995918	+	0.0902679i	$0.0287723\pi$
$661$	10.5912	+	23.1915i	0.411950	+	0.902045i	−0.583967	+	0.811777i	$0.698500\pi$
$662$	−9.80666	+	2.87950i	−0.381147	+	0.111915i
$663$	4.09036	−	8.95664i	0.158856	−	0.347847i
$664$	−0.916759	+	6.37620i	−0.0355772	+	0.247445i
$665$	−8.02663	+	5.15840i	−0.311259	+	0.200034i
$666$	−8.12717			−0.314922
$667$	−30.2878	+	7.01240i	−1.17275	+	0.271521i
$668$	19.6558			0.760506
$669$	9.39401	−	6.03716i	0.363193	−	0.233410i
$670$	0.727107	−	5.05714i	0.0280906	−	0.195374i
$671$	2.47082	−	5.41034i	0.0953850	−	0.208864i
$672$	2.57879	−	0.757200i	0.0994788	−	0.0292096i
$673$	−10.1851	−	22.3022i	−0.392606	−	0.859688i	−0.997967	−	0.0637367i	$-0.979698\pi$
$673$	−10.1851	−	22.3022i	−0.392606	−	0.859688i	0.605360	−	0.795952i	$-0.293029\pi$
$674$	−1.41737	−	1.63574i	−0.0545952	−	0.0630062i
$675$	−0.142315	−	0.989821i	−0.00547770	−	0.0380982i
$676$	8.32551	+	2.44459i	0.320212	+	0.0940227i
$677$	20.0769	−	23.1700i	0.771617	−	0.890494i	−0.224857	−	0.974392i	$-0.572192\pi$
$677$	20.0769	−	23.1700i	0.771617	−	0.890494i	0.996474	+	0.0838980i	$0.0267370\pi$
$678$	−6.54469	−	4.20602i	−0.251347	−	0.161531i
$679$	6.53028	+	4.19676i	0.250609	+	0.161057i
$680$	−3.10124	+	3.57902i	−0.118927	+	0.137249i
$681$	24.3000	+	7.13513i	0.931179	+	0.273419i
$682$	−0.660321	−	4.59263i	−0.0252850	−	0.175861i
$683$	−18.5011	−	21.3514i	−0.707924	−	0.816987i	0.281876	−	0.959451i	$-0.409043\pi$
$683$	−18.5011	−	21.3514i	−0.707924	−	0.816987i	−0.989800	+	0.142463i	$0.954498\pi$
$684$	1.47474	+	3.22923i	0.0563881	+	0.123473i
$685$	−4.06149	+	1.19256i	−0.155182	+	0.0455654i
$686$	7.56592	−	16.5671i	0.288868	−	0.632533i
$687$	3.24918	−	22.5986i	0.123964	−	0.862189i
$688$	−3.02745	+	1.94562i	−0.115420	+	0.0741762i
$689$	8.16698			0.311137
$690$	4.17822	−	2.35425i	0.159062	−	0.0896247i
$691$	17.6587			0.671769			0.335885	−	0.941903i	$-0.390965\pi$
$691$	17.6587			0.671769			0.335885	+	0.941903i	$0.390965\pi$
$692$	−2.42124	+	1.55604i	−0.0920418	+	0.0591517i
$693$	0.900349	−	6.26206i	0.0342014	−	0.237876i
$694$	9.74649	−	21.3418i	0.369972	−	0.810125i
$695$	8.70190	−	2.55511i	0.330082	−	0.0969208i
$696$	2.69293	+	5.89669i	0.102075	+	0.223513i
$697$	−2.95541	−	3.41073i	−0.111944	−	0.129191i
$698$	0.744967	+	5.18136i	0.0281974	+	0.196117i
$699$	−22.2164	−	6.52333i	−0.840302	−	0.246735i
$700$	1.76004	−	2.03119i	0.0665232	−	0.0767719i
$701$	−0.0219128	−	0.0140825i	−0.000827634	−	0.000531888i	0.540227	−	0.841519i	$-0.318338\pi$
$701$	−0.0219128	−	0.0140825i	−0.000827634	−	0.000531888i	−0.541055	+	0.840987i	$0.681975\pi$
$702$	1.74912	+	1.12409i	0.0660163	+	0.0424261i
$703$	18.8939	−	21.8047i	0.712597	−	0.822381i
$704$	−2.25855	−	0.663169i	−0.0851222	−	0.0249941i
$705$	0.183210	+	1.27425i	0.00690009	+	0.0479912i
$706$	17.7991	+	20.5413i	0.669878	+	0.773081i
$707$	−7.57665	−	16.5905i	−0.284949	−	0.623952i
$708$	−1.35894	+	0.399021i	−0.0510721	+	0.0149961i
$709$	8.15230	−	17.8510i	0.306166	−	0.670410i	−0.692534	−	0.721385i	$-0.743506\pi$
$709$	8.15230	−	17.8510i	0.306166	−	0.670410i	0.998700	+	0.0509754i	$0.0162330\pi$
$710$	−0.0780305	+	0.542714i	−0.00292843	+	0.0203677i
$711$	−0.713374	+	0.458458i	−0.0267536	+	0.0171935i
$712$	−11.6143			−0.435263
$713$	9.43732	+	0.548760i	0.353430	+	0.0205512i
$714$	−12.7280			−0.476333
$715$	4.11725	−	2.64600i	0.153976	−	0.0989546i
$716$	−1.23377	+	8.58109i	−0.0461083	+	0.320690i
