LMFDB - Embedded newform 297.2.n.b.181.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,2,Mod(37,297)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(297, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 6]))

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

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

chi := DirichletCharacter("297.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.n (of order $15$, degree $8$, not 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:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			181.5
Character	$\chi$	$=$	297.181
Dual form			297.2.n.b.64.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.278917 + 0.0592857i) q^{2} +(-1.75281 - 0.780402i) q^{4} +(2.64954 - 0.563177i) q^{5} +(0.425779 + 4.05102i) q^{7} +(-0.904002 - 0.656796i) q^{8} +O(q^{10})$	\(q+(0.278917 + 0.0592857i) q^{2} +(-1.75281 - 0.780402i) q^{4} +(2.64954 - 0.563177i) q^{5} +(0.425779 + 4.05102i) q^{7} +(-0.904002 - 0.656796i) q^{8} +0.772391 q^{10} +(3.31056 - 0.200500i) q^{11} +(2.57679 - 2.86182i) q^{13} +(-0.121410 + 1.15514i) q^{14} +(2.35451 + 2.61494i) q^{16} +(1.33502 - 4.10876i) q^{17} +(1.31246 + 0.953561i) q^{19} +(-5.08365 - 1.08056i) q^{20} +(0.935259 + 0.140346i) q^{22} +(-0.932117 - 1.61447i) q^{23} +(2.13517 - 0.950641i) q^{25} +(0.888377 - 0.645443i) q^{26} +(2.41511 - 7.43295i) q^{28} +(0.371426 + 3.53388i) q^{29} +(-3.25505 + 3.61509i) q^{31} +(1.61909 + 2.80435i) q^{32} +(0.615950 - 1.06686i) q^{34} +(3.40956 + 10.4936i) q^{35} +(-6.26542 + 4.55210i) q^{37} +(0.309536 + 0.343775i) q^{38} +(-2.76508 - 1.23109i) q^{40} +(0.718335 - 6.83450i) q^{41} +(-0.492496 + 0.853027i) q^{43} +(-5.95925 - 2.23213i) q^{44} +(-0.164268 - 0.505566i) q^{46} +(-5.35918 + 2.38606i) q^{47} +(-9.38245 + 1.99430i) q^{49} +(0.651896 - 0.138565i) q^{50} +(-6.75000 + 3.00529i) q^{52} +(0.485721 + 1.49489i) q^{53} +(8.65855 - 2.39567i) q^{55} +(2.27579 - 3.94178i) q^{56} +(-0.105911 + 1.00768i) q^{58} +(-10.3802 - 4.62154i) q^{59} +(-5.75953 - 6.39660i) q^{61} +(-1.12221 + 0.815335i) q^{62} +(-1.88937 - 5.81490i) q^{64} +(5.21561 - 9.03370i) q^{65} +(0.870282 + 1.50737i) q^{67} +(-5.54651 + 6.16003i) q^{68} +(0.328868 + 3.12897i) q^{70} +(1.77418 - 5.46036i) q^{71} +(3.27379 - 2.37855i) q^{73} +(-2.01741 + 0.898208i) q^{74} +(-1.55634 - 2.69566i) q^{76} +(2.22180 + 13.3258i) q^{77} +(4.18662 + 0.889893i) q^{79} +(7.71104 + 5.60240i) q^{80} +(0.605544 - 1.86367i) q^{82} +(4.34947 + 4.83058i) q^{83} +(1.22322 - 11.6382i) q^{85} +(-0.187938 + 0.208726i) q^{86} +(-3.12444 - 1.99311i) q^{88} -9.26243 q^{89} +(12.6904 + 9.22014i) q^{91} +(0.373887 + 3.55729i) q^{92} +(-1.63623 + 0.347790i) q^{94} +(4.01445 + 1.78735i) q^{95} +(7.25070 + 1.54118i) q^{97} -2.73516 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8}+O(q^{10}) $ 72 * q + q^2 + 11 * q^4 + 8 * q^5 - 2 * q^7 - 6 * q^8	$ 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8} - 8 q^{10} + 2 q^{11} - 11 q^{13} + 10 q^{14} - 9 q^{16} + 20 q^{17} + 8 q^{19} + 45 q^{20} - 16 q^{22} - 20 q^{23} + 11 q^{25} + 12 q^{26} - 54 q^{28} + 23 q^{29} + 3 q^{31} - 18 q^{32} + 8 q^{34} - 18 q^{35} - 42 q^{37} + q^{38} - 25 q^{40} - 10 q^{41} - 8 q^{43} - 38 q^{44} - 18 q^{46} + 34 q^{47} + q^{49} - 27 q^{52} - 4 q^{53} + 18 q^{55} - 114 q^{56} + q^{58} + 16 q^{59} - 3 q^{61} - 184 q^{62} + 26 q^{64} - 84 q^{65} + 10 q^{67} + 23 q^{68} - 46 q^{70} + 48 q^{71} - 40 q^{73} - 68 q^{74} + 16 q^{76} + 26 q^{77} + 19 q^{79} + 56 q^{80} + 94 q^{82} - 7 q^{83} + 25 q^{85} + 77 q^{86} + 18 q^{88} + 56 q^{89} + 20 q^{91} - 50 q^{92} - 63 q^{94} + 77 q^{95} - 33 q^{97} + 328 q^{98}+O(q^{100}) $ 72 * q + q^2 + 11 * q^4 + 8 * q^5 - 2 * q^7 - 6 * q^8 - 8 * q^10 + 2 * q^11 - 11 * q^13 + 10 * q^14 - 9 * q^16 + 20 * q^17 + 8 * q^19 + 45 * q^20 - 16 * q^22 - 20 * q^23 + 11 * q^25 + 12 * q^26 - 54 * q^28 + 23 * q^29 + 3 * q^31 - 18 * q^32 + 8 * q^34 - 18 * q^35 - 42 * q^37 + q^38 - 25 * q^40 - 10 * q^41 - 8 * q^43 - 38 * q^44 - 18 * q^46 + 34 * q^47 + q^49 - 27 * q^52 - 4 * q^53 + 18 * q^55 - 114 * q^56 + q^58 + 16 * q^59 - 3 * q^61 - 184 * q^62 + 26 * q^64 - 84 * q^65 + 10 * q^67 + 23 * q^68 - 46 * q^70 + 48 * q^71 - 40 * q^73 - 68 * q^74 + 16 * q^76 + 26 * q^77 + 19 * q^79 + 56 * q^80 + 94 * q^82 - 7 * q^83 + 25 * q^85 + 77 * q^86 + 18 * q^88 + 56 * q^89 + 20 * q^91 - 50 * q^92 - 63 * q^94 + 77 * q^95 - 33 * q^97 + 328 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.278917	+	0.0592857i	0.197224	+	0.0419213i	0.305465	−	0.952203i	$-0.401188\pi$
$2$	0.278917	+	0.0592857i	0.197224	+	0.0419213i	−0.108240	+	0.994125i	$0.534522\pi$
$3$		0			0
$3$		0			0
$4$	−1.75281	−	0.780402i	−0.876405	−	0.390201i
$5$	2.64954	−	0.563177i	1.18491	−	0.251861i	0.427020	−	0.904242i	$-0.359563\pi$
$5$	2.64954	−	0.563177i	1.18491	−	0.251861i	0.757891	+	0.652381i	$0.226230\pi$
$6$		0			0
$7$	0.425779	+	4.05102i	0.160930	+	1.53114i	0.715268	+	0.698851i	$0.246305\pi$
$7$	0.425779	+	4.05102i	0.160930	+	1.53114i	−0.554338	+	0.832291i	$0.687029\pi$
$8$	−0.904002	−	0.656796i	−0.319613	−	0.232212i
$9$		0			0
$10$	0.772391			0.244251
