LMFDB - Embedded newform 639.2.z.a.53.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [639,2,Mod(35,639)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(639, base_ring=CyclotomicField(70))

chi = DirichletCharacter(H, H._module([35, 29]))

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

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

chi := DirichletCharacter("639.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 639 = 3^{2} \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	639.z (of order $70$, degree $24$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.10244068916$
Analytic rank:	$0$
Dimension:	$576$
Relative dimension:	$24$ over $\Q(\zeta_{70})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{70}]$

Embedding invariants

Embedding label			53.5
Character	$\chi$	$=$	639.53
Dual form			639.2.z.a.422.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.180328 - 2.00361i) q^{2} +(-2.01408 + 0.365501i) q^{4} +(0.521198 - 0.717368i) q^{5} +(-0.352855 - 0.590579i) q^{7} +(0.0251400 + 0.0910928i) q^{8} +O(q^{10})$	\(q+(-0.180328 - 2.00361i) q^{2} +(-2.01408 + 0.365501i) q^{4} +(0.521198 - 0.717368i) q^{5} +(-0.352855 - 0.590579i) q^{7} +(0.0251400 + 0.0910928i) q^{8} +(-1.53131 - 0.914916i) q^{10} +(-0.768209 + 1.16379i) q^{11} +(-4.65350 + 3.07175i) q^{13} +(-1.11966 + 0.813481i) q^{14} +(-3.65492 + 1.37171i) q^{16} +(2.27312 - 6.99594i) q^{17} +(-5.61850 - 5.87649i) q^{19} +(-0.787535 + 1.63533i) q^{20} +(2.47031 + 1.32933i) q^{22} +(-1.32447 - 5.80286i) q^{23} +(1.30212 + 4.00750i) q^{25} +(6.99375 + 8.76988i) q^{26} +(0.926534 + 1.06050i) q^{28} +(-1.96472 + 1.05726i) q^{29} +(2.21005 - 5.88866i) q^{31} +(3.48947 + 7.24595i) q^{32} +(-14.4271 - 3.29288i) q^{34} +(-0.607569 - 0.0546822i) q^{35} +(-1.56286 + 6.84735i) q^{37} +(-10.7610 + 12.3170i) q^{38} +(0.0784500 + 0.0294428i) q^{40} +(1.13399 - 1.42197i) q^{41} +(1.99491 - 1.74290i) q^{43} +(1.12187 - 2.62474i) q^{44} +(-11.3878 + 3.70013i) q^{46} +(0.987800 + 7.29223i) q^{47} +(3.09280 - 5.74739i) q^{49} +(7.79466 - 3.33160i) q^{50} +(8.24979 - 7.88760i) q^{52} +(-6.83469 - 1.24031i) q^{53} +(0.434474 + 1.15765i) q^{55} +(0.0449267 - 0.0469897i) q^{56} +(2.47264 + 3.74589i) q^{58} +(-0.111884 - 2.49130i) q^{59} +(-0.319769 + 0.535203i) q^{61} +(-12.1971 - 3.36619i) q^{62} +(7.18631 - 4.29362i) q^{64} +(-0.221822 + 4.93926i) q^{65} +(2.86556 + 15.7905i) q^{67} +(-2.02121 + 14.9212i) q^{68} +1.22719i q^{70} +(6.74102 - 5.05556i) q^{71} +(-1.50301 + 0.135273i) q^{73} +(14.0013 + 1.89660i) q^{74} +(13.4640 + 9.78214i) q^{76} +(0.958375 + 0.0430407i) q^{77} +(10.3091 - 2.84513i) q^{79} +(-0.920913 + 3.33685i) q^{80} +(-3.05357 - 2.01565i) q^{82} +(6.14686 - 0.276056i) q^{83} +(-3.83392 - 5.27693i) q^{85} +(-3.85184 - 3.68274i) q^{86} +(-0.125325 - 0.0407207i) q^{88} +(1.54601 - 8.51921i) q^{89} +(3.45612 + 1.66438i) q^{91} +(4.78853 + 11.2033i) q^{92} +(14.4327 - 3.29416i) q^{94} +(-7.14396 + 0.967715i) q^{95} +(11.1237 - 8.87087i) q^{97} +(-12.0733 - 5.16036i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 576 q - 24 q^{4}+O(q^{10}) $ 576 * q - 24 * q^4	$ 576 q - 24 q^{4} - 16 q^{10} + 76 q^{16} - 8 q^{19} + 20 q^{22} + 168 q^{25} - 20 q^{28} - 28 q^{31} + 40 q^{37} + 32 q^{40} + 52 q^{43} - 20 q^{46} - 208 q^{52} - 92 q^{55} + 56 q^{58} + 56 q^{61} - 144 q^{64} - 16 q^{67} - 44 q^{73} - 336 q^{76} + 88 q^{79} - 124 q^{82} + 60 q^{85} - 260 q^{88} + 80 q^{91} + 56 q^{94} - 56 q^{97}+O(q^{100}) $ 576 * q - 24 * q^4 - 16 * q^10 + 76 * q^16 - 8 * q^19 + 20 * q^22 + 168 * q^25 - 20 * q^28 - 28 * q^31 + 40 * q^37 + 32 * q^40 + 52 * q^43 - 20 * q^46 - 208 * q^52 - 92 * q^55 + 56 * q^58 + 56 * q^61 - 144 * q^64 - 16 * q^67 - 44 * q^73 - 336 * q^76 + 88 * q^79 - 124 * q^82 + 60 * q^85 - 260 * q^88 + 80 * q^91 + 56 * q^94 - 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/639\mathbb{Z}\right)^\times$.

$n$	$433$	$569$
$\chi(n)$	$e\left(\frac{23}{70}\right)$	$-1$

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 $

$2$	−0.180328	−	2.00361i	−0.127511	−	1.41677i	−0.763868	−	0.645372i	$-0.776702\pi$
$2$	−0.180328	−	2.00361i	−0.127511	−	1.41677i	0.636357	−	0.771395i	$-0.280441\pi$
$3$		0			0
$3$		0			0
$4$	−2.01408	+	0.365501i	−1.00704	+	0.182751i
$5$	0.521198	−	0.717368i	0.233087	−	0.320817i	−0.676412	−	0.736524i	$-0.736466\pi$
$5$	0.521198	−	0.717368i	0.233087	−	0.320817i	0.909498	+	0.415707i	$0.136466\pi$
$6$		0			0
$7$	−0.352855	−	0.590579i	−0.133366	−	0.223218i	0.784479	−	0.620155i	$-0.212930\pi$
$7$	−0.352855	−	0.590579i	−0.133366	−	0.223218i	−0.917846	+	0.396937i	$0.870073\pi$
$8$	0.0251400	+	0.0910928i	0.00888834	+	0.0322062i
$9$		0			0
$10$	−1.53131	−	0.914916i	−0.484243	−	0.289322i
$11$	−0.768209	+	1.16379i	−0.231624	+	0.350895i	−0.931735	−	0.363139i	$-0.881705\pi$
$11$	−0.768209	+	1.16379i	−0.231624	+	0.350895i	0.700111	+	0.714034i	$0.253134\pi$
$12$		0			0
$13$	−4.65350	+	3.07175i	−1.29065	+	0.851950i	−0.994656	−	0.103241i	$-0.967079\pi$
$13$	−4.65350	+	3.07175i	−1.29065	+	0.851950i	−0.295992	+	0.955190i	$0.595650\pi$
$14$	−1.11966	+	0.813481i	−0.299242	+	0.217412i
$15$		0			0
$16$	−3.65492	+	1.37171i	−0.913729	+	0.342928i
$17$	2.27312	−	6.99594i	0.551312	−	1.69677i	−0.154176	−	0.988043i	$-0.549272\pi$
$17$	2.27312	−	6.99594i	0.551312	−	1.69677i	0.705488	−	0.708722i	$-0.250728\pi$
$18$		0			0
$19$	−5.61850	−	5.87649i	−1.28897	−	1.34816i	−0.905348	−	0.424670i	$-0.860390\pi$
$19$	−5.61850	−	5.87649i	−1.28897	−	1.34816i	−0.383624	−	0.923489i	$-0.625324\pi$
$20$	−0.787535	+	1.63533i	−0.176098	+	0.365672i
$21$		0			0
$22$	2.47031	+	1.32933i	0.526671	+	0.283414i
$23$	−1.32447	−	5.80286i	−0.276170	−	1.20998i	−0.902592	−	0.430497i	$-0.858338\pi$
$23$	−1.32447	−	5.80286i	−0.276170	−	1.20998i	0.626422	−	0.779484i	$-0.284519\pi$
$24$		0			0
$25$	1.30212	+	4.00750i	0.260423	+	0.801500i
$26$	6.99375	+	8.76988i	1.37159	+	1.71991i
$27$		0			0
$28$	0.926534	+	1.06050i	0.175098	+	0.200416i
$29$	−1.96472	+	1.05726i	−0.364840	+	0.196329i	−0.646010	−	0.763329i	$-0.723563\pi$
$29$	−1.96472	+	1.05726i	−0.364840	+	0.196329i	0.281170	+	0.959658i	$0.409278\pi$
$30$		0			0
$31$	2.21005	−	5.88866i	0.396937	−	1.05763i	−0.574117	−	0.818773i	$-0.694655\pi$
$31$	2.21005	−	5.88866i	0.396937	−	1.05763i	0.971054	−	0.238861i	$-0.0767740\pi$
$32$	3.48947	+	7.24595i	0.616856	+	1.28092i
$33$		0			0
$34$	−14.4271	−	3.29288i	−2.47422	−	0.564724i
$35$	−0.607569	−	0.0546822i	−0.102698	−	0.00924298i
$36$		0			0
$37$	−1.56286	+	6.84735i	−0.256933	+	1.12570i	0.667577	+	0.744541i	$0.267331\pi$
$37$	−1.56286	+	6.84735i	−0.256933	+	1.12570i	−0.924510	+	0.381157i	$0.875526\pi$
$38$	−10.7610	+	12.3170i	−1.74567	+	1.99808i
$39$		0			0
$40$	0.0784500	+	0.0294428i	0.0124040	+	0.00465531i
$41$	1.13399	−	1.42197i	0.177099	−	0.222075i	−0.685357	−	0.728207i	$-0.740354\pi$
$41$	1.13399	−	1.42197i	0.177099	−	0.222075i	0.862456	+	0.506132i	$0.168925\pi$
$42$		0			0
$43$	1.99491	−	1.74290i	0.304221	−	0.265790i	−0.492267	−	0.870444i	$-0.663832\pi$
$43$	1.99491	−	1.74290i	0.304221	−	0.265790i	0.796488	+	0.604654i	$0.206689\pi$
$44$	1.12187	−	2.62474i	0.169128	−	0.395695i
$45$		0			0
$46$	−11.3878	+	3.70013i	−1.67905	+	0.545555i
$47$	0.987800	+	7.29223i	0.144085	+	1.06368i	0.908181	+	0.418578i	$0.137471\pi$
$47$	0.987800	+	7.29223i	0.144085	+	1.06368i	−0.764095	+	0.645103i	$0.776814\pi$
$48$		0			0
$49$	3.09280	−	5.74739i	0.441829	−	0.821056i
$50$	7.79466	−	3.33160i	1.10233	−	0.471159i
$51$		0			0
$52$	8.24979	−	7.88760i	1.14404	−	1.09381i
$53$	−6.83469	−	1.24031i	−0.938817	−	0.170370i	−0.312481	−	0.949924i	$-0.601160\pi$
$53$	−6.83469	−	1.24031i	−0.938817	−	0.170370i	−0.626335	+	0.779554i	$0.715446\pi$
$54$		0			0
$55$	0.434474	+	1.15765i	0.0585845	+	0.156098i
$56$	0.0449267	−	0.0469897i	0.00600359	−	0.00627926i
$57$		0			0
$58$	2.47264	+	3.74589i	0.324673	+	0.491859i
$59$	−0.111884	−	2.49130i	−0.0145661	−	0.324339i	−0.993025	−	0.117900i	$-0.962384\pi$