$717$	0.174681	−	0.382498i	0.00652359	−	0.0142847i
$718$	−27.1950	+	7.98518i	−1.01491	+	0.298004i
$719$	−6.13191	−	13.4270i	−0.228682	−	0.500743i	0.760156	−	0.649741i	$-0.225123\pi$
$719$	−6.13191	−	13.4270i	−0.228682	−	0.500743i	−0.988838	+	0.148998i	$0.952395\pi$
$720$	−0.654861	−	0.755750i	−0.0244052	−	0.0281651i
$721$	−2.06349	−	14.3519i	−0.0768485	−	0.534493i
$722$	6.13809	+	1.80231i	0.228436	+	0.0670749i
$723$	−0.667192	+	0.769981i	−0.0248132	+	0.0286359i
$724$	−11.5035	−	7.39287i	−0.427526	−	0.274754i
$725$	5.45343	+	3.50470i	0.202535	+	0.130161i
$726$	3.57500	−	4.12577i	0.132681	−	0.153122i
$727$	6.16919	+	1.81144i	0.228803	+	0.0671826i	0.394124	−	0.919057i	$-0.371048\pi$
$727$	6.16919	+	1.81144i	0.228803	+	0.0671826i	−0.165321	+	0.986240i	$0.552866\pi$
$728$	0.795274	+	5.53125i	0.0294748	+	0.205002i
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$	3.91085	+	8.56356i	0.144747	+	0.316951i
$731$	16.3523	−	4.80146i	0.604810	−	0.177588i
$732$	1.04967	−	2.29846i	0.0387970	−	0.0849536i
$733$	3.51682	−	24.4600i	0.129897	−	0.903450i	−0.815785	−	0.578355i	$-0.803695\pi$
$733$	3.51682	−	24.4600i	0.129897	−	0.903450i	0.945681	−	0.325095i	$-0.105396\pi$
$734$	−17.8332	+	11.4607i	−0.658237	+	0.423023i
$735$	0.223487			0.00824343
$736$	2.24214	−	4.23943i	0.0826464	−	0.156268i
$737$	−12.0264			−0.442998
$738$	0.801696	−	0.515219i	0.0295108	−	0.0189655i
$739$	4.57407	−	31.8134i	0.168260	−	1.17027i	−0.714219	−	0.699922i	$-0.753218\pi$
$739$	4.57407	−	31.8134i	0.168260	−	1.17027i	0.882479	−	0.470352i	$-0.155873\pi$
$740$	−3.37615	+	7.39274i	−0.124110	+	0.271762i
$741$	−7.08220	+	2.07952i	−0.260171	+	0.0763931i
$742$	−4.38555	−	9.60302i	−0.160999	−	0.352538i
$743$	−24.4724	−	28.2426i	−0.897805	−	1.03612i	−0.999148	−	0.0412702i	$-0.986860\pi$
$743$	−24.4724	−	28.2426i	−0.897805	−	1.03612i	0.101343	−	0.994852i	$-0.467686\pi$
$744$	−0.280522	−	1.95108i	−0.0102845	−	0.0715299i
$745$	−12.0046	−	3.52486i	−0.439814	−	0.129141i
$746$	7.48345	−	8.63636i	0.273989	−	0.316200i
$747$	5.41916	+	3.48268i	0.198277	+	0.127425i
$748$	9.37779	+	6.02674i	0.342886	+	0.220359i
$749$	6.33741	−	7.31376i	0.231564	−	0.267239i
$750$	−0.959493	−	0.281733i	−0.0350357	−	0.0102874i
$751$	6.32545	+	43.9945i	0.230819	+	1.60538i	0.694576	+	0.719419i	$0.255592\pi$
$751$	6.32545	+	43.9945i	0.230819	+	1.60538i	−0.463757	+	0.885963i	$0.653499\pi$
$752$	0.843040	+	0.972920i	0.0307425	+	0.0354787i
$753$	−4.76930	−	10.4433i	−0.173803	−	0.380576i
$754$	−12.9324	+	3.79728i	−0.470968	+	0.138289i
$755$	0.140722	−	0.308137i	0.00512138	−	0.0112143i
$756$	0.382493	−	2.66030i	0.0139111	−	0.0967541i
$757$	10.4193	−	6.69610i	0.378697	−	0.243374i	−0.337420	−	0.941354i	$-0.609554\pi$
$757$	10.4193	−	6.69610i	0.378697	−	0.243374i	0.716117	+	0.697980i	$0.245918\pi$
$758$	−2.43401			−0.0884074
$759$	−6.88493	−	8.94633i	−0.249907	−	0.324731i
$760$	3.55004			0.128773
$761$	21.4150	−	13.7626i	0.776295	−	0.498894i	−0.0915073	−	0.995804i	$-0.529168\pi$
$761$	21.4150	−	13.7626i	0.776295	−	0.498894i	0.867802	+	0.496910i	$0.165532\pi$
$762$	−2.74690	+	19.1051i	−0.0995097	+	0.692105i
$763$	18.2759	−	40.0186i	0.661632	−	1.44877i
$764$	−11.0555	+	3.24619i	−0.399974	+	0.117443i
$765$	1.96729	+	4.30776i	0.0711275	+	0.155748i
$766$	−11.8147	−	13.6349i	−0.426882	−	0.492648i
$767$	−0.419084	−	2.91480i	−0.0151323	−	0.105247i
$768$	−0.959493	−	0.281733i	−0.0346227	−	0.0101661i
