LMFDB - Embedded newform 690.2.q.b.251.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(11,690)]

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([11, 0, 9]))

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

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

chi := DirichletCharacter("690.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.q (of order $22$, 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:	$160$
Relative dimension:	$16$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			251.6
Character	$\chi$	$=$	690.251
Dual form			690.2.q.b.11.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.540641 + 0.841254i) q^{2} +(0.869657 - 1.49790i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(0.959493 + 0.281733i) q^{5} +(0.789940 + 1.54143i) q^{6} +(3.70222 + 3.20799i) q^{7} +(0.989821 + 0.142315i) q^{8} +(-1.48739 - 2.60531i) q^{9} +O(q^{10})$	\(q+(-0.540641 + 0.841254i) q^{2} +(0.869657 - 1.49790i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(0.959493 + 0.281733i) q^{5} +(0.789940 + 1.54143i) q^{6} +(3.70222 + 3.20799i) q^{7} +(0.989821 + 0.142315i) q^{8} +(-1.48739 - 2.60531i) q^{9} +(-0.755750 + 0.654861i) q^{10} +(-2.80081 + 1.79997i) q^{11} +(-1.72380 - 0.168818i) q^{12} +(3.81776 + 4.40593i) q^{13} +(-4.70031 + 1.38014i) q^{14} +(1.25644 - 1.19221i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-2.40866 + 5.27422i) q^{17} +(2.99588 + 0.157263i) q^{18} +(-1.05335 + 0.481051i) q^{19} +(-0.142315 - 0.989821i) q^{20} +(8.02491 - 2.75570i) q^{21} -3.32933i q^{22} +(3.28761 - 3.49165i) q^{23} +(1.07398 - 1.35889i) q^{24} +(0.841254 + 0.540641i) q^{25} +(-5.77054 + 0.829678i) q^{26} +(-5.19602 - 0.0377638i) q^{27} +(1.38014 - 4.70031i) q^{28} +(-1.40873 - 0.643347i) q^{29} +(0.323672 + 1.70154i) q^{30} +(0.0108063 - 0.0751597i) q^{31} +(-0.281733 - 0.959493i) q^{32} +(0.260430 + 5.76069i) q^{33} +(-3.13474 - 4.87775i) q^{34} +(2.64846 + 4.12108i) q^{35} +(-1.75199 + 2.43527i) q^{36} +(-2.82705 - 9.62804i) q^{37} +(0.164801 - 1.14621i) q^{38} +(9.91977 - 1.88697i) q^{39} +(0.909632 + 0.415415i) q^{40} +(1.93806 - 6.60042i) q^{41} +(-2.02035 + 8.24083i) q^{42} +(3.74808 - 0.538893i) q^{43} +(2.80081 + 1.79997i) q^{44} +(-0.693143 - 2.91883i) q^{45} +(1.15995 + 4.65344i) q^{46} +6.09793i q^{47} +(0.562531 + 1.63816i) q^{48} +(2.41902 + 16.8247i) q^{49} +(-0.909632 + 0.415415i) q^{50} +(5.80554 + 8.19468i) q^{51} +(2.42182 - 5.30304i) q^{52} +(2.15669 - 2.48895i) q^{53} +(2.84095 - 4.35075i) q^{54} +(-3.19447 + 0.937982i) q^{55} +(3.20799 + 3.70222i) q^{56} +(-0.195492 + 1.99617i) q^{57} +(1.30284 - 0.837282i) q^{58} +(-1.85353 + 1.60609i) q^{59} +(-1.60642 - 0.647632i) q^{60} +(11.3125 + 1.62650i) q^{61} +(0.0573860 + 0.0497252i) q^{62} +(2.85117 - 14.4170i) q^{63} +(0.959493 + 0.281733i) q^{64} +(2.42182 + 5.30304i) q^{65} +(-4.98700 - 2.89538i) q^{66} +(4.35207 - 6.77195i) q^{67} +5.79819 q^{68} +(-2.37104 - 7.96104i) q^{69} -4.89874 q^{70} +(0.0737642 - 0.114779i) q^{71} +(-1.10148 - 2.79047i) q^{72} +(-2.95980 - 6.48106i) q^{73} +(9.62804 + 2.82705i) q^{74} +(1.54143 - 0.789940i) q^{75} +(0.875159 + 0.758330i) q^{76} +(-16.1435 - 2.32109i) q^{77} +(-3.77561 + 9.36521i) q^{78} +(4.93755 - 4.27841i) q^{79} +(-0.841254 + 0.540641i) q^{80} +(-4.57532 + 7.75026i) q^{81} +(4.50483 + 5.19886i) q^{82} +(-9.78245 + 2.87239i) q^{83} +(-5.84034 - 6.15496i) q^{84} +(-3.79701 + 4.38198i) q^{85} +(-1.57302 + 3.44444i) q^{86} +(-2.18878 + 1.55065i) q^{87} +(-3.02847 + 1.38306i) q^{88} +(-2.62988 - 18.2912i) q^{89} +(2.83022 + 0.994928i) q^{90} +28.5591i q^{91} +(-4.54184 - 1.54003i) q^{92} +(-0.103184 - 0.0815499i) q^{93} +(-5.12990 - 3.29679i) q^{94} +(-1.14621 + 0.164801i) q^{95} +(-1.68223 - 0.412423i) q^{96} +(-3.87364 + 13.1924i) q^{97} +(-15.4616 - 7.06109i) q^{98} +(8.85541 + 4.61973i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 16 q^{4} + 16 q^{5} - 2 q^{6} - 46 q^{9}+O(q^{10}) $ 160 * q + 16 * q^4 + 16 * q^5 - 2 * q^6 - 46 * q^9	$ 160 q + 16 q^{4} + 16 q^{5} - 2 q^{6} - 46 q^{9} + 12 q^{11} + 12 q^{14} - 16 q^{16} - 8 q^{18} - 16 q^{20} + 70 q^{21} - 4 q^{23} + 2 q^{24} - 16 q^{25} + 42 q^{27} + 2 q^{30} - 4 q^{31} - 16 q^{33} + 2 q^{36} - 72 q^{38} + 140 q^{39} - 44 q^{41} + 44 q^{43} - 12 q^{44} + 2 q^{45} + 4 q^{46} + 70 q^{49} + 2 q^{51} + 52 q^{53} - 62 q^{54} + 10 q^{55} + 54 q^{56} - 94 q^{57} - 36 q^{58} - 44 q^{61} + 16 q^{64} - 54 q^{66} - 44 q^{67} - 30 q^{69} - 12 q^{70} - 36 q^{72} - 28 q^{73} + 24 q^{74} + 88 q^{77} - 54 q^{78} - 44 q^{79} + 16 q^{80} - 66 q^{81} - 28 q^{82} - 4 q^{83} - 4 q^{84} - 158 q^{86} + 156 q^{87} - 80 q^{89} + 8 q^{90} + 4 q^{92} + 4 q^{93} + 24 q^{94} - 2 q^{96} + 88 q^{98} - 58 q^{99}+O(q^{100}) $ 160 * q + 16 * q^4 + 16 * q^5 - 2 * q^6 - 46 * q^9 + 12 * q^11 + 12 * q^14 - 16 * q^16 - 8 * q^18 - 16 * q^20 + 70 * q^21 - 4 * q^23 + 2 * q^24 - 16 * q^25 + 42 * q^27 + 2 * q^30 - 4 * q^31 - 16 * q^33 + 2 * q^36 - 72 * q^38 + 140 * q^39 - 44 * q^41 + 44 * q^43 - 12 * q^44 + 2 * q^45 + 4 * q^46 + 70 * q^49 + 2 * q^51 + 52 * q^53 - 62 * q^54 + 10 * q^55 + 54 * q^56 - 94 * q^57 - 36 * q^58 - 44 * q^61 + 16 * q^64 - 54 * q^66 - 44 * q^67 - 30 * q^69 - 12 * q^70 - 36 * q^72 - 28 * q^73 + 24 * q^74 + 88 * q^77 - 54 * q^78 - 44 * q^79 + 16 * q^80 - 66 * q^81 - 28 * q^82 - 4 * q^83 - 4 * q^84 - 158 * q^86 + 156 * q^87 - 80 * q^89 + 8 * q^90 + 4 * q^92 + 4 * q^93 + 24 * q^94 - 2 * q^96 + 88 * q^98 - 58 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$-1$	$e\left(\frac{13}{22}\right)$

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 $

$2$	−0.540641	+	0.841254i	−0.382291	+	0.594856i
$2$	−0.540641	+	0.841254i	−0.382291	+	0.594856i
$3$	0.869657	−	1.49790i	0.502097	−	0.864812i
$3$	0.869657	−	1.49790i	0.502097	−	0.864812i
$4$	−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
$6$	0.789940	+	1.54143i	0.322492	+	0.629285i
$7$	3.70222	+	3.20799i	1.39931	+	1.21251i	0.947240	+	0.320525i	$0.103859\pi$
$7$	3.70222	+	3.20799i	1.39931	+	1.21251i	0.452069	+	0.891983i	$0.350686\pi$
$8$	0.989821	+	0.142315i	0.349955	+	0.0503159i
$9$	−1.48739	−	2.60531i	−0.495798	−	0.868438i
$10$	−0.755750	+	0.654861i	−0.238989	+	0.207085i
$11$	−2.80081	+	1.79997i	−0.844477	+	0.542713i	−0.889848	−	0.456258i	$-0.849190\pi$
$11$	−2.80081	+	1.79997i	−0.844477	+	0.542713i	0.0453705	+	0.998970i	$0.485553\pi$
$12$	−1.72380	−	0.168818i	−0.497619	−	0.0487337i
$13$	3.81776	+	4.40593i	1.05886	+	1.22198i	0.974227	+	0.225572i	$0.0724251\pi$
$13$	3.81776	+	4.40593i	1.05886	+	1.22198i	0.0846290	+	0.996413i	$0.473029\pi$
$14$	−4.70031	+	1.38014i	−1.25621	+	0.368857i
$15$	1.25644	−	1.19221i	0.324410	−	0.307828i
$16$	−0.654861	+	0.755750i	−0.163715	+	0.188937i
$17$	−2.40866	+	5.27422i	−0.584185	+	1.27919i	0.354708	+	0.934977i	$0.384580\pi$
$17$	−2.40866	+	5.27422i	−0.584185	+	1.27919i	−0.938893	+	0.344209i	$0.888147\pi$
$18$	2.99588	+	0.157263i	0.706135	+	0.0370672i
$19$	−1.05335	+	0.481051i	−0.241656	+	0.110361i	−0.532562	−	0.846391i	$-0.678771\pi$
$19$	−1.05335	+	0.481051i	−0.241656	+	0.110361i	0.290906	+	0.956752i	$0.406043\pi$
$20$	−0.142315	−	0.989821i	−0.0318226	−	0.221331i
$21$	8.02491	−	2.75570i	1.75118	−	0.601342i
$22$		−	3.32933i		−	0.709816i
$23$	3.28761	−	3.49165i	0.685514	−	0.728059i
$23$	3.28761	−	3.49165i	0.685514	−	0.728059i
$24$	1.07398	−	1.35889i	0.219225	−	0.277381i
$25$	0.841254	+	0.540641i	0.168251	+	0.108128i
$26$	−5.77054	+	0.829678i	−1.13170	+	0.162713i
$27$	−5.19602	−	0.0377638i	−0.999974	−	0.00726765i
$28$	1.38014	−	4.70031i	0.260821	−	0.888275i
$29$	−1.40873	−	0.643347i	−0.261595	−	0.119467i	0.280300	−	0.959912i	$-0.409566\pi$
$29$	−1.40873	−	0.643347i	−0.261595	−	0.119467i	−0.541896	+	0.840446i	$0.682293\pi$
$30$	0.323672	+	1.70154i	0.0590941	+	0.310657i
$31$	0.0108063	−	0.0751597i	0.00194087	−	0.0134991i	−0.988828	−	0.149061i	$-0.952375\pi$
$31$	0.0108063	−	0.0751597i	0.00194087	−	0.0134991i	0.990769	+	0.135562i	$0.0432840\pi$
$32$	−0.281733	−	0.959493i	−0.0498038	−	0.169616i
$33$	0.260430	+	5.76069i	0.0453350	+	1.00281i
$34$	−3.13474	−	4.87775i	−0.537603	−	0.836527i
$35$	2.64846	+	4.12108i	0.447672	+	0.696590i
$36$	−1.75199	+	2.43527i	−0.291998	+	0.405878i
$37$	−2.82705	−	9.62804i	−0.464764	−	1.58284i	−0.774859	−	0.632134i	$-0.782179\pi$
$37$	−2.82705	−	9.62804i	−0.464764	−	1.58284i	0.310095	−	0.950705i	$-0.399639\pi$
$38$	0.164801	−	1.14621i	0.0267342	−	0.185941i
$39$	9.91977	−	1.88697i	1.58843	−	0.302156i
$40$	0.909632	+	0.415415i	0.143825	+	0.0656829i
$41$	1.93806	−	6.60042i	0.302674	−	1.03081i	−0.657973	−	0.753041i	$-0.728586\pi$
$41$	1.93806	−	6.60042i	0.302674	−	1.03081i	0.960647	−	0.277771i	$-0.0895957\pi$
$42$	−2.02035	+	8.24083i	−0.311747	+	1.27159i
$43$	3.74808	−	0.538893i	0.571577	−	0.0821804i	0.149535	−	0.988756i	$-0.452222\pi$
$43$	3.74808	−	0.538893i	0.571577	−	0.0821804i	0.422043	+	0.906576i	$0.361313\pi$
$44$	2.80081	+	1.79997i	0.422239	+	0.271356i
$45$	−0.693143	−	2.91883i	−0.103328	−	0.435113i
$46$	1.15995	+	4.65344i	0.171025	+	0.686113i
$47$			6.09793i			0.889474i	0.895661	+	0.444737i	$0.146703\pi$
$47$			6.09793i			0.889474i	−0.895661	+	0.444737i	$0.853297\pi$
$48$	0.562531	+	1.63816i	0.0811944	+	0.236448i
$49$	2.41902	+	16.8247i	0.345575	+	2.40352i
$50$	−0.909632	+	0.415415i	−0.128641	+	0.0587486i
$51$	5.80554	+	8.19468i	0.812938	+	1.14748i
$52$	2.42182	−	5.30304i	0.335846	−	0.735400i
$53$	2.15669	−	2.48895i	0.296244	−	0.341884i	−0.588041	−	0.808831i	$-0.700101\pi$
$53$	2.15669	−	2.48895i	0.296244	−	0.341884i	0.884285	+	0.466947i	$0.154646\pi$
$54$	2.84095	−	4.35075i	0.386604	−	0.592062i
$55$	−3.19447	+	0.937982i	−0.430743	+	0.126477i
$56$	3.20799	+	3.70222i	0.428686	+	0.494730i
$57$	−0.195492	+	1.99617i	−0.0258935	+	0.264399i