$59$	−0.111884	−	2.49130i	−0.0145661	−	0.324339i	0.978459	−	0.206439i	$-0.0661876\pi$
$60$		0			0
$61$	−0.319769	+	0.535203i	−0.0409422	+	0.0685258i	−0.878236	−	0.478228i	$-0.841279\pi$
$61$	−0.319769	+	0.535203i	−0.0409422	+	0.0685258i	0.837294	+	0.546753i	$0.184137\pi$
$62$	−12.1971	−	3.36619i	−1.54904	−	0.427506i
$63$		0			0
$64$	7.18631	−	4.29362i	0.898289	−	0.536703i
$65$	−0.221822	+	4.93926i	−0.0275137	+	0.612640i
$66$		0			0
$67$	2.86556	+	15.7905i	0.350084	+	1.92912i	0.369311	+	0.929306i	$0.379594\pi$
$67$	2.86556	+	15.7905i	0.350084	+	1.92912i	−0.0192274	+	0.999815i	$0.506121\pi$
$68$	−2.02121	+	14.9212i	−0.245108	+	1.80946i
$69$		0			0
$70$			1.22719i			0.146678i
$71$	6.74102	−	5.05556i	0.800012	−	0.599985i
$71$	6.74102	−	5.05556i	0.800012	−	0.599985i
$72$		0			0
$73$	−1.50301	+	0.135273i	−0.175914	+	0.0158325i	−0.177246	−	0.984167i	$-0.556719\pi$
$73$	−1.50301	+	0.135273i	−0.175914	+	0.0158325i	0.00133229	+	0.999999i	$0.499576\pi$
$74$	14.0013	+	1.89660i	1.62761	+	0.220475i
$75$		0			0
$76$	13.4640	+	9.78214i	1.54442	+	1.12209i
$77$	0.958375	+	0.0430407i	0.109217	+	0.00490494i
$78$		0			0
$79$	10.3091	−	2.84513i	1.15987	−	0.320103i	0.367426	−	0.930053i	$-0.380239\pi$
$79$	10.3091	−	2.84513i	1.15987	−	0.320103i	0.792440	+	0.609950i	$0.208811\pi$
$80$	−0.920913	+	3.33685i	−0.102961	+	0.373071i
$81$		0			0
$82$	−3.05357	−	2.01565i	−0.337211	−	0.222591i
$83$	6.14686	−	0.276056i	0.674706	−	0.0303011i	0.295124	−	0.955459i	$-0.404639\pi$
$83$	6.14686	−	0.276056i	0.674706	−	0.0303011i	0.379582	+	0.925158i	$0.376068\pi$
$84$		0			0
$85$	−3.83392	−	5.27693i	−0.415847	−	0.572364i
$86$	−3.85184	−	3.68274i	−0.415354	−	0.397120i
$87$		0			0
$88$	−0.125325	−	0.0407207i	−0.0133597	−	0.00434084i
$89$	1.54601	−	8.51921i	0.163877	−	0.903035i	−0.792275	−	0.610164i	$-0.791104\pi$
$89$	1.54601	−	8.51921i	0.163877	−	0.903035i	0.956152	−	0.292871i	$-0.0946107\pi$
$90$		0			0
$91$	3.45612	+	1.66438i	0.362300	+	0.174474i
$92$	4.78853	+	11.2033i	0.499239	+	1.16803i
$93$		0			0
$94$	14.4327	−	3.29416i	1.48862	−	0.339767i
$95$	−7.14396	+	0.967715i	−0.732954	+	0.0992854i
$96$		0			0
$97$	11.1237	−	8.87087i	1.12944	−	0.900701i	0.133532	−	0.991044i	$-0.457368\pi$
$97$	11.1237	−	8.87087i	1.12944	−	0.900701i	0.995911	+	0.0903438i	$0.0287966\pi$
$98$	−12.0733	−	5.16036i	−1.21958	−	0.521275i
$99$		0			0
$100$	−4.08731	−	7.59550i	−0.408731	−	0.759550i
$101$	−9.71099	−	7.74426i	−0.966280	−	0.770582i	0.00705433	−	0.999975i	$-0.497755\pi$
$101$	−9.71099	−	7.74426i	−0.966280	−	0.770582i	−0.973334	+	0.229393i	$0.926326\pi$
$102$		0			0
$103$	10.0100	−	4.82057i	0.986317	−	0.474985i	0.130043	−	0.991508i	$-0.458488\pi$
$103$	10.0100	−	4.82057i	0.986317	−	0.474985i	0.856273	+	0.516523i	$0.172774\pi$
$104$	−0.396803	−	0.346677i	−0.0389098	−	0.0339944i
$105$		0			0
$106$	−1.25262	+	13.9177i	−0.121665	+	1.35181i
$107$	1.31379	−	14.5974i	0.127009	−	1.41119i	−0.639419	−	0.768858i	$-0.720825\pi$
$107$	1.31379	−	14.5974i	0.127009	−	1.41119i	0.766428	−	0.642330i	$-0.222032\pi$
$108$		0			0
$109$	−10.2842	−	8.98500i	−0.985043	−	0.860607i	0.00519557	−	0.999987i	$-0.498346\pi$
$109$	−10.2842	−	8.98500i	−0.985043	−	0.860607i	−0.990239	+	0.139380i	$0.955489\pi$
$110$	2.24114	−	1.07927i	0.213684	−	0.102905i
$111$		0			0
$112$	2.09976	+	1.67450i	0.198409	+	0.158226i
$113$	3.72726	+	6.92641i	0.350631	+	0.651582i	0.993429	−	0.114454i	$-0.0365120\pi$
$113$	3.72726	+	6.92641i	0.350631	+	0.651582i	−0.642797	+	0.766036i	$0.722226\pi$
$114$		0			0
$115$	−4.85310	−	2.07431i	−0.452554	−	0.193431i
$116$	3.57068	−	2.84752i	0.331529	−	0.264385i
$117$		0			0
$118$	−4.97142	+	0.673424i	−0.457656	+	0.0619937i
$119$	−4.93374	+	1.12609i	−0.452275	+	0.103229i
$120$		0			0
$121$	3.55902	+	8.32674i	0.323547	+	0.756976i
$122$	1.13000	+	0.544181i	0.102306	+	0.0492678i
$123$		0			0
$124$	−2.29890	+	12.6680i	−0.206448	+	1.13762i
$125$	7.77009	+	2.52466i	0.694978	+	0.225812i
$126$		0			0
$127$	−3.21647	−	3.07526i	−0.285415	−	0.272885i	0.534752	−	0.845009i	$-0.320405\pi$
$127$	−3.21647	−	3.07526i	−0.285415	−	0.272885i	−0.820167	+	0.572124i	$0.806119\pi$
$128$	−0.444235	−	0.611437i	−0.0392652	−	0.0540439i
$129$		0			0
$130$	9.93635	−	0.446242i	0.871476	−	0.0391380i
$131$	−10.8817	−	7.18294i	−0.950737	−	0.627576i	−0.0225721	−	0.999745i	$-0.507186\pi$
$131$	−10.8817	−	7.18294i	−0.950737	−	0.627576i	−0.928165	+	0.372169i	$0.878614\pi$
$132$		0			0
$133$	−1.48802	+	5.39172i	−0.129028	+	0.467521i
$134$	31.1213	−	8.58895i	2.68847	−	0.741972i
$135$		0			0
$136$	0.694426	+	0.0311867i	0.0595466	+	0.00267424i
$137$	−11.6383	−	8.45569i	−0.994323	−	0.722418i	−0.0334595	−	0.999440i	$-0.510652\pi$
$137$	−11.6383	−	8.45569i	−0.994323	−	0.722418i	−0.960864	+	0.277022i	$0.910652\pi$
$138$		0			0
$139$	12.4377	+	1.68480i	1.05495	+	0.142903i	0.641113	−	0.767446i	$-0.278473\pi$
$139$	12.4377	+	1.68480i	1.05495	+	0.142903i	0.413840	+	0.910349i	$0.364187\pi$
$140$	1.24368	−	0.111933i	0.105110	−	0.00946007i
$141$		0			0
$142$	−11.3450	−	12.5947i	−0.952049	−	1.05692i
$143$		−	7.77543i		−	0.650214i
$144$		0			0
$145$	−0.265564	+	1.96047i	−0.0220539	+	0.162808i
$146$	0.542069	+	2.98705i	0.0448619	+	0.247210i
$147$		0			0
$148$	0.645013	−	14.3623i	0.0530197	−	1.18058i
$149$	−1.57542	+	0.941272i	−0.129064	+	0.0771120i	−0.575980	−	0.817464i	$-0.695379\pi$
$149$	−1.57542	+	0.941272i	−0.129064	+	0.0771120i	0.446916	+	0.894576i	$0.352522\pi$
$150$		0			0
$151$	−4.18543	−	1.15510i	−0.340605	−	0.0940011i	0.0915495	−	0.995801i	$-0.470818\pi$
$151$	−4.18543	−	1.15510i	−0.340605	−	0.0940011i	−0.432155	+	0.901799i	$0.642247\pi$
$152$	0.394057	−	0.659540i	0.0319622	−	0.0534958i
$153$		0			0
$154$	−0.0865853	−	1.92797i	−0.00697724	−	0.155360i
$155$	−3.07246	−	4.65458i	−0.246786	−	0.373865i
$156$		0			0
$157$	−14.4818	+	15.1467i	−1.15577	+	1.20884i	−0.181516	+	0.983388i	$0.558100\pi$
$157$	−14.4818	+	15.1467i	−1.15577	+	1.20884i	−0.974254	+	0.225453i	$0.927614\pi$
$158$	−7.55956	−	20.1424i	−0.601407	−	1.60244i
$159$		0			0
$160$	7.01671	+	1.27335i	0.554720	+	0.100667i
$161$	−2.95971	+	2.82977i	−0.233258	+	0.223017i
$162$		0			0
$163$	−2.37152	+	1.01364i	−0.185752	+	0.0793940i	−0.483891	−	0.875128i	$-0.660777\pi$
$163$	−2.37152	+	1.01364i	−0.185752	+	0.0793940i	0.298139	+	0.954522i	$0.403634\pi$
$164$	−1.76420	+	3.27844i	−0.137761	+	0.256003i
$165$		0			0
$166$	−1.66156	−	12.2661i	−0.128962	−	0.952037i
$167$	11.7413	−	3.81499i	0.908570	−	0.295212i	0.182801	−	0.983150i	$-0.441484\pi$
$167$	11.7413	−	3.81499i	0.908570	−	0.295212i	0.725770	+	0.687938i	$0.241484\pi$
$168$		0			0
$169$	7.11010	−	16.6349i	0.546931	−	1.27961i
$170$	−9.88156	+	8.63326i	−0.757881	+	0.662141i
$171$		0			0
$172$	−3.38088	+	4.23949i	−0.257790	+	0.323258i
$173$	7.10519	+	2.66662i	0.540197	+	0.202739i	0.606534	−	0.795058i	$-0.292560\pi$
$173$	7.10519	+	2.66662i	0.540197	+	0.202739i	−0.0663362	+	0.997797i	$0.521131\pi$
$174$		0			0
$175$	1.90729	−	2.18307i	0.144177	−	0.165024i
$176$	1.21136	−	5.30731i	0.0913096	−	0.400053i
$177$		0			0
$178$	−17.3480	−	1.56135i	−1.30029	−	0.117028i
$179$	−4.52413	−	1.03260i	−0.338149	−	0.0771803i	0.0500746	−	0.998745i	$-0.484054\pi$
$179$	−4.52413	−	1.03260i	−0.338149	−	0.0771803i	−0.388224	+	0.921565i	$0.626911\pi$
$180$		0			0
$181$	2.63126	+	5.46387i	0.195580	+	0.406126i	0.975577	−	0.219657i	$-0.0704938\pi$
$181$	2.63126	+	5.46387i	0.195580	+	0.406126i	−0.779997	+	0.625783i	$0.784780\pi$
$182$	2.71153	−	7.22485i	0.200992	−	0.535542i
$183$		0			0
$184$	0.495302	−	0.266533i	0.0365142	−	0.0196491i
$185$	4.09751	+	4.68997i	0.301255	+	0.344814i
$186$		0			0
$187$	6.39556	+	8.01978i	0.467690	+	0.586464i
$188$	−4.65483	−	14.3261i	−0.339488	−	1.04484i
$189$		0			0
$190$	3.22718	+	14.1392i	0.234124	+	1.02577i
$191$	−12.4395	−	6.69396i	−0.900088	−	0.484358i	−0.0427348	−	0.999086i	$-0.513607\pi$
$191$	−12.4395	−	6.69396i	−0.900088	−	0.484358i	−0.857353	+	0.514728i	$0.827893\pi$
$192$		0			0
$193$	1.46610	−	3.04439i	0.105532	−	0.219140i	−0.841515	−	0.540233i	$-0.818336\pi$
