LMFDB - Embedded newform 525.2.bv.a.52.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(52,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("525.52");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bv (of order $60$, degree $16$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$640$
Relative dimension:	$40$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			52.10
Character	$\chi$	$=$	525.52
Dual form			525.2.bv.a.313.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.611789 - 1.59376i) q^{2} +(-0.0523360 + 0.998630i) q^{3} +(-0.679511 + 0.611834i) q^{4} +(-1.29445 - 1.82330i) q^{5} +(1.62360 - 0.527539i) q^{6} +(-2.56289 - 0.656955i) q^{7} +(-1.65133 - 0.841396i) q^{8} +(-0.994522 - 0.104528i) q^{9} +O(q^{10})$	\(q+(-0.611789 - 1.59376i) q^{2} +(-0.0523360 + 0.998630i) q^{3} +(-0.679511 + 0.611834i) q^{4} +(-1.29445 - 1.82330i) q^{5} +(1.62360 - 0.527539i) q^{6} +(-2.56289 - 0.656955i) q^{7} +(-1.65133 - 0.841396i) q^{8} +(-0.994522 - 0.104528i) q^{9} +(-2.11398 + 3.17852i) q^{10} +(0.404222 + 3.84592i) q^{11} +(-0.575433 - 0.710600i) q^{12} +(0.0989636 + 0.624832i) q^{13} +(0.520917 + 4.48656i) q^{14} +(1.88854 - 1.19725i) q^{15} +(-0.521876 + 4.96532i) q^{16} +(4.15179 - 2.69621i) q^{17} +(0.441844 + 1.64898i) q^{18} +(-4.42613 + 4.91572i) q^{19} +(1.99515 + 0.446963i) q^{20} +(0.790186 - 2.52500i) q^{21} +(5.88219 - 2.99712i) q^{22} +(2.14402 - 0.823013i) q^{23} +(0.926667 - 1.60503i) q^{24} +(-1.64882 + 4.72032i) q^{25} +(0.935290 - 0.539990i) q^{26} +(0.156434 - 0.987688i) q^{27} +(2.14346 - 1.12166i) q^{28} +(-8.17116 - 2.65497i) q^{29} +(-3.06352 - 2.27743i) q^{30} +(-1.65314 + 7.77743i) q^{31} +(4.65246 - 1.24662i) q^{32} +(-3.86180 + 0.202388i) q^{33} +(-6.83714 - 4.96747i) q^{34} +(2.11970 + 5.52330i) q^{35} +(0.739742 - 0.537454i) q^{36} +(-7.15837 + 5.79673i) q^{37} +(10.5424 + 4.04683i) q^{38} +(-0.629155 + 0.0661268i) q^{39} +(0.603447 + 4.10001i) q^{40} +(2.15095 - 2.96053i) q^{41} +(-4.50768 + 0.285395i) q^{42} +(0.180290 - 0.180290i) q^{43} +(-2.62774 - 2.36602i) q^{44} +(1.09677 + 1.94861i) q^{45} +(-2.62338 - 2.91356i) q^{46} +(2.48721 - 3.82996i) q^{47} +(-4.93120 - 0.781025i) q^{48} +(6.13682 + 3.36741i) q^{49} +(8.53180 - 0.260011i) q^{50} +(2.47522 + 4.28721i) q^{51} +(-0.449540 - 0.364031i) q^{52} +(-10.8752 - 0.569943i) q^{53} +(-1.66985 + 0.354937i) q^{54} +(6.48900 - 5.71535i) q^{55} +(3.67943 + 3.24126i) q^{56} +(-4.67733 - 4.67733i) q^{57} +(0.767626 + 14.6472i) q^{58} +(-9.59811 + 4.27336i) q^{59} +(-0.550768 + 1.96902i) q^{60} +(5.33592 - 11.9847i) q^{61} +(13.4068 - 2.12342i) q^{62} +(2.48018 + 0.921251i) q^{63} +(1.03608 + 1.42605i) q^{64} +(1.01115 - 0.989251i) q^{65} +(2.68517 + 6.03098i) q^{66} +(-4.25501 - 6.55214i) q^{67} +(-1.17156 + 4.37231i) q^{68} +(0.709676 + 2.18416i) q^{69} +(7.50603 - 6.75740i) q^{70} +(-0.528338 + 1.62606i) q^{71} +(1.55434 + 1.00940i) q^{72} +(0.295639 - 0.365083i) q^{73} +(13.6180 + 7.86238i) q^{74} +(-4.62756 - 1.89360i) q^{75} -6.04834i q^{76} +(1.49062 - 10.1222i) q^{77} +(0.490301 + 0.962269i) q^{78} +(-0.0170177 - 0.0800622i) q^{79} +(9.72878 - 5.47580i) q^{80} +(0.978148 + 0.207912i) q^{81} +(-6.03432 - 1.61689i) q^{82} +(2.68822 - 5.27592i) q^{83} +(1.00794 + 2.19922i) q^{84} +(-10.2903 - 4.07985i) q^{85} +(-0.397639 - 0.177040i) q^{86} +(3.07898 - 8.02101i) q^{87} +(2.56843 - 6.69100i) q^{88} +(-3.30376 - 1.47093i) q^{89} +(2.43464 - 2.94013i) q^{90} +(0.156853 - 1.66639i) q^{91} +(-0.953339 + 1.87103i) q^{92} +(-7.68025 - 2.05792i) q^{93} +(-7.62571 - 1.62089i) q^{94} +(14.6922 + 1.70702i) q^{95} +(1.00142 + 4.71133i) q^{96} +(4.27250 + 8.38526i) q^{97} +(1.61242 - 11.8408i) q^{98} -3.86710i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640 q + 12 q^{5} - 8 q^{7} + 24 q^{8}+O(q^{10}) $ 640 * q + 12 * q^5 - 8 * q^7 + 24 * q^8	$ 640 q + 12 q^{5} - 8 q^{7} + 24 q^{8} + 12 q^{10} + 8 q^{15} - 80 q^{16} - 72 q^{22} + 48 q^{23} - 12 q^{25} - 36 q^{28} - 80 q^{29} + 32 q^{30} - 24 q^{32} + 36 q^{33} - 64 q^{35} + 160 q^{36} - 4 q^{37} - 192 q^{38} - 12 q^{40} - 16 q^{42} + 120 q^{43} + 60 q^{47} + 288 q^{50} - 432 q^{52} - 136 q^{53} - 16 q^{57} - 4 q^{58} - 240 q^{59} - 20 q^{60} - 4 q^{63} + 120 q^{64} + 4 q^{65} - 8 q^{67} - 132 q^{68} + 76 q^{70} - 12 q^{72} - 36 q^{73} - 48 q^{75} - 60 q^{77} - 80 q^{78} + 12 q^{80} - 80 q^{81} - 252 q^{82} - 160 q^{84} + 72 q^{85} + 24 q^{87} + 152 q^{88} + 56 q^{92} - 96 q^{93} + 172 q^{95} - 488 q^{98}+O(q^{100}) $ 640 * q + 12 * q^5 - 8 * q^7 + 24 * q^8 + 12 * q^10 + 8 * q^15 - 80 * q^16 - 72 * q^22 + 48 * q^23 - 12 * q^25 - 36 * q^28 - 80 * q^29 + 32 * q^30 - 24 * q^32 + 36 * q^33 - 64 * q^35 + 160 * q^36 - 4 * q^37 - 192 * q^38 - 12 * q^40 - 16 * q^42 + 120 * q^43 + 60 * q^47 + 288 * q^50 - 432 * q^52 - 136 * q^53 - 16 * q^57 - 4 * q^58 - 240 * q^59 - 20 * q^60 - 4 * q^63 + 120 * q^64 + 4 * q^65 - 8 * q^67 - 132 * q^68 + 76 * q^70 - 12 * q^72 - 36 * q^73 - 48 * q^75 - 60 * q^77 - 80 * q^78 + 12 * q^80 - 80 * q^81 - 252 * q^82 - 160 * q^84 + 72 * q^85 + 24 * q^87 + 152 * q^88 + 56 * q^92 - 96 * q^93 + 172 * q^95 - 488 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{20}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.611789	−	1.59376i	−0.432600	−	1.12696i	−0.960653	−	0.277751i	$-0.910411\pi$
$2$	−0.611789	−	1.59376i	−0.432600	−	1.12696i	0.528053	−	0.849211i	$-0.322922\pi$
$3$	−0.0523360	+	0.998630i	−0.0302162	+	0.576559i
$3$	−0.0523360	+	0.998630i	−0.0302162	+	0.576559i
$4$	−0.679511	+	0.611834i	−0.339755	+	0.305917i
$5$	−1.29445	−	1.82330i	−0.578894	−	0.815403i
$5$	−1.29445	−	1.82330i	−0.578894	−	0.815403i
$6$	1.62360	−	0.527539i	0.662832	−	0.215367i
$7$	−2.56289	−	0.656955i	−0.968682	−	0.248306i
$7$	−2.56289	−	0.656955i	−0.968682	−	0.248306i
$8$	−1.65133	−	0.841396i	−0.583834	−	0.297478i
$9$	−0.994522	−	0.104528i	−0.331507	−	0.0348428i
$10$	−2.11398	+	3.17852i	−0.668498	+	1.00513i
$11$	0.404222	+	3.84592i	0.121878	+	1.15959i	0.868969	+	0.494866i	$0.164783\pi$
$11$	0.404222	+	3.84592i	0.121878	+	1.15959i	−0.747092	+	0.664721i	$0.768550\pi$
$12$	−0.575433	−	0.710600i	−0.166113	−	0.205133i
$13$	0.0989636	+	0.624832i	0.0274476	+	0.173297i	0.997604	−	0.0691827i	$-0.0220392\pi$
$13$	0.0989636	+	0.624832i	0.0274476	+	0.173297i	−0.970156	+	0.242480i	$0.922039\pi$
$14$	0.520917	+	4.48656i	0.139221	+	1.19908i
$15$	1.88854	−	1.19725i	0.487620	−	0.309128i
$16$	−0.521876	+	4.96532i	−0.130469	+	1.24133i
$17$	4.15179	−	2.69621i	1.00696	−	0.653926i	0.0679024	−	0.997692i	$-0.478369\pi$
$17$	4.15179	−	2.69621i	1.00696	−	0.653926i	0.939055	+	0.343766i	$0.111703\pi$
$18$	0.441844	+	1.64898i	0.104144	+	0.388669i
$19$	−4.42613	+	4.91572i	−1.01542	+	1.12774i	−0.0236526	+	0.999720i	$0.507530\pi$
$19$	−4.42613	+	4.91572i	−1.01542	+	1.12774i	−0.991771	+	0.128022i	$0.959137\pi$
$20$	1.99515	+	0.446963i	0.446128	+	0.0999439i
$21$	0.790186	−	2.52500i	0.172433	−	0.550999i
$22$	5.88219	−	2.99712i	1.25409	−	0.638989i
$23$	2.14402	−	0.823013i	0.447060	−	0.171610i	−0.124414	−	0.992230i	$-0.539705\pi$
$23$	2.14402	−	0.823013i	0.447060	−	0.171610i	0.571474	+	0.820620i	$0.306372\pi$
$24$	0.926667	−	1.60503i	0.189155	−	0.327626i
$25$	−1.64882	+	4.72032i	−0.329763	+	0.944064i
$26$	0.935290	−	0.539990i	0.183425	−	0.105901i
$27$	0.156434	−	0.987688i	0.0301058	−	0.190081i
$28$	2.14346	−	1.12166i	0.405076	−	0.211973i
$29$	−8.17116	−	2.65497i	−1.51735	−	0.493016i	−0.572325	−	0.820027i	$-0.693959\pi$
$29$	−8.17116	−	2.65497i	−1.51735	−	0.493016i	−0.945021	+	0.327011i	$0.893959\pi$
$30$	−3.06352	−	2.27743i	−0.559320	−	0.415800i
$31$	−1.65314	+	7.77743i	−0.296913	+	1.39687i	0.536352	+	0.843994i	$0.319802\pi$
$31$	−1.65314	+	7.77743i	−0.296913	+	1.39687i	−0.833266	+	0.552873i	$0.813531\pi$
$32$	4.65246	−	1.24662i	0.822447	−	0.220374i
$33$	−3.86180	+	0.202388i	−0.672253	+	0.0352313i
$34$	−6.83714	−	4.96747i	−1.17256	−	0.851915i
$35$	2.11970	+	5.52330i	0.358295	+	0.933608i
$36$	0.739742	−	0.537454i	0.123290	−	0.0895757i
$37$	−7.15837	+	5.79673i	−1.17683	+	0.952977i	−0.999514	−	0.0311778i	$-0.990074\pi$
$37$	−7.15837	+	5.79673i	−1.17683	+	0.952977i	−0.177314	+	0.984154i	$0.556741\pi$
$38$	10.5424	+	4.04683i	1.71020	+	0.656482i
$39$	−0.629155	+	0.0661268i	−0.100745	+	0.0105888i
$40$	0.603447	+	4.10001i	0.0954134	+	0.648268i
$41$	2.15095	−	2.96053i	0.335922	−	0.462357i	−0.607323	−	0.794455i	$-0.707756\pi$
$41$	2.15095	−	2.96053i	0.335922	−	0.462357i	0.943245	+	0.332098i	$0.107756\pi$
$42$	−4.50768	+	0.285395i	−0.695550	+	0.0440373i
$43$	0.180290	−	0.180290i	0.0274940	−	0.0274940i	−0.693226	−	0.720720i	$-0.743811\pi$
$43$	0.180290	−	0.180290i	0.0274940	−	0.0274940i	0.720720	+	0.693226i	$0.243811\pi$
$44$	−2.62774	−	2.36602i	−0.396146	−	0.356692i
$45$	1.09677	+	1.94861i	0.163497	+	0.290482i
$46$	−2.62338	−	2.91356i	−0.386796	−	0.429581i
$47$	2.48721	−	3.82996i	0.362797	−	0.558658i	−0.609388	−	0.792872i	$-0.708585\pi$
$47$	2.48721	−	3.82996i	0.362797	−	0.558658i	0.972185	+	0.234214i	$0.0752517\pi$
$48$	−4.93120	−	0.781025i	−0.711757	−	0.112731i
$49$	6.13682	+	3.36741i	0.876689	+	0.481058i
$50$	8.53180	−	0.260011i	1.20658	−	0.0367712i
$51$	2.47522	+	4.28721i	0.346601	+	0.600330i
$52$	−0.449540	−	0.364031i	−0.0623400	−	0.0504820i
$53$	−10.8752	−	0.569943i	−1.49382	−	0.0782877i	−0.712170	−	0.702007i	$-0.752288\pi$
$53$	−10.8752	−	0.569943i	−1.49382	−	0.0782877i	−0.781649	+	0.623719i	$0.785621\pi$
$54$	−1.66985	+	0.354937i	−0.227238	+	0.0483008i
$55$	6.48900	−	5.71535i	0.874977	−	0.770657i
$56$	3.67943	+	3.24126i	0.491684	+	0.433131i
$57$	−4.67733	−	4.67733i	−0.619528	−	0.619528i
$58$	0.767626	+	14.6472i	0.100794	+	1.92327i
$59$	−9.59811	+	4.27336i	−1.24957	+	0.556343i	−0.921525	−	0.388319i	$-0.873056\pi$
$59$	−9.59811	+	4.27336i	−1.24957	+	0.556343i	−0.328043	+	0.944663i	$0.606389\pi$
