LMFDB - Embedded newform 175.2.h.c.36.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(36,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

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

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

chi := DirichletCharacter("175.36");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.h (of order $5$, degree $4$, 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:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			36.1
Character	$\chi$	$=$	175.36
Dual form			175.2.h.c.141.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.25360 + 1.63734i) q^{2} +(-0.295516 + 0.909504i) q^{3} +(1.77981 - 5.47769i) q^{4} +(1.23160 + 1.86632i) q^{5} +(-0.823190 - 2.53352i) q^{6} +1.00000 q^{7} +(3.23625 + 9.96014i) q^{8} +(1.68718 + 1.22581i) q^{9} +O(q^{10})$	\(q+(-2.25360 + 1.63734i) q^{2} +(-0.295516 + 0.909504i) q^{3} +(1.77981 - 5.47769i) q^{4} +(1.23160 + 1.86632i) q^{5} +(-0.823190 - 2.53352i) q^{6} +1.00000 q^{7} +(3.23625 + 9.96014i) q^{8} +(1.68718 + 1.22581i) q^{9} +(-5.83133 - 2.18940i) q^{10} +(-1.55534 + 1.13002i) q^{11} +(4.45602 + 3.23749i) q^{12} +(1.07988 + 0.784580i) q^{13} +(-2.25360 + 1.63734i) q^{14} +(-2.06139 + 0.568617i) q^{15} +(-14.2821 - 10.3766i) q^{16} +(-0.788110 - 2.42555i) q^{17} -5.80930 q^{18} +(-0.112176 - 0.345244i) q^{19} +(12.4152 - 3.42462i) q^{20} +(-0.295516 + 0.909504i) q^{21} +(1.65489 - 5.09323i) q^{22} +(-4.44538 + 3.22976i) q^{23} -10.0151 q^{24} +(-1.96632 + 4.59713i) q^{25} -3.71824 q^{26} +(-3.93448 + 2.85857i) q^{27} +(1.77981 - 5.47769i) q^{28} +(1.14619 - 3.52762i) q^{29} +(3.71452 - 4.65662i) q^{30} +(1.91551 + 5.89532i) q^{31} +28.2306 q^{32} +(-0.568131 - 1.74853i) q^{33} +(5.74753 + 4.17582i) q^{34} +(1.23160 + 1.86632i) q^{35} +(9.71748 - 7.06016i) q^{36} +(-2.12915 - 1.54692i) q^{37} +(0.818081 + 0.594371i) q^{38} +(-1.03270 + 0.750301i) q^{39} +(-14.6031 + 18.3068i) q^{40} +(8.03587 + 5.83840i) q^{41} +(-0.823190 - 2.53352i) q^{42} +0.423079 q^{43} +(3.42170 + 10.5309i) q^{44} +(-0.209823 + 4.65854i) q^{45} +(4.72991 - 14.5572i) q^{46} +(4.11939 - 12.6782i) q^{47} +(13.6581 - 9.92319i) q^{48} +1.00000 q^{49} +(-3.09574 - 13.5796i) q^{50} +2.43895 q^{51} +(6.21967 - 4.51885i) q^{52} +(-1.99004 + 6.12473i) q^{53} +(4.18631 - 12.8841i) q^{54} +(-4.02454 - 1.51103i) q^{55} +(3.23625 + 9.96014i) q^{56} +0.347150 q^{57} +(3.19284 + 9.82654i) q^{58} +(-7.91087 - 5.74758i) q^{59} +(-0.554163 + 12.3037i) q^{60} +(5.74583 - 4.17459i) q^{61} +(-13.9694 - 10.1494i) q^{62} +(1.68718 + 1.22581i) q^{63} +(-35.0564 + 25.4699i) q^{64} +(-0.134297 + 2.98170i) q^{65} +(4.14327 + 3.01026i) q^{66} +(0.929121 + 2.85954i) q^{67} -14.6891 q^{68} +(-1.62380 - 4.99753i) q^{69} +(-5.83133 - 2.18940i) q^{70} +(-1.27465 + 3.92298i) q^{71} +(-6.74910 + 20.7716i) q^{72} +(9.91233 - 7.20173i) q^{73} +7.33108 q^{74} +(-3.60003 - 3.14690i) q^{75} -2.09079 q^{76} +(-1.55534 + 1.13002i) q^{77} +(1.09880 - 3.38175i) q^{78} +(3.70356 - 11.3984i) q^{79} +(1.77616 - 39.4348i) q^{80} +(0.496163 + 1.52703i) q^{81} -27.6691 q^{82} +(-1.05259 - 3.23954i) q^{83} +(4.45602 + 3.23749i) q^{84} +(3.55623 - 4.45818i) q^{85} +(-0.953450 + 0.692722i) q^{86} +(2.86966 + 2.08493i) q^{87} +(-16.2886 - 11.8344i) q^{88} +(6.89171 - 5.00712i) q^{89} +(-7.15474 - 10.8420i) q^{90} +(1.07988 + 0.784580i) q^{91} +(9.77968 + 30.0988i) q^{92} -5.92788 q^{93} +(11.4750 + 35.3163i) q^{94} +(0.506180 - 0.634560i) q^{95} +(-8.34260 + 25.6759i) q^{96} +(3.71937 - 11.4470i) q^{97} +(-2.25360 + 1.63734i) q^{98} -4.00934 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 3 q^{2} - 4 q^{3} - 9 q^{4} + q^{5} + 15 q^{6} + 32 q^{7} - 9 q^{8} - 6 q^{9}+O(q^{10}) $ 32 * q - 3 * q^2 - 4 * q^3 - 9 * q^4 + q^5 + 15 * q^6 + 32 * q^7 - 9 * q^8 - 6 * q^9	\( 32 q - 3 q^{2} - 4 q^{3} - 9 q^{4} + q^{5} + 15 q^{6} + 32 q^{7} - 9 q^{8} - 6 q^{9} - 15 q^{10} + 2 q^{11} - 2 q^{12} - 16 q^{13} - 3 q^{14} - 9 q^{15} - 15 q^{16} - 18 q^{17} + 26 q^{18} - 8 q^{19} - 12 q^{20} - 4 q^{21} + 9 q^{22} - 11 q^{23} - 46 q^{24} + 19 q^{25} - 34 q^{26} - 7 q^{27} - 9 q^{28} + 13 q^{29} - 10 q^{30} + 5 q^{31} + 64 q^{32} - 25 q^{33} + 25 q^{34} + q^{35} + 64 q^{36} + 6 q^{37} - 15 q^{38} - 18 q^{39} + 20 q^{40} - 26 q^{41} + 15 q^{42} - 6 q^{43} - 37 q^{44} - 37 q^{45} - 12 q^{46} + 15 q^{48} + 32 q^{49} + 20 q^{50} - 10 q^{51} - 38 q^{52} - 27 q^{53} + 108 q^{54} + 42 q^{55} - 9 q^{56} + 2 q^{57} + 49 q^{58} + 13 q^{59} + 18 q^{60} + 40 q^{61} - 14 q^{62} - 6 q^{63} + q^{64} + 40 q^{65} - 37 q^{66} - 15 q^{67} + 4 q^{68} - 45 q^{69} - 15 q^{70} - 24 q^{71} - 75 q^{72} - 38 q^{73} - 40 q^{74} - 56 q^{75} - 70 q^{76} + 2 q^{77} + 93 q^{78} + 66 q^{79} - 11 q^{80} - 7 q^{81} - 32 q^{82} - 52 q^{83} - 2 q^{84} + 13 q^{85} + 60 q^{86} + 54 q^{87} - 66 q^{88} + 28 q^{89} - 135 q^{90} - 16 q^{91} - 44 q^{92} + 56 q^{93} - 4 q^{94} - 23 q^{95} - 34 q^{96} - 44 q^{97} - 3 q^{98} - 66 q^{99}+O(q^{100}) \) 32 * q - 3 * q^2 - 4 * q^3 - 9 * q^4 + q^5 + 15 * q^6 + 32 * q^7 - 9 * q^8 - 6 * q^9 - 15 * q^10 + 2 * q^11 - 2 * q^12 - 16 * q^13 - 3 * q^14 - 9 * q^15 - 15 * q^16 - 18 * q^17 + 26 * q^18 - 8 * q^19 - 12 * q^20 - 4 * q^21 + 9 * q^22 - 11 * q^23 - 46 * q^24 + 19 * q^25 - 34 * q^26 - 7 * q^27 - 9 * q^28 + 13 * q^29 - 10 * q^30 + 5 * q^31 + 64 * q^32 - 25 * q^33 + 25 * q^34 + q^35 + 64 * q^36 + 6 * q^37 - 15 * q^38 - 18 * q^39 + 20 * q^40 - 26 * q^41 + 15 * q^42 - 6 * q^43 - 37 * q^44 - 37 * q^45 - 12 * q^46 + 15 * q^48 + 32 * q^49 + 20 * q^50 - 10 * q^51 - 38 * q^52 - 27 * q^53 + 108 * q^54 + 42 * q^55 - 9 * q^56 + 2 * q^57 + 49 * q^58 + 13 * q^59 + 18 * q^60 + 40 * q^61 - 14 * q^62 - 6 * q^63 + q^64 + 40 * q^65 - 37 * q^66 - 15 * q^67 + 4 * q^68 - 45 * q^69 - 15 * q^70 - 24 * q^71 - 75 * q^72 - 38 * q^73 - 40 * q^74 - 56 * q^75 - 70 * q^76 + 2 * q^77 + 93 * q^78 + 66 * q^79 - 11 * q^80 - 7 * q^81 - 32 * q^82 - 52 * q^83 - 2 * q^84 + 13 * q^85 + 60 * q^86 + 54 * q^87 - 66 * q^88 + 28 * q^89 - 135 * q^90 - 16 * q^91 - 44 * q^92 + 56 * q^93 - 4 * q^94 - 23 * q^95 - 34 * q^96 - 44 * q^97 - 3 * q^98 - 66 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−2.25360	+	1.63734i	−1.59354	+	1.15777i	−0.694873	+	0.719133i	$0.744539\pi$
$2$	−2.25360	+	1.63734i	−1.59354	+	1.15777i	−0.898663	+	0.438639i	$0.855461\pi$
$3$	−0.295516	+	0.909504i	−0.170616	+	0.525102i	−0.999406	−	0.0344573i	$-0.989030\pi$
$3$	−0.295516	+	0.909504i	−0.170616	+	0.525102i	0.828790	+	0.559560i	$0.189030\pi$
$4$	1.77981	−	5.47769i	0.889905	−	2.73885i
$5$	1.23160	+	1.86632i	0.550788	+	0.834645i
$5$	1.23160	+	1.86632i	0.550788	+	0.834645i
$6$	−0.823190	−	2.53352i	−0.336066	−	1.03430i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	3.23625	+	9.96014i	1.14419	+	3.52144i
$9$	1.68718	+	1.22581i	0.562394	+	0.408603i
$10$	−5.83133	−	2.18940i	−1.84403	−	0.692350i
$11$	−1.55534	+	1.13002i	−0.468953	+	0.340714i	−0.797033	−	0.603936i	$-0.793598\pi$
$11$	−1.55534	+	1.13002i	−0.468953	+	0.340714i	0.328080	+	0.944650i	$0.393598\pi$
$12$	4.45602	+	3.23749i	1.28634	+	0.934582i
$13$	1.07988	+	0.784580i	0.299505	+	0.217603i	0.727380	−	0.686235i	$-0.240738\pi$
$13$	1.07988	+	0.784580i	0.299505	+	0.217603i	−0.427875	+	0.903838i	$0.640738\pi$
$14$	−2.25360	+	1.63734i	−0.602300	+	0.437597i
$15$	−2.06139	+	0.568617i	−0.532247	+	0.146816i
$16$	−14.2821	−	10.3766i	−3.57053	−	2.59414i
$17$	−0.788110	−	2.42555i	−0.191145	−	0.588283i	−1.00000		0.000275089i	$-0.999912\pi$
$17$	−0.788110	−	2.42555i	−0.191145	−	0.588283i	0.808855	−	0.588008i	$-0.200088\pi$
$18$	−5.80930			−1.36927
$19$	−0.112176	−	0.345244i	−0.0257351	−	0.0792043i	0.937364	−	0.348351i	$-0.113258\pi$
$19$	−0.112176	−	0.345244i	−0.0257351	−	0.0792043i	−0.963099	+	0.269147i	$0.913258\pi$
$20$	12.4152	−	3.42462i	2.77611	−	0.765769i
$21$	−0.295516	+	0.909504i	−0.0644868	+	0.198470i
$22$	1.65489	−	5.09323i	0.352824	−	1.08588i
$23$	−4.44538	+	3.22976i	−0.926926	+	0.673451i	−0.945238	−	0.326381i	$-0.894171\pi$
$23$	−4.44538	+	3.22976i	−0.926926	+	0.673451i	0.0183126	+	0.999832i	$0.494171\pi$
$24$	−10.0151			−2.04433
$25$	−1.96632	+	4.59713i	−0.393264	+	0.919425i
$26$	−3.71824			−0.729207
$27$	−3.93448	+	2.85857i	−0.757191	+	0.550131i
$28$	1.77981	−	5.47769i	0.336352	−	1.03519i
$29$	1.14619	−	3.52762i	0.212843	−	0.655062i	−0.786457	−	0.617645i	$-0.788087\pi$
$29$	1.14619	−	3.52762i	0.212843	−	0.655062i	0.999300	−	0.0374173i	$-0.0119131\pi$
$30$	3.71452	−	4.65662i	0.678175	−	0.850178i
$31$	1.91551	+	5.89532i	0.344035	+	1.05883i	0.962098	+	0.272703i	$0.0879175\pi$
$31$	1.91551	+	5.89532i	0.344035	+	1.05883i	−0.618063	+	0.786128i	$0.712082\pi$
$32$	28.2306			4.99052
$33$	−0.568131	−	1.74853i	−0.0988989	−	0.304380i
$34$	5.74753	+	4.17582i	0.985693	+	0.716148i
$35$	1.23160	+	1.86632i	0.208178	+	0.315466i
$36$	9.71748	−	7.06016i	1.61958	−	1.17669i
$37$	−2.12915	−	1.54692i	−0.350030	−	0.254312i	0.398851	−	0.917016i	$-0.369409\pi$
$37$	−2.12915	−	1.54692i	−0.350030	−	0.254312i	−0.748882	+	0.662704i	$0.769409\pi$
$38$	0.818081	+	0.594371i	0.132710	+	0.0964197i
$39$	−1.03270	+	0.750301i	−0.165364	+	0.120144i
$40$	−14.6031	+	18.3068i	−2.30895	+	2.89456i
$41$	8.03587	+	5.83840i	1.25499	+	0.911805i	0.998501	−	0.0547413i	$-0.0174334\pi$
$41$	8.03587	+	5.83840i	1.25499	+	0.911805i	0.256492	+	0.966546i	$0.417433\pi$
$42$	−0.823190	−	2.53352i	−0.127021	−	0.390930i
$43$	0.423079			0.0645189			0.0322594	−	0.999480i	$-0.489730\pi$
$43$	0.423079			0.0645189			0.0322594	+	0.999480i	$0.489730\pi$
$44$	3.42170	+	10.5309i	0.515840	+	1.58759i