$193$	1.46610	−	3.04439i	0.105532	−	0.219140i	0.947048	+	0.321093i	$0.104050\pi$
$194$	−19.7797	−	20.6879i	−1.42010	−	1.48531i
$195$		0			0
$196$	−4.12847	+	12.7061i	−0.294891	+	0.907580i
$197$	17.2668	−	6.48034i	1.23021	−	0.461705i	0.350206	−	0.936673i	$-0.386112\pi$
$197$	17.2668	−	6.48034i	1.23021	−	0.461705i	0.880003	+	0.474967i	$0.157540\pi$
$198$		0			0
$199$	8.62762	−	6.26834i	0.611596	−	0.444351i	−0.238380	−	0.971172i	$-0.576616\pi$
$199$	8.62762	−	6.26834i	0.611596	−	0.444351i	0.849976	+	0.526821i	$0.176616\pi$
$200$	−0.332319	+	0.219362i	−0.0234985	+	0.0155112i
$201$		0			0
$202$	−13.7653	+	20.8536i	−0.968524	+	1.46725i
$203$	1.31766	+	0.787264i	0.0924815	+	0.0552551i
$204$		0			0
$205$	−0.429047	−	1.55462i	−0.0299659	−	0.108579i
$206$	−11.4636	−	19.1869i	−0.798710	−	1.33681i
$207$		0			0
$208$	12.7946	−	17.6102i	0.887146	−	1.22105i
$209$	11.1552	−	2.02437i	0.771619	−	0.140028i
$210$		0			0
$211$	−0.853800	−	9.48650i	−0.0587780	−	0.653078i	−0.970313	−	0.241854i	$-0.922244\pi$
$211$	−0.853800	−	9.48650i	−0.0587780	−	0.653078i	0.911535	−	0.411223i	$-0.134898\pi$
$212$	14.2189			0.976561
$213$		0			0
$214$	−29.4845			−2.01552
$215$	−0.210557	−	2.33948i	−0.0143599	−	0.159551i
$216$		0			0
$217$	−4.25754	+	0.772630i	−0.289021	+	0.0524496i
$218$	−16.1479	+	22.2257i	−1.09367	+	1.50531i
$219$		0			0
$220$	−1.29819	−	2.17280i	−0.0875239	−	0.146490i
$221$	10.9118	+	39.5381i	0.734008	+	2.65962i
$222$		0			0
$223$	−6.18659	−	3.69632i	−0.414285	−	0.247524i	0.290601	−	0.956844i	$-0.406145\pi$
$223$	−6.18659	−	3.69632i	−0.414285	−	0.247524i	−0.704886	+	0.709321i	$0.749002\pi$
$224$	3.04803	−	4.61757i	0.203655	−	0.308524i
$225$		0			0
$226$	13.2057	−	8.71701i	0.878430	−	0.579847i
$227$	15.1583	−	11.0132i	1.00609	−	0.730971i	0.0427085	−	0.999088i	$-0.486401\pi$
$227$	15.1583	−	11.0132i	1.00609	−	0.730971i	0.963386	+	0.268117i	$0.0864013\pi$
$228$		0			0
$229$	5.00167	−	1.87716i	0.330519	−	0.124046i	−0.180598	−	0.983557i	$-0.557803\pi$
$229$	5.00167	−	1.87716i	0.330519	−	0.124046i	0.511117	+	0.859511i	$0.329232\pi$
$230$	−3.28097	+	10.0978i	−0.216340	+	0.665827i
$231$		0			0
$232$	−0.145702	−	0.152393i	−0.00956582	−	0.0100051i
$233$	−2.63679	+	5.47536i	−0.172742	+	0.358702i	−0.969308	−	0.245849i	$-0.920933\pi$
$233$	−2.63679	+	5.47536i	−0.172742	+	0.358702i	0.796566	+	0.604551i	$0.206648\pi$
$234$		0			0
$235$	5.74605	+	3.09208i	0.374831	+	0.201705i
$236$	1.13592	+	4.97678i	0.0739419	+	0.323961i
$237$		0			0
$238$	3.14594	+	9.68222i	0.203921	+	0.627605i
$239$	−2.67977	−	3.36032i	−0.173340	−	0.217361i	0.687571	−	0.726117i	$-0.258677\pi$
$239$	−2.67977	−	3.36032i	−0.173340	−	0.217361i	−0.860911	+	0.508756i	$0.830106\pi$
$240$		0			0
$241$	13.4740	+	15.4222i	0.867936	+	0.993433i	0.999998	+	0.00219163i	$0.000697620\pi$
$241$	13.4740	+	15.4222i	0.867936	+	0.993433i	−0.132061	+	0.991242i	$0.542160\pi$
$242$	16.0418	−	8.63244i	1.03120	−	0.554914i
$243$		0			0
$244$	0.448423	−	1.19482i	0.0287073	−	0.0764904i
$245$	−2.51103	−	5.21421i	−0.160424	−	0.333123i
$246$		0			0
$247$	44.1968	+	10.0876i	2.81217	+	0.641861i
$248$	0.591975	+	0.0532787i	0.0375905	+	0.00338320i
$249$		0			0
$250$	3.65726	−	16.0235i	0.231306	−	1.01342i
$251$	0.472256	−	0.540540i	0.0298085	−	0.0341186i	−0.737974	−	0.674829i	$-0.764217\pi$
$251$	0.472256	−	0.540540i	0.0298085	−	0.0341186i	0.767782	+	0.640711i	$0.221360\pi$
$252$		0			0
$253$	7.77077	+	2.91642i	0.488544	+	0.183354i
$254$	−5.58160	+	6.99910i	−0.350221	+	0.439163i
$255$		0			0
$256$	11.4634	−	10.0152i	0.716460	−	0.625953i
$257$	−10.2349	+	23.9459i	−0.638439	+	1.49370i	0.217200	+	0.976127i	$0.430308\pi$
$257$	−10.2349	+	23.9459i	−0.638439	+	1.49370i	−0.855638	+	0.517574i	$0.826835\pi$
$258$		0			0
$259$	4.59537	−	1.49312i	0.285542	−	0.0927783i
$260$	−1.35854	−	10.0291i	−0.0842530	−	0.621980i
$261$		0			0
$262$	−12.4295	+	23.0979i	−0.767899	+	1.42700i
$263$	−17.6267	+	7.53400i	−1.08691	+	0.464566i	−0.860492	−	0.509465i	$-0.829844\pi$
$263$	−17.6267	+	7.53400i	−1.08691	+	0.464566i	−0.226415	+	0.974031i	$0.572701\pi$
$264$		0			0
$265$	−4.45199	+	4.25654i	−0.273483	+	0.261477i
$266$	11.0712	+	2.00913i	0.678821	+	0.123188i
$267$		0			0
$268$	−11.5429	−	30.7560i	−0.705096	−	1.87872i
$269$	−2.65806	+	2.78012i	−0.162065	+	0.169507i	−0.798841	−	0.601542i	$-0.794553\pi$
$269$	−2.65806	+	2.78012i	−0.162065	+	0.169507i	0.636776	+	0.771049i	$0.280268\pi$
$270$		0			0
$271$	2.14858	+	3.25496i	0.130517	+	0.197725i	0.893956	−	0.448156i	$-0.147919\pi$
$271$	2.14858	+	3.25496i	0.130517	+	0.197725i	−0.763438	+	0.645881i	$0.776490\pi$
$272$	1.28836	+	28.6877i	0.0781185	+	1.73944i
$273$		0			0
$274$	−14.8432	+	24.8433i	−0.896710	+	1.50084i
$275$	−5.66418	−	1.56321i	−0.341563	−	0.0942653i
$276$		0			0
$277$	−15.9452	+	9.52683i	−0.958056	+	0.572412i	−0.904647	−	0.426161i	$-0.859866\pi$
$277$	−15.9452	+	9.52683i	−0.958056	+	0.572412i	−0.0534088	+	0.998573i	$0.517009\pi$
$278$	1.13282	−	25.2242i	0.0679420	−	1.51285i
$279$		0			0
$280$	−0.0102931	−	0.0567199i	−0.000615133	−	0.00338966i
$281$	0.490575	−	3.62157i	0.0292653	−	0.216045i	−0.970412	−	0.241456i	$-0.922375\pi$
$281$	0.490575	−	3.62157i	0.0292653	−	0.216045i	0.999677	+	0.0254109i	$0.00808940\pi$
$282$		0			0
$283$		−	25.9357i		−	1.54172i	−0.637004	−	0.770860i	$-0.719827\pi$
$283$		−	25.9357i		−	1.54172i	0.637004	−	0.770860i	$-0.280173\pi$
$284$	−11.7291	+	12.6461i	−0.695995	+	0.750411i
$285$		0			0
$286$	−15.5789	+	1.40213i	−0.921202	+	0.0829097i
$287$	−1.23992	−	0.167959i	−0.0731902	−	0.00991429i
$288$		0			0
$289$	−30.0229	−	21.8129i	−1.76605	−	1.28311i
$290$	3.97591	+	0.178558i	0.233474	+	0.0104853i
$291$		0			0
$292$	2.97773	−	0.821801i	0.174258	−	0.0480923i
$293$	−6.84825	+	24.8141i	−0.400079	+	1.44965i	0.435453	+	0.900211i	$0.356588\pi$
$293$	−6.84825	+	24.8141i	−0.400079	+	1.44965i	−0.835532	+	0.549442i	$0.814840\pi$
$294$		0			0
$295$	−1.84549	−	1.21820i	−0.107449	−	0.0709262i
$296$	−0.663035	+	0.0297769i	−0.0385381	+	0.00173075i
$297$		0			0
$298$	2.17004	+	2.98680i	0.125707	+	0.173021i
$299$	23.9883	+	22.9352i	1.38728	+	1.32638i
$300$		0			0
$301$	−1.73324	−	0.563163i	−0.0999021	−	0.0324602i
$302$	−1.55963	+	8.59427i	−0.0897466	+	0.494544i
$303$		0			0
$304$	28.5960	+	13.7711i	1.64009	+	0.789827i
$305$	0.217275	+	0.508339i	0.0124411	+	0.0291074i
$306$		0			0
$307$	4.08332	−	0.931991i	0.233047	−	0.0531915i	−0.104402	−	0.994535i	$-0.533293\pi$
$307$	4.08332	−	0.931991i	0.233047	−	0.0531915i	0.337449	+	0.941344i	$0.390436\pi$
$308$	−1.94597	+	0.263600i	−0.110882	+	0.0150200i
$309$		0			0
$310$	−8.77191	+	6.99536i	−0.498211	+	0.397310i
$311$	26.2705	+	11.2285i	1.48966	+	0.636712i	0.975304	−	0.220865i	$-0.0708880\pi$
$311$	26.2705	+	11.2285i	1.48966	+	0.636712i	0.514356	+	0.857577i	$0.328031\pi$
$312$		0			0
$313$	1.64329	+	3.05374i	0.0928840	+	0.172607i	0.922798	−	0.385284i	$-0.125896\pi$
$313$	1.64329	+	3.05374i	0.0928840	+	0.172607i	−0.829914	+	0.557891i	$0.811611\pi$
$314$	32.9596	+	26.2844i	1.86002	+	1.48332i
$315$		0			0
$316$	−19.7235	+	9.49832i	−1.10953	+	0.534322i
$317$	9.76489	+	8.53133i	0.548451	+	0.479167i	0.886992	−	0.461784i	$-0.152791\pi$
$317$	9.76489	+	8.53133i	0.548451	+	0.479167i	−0.338541	+	0.940952i	$0.609933\pi$
$318$		0			0
$319$	0.278890	−	3.09872i	0.0156148	−	0.173495i
$320$	0.665387	−	7.39305i	0.0371963	−	0.413284i
$321$		0			0
$322$	6.20347	+	5.41981i	0.345706	+	0.302034i
$323$	−53.8831	+	25.9487i	−2.99814	+	1.44383i
$324$		0			0
$325$	−18.3694	−	14.6491i	−1.01895	−	0.812588i
$326$	2.45858	+	4.56881i	0.136168	+	0.253043i
$327$		0			0
$328$	0.158040	+	0.0675496i	0.00872631	+	0.00372980i
$329$	3.95809	−	3.15647i	0.218217	−	0.174022i
$330$		0			0
$331$	24.7900	−	3.35804i	1.36258	−	0.184575i	0.583816	−	0.811886i	$-0.301559\pi$
$331$	24.7900	−	3.35804i	1.36258	−	0.184575i	0.778768	+	0.627312i	$0.215845\pi$
$332$	−12.2794	+	2.80268i	−0.673918	+	0.153817i
$333$		0			0
$334$	−9.76104	−	22.8371i	−0.534100	−	1.24959i
$335$	12.8211	+	6.17434i	0.700494	+	0.337340i
