LMFDB - Embedded newform 690.2.q.b.11.5

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			11.5
Character	$\chi$	$=$	690.11
Dual form			690.2.q.b.251.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.540641 - 0.841254i) q^{2} +(-0.0752308 - 1.73042i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(0.959493 - 0.281733i) q^{5} +(-1.41505 + 0.998822i) q^{6} +(-2.94981 + 2.55602i) q^{7} +(0.989821 - 0.142315i) q^{8} +(-2.98868 + 0.260361i) q^{9} +O(q^{10})$	\(q+(-0.540641 - 0.841254i) q^{2} +(-0.0752308 - 1.73042i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(0.959493 - 0.281733i) q^{5} +(-1.41505 + 0.998822i) q^{6} +(-2.94981 + 2.55602i) q^{7} +(0.989821 - 0.142315i) q^{8} +(-2.98868 + 0.260361i) q^{9} +(-0.755750 - 0.654861i) q^{10} +(1.62713 + 1.04569i) q^{11} +(1.60529 + 0.650409i) q^{12} +(-1.51588 + 1.74942i) q^{13} +(3.74505 + 1.09965i) q^{14} +(-0.559698 - 1.63913i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(2.62149 + 5.74026i) q^{17} +(1.83483 + 2.37348i) q^{18} +(-3.93948 - 1.79910i) q^{19} +(-0.142315 + 0.989821i) q^{20} +(4.64490 + 4.91210i) q^{21} -1.93417i q^{22} +(-2.02820 + 4.34585i) q^{23} +(-0.320729 - 1.70210i) q^{24} +(0.841254 - 0.540641i) q^{25} +(2.29125 + 0.329432i) q^{26} +(0.675374 + 5.15207i) q^{27} +(-1.09965 - 3.74505i) q^{28} +(3.24492 - 1.48190i) q^{29} +(-1.07633 + 1.35703i) q^{30} +(0.896737 + 6.23694i) q^{31} +(-0.281733 + 0.959493i) q^{32} +(1.68707 - 2.89428i) q^{33} +(3.41173 - 5.30875i) q^{34} +(-2.11021 + 3.28354i) q^{35} +(1.00471 - 2.82676i) q^{36} +(-1.18792 + 4.04568i) q^{37} +(0.616344 + 4.28677i) q^{38} +(3.14127 + 2.49150i) q^{39} +(0.909632 - 0.415415i) q^{40} +(-1.79159 - 6.10159i) q^{41} +(1.62110 - 6.56322i) q^{42} +(-6.08292 - 0.874592i) q^{43} +(-1.62713 + 1.04569i) q^{44} +(-2.79427 + 1.09182i) q^{45} +(4.75249 - 0.643315i) q^{46} -1.53681i q^{47} +(-1.25850 + 1.19004i) q^{48} +(1.17191 - 8.15081i) q^{49} +(-0.909632 - 0.415415i) q^{50} +(9.73581 - 4.96811i) q^{51} +(-0.961609 - 2.10563i) q^{52} +(0.712176 + 0.821895i) q^{53} +(3.96907 - 3.35358i) q^{54} +(1.85582 + 0.544919i) q^{55} +(-2.55602 + 2.94981i) q^{56} +(-2.81682 + 6.95229i) q^{57} +(-3.00099 - 1.92862i) q^{58} +(-4.45591 - 3.86107i) q^{59} +(1.72351 + 0.171799i) q^{60} +(11.2928 - 1.62366i) q^{61} +(4.76204 - 4.12633i) q^{62} +(8.15055 - 8.40715i) q^{63} +(0.959493 - 0.281733i) q^{64} +(-0.961609 + 2.10563i) q^{65} +(-3.34692 + 0.145509i) q^{66} +(3.69201 + 5.74488i) q^{67} -6.31052 q^{68} +(7.67271 + 3.18269i) q^{69} +3.90316 q^{70} +(-0.0295383 - 0.0459624i) q^{71} +(-2.92121 + 0.683045i) q^{72} +(-4.05026 + 8.86883i) q^{73} +(4.04568 - 1.18792i) q^{74} +(-0.998822 - 1.41505i) q^{75} +(3.27304 - 2.83610i) q^{76} +(-7.47253 + 1.07439i) q^{77} +(0.397683 - 3.98961i) q^{78} +(-4.69071 - 4.06452i) q^{79} +(-0.841254 - 0.540641i) q^{80} +(8.86442 - 1.55627i) q^{81} +(-4.16438 + 4.80595i) q^{82} +(11.9112 + 3.49743i) q^{83} +(-6.39777 + 2.18459i) q^{84} +(4.13251 + 4.76918i) q^{85} +(2.55292 + 5.59012i) q^{86} +(-2.80843 - 5.50357i) q^{87} +(1.75938 + 0.803484i) q^{88} +(-1.74485 + 12.1357i) q^{89} +(2.42919 + 1.76040i) q^{90} -9.03508i q^{91} +(-3.11058 - 3.65025i) q^{92} +(10.7250 - 2.02094i) q^{93} +(-1.29284 + 0.830860i) q^{94} +(-4.28677 - 0.616344i) q^{95} +(1.68152 + 0.415331i) q^{96} +(-4.23230 - 14.4139i) q^{97} +(-7.49048 + 3.42079i) q^{98} +(-5.13522 - 2.70160i) 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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$-1$	$e\left(\frac{9}{22}\right)$

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
$3$	−0.0752308	−	1.73042i	−0.0434345	−	0.999056i
$3$	−0.0752308	−	1.73042i	−0.0434345	−	0.999056i
$4$	−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
$6$	−1.41505	+	0.998822i	−0.577690	+	0.407767i
$7$	−2.94981	+	2.55602i	−1.11492	+	0.966086i	−0.999629	−	0.0272453i	$-0.991326\pi$
$7$	−2.94981	+	2.55602i	−1.11492	+	0.966086i	−0.115294	+	0.993331i	$0.536781\pi$
$8$	0.989821	−	0.142315i	0.349955	−	0.0503159i
$9$	−2.98868	+	0.260361i	−0.996227	+	0.0867871i
$10$	−0.755750	−	0.654861i	−0.238989	−	0.207085i
$11$	1.62713	+	1.04569i	0.490598	+	0.315288i	0.762446	−	0.647052i	$-0.223998\pi$
$11$	1.62713	+	1.04569i	0.490598	+	0.315288i	−0.271848	+	0.962340i	$0.587635\pi$
$12$	1.60529	+	0.650409i	0.463408	+	0.187757i
$13$	−1.51588	+	1.74942i	−0.420430	+	0.485202i	−0.925968	−	0.377602i	$-0.876749\pi$
$13$	−1.51588	+	1.74942i	−0.420430	+	0.485202i	0.505538	+	0.862804i	$0.331294\pi$
$14$	3.74505	+	1.09965i	1.00091	+	0.293893i
$15$	−0.559698	−	1.63913i	−0.144513	−	0.423221i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	2.62149	+	5.74026i	0.635804	+	1.39222i	0.903448	+	0.428698i	$0.141028\pi$
$17$	2.62149	+	5.74026i	0.635804	+	1.39222i	−0.267644	+	0.963518i	$0.586245\pi$
$18$	1.83483	+	2.37348i	0.432474	+	0.559434i
$19$	−3.93948	−	1.79910i	−0.903779	−	0.412742i	−0.0913610	−	0.995818i	$-0.529122\pi$
$19$	−3.93948	−	1.79910i	−0.903779	−	0.412742i	−0.812418	+	0.583076i	$0.801849\pi$
$20$	−0.142315	+	0.989821i	−0.0318226	+	0.221331i
$21$	4.64490	+	4.91210i	1.01360	+	1.07191i
$22$		−	1.93417i		−	0.412367i
$23$	−2.02820	+	4.34585i	−0.422909	+	0.906172i
$23$	−2.02820	+	4.34585i	−0.422909	+	0.906172i
$24$	−0.320729	−	1.70210i	−0.0654685	−	0.347439i
$25$	0.841254	−	0.540641i	0.168251	−	0.108128i
$26$	2.29125	+	0.329432i	0.449352	+	0.0646070i
$27$	0.675374	+	5.15207i	0.129976	+	0.991517i
$28$	−1.09965	−	3.74505i	−0.207814	−	0.707748i
$29$	3.24492	−	1.48190i	0.602566	−	0.275183i	−0.0906841	−	0.995880i	$-0.528905\pi$
$29$	3.24492	−	1.48190i	0.602566	−	0.275183i	0.693250	+	0.720697i	$0.256178\pi$
$30$	−1.07633	+	1.35703i	−0.196509	+	0.247758i
$31$	0.896737	+	6.23694i	0.161059	+	1.12019i	0.896643	+	0.442755i	$0.145999\pi$
$31$	0.896737	+	6.23694i	0.161059	+	1.12019i	−0.735584	+	0.677434i	$0.763092\pi$
$32$	−0.281733	+	0.959493i	−0.0498038	+	0.169616i
$33$	1.68707	−	2.89428i	0.293682	−	0.503829i
$34$	3.41173	−	5.30875i	0.585106	−	0.910443i
$35$	−2.11021	+	3.28354i	−0.356690	+	0.555020i
$36$	1.00471	−	2.82676i	0.167452	−	0.471126i
$37$	−1.18792	+	4.04568i	−0.195293	+	0.665105i	0.802373	+	0.596822i	$0.203570\pi$
$37$	−1.18792	+	4.04568i	−0.195293	+	0.665105i	−0.997666	+	0.0682831i	$0.978248\pi$
$38$	0.616344	+	4.28677i	0.0999842	+	0.695406i
$39$	3.14127	+	2.49150i	0.503005	+	0.398959i
$40$	0.909632	−	0.415415i	0.143825	−	0.0656829i
$41$	−1.79159	−	6.10159i	−0.279799	−	0.952908i	−0.972737	−	0.231911i	$-0.925502\pi$
$41$	−1.79159	−	6.10159i	−0.279799	−	0.952908i	0.692938	−	0.720997i	$-0.256316\pi$
$42$	1.62110	−	6.56322i	0.250142	−	1.01273i
$43$	−6.08292	−	0.874592i	−0.927636	−	0.133374i	−0.338095	−	0.941112i	$-0.609782\pi$
$43$	−6.08292	−	0.874592i	−0.927636	−	0.133374i	−0.589542	+	0.807738i	$0.700692\pi$
$44$	−1.62713	+	1.04569i	−0.245299	+	0.157644i
$45$	−2.79427	+	1.09182i	−0.416545	+	0.162759i
$46$	4.75249	−	0.643315i	0.700716	−	0.0948516i
$47$		−	1.53681i		−	0.224166i	−0.993699	−	0.112083i	$-0.964248\pi$
$47$		−	1.53681i		−	0.224166i	0.993699	−	0.112083i	$-0.0357523\pi$
$48$	−1.25850	+	1.19004i	−0.181648	+	0.171767i
$49$	1.17191	−	8.15081i	0.167416	−	1.16440i
$50$	−0.909632	−	0.415415i	−0.128641	−	0.0587486i
$51$	9.73581	−	4.96811i	1.36329	−	0.695674i
$52$	−0.961609	−	2.10563i	−0.133351	−	0.291998i
$53$	0.712176	+	0.821895i	0.0978249	+	0.112896i	0.802551	−	0.596584i	$-0.203476\pi$
$53$	0.712176	+	0.821895i	0.0978249	+	0.112896i	−0.704726	+	0.709479i	$0.748930\pi$
$54$	3.96907	−	3.35358i	0.540121	−	0.456365i
$55$	1.85582	+	0.544919i	0.250239	+	0.0734769i
$56$	−2.55602	+	2.94981i	−0.341563	+	0.394185i
$57$	−2.81682	+	6.95229i	−0.373097	+	0.920853i
$58$	−3.00099	−	1.92862i	−0.394050	−	0.253240i
$59$	−4.45591	−	3.86107i	−0.580110	−	0.502669i	0.314654	−	0.949206i	$-0.398111\pi$
$59$	−4.45591	−	3.86107i	−0.580110	−	0.502669i	−0.894765	+	0.446538i	$0.852657\pi$
$60$	1.72351	+	0.171799i	0.222504	+	0.0221791i
$61$	11.2928	−	1.62366i	1.44590	−	0.207889i	0.625743	−	0.780029i	$-0.284796\pi$
$61$	11.2928	−	1.62366i	1.44590	−	0.207889i	0.820156	+	0.572140i	$0.193887\pi$
$62$	4.76204	−	4.12633i	0.604780	−	0.524044i
$63$	8.15055	−	8.40715i	1.02687	−	1.05920i
$64$	0.959493	−	0.281733i	0.119937	−	0.0352166i
$65$	−0.961609	+	2.10563i	−0.119273	+	0.261171i
$66$	−3.34692	+	0.145509i	−0.411977	+	0.0179109i
$67$	3.69201	+	5.74488i	0.451051	+	0.701848i	0.990090	−	0.140432i	$-0.0448491\pi$
$67$	3.69201	+	5.74488i	0.451051	+	0.701848i	−0.539040	+	0.842280i	$0.681213\pi$
$68$	−6.31052			−0.765264
$69$	7.67271	+	3.18269i	0.923686	+	0.383150i
$70$	3.90316			0.466516
$71$	−0.0295383	−	0.0459624i	−0.00350555	−	0.00545474i	0.839496	−	0.543365i	$-0.182850\pi$
$71$	−0.0295383	−	0.0459624i	−0.00350555	−	0.00545474i	−0.843002	+	0.537911i	$0.819214\pi$
$72$	−2.92121	+	0.683045i	−0.344268	+	0.0804976i
$73$	−4.05026	+	8.86883i	−0.474047	+	1.03802i	0.510011	+	0.860168i	$0.329641\pi$
$73$	−4.05026	+	8.86883i	−0.474047	+	1.03802i	−0.984058	+	0.177850i	$0.943086\pi$
$74$	4.04568	−	1.18792i	0.470301	−	0.138093i
$75$	−0.998822	−	1.41505i	−0.115334	−	0.163395i
$76$	3.27304	−	2.83610i	0.375443	−	0.325323i
$77$	−7.47253	+	1.07439i	−0.851574	+	0.122438i
$78$	0.397683	−	3.98961i	0.0450287	−	0.451734i