$60$	−0.550768	+	1.96902i	−0.0711039	+	0.254199i
$61$	5.33592	−	11.9847i	0.683194	−	1.53448i	−0.154295	−	0.988025i	$-0.549311\pi$
$61$	5.33592	−	11.9847i	0.683194	−	1.53448i	0.837489	−	0.546454i	$-0.184023\pi$
$62$	13.4068	−	2.12342i	1.70266	−	0.269675i
$63$	2.48018	+	0.921251i	0.312473	+	0.116067i
$64$	1.03608	+	1.42605i	0.129511	+	0.178256i
$65$	1.01115	−	0.989251i	0.125418	−	0.122702i
$66$	2.68517	+	6.03098i	0.330521	+	0.742363i
$67$	−4.25501	−	6.55214i	−0.519832	−	0.800472i	0.477091	−	0.878854i	$-0.341691\pi$
$67$	−4.25501	−	6.55214i	−0.519832	−	0.800472i	−0.996923	+	0.0783822i	$0.975025\pi$
$68$	−1.17156	+	4.37231i	−0.142072	+	0.530221i
$69$	0.709676	+	2.18416i	0.0854349	+	0.262942i
$70$	7.50603	−	6.75740i	0.897143	−	0.807664i
$71$	−0.528338	+	1.62606i	−0.0627021	+	0.192977i	−0.977500	−	0.210934i	$-0.932350\pi$
$71$	−0.528338	+	1.62606i	−0.0627021	+	0.192977i	0.914798	+	0.403911i	$0.132350\pi$
$72$	1.55434	+	1.00940i	0.183180	+	0.118959i
$73$	0.295639	−	0.365083i	0.0346019	−	0.0427298i	−0.759551	−	0.650447i	$-0.774581\pi$
$73$	0.295639	−	0.365083i	0.0346019	−	0.0427298i	0.794153	+	0.607718i	$0.207915\pi$
$74$	13.6180	+	7.86238i	1.58306	+	0.913983i
$75$	−4.62756	−	1.89360i	−0.534344	−	0.218654i
$76$		−	6.04834i		−	0.693792i
$77$	1.49062	−	10.1222i	0.169871	−	1.15353i
$78$	0.490301	+	0.962269i	0.0555156	+	0.108956i
$79$	−0.0170177	−	0.0800622i	−0.00191465	−	0.00900770i	0.977180	−	0.212413i	$-0.0681323\pi$
$79$	−0.0170177	−	0.0800622i	−0.00191465	−	0.00900770i	−0.979095	+	0.203406i	$0.934799\pi$
$80$	9.72878	−	5.47580i	1.08771	−	0.612213i
$81$	0.978148	+	0.207912i	0.108683	+	0.0231013i
$82$	−6.03432	−	1.61689i	−0.666379	−	0.178556i
$83$	2.68822	−	5.27592i	0.295070	−	0.579108i	−0.695110	−	0.718903i	$-0.744644\pi$
$83$	2.68822	−	5.27592i	0.295070	−	0.579108i	0.990180	+	0.139795i	$0.0446445\pi$
$84$	1.00794	+	2.19922i	0.109975	+	0.239955i
$85$	−10.2903	−	4.07985i	−1.11613	−	0.442522i
$86$	−0.397639	−	0.177040i	−0.0428786	−	0.0190908i
$87$	3.07898	−	8.02101i	0.330101	−	0.859942i
$88$	2.56843	−	6.69100i	0.273796	−	0.713262i
$89$	−3.30376	−	1.47093i	−0.350198	−	0.155918i	0.224096	−	0.974567i	$-0.428057\pi$
$89$	−3.30376	−	1.47093i	−0.350198	−	0.155918i	−0.574295	+	0.818649i	$0.694724\pi$
$90$	2.43464	−	2.94013i	0.256634	−	0.309917i
$91$	0.156853	−	1.66639i	0.0164427	−	0.174685i
$92$	−0.953339	+	1.87103i	−0.0993924	+	0.195069i
$93$	−7.68025	−	2.05792i	−0.796405	−	0.213396i
$94$	−7.62571	−	1.62089i	−0.786532	−	0.167183i
$95$	14.6922	+	1.70702i	1.50739	+	0.175136i
$96$	1.00142	+	4.71133i	0.102207	+	0.480848i
$97$	4.27250	+	8.38526i	0.433807	+	0.851394i	0.999639	+	0.0268732i	$0.00855504\pi$
$97$	4.27250	+	8.38526i	0.433807	+	0.851394i	−0.565832	+	0.824520i	$0.691445\pi$
$98$	1.61242	−	11.8408i	0.162879	−	1.19610i
$99$		−	3.86710i		−	0.388658i
$100$	−1.76766	−	4.21631i	−0.176766	−	0.421631i
$101$	3.11176	+	1.79658i	0.309632	+	0.178766i	0.646762	−	0.762692i	$-0.276123\pi$
$101$	3.11176	+	1.79658i	0.309632	+	0.178766i	−0.337130	+	0.941458i	$0.609456\pi$
$102$	5.31849	−	6.56779i	0.526609	−	0.650308i
$103$	−6.11374	−	3.97031i	−0.602405	−	0.391206i	0.207100	−	0.978320i	$-0.433598\pi$
$103$	−6.11374	−	3.97031i	−0.602405	−	0.391206i	−0.809505	+	0.587113i	$0.800264\pi$
$104$	0.362309	−	1.11507i	0.0355273	−	0.109342i
$105$	−5.62667	+	1.82773i	−0.549107	+	0.178368i
$106$	5.74495	+	17.6811i	0.557999	+	1.71734i
$107$	−4.90192	+	18.2942i	−0.473886	+	1.76857i	0.151716	+	0.988424i	$0.451520\pi$
$107$	−4.90192	+	18.2942i	−0.473886	+	1.76857i	−0.625602	+	0.780143i	$0.715146\pi$
$108$	0.498003	+	0.766857i	0.0479203	+	0.0737908i
$109$	−3.22153	−	7.23568i	−0.308567	−	0.693052i	0.690989	−	0.722865i	$-0.257175\pi$
$109$	−3.22153	−	7.23568i	−0.308567	−	0.693052i	−0.999555	+	0.0298133i	$0.990509\pi$
$110$	−13.0788	−	6.84535i	−1.24702	−	0.652679i
$111$	−5.41415	−	7.45193i	−0.513888	−	0.707306i
$112$	4.59950	−	12.3827i	0.434612	−	1.17006i
$113$	−5.11544	+	0.810206i	−0.481220	+	0.0762178i	−0.392332	−	0.919824i	$-0.628331\pi$
$113$	−5.11544	+	0.810206i	−0.481220	+	0.0762178i	−0.0888885	+	0.996042i	$0.528331\pi$
$114$	−4.59303	+	10.3161i	−0.430176	+	0.966192i
$115$	−4.27592	−	2.84384i	−0.398731	−	0.265190i
$116$	7.17679	−	3.19531i	0.666348	−	0.296677i
$117$	−0.0331088	−	0.631753i	−0.00306091	−	0.0584056i
$118$	12.6827	+	12.6827i	1.16754	+	1.16754i
$119$	−12.4119	+	4.18254i	−1.13780	+	0.383413i
$120$	−4.12597	+	0.388042i	−0.376648	+	0.0354233i
$121$	−3.86805	+	0.822179i	−0.351641	+	0.0747436i
$122$	−22.3652	−	1.17211i	−2.02485	−	0.106118i
$123$	2.84390	+	2.30295i	0.256426	+	0.207650i
$124$	−3.63517	−	6.29630i	−0.326448	−	0.565424i
$125$	10.7408	−	3.10392i	0.960690	−	0.277623i
$126$	−0.0490899	−	4.51644i	−0.00437328	−	0.402356i
$127$	−18.1122	−	2.86869i	−1.60720	−	0.254555i	−0.712648	−	0.701522i	$-0.752504\pi$
$127$	−18.1122	−	2.86869i	−1.60720	−	0.254555i	−0.894550	+	0.446967i	$0.852504\pi$
$128$	6.88552	−	10.6028i	0.608599	−	0.937161i
$129$	0.170607	+	0.189479i	0.0150211	+	0.0166827i
$130$	−2.19524	−	1.00632i	−0.192536	−	0.0882603i
$131$	−6.30349	−	5.67568i	−0.550738	−	0.495887i	0.346129	−	0.938187i	$-0.387496\pi$
$131$	−6.30349	−	5.67568i	−0.550738	−	0.495887i	−0.896867	+	0.442300i	$0.854163\pi$
$132$	2.50031	−	2.50031i	0.217624	−	0.217624i
$133$	14.5731	−	9.69068i	1.26365	−	0.840288i
$134$	−7.83941	+	10.7900i	−0.677222	+	0.932115i
$135$	−2.00334	+	0.993283i	−0.172420	+	0.0854882i
$136$	−9.12457	+	0.959031i	−0.782425	+	0.0822362i
$137$	−8.35946	−	3.20890i	−0.714197	−	0.274155i	−0.0259831	−	0.999662i	$-0.508272\pi$
$137$	−8.35946	−	3.20890i	−0.714197	−	0.274155i	−0.688214	+	0.725508i	$0.741605\pi$
$138$	3.04686	−	2.46730i	0.259366	−	0.210030i
$139$	13.6127	−	9.89020i	1.15461	−	0.838876i	0.165526	−	0.986205i	$-0.447068\pi$
$139$	13.6127	−	9.89020i	1.15461	−	0.838876i	0.989087	+	0.147329i	$0.0470677\pi$
$140$	−4.81971	−	2.45624i	−0.407339	−	0.207590i
$141$	3.69455	+	2.68424i	0.311137	+	0.226054i
$142$	2.91478	−	0.152757i	0.244603	−	0.0128191i
$143$	−2.36305	+	0.633177i	−0.197608	+	0.0529489i
$144$	1.03803	−	4.88357i	0.0865028	−	0.406964i
$145$	5.73633	+	18.3352i	0.476376	+	1.52265i
$146$	−0.762725	−	0.247824i	−0.0631236	−	0.0205101i
$147$	−3.68397	+	5.95217i	−0.303849	+	0.490927i
$148$	1.31755	−	8.31867i	0.108302	−	0.683791i
$149$	−2.82688	+	1.63210i	−0.231587	+	0.133707i	−0.611304	−	0.791396i	$-0.709355\pi$
$149$	−2.82688	+	1.63210i	−0.231587	+	0.133707i	0.379717	+	0.925103i	$0.376021\pi$
$150$	−0.186865	+	8.53372i	−0.0152575	+	0.696775i
$151$	−7.98817	+	13.8359i	−0.650068	+	1.12595i	0.333038	+	0.942913i	$0.391926\pi$
$151$	−7.98817	+	13.8359i	−0.650068	+	1.12595i	−0.983106	+	0.183037i	$0.941407\pi$
$152$	11.4451	−	4.39335i	0.928318	−	0.356348i
$153$	−4.41088	+	2.24746i	−0.356598	+	0.181696i
$154$	−17.0444	+	3.81697i	−1.37348	+	0.307580i
$155$	16.3205	−	7.05329i	1.31089	−	0.566534i
$156$	0.387059	−	0.429872i	0.0309895	−	0.0344173i
$157$	−4.21734	−	15.7393i	−0.336580	−	1.25614i	−0.902146	−	0.431432i	$-0.858009\pi$
$157$	−4.21734	−	15.7393i	−0.336580	−	1.25614i	0.565565	−	0.824704i	$-0.308658\pi$
$158$	−0.117189	+	0.0761035i	−0.00932306	+	0.00605447i
$159$	1.13832	−	10.8304i	0.0902750	−	0.858909i
$160$	−8.29532	−	6.86913i	−0.655803	−	0.543052i
$161$	−6.03558	+	0.700767i	−0.475670	+	0.0552282i
$162$	−0.267058	−	1.68614i	−0.0209820	−	0.132475i
$163$	0.0330788	+	0.0408489i	0.00259093	+	0.00319953i	0.778440	−	0.627719i	$-0.216011\pi$
$163$	0.0330788	+	0.0408489i	0.00259093	+	0.00319953i	−0.775849	+	0.630919i	$0.782678\pi$
$164$	0.349759	+	3.32774i	0.0273116	+	0.259853i
$165$	5.36791	+	6.77923i	0.417891	+	0.527762i
$166$	−10.0532	−	1.05663i	−0.780280	−	0.0820107i
$167$	7.52268	+	3.83300i	0.582123	+	0.296606i	0.720146	−	0.693823i	$-0.244075\pi$
$167$	7.52268	+	3.83300i	0.582123	+	0.296606i	−0.138023	+	0.990429i	$0.544075\pi$
$168$	−3.42938	+	3.50475i	−0.264582	+	0.270397i
$169$	11.9831	−	3.89355i	0.921778	−	0.299504i
$170$	−0.206863	+	18.8963i	−0.0158657	+	1.44928i
$171$	4.91572	−	4.42613i	0.375914	−	0.338475i
$172$	−0.0122014	+	0.232817i	−0.000930348	+	0.0177521i
$173$	−6.98507	−	18.1967i	−0.531065	−	1.38347i	−0.892489	−	0.451070i	$-0.851043\pi$
$173$	−6.98507	−	18.1967i	−0.531065	−	1.38347i	0.361424	−	0.932402i	$-0.382291\pi$
$174$	−14.6673			−1.11192
$175$	7.32677	−	11.0145i	0.553852	−	0.832615i
$176$	−19.3071			−1.45533
$177$	−3.76517	−	9.80861i	−0.283008	−	0.737260i
$178$	−0.323111	+	6.16532i	−0.0242182	+	0.462111i
$179$	−5.43369	+	4.89252i	−0.406133	+	0.365684i	−0.846732	−	0.532020i	$-0.821433\pi$
$179$	−5.43369	+	4.89252i	−0.406133	+	0.365684i	0.440598	+	0.897704i	$0.354766\pi$
$180$	−1.93750	−	0.653064i	−0.144412	−	0.0486765i
$181$	−13.0722	+	4.24740i	−0.971646	+	0.315707i	−0.751480	−	0.659755i	$-0.770660\pi$
$181$	−13.0722	+	4.24740i	−0.971646	+	0.315707i	−0.220166	+	0.975462i	$0.570660\pi$
$182$	−2.75180	+	0.769492i	−0.203977	+	0.0570386i
$183$	11.6890	+	5.95583i	0.864074	+	0.440268i
$184$	−4.23297	−	0.444903i	−0.312059	−	0.0327987i
$185$	19.8353	+	5.54826i	1.45832	+	0.407916i
$186$	1.41886	+	13.4995i	0.104036	+	0.989833i
$187$	12.0476	+	14.8776i	0.881010	+	1.08796i
$188$	0.653219	+	4.12426i	0.0476409	+	0.300793i
$189$	−1.04979	+	2.42857i	−0.0763611	+	0.176652i
$190$	−6.26794	−	24.4602i	−0.454724	−	1.77453i
$191$	0.0923731	−	0.878871i	0.00668388	−	0.0635929i	−0.990672	−	0.136271i	$-0.956488\pi$
$191$	0.0923731	−	0.878871i	0.00668388	−	0.0635929i	0.997355	+	0.0726786i	$0.0231547\pi$
$192$	−1.47832	+	0.960031i	−0.106688	+	0.0692843i
$193$	0.315877	+	1.17887i	0.0227373	+	0.0848569i	0.976362	−	0.216141i	$-0.0693470\pi$
$193$	0.315877	+	1.17887i	0.0227373	+	0.0848569i	−0.953625	+	0.300998i	$0.902680\pi$
$194$	10.7503	−	11.9394i	0.771823	−	0.857197i
$195$	0.934976	+	1.06154i	0.0669550	+	0.0760183i