$336$		0			0
$337$	0.0739927	−	0.407734i	0.00403064	−	0.0222107i	−0.981852	−	0.189651i	$-0.939264\pi$
$337$	0.0739927	−	0.407734i	0.00403064	−	0.0222107i	0.985882	+	0.167440i	$0.0535501\pi$
$338$	−34.6120	−	11.2461i	−1.88265	−	0.611709i
$339$		0			0
$340$	9.65054	+	9.22686i	0.523374	+	0.500397i
$341$	5.15537	+	7.09575i	0.279179	+	0.384257i
$342$		0			0
$343$	−9.29647	+	0.417505i	−0.501962	+	0.0225432i
$344$	0.208918	+	0.137906i	0.0112641	+	0.00743537i
$345$		0			0
$346$	4.06161	−	14.7169i	0.218353	−	0.791185i
$347$	−4.99111	+	1.37746i	−0.267937	+	0.0739459i	−0.397424	−	0.917635i	$-0.630096\pi$
$347$	−4.99111	+	1.37746i	−0.267937	+	0.0739459i	0.129487	+	0.991581i	$0.458667\pi$
$348$		0			0
$349$	1.38046	+	0.0619964i	0.0738942	+	0.00331859i	0.0817812	−	0.996650i	$-0.473939\pi$
$349$	1.38046	+	0.0619964i	0.0738942	+	0.00331859i	−0.00788704	+	0.999969i	$0.502511\pi$
$350$	−4.71796	−	3.42780i	−0.252185	−	0.183223i
$351$		0			0
$352$	−11.1134	−	1.50541i	−0.592346	−	0.0802387i
$353$	−32.8269	+	2.95448i	−1.74720	+	0.157251i	−0.916650	−	0.399692i	$-0.869117\pi$
$353$	−32.8269	+	2.95448i	−1.74720	+	0.157251i	−0.830551	+	0.556943i	$0.811974\pi$
$354$		0			0
$355$	−0.113291	−	7.47074i	−0.00601284	−	0.396505i
$356$			17.7234i			0.939340i
$357$		0			0
$358$	−1.25311	+	9.25080i	−0.0662287	+	0.488920i
$359$	4.66097	+	25.6840i	0.245996	+	1.35555i	0.836256	+	0.548338i	$0.184739\pi$
$359$	4.66097	+	25.6840i	0.245996	+	1.35555i	−0.590260	+	0.807213i	$0.700975\pi$
$360$		0			0
$361$	−2.11316	+	47.0533i	−0.111219	+	2.47649i
$362$	10.4730	−	6.25731i	0.550447	−	0.328877i
$363$		0			0
$364$	−7.56923	−	2.08897i	−0.396735	−	0.109492i
$365$	−0.686323	+	1.14871i	−0.0359238	+	0.0601263i
$366$		0			0
$367$	0.478368	+	10.6517i	0.0249706	+	0.556013i	0.972016	+	0.234914i	$0.0754809\pi$
$367$	0.478368	+	10.6517i	0.0249706	+	0.556013i	−0.947046	+	0.321099i	$0.895948\pi$
$368$	12.8007	+	19.3922i	0.667281	+	1.01089i
$369$		0			0
$370$	8.65799	−	9.05554i	0.450107	−	0.470775i
$371$	1.67915	+	4.47407i	0.0871770	+	0.232282i
$372$		0			0
$373$	−22.0713	−	4.00536i	−1.14281	−	0.207389i	−0.426043	−	0.904703i	$-0.640093\pi$
$373$	−22.0713	−	4.00536i	−1.14281	−	0.207389i	−0.716766	+	0.697313i	$0.754379\pi$
$374$	14.9152	−	14.2604i	0.771247	−	0.737388i
$375$		0			0
$376$	−0.639437	+	0.273308i	−0.0329764	+	0.0140948i
$377$	5.89519	−	10.9551i	0.303618	−	0.564217i
$378$		0			0
$379$	−3.55665	−	26.2562i	−0.182693	−	1.34869i	−0.817459	−	0.575987i	$-0.804618\pi$
$379$	−3.55665	−	26.2562i	−0.182693	−	1.34869i	0.634766	−	0.772704i	$-0.281096\pi$
$380$	14.0348	−	4.56018i	0.719969	−	0.233932i
$381$		0			0
$382$	−11.1689	+	26.1310i	−0.571451	+	1.33698i
$383$	13.8657	−	12.1141i	0.708505	−	0.619002i	−0.226344	−	0.974047i	$-0.572677\pi$
$383$	13.8657	−	12.1141i	0.708505	−	0.619002i	0.934849	+	0.355045i	$0.115534\pi$
$384$		0			0
$385$	0.530379	−	0.665074i	0.0270306	−	0.0338953i
$386$	−6.36416	−	2.38851i	−0.323927	−	0.121572i
$387$		0			0
$388$	−19.1617	+	21.9324i	−0.972790	+	1.11345i
$389$	6.04797	−	26.4979i	0.306644	−	1.34350i	−0.553247	−	0.833018i	$-0.686611\pi$
$389$	6.04797	−	26.4979i	0.306644	−	1.34350i	0.859891	−	0.510478i	$-0.170532\pi$
$390$		0			0
$391$	−43.6072	−	3.92472i	−2.20531	−	0.198481i
$392$	0.601299	+	0.137243i	0.0303702	+	0.00693180i
$393$		0			0
$394$	−16.0978	−	33.4274i	−0.810994	−	1.68405i
$395$	3.33208	−	8.87830i	0.167655	−	0.446716i
$396$		0			0
$397$	9.66294	−	5.19985i	0.484969	−	0.260973i	−0.213064	−	0.977038i	$-0.568344\pi$
$397$	9.66294	−	5.19985i	0.484969	−	0.260973i	0.698033	+	0.716065i	$0.254059\pi$
$398$	−14.1151	−	16.1560i	−0.707527	−	0.809829i
$399$		0			0
$400$	−10.2563	−	12.8610i	−0.512813	−	0.643048i
$401$	−7.37011	−	22.6829i	−0.368046	−	1.13273i	−0.948052	−	0.318116i	$-0.896950\pi$
$401$	−7.37011	−	22.6829i	−0.368046	−	1.13273i	0.580006	−	0.814612i	$-0.303050\pi$
$402$		0			0
$403$	7.80401	+	34.1916i	0.388745	+	1.70320i
$404$	22.3892	+	12.0482i	1.11391	+	0.599418i
$405$		0			0
$406$	1.33976	−	2.78204i	0.0664912	−	0.138070i
$407$	−6.76826	−	7.07904i	−0.335490	−	0.350895i
$408$		0			0
$409$	−6.69523	+	20.6058i	−0.331058	+	1.01889i	0.637574	+	0.770389i	$0.279938\pi$
$409$	−6.69523	+	20.6058i	−0.331058	+	1.01889i	−0.968632	+	0.248501i	$0.920062\pi$
$410$	−3.03748	+	1.13998i	−0.150010	+	0.0562998i
$411$		0			0
$412$	−18.3990	+	13.3677i	−0.906456	+	0.658579i
$413$	−1.43183	+	0.945142i	−0.0704557	+	0.0465074i
$414$		0			0
$415$	3.00570	−	4.55344i	0.147544	−	0.223520i
$416$	−38.4960	−	23.0003i	−1.88742	−	1.12768i
$417$		0			0
$418$	−6.06763	−	21.9856i	−0.296778	−	1.07535i
$419$	−2.23712	−	3.74430i	−0.109290	−	0.182921i	0.798918	−	0.601441i	$-0.205406\pi$
$419$	−2.23712	−	3.74430i	−0.109290	−	0.182921i	−0.908208	+	0.418519i	$0.862549\pi$
$420$		0			0
$421$	4.77006	−	6.56543i	0.232479	−	0.319979i	−0.676800	−	0.736167i	$-0.736634\pi$
$421$	4.77006	−	6.56543i	0.232479	−	0.319979i	0.909279	+	0.416187i	$0.136634\pi$
$422$	−18.8533	+	3.42137i	−0.917764	+	0.166550i
$423$		0			0
$424$	−0.0588406	−	0.653773i	−0.00285755	−	0.0317500i
$425$	30.9961			1.50353
$426$		0			0
$427$	0.428912			0.0207565
$428$	2.68930	+	29.8806i	0.129992	+	1.44433i
$429$		0			0
$430$	−4.64945	+	0.843750i	−0.224216	+	0.0406892i
$431$	14.4016	−	19.8222i	0.693702	−	0.954800i	−0.306293	−	0.951937i	$-0.599089\pi$
$431$	14.4016	−	19.8222i	0.693702	−	0.954800i	0.999996	−	0.00286242i	$-0.000911137\pi$
$432$		0			0
$433$	15.3188	+	25.6393i	0.736173	+	1.23215i	0.965906	+	0.258893i	$0.0833576\pi$
$433$	15.3188	+	25.6393i	0.736173	+	1.23215i	−0.229733	+	0.973254i	$0.573785\pi$
$434$	2.31581	+	8.39113i	0.111162	+	0.402787i
$435$		0			0
$436$	23.9971	+	14.3376i	1.14925	+	0.686647i
$437$	−26.6590	+	40.3866i	−1.27527	+	1.93195i
$438$		0			0
$439$	−7.46187	+	4.92554i	−0.356136	+	0.235083i	−0.716279	−	0.697814i	$-0.754156\pi$
$439$	−7.46187	+	4.92554i	−0.356136	+	0.235083i	0.360144	+	0.932897i	$0.382728\pi$
$440$	−0.0945311	+	0.0686809i	−0.00450659	+	0.00327423i
$441$		0			0
$442$	77.2512	−	28.9929i	3.67446	−	1.37905i
$443$	0.246293	−	0.758011i	0.0117017	−	0.0360142i	−0.945035	−	0.326969i	$-0.893973\pi$
$443$	0.246293	−	0.758011i	0.0117017	−	0.0360142i	0.956737	+	0.290954i	$0.0939728\pi$
$444$		0			0
$445$	−5.30563	−	5.54926i	−0.251511	−	0.263060i
$446$	−6.29036	+	13.0621i	−0.297857	+	0.618507i
$447$		0			0
$448$	−5.07145	−	2.72906i	−0.239603	−	0.128936i
$449$	−2.91028	−	12.7508i	−0.137345	−	0.601747i	−0.996012	−	0.0892141i	$-0.971564\pi$
$449$	−2.91028	−	12.7508i	−0.137345	−	0.601747i	0.858668	−	0.512533i	$-0.171293\pi$
$450$		0			0
$451$	0.783737	+	2.41209i	0.0369047	+	0.113581i
$452$	−10.0386	−	12.5880i	−0.472176	−	0.592090i
$453$		0			0
$454$	−24.7996	−	28.3854i	−1.16390	−	1.33219i
$455$	2.99529	−	1.61184i	0.140422	−	0.0755641i
$456$		0			0
$457$	10.3765	−	27.6482i	0.485394	−	1.29333i	−0.434327	−	0.900755i	$-0.643014\pi$
$457$	10.3765	−	27.6482i	0.485394	−	1.29333i	0.919721	−	0.392573i	$-0.128415\pi$
$458$	−4.66303	−	9.68289i	−0.217889	−	0.452452i
$459$		0			0
$460$	10.5327	+	2.40402i	0.491089	+	0.112088i
$461$	40.0172	+	3.60161i	1.86379	+	0.167744i	0.963527	−	0.267611i	$-0.0862341\pi$
$461$	40.0172	+	3.60161i	1.86379	+	0.167744i	0.900259	+	0.435355i	$0.143377\pi$
$462$		0			0
$463$	−4.86007	+	21.2933i	−0.225867	+	0.989586i	0.727105	+	0.686526i	$0.240865\pi$
$463$	−4.86007	+	21.2933i	−0.225867	+	0.989586i	−0.952972	+	0.303060i	$0.901992\pi$
$464$	5.73064	−	6.55924i	0.266038	−	0.304505i
$465$		0			0
$466$	11.4460	+	4.29574i	0.530224	+	0.198996i
$467$	3.68243	−	4.61762i	0.170403	−	0.213678i	−0.689296	−	0.724480i	$-0.742080\pi$
$467$	3.68243	−	4.61762i	0.170403	−	0.213678i	0.859698	+	0.510802i	$0.170651\pi$
$468$		0			0
$469$	8.31443	−	7.26410i	0.383925	−	0.335425i
$470$	5.15915	−	12.0704i	0.237974	−	0.556768i
$471$		0			0
$472$	0.224127	−	0.0728232i	0.0103163	−	0.00335196i
$473$	0.495858	+	3.66057i	0.0227996	+	0.168313i
$474$		0			0
$475$	16.2341	−	30.1680i	0.744872	−	1.38420i