$79$	−4.69071	−	4.06452i	−0.527746	−	0.457294i	0.349775	−	0.936834i	$-0.386258\pi$
$79$	−4.69071	−	4.06452i	−0.527746	−	0.457294i	−0.877520	+	0.479540i	$0.840804\pi$
$80$	−0.841254	−	0.540641i	−0.0940550	−	0.0604455i
$81$	8.86442	−	1.55627i	0.984936	−	0.172919i
$82$	−4.16438	+	4.80595i	−0.459879	+	0.530728i
$83$	11.9112	+	3.49743i	1.30742	+	0.383893i	0.859937	−	0.510400i	$-0.170503\pi$
$83$	11.9112	+	3.49743i	1.30742	+	0.383893i	0.447482	+	0.894293i	$0.352321\pi$
$84$	−6.39777	+	2.18459i	−0.698054	+	0.238358i
$85$	4.13251	+	4.76918i	0.448234	+	0.517290i
$86$	2.55292	+	5.59012i	0.275289	+	0.602798i
$87$	−2.80843	−	5.50357i	−0.301095	−	0.590045i
$88$	1.75938	+	0.803484i	0.187551	+	0.0856516i
$89$	−1.74485	+	12.1357i	−0.184954	+	1.28638i	0.659888	+	0.751364i	$0.270604\pi$
$89$	−1.74485	+	12.1357i	−0.184954	+	1.28638i	−0.844842	+	0.535016i	$0.820305\pi$
$90$	2.42919	+	1.76040i	0.256060	+	0.185563i
$91$		−	9.03508i		−	0.947134i
$92$	−3.11058	−	3.65025i	−0.324300	−	0.380564i
$93$	10.7250	−	2.02094i	1.11214	−	0.209562i
$94$	−1.29284	+	0.830860i	−0.133347	+	0.0856967i
$95$	−4.28677	−	0.616344i	−0.439813	−	0.0632356i
$96$	1.68152	+	0.415331i	0.171619	+	0.0423896i
$97$	−4.23230	−	14.4139i	−0.429725	−	1.46351i	−0.835477	−	0.549525i	$-0.814809\pi$
$97$	−4.23230	−	14.4139i	−0.429725	−	1.46351i	0.405752	−	0.913983i	$-0.367010\pi$
$98$	−7.49048	+	3.42079i	−0.756653	+	0.345552i
$99$	−5.13522	−	2.70160i	−0.516109	−	0.271521i
$100$	0.142315	+	0.989821i	0.0142315	+	0.0989821i
$101$	−2.66597	+	9.07945i	−0.265274	+	0.903439i	0.713872	+	0.700277i	$0.246940\pi$
$101$	−2.66597	+	9.07945i	−0.265274	+	0.903439i	−0.979145	+	0.203162i	$0.934878\pi$
$102$	−9.44302	−	5.50433i	−0.934998	−	0.545010i
$103$	−5.26160	+	8.18722i	−0.518441	+	0.806710i	−0.997470	−	0.0710889i	$-0.977353\pi$
$103$	−5.26160	+	8.18722i	−0.518441	+	0.806710i	0.479029	+	0.877799i	$0.340989\pi$
$104$	−1.25148	+	1.94735i	−0.122718	+	0.190953i
$105$	5.84065	+	3.40451i	0.569989	+	0.332246i
$106$	0.306390	−	1.04347i	0.0297593	−	0.101351i
$107$	0.242893	+	1.68936i	0.0234813	+	0.163316i	0.998188	−	0.0601715i	$-0.0191648\pi$
$107$	0.242893	+	1.68936i	0.0234813	+	0.163316i	−0.974707	+	0.223488i	$0.928256\pi$
$108$	−4.96705	−	1.52591i	−0.477955	−	0.146830i
$109$	9.90294	−	4.52252i	0.948530	−	0.433179i	0.119781	−	0.992800i	$-0.461781\pi$
$109$	9.90294	−	4.52252i	0.948530	−	0.433179i	0.828748	+	0.559621i	$0.189053\pi$
$110$	−0.544919	−	1.85582i	−0.0519560	−	0.176946i
$111$	7.09008	+	1.75123i	0.672960	+	0.166220i
$112$	3.86343	+	0.555477i	0.365060	+	0.0524876i
$113$	−11.0302	+	7.08867i	−1.03763	+	0.666846i	−0.944400	−	0.328798i	$-0.893356\pi$
$113$	−11.0302	+	7.08867i	−1.03763	+	0.666846i	−0.0932327	+	0.995644i	$0.529720\pi$
$114$	7.37152	−	1.38903i	0.690407	−	0.130094i
$115$	−0.721674	+	4.74122i	−0.0672965	+	0.442121i
$116$			3.56729i			0.331214i
$117$	4.07500	−	5.62314i	0.376734	−	0.519859i
$118$	−0.839091	+	5.83601i	−0.0772446	+	0.537248i
$119$	−22.4051	−	10.2321i	−2.05387	−	0.937972i
$120$	−0.787273	−	1.54279i	−0.0718679	−	0.140837i
$121$	−3.01549	−	6.60300i	−0.274135	−	0.600273i
$122$	−7.47128	−	8.62232i	−0.676418	−	0.780628i
$123$	−10.4235	+	3.55922i	−0.939856	+	0.320924i
$124$	−6.04584	−	1.77522i	−0.542933	−	0.159419i
$125$	0.654861	−	0.755750i	0.0585725	−	0.0675963i
$126$	−11.4791	−	2.31143i	−1.02264	−	0.205918i
$127$	−15.4730	−	9.94391i	−1.37301	−	0.882379i	−0.374023	−	0.927419i	$-0.622022\pi$
$127$	−15.4730	−	9.94391i	−1.37301	−	0.882379i	−0.998985	+	0.0450401i	$0.985658\pi$
$128$	−0.755750	−	0.654861i	−0.0667995	−	0.0578821i
$129$	−1.05578	+	10.5918i	−0.0929567	+	0.932554i
$130$	2.29125	−	0.329432i	0.200956	−	0.0288931i
$131$	−6.54865	+	5.67444i	−0.572158	+	0.495778i	−0.892209	−	0.451622i	$-0.850845\pi$
$131$	−6.54865	+	5.67444i	−0.572158	+	0.495778i	0.320051	+	0.947400i	$0.396300\pi$
$132$	1.93189	+	2.73694i	0.168150	+	0.238220i
$133$	16.2193	−	4.76240i	1.40639	−	0.412953i
$134$	2.83685	−	6.21183i	0.245066	−	0.536620i
$135$	2.09952	+	4.75310i	0.180698	+	0.409082i
$136$	3.41173	+	5.30875i	0.292553	+	0.455222i
$137$	6.85187			0.585395			0.292697	−	0.956205i	$-0.405447\pi$
$137$	6.85187			0.585395			0.292697	+	0.956205i	$0.405447\pi$
$138$	−1.47074	−	8.17539i	−0.125197	−	0.695935i
$139$	−1.54645			−0.131168			−0.0655839	−	0.997847i	$-0.520891\pi$
$139$	−1.54645			−0.131168			−0.0655839	+	0.997847i	$0.520891\pi$
$140$	−2.11021	−	3.28354i	−0.178345	−	0.277510i
$141$	−2.65931	+	0.115615i	−0.223955	+	0.00973655i
$142$	−0.0226965	+	0.0496983i	−0.00190465	+	0.00417059i
$143$	−4.29589	+	1.26139i	−0.359240	+	0.105482i
$144$	2.15394	+	2.08819i	0.179495	+	0.174016i
$145$	2.69597	−	2.33608i	0.223889	−	0.194001i
$146$	9.65067	−	1.38756i	0.798695	−	0.114835i
$147$	−14.1925	−	1.41470i	−1.17057	−	0.116682i
$148$	−3.18660	−	2.76120i	−0.261937	−	0.226970i
$149$	−1.21829	−	0.782949i	−0.0998064	−	0.0641417i	0.489786	−	0.871843i	$-0.337075\pi$
$149$	−1.21829	−	0.782949i	−0.0998064	−	0.0641417i	−0.589592	+	0.807701i	$0.700711\pi$
$150$	−0.650409	+	1.60529i	−0.0531056	+	0.131072i
$151$	−8.98064	+	10.3642i	−0.730834	+	0.843428i	−0.992565	−	0.121713i	$-0.961161\pi$
$151$	−8.98064	+	10.3642i	−0.730834	+	0.843428i	0.261731	+	0.965141i	$0.415707\pi$
$152$	−4.15542	−	1.22014i	−0.337049	−	0.0989665i
$153$	−9.32933	−	16.4733i	−0.754231	−	1.33178i
$154$	4.94379	+	5.70543i	0.398382	+	0.459757i
$155$	2.61756	+	5.73166i	0.210248	+	0.460378i
$156$	−3.57127	+	1.82239i	−0.285931	+	0.145908i
$157$	−4.22579	−	1.92985i	−0.337255	−	0.154019i	0.239587	−	0.970875i	$-0.422988\pi$
$157$	−4.22579	−	1.92985i	−0.337255	−	0.154019i	−0.576842	+	0.816856i	$0.695715\pi$
$158$	−0.883305	+	6.14352i	−0.0702719	+	0.488752i
$159$	1.36864	−	1.29419i	0.108540	−	0.102636i
$160$			1.00000i			0.0790569i
$161$	−5.12530	−	18.0035i	−0.403930	−	1.41888i
$162$	−6.10169	−	6.61584i	−0.479394	−	0.519790i
$163$	−16.8553	+	10.8322i	−1.32021	+	0.848447i	−0.995257	−	0.0972834i	$-0.968985\pi$
$163$	−16.8553	+	10.8322i	−1.32021	+	0.848447i	−0.324952	+	0.945730i	$0.605348\pi$
$164$	6.29445	+	0.905006i	0.491514	+	0.0706691i
$165$	0.803322	−	3.25234i	0.0625385	−	0.253194i
$166$	−3.49743	−	11.9112i	−0.271453	−	0.924485i
$167$	−0.756192	+	0.345341i	−0.0585159	+	0.0267233i	−0.444458	−	0.895800i	$-0.646604\pi$
$167$	−0.756192	+	0.345341i	−0.0585159	+	0.0267233i	0.385942	+	0.922523i	$0.373876\pi$
$168$	5.29669	+	4.20107i	0.408648	+	0.324119i
$169$	1.08752	+	7.56385i	0.0836552	+	0.581835i
$170$	1.77788	−	6.05490i	0.136357	−	0.464390i
$171$	12.2423	+	4.35125i	0.936189	+	0.332748i
$172$	3.32249	−	5.16990i	0.253338	−	0.394201i
$173$	5.57100	−	8.66864i	0.423555	−	0.659065i	−0.562248	−	0.826969i	$-0.690063\pi$
$173$	5.57100	−	8.66864i	0.423555	−	0.659065i	0.985803	+	0.167904i	$0.0536998\pi$
$174$	−3.11155	+	5.33806i	−0.235886	+	0.404677i
$175$	−1.09965	+	3.74505i	−0.0831254	+	0.283099i
$176$	−0.275261	−	1.91448i	−0.0207486	−	0.144310i
$177$	−6.34604	+	8.00106i	−0.476997	+	0.601396i
$178$	11.1525	−	5.09319i	0.835917	−	0.381750i
$179$	−7.35072	−	25.0343i	−0.549419	−	1.87115i	−0.487612	−	0.873060i	$-0.662132\pi$
$179$	−7.35072	−	25.0343i	−0.549419	−	1.87115i	−0.0618064	−	0.998088i	$-0.519686\pi$
$180$	0.167623	−	2.99531i	0.0124938	−	0.223257i
$181$	20.7846	+	2.98837i	1.54491	+	0.222124i	0.861441	−	0.507858i	$-0.169563\pi$
$181$	20.7846	+	2.98837i	1.54491	+	0.222124i	0.683466	+	0.729982i	$0.260472\pi$
$182$	−7.60080	+	4.88473i	−0.563408	+	0.362081i
$183$	−3.65918	−	19.4191i	−0.270495	−	1.43550i
$184$	−1.38907	+	4.59026i	−0.102404	+	0.338398i
$185$			4.21648i			0.310001i
$186$	−7.49852	−	7.92988i	−0.549818	−	0.581447i
$187$	−1.73704	+	12.0814i	−0.127025	+	0.883479i
$188$	1.39793	+	0.638412i	0.101954	+	0.0465610i
$189$	−15.1610	−	13.4714i	−1.10280	−	0.979897i
$190$	1.79910	+	3.93948i	0.130520	+	0.285800i
$191$	16.9708	+	19.5854i	1.22796	+	1.41715i	0.876815	+	0.480828i	$0.159664\pi$
$191$	16.9708	+	19.5854i	1.22796	+	1.41715i	0.351150	+	0.936319i	$0.385791\pi$
$192$	−0.559698	−	1.63913i	−0.0403927	−	0.118294i
$193$	−5.03861	−	1.47947i	−0.362687	−	0.106495i	0.0953114	−	0.995448i	$-0.469615\pi$
$193$	−5.03861	−	1.47947i	−0.362687	−	0.106495i	−0.457998	+	0.888953i	$0.651433\pi$
$194$	−9.83758	+	11.3532i	−0.706297	+	0.815110i
$195$	3.71596	+	1.50558i	0.266105	+	0.107816i
$196$	6.92741	+	4.45198i	0.494815	+	0.317998i
$197$	9.40784	+	8.15194i	0.670281	+	0.580802i	0.922090	−	0.386975i	$-0.126480\pi$
$197$	9.40784	+	8.15194i	0.670281	+	0.580802i	−0.251809	+	0.967777i	$0.581026\pi$
$198$	0.503583	+	5.78062i	0.0357881	+	0.410811i
$199$	−27.3942	+	3.93869i	−1.94192	+	0.279207i	−0.998611	−	0.0526960i	$-0.983219\pi$
$199$	−27.3942	+	3.93869i	−1.94192	+	0.279207i	−0.943314	+	0.331903i	$0.892309\pi$
$200$	0.755750	−	0.654861i	0.0534396	−	0.0463056i
$201$	9.66328	−	6.82090i	0.681595	−	0.481109i
$202$	9.07945	−	2.66597i	0.638828	−	0.187577i
$203$	−5.78410	+	12.6654i	−0.405964	+	0.888938i
$204$	0.474746	+	10.9198i	0.0332389	+	0.764541i
$205$	−3.43803	−	5.34968i	−0.240123	−	0.373638i
$206$	9.73216			0.678072
$207$	4.93015	−	13.5164i	0.342669	−	0.939456i
$208$	2.31481			0.160504
$209$	−4.52873	−	7.04685i	−0.313259	−	0.487441i
$210$	−0.293638	−	6.75408i	−0.0202629	−	0.466076i
$211$	−1.38096	+	3.02388i	−0.0950691	+	0.208172i	−0.951192	−	0.308600i	$-0.900139\pi$