$45$	−0.209823	+	4.65854i	−0.0312786	+	0.694454i
$46$	4.72991	−	14.5572i	0.697387	−	2.14634i
$47$	4.11939	−	12.6782i	0.600874	−	1.84930i	0.0778832	−	0.996962i	$-0.475184\pi$
$47$	4.11939	−	12.6782i	0.600874	−	1.84930i	0.522991	−	0.852338i	$-0.324816\pi$
$48$	13.6581	−	9.92319i	1.97138	−	1.43229i
$49$	1.00000			0.142857
$50$	−3.09574	−	13.5796i	−0.437804	−	1.92045i
$51$	2.43895			0.341521
$52$	6.21967	−	4.51885i	0.862513	−	0.626652i
$53$	−1.99004	+	6.12473i	−0.273354	+	0.841296i	0.716297	+	0.697796i	$0.245836\pi$
$53$	−1.99004	+	6.12473i	−0.273354	+	0.841296i	−0.989650	+	0.143500i	$0.954164\pi$
$54$	4.18631	−	12.8841i	0.569684	−	1.75331i
$55$	−4.02454	−	1.51103i	−0.542669	−	0.203748i
$56$	3.23625	+	9.96014i	0.432462	+	1.33098i
$57$	0.347150			0.0459812
$58$	3.19284	+	9.82654i	0.419240	+	1.29029i
$59$	−7.91087	−	5.74758i	−1.02991	−	0.748271i	−0.0616169	−	0.998100i	$-0.519626\pi$
$59$	−7.91087	−	5.74758i	−1.02991	−	0.748271i	−0.968290	+	0.249829i	$0.919626\pi$
$60$	−0.554163	+	12.3037i	−0.0715422	+	1.58840i
$61$	5.74583	−	4.17459i	0.735678	−	0.534502i	−0.155676	−	0.987808i	$-0.549756\pi$
$61$	5.74583	−	4.17459i	0.735678	−	0.534502i	0.891355	+	0.453306i	$0.149756\pi$
$62$	−13.9694	−	10.1494i	−1.77412	−	1.28897i
$63$	1.68718	+	1.22581i	0.212565	+	0.154438i
$64$	−35.0564	+	25.4699i	−4.38205	+	3.18374i
$65$	−0.134297	+	2.98170i	−0.0166575	+	0.369834i
$66$	4.14327	+	3.01026i	0.510001	+	0.370537i
$67$	0.929121	+	2.85954i	0.113510	+	0.349349i	0.991633	−	0.129086i	$-0.0412044\pi$
$67$	0.929121	+	2.85954i	0.113510	+	0.349349i	−0.878123	+	0.478435i	$0.841204\pi$
$68$	−14.6891			−1.78132
$69$	−1.62380	−	4.99753i	−0.195482	−	0.601632i
$70$	−5.83133	−	2.18940i	−0.696978	−	0.261684i
$71$	−1.27465	+	3.92298i	−0.151274	+	0.465573i	−0.997764	−	0.0668311i	$-0.978711\pi$
$71$	−1.27465	+	3.92298i	−0.151274	+	0.465573i	0.846491	+	0.532404i	$0.178711\pi$
$72$	−6.74910	+	20.7716i	−0.795390	+	2.44796i
$73$	9.91233	−	7.20173i	1.16015	−	0.842899i	0.170353	−	0.985383i	$-0.445509\pi$
$73$	9.91233	−	7.20173i	1.16015	−	0.842899i	0.989797	+	0.142484i	$0.0455090\pi$
$74$	7.33108			0.852221
$75$	−3.60003	−	3.14690i	−0.415695	−	0.363373i
$76$	−2.09079			−0.239830
$77$	−1.55534	+	1.13002i	−0.177248	+	0.128778i
$78$	1.09880	−	3.38175i	0.124414	−	0.382908i
$79$	3.70356	−	11.3984i	0.416683	−	1.28242i	−0.494054	−	0.869431i	$-0.664486\pi$
$79$	3.70356	−	11.3984i	0.416683	−	1.28242i	0.910737	−	0.412987i	$-0.135514\pi$
$80$	1.77616	−	39.4348i	0.198581	−	4.40894i
$81$	0.496163	+	1.52703i	0.0551293	+	0.169670i
$82$	−27.6691			−3.05554
$83$	−1.05259	−	3.23954i	−0.115537	−	0.355586i	0.876522	−	0.481362i	$-0.159858\pi$
$83$	−1.05259	−	3.23954i	−0.115537	−	0.355586i	−0.992059	+	0.125776i	$0.959858\pi$
$84$	4.45602	+	3.23749i	0.486192	+	0.353239i
$85$	3.55623	−	4.45818i	0.385727	−	0.483557i
$86$	−0.953450	+	0.692722i	−0.102813	+	0.0746981i
$87$	2.86966	+	2.08493i	0.307660	+	0.223528i
$88$	−16.2886	−	11.8344i	−1.73637	−	1.26155i
$89$	6.89171	−	5.00712i	0.730520	−	0.530754i	−0.159208	−	0.987245i	$-0.550894\pi$
$89$	6.89171	−	5.00712i	0.730520	−	0.530754i	0.889728	+	0.456491i	$0.150894\pi$
$90$	−7.15474	−	10.8420i	−0.754175	−	1.14285i
$91$	1.07988	+	0.784580i	0.113202	+	0.0822463i
$92$	9.77968	+	30.0988i	1.01960	+	3.13801i
$93$	−5.92788			−0.614692
$94$	11.4750	+	35.3163i	1.18355	+	3.64260i
$95$	0.506180	−	0.634560i	0.0519329	−	0.0651045i
$96$	−8.34260	+	25.6759i	−0.851463	+	2.62053i
$97$	3.71937	−	11.4470i	0.377645	−	1.16227i	−0.564032	−	0.825753i	$-0.690751\pi$
$97$	3.71937	−	11.4470i	0.377645	−	1.16227i	0.941677	−	0.336518i	$-0.109249\pi$
$98$	−2.25360	+	1.63734i	−0.227648	+	0.165396i
$99$	−4.00934			−0.402953
$100$	21.6820	+	18.9529i	2.16820	+	1.89529i
$101$	−1.35809			−0.135135			−0.0675675	−	0.997715i	$-0.521524\pi$
$101$	−1.35809			−0.135135			−0.0675675	+	0.997715i	$0.521524\pi$
$102$	−5.49641	+	3.99338i	−0.544226	+	0.395403i
$103$	0.442149	−	1.36080i	0.0435663	−	0.134083i	−0.926908	−	0.375290i	$-0.877543\pi$
$103$	0.442149	−	1.36080i	0.0435663	−	0.134083i	0.970474	+	0.241207i	$0.0775432\pi$
$104$	−4.31976	+	13.2949i	−0.423588	+	1.30367i
$105$	−2.06139	+	0.568617i	−0.201171	+	0.0554914i
$106$	−5.54347	−	17.0611i	−0.538430	−	1.65712i
$107$	2.08436			0.201503			0.100752	−	0.994912i	$-0.467875\pi$
$107$	2.08436			0.201503			0.100752	+	0.994912i	$0.467875\pi$
$108$	8.65572	+	26.6396i	0.832897	+	2.56339i
$109$	9.77141	+	7.09934i	0.935931	+	0.679994i	0.947438	−	0.319940i	$-0.103663\pi$
$109$	9.77141	+	7.09934i	0.935931	+	0.679994i	−0.0115067	+	0.999934i	$0.503663\pi$
$110$	11.5438	−	3.18426i	1.10066	−	0.303608i
$111$	2.03613	−	1.47933i	0.193261	−	0.140412i
$112$	−14.2821	−	10.3766i	−1.34953	−	0.980492i
$113$	6.45512	+	4.68992i	0.607246	+	0.441190i	0.848444	−	0.529286i	$-0.177540\pi$
$113$	6.45512	+	4.68992i	0.607246	+	0.441190i	−0.241197	+	0.970476i	$0.577540\pi$
$114$	−0.782338	+	0.568402i	−0.0732727	+	0.0532357i
$115$	−11.5027	−	4.31874i	−1.07263	−	0.402725i
$116$	−17.2832	−	12.5570i	−1.60470	−	1.16589i
$117$	0.860212	+	2.64746i	0.0795266	+	0.244758i
$118$	27.2387			2.50752
$119$	−0.788110	−	2.42555i	−0.0722459	−	0.222350i
$120$	−12.3347	−	18.6915i	−1.12599	−	1.70629i
$121$	−2.25705	+	6.94649i	−0.205186	+	0.631499i
$122$	−6.11360	+	18.8157i	−0.553499	+	1.70350i
$123$	−7.68477	+	5.58332i	−0.692913	+	0.503431i
$124$	35.7020			3.20613
$125$	−11.0014	+	1.99203i	−0.983999	+	0.178173i
$126$	−5.80930			−0.517534
$127$	5.96258	−	4.33207i	0.529094	−	0.384409i	−0.290925	−	0.956746i	$-0.593963\pi$
$127$	5.96258	−	4.33207i	0.529094	−	0.384409i	0.820019	+	0.572337i	$0.193963\pi$
$128$	19.8527	−	61.1003i	1.75475	−	5.40055i
$129$	−0.125026	+	0.384792i	−0.0110080	+	0.0338790i
$130$	−4.57939	−	6.93944i	−0.401639	−	0.608629i
$131$	−5.34430	−	16.4481i	−0.466934	−	1.43707i	−0.856534	−	0.516091i	$-0.827387\pi$
$131$	−5.34430	−	16.4481i	−0.466934	−	1.43707i	0.389600	−	0.920984i	$-0.372613\pi$
$132$	−10.5891			−0.921659
$133$	−0.112176	−	0.345244i	−0.00972694	−	0.0299364i
$134$	−6.77590	−	4.92298i	−0.585348	−	0.425281i
$135$	−10.1807	−	3.82240i	−0.876216	−	0.328980i
$136$	21.6083	−	15.6994i	1.85290	−	1.34621i
$137$	−5.49228	−	3.99038i	−0.469237	−	0.340921i	0.327907	−	0.944710i	$-0.393657\pi$
$137$	−5.49228	−	3.99038i	−0.469237	−	0.340921i	−0.797144	+	0.603789i	$0.793657\pi$
$138$	11.8420	+	8.60374i	1.00806	+	0.732399i
$139$	0.677130	−	0.491964i	0.0574334	−	0.0417278i	−0.558698	−	0.829371i	$-0.688699\pi$
$139$	0.677130	−	0.491964i	0.0574334	−	0.0417278i	0.616132	+	0.787643i	$0.288699\pi$
$140$	12.4152	−	3.42462i	1.04927	−	0.289434i
$141$	10.3135	+	7.49319i	0.868553	+	0.631041i
$142$	−3.55068	−	10.9279i	−0.297967	−	0.917047i
$143$	−2.56617			−0.214594
$144$	−11.3768	−	35.0143i	−0.948070	−	2.91786i
$145$	7.99532	−	2.20545i	0.663975	−	0.183153i
$146$	−10.5468	+	32.4596i	−0.872857	+	2.68638i
$147$	−0.295516	+	0.909504i	−0.0243737	+	0.0750146i
$148$	−12.2630	+	8.90961i	−1.00801	+	0.732366i
$149$	−2.83497			−0.232250			−0.116125	−	0.993235i	$-0.537047\pi$
$149$	−2.83497			−0.232250			−0.116125	+	0.993235i	$0.537047\pi$
$150$	13.2656	+	1.19740i	1.08313	+	0.0977676i
$151$	1.27013			0.103361			0.0516807	−	0.998664i	$-0.483542\pi$
$151$	1.27013			0.103361			0.0516807	+	0.998664i	$0.483542\pi$
$152$	3.07565	−	2.23459i	0.249468	−	0.181249i
$153$	1.64358	−	5.05842i	0.132876	−	0.408949i
$154$	1.65489	−	5.09323i	0.133355	−	0.410424i
$155$	−8.64344	+	10.8356i	−0.694257	+	0.870339i
$156$	2.27190	+	6.99220i	0.181898	+	0.559824i
$157$	−10.6488			−0.849869			−0.424935	−	0.905224i	$-0.639703\pi$
$157$	−10.6488			−0.849869			−0.424935	+	0.905224i	$0.639703\pi$
$158$	10.3166	+	31.7514i	0.820748	+	2.52600i
$159$	−4.98237	−	3.61991i	−0.395128	−	0.287077i
$160$	34.7689	+	52.6875i	2.74872	+	4.16531i
$161$	−4.44538	+	3.22976i	−0.350345	+	0.254540i
$162$	−3.61842	−	2.62894i	−0.284290	−	0.206549i
$163$	1.54490	+	1.12243i	0.121006	+	0.0879158i	0.646642	−	0.762794i	$-0.276173\pi$
$163$	1.54490	+	1.12243i	0.121006	+	0.0879158i	−0.525636	+	0.850709i	$0.676173\pi$
$164$	46.2833	−	33.6268i	3.61412	−	2.62581i
$165$	2.56361	−	3.21380i	0.199576	−	0.250194i
$166$	7.67633	+	5.57718i	0.595799	+	0.432873i
$167$	4.59022	+	14.1273i	0.355202	+	1.09320i	0.955892	+	0.293718i	$0.0948925\pi$
$167$	4.59022	+	14.1273i	0.355202	+	1.09320i	−0.600690	+	0.799482i	$0.705107\pi$
$168$	−10.0151			−0.772685
$169$	−3.46664	−	10.6692i	−0.266665	−	0.820710i
$170$	−0.714779	+	15.8697i	−0.0548211	+	1.21715i
$171$	0.233941	−	0.719997i	0.0178899	−	0.0550595i
$172$	0.752999	−	2.31749i	0.0574157	−	0.176707i
$173$	3.26354	−	2.37110i	0.248122	−	0.180271i	−0.456772	−	0.889584i	$-0.650994\pi$
$173$	3.26354	−	2.37110i	0.248122	−	0.180271i	0.704894	+	0.709312i	$0.250994\pi$
$174$	−9.88081			−0.749062
$175$	−1.96632	+	4.59713i	−0.148640	+	0.347510i
$176$	33.9393			2.55827
$177$	7.56523	−	5.49646i	0.568638	−	0.413139i
$178$	−7.33282	+	22.5681i	−0.549618	+	1.69155i
$179$	−5.31171	+	16.3478i	−0.397016	+	1.22189i	0.530365	+	0.847770i	$0.322055\pi$
$179$	−5.31171	+	16.3478i	−0.397016	+	1.22189i	−0.927381	+	0.374119i	$0.877945\pi$
$180$	25.1446	+	9.44065i	1.87417	+	0.703665i
$181$	2.46627	+	7.59040i	0.183316	+	0.564190i	0.999915	−	0.0130156i	$-0.00414310\pi$
$181$	2.46627	+	7.59040i	0.183316	+	0.564190i	−0.816599	+	0.577206i	$0.804143\pi$
$182$	−3.71824			−0.275614
$183$	2.09882	+	6.45951i	0.155149	+	0.477501i
$184$	−46.5552	−	33.8243i	−3.43209	−	2.49356i
$185$	0.264787	−	5.87887i	0.0194676	−	0.432223i
$186$	13.3591	−	9.70593i	0.979535	−	0.711674i
$187$	3.96670	+	2.88198i	0.290074	+	0.210751i