$476$	9.52535	−	4.07133i	0.436593	−	0.186609i
$477$		0			0
$478$	−6.24954	+	5.97517i	−0.285847	+	0.273298i
$479$	−42.4001	−	7.69449i	−1.93731	−	0.351570i	−0.999995	−	0.00309150i	$-0.999016\pi$
$479$	−42.4001	−	7.69449i	−1.93731	−	0.351570i	−0.937317	−	0.348479i	$-0.886698\pi$
$480$		0			0
$481$	−13.7606	−	36.6649i	−0.627427	−	1.67177i
$482$	28.4704	−	29.7777i	1.29679	−	1.35634i
$483$		0			0
$484$	−10.2116	−	15.4699i	−0.464163	−	0.703176i
$485$	−0.566014	−	12.6033i	−0.0257014	−	0.572285i
$486$		0			0
$487$	−12.3787	+	20.7185i	−0.560934	+	0.938845i	0.438266	+	0.898845i	$0.355593\pi$
$487$	−12.3787	+	20.7185i	−0.560934	+	0.938845i	−0.999200	+	0.0399999i	$0.987264\pi$
$488$	−0.0567922	−	0.0156736i	−0.00257086	−	0.000709513i
$489$		0			0
$490$	−9.99443	+	5.97139i	−0.451502	+	0.269760i
$491$	0.0908134	−	2.02212i	0.00409835	−	0.0912569i	−0.995901	−	0.0904465i	$-0.971171\pi$
$491$	0.0908134	−	2.02212i	0.00409835	−	0.0912569i	1.00000		0.000810455i	$-0.000257976\pi$
$492$		0			0
$493$	2.93050	+	16.1484i	0.131983	+	0.727286i
$494$	12.2418	−	90.3723i	0.550783	−	4.06604i
$495$		0			0
$496$			24.5541i			1.10251i
$497$	−5.36431	−	2.19723i	−0.240622	−	0.0985590i
$498$		0			0
$499$	−24.1913	+	2.17726i	−1.08295	+	0.0974675i	−0.616711	−	0.787190i	$-0.711535\pi$
$499$	−24.1913	+	2.17726i	−1.08295	+	0.0974675i	−0.466242	+	0.884657i	$0.654392\pi$
$500$	−16.5723	−	2.24488i	−0.741138	−	0.100394i
$501$		0			0
$502$	−1.16819	−	0.848742i	−0.0521390	−	0.0378812i
$503$	7.61884	+	0.342163i	0.339707	+	0.0152563i	0.214065	−	0.976819i	$-0.431329\pi$
$503$	7.61884	+	0.342163i	0.339707	+	0.0152563i	0.125642	+	0.992076i	$0.459901\pi$
$504$		0			0
$505$	−10.6168	+	2.93006i	−0.472443	+	0.130386i
$506$	4.44208	−	16.0955i	0.197474	−	0.715533i
$507$		0			0
$508$	7.60223	+	5.01819i	0.337294	+	0.222646i
$509$	26.2723	−	1.17989i	1.16450	−	0.0522978i	0.545793	−	0.837920i	$-0.316228\pi$
$509$	26.2723	−	1.17989i	1.16450	−	0.0522978i	0.618707	+	0.785622i	$0.287657\pi$
$510$		0			0
$511$	0.610232	+	0.839912i	0.0269951	+	0.0371555i
$512$	−23.2264	−	22.2067i	−1.02647	−	0.981405i
$513$		0			0
$514$	49.8238	+	16.1887i	2.19763	+	0.714055i
$515$	1.75908	−	9.69334i	0.0775144	−	0.427139i
$516$		0			0
$517$	−9.24545	−	4.45237i	−0.406614	−	0.195815i
$518$	−3.82031	−	8.93807i	−0.167855	−	0.392716i
$519$		0			0
$520$	−0.455508	+	0.103967i	−0.0199753	+	0.00455924i
$521$	−21.1511	+	2.86511i	−0.926646	+	0.125523i	−0.581980	−	0.813203i	$-0.697722\pi$
$521$	−21.1511	+	2.86511i	−0.926646	+	0.125523i	−0.344666	+	0.938725i	$0.612008\pi$
$522$		0			0
$523$	10.4564	−	8.33868i	0.457226	−	0.364625i	−0.367627	−	0.929973i	$-0.619830\pi$
$523$	10.4564	−	8.33868i	0.457226	−	0.364625i	0.824852	+	0.565348i	$0.191258\pi$
$524$	24.5419	+	10.4897i	1.07212	+	0.458246i
$525$		0			0
$526$	18.2738	+	33.9584i	0.796775	+	1.48066i
$527$	−36.1730	−	28.8470i	−1.57572	−	1.25660i
$528$		0			0
$529$	−11.1967	+	5.39207i	−0.486815	+	0.234438i
$530$	9.33126	+	8.15248i	0.405324	+	0.354121i
$531$		0			0
$532$	1.02631	−	11.4032i	0.0444961	−	0.494392i
$533$	−0.909060	+	10.1005i	−0.0393757	+	0.437500i
$534$		0			0
$535$	−9.78699	−	8.55063i	−0.423128	−	0.369676i
$536$	−1.36636	+	0.658006i	−0.0590179	+	0.0284215i
$537$		0			0
$538$	6.04960	+	4.82439i	0.260817	+	0.207994i
$539$	4.31282	+	8.01457i	0.185766	+	0.345212i
$540$		0			0
$541$	11.3240	+	4.84010i	0.486856	+	0.208092i	0.622431	−	0.782675i	$-0.286145\pi$
$541$	11.3240	+	4.84010i	0.486856	+	0.208092i	−0.135575	+	0.990767i	$0.543288\pi$
$542$	6.13423	−	4.89188i	0.263488	−	0.210124i
$543$		0			0
$544$	58.6242	−	7.94119i	2.51349	−	0.340476i
$545$	−11.8056	+	2.69456i	−0.505697	+	0.115422i
$546$		0			0
$547$	0.598172	+	1.39949i	0.0255760	+	0.0598380i	0.931829	−	0.362898i	$-0.118213\pi$
$547$	0.598172	+	1.39949i	0.0255760	+	0.0598380i	−0.906253	+	0.422736i	$0.861070\pi$
$548$	26.5309	+	12.7766i	1.13334	+	0.545790i
$549$		0			0
$550$	−2.11066	+	11.6307i	−0.0899989	+	0.495935i
$551$	17.2518	+	5.60545i	0.734951	+	0.238800i
$552$		0			0
$553$	−5.31789	−	5.08443i	−0.226140	−	0.216212i
$554$	21.9634	+	30.2301i	0.933137	+	1.28435i
$555$		0			0
$556$	−25.6663	+	1.15268i	−1.08850	+	0.0488844i
$557$	2.76808	+	1.82719i	0.117287	+	0.0774206i	0.608179	−	0.793800i	$-0.291900\pi$
$557$	2.76808	+	1.82719i	0.117287	+	0.0774206i	−0.490892	+	0.871221i	$0.663329\pi$
$558$		0			0
$559$	−3.92957	+	14.2385i	−0.166203	+	0.602223i
$560$	2.29562	−	0.633552i	0.0970078	−	0.0267724i
$561$		0			0
$562$	−7.34469	−	0.329850i	−0.309817	−	0.0139139i
$563$	11.1875	+	8.12820i	0.471497	+	0.342563i	0.798025	−	0.602625i	$-0.205878\pi$
$563$	11.1875	+	8.12820i	0.471497	+	0.342563i	−0.326527	+	0.945188i	$0.605878\pi$
$564$		0			0
$565$	6.91142	+	0.936216i	0.290766	+	0.0393869i
$566$	−51.9651	+	4.67695i	−2.18426	+	0.196587i
$567$		0			0
$568$	0.629995	+	0.486961i	0.0264340	+	0.0204324i
$569$		−	19.6945i		−	0.825635i	−0.910814	−	0.412817i	$-0.864545\pi$
$569$		−	19.6945i		−	0.825635i	0.910814	−	0.412817i	$-0.135455\pi$
$570$		0			0
$571$	−0.182684	+	1.34863i	−0.00764509	+	0.0564383i	−0.994370	−	0.105960i	$-0.966209\pi$
$571$	−0.182684	+	1.34863i	−0.00764509	+	0.0564383i	0.986725	+	0.162398i	$0.0519228\pi$
$572$	2.84193	+	15.6603i	0.118827	+	0.654791i
$573$		0			0
$574$	−0.112931	+	2.51461i	−0.00471365	+	0.104958i
$575$	21.5304	−	12.8638i	0.897879	−	0.536458i
$576$		0			0
$577$	−24.2617	−	6.69580i	−1.01003	−	0.278750i	−0.278408	−	0.960463i	$-0.589807\pi$
$577$	−24.2617	−	6.69580i	−1.01003	−	0.278750i	−0.731620	+	0.681713i	$0.761235\pi$
$578$	−38.2906	+	64.0876i	−1.59268	+	2.66569i
$579$		0			0
$580$	−0.181688	−	4.04561i	−0.00754420	−	0.167985i
$581$	−2.33198	−	3.53280i	−0.0967469	−	0.146565i
$582$		0			0
$583$	6.69393	−	7.00131i	0.277234	−	0.289965i
$584$	−0.0501080	−	0.133512i	−0.00207348	−	0.00552478i
$585$		0			0
$586$	50.9527	+	9.24655i	2.10484	+	0.381971i
$587$	8.32119	−	7.95587i	0.343452	−	0.328374i	−0.499549	−	0.866286i	$-0.666501\pi$
$587$	8.32119	−	7.95587i	0.343452	−	0.328374i	0.843001	+	0.537912i	$0.180787\pi$
$588$		0			0
$589$	−47.0218	+	20.0981i	−1.93750	+	0.828127i
$590$	−2.10800	+	3.91732i	−0.0867850	+	0.161274i
$591$		0			0
$592$	−3.68047	−	27.1703i	−0.151266	−	1.11669i
$593$	−14.3897	+	4.67549i	−0.590914	+	0.191999i	−0.589184	−	0.807999i	$-0.700551\pi$
$593$	−14.3897	+	4.67549i	−0.590914	+	0.191999i	−0.00172982	+	0.999999i	$0.500551\pi$
$594$		0			0
$595$	−1.76363	+	4.12622i	−0.0723018	+	0.169159i
$596$	2.82899	−	2.47162i	0.115880	−	0.101241i
$597$		0			0
$598$	41.6274	−	52.1992i	1.70227	−	2.13458i
$599$	−30.4288	−	11.4201i	−1.24329	−	0.466614i	−0.358905	−	0.933374i	$-0.616850\pi$
$599$	−30.4288	−	11.4201i	−1.24329	−	0.466614i	−0.884384	+	0.466760i	$0.845421\pi$
$600$		0			0
$601$	−6.20827	+	7.10594i	−0.253241	+	0.289857i	−0.865614	−	0.500711i	$-0.833072\pi$
$601$	−6.20827	+	7.10594i	−0.253241	+	0.289857i	0.612374	+	0.790568i	$0.290215\pi$
$602$	−0.815807	+	3.57428i	−0.0332498	+	0.145677i
$603$		0			0
$604$	8.85197	+	0.796692i	0.360182	+	0.0324169i
$605$	7.82829	+	1.78676i	0.318265	+	0.0726419i
$606$		0			0
$607$	7.75202	+	16.0972i	0.314645	+	0.653366i	0.996979	−	0.0776741i	$-0.0247494\pi$
$607$	7.75202	+	16.0972i	0.314645	+	0.653366i	−0.682334	+	0.731040i	$0.739035\pi$
$608$	22.9752	−	61.2172i	0.931767	−	2.48268i
$609$		0			0
$610$	0.979333	−	0.527001i	0.0396520	−	0.0213377i
$611$	−26.9966	−	30.9001i	−1.09217	−	1.25009i
$612$		0			0
$613$	−22.2728	−	27.9293i	−0.899592	−	1.12805i	−0.991215	−	0.132258i	$-0.957777\pi$
$613$	−22.2728	−	27.9293i	−0.899592	−	1.12805i	0.0916236	−	0.995794i	$-0.470794\pi$
$614$	−2.60368	−	8.01332i	−0.105076	−	0.323391i
$615$		0			0
$616$	0.0201729	+	0.0883831i	0.000812788	+	0.00356106i
$617$	22.9767	+	12.3643i	0.925005	+	0.497767i	0.865750	−	0.500476i	$-0.166842\pi$
$617$	22.9767	+	12.3643i	0.925005	+	0.497767i	0.0592552	+	0.998243i	$0.481127\pi$
$618$		0			0
$619$	5.45332	−	11.3239i	0.219187	−	0.455147i	−0.762160	−	0.647388i	$-0.775861\pi$
$619$	5.45332	−	11.3239i	0.219187	−	0.455147i	0.981348	+	0.192241i	$0.0615756\pi$