$211$	−1.38096	+	3.02388i	−0.0950691	+	0.208172i	0.856123	+	0.516773i	$0.172867\pi$
$212$	−1.04347	+	0.306390i	−0.0716658	+	0.0210430i
$213$	−0.0773120	+	0.0545713i	−0.00529733	+	0.00373916i
$214$	1.28986	−	1.11767i	0.0881730	−	0.0764024i
$215$	−6.08292	+	0.874592i	−0.414852	+	0.0596467i
$216$	1.40172	+	5.00352i	0.0953747	+	0.340446i
$217$	−18.5870	−	16.1057i	−1.26177	−	1.09333i
$218$	−9.15852	−	5.88582i	−0.620293	−	0.398638i
$219$	15.6515	+	6.34143i	1.05763	+	0.428514i
$220$	−1.26661	+	1.46175i	−0.0853950	+	0.0985511i
$221$	−14.0160	−	4.11546i	−0.942817	−	0.276836i
$222$	−2.35995	−	6.91134i	−0.158390	−	0.463859i
$223$	−0.952838	−	1.09963i	−0.0638067	−	0.0736369i	0.722949	−	0.690902i	$-0.242786\pi$
$223$	−0.952838	−	1.09963i	−0.0638067	−	0.0736369i	−0.786756	+	0.617265i	$0.788241\pi$
$224$	−1.62143	−	3.55044i	−0.108336	−	0.237223i
$225$	−2.37348	+	1.83483i	−0.158232	+	0.122322i
$226$	11.9267	+	5.44676i	0.793355	+	0.362313i
$227$	3.18102	−	22.1245i	0.211132	−	1.46846i	−0.558253	−	0.829671i	$-0.688528\pi$
$227$	3.18102	−	22.1245i	0.211132	−	1.46846i	0.769385	−	0.638785i	$-0.220563\pi$
$228$	−5.15387	−	5.45036i	−0.341324	−	0.360959i
$229$			25.5963i			1.69145i	0.533616	+	0.845727i	$0.320833\pi$
$229$			25.5963i			1.69145i	−0.533616	+	0.845727i	$0.679167\pi$
$230$	4.37874	−	1.95619i	0.288725	−	0.128987i
$231$	2.42130	+	12.8498i	0.159310	+	0.845452i
$232$	3.00099	−	1.92862i	0.197025	−	0.126620i
$233$	24.4232	+	3.51152i	1.60001	+	0.230047i	0.883811	−	0.467844i	$-0.154969\pi$
$233$	24.4232	+	3.51152i	1.60001	+	0.230047i	0.716204	+	0.697891i	$0.245878\pi$
$234$	−6.93360	−	0.388015i	−0.453263	−	0.0253653i
$235$	−0.432968	−	1.47455i	−0.0282437	−	0.0961893i
$236$	5.36321	−	2.44929i	0.349115	−	0.159435i
$237$	−6.68043	+	8.42265i	−0.433940	+	0.547110i
$238$	3.50535	+	24.3803i	0.227218	+	1.58034i
$239$	−1.95989	+	6.67479i	−0.126775	+	0.431756i	−0.998280	−	0.0586311i	$-0.981326\pi$
$239$	−1.95989	+	6.67479i	−0.126775	+	0.431756i	0.871505	+	0.490387i	$0.163145\pi$
$240$	−0.872245	+	1.49639i	−0.0563032	+	0.0965917i
$241$	3.52414	−	5.48367i	0.227010	−	0.353234i	−0.709000	−	0.705209i	$-0.750853\pi$
$241$	3.52414	−	5.48367i	0.227010	−	0.353234i	0.936010	+	0.351974i	$0.114490\pi$
$242$	−3.92450	+	6.10664i	−0.252277	+	0.392550i
$243$	−3.35988	−	15.2221i	−0.215536	−	0.976496i
$244$	−3.21428	+	10.9468i	−0.205773	+	0.700798i
$245$	−1.17191	−	8.15081i	−0.0748706	−	0.520736i
$246$	8.62958	+	6.84455i	0.550202	+	0.436393i
$247$	9.11917	−	4.16458i	0.580239	−	0.264986i
$248$	1.77522	+	6.04584i	0.112727	+	0.383911i
$249$	5.15593	−	20.8744i	0.326744	−	1.32286i
$250$	−0.989821	−	0.142315i	−0.0626018	−	0.00900078i
$251$	−4.01980	+	2.58337i	−0.253728	+	0.163061i	−0.661322	−	0.750102i	$-0.730004\pi$
$251$	−4.01980	+	2.58337i	−0.253728	+	0.163061i	0.407594	+	0.913163i	$0.366368\pi$
$252$	4.26156	+	10.9065i	0.268453	+	0.687042i
$253$	−7.84456	+	4.95039i	−0.493183	+	0.311228i
$254$			18.3928i			1.15407i
$255$	7.94177	−	7.50976i	0.497333	−	0.470279i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	−4.52121	−	2.06477i	−0.282025	−	0.128797i	0.269380	−	0.963034i	$-0.413181\pi$
$257$	−4.52121	−	2.06477i	−0.282025	−	0.128797i	−0.551406	+	0.834237i	$0.685908\pi$
$258$	9.48117	−	4.83816i	0.590272	−	0.301211i
$259$	−6.83672	−	14.9703i	−0.424813	−	0.930211i
$260$	−1.51588	−	1.74942i	−0.0940110	−	0.108494i
$261$	−9.31219	+	5.27379i	−0.576410	+	0.326439i
$262$	8.31411	+	2.44124i	0.513647	+	0.150820i
$263$	19.7613	−	22.8057i	1.21853	−	1.40626i	0.332204	−	0.943208i	$-0.392208\pi$
$263$	19.7613	−	22.8057i	1.21853	−	1.40626i	0.886330	−	0.463055i	$-0.153247\pi$
$264$	1.25800	−	3.10491i	0.0774246	−	0.191094i
$265$	0.914882	+	0.587959i	0.0562008	+	0.0361180i
$266$	−12.7752	−	11.0698i	−0.783296	−	0.678730i
$267$	21.1311	+	2.10634i	1.29320	+	0.128906i
$268$	−6.75944	+	0.971861i	−0.412899	+	0.0593658i
$269$	6.04625	−	5.23911i	0.368646	−	0.319434i	−0.450762	−	0.892644i	$-0.648848\pi$
$269$	6.04625	−	5.23911i	0.368646	−	0.319434i	0.819408	+	0.573210i	$0.194302\pi$
$270$	2.86348	−	4.33595i	0.174266	−	0.263878i
$271$	30.2788	−	8.89065i	1.83930	−	0.540068i	0.839310	−	0.543653i	$-0.182959\pi$
$271$	30.2788	−	8.89065i	1.83930	−	0.540068i	0.999994	+	0.00358477i	$0.00114107\pi$
$272$	2.62149	−	5.74026i	0.158951	−	0.348054i
$273$	−15.6345	+	0.679716i	−0.946240	+	0.0411383i
$274$	−3.70440	−	5.76416i	−0.223791	−	0.348226i
$275$	1.93417			0.116635
$276$	−6.08243	+	5.65721i	−0.366119	+	0.340524i
$277$	17.9196			1.07668			0.538342	−	0.842726i	$-0.319051\pi$
$277$	17.9196			1.07668			0.538342	+	0.842726i	$0.319051\pi$
$278$	0.836072	+	1.30095i	0.0501443	+	0.0780260i
$279$	−4.30392	−	18.4068i	−0.257669	−	1.10198i
$280$	−1.62143	+	3.55044i	−0.0968990	+	0.212179i
$281$	−10.6213	+	3.11869i	−0.633613	+	0.186046i	−0.582739	−	0.812659i	$-0.698019\pi$
$281$	−10.6213	+	3.11869i	−0.633613	+	0.186046i	−0.0508743	+	0.998705i	$0.516201\pi$
$282$	1.53500	+	2.17465i	0.0914076	+	0.129499i
$283$	5.38019	−	4.66196i	0.319819	−	0.277125i	−0.480124	−	0.877201i	$-0.659408\pi$
$283$	5.38019	−	4.66196i	0.319819	−	0.277125i	0.799943	+	0.600076i	$0.204863\pi$
$284$	0.0540795	−	0.00777546i	0.00320903	−	0.000461389i
$285$	−0.744035	+	7.46426i	−0.0440728	+	0.442145i
$286$	3.38368	+	2.93197i	0.200081	+	0.173371i
$287$	20.8807	+	13.4192i	1.23255	+	0.792109i
$288$	0.592194	−	2.94097i	0.0348954	−	0.173298i
$289$	−14.9457	+	17.2483i	−0.879159	+	1.01460i
$290$	−3.42279	−	1.00502i	−0.200993	−	0.0590168i
$291$	−24.6236	+	8.40801i	−1.44346	+	0.492886i
$292$	−6.38483	−	7.36849i	−0.373644	−	0.431208i
$293$	0.0544576	+	0.119245i	0.00318144	+	0.00696639i	0.911216	−	0.411929i	$-0.135145\pi$
$293$	0.0544576	+	0.119245i	0.00318144	+	0.00696639i	−0.908035	+	0.418895i	$0.862417\pi$
$294$	6.48290	+	12.7043i	0.378091	+	0.740930i
$295$	−5.36321	−	2.44929i	−0.312258	−	0.142603i
$296$	−0.600067	+	4.17356i	−0.0348782	+	0.242583i
$297$	−4.28856	+	9.08932i	−0.248848	+	0.527416i
$298$			1.44819i			0.0838912i
$299$	−4.52821	−	10.1360i	−0.261873	−	0.586178i
$300$	1.70210	−	0.320729i	0.0982706	−	0.0185173i
$301$	20.1789	−	12.9682i	1.16309	−	0.747475i
$302$	13.5742	+	1.95168i	0.781109	+	0.112307i
$303$	15.9118	+	3.93018i	0.914108	+	0.225783i
$304$	1.22014	+	4.15542i	0.0699799	+	0.238330i
$305$	10.3780	−	4.73945i	0.594240	−	0.271380i
$306$	−8.81437	+	16.7544i	−0.503884	+	0.957788i
$307$	−2.17055	−	15.0965i	−0.123880	−	0.861605i	−0.953094	−	0.302674i	$-0.902121\pi$
$307$	−2.17055	−	15.0965i	−0.123880	−	0.861605i	0.829214	−	0.558931i	$-0.188788\pi$
$308$	2.12690	−	7.24357i	0.121192	−	0.412741i
$309$	14.5631	+	8.48883i	0.828467	+	0.482913i
$310$	3.40662	−	5.30081i	0.193483	−	0.301066i
$311$	−7.78247	+	12.1098i	−0.441303	+	0.686682i	−0.988652	−	0.150223i	$-0.952001\pi$
$311$	−7.78247	+	12.1098i	−0.441303	+	0.686682i	0.547349	+	0.836905i	$0.315637\pi$
$312$	3.46387	+	2.01909i	0.196103	+	0.114308i
$313$	5.20775	−	17.7360i	0.294359	−	1.00250i	−0.670975	−	0.741480i	$-0.734124\pi$
$313$	5.20775	−	17.7360i	0.294359	−	1.00250i	0.965335	−	0.261016i	$-0.0840574\pi$
$314$	0.661138	+	4.59832i	0.0373102	+	0.259498i
$315$	5.45182	−	10.3629i	0.307175	−	0.583882i
$316$	5.64581	−	2.57835i	0.317601	−	0.145044i
$317$	4.58792	+	15.6250i	0.257683	+	0.877588i	0.982121	+	0.188248i	$0.0602810\pi$
$317$	4.58792	+	15.6250i	0.257683	+	0.877588i	−0.724438	+	0.689340i	$0.757901\pi$
$318$	−1.82869	−	0.451682i	−0.102548	−	0.0253291i
$319$	6.82951	+	0.981936i	0.382379	+	0.0549778i
$320$	0.841254	−	0.540641i	0.0470275	−	0.0302227i
$321$	2.90502	−	0.547398i	0.162142	−	0.0305528i
$322$	−12.3746	+	14.0451i	−0.689610	+	0.782704i
$323$		−	27.3299i		−	1.52068i
$324$	−2.26678	+	8.70986i	−0.125932	+	0.483881i
$325$	−0.329432	+	2.29125i	−0.0182736	+	0.127096i
$326$	18.2253	+	8.32323i	1.00941	+	0.460981i
$327$	−8.57085	−	16.7960i	−0.473969	−	0.928820i
$328$	−2.64170	−	5.78452i	−0.145863	−	0.319396i
$329$	3.92811	+	4.53328i	0.216564	+	0.249928i
$330$	−3.17035	+	1.08255i	−0.174522	+	0.0595925i
$331$	−15.5433	−	4.56393i	−0.854338	−	0.250856i	−0.174897	−	0.984587i	$-0.555959\pi$
$331$	−15.5433	−	4.56393i	−0.854338	−	0.250856i	−0.679441	+	0.733730i	$0.737778\pi$
$332$	−8.12945	+	9.38189i	−0.446162	+	0.514898i
$333$	2.49697	−	12.4005i	0.136833	−	0.679545i
$334$	0.699348	+	0.449444i	0.0382666	+	0.0245925i
$335$	5.16098	+	4.47201i	0.281974	+	0.244332i
$336$	0.670558	−	6.72713i	0.0365819	−	0.366995i
$337$	−5.62293	+	0.808455i	−0.306300	+	0.0440394i	−0.293751	−	0.955882i	$-0.594904\pi$
$337$	−5.62293	+	0.808455i	−0.306300	+	0.0440394i	−0.0125492	+	0.999921i	$0.503995\pi$
$338$	5.77516	−	5.00421i	0.314127	−	0.272193i
$339$	13.0962	+	18.5535i	0.711286	+	1.00769i
$340$	−6.05490	+	1.77788i	−0.328373	+	0.0964191i
$341$	−5.06282	+	11.0860i	−0.274167	+	0.600342i
$342$	−2.95816	−	12.6513i	−0.159959	−	0.684104i
$343$	2.60532	+	4.05395i	0.140674	+	0.218893i
$344$	−6.14547			−0.331342
$345$	8.25858	+	0.892111i	0.444627	+	0.0480296i
$346$	−10.3044			−0.553970
$347$	16.8146	+	26.1640i	0.902654	+	1.40456i	0.914482	+	0.404627i	$0.132599\pi$
$347$	16.8146	+	26.1640i	0.902654	+	1.40456i	−0.0118281	+	0.999930i	$0.503765\pi$
$348$	6.17289	−	0.268370i	0.330902	−	0.0143861i