$188$	−62.1154	−	45.1294i	−4.53023	−	3.29140i
$189$	−3.93448	+	2.85857i	−0.286191	+	0.207930i
$190$	−0.101739	+	2.25883i	−0.00738092	+	0.163873i
$191$	4.86708	+	3.53614i	0.352170	+	0.255866i	0.749779	−	0.661689i	$-0.230160\pi$
$191$	4.86708	+	3.53614i	0.352170	+	0.255866i	−0.397609	+	0.917555i	$0.630160\pi$
$192$	−12.8053	−	39.4107i	−0.924143	−	2.84422i
$193$	3.07641			0.221445			0.110722	−	0.993851i	$-0.464684\pi$
$193$	3.07641			0.221445			0.110722	+	0.993851i	$0.464684\pi$
$194$	10.3607	+	31.8869i	0.743854	+	2.28935i
$195$	−2.67218	−	1.00328i	−0.191359	−	0.0718465i
$196$	1.77981	−	5.47769i	0.127129	−	0.391264i
$197$	4.35634	−	13.4074i	0.310376	−	0.955240i	−0.667240	−	0.744843i	$-0.732524\pi$
$197$	4.35634	−	13.4074i	0.310376	−	0.955240i	0.977616	−	0.210397i	$-0.0674757\pi$
$198$	9.03544	−	6.56463i	0.642121	−	0.466528i
$199$	−10.3605			−0.734438			−0.367219	−	0.930135i	$-0.619690\pi$
$199$	−10.3605			−0.734438			−0.367219	+	0.930135i	$0.619690\pi$
$200$	−52.1515	−	4.70741i	−3.68767	−	0.332865i
$201$	−2.87533			−0.202810
$202$	3.06059	−	2.22365i	0.215342	−	0.156455i
$203$	1.14619	−	3.52762i	0.0804469	−	0.247590i
$204$	4.34086	−	13.3598i	0.303921	−	0.935373i
$205$	−0.999364	+	22.1881i	−0.0697986	+	1.54968i
$206$	1.23165	+	3.79064i	0.0858133	+	0.264106i
$207$	−11.4592			−0.796472
$208$	−7.28174	−	22.4109i	−0.504898	−	1.55392i
$209$	0.564605	+	0.410210i	0.0390546	+	0.0283748i
$210$	3.71452	−	4.65662i	0.256326	−	0.321337i
$211$	−6.54107	+	4.75236i	−0.450306	+	0.327166i	−0.789716	−	0.613472i	$-0.789772\pi$
$211$	−6.54107	+	4.75236i	−0.450306	+	0.327166i	0.339411	+	0.940638i	$0.389772\pi$
$212$	30.0075	+	21.8017i	2.06092	+	1.49735i
$213$	−3.19129	−	2.31861i	−0.218664	−	0.158868i
$214$	−4.69732	+	3.41281i	−0.321102	+	0.233295i
$215$	0.521064	+	0.789601i	0.0355362	+	0.0538504i
$216$	−41.2047	−	29.9369i	−2.80362	−	2.03695i
$217$	1.91551	+	5.89532i	0.130033	+	0.400200i
$218$	−33.6449			−2.27872
$219$	3.62075	+	11.1435i	0.244668	+	0.753010i
$220$	−15.4399	+	19.3558i	−1.04096	+	1.30497i
$221$	1.05197	−	3.23764i	0.0707634	−	0.217787i
$222$	−2.16645	+	6.66765i	−0.145403	+	0.447503i
$223$	11.7809	−	8.55930i	0.788905	−	0.573173i	−0.118733	−	0.992926i	$-0.537883\pi$
$223$	11.7809	−	8.55930i	0.788905	−	0.573173i	0.907638	+	0.419753i	$0.137883\pi$
$224$	28.2306			1.88624
$225$	−8.95275	+	5.34586i	−0.596850	+	0.356390i
$226$	−22.2262			−1.47847
$227$	10.9789	−	7.97667i	0.728698	−	0.529430i	−0.160453	−	0.987043i	$-0.551296\pi$
$227$	10.9789	−	7.97667i	0.728698	−	0.529430i	0.889151	+	0.457613i	$0.151296\pi$
$228$	0.617862	−	1.90158i	0.0409189	−	0.125935i
$229$	−0.882465	+	2.71595i	−0.0583149	+	0.179475i	−0.975971	−	0.217901i	$-0.930079\pi$
$229$	−0.882465	+	2.71595i	−0.0583149	+	0.179475i	0.917656	+	0.397376i	$0.130079\pi$
$230$	32.9937	−	9.10106i	2.17554	−	0.600106i
$231$	−0.568131	−	1.74853i	−0.0373803	−	0.115045i
$232$	38.8449			2.55029
$233$	−3.35600	−	10.3287i	−0.219859	−	0.676657i	−0.998773	−	0.0495256i	$-0.984229\pi$
$233$	−3.35600	−	10.3287i	−0.219859	−	0.676657i	0.778914	−	0.627131i	$-0.215771\pi$
$234$	−6.27335	−	4.55786i	−0.410102	−	0.297957i
$235$	28.7350	−	7.92633i	1.87446	−	0.517057i
$236$	−45.5633	+	33.1037i	−2.96592	+	2.15487i
$237$	9.27241	+	6.73680i	0.602308	+	0.437602i
$238$	5.74753	+	4.17582i	0.372557	+	0.270679i
$239$	−12.6115	+	9.16277i	−0.815768	+	0.592690i	−0.915497	−	0.402324i	$-0.868202\pi$
$239$	−12.6115	+	9.16277i	−0.815768	+	0.592690i	0.0997291	+	0.995015i	$0.468202\pi$
$240$	35.3412	+	13.2690i	2.28126	+	0.856512i
$241$	−1.93212	−	1.40377i	−0.124459	−	0.0904245i	0.523815	−	0.851832i	$-0.324508\pi$
$241$	−1.93212	−	1.40377i	−0.124459	−	0.0904245i	−0.648273	+	0.761408i	$0.724508\pi$
$242$	−6.28725	−	19.3502i	−0.404160	−	1.24388i
$243$	−16.1253			−1.03444
$244$	−12.6406	−	38.9039i	−0.809234	−	2.49056i
$245$	1.23160	+	1.86632i	0.0786840	+	0.119235i
$246$	8.17664	−	25.1651i	0.521324	−	1.60447i
$247$	0.149734	−	0.460834i	0.00952734	−	0.0293221i
$248$	−52.5192	+	38.1574i	−3.33497	+	2.42300i
$249$	3.25743			0.206431
$250$	21.5312	−	22.5023i	1.36176	−	1.42317i
$251$	−0.344184			−0.0217247			−0.0108623	−	0.999941i	$-0.503458\pi$
$251$	−0.344184			−0.0217247			−0.0108623	+	0.999941i	$0.503458\pi$
$252$	9.71748	−	7.06016i	0.612143	−	0.444748i
$253$	3.26438	−	10.0467i	0.205230	−	0.631633i
$254$	−6.34422	+	19.5255i	−0.398072	+	1.22514i
$255$	3.00381	+	4.55186i	0.188106	+	0.285049i
$256$	28.5210	+	87.7786i	1.78256	+	5.48616i
$257$	4.24541			0.264821			0.132411	−	0.991195i	$-0.457728\pi$
$257$	4.24541			0.264821			0.132411	+	0.991195i	$0.457728\pi$
$258$	−0.348274	−	1.07188i	−0.0216826	−	0.0667321i
$259$	−2.12915	−	1.54692i	−0.132299	−	0.0961209i
$260$	16.0938	+	6.04249i	0.998094	+	0.374739i
$261$	6.25803	−	4.54672i	0.387362	−	0.281435i
$262$	38.9750	+	28.3170i	2.40788	+	1.74943i
$263$	−3.37251	−	2.45027i	−0.207958	−	0.151090i	0.478931	−	0.877852i	$-0.341024\pi$
$263$	−3.37251	−	2.45027i	−0.207958	−	0.151090i	−0.686889	+	0.726762i	$0.741024\pi$
$264$	15.5770	−	11.3173i	0.958696	−	0.696533i
$265$	−13.8817	+	3.82915i	−0.852743	+	0.235223i
$266$	0.818081	+	0.594371i	0.0501598	+	0.0364432i
$267$	2.51739	+	7.74772i	0.154062	+	0.474153i
$268$	17.3173			1.05782
$269$	−5.80964	−	17.8802i	−0.354220	−	1.09018i	−0.956460	−	0.291862i	$-0.905725\pi$
$269$	−5.80964	−	17.8802i	−0.354220	−	1.09018i	0.602240	−	0.798315i	$-0.294275\pi$
$270$	29.2018	−	8.05509i	1.77717	−	0.490217i
$271$	1.46804	−	4.51817i	0.0891773	−	0.274460i	−0.896515	−	0.443013i	$-0.853910\pi$
$271$	1.46804	−	4.51817i	0.0891773	−	0.274460i	0.985693	+	0.168553i	$0.0539096\pi$
$272$	−13.9130	+	42.8198i	−0.843600	+	2.59633i
$273$	−1.03270	+	0.750301i	−0.0625019	+	0.0454103i
$274$	18.9110			1.14246
$275$	−2.13655	−	9.37208i	−0.128839	−	0.565158i
$276$	−30.2650			−1.82174
$277$	−24.1534	+	17.5485i	−1.45124	+	1.05439i	−0.465697	+	0.884944i	$0.654196\pi$
$277$	−24.1534	+	17.5485i	−1.45124	+	1.05439i	−0.985540	+	0.169441i	$0.945804\pi$
$278$	−0.720470	+	2.21738i	−0.0432109	+	0.132990i
$279$	−3.99474	+	12.2945i	−0.239159	+	0.736055i
$280$	−14.6031	+	18.3068i	−0.872701	+	1.09404i
$281$	−2.46516	−	7.58698i	−0.147059	−	0.452601i	0.850211	−	0.526442i	$-0.176474\pi$
$281$	−2.46516	−	7.58698i	−0.147059	−	0.452601i	−0.997270	+	0.0738408i	$0.976474\pi$
$282$	−35.5114			−2.11467
$283$	−3.40521	−	10.4801i	−0.202418	−	0.622980i	−0.999810	−	0.0195171i	$-0.993787\pi$
$283$	−3.40521	−	10.4801i	−0.202418	−	0.622980i	0.797391	−	0.603463i	$-0.206213\pi$
$284$	19.2203	+	13.9643i	1.14051	+	0.828631i
$285$	0.427550	+	0.647895i	0.0253259	+	0.0383780i
$286$	5.78313	−	4.20169i	0.341964	−	0.248451i
$287$	8.03587	+	5.83840i	0.474342	+	0.344630i
$288$	47.6303	+	34.6054i	2.80664	+	2.03914i
$289$	8.49110	−	6.16915i	0.499477	−	0.362891i
$290$	−14.4072	+	18.0612i	−0.846020	+	1.06059i
$291$	9.31200	+	6.76556i	0.545879	+	0.396604i
$292$	−21.8068	−	67.1144i	−1.27615	−	3.92757i
$293$	13.2329			0.773076			0.386538	−	0.922273i	$-0.373671\pi$
$293$	13.2329			0.773076			0.386538	+	0.922273i	$0.373671\pi$
$294$	−0.823190	−	2.53352i	−0.0480094	−	0.147758i
$295$	0.983818	−	21.8430i	0.0572801	−	1.27175i
$296$	8.51707	−	26.2129i	0.495045	−	1.52359i
$297$	2.88921	−	8.89209i	0.167649	−	0.515971i
$298$	6.38888	−	4.64180i	0.370098	−	0.268892i
$299$	−7.33448			−0.424164
$300$	−23.6451	+	14.1189i	−1.36515	+	0.815157i
$301$	0.423079			0.0243858
$302$	−2.86235	+	2.07962i	−0.164710	+	0.119669i
$303$	0.401337	−	1.23519i	0.0230562	−	0.0709597i
$304$	−1.98032	+	6.09481i	−0.113579	+	0.349561i
$305$	14.8677	+	5.58215i	0.851322	+	0.319633i
$306$	4.57837	+	14.0908i	0.261728	+	0.805515i
$307$	6.35178			0.362515			0.181258	−	0.983436i	$-0.441983\pi$
$307$	6.35178			0.362515			0.181258	+	0.983436i	$0.441983\pi$
$308$	3.42170	+	10.5309i	0.194969	+	0.600054i
$309$	1.10699	+	0.804273i	0.0629743	+	0.0457535i
$310$	1.73728	−	38.5714i	0.0986706	−	2.19071i
$311$	2.48219	−	1.80342i	0.140752	−	0.102263i	−0.515181	−	0.857081i	$-0.672275\pi$
$311$	2.48219	−	1.80342i	0.140752	−	0.102263i	0.655933	+	0.754819i	$0.272275\pi$
$312$	−10.8152	−	7.85768i	−0.612288	−	0.444854i
$313$	1.99063	+	1.44628i	0.112517	+	0.0817486i	0.642621	−	0.766184i	$-0.277847\pi$
$313$	1.99063	+	1.44628i	0.112517	+	0.0817486i	−0.530104	+	0.847933i	$0.677847\pi$
$314$	23.9982	−	17.4357i	1.35430	−	0.983955i
$315$	−0.209823	+	4.65854i	−0.0118222	+	0.262479i
$316$	−55.8452	−	40.5739i	−3.14154	−	2.28246i
$317$	−2.31175	−	7.11485i	−0.129841	−	0.399610i	0.864911	−	0.501925i	$-0.167375\pi$
$317$	−2.31175	−	7.11485i	−0.129841	−	0.399610i	−0.994752	+	0.102316i	$0.967375\pi$
$318$	17.1553			0.962020
$319$	2.20356	+	6.78187i	0.123376	+	0.379712i
$320$	−90.7106	−	34.0577i	−5.07087	−	1.90388i
$321$	−0.615962	+	1.89574i	−0.0343797	+	0.105810i
$322$	4.72991	−	14.5572i	0.263587	−	0.811239i
$323$	−0.748999	+	0.544180i	−0.0416754	+	0.0302790i
$324$	9.24769			0.513761
$325$	−5.73021	+	3.42161i	−0.317855	+	0.189797i
$326$	−5.31938			−0.294613
$327$	−9.34448	+	6.78917i	−0.516751	+	0.375442i
$328$	−32.1452	+	98.9329i	−1.77492	+	5.46266i
$329$	4.11939	−	12.6782i	0.227109	−	0.698970i
$330$	−0.515269	+	11.4401i	−0.0283646	+	0.629757i
$331$	−3.72080	−	11.4514i	−0.204514	−	0.629428i	−0.999733	−	0.0231066i	$-0.992644\pi$
$331$	−3.72080	−	11.4514i	−0.204514	−	0.629428i	0.795219	−	0.606322i	$-0.207356\pi$
$332$	−19.6186			−1.07671
$333$	−1.69604	−	5.21987i	−0.0929424	−	0.286047i
$334$	−33.4756	−	24.3214i	−1.83170	−	1.33081i
$335$	−4.19252	+	5.25585i	−0.229062	+	0.287158i
$336$	13.6581	−	9.92319i	0.745111	−	0.541354i