$769$	−5.66807	+	6.54131i	−0.204396	+	0.235886i	−0.848688	−	0.528894i	$-0.822607\pi$
$769$	−5.66807	+	6.54131i	−0.204396	+	0.235886i	0.644292	+	0.764780i	$0.277152\pi$
$770$	−5.32216	−	3.42034i	−0.191797	−	0.123261i
$771$	−6.38309	−	4.10216i	−0.229881	−	0.147736i
$772$	1.68836	−	1.94847i	0.0607654	−	0.0701270i
$773$	−4.66484	−	1.36972i	−0.167783	−	0.0492654i	0.196762	−	0.980451i	$-0.436957\pi$
$773$	−4.66484	−	1.36972i	−0.167783	−	0.0492654i	−0.364545	+	0.931186i	$0.618775\pi$
$774$	0.512153	+	3.56210i	0.0184090	+	0.128037i
$775$	−1.29082	−	1.48969i	−0.0463677	−	0.0535112i
$776$	−1.19981	−	2.62723i	−0.0430708	−	0.0943119i
$777$	−20.9582	+	6.15389i	−0.751873	+	0.220770i
$778$	13.3361	−	29.2020i	0.478123	−	1.04694i
$779$	−0.481467	+	3.34867i	−0.0172503	+	0.119979i
$780$	1.74912	−	1.12409i	0.0626286	−	0.0402490i
$781$	1.29063			0.0461823
$782$	−15.8443	+	16.2721i	−0.566592	+	0.581887i
$783$	6.48250			0.231666
$784$	0.188009	−	0.120826i	0.00671460	−	0.00431521i
$785$	−2.89623	+	20.1438i	−0.103371	+	0.718961i
$786$	6.77729	−	14.8402i	0.241738	−	0.529332i
$787$	9.15033	−	2.68678i	0.326174	−	0.0957734i	−0.114546	−	0.993418i	$-0.536541\pi$
$787$	9.15033	−	2.68678i	0.326174	−	0.0957734i	0.440720	+	0.897645i	$0.354723\pi$
$788$	−8.04548	−	17.6171i	−0.286608	−	0.627585i
$789$	−18.8393	−	21.7417i	−0.670698	−	0.774026i
$790$	0.120682	+	0.839358i	0.00429366	+	0.0298630i
$791$	−20.0622	−	5.89078i	−0.713328	−	0.209452i
$792$	−1.54147	+	1.77896i	−0.0547739	+	0.0632124i
$793$	4.41969	+	2.84036i	0.156948	+	0.100864i
$794$	10.1654	+	6.53292i	0.360758	+	0.231845i
$795$	−2.57228	+	2.96856i	−0.0912292	+	0.105284i
$796$	15.8850	+	4.66425i	0.563028	+	0.165320i
$797$	4.26786	+	29.6836i	0.151175	+	1.05145i	0.914254	+	0.405142i	$0.132778\pi$
$797$	4.26786	+	29.6836i	0.151175	+	1.05145i	−0.763078	+	0.646306i	$0.776313\pi$
$798$	6.24821	+	7.21082i	0.221184	+	0.255260i
$799$	−2.53261	−	5.54563i	−0.0895971	−	0.196190i
$800$	−0.959493	+	0.281733i	−0.0339232	+	0.00996075i
$801$	−4.82474	+	10.5647i	−0.170474	+	0.373286i
$802$	1.47174	−	10.2362i	0.0519690	−	0.361453i
$803$	18.6424	−	11.9808i	0.657877	−	0.422792i
$804$	−5.10914			−0.180186
$805$	8.99210	−	9.23485i	0.316930	−	0.325486i
$806$	4.09837			0.144359
$807$	−2.41572	+	1.55249i	−0.0850372	+	0.0546501i
$808$	−0.965765	+	6.71705i	−0.0339755	+	0.236305i
$809$	−22.7547	+	49.8258i	−0.800012	+	1.75178i	−0.154557	+	0.987984i	$0.549395\pi$
$809$	−22.7547	+	49.8258i	−0.800012	+	1.75178i	−0.645455	+	0.763798i	$0.723332\pi$
$810$	−0.959493	+	0.281733i	−0.0337131	+	0.00989907i
$811$	10.7722	+	23.5879i	0.378264	+	0.828283i	0.999019	+	0.0442787i	$0.0140990\pi$
$811$	10.7722	+	23.5879i	0.378264	+	0.828283i	−0.620755	+	0.784005i	$0.713174\pi$
$812$	11.4095	+	13.1672i	0.400393	+	0.462079i
$813$	2.63996	+	18.3613i	0.0925873	+	0.643959i
$814$	18.3556	+	5.38969i	0.643363	+	0.188909i
$815$	−13.1619	+	15.1897i	−0.461043	+	0.532072i
$816$	3.98394	+	2.56032i	0.139466	+	0.0896293i
$817$	−10.7476	−	6.90703i	−0.376009	−	0.241647i
$818$	−12.7801	+	14.7490i	−0.446846	+	0.515687i
$819$	5.36177	+	1.57436i	0.187355	+	0.0550125i
$820$	−0.135623	−	0.943278i	−0.00473616	−	0.0329407i
$821$	30.8831	+	35.6410i	1.07783	+	1.24388i	0.968272	+	0.249899i	$0.0803975\pi$
$821$	30.8831	+	35.6410i	1.07783	+	1.24388i	0.109556	+	0.993981i	$0.465057\pi$
$822$	1.75843	+	3.85043i	0.0613324	+	0.134299i