$58$	1.30284	−	0.837282i	0.171071	−	0.109941i
$59$	−1.85353	+	1.60609i	−0.241309	+	0.209096i	−0.767116	−	0.641508i	$-0.778309\pi$
$59$	−1.85353	+	1.60609i	−0.241309	+	0.209096i	0.525807	+	0.850604i	$0.323763\pi$
$60$	−1.60642	−	0.647632i	−0.207387	−	0.0836089i
$61$	11.3125	+	1.62650i	1.44842	+	0.208252i	0.821223	−	0.570608i	$-0.193292\pi$
$61$	11.3125	+	1.62650i	1.44842	+	0.208252i	0.627199	+	0.778859i	$0.284201\pi$
$62$	0.0573860	+	0.0497252i	0.00728803	+	0.00631511i
$63$	2.85117	−	14.4170i	0.359213	−	1.81637i
$64$	0.959493	+	0.281733i	0.119937	+	0.0352166i
$65$	2.42182	+	5.30304i	0.300390	+	0.657762i
$66$	−4.98700	−	2.89538i	−0.613857	−	0.356396i
$67$	4.35207	−	6.77195i	0.531690	−	0.827325i	−0.466679	−	0.884427i	$-0.654550\pi$
$67$	4.35207	−	6.77195i	0.531690	−	0.827325i	0.998368	+	0.0571015i	$0.0181859\pi$
$68$	5.79819			0.703134
$69$	−2.37104	−	7.96104i	−0.285440	−	0.958397i
$70$	−4.89874			−0.585512
$71$	0.0737642	−	0.114779i	0.00875420	−	0.0136218i	−0.836849	−	0.547434i	$-0.815605\pi$
$71$	0.0737642	−	0.114779i	0.00875420	−	0.0136218i	0.845603	+	0.533812i	$0.179241\pi$
$72$	−1.10148	−	2.79047i	−0.129811	−	0.328860i
$73$	−2.95980	−	6.48106i	−0.346418	−	0.758550i	−0.999999	−	0.00169305i	$-0.999461\pi$
$73$	−2.95980	−	6.48106i	−0.346418	−	0.758550i	0.653580	−	0.756857i	$-0.273266\pi$
$74$	9.62804	+	2.82705i	1.11924	+	0.328638i
$75$	1.54143	−	0.789940i	0.177989	−	0.0912144i
$76$	0.875159	+	0.758330i	0.100388	+	0.0869864i
$77$	−16.1435	−	2.32109i	−1.83973	−	0.264513i
$78$	−3.77561	+	9.36521i	−0.427504	+	1.06040i
$79$	4.93755	−	4.27841i	0.555517	−	0.481358i	−0.331270	−	0.943536i	$-0.607477\pi$
$79$	4.93755	−	4.27841i	0.555517	−	0.481358i	0.886787	+	0.462178i	$0.152932\pi$
$80$	−0.841254	+	0.540641i	−0.0940550	+	0.0604455i
$81$	−4.57532	+	7.75026i	−0.508368	+	0.861140i
$82$	4.50483	+	5.19886i	0.497476	+	0.574117i
$83$	−9.78245	+	2.87239i	−1.07376	+	0.315285i	−0.770381	−	0.637584i	$-0.779934\pi$
$83$	−9.78245	+	2.87239i	−1.07376	+	0.315285i	−0.303382	+	0.952869i	$0.598116\pi$
$84$	−5.84034	−	6.15496i	−0.637233	−	0.671561i
$85$	−3.79701	+	4.38198i	−0.411843	+	0.475293i
$86$	−1.57302	+	3.44444i	−0.169623	+	0.371423i
$87$	−2.18878	+	1.55065i	−0.234662	+	0.166247i
$88$	−3.02847	+	1.38306i	−0.322836	+	0.147434i
$89$	−2.62988	−	18.2912i	−0.278767	−	1.93887i	−0.339247	−	0.940697i	$-0.610172\pi$
$89$	−2.62988	−	18.2912i	−0.278767	−	1.93887i	0.0604799	−	0.998169i	$-0.480737\pi$
$90$	2.83022	+	0.994928i	0.298331	+	0.104875i
$91$			28.5591i			2.99380i
$92$	−4.54184	−	1.54003i	−0.473519	−	0.160559i
$93$	−0.103184	−	0.0815499i	−0.0106996	−	0.00845633i
$94$	−5.12990	−	3.29679i	−0.529109	−	0.340038i
$95$	−1.14621	+	0.164801i	−0.117599	+	0.0169082i
$96$	−1.68223	−	0.412423i	−0.171692	−	0.0420927i
$97$	−3.87364	+	13.1924i	−0.393308	+	1.33949i	0.490421	+	0.871486i	$0.336843\pi$
$97$	−3.87364	+	13.1924i	−0.393308	+	1.33949i	−0.883729	+	0.467999i	$0.844975\pi$
$98$	−15.4616	−	7.06109i	−1.56186	−	0.713278i
$99$	8.85541	+	4.61973i	0.890002	+	0.464300i
$100$	0.142315	−	0.989821i	0.0142315	−	0.0989821i
$101$	1.82251	+	6.20689i	0.181346	+	0.617609i	0.999115	+	0.0420619i	$0.0133927\pi$
$101$	1.82251	+	6.20689i	0.181346	+	0.617609i	−0.817769	+	0.575547i	$0.804789\pi$
$102$	−10.0325	+	0.453551i	−0.993367	+	0.0449082i
$103$	−9.69259	−	15.0820i	−0.955039	−	1.48607i	−0.871989	−	0.489525i	$-0.837170\pi$
$103$	−9.69259	−	15.0820i	−0.955039	−	1.48607i	−0.0830500	−	0.996545i	$-0.526466\pi$
$104$	3.15187	+	4.90441i	0.309066	+	0.480916i
$105$	8.47621	−	0.383193i	0.827194	−	0.0373958i
$106$	0.927845	+	3.15995i	0.0901203	+	0.306921i
$107$	1.46787	−	10.2093i	0.141904	−	0.986966i	−0.787081	−	0.616850i	$-0.788409\pi$
$107$	1.46787	−	10.2093i	0.141904	−	0.986966i	0.928985	−	0.370116i	$-0.120682\pi$
$108$	2.12415	+	4.74215i	0.204397	+	0.456314i
$109$	−1.41677	−	0.647018i	−0.135702	−	0.0619731i	0.346407	−	0.938084i	$-0.387402\pi$
$109$	−1.41677	−	0.647018i	−0.135702	−	0.0619731i	−0.482109	+	0.876111i	$0.660129\pi$
$110$	0.937982	−	3.19447i	0.0894331	−	0.304581i
$111$	−16.8804	−	4.13846i	−1.60221	−	0.392805i
$112$	−4.84888	+	0.697164i	−0.458176	+	0.0658758i
$113$	8.85931	+	5.69354i	0.833414	+	0.535603i	0.886361	−	0.462995i	$-0.153225\pi$
$113$	8.85931	+	5.69354i	0.833414	+	0.535603i	−0.0529469	+	0.998597i	$0.516861\pi$
$114$	−1.57359	−	1.24367i	−0.147380	−	0.116480i
$115$	4.13815	−	2.42399i	0.385884	−	0.226038i
$116$			1.54868i			0.143792i
$117$	5.80031	−	16.4998i	0.536239	−	1.52541i
$118$	−0.349037	−	2.42761i	−0.0321315	−	0.223479i
$119$	−25.8371	+	11.7994i	−2.36848	+	1.08165i
$120$	1.41332	−	1.00127i	0.129018	−	0.0914028i
$121$	0.0350886	−	0.0768333i	0.00318987	−	0.00698484i
$122$	−7.48431	+	8.63736i	−0.677598	+	0.781990i
$123$	−8.20131	−	8.64311i	−0.739487	−	0.779323i
$124$	−0.0728567	+	0.0213927i	−0.00654273	+	0.00192112i
$125$	0.654861	+	0.755750i	0.0585725	+	0.0675963i
$126$	10.5869	+	10.1930i	0.943156	+	0.908062i
$127$	10.8270	−	6.95808i	0.960740	−	0.617430i	0.0365372	−	0.999332i	$-0.488367\pi$
$127$	10.8270	−	6.95808i	0.960740	−	0.617430i	0.924203	+	0.381902i	$0.124731\pi$
$128$	−0.755750	+	0.654861i	−0.0667995	+	0.0578821i
$129$	2.45234	−	6.08290i	0.215916	−	0.535569i
$130$	−5.77054	−	0.829678i	−0.506110	−	0.0727676i
$131$	−9.65854	−	8.36917i	−0.843871	−	0.731218i	0.121363	−	0.992608i	$-0.461274\pi$
$131$	−9.65854	−	8.36917i	−0.843871	−	0.731218i	−0.965233	+	0.261390i	$0.915819\pi$
$132$	5.13192	−	2.62997i	0.446677	−	0.228910i
$133$	−5.44296	−	1.59820i	−0.471965	−	0.138581i
$134$	3.34402	+	7.32239i	0.288879	+	0.632558i
$135$	−4.97490	−	1.50012i	−0.428171	−	0.129110i
$136$	−3.13474	+	4.87775i	−0.268802	+	0.418264i
$137$	10.5804			0.903946			0.451973	−	0.892032i	$-0.350720\pi$
$137$	10.5804			0.903946			0.451973	+	0.892032i	$0.350720\pi$
$138$	7.97914	+	2.30942i	0.679229	+	0.196590i
$139$	−20.1327			−1.70764			−0.853818	−	0.520572i	$-0.825719\pi$
$139$	−20.1327			−1.70764			−0.853818	+	0.520572i	$0.825719\pi$
$140$	2.64846	−	4.12108i	0.223836	−	0.348295i
$141$	9.13407	+	5.30310i	0.769228	+	0.446602i
$142$	0.0566786	+	0.124109i	0.00475636	+	0.0104150i
$143$	−18.6234	−	5.46832i	−1.55737	−	0.457284i
$144$	2.94300	+	0.582020i	0.245250	+	0.0485016i
$145$	−1.17042	−	1.01417i	−0.0971979	−	0.0842225i
$146$	7.05240	+	1.01398i	0.583661	+	0.0839177i
$147$	27.3054	+	11.0082i	2.25211	+	0.907944i
$148$	−7.58357	+	6.57120i	−0.623366	+	0.540150i
$149$	16.3214	−	10.4891i	1.33710	−	0.859304i	0.340387	−	0.940285i	$-0.389442\pi$
$149$	16.3214	−	10.4891i	1.33710	−	0.859304i	0.996716	+	0.0809813i	$0.0258054\pi$
$150$	−0.168818	+	1.72380i	−0.0137840	+	0.140748i
$151$	−5.49774	−	6.34473i	−0.447400	−	0.516327i	0.486588	−	0.873632i	$-0.338241\pi$
$151$	−5.49774	−	6.34473i	−0.447400	−	0.516327i	−0.933988	+	0.357304i	$0.883696\pi$
$152$	−1.11109	+	0.326247i	−0.0901216	+	0.0264621i
$153$	17.3236	−	1.56954i	1.40053	−	0.126890i
$154$	10.6805	−	12.3259i	0.860658	−	0.993252i
$155$	0.0315435	−	0.0690707i	0.00253364	−	0.00554789i
$156$	−5.83726	−	8.23946i	−0.467355	−	0.659685i
$157$	9.61878	−	4.39275i	0.767662	−	0.350580i	0.00721050	−	0.999974i	$-0.497705\pi$
$157$	9.61878	−	4.39275i	0.767662	−	0.350580i	0.760452	+	0.649394i	$0.224978\pi$
$158$	0.929787	+	6.46681i	0.0739699	+	0.514472i
$159$	−1.85261	−	5.39503i	−0.146922	−	0.427854i
$160$		−	1.00000i		−	0.0790569i
$161$	23.3727	−	2.38023i	1.84202	−	0.187589i
$162$	−4.04633	−	8.03911i	−0.317910	−	0.631612i
$163$	−10.2795	−	6.60623i	−0.805153	−	0.517440i	0.0721409	−	0.997394i	$-0.477017\pi$
$163$	−10.2795	−	6.60623i	−0.805153	−	0.517440i	−0.877293	+	0.479954i	$0.840653\pi$
$164$	−6.80905	+	0.978994i	−0.531698	+	0.0764466i
$165$	−1.37309	+	5.60072i	−0.106895	+	0.436015i
$166$	2.87239	−	9.78245i	0.222940	−	0.759265i
$167$	−3.00432	−	1.37203i	−0.232481	−	0.106171i	0.295768	−	0.955260i	$-0.404424\pi$
$167$	−3.00432	−	1.37203i	−0.232481	−	0.106171i	−0.528250	+	0.849089i	$0.677152\pi$
$168$	8.33540	−	1.58558i	0.643090	−	0.122330i
$169$	−2.98683	+	20.7739i	−0.229756	+	1.59799i
$170$	−1.63354	−	5.56332i	−0.125287	−	0.426687i
$171$	2.82004	+	2.02881i	0.215654	+	0.155147i
$172$	−2.04720	−	3.18551i	−0.156098	−	0.242893i
$173$	0.829595	+	1.29088i	0.0630729	+	0.0981434i	0.871358	−	0.490649i	$-0.163240\pi$
$173$	0.829595	+	1.29088i	0.0630729	+	0.0981434i	−0.808285	+	0.588792i	$0.799604\pi$
$174$	−0.121142	−	2.67966i	−0.00918378	−	0.203145i
$175$	1.38014	+	4.70031i	0.104328	+	0.355310i
$176$	0.473814	−	3.29545i	0.0357150	−	0.248404i
$177$	0.793828	+	4.17315i	0.0596678	+	0.313673i
$178$	16.8094	+	7.67659i	1.25992	+	0.575385i
$179$	−2.50918	+	8.54547i	−0.187545	+	0.638719i	0.811013	+	0.585028i	$0.198917\pi$
$179$	−2.50918	+	8.54547i	−0.187545	+	0.638719i	−0.998558	+	0.0536904i	$0.982902\pi$
$180$	−2.36712	+	1.84303i	−0.176434	+	0.137371i
$181$	−6.81543	+	0.979911i	−0.506587	+	0.0728362i	−0.390870	−	0.920446i	$-0.627826\pi$
$181$	−6.81543	+	0.979911i	−0.506587	+	0.0728362i	−0.115717	+	0.993282i	$0.536917\pi$
$182$	−24.0254	−	15.4402i	−1.78088	−	1.14450i
$183$	12.2743	−	15.5305i	0.907346	−	1.14805i
$184$	3.75106	−	2.98823i	0.276532	−	0.220296i
$185$		−	10.0345i		−	0.737752i
$186$	0.124389	−	0.0427144i	0.00912068	−	0.00313197i
$187$	−2.74726	−	19.1076i	−0.200900	−	1.39729i
$188$	5.54687	−	2.53317i	0.404547	−	0.184750i
$189$	−19.1157	−	16.8086i	−1.39046	−	1.22265i
$190$	0.481051	−	1.05335i	0.0348991	−	0.0764184i
$191$	1.06729	−	1.23171i	0.0772261	−	0.0891237i	−0.715822	−	0.698283i	$-0.753948\pi$
$191$	1.06729	−	1.23171i	0.0772261	−	0.0891237i	0.793048	+	0.609159i	$0.208493\pi$
$192$	1.25644	−	1.19221i	0.0906755	−	0.0860405i
$193$	−16.5375	+	4.85585i	−1.19040	+	0.349532i	−0.816173	−	0.577807i	$-0.803909\pi$