$196$	−6.23033	+	1.46653i	−0.445024	+	0.104752i
$197$	−11.6177	+	5.91954i	−0.827730	+	0.421750i	−0.815909	−	0.578181i	$-0.803763\pi$
$197$	−11.6177	+	5.91954i	−0.827730	+	0.421750i	−0.0118212	+	0.999930i	$0.503763\pi$
$198$	−6.16325	+	2.36585i	−0.438003	+	0.168134i
$199$	10.4135	−	18.0367i	0.738194	−	1.27859i	−0.215114	−	0.976589i	$-0.569012\pi$
$199$	10.4135	−	18.0367i	0.738194	−	1.27859i	0.953308	−	0.302000i	$-0.0976543\pi$
$200$	6.69440	−	6.40750i	0.473366	−	0.453079i
$201$	6.76585	−	3.90627i	0.477227	−	0.275527i
$202$	0.959579	−	6.05854i	0.0675157	−	0.426278i
$203$	19.1976	+	12.1725i	1.34741	+	0.854341i
$204$	−4.30500	−	1.39878i	−0.301411	−	0.0979342i
$205$	−8.18221	−	0.0895733i	−0.571471	−	0.00625607i
$206$	−2.58742	+	12.1729i	−0.180274	+	0.848124i
$207$	−2.21831	+	0.594393i	−0.154183	+	0.0413132i
$208$	−3.15413	+	0.165301i	−0.218700	+	0.0114616i
$209$	−20.6946	−	15.0355i	−1.43147	−	1.04003i
$210$	6.35531	+	7.84940i	0.438558	+	0.541660i
$211$	7.86431	−	5.71376i	0.541402	−	0.393351i	−0.283204	−	0.959060i	$-0.591397\pi$
$211$	7.86431	−	5.71376i	0.541402	−	0.393351i	0.824605	+	0.565708i	$0.191397\pi$
$212$	7.73850	−	6.26652i	0.531483	−	0.430386i
$213$	−1.59618	−	0.612715i	−0.109368	−	0.0419825i
$214$	32.1556	−	3.37969i	2.19811	−	0.231031i
$215$	−0.562098	−	0.0953464i	−0.0383348	−	0.00650257i
$216$	−1.08936	+	1.49938i	−0.0741217	+	0.102020i
$217$	9.34624	−	18.8467i	0.634464	−	1.27939i
$218$	−9.56107	+	9.56107i	−0.647557	+	0.647557i
$219$	0.349110	+	0.314340i	0.0235907	+	0.0212412i
$220$	−0.912500	+	7.85383i	−0.0615207	+	0.529505i
$221$	2.09555	+	2.32735i	0.140962	+	0.156554i
$222$	−8.56431	+	13.1879i	−0.574799	+	0.885113i
$223$	17.0398	+	2.69883i	1.14107	+	0.180727i	0.698229	−	0.715875i	$-0.253972\pi$
$223$	17.0398	+	2.69883i	1.14107	+	0.180727i	0.442838	+	0.896602i	$0.353972\pi$
$224$	−12.7427	+	0.138503i	−0.851409	+	0.00925411i
$225$	2.13319	−	4.52211i	0.142213	−	0.301474i
$226$	4.42085	+	7.65714i	0.294071	+	0.509345i
$227$	−1.97826	−	1.60196i	−0.131302	−	0.106326i	0.561420	−	0.827531i	$-0.310255\pi$
$227$	−1.97826	−	1.60196i	−0.131302	−	0.106326i	−0.692722	+	0.721205i	$0.743589\pi$
$228$	6.04005	+	0.316546i	0.400012	+	0.0209637i
$229$	−0.143084	+	0.0304135i	−0.00945527	+	0.00200978i	−0.212637	−	0.977131i	$-0.568205\pi$
$229$	−0.143084	+	0.0304135i	−0.00945527	+	0.00200978i	0.203182	+	0.979141i	$0.434872\pi$
$230$	−1.91645	+	8.55464i	−0.126367	+	0.564076i
$231$	10.0303	+	2.01833i	0.659948	+	0.132796i
$232$	11.2594	+	11.2594i	0.739217	+	0.739217i
$233$	1.04590	+	19.9570i	0.0685194	+	1.30743i	0.789190	+	0.614150i	$0.210501\pi$
$233$	1.04590	+	19.9570i	0.0685194	+	1.30743i	−0.720670	+	0.693278i	$0.756166\pi$
$234$	−0.986611	+	0.439267i	−0.0644968	+	0.0287158i
$235$	−10.2027	+	0.422767i	−0.665552	+	0.0275783i
$236$	3.90744	−	8.77625i	0.254352	−	0.571285i
$237$	0.0808431	−	0.0128043i	0.00525133	−	0.000831728i
$238$	14.2594	+	17.2228i	0.924302	+	1.11639i
$239$	14.5132	+	19.9757i	0.938779	+	1.29212i	0.956335	+	0.292273i	$0.0944116\pi$
$239$	14.5132	+	19.9757i	0.938779	+	1.29212i	−0.0175557	+	0.999846i	$0.505588\pi$
$240$	4.95913	+	10.0020i	0.320111	+	0.645628i
$241$	9.42343	+	21.1654i	0.607016	+	1.36338i	0.911672	+	0.410919i	$0.134792\pi$
$241$	9.42343	+	21.1654i	0.607016	+	1.36338i	−0.304656	+	0.952463i	$0.598541\pi$
$242$	3.67679	+	5.66176i	0.236353	+	0.363952i
$243$	−0.258819	+	0.965926i	−0.0166032	+	0.0619642i
$244$	3.70681	+	11.4084i	0.237304	+	0.730348i
$245$	−1.80401	−	15.5482i	−0.115254	−	0.993336i
$246$	1.93049	−	5.94143i	0.123083	−	0.378811i
$247$	−3.50952	−	2.27911i	−0.223305	−	0.145016i
$248$	9.27378	−	11.4522i	0.588886	−	0.727213i
$249$	5.12800	+	2.96065i	0.324974	+	0.187624i
$250$	−11.5180	−	15.2194i	−0.728465	−	0.962562i
$251$			12.8167i			0.808981i	0.914542	+	0.404490i	$0.132551\pi$
$251$			12.8167i			0.808981i	−0.914542	+	0.404490i	$0.867449\pi$
$252$	−2.24896	+	0.891460i	−0.141671	+	0.0561567i
$253$	4.03190	+	7.91305i	0.253483	+	0.497489i
$254$	6.50883	+	30.6216i	0.408400	+	1.92137i
$255$	4.61281	−	10.0626i	0.288866	−	0.630146i
$256$	−17.6625	−	3.75427i	−1.10390	−	0.234642i
$257$	−9.02437	−	2.41807i	−0.562925	−	0.150835i	−0.0338750	−	0.999426i	$-0.510785\pi$
$257$	−9.02437	−	2.41807i	−0.562925	−	0.150835i	−0.529050	+	0.848591i	$0.677451\pi$
$258$	0.197609	−	0.387829i	0.0123026	−	0.0241452i
$259$	22.1543	−	10.1537i	1.37660	−	0.630918i
$260$	−0.0818297	+	1.29086i	−0.00507486	+	0.0800559i
$261$	7.84888	+	3.49454i	0.485833	+	0.216307i
$262$	−5.18930	+	13.5186i	−0.320596	+	0.835182i
$263$	9.63629	−	25.1034i	0.594199	−	1.54794i	−0.224955	−	0.974369i	$-0.572224\pi$
$263$	9.63629	−	25.1034i	0.594199	−	1.54794i	0.819154	−	0.573573i	$-0.194443\pi$
$264$	6.54740	+	2.91509i	0.402965	+	0.179412i
$265$	13.0381	+	20.5664i	0.800927	+	1.26338i
$266$	−24.3603	−	17.2974i	−1.49363	−	1.06057i
$267$	1.64182	−	3.22225i	0.100478	−	0.197199i
$268$	6.90015	+	1.84889i	0.421494	+	0.112939i
$269$	5.77138	+	1.22675i	0.351887	+	0.0747960i	0.380464	−	0.924796i	$-0.375764\pi$
$269$	5.77138	+	1.22675i	0.351887	+	0.0747960i	−0.0285768	+	0.999592i	$0.509098\pi$
$270$	2.80868	+	2.58518i	0.170931	+	0.157329i
$271$	4.34048	+	20.4204i	0.263666	+	1.24045i	0.888202	+	0.459453i	$0.151955\pi$
$271$	4.34048	+	20.4204i	0.263666	+	1.24045i	−0.624536	+	0.780996i	$0.714712\pi$
$272$	11.2208	+	22.0221i	0.680361	+	1.33528i
$273$	1.65590	+	0.243850i	0.100219	+	0.0147585i
$274$			15.2862i			0.923472i
$275$	−18.8204	−	4.43316i	−1.13491	−	0.267329i
$276$	−1.81857	−	1.04995i	−0.109465	−	0.0631998i
$277$	−4.97831	+	6.14770i	−0.299117	+	0.369379i	−0.904440	−	0.426601i	$-0.859711\pi$
$277$	−4.97831	+	6.14770i	−0.299117	+	0.369379i	0.605322	+	0.795980i	$0.293044\pi$
$278$	−24.0908	−	15.6447i	−1.44487	−	0.938308i
$279$	2.45705	−	7.56202i	0.147100	−	0.452726i
$280$	1.14695	−	10.9043i	0.0685434	−	0.651657i
$281$	0.455904	+	1.40313i	0.0271969	+	0.0837035i	0.963734	−	0.266866i	$-0.0859881\pi$
$281$	0.455904	+	1.40313i	0.0271969	+	0.0837035i	−0.936537	+	0.350569i	$0.885988\pi$
$282$	2.01777	−	7.53043i	0.120157	−	0.448430i
$283$	8.60358	+	13.2483i	0.511430	+	0.787532i	0.996199	−	0.0871097i	$-0.0277631\pi$
$283$	8.60358	+	13.2483i	0.511430	+	0.787532i	−0.484769	+	0.874642i	$0.661096\pi$
$284$	−0.635866	−	1.42818i	−0.0377317	−	0.0847467i
$285$	−2.47361	+	14.5827i	−0.146524	+	0.863806i
$286$	2.45482	+	3.37877i	0.145157	+	0.199791i
$287$	−7.45759	+	6.17444i	−0.440207	+	0.364466i
$288$	−4.75728	+	0.753479i	−0.280326	+	0.0443992i
$289$	3.05334	−	6.85791i	0.179608	−	0.403406i
$290$	25.7125	−	20.3596i	1.50989	−	1.19556i
$291$	−8.59737	+	3.82780i	−0.503987	+	0.224389i
$292$	0.0224808	+	0.428960i	0.00131559	+	0.0251030i
$293$	0.772035	+	0.772035i	0.0451028	+	0.0451028i	0.729298	−	0.684196i	$-0.239847\pi$
$293$	0.772035	+	0.772035i	0.0451028	+	0.0451028i	−0.684196	+	0.729298i	$0.739847\pi$
$294$	11.7402	+	2.22990i	0.684701	+	0.130051i
$295$	20.2158	+	11.9686i	1.17701	+	0.696837i
$296$	16.6982	−	3.54931i	0.970562	−	0.206299i
$297$	3.86180	+	0.202388i	0.224084	+	0.0117438i
$298$	4.33064	+	3.50688i	0.250867	+	0.203148i
$299$	0.726425	+	1.25820i	0.0420102	+	0.0727639i
$300$	4.30304	−	1.54458i	0.248436	−	0.0891761i
$301$	−0.580506	+	0.343621i	−0.0334598	+	0.0198060i
$302$	26.9383	+	4.26660i	1.55012	+	0.245515i
$303$	−1.95697	+	3.01347i	−0.112425	+	0.173119i
$304$	−22.0982	−	24.5425i	−1.26742	−	1.40761i
$305$	−28.7586	+	5.78455i	−1.64672	+	0.331222i
$306$	6.28044	+	5.65494i	0.359029	+	0.323271i
$307$	−15.6009	+	15.6009i	−0.890389	+	0.890389i	−0.994559	−	0.104171i	$-0.966781\pi$
$307$	−15.6009	+	15.6009i	−0.890389	+	0.890389i	0.104171	+	0.994559i	$0.466781\pi$
$308$	5.18023	+	7.79017i	0.295171	+	0.443886i
$309$	4.28484	−	5.89758i	0.243756	−	0.335501i
$310$	−21.2260	−	21.6958i	−1.20555	−	1.23224i
$311$	−17.3641	+	1.82504i	−0.984628	+	0.103489i	−0.583136	−	0.812374i	$-0.698175\pi$
$311$	−17.3641	+	1.82504i	−0.984628	+	0.103489i	−0.401491	+	0.915863i	$0.631508\pi$
$312$	1.09458	+	0.420171i	0.0619685	+	0.0237875i
$313$	−14.7466	+	11.9416i	−0.833528	+	0.674978i	−0.947938	−	0.318456i	$-0.896836\pi$
$313$	−14.7466	+	11.9416i	−0.833528	+	0.674978i	0.114409	+	0.993434i	$0.463502\pi$
$314$	−22.5047	+	16.3506i	−1.27001	+	0.922718i
$315$	−1.53075	−	5.71461i	−0.0862479	−	0.321982i
$316$	0.0605485	+	0.0439911i	0.00340612	+	0.00247469i
$317$	−24.6085	+	1.28968i	−1.38215	+	0.0724354i	−0.728855	−	0.684668i	$-0.759947\pi$
$317$	−24.6085	+	1.28968i	−1.38215	+	0.0724354i	−0.653295	+	0.757103i	$0.726614\pi$
$318$	−17.9576	+	4.81172i	−1.00701	+	0.269828i
$319$	6.90783	−	32.4988i	0.386764	−	1.81958i
$320$	1.25895	−	3.73503i	0.0703776	−	0.208795i
$321$	−18.0126	−	5.85264i	−1.00536	−	0.326663i
$322$	4.80936	+	9.19057i	0.268015	+	0.512170i
$323$	−5.12260	+	32.3428i	−0.285029	+	1.79960i
$324$	−0.791869	+	0.457186i	−0.0439927	+	0.0253992i
$325$	−3.11258	−	0.563094i	−0.172655	−	0.0312348i
$326$	0.0448663	−	0.0777107i	0.00248491	−	0.00430400i
$327$	7.39436	−	2.83843i	0.408909	−	0.156966i
$328$	−6.04291	+	3.07902i	−0.333664	+	0.170010i
$329$	−8.89056	+	8.18180i	−0.490152	+	0.451077i
$330$	7.52046	−	12.7026i	0.413988	−	0.699257i
$331$	15.7785	−	17.5238i	0.867266	−	0.963196i	−0.132342	−	0.991204i	$-0.542250\pi$
$331$	15.7785	−	17.5238i	0.867266	−	0.963196i	0.999608	+	0.0280078i	$0.00891631\pi$
$332$	1.40132	+	5.22979i	0.0769073	+	0.287022i
$333$	7.72507	−	5.01672i	0.423331	−	0.274915i
$334$	1.50660	−	14.3344i	0.0824377	−	0.784342i
$335$	−6.43861	+	16.2395i	−0.351779	+	0.887261i
$336$	12.1250	+	5.24126i	0.661475	+	0.285934i
$337$	3.69747	+	23.3449i	0.201414	+	1.27168i	0.856509	+	0.516132i	$0.172629\pi$
$337$	3.69747	+	23.3449i	0.201414	+	1.27168i	−0.655095	+	0.755547i	$0.727371\pi$
$338$	−13.5365	−	16.7162i	−0.736291	−	0.909243i
$339$	−0.541375	−	5.15083i	−0.0294034	−	0.279755i