$349$	1.39547	−	3.05566i	0.0746979	−	0.163565i	−0.868599	−	0.495515i	$-0.834979\pi$
$349$	1.39547	−	3.05566i	0.0746979	−	0.163565i	0.943297	+	0.331950i	$0.107706\pi$
$350$	3.74505	−	1.09965i	0.200181	−	0.0587786i
$351$	−10.0369	−	6.62842i	−0.535732	−	0.353799i
$352$	−1.46175	+	1.26661i	−0.0779115	+	0.0675107i
$353$	−19.7400	+	2.83819i	−1.05065	+	0.151061i	−0.645945	−	0.763384i	$-0.723537\pi$
$353$	−19.7400	+	2.83819i	−1.05065	+	0.151061i	−0.404710	+	0.914445i	$0.632627\pi$
$354$	10.1618	+	1.01293i	0.540096	+	0.0538366i
$355$	−0.0412909	−	0.0357787i	−0.00219149	−	0.00189894i
$356$	−10.3142	−	6.62851i	−0.546650	−	0.351311i
$357$	−16.0202	+	39.5399i	−0.847878	+	2.09268i
$358$	−17.0861	+	19.7184i	−0.903026	+	1.04215i
$359$	33.9002	+	9.95400i	1.78918	+	0.525352i	0.996448	−	0.0842117i	$-0.0268372\pi$
$359$	33.9002	+	9.95400i	1.78918	+	0.525352i	0.792737	+	0.609564i	$0.208655\pi$
$360$	−2.61044	+	1.47838i	−0.137582	+	0.0779172i
$361$	−0.159616	−	0.184207i	−0.00840087	−	0.00969512i
$362$	−8.72302	−	19.1007i	−0.458472	−	1.00391i
$363$	−11.1991	+	5.71480i	−0.587800	+	0.299949i
$364$	8.21860	+	3.75331i	0.430772	+	0.196727i
$365$	−1.38756	+	9.65067i	−0.0726281	+	0.505139i
$366$	−14.3581	+	13.5771i	−0.750511	+	0.709686i
$367$		−	21.0372i		−	1.09813i	−0.835778	−	0.549067i	$-0.814983\pi$
$367$		−	21.0372i		−	1.09813i	0.835778	−	0.549067i	$-0.185017\pi$
$368$	4.61256	−	1.31312i	0.240446	−	0.0684509i
$369$	6.94310	+	17.7692i	0.361444	+	0.925030i
$370$	3.54712	−	2.27960i	0.184406	−	0.118511i
$371$	−4.20156	−	0.604094i	−0.218134	−	0.0313630i
$372$	−2.61704	+	10.5954i	−0.135687	+	0.549345i
$373$	7.82227	+	26.6402i	0.405022	+	1.37938i	0.869561	+	0.493825i	$0.164402\pi$
$373$	7.82227	+	26.6402i	0.405022	+	1.37938i	−0.464539	+	0.885552i	$0.653780\pi$
$374$	11.1026	−	5.07040i	0.574104	−	0.262184i
$375$	−1.35703	−	1.07633i	−0.0700766	−	0.0555812i
$376$	−0.218710	−	1.52116i	−0.0112791	−	0.0784480i
$377$	−2.32644	+	7.92312i	−0.119818	+	0.408061i
$378$	−3.13615	+	20.0375i	−0.161306	+	1.03062i
$379$	−1.92560	+	2.99629i	−0.0989115	+	0.153909i	−0.887182	−	0.461419i	$-0.847340\pi$
$379$	−1.92560	+	2.99629i	−0.0989115	+	0.153909i	0.788271	+	0.615329i	$0.210977\pi$
$380$	2.34143	−	3.64334i	0.120113	−	0.186900i
$381$	−16.0431	+	27.5229i	−0.821910	+	1.41004i
$382$	7.30114	−	24.8654i	0.373559	−	1.27222i
$383$	1.44160	+	10.0265i	0.0736621	+	0.512331i	0.992930	+	0.118699i	$0.0378724\pi$
$383$	1.44160	+	10.0265i	0.0736621	+	0.512331i	−0.919268	+	0.393632i	$0.871218\pi$
$384$	−1.07633	+	1.35703i	−0.0549260	+	0.0692505i
$385$	−6.86715	+	3.13612i	−0.349982	+	0.159832i
$386$	1.47947	+	5.03861i	0.0753030	+	0.256458i
$387$	18.4076	+	1.03012i	0.935711	+	0.0523639i
$388$	14.8695	+	2.13791i	0.754884	+	0.108536i
$389$	8.19325	−	5.26548i	0.415414	−	0.266971i	−0.316196	−	0.948694i	$-0.602406\pi$
$389$	8.19325	−	5.26548i	0.415414	−	0.266971i	0.731610	+	0.681723i	$0.238769\pi$
$390$	−0.742428	−	3.94004i	−0.0375943	−	0.199512i
$391$	−30.2632	−	0.249786i	−1.53047	−	0.0126322i
$392$		−	8.23463i		−	0.415911i
$393$	10.3118	+	10.9050i	0.520162	+	0.550085i
$394$	1.77159	−	12.3217i	0.0892512	−	0.620756i
$395$	−5.64581	−	2.57835i	−0.284071	−	0.129731i
$396$	4.59071	−	3.54888i	0.230692	−	0.178338i
$397$	0.641907	+	1.40558i	0.0322164	+	0.0705440i	0.925056	−	0.379831i	$-0.124018\pi$
$397$	0.641907	+	1.40558i	0.0322164	+	0.0705440i	−0.892840	+	0.450375i	$0.851290\pi$
$398$	18.1239	+	20.9161i	0.908467	+	1.04843i
$399$	−9.46113	−	27.7078i	−0.473649	−	1.38712i
$400$	−0.959493	−	0.281733i	−0.0479746	−	0.0140866i
$401$	17.0307	−	19.6544i	0.850471	−	0.981496i	−0.149502	−	0.988761i	$-0.547767\pi$
$401$	17.0307	−	19.6544i	0.850471	−	0.981496i	0.999974	+	0.00726520i	$0.00231260\pi$
$402$	−10.9625	−	4.44161i	−0.546758	−	0.221527i
$403$	−12.2704	−	7.88570i	−0.611231	−	0.392815i
$404$	−7.15147	−	6.19679i	−0.355799	−	0.308302i
$405$	8.06690	−	3.99063i	0.400847	−	0.198296i
$406$	13.7820	−	1.98155i	0.683987	−	0.0983425i
$407$	−6.16343	+	5.34064i	−0.305510	+	0.264726i
$408$	8.92968	−	6.30309i	0.442085	−	0.312049i
$409$	31.0643	−	9.12130i	1.53603	−	0.451019i	0.599140	−	0.800644i	$-0.295509\pi$
$409$	31.0643	−	9.12130i	1.53603	−	0.451019i	0.936890	+	0.349625i	$0.113691\pi$
$410$	−2.64170	+	5.78452i	−0.130464	+	0.285677i
$411$	−0.515472	−	11.8566i	−0.0254263	−	0.584842i
$412$	−5.26160	−	8.18722i	−0.259221	−	0.403355i
$413$	23.0131			1.13240
$414$	−14.0362	+	3.16003i	−0.689840	+	0.155307i
$415$	12.4140			0.609380
$416$	−1.25148	−	1.94735i	−0.0613590	−	0.0954765i
$417$	0.116340	+	2.67600i	0.00569721	+	0.131044i
$418$	−3.47977	+	7.61963i	−0.170201	+	0.372688i
$419$	18.6722	−	5.48266i	0.912198	−	0.267845i	0.208232	−	0.978079i	$-0.433229\pi$
$419$	18.6722	−	5.48266i	0.912198	−	0.267845i	0.703966	+	0.710234i	$0.251411\pi$
$420$	−5.52315	+	3.89856i	−0.269502	+	0.190230i
$421$	8.35809	−	7.24233i	0.407348	−	0.352969i	−0.426957	−	0.904272i	$-0.640414\pi$
$421$	8.35809	−	7.24233i	0.407348	−	0.352969i	0.834305	+	0.551303i	$0.185869\pi$
$422$	3.29045	−	0.473095i	0.160177	−	0.0230299i
$423$	0.400125	+	4.59302i	0.0194547	+	0.223320i
$424$	0.821895	+	0.712176i	0.0399147	+	0.0345863i
$425$	5.30875	+	3.41173i	0.257512	+	0.165493i
$426$	0.0877063	+	0.0355355i	0.00424938	+	0.00172170i
$427$	−29.1616	+	33.6542i	−1.41123	+	1.62864i
$428$	−1.63760	−	0.480841i	−0.0791562	−	0.0232423i
$429$	2.50591	+	7.33878i	0.120986	+	0.354320i
$430$	4.02443	+	4.64444i	0.194075	+	0.223975i
$431$	4.99683	+	10.9415i	0.240689	+	0.527035i	0.990970	−	0.134084i	$-0.0428092\pi$
$431$	4.99683	+	10.9415i	0.240689	+	0.527035i	−0.750281	+	0.661119i	$0.770082\pi$
$432$	3.45140	−	3.88430i	0.166056	−	0.186884i
$433$	12.1668	+	5.55639i	0.584699	+	0.267023i	0.685725	−	0.727861i	$-0.259485\pi$
$433$	12.1668	+	5.55639i	0.584699	+	0.267023i	−0.101026	+	0.994884i	$0.532213\pi$
$434$	−3.50011	+	24.3438i	−0.168010	+	1.16854i
$435$	−4.24520	−	4.48941i	−0.203542	−	0.215251i
$436$			10.8868i			0.521381i
$437$	15.8087	−	13.4715i	0.756231	−	0.644427i
$438$	−3.12708	−	16.5953i	−0.149418	−	0.792954i
$439$	22.9549	−	14.7522i	1.09558	−	0.704086i	0.137475	−	0.990505i	$-0.456101\pi$
$439$	22.9549	−	14.7522i	1.09558	−	0.704086i	0.958104	+	0.286419i	$0.0924650\pi$
$440$	1.91448	+	0.275261i	0.0912694	+	0.0131226i
$441$	−1.38031	+	24.6653i	−0.0657290	+	1.17454i
$442$	4.11546	+	14.0160i	0.195753	+	0.666672i
$443$	−22.3682	+	10.2152i	−1.06275	+	0.485340i	−0.868540	−	0.495620i	$-0.834941\pi$
$443$	−22.3682	+	10.2152i	−1.06275	+	0.485340i	−0.194208	+	0.980960i	$0.562214\pi$
$444$	−4.53830	+	5.72187i	−0.215378	+	0.271548i
$445$	1.74485	+	12.1357i	0.0827137	+	0.575287i
$446$	−0.409927	+	1.39608i	−0.0194106	+	0.0661065i
$447$	−1.26317	+	2.16705i	−0.0597461	+	0.102498i
$448$	−2.11021	+	3.28354i	−0.0996978	+	0.155133i
$449$	3.52002	−	5.47726i	0.166120	−	0.258488i	−0.748206	−	0.663466i	$-0.769085\pi$
$449$	3.52002	−	5.47726i	0.166120	−	0.258488i	0.914326	+	0.404979i	$0.132721\pi$
$450$	2.82676	+	1.00471i	0.133255	+	0.0473625i
$451$	3.46524	−	11.8015i	0.163172	−	0.555712i
$452$	−1.86598	−	12.9782i	−0.0877682	−	0.610441i
$453$	18.6100	+	14.7605i	0.874375	+	0.693511i
$454$	−20.3321	+	9.28537i	−0.954233	+	0.435784i
$455$	−2.54548	−	8.66910i	−0.119334	−	0.406414i
$456$	−1.79874	+	7.28240i	−0.0842336	+	0.341030i
$457$	9.59794	+	1.37998i	0.448973	+	0.0645525i	0.363093	−	0.931753i	$-0.381721\pi$
$457$	9.59794	+	1.37998i	0.448973	+	0.0645525i	0.0858799	+	0.996306i	$0.472630\pi$
$458$	21.5330	−	13.8384i	1.00617	−	0.646627i
$459$	−27.8037	+	17.3829i	−1.29777	+	0.811365i
$460$	−4.01297	−	2.62603i	−0.187106	−	0.122439i
$461$		−	10.4902i		−	0.488576i	−0.969703	−	0.244288i	$-0.921446\pi$
$461$		−	10.4902i		−	0.488576i	0.969703	−	0.244288i	$-0.0785542\pi$
$462$	9.50085	−	8.98403i	0.442020	−	0.417975i
$463$	−3.37874	+	23.4996i	−0.157023	+	1.09212i	0.747057	+	0.664760i	$0.231466\pi$
$463$	−3.37874	+	23.4996i	−0.157023	+	1.09212i	−0.904081	+	0.427362i	$0.859443\pi$
$464$	−3.24492	−	1.48190i	−0.150642	−	0.0687957i
$465$	9.72124	−	4.96067i	0.450812	−	0.230046i
$466$	−10.2501	−	22.4445i	−0.474826	−	1.03972i
$467$	−9.54507	−	11.0156i	−0.441693	−	0.509741i	0.490630	−	0.871368i	$-0.336767\pi$
$467$	−9.54507	−	11.0156i	−0.441693	−	0.509741i	−0.932323	+	0.361627i	$0.882221\pi$
$468$	3.42217	+	6.04269i	0.158190	+	0.279323i
$469$	−25.5748	−	7.50943i	−1.18093	−	0.346753i
$470$	−1.00639	+	1.16144i	−0.0464215	+	0.0535733i
$471$	−3.02154	+	7.45756i	−0.139225	+	0.343626i
$472$	−4.96005	−	3.18763i	−0.228305	−	0.146722i
$473$	−8.98313	−	7.78393i	−0.413045	−	0.357906i
$474$	10.6973	+	1.06630i	0.491343	+	0.0489769i
$475$	−4.28677	+	0.616344i	−0.196690	+	0.0282798i
$476$	18.6148	−	16.1299i	0.853210	−	0.739310i
$477$	−2.34246	−	2.27096i	−0.107254	−	0.103980i
$478$	6.67479	−	1.95989i	0.305298	−	0.0896435i
$479$	13.1312	−	28.7534i	0.599981	−	1.31378i	−0.329238	−	0.944247i	$-0.606792\pi$
$479$	13.1312	−	28.7534i	0.599981	−	1.31378i	0.929219	−	0.369529i	$-0.120481\pi$
$480$	1.73042	−	0.0752308i	0.0789823	−	0.00343380i
$481$	−5.27685	−	8.21094i	−0.240604	−	0.374387i
$482$	−6.51845			−0.296907
$483$	−30.7681	+	10.2233i	−1.39999	+	0.465177i
$484$	7.25898			0.329954
$485$	−8.12172	−	12.6376i	−0.368788	−	0.573846i
$486$	−10.9891	+	11.0562i	−0.498477	+	0.501518i