$823$	−21.8092	+	6.40376i	−0.760221	+	0.223221i	−0.638792	−	0.769379i	$-0.720566\pi$
$823$	−21.8092	+	6.40376i	−0.760221	+	0.223221i	−0.121429	+	0.992600i	$0.538748\pi$
$824$	−2.24110	+	4.90733i	−0.0780725	+	0.170955i
$825$	−0.334994	+	2.32994i	−0.0116630	+	0.0811180i
$826$	−3.20227	+	2.05798i	−0.111421	+	0.0716062i
$827$	1.46436			0.0509209			0.0254604	−	0.999676i	$-0.491895\pi$
$827$	1.46436			0.0509209			0.0254604	+	0.999676i	$0.491895\pi$
$828$	−2.92491	−	3.80065i	−0.101648	−	0.132082i
$829$	9.24247			0.321004			0.160502	−	0.987036i	$-0.448689\pi$
$829$	9.24247			0.321004			0.160502	+	0.987036i	$0.448689\pi$
$830$	5.41916	−	3.48268i	0.188102	−	0.120886i
$831$	−4.65536	+	32.3787i	−0.161493	+	1.12321i
$832$	0.863725	−	1.89129i	0.0299443	−	0.0655688i
$833$	−1.01550	+	0.298177i	−0.0351850	+	0.0103312i
$834$	−3.76751	−	8.24970i	−0.130458	−	0.285664i
$835$	−12.8718	−	14.8549i	−0.445448	−	0.514074i
$836$	−1.18924	−	8.27136i	−0.0411308	−	0.286071i
$837$	−1.89130	−	0.555334i	−0.0653727	−	0.0191952i
$838$	6.99381	−	8.07129i	0.241597	−	0.278818i
$839$	−14.0375	−	9.02134i	−0.484628	−	0.311451i	0.275414	−	0.961326i	$-0.411185\pi$
$839$	−14.0375	−	9.02134i	−0.484628	−	0.311451i	−0.760042	+	0.649875i	$0.774821\pi$
$840$	−2.26100	−	1.45306i	−0.0780119	−	0.0501352i
$841$	−8.52812	+	9.84198i	−0.294073	+	0.339379i
$842$	−36.7184	−	10.7815i	−1.26540	−	0.371555i
$843$	4.04617	+	28.1417i	0.139357	+	0.969252i
$844$	14.1127	+	16.2870i	0.485781	+	0.560621i
$845$	−3.60455	−	7.89287i	−0.124000	−	0.271523i
$846$	1.23521	−	0.362690i	0.0424674	−	0.0124696i
$847$	6.09512	−	13.3465i	0.209431	−	0.458590i
$848$	−0.559009	+	3.88799i	−0.0191964	+	0.133514i
$849$	12.6436	−	8.12557i	0.433929	−	0.278869i
$850$	4.73572			0.162434
$851$	−18.2223	+	34.4546i	−0.624651	+	1.18109i
$852$	0.548295			0.0187843
$853$	−39.6690	+	25.4937i	−1.35824	+	0.872887i	−0.998195	−	0.0600483i	$-0.980875\pi$
$853$	−39.6690	+	25.4937i	−1.35824	+	0.872887i	−0.360044	+	0.932935i	$0.617238\pi$
$854$	0.966486	−	6.72205i	0.0330725	−	0.230024i
$855$	1.47474	−	3.22923i	0.0504350	−	0.110437i
$856$	−3.45487	+	1.01444i	−0.118085	+	0.0346728i
$857$	−4.25807	−	9.32388i	−0.145453	−	0.318498i	0.822857	−	0.568248i	$-0.192379\pi$
$857$	−4.25807	−	9.32388i	−0.145453	−	0.318498i	−0.968310	+	0.249751i	$0.919651\pi$
$858$	−3.20501	−	3.69878i	−0.109417	−	0.126274i
$859$	−1.45003	−	10.0852i	−0.0494744	−	0.344102i	−0.999491	−	0.0319024i	$-0.989843\pi$
$859$	−1.45003	−	10.0852i	−0.0494744	−	0.344102i	0.950017	−	0.312199i	$-0.101066\pi$
$860$	3.45296	+	1.01388i	0.117745	+	0.0345730i
$861$	1.67728	−	1.93568i	0.0571615	−	0.0659679i
$862$	31.5583	+	20.2813i	1.07488	+	0.690784i
$863$	15.1259	+	9.72080i	0.514890	+	0.330900i	0.772148	−	0.635443i	$-0.219182\pi$
$863$	15.1259	+	9.72080i	0.514890	+	0.330900i	−0.257257	+	0.966343i	$0.582819\pi$
$864$	−0.654861	+	0.755750i	−0.0222788	+	0.0257111i
$865$	2.76155	+	0.810865i	0.0938956	+	0.0275702i
$866$	−0.0731420	−	0.508714i	−0.00248547	−	0.0172868i
$867$	−3.55397	−	4.10150i	−0.120699	−	0.139294i
$868$	−2.20076	−	4.81900i	−0.0746987	−	0.163567i
$869$	1.91522	−	0.562361i	0.0649695	−	0.0190768i
$870$	2.69293	−	5.89669i	0.0912988	−	0.199916i
$871$	1.51179	−	10.5147i	0.0512251	−	0.356278i
$872$	−13.7705	+	8.84977i	−0.466328	+	0.299691i
$873$	−2.88823			−0.0977517
$874$	16.9967	+	0.988322i	0.574921	+	0.0334305i
$875$	−2.68765			−0.0908593