$620$	7.88943	+	8.25169i	0.316847	+	0.331396i
$621$		0			0
$622$	17.7603	−	54.6606i	0.712123	−	2.19169i
$623$	−5.57679	+	2.09300i	−0.223429	+	0.0838544i
$624$		0			0
$625$	−11.1841	+	8.12569i	−0.447362	+	0.325028i
$626$	5.82217	−	3.84318i	0.232701	−	0.153604i
$627$		0			0
$628$	23.6312	−	35.7998i	0.942989	−	1.42857i
$629$	44.3511	+	26.4986i	1.76839	+	1.05657i
$630$		0			0
$631$	2.14151	+	7.75958i	0.0852521	+	0.308904i	0.994135	−	0.108148i	$-0.0344920\pi$
$631$	2.14151	+	7.75958i	0.0852521	+	0.308904i	−0.908883	+	0.417052i	$0.863063\pi$
$632$	0.518342	+	0.867559i	0.0206186	+	0.0345097i
$633$		0			0
$634$	15.3326	−	21.1035i	0.608934	−	0.838126i
$635$	−3.88251	+	0.704571i	−0.154073	+	0.0279600i
$636$		0			0
$637$	3.26218	+	36.2458i	0.129252	+	1.43611i
$638$	−6.25892			−0.247793
$639$		0			0
$640$	−0.670159			−0.0264904
$641$	2.59483	+	28.8309i	0.102490	+	1.13875i	0.868420	+	0.495830i	$0.165136\pi$
$641$	2.59483	+	28.8309i	0.102490	+	1.13875i	−0.765930	+	0.642924i	$0.777721\pi$
$642$		0			0
$643$	−47.8286	+	8.67962i	−1.88618	+	0.342291i	−0.993999	−	0.109392i	$-0.965110\pi$
$643$	−47.8286	+	8.67962i	−1.88618	+	0.342291i	−0.892179	+	0.451682i	$0.850824\pi$
$644$	4.92680	−	6.78115i	0.194143	−	0.267215i
$645$		0			0
$646$	61.7078	+	103.282i	2.42786	+	4.06356i
$647$	4.11856	+	14.9233i	0.161917	+	0.586694i	0.999203	+	0.0399275i	$0.0127127\pi$
$647$	4.11856	+	14.9233i	0.161917	+	0.586694i	−0.837285	+	0.546766i	$0.815859\pi$
$648$		0			0
$649$	2.98529	+	1.78363i	0.117183	+	0.0700136i
$650$	−26.0386	+	39.4468i	−1.02132	+	1.54723i
$651$		0			0
$652$	4.40594	−	2.90833i	0.172550	−	0.113899i
$653$	−23.6307	+	17.1687i	−0.924739	+	0.671862i	−0.944699	−	0.327939i	$-0.893646\pi$
$653$	−23.6307	+	17.1687i	−0.924739	+	0.671862i	0.0199600	+	0.999801i	$0.493646\pi$
$654$		0			0
$655$	−10.8243	+	4.06243i	−0.422941	+	0.158732i
$656$	−2.19409	+	6.75270i	−0.0856647	+	0.263649i
$657$		0			0
$658$	−7.03810	−	7.36127i	−0.274374	−	0.286972i
$659$	−12.1950	+	25.3231i	−0.475048	+	0.986448i	0.516448	+	0.856318i	$0.327254\pi$
$659$	−12.1950	+	25.3231i	−0.475048	+	0.986448i	−0.991497	+	0.130130i	$0.958461\pi$
$660$		0			0
$661$	−7.52647	−	4.05016i	−0.292746	−	0.157533i	0.320904	−	0.947112i	$-0.396013\pi$
$661$	−7.52647	−	4.05016i	−0.292746	−	0.157533i	−0.613649	+	0.789579i	$0.710299\pi$
$662$	−11.1985	−	49.0641i	−0.435244	−	1.90693i
$663$		0			0
$664$	0.179679	+	0.552995i	0.00697290	+	0.0214604i
$665$	3.09229	+	3.87761i	0.119914	+	0.150367i
$666$		0			0
$667$	8.73736	+	10.0007i	0.338312	+	0.387229i
$668$	−22.2536	+	11.9751i	−0.861016	+	0.463332i
$669$		0			0
$670$	10.0590	−	26.8020i	0.388611	−	1.03545i
$671$	−0.377213	−	0.783292i	−0.0145622	−	0.0302386i
$672$		0			0
$673$	17.4841	+	3.99063i	0.673962	+	0.153827i	0.545787	−	0.837924i	$-0.316231\pi$
$673$	17.4841	+	3.99063i	0.673962	+	0.153827i	0.128175	+	0.991752i	$0.459088\pi$
$674$	−0.830282	−	0.0747268i	−0.0319813	−	0.00287837i
$675$		0			0
$676$	−8.24022	+	36.1027i	−0.316931	+	1.38857i
$677$	−21.6074	+	24.7317i	−0.830441	+	0.950516i	−0.999383	−	0.0351098i	$-0.988822\pi$
$677$	−21.6074	+	24.7317i	−0.830441	+	0.950516i	0.168943	+	0.985626i	$0.445965\pi$
$678$		0			0
$679$	−9.16401	−	3.43931i	−0.351682	−	0.131989i
$680$	0.384306	−	0.481905i	0.0147375	−	0.0184802i
$681$		0			0
$682$	13.2875	−	11.6089i	0.508803	−	0.444528i
$683$	16.6326	−	38.9140i	0.636430	−	1.48900i	−0.221461	−	0.975169i	$-0.571082\pi$
$683$	16.6326	−	38.9140i	0.636430	−	1.48900i	0.857891	−	0.513832i	$-0.171775\pi$
$684$		0			0
$685$	−12.1317	+	3.94182i	−0.463527	+	0.150609i
$686$	2.51293	+	18.5512i	0.0959443	+	0.708289i
$687$		0			0
$688$	−4.90048	+	9.10661i	−0.186829	+	0.347186i
$689$	35.6152	−	15.2227i	1.35683	−	0.579937i
$690$		0			0
$691$	14.3912	−	13.7594i	0.547467	−	0.523432i	−0.365854	−	0.930672i	$-0.619223\pi$
$691$	14.3912	−	13.7594i	0.547467	−	0.523432i	0.913321	+	0.407240i	$0.133509\pi$
$692$	−15.2851	−	2.77383i	−0.581051	−	0.105445i
$693$		0			0
$694$	3.65993	+	9.75185i	0.138929	+	0.370175i
$695$	7.69114	−	8.04430i	0.291742	−	0.305138i
$696$		0			0
$697$	−7.37036	−	11.1656i	−0.279172	−	0.422928i
$698$	−0.124719	−	2.77708i	−0.00472067	−	0.105114i
$699$		0			0
$700$	−3.04351	+	5.09399i	−0.115034	+	0.192535i
$701$	6.55579	+	1.80928i	0.247609	+	0.0683357i	0.387638	−	0.921812i	$-0.373291\pi$
$701$	6.55579	+	1.80928i	0.247609	+	0.0683357i	−0.140029	+	0.990147i	$0.544720\pi$
$702$		0			0
$703$	49.0193	−	29.2877i	1.84880	−	1.10461i
$704$	−0.523729	+	11.6617i	−0.0197388	+	0.439518i
$705$		0			0
$706$	11.8392	+	65.2396i	0.445576	+	2.45532i
$707$	−1.14703	+	8.46770i	−0.0431384	+	0.318461i
$708$		0			0
$709$		−	2.38810i		−	0.0896869i	−0.998994	−	0.0448434i	$-0.985721\pi$
$709$		−	2.38810i		−	0.0896869i	0.998994	−	0.0448434i	$-0.0142789\pi$
$710$	−14.9480	+	1.57417i	−0.560989	+	0.0590777i
$711$		0			0
$712$	0.814906	−	0.0733429i	0.0305399	−	0.00274864i
$713$	−37.0982	−	5.02530i	−1.38934	−	0.188199i
$714$		0			0
$715$	−5.57784	−	4.05254i	−0.208599	−	0.151556i
$716$	9.48937	+	0.426168i	0.354634	+	0.0159266i
$717$		0			0
$718$	50.6203	−	13.9703i	1.88913	−	0.521368i
$719$	3.15973	−	11.4490i	0.117838	−	0.426976i	−0.881106	−	0.472919i	$-0.843200\pi$
$719$	3.15973	−	11.4490i	0.117838	−	0.426976i	0.998944	+	0.0459424i	$0.0146291\pi$
$720$		0			0
$721$	−6.37901	−	4.21075i	−0.237567	−	0.156816i
$722$	94.6575	−	4.25107i	3.52279	−	0.158209i
$723$		0			0
$724$	−7.29661	−	10.0429i	−0.271176	−	0.373242i
$725$	−6.79528	−	6.49695i	−0.252370	−	0.241291i
$726$		0			0
$727$	45.8703	+	14.9042i	1.70123	+	0.552764i	0.988836	−	0.149011i	$-0.0476089\pi$
$727$	45.8703	+	14.9042i	1.70123	+	0.552764i	0.712399	+	0.701775i	$0.247609\pi$
$728$	−0.0647261	+	0.356670i	−0.00239891	+	0.0132191i
$729$		0			0
$730$	2.42534	+	1.16798i	0.0897657	+	0.0432289i
$731$	−7.65858	−	17.9181i	−0.283263	−	0.662726i
$732$		0			0
$733$	15.7840	−	3.60260i	0.582996	−	0.133065i	0.0791562	−	0.996862i	$-0.474777\pi$
$733$	15.7840	−	3.60260i	0.582996	−	0.133065i	0.503840	+	0.863797i	$0.331920\pi$
$734$	21.2556	−	2.87926i	0.784557	−	0.106275i
$735$		0			0
$736$	37.4256	−	29.8459i	1.37953	−	1.10013i
$737$	−20.5782	−	8.79554i	−0.758007	−	0.323988i
$738$		0			0
$739$	4.22027	+	7.84257i	0.155245	+	0.288494i	0.946323	−	0.323221i	$-0.104766\pi$
$739$	4.22027	+	7.84257i	0.155245	+	0.288494i	−0.791078	+	0.611715i	$0.790480\pi$
$740$	−9.96689	−	7.94833i	−0.366390	−	0.292186i
$741$		0			0
$742$	8.66151	−	4.17116i	0.317974	−	0.153128i
$743$	−3.31490	−	2.89614i	−0.121612	−	0.106249i	0.594984	−	0.803737i	$-0.297158\pi$
$743$	−3.31490	−	2.89614i	−0.121612	−	0.106249i	−0.716596	+	0.697488i	$0.754301\pi$
$744$		0			0
$745$	−0.145870	+	1.62075i	−0.00534426	+	0.0593796i
$746$	−4.04509	+	44.9446i	−0.148101	+	1.64554i
$747$		0			0
$748$	−15.8124	−	13.8149i	−0.578159	−	0.505122i
$749$	−9.08452	+	4.37488i	−0.331941	+	0.159854i
$750$		0			0
$751$	−23.5980	−	18.8188i	−0.861105	−	0.686708i	0.0898776	−	0.995953i	$-0.471352\pi$
$751$	−23.5980	−	18.8188i	−0.861105	−	0.686708i	−0.950983	+	0.309245i	$0.899924\pi$
$752$	−13.6132	−	25.2975i	−0.496422	−	0.922506i
$753$		0			0
$754$	−23.0128	−	9.83616i	−0.838078	−	0.358212i
$755$	−3.01007	+	2.40045i	−0.109548	+	0.0873614i
$756$		0			0
$757$	7.22385	−	0.978537i	0.262555	−	0.0355655i	−0.00177249	−	0.999998i	$-0.500564\pi$
$757$	7.22385	−	0.978537i	0.262555	−	0.0355655i	0.264328	+	0.964433i	$0.414850\pi$
$758$	−51.9659	+	11.8609i	−1.88749	+	0.430806i
$759$		0			0
$760$	−0.267751	−	0.626435i	−0.00971235	−	0.0227232i
$761$	29.8449	+	14.3726i	1.08188	+	0.521005i	0.887917	−	0.460004i	$-0.152152\pi$
$761$	29.8449	+	14.3726i	1.08188	+	0.521005i	0.193961	+	0.981009i	$0.437866\pi$
$762$		0			0
$763$	−1.67754	+	9.24400i	−0.0607310	+	0.334655i
$764$	27.5007	+	8.93552i	0.994941	+	0.323276i
$765$		0			0
$766$	−26.7724	−	25.5970i	−0.967325	−	0.924857i
$767$	8.17330	+	11.2496i	0.295121	+	0.406199i
$768$		0			0
$769$	9.34417	−	0.419647i	0.336959	−	0.0151329i	0.124257	−	0.992250i	$-0.460345\pi$