$487$	1.74579	−	3.82274i	0.0791091	−	0.173225i	−0.865945	−	0.500140i	$-0.833282\pi$
$487$	1.74579	−	3.82274i	0.0791091	−	0.173225i	0.945054	+	0.326915i	$0.106009\pi$
$488$	10.9468	−	3.21428i	0.495539	−	0.145503i
$489$	20.0123	+	28.3518i	0.904989	+	1.28211i
$490$	−6.22332	+	5.39253i	−0.281141	+	0.243610i
$491$	33.3774	−	4.79894i	1.50630	−	0.216573i	0.660806	−	0.750557i	$-0.270215\pi$
$491$	33.3774	−	4.79894i	1.50630	−	0.216573i	0.845495	+	0.533984i	$0.179306\pi$
$492$	1.09250	−	10.9601i	0.0492537	−	0.494120i
$493$	17.0130	+	14.7419i	0.766228	+	0.663940i
$494$	−8.43366	−	5.41999i	−0.379448	−	0.243857i
$495$	−5.68834	−	1.14540i	−0.255672	−	0.0514821i
$496$	4.12633	−	4.76204i	0.185278	−	0.213822i
$497$	0.204613	+	0.0600799i	0.00917816	+	0.00269495i
$498$	−20.3482	+	6.94810i	−0.911822	+	0.311352i
$499$	−8.19340	−	9.45569i	−0.366787	−	0.423295i	0.542115	−	0.840304i	$-0.317624\pi$
$499$	−8.19340	−	9.45569i	−0.366787	−	0.423295i	−0.908902	+	0.417009i	$0.863078\pi$
$500$	0.415415	+	0.909632i	0.0185779	+	0.0406800i
$501$	0.654473	+	1.28255i	0.0292397	+	0.0573000i
$502$	4.34654	+	1.98500i	0.193995	+	0.0885948i
$503$	5.48633	−	38.1583i	0.244623	−	1.70139i	−0.383714	−	0.923452i	$-0.625355\pi$
$503$	5.48633	−	38.1583i	0.244623	−	1.70139i	0.628338	−	0.777941i	$-0.283736\pi$
$504$	6.87112	−	9.48153i	0.306064	−	0.422341i
$505$			9.46276i			0.421087i
$506$	8.40562	+	3.92288i	0.373675	+	0.174393i
$507$	13.0068	−	2.45089i	0.577652	−	0.108848i
$508$	15.4730	−	9.94391i	0.686504	−	0.441190i
$509$	−35.7326	−	5.13757i	−1.58382	−	0.227719i	−0.706531	−	0.707682i	$-0.749741\pi$
$509$	−35.7326	−	5.13757i	−1.58382	−	0.227719i	−0.877289	+	0.479963i	$0.840650\pi$
$510$	−10.6113	−	2.62096i	−0.469874	−	0.116058i
$511$	−10.7215	−	36.5139i	−0.474289	−	1.61528i
$512$	0.909632	−	0.415415i	0.0402004	−	0.0183589i
$513$	6.60847	−	21.5116i	0.291771	−	0.949758i
$514$	0.707358	+	4.91978i	0.0312002	+	0.217002i
$515$	−2.74187	+	9.33794i	−0.120821	+	0.411479i
$516$	−9.19603	−	5.36036i	−0.404833	−	0.235977i
$517$	1.60703	−	2.50058i	0.0706769	−	0.109975i
$518$	−8.89763	+	13.8450i	−0.390939	+	0.608314i
$519$	−15.4195	−	8.98800i	−0.676840	−	0.394529i
$520$	−0.652159	+	2.22105i	−0.0285991	+	0.0973994i
$521$	−4.99489	−	34.7402i	−0.218830	−	1.52200i	−0.742367	−	0.669993i	$-0.766297\pi$
$521$	−4.99489	−	34.7402i	−0.218830	−	1.52200i	0.523537	−	0.852003i	$-0.324612\pi$
$522$	9.47114	+	4.98269i	0.414541	+	0.218086i
$523$	−5.88063	+	2.68560i	−0.257142	+	0.117433i	−0.539816	−	0.841783i	$-0.681506\pi$
$523$	−5.88063	+	2.68560i	−0.257142	+	0.117433i	0.282673	+	0.959216i	$0.408779\pi$
$524$	−2.44124	−	8.31411i	−0.106646	−	0.363204i
$525$	6.56322	+	1.62110i	0.286443	+	0.0707507i
$526$	−29.8692	−	4.29454i	−1.30236	−	0.187251i
$527$	−33.4509	+	21.4976i	−1.45714	+	0.936449i
$528$	−3.29215	+	0.620345i	−0.143272	+	0.0269970i
$529$	−14.7728	−	17.6285i	−0.642297	−	0.766456i
$530$		−	1.08752i		−	0.0472390i
$531$	14.3226	+	10.3794i	0.621547	+	0.450426i
$532$	−2.40569	+	16.7319i	−0.104300	+	0.725421i
$533$	13.3901	+	6.11505i	0.579989	+	0.264872i
$534$	−9.65235	−	18.9153i	−0.417698	−	0.818547i
$535$	0.709001	+	1.55250i	0.0306528	+	0.0671203i
$536$	4.47201	+	5.16098i	0.193161	+	0.222920i
$537$	−42.7667	+	14.6032i	−1.84552	+	0.630173i
$538$	−7.67627	−	2.25396i	−0.330947	−	0.0971749i
$539$	10.4301	−	12.0370i	0.449255	−	0.518468i
$540$	−5.19575	−	0.0647169i	−0.223589	−	0.00278497i
$541$	−32.5426	−	20.9139i	−1.39912	−	0.899158i	−0.399273	−	0.916832i	$-0.630738\pi$
$541$	−32.5426	−	20.9139i	−1.39912	−	0.899158i	−0.999844	+	0.0176739i	$0.994374\pi$
$542$	−23.8492	−	20.6655i	−1.02441	−	0.887658i
$543$	3.60749	−	36.1908i	0.154812	−	1.55310i
$544$	−6.24629	+	0.898081i	−0.267808	+	0.0385049i
$545$	8.22766	−	7.12931i	0.352434	−	0.305386i
$546$	9.02444	+	12.7851i	0.386210	+	0.547150i
$547$	15.9726	−	4.68999i	0.682941	−	0.200530i	0.0781832	−	0.996939i	$-0.475088\pi$
$547$	15.9726	−	4.68999i	0.682941	−	0.200530i	0.604758	+	0.796409i	$0.293270\pi$
$548$	−2.84637	+	6.23268i	−0.121591	+	0.266247i
$549$	−33.3279	+	7.79283i	−1.42240	+	0.332590i
$550$	−1.04569	−	1.62713i	−0.0445884	−	0.0693810i
$551$	−15.4494			−0.658166
$552$	8.04756	+	2.05835i	0.342527	+	0.0876092i
$553$	24.2257			1.03018
$554$	−9.68807	−	15.0749i	−0.411606	−	0.640472i
$555$	7.29626	−	0.317209i	0.309709	−	0.0134648i
$556$	0.642417	−	1.40670i	0.0272445	−	0.0596572i
$557$	40.1397	−	11.7861i	1.70077	−	0.499392i	0.719905	−	0.694072i	$-0.244185\pi$
$557$	40.1397	−	11.7861i	1.70077	−	0.499392i	0.980867	+	0.194680i	$0.0623670\pi$
$558$	−13.1579	+	13.5721i	−0.557017	+	0.574554i
$559$	10.7510	−	9.31580i	0.454719	−	0.394017i
$560$	3.86343	−	0.555477i	0.163260	−	0.0234732i
$561$	21.0365	+	2.09691i	0.888163	+	0.0885318i
$562$	8.36592	+	7.24911i	0.352895	+	0.305785i
$563$	5.37268	+	3.45281i	0.226431	+	0.145519i	0.648938	−	0.760841i	$-0.275213\pi$
$563$	5.37268	+	3.45281i	0.226431	+	0.145519i	−0.422507	+	0.906360i	$0.638850\pi$
$564$	0.999552	−	2.46703i	0.0420887	−	0.103881i
$565$	−8.58628	+	9.90909i	−0.361227	+	0.416879i
$566$	−6.83064	−	2.00566i	−0.287113	−	0.0843040i
$567$	−22.1705	+	27.2484i	−0.931073	+	1.14432i
$568$	−0.0357787	−	0.0412909i	−0.00150124	−	0.00173253i
$569$	−12.1155	−	26.5293i	−0.507910	−	1.11217i	−0.973817	−	0.227333i	$-0.926999\pi$
$569$	−12.1155	−	26.5293i	−0.507910	−	1.11217i	0.465907	−	0.884833i	$-0.345728\pi$
$570$	6.68159	−	3.40956i	0.279861	−	0.142811i
$571$	8.67285	+	3.96076i	0.362948	+	0.165753i	0.588538	−	0.808470i	$-0.299704\pi$
$571$	8.67285	+	3.96076i	0.362948	+	0.165753i	−0.225590	+	0.974222i	$0.572431\pi$
$572$	0.637179	−	4.43168i	0.0266418	−	0.185298i
$573$	32.6141	−	30.8400i	1.36247	−	1.28836i
$574$		−	24.8209i		−	1.03600i
$575$	0.643315	+	4.75249i	0.0268281	+	0.198192i
$576$	−2.79427	+	1.09182i	−0.116428	+	0.0454926i
$577$	−22.0367	+	14.1621i	−0.917398	+	0.589576i	−0.911902	−	0.410409i	$-0.865386\pi$
$577$	−22.0367	+	14.1621i	−0.917398	+	0.589576i	−0.00549631	+	0.999985i	$0.501750\pi$
$578$	22.5904	+	3.24801i	0.939638	+	0.135099i
$579$	−2.18104	+	8.83019i	−0.0906409	+	0.366970i
$580$	1.00502	+	3.42279i	0.0417312	+	0.142123i
$581$	−44.0752	+	20.1285i	−1.82855	+	0.835069i
$582$	20.3858	+	16.1690i	0.845019	+	0.670227i
$583$	0.299353	+	2.08204i	0.0123979	+	0.0862295i
$584$	−2.74687	+	9.35497i	−0.113666	+	0.387111i
$585$	2.32572	−	6.54342i	0.0961566	−	0.270537i
$586$	0.0708737	−	0.110282i	0.00292776	−	0.00455569i
$587$	8.18990	−	12.7437i	0.338033	−	0.525990i	−0.630071	−	0.776537i	$-0.716974\pi$
$587$	8.18990	−	12.7437i	0.338033	−	0.525990i	0.968104	+	0.250548i	$0.0806106\pi$
$588$	7.18262	−	12.3222i	0.296206	−	0.508160i
$589$	7.68821	−	26.1836i	0.316787	−	1.07888i
$590$	0.839091	+	5.83601i	0.0345448	+	0.240265i
$591$	13.3985	−	16.8928i	0.551140	−	0.694875i
$592$	3.83544	−	1.75159i	0.157636	−	0.0719898i
$593$	6.34012	+	21.5925i	0.260358	+	0.886697i	0.981101	+	0.193495i	$0.0619823\pi$
$593$	6.34012	+	21.5925i	0.260358	+	0.886697i	−0.720744	+	0.693202i	$0.756200\pi$
$594$	9.96499	−	1.30629i	0.408869	−	0.0535977i
$595$	−24.3803	−	3.50535i	−0.999493	−	0.143705i
$596$	1.21829	−	0.782949i	0.0499032	−	0.0320708i
$597$	8.87647	+	47.1071i	0.363290	+	1.92796i
$598$	−6.07878	+	9.28929i	−0.248580	+	0.379867i
$599$		−	3.12032i		−	0.127493i	−0.997966	−	0.0637464i	$-0.979695\pi$
$599$		−	3.12032i		−	0.127493i	0.997966	−	0.0637464i	$-0.0203049\pi$
$600$	−1.19004	−	1.25850i	−0.0485831	−	0.0513779i
$601$	−1.49812	+	10.4196i	−0.0611095	+	0.425026i	0.936185	+	0.351509i	$0.114331\pi$
$601$	−1.49812	+	10.4196i	−0.0611095	+	0.425026i	−0.997294	+	0.0735167i	$0.976578\pi$
$602$	−21.8191	−	9.96445i	−0.889280	−	0.406121i
$603$	−12.5300	−	16.2083i	−0.510260	−	0.660055i
$604$	−5.69693	−	12.4745i	−0.231805	−	0.507581i
$605$	−4.75362	−	5.48597i	−0.193262	−	0.223037i
$606$	−5.29629	−	15.5107i	−0.215147	−	0.630078i
$607$	35.4831	+	10.4188i	1.44021	+	0.422885i	0.906293	−	0.422649i	$-0.138900\pi$
$607$	35.4831	+	10.4188i	1.44021	+	0.422885i	0.533921	+	0.845534i	$0.320718\pi$
$608$	2.83610	−	3.27304i	0.115019	−	0.132739i
$609$	22.3516	+	9.05608i	0.905732	+	0.366971i
$610$	−9.59783	−	6.16815i	−0.388605	−	0.249741i
$611$	2.68852	+	2.32962i	0.108766	+	0.0942462i
$612$	18.8601	−	1.64302i	0.762376	−	0.0664150i
$613$	−38.4091	+	5.52239i	−1.55133	+	0.223047i	−0.864072	−	0.503368i	$-0.832094\pi$
$613$	−38.4091	+	5.52239i	−1.55133	+	0.223047i	−0.687256	+	0.726415i	$0.741185\pi$
$614$	−11.5265	+	9.98779i	−0.465173	+	0.403074i
$615$	−8.99853	+	6.35169i	−0.362856	+	0.256125i
$616$	−7.24357	+	2.12690i	−0.291852	+	0.0856954i
$617$	−11.5147	+	25.2136i	−0.463564	+	1.01506i	0.523097	+	0.852273i	$0.324777\pi$
$617$	−11.5147	+	25.2136i	−0.463564	+	1.01506i	−0.986661	+	0.162790i	$0.947951\pi$
$618$	−0.732158	−	16.8407i	−0.0294517	−	0.677432i
$619$	5.57316	+	8.67201i	0.224004	+	0.348557i	0.935005	−	0.354633i	$-0.115394\pi$
$619$	5.57316	+	8.67201i	0.224004	+	0.348557i	−0.711001	+	0.703191i	$0.751758\pi$
$620$	−6.30108			−0.253057
$621$	−23.7599	−	7.51435i	−0.953453	−	0.301541i
$622$	14.3949			0.577183
$623$	−25.8721	−	40.2578i	−1.03654	−	1.61290i
$624$	−0.174145	−	4.00559i	−0.00697139	−	0.160352i
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$	−17.7360	+	5.20775i	−0.708871	+	0.208143i
$627$	−11.8533	+	8.36673i	−0.473374	+	0.334135i