$340$	9.48853	−	3.52363i	0.514588	−	0.191095i
$341$	−30.5796	−	3.21404i	−1.65598	−	0.174050i
$342$	−10.0616	−	5.12664i	−0.544069	−	0.277217i
$343$	−13.5158	−	12.6619i	−0.729783	−	0.683679i
$344$	−0.449414	+	0.146023i	−0.0242308	+	0.00787306i
$345$	3.06373	−	4.12122i	0.164946	−	0.221879i
$346$	−24.7279	+	22.2651i	−1.32938	+	1.19698i
$347$	0.904484	−	17.2586i	0.0485552	−	0.926489i	−0.860406	−	0.509609i	$-0.829790\pi$
$347$	0.904484	−	17.2586i	0.0485552	−	0.926489i	0.908961	−	0.416880i	$-0.136877\pi$
$348$	2.81533	+	7.33419i	0.150918	+	0.393154i
$349$	5.74542			0.307545			0.153773	−	0.988106i	$-0.450858\pi$
$349$	5.74542			0.307545			0.153773	+	0.988106i	$0.450858\pi$
$350$	−22.0369	−	4.93863i	−1.17792	−	0.263981i
$351$	0.632620			0.0337668
$352$	6.67504	+	17.3891i	0.355781	+	0.926840i
$353$	0.477915	−	9.11916i	0.0254369	−	0.485364i	−0.955975	−	0.293449i	$-0.905197\pi$
$353$	0.477915	−	9.11916i	0.0254369	−	0.485364i	0.981412	−	0.191915i	$-0.0614698\pi$
$354$	−13.3291	+	12.0016i	−0.708435	+	0.637878i
$355$	3.64869	−	1.14153i	0.193652	−	0.0605859i
$356$	3.14491	−	1.02184i	0.166680	−	0.0541576i
$357$	−3.52722	−	12.6138i	−0.186680	−	0.667591i
$358$	11.1218	+	5.66684i	0.587805	+	0.299502i
$359$	14.2245	+	1.49506i	0.750741	+	0.0789061i	0.472167	−	0.881509i	$-0.343472\pi$
$359$	14.2245	+	1.49506i	0.750741	+	0.0789061i	0.278573	+	0.960415i	$0.410138\pi$
$360$	−0.171574	−	4.14063i	−0.00904273	−	0.218230i
$361$	−2.58759	−	24.6193i	−0.136189	−	1.29575i
$362$	14.7668	+	18.2354i	0.776124	+	0.958434i
$363$	−0.618615	−	3.90578i	−0.0324688	−	0.205000i
$364$	0.912971	+	1.22830i	0.0478527	+	0.0643803i
$365$	−1.04834	−	0.0664560i	−0.0548728	−	0.00347847i
$366$	2.34101	−	22.2732i	0.122366	−	1.16424i
$367$	−11.3640	+	7.37984i	−0.593194	+	0.385224i	−0.806040	−	0.591861i	$-0.798393\pi$
$367$	−11.3640	+	7.37984i	−0.593194	+	0.385224i	0.212846	+	0.977086i	$0.431727\pi$
$368$	2.96761	+	11.0753i	0.154697	+	0.577338i
$369$	−2.44863	+	2.71948i	−0.127470	+	0.141570i
$370$	−3.29238	−	35.0071i	−0.171162	−	1.81993i
$371$	27.4974	+	8.60520i	1.42760	+	0.446760i
$372$	6.47792	−	3.30066i	0.335864	−	0.171131i
$373$	24.9089	−	9.56164i	1.28973	−	0.495083i	0.385733	−	0.922611i	$-0.373949\pi$
$373$	24.9089	−	9.56164i	1.28973	−	0.495083i	0.904002	+	0.427528i	$0.140615\pi$
$374$	16.3408	−	28.3030i	0.844961	−	1.46351i
$375$	2.53753	+	10.8886i	0.131037	+	0.562283i
$376$	−7.32972	+	4.23182i	−0.378002	+	0.218239i
$377$	0.850262	−	5.36834i	0.0437907	−	0.276484i
$378$	4.51282	+	0.187349i	0.232114	+	0.00963621i
$379$	−5.80874	−	1.88737i	−0.298375	−	0.0969479i	0.156004	−	0.987756i	$-0.450139\pi$
$379$	−5.80874	−	1.88737i	−0.298375	−	0.0969479i	−0.454379	+	0.890809i	$0.650139\pi$
$380$	−11.0279	+	7.82925i	−0.565720	+	0.401632i
$381$	3.81268	−	17.9372i	0.195329	−	0.918953i
$382$	−1.45723	+	0.390463i	−0.0745582	+	0.0199778i
$383$	11.9783	−	0.627756i	0.612062	−	0.0320768i	0.256213	−	0.966620i	$-0.417525\pi$
$383$	11.9783	−	0.627756i	0.612062	−	0.0320768i	0.355849	+	0.934543i	$0.384192\pi$
$384$	10.2279	+	7.43099i	0.521939	+	0.379211i
$385$	−20.3853	+	10.3848i	−1.03893	+	0.529260i
$386$	1.68559	−	1.22465i	0.0857943	−	0.0623332i
$387$	−0.198148	+	0.160457i	−0.0100724	+	0.00815649i
$388$	−8.03360	−	3.08381i	−0.407844	−	0.156557i
$389$	28.8005	−	3.02706i	1.46024	−	0.153478i	0.659148	−	0.752013i	$-0.270917\pi$
$389$	28.8005	−	3.02706i	1.46024	−	0.153478i	0.801097	+	0.598535i	$0.204250\pi$
$390$	1.11983	−	2.13957i	0.0567050	−	0.108341i
$391$	6.68252	−	9.19771i	0.337950	−	0.465148i
$392$	−7.30061	−	10.7242i	−0.368736	−	0.541654i
$393$	5.99780	−	5.99780i	0.302549	−	0.302549i
$394$	16.5420	+	14.8944i	0.833372	+	0.750371i
$395$	−0.123949	+	0.134665i	−0.00623653	+	0.00677571i
$396$	2.36602	+	2.62774i	0.118897	+	0.132049i
$397$	−6.62571	+	10.2027i	−0.332535	+	0.512058i	−0.964902	−	0.262610i	$-0.915417\pi$
$397$	−6.62571	+	10.2027i	−0.332535	+	0.512058i	0.632367	+	0.774669i	$0.282083\pi$
$398$	−35.1172	−	5.56201i	−1.76026	−	0.278798i
$399$	8.91470	+	15.0603i	0.446293	+	0.753958i
$400$	−22.5774	−	10.6503i	−1.12887	−	0.532516i
$401$	−8.92868	−	15.4649i	−0.445877	−	0.772281i	0.552236	−	0.833688i	$-0.313775\pi$
$401$	−8.92868	−	15.4649i	−0.445877	−	0.772281i	−0.998113	+	0.0614064i	$0.980441\pi$
$402$	−10.3649	−	8.39337i	−0.516957	−	0.418623i
$403$	−5.02318	−	0.263254i	−0.250223	−	0.0131136i
$404$	−3.21368	+	0.683090i	−0.159887	+	0.0339850i
$405$	−0.887075	−	2.05258i	−0.0440791	−	0.101994i
$406$	7.65520	−	38.0434i	0.379921	−	1.88806i
$407$	−25.1873	−	25.1873i	−1.24849	−	1.24849i
$408$	−0.480173	−	9.16225i	−0.0237721	−	0.453599i
$409$	−5.56889	+	2.47943i	−0.275364	+	0.122600i	−0.539773	−	0.841811i	$-0.681490\pi$
$409$	−5.56889	+	2.47943i	−0.275364	+	0.122600i	0.264409	+	0.964411i	$0.414823\pi$
$410$	4.86303	+	13.0953i	0.240168	+	0.646732i
$411$	3.64200	−	8.18006i	0.179647	−	0.403493i
$412$	6.58353	−	1.04273i	0.324347	−	0.0513715i
$413$	27.4063	−	4.64662i	1.34858	−	0.228645i
$414$	2.30446	+	3.17181i	0.113258	+	0.155886i
$415$	−13.0993	+	1.92798i	−0.643020	+	0.0946410i
$416$	1.23935	+	2.78363i	0.0607643	+	0.136479i
$417$	9.16421	+	14.1117i	0.448773	+	0.691051i
$418$	−11.3023	+	42.1808i	−0.552814	+	2.06313i
$419$	−1.13672	−	3.49845i	−0.0555322	−	0.170910i	0.919443	−	0.393222i	$-0.128640\pi$
$419$	−1.13672	−	3.49845i	−0.0555322	−	0.170910i	−0.974976	+	0.222312i	$0.928640\pi$
$420$	2.70511	−	4.68455i	0.131996	−	0.228583i
$421$	0.213774	−	0.657927i	0.0104187	−	0.0320654i	−0.945712	−	0.325006i	$-0.894634\pi$
$421$	0.213774	−	0.657927i	0.0104187	−	0.0320654i	0.956131	+	0.292940i	$0.0946337\pi$
$422$	−13.9177	−	9.03825i	−0.677502	−	0.439975i
$423$	−2.87392	+	3.54900i	−0.139735	+	0.172558i
$424$	17.4790	+	10.0915i	0.848854	+	0.490086i
$425$	5.88140	+	24.0433i	0.285290	+	1.16627i
$426$			2.91878i			0.141415i
$427$	−21.5487	+	27.2099i	−1.04282	+	1.31678i
$428$	−7.86211	−	15.4303i	−0.380030	−	0.745850i
$429$	−0.508636	−	2.39295i	−0.0245572	−	0.115533i
$430$	0.191926	+	0.954184i	0.00925548	+	0.0460148i
$431$	−11.9191	−	2.53349i	−0.574124	−	0.122034i	−0.0883054	−	0.996093i	$-0.528145\pi$
$431$	−11.9191	−	2.53349i	−0.574124	−	0.122034i	−0.485819	+	0.874060i	$0.661478\pi$
$432$	4.82255	+	1.29220i	0.232025	+	0.0621709i
$433$	−13.5934	+	26.6785i	−0.653256	+	1.28209i	0.292206	+	0.956355i	$0.405611\pi$
$433$	−13.5934	+	26.6785i	−0.653256	+	1.28209i	−0.945462	+	0.325732i	$0.894389\pi$
$434$	−35.7551	−	3.36554i	−1.71630	−	0.161551i
$435$	−18.6102	+	4.76888i	−0.892293	+	0.228650i
$436$	6.61610	+	2.94568i	0.316854	+	0.141072i
$437$	−5.44402	+	14.1822i	−0.260423	+	0.678425i
$438$	0.287403	−	0.748710i	0.0137326	−	0.0357747i
$439$	11.3241	+	5.04180i	0.540468	+	0.240632i	0.658768	−	0.752346i	$-0.271078\pi$
$439$	11.3241	+	5.04180i	0.540468	+	0.240632i	−0.118300	+	0.992978i	$0.537744\pi$
$440$	−15.5244	+	3.97812i	−0.740095	+	0.189649i
$441$	−5.75121	−	3.99043i	−0.273867	−	0.190021i
$442$	2.42721	−	4.76366i	0.115450	−	0.226584i
$443$	−18.7283	−	5.01823i	−0.889808	−	0.238423i	−0.215174	−	0.976576i	$-0.569032\pi$
$443$	−18.7283	−	5.01823i	−0.889808	−	0.238423i	−0.674634	+	0.738152i	$0.735699\pi$
$444$	8.23832	+	1.75111i	0.390973	+	0.0831039i
$445$	1.59460	+	7.92778i	0.0755915	+	0.375813i
$446$	−6.12343	−	28.8085i	−0.289953	−	1.36412i
$447$	−1.48192	−	2.90843i	−0.0700923	−	0.137564i
$448$	−1.71852	−	4.33547i	−0.0811926	−	0.204832i
$449$		−	2.32228i		−	0.109595i	−0.998497	−	0.0547976i	$-0.982549\pi$
$449$		−	2.32228i		−	0.109595i	0.998497	−	0.0547976i	$-0.0174514\pi$
$450$	−8.51225	−	0.633229i	−0.401271	−	0.0298507i
$451$	12.2554	+	7.07567i	0.577085	+	0.333180i
$452$	2.98029	−	3.68035i	0.140181	−	0.173109i
$453$	−13.3989	−	8.70134i	−0.629534	−	0.408824i
$454$	−1.34287	+	4.13294i	−0.0630242	+	0.193969i
$455$	−3.24136	+	1.87106i	−0.151957	+	0.0877168i
$456$	3.78834	+	11.6593i	0.177405	+	0.545998i
$457$	−4.30390	+	16.0624i	−0.201328	+	0.751366i	0.789210	+	0.614124i	$0.210491\pi$
$457$	−4.30390	+	16.0624i	−0.201328	+	0.751366i	−0.990538	+	0.137242i	$0.956176\pi$
$458$	0.136009	+	0.209436i	0.00635530	+	0.00978630i
$459$	−2.01353	−	4.52246i	−0.0939834	−	0.211090i
$460$	4.64549	−	0.683732i	0.216597	−	0.0318792i
$461$	6.12590	+	8.43158i	0.285312	+	0.392698i	0.927484	−	0.373862i	$-0.121967\pi$
$461$	6.12590	+	8.43158i	0.285312	+	0.392698i	−0.642173	+	0.766560i	$0.721967\pi$
$462$	−2.91971	−	17.2208i	−0.135837	−	0.801183i
$463$	14.5420	−	2.30322i	0.675822	−	0.107040i	0.190917	−	0.981606i	$-0.438854\pi$
$463$	14.5420	−	2.30322i	0.675822	−	0.107040i	0.484905	+	0.874567i	$0.338854\pi$
$464$	17.4471	−	39.1868i	0.809961	−	1.81920i
$465$	6.18948	+	16.6672i	0.287030	+	0.772924i
$466$	31.1669	−	13.8764i	1.44378	−	0.642812i
$467$	0.471084	+	8.98882i	0.0217992	+	0.415953i	0.987632	+	0.156788i	$0.0501140\pi$
$467$	0.471084	+	8.98882i	0.0217992	+	0.415953i	−0.965833	+	0.259165i	$0.916553\pi$
$468$	0.409026	+	0.409026i	0.0189072	+	0.0189072i
$469$	6.60067	+	19.5878i	0.304791	+	0.904480i
$470$	6.91570	+	16.0021i	0.318997	+	0.738121i
$471$	15.9385	−	3.38783i	0.734406	−	0.156103i
$472$	19.4453	+	1.01908i	0.895040	+	0.0469071i
$473$	0.766258	+	0.620503i	0.0352326	+	0.0285308i
$474$	−0.0698660	−	0.121011i	−0.00320905	−	0.00555824i
$475$	−15.9059	−	28.9979i	−0.729811	−	1.33051i
$476$	5.87498	−	10.4361i	0.269279	−	0.478338i
$477$	10.7560	+	1.70359i	0.492484	+	0.0780018i
$478$	22.9575	−	35.3515i	1.05005	−	1.61694i
$479$	−23.7855	−	26.4165i	−1.08679	−	1.20700i	−0.977044	−	0.213039i	$-0.931664\pi$
$479$	−23.7855	−	26.4165i	−1.08679	−	1.20700i	−0.109743	−	0.993960i	$-0.535003\pi$
$480$	7.29386	−	7.92445i	0.332918	−	0.361700i
$481$	−4.33040	−	3.89911i	−0.197449	−	0.177784i
$482$	27.9675	−	27.9675i	1.27388	−	1.27388i
$483$	−0.383929	−	6.06398i	−0.0174694	−	0.275921i