$193$	−16.5375	+	4.85585i	−1.19040	+	0.349532i	−0.374222	+	0.927339i	$0.622090\pi$
$194$	−9.00391	−	10.3911i	−0.646443	−	0.746035i
$195$	10.0496	+	0.984191i	0.719664	+	0.0704794i
$196$	14.2994	−	9.18964i	1.02138	−	0.656403i
$197$	−1.73164	+	1.50047i	−0.123374	+	0.106904i	−0.714363	−	0.699776i	$-0.753283\pi$
$197$	−1.73164	+	1.50047i	−0.123374	+	0.106904i	0.590989	+	0.806680i	$0.298738\pi$
$198$	−8.67396	+	4.95203i	−0.616431	+	0.351926i
$199$	2.01184	+	0.289259i	0.142616	+	0.0205050i	0.213253	−	0.976997i	$-0.431594\pi$
$199$	2.01184	+	0.289259i	0.142616	+	0.0205050i	−0.0706372	+	0.997502i	$0.522503\pi$
$200$	0.755750	+	0.654861i	0.0534396	+	0.0463056i
$201$	−6.35888	−	12.4082i	−0.448521	−	0.875209i
$202$	−6.20689	−	1.82251i	−0.436715	−	0.128231i
$203$	−3.15159	−	6.90102i	−0.221198	−	0.484357i
$204$	5.04244	−	8.68510i	0.353041	−	0.608078i
$205$	3.71911	−	5.78704i	0.259754	−	0.404185i
$206$	17.9280			1.24910
$207$	−13.9868	−	3.37179i	−0.972151	−	0.234356i
$208$	−5.82988			−0.404229
$209$	2.08437	−	3.24335i	0.144179	−	0.224347i
$210$	−4.26022	+	7.33782i	−0.293983	+	0.506357i
$211$	−4.52663	−	9.91193i	−0.311626	−	0.682366i	0.687410	−	0.726270i	$-0.258748\pi$
$211$	−4.52663	−	9.91193i	−0.311626	−	0.682366i	−0.999036	+	0.0439042i	$0.986020\pi$
$212$	−3.15995	−	0.927845i	−0.217026	−	0.0637246i
$213$	−0.107778	−	0.210310i	−0.00738483	−	0.0144102i
$214$	7.79498	+	6.75439i	0.532854	+	0.461721i
$215$	3.74808	+	0.538893i	0.255617	+	0.0367522i
$216$	−5.13775	−	0.776850i	−0.349580	−	0.0528579i
$217$	0.281119	−	0.243591i	0.0190836	−	0.0165360i
$218$	1.31027	−	0.842060i	0.0887428	−	0.0570315i
$219$	−12.2820	−	1.20282i	−0.829938	−	0.0812789i
$220$	2.18025	+	2.51614i	0.146992	+	0.169638i
$221$	−32.4335	+	9.52333i	−2.18171	+	0.640609i
$222$	12.6077	−	11.9633i	0.846174	−	0.802921i
$223$	−14.0160	+	16.1753i	−0.938579	+	1.08318i	0.0578152	+	0.998327i	$0.481587\pi$
$223$	−14.0160	+	16.1753i	−0.938579	+	1.08318i	−0.996394	+	0.0848500i	$0.972959\pi$
$224$	2.03501	−	4.45605i	0.135970	−	0.297733i
$225$	0.157263	−	2.99588i	0.0104842	−	0.199725i
$226$	−9.57941	+	4.37477i	−0.637213	+	0.291005i
$227$	−0.437069	−	3.03989i	−0.0290093	−	0.201764i	0.970162	−	0.242456i	$-0.0779530\pi$
$227$	−0.437069	−	3.03989i	−0.0290093	−	0.201764i	−0.999172	+	0.0406916i	$0.987044\pi$
$228$	1.89699	−	0.651412i	0.125631	−	0.0431408i
$229$			11.8517i			0.783183i	0.920139	+	0.391591i	$0.128075\pi$
$229$			11.8517i			0.783183i	−0.920139	+	0.391591i	$0.871925\pi$
$230$	−0.198065	+	4.79174i	−0.0130600	+	0.315958i
$231$	−17.5161	+	22.1628i	−1.15247	+	1.45821i
$232$	−1.30284	−	0.837282i	−0.0855354	−	0.0549703i
$233$	7.79717	−	1.12106i	0.510809	−	0.0734433i	0.117909	−	0.993024i	$-0.462381\pi$
$233$	7.79717	−	1.12106i	0.510809	−	0.0734433i	0.392900	+	0.919581i	$0.371472\pi$
$234$	10.7446	+	13.8000i	0.702399	+	0.902134i
$235$	−1.71798	+	5.85092i	−0.112069	+	0.381672i
$236$	2.23094	+	1.01884i	0.145222	+	0.0663205i
$237$	−2.11465	−	11.1167i	−0.137361	−	0.722106i
$238$	4.04229	−	28.1147i	0.262023	−	1.82241i
$239$	6.51727	+	22.1958i	0.421567	+	1.43572i	0.847415	+	0.530930i	$0.178157\pi$
$239$	6.51727	+	22.1958i	0.421567	+	1.43572i	−0.425849	+	0.904794i	$0.640024\pi$
$240$	0.0782228	+	1.73028i	0.00504926	+	0.111689i
$241$	10.4575	+	16.2722i	0.673626	+	1.04818i	0.994868	+	0.101185i	$0.0322635\pi$
$241$	10.4575	+	16.2722i	0.673626	+	1.04818i	−0.321241	+	0.946997i	$0.604100\pi$
$242$	0.0456660	+	0.0710576i	0.00293552	+	0.00456776i
$243$	7.63014	+	13.5934i	0.489474	+	0.872018i
$244$	−3.21988	−	10.9659i	−0.206132	−	0.702021i
$245$	−2.41902	+	16.8247i	−0.154546	+	1.07489i
$246$	11.7050	−	2.22656i	0.746284	−	0.141960i
$247$	−6.14093	−	2.80447i	−0.390738	−	0.178444i
$248$	0.0213927	−	0.0728567i	0.00135844	−	0.00462641i
$249$	−4.20483	+	17.1511i	−0.266470	+	1.08691i
$250$	−0.989821	+	0.142315i	−0.0626018	+	0.00900078i
$251$	−9.61375	−	6.17838i	−0.606814	−	0.389976i	0.200847	−	0.979623i	$-0.435631\pi$
$251$	−9.61375	−	6.17838i	−0.606814	−	0.389976i	−0.807661	+	0.589647i	$0.799267\pi$
$252$	−14.2986	+	3.39553i	−0.900726	+	0.213898i
$253$	−2.92310	+	15.6971i	−0.183774	+	0.986867i
$254$			12.8701i			0.807540i
$255$	3.26166	+	9.49835i	0.204253	+	0.594810i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	3.76268	−	1.71836i	0.234710	−	0.107188i	−0.294589	−	0.955624i	$-0.595183\pi$
$257$	3.76268	−	1.71836i	0.234710	−	0.107188i	0.529298	+	0.848436i	$0.322455\pi$
$258$	3.79142	+	5.35170i	0.236044	+	0.333182i
$259$	20.4203	−	44.7143i	1.26886	−	2.77841i
$260$	3.81776	−	4.40593i	0.236767	−	0.273244i
$261$	0.419222	+	4.62710i	0.0259492	+	0.286410i
$262$	12.2624	−	3.60057i	0.757574	−	0.222444i
$263$	−4.44615	−	5.13113i	−0.274161	−	0.316399i	0.601926	−	0.798552i	$-0.294400\pi$
$263$	−4.44615	−	5.13113i	−0.274161	−	0.316399i	−0.876087	+	0.482153i	$0.839855\pi$
$264$	−0.562053	+	5.73912i	−0.0345920	+	0.353218i
$265$	2.77055	−	1.78052i	0.170193	−	0.109377i
$266$	4.28718	−	3.71486i	0.262864	−	0.227773i
$267$	−29.6855	−	11.9678i	−1.81672	−	0.732417i
$268$	−7.96790	−	1.14561i	−0.486717	−	0.0699793i
$269$	−7.16937	−	6.21229i	−0.437124	−	0.378770i	0.408316	−	0.912841i	$-0.366116\pi$
$269$	−7.16937	−	6.21229i	−0.437124	−	0.378770i	−0.845440	+	0.534071i	$0.820662\pi$
$270$	3.95162	−	3.37413i	0.240488	−	0.205343i
$271$	−5.91719	−	1.73744i	−0.359444	−	0.105542i	0.0970242	−	0.995282i	$-0.469068\pi$
$271$	−5.91719	−	1.73744i	−0.359444	−	0.105542i	−0.456468	+	0.889740i	$0.650886\pi$
$272$	−2.40866	−	5.27422i	−0.146046	−	0.319797i
$273$	42.7786	+	24.8366i	2.58908	+	1.50318i
$274$	−5.72021	+	8.90082i	−0.345570	+	0.537718i
$275$	−3.32933			−0.200766
$276$	−6.25665	+	5.46391i	−0.376606	+	0.328889i
$277$	−2.47047			−0.148436			−0.0742180	−	0.997242i	$-0.523646\pi$
$277$	−2.47047			−0.148436			−0.0742180	+	0.997242i	$0.523646\pi$
$278$	10.8846	−	16.9367i	0.652813	−	1.01580i
$279$	−0.211888	+	0.0836382i	−0.0126854	+	0.00500729i
$280$	2.03501	+	4.45605i	0.121615	+	0.266300i
$281$	17.0094	+	4.99442i	1.01470	+	0.297942i	0.746474	−	0.665414i	$-0.231745\pi$
$281$	17.0094	+	4.99442i	1.01470	+	0.297942i	0.268224	+	0.963357i	$0.413563\pi$
$282$	−9.39951	+	4.81700i	−0.559732	+	0.286848i
$283$	−4.41850	−	3.82865i	−0.262652	−	0.227590i	0.513572	−	0.858047i	$-0.328322\pi$
$283$	−4.41850	−	3.82865i	−0.262652	−	0.227590i	−0.776224	+	0.630457i	$0.782867\pi$
$284$	−0.135050	−	0.0194172i	−0.00801372	−	0.00115220i
$285$	−0.749958	+	1.86023i	−0.0444237	+	0.110191i
$286$	14.6688	−	12.7106i	0.867385	−	0.751593i
$287$	28.3492	−	18.2189i	1.67340	−	1.07543i
$288$	−2.08073	+	2.16115i	−0.122608	+	0.127347i
$289$	−10.8831	−	12.5598i	−0.640185	−	0.738813i
$290$	1.48595	−	0.436315i	0.0872581	−	0.0256213i
$291$	16.3921	+	17.2752i	0.960923	+	1.01269i
$292$	−4.66583	+	5.38466i	−0.273047	+	0.315113i
$293$	−2.43967	+	5.34213i	−0.142527	+	0.312090i	−0.967411	−	0.253212i	$-0.918513\pi$
$293$	−2.43967	+	5.34213i	−0.142527	+	0.312090i	0.824884	+	0.565302i	$0.191240\pi$
$294$	−24.0231	+	17.0192i	−1.40106	+	0.992581i
$295$	−2.23094	+	1.01884i	−0.129890	+	0.0593189i
$296$	−1.42806	−	9.93237i	−0.0830042	−	0.577307i
$297$	14.6210	−	9.24692i	0.848399	−	0.536561i
$298$			19.4013i			1.12389i
$299$	27.9353	+	1.15469i	1.61554	+	0.0667777i
$300$	−1.35889	−	1.07398i	−0.0784553	−	0.0620061i
$301$	15.6050	+	10.0287i	0.899458	+	0.578046i
$302$	8.30983	−	1.19477i	0.478177	−	0.0687515i
$303$	10.8822	+	2.66794i	0.625169	+	0.153269i
$304$	0.326247	−	1.11109i	0.0187115	−	0.0637256i
$305$	10.3961	+	4.74772i	0.595277	+	0.271854i
$306$	−8.04547	+	15.4221i	−0.459929	+	0.881624i
$307$	2.39718	−	16.6727i	0.136814	−	0.951563i	−0.799567	−	0.600577i	$-0.794938\pi$
$307$	2.39718	−	16.6727i	0.136814	−	0.951563i	0.936381	−	0.350986i	$-0.114153\pi$
$308$	4.59493	+	15.6489i	0.261821	+	0.891679i
$309$	−31.0205	+	1.40238i	−1.76469	+	0.0797784i
$310$	0.0410522	+	0.0638785i	0.00233161	+	0.00362806i
$311$	9.12245	+	14.1948i	0.517287	+	0.804914i	0.997383	−	0.0723019i	$-0.0230345\pi$
$311$	9.12245	+	14.1948i	0.517287	+	0.804914i	−0.480096	+	0.877216i	$0.659398\pi$
$312$	10.0873	−	0.456029i	0.571083	−	0.0258176i
$313$	5.38827	+	18.3508i	0.304563	+	1.03725i	0.959534	+	0.281592i	$0.0908625\pi$
$313$	5.38827	+	18.3508i	0.304563	+	1.03725i	−0.654971	+	0.755654i	$0.727319\pi$
$314$	−1.50489	+	10.4667i	−0.0849258	+	0.590672i
$315$	6.79741	−	13.0297i	0.382991	−	0.734143i
$316$	−5.94291	−	2.71403i	−0.334315	−	0.152676i
$317$	0.0495520	−	0.168759i	0.00278312	−	0.00947843i	−0.958090	−	0.286468i	$-0.907519\pi$
$317$	0.0495520	−	0.168759i	0.00278312	−	0.00947843i	0.960873	+	0.276990i	$0.0893369\pi$
$318$	5.54019	+	1.35825i	0.310678	+	0.0761671i
$319$	5.10361	−	0.733788i	0.285747	−	0.0410842i
$320$	0.841254	+	0.540641i	0.0470275	+	0.0302227i
$321$	−14.0159	−	11.0773i	−0.782290	−	0.618273i
$322$	−10.6338	+	20.9492i	−0.592600	+	1.16745i
$323$		−	6.71431i		−	0.373594i
$324$	8.95054	+	0.942281i	0.497252	+	0.0523489i
$325$	0.829678	+	5.77054i	0.0460223	+	0.320092i
$326$	11.1150	−	5.07607i	0.615605	−	0.281137i
$327$	−2.20127	+	1.55950i	−0.121731	+	0.0862403i
$328$	2.85767	−	6.25742i	0.157788	−	0.345508i
$329$	−19.5621	+	22.5759i	−1.07849	+	1.24465i
$330$	−3.96927	−	4.18310i	−0.218501	−	0.230272i
$331$	11.1122	−	3.26284i	0.610783	−	0.179342i	0.0383101	−	0.999266i	$-0.487803\pi$
$331$	11.1122	−	3.26284i	0.610783	−	0.179342i	0.572472	+	0.819924i	$0.305984\pi$
$332$	6.67659	+	7.70520i	0.366425	+	0.422878i
$333$	−20.8791	+	21.6860i	−1.14417	+	1.18839i
$334$	2.77848	−	1.78562i	0.152032	−	0.0977049i
$335$	6.08366	−	5.27152i	0.332386	−	0.288014i
$336$	−3.17258	+	7.86942i	−0.173079	+	0.429312i
$337$	4.55302	+	0.654626i	0.248019	+	0.0356597i	0.265203	−	0.964193i	$-0.414561\pi$
$337$	4.55302	+	0.654626i	0.248019	+	0.0356597i	−0.0171841	+	0.999852i	$0.505470\pi$