$876$	7.91982	−	5.08976i	0.267586	−	0.171967i
$877$	−1.20492	+	8.38042i	−0.0406874	+	0.282987i	0.959312	+	0.282347i	$0.0911128\pi$
$877$	−1.20492	+	8.38042i	−0.0406874	+	0.282987i	−1.00000		0.000640086i	$0.999796\pi$
$878$	9.87580	−	21.6250i	0.333292	−	0.729808i
$879$	−22.3837	+	6.57244i	−0.754982	+	0.221683i
$880$	0.977844	+	2.14118i	0.0329631	+	0.0721791i
$881$	12.0572	+	13.9147i	0.406216	+	0.468798i	0.921589	−	0.388168i	$-0.126892\pi$
$881$	12.0572	+	13.9147i	0.406216	+	0.468798i	−0.515373	+	0.856966i	$0.672347\pi$
$882$	−0.0318055	−	0.221212i	−0.00107095	−	0.00744859i
$883$	25.9972	+	7.63345i	0.874874	+	0.256886i	0.688187	−	0.725533i	$-0.258407\pi$
$883$	25.9972	+	7.63345i	0.874874	+	0.256886i	0.186687	+	0.982419i	$0.440225\pi$
$884$	−6.44805	+	7.44144i	−0.216871	+	0.250283i
$885$	1.19148	+	0.765715i	0.0400510	+	0.0257392i
$886$	4.58455	+	2.94631i	0.154021	+	0.0989833i
$887$	1.44891	−	1.67213i	0.0486495	−	0.0561445i	−0.730903	−	0.682481i	$-0.760901\pi$
$887$	1.44891	−	1.67213i	0.0486495	−	0.0561445i	0.779553	+	0.626337i	$0.215446\pi$
$888$	7.79797	+	2.28969i	0.261683	+	0.0768369i
$889$	7.38272	+	51.3479i	0.247608	+	1.72215i
$890$	7.60573	+	8.77748i	0.254945	+	0.294222i
$891$	0.977844	+	2.14118i	0.0327590	+	0.0717322i
$892$	−10.7144	+	3.14602i	−0.358743	+	0.105336i
$893$	−1.89852	+	4.15717i	−0.0635314	+	0.139114i
$894$	−1.78055	+	12.3840i	−0.0595506	+	0.414184i
$895$	7.29310	−	4.68699i	0.243781	−	0.156669i
$896$	−2.68765			−0.0897882
$897$	8.68729	−	4.89492i	0.290060	−	0.163436i
$898$	0.502197			0.0167585
$899$	10.7495	−	6.90826i	0.358515	−	0.230403i
$900$	−0.142315	+	0.989821i	−0.00474383	+	0.0329940i
$901$	7.72746	−	16.9208i	0.257439	−	0.563713i
$902$	−2.15235	+	0.631986i	−0.0716653	+	0.0210428i
$903$	4.01796	+	8.79810i	0.133709	+	0.292782i
$904$	5.09461	+	5.87950i	0.169444	+	0.195549i
$905$	1.94605	+	13.5351i	0.0646890	+	0.449922i
$906$	−0.325028	−	0.0954367i	−0.0107983	−	0.00317067i
$907$	−4.86203	+	5.61109i	−0.161441	+	0.186313i	−0.830707	−	0.556710i	$-0.812063\pi$
$907$	−4.86203	+	5.61109i	−0.161441	+	0.186313i	0.669266	+	0.743023i	$0.266609\pi$
$908$	−21.3055	−	13.6922i	−0.707048	−	0.454392i
$909$	5.70885	+	3.66885i	0.189350	+	0.121688i
$910$	3.65945	−	4.22323i	0.121310	−	0.139999i
$911$	32.8257	+	9.63850i	1.08756	+	0.319338i	0.775901	−	0.630855i	$-0.217296\pi$
$911$	32.8257	+	9.63850i	1.08756	+	0.319338i	0.311663	+	0.950193i	$0.399114\pi$
$912$	−0.505223	−	3.51390i	−0.0167296	−	0.116357i
$913$	−9.92982	−	11.4596i	−0.328629	−	0.379258i
$914$	−0.684464	−	1.49877i	−0.0226400	−	0.0495748i
$915$	−2.42445	+	0.711883i	−0.0801499	+	0.0235341i
$916$	−9.48432	+	20.7678i	−0.313371	+	0.686186i
$917$	6.24019	−	43.4015i	0.206069	−	1.43324i
$918$	3.98394	−	2.56032i	0.131490	−	0.0845033i
$919$	39.7353			1.31075			0.655374	−	0.755304i	$-0.272511\pi$
$919$	39.7353			1.31075			0.655374	+	0.755304i	$0.272511\pi$
$920$	−4.67224	+	1.08174i	−0.154039	+	0.0356640i
$921$	−4.17847			−0.137685
$922$	31.5167	−	20.2545i	1.03795	−	0.667048i
$923$	−0.162240	+	1.12840i	−0.00534019	+	0.0371418i
$924$	−2.62811	+	5.75475i	−0.0864583	+	0.189317i
$925$	7.79797	−	2.28969i	0.256396	−	0.0752845i
$926$	5.92013	+	12.9633i	0.194547	+	0.425999i
$927$	3.53288	+	4.07716i	0.116035	+	0.133911i
$928$	−0.922556	−	6.41652i	−0.0302844	−	0.210633i
$929$	−24.8365	−	7.29264i	−0.814858	−	0.239264i	−0.152357	−	0.988325i	$-0.548686\pi$