$484$	2.12534	−	2.92529i	0.0966066	−	0.132968i
$485$	9.75828	−	18.6443i	0.443101	−	0.846594i
$486$	1.69780	−	0.178446i	0.0770138	−	0.00809448i
$487$	11.8287	+	4.54060i	0.536008	+	0.205754i	0.611288	−	0.791408i	$-0.290652\pi$
$487$	11.8287	+	4.54060i	0.536008	+	0.205754i	−0.0752800	+	0.997162i	$0.523985\pi$
$488$	−18.8952	+	15.3010i	−0.855346	+	0.692646i
$489$	−0.0425241	+	0.0308956i	−0.00192301	+	0.00139715i
$490$	−23.6765	+	12.3874i	−1.06959	+	0.559604i
$491$	16.4009	+	11.9159i	0.740161	+	0.537759i	0.892762	−	0.450529i	$-0.148765\pi$
$491$	16.4009	+	11.9159i	0.740161	+	0.537759i	−0.152600	+	0.988288i	$0.548765\pi$
$492$	−3.34148	+	0.175120i	−0.150646	+	0.00789500i
$493$	−41.0833	+	11.0082i	−1.85030	+	0.495786i
$494$	−1.48528	+	6.98769i	−0.0668258	+	0.314391i
$495$	−7.05087	+	5.00575i	−0.316913	+	0.224992i
$496$	−37.7547	−	12.2672i	−1.69523	−	0.550815i
$497$	2.42232	−	3.82031i	0.108656	−	0.171364i
$498$	1.58133	−	9.98412i	0.0708611	−	0.447399i
$499$	−22.2933	+	12.8710i	−0.997984	+	0.576186i	−0.907651	−	0.419725i	$-0.862126\pi$
$499$	−22.2933	+	12.8710i	−0.997984	+	0.576186i	−0.0903330	+	0.995912i	$0.528793\pi$
$500$	−5.39944	+	8.68076i	−0.241470	+	0.388215i
$501$	−4.22145	+	7.31177i	−0.188601	+	0.326666i
$502$	20.4268	−	7.84110i	0.911691	−	0.349965i
$503$	31.4656	−	16.0325i	1.40298	−	0.714854i	0.421573	−	0.906794i	$-0.361478\pi$
$503$	31.4656	−	16.0325i	1.40298	−	0.714854i	0.981407	+	0.191940i	$0.0614780\pi$
$504$	−3.32047	−	3.60810i	−0.147905	−	0.160718i
$505$	−0.752318	−	7.99924i	−0.0334777	−	0.355961i
$506$	10.1449	−	11.2670i	0.450994	−	0.500880i
$507$	3.26107	+	12.1705i	0.144829	+	0.540509i
$508$	14.0626	−	9.13236i	0.623927	−	0.405183i
$509$	2.58311	−	24.5767i	0.114495	−	1.08934i	−0.774863	−	0.632130i	$-0.782181\pi$
$509$	2.58311	−	24.5767i	0.114495	−	1.08934i	0.889357	−	0.457213i	$-0.151152\pi$
$510$	−18.8595	−	1.19553i	−0.835114	−	0.0529391i
$511$	−0.997532	+	0.741447i	−0.0441282	+	0.0327997i
$512$	0.866872	+	5.47321i	0.0383107	+	0.241884i
$513$	4.16280	+	5.14062i	0.183792	+	0.226964i
$514$	1.66717	+	15.8621i	0.0735358	+	0.699646i
$515$	0.674859	+	16.2865i	0.0297379	+	0.717670i
$516$	−0.231859	−	0.0243694i	−0.0102070	−	0.00107280i
$517$	15.7351	+	8.01744i	0.692029	+	0.352606i
$518$	−29.7363	−	29.0968i	−1.30654	−	1.27844i
$519$	18.5374	−	6.02315i	0.813700	−	0.264387i
$520$	−2.50210	+	0.782805i	−0.109724	+	0.0343283i
$521$	9.48303	−	8.53856i	0.415459	−	0.374081i	−0.434728	−	0.900562i	$-0.643155\pi$
$521$	9.48303	−	8.53856i	0.415459	−	0.374081i	0.850187	+	0.526481i	$0.176489\pi$
$522$	0.767626	−	14.6472i	0.0335981	−	0.641090i
$523$	−5.81268	−	15.1425i	−0.254171	−	0.662137i	0.745821	−	0.666146i	$-0.232057\pi$
$523$	−5.81268	−	15.1425i	−0.254171	−	0.662137i	−0.999992	+	0.00400899i	$0.998724\pi$
$524$	7.75586			0.338817
$525$	10.6159	+	7.89319i	0.463316	+	0.344487i
$526$	−45.9043			−2.00152
$527$	14.1060	+	36.7475i	0.614469	+	1.60075i
$528$	1.01046	−	19.2807i	0.0439745	−	0.839084i
$529$	−13.1729	+	11.8609i	−0.572733	+	0.515691i
$530$	24.8014	−	33.3620i	1.07731	−	1.44915i
$531$	9.99222	−	3.24667i	0.433625	−	0.140893i
$532$	−3.97349	+	15.5012i	−0.172272	+	0.672064i
$533$	2.06270	+	1.05100i	0.0893454	+	0.0455238i
$534$	−6.13996	−	0.645336i	−0.265702	−	0.0279264i
$535$	39.7010	−	14.7432i	1.71642	−	0.637405i
$536$	1.51349	+	14.3999i	0.0653729	+	0.621981i
$537$	−4.60143	−	5.68230i	−0.198567	−	0.245209i
$538$	−1.57573	−	9.94874i	−0.0679343	−	0.428920i
$539$	−10.4701	+	24.9629i	−0.450980	+	1.07523i
$540$	0.753569	−	1.90066i	0.0324285	−	0.0817914i
$541$	−1.60565	+	15.2767i	−0.0690322	+	0.656798i	0.904221	+	0.427064i	$0.140452\pi$
$541$	−1.60565	+	15.2767i	−0.0690322	+	0.656798i	−0.973254	+	0.229734i	$0.926215\pi$
$542$	29.8898	−	19.4107i	1.28388	−	0.833760i
$543$	−3.55744	−	13.2765i	−0.152664	−	0.569751i
$544$	15.9549	−	17.7197i	0.684061	−	0.759727i
$545$	−9.02268	+	15.2400i	−0.386489	+	0.652810i
$546$	−0.624420	−	2.78830i	−0.0267227	−	0.119328i
$547$	26.1047	−	13.3010i	1.11616	−	0.568710i	0.204172	−	0.978935i	$-0.434550\pi$
$547$	26.1047	−	13.3010i	1.11616	−	0.568710i	0.911984	+	0.410225i	$0.134550\pi$
$548$	7.64366	−	2.93412i	0.326521	−	0.125340i
$549$	−6.55942	+	11.3613i	−0.279949	+	0.484886i
$550$	4.44873	+	32.7075i	0.189694	+	1.39465i
$551$	49.2177	−	28.4158i	2.09674	−	1.21056i
$552$	0.665830	−	4.20389i	0.0283396	−	0.178929i
$553$	−0.00898262	+	0.216371i	−0.000381980	+	0.00920101i
$554$	12.8437	+	4.17316i	0.545675	+	0.177300i
$555$	−6.57876	+	19.5177i	−0.279253	+	0.828481i
$556$	−3.19881	+	15.0492i	−0.135660	+	0.638229i
$557$	−14.9183	+	3.99736i	−0.632110	+	0.169373i	−0.560627	−	0.828068i	$-0.689440\pi$
$557$	−14.9183	+	3.99736i	−0.632110	+	0.169373i	−0.0714830	+	0.997442i	$0.522773\pi$
$558$	−13.5553	+	0.710402i	−0.573841	+	0.0300737i
$559$	0.130493	+	0.0948088i	0.00551927	+	0.00400998i
$560$	−28.5312	+	7.64251i	−1.20566	+	0.322955i
$561$	−15.4877	+	11.2525i	−0.653892	+	0.475080i
$562$	1.95734	−	1.58502i	0.0825653	−	0.0668601i
$563$	−5.50749	−	2.11413i	−0.232113	−	0.0890998i	0.239532	−	0.970889i	$-0.423006\pi$
$563$	−5.50749	−	2.11413i	−0.232113	−	0.0890998i	−0.471645	+	0.881789i	$0.656339\pi$
$564$	−4.15280	+	0.436476i	−0.174864	+	0.0183790i
$565$	8.09891	+	8.27820i	0.340724	+	0.348266i
$566$	15.8512	−	21.8173i	0.666275	−	0.917048i
$567$	−2.37030	−	1.17545i	−0.0995431	−	0.0493644i
$568$	2.24062	−	2.24062i	0.0940142	−	0.0940142i
$569$	22.6155	+	20.3631i	0.948092	+	0.853666i	0.989361	−	0.145482i	$-0.0464732\pi$
$569$	22.6155	+	20.3631i	0.948092	+	0.853666i	−0.0412685	+	0.999148i	$0.513140\pi$
$570$	24.7548	−	4.97920i	1.03686	−	0.208556i
$571$	−13.7366	−	15.2560i	−0.574857	−	0.638444i	0.383661	−	0.923474i	$-0.374663\pi$
$571$	−13.7366	−	15.2560i	−0.574857	−	0.638444i	−0.958518	+	0.285030i	$0.907996\pi$
$572$	1.21832	−	1.87604i	0.0509404	−	0.0784413i
$573$	0.872832	+	0.138243i	0.0364631	+	0.00577519i
$574$	14.4031	+	8.10819i	0.601173	+	0.338429i
$575$	0.349782	+	11.4775i	0.0145869	+	0.478643i
$576$	−0.881346	−	1.52654i	−0.0367228	−	0.0636057i
$577$	−13.2042	−	10.6925i	−0.549698	−	0.445136i	0.313800	−	0.949489i	$-0.398398\pi$
$577$	−13.2042	−	10.6925i	−0.549698	−	0.445136i	−0.863498	+	0.504353i	$0.831731\pi$
$578$	−12.7979	−	0.670709i	−0.532322	−	0.0278978i
$579$	−1.19379	+	0.253747i	−0.0496120	+	0.0105454i
$580$	−15.1160	−	8.94925i	−0.627657	−	0.371598i
$581$	−10.3556	+	11.7556i	−0.429625	+	0.487704i
$582$	11.3604	+	11.3604i	0.470903	+	0.470903i
$583$	−2.20403	−	42.0554i	−0.0912815	−	1.74176i
$584$	−0.795377	+	0.354125i	−0.0329129	+	0.0146538i
$585$	−1.10902	+	0.878138i	−0.0458522	+	0.0363065i
$586$	0.758120	−	1.70277i	0.0313176	−	0.0703406i
$587$	2.84747	−	0.450995i	0.117528	−	0.0186145i	−0.0973935	−	0.995246i	$-0.531051\pi$
$587$	2.84747	−	0.450995i	0.117528	−	0.0186145i	0.214921	+	0.976631i	$0.431051\pi$
$588$	−1.13845	−	6.29854i	−0.0469488	−	0.259748i
$589$	−30.9146	−	42.5503i	−1.27381	−	1.75325i
$590$	6.70727	−	39.5415i	0.276134	−	1.62790i
$591$	−5.30340	−	11.9116i	−0.218153	−	0.489979i
$592$	−25.0468	−	38.5687i	−1.02942	−	1.58517i
$593$	−4.53414	+	16.9217i	−0.186195	+	0.694889i	0.808177	+	0.588940i	$0.200455\pi$
$593$	−4.53414	+	16.9217i	−0.186195	+	0.694889i	−0.994372	+	0.105949i	$0.966212\pi$
$594$	−2.04005	−	6.27862i	−0.0837042	−	0.257615i
$595$	23.6925	+	17.2165i	0.971299	+	0.705806i
$596$	0.922322	−	2.83861i	0.0377798	−	0.116274i
$597$	17.4670	+	11.3432i	0.714877	+	0.464246i
$598$	1.56086	−	1.92751i	0.0638285	−	0.0788216i
$599$	−28.3509	−	16.3684i	−1.15839	−	0.668796i	−0.207471	−	0.978241i	$-0.566523\pi$
$599$	−28.3509	−	16.3684i	−1.15839	−	0.668796i	−0.950917	+	0.309446i	$0.899857\pi$
$600$	6.04837	+	7.02057i	0.246923	+	0.286614i
$601$		−	47.4755i		−	1.93657i	−0.249853	−	0.968284i	$-0.580382\pi$
$601$		−	47.4755i		−	1.93657i	0.249853	−	0.968284i	$-0.419618\pi$
$602$	0.902799	+	0.714967i	0.0367953	+	0.0291399i
$603$	3.54682	+	6.96102i	0.144438	+	0.283475i
$604$	−3.03724	−	14.2891i	−0.123584	−	0.581415i
$605$	6.50606	+	5.98833i	0.264509	+	0.243460i
$606$	6.00002	+	1.27534i	0.243734	+	0.0518073i
$607$	23.8286	+	6.38486i	0.967174	+	0.259154i	0.707634	−	0.706579i	$-0.249762\pi$
$607$	23.8286	+	6.38486i	0.967174	+	0.259154i	0.259540	+	0.965732i	$0.416429\pi$
$608$	−14.4644	+	28.3879i	−0.586607	+	1.15128i
$609$	−13.1605	+	18.5342i	−0.533291	+	0.751045i
$610$	26.8134	+	42.2956i	1.08564	+	1.71250i
$611$	2.63923	+	1.17506i	0.106772	+	0.0475378i
$612$	1.62217	−	4.22590i	0.0655723	−	0.170822i
$613$	−4.12429	+	10.7441i	−0.166578	+	0.433951i	−0.991306	−	0.131579i	$-0.957995\pi$
$613$	−4.12429	+	10.7441i	−0.166578	+	0.433951i	0.824727	+	0.565531i	$0.191329\pi$
$614$	34.4086	+	15.3197i	1.38862	+	0.618252i
$615$	0.517675	−	8.16631i	0.0208747	−	0.329298i
$616$	−10.9783	+	15.4609i	−0.442328	+	0.622939i
$617$	16.8162	−	33.0037i	0.676996	−	1.32868i	−0.255257	−	0.966873i	$-0.582160\pi$
$617$	16.8162	−	33.0037i	0.676996	−	1.32868i	0.932253	−	0.361807i	$-0.117840\pi$
$618$	−12.0208	−	3.22095i	−0.483546	−	0.129566i
$619$	27.0761	+	5.75520i	1.08828	+	0.231321i	0.716911	−	0.697165i	$-0.245555\pi$
$619$	27.0761	+	5.75520i	1.08828	+	0.231321i	0.371368	+	0.928486i	$0.378889\pi$
$620$	−6.77448	+	14.7782i	−0.272070	+	0.593507i
$621$	−0.477481	−	2.24637i	−0.0191607	−	0.0901439i
$622$	13.5319	+	26.5578i	0.542578	+	1.06487i
$623$	7.50085	+	5.94026i	0.300515	+	0.237991i
$624$		−	3.15846i		−	0.126440i
$625$	−19.5628	−	15.5659i	−0.782512	−	0.622635i
$626$	28.0539	+	16.1969i	1.12126	+	0.647359i
$627$	16.0979	−	19.8793i	0.642890	−	0.793903i
$628$	12.4956	+	8.11473i	0.498628	+	0.323813i
$629$	−14.0909	+	43.3673i	−0.561840	+	1.72917i
$630$	−8.17126	+	5.93579i	−0.325551	+	0.236488i
$631$	−2.67697	−	8.23888i	−0.106569	−	0.327984i	0.883527	−	0.468381i	$-0.155162\pi$
$631$	−2.67697	−	8.23888i	−0.106569	−	0.327984i	−0.990095	+	0.140396i	$0.955162\pi$