$337$	12.9342	+	9.39723i	0.704570	+	0.511900i	0.881417	−	0.472338i	$-0.156590\pi$
$337$	12.9342	+	9.39723i	0.704570	+	0.511900i	−0.176848	+	0.984238i	$0.556590\pi$
$338$	25.2815	+	18.3681i	1.37513	+	0.999094i
$339$	−6.17308	+	4.48501i	−0.335276	+	0.243592i
$340$	−18.0911	−	27.4146i	−0.981128	−	1.48677i
$341$	−9.64110	−	7.00467i	−0.522095	−	0.379324i
$342$	0.651667	+	2.00562i	0.0352381	+	0.108452i
$343$	1.00000			0.0539949
$344$	1.36919	+	4.21392i	0.0738216	+	0.227199i
$345$	7.32714	−	9.18549i	0.394480	−	0.494530i
$346$	−3.47242	+	10.6870i	−0.186679	+	0.574538i
$347$	8.60549	−	26.4850i	0.461967	−	1.42179i	−0.400791	−	0.916170i	$-0.631265\pi$
$347$	8.60549	−	26.4850i	0.461967	−	1.42179i	0.862758	−	0.505618i	$-0.168735\pi$
$348$	16.5281	−	12.0083i	0.885998	−	0.643715i
$349$	13.0729			0.699778			0.349889	−	0.936791i	$-0.386219\pi$
$349$	13.0729			0.699778			0.349889	+	0.936791i	$0.386219\pi$
$350$	−3.09574	−	13.5796i	−0.165474	−	0.725861i
$351$	−6.49154			−0.346493
$352$	−43.9082	+	31.9012i	−2.34032	+	1.70034i
$353$	8.59237	−	26.4446i	0.457326	−	1.40750i	−0.411057	−	0.911610i	$-0.634840\pi$
$353$	8.59237	−	26.4446i	0.457326	−	1.40750i	0.868383	−	0.495895i	$-0.165160\pi$
$354$	−8.04945	+	24.7737i	−0.427823	+	1.31671i
$355$	−8.89142	+	2.45263i	−0.471908	+	0.130172i
$356$	−15.1615	−	46.6624i	−0.803559	−	2.47310i
$357$	2.43895			0.129083
$358$	−14.7963	−	45.5384i	−0.782009	−	2.40678i
$359$	13.0879	+	9.50888i	0.690751	+	0.501860i	0.876907	−	0.480660i	$-0.159603\pi$
$359$	13.0879	+	9.50888i	0.690751	+	0.501860i	−0.186156	+	0.982520i	$0.559603\pi$
$360$	−47.0787	+	12.9863i	−2.48127	+	0.684438i
$361$	15.2647	−	11.0905i	0.803406	−	0.583709i
$362$	−17.9860	−	13.0676i	−0.945325	−	0.686819i
$363$	−5.65086	−	4.10559i	−0.296593	−	0.215488i
$364$	6.21967	−	4.51885i	0.325999	−	0.236852i
$365$	25.6488	+	9.62996i	1.34252	+	0.504055i
$366$	−15.3063	−	11.1207i	−0.800073	−	0.581287i
$367$	10.2543	+	31.5595i	0.535271	+	1.64739i	0.743063	+	0.669221i	$0.233372\pi$
$367$	10.2543	+	31.5595i	0.535271	+	1.64739i	−0.207793	+	0.978173i	$0.566628\pi$
$368$	97.0031			5.05664
$369$	6.40121	+	19.7009i	0.333234	+	1.02559i
$370$	9.02896	+	13.6822i	0.469393	+	0.711302i
$371$	−1.99004	+	6.12473i	−0.103318	+	0.317980i
$372$	−10.5505	+	32.4711i	−0.547018	+	1.68355i
$373$	−24.8953	+	18.0875i	−1.28903	+	0.936533i	−0.999785	−	0.0207227i	$-0.993403\pi$
$373$	−24.8953	+	18.0875i	−1.28903	+	0.936533i	−0.289242	+	0.957256i	$0.593403\pi$
$374$	−13.6581			−0.706245
$375$	1.43934	−	10.5945i	0.0743273	−	0.547099i
$376$	139.608			7.19972
$377$	4.00545	−	2.91013i	0.206291	−	0.149879i
$378$	4.18631	−	12.8841i	0.215320	−	0.662688i
$379$	−4.33718	+	13.3485i	−0.222786	+	0.685665i	0.775723	+	0.631074i	$0.217385\pi$
$379$	−4.33718	+	13.3485i	−0.222786	+	0.685665i	−0.998509	+	0.0545909i	$0.982615\pi$
$380$	−2.57502	−	3.90209i	−0.132096	−	0.200173i
$381$	2.17800	+	6.70319i	0.111582	+	0.343415i
$382$	−16.7583			−0.857429
$383$	2.65399	+	8.16813i	0.135612	+	0.417372i	0.995685	−	0.0928001i	$-0.0295817\pi$
$383$	2.65399	+	8.16813i	0.135612	+	0.417372i	−0.860072	+	0.510172i	$0.829582\pi$
$384$	49.7041	+	36.1122i	2.53645	+	1.84284i
$385$	−4.02454	−	1.51103i	−0.205110	−	0.0770094i
$386$	−6.93299	+	5.03711i	−0.352880	+	0.256382i
$387$	0.713811	+	0.518614i	0.0362851	+	0.0263626i
$388$	−56.0836	−	40.7471i	−2.84721	−	2.06862i
$389$	−22.0883	+	16.0481i	−1.11992	+	0.813669i	−0.984197	−	0.177078i	$-0.943335\pi$
$389$	−22.0883	+	16.0481i	−1.11992	+	0.813669i	−0.135722	+	0.990747i	$0.543335\pi$
$390$	7.66473	−	2.11426i	0.388119	−	0.107060i
$391$	11.3374	+	8.23710i	0.573356	+	0.416568i
$392$	3.23625	+	9.96014i	0.163455	+	0.503063i
$393$	16.5389			0.834278
$394$	12.1350	+	37.3478i	0.611354	+	1.88155i
$395$	25.8344	−	7.12621i	1.29987	−	0.358558i
$396$	−7.13585	+	21.9619i	−0.358590	+	1.10363i
$397$	−5.73365	+	17.6464i	−0.287764	+	0.885646i	0.697793	+	0.716300i	$0.254166\pi$
$397$	−5.73365	+	17.6464i	−0.287764	+	0.885646i	−0.985557	+	0.169346i	$0.945834\pi$
$398$	23.3485	−	16.9637i	1.17035	−	0.850311i
$399$	0.347150			0.0173793
$400$	75.7856	−	45.2530i	3.78928	−	2.26265i
$401$	−30.0782			−1.50203			−0.751016	−	0.660284i	$-0.770436\pi$
$401$	−30.0782			−1.50203			−0.751016	+	0.660284i	$0.770436\pi$
$402$	6.47985	−	4.70789i	0.323186	−	0.234808i
$403$	−2.55683	+	7.86911i	−0.127365	+	0.391988i
$404$	−2.41714	+	7.43920i	−0.120257	+	0.370114i
$405$	−2.23886	+	2.80670i	−0.111250	+	0.139466i
$406$	3.19284	+	9.82654i	0.158458	+	0.487683i
$407$	5.05961			0.250795
$408$	7.89304	+	24.2923i	0.390763	+	1.20265i
$409$	−5.13345	−	3.72967i	−0.253833	−	0.184420i	0.453591	−	0.891210i	$-0.350143\pi$
$409$	−5.13345	−	3.72967i	−0.253833	−	0.184420i	−0.707424	+	0.706790i	$0.750143\pi$
$410$	−34.0772	−	51.6394i	−1.68295	−	2.55029i
$411$	5.25232	−	3.81603i	0.259078	−	0.188231i
$412$	−6.66707	−	4.84391i	−0.328463	−	0.238642i
$413$	−7.91087	−	5.74758i	−0.389268	−	0.282820i
$414$	25.8245	−	18.7626i	1.26921	−	0.922133i
$415$	4.74966	−	5.95429i	0.233151	−	0.292285i
$416$	30.4857	+	22.1492i	1.49469	+	1.08595i
$417$	0.247340	+	0.761236i	0.0121123	+	0.0372779i
$418$	−1.94405			−0.0950864
$419$	−9.17497	−	28.2376i	−0.448226	−	1.37950i	−0.878906	−	0.476994i	$-0.841726\pi$
$419$	−9.17497	−	28.2376i	−0.448226	−	1.37950i	0.430680	−	0.902505i	$-0.358274\pi$
$420$	−0.554163	+	12.3037i	−0.0270404	+	0.600357i
$421$	−11.3562	+	34.9509i	−0.553468	+	1.70340i	0.146486	+	0.989213i	$0.453204\pi$
$421$	−11.3562	+	34.9509i	−0.553468	+	1.70340i	−0.699954	+	0.714188i	$0.746796\pi$
$422$	6.95973	−	21.4199i	0.338794	−	1.04270i
$423$	22.4912	−	16.3408i	1.09356	−	0.794517i
$424$	−67.4434			−3.27534
$425$	12.7003	+	1.14638i	0.616053	+	0.0556075i
$426$	10.9882			0.532381
$427$	5.74583	−	4.17459i	0.278060	−	0.202023i
$428$	3.70977	−	11.4175i	0.179319	−	0.551886i
$429$	0.758345	−	2.33395i	0.0366132	−	0.112684i
$430$	−2.46711	−	0.926289i	−0.118975	−	0.0446696i
$431$	−9.71955	−	29.9137i	−0.468174	−	1.44089i	−0.854946	−	0.518717i	$-0.826410\pi$
$431$	−9.71955	−	29.9137i	−0.468174	−	1.44089i	0.386772	−	0.922175i	$-0.373590\pi$
$432$	85.8547			4.13069
$433$	−8.81402	−	27.1268i	−0.423575	−	1.30363i	−0.904352	−	0.426787i	$-0.859645\pi$
$433$	−8.81402	−	27.1268i	−0.423575	−	1.30363i	0.480777	−	0.876843i	$-0.340355\pi$
$434$	−13.9694	−	10.1494i	−0.670553	−	0.487185i
$435$	−0.356880	+	7.92352i	−0.0171111	+	0.379904i
$436$	56.2792	−	40.8893i	2.69529	−	1.95824i
$437$	1.61372	+	1.17244i	0.0771947	+	0.0560852i
$438$	−26.4054	−	19.1847i	−1.26170	−	0.916679i
$439$	−22.6580	+	16.4620i	−1.08141	+	0.785689i	−0.977928	−	0.208943i	$-0.932998\pi$
$439$	−22.6580	+	16.4620i	−1.08141	+	0.785689i	−0.103480	+	0.994632i	$0.532998\pi$
$440$	2.02570	−	44.9751i	0.0965715	−	2.14410i
$441$	1.68718	+	1.22581i	0.0803421	+	0.0583719i
$442$	2.93038	+	9.01879i	0.139384	+	0.428980i
$443$	6.99989			0.332575			0.166287	−	0.986077i	$-0.446822\pi$
$443$	6.99989			0.332575			0.166287	+	0.986077i	$0.446822\pi$
$444$	−4.47941	−	13.7862i	−0.212583	−	0.654264i
$445$	17.8327	+	6.69539i	0.845353	+	0.317392i
$446$	−12.5349	+	38.5785i	−0.593545	+	1.82674i
$447$	0.837777	−	2.57841i	0.0396255	−	0.121955i
$448$	−35.0564	+	25.4699i	−1.65626	+	1.20334i
$449$	−8.73071			−0.412028			−0.206014	−	0.978549i	$-0.566049\pi$
$449$	−8.73071			−0.412028			−0.206014	+	0.978549i	$0.566049\pi$
$450$	11.4230	−	26.7061i	0.538483	−	1.25894i
$451$	−19.0960			−0.899197
$452$	37.1788	−	27.0120i	1.74874	−	1.27054i
$453$	−0.375342	+	1.15518i	−0.0176351	+	0.0542753i
$454$	−11.6817	+	35.9525i	−0.548248	+	1.68733i
$455$	−0.134297	+	2.98170i	−0.00629595	+	0.139784i
$456$	1.12346	+	3.45767i	0.0526110	+	0.161920i
$457$	−36.5618			−1.71029			−0.855144	−	0.518391i	$-0.826531\pi$
$457$	−36.5618			−1.71029			−0.855144	+	0.518391i	$0.826531\pi$
$458$	−2.45820	−	7.56555i	−0.114864	−	0.353515i
$459$	10.0344	+	7.29042i	0.468366	+	0.340288i
$460$	−44.1294	+	55.3217i	−2.05754	+	2.57939i
$461$	−26.1595	+	19.0060i	−1.21837	+	0.885197i	−0.995964	−	0.0897578i	$-0.971391\pi$
$461$	−26.1595	+	19.0060i	−1.21837	+	0.885197i	−0.222405	+	0.974954i	$0.571391\pi$
$462$	4.14327	+	3.01026i	0.192762	+	0.140050i
$463$	1.23827	+	0.899657i	0.0575474	+	0.0418106i	0.616187	−	0.787600i	$-0.288677\pi$
$463$	1.23827	+	0.899657i	0.0575474	+	0.0418106i	−0.558640	+	0.829410i	$0.688677\pi$
$464$	−52.9745	+	38.4883i	−2.45928	+	1.78677i
$465$	−7.30078	−	11.0633i	−0.338565	−	0.513050i
$466$	24.4747	+	17.7819i	1.13377	+	0.823730i
$467$	7.51126	+	23.1173i	0.347580	+	1.06974i	0.960188	+	0.279354i	$0.0901202\pi$
$467$	7.51126	+	23.1173i	0.347580	+	1.06974i	−0.612609	+	0.790386i	$0.709880\pi$
$468$	16.0330			0.741125
$469$	0.929121	+	2.85954i	0.0429028	+	0.132041i
$470$	−51.7791	+	64.9116i	−2.38839	+	2.99415i
$471$	3.14690	−	9.68515i	0.145001	−	0.446268i
$472$	31.6452	−	97.3939i	1.45659	−	4.48292i
$473$	−0.658031	+	0.478088i	−0.0302563	+	0.0219825i
$474$	−31.9267			−1.46644
$475$	1.80770	+	0.163171i	0.0829432	+	0.00748680i
$476$	−14.6891			−0.673274
$477$	−10.8653	+	7.89412i	−0.497489	+	0.361447i
$478$	13.4187	−	41.2984i	0.613756	−	1.88895i
$479$	1.96658	−	6.05250i	0.0898552	−	0.276546i	−0.896024	−	0.444007i	$-0.853557\pi$
$479$	1.96658	−	6.05250i	0.0898552	−	0.276546i	0.985879	+	0.167461i	$0.0535567\pi$
$480$	−58.1942	+	16.0524i	−2.65619	+	0.732690i
$481$	−1.08555	−	3.34098i	−0.0494968	−	0.152335i
$482$	6.65266			0.303020
$483$	−1.62380	−	4.99753i	−0.0738853	−	0.227396i
$484$	34.0336	+	24.7268i	1.54698	+	1.12395i
$485$	25.9446	−	7.15663i	1.17809	−	0.324966i
$486$	36.3400	−	26.4026i	1.64842	−	1.19764i