$338$	−15.8613	−	13.7439i	−0.862740	−	0.747568i
$339$	16.2329	−	8.31892i	0.881650	−	0.451822i
$340$	5.56332	+	1.63354i	0.301714	+	0.0885911i
$341$	0.105019	+	0.229959i	0.00568709	+	0.0124530i
$342$	−3.23137	+	1.27552i	−0.174733	+	0.0689720i
$343$	−26.4785	+	41.2013i	−1.42970	+	2.22466i
$344$	3.78663			0.204161
$345$	−0.0321146	−	8.30656i	−0.00172899	−	0.447210i
$346$	−1.53447			−0.0824934
$347$	−3.33102	+	5.18318i	−0.178819	+	0.278247i	−0.919079	−	0.394073i	$-0.871066\pi$
$347$	−3.33102	+	5.18318i	−0.178819	+	0.278247i	0.740260	+	0.672320i	$0.234702\pi$
$348$	2.31977	+	1.34682i	0.124353	+	0.0721973i
$349$	7.46343	+	16.3426i	0.399508	+	0.874801i	0.997320	+	0.0731645i	$0.0233098\pi$
$349$	7.46343	+	16.3426i	0.399508	+	0.874801i	−0.597812	+	0.801637i	$0.703963\pi$
$350$	−4.70031	−	1.38014i	−0.251242	−	0.0737713i
$351$	−19.6707	−	23.0374i	−1.04995	−	1.22965i
$352$	2.51614	+	2.18025i	0.134111	+	0.116208i
$353$	−10.8295	−	1.55704i	−0.576394	−	0.0828730i	−0.152048	−	0.988373i	$-0.548587\pi$
$353$	−10.8295	−	1.55704i	−0.576394	−	0.0828730i	−0.424346	+	0.905500i	$0.639496\pi$
$354$	−3.93985	−	1.58836i	−0.209401	−	0.0844206i
$355$	0.103113	−	0.0893481i	0.00547268	−	0.00474211i
$356$	−15.5458	+	9.99068i	−0.823926	+	0.529505i
$357$	−4.79509	+	48.9627i	−0.253783	+	2.59138i
$358$	−5.83235	−	6.73089i	−0.308249	−	0.355738i
$359$	6.42730	−	1.88722i	0.339220	−	0.0996039i	−0.107686	−	0.994185i	$-0.534344\pi$
$359$	6.42730	−	1.88722i	0.339220	−	0.0996039i	0.446906	+	0.894581i	$0.352526\pi$
$360$	−0.270695	−	2.98776i	−0.0142669	−	0.157469i
$361$	−11.5642	+	13.3458i	−0.608642	+	0.702411i
$362$	2.86035	−	6.26328i	0.150336	−	0.329191i
$363$	−0.0845734	−	0.119378i	−0.00443895	−	0.00626570i
$364$	25.9782	−	11.8639i	1.36163	−	0.621836i
$365$	−1.01398	−	7.05240i	−0.0530742	−	0.369139i
$366$	6.42910	+	18.7223i	0.336054	+	0.978629i
$367$			3.14108i			0.163963i	0.996634	+	0.0819816i	$0.0261249\pi$
$367$			3.14108i			0.163963i	−0.996634	+	0.0819816i	$0.973875\pi$
$368$	0.485887	+	4.77115i	0.0253286	+	0.248714i
$369$	−20.0788	+	4.76818i	−1.04526	+	0.248221i
$370$	8.44156	+	5.42506i	0.438856	+	0.282036i
$371$	15.9691	−	2.29601i	0.829073	−	0.119203i
$372$	−0.0313163	+	0.127736i	−0.00162368	+	0.00662281i
$373$	6.91810	−	23.5609i	0.358206	−	1.21994i	−0.561549	−	0.827443i	$-0.689794\pi$
$373$	6.91810	−	23.5609i	0.358206	−	1.21994i	0.919755	−	0.392493i	$-0.128387\pi$
$374$	17.5596	+	8.01922i	0.907987	+	0.414664i
$375$	1.70154	−	0.323672i	0.0878671	−	0.0167143i
$376$	−0.867826	+	6.03586i	−0.0447547	+	0.311276i
$377$	−2.54366	−	8.66292i	−0.131005	−	0.446163i
$378$	24.4750	−	6.99370i	1.25886	−	0.359717i
$379$	−14.9462	−	23.2568i	−0.767736	−	1.19462i	−0.976260	−	0.216603i	$-0.930502\pi$
$379$	−14.9462	−	23.2568i	−0.767736	−	1.19462i	0.208524	−	0.978017i	$-0.433134\pi$
$380$	0.626063	+	0.974173i	0.0321163	+	0.0499740i
$381$	−1.00673	−	22.2689i	−0.0515765	−	1.14087i
$382$	0.459165	+	1.56377i	0.0234929	+	0.0800096i
$383$	−2.51842	+	17.5160i	−0.128685	+	0.895027i	0.818538	+	0.574453i	$0.194785\pi$
$383$	−2.51842	+	17.5160i	−0.128685	+	0.895027i	−0.947223	+	0.320574i	$0.896124\pi$
$384$	0.323672	+	1.70154i	0.0165173	+	0.0868313i
$385$	−14.8357	−	6.77523i	−0.756097	−	0.345298i
$386$	4.85585	−	16.5375i	0.247156	−	0.841737i
$387$	−6.97886	−	8.96339i	−0.354756	−	0.455634i
$388$	13.6094	−	1.95674i	0.690912	−	0.0993382i
$389$	20.7460	+	13.3327i	1.05187	+	0.675993i	0.947894	−	0.318587i	$-0.103208\pi$
$389$	20.7460	+	13.3327i	1.05187	+	0.675993i	0.103972	+	0.994580i	$0.466845\pi$
$390$	−6.26116	+	7.92214i	−0.317046	+	0.401153i
$391$	10.4970	+	25.7498i	0.530857	+	1.30222i
$392$			16.9977i			0.858513i
$393$	−20.9358	+	7.18920i	−1.05607	+	0.362647i
$394$	−0.326083	−	2.26796i	−0.0164278	−	0.114258i
$395$	5.94291	−	2.71403i	0.299020	−	0.136558i
$396$	0.523581	−	9.97427i	0.0263109	−	0.501226i
$397$	9.53510	−	20.8790i	0.478553	−	1.04788i	−0.504306	−	0.863525i	$-0.668252\pi$
$397$	9.53510	−	20.8790i	0.478553	−	1.04788i	0.982859	−	0.184360i	$-0.0590211\pi$
$398$	−1.33102	+	1.53608i	−0.0667182	+	0.0769969i
$399$	−7.12745	+	6.76312i	−0.356819	+	0.338579i
$400$	−0.959493	+	0.281733i	−0.0479746	+	0.0140866i
$401$	5.85844	+	6.76100i	0.292557	+	0.337628i	0.882932	−	0.469500i	$-0.155566\pi$
$401$	5.85844	+	6.76100i	0.292557	+	0.337628i	−0.590376	+	0.807128i	$0.701020\pi$
$402$	13.8763	+	1.35896i	0.692089	+	0.0677788i
$403$	0.372404	−	0.239329i	0.0185508	−	0.0119219i
$404$	4.88889	−	4.23625i	0.243231	−	0.210761i
$405$	−6.57348	+	6.14730i	−0.326639	+	0.305462i
$406$	7.50939	+	1.07969i	0.372685	+	0.0535840i
$407$	25.2482	+	21.8777i	1.25151	+	1.08444i
$408$	4.58022	+	8.93748i	0.226755	+	0.442471i
$409$	−11.1899	−	3.28564i	−0.553303	−	0.162464i	−0.00688382	−	0.999976i	$-0.502191\pi$
$409$	−11.1899	−	3.28564i	−0.553303	−	0.162464i	−0.546419	+	0.837512i	$0.684009\pi$
$410$	2.85767	+	6.25742i	0.141130	+	0.309032i
$411$	9.20133	−	15.8484i	0.453868	−	0.781743i
$412$	−9.69259	+	15.0820i	−0.477520	+	0.743035i
$413$	−12.0145			−0.591196
$414$	10.3984	−	9.94353i	0.511052	−	0.488698i
$415$	−10.1954			−0.500474
$416$	3.15187	−	4.90441i	0.154533	−	0.240458i
$417$	−17.5086	+	30.1568i	−0.857398	+	1.47678i
$418$	1.60158	+	3.50697i	0.0783358	+	0.171532i
$419$	−23.8529	−	7.00384i	−1.16529	−	0.342160i	−0.358804	−	0.933413i	$-0.616815\pi$
$419$	−23.8529	−	7.00384i	−1.16529	−	0.342160i	−0.806486	+	0.591253i	$0.798633\pi$
$420$	−3.86971	−	7.55105i	−0.188823	−	0.368454i
$421$	−17.5759	−	15.2296i	−0.856599	−	0.742247i	0.111246	−	0.993793i	$-0.464516\pi$
$421$	−17.5759	−	15.2296i	−0.856599	−	0.742247i	−0.967845	+	0.251545i	$0.919061\pi$
$422$	10.7857	+	1.55075i	0.525041	+	0.0754895i
$423$	15.8870	−	9.07002i	0.772453	−	0.441000i
$424$	2.48895	−	2.15669i	0.120874	−	0.104738i
$425$	−4.87775	+	3.13474i	−0.236606	+	0.152057i
$426$	0.235193	+	0.0230333i	0.0113951	+	0.00111597i
$427$	36.6637	+	42.3122i	1.77428	+	2.04763i
$428$	−9.89644	+	2.90586i	−0.478363	+	0.140460i
$429$	−24.3869	+	23.1404i	−1.17741	+	1.11723i
$430$	−2.47971	+	2.86174i	−0.119582	+	0.138005i
$431$	−1.10799	+	2.42616i	−0.0533699	+	0.116864i	−0.934438	−	0.356125i	$-0.884098\pi$
$431$	−1.10799	+	2.42616i	−0.0533699	+	0.116864i	0.881068	+	0.472989i	$0.156825\pi$
$432$	3.43121	−	3.90216i	0.165084	−	0.187743i
$433$	−14.0489	+	6.41593i	−0.675148	+	0.308330i	−0.723324	−	0.690509i	$-0.757387\pi$
$433$	−14.0489	+	6.41593i	−0.675148	+	0.308330i	0.0481755	+	0.998839i	$0.484659\pi$
$434$	0.0529374	+	0.368188i	0.00254108	+	0.0176736i
$435$	−2.53699	+	0.871184i	−0.121639	+	0.0417701i
$436$			1.55752i			0.0745918i
$437$	−1.78336	+	5.25946i	−0.0853096	+	0.251594i
$438$	7.65201	−	9.68196i	0.365627	−	0.462622i
$439$	16.0963	+	10.3444i	0.768233	+	0.493714i	0.865110	−	0.501583i	$-0.167249\pi$
$439$	16.0963	+	10.3444i	0.768233	+	0.493714i	−0.0968763	+	0.995296i	$0.530885\pi$
$440$	−3.29545	+	0.473814i	−0.157104	+	0.0225882i
$441$	40.2355	−	31.3272i	1.91598	−	1.49177i
$442$	9.52333	−	32.4335i	0.452979	−	1.54270i
$443$	−24.3091	−	11.1016i	−1.15496	−	0.527454i	−0.256517	−	0.966540i	$-0.582575\pi$
$443$	−24.3091	−	11.1016i	−1.15496	−	0.527454i	−0.898445	+	0.439086i	$0.855302\pi$
$444$	3.24788	+	17.0741i	0.154138	+	0.810301i
$445$	2.62988	−	18.2912i	0.124668	−	0.867088i
$446$	−6.02991	−	20.5360i	−0.285525	−	0.972408i
$447$	−1.51762	−	33.5698i	−0.0717812	−	1.58780i
$448$	2.64846	+	4.12108i	0.125128	+	0.194703i
$449$	10.5191	+	16.3680i	0.496426	+	0.772455i	0.995566	−	0.0940671i	$-0.0299868\pi$
$449$	10.5191	+	16.3680i	0.496426	+	0.772455i	−0.499139	+	0.866522i	$0.666350\pi$
$450$	2.43527	+	1.75199i	0.114800	+	0.0825896i
$451$	6.45244	+	21.9750i	0.303834	+	1.03476i
$452$	1.49873	−	10.4239i	0.0704943	−	0.490299i
$453$	−14.2849	+	2.71732i	−0.671164	+	0.127671i
$454$	2.79361	+	1.27580i	0.131111	+	0.0598762i
$455$	−8.04602	+	27.4022i	−0.377203	+	1.28464i
$456$	−0.477586	+	1.94803i	−0.0223650	+	0.0912248i
$457$	23.0420	−	3.31294i	1.07786	−	0.154973i	0.419558	−	0.907728i	$-0.362185\pi$
$457$	23.0420	−	3.31294i	1.07786	−	0.154973i	0.658300	+	0.752756i	$0.271276\pi$
$458$	−9.97029	−	6.40752i	−0.465881	−	0.299404i
$459$	12.7146	−	27.3140i	0.593466	−	1.27491i
$460$	−3.92399	−	2.75723i	−0.182957	−	0.128557i
$461$			24.4776i			1.14003i	0.821633	+	0.570017i	$0.193063\pi$
$461$			24.4776i			1.14003i	−0.821633	+	0.570017i	$0.806937\pi$
$462$	−9.17464	−	26.7176i	−0.426843	−	1.24302i
$463$	−1.85526	−	12.9036i	−0.0862211	−	0.599681i	−0.986425	−	0.164212i	$-0.947492\pi$
$463$	−1.85526	−	12.9036i	−0.0862211	−	0.599681i	0.900204	−	0.435469i	$-0.143417\pi$
$464$	1.40873	−	0.643347i	0.0653988	−	0.0298666i
$465$	−0.0760288	−	0.107317i	−0.00352575	−	0.00497669i
$466$	−3.27237	+	7.16549i	−0.151590	+	0.331935i
$467$	4.93693	−	5.69752i	0.228454	−	0.263650i	−0.629937	−	0.776646i	$-0.716919\pi$
$467$	4.93693	−	5.69752i	0.228454	−	0.263650i	0.858391	+	0.512997i	$0.171465\pi$
$468$	−17.4183	+	1.57812i	−0.805161	+	0.0729486i
$469$	37.8367	−	11.1099i	1.74714	−	0.513006i
$470$	−3.99329	−	4.60851i	−0.184197	−	0.212575i
$471$	1.78515	−	18.2281i	0.0822553	−	0.839908i
$472$	−2.06324	+	1.32596i	−0.0949681	+	0.0610323i
$473$	−9.52769	+	8.25579i	−0.438084	+	0.379602i
$474$	10.4952	+	4.23118i	0.482061	+	0.194344i
$475$	−1.14621	−	0.164801i	−0.0525919	−	0.00756158i
$476$	21.4662	+	18.6006i	0.983902	+	0.852556i
$477$	−9.69234	−	1.91680i	−0.443782	−	0.0877641i
$478$	−22.1958	−	6.51727i	−1.01521	−	0.298093i
$479$	−12.3761	−	27.0998i	−0.565477	−	1.23822i	−0.949171	−	0.314762i	$-0.898075\pi$
$479$	−12.3761	−	27.0998i	−0.565477	−	1.23822i	0.383693	−	0.923461i	$-0.374652\pi$
$480$	−1.49790	−	0.869657i	−0.0683694	−	0.0396942i
$481$	31.6275	−	49.2133i	1.44209	−	2.24393i
$482$	−19.3428			−0.881039