$632$	−0.0392620	+	0.146528i	−0.00156176	+	0.00582857i
$633$	5.29434	+	8.15257i	0.210431	+	0.324036i
$634$	17.1106	+	38.4311i	0.679550	+	1.52629i
$635$	18.2148	+	36.7373i	0.722832	+	1.45787i
$636$	5.85293	+	8.05586i	0.232084	+	0.319436i
$637$	−1.49674	+	4.16773i	−0.0593030	+	0.165132i
$638$	−56.0216	+	8.87294i	−2.21791	+	0.351283i
$639$	0.695412	−	1.56192i	0.0275101	−	0.0617887i
$640$	−28.2449	+	1.17038i	−1.11648	+	0.0462632i
$641$	−30.4772	+	13.5693i	−1.20378	+	0.535957i	−0.907867	−	0.419259i	$-0.862290\pi$
$641$	−30.4772	+	13.5693i	−1.20378	+	0.535957i	−0.295912	+	0.955215i	$0.595623\pi$
$642$	1.69216	+	32.2884i	0.0667843	+	1.27432i
$643$	1.70175	+	1.70175i	0.0671103	+	0.0671103i	0.739865	−	0.672755i	$-0.234889\pi$
$643$	1.70175	+	1.70175i	0.0671103	+	0.0671103i	−0.672755	+	0.739865i	$0.734889\pi$
$644$	3.67249	−	4.16895i	0.144716	−	0.164280i
$645$	0.124634	−	0.556338i	0.00490744	−	0.0219058i
$646$	54.6808	−	11.6228i	2.15139	−	0.457291i
$647$	−16.8215	−	0.881579i	−0.661323	−	0.0346585i	−0.281278	−	0.959626i	$-0.590758\pi$
$647$	−16.8215	−	0.881579i	−0.661323	−	0.0346585i	−0.380045	+	0.924968i	$0.624092\pi$
$648$	−1.44031	−	1.16634i	−0.0565807	−	0.0458182i
$649$	−20.3147	−	35.1862i	−0.797423	−	1.38118i
$650$	1.00680	+	5.30521i	0.0394900	+	0.208087i
$651$	18.3317	+	10.3198i	0.718475	+	0.404465i
$652$	−0.0474701	−	0.00751853i	−0.00185907	−	0.000294448i
$653$	−2.60569	+	4.01241i	−0.101968	+	0.157018i	−0.885972	−	0.463739i	$-0.846508\pi$
$653$	−2.60569	+	4.01241i	−0.101968	+	0.157018i	0.784004	+	0.620756i	$0.213174\pi$
$654$	−9.04758	−	10.0484i	−0.353788	−	0.392922i
$655$	−2.18893	+	18.8400i	−0.0855285	+	0.736139i
$656$	13.5774	+	12.2252i	0.530110	+	0.477313i
$657$	−0.332181	+	0.332181i	−0.0129596	+	0.0129596i
$658$	18.4790	+	9.16392i	0.720387	+	0.357247i
$659$	−10.5286	+	14.4913i	−0.410134	+	0.564502i	−0.963251	−	0.268602i	$-0.913438\pi$
$659$	−10.5286	+	14.4913i	−0.410134	+	0.564502i	0.553117	+	0.833104i	$0.313438\pi$
$660$	−7.79531	−	1.32229i	−0.303432	−	0.0514699i
$661$	1.89952	−	0.199647i	0.0738826	−	0.00776537i	−0.0675150	−	0.997718i	$-0.521507\pi$
$661$	1.89952	−	0.199647i	0.0738826	−	0.00776537i	0.141398	+	0.989953i	$0.454840\pi$
$662$	−37.5820	−	14.4264i	−1.46066	−	0.560697i
$663$	−2.43383	+	1.97088i	−0.0945221	+	0.0765425i
$664$	−8.87828	+	6.45045i	−0.344544	+	0.250326i
$665$	−36.5331	−	14.0270i	−1.41669	−	0.543944i
$666$	−12.7216	−	9.24278i	−0.492952	−	0.358150i
$667$	−19.7042	+	1.03265i	−0.762950	+	0.0399845i
$668$	−7.45690	+	1.99807i	−0.288516	+	0.0773077i
$669$	−3.58693	+	16.8752i	−0.138679	+	0.652431i
$670$	29.8211	+	0.326461i	1.15209	+	0.0126123i
$671$	48.2489	+	15.6770i	1.86263	+	0.605205i
$672$	0.528590	−	12.7325i	0.0203908	−	0.491167i
$673$	7.57679	−	47.8379i	0.292064	−	1.84402i	−0.208127	−	0.978102i	$-0.566737\pi$
$673$	7.57679	−	47.8379i	0.292064	−	1.84402i	0.500190	−	0.865916i	$-0.333263\pi$
$674$	34.9442	−	20.1751i	1.34600	−	0.777115i
$675$	4.40427	+	2.36694i	0.169520	+	0.0911035i
$676$	−5.76045	+	9.97739i	−0.221556	+	0.383746i
$677$	30.2570	−	11.6146i	1.16287	−	0.446384i	0.301055	−	0.953607i	$-0.402661\pi$
$677$	30.2570	−	11.6146i	1.16287	−	0.446384i	0.861815	+	0.507222i	$0.169328\pi$
$678$	−7.87801	+	4.01405i	−0.302553	+	0.154159i
$679$	−5.44122	−	24.2973i	−0.208815	−	0.932446i
$680$	13.5599	+	15.3954i	0.519997	+	0.590386i
$681$	1.70330	−	1.89171i	0.0652706	−	0.0724904i
$682$	13.5858	+	50.7030i	0.520228	+	1.94152i
$683$	22.1564	−	14.3886i	0.847793	−	0.550563i	−0.0460524	−	0.998939i	$-0.514664\pi$
$683$	22.1564	−	14.3886i	0.847793	−	0.550563i	0.893845	+	0.448376i	$0.147997\pi$
$684$	−0.632224	+	6.01521i	−0.0241737	+	0.229997i
$685$	4.97011	+	19.3955i	0.189898	+	0.741065i
$686$	−11.9113	+	29.2874i	−0.454776	+	1.11820i
$687$	−0.0228834	−	0.144480i	−0.000873054	−	0.00551225i
$688$	0.801108	+	0.989286i	0.0305420	+	0.0377162i
$689$	−0.720127	−	6.85155i	−0.0274347	−	0.261023i
$690$	−8.44262	−	2.36154i	−0.321405	−	0.0899024i
$691$	22.4491	+	2.35949i	0.854002	+	0.0897593i	0.521405	−	0.853310i	$-0.325408\pi$
$691$	22.4491	+	2.35949i	0.854002	+	0.0897593i	0.332598	+	0.943069i	$0.392075\pi$
$692$	15.8798	+	8.09117i	0.603660	+	0.307580i
$693$	−2.54051	+	9.91096i	−0.0965060	+	0.376486i
$694$	−28.0595	+	9.11707i	−1.06512	+	0.346079i
$695$	−35.6537	−	12.0176i	−1.35242	−	0.455855i
$696$	−11.8333	+	10.6547i	−0.448538	+	0.403866i
$697$	0.948105	−	18.0909i	0.0359120	−	0.685242i
$698$	−3.51499	−	9.15685i	−0.133044	−	0.346592i
$699$	−19.9844			−0.755880
$700$	1.76040	+	11.9672i	0.0665370	+	0.452318i
$701$	3.53363			0.133464			0.0667318	−	0.997771i	$-0.478743\pi$
$701$	3.53363			0.133464			0.0667318	+	0.997771i	$0.478743\pi$
$702$	−0.387030	−	1.00825i	−0.0146075	−	0.0380539i
$703$	3.18878	−	60.8456i	0.120267	−	2.29483i
$704$	−5.06565	+	4.56113i	−0.190919	+	0.171904i
$705$	0.111782	−	10.2109i	0.00420994	−	0.384563i
$706$	−14.8262	+	4.81732i	−0.557991	+	0.181302i
$707$	−6.79484	−	6.64872i	−0.255546	−	0.250051i
$708$	8.55972	+	4.36139i	0.321694	+	0.163911i
$709$	0.203172	+	0.0213543i	0.00763030	+	0.000801977i	0.108343	−	0.994114i	$-0.465446\pi$
$709$	0.203172	+	0.0213543i	0.00763030	+	0.000801977i	−0.100713	+	0.994916i	$0.532112\pi$
$710$	−4.05155	−	5.11677i	−0.152052	−	0.192029i
$711$	0.00855574	+	0.0814025i	0.000320865	+	0.00305283i
$712$	4.21798	+	5.20877i	0.158075	+	0.195207i
$713$	2.85655	+	18.0355i	0.106979	+	0.675436i
$714$	−17.9455	+	13.3385i	−0.671592	+	0.499182i
$715$	4.21331	+	3.48892i	0.157569	+	0.130478i
$716$	0.698842	−	6.64904i	0.0261169	−	0.248486i
$717$	−20.7079	+	13.4478i	−0.773349	+	0.502219i
$718$	−6.31963	−	23.5852i	−0.235847	−	0.880191i
$719$	−16.4509	+	18.2706i	−0.613515	+	0.681377i	−0.967208	−	0.253984i	$-0.918259\pi$
$719$	−16.4509	+	18.2706i	−0.613515	+	0.681377i	0.353694	+	0.935361i	$0.384926\pi$
$720$	−10.2479	+	4.42887i	−0.381915	+	0.165054i
$721$	13.0605	+	14.1919i	0.486400	+	0.528535i
$722$	−37.6543	+	19.1858i	−1.40135	+	0.714022i
$723$	−21.6295	+	8.30280i	−0.804411	+	0.308785i
$724$	6.28397	−	10.8842i	0.233542	−	0.404506i
$725$	26.0051	−	34.1929i	0.965803	−	1.26989i
$726$	−5.84643	+	3.37544i	−0.216981	+	0.125274i
$727$	−5.27989	+	33.3359i	−0.195820	+	1.23636i	0.672402	+	0.740186i	$0.265263\pi$
$727$	−5.27989	+	33.3359i	−0.195820	+	1.23636i	−0.868223	+	0.496175i	$0.834737\pi$
$728$	−1.66111	+	2.61979i	−0.0615648	+	0.0970958i
$729$	−0.951057	−	0.309017i	−0.0352243	−	0.0114451i
$730$	0.535449	+	1.71147i	0.0198179	+	0.0633443i
$731$	0.262428	−	1.23463i	0.00970625	−	0.0456643i
$732$	−11.5868	+	3.10467i	−0.428259	+	0.114752i
$733$	−5.78596	+	0.303229i	−0.213709	+	0.0112000i	−0.158890	−	0.987296i	$-0.550792\pi$
$733$	−5.78596	+	0.303229i	−0.213709	+	0.0112000i	−0.0548191	+	0.998496i	$0.517458\pi$
$734$	18.7141	+	13.5966i	0.690749	+	0.501858i
$735$	15.6213	−	0.987805i	0.576199	−	0.0364357i
$736$	8.94899	−	6.50182i	0.329864	−	0.239660i
$737$	23.4790	−	19.0129i	0.864861	−	0.700351i
$738$	5.83225	+	2.23879i	0.214688	+	0.0824110i
$739$	−11.0278	+	1.15907i	−0.405664	+	0.0426370i	−0.305163	−	0.952300i	$-0.598711\pi$
$739$	−11.0278	+	1.15907i	−0.405664	+	0.0426370i	−0.100500	+	0.994937i	$0.532044\pi$
$740$	−16.8729	+	8.36580i	−0.620260	+	0.307533i
$741$	2.45966	−	3.38543i	0.0903579	−	0.124367i
$742$	−3.10797	−	49.0890i	−0.114097	−	1.80211i
$743$	−28.9553	+	28.9553i	−1.06227	+	1.06227i	−0.0643391	+	0.997928i	$0.520494\pi$
$743$	−28.9553	+	28.9553i	−1.06227	+	1.06227i	−0.997928	+	0.0643391i	$0.979506\pi$
$744$	10.9511	+	9.86043i	0.401488	+	0.361501i
$745$	6.63505	+	3.04158i	0.243090	+	0.111435i
$746$	−30.4780	−	33.8493i	−1.11588	−	1.23931i
$747$	−3.22497	+	4.96603i	−0.117996	+	0.181697i
$748$	−17.2891	−	2.73833i	−0.632152	−	0.100123i
$749$	24.5815	−	43.6657i	0.898190	−	1.59551i
$750$	15.8014	−	10.7057i	0.576985	−	0.390918i
$751$	9.24038	+	16.0048i	0.337186	+	0.584024i	0.983902	−	0.178707i	$-0.0571914\pi$
$751$	9.24038	+	16.0048i	0.337186	+	0.584024i	−0.646716	+	0.762731i	$0.723858\pi$
$752$	17.7190	+	14.3485i	0.646145	+	0.523238i
$753$	−12.7991	−	0.670773i	−0.466425	−	0.0244443i
$754$	−9.07606	+	1.92918i	−0.330531	+	0.0702564i
$755$	35.5672	−	3.34505i	1.29442	−	0.121739i
$756$	−0.772536	−	2.29254i	−0.0280969	−	0.0833787i
$757$	−12.7466	−	12.7466i	−0.463282	−	0.463282i	0.436448	−	0.899730i	$-0.356236\pi$
$757$	−12.7466	−	12.7466i	−0.463282	−	0.463282i	−0.899730	+	0.436448i	$0.856236\pi$
$758$	0.545693	+	10.4124i	0.0198205	+	0.378197i
$759$	−8.11322	+	3.61224i	−0.294491	+	0.131116i
$760$	−22.8254	−	15.1808i	−0.827965	−	0.550665i
$761$	7.86537	−	17.6659i	0.285119	−	0.640388i	−0.713034	−	0.701129i	$-0.752680\pi$
$761$	7.86537	−	17.6659i	0.285119	−	0.640388i	0.998154	+	0.0607408i	$0.0193463\pi$
$762$	−30.9203	+	4.89729i	−1.12012	+	0.177410i
$763$	3.50292	+	20.6607i	0.126814	+	0.747966i
$764$	0.474955	+	0.653719i	0.0171833	+	0.0236507i
$765$	9.80742	+	5.13313i	0.354588	+	0.185589i
$766$	−8.32869	−	18.7065i	−0.300928	−	0.675895i
$767$	−3.61999	−	5.57430i	−0.130710	−	0.201276i
$768$	4.67351	−	17.4418i	0.168641	−	0.629375i
$769$	−13.8576	−	42.6492i	−0.499717	−	1.53797i	−0.809474	−	0.587155i	$-0.800248\pi$
$769$	−13.8576	−	42.6492i	−0.499717	−	1.53797i	0.309758	−	0.950816i	$-0.399752\pi$
$770$	29.0225	+	26.1361i	1.04590	+	0.941879i
$771$	2.88706	−	8.88545i	0.103975	−	0.320002i
$772$	−0.935915	−	0.607790i	−0.0336843	−	0.0218748i
$773$	−31.2303	+	38.5662i	−1.12327	+	1.38713i	−0.211031	+	0.977479i	$0.567682\pi$
$773$	−31.2303	+	38.5662i	−1.12327	+	1.38713i	−0.912243	+	0.409649i	$0.865651\pi$
$774$	0.376955	+	0.217635i	0.0135494	+	0.00782274i
$775$	−33.9862	−	20.6269i	−1.22082	−	0.740941i
$776$		−	17.4417i		−	0.626121i
$777$	8.98028	+	22.6553i	0.322166	+	0.812756i
$778$	−22.4443	−	44.0493i	−0.804666	−	1.57925i
$779$	5.03274	+	23.6772i	0.180316	+	0.848322i