$628$	3.51091	−	3.04222i	0.140101	−	0.121398i
$629$	−26.3373	+	3.78674i	−1.05014	+	0.150987i
$630$	−11.6653	+	1.01623i	−0.464756	+	0.0404876i
$631$	21.2299	+	18.3958i	0.845149	+	0.732326i	0.965499	−	0.260405i	$-0.0838562\pi$
$631$	21.2299	+	18.3958i	0.845149	+	0.732326i	−0.120350	+	0.992732i	$0.538402\pi$
$632$	−5.22140	−	3.35559i	−0.207696	−	0.133478i
$633$	5.33646	+	2.16214i	0.212105	+	0.0859375i
$634$	10.6642	−	12.3071i	0.423529	−	0.488778i
$635$	−17.6478	−	5.18186i	−0.700331	−	0.205636i
$636$	0.608684	+	1.78259i	0.0241359	+	0.0706842i
$637$	12.4827	+	14.4058i	0.494583	+	0.570780i
$638$	−2.86626	−	6.27623i	−0.113476	−	0.248478i
$639$	0.100247	+	0.129676i	0.00396572	+	0.00512992i
$640$	−0.909632	−	0.415415i	−0.0359564	−	0.0164207i
$641$	−4.55953	+	31.7123i	−0.180091	+	1.25256i	0.676453	+	0.736485i	$0.263516\pi$
$641$	−4.55953	+	31.7123i	−0.180091	+	1.25256i	−0.856544	+	0.516074i	$0.827393\pi$
$642$	−2.03107	−	2.14791i	−0.0801600	−	0.0847713i
$643$			20.9604i			0.826598i	0.910595	+	0.413299i	$0.135623\pi$
$643$			20.9604i			0.826598i	−0.910595	+	0.413299i	$0.864377\pi$
$644$	18.5057	+	2.81681i	0.729228	+	0.110998i
$645$	1.97103	+	10.4602i	0.0776092	+	0.411869i
$646$	−22.9914	+	14.7757i	−0.904585	+	0.581341i
$647$	−16.1780	−	2.32605i	−0.636023	−	0.0914463i	−0.183242	−	0.983068i	$-0.558659\pi$
$647$	−16.1780	−	2.32605i	−0.636023	−	0.0914463i	−0.452781	+	0.891622i	$0.649568\pi$
$648$	8.55272	−	2.80197i	0.335982	−	0.110072i
$649$	−3.21285	−	10.9420i	−0.126115	−	0.429510i
$650$	2.10563	−	0.961609i	0.0825896	−	0.0377174i
$651$	−26.4713	+	33.3749i	−1.03749	+	1.30806i
$652$	−2.85141	−	19.8320i	−0.111670	−	0.776681i
$653$	−11.8913	+	40.4980i	−0.465342	+	1.58481i	0.308367	+	0.951267i	$0.400217\pi$
$653$	−11.8913	+	40.4980i	−0.465342	+	1.58481i	−0.773709	+	0.633541i	$0.781601\pi$
$654$	−9.49592	+	16.2908i	−0.371320	+	0.637023i
$655$	−4.68471	+	7.28955i	−0.183047	+	0.284826i
$656$	−3.43803	+	5.34968i	−0.134233	+	0.208870i
$657$	9.79583	−	27.5606i	0.382172	−	1.07524i
$658$	1.68994	−	5.75542i	0.0658808	−	0.224370i
$659$	6.39908	+	44.5066i	0.249273	+	1.73373i	0.602435	+	0.798168i	$0.294197\pi$
$659$	6.39908	+	44.5066i	0.249273	+	1.73373i	−0.353162	+	0.935562i	$0.614894\pi$
$660$	2.62472	+	2.08180i	0.102167	+	0.0810339i
$661$	−11.0913	+	5.06523i	−0.431402	+	0.197015i	−0.619268	−	0.785180i	$-0.712570\pi$
$661$	−11.0913	+	5.06523i	−0.431402	+	0.197015i	0.187865	+	0.982195i	$0.439843\pi$
$662$	4.56393	+	15.5433i	0.177382	+	0.604108i
$663$	−6.06703	+	24.5631i	−0.235624	+	0.953951i
$664$	12.2877	+	1.76670i	0.476854	+	0.0685612i
$665$	14.2205	−	9.13898i	0.551449	−	0.354395i
$666$	−11.7820	+	4.60365i	−0.456541	+	0.178388i
$667$	−0.141202	+	17.1075i	−0.00546736	+	0.662406i
$668$		−	0.831316i		−	0.0321646i
$669$	−1.83114	+	1.73153i	−0.0707960	+	0.0669449i
$670$	0.971861	−	6.75944i	0.0375463	−	0.261140i
$671$	20.0727	+	9.16691i	0.774899	+	0.353885i
$672$	−6.02175	+	3.07285i	−0.232294	+	0.118538i
$673$	−17.2822	−	37.8428i	−0.666181	−	1.45873i	−0.876649	−	0.481131i	$-0.840226\pi$
$673$	−17.2822	−	37.8428i	−0.666181	−	1.45873i	0.210468	−	0.977601i	$-0.432501\pi$
$674$	3.72010	+	4.29323i	0.143293	+	0.165369i
$675$	3.35358	+	3.96907i	0.129079	+	0.152769i
$676$	−7.33209	−	2.15290i	−0.282004	−	0.0828037i
$677$	1.92344	−	2.21976i	0.0739236	−	0.0853124i	−0.717583	−	0.696473i	$-0.754752\pi$
$677$	1.92344	−	2.21976i	0.0739236	−	0.0853124i	0.791507	+	0.611161i	$0.209297\pi$
$678$	8.52790	−	21.0480i	0.327512	−	0.808343i
$679$	49.3267	+	31.7004i	1.89299	+	1.21655i
$680$	4.76918	+	4.13251i	0.182890	+	0.158475i
$681$	−38.5239	−	3.84005i	−1.47624	−	0.147151i
$682$	12.0633	−	1.73444i	0.461928	−	0.0664153i
$683$	−34.9509	+	30.2851i	−1.33736	+	1.15883i	−0.363518	+	0.931587i	$0.618425\pi$
$683$	−34.9509	+	30.2851i	−1.33736	+	1.15883i	−0.973839	+	0.227240i	$0.927030\pi$
$684$	−9.04365	+	9.32838i	−0.345793	+	0.356679i
$685$	6.57432	−	1.93039i	0.251192	−	0.0737566i
$686$	2.00186	−	4.38347i	0.0764314	−	0.167361i
$687$	44.2923	−	1.92563i	1.68986	−	0.0734675i
$688$	3.32249	+	5.16990i	0.126669	+	0.197101i
$689$	−2.51741			−0.0959058
$690$	−3.71443	−	7.42987i	−0.141406	−	0.282850i
$691$	−16.1151			−0.613049			−0.306524	−	0.951863i	$-0.599166\pi$
$691$	−16.1151			−0.613049			−0.306524	+	0.951863i	$0.599166\pi$
$692$	5.57100	+	8.66864i	0.211778	+	0.329532i
$693$	22.0533	−	5.15656i	0.837735	−	0.195881i
$694$	12.9199	−	28.2906i	0.490433	−	1.07390i
$695$	−1.48380	+	0.435684i	−0.0562839	+	0.0165264i
$696$	−3.56308	−	5.04787i	−0.135058	−	0.191339i
$697$	30.3281	−	26.2794i	1.14876	−	0.995404i
$698$	−3.32503	+	0.478067i	−0.125854	+	0.0180951i
$699$	4.23902	−	42.5264i	0.160334	−	1.60850i
$700$	−2.94981	−	2.55602i	−0.111492	−	0.0966086i
$701$	−30.2943	−	19.4690i	−1.14420	−	0.735334i	−0.175725	−	0.984439i	$-0.556227\pi$
$701$	−30.2943	−	19.4690i	−1.14420	−	0.735334i	−0.968476	+	0.249106i	$0.919863\pi$
$702$	−0.149808	+	12.0272i	−0.00565413	+	0.453937i
$703$	11.9584	−	13.8007i	0.451018	−	0.520503i
$704$	1.85582	+	0.544919i	0.0699440	+	0.0205374i
$705$	−2.51902	+	0.860147i	−0.0948718	+	0.0323950i
$706$	13.0599	+	15.0719i	0.491515	+	0.567239i
$707$	−15.3432	−	33.5969i	−0.577040	−	1.26354i
$708$	−4.64178	−	9.09632i	−0.174449	−	0.341861i
$709$	39.7260	+	18.1423i	1.49194	+	0.681347i	0.983692	−	0.179862i	$-0.0575650\pi$
$709$	39.7260	+	18.1423i	1.49194	+	0.681347i	0.508251	+	0.861209i	$0.330292\pi$
$710$	−0.00777546	+	0.0540795i	−0.000291808	+	0.00202957i
$711$	15.0773	+	10.9263i	0.565442	+	0.409767i
$712$			12.2605i			0.459481i
$713$	−28.9236	−	8.75267i	−1.08320	−	0.327790i
$714$	41.9243	−	7.89986i	1.56898	−	0.295645i
$715$	−3.76650	+	2.42058i	−0.140859	+	0.0905247i
$716$	25.8256	+	3.71316i	0.965147	+	0.138767i
$717$	11.6976	+	2.88928i	0.436855	+	0.107902i
$718$	−9.95400	−	33.9002i	−0.371480	−	1.26514i
$719$	38.7736	−	17.7073i	1.44601	−	0.660371i	0.470919	−	0.882176i	$-0.343922\pi$
$719$	38.7736	−	17.7073i	1.44601	−	0.660371i	0.975091	+	0.221806i	$0.0711950\pi$
$720$	2.65500	+	1.39677i	0.0989460	+	0.0520547i
$721$	−5.40599	−	37.5995i	−0.201330	−	1.40028i
$722$	−0.0686698	+	0.233868i	−0.00255563	+	0.00870366i
$723$	−9.75416	−	5.68569i	−0.362761	−	0.211453i
$724$	−11.3526	+	17.6649i	−0.421914	+	0.656511i
$725$	1.92862	−	3.00099i	0.0716272	−	0.111454i
$726$	10.8623	+	6.33161i	0.403137	+	0.234988i
$727$	−3.01521	+	10.2689i	−0.111828	+	0.380851i	−0.996321	−	0.0857030i	$-0.972686\pi$
$727$	−3.01521	+	10.2689i	−0.111828	+	0.380851i	0.884493	+	0.466554i	$0.154505\pi$
$728$	−1.28583	−	8.94312i	−0.0476559	−	0.331454i
$729$	−26.0877	+	6.95915i	−0.966213	+	0.257746i
$730$	8.86883	−	4.05026i	0.328250	−	0.149907i
$731$	−10.9259	−	37.2102i	−0.404109	−	1.37627i
$732$	19.1844	+	4.73850i	0.709074	+	0.175140i
$733$	−34.7857	−	5.00143i	−1.28484	−	0.184732i	−0.534152	−	0.845388i	$-0.679369\pi$
$733$	−34.7857	−	5.00143i	−1.28484	−	0.184732i	−0.750689	+	0.660656i	$0.770278\pi$
$734$	−17.6976	+	11.3736i	−0.653232	+	0.419806i
$735$	−14.0161	+	2.64108i	−0.516993	+	0.0974178i
$736$	−3.59840	−	3.17041i	−0.132639	−	0.116863i
$737$			13.2084i			0.486536i
$738$	11.1947	−	15.4477i	0.412083	−	0.568637i
$739$	−5.13442	+	35.7107i	−0.188873	+	1.31364i	0.646060	+	0.763287i	$0.276416\pi$
$739$	−5.13442	+	35.7107i	−0.188873	+	1.31364i	−0.834933	+	0.550352i	$0.814494\pi$
$740$	−3.83544	−	1.75159i	−0.140994	−	0.0643896i
$741$	−7.89250	−	15.4666i	−0.289938	−	0.568181i
$742$	1.76334	+	3.86118i	0.0647343	+	0.141748i
$743$	−16.9930	−	19.6110i	−0.623414	−	0.719458i	0.352938	−	0.935647i	$-0.385183\pi$
$743$	−16.9930	−	19.6110i	−0.623414	−	0.719458i	−0.976352	+	0.216189i	$0.930637\pi$
$744$	10.3283	−	3.52670i	0.378653	−	0.129295i
$745$	−1.38952	−	0.408001i	−0.0509082	−	0.0149480i
$746$	18.1821	−	20.9833i	0.665695	−	0.768253i
$747$	−36.5093	−	7.35150i	−1.33580	−	0.268977i
$748$	−10.2680	−	6.59886i	−0.375436	−	0.241278i
$749$	−5.03453	−	4.36244i	−0.183958	−	0.159400i
$750$	−0.171799	+	1.72351i	−0.00627321	+	0.0629337i
$751$	−0.734918	+	0.105665i	−0.0268175	+	0.00385578i	−0.155711	−	0.987803i	$-0.549767\pi$
$751$	−0.734918	+	0.105665i	−0.0268175	+	0.00385578i	0.128893	+	0.991659i	$0.458858\pi$
$752$	−1.16144	+	1.00639i	−0.0423534	+	0.0366994i
$753$	4.77272	+	6.76158i	0.173928	+	0.246406i
$754$	7.92312	−	2.32644i	0.288543	−	0.0847238i
$755$	−5.69693	+	12.4745i	−0.207332	+	0.453994i
$756$	18.5521	−	8.19477i	0.674734	−	0.298041i
$757$	−4.21214	−	6.55421i	−0.153093	−	0.238217i	0.756233	−	0.654303i	$-0.227038\pi$
$757$	−4.21214	−	6.55421i	−0.153093	−	0.238217i	−0.909325	+	0.416086i	$0.863402\pi$
$758$	3.56170			0.129367
$759$	9.15638	+	13.2019i	0.332356	+	0.479200i
$760$	−4.33085			−0.157096
$761$	16.7006	+	25.9867i	0.605397	+	0.942017i	0.999734	+	0.0230509i	$0.00733797\pi$
$761$	16.7006	+	25.9867i	0.605397	+	0.942017i	−0.394337	+	0.918966i	$0.629026\pi$
$762$	31.8272	−	1.38371i	1.15298	−	0.0501264i
$763$	−17.6521	+	38.6527i	−0.639049	+	1.39932i
$764$	−24.8654	+	7.30114i	−0.899599	+	0.264146i
$765$	−13.5925	−	13.1776i	−0.491437	−	0.476437i
$766$	7.65546	−	6.63349i	0.276603	−	0.239678i
$767$	13.5093	−	1.94234i	0.487791	−	0.0701338i
$768$	1.72351	+	0.171799i	0.0621918	+	0.00619926i
$769$	−21.1625	−	18.3374i	−0.763139	−	0.661264i	0.183696	−	0.982983i	$-0.441194\pi$