$487$	−6.10025	−	4.43209i	−0.276429	−	0.200837i	0.440929	−	0.897542i	$-0.354649\pi$
$487$	−6.10025	−	4.43209i	−0.276429	−	0.200837i	−0.717358	+	0.696704i	$0.754649\pi$
$488$	60.1744	+	43.7193i	2.72397	+	1.97908i
$489$	−1.47740	+	1.07339i	−0.0668103	+	0.0485405i
$490$	−5.83133	−	2.18940i	−0.263433	−	0.0989071i
$491$	16.6381	+	12.0883i	0.750865	+	0.545535i	0.896095	−	0.443862i	$-0.146392\pi$
$491$	16.6381	+	12.0883i	0.750865	+	0.545535i	−0.145230	+	0.989398i	$0.546392\pi$
$492$	16.9062	+	52.0321i	0.762192	+	2.34579i
$493$	−9.45975			−0.426046
$494$	0.417099	+	1.28370i	0.0187662	+	0.0577564i
$495$	−4.93790	−	7.48272i	−0.221942	−	0.336323i
$496$	33.8157	−	104.074i	1.51837	−	4.67306i
$497$	−1.27465	+	3.92298i	−0.0571761	+	0.175970i
$498$	−7.34095	+	5.33351i	−0.328956	+	0.239000i
$499$	−1.82827			−0.0818445			−0.0409223	−	0.999162i	$-0.513030\pi$
$499$	−1.82827			−0.0818445			−0.0409223	+	0.999162i	$0.513030\pi$
$500$	−8.66876	+	63.8080i	−0.387679	+	2.85358i
$501$	−14.2053			−0.634645
$502$	0.775653	−	0.563545i	0.0346191	−	0.0251522i
$503$	−8.59788	+	26.4615i	−0.383360	+	1.17986i	0.554302	+	0.832315i	$0.312985\pi$
$503$	−8.59788	+	26.4615i	−0.383360	+	1.17986i	−0.937663	+	0.347547i	$0.887015\pi$
$504$	−6.74910	+	20.7716i	−0.300629	+	0.925241i
$505$	−1.67262	−	2.53463i	−0.0744308	−	0.112790i
$506$	9.09328	+	27.9862i	0.404246	+	1.24414i
$507$	10.7282			0.476454
$508$	−13.1175	−	40.3714i	−0.581994	−	1.79119i
$509$	31.7397	+	23.0603i	1.40684	+	1.02213i	0.993773	+	0.111428i	$0.0355423\pi$
$509$	31.7397	+	23.0603i	1.40684	+	1.02213i	0.413067	+	0.910701i	$0.364458\pi$
$510$	−14.2223	−	5.33984i	−0.629775	−	0.236452i
$511$	9.91233	−	7.20173i	0.438496	−	0.318586i
$512$	−104.048	−	75.5954i	−4.59832	−	3.34088i
$513$	1.42826	+	1.03769i	0.0630591	+	0.0458151i
$514$	−9.56746	+	6.95117i	−0.422002	+	0.306603i
$515$	3.08423	−	0.850762i	0.135908	−	0.0374891i
$516$	1.88525	+	1.36971i	0.0829933	+	0.0602982i
$517$	7.91955	+	24.3739i	0.348301	+	1.07196i
$518$	7.33108			0.322109
$519$	1.19210	+	3.66890i	0.0523273	+	0.161047i
$520$	−30.1327	+	8.31188i	−1.32141	+	0.364500i
$521$	−7.05062	+	21.6996i	−0.308893	+	0.950676i	0.669302	+	0.742990i	$0.266593\pi$
$521$	−7.05062	+	21.6996i	−0.308893	+	0.950676i	−0.978196	+	0.207686i	$0.933407\pi$
$522$	−6.65858	+	20.4930i	−0.291438	+	0.896954i
$523$	−21.9126	+	15.9204i	−0.958170	+	0.696151i	−0.952725	−	0.303834i	$-0.901733\pi$
$523$	−21.9126	+	15.9204i	−0.958170	+	0.696151i	−0.00544494	+	0.999985i	$0.501733\pi$
$524$	−99.6093			−4.35145
$525$	−3.60003	−	3.14690i	−0.157118	−	0.137342i
$526$	11.6122			0.506317
$527$	12.7898	−	9.29232i	0.557132	−	0.404780i
$528$	−10.0296	+	30.8679i	−0.436482	+	1.34335i
$529$	2.22267	−	6.84068i	0.0966380	−	0.297421i
$530$	25.0141	−	31.3583i	1.08654	−	1.36212i
$531$	−6.30164	−	19.3944i	−0.273468	−	0.841647i
$532$	−2.09079			−0.0906473
$533$	4.09709	+	12.6096i	0.177465	+	0.546181i
$534$	−18.3588	−	13.3385i	−0.794464	−	0.577212i
$535$	2.56710	+	3.89010i	0.110986	+	0.168184i
$536$	−25.4746	+	18.5084i	−1.10033	+	0.799439i
$537$	−13.2987	−	9.66204i	−0.573879	−	0.416948i
$538$	42.3686	+	30.7826i	1.82664	+	1.32713i
$539$	−1.55534	+	1.13002i	−0.0669933	+	0.0486735i
$540$	−39.0576	+	48.9637i	−1.68077	+	2.10706i
$541$	−4.00857	−	2.91240i	−0.172342	−	0.125214i	0.498271	−	0.867022i	$-0.333969\pi$
$541$	−4.00857	−	2.91240i	−0.172342	−	0.125214i	−0.670612	+	0.741808i	$0.733969\pi$
$542$	4.08939	+	12.5858i	0.175654	+	0.540608i
$543$	−7.63232			−0.327534
$544$	−22.2488	−	68.4749i	−0.953911	−	2.93584i
$545$	−1.21520	+	26.9802i	−0.0520535	+	1.15570i
$546$	1.09880	−	3.38175i	0.0470242	−	0.144726i
$547$	−0.0393171	+	0.121006i	−0.00168108	+	0.00517383i	−0.951894	−	0.306429i	$-0.900866\pi$
$547$	−0.0393171	+	0.121006i	−0.00168108	+	0.00517383i	0.950212	+	0.311603i	$0.100866\pi$
$548$	−31.6333	+	22.9829i	−1.35131	+	0.981781i
$549$	14.8115			0.632141
$550$	20.1602	+	17.6227i	0.859633	+	0.751434i
$551$	−1.34646			−0.0573613
$552$	44.5211	−	32.3465i	1.89494	−	1.37676i
$553$	3.70356	−	11.3984i	0.157491	−	0.484708i
$554$	25.6994	−	79.0945i	1.09186	−	3.36040i
$555$	5.26861	+	1.97812i	0.223640	+	0.0839667i
$556$	−1.48966	−	4.58471i	−0.0631758	−	0.194435i
$557$	−43.9843			−1.86368			−0.931838	−	0.362874i	$-0.881795\pi$
$557$	−43.9843			−1.86368			−0.931838	+	0.362874i	$0.881795\pi$
$558$	−11.1278	−	34.2477i	−0.471075	−	1.44982i
$559$	0.456875	+	0.331939i	0.0193237	+	0.0140395i
$560$	1.77616	−	39.4348i	0.0750566	−	1.66642i
$561$	−3.79339	+	2.75606i	−0.160157	+	0.116361i
$562$	17.9779	+	13.0617i	0.758353	+	0.550976i
$563$	34.4028	+	24.9951i	1.44991	+	1.05342i	0.985853	+	0.167610i	$0.0536050\pi$
$563$	34.4028	+	24.9951i	1.44991	+	1.05342i	0.464052	+	0.885808i	$0.346395\pi$
$564$	59.4015	−	43.1577i	2.50125	−	1.81727i
$565$	−0.802777	+	17.8234i	−0.0337731	+	0.749837i
$566$	24.8335	+	18.0426i	1.04383	+	0.758387i
$567$	0.496163	+	1.52703i	0.0208369	+	0.0641294i
$568$	−43.1986			−1.81257
$569$	−10.5815	−	32.5666i	−0.443601	−	1.36526i	−0.884011	−	0.467467i	$-0.845167\pi$
$569$	−10.5815	−	32.5666i	−0.443601	−	1.36526i	0.440410	−	0.897797i	$-0.354833\pi$
$570$	−2.02435	−	0.760052i	−0.0847907	−	0.0318351i
$571$	4.67192	−	14.3787i	0.195514	−	0.601730i	−0.804456	−	0.594012i	$-0.797543\pi$
$571$	4.67192	−	14.3787i	0.195514	−	0.601730i	0.999970	−	0.00771798i	$-0.00245673\pi$
$572$	−4.56730	+	14.0567i	−0.190968	+	0.587741i
$573$	−4.65443	+	3.38164i	−0.194442	+	0.141270i
$574$	−27.6691			−1.15488
$575$	−6.10655	−	26.7867i	−0.254661	−	1.11708i
$576$	−90.3678			−3.76533
$577$	−8.52108	+	6.19093i	−0.354737	+	0.257732i	−0.750854	−	0.660469i	$-0.770358\pi$
$577$	−8.52108	+	6.19093i	−0.354737	+	0.257732i	0.396116	+	0.918200i	$0.370358\pi$
$578$	−9.03458	+	27.8056i	−0.375789	+	1.15656i
$579$	−0.909127	+	2.79800i	−0.0377820	+	0.116281i
$580$	2.14939	−	47.7212i	0.0892485	−	1.98151i
$581$	−1.05259	−	3.23954i	−0.0436688	−	0.134399i
$582$	−32.0630			−1.32905
$583$	−3.82587	−	11.7748i	−0.158451	−	0.487664i
$584$	103.809	+	75.4216i	4.29565	+	3.12097i
$585$	−3.88158	+	4.86604i	−0.160483	+	0.201186i
$586$	−29.8217	+	21.6668i	−1.23192	+	0.895046i
$587$	16.5759	+	12.0431i	0.684162	+	0.497073i	0.874736	−	0.484600i	$-0.161035\pi$
$587$	16.5759	+	12.0431i	0.684162	+	0.497073i	−0.190574	+	0.981673i	$0.561035\pi$
$588$	4.45602	+	3.23749i	0.183763	+	0.133512i
$589$	1.82045	−	1.32263i	0.0750102	−	0.0544981i
$590$	33.5471	+	50.8361i	1.38111	+	2.09289i
$591$	10.9067	+	7.92422i	0.448644	+	0.325959i
$592$	14.3571	+	44.1865i	0.590072	+	1.81605i
$593$	−8.92342			−0.366441			−0.183221	−	0.983072i	$-0.558652\pi$
$593$	−8.92342			−0.366441			−0.183221	+	0.983072i	$0.558652\pi$
$594$	8.04821	+	24.7698i	0.330222	+	1.01632i
$595$	3.55623	−	4.45818i	0.145791	−	0.182767i
$596$	−5.04570	+	15.5291i	−0.206680	+	0.636096i
$597$	3.06170	−	9.42293i	0.125307	−	0.385655i
$598$	16.5290	−	12.0090i	0.675921	−	0.491085i
$599$	44.3647			1.81269			0.906346	−	0.422536i	$-0.138860\pi$
$599$	44.3647			1.81269			0.906346	+	0.422536i	$0.138860\pi$
$600$	19.6930	−	46.0409i	0.803964	−	1.87961i
$601$	−14.4688			−0.590196			−0.295098	−	0.955467i	$-0.595352\pi$
$601$	−14.4688			−0.590196			−0.295098	+	0.955467i	$0.595352\pi$
$602$	−0.953450	+	0.692722i	−0.0388597	+	0.0282332i
$603$	−1.93766	+	5.96350i	−0.0789075	+	0.242852i
$604$	2.26058	−	6.95735i	0.0919817	−	0.283091i
$605$	−15.7442	+	4.34291i	−0.640092	+	0.176564i
$606$	1.11797	+	3.44074i	0.0454142	+	0.139771i
$607$	−18.1939			−0.738468			−0.369234	−	0.929336i	$-0.620380\pi$
$607$	−18.1939			−0.738468			−0.369234	+	0.929336i	$0.620380\pi$
$608$	−3.16681	−	9.74645i	−0.128431	−	0.395271i
$609$	2.86966	+	2.08493i	0.116285	+	0.0844857i
$610$	−42.6457	+	11.7635i	−1.72667	+	0.476290i
$611$	14.3955	−	10.4589i	0.582379	−	0.423123i
$612$	−24.7832	−	18.0061i	−1.00180	−	0.727852i
$613$	−5.34240	−	3.88148i	−0.215778	−	0.156772i	0.474646	−	0.880177i	$-0.342576\pi$
$613$	−5.34240	−	3.88148i	−0.215778	−	0.156772i	−0.690424	+	0.723405i	$0.742576\pi$
$614$	−14.3144	+	10.4000i	−0.577681	+	0.419710i
$615$	−19.8848	−	7.46586i	−0.801834	−	0.301053i
$616$	−16.2886	−	11.8344i	−0.656288	−	0.476821i
$617$	−8.99839	−	27.6942i	−0.362262	−	1.11493i	−0.951678	−	0.307097i	$-0.900642\pi$
$617$	−8.99839	−	27.6942i	−0.362262	−	1.11493i	0.589416	−	0.807829i	$-0.299358\pi$
$618$	−3.81157			−0.153324
$619$	−8.41261	−	25.8914i	−0.338131	−	1.04066i	−0.965159	−	0.261664i	$-0.915729\pi$
$619$	−8.41261	−	25.8914i	−0.338131	−	1.04066i	0.627027	−	0.778997i	$-0.284271\pi$
$620$	43.9706	+	66.6314i	1.76590	+	2.67598i
$621$	8.25778	−	25.4148i	0.331373	−	1.01986i
$622$	−2.64107	+	8.12837i	−0.105897	+	0.325918i
$623$	6.89171	−	5.00712i	0.276111	−	0.200606i
$624$	22.5347			0.902108
$625$	−17.2672	−	18.0789i	−0.690686	−	0.723155i
$626$	−6.85414			−0.273947
$627$	−0.539937	+	0.392287i	−0.0215630	+	0.0156664i
$628$	−18.9529	+	58.3310i	−0.756303	+	2.32766i
$629$	−2.07413	+	6.38351i	−0.0827009	+	0.254527i
$630$	−7.15474	−	10.8420i	−0.285051	−	0.431957i
$631$	4.52828	+	13.9366i	0.180268	+	0.554807i	0.999835	−	0.0181760i	$-0.00578592\pi$
$631$	4.52828	+	13.9366i	0.180268	+	0.554807i	−0.819567	+	0.572983i	$0.805786\pi$
$632$	125.515			4.99272
$633$	−2.38930	−	7.35352i	−0.0949663	−	0.292276i
$634$	16.8592	+	12.2489i	0.669563	+	0.486466i
$635$	15.4286	+	5.79273i	0.612264	+	0.229877i
$636$	−28.6964	+	20.8492i	−1.13789	+	0.826723i
$637$	1.07988	+	0.784580i	0.0427865	+	0.0310862i
$638$	−16.0701	−	11.6756i	−0.636223	−	0.462243i
$639$	−6.95941	+	5.05631i	−0.275310	+	0.200024i