$483$	16.7608	−	37.0798i	0.762645	−	1.68719i
$484$	−0.0844663			−0.00383938
$485$	−7.43346	+	11.5667i	−0.337536	+	0.525216i
$486$	−15.5607	−	0.930277i	−0.705847	−	0.0421982i
$487$	1.92969	+	4.22543i	0.0874427	+	0.191473i	0.948301	−	0.317371i	$-0.102800\pi$
$487$	1.92969	+	4.22543i	0.0874427	+	0.191473i	−0.860859	+	0.508844i	$0.830073\pi$
$488$	10.9659	+	3.21988i	0.496404	+	0.145757i
$489$	−18.8351	+	9.65248i	−0.851753	+	0.436500i
$490$	−12.8460	−	11.1311i	−0.580323	−	0.502853i
$491$	21.2893	+	3.06093i	0.960770	+	0.138138i	0.604816	−	0.796365i	$-0.293247\pi$
$491$	21.2893	+	3.06093i	0.960770	+	0.138138i	0.355955	+	0.934503i	$0.384156\pi$
$492$	−4.45511	+	11.0507i	−0.200852	+	0.498202i
$493$	6.78631	−	5.88037i	0.305640	−	0.264838i
$494$	5.67931	−	3.64987i	0.255524	−	0.164215i
$495$	7.19518	+	6.92745i	0.323399	+	0.311366i
$496$	0.0497252	+	0.0573860i	0.00223273	+	0.00257671i
$497$	0.641303	−	0.188303i	0.0287664	−	0.00844656i
$498$	−12.1551	−	12.8099i	−0.544684	−	0.574026i
$499$	−27.5809	+	31.8300i	−1.23469	+	1.42491i	−0.365220	+	0.930921i	$0.619006\pi$
$499$	−27.5809	+	31.8300i	−1.23469	+	1.42491i	−0.869469	+	0.493987i	$0.835539\pi$
$500$	0.415415	−	0.909632i	0.0185779	−	0.0406800i
$501$	−4.66789	+	3.30697i	−0.208546	+	0.147745i
$502$	10.3952	−	4.74731i	0.463959	−	0.211883i
$503$	5.45635	+	37.9498i	0.243287	+	1.69210i	0.635403	+	0.772181i	$0.280834\pi$
$503$	5.45635	+	37.9498i	0.243287	+	1.69210i	−0.392116	+	0.919916i	$0.628257\pi$
$504$	4.87390	−	13.8645i	0.217101	−	0.617574i
$505$			6.46893i			0.287864i
$506$	−11.6249	−	10.9456i	−0.516789	−	0.486589i
$507$	28.5196	+	22.5401i	1.26660	+	1.00104i
$508$	−10.8270	−	6.95808i	−0.480370	−	0.308715i
$509$	−9.98240	+	1.43525i	−0.442462	+	0.0636165i	−0.359946	−	0.932973i	$-0.617205\pi$
$509$	−9.98240	+	1.43525i	−0.442462	+	0.0636165i	−0.0825165	+	0.996590i	$0.526296\pi$
$510$	−9.75391	−	2.39131i	−0.431910	−	0.105889i
$511$	9.83336	−	33.4893i	0.435002	−	1.48148i
$512$	0.909632	+	0.415415i	0.0402004	+	0.0183589i
$513$	5.49141	−	2.45977i	0.242452	−	0.108601i
$514$	−0.588684	+	4.09438i	−0.0259657	+	0.180596i
$515$	−5.05089	−	17.2018i	−0.222569	−	0.758000i
$516$	−6.55194	+	0.296200i	−0.288433	+	0.0130395i
$517$	−10.9761	−	17.0792i	−0.482729	−	0.751141i
$518$	26.5760	+	41.3530i	1.16768	+	1.81695i
$519$	2.65506	−	0.120030i	0.116544	−	0.00526874i
$520$	1.64247	+	5.59373i	0.0720269	+	0.245301i
$521$	5.46189	−	37.9883i	0.239290	−	1.66430i	−0.416336	−	0.909211i	$-0.636686\pi$
$521$	5.46189	−	37.9883i	0.239290	−	1.66430i	0.655626	−	0.755086i	$-0.272405\pi$
$522$	−4.11921	−	2.14893i	−0.180293	−	0.0940560i
$523$	−37.8416	−	17.2817i	−1.65470	−	0.755674i	−0.654696	−	0.755892i	$-0.727203\pi$
$523$	−37.8416	−	17.2817i	−1.65470	−	0.755674i	−1.00000		0.000217648i	$0.999931\pi$
$524$	−3.60057	+	12.2624i	−0.157291	+	0.535685i
$525$	8.24083	+	2.02035i	0.359659	+	0.0881755i
$526$	6.72035	−	0.966241i	0.293021	−	0.0421301i
$527$	0.370380	+	0.238029i	0.0161340	+	0.0103687i
$528$	−4.52419	−	3.57563i	−0.196890	−	0.155609i
$529$	−1.38324	−	22.9584i	−0.0601410	−	0.998190i
$530$			3.29335i			0.143054i
$531$	6.94131	+	2.44013i	0.301227	+	0.105893i
$532$	0.807317	+	5.61501i	0.0350016	+	0.243442i
$533$	36.4800	−	16.6599i	1.58012	−	0.721619i
$534$	26.1171	−	18.5027i	1.13020	−	0.800692i
$535$	4.28469	−	9.38216i	0.185243	−	0.405626i
$536$	5.27152	−	6.08366i	0.227695	−	0.262774i
$537$	10.6181	+	11.1901i	0.458206	+	0.482889i
$538$	9.10216	−	2.67264i	0.392422	−	0.115226i
$539$	−37.0592	−	42.7686i	−1.59625	−	1.84217i
$540$	0.702091	+	5.14850i	0.0302132	+	0.221556i
$541$	−4.25568	+	2.73496i	−0.182966	+	0.117585i	−0.628917	−	0.777472i	$-0.716502\pi$
$541$	−4.25568	+	2.73496i	−0.182966	+	0.117585i	0.445952	+	0.895057i	$0.352865\pi$
$542$	4.66071	−	4.03853i	0.200195	−	0.173470i
$543$	−4.45928	+	11.0610i	−0.191366	+	0.474673i
$544$	5.73917	+	0.825169i	0.246065	+	0.0353788i
$545$	−1.17710	−	1.01996i	−0.0504213	−	0.0436903i
$546$	−44.0217	+	22.5599i	−1.88396	+	0.965477i
$547$	−18.4259	−	5.41033i	−0.787834	−	0.231329i	−0.137022	−	0.990568i	$-0.543753\pi$
$547$	−18.4259	−	5.41033i	−0.787834	−	0.231329i	−0.650812	+	0.759239i	$0.725571\pi$
$548$	−4.39527	−	9.62429i	−0.187756	−	0.411129i
$549$	−12.5887	−	31.8919i	−0.537271	−	1.36111i
$550$	1.79997	−	2.80081i	0.0767511	−	0.119427i
$551$	1.79338			0.0764005
$552$	−1.21393	−	8.21744i	−0.0516685	−	0.349758i
$553$	32.0050			1.36099
$554$	1.33564	−	2.07829i	0.0567458	−	0.0882981i
$555$	−15.0307	−	8.72657i	−0.638016	−	0.370422i
$556$	8.36344	+	18.3134i	0.354689	+	0.776660i
$557$	15.5246	+	4.55843i	0.657798	+	0.193147i	0.593563	−	0.804788i	$-0.297721\pi$
$557$	15.5246	+	4.55843i	0.657798	+	0.193147i	0.0642356	+	0.997935i	$0.479539\pi$
$558$	0.0441942	−	0.223470i	0.00187089	−	0.00946022i
$559$	16.6836	+	14.4564i	0.705641	+	0.611441i
$560$	−4.84888	−	0.697164i	−0.204903	−	0.0294605i
$561$	−31.0104	−	12.5020i	−1.30926	−	0.527833i
$562$	−13.3976	+	11.6091i	−0.565142	+	0.489699i
$563$	19.9942	−	12.8495i	0.842656	−	0.541542i	−0.0466201	−	0.998913i	$-0.514845\pi$
$563$	19.9942	−	12.8495i	0.842656	−	0.541542i	0.889276	+	0.457370i	$0.151209\pi$
$564$	1.02944	−	10.5116i	0.0433474	−	0.442620i
$565$	6.89640	+	7.95886i	0.290134	+	0.334832i
$566$	5.60968	−	1.64715i	0.235793	−	0.0692350i
$567$	−41.8016	+	14.0156i	−1.75550	+	0.588600i
$568$	0.0893481	−	0.103113i	0.00374896	−	0.00432654i
$569$	15.6152	−	34.1925i	0.654623	−	1.43342i	−0.232827	−	0.972518i	$-0.574798\pi$
$569$	15.6152	−	34.1925i	0.654623	−	1.43342i	0.887449	−	0.460905i	$-0.152475\pi$
$570$	−1.15947	−	1.63662i	−0.0485648	−	0.0685506i
$571$	−7.74485	+	3.53695i	−0.324112	+	0.148017i	−0.570825	−	0.821072i	$-0.693377\pi$
$571$	−7.74485	+	3.53695i	−0.324112	+	0.148017i	0.246713	+	0.969088i	$0.420649\pi$
$572$	2.76228	+	19.2120i	0.115497	+	0.803296i
$573$	−0.916809	−	2.66985i	−0.0383002	−	0.111535i
$574$			33.6988i			1.40656i
$575$	4.65344	−	1.15995i	0.194062	−	0.0483731i
$576$	−0.693143	−	2.91883i	−0.0288810	−	0.121618i
$577$	30.4170	+	19.5478i	1.26627	+	0.813785i	0.989130	−	0.147043i	$-0.0469755\pi$
$577$	30.4170	+	19.5478i	1.26627	+	0.813785i	0.277145	+	0.960828i	$0.410612\pi$
$578$	16.4499	−	2.36513i	0.684224	−	0.0983766i
$579$	−7.10839	+	28.9944i	−0.295414	+	1.20497i
$580$	−0.436315	+	1.48595i	−0.0181170	+	0.0617008i
$581$	−45.4314	−	20.7478i	−1.88481	−	0.860765i
$582$	−23.3951	+	4.45027i	−0.969756	+	0.184470i
$583$	−1.56044	+	10.8531i	−0.0646266	+	0.449488i
$584$	−2.00732	−	6.83631i	−0.0830636	−	0.282889i
$585$	10.2139	−	14.1973i	0.422292	−	0.586987i
$586$	−3.17510	−	4.94055i	−0.131162	−	0.204092i
$587$	−7.66289	−	11.9237i	−0.316281	−	0.492143i	0.646320	−	0.763067i	$-0.276307\pi$
$587$	−7.66289	−	11.9237i	−0.316281	−	0.492143i	−0.962601	+	0.270924i	$0.912671\pi$
$588$	−1.32961	−	29.4108i	−0.0548320	−	1.21288i
$589$	0.0247727	+	0.0843682i	0.00102074	+	0.00347633i
$590$	0.349037	−	2.42761i	0.0143696	−	0.0999431i
$591$	0.741623	+	3.89871i	0.0305063	+	0.160371i
$592$	9.12771	+	4.16848i	0.375146	+	0.171324i
$593$	4.66749	−	15.8960i	0.191671	−	0.652771i	−0.806439	−	0.591317i	$-0.798608\pi$
$593$	4.66749	−	15.8960i	0.191671	−	0.652771i	0.998110	−	0.0614540i	$-0.0195738\pi$
$594$	−0.125728	+	17.2993i	−0.00515870	+	0.709798i
$595$	−28.1147	+	4.04229i	−1.15259	+	0.165718i
$596$	−16.3214	−	10.4891i	−0.668552	−	0.429652i
$597$	2.18289	−	2.76198i	0.0893398	−	0.113040i
$598$	−16.0743	+	22.8764i	−0.657328	+	0.935484i
$599$		−	0.452727i		−	0.0184979i	−0.999957	−	0.00924896i	$-0.997056\pi$
$599$		−	0.452727i		−	0.0184979i	0.999957	−	0.00924896i	$-0.00294408\pi$
$600$	1.63816	−	0.562531i	0.0668775	−	0.0229652i
$601$	−1.63673	−	11.3837i	−0.0667638	−	0.464352i	−0.995588	−	0.0938317i	$-0.970088\pi$
$601$	−1.63673	−	11.3837i	−0.0667638	−	0.464352i	0.928824	−	0.370520i	$-0.120821\pi$
$602$	−16.8734	+	7.70583i	−0.687709	+	0.314066i
$603$	−24.1163	−	1.26594i	−0.982091	−	0.0515531i
$604$	−3.48753	+	7.63662i	−0.141906	+	0.310730i
$605$	0.0553137	−	0.0638354i	0.00224882	−	0.00259528i
$606$	−8.12780	+	7.71233i	−0.330169	+	0.313292i
$607$	−11.6500	+	3.42076i	−0.472861	+	0.138844i	−0.509476	−	0.860485i	$-0.670161\pi$
$607$	−11.6500	+	3.42076i	−0.472861	+	0.138844i	0.0366151	+	0.999329i	$0.488342\pi$
$608$	0.758330	+	0.875159i	0.0307543	+	0.0354924i
$609$	−13.0778	−	1.28076i	−0.529940	−	0.0518990i
$610$	−9.61457	+	6.17891i	−0.389283	+	0.250177i
$611$	−26.8670	+	23.2804i	−1.08692	+	0.941825i
$612$	−8.62420	−	15.1061i	−0.348613	−	0.610628i
$613$	41.9749	+	6.03508i	1.69535	+	0.243755i	0.921156	−	0.389194i	$-0.127246\pi$
$613$	41.9749	+	6.03508i	1.69535	+	0.243755i	0.774194	+	0.632948i	$0.218155\pi$
$614$	12.7300	+	11.0306i	0.513740	+	0.445158i
$615$	−5.43405	−	10.6036i	−0.219122	−	0.427578i
$616$	−15.6489	−	4.59493i	−0.630512	−	0.185135i
$617$	4.69795	+	10.2871i	0.189132	+	0.414142i	0.980316	−	0.197437i	$-0.0632618\pi$
$617$	4.69795	+	10.2871i	0.189132	+	0.414142i	−0.791183	+	0.611579i	$0.790535\pi$
$618$	15.5912	−	26.8543i	0.627169	−	1.08024i
$619$	−2.49418	+	3.88102i	−0.100250	+	0.155991i	−0.887755	−	0.460317i	$-0.847736\pi$
$619$	−2.49418	+	3.88102i	−0.100250	+	0.155991i	0.787505	+	0.616308i	$0.211372\pi$
$620$	−0.0759325			−0.00304952
$621$	−17.2143	+	18.0185i	−0.690787	+	0.723058i
$622$	−16.8734			−0.676562
$623$	48.9418	−	76.1549i	1.96081	−	3.05108i
$624$	−5.06999	+	8.73256i	−0.202962	+	0.349582i
$625$	0.415415	+	0.909632i	0.0166166	+	0.0363853i
$626$	−18.3508	−	5.38827i	−0.733444	−	0.215358i
$627$	−3.04551	−	5.94277i	−0.121626	−	0.237332i
$628$	−7.99157	−	6.92474i	−0.318898	−	0.276327i
$629$	57.5898	+	8.28016i	2.29625	+	0.330152i
$630$	7.28636	+	12.7628i	0.290296	+	0.508481i
$631$	2.98801	−	2.58913i	0.118951	−	0.103071i	−0.593354	−	0.804941i	$-0.702197\pi$