$929$	−24.8365	−	7.29264i	−0.814858	−	0.239264i	−0.662500	+	0.749062i	$0.730505\pi$
$930$	−1.29082	+	1.48969i	−0.0423277	+	0.0488488i
$931$	0.667439	+	0.428937i	0.0218744	+	0.0140578i
$932$	19.4787	+	12.5182i	0.638045	+	0.410046i
$933$	−6.68867	+	7.71913i	−0.218977	+	0.252713i
$934$	−19.8639	−	5.83256i	−0.649966	−	0.190847i
$935$	−1.58644	−	11.0339i	−0.0518821	−	0.360848i
$936$	−1.36158	−	1.57134i	−0.0445045	−	0.0513610i
$937$	−4.22364	−	9.24849i	−0.137980	−	0.302135i	0.828010	−	0.560714i	$-0.189473\pi$
$937$	−4.22364	−	9.24849i	−0.137980	−	0.302135i	−0.965990	+	0.258579i	$0.916746\pi$
$938$	−13.1754	+	3.86864i	−0.430192	+	0.126316i
$939$	−5.69503	+	12.4704i	−0.185850	+	0.406955i
$940$	0.183210	−	1.27425i	0.00597565	−	0.0415616i
$941$	−26.9922	+	17.3468i	−0.879920	+	0.565490i	−0.900772	−	0.434293i	$-0.856998\pi$
$941$	−26.9922	+	17.3468i	−0.879920	+	0.565490i	0.0208522	+	0.999783i	$0.493362\pi$
$942$	20.3509			0.663068
$943$	−0.386722	−	4.55393i	−0.0125934	−	0.148296i
$944$	1.41631			0.0460970
$945$	−2.26100	+	1.45306i	−0.0735503	+	0.0472679i
$946$	1.20556	−	8.38482i	0.0391960	−	0.272614i
$947$	1.06715	−	2.33673i	0.0346776	−	0.0759334i	−0.891500	−	0.453020i	$-0.850347\pi$
$947$	1.06715	−	2.33673i	0.0346776	−	0.0759334i	0.926178	+	0.377086i	$0.123074\pi$
$948$	0.813640	−	0.238906i	0.0264258	−	0.00775932i
$949$	8.13137	+	17.8052i	0.263956	+	0.577982i
$950$	−2.32478	−	2.68294i	−0.0754259	−	0.0870461i
$951$	3.05837	+	21.2715i	0.0991746	+	0.689774i
$952$	12.2124	+	3.58589i	0.395807	+	0.116219i
$953$	−17.9864	+	20.7575i	−0.582638	+	0.672400i	−0.968170	−	0.250294i	$-0.919473\pi$
$953$	−17.9864	+	20.7575i	−0.582638	+	0.672400i	0.385532	+	0.922695i	$0.374018\pi$
$954$	3.30442	+	2.12362i	0.106985	+	0.0687548i
$955$	9.69312	+	6.22939i	0.313662	+	0.201578i
$956$	−0.275368	+	0.317791i	−0.00890602	+	0.0102781i
$957$	−14.6410	−	4.29899i	−0.473277	−	0.138967i
$958$	2.51615	+	17.5002i	0.0812932	+	0.565407i
$959$	7.45017	+	8.59795i	0.240578	+	0.277642i
$960$	0.415415	+	0.909632i	0.0134075	+	0.0293582i
$961$	26.0163	−	7.63907i	0.839235	−	0.246422i
$962$	−7.01964	+	15.3709i	−0.226322	+	0.495577i
$963$	−0.512436	+	3.56407i	−0.0165130	+	0.114851i
$964$	0.857095	−	0.550822i	0.0276052	−	0.0177408i
$965$	−2.57820			−0.0829951
$966$	−10.4206	−	7.58632i	−0.335276	−	0.244086i
$967$	27.8476			0.895519			0.447759	−	0.894154i	$-0.352222\pi$
$967$	27.8476			0.895519			0.447759	+	0.894154i	$0.352222\pi$
$968$	−4.59255	+	2.95145i	−0.147610	+	0.0948633i
$969$	−2.39260	+	16.6409i	−0.0768613	+	0.534582i
$970$	−1.19981	+	2.62723i	−0.0385237	+	0.0843551i
$971$	7.91615	−	2.32439i	0.254041	−	0.0745932i	−0.152232	−	0.988345i	$-0.548646\pi$
$971$	7.91615	−	2.32439i	0.254041	−	0.0745932i	0.406274	+	0.913752i	$0.366828\pi$
$972$	0.415415	+	0.909632i	0.0133244	+	0.0291765i
$973$	−15.9623	−	18.4215i	−0.511727	−	0.590565i
$974$	5.53754	+	38.5145i	0.177434	+	1.23408i
$975$	−1.99496	−	0.585774i	−0.0638900	−	0.0187598i
$976$	−1.65471	+	1.90963i	−0.0529658	+	0.0611258i
$977$	−36.8181	−	23.6616i	−1.17792	−	0.757000i	−0.202914	−	0.979197i	$-0.565041\pi$
$977$	−36.8181	−	23.6616i	−1.17792	−	0.757000i	−0.975002	+	0.222196i	$0.928677\pi$
$978$	16.9082	+	10.8663i	0.540666	+	0.347465i
$979$	17.9031	−	20.6613i	0.572185	−	0.660337i
$980$	−0.214434	−	0.0629635i	−0.00684984	−	0.00201129i
$981$	2.32956	+	16.2024i	0.0743770	+	0.517303i