$780$	−1.28481	−	0.149276i	−0.0460036	−	0.00534494i
$781$	−6.46724	−	1.37465i	−0.231416	−	0.0491890i
$782$	−18.7473	−	5.02332i	−0.670401	−	0.179633i
$783$	−3.90053	+	7.65523i	−0.139394	+	0.273576i
$784$	−19.9229	+	28.7139i	−0.711532	+	1.02550i
$785$	−23.2383	+	28.0632i	−0.829412	+	1.00162i
$786$	−13.2285	−	5.88970i	−0.471844	−	0.210079i
$787$	3.82817	−	9.97271i	0.136459	−	0.355489i	−0.848274	−	0.529557i	$-0.822358\pi$
$787$	3.82817	−	9.97271i	0.136459	−	0.355489i	0.984734	+	0.174068i	$0.0556914\pi$
$788$	4.27261	−	11.1305i	0.152205	−	0.396508i
$789$	24.5647	+	10.9369i	0.874526	+	0.389364i
$790$	0.290454	+	0.115158i	0.0103339	+	0.00409716i
$791$	13.6426	+	1.28414i	0.485075	+	0.0456589i
$792$	−3.25376	+	6.38587i	−0.115617	+	0.226912i
$793$	8.01646	+	2.14800i	0.284673	+	0.0762778i
$794$	20.3142	+	4.31792i	0.720925	+	0.153237i
$795$	−21.2206	+	11.9439i	−0.752617	+	0.423607i
$796$	3.95939	+	18.6275i	0.140337	+	0.660234i
$797$	−1.66836	−	3.27433i	−0.0590962	−	0.115983i	0.859569	−	0.511019i	$-0.170732\pi$
$797$	−1.66836	−	3.27433i	−0.0590962	−	0.115983i	−0.918665	+	0.395037i	$0.870732\pi$
$798$	18.5486	−	23.4217i	0.656615	−	0.829118i
$799$		−	22.6072i		−	0.799787i
$800$	−1.78660	+	24.0165i	−0.0631659	+	0.849113i
$801$	3.13191	+	1.80821i	0.110661	+	0.0638900i
$802$	−19.1850	+	23.6915i	−0.677445	+	0.836575i
$803$	1.52358	+	0.989426i	0.0537661	+	0.0349161i
$804$	−2.20748	+	6.79393i	−0.0778519	+	0.239604i
$805$	9.09044	+	10.0975i	0.320396	+	0.355892i
$806$	2.65356	+	8.16683i	0.0934678	+	0.287664i
$807$	−1.52712	+	5.69927i	−0.0537570	+	0.200624i
$808$	−3.62692	−	5.58497i	−0.127595	−	0.196479i
$809$	2.57740	+	5.78894i	0.0906167	+	0.203528i	0.953168	−	0.302441i	$-0.0978015\pi$
$809$	2.57740	+	5.78894i	0.0906167	+	0.203528i	−0.862551	+	0.505969i	$0.831135\pi$
$810$	−2.72863	+	2.66954i	−0.0958744	+	0.0937980i
$811$	−19.6719	−	27.0761i	−0.690774	−	0.950769i	0.309226	−	0.950989i	$-0.399930\pi$
$811$	−19.6719	−	27.0761i	−0.690774	−	0.950769i	−1.00000		0.000219594i	$0.999930\pi$
$812$	−20.4925	+	3.47441i	−0.719146	+	0.121928i
$813$	−20.6196	+	3.26582i	−0.723159	+	0.114537i
$814$	−24.7333	+	55.5520i	−0.866903	+	1.94710i
$815$	0.0316609	−	0.113189i	0.00110903	−	0.00396484i
$816$	−22.5791	+	10.0529i	−0.790428	+	0.351921i
$817$	0.0882674	+	1.68424i	0.00308808	+	0.0589242i
$818$	7.35861	+	7.35861i	0.257288	+	0.257288i
$819$	−0.330179	+	1.64087i	−0.0115374	+	0.0573365i
$820$	5.61471	−	4.94529i	0.196074	−	0.172697i
$821$	−45.7717	+	9.72907i	−1.59744	+	0.339547i	−0.918739	−	0.394866i	$-0.870791\pi$
$821$	−45.7717	+	9.72907i	−1.59744	+	0.339547i	−0.678703	+	0.734413i	$0.737458\pi$
$822$	−15.2652	−	0.800017i	−0.532436	−	0.0279038i
$823$	14.9305	+	12.0905i	0.520444	+	0.421447i	0.853214	−	0.521561i	$-0.174650\pi$
$823$	14.9305	+	12.0905i	0.520444	+	0.421447i	−0.332770	+	0.943008i	$0.607983\pi$
$824$	6.75522	+	11.7004i	0.235329	+	0.407602i
$825$	5.41207	−	18.5626i	0.188424	−	0.646268i
$826$	−24.1725	−	40.8365i	−0.841069	−	1.42088i
$827$	−27.5036	−	4.35614i	−0.956393	−	0.151478i	−0.341319	−	0.939947i	$-0.610874\pi$
$827$	−27.5036	−	4.35614i	−0.956393	−	0.151478i	−0.615074	+	0.788470i	$0.710874\pi$
$828$	1.14369	−	1.76113i	0.0397461	−	0.0612036i
$829$	−12.0932	−	13.4309i	−0.420015	−	0.466474i	0.495588	−	0.868558i	$-0.334953\pi$
$829$	−12.0932	−	13.4309i	−0.420015	−	0.466474i	−0.915603	+	0.402084i	$0.868286\pi$
$830$	11.0868	+	19.6977i	0.384828	+	0.683718i
$831$	−5.87873	−	5.29323i	−0.203931	−	0.183620i
$832$	−0.788505	+	0.788505i	−0.0273365	+	0.0273365i
$833$	34.5580	−	2.56536i	1.19736	−	0.0888843i
$834$	16.8841	−	23.2390i	0.584648	−	0.804699i
$835$	−2.74902	−	18.6777i	−0.0951337	−	0.646368i
$836$	23.2614	−	2.44487i	0.804513	−	0.0845577i
$837$	7.42307	+	2.84945i	0.256579	+	0.0984913i
$838$	−4.88028	+	3.95197i	−0.168586	+	0.136519i
$839$	−21.9662	+	15.9594i	−0.758357	+	0.550979i	−0.898406	−	0.439166i	$-0.855274\pi$
$839$	−21.9662	+	15.9594i	−0.758357	+	0.550979i	0.140049	+	0.990145i	$0.455274\pi$
$840$	10.8293	+	1.71607i	0.373648	+	0.0592099i
$841$	36.2575	+	26.3426i	1.25026	+	0.908365i
$842$	−1.17937	+	0.0618079i	−0.0406436	+	0.00213004i
$843$	−1.42506	+	0.381845i	−0.0490818	+	0.0131514i
$844$	−1.84801	+	8.69422i	−0.0636112	+	0.299267i
$845$	−22.6106	−	16.8088i	−0.777828	−	0.578239i
$846$	7.41451	+	2.40912i	0.254916	+	0.0828272i
$847$	10.4535	+	0.433978i	0.359187	+	0.0149116i
$848$	8.50544	−	53.7012i	0.292078	−	1.84411i
$849$	−13.6805	+	7.89842i	−0.469512	+	0.271073i
$850$	34.7212	−	24.0830i	1.19093	−	0.826041i
$851$	−10.5769	+	18.3197i	−0.362572	+	0.627993i
$852$	1.45950	−	0.560249i	0.0500016	−	0.0191938i
$853$	−24.0924	+	12.2757i	−0.824907	+	0.420311i	−0.814874	−	0.579638i	$-0.803194\pi$
$853$	−24.0924	+	12.2757i	−0.824907	+	0.420311i	−0.0100334	+	0.999950i	$0.503194\pi$
$854$	56.5495	+	17.6969i	1.93508	+	0.605576i
$855$	−14.4333	−	3.23342i	−0.493608	−	0.110581i
$856$	23.4873	−	26.0853i	0.802781	−	0.891579i
$857$	−0.724502	−	2.70388i	−0.0247485	−	0.0923628i	0.952447	−	0.304704i	$-0.0985577\pi$
$857$	−0.724502	−	2.70388i	−0.0247485	−	0.0923628i	−0.977195	+	0.212342i	$0.931891\pi$
$858$	−3.50262	+	2.27463i	−0.119577	+	0.0776544i
$859$	−3.68411	+	35.0520i	−0.125700	+	1.19596i	0.731816	+	0.681502i	$0.238673\pi$
$859$	−3.68411	+	35.0520i	−0.125700	+	1.19596i	−0.857516	+	0.514457i	$0.827994\pi$
$860$	0.440288	−	0.279122i	0.0150137	−	0.00951798i
$861$	−5.77568	−	7.77051i	−0.196835	−	0.264818i
$862$	3.25420	+	20.5462i	0.110839	+	0.699808i
$863$	13.2488	+	16.3609i	0.450994	+	0.556931i	0.951040	−	0.309068i	$-0.100017\pi$
$863$	13.2488	+	16.3609i	0.450994	+	0.556931i	−0.500046	+	0.865999i	$0.666684\pi$
$864$	−0.503470	−	4.79020i	−0.0171284	−	0.162966i
$865$	−24.1362	+	36.2905i	−0.820656	+	1.23392i
$866$	50.8355	+	5.34303i	1.72746	+	0.181564i
$867$	6.68871	+	3.40807i	0.227160	+	0.115744i
$868$	5.18016	+	18.5249i	0.175826	+	0.628775i
$869$	0.301034	−	0.0978117i	0.0102119	−	0.00331804i
$870$	18.9860	+	26.7428i	0.643686	+	0.906666i
$871$	3.67290	−	3.30709i	0.124451	−	0.112056i
$872$	−0.768250	+	14.6591i	−0.0260162	+	0.496419i
$873$	−3.37260	−	8.78592i	−0.114145	−	0.297358i
$874$	25.9336			0.877218
$875$	−29.5667	+	0.898750i	−0.999538	+	0.0303833i
$876$	−0.429548			−0.0145131
$877$	−13.1409	−	34.2333i	−0.443738	−	1.15598i	−0.955014	−	0.296560i	$-0.904160\pi$
$877$	−13.1409	−	34.2333i	−0.443738	−	1.15598i	0.511276	−	0.859416i	$-0.329173\pi$
$878$	1.10750	−	21.1324i	0.0373764	−	0.713184i
$879$	−0.811382	+	0.730572i	−0.0273672	+	0.0246416i
$880$	24.9921	+	35.2026i	0.842482	+	1.18668i
$881$	45.6777	−	14.8416i	1.53892	−	0.500026i	0.587843	−	0.808975i	$-0.299977\pi$
$881$	45.6777	−	14.8416i	1.53892	−	0.500026i	0.951078	+	0.308950i	$0.0999774\pi$
$882$	−2.84128	+	11.6074i	−0.0956709	+	0.390841i
$883$	2.42995	+	1.23812i	0.0817744	+	0.0416661i	0.494399	−	0.869235i	$-0.335388\pi$
$883$	2.42995	+	1.23812i	0.0817744	+	0.0416661i	−0.412625	+	0.910901i	$0.635388\pi$
$884$	−2.84790	−	0.299326i	−0.0957852	−	0.0100674i
$885$	−13.0102	+	19.5617i	−0.437333	+	0.657561i
$886$	3.45988	+	32.9186i	0.116237	+	1.10592i
$887$	−10.6723	−	13.1792i	−0.358340	−	0.442514i	0.565814	−	0.824533i	$-0.308562\pi$
$887$	−10.6723	−	13.1792i	−0.358340	−	0.442514i	−0.924154	+	0.382019i	$0.875229\pi$
$888$	2.67053	+	16.8611i	0.0896171	+	0.565820i
$889$	44.5350	+	19.2510i	1.49366	+	0.645659i
$890$	11.6595	−	7.39155i	0.390826	−	0.247765i
$891$	−0.404222	+	3.84592i	−0.0135419	+	0.128843i
$892$	−13.2299	+	8.59162i	−0.442971	+	0.287669i
$893$	7.81831	+	29.1783i	0.261630	+	0.976416i
$894$	−3.72873	+	4.14117i	−0.124707	+	0.138501i
$895$	15.9541	+	3.57413i	0.533288	+	0.119470i
$896$	−24.6124	+	22.6503i	−0.822242	+	0.756692i
$897$	−1.29450	+	0.659580i	−0.0432221	+	0.0220227i
$898$	−3.70117	+	1.42074i	−0.123510	+	0.0474109i
$899$	34.1569	−	59.1615i	1.13920	−	1.97315i
$900$	1.31726	+	4.37798i	0.0439085	+	0.145933i
$901$	−46.6881	+	26.9554i	−1.55541	+	0.898015i
$902$	3.77922	−	23.8611i	0.125834	−	0.794486i
$903$	−0.312769	−	0.597694i	−0.0104083	−	0.0198900i
$904$	9.12900	+	2.96619i	0.303626	+	0.0986541i
$905$	24.6655	+	18.3364i	0.819909	+	0.609522i
$906$	−5.67059	+	26.6781i	−0.188393	+	0.886319i
$907$	−19.6432	+	5.26338i	−0.652242	+	0.174768i	−0.569742	−	0.821823i	$-0.692957\pi$
$907$	−19.6432	+	5.26338i	−0.652242	+	0.174768i	−0.0824995	+	0.996591i	$0.526290\pi$
$908$	2.32438	−	0.121816i	0.0771373	−	0.00404260i
$909$	−2.90692	−	2.11200i	−0.0964165	−	0.0700507i
$910$	4.96506	+	4.02127i	0.164590	+	0.133304i
$911$	19.1017	−	13.8782i	0.632868	−	0.459806i	−0.224525	−	0.974468i	$-0.572083\pi$
$911$	19.1017	−	13.8782i	0.632868	−	0.459806i	0.857393	+	0.514663i	$0.172083\pi$
$912$	25.6654	−	20.7835i	0.849867	−	0.688209i
$913$	21.3774	+	8.20601i	0.707488	+	0.271579i
$914$	28.2327	−	2.96738i	0.933856	−	0.0981522i
$915$	−4.27151	−	29.0220i	−0.141212	−	0.959437i
$916$	0.0786192	−	0.108210i	0.00259765	−	0.00357536i
$917$	12.4265	+	18.6873i	0.410358	+	0.617108i
$918$	−5.97588	+	5.97588i	−0.197233	+	0.197233i
$919$	19.8837	+	17.9034i	0.655902	+	0.590577i	0.928401	−	0.371579i	$-0.121183\pi$
$919$	19.8837	+	17.9034i	0.655902	+	0.590577i	−0.272499	+	0.962156i	$0.587850\pi$
$920$	4.66817	+	8.29387i	0.153905	+	0.273441i
$921$	−14.7630	−	16.3960i	−0.486457	−	0.540266i
$922$	9.69020	−	14.9216i	0.319130	−	0.491417i
$923$	−1.06830	−	0.169202i	−0.0351634	−	0.00556934i
$924$	−8.05060	+	4.76543i	−0.264845	+	0.156771i
$925$	−15.5596	−	43.3475i	−0.511596	−	1.42526i
$926$	−12.5674	−	21.7674i	−0.412990	−	0.715320i
$927$	5.66524	+	4.58762i	0.186071	+	0.150677i
$928$	−41.3257	−	2.16579i	−1.35658	−	0.0710955i
$929$	22.3504	−	4.75071i	0.733291	−	0.155866i	0.173893	−	0.984765i	$-0.444365\pi$
$929$	22.3504	−	4.75071i	0.733291	−	0.155866i	0.559399	+	0.828899i	$0.311032\pi$