$640$	138.483	−	38.1996i	5.47404	−	1.50997i
$641$	−35.1013	−	25.5026i	−1.38642	−	1.00729i	−0.996248	−	0.0865476i	$-0.972417\pi$
$641$	−35.1013	−	25.5026i	−1.38642	−	1.00729i	−0.390169	−	0.920743i	$-0.627583\pi$
$642$	−1.71583	−	5.28077i	−0.0677183	−	0.208415i
$643$	0.806446			0.0318031			0.0159016	−	0.999874i	$-0.494938\pi$
$643$	0.806446			0.0318031			0.0159016	+	0.999874i	$0.494938\pi$
$644$	9.77968	+	30.0988i	0.385373	+	1.18606i
$645$	−0.872128	+	0.240570i	−0.0343400	+	0.00947243i
$646$	0.796940	−	2.45273i	0.0313552	−	0.0965013i
$647$	4.37079	−	13.4519i	0.171833	−	0.528849i	−0.827641	−	0.561257i	$-0.810318\pi$
$647$	4.37079	−	13.4519i	0.171833	−	0.528849i	0.999475	+	0.0324087i	$0.0103178\pi$
$648$	−13.6038	+	9.88371i	−0.534406	+	0.388269i
$649$	18.7990			0.737924
$650$	7.31126	−	17.0932i	0.286771	−	0.670452i
$651$	−5.92788			−0.232332
$652$	8.89797	−	6.46475i	0.348471	−	0.253179i
$653$	−1.52105	+	4.68132i	−0.0595235	+	0.183194i	−0.976397	−	0.215983i	$-0.930704\pi$
$653$	−1.52105	+	4.68132i	−0.0595235	+	0.183194i	0.916874	+	0.399178i	$0.130704\pi$
$654$	9.94258	−	30.6001i	0.388786	−	1.19656i
$655$	24.1154	−	30.2316i	0.942266	−	1.18125i
$656$	−54.1866	−	166.769i	−2.11563	−	6.51125i
$657$	25.5519			0.996874
$658$	11.4750	+	35.3163i	0.447341	+	1.37677i
$659$	−33.6999	−	24.4844i	−1.31276	−	0.953779i	−0.999992	−	0.00395009i	$-0.998743\pi$
$659$	−33.6999	−	24.4844i	−1.31276	−	0.953779i	−0.312771	−	0.949828i	$-0.601257\pi$
$660$	−13.0415	−	19.7626i	−0.507639	−	0.769258i
$661$	−17.3342	+	12.5940i	−0.674222	+	0.489851i	−0.871436	−	0.490510i	$-0.836811\pi$
$661$	−17.3342	+	12.5940i	−0.674222	+	0.489851i	0.197214	+	0.980360i	$0.436811\pi$
$662$	27.1351	+	19.7148i	1.05463	+	0.766237i
$663$	2.63377	+	1.91355i	0.102287	+	0.0743161i
$664$	28.8598	−	20.9679i	1.11998	−	0.813712i
$665$	0.506180	−	0.634560i	0.0196288	−	0.0246072i
$666$	12.3689	+	8.98652i	0.479284	+	0.348220i
$667$	6.29809	+	19.3835i	0.243863	+	0.750533i
$668$	85.5544			3.31020
$669$	4.30328	+	13.2441i	0.166375	+	0.512048i
$670$	0.842670	−	18.7092i	0.0325552	−	0.722798i
$671$	−4.21935	+	12.9858i	−0.162886	+	0.501312i
$672$	−8.34260	+	25.6759i	−0.321823	+	0.990468i
$673$	21.6292	−	15.7145i	0.833743	−	0.605750i	−0.0868729	−	0.996219i	$-0.527687\pi$
$673$	21.6292	−	15.7145i	0.833743	−	0.605750i	0.920616	+	0.390470i	$0.127687\pi$
$674$	−44.5349			−1.71542
$675$	−5.40474	−	23.7082i	−0.208028	−	0.912528i
$676$	−64.6127			−2.48510
$677$	8.87810	−	6.45032i	0.341213	−	0.247906i	−0.403960	−	0.914776i	$-0.632367\pi$
$677$	8.87810	−	6.45032i	0.341213	−	0.247906i	0.745173	+	0.666871i	$0.232367\pi$
$678$	6.56820	−	20.2148i	0.252250	−	0.776346i
$679$	3.71937	−	11.4470i	0.142736	−	0.439297i
$680$	55.9129	+	20.9928i	2.14416	+	0.805036i
$681$	4.01036	+	12.3426i	0.153677	+	0.472970i
$682$	33.1962			1.27115
$683$	15.6645	+	48.2102i	0.599384	+	1.84471i	0.531568	+	0.847016i	$0.321603\pi$
$683$	15.6645	+	48.2102i	0.599384	+	1.84471i	0.0678162	+	0.997698i	$0.478397\pi$
$684$	−3.52755	−	2.56291i	−0.134879	−	0.0979954i
$685$	0.683036	−	15.1649i	0.0260975	−	0.579422i
$686$	−2.25360	+	1.63734i	−0.0860429	+	0.0625138i
$687$	−2.20938	−	1.60521i	−0.0842932	−	0.0612426i
$688$	−6.04245	−	4.39010i	−0.230366	−	0.167371i
$689$	−6.95435	+	5.05263i	−0.264940	+	0.192490i
$690$	−1.47271	+	32.6974i	−0.0560651	+	1.24477i
$691$	−18.1024	−	13.1522i	−0.688648	−	0.500332i	0.187567	−	0.982252i	$-0.439940\pi$
$691$	−18.1024	−	13.1522i	−0.688648	−	0.500332i	−0.876215	+	0.481920i	$0.839940\pi$
$692$	−7.17967	−	22.0968i	−0.272930	−	0.839993i
$693$	−4.00934			−0.152302
$694$	23.9715	+	73.7766i	0.909945	+	2.80052i
$695$	1.75212	+	0.657841i	0.0664616	+	0.0249533i
$696$	−11.4793	+	35.3296i	−0.435121	+	1.33917i
$697$	7.82820	−	24.0927i	0.296514	−	0.912577i
$698$	−29.4612	+	21.4048i	−1.11512	+	0.810183i
$699$	10.3858			0.392825
$700$	21.6820	+	18.9529i	0.819501	+	0.716353i
$701$	−22.1023			−0.834792			−0.417396	−	0.908725i	$-0.637057\pi$
$701$	−22.1023			−0.834792			−0.417396	+	0.908725i	$0.637057\pi$
$702$	14.6293	−	10.6288i	0.552149	−	0.401160i
$703$	−0.295223	+	0.908604i	−0.0111346	+	0.0342687i
$704$	25.7430	−	79.2289i	0.970226	−	2.98605i
$705$	−1.28262	+	28.4769i	−0.0483061	+	1.07250i
$706$	23.9349	+	73.6642i	0.900804	+	2.77239i
$707$	−1.35809			−0.0510762
$708$	−16.6432	−	51.2227i	−0.625492	−	1.92507i
$709$	33.0716	+	24.0279i	1.24203	+	0.902387i	0.997732	−	0.0673139i	$-0.0214429\pi$
$709$	33.0716	+	24.0279i	1.24203	+	0.902387i	0.244297	+	0.969701i	$0.421443\pi$
$710$	16.0219	−	20.0855i	0.601292	−	0.753795i
$711$	20.2208	−	14.6913i	0.758340	−	0.550966i
$712$	72.1749	+	52.4381i	2.70487	+	1.96520i
$713$	−27.5556	−	20.0203i	−1.03197	−	0.749767i
$714$	−5.49641	+	3.99338i	−0.205698	+	0.149448i
$715$	−3.16050	−	4.78931i	−0.118196	−	0.179110i
$716$	80.0941	+	58.1918i	2.99326	+	2.17473i
$717$	−4.60669	−	14.1779i	−0.172040	−	0.529484i
$718$	−45.0640			−1.68177
$719$	−2.71765	−	8.36405i	−0.101351	−	0.311927i	0.887506	−	0.460797i	$-0.152436\pi$
$719$	−2.71765	−	8.36405i	−0.101351	−	0.311927i	−0.988857	+	0.148870i	$0.952436\pi$
$720$	51.3363	−	64.3565i	1.91319	−	2.39842i
$721$	0.442149	−	1.36080i	0.0164665	−	0.0506787i
$722$	−16.2417	+	49.9869i	−0.604455	+	1.86032i
$723$	1.84770	−	1.34243i	0.0687167	−	0.0499256i
$724$	45.9674			1.70836
$725$	13.9631	+	12.2056i	0.518577	+	0.453306i
$726$	19.4570			0.722118
$727$	−27.6838	+	20.1135i	−1.02674	+	0.745968i	−0.967653	−	0.252285i	$-0.918818\pi$
$727$	−27.6838	+	20.1135i	−1.02674	+	0.745968i	−0.0590837	+	0.998253i	$0.518818\pi$
$728$	−4.31976	+	13.2949i	−0.160101	+	0.492740i
$729$	3.27679	−	10.0849i	0.121363	−	0.373516i
$730$	−73.5696	+	20.2936i	−2.72293	+	0.751100i
$731$	−0.333432	−	1.02620i	−0.0123324	−	0.0379554i
$732$	39.1187			1.44587
$733$	11.9030	+	36.6338i	0.439649	+	1.35310i	0.888247	+	0.459366i	$0.151923\pi$
$733$	11.9030	+	36.6338i	0.439649	+	1.35310i	−0.448598	+	0.893734i	$0.648077\pi$
$734$	−74.7827	−	54.3328i	−2.76028	−	2.00546i
$735$	−2.06139	+	0.568617i	−0.0760353	+	0.0209738i
$736$	−125.496	+	91.1781i	−4.62584	+	3.36087i
$737$	−4.67644	−	3.39763i	−0.172259	−	0.125153i
$738$	−46.6828	−	33.9170i	−1.71842	−	1.24850i
$739$	20.2677	−	14.7254i	0.745560	−	0.541681i	−0.148888	−	0.988854i	$-0.547569\pi$
$739$	20.2677	−	14.7254i	0.745560	−	0.541681i	0.894447	+	0.447173i	$0.147569\pi$
$740$	−31.7314	−	11.9137i	−1.16647	−	0.437956i
$741$	0.374881	+	0.272367i	0.0137716	+	0.0100057i
$742$	−5.54347	−	17.0611i	−0.203507	−	0.626331i
$743$	24.2645			0.890178			0.445089	−	0.895486i	$-0.353172\pi$
$743$	24.2645			0.890178			0.445089	+	0.895486i	$0.353172\pi$
$744$	−19.1841	−	59.0425i	−0.703322	−	2.16460i
$745$	−3.49155	−	5.29096i	−0.127920	−	0.193846i
$746$	26.4887	−	81.5238i	0.969820	−	2.98480i
$747$	2.19515	−	6.75597i	0.0803163	−	0.247188i
$748$	22.8466	−	16.5990i	0.835353	−	0.606920i
$749$	2.08436			0.0761610
$750$	14.1031	+	26.2325i	0.514973	+	0.957877i
$751$	46.4177			1.69380			0.846902	−	0.531749i	$-0.178465\pi$
$751$	46.4177			1.69380			0.846902	+	0.531749i	$0.178465\pi$
$752$	−190.389	+	138.326i	−6.94278	+	5.04422i
$753$	0.101712	−	0.313037i	0.00370658	−	0.0114077i
$754$	−4.26182	+	13.1165i	−0.155206	+	0.477676i
$755$	1.56429	+	2.37046i	0.0569302	+	0.0862700i
$756$	8.65572	+	26.6396i	0.314805	+	0.968872i
$757$	−38.0656			−1.38352			−0.691759	−	0.722128i	$-0.743164\pi$
$757$	−38.0656			−1.38352			−0.691759	+	0.722128i	$0.743164\pi$
$758$	−12.0817	−	37.1835i	−0.438826	−	1.35057i
$759$	8.17287	+	5.93794i	0.296657	+	0.215534i
$760$	7.95843	+	2.98803i	0.288682	+	0.108387i
$761$	23.4725	−	17.0538i	0.850878	−	0.618199i	−0.0745097	−	0.997220i	$-0.523739\pi$
$761$	23.4725	−	17.0538i	0.850878	−	0.618199i	0.925388	+	0.379021i	$0.123739\pi$
$762$	−15.8837	−	11.5402i	−0.575406	−	0.418057i
$763$	9.77141	+	7.09934i	0.353749	+	0.257013i
$764$	28.0324	−	20.3667i	1.01418	−	0.736841i
$765$	11.4649	−	3.16250i	0.414514	−	0.114340i
$766$	−19.3550	−	14.0622i	−0.699325	−	0.508089i
$767$	−4.03336	−	12.4134i	−0.145636	−	0.448222i
$768$	−88.2634			−3.18493
$769$	−14.9005	−	45.8590i	−0.537325	−	1.65372i	−0.738570	−	0.674176i	$-0.764499\pi$
$769$	−14.9005	−	45.8590i	−0.537325	−	1.65372i	0.201245	−	0.979541i	$-0.435501\pi$
$770$	11.5438	−	3.18426i	0.416009	−	0.114753i
$771$	−1.25459	+	3.86122i	−0.0451828	+	0.139058i
$772$	5.47542	−	16.8516i	0.197065	−	0.606503i
$773$	−27.0590	+	19.6595i	−0.973245	+	0.707104i	−0.956189	−	0.292750i	$-0.905429\pi$
$773$	−27.0590	+	19.6595i	−0.973245	+	0.707104i	−0.0170564	+	0.999855i	$0.505429\pi$
$774$	−2.45779			−0.0883435
$775$	−30.8680	−	2.78628i	−1.10881	−	0.100086i
$776$	126.051			4.52496
$777$	2.03613	−	1.47933i	0.0730456	−	0.0530708i
$778$	23.5020	−	72.3318i	0.842589	−	2.59322i
$779$	1.11424	−	3.42927i	0.0399216	−	0.122866i
$780$	−10.2516	+	12.8517i	−0.367067	+	0.460165i
$781$	−2.45053	−	7.54196i	−0.0876869	−	0.269873i
$782$	−39.0368			−1.39595
$783$	5.57426	+	17.1558i	0.199208	+	0.613098i
$784$	−14.2821	−	10.3766i	−0.510075	−	0.370591i
$785$	−13.1151	−	19.8742i	−0.468098	−	0.709339i
$786$	−37.2721	+	27.0798i	−1.32945	+	0.965903i
$787$	−29.1647	−	21.1894i	−1.03961	−	0.755321i	−0.0694007	−	0.997589i	$-0.522109\pi$
$787$	−29.1647	−	21.1894i	−1.03961	−	0.755321i	−0.970209	+	0.242268i	$0.922109\pi$
$788$	−65.6883	−	47.7254i	−2.34005	−	1.70015i
$789$	3.22516	−	2.34322i	0.114819	−	0.0834208i
$790$	−46.5523	+	58.3592i	−1.65626	+	2.07633i
$791$	6.45512	+	4.68992i	0.229517	+	0.166754i
$792$	−12.9752	−	39.9335i	−0.461054	−	1.41898i
$793$	9.48012			0.336649
$794$	−15.9717	−	49.1558i	−0.566814	−	1.74447i