$982$	0.883780	+	1.01994i	0.0282026	+	0.0325475i
$983$	−9.81316	−	21.4878i	−0.312991	−	0.685355i	0.686121	−	0.727488i	$-0.259312\pi$
$983$	−9.81316	−	21.4878i	−0.312991	−	0.685355i	−0.999112	+	0.0421325i	$0.986585\pi$
$984$	−0.914376	+	0.268485i	−0.0291492	+	0.00855899i
$985$	−8.04548	+	17.6171i	−0.256350	+	0.561329i
$986$	−4.36897	+	30.3868i	−0.139136	+	0.967714i
$987$	2.91071	−	1.87060i	0.0926490	−	0.0595419i
$988$	7.38119			0.234827
$989$	16.2496	+	5.81550i	0.516708	+	0.184922i
$990$	2.35390			0.0748117
$991$	−25.7828	+	16.5696i	−0.819018	+	0.526351i	−0.881771	−	0.471678i	$-0.843648\pi$
$991$	−25.7828	+	16.5696i	−0.819018	+	0.526351i	0.0627530	+	0.998029i	$0.480012\pi$
$992$	−0.280522	+	1.95108i	−0.00890660	+	0.0619468i
$993$	4.24582	−	9.29705i	0.134737	−	0.295033i
$994$	1.41394	−	0.415169i	0.0448473	−	0.0131684i
$995$	−6.87745	−	15.0595i	−0.218030	−	0.477418i
$996$	−4.21846	−	4.86836i	−0.133667	−	0.154260i
$997$	4.78135	+	33.2550i	0.151427	+	1.05320i	0.913831	+	0.406095i	$0.133110\pi$
$997$	4.78135	+	33.2550i	0.151427	+	1.05320i	−0.762404	+	0.647101i	$0.775981\pi$
$998$	7.92261	+	2.32629i	0.250786	+	0.0736374i
$999$	5.32217	−	6.14211i	0.168386	−	0.194328i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.g.541.3	yes	30
23.2	even	11	inner	690.2.m.g.301.3	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.g.301.3	✓	30	23.2	even	11	inner
690.2.m.g.541.3	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)

\(f(q)\)	\(=\)	\(q+(0.841254 - 0.540641i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(0.415415 + 0.909632i) q^{6} +(1.76004 + 2.03119i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(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} +(1.76004 + 2.03119i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(-0.654861 + 0.755750i) q^{10} +(1.98022 + 1.27261i) q^{11} +(0.841254 + 0.540641i) q^{12} +(-1.36158 + 1.57134i) q^{13} +(2.57879 + 0.757200i) q^{14} +(-0.142315 - 0.989821i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(1.96729 + 4.30776i) q^{17} +(-0.959493 + 0.281733i) q^{18} +(1.47474 - 3.22923i) q^{19} +(-0.142315 + 0.989821i) q^{20} +(-2.26100 + 1.45306i) q^{21} +2.35390 q^{22} +(-0.956931 + 4.69939i) q^{23} +1.00000 q^{24} +(0.841254 - 0.540641i) q^{25} +(-0.295899 + 2.05802i) q^{26} +(0.415415 - 0.909632i) q^{27} +(2.57879 - 0.757200i) q^{28} +(2.69293 + 5.89669i) q^{29} +(-0.654861 - 0.755750i) q^{30} +(-0.280522 - 1.95108i) q^{31} +(-0.959493 - 0.281733i) q^{32} +(-1.54147 + 1.77896i) q^{33} +(3.98394 + 2.56032i) q^{34} +(-2.26100 - 1.45306i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(7.79797 + 2.28969i) q^{37} +(-0.505223 - 3.51390i) q^{38} +(-1.36158 - 1.57134i) q^{39} +(0.415415 + 0.909632i) q^{40} +(-0.914376 + 0.268485i) q^{41} +(-1.11649 + 2.44478i) q^{42} +(0.512153 - 3.56210i) q^{43} +(1.98022 - 1.27261i) q^{44} +1.00000 q^{45} +(1.73566 + 4.47074i) q^{46} -1.28736 q^{47} +(0.841254 - 0.540641i) q^{48} +(-0.0318055 + 0.221212i) q^{49} +(0.415415 - 0.909632i) q^{50} +(-4.54389 + 1.33421i) q^{51} +(0.863725 + 1.89129i) q^{52} +(-2.57228 - 2.96856i) q^{53} +(-0.142315 - 0.989821i) q^{54} +(-2.25855 - 0.663169i) q^{55} +(1.76004 - 2.03119i) q^{56} +(2.98648 + 1.91930i) q^{57} +(5.45343 + 3.50470i) q^{58} +(-0.927486 + 1.07038i) q^{59} +(-0.959493 - 0.281733i) q^{60} +(-0.359602 - 2.50109i) q^{61} +(-1.29082 - 1.48969i) q^{62} +(-1.11649 - 2.44478i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(0.863725 - 1.89129i) q^{65} +(-0.334994 + 2.32994i) q^{66} +(-4.29809 + 2.76221i) q^{67} +4.73572 q^{68} +(-4.51537 - 1.61598i) q^{69} -2.68765 q^{70} +(0.461255 - 0.296431i) q^{71} +(-0.142315 + 0.989821i) q^{72} +(3.91085 - 8.56356i) q^{73} +(7.79797 - 2.28969i) q^{74} +(0.415415 + 0.909632i) q^{75} +(-2.32478 - 2.68294i) q^{76} +(0.900349 + 6.26206i) q^{77} +(-1.99496 - 0.585774i) q^{78} +(0.555315 - 0.640868i) q^{79} +(0.841254 + 0.540641i) q^{80} +(0.841254 + 0.540641i) q^{81} +(-0.624068 + 0.720213i) q^{82} +(-6.18083 - 1.81486i) q^{83} +(0.382493 + 2.66030i) q^{84} +(-3.10124 - 3.57902i) q^{85} +(-1.49497 - 3.27352i) q^{86} +(-6.21991 + 1.82633i) q^{87} +(0.977844 - 2.14118i) q^{88} +(1.65288 - 11.4960i) q^{89} +(0.841254 - 0.540641i) q^{90} -5.58813 q^{91} +(3.87719 + 2.82265i) q^{92} +1.97114 q^{93} +(-1.08299 + 0.695998i) q^{94} +(-0.505223 + 3.51390i) q^{95} +(0.415415 - 0.909632i) q^{96} +(2.77124 - 0.813708i) q^{97} +(0.0928397 + 0.203291i) q^{98} +(-1.54147 - 1.77896i) 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	\( 30 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} - 3 q^{9} - 3 q^{10} + 8 q^{11} - 3 q^{12} - 5 q^{13} - 8 q^{14} - 3 q^{15} - 3 q^{16} + 4 q^{17} - 3 q^{18} + 6 q^{19} - 3 q^{20} + 3 q^{21} + 8 q^{22} + q^{23} + 30 q^{24} - 3 q^{25} - 5 q^{26} - 3 q^{27} - 8 q^{28} - 10 q^{29} - 3 q^{30} - 10 q^{31} - 3 q^{32} - 14 q^{33} - 7 q^{34} + 3 q^{35} - 3 q^{36} - 12 q^{37} - 5 q^{38} - 5 q^{39} - 3 q^{40} + 5 q^{41} + 3 q^{42} + 2 q^{43} + 8 q^{44} + 30 q^{45} - 21 q^{46} + 96 q^{47} - 3 q^{48} - 43 q^{49} - 3 q^{50} + 15 q^{51} - 16 q^{52} + 12 q^{53} - 3 q^{54} + 8 q^{55} - 8 q^{56} + 17 q^{57} + q^{58} - 9 q^{59} - 3 q^{60} + q^{61} - 32 q^{62} + 3 q^{63} - 3 q^{64} - 16 q^{65} - 3 q^{66} - 28 q^{67} + 4 q^{68} + 23 q^{69} + 14 q^{70} + 3 q^{71} - 3 q^{72} - 27 q^{73} - 12 q^{74} - 3 q^{75} - 16 q^{76} + 47 q^{77} + 6 q^{78} + 2 q^{79} - 3 q^{80} - 3 q^{81} + 27 q^{82} + 11 q^{83} + 3 q^{84} - 7 q^{85} + 2 q^{86} - 32 q^{87} - 3 q^{88} + 25 q^{89} - 3 q^{90} - 90 q^{91} - 10 q^{92} + 56 q^{93} - 25 q^{94} - 5 q^{95} - 3 q^{96} - 7 q^{97} - 32 q^{98} - 14 q^{99}+O(q^{100}) \) 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 + 8 * q^11 - 3 * q^12 - 5 * q^13 - 8 * q^14 - 3 * q^15 - 3 * q^16 + 4 * q^17 - 3 * q^18 + 6 * q^19 - 3 * q^20 + 3 * q^21 + 8 * q^22 + q^23 + 30 * q^24 - 3 * q^25 - 5 * q^26 - 3 * q^27 - 8 * q^28 - 10 * q^29 - 3 * q^30 - 10 * q^31 - 3 * q^32 - 14 * q^33 - 7 * q^34 + 3 * q^35 - 3 * q^36 - 12 * q^37 - 5 * q^38 - 5 * q^39 - 3 * q^40 + 5 * q^41 + 3 * q^42 + 2 * q^43 + 8 * q^44 + 30 * q^45 - 21 * q^46 + 96 * q^47 - 3 * q^48 - 43 * q^49 - 3 * q^50 + 15 * q^51 - 16 * q^52 + 12 * q^53 - 3 * q^54 + 8 * q^55 - 8 * q^56 + 17 * q^57 + q^58 - 9 * q^59 - 3 * q^60 + q^61 - 32 * q^62 + 3 * q^63 - 3 * q^64 - 16 * q^65 - 3 * q^66 - 28 * q^67 + 4 * q^68 + 23 * q^69 + 14 * q^70 + 3 * q^71 - 3 * q^72 - 27 * q^73 - 12 * q^74 - 3 * q^75 - 16 * q^76 + 47 * q^77 + 6 * q^78 + 2 * q^79 - 3 * q^80 - 3 * q^81 + 27 * q^82 + 11 * q^83 + 3 * q^84 - 7 * q^85 + 2 * q^86 - 32 * q^87 - 3 * q^88 + 25 * q^89 - 3 * q^90 - 90 * q^91 - 10 * q^92 + 56 * q^93 - 25 * q^94 - 5 * q^95 - 3 * q^96 - 7 * q^97 - 32 * q^98 - 14 * q^99

Introduction

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