$769$	−21.1625	−	18.3374i	−0.763139	−	0.661264i	−0.946835	+	0.321719i	$0.895739\pi$
$770$	6.35094	+	4.08150i	0.228872	+	0.147087i
$771$	−3.23277	+	7.97891i	−0.116425	+	0.287353i
$772$	3.43889	−	3.96869i	0.123768	−	0.142836i
$773$	20.2276	+	5.93935i	0.727535	+	0.213624i	0.624468	−	0.781051i	$-0.285316\pi$
$773$	20.2276	+	5.93935i	0.727535	+	0.213624i	0.103068	+	0.994674i	$0.467134\pi$
$774$	−9.08531	−	16.0424i	−0.326565	−	0.576632i
$775$	4.12633	+	4.76204i	0.148222	+	0.171057i
$776$	−6.24053	−	13.6649i	−0.224022	−	0.490540i
$777$	−25.3906	+	12.9566i	−0.910881	+	0.464815i
$778$	−8.85921	−	4.04587i	−0.317618	−	0.145051i
$779$	−3.91944	+	27.2603i	−0.140429	+	0.976703i
$780$	−2.91318	+	2.75472i	−0.104309	+	0.0986347i
$781$		−	0.105675i		−	0.00378134i
$782$	16.1514	+	25.5941i	0.577572	+	0.915241i
$783$	9.82641	+	15.7172i	0.351167	+	0.561688i
$784$	−6.92741	+	4.45198i	−0.247407	+	0.158999i
$785$	−4.59832	−	0.661138i	−0.164121	−	0.0235970i
$786$	3.59889	−	14.5705i	0.128368	−	0.519714i
$787$	−8.57035	−	29.1879i	−0.305500	−	1.04044i	−0.958975	−	0.283489i	$-0.908508\pi$
$787$	−8.57035	−	29.1879i	−0.305500	−	1.04044i	0.653476	−	0.756948i	$-0.273310\pi$
$788$	−11.3234	+	5.17124i	−0.403380	+	0.184218i
$789$	−40.9501	−	32.4796i	−1.45786	−	1.15630i
$790$	0.883305	+	6.14352i	0.0314266	+	0.218577i
$791$	14.4181	−	49.1037i	0.512650	−	1.74592i
$792$	−5.46743	−	1.94328i	−0.194277	−	0.0690515i
$793$	−14.2781	+	22.2172i	−0.507031	+	0.788956i
$794$	0.835408	−	1.29992i	0.0296475	−	0.0461324i
$795$	0.948586	−	1.62736i	0.0336429	−	0.0577165i
$796$	7.79721	−	26.5548i	0.276365	−	0.941212i
$797$	−3.04361	−	21.1688i	−0.107810	−	0.749837i	−0.969974	−	0.243207i	$-0.921800\pi$
$797$	−3.04361	−	21.1688i	−0.107810	−	0.749837i	0.862164	−	0.506629i	$-0.169109\pi$
$798$	−18.1942	+	22.9392i	−0.644068	+	0.812037i
$799$	8.82166	−	4.02872i	0.312088	−	0.142526i
$800$	0.281733	+	0.959493i	0.00996075	+	0.0339232i
$801$	2.05513	−	36.7240i	0.0726145	−	1.29758i
$802$	−25.7418	−	3.70112i	−0.908976	−	0.130691i
$803$	−15.8644	+	10.1954i	−0.559841	+	0.359788i
$804$	2.19024	+	11.6235i	0.0772439	+	0.409930i
$805$	−9.98987	−	15.8303i	−0.352097	−	0.557945i
$806$			14.5858i			0.513764i
$807$	−9.52070	−	10.0684i	−0.335144	−	0.354424i
$808$	−1.34669	+	9.36644i	−0.0473764	+	0.329510i
$809$	20.1327	+	9.19431i	0.707829	+	0.323255i	0.736598	−	0.676331i	$-0.236431\pi$
$809$	20.1327	+	9.19431i	0.707829	+	0.323255i	−0.0287683	+	0.999586i	$0.509158\pi$
$810$	−7.71843	−	4.62881i	−0.271198	−	0.162640i
$811$	4.57710	+	10.0224i	0.160724	+	0.351936i	0.972811	−	0.231600i	$-0.0743961\pi$
$811$	4.57710	+	10.0224i	0.160724	+	0.351936i	−0.812087	+	0.583536i	$0.801669\pi$
$812$	−9.11807	−	10.5228i	−0.319981	−	0.369278i
$813$	−17.6624	−	51.7260i	−0.619448	−	1.81411i
$814$	7.82503	+	2.29764i	0.274267	+	0.0805322i
$815$	−13.1207	+	15.1422i	−0.459600	+	0.530406i
$816$	−10.1302	−	4.10442i	−0.354630	−	0.143683i
$817$	22.3901	+	14.3892i	0.783329	+	0.503415i
$818$	−24.4679	−	21.2016i	−0.855501	−	0.741296i
$819$	2.35238	+	27.0030i	0.0821990	+	0.943560i
$820$	6.29445	−	0.905006i	0.219812	−	0.0316042i
$821$	−12.5194	+	10.8481i	−0.436930	+	0.378602i	−0.845368	−	0.534184i	$-0.820619\pi$
$821$	−12.5194	+	10.8481i	−0.436930	+	0.378602i	0.408438	+	0.912786i	$0.366074\pi$
$822$	−9.69571	+	6.84380i	−0.338177	+	0.238705i
$823$	19.9036	−	5.84421i	0.693794	−	0.203716i	0.0842222	−	0.996447i	$-0.473159\pi$
$823$	19.9036	−	5.84421i	0.693794	−	0.203716i	0.609572	+	0.792731i	$0.291341\pi$
$824$	−4.04289	+	8.85269i	−0.140841	+	0.308398i
$825$	−0.145509	−	3.34692i	−0.00506598	−	0.116525i
$826$	−12.4418	−	19.3598i	−0.432906	−	0.673615i
$827$	17.9349			0.623659			0.311830	−	0.950138i	$-0.399058\pi$
$827$	17.9349			0.623659			0.311830	+	0.950138i	$0.399058\pi$
$828$	10.2469	+	10.0995i	0.356105	+	0.350983i
$829$	55.4840			1.92704			0.963519	−	0.267641i	$-0.0862440\pi$
$829$	55.4840			1.92704			0.963519	+	0.267641i	$0.0862440\pi$
$830$	−6.71152	−	10.4433i	−0.232960	−	0.362493i
$831$	−1.34811	−	31.0084i	−0.0467653	−	1.07567i
$832$	−0.961609	+	2.10563i	−0.0333378	+	0.0729996i
$833$	49.8599	−	14.6402i	1.72754	−	0.507252i
$834$	2.18829	−	1.54462i	0.0757744	−	0.0534860i
$835$	−0.628267	+	0.544397i	−0.0217421	+	0.0188396i
$836$	8.29134	−	1.19212i	0.286762	−	0.0412302i
$837$	−31.5276	+	8.83233i	−1.08975	+	0.305290i
$838$	−14.7073	−	12.7439i	−0.508054	−	0.440232i
$839$	31.6919	+	20.3672i	1.09413	+	0.703153i	0.957778	−	0.287508i	$-0.0928267\pi$
$839$	31.6919	+	20.3672i	1.09413	+	0.703153i	0.136349	+	0.990661i	$0.456463\pi$
$840$	6.26571	+	2.53865i	0.216188	+	0.0875916i
$841$	−10.6575	+	12.2994i	−0.367500	+	0.424118i
$842$	−10.6114	−	3.11578i	−0.365692	−	0.107377i
$843$	6.19569	+	18.1446i	0.213391	+	0.624934i
$844$	−2.17694	−	2.51233i	−0.0749335	−	0.0864779i
$845$	3.17445	+	6.95107i	0.109204	+	0.239124i
$846$	3.64757	−	2.81978i	0.125406	−	0.0969461i
$847$	25.7726	+	11.7699i	0.885555	+	0.404420i
$848$	0.154771	−	1.07645i	0.00531484	−	0.0369655i
$849$	−8.47189	−	8.95924i	−0.290754	−	0.307480i
$850$		−	6.31052i		−	0.216449i
$851$	−15.1726	−	13.3680i	−0.520109	−	0.458248i
$852$	−0.0175232	−	0.0929952i	−0.000600336	−	0.00318596i
$853$	−20.7332	+	13.3244i	−0.709892	+	0.456220i	−0.845108	−	0.534596i	$-0.820464\pi$
$853$	−20.7332	+	13.3244i	−0.709892	+	0.456220i	0.135215	+	0.990816i	$0.456827\pi$
$854$	44.0777	+	6.33741i	1.50831	+	0.216862i
$855$	12.9723	+	0.725948i	0.443642	+	0.0248269i
$856$	0.480841	+	1.63760i	0.0164348	+	0.0559719i
$857$	30.0675	−	13.7314i	1.02709	−	0.469054i	0.170663	−	0.985330i	$-0.445409\pi$
$857$	30.0675	−	13.7314i	1.02709	−	0.469054i	0.856423	+	0.516275i	$0.172682\pi$
$858$	4.81898	−	6.07575i	0.164517	−	0.207423i
$859$	4.02069	+	27.9645i	0.137184	+	0.954137i	0.935859	+	0.352374i	$0.114626\pi$
$859$	4.02069	+	27.9645i	0.137184	+	0.954137i	−0.798675	+	0.601763i	$0.794465\pi$
$860$	1.73138	−	5.89654i	0.0590395	−	0.201070i
$861$	21.6499	−	37.1418i	0.737827	−	1.26579i
$862$	6.50311	−	10.1190i	0.221497	−	0.344656i
$863$	−12.4962	+	19.4445i	−0.425375	+	0.661897i	−0.986109	−	0.166099i	$-0.946883\pi$
$863$	−12.4962	+	19.4445i	−0.425375	+	0.661897i	0.560734	+	0.827996i	$0.310519\pi$
$864$	−5.13365	−	0.803490i	−0.174650	−	0.0273353i
$865$	2.90310	−	9.88703i	0.0987082	−	0.336169i
$866$	−1.90353	−	13.2394i	−0.0646847	−	0.449892i
$867$	30.9710	+	24.5647i	1.05183	+	0.834261i
$868$	22.3716	−	10.2168i	0.759341	−	0.346779i
$869$	−3.38214	−	11.5185i	−0.114731	−	0.390739i
$870$	−1.48161	+	5.99845i	−0.0502311	+	0.203367i
$871$	−15.6469	−	2.24968i	−0.530173	−	0.0762274i
$872$	9.15852	−	5.88582i	0.310147	−	0.199319i
$873$	16.4018	+	41.9766i	0.555117	+	1.42069i
$874$	−19.8797	−	6.01587i	−0.672442	−	0.203490i
$875$			3.90316i			0.131951i
$876$	−12.2702	+	11.6028i	−0.414572	+	0.392021i
$877$	−0.913491	+	6.35347i	−0.0308464	+	0.214541i	−0.999415	−	0.0342059i	$-0.989110\pi$
$877$	−0.913491	+	6.35347i	−0.0308464	+	0.214541i	0.968568	+	0.248747i	$0.0800189\pi$
$878$	−24.8208	−	11.3353i	−0.837660	−	0.382546i
$879$	0.202247	−	0.103205i	0.00682163	−	0.00348102i
$880$	−0.803484	−	1.75938i	−0.0270854	−	0.0593088i
$881$	23.8081	+	27.4761i	0.802117	+	0.925692i	0.998495	−	0.0548362i	$-0.0174637\pi$
$881$	23.8081	+	27.4761i	0.802117	+	0.925692i	−0.196379	+	0.980528i	$0.562918\pi$
$882$	21.4960	−	12.1739i	0.723808	−	0.409916i
$883$	18.3044	+	5.37466i	0.615993	+	0.180872i	0.574819	−	0.818280i	$-0.305072\pi$
$883$	18.3044	+	5.37466i	0.615993	+	0.180872i	0.0411731	+	0.999152i	$0.486890\pi$
$884$	9.56601	−	11.0398i	0.321740	−	0.371307i
$885$	−3.83482	+	9.46484i	−0.128906	+	0.318157i
$886$	20.6868	+	13.2946i	0.694986	+	0.446641i
$887$	43.2994	+	37.5192i	1.45385	+	1.25977i	0.906055	+	0.423160i	$0.139079\pi$
$887$	43.2994	+	37.5192i	1.45385	+	1.25977i	0.547798	+	0.836611i	$0.315466\pi$
$888$	7.26714	+	0.724386i	0.243869	+	0.0243088i
$889$	71.0593	−	10.2168i	2.38325	−	0.342660i
$890$	9.26585	−	8.02891i	0.310592	−	0.269130i
$891$	16.0509	+	6.73720i	0.537727	+	0.225705i
$892$	1.39608	−	0.409927i	0.0467444	−	0.0137254i
$893$	−2.76487	+	6.05422i	−0.0925228	+	0.202597i
$894$	2.50597	−	0.108948i	0.0838120	−	0.00364377i
$895$	−14.1059	−	21.9493i	−0.471509	−	0.733683i
$896$	3.90316			0.130395
$897$	−17.1988	+	8.59823i	−0.574250	+	0.287086i
$898$	−6.51083			−0.217269
$899$	12.1524	+	18.9095i	0.405305	+	0.630667i
$900$	−0.683045	−	2.92121i	−0.0227682	−	0.0973736i
$901$	−2.85093	+	6.24266i	−0.0949781	+	0.207973i
$902$	−11.8015	+	3.46524i	−0.392948	+	0.115380i
$903$	−23.9585	−	33.9423i	−0.797288	−	1.12953i
$904$	−9.90909	+	8.58628i	−0.329572	+	0.285575i
$905$	20.7846	−	2.98837i	0.690903	−	0.0993369i
$906$	2.35602	−	23.6359i	0.0782735	−	0.785250i
$907$	18.3239	+	15.8778i	0.608436	+	0.527213i	0.903680	−	0.428209i	$-0.140855\pi$
$907$	18.3239	+	15.8778i	0.608436	+	0.527213i	−0.295244	+	0.955422i	$0.595401\pi$
$908$	18.8037	+	12.0844i	0.624023	+	0.401035i
$909$	5.60379	−	27.8297i	0.185866	−	0.923052i
$910$	−5.91672	+	6.82826i	−0.196137	+	0.226355i
$911$	12.2430	+	3.59488i	0.405630	+	0.119104i	0.478182	−	0.878261i	$-0.341296\pi$
$911$	12.2430	+	3.59488i	0.405630	+	0.119104i	−0.0725516	+	0.997365i	$0.523114\pi$
$912$	7.09881	−	2.42397i	0.235065	−	0.0802656i
$913$	15.7237	+	18.1462i	0.520380	+	0.600551i