$769$	9.34417	−	0.419647i	0.336959	−	0.0151329i	0.212702	+	0.977117i	$0.431774\pi$
$770$	−1.42819	−	0.942741i	−0.0514685	−	0.0339740i
$771$		0			0
$772$	−1.84012	+	6.66751i	−0.0662272	+	0.239969i
$773$	34.6499	−	9.56278i	1.24627	−	0.343949i	0.420157	−	0.907451i	$-0.361975\pi$
$773$	34.6499	−	9.56278i	1.24627	−	0.343949i	0.826115	+	0.563502i	$0.190546\pi$
$774$		0			0
$775$	26.4765	+	1.18906i	0.951066	+	0.0427124i
$776$	1.08772	+	0.790277i	0.0390470	+	0.0283693i
$777$		0			0
$778$	−54.1820	−	7.33946i	−1.94252	−	0.263132i
$779$	−14.7275	+	1.32550i	−0.527668	+	0.0474910i
$780$		0			0
$781$	0.705086	+	11.7288i	0.0252300	+	0.419691i
$782$			88.0795i			3.14972i
$783$		0			0
$784$	−3.42017	+	25.2487i	−0.122149	+	0.901738i
$785$	3.31791	+	18.2832i	0.118421	+	0.652555i
$786$		0			0
$787$	1.34519	−	29.9529i	0.0479507	−	1.06770i	−0.820411	−	0.571774i	$-0.806255\pi$
$787$	1.34519	−	29.9529i	0.0479507	−	1.06770i	0.868362	−	0.495931i	$-0.165173\pi$
$788$	−32.4081	+	19.3630i	−1.15449	+	0.689777i
$789$		0			0
$790$	−18.3895	−	5.07519i	−0.654270	−	0.180567i
$791$	2.77541	−	4.64526i	0.0986823	−	0.165166i
$792$		0			0
$793$	−0.155964	−	3.47282i	−0.00553846	−	0.123323i
$794$	−12.1610	−	18.4231i	−0.431577	−	0.653811i
$795$		0			0
$796$	−15.0856	+	15.7783i	−0.534696	+	0.559248i
$797$	8.72475	+	23.2470i	0.309046	+	0.823451i	0.995367	+	0.0961517i	$0.0306534\pi$
$797$	8.72475	+	23.2470i	0.309046	+	0.823451i	−0.686320	+	0.727299i	$0.740775\pi$
$798$		0			0
$799$	53.2614	+	9.66553i	1.88425	+	0.341942i
$800$	−24.4945	+	23.4191i	−0.866010	+	0.827990i
$801$		0			0
$802$	−44.1186	+	18.8572i	−1.55788	+	0.665870i
$803$	0.997194	−	1.85310i	0.0351902	−	0.0653944i
$804$		0			0
$805$	0.487391	+	3.59807i	0.0171783	+	0.126815i
$806$	67.0994	−	21.8019i	2.36347	−	0.767939i
$807$		0			0
$808$	0.461312	−	1.07929i	0.0162289	−	0.0379694i
$809$	−31.9548	+	27.9181i	−1.12347	+	0.981548i	−0.999942	−	0.0107931i	$-0.996564\pi$
$809$	−31.9548	+	27.9181i	−1.12347	+	0.981548i	−0.123530	+	0.992341i	$0.539422\pi$
$810$		0			0
$811$	9.54085	−	11.9639i	0.335025	−	0.420108i	−0.585573	−	0.810620i	$-0.699131\pi$
$811$	9.54085	−	11.9639i	0.335025	−	0.420108i	0.920598	+	0.390512i	$0.127702\pi$
$812$	−2.94161	−	1.10401i	−0.103230	−	0.0387430i
$813$		0			0
$814$	−12.9631	+	14.8375i	−0.454358	+	0.520054i
$815$	−0.508881	+	2.22955i	−0.0178253	+	0.0780979i
$816$		0			0
$817$	−21.4506	−	1.93059i	−0.750461	−	0.0675427i
$818$	42.4933	+	9.69882i	1.48574	+	0.339111i
$819$		0			0
$820$	1.43235	+	2.97430i	0.0500198	+	0.103867i
$821$	13.8385	−	36.8725i	0.482966	−	1.28686i	−0.438616	−	0.898674i	$-0.644531\pi$
$821$	13.8385	−	36.8725i	0.482966	−	1.28686i	0.921582	−	0.388183i	$-0.126897\pi$
$822$		0			0
$823$	18.1400	−	9.76155i	0.632321	−	0.340266i	−0.126114	−	0.992016i	$-0.540250\pi$
$823$	18.1400	−	9.76155i	0.632321	−	0.340266i	0.758434	+	0.651750i	$0.225965\pi$
$824$	0.690772	+	0.790652i	0.0240642	+	0.0275437i
$825$		0			0
$826$	2.15190	+	2.69839i	0.0748741	+	0.0938891i
$827$	−14.0185	−	43.1446i	−0.487472	−	1.50028i	−0.828369	−	0.560183i	$-0.810731\pi$
$827$	−14.0185	−	43.1446i	−0.487472	−	1.50028i	0.340897	−	0.940100i	$-0.389269\pi$
$828$		0			0
$829$	6.71005	+	29.3986i	0.233050	+	1.02106i	0.947094	+	0.320957i	$0.104004\pi$
$829$	6.71005	+	29.3986i	0.233050	+	1.02106i	−0.714044	+	0.700101i	$0.753138\pi$
$830$	−9.66533	−	5.20114i	−0.335489	−	0.180534i
$831$		0			0
$832$	−20.2526	+	42.0549i	−0.702132	+	1.45799i
$833$	−33.1781	−	34.7016i	−1.14955	−	1.20234i
$834$		0			0
$835$	3.38281	−	10.4112i	0.117067	−	0.360295i
$836$	−21.7275	+	8.15446i	−0.751461	+	0.282028i
$837$		0			0
$838$	−7.09871	+	5.15751i	−0.245221	+	0.178163i
$839$	0.0279117	−	0.0184244i	0.000963620	−	0.000636080i	−0.550415	−	0.834891i	$-0.685531\pi$
$839$	0.0279117	−	0.0184244i	0.000963620	−	0.000636080i	0.551379	+	0.834255i	$0.314102\pi$
$840$		0			0
$841$	−13.2337	+	20.0482i	−0.456334	+	0.691316i
$842$	−14.0147	−	8.37341i	−0.482980	−	0.288567i
$843$		0			0
$844$	5.18695	+	18.7945i	0.178542	+	0.646933i
$845$	−8.22757	−	13.7706i	−0.283037	−	0.473724i
$846$		0			0
$847$	3.66178	−	5.04001i	0.125820	−	0.173177i
$848$	26.6816	−	4.84199i	0.916249	−	0.166275i
$849$		0			0
$850$	−5.58947	−	62.1041i	−0.191717	−	2.13015i
$851$	41.8042			1.43303
$852$		0			0
$853$	−34.0382			−1.16545			−0.582723	−	0.812671i	$-0.698013\pi$
$853$	−34.0382			−1.16545			−0.582723	+	0.812671i	$0.698013\pi$
$854$	−0.0773449	−	0.859372i	−0.00264669	−	0.0294071i
$855$		0			0
$856$	1.36275	−	0.247303i	0.0465779	−	0.00845264i
$857$	−11.0674	+	15.2329i	−0.378054	+	0.520346i	−0.955068	−	0.296388i	$-0.904218\pi$
$857$	−11.0674	+	15.2329i	−0.378054	+	0.520346i	0.577014	+	0.816734i	$0.304218\pi$
$858$		0			0
$859$	8.83231	+	14.7828i	0.301355	+	0.504383i	0.971247	−	0.238076i	$-0.0765167\pi$
$859$	8.83231	+	14.7828i	0.301355	+	0.504383i	−0.669892	+	0.742459i	$0.733660\pi$
$860$	1.27916	+	4.63495i	0.0436191	+	0.158050i
$861$		0			0
$862$	−42.3129	−	25.2808i	−1.44118	−	0.861067i
$863$	9.16614	−	13.8861i	0.312019	−	0.472689i	−0.644399	−	0.764689i	$-0.722892\pi$
$863$	9.16614	−	13.8861i	0.312019	−	0.472689i	0.956418	+	0.292001i	$0.0943210\pi$
$864$		0			0
$865$	5.61616	−	3.70719i	0.190955	−	0.126048i
$866$	48.6088	−	35.3163i	1.65179	−	1.20010i
$867$		0			0
$868$	8.29263	−	3.11228i	0.281470	−	0.105638i
$869$	−4.60843	+	14.1833i	−0.156330	+	0.481135i
$870$		0			0
$871$	−61.8394	−	64.6790i	−2.09535	−	2.19156i
$872$	0.559925	−	1.16270i	0.0189614	−	0.0393738i
$873$		0			0
$874$	85.7264	+	46.1313i	2.89974	+	1.56042i
$875$	−1.25070	−	5.47969i	−0.0422815	−	0.185247i
$876$		0			0
$877$	2.79220	+	8.59349i	0.0942857	+	0.290182i	0.987067	−	0.160309i	$-0.0512491\pi$
$877$	2.79220	+	8.59349i	0.0942857	+	0.290182i	−0.892781	+	0.450491i	$0.851249\pi$
$878$	11.2144	+	14.0625i	0.378469	+	0.474585i
$879$		0			0
$880$	−3.17593	−	3.63515i	−0.107061	−	0.122541i
$881$	9.31827	−	5.01438i	0.313941	−	0.168939i	−0.309309	−	0.950962i	$-0.600098\pi$
$881$	9.31827	−	5.01438i	0.313941	−	0.168939i	0.623250	+	0.782023i	$0.285812\pi$
$882$		0			0
$883$	0.905100	−	2.41163i	0.0304590	−	0.0811578i	−0.920126	−	0.391624i	$-0.871914\pi$
$883$	0.905100	−	2.41163i	0.0304590	−	0.0811578i	0.950585	+	0.310466i	$0.100485\pi$
$884$	−36.4285	−	75.6445i	−1.22522	−	2.54420i
$885$		0			0
$886$	−1.56317	−	0.356784i	−0.0525158	−	0.0119864i
$887$	−0.159354	−	0.0143421i	−0.00535058	−	0.000481561i	0.0869637	−	0.996211i	$-0.472284\pi$
$887$	−0.159354	−	0.0143421i	−0.00535058	−	0.000481561i	−0.0923143	+	0.995730i	$0.529426\pi$
$888$		0			0
$889$	−0.681237	+	2.98470i	−0.0228480	+	0.100103i
$890$	−10.1618	+	11.6311i	−0.340624	+	0.389876i
$891$		0			0
$892$	13.8113	+	5.18346i	0.462436	+	0.173555i
$893$	37.3028	−	46.7762i	1.24829	−	1.56531i
$894$		0			0
$895$	−3.09872	+	2.70727i	−0.103579	+	0.0904941i
$896$	−0.204351	+	0.478104i	−0.00682690	+	0.0159723i
$897$		0			0
$898$	−25.0228	+	8.13040i	−0.835022	+	0.271315i
$899$	1.88372	+	13.9062i	0.0628256	+	0.463797i
$900$		0			0
$901$	−24.2132	+	44.9957i	−0.806660	+	1.49902i
$902$	4.69157	−	2.00527i	0.156212	−	0.0667683i
$903$		0			0
$904$	−0.537243	+	0.513657i	−0.0178684	+	0.0170840i
$905$	5.29101	+	0.960176i	0.175879	+	0.0319173i
$906$		0			0
$907$	0.440739	+	1.17434i	0.0146345	+	0.0389934i	0.943349	−	0.331802i	$-0.107657\pi$
$907$	0.440739	+	1.17434i	0.0146345	+	0.0389934i	−0.928715	+	0.370795i	$0.879085\pi$
$908$	−26.5048	+	27.7218i	−0.879592	+	0.919981i
$909$		0			0
$910$	−3.76963	−	5.71074i	−0.124962	−	0.189309i
$911$	1.24756	+	27.7791i	0.0413335	+	0.920362i	0.907358	+	0.420359i	$0.138096\pi$
$911$	1.24756	+	27.7791i	0.0413335	+	0.920362i	−0.866024	+	0.500002i	$0.833333\pi$
$912$		0			0
$913$	−4.40081	+	7.36571i	−0.145645	+	0.243769i
$914$	−57.2674	−	15.8048i	−1.89424	−	0.522776i
$915$		0			0
$916$	−9.38765	+	5.60886i	−0.310177	+	0.185322i
$917$	−0.402440	+	8.96102i	−0.0132897	+	0.295919i
$918$		0			0
$919$	1.44664	+	7.97162i	0.0477201	+	0.262960i	0.998965	−	0.0454758i	$-0.0144804\pi$