$795$	0.619622	−	13.7570i	0.0219757	−	0.487910i
$796$	−18.4398	+	56.7517i	−0.653580	+	2.01151i
$797$	16.1042	−	49.5636i	0.570440	−	1.75563i	−0.0807658	−	0.996733i	$-0.525737\pi$
$797$	16.1042	−	49.5636i	0.570440	−	1.75563i	0.651206	−	0.758901i	$-0.274263\pi$
$798$	−0.782338	+	0.568402i	−0.0276945	+	0.0201212i
$799$	−33.9981			−1.20277
$800$	−55.5105	+	129.780i	−1.96259	+	4.58841i
$801$	17.7654			0.627708
$802$	67.7842	−	49.2481i	2.39354	−	1.73901i
$803$	−7.27894	+	22.4023i	−0.256868	+	0.790559i
$804$	−5.11755	+	15.7502i	−0.180482	+	0.555466i
$805$	−11.5027	−	4.31874i	−0.405417	−	0.152216i
$806$	−7.12231	−	21.9202i	−0.250873	−	0.772107i
$807$	17.9790			0.632890
$808$	−4.39511	−	13.5268i	−0.154620	−	0.475870i
$809$	−26.1970	−	19.0332i	−0.921037	−	0.669173i	0.0227447	−	0.999741i	$-0.492760\pi$
$809$	−26.1970	−	19.0332i	−0.921037	−	0.669173i	−0.943782	+	0.330569i	$0.892760\pi$
$810$	0.449997	−	9.99094i	0.0158113	−	0.351046i
$811$	31.5932	−	22.9538i	1.10939	−	0.806018i	0.126821	−	0.991926i	$-0.459523\pi$
$811$	31.5932	−	22.9538i	1.10939	−	0.806018i	0.982567	+	0.185908i	$0.0595226\pi$
$812$	−17.2832	−	12.5570i	−0.606521	−	0.440663i
$813$	3.67547	+	2.67038i	0.128904	+	0.0936544i
$814$	−11.4023	+	8.28428i	−0.399651	+	0.290364i
$815$	−0.192128	+	4.26567i	−0.00672995	+	0.149420i
$816$	−34.8333	−	25.3079i	−1.21941	−	0.885953i
$817$	−0.0474595	−	0.146065i	−0.00166040	−	0.00511018i
$818$	17.6755			0.618008
$819$	0.860212	+	2.64746i	0.0300582	+	0.0925097i
$820$	119.761	+	44.9648i	4.18223	+	1.57024i
$821$	11.6638	−	35.8976i	0.407071	−	1.25284i	−0.512083	−	0.858936i	$-0.671126\pi$
$821$	11.6638	−	35.8976i	0.407071	−	1.25284i	0.919154	−	0.393899i	$-0.128874\pi$
$822$	−5.58850	+	17.1996i	−0.194921	+	0.599906i
$823$	−37.0888	+	26.9466i	−1.29283	+	0.939299i	−0.999859	−	0.0168202i	$-0.994646\pi$
$823$	−37.0888	+	26.9466i	−1.29283	+	0.939299i	−0.292976	+	0.956120i	$0.594646\pi$
$824$	14.9846			0.522014
$825$	9.15533	+	0.826398i	0.318748	+	0.0287715i
$826$	27.2387			0.947754
$827$	23.4224	−	17.0174i	0.814476	−	0.591751i	−0.100649	−	0.994922i	$-0.532092\pi$
$827$	23.4224	−	17.0174i	0.814476	−	0.591751i	0.915125	+	0.403171i	$0.132092\pi$
$828$	−20.3953	+	62.7702i	−0.708784	+	2.18141i
$829$	−9.34130	+	28.7496i	−0.324437	+	0.998514i	0.647257	+	0.762272i	$0.275916\pi$
$829$	−9.34130	+	28.7496i	−0.324437	+	0.998514i	−0.971694	+	0.236242i	$0.924084\pi$
$830$	−0.954651	+	21.1954i	−0.0331364	+	0.735702i
$831$	−8.82269	−	27.1535i	−0.306056	−	0.941943i
$832$	−57.8399			−2.00524
$833$	−0.788110	−	2.42555i	−0.0273064	−	0.0840404i
$834$	−1.80381	−	1.31054i	−0.0624607	−	0.0453803i
$835$	−20.7127	+	25.9660i	−0.716792	+	0.898589i
$836$	3.25189	−	2.36264i	0.112469	−	0.0817135i
$837$	−24.3887	−	17.7194i	−0.842996	−	0.612473i
$838$	66.9112	+	48.6138i	2.31141	+	1.67934i
$839$	0.540260	−	0.392522i	0.0186518	−	0.0135514i	−0.578420	−	0.815739i	$-0.696331\pi$
$839$	0.540260	−	0.392522i	0.0186518	−	0.0135514i	0.597072	+	0.802188i	$0.296331\pi$
$840$	−12.3347	−	18.6915i	−0.425586	−	0.644918i
$841$	12.3312	+	8.95912i	0.425213	+	0.308935i
$842$	−31.6339	−	97.3592i	−1.09018	−	3.35522i
$843$	7.62888			0.262753
$844$	14.3901	+	44.2882i	0.495328	+	1.52446i
$845$	15.6427	−	19.6101i	0.538126	−	0.674608i
$846$	−23.9308	+	73.6513i	−0.822756	+	2.53218i
$847$	−2.25705	+	6.94649i	−0.0775532	+	0.238684i
$848$	91.9756	−	66.8242i	3.15845	−	2.29475i
$849$	10.5380			0.361664
$850$	−30.4983	+	18.2111i	−1.04608	+	0.624636i
$851$	14.4611			0.495719
$852$	−18.3805	+	13.3542i	−0.629706	+	0.457508i
$853$	1.35047	−	4.15632i	0.0462392	−	0.142310i	−0.925271	−	0.379306i	$-0.876163\pi$
$853$	1.35047	−	4.15632i	0.0462392	−	0.142310i	0.971511	+	0.236996i	$0.0761629\pi$
$854$	−6.11360	+	18.8157i	−0.209203	+	0.643861i
$855$	1.63187	−	0.450138i	0.0558087	−	0.0153944i
$856$	6.74551	+	20.7606i	0.230557	+	0.709581i
$857$	20.3556			0.695335			0.347667	−	0.937618i	$-0.386974\pi$
$857$	20.3556			0.695335			0.347667	+	0.937618i	$0.386974\pi$
$858$	2.11245	+	6.50145i	0.0721178	+	0.221956i
$859$	29.5576	+	21.4749i	1.00849	+	0.732713i	0.963892	−	0.266292i	$-0.0857985\pi$
$859$	29.5576	+	21.4749i	1.00849	+	0.732713i	0.0446005	+	0.999005i	$0.485799\pi$
$860$	5.25259	−	1.44889i	0.179112	−	0.0494066i
$861$	−7.68477	+	5.58332i	−0.261896	+	0.190279i
$862$	70.8828	+	51.4994i	2.41428	+	1.75407i
$863$	−4.95094	−	3.59707i	−0.168532	−	0.122446i	0.500322	−	0.865839i	$-0.333215\pi$
$863$	−4.95094	−	3.59707i	−0.168532	−	0.122446i	−0.668854	+	0.743394i	$0.733215\pi$
$864$	−111.073	+	80.6991i	−3.77877	+	2.74544i
$865$	8.44461	+	3.17057i	0.287125	+	0.107803i
$866$	64.2789	+	46.7014i	2.18429	+	1.58698i
$867$	3.10161	+	9.54577i	0.105336	+	0.324191i
$868$	35.7020			1.21180
$869$	7.12011	+	21.9135i	0.241533	+	0.743363i
$870$	−12.1692	−	18.4408i	−0.412575	−	0.625201i
$871$	−1.24020	+	3.81693i	−0.0420225	+	0.129332i
$872$	−39.0878	+	120.300i	−1.32368	+	4.07387i
$873$	20.3072	−	14.7540i	0.687293	−	0.499348i
$874$	−5.55635			−0.187946
$875$	−11.0014	+	1.99203i	−0.371917	+	0.0673429i
$876$	67.4850			2.28011
$877$	−33.5844	+	24.4005i	−1.13406	+	0.823946i	−0.986281	−	0.165074i	$-0.947214\pi$
$877$	−33.5844	+	24.4005i	−1.13406	+	0.823946i	−0.147783	+	0.989020i	$0.547214\pi$
$878$	24.1083	−	74.1976i	0.813614	−	2.50405i
$879$	−3.91054	+	12.0354i	−0.131899	+	0.405944i
$880$	41.7996	+	63.3416i	1.40906	+	2.13525i
$881$	6.91214	+	21.2734i	0.232876	+	0.716718i	0.997396	+	0.0721184i	$0.0229759\pi$
$881$	6.91214	+	21.2734i	0.232876	+	0.716718i	−0.764520	+	0.644600i	$0.777024\pi$
$882$	−5.80930			−0.195609
$883$	−6.47433	−	19.9259i	−0.217879	−	0.670562i	−0.998937	−	0.0461031i	$-0.985320\pi$
$883$	−6.47433	−	19.9259i	−0.217879	−	0.670562i	0.781058	−	0.624458i	$-0.214680\pi$
$884$	−15.8625	−	11.5248i	−0.533513	−	0.387620i
$885$	19.5755	+	7.34972i	0.658024	+	0.247058i
$886$	−15.7749	+	11.4612i	−0.529970	+	0.385045i
$887$	−1.70599	−	1.23947i	−0.0572814	−	0.0416174i	0.558776	−	0.829319i	$-0.311271\pi$
$887$	−1.70599	−	1.23947i	−0.0572814	−	0.0416174i	−0.616058	+	0.787701i	$0.711271\pi$
$888$	21.3238	+	15.4926i	0.715579	+	0.519898i
$889$	5.96258	−	4.33207i	0.199979	−	0.145293i
$890$	−51.1505	+	14.1095i	−1.71457	+	0.472950i
$891$	−2.49728	−	1.81438i	−0.0836621	−	0.0607841i
$892$	−25.9175	−	79.7658i	−0.867782	−	2.67076i
$893$	−4.83916			−0.161936
$894$	2.33372	+	7.18244i	0.0780511	+	0.240217i
$895$	−37.0521	+	10.2205i	−1.23852	+	0.341635i
$896$	19.8527	−	61.1003i	0.663231	−	2.04122i
$897$	2.16745	−	6.67074i	0.0723692	−	0.222730i
$898$	19.6755	−	14.2951i	0.656581	−	0.477034i
$899$	22.9920			0.766825
$900$	13.3488	+	58.5550i	0.444959	+	1.95183i
$901$	16.4242			0.547170
$902$	43.0348	−	31.2666i	1.43290	−	1.04106i
$903$	−0.125026	+	0.384792i	−0.00416062	+	0.0128051i
$904$	−25.8219	+	79.4716i	−0.858823	+	2.64319i
$905$	−11.1287	+	13.9512i	−0.369930	+	0.463753i
$906$	−1.04555	−	3.21788i	−0.0347362	−	0.106907i
$907$	21.9287			0.728131			0.364066	−	0.931373i	$-0.381388\pi$
$907$	21.9287			0.728131			0.364066	+	0.931373i	$0.381388\pi$
$908$	−24.1533	−	74.3362i	−0.801556	−	2.46693i
$909$	−2.29135	−	1.66476i	−0.0759992	−	0.0552166i
$910$	−4.57939	−	6.93944i	−0.151805	−	0.230040i
$911$	−3.92195	+	2.84946i	−0.129940	+	0.0944069i	−0.650857	−	0.759201i	$-0.725590\pi$
$911$	−3.92195	+	2.84946i	−0.129940	+	0.0944069i	0.520917	+	0.853607i	$0.325590\pi$
$912$	−4.95804	−	3.60223i	−0.164177	−	0.119282i
$913$	5.29788	+	3.84914i	0.175334	+	0.127388i
$914$	82.3956	−	59.8639i	2.72541	−	1.98012i
$915$	−9.47063	+	11.8726i	−0.313089	+	0.392497i
$916$	13.3065	+	9.66774i	0.439659	+	0.319431i
$917$	−5.34430	−	16.4481i	−0.176484	−	0.543163i
$918$	−34.5504			−1.14033
$919$	0.713632	+	2.19633i	0.0235405	+	0.0724503i	0.962137	−	0.272568i	$-0.0878728\pi$
$919$	0.713632	+	2.19633i	0.0235405	+	0.0724503i	−0.938596	+	0.345018i	$0.887873\pi$
$920$	5.78973	−	128.545i	0.190882	−	4.23800i
$921$	−1.87705	+	5.77697i	−0.0618509	+	0.190358i
$922$	27.8338	−	85.6637i	0.916659	−	2.82119i
$923$	−4.45437	+	3.23629i	−0.146617	+	0.106524i
$924$	−10.5891			−0.348354
$925$	11.2980	−	6.74624i	0.371475	−	0.221815i
$926$	−4.26361			−0.140111
$927$	2.41406	−	1.75392i	0.0792883	−	0.0576063i
$928$	32.3577	−	99.5869i	1.06219	−	3.26910i
$929$	8.22957	−	25.3280i	0.270003	−	0.830985i	−0.720495	−	0.693460i	$-0.756085\pi$
$929$	8.22957	−	25.3280i	0.270003	−	0.830985i	0.990498	−	0.137525i	$-0.0439147\pi$
$930$	34.5674	+	12.9785i	1.13351	+	0.425582i
$931$	−0.112176	−	0.345244i	−0.00367644	−	0.0113149i
$932$	−62.5506			−2.04891
$933$	0.906689	+	2.79050i	0.0296837	+	0.0913570i
$934$	−54.7782	−	39.7987i	−1.79240	−	1.30225i
$935$	−0.493311	+	10.9526i	−0.0161330	+	0.358188i
$936$	−23.5852	+	17.1357i	−0.770907	+	0.560096i
$937$	1.88234	+	1.36760i	0.0614932	+	0.0446775i	0.618107	−	0.786094i	$-0.287900\pi$
$937$	1.88234	+	1.36760i	0.0614932	+	0.0446775i	−0.556614	+	0.830771i	$0.687900\pi$
$938$	−6.77590	−	4.92298i	−0.221241	−	0.160741i
$939$	−1.90366	+	1.38309i	−0.0621236	+	0.0451355i
$940$	7.72484	−	171.509i	0.251957	−	5.59400i
$941$	−7.31710	−	5.31618i	−0.238531	−	0.173303i	0.462098	−	0.886829i	$-0.347097\pi$
$941$	−7.31710	−	5.31618i	−0.238531	−	0.173303i	−0.700628	+	0.713526i	$0.747097\pi$
$942$	8.76601	+	26.9790i	0.285612	+	0.879023i
$943$	−54.5791			−1.77734
$944$	53.3437	+	164.175i	1.73619	+	5.34344i
$945$	−10.1807	−	3.82240i	−0.331179	−	0.124343i
$946$	0.700149	−	2.15484i	0.0227638	−	0.0700598i
$947$	−8.22989	+	25.3290i	−0.267435	+	0.823082i	0.723687	+	0.690128i	$0.242446\pi$
$947$	−8.22989	+	25.3290i	−0.267435	+	0.823082i	−0.991122	+	0.132953i	$0.957554\pi$