$631$	2.98801	−	2.58913i	0.118951	−	0.103071i	0.712305	+	0.701870i	$0.247651\pi$
$632$	5.49617	−	3.53217i	0.218626	−	0.140502i
$633$	−18.7837	−	1.83955i	−0.746584	−	0.0731157i
$634$	0.115179	+	0.132924i	0.00457434	+	0.00527907i
$635$	12.3487	−	3.62592i	0.490045	−	0.143890i
$636$	−4.13789	+	3.92637i	−0.164078	+	0.155691i
$637$	−64.8930	+	74.8906i	−2.57116	+	2.96727i
$638$	−2.14192	+	4.69014i	−0.0847993	+	0.185685i
$639$	−0.408752	−	0.0214567i	−0.0161700	−	0.000848814i
$640$	−0.909632	+	0.415415i	−0.0359564	+	0.0164207i
$641$	−4.44630	−	30.9247i	−0.175618	−	1.22145i	−0.866757	−	0.498731i	$-0.833800\pi$
$641$	−4.44630	−	30.9247i	−0.175618	−	1.22145i	0.691138	−	0.722722i	$-0.257109\pi$
$642$	16.8963	−	5.80208i	0.666846	−	0.228990i
$643$		−	17.6159i		−	0.694703i	−0.937735	−	0.347351i	$-0.887081\pi$
$643$		−	17.6159i		−	0.694703i	0.937735	−	0.347351i	$-0.112919\pi$
$644$	−11.8745	−	20.2717i	−0.467920	−	0.798818i
$645$	4.06675	−	5.14559i	0.160128	−	0.202608i
$646$	5.64844	+	3.63003i	0.222235	+	0.142822i
$647$	36.8500	−	5.29823i	1.44872	−	0.208295i	0.627373	−	0.778719i	$-0.284130\pi$
$647$	36.8500	−	5.29823i	1.44872	−	0.208295i	0.821350	+	0.570424i	$0.193221\pi$
$648$	−5.63172	+	7.02024i	−0.221235	+	0.275781i
$649$	2.30047	−	7.83468i	0.0903013	−	0.307538i
$650$	−5.30304	−	2.42182i	−0.208002	−	0.0949915i
$651$	−0.120397	−	0.632929i	−0.00471875	−	0.0248064i
$652$	−1.73898	+	12.0949i	−0.0681038	+	0.473672i
$653$	2.00598	+	6.83173i	0.0785000	+	0.267346i	0.989386	−	0.145312i	$-0.0464186\pi$
$653$	2.00598	+	6.83173i	0.0785000	+	0.267346i	−0.910886	+	0.412658i	$0.864600\pi$
$654$	−0.121834	−	2.69496i	−0.00476408	−	0.105381i
$655$	−6.90943	−	10.7513i	−0.269974	−	0.420088i
$656$	3.71911	+	5.78704i	0.145207	+	0.225946i
$657$	−12.4828	+	17.3511i	−0.487000	+	0.676931i
$658$	−8.41597	−	28.6621i	−0.328089	−	1.11737i
$659$	6.06757	−	42.2009i	0.236359	−	1.64391i	−0.433303	−	0.901248i	$-0.642652\pi$
$659$	6.06757	−	42.2009i	0.236359	−	1.64391i	0.669662	−	0.742666i	$-0.266439\pi$
$660$	5.66499	−	1.07761i	0.220510	−	0.0419460i
$661$	10.2077	+	4.66170i	0.397033	+	0.181319i	0.603918	−	0.797046i	$-0.293605\pi$
$661$	10.2077	+	4.66170i	0.397033	+	0.181319i	−0.206885	+	0.978365i	$0.566333\pi$
$662$	−3.26284	+	11.1122i	−0.126814	+	0.431889i
$663$	−13.9410	+	56.8641i	−0.541425	+	2.20842i
$664$	−10.0917	+	1.45096i	−0.391632	+	0.0563082i
$665$	−4.77222	−	3.06692i	−0.185059	−	0.118930i
$666$	−6.95535	−	29.2890i	−0.269514	−	1.13493i
$667$	−6.87771	+	2.80373i	−0.266306	+	0.108561i
$668$			3.30279i			0.127789i
$669$	12.0398	+	35.0614i	0.465487	+	1.35555i
$670$	1.14561	+	7.96790i	0.0442588	+	0.307827i
$671$	−34.6120	+	15.8068i	−1.33618	+	0.610213i
$672$	−4.90495	−	6.92348i	−0.189213	−	0.267079i
$673$	0.192056	−	0.420545i	0.00740323	−	0.0162108i	−0.905894	−	0.423504i	$-0.860800\pi$
$673$	0.192056	−	0.420545i	0.00740323	−	0.0162108i	0.913297	+	0.407293i	$0.133527\pi$
$674$	−3.01225	+	3.47633i	−0.116028	+	0.133903i
$675$	−4.35075	−	2.84095i	−0.167460	−	0.109348i
$676$	20.1373	−	5.91285i	0.774513	−	0.227417i
$677$	−0.961607	−	1.10975i	−0.0369575	−	0.0426513i	0.736970	−	0.675926i	$-0.236256\pi$
$677$	−0.961607	−	1.10975i	−0.0369575	−	0.0426513i	−0.773927	+	0.633274i	$0.781710\pi$
$678$	−1.77784	+	18.1535i	−0.0682776	+	0.697182i
$679$	−56.6622	+	36.4146i	−2.17450	+	1.39746i
$680$	−4.38198	+	3.79701i	−0.168041	+	0.145609i
$681$	−4.93354	−	1.98897i	−0.189054	−	0.0762175i
$682$	−0.250232	−	0.0359779i	−0.00958186	−	0.00137766i
$683$	13.5967	+	11.7816i	0.520265	+	0.450812i	0.874978	−	0.484163i	$-0.160876\pi$
$683$	13.5967	+	11.7816i	0.520265	+	0.450812i	−0.354713	+	0.934975i	$0.615421\pi$
$684$	0.673980	−	3.40800i	0.0257703	−	0.130308i
$685$	10.1518	+	2.98085i	0.387882	+	0.113892i
$686$	−20.3454	−	44.5502i	−0.776791	−	1.70093i
$687$	17.7526	+	10.3069i	0.677305	+	0.393233i
$688$	−2.04720	+	3.18551i	−0.0780489	+	0.121447i
$689$	19.1998			0.731456
$690$	7.00529	+	4.46385i	0.266687	+	0.169936i
$691$	34.0057			1.29364			0.646818	−	0.762644i	$-0.276099\pi$
$691$	34.0057			1.29364			0.646818	+	0.762644i	$0.276099\pi$
$692$	0.829595	−	1.29088i	0.0315365	−	0.0490717i
$693$	17.9646	+	45.5114i	0.682421	+	1.72883i
$694$	−2.55948	−	5.60447i	−0.0971564	−	0.212743i
$695$	−19.3172	−	5.67205i	−0.732744	−	0.215153i
$696$	−2.38718	+	1.22337i	−0.0904860	+	0.0463716i
$697$	30.1440	+	26.1199i	1.14178	+	0.989361i
$698$	−17.7833	−	2.55686i	−0.673109	−	0.0967785i
$699$	5.10162	−	12.6543i	0.192961	−	0.478629i
$700$	3.70222	−	3.20799i	0.139931	−	0.121251i
$701$	12.5471	−	8.06352i	0.473897	−	0.304555i	−0.281804	−	0.959472i	$-0.590933\pi$
$701$	12.5471	−	8.06352i	0.473897	−	0.304555i	0.755701	+	0.654917i	$0.227296\pi$
$702$	30.0151	−	4.09310i	1.13285	−	0.154484i
$703$	7.60946	+	8.78179i	0.286996	+	0.331211i
$704$	−3.19447	+	0.937982i	−0.120396	+	0.0353515i
$705$	7.27002	+	7.66166i	0.273805	+	0.288555i
$706$	7.16472	−	8.26852i	0.269648	−	0.311190i
$707$	−13.1643	+	28.8259i	−0.495096	+	1.08411i
$708$	3.46626	−	2.45568i	0.130270	−	0.0922901i
$709$	−3.64079	+	1.66269i	−0.136733	+	0.0624438i	−0.482606	−	0.875837i	$-0.660310\pi$
$709$	−3.64079	+	1.66269i	−0.136733	+	0.0624438i	0.345874	+	0.938281i	$0.387583\pi$
$710$	0.0194172	+	0.135050i	0.000728715	+	0.00506832i
$711$	−18.4907	−	6.50017i	−0.693454	−	0.243776i
$712$		−	18.4793i		−	0.692542i
$713$	−0.226904	−	0.284828i	−0.00849763	−	0.0106669i
$714$	−38.5976	−	30.5051i	−1.44448	−	1.14162i
$715$	−16.3284	−	10.4936i	−0.610648	−	0.392439i
$716$	8.81559	−	1.26749i	0.329454	−	0.0473683i
$717$	38.9148	+	9.54050i	1.45330	+	0.356297i
$718$	−1.88722	+	6.42730i	−0.0704306	+	0.239865i
$719$	17.7331	+	8.09845i	0.661335	+	0.302021i	0.717663	−	0.696391i	$-0.245212\pi$
$719$	17.7331	+	8.09845i	0.661335	+	0.302021i	−0.0563280	+	0.998412i	$0.517939\pi$
$720$	2.65981	+	1.38758i	0.0991254	+	0.0517122i
$721$	12.4987	−	86.9306i	0.465477	−	3.23746i
$722$	−4.97512	−	16.9437i	−0.185155	−	0.630580i
$723$	33.4685	−	1.51305i	1.24471	−	0.0562708i
$724$	3.72259	+	5.79246i	0.138349	+	0.215275i
$725$	−0.837282	−	1.30284i	−0.0310959	−	0.0483861i
$726$	0.146151	−	0.00660719i	0.00542416	−	0.000245216i
$727$	−9.65750	−	32.8904i	−0.358177	−	1.21984i	−0.919781	−	0.392432i	$-0.871634\pi$
$727$	−9.65750	−	32.8904i	−0.358177	−	1.21984i	0.561604	−	0.827406i	$-0.310184\pi$
$728$	−4.06438	+	28.2684i	−0.150636	+	1.04770i
$729$	26.9971	+	0.392443i	0.999894	+	0.0145349i
$730$	6.48106	+	2.95980i	0.239875	+	0.109547i
$731$	−6.18560	+	21.0662i	−0.228783	+	0.779163i
$732$	−19.2260	−	4.71353i	−0.710614	−	0.174217i
$733$	−26.5003	+	3.81016i	−0.978810	+	0.140732i	−0.613107	−	0.790000i	$-0.710081\pi$
$733$	−26.5003	+	3.81016i	−0.978810	+	0.140732i	−0.365703	+	0.930732i	$0.619171\pi$
$734$	−2.64245	−	1.69820i	−0.0975345	−	0.0626816i
$735$	23.0979	+	18.2551i	0.851979	+	0.673351i
$736$	−4.27644	−	2.17073i	−0.157632	−	0.0800141i
$737$			26.8006i			0.987212i
$738$	6.84418	−	19.4693i	0.251938	−	0.716673i
$739$	−1.20643	−	8.39090i	−0.0443792	−	0.308664i	−0.999905	−	0.0137578i	$-0.995621\pi$
$739$	−1.20643	−	8.39090i	−0.0443792	−	0.308664i	0.955526	−	0.294906i	$-0.0952885\pi$
$740$	−9.12771	+	4.16848i	−0.335541	+	0.153237i
$741$	−9.54131	+	6.75956i	−0.350509	+	0.248319i
$742$	−6.70201	+	14.6754i	−0.246039	+	0.538749i
$743$	16.7358	−	19.3142i	0.613978	−	0.708568i	−0.360574	−	0.932731i	$-0.617419\pi$
$743$	16.7358	−	19.3142i	0.613978	−	0.708568i	0.974552	+	0.224163i	$0.0719647\pi$
$744$	−0.0905277	−	0.0954044i	−0.00331891	−	0.00349769i
$745$	18.6154	−	5.46598i	0.682016	−	0.200258i
$746$	16.0805	+	18.5579i	0.588748	+	0.679451i
$747$	22.0338	+	21.2140i	0.806175	+	0.776179i
$748$	−16.2397	+	10.4366i	−0.593781	+	0.381600i
$749$	38.1856	−	33.0880i	1.39527	−	1.20901i
$750$	−0.647632	+	1.60642i	−0.0236482	+	0.0586580i
$751$	−6.69390	−	0.962437i	−0.244264	−	0.0351198i	0.0190955	−	0.999818i	$-0.493921\pi$
$751$	−6.69390	−	0.962437i	−0.244264	−	0.0351198i	−0.263359	+	0.964698i	$0.584830\pi$
$752$	−4.60851	−	3.99329i	−0.168055	−	0.145620i
$753$	−17.6152	+	9.02734i	−0.641935	+	0.328974i
$754$	8.66292	+	2.54366i	0.315485	+	0.0926347i
$755$	−3.48753	−	7.63662i	−0.126924	−	0.277925i
$756$	−7.34871	+	24.3708i	−0.267270	+	0.886356i
$757$	4.46861	−	6.95329i	0.162414	−	0.252722i	−0.750502	−	0.660868i	$-0.770188\pi$
$757$	4.46861	−	6.95329i	0.162414	−	0.252722i	0.912917	+	0.408146i	$0.133825\pi$
$758$	27.6454			1.00413
$759$	20.9705	+	18.0296i	0.761181	+	0.654432i
$760$	−1.15800			−0.0420051
$761$	−26.9587	+	41.9485i	−0.977250	+	1.52063i	−0.128587	+	0.991698i	$0.541044\pi$
$761$	−26.9587	+	41.9485i	−0.977250	+	1.52063i	−0.848664	+	0.528933i	$0.822592\pi$
$762$	19.2780	+	11.1925i	0.698370	+	0.405463i
$763$	−3.16958	−	6.94040i	−0.114746	−	0.251260i
$764$	−1.56377	−	0.459165i	−0.0565753	−	0.0166120i
$765$	17.0641	+	3.37466i	0.616953	+	0.122011i
$766$	−13.3739	−	11.5885i	−0.483217	−	0.418710i
$767$	−14.1527	−	2.03485i	−0.511023	−	0.0734740i
$768$	−1.60642	−	0.647632i	−0.0579666	−	0.0233694i
$769$	−11.0690	+	9.59138i	−0.399160	+	0.345874i	−0.831193	−	0.555984i	$-0.812342\pi$
$769$	−11.0690	+	9.59138i	−0.399160	+	0.345874i	0.432033	+	0.901858i	$0.357796\pi$
$770$	13.7205	−	8.81761i	0.494451	−	0.317765i
$771$	0.698315	−	7.13049i	0.0251492	−	0.256798i
$772$	11.2870	+	13.0259i	0.406227	+	0.468811i
$773$	−29.4462	+	8.64619i	−1.05911	+	0.310982i	−0.764491	−	0.644634i	$-0.777010\pi$
$773$	−29.4462	+	8.64619i	−1.05911	+	0.310982i	−0.294616	+	0.955616i	$0.595192\pi$
$774$	11.3135	−	1.02502i	0.406657	−	0.0368436i
$775$	0.0497252	−	0.0573860i	0.00178618	−	0.00206137i
$776$	−5.71168	+	12.5068i	−0.205037	+	0.448969i
$777$	−49.2187	−	69.4737i	−1.76571	−	2.49235i
$778$	−22.4323	+	10.2445i	−0.804237	+	0.367283i
$779$	1.13368	+	7.88489i	0.0406182	+	0.282506i