$919$	1.44664	+	7.97162i	0.0477201	+	0.262960i	−0.951245	+	0.308435i	$0.900195\pi$
$920$	0.0669481	−	0.494230i	0.00220721	−	0.0162943i
$921$		0			0
$922$		−	80.8283i		−	2.66194i
$923$	−15.8399	+	44.2328i	−0.521377	+	1.45594i
$924$		0			0
$925$	−29.4758	+	2.65287i	−0.969158	+	0.0872258i
$926$	43.5400	+	5.89789i	1.43081	+	0.193817i
$927$		0			0
$928$	−14.5167	−	10.5470i	−0.476534	−	0.346222i
$929$	−6.44827	−	0.289592i	−0.211561	−	0.00950121i	−0.0611678	−	0.998127i	$-0.519482\pi$
$929$	−6.44827	−	0.289592i	−0.211561	−	0.00950121i	−0.150393	+	0.988626i	$0.548054\pi$
$930$		0			0
$931$	−51.1514	+	14.1169i	−1.67642	+	0.462662i
$932$	3.30946	−	11.9915i	0.108405	−	0.392796i
$933$		0			0
$934$	−9.91596	−	6.54547i	−0.324460	−	0.214174i
$935$	9.08648	−	0.408074i	0.297160	−	0.0133455i
$936$		0			0
$937$	−31.7286	−	43.6706i	−1.03653	−	1.42666i	−0.899932	−	0.436031i	$-0.856384\pi$
$937$	−31.7286	−	43.6706i	−1.03653	−	1.42666i	−0.136595	−	0.990627i	$-0.543616\pi$
$938$	−16.0538	−	15.3490i	−0.524174	−	0.501161i
$939$		0			0
$940$	−12.7032	−	4.12751i	−0.414331	−	0.134624i
$941$	8.83546	−	48.6874i	0.288028	−	1.58716i	−0.437661	−	0.899140i	$-0.644193\pi$
$941$	8.83546	−	48.6874i	0.288028	−	1.58716i	0.725689	−	0.688023i	$-0.241521\pi$
$942$		0			0
$943$	−9.75345	−	4.69701i	−0.317616	−	0.152956i
$944$	3.82627	+	8.95201i	0.124535	+	0.291363i
$945$		0			0
$946$	7.24494	−	1.65361i	0.235553	−	0.0537635i
$947$	−47.9760	+	6.49878i	−1.55901	+	0.211182i	−0.862385	−	0.506254i	$-0.831030\pi$
$947$	−47.9760	+	6.49878i	−1.55901	+	0.211182i	−0.696624	+	0.717436i	$0.745316\pi$
$948$		0			0
$949$	6.57871	−	5.24635i	0.213554	−	0.170304i
$950$	−63.3724	−	27.0867i	−2.05607	−	0.878808i
$951$		0			0
$952$	−0.226613	−	0.421118i	−0.00734458	−	0.0136485i
$953$	7.11211	+	5.67172i	0.230384	+	0.183725i	0.731877	−	0.681436i	$-0.238644\pi$
$953$	7.11211	+	5.67172i	0.230384	+	0.183725i	−0.501493	+	0.865161i	$0.667216\pi$
$954$		0			0
$955$	−11.2855	+	5.43479i	−0.365189	+	0.175866i
$956$	6.62546	+	5.78849i	0.214283	+	0.187213i
$957$		0			0
$958$	−7.77082	+	86.3409i	−0.251064	+	2.78955i
$959$	−0.887140	+	9.85693i	−0.0286472	+	0.318297i
$960$		0			0
$961$	−6.44676	−	5.63237i	−0.207960	−	0.181689i
$962$	−70.9807	+	34.1825i	−2.28851	+	1.10209i
$963$		0			0
$964$	−32.7745	−	26.1368i	−1.05560	−	0.841810i
$965$	−1.41982	−	2.63847i	−0.0457056	−	0.0849353i
$966$		0			0
$967$	−0.479344	−	0.204882i	−0.0154147	−	0.00658855i	0.385304	−	0.922790i	$-0.374097\pi$
$967$	−0.479344	−	0.204882i	−0.0154147	−	0.00658855i	−0.400719	+	0.916201i	$0.631239\pi$
$968$	−0.669032	+	0.533536i	−0.0215035	+	0.0171485i
$969$		0			0
$970$	−25.1500	+	3.40680i	−0.807518	+	0.109386i
$971$	28.5768	−	6.52246i	0.917072	−	0.209316i	0.262163	−	0.965024i	$-0.415564\pi$
$971$	28.5768	−	6.52246i	0.917072	−	0.209316i	0.654909	+	0.755708i	$0.272707\pi$
$972$		0			0
$973$	−3.39370	−	7.93995i	−0.108797	−	0.254543i
$974$	43.7441	+	21.0660i	1.40165	+	0.674999i
$975$		0			0
$976$	0.434584	−	2.39475i	0.0139107	−	0.0766542i
$977$	−3.13108	−	1.01735i	−0.100172	−	0.0325479i	0.258502	−	0.966011i	$-0.416771\pi$
$977$	−3.13108	−	1.01735i	−0.100172	−	0.0325479i	−0.358674	+	0.933463i	$0.616771\pi$
$978$		0			0
$979$	8.72690	+	8.34377i	0.278913	+	0.266668i
$980$	6.96321	+	9.58404i	0.222432	+	0.306151i
$981$		0			0
$982$	−4.06791	+	0.182690i	−0.129812	+	0.00582988i
$983$	−3.12958	−	2.06582i	−0.0998180	−	0.0658893i	0.500002	−	0.866024i	$-0.333333\pi$
$983$	−3.12958	−	2.06582i	−0.0998180	−	0.0658893i	−0.599820	+	0.800135i	$0.704761\pi$
$984$		0			0
$985$	4.35064	−	15.7642i	0.138623	−	0.502289i
$986$	31.8266	−	8.78359i	1.01357	−	0.279726i
$987$		0			0
$988$	−92.7029	−	4.16329i	−2.94927	−	0.132452i
$989$	−12.7560	−	9.26780i	−0.405618	−	0.294699i
$990$		0			0
$991$	−25.6286	−	3.47162i	−0.814118	−	0.110280i	−0.284674	−	0.958625i	$-0.591885\pi$
$991$	−25.6286	−	3.47162i	−0.814118	−	0.110280i	−0.529444	+	0.848345i	$0.677600\pi$
$992$	50.3808	−	4.53436i	1.59959	−	0.143966i
$993$		0			0
$994$	−3.43505	+	11.1442i	−0.108953	+	0.353473i
$995$		−	9.45622i		−	0.299782i
$996$		0			0
$997$	−7.41087	+	54.7092i	−0.234705	+	1.73266i	0.363745	+	0.931499i	$0.381498\pi$
$997$	−7.41087	+	54.7092i	−0.234705	+	1.73266i	−0.598450	+	0.801160i	$0.704216\pi$
$998$	8.72476	+	48.0774i	0.276177	+	1.52186i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	639.2.z.a.53.5	✓	576
3.2	odd	2	inner	639.2.z.a.53.20	yes	576
71.67	odd	70	inner	639.2.z.a.422.20	yes	576
213.209	even	70	inner	639.2.z.a.422.5	yes	576

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
639.2.z.a.53.5	✓	576	1.1	even	1	trivial
639.2.z.a.53.20	yes	576	3.2	odd	2	inner
639.2.z.a.422.5	yes	576	213.209	even	70	inner
639.2.z.a.422.20	yes	576	71.67	odd	70	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:	\( N \)	\(=\)	\( 639 = 3^{2} \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	639.z (of order \(70\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.180328 - 2.00361i) q^{2} +(-2.01408 + 0.365501i) q^{4} +(0.521198 - 0.717368i) q^{5} +(-0.352855 - 0.590579i) q^{7} +(0.0251400 + 0.0910928i) q^{8} +O(q^{10})\)	\(q+(-0.180328 - 2.00361i) q^{2} +(-2.01408 + 0.365501i) q^{4} +(0.521198 - 0.717368i) q^{5} +(-0.352855 - 0.590579i) q^{7} +(0.0251400 + 0.0910928i) q^{8} +(-1.53131 - 0.914916i) q^{10} +(-0.768209 + 1.16379i) q^{11} +(-4.65350 + 3.07175i) q^{13} +(-1.11966 + 0.813481i) q^{14} +(-3.65492 + 1.37171i) q^{16} +(2.27312 - 6.99594i) q^{17} +(-5.61850 - 5.87649i) q^{19} +(-0.787535 + 1.63533i) q^{20} +(2.47031 + 1.32933i) q^{22} +(-1.32447 - 5.80286i) q^{23} +(1.30212 + 4.00750i) q^{25} +(6.99375 + 8.76988i) q^{26} +(0.926534 + 1.06050i) q^{28} +(-1.96472 + 1.05726i) q^{29} +(2.21005 - 5.88866i) q^{31} +(3.48947 + 7.24595i) q^{32} +(-14.4271 - 3.29288i) q^{34} +(-0.607569 - 0.0546822i) q^{35} +(-1.56286 + 6.84735i) q^{37} +(-10.7610 + 12.3170i) q^{38} +(0.0784500 + 0.0294428i) q^{40} +(1.13399 - 1.42197i) q^{41} +(1.99491 - 1.74290i) q^{43} +(1.12187 - 2.62474i) q^{44} +(-11.3878 + 3.70013i) q^{46} +(0.987800 + 7.29223i) q^{47} +(3.09280 - 5.74739i) q^{49} +(7.79466 - 3.33160i) q^{50} +(8.24979 - 7.88760i) q^{52} +(-6.83469 - 1.24031i) q^{53} +(0.434474 + 1.15765i) q^{55} +(0.0449267 - 0.0469897i) q^{56} +(2.47264 + 3.74589i) q^{58} +(-0.111884 - 2.49130i) q^{59} +(-0.319769 + 0.535203i) q^{61} +(-12.1971 - 3.36619i) q^{62} +(7.18631 - 4.29362i) q^{64} +(-0.221822 + 4.93926i) q^{65} +(2.86556 + 15.7905i) q^{67} +(-2.02121 + 14.9212i) q^{68} +1.22719i q^{70} +(6.74102 - 5.05556i) q^{71} +(-1.50301 + 0.135273i) q^{73} +(14.0013 + 1.89660i) q^{74} +(13.4640 + 9.78214i) q^{76} +(0.958375 + 0.0430407i) q^{77} +(10.3091 - 2.84513i) q^{79} +(-0.920913 + 3.33685i) q^{80} +(-3.05357 - 2.01565i) q^{82} +(6.14686 - 0.276056i) q^{83} +(-3.83392 - 5.27693i) q^{85} +(-3.85184 - 3.68274i) q^{86} +(-0.125325 - 0.0407207i) q^{88} +(1.54601 - 8.51921i) q^{89} +(3.45612 + 1.66438i) q^{91} +(4.78853 + 11.2033i) q^{92} +(14.4327 - 3.29416i) q^{94} +(-7.14396 + 0.967715i) q^{95} +(11.1237 - 8.87087i) q^{97} +(-12.0733 - 5.16036i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 576 q - 24 q^{4}+O(q^{10}) \) 576 * q - 24 * q^4	\( 576 q - 24 q^{4} - 16 q^{10} + 76 q^{16} - 8 q^{19} + 20 q^{22} + 168 q^{25} - 20 q^{28} - 28 q^{31} + 40 q^{37} + 32 q^{40} + 52 q^{43} - 20 q^{46} - 208 q^{52} - 92 q^{55} + 56 q^{58} + 56 q^{61} - 144 q^{64} - 16 q^{67} - 44 q^{73} - 336 q^{76} + 88 q^{79} - 124 q^{82} + 60 q^{85} - 260 q^{88} + 80 q^{91} + 56 q^{94} - 56 q^{97}+O(q^{100}) \) 576 * q - 24 * q^4 - 16 * q^10 + 76 * q^16 - 8 * q^19 + 20 * q^22 + 168 * q^25 - 20 * q^28 - 28 * q^31 + 40 * q^37 + 32 * q^40 + 52 * q^43 - 20 * q^46 - 208 * q^52 - 92 * q^55 + 56 * q^58 + 56 * q^61 - 144 * q^64 - 16 * q^67 - 44 * q^73 - 336 * q^76 + 88 * q^79 - 124 * q^82 + 60 * q^85 - 260 * q^88 + 80 * q^91 + 56 * q^94 - 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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