$914$	−4.02813	−	8.82037i	−0.133239	−	0.291752i
$915$	−8.98197	−	17.6016i	−0.296935	−	0.581892i
$916$	−23.2833	−	10.6331i	−0.769300	−	0.351328i
$917$	4.81327	−	33.4770i	0.158948	−	1.10551i
$918$	29.6553	+	13.9921i	0.978770	+	0.461807i
$919$			24.2450i			0.799768i	0.916566	+	0.399884i	$0.130950\pi$
$919$			24.2450i			0.799768i	−0.916566	+	0.399884i	$0.869050\pi$
$920$	−0.0395825	+	4.79567i	−0.00130500	+	0.158108i
$921$	−25.9600	+	4.89169i	−0.855411	+	0.161187i
$922$	−8.82490	+	5.67142i	−0.290632	+	0.186778i
$923$	0.125184	+	0.0179988i	0.00412049	+	0.000592436i
$924$	−12.6944	−	3.13549i	−0.417615	−	0.103150i
$925$	1.18792	+	4.04568i	0.0390585	+	0.133021i
$926$	21.5958	−	9.86249i	0.709684	−	0.324102i
$927$	13.5936	−	25.8389i	0.446473	−	0.848661i
$928$	0.507678	+	3.53098i	0.0166653	+	0.115910i
$929$	−13.1474	+	44.7759i	−0.431352	+	1.46905i	0.401656	+	0.915791i	$0.368435\pi$
$929$	−13.1474	+	44.7759i	−0.431352	+	1.46905i	−0.833008	+	0.553260i	$0.813383\pi$
$930$	−9.42888	−	5.49609i	−0.309185	−	0.180224i
$931$	−19.2808	+	30.0016i	−0.631904	+	0.983262i
$932$	−13.3399	+	20.7574i	−0.436964	+	0.679930i
$933$	21.5404	+	12.5559i	0.705201	+	0.411061i
$934$	−4.10646	+	13.9853i	−0.134367	+	0.457613i
$935$	1.73704	+	12.0814i	0.0568074	+	0.395104i
$936$	3.23327	−	6.14583i	0.105683	−	0.200883i
$937$	33.2301	−	15.1757i	1.08558	−	0.495768i	0.209438	−	0.977822i	$-0.432836\pi$
$937$	33.2301	−	15.1757i	1.08558	−	0.495768i	0.876141	+	0.482054i	$0.160109\pi$
$938$	7.50943	+	25.5748i	0.245191	+	0.835046i
$939$	−31.0824	−	7.67728i	−1.01433	−	0.250538i
$940$	1.52116	+	0.218710i	0.0496149	+	0.00713354i
$941$	−23.2046	+	14.9127i	−0.756447	+	0.486139i	−0.861142	−	0.508365i	$-0.830250\pi$
$941$	−23.2046	+	14.9127i	−0.756447	+	0.486139i	0.104694	+	0.994504i	$0.466614\pi$
$942$	7.90726	−	1.48998i	0.257633	−	0.0485461i
$943$	30.1503	+	4.58926i	0.981829	+	0.149447i
$944$			5.89602i			0.191899i
$945$	−18.3422	−	8.65432i	−0.596673	−	0.281525i
$946$	−1.69161	+	11.7654i	−0.0549990	+	0.382526i
$947$	7.85751	+	3.58841i	0.255335	+	0.116608i	0.538971	−	0.842325i	$-0.318813\pi$
$947$	7.85751	+	3.58841i	0.255335	+	0.116608i	−0.283636	+	0.958932i	$0.591541\pi$
$948$	−4.88636	−	9.57562i	−0.158702	−	0.311002i
$949$	−9.37560	−	20.5297i	−0.304345	−	0.666422i
$950$	2.83610	+	3.27304i	0.0920153	+	0.106191i
$951$	26.6926	−	9.11449i	0.865567	−	0.295557i
$952$	−23.6332	−	6.93934i	−0.765958	−	0.224905i
$953$	17.2780	−	19.9399i	0.559691	−	0.645917i	−0.403423	−	0.915014i	$-0.632180\pi$
$953$	17.2780	−	19.9399i	0.559691	−	0.645917i	0.963113	+	0.269096i	$0.0867250\pi$
$954$	−0.644024	+	3.19837i	−0.0208511	+	0.103551i
$955$	21.8012	+	14.0108i	0.705471	+	0.453378i
$956$	−5.25743	−	4.55559i	−0.170037	−	0.147338i
$957$	1.18537	−	11.8918i	0.0383175	−	0.384406i
$958$	−31.2882	+	4.49856i	−1.01087	+	0.145342i
$959$	−20.2117	+	17.5135i	−0.652670	+	0.565542i
$960$	−0.998822	−	1.41505i	−0.0322368	−	0.0456704i
$961$	−8.35106	+	2.45209i	−0.269389	+	0.0790998i
$962$	−4.05460	+	8.87834i	−0.130726	+	0.286249i
$963$	−1.16577	−	4.98571i	−0.0375665	−	0.160662i
$964$	3.52414	+	5.48367i	0.113505	+	0.176617i
$965$	−5.25133			−0.169046
$966$	25.2349	+	20.3566i	0.811919	+	0.654962i
$967$	22.0085			0.707746			0.353873	−	0.935293i	$-0.384864\pi$
$967$	22.0085			0.707746			0.353873	+	0.935293i	$0.384864\pi$
$968$	−3.92450	−	6.10664i	−0.126138	−	0.196275i
$969$	−47.2922	+	2.05605i	−1.51924	+	0.0660499i
$970$	−6.24053	+	13.6649i	−0.200371	+	0.438752i
$971$	−18.8239	+	5.52720i	−0.604089	+	0.177376i	−0.569453	−	0.822024i	$-0.692845\pi$
$971$	−18.8239	+	5.52720i	−0.604089	+	0.177376i	−0.0346352	+	0.999400i	$0.511027\pi$
$972$	15.2422	+	3.26722i	0.488894	+	0.104796i
$973$	4.56172	−	3.95275i	0.146242	−	0.126719i
$974$	−4.15974	+	0.598080i	−0.133287	+	0.0191637i
$975$	3.98961	+	0.397683i	0.127770	+	0.0127360i
$976$	−8.62232	−	7.47128i	−0.275994	−	0.239150i
$977$	−33.8855	−	21.7769i	−1.08409	−	0.696705i	−0.128594	−	0.991697i	$-0.541046\pi$
$977$	−33.8855	−	21.7769i	−1.08409	−	0.696705i	−0.955500	+	0.294992i	$0.904683\pi$
$978$	13.0315	−	32.1636i	0.416703	−	1.02848i
$979$	−15.5293	+	17.9217i	−0.496318	+	0.572781i
$980$	7.90107	+	2.31996i	0.252390	+	0.0741085i
$981$	−28.4192	+	16.0947i	−0.907356	+	0.513865i
$982$	−22.0823	−	25.4843i	−0.704675	−	0.813238i
$983$	−16.6171	−	36.3863i	−0.530002	−	1.16054i	−0.965512	−	0.260358i	$-0.916159\pi$
$983$	−16.6171	−	36.3863i	−0.530002	−	1.16054i	0.435511	−	0.900184i	$-0.356568\pi$
$984$	−9.81088	+	5.00641i	−0.312760	+	0.159599i
$985$	11.3234	+	5.17124i	0.360794	+	0.164769i
$986$	3.20371	−	22.2823i	0.102027	−	0.709613i
$987$	7.54895	−	7.13831i	0.240286	−	0.227215i
$988$			10.0251i			0.318941i
$989$	16.1382	−	24.6616i	0.513165	−	0.784193i
$990$	2.11177	+	5.40459i	0.0671166	+	0.171769i
$991$	−12.2644	+	7.88188i	−0.389593	+	0.250376i	−0.720744	−	0.693202i	$-0.756199\pi$
$991$	−12.2644	+	7.88188i	−0.389593	+	0.250376i	0.331151	+	0.943578i	$0.392563\pi$
$992$	−6.23694	−	0.896737i	−0.198023	−	0.0284714i
$993$	−6.72816	+	27.2398i	−0.213512	+	0.864428i
$994$	−0.0600799	−	0.204613i	−0.00190562	−	0.00648994i
$995$	−25.1749	+	11.4970i	−0.798098	+	0.364479i
$996$	16.8462	+	13.3615i	0.533791	+	0.423376i
$997$	2.75199	+	19.1405i	0.0871564	+	0.606186i	0.985853	+	0.167614i	$0.0536064\pi$
$997$	2.75199	+	19.1405i	0.0871564	+	0.606186i	−0.898696	+	0.438572i	$0.855485\pi$
$998$	−3.52495	+	12.0049i	−0.111580	+	0.380007i
$999$	−21.6459	−	3.38790i	−0.684847	−	0.107188i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.q.b.11.5	yes	160
3.2	odd	2		690.2.q.a.11.13	✓	160
23.21	odd	22		690.2.q.a.251.13	yes	160
69.44	even	22	inner	690.2.q.b.251.5	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.q.a.11.13	✓	160	3.2	odd	2
690.2.q.a.251.13	yes	160	23.21	odd	22
690.2.q.b.11.5	yes	160	1.1	even	1	trivial
690.2.q.b.251.5	yes	160	69.44	even	22	inner

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)

\(f(q)\)	\(=\)	\(q+(-0.540641 - 0.841254i) q^{2} +(-0.0752308 - 1.73042i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(0.959493 - 0.281733i) q^{5} +(-1.41505 + 0.998822i) q^{6} +(-2.94981 + 2.55602i) q^{7} +(0.989821 - 0.142315i) q^{8} +(-2.98868 + 0.260361i) q^{9} +O(q^{10})\)	\(q+(-0.540641 - 0.841254i) q^{2} +(-0.0752308 - 1.73042i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(0.959493 - 0.281733i) q^{5} +(-1.41505 + 0.998822i) q^{6} +(-2.94981 + 2.55602i) q^{7} +(0.989821 - 0.142315i) q^{8} +(-2.98868 + 0.260361i) q^{9} +(-0.755750 - 0.654861i) q^{10} +(1.62713 + 1.04569i) q^{11} +(1.60529 + 0.650409i) q^{12} +(-1.51588 + 1.74942i) q^{13} +(3.74505 + 1.09965i) q^{14} +(-0.559698 - 1.63913i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(2.62149 + 5.74026i) q^{17} +(1.83483 + 2.37348i) q^{18} +(-3.93948 - 1.79910i) q^{19} +(-0.142315 + 0.989821i) q^{20} +(4.64490 + 4.91210i) q^{21} -1.93417i q^{22} +(-2.02820 + 4.34585i) q^{23} +(-0.320729 - 1.70210i) q^{24} +(0.841254 - 0.540641i) q^{25} +(2.29125 + 0.329432i) q^{26} +(0.675374 + 5.15207i) q^{27} +(-1.09965 - 3.74505i) q^{28} +(3.24492 - 1.48190i) q^{29} +(-1.07633 + 1.35703i) q^{30} +(0.896737 + 6.23694i) q^{31} +(-0.281733 + 0.959493i) q^{32} +(1.68707 - 2.89428i) q^{33} +(3.41173 - 5.30875i) q^{34} +(-2.11021 + 3.28354i) q^{35} +(1.00471 - 2.82676i) q^{36} +(-1.18792 + 4.04568i) q^{37} +(0.616344 + 4.28677i) q^{38} +(3.14127 + 2.49150i) q^{39} +(0.909632 - 0.415415i) q^{40} +(-1.79159 - 6.10159i) q^{41} +(1.62110 - 6.56322i) q^{42} +(-6.08292 - 0.874592i) q^{43} +(-1.62713 + 1.04569i) q^{44} +(-2.79427 + 1.09182i) q^{45} +(4.75249 - 0.643315i) q^{46} -1.53681i q^{47} +(-1.25850 + 1.19004i) q^{48} +(1.17191 - 8.15081i) q^{49} +(-0.909632 - 0.415415i) q^{50} +(9.73581 - 4.96811i) q^{51} +(-0.961609 - 2.10563i) q^{52} +(0.712176 + 0.821895i) q^{53} +(3.96907 - 3.35358i) q^{54} +(1.85582 + 0.544919i) q^{55} +(-2.55602 + 2.94981i) q^{56} +(-2.81682 + 6.95229i) q^{57} +(-3.00099 - 1.92862i) q^{58} +(-4.45591 - 3.86107i) q^{59} +(1.72351 + 0.171799i) q^{60} +(11.2928 - 1.62366i) q^{61} +(4.76204 - 4.12633i) q^{62} +(8.15055 - 8.40715i) q^{63} +(0.959493 - 0.281733i) q^{64} +(-0.961609 + 2.10563i) q^{65} +(-3.34692 + 0.145509i) q^{66} +(3.69201 + 5.74488i) q^{67} -6.31052 q^{68} +(7.67271 + 3.18269i) q^{69} +3.90316 q^{70} +(-0.0295383 - 0.0459624i) q^{71} +(-2.92121 + 0.683045i) q^{72} +(-4.05026 + 8.86883i) q^{73} +(4.04568 - 1.18792i) q^{74} +(-0.998822 - 1.41505i) q^{75} +(3.27304 - 2.83610i) q^{76} +(-7.47253 + 1.07439i) q^{77} +(0.397683 - 3.98961i) q^{78} +(-4.69071 - 4.06452i) q^{79} +(-0.841254 - 0.540641i) q^{80} +(8.86442 - 1.55627i) q^{81} +(-4.16438 + 4.80595i) q^{82} +(11.9112 + 3.49743i) q^{83} +(-6.39777 + 2.18459i) q^{84} +(4.13251 + 4.76918i) q^{85} +(2.55292 + 5.59012i) q^{86} +(-2.80843 - 5.50357i) q^{87} +(1.75938 + 0.803484i) q^{88} +(-1.74485 + 12.1357i) q^{89} +(2.42919 + 1.76040i) q^{90} -9.03508i q^{91} +(-3.11058 - 3.65025i) q^{92} +(10.7250 - 2.02094i) q^{93} +(-1.29284 + 0.830860i) q^{94} +(-4.28677 - 0.616344i) q^{95} +(1.68152 + 0.415331i) q^{96} +(-4.23230 - 14.4139i) q^{97} +(-7.49048 + 3.42079i) q^{98} +(-5.13522 - 2.70160i) 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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