$780$	−3.27949	−	9.55025i	−0.117425	−	0.341954i
$781$			0.454249i			0.0162543i
$782$	−27.3372	−	5.09072i	−0.977576	−	0.182044i
$783$	7.29550	+	3.39604i	0.260720	+	0.121365i
$784$	−14.2994	−	9.18964i	−0.510691	−	0.328201i
$785$	10.4667	−	1.50489i	0.373574	−	0.0537118i
$786$	5.27080	−	21.4991i	0.188003	−	0.766847i
$787$	−3.32582	+	11.3267i	−0.118553	+	0.403753i	−0.997292	−	0.0735496i	$-0.976567\pi$
$787$	−3.32582	+	11.3267i	−0.118553	+	0.403753i	0.878739	+	0.477303i	$0.158385\pi$
$788$	2.08422	+	0.951833i	0.0742474	+	0.0339076i
$789$	−11.5525	+	2.19756i	−0.411281	+	0.0782350i
$790$	−0.929787	+	6.46681i	−0.0330803	+	0.230079i
$791$	14.5343	+	49.4994i	0.516781	+	1.75999i
$792$	8.10782	+	5.83296i	0.288099	+	0.207265i
$793$	36.0223	+	56.0518i	1.27919	+	1.99046i
$794$	12.4094	+	19.3095i	0.440394	+	0.685267i
$795$	−0.257615	−	5.69843i	−0.00913667	−	0.202103i
$796$	−0.572630	−	1.95020i	−0.0202963	−	0.0691229i
$797$	4.64416	−	32.3008i	0.164504	−	1.14415i	−0.725507	−	0.688215i	$-0.758395\pi$
$797$	4.64416	−	32.3008i	0.164504	−	1.14415i	0.890011	−	0.455939i	$-0.150696\pi$
$798$	−1.83611	−	9.65241i	−0.0649975	−	0.341692i
$799$	−32.1618	−	14.6878i	−1.13780	−	0.519617i
$800$	0.281733	−	0.959493i	0.00996075	−	0.0339232i
$801$	−43.7427	+	34.0579i	−1.54557	+	1.20338i
$802$	−8.85503	+	1.27316i	−0.312682	+	0.0449569i
$803$	19.9556	+	12.8247i	0.704217	+	0.452573i
$804$	−8.64534	+	10.9388i	−0.304898	+	0.385782i
$805$	23.0965	+	4.30102i	0.814044	+	0.151591i
$806$			0.442677i			0.0155926i
$807$	−15.5403	+	5.33642i	−0.547043	+	0.187851i
$808$	0.920625	+	6.40309i	0.0323875	+	0.225260i
$809$	−15.1046	+	6.89804i	−0.531050	+	0.242522i	−0.662848	−	0.748754i	$-0.730652\pi$
$809$	−15.1046	+	6.89804i	−0.531050	+	0.242522i	0.131798	+	0.991277i	$0.457925\pi$
$810$	−1.61755	−	8.85345i	−0.0568348	−	0.311078i
$811$	−18.6114	+	40.7532i	−0.653534	+	1.43104i	0.234893	+	0.972021i	$0.424526\pi$
$811$	−18.6114	+	40.7532i	−0.653534	+	1.43104i	−0.888427	+	0.459019i	$0.848201\pi$
$812$	−4.96817	+	5.73358i	−0.174349	+	0.201209i
$813$	−7.74844	+	7.35237i	−0.271750	+	0.257859i
$814$	−32.0550	+	9.41218i	−1.12353	+	0.329897i
$815$	−8.00192	−	9.23470i	−0.280295	−	0.323478i
$816$	−9.99495	−	0.978842i	−0.349893	−	0.0342663i
$817$	−3.68883	+	2.37067i	−0.129056	+	0.0829391i
$818$	8.81375	−	7.63716i	0.308166	−	0.267027i
$819$	74.4053	−	42.4786i	2.59993	−	1.48432i
$820$	−6.80905	−	0.978994i	−0.237782	−	0.0341879i
$821$	7.68658	+	6.66046i	0.268264	+	0.232452i	0.778596	−	0.627526i	$-0.215932\pi$
$821$	7.68658	+	6.66046i	0.268264	+	0.232452i	−0.510332	+	0.859977i	$0.670478\pi$
$822$	8.35790	+	16.3089i	0.291515	+	0.568840i
$823$	−18.2627	−	5.36242i	−0.636599	−	0.186922i	−0.0525209	−	0.998620i	$-0.516726\pi$
$823$	−18.2627	−	5.36242i	−0.636599	−	0.186922i	−0.584078	+	0.811697i	$0.698544\pi$
$824$	−7.44755	−	16.3079i	−0.259448	−	0.568111i
$825$	−2.89538	+	4.98700i	−0.100804	+	0.173625i
$826$	6.49554	−	10.1073i	0.226009	−	0.351677i
$827$	16.2099			0.563673			0.281837	−	0.959462i	$-0.409056\pi$
$827$	16.2099			0.563673			0.281837	+	0.959462i	$0.409056\pi$
$828$	2.74324	+	14.1235i	0.0953343	+	0.490827i
$829$	−3.71257			−0.128943			−0.0644714	−	0.997920i	$-0.520536\pi$
$829$	−3.71257			−0.128943			−0.0644714	+	0.997920i	$0.520536\pi$
$830$	5.51207	−	8.57695i	0.191327	−	0.297710i
$831$	−2.14846	+	3.70051i	−0.0745292	+	0.128369i
$832$	2.42182	+	5.30304i	0.0839615	+	0.183850i
$833$	−94.5636	−	27.7664i	−3.27644	−	0.962048i
$834$	−15.9036	−	31.0331i	−0.550698	−	1.07459i
$835$	−2.49608	−	2.16287i	−0.0863805	−	0.0748491i
$836$	−3.81613	−	0.548677i	−0.131984	−	0.0189764i
$837$	−0.0589882	+	0.390123i	−0.00203893	+	0.0134846i
$838$	18.7878	−	16.2798i	0.649015	−	0.562375i
$839$	−36.8906	+	23.7081i	−1.27360	+	0.818495i	−0.990085	−	0.140472i	$-0.955138\pi$
$839$	−36.8906	+	23.7081i	−1.27360	+	0.818495i	−0.283519	+	0.958967i	$0.591502\pi$
$840$	8.44447	+	0.826998i	0.291362	+	0.0285341i
$841$	−17.4203	−	20.1041i	−0.600701	−	0.693246i
$842$	22.3143	−	6.55206i	0.769000	−	0.225799i
$843$	22.2735	−	21.1350i	0.767140	−	0.727927i
$844$	−7.13578	+	8.23513i	−0.245624	+	0.283465i
$845$	−8.71851	+	19.0909i	−0.299926	+	0.656746i
$846$	−0.958978	+	18.2686i	−0.0329704	+	0.628088i
$847$	0.376387	−	0.171890i	0.0129328	−	0.00590621i
$848$	0.468693	+	3.25983i	0.0160950	+	0.111943i
$849$	−9.57750	+	3.28885i	−0.328699	+	0.112873i
$850$		−	5.79819i		−	0.198876i
$851$	−42.9120	−	21.7822i	−1.47100	−	0.746683i
$852$	−0.146532	+	0.185404i	−0.00502010	+	0.00635184i
$853$	−32.8779	−	21.1293i	−1.12572	−	0.723454i	−0.161055	−	0.986946i	$-0.551489\pi$
$853$	−32.8779	−	21.1293i	−1.12572	−	0.723454i	−0.964662	+	0.263492i	$0.915126\pi$
$854$	−55.4172	+	7.96779i	−1.89634	+	0.272652i
$855$	2.13423	+	2.74112i	0.0729891	+	0.0937445i
$856$	2.90586	−	9.89644i	0.0993202	−	0.338253i
$857$	44.7098	+	20.4183i	1.52726	+	0.697475i	0.989354	−	0.145531i	$-0.0464890\pi$
$857$	44.7098	+	20.4183i	1.52726	+	0.697475i	0.537904	+	0.843006i	$0.319216\pi$
$858$	−6.28234	−	33.0262i	−0.214476	−	1.12750i
$859$	2.89003	−	20.1006i	0.0986067	−	0.685825i	−0.879221	−	0.476414i	$-0.841936\pi$
$859$	2.89003	−	20.1006i	0.0986067	−	0.685825i	0.977828	−	0.209411i	$-0.0671545\pi$
$860$	−1.06682	−	3.63324i	−0.0363781	−	0.123892i
$861$	−2.63601	−	58.3085i	−0.0898351	−	1.98715i
$862$	−1.44199	−	2.24378i	−0.0491143	−	0.0764234i
$863$	−17.5450	−	27.3005i	−0.597238	−	0.929320i	−0.999902	−	0.0139726i	$-0.995552\pi$
$863$	−17.5450	−	27.3005i	−0.597238	−	0.929320i	0.402665	−	0.915348i	$-0.368084\pi$
$864$	1.42765	+	4.99618i	0.0485697	+	0.169973i
$865$	0.432309	+	1.47231i	0.0146990	+	0.0500600i
$866$	2.19800	−	15.2874i	0.0746911	−	0.519488i
$867$	−28.2779	+	5.37911i	−0.960369	+	0.182684i
$868$	−0.338359	−	0.154524i	−0.0114847	−	0.00524487i
$869$	−6.12812	+	20.8705i	−0.207882	+	0.707982i
$870$	0.638713	−	2.60525i	0.0216544	−	0.0883262i
$871$	46.4519	−	6.67877i	1.57396	−	0.226301i
$872$	−1.31027	−	0.842060i	−0.0443714	−	0.0285158i
$873$	40.1320	−	9.53026i	1.35826	−	0.322550i
$874$	−3.46038	−	4.34373i	−0.117049	−	0.146929i
$875$			4.89874i			0.165608i
$876$	4.00799	+	11.6717i	0.135418	+	0.394352i
$877$	−4.17664	−	29.0492i	−0.141035	−	0.980921i	−0.930282	−	0.366845i	$-0.880438\pi$
$877$	−4.17664	−	29.0492i	−0.141035	−	0.980921i	0.789247	−	0.614076i	$-0.210471\pi$
$878$	−17.4046	+	7.94842i	−0.587377	+	0.268246i
$879$	5.88028	+	8.30019i	0.198337	+	0.279958i
$880$	1.38306	−	3.02847i	0.0466228	−	0.102090i
$881$	−12.7779	+	14.7465i	−0.430499	+	0.496822i	−0.929007	−	0.370063i	$-0.879336\pi$
$881$	−12.7779	+	14.7465i	−0.430499	+	0.496822i	0.498508	+	0.866885i	$0.333882\pi$
$882$	4.60119	+	50.7850i	0.154930	+	1.71002i
$883$	41.9855	−	12.3281i	1.41293	−	0.414872i	0.515823	−	0.856695i	$-0.327486\pi$
$883$	41.9855	−	12.3281i	1.41293	−	0.414872i	0.897102	+	0.441823i	$0.145668\pi$
$884$	22.1361	+	25.5464i	0.744517	+	0.859219i
$885$	−0.414039	+	4.22775i	−0.0139178	+	0.142114i
$886$	22.4818	−	14.4482i	0.755290	−	0.485396i
$887$	−3.81866	+	3.30889i	−0.128218	+	0.111102i	−0.716609	−	0.697475i	$-0.754307\pi$
$887$	−3.81866	+	3.30889i	−0.128218	+	0.111102i	0.588391	+	0.808576i	$0.299762\pi$
$888$	−16.1196	−	6.49866i	−0.540938	−	0.218081i
$889$	62.4054	+	8.97254i	2.09301	+	0.300929i
$890$	13.9657	+	12.1014i	0.468133	+	0.405639i
$891$	−1.13565	−	29.9425i	−0.0380458	−	1.00311i
$892$	20.5360	+	6.02991i	0.687596	+	0.201896i
$893$	−2.93341	−	6.42328i	−0.0981630	−	0.214947i
$894$	29.0612	+	16.8725i	0.971951	+	0.564300i
$895$	−4.81508	+	7.49240i	−0.160950	+	0.250443i
$896$	−4.89874			−0.163656
$897$	26.0237	−	40.8400i	0.868906	−	1.36361i
$898$	−19.4567			−0.649278
$899$	−0.0635770	+	0.0989277i	−0.00212041	+	0.00329942i
$900$	−2.79047	+	1.10148i	−0.0930158	+	0.0367160i
$901$	7.93255	+	17.3699i	0.264272	+	0.578674i
$902$	−21.9750	−	6.45244i	−0.731688	−	0.214843i
$903$	28.5930	−	14.6532i	0.951516	−	0.487626i
$904$	7.95886	+	6.89640i	0.264708	+	0.229371i
$905$	−6.81543	−	0.979911i	−0.226553	−	0.0325733i
$906$	5.43705	−	13.4863i	0.180634	−	0.448053i
$907$	−11.7819	+	10.2090i	−0.391210	+	0.338986i	−0.828151	−	0.560505i	$-0.810607\pi$
$907$	−11.7819	+	10.2090i	−0.391210	+	0.338986i	0.436941	+	0.899490i	$0.356062\pi$
$908$	−2.58361	+	1.66039i	−0.0857402	+	0.0551019i
$909$	13.4601	−	13.9803i	0.446444	−	0.463697i
$910$	−18.7022	−	21.5835i	−0.619972	−	0.715486i
$911$	−43.1223	+	12.6618i	−1.42871	+	0.419506i	−0.902440	−	0.430815i	$-0.858226\pi$
$911$	−43.1223	+	12.6618i	−1.42871	+	0.419506i	−0.526265	+	0.850321i	$0.676408\pi$
$912$	−1.38058	−	1.45495i	−0.0457157	−	0.0481784i
$913$	22.2286	−	25.6532i	0.735659	−	0.848996i
$914$	−9.67042	+	21.1753i	−0.319869	+	0.700415i
$915$	16.1526	−	11.4433i	0.533989	−	0.378305i
$916$	10.7807	−	4.92338i	0.356204	−	0.162673i
$917$	−8.90981	−	61.9691i	−0.294228	−	2.04640i
$918$	16.1039	+	25.4632i	0.531509	+	0.840412i
$919$			50.6555i			1.67097i	0.549512	+	0.835486i	$0.314814\pi$
$919$			50.6555i			1.67097i	−0.549512	+	0.835486i	$0.685186\pi$
$920$	4.44100	−	1.81039i	0.146415	−	0.0596869i
$921$	−22.8893	−	18.0903i	−0.754229	−	0.596095i
$922$	−20.5918	−	13.2336i	−0.678156	−	0.435825i
$923$	0.787323	−	0.113200i	0.0259150	−	0.00372602i
$924$	27.4365	+	6.72643i	0.902593	+	0.221283i
$925$	2.82705	−	9.62804i	0.0929527	−	0.316568i
$926$	11.8582	+	5.41547i	0.389686	+	0.177963i
$927$	−24.8765	+	47.6851i	−0.817053	+	1.56618i
$928$	−0.220401	+	1.53292i	−0.00723501	+	0.0503206i
$929$	−6.78000	−	23.0905i	−0.222444	−	0.757576i	−0.992781	−	0.119939i	$-0.961730\pi$
$929$	−6.78000	−	23.0905i	−0.222444	−	0.757576i	0.770337	−	0.637637i	$-0.220088\pi$
$930$	0.131385	−	0.00593966i	0.00430828	−	0.000194769i
$931$	−10.6416	−	16.5587i	−0.348765	−	0.542689i
$932$	−4.25882	−	6.62685i	−0.139502	−	0.217070i