$930$	22.7770	−	20.0614i	0.746887	−	0.657839i
$931$	−43.7156	+	15.2623i	−1.43272	+	0.500201i
$932$	−12.9211	−	12.9211i	−0.423244	−	0.423244i
$933$	−0.913773	−	17.4358i	−0.0299156	−	0.570823i
$934$	14.0379	−	6.25006i	0.459333	−	0.204508i
$935$	11.5312	−	41.2246i	0.377112	−	1.34819i
$936$	−0.476881	+	1.07109i	−0.0155873	+	0.0350097i
$937$	40.5664	−	6.42508i	1.32525	−	0.209898i	0.546617	−	0.837383i	$-0.315916\pi$
$937$	40.5664	−	6.42508i	1.32525	−	0.209898i	0.778629	+	0.627485i	$0.215916\pi$
$938$	27.1801	−	22.5035i	0.887462	−	0.734765i
$939$	−11.1534	−	15.3514i	−0.363979	−	0.500974i
$940$	6.67419	−	6.52965i	0.217688	−	0.212974i
$941$	5.86225	+	13.1668i	0.191104	+	0.429226i	0.983531	−	0.180741i	$-0.0578494\pi$
$941$	5.86225	+	13.1668i	0.191104	+	0.429226i	−0.792427	+	0.609967i	$0.791183\pi$
$942$	−15.1504	−	23.3296i	−0.493626	−	0.760118i
$943$	2.17513	−	8.11770i	0.0708320	−	0.264349i
$944$	−16.2095	−	49.8878i	−0.527576	−	1.62371i
$945$	5.78690	−	1.22957i	0.188248	−	0.0399979i
$946$	0.520148	−	1.60085i	0.0169115	−	0.0520482i
$947$	17.2819	+	11.2230i	0.561588	+	0.364699i	0.794000	−	0.607918i	$-0.207995\pi$
$947$	17.2819	+	11.2230i	0.561588	+	0.364699i	−0.232412	+	0.972617i	$0.574662\pi$
$948$	−0.0470997	+	0.0581632i	−0.00152973	+	0.00188905i
$949$	0.257373	+	0.148594i	0.00835468	+	0.00482358i
$950$	−36.4847	+	43.0908i	−1.18372	+	1.39805i
$951$		−	24.6423i		−	0.799080i
$952$	24.0153	+	3.53654i	0.778341	+	0.114620i
$953$	15.6838	+	30.7811i	0.508047	+	0.997099i	0.992496	+	0.122279i	$0.0390203\pi$
$953$	15.6838	+	30.7811i	0.508047	+	0.997099i	−0.484448	+	0.874820i	$0.660980\pi$
$954$	−3.86530	−	18.1848i	−0.125144	−	0.588755i
$955$	−1.72201	+	0.969228i	−0.0557231	+	0.0313635i
$956$	−22.0837	−	4.69403i	−0.714237	−	0.151816i
$957$	32.0927	+	8.59922i	1.03741	+	0.277973i
$958$	−27.5499	+	54.0698i	−0.890098	+	1.74692i
$959$	19.3163	+	13.7158i	0.623755	+	0.442908i
$960$	3.66402	+	1.45270i	0.118256	+	0.0468858i
$961$	−29.4356	−	13.1056i	−0.949535	−	0.422760i
$962$	−3.56497	+	9.28707i	−0.114939	+	0.299427i
$963$	6.78733	−	17.6816i	0.218719	−	0.569781i
$964$	−19.3530	−	8.61652i	−0.623319	−	0.277519i
$965$	1.74054	−	2.10192i	0.0560300	−	0.0676632i
$966$	−9.42968	+	4.32177i	−0.303395	+	0.139051i
$967$	−19.3626	+	38.0013i	−0.622660	+	1.22204i	0.337167	+	0.941445i	$0.390531\pi$
$967$	−19.3626	+	38.0013i	−0.622660	+	1.22204i	−0.959827	+	0.280593i	$0.909469\pi$
$968$	7.07921	+	1.89687i	0.227535	+	0.0609677i
$969$	−32.0304	−	6.80827i	−1.02896	−	0.218713i
$970$	−35.6846	−	4.14603i	−1.14576	−	0.133121i
$971$	7.92956	+	37.3056i	0.254472	+	1.19719i	0.900834	+	0.434164i	$0.142956\pi$
$971$	7.92956	+	37.3056i	0.254472	+	1.19719i	−0.646362	+	0.763031i	$0.723711\pi$
$972$	−0.415116	−	0.814711i	−0.0133149	−	0.0261319i
$973$	−41.3853	+	16.4046i	−1.32675	+	0.525907i
$974$		−	21.6300i		−	0.693070i
$975$	0.725222	−	3.07884i	0.0232257	−	0.0986018i
$976$	56.7230	+	32.7490i	1.81566	+	1.04827i
$977$	8.71405	−	10.7610i	0.278787	−	0.344274i	−0.618449	−	0.785825i	$-0.712238\pi$
$977$	8.71405	−	10.7610i	0.278787	−	0.344274i	0.897236	+	0.441552i	$0.145572\pi$
$978$	0.0752561	+	0.0488719i	0.00240642	+	0.00156275i
$979$	4.32162	−	13.3006i	0.138120	−	0.425089i
$980$	10.7387	+	9.46140i	0.343037	+	0.302233i
$981$	2.44755	+	7.53278i	0.0781442	+	0.240503i
$982$	8.95732	−	33.4292i	0.285840	−	1.06677i
$983$	−7.72816	−	11.9003i	−0.246490	−	0.379562i	0.693671	−	0.720292i	$-0.255992\pi$
$983$	−7.72816	−	11.9003i	−0.246490	−	0.379562i	−0.940161	+	0.340731i	$0.889326\pi$
$984$	−2.75854	−	6.19577i	−0.0879389	−	0.197514i
$985$	25.8316	+	13.5201i	0.823064	+	0.430785i
$986$	42.6789	+	58.7424i	1.35917	+	1.87074i
$987$	−7.70529	−	9.30657i	−0.245262	−	0.296232i
$988$	3.77919	−	0.598566i	0.120232	−	0.0190429i
$989$	0.238165	−	0.534927i	0.00757320	−	0.0170097i
$990$	12.2916	+	8.17496i	0.390654	+	0.259817i
$991$	−9.55333	+	4.25341i	−0.303471	+	0.135114i	−0.552823	−	0.833299i	$-0.686449\pi$
$991$	−9.55333	+	4.25341i	−0.303471	+	0.135114i	0.249351	+	0.968413i	$0.419783\pi$
$992$	2.00434	+	38.2450i	0.0636378	+	1.21428i
$993$	16.6740	+	16.6740i	0.529134	+	0.529134i
$994$	−7.57062	−	1.52338i	−0.240126	−	0.0483187i
$995$	−46.3660	+	4.36066i	−1.46990	+	0.138242i
$996$	−5.29596	+	1.12569i	−0.167809	+	0.0356689i
$997$	13.0782	+	0.685402i	0.414192	+	0.0217069i	0.258294	−	0.966066i	$-0.416840\pi$
$997$	13.0782	+	0.685402i	0.414192	+	0.0217069i	0.155898	+	0.987773i	$0.450173\pi$
$998$	34.1522	+	27.6559i	1.08107	+	0.875432i
$999$	4.60555	+	7.97704i	0.145713	+	0.252382i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bv.a.52.10	✓	640
7.5	odd	6	inner	525.2.bv.a.502.10	yes	640
25.13	odd	20	inner	525.2.bv.a.388.10	yes	640
175.138	even	60	inner	525.2.bv.a.313.10	yes	640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bv.a.52.10	✓	640	1.1	even	1	trivial
525.2.bv.a.313.10	yes	640	175.138	even	60	inner
525.2.bv.a.388.10	yes	640	25.13	odd	20	inner
525.2.bv.a.502.10	yes	640	7.5	odd	6	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bv (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.611789 - 1.59376i) q^{2} +(-0.0523360 + 0.998630i) q^{3} +(-0.679511 + 0.611834i) q^{4} +(-1.29445 - 1.82330i) q^{5} +(1.62360 - 0.527539i) q^{6} +(-2.56289 - 0.656955i) q^{7} +(-1.65133 - 0.841396i) q^{8} +(-0.994522 - 0.104528i) q^{9} +O(q^{10})\)	\(q+(-0.611789 - 1.59376i) q^{2} +(-0.0523360 + 0.998630i) q^{3} +(-0.679511 + 0.611834i) q^{4} +(-1.29445 - 1.82330i) q^{5} +(1.62360 - 0.527539i) q^{6} +(-2.56289 - 0.656955i) q^{7} +(-1.65133 - 0.841396i) q^{8} +(-0.994522 - 0.104528i) q^{9} +(-2.11398 + 3.17852i) q^{10} +(0.404222 + 3.84592i) q^{11} +(-0.575433 - 0.710600i) q^{12} +(0.0989636 + 0.624832i) q^{13} +(0.520917 + 4.48656i) q^{14} +(1.88854 - 1.19725i) q^{15} +(-0.521876 + 4.96532i) q^{16} +(4.15179 - 2.69621i) q^{17} +(0.441844 + 1.64898i) q^{18} +(-4.42613 + 4.91572i) q^{19} +(1.99515 + 0.446963i) q^{20} +(0.790186 - 2.52500i) q^{21} +(5.88219 - 2.99712i) q^{22} +(2.14402 - 0.823013i) q^{23} +(0.926667 - 1.60503i) q^{24} +(-1.64882 + 4.72032i) q^{25} +(0.935290 - 0.539990i) q^{26} +(0.156434 - 0.987688i) q^{27} +(2.14346 - 1.12166i) q^{28} +(-8.17116 - 2.65497i) q^{29} +(-3.06352 - 2.27743i) q^{30} +(-1.65314 + 7.77743i) q^{31} +(4.65246 - 1.24662i) q^{32} +(-3.86180 + 0.202388i) q^{33} +(-6.83714 - 4.96747i) q^{34} +(2.11970 + 5.52330i) q^{35} +(0.739742 - 0.537454i) q^{36} +(-7.15837 + 5.79673i) q^{37} +(10.5424 + 4.04683i) q^{38} +(-0.629155 + 0.0661268i) q^{39} +(0.603447 + 4.10001i) q^{40} +(2.15095 - 2.96053i) q^{41} +(-4.50768 + 0.285395i) q^{42} +(0.180290 - 0.180290i) q^{43} +(-2.62774 - 2.36602i) q^{44} +(1.09677 + 1.94861i) q^{45} +(-2.62338 - 2.91356i) q^{46} +(2.48721 - 3.82996i) q^{47} +(-4.93120 - 0.781025i) q^{48} +(6.13682 + 3.36741i) q^{49} +(8.53180 - 0.260011i) q^{50} +(2.47522 + 4.28721i) q^{51} +(-0.449540 - 0.364031i) q^{52} +(-10.8752 - 0.569943i) q^{53} +(-1.66985 + 0.354937i) q^{54} +(6.48900 - 5.71535i) q^{55} +(3.67943 + 3.24126i) q^{56} +(-4.67733 - 4.67733i) q^{57} +(0.767626 + 14.6472i) q^{58} +(-9.59811 + 4.27336i) q^{59} +(-0.550768 + 1.96902i) q^{60} +(5.33592 - 11.9847i) q^{61} +(13.4068 - 2.12342i) q^{62} +(2.48018 + 0.921251i) q^{63} +(1.03608 + 1.42605i) q^{64} +(1.01115 - 0.989251i) q^{65} +(2.68517 + 6.03098i) q^{66} +(-4.25501 - 6.55214i) q^{67} +(-1.17156 + 4.37231i) q^{68} +(0.709676 + 2.18416i) q^{69} +(7.50603 - 6.75740i) q^{70} +(-0.528338 + 1.62606i) q^{71} +(1.55434 + 1.00940i) q^{72} +(0.295639 - 0.365083i) q^{73} +(13.6180 + 7.86238i) q^{74} +(-4.62756 - 1.89360i) q^{75} -6.04834i q^{76} +(1.49062 - 10.1222i) q^{77} +(0.490301 + 0.962269i) q^{78} +(-0.0170177 - 0.0800622i) q^{79} +(9.72878 - 5.47580i) q^{80} +(0.978148 + 0.207912i) q^{81} +(-6.03432 - 1.61689i) q^{82} +(2.68822 - 5.27592i) q^{83} +(1.00794 + 2.19922i) q^{84} +(-10.2903 - 4.07985i) q^{85} +(-0.397639 - 0.177040i) q^{86} +(3.07898 - 8.02101i) q^{87} +(2.56843 - 6.69100i) q^{88} +(-3.30376 - 1.47093i) q^{89} +(2.43464 - 2.94013i) q^{90} +(0.156853 - 1.66639i) q^{91} +(-0.953339 + 1.87103i) q^{92} +(-7.68025 - 2.05792i) q^{93} +(-7.62571 - 1.62089i) q^{94} +(14.6922 + 1.70702i) q^{95} +(1.00142 + 4.71133i) q^{96} +(4.27250 + 8.38526i) q^{97} +(1.61242 - 11.8408i) q^{98} -3.86710i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q + 12 q^{5} - 8 q^{7} + 24 q^{8}+O(q^{10}) \) 640 * q + 12 * q^5 - 8 * q^7 + 24 * q^8	\( 640 q + 12 q^{5} - 8 q^{7} + 24 q^{8} + 12 q^{10} + 8 q^{15} - 80 q^{16} - 72 q^{22} + 48 q^{23} - 12 q^{25} - 36 q^{28} - 80 q^{29} + 32 q^{30} - 24 q^{32} + 36 q^{33} - 64 q^{35} + 160 q^{36} - 4 q^{37} - 192 q^{38} - 12 q^{40} - 16 q^{42} + 120 q^{43} + 60 q^{47} + 288 q^{50} - 432 q^{52} - 136 q^{53} - 16 q^{57} - 4 q^{58} - 240 q^{59} - 20 q^{60} - 4 q^{63} + 120 q^{64} + 4 q^{65} - 8 q^{67} - 132 q^{68} + 76 q^{70} - 12 q^{72} - 36 q^{73} - 48 q^{75} - 60 q^{77} - 80 q^{78} + 12 q^{80} - 80 q^{81} - 252 q^{82} - 160 q^{84} + 72 q^{85} + 24 q^{87} + 152 q^{88} + 56 q^{92} - 96 q^{93} + 172 q^{95} - 488 q^{98}+O(q^{100}) \) 640 * q + 12 * q^5 - 8 * q^7 + 24 * q^8 + 12 * q^10 + 8 * q^15 - 80 * q^16 - 72 * q^22 + 48 * q^23 - 12 * q^25 - 36 * q^28 - 80 * q^29 + 32 * q^30 - 24 * q^32 + 36 * q^33 - 64 * q^35 + 160 * q^36 - 4 * q^37 - 192 * q^38 - 12 * q^40 - 16 * q^42 + 120 * q^43 + 60 * q^47 + 288 * q^50 - 432 * q^52 - 136 * q^53 - 16 * q^57 - 4 * q^58 - 240 * q^59 - 20 * q^60 - 4 * q^63 + 120 * q^64 + 4 * q^65 - 8 * q^67 - 132 * q^68 + 76 * q^70 - 12 * q^72 - 36 * q^73 - 48 * q^75 - 60 * q^77 - 80 * q^78 + 12 * q^80 - 80 * q^81 - 252 * q^82 - 160 * q^84 + 72 * q^85 + 24 * q^87 + 152 * q^88 + 56 * q^92 - 96 * q^93 + 172 * q^95 - 488 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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