$948$	53.4052	−	38.8012i	1.73452	−	1.26020i
$949$	16.3545			0.530889
$950$	−4.34101	+	2.59210i	−0.140841	+	0.0840988i
$951$	7.15414			0.231989
$952$	21.6083	−	15.6994i	0.700330	−	0.508819i
$953$	−12.8468	+	39.5385i	−0.416150	+	1.28078i	0.495069	+	0.868854i	$0.335143\pi$
$953$	−12.8468	+	39.5385i	−0.416150	+	1.28078i	−0.911219	+	0.411923i	$0.864857\pi$
$954$	11.5608	−	35.5804i	0.374294	−	1.15196i
$955$	−0.605284	+	13.4387i	−0.0195865	+	0.434865i
$956$	27.7448	+	85.3897i	0.897331	+	2.76170i
$957$	−6.81932			−0.220437
$958$	5.47810	+	16.8599i	0.176990	+	0.544718i
$959$	−5.49228	−	3.99038i	−0.177355	−	0.128856i
$960$	57.7820	−	72.4370i	1.86491	−	2.33789i
$961$	−6.00612	+	4.36370i	−0.193746	+	0.140765i
$962$	7.91670	+	5.75182i	0.255245	+	0.185446i
$963$	3.51670	+	2.55504i	0.113324	+	0.0823349i
$964$	−11.1282	+	8.08510i	−0.358415	+	0.260404i
$965$	3.78890	+	5.74157i	0.121969	+	0.184828i
$966$	11.8420	+	8.60374i	0.381011	+	0.276821i
$967$	−5.55204	−	17.0874i	−0.178542	−	0.549495i	0.821236	−	0.570589i	$-0.193285\pi$
$967$	−5.55204	−	17.0874i	−0.178542	−	0.549495i	−0.999777	+	0.0210943i	$0.993285\pi$
$968$	−76.4924			−2.45856
$969$	−0.273593	−	0.842032i	−0.00878906	−	0.0270499i
$970$	−46.7511	+	58.6083i	−1.50109	+	1.88180i
$971$	−9.75815	+	30.0325i	−0.313154	+	0.963788i	0.663354	+	0.748306i	$0.269132\pi$
$971$	−9.75815	+	30.0325i	−0.313154	+	0.963788i	−0.976508	+	0.215483i	$0.930868\pi$
$972$	−28.7000	+	88.3295i	−0.920553	+	2.83317i
$973$	0.677130	−	0.491964i	0.0217078	−	0.0157716i
$974$	21.0044			0.673023
$975$	−1.41861	−	6.22279i	−0.0454317	−	0.199289i
$976$	−125.380			−4.01333
$977$	−28.7518	+	20.8894i	−0.919853	+	0.668312i	−0.943487	−	0.331408i	$-0.892476\pi$
$977$	−28.7518	+	20.8894i	−0.919853	+	0.668312i	0.0236346	+	0.999721i	$0.492476\pi$
$978$	1.57196	−	4.83800i	0.0502658	−	0.154702i
$979$	−5.06081	+	15.5756i	−0.161744	+	0.497797i
$980$	12.4152	−	3.42462i	0.396588	−	0.109396i
$981$	7.78371	+	23.9558i	0.248515	+	0.764849i
$982$	−57.2881			−1.82814
$983$	17.2032	+	52.9460i	0.548696	+	1.68871i	0.712035	+	0.702144i	$0.247774\pi$
$983$	17.2032	+	52.9460i	0.548696	+	1.68871i	−0.163339	+	0.986570i	$0.552226\pi$
$984$	−80.4804	−	58.4725i	−2.56562	−	1.86403i
$985$	30.3879	−	8.38226i	0.968238	−	0.267081i
$986$	21.3185	−	15.4888i	0.678919	−	0.493263i
$987$	10.3135	+	7.49319i	0.328282	+	0.238511i
$988$	−2.25781	−	1.64039i	−0.0718304	−	0.0521878i
$989$	−1.88074	+	1.36644i	−0.0598042	+	0.0434503i
$990$	23.3798	+	8.77805i	0.743058	+	0.278985i
$991$	1.89040	+	1.37346i	0.0600506	+	0.0436293i	0.617406	−	0.786645i	$-0.288184\pi$
$991$	1.89040	+	1.37346i	0.0600506	+	0.0436293i	−0.557355	+	0.830274i	$0.688184\pi$
$992$	54.0759	+	166.429i	1.71691	+	5.28412i
$993$	11.5147			0.365408
$994$	−3.55068	−	10.9279i	−0.112621	−	0.346611i
$995$	−12.7600	−	19.3361i	−0.404520	−	0.612995i
$996$	5.79761	−	17.8432i	0.183704	−	0.565383i
$997$	−7.12362	+	21.9243i	−0.225607	+	0.694348i	0.772622	+	0.634866i	$0.218945\pi$
$997$	−7.12362	+	21.9243i	−0.225607	+	0.694348i	−0.998229	+	0.0594819i	$0.981055\pi$
$998$	4.12019	−	2.99349i	0.130422	−	0.0947573i
$999$	12.7991			0.404945

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.h.c.36.1	✓	32
5.2	odd	4		875.2.n.d.449.1		64
5.3	odd	4		875.2.n.d.449.16		64
5.4	even	2		875.2.h.c.176.8		32
25.4	even	10		4375.2.a.i.1.1		16
25.9	even	10		875.2.h.c.701.8		32
25.12	odd	20		875.2.n.d.799.16		64
25.13	odd	20		875.2.n.d.799.1		64
25.16	even	5	inner	175.2.h.c.141.1	yes	32
25.21	even	5		4375.2.a.l.1.16		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.h.c.36.1	✓	32	1.1	even	1	trivial
175.2.h.c.141.1	yes	32	25.16	even	5	inner
875.2.h.c.176.8		32	5.4	even	2
875.2.h.c.701.8		32	25.9	even	10
875.2.n.d.449.1		64	5.2	odd	4
875.2.n.d.449.16		64	5.3	odd	4
875.2.n.d.799.1		64	25.13	odd	20
875.2.n.d.799.16		64	25.12	odd	20
4375.2.a.i.1.1		16	25.4	even	10
4375.2.a.l.1.16		16	25.21	even	5

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.25360 + 1.63734i) q^{2} +(-0.295516 + 0.909504i) q^{3} +(1.77981 - 5.47769i) q^{4} +(1.23160 + 1.86632i) q^{5} +(-0.823190 - 2.53352i) q^{6} +1.00000 q^{7} +(3.23625 + 9.96014i) q^{8} +(1.68718 + 1.22581i) q^{9} +O(q^{10})\)	\(q+(-2.25360 + 1.63734i) q^{2} +(-0.295516 + 0.909504i) q^{3} +(1.77981 - 5.47769i) q^{4} +(1.23160 + 1.86632i) q^{5} +(-0.823190 - 2.53352i) q^{6} +1.00000 q^{7} +(3.23625 + 9.96014i) q^{8} +(1.68718 + 1.22581i) q^{9} +(-5.83133 - 2.18940i) q^{10} +(-1.55534 + 1.13002i) q^{11} +(4.45602 + 3.23749i) q^{12} +(1.07988 + 0.784580i) q^{13} +(-2.25360 + 1.63734i) q^{14} +(-2.06139 + 0.568617i) q^{15} +(-14.2821 - 10.3766i) q^{16} +(-0.788110 - 2.42555i) q^{17} -5.80930 q^{18} +(-0.112176 - 0.345244i) q^{19} +(12.4152 - 3.42462i) q^{20} +(-0.295516 + 0.909504i) q^{21} +(1.65489 - 5.09323i) q^{22} +(-4.44538 + 3.22976i) q^{23} -10.0151 q^{24} +(-1.96632 + 4.59713i) q^{25} -3.71824 q^{26} +(-3.93448 + 2.85857i) q^{27} +(1.77981 - 5.47769i) q^{28} +(1.14619 - 3.52762i) q^{29} +(3.71452 - 4.65662i) q^{30} +(1.91551 + 5.89532i) q^{31} +28.2306 q^{32} +(-0.568131 - 1.74853i) q^{33} +(5.74753 + 4.17582i) q^{34} +(1.23160 + 1.86632i) q^{35} +(9.71748 - 7.06016i) q^{36} +(-2.12915 - 1.54692i) q^{37} +(0.818081 + 0.594371i) q^{38} +(-1.03270 + 0.750301i) q^{39} +(-14.6031 + 18.3068i) q^{40} +(8.03587 + 5.83840i) q^{41} +(-0.823190 - 2.53352i) q^{42} +0.423079 q^{43} +(3.42170 + 10.5309i) q^{44} +(-0.209823 + 4.65854i) q^{45} +(4.72991 - 14.5572i) q^{46} +(4.11939 - 12.6782i) q^{47} +(13.6581 - 9.92319i) q^{48} +1.00000 q^{49} +(-3.09574 - 13.5796i) q^{50} +2.43895 q^{51} +(6.21967 - 4.51885i) q^{52} +(-1.99004 + 6.12473i) q^{53} +(4.18631 - 12.8841i) q^{54} +(-4.02454 - 1.51103i) q^{55} +(3.23625 + 9.96014i) q^{56} +0.347150 q^{57} +(3.19284 + 9.82654i) q^{58} +(-7.91087 - 5.74758i) q^{59} +(-0.554163 + 12.3037i) q^{60} +(5.74583 - 4.17459i) q^{61} +(-13.9694 - 10.1494i) q^{62} +(1.68718 + 1.22581i) q^{63} +(-35.0564 + 25.4699i) q^{64} +(-0.134297 + 2.98170i) q^{65} +(4.14327 + 3.01026i) q^{66} +(0.929121 + 2.85954i) q^{67} -14.6891 q^{68} +(-1.62380 - 4.99753i) q^{69} +(-5.83133 - 2.18940i) q^{70} +(-1.27465 + 3.92298i) q^{71} +(-6.74910 + 20.7716i) q^{72} +(9.91233 - 7.20173i) q^{73} +7.33108 q^{74} +(-3.60003 - 3.14690i) q^{75} -2.09079 q^{76} +(-1.55534 + 1.13002i) q^{77} +(1.09880 - 3.38175i) q^{78} +(3.70356 - 11.3984i) q^{79} +(1.77616 - 39.4348i) q^{80} +(0.496163 + 1.52703i) q^{81} -27.6691 q^{82} +(-1.05259 - 3.23954i) q^{83} +(4.45602 + 3.23749i) q^{84} +(3.55623 - 4.45818i) q^{85} +(-0.953450 + 0.692722i) q^{86} +(2.86966 + 2.08493i) q^{87} +(-16.2886 - 11.8344i) q^{88} +(6.89171 - 5.00712i) q^{89} +(-7.15474 - 10.8420i) q^{90} +(1.07988 + 0.784580i) q^{91} +(9.77968 + 30.0988i) q^{92} -5.92788 q^{93} +(11.4750 + 35.3163i) q^{94} +(0.506180 - 0.634560i) q^{95} +(-8.34260 + 25.6759i) q^{96} +(3.71937 - 11.4470i) q^{97} +(-2.25360 + 1.63734i) q^{98} -4.00934 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 3 q^{2} - 4 q^{3} - 9 q^{4} + q^{5} + 15 q^{6} + 32 q^{7} - 9 q^{8} - 6 q^{9}+O(q^{10}) \) 32 * q - 3 * q^2 - 4 * q^3 - 9 * q^4 + q^5 + 15 * q^6 + 32 * q^7 - 9 * q^8 - 6 * q^9	\( 32 q - 3 q^{2} - 4 q^{3} - 9 q^{4} + q^{5} + 15 q^{6} + 32 q^{7} - 9 q^{8} - 6 q^{9} - 15 q^{10} + 2 q^{11} - 2 q^{12} - 16 q^{13} - 3 q^{14} - 9 q^{15} - 15 q^{16} - 18 q^{17} + 26 q^{18} - 8 q^{19} - 12 q^{20} - 4 q^{21} + 9 q^{22} - 11 q^{23} - 46 q^{24} + 19 q^{25} - 34 q^{26} - 7 q^{27} - 9 q^{28} + 13 q^{29} - 10 q^{30} + 5 q^{31} + 64 q^{32} - 25 q^{33} + 25 q^{34} + q^{35} + 64 q^{36} + 6 q^{37} - 15 q^{38} - 18 q^{39} + 20 q^{40} - 26 q^{41} + 15 q^{42} - 6 q^{43} - 37 q^{44} - 37 q^{45} - 12 q^{46} + 15 q^{48} + 32 q^{49} + 20 q^{50} - 10 q^{51} - 38 q^{52} - 27 q^{53} + 108 q^{54} + 42 q^{55} - 9 q^{56} + 2 q^{57} + 49 q^{58} + 13 q^{59} + 18 q^{60} + 40 q^{61} - 14 q^{62} - 6 q^{63} + q^{64} + 40 q^{65} - 37 q^{66} - 15 q^{67} + 4 q^{68} - 45 q^{69} - 15 q^{70} - 24 q^{71} - 75 q^{72} - 38 q^{73} - 40 q^{74} - 56 q^{75} - 70 q^{76} + 2 q^{77} + 93 q^{78} + 66 q^{79} - 11 q^{80} - 7 q^{81} - 32 q^{82} - 52 q^{83} - 2 q^{84} + 13 q^{85} + 60 q^{86} + 54 q^{87} - 66 q^{88} + 28 q^{89} - 135 q^{90} - 16 q^{91} - 44 q^{92} + 56 q^{93} - 4 q^{94} - 23 q^{95} - 34 q^{96} - 44 q^{97} - 3 q^{98} - 66 q^{99}+O(q^{100}) \) 32 * q - 3 * q^2 - 4 * q^3 - 9 * q^4 + q^5 + 15 * q^6 + 32 * q^7 - 9 * q^8 - 6 * q^9 - 15 * q^10 + 2 * q^11 - 2 * q^12 - 16 * q^13 - 3 * q^14 - 9 * q^15 - 15 * q^16 - 18 * q^17 + 26 * q^18 - 8 * q^19 - 12 * q^20 - 4 * q^21 + 9 * q^22 - 11 * q^23 - 46 * q^24 + 19 * q^25 - 34 * q^26 - 7 * q^27 - 9 * q^28 + 13 * q^29 - 10 * q^30 + 5 * q^31 + 64 * q^32 - 25 * q^33 + 25 * q^34 + q^35 + 64 * q^36 + 6 * q^37 - 15 * q^38 - 18 * q^39 + 20 * q^40 - 26 * q^41 + 15 * q^42 - 6 * q^43 - 37 * q^44 - 37 * q^45 - 12 * q^46 + 15 * q^48 + 32 * q^49 + 20 * q^50 - 10 * q^51 - 38 * q^52 - 27 * q^53 + 108 * q^54 + 42 * q^55 - 9 * q^56 + 2 * q^57 + 49 * q^58 + 13 * q^59 + 18 * q^60 + 40 * q^61 - 14 * q^62 - 6 * q^63 + q^64 + 40 * q^65 - 37 * q^66 - 15 * q^67 + 4 * q^68 - 45 * q^69 - 15 * q^70 - 24 * q^71 - 75 * q^72 - 38 * q^73 - 40 * q^74 - 56 * q^75 - 70 * q^76 + 2 * q^77 + 93 * q^78 + 66 * q^79 - 11 * q^80 - 7 * q^81 - 32 * q^82 - 52 * q^83 - 2 * q^84 + 13 * q^85 + 60 * q^86 + 54 * q^87 - 66 * q^88 + 28 * q^89 - 135 * q^90 - 16 * q^91 - 44 * q^92 + 56 * q^93 - 4 * q^94 - 23 * q^95 - 34 * q^96 - 44 * q^97 - 3 * q^98 - 66 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more