$933$	29.1958	−	1.31989i	0.955827	−	0.0432111i
$934$	2.12395	+	7.23352i	0.0694979	+	0.236688i
$935$	2.74726	−	19.1076i	0.0898451	−	0.624886i
$936$	8.08944	−	15.5064i	0.264412	−	0.506842i
$937$	32.6584	+	14.9146i	1.06690	+	0.487238i	0.869932	−	0.493171i	$-0.164162\pi$
$937$	32.6584	+	14.9146i	1.06690	+	0.487238i	0.196971	+	0.980409i	$0.436890\pi$
$938$	−11.1099	+	37.8367i	−0.362750	+	1.23541i
$939$	32.1735	+	7.88778i	1.04994	+	0.257408i
$940$	6.03586	−	0.867826i	0.196868	−	0.0283053i
$941$	47.6822	+	30.6435i	1.55440	+	0.998950i	0.984122	+	0.177495i	$0.0567994\pi$
$941$	47.6822	+	30.6435i	1.55440	+	0.998950i	0.570274	+	0.821454i	$0.306837\pi$
$942$	14.3694	+	11.3566i	0.468179	+	0.370019i
$943$	−16.6748	−	28.4666i	−0.543006	−	0.927001i
$944$		−	2.45257i		−	0.0798244i
$945$	−13.6058	−	21.5132i	−0.442597	−	0.699826i
$946$	−1.79416	−	12.4786i	−0.0583330	−	0.405715i
$947$	35.7086	−	16.3075i	1.16037	−	0.529924i	0.260241	−	0.965544i	$-0.416198\pi$
$947$	35.7086	−	16.3075i	1.16037	−	0.529924i	0.900131	+	0.435619i	$0.143471\pi$
$948$	−9.23363	+	6.54159i	−0.299895	+	0.212461i
$949$	17.2553	−	37.7838i	0.560130	−	1.22651i
$950$	0.758330	−	0.875159i	0.0246035	−	0.0283939i
$951$	−0.209690	−	0.220986i	−0.00679966	−	0.00716596i
$952$	−27.2533	+	8.00229i	−0.883284	+	0.259356i
$953$	23.6928	+	27.3430i	0.767486	+	0.885726i	0.996140	−	0.0877818i	$-0.0279778\pi$
$953$	23.6928	+	27.3430i	0.767486	+	0.885726i	−0.228654	+	0.973508i	$0.573432\pi$
$954$	6.85259	−	7.11742i	0.221861	−	0.230435i
$955$	1.37107	−	0.881132i	0.0443667	−	0.0285128i
$956$	17.4826	−	15.1488i	0.565428	−	0.489946i
$957$	3.33925	−	8.28282i	0.107943	−	0.267746i
$958$	29.4888	+	4.23985i	0.952741	+	0.136983i
$959$	39.1711	+	33.9419i	1.26490	+	1.09604i
$960$	1.54143	−	0.789940i	0.0497493	−	0.0254952i
$961$	29.7387	+	8.73208i	0.959315	+	0.281680i
$962$	24.3018	+	53.2134i	0.783520	+	1.71567i
$963$	−28.7816	+	11.3609i	−0.927475	+	0.366101i
$964$	10.4575	−	16.2722i	0.336813	−	0.524091i
$965$	−17.2357			−0.554836
$966$	22.1319	+	34.1470i	0.712084	+	1.09866i
$967$	9.75777			0.313789			0.156894	−	0.987615i	$-0.449852\pi$
$967$	9.75777			0.313789			0.156894	+	0.987615i	$0.449852\pi$
$968$	0.0456660	−	0.0710576i	0.00146776	−	0.00228388i
$969$	−10.0574	−	5.83915i	−0.323089	−	0.187580i
$970$	−5.71168	−	12.5068i	−0.183391	−	0.401571i
$971$	8.02687	+	2.35690i	0.257594	+	0.0756365i	0.407980	−	0.912991i	$-0.366233\pi$
$971$	8.02687	+	2.35690i	0.257594	+	0.0756365i	−0.150386	+	0.988627i	$0.548052\pi$
$972$	9.19533	−	12.5875i	0.294940	−	0.403745i
$973$	−74.5359	−	64.5857i	−2.38951	−	2.07052i
$974$	−4.59793	−	0.661083i	−0.147327	−	0.0211825i
$975$	9.36521	+	3.77561i	0.299927	+	0.120916i
$976$	−8.63736	+	7.48431i	−0.276475	+	0.239567i
$977$	−42.7832	+	27.4951i	−1.36875	+	0.879645i	−0.998779	−	0.0493960i	$-0.984270\pi$
$977$	−42.7832	+	27.4951i	−1.36875	+	0.879645i	−0.369976	+	0.929041i	$0.620634\pi$
$978$	2.06284	−	21.0636i	0.0659623	−	0.673540i
$979$	40.2896	+	46.4966i	1.28766	+	1.48604i
$980$	16.3092	−	4.78880i	0.520977	−	0.152973i
$981$	0.421614	+	4.65351i	0.0134611	+	0.148575i
$982$	−14.0849	+	16.2548i	−0.449466	+	0.518711i
$983$	−16.8501	+	36.8966i	−0.537434	+	1.17682i	0.424973	+	0.905206i	$0.360284\pi$
$983$	−16.8501	+	36.8966i	−0.537434	+	1.17682i	−0.962407	+	0.271611i	$0.912444\pi$
$984$	−6.88779	−	9.72231i	−0.219575	−	0.309936i
$985$	−2.08422	+	0.951833i	−0.0664089	+	0.0303279i
$986$	1.27793	+	8.88817i	0.0406975	+	0.283057i
$987$	16.8040	+	48.9353i	0.534879	+	1.55763i
$988$			6.75101i			0.214778i
$989$	10.4406	−	14.8587i	0.331992	−	0.472478i
$990$	−9.71775	+	2.30770i	−0.308850	+	0.0733437i
$991$	41.4978	+	26.6690i	1.31822	+	0.847168i	0.995070	−	0.0991795i	$-0.0316218\pi$
$991$	41.4978	+	26.6690i	1.31822	+	0.847168i	0.323150	+	0.946348i	$0.395258\pi$
$992$	−0.0751597	+	0.0108063i	−0.00238632	+	0.000343101i
$993$	4.77641	−	19.4825i	0.151575	−	0.618259i
$994$	−0.188303	+	0.641303i	−0.00597262	+	0.0203409i
$995$	1.84885	+	0.844343i	0.0586126	+	0.0267675i
$996$	17.3479	−	3.29997i	0.549690	−	0.104564i
$997$	−0.767507	+	5.33813i	−0.0243072	+	0.169060i	−0.998359	−	0.0572648i	$-0.981762\pi$
$997$	−0.767507	+	5.33813i	−0.0243072	+	0.169060i	0.974052	+	0.226325i	$0.0726711\pi$
$998$	−11.8658	−	40.4111i	−0.375605	−	1.27919i
$999$	14.3258	+	50.1342i	0.453248	+	1.58618i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.q.b.251.6	yes	160
3.2	odd	2		690.2.q.a.251.10	yes	160
23.11	odd	22		690.2.q.a.11.10	✓	160
69.11	even	22	inner	690.2.q.b.11.6	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.q.a.11.10	✓	160	23.11	odd	22
690.2.q.a.251.10	yes	160	3.2	odd	2
690.2.q.b.11.6	yes	160	69.11	even	22	inner
690.2.q.b.251.6	yes	160	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.q (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.540641 + 0.841254i) q^{2} +(0.869657 - 1.49790i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(0.959493 + 0.281733i) q^{5} +(0.789940 + 1.54143i) q^{6} +(3.70222 + 3.20799i) q^{7} +(0.989821 + 0.142315i) q^{8} +(-1.48739 - 2.60531i) q^{9} +O(q^{10})\)	\(q+(-0.540641 + 0.841254i) q^{2} +(0.869657 - 1.49790i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(0.959493 + 0.281733i) q^{5} +(0.789940 + 1.54143i) q^{6} +(3.70222 + 3.20799i) q^{7} +(0.989821 + 0.142315i) q^{8} +(-1.48739 - 2.60531i) q^{9} +(-0.755750 + 0.654861i) q^{10} +(-2.80081 + 1.79997i) q^{11} +(-1.72380 - 0.168818i) q^{12} +(3.81776 + 4.40593i) q^{13} +(-4.70031 + 1.38014i) q^{14} +(1.25644 - 1.19221i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-2.40866 + 5.27422i) q^{17} +(2.99588 + 0.157263i) q^{18} +(-1.05335 + 0.481051i) q^{19} +(-0.142315 - 0.989821i) q^{20} +(8.02491 - 2.75570i) q^{21} -3.32933i q^{22} +(3.28761 - 3.49165i) q^{23} +(1.07398 - 1.35889i) q^{24} +(0.841254 + 0.540641i) q^{25} +(-5.77054 + 0.829678i) q^{26} +(-5.19602 - 0.0377638i) q^{27} +(1.38014 - 4.70031i) q^{28} +(-1.40873 - 0.643347i) q^{29} +(0.323672 + 1.70154i) q^{30} +(0.0108063 - 0.0751597i) q^{31} +(-0.281733 - 0.959493i) q^{32} +(0.260430 + 5.76069i) q^{33} +(-3.13474 - 4.87775i) q^{34} +(2.64846 + 4.12108i) q^{35} +(-1.75199 + 2.43527i) q^{36} +(-2.82705 - 9.62804i) q^{37} +(0.164801 - 1.14621i) q^{38} +(9.91977 - 1.88697i) q^{39} +(0.909632 + 0.415415i) q^{40} +(1.93806 - 6.60042i) q^{41} +(-2.02035 + 8.24083i) q^{42} +(3.74808 - 0.538893i) q^{43} +(2.80081 + 1.79997i) q^{44} +(-0.693143 - 2.91883i) q^{45} +(1.15995 + 4.65344i) q^{46} +6.09793i q^{47} +(0.562531 + 1.63816i) q^{48} +(2.41902 + 16.8247i) q^{49} +(-0.909632 + 0.415415i) q^{50} +(5.80554 + 8.19468i) q^{51} +(2.42182 - 5.30304i) q^{52} +(2.15669 - 2.48895i) q^{53} +(2.84095 - 4.35075i) q^{54} +(-3.19447 + 0.937982i) q^{55} +(3.20799 + 3.70222i) q^{56} +(-0.195492 + 1.99617i) q^{57} +(1.30284 - 0.837282i) q^{58} +(-1.85353 + 1.60609i) q^{59} +(-1.60642 - 0.647632i) q^{60} +(11.3125 + 1.62650i) q^{61} +(0.0573860 + 0.0497252i) q^{62} +(2.85117 - 14.4170i) q^{63} +(0.959493 + 0.281733i) q^{64} +(2.42182 + 5.30304i) q^{65} +(-4.98700 - 2.89538i) q^{66} +(4.35207 - 6.77195i) q^{67} +5.79819 q^{68} +(-2.37104 - 7.96104i) q^{69} -4.89874 q^{70} +(0.0737642 - 0.114779i) q^{71} +(-1.10148 - 2.79047i) q^{72} +(-2.95980 - 6.48106i) q^{73} +(9.62804 + 2.82705i) q^{74} +(1.54143 - 0.789940i) q^{75} +(0.875159 + 0.758330i) q^{76} +(-16.1435 - 2.32109i) q^{77} +(-3.77561 + 9.36521i) q^{78} +(4.93755 - 4.27841i) q^{79} +(-0.841254 + 0.540641i) q^{80} +(-4.57532 + 7.75026i) q^{81} +(4.50483 + 5.19886i) q^{82} +(-9.78245 + 2.87239i) q^{83} +(-5.84034 - 6.15496i) q^{84} +(-3.79701 + 4.38198i) q^{85} +(-1.57302 + 3.44444i) q^{86} +(-2.18878 + 1.55065i) q^{87} +(-3.02847 + 1.38306i) q^{88} +(-2.62988 - 18.2912i) q^{89} +(2.83022 + 0.994928i) q^{90} +28.5591i q^{91} +(-4.54184 - 1.54003i) q^{92} +(-0.103184 - 0.0815499i) q^{93} +(-5.12990 - 3.29679i) q^{94} +(-1.14621 + 0.164801i) q^{95} +(-1.68223 - 0.412423i) q^{96} +(-3.87364 + 13.1924i) q^{97} +(-15.4616 - 7.06109i) q^{98} +(8.85541 + 4.61973i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 16 q^{4} + 16 q^{5} - 2 q^{6} - 46 q^{9}+O(q^{10}) \) 160 * q + 16 * q^4 + 16 * q^5 - 2 * q^6 - 46 * q^9	\( 160 q + 16 q^{4} + 16 q^{5} - 2 q^{6} - 46 q^{9} + 12 q^{11} + 12 q^{14} - 16 q^{16} - 8 q^{18} - 16 q^{20} + 70 q^{21} - 4 q^{23} + 2 q^{24} - 16 q^{25} + 42 q^{27} + 2 q^{30} - 4 q^{31} - 16 q^{33} + 2 q^{36} - 72 q^{38} + 140 q^{39} - 44 q^{41} + 44 q^{43} - 12 q^{44} + 2 q^{45} + 4 q^{46} + 70 q^{49} + 2 q^{51} + 52 q^{53} - 62 q^{54} + 10 q^{55} + 54 q^{56} - 94 q^{57} - 36 q^{58} - 44 q^{61} + 16 q^{64} - 54 q^{66} - 44 q^{67} - 30 q^{69} - 12 q^{70} - 36 q^{72} - 28 q^{73} + 24 q^{74} + 88 q^{77} - 54 q^{78} - 44 q^{79} + 16 q^{80} - 66 q^{81} - 28 q^{82} - 4 q^{83} - 4 q^{84} - 158 q^{86} + 156 q^{87} - 80 q^{89} + 8 q^{90} + 4 q^{92} + 4 q^{93} + 24 q^{94} - 2 q^{96} + 88 q^{98} - 58 q^{99}+O(q^{100}) \) 160 * q + 16 * q^4 + 16 * q^5 - 2 * q^6 - 46 * q^9 + 12 * q^11 + 12 * q^14 - 16 * q^16 - 8 * q^18 - 16 * q^20 + 70 * q^21 - 4 * q^23 + 2 * q^24 - 16 * q^25 + 42 * q^27 + 2 * q^30 - 4 * q^31 - 16 * q^33 + 2 * q^36 - 72 * q^38 + 140 * q^39 - 44 * q^41 + 44 * q^43 - 12 * q^44 + 2 * q^45 + 4 * q^46 + 70 * q^49 + 2 * q^51 + 52 * q^53 - 62 * q^54 + 10 * q^55 + 54 * q^56 - 94 * q^57 - 36 * q^58 - 44 * q^61 + 16 * q^64 - 54 * q^66 - 44 * q^67 - 30 * q^69 - 12 * q^70 - 36 * q^72 - 28 * q^73 + 24 * q^74 + 88 * q^77 - 54 * q^78 - 44 * q^79 + 16 * q^80 - 66 * q^81 - 28 * q^82 - 4 * q^83 - 4 * q^84 - 158 * q^86 + 156 * q^87 - 80 * q^89 + 8 * q^90 + 4 * q^92 + 4 * q^93 + 24 * q^94 - 2 * q^96 + 88 * q^98 - 58 * q^99

Introduction

L-functions

Modular forms

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