$11$	3.31056	−	0.200500i	0.998171	−	0.0604531i
$11$	3.31056	−	0.200500i	0.998171	−	0.0604531i
$12$		0			0
$13$	2.57679	−	2.86182i	0.714674	−	0.793726i	−0.270966	−	0.962589i	$-0.587343\pi$
$13$	2.57679	−	2.86182i	0.714674	−	0.793726i	0.985639	+	0.168863i	$0.0540097\pi$
$14$	−0.121410	+	1.15514i	−0.0324483	+	0.308725i
$15$		0			0
$16$	2.35451	+	2.61494i	0.588626	+	0.653736i
$17$	1.33502	−	4.10876i	0.323789	−	0.996520i	−0.648195	−	0.761474i	$-0.724476\pi$
$17$	1.33502	−	4.10876i	0.323789	−	0.996520i	0.971984	−	0.235046i	$-0.0755241\pi$
$18$		0			0
$19$	1.31246	+	0.953561i	0.301100	+	0.218762i	0.728068	−	0.685505i	$-0.240418\pi$
$19$	1.31246	+	0.953561i	0.301100	+	0.218762i	−0.426968	+	0.904267i	$0.640418\pi$
$20$	−5.08365	−	1.08056i	−1.13674	−	0.241621i
$21$		0			0
$22$	0.935259	+	0.140346i	0.199398	+	0.0299218i
$23$	−0.932117	−	1.61447i	−0.194360	−	0.336641i	0.752331	−	0.658786i	$-0.228930\pi$
$23$	−0.932117	−	1.61447i	−0.194360	−	0.336641i	−0.946691	+	0.322145i	$0.895596\pi$
$24$		0			0
$25$	2.13517	−	0.950641i	0.427035	−	0.190128i
$26$	0.888377	−	0.645443i	0.174225	−	0.126582i
$27$		0			0
$28$	2.41511	−	7.43295i	0.456413	−	1.40470i
$29$	0.371426	+	3.53388i	0.0689720	+	0.656225i	0.973324	+	0.229437i	$0.0736884\pi$
$29$	0.371426	+	3.53388i	0.0689720	+	0.656225i	−0.904352	+	0.426788i	$0.859645\pi$
$30$		0			0
$31$	−3.25505	+	3.61509i	−0.584624	+	0.649290i	−0.960795	−	0.277260i	$-0.910574\pi$
$31$	−3.25505	+	3.61509i	−0.584624	+	0.649290i	0.376171	+	0.926550i	$0.377240\pi$
$32$	1.61909	+	2.80435i	0.286218	+	0.495744i
$33$		0			0
$34$	0.615950	−	1.06686i	0.105634	−	0.182964i
$35$	3.40956	+	10.4936i	0.576321	+	1.77374i
$36$		0			0
$37$	−6.26542	+	4.55210i	−1.03003	+	0.748360i	−0.968314	−	0.249734i	$-0.919657\pi$
$37$	−6.26542	+	4.55210i	−1.03003	+	0.748360i	−0.0617145	+	0.998094i	$0.519657\pi$
$38$	0.309536	+	0.343775i	0.0502134	+	0.0557676i
$39$		0			0
$40$	−2.76508	−	1.23109i	−0.437198	−	0.194653i
$41$	0.718335	−	6.83450i	0.112185	−	1.06737i	−0.783106	−	0.621888i	$-0.786366\pi$
$41$	0.718335	−	6.83450i	0.112185	−	1.06737i	0.895291	−	0.445481i	$-0.146967\pi$
$42$		0			0
$43$	−0.492496	+	0.853027i	−0.0751049	+	0.130085i	−0.901132	−	0.433545i	$-0.857262\pi$
$43$	−0.492496	+	0.853027i	−0.0751049	+	0.130085i	0.826027	+	0.563631i	$0.190596\pi$
$44$	−5.95925	−	2.23213i	−0.898391	−	0.336506i
$45$		0			0
$46$	−0.164268	−	0.505566i	−0.0242200	−	0.0745416i
$47$	−5.35918	+	2.38606i	−0.781716	+	0.348042i	−0.758487	−	0.651688i	$-0.774061\pi$
$47$	−5.35918	+	2.38606i	−0.781716	+	0.348042i	−0.0232288	+	0.999730i	$0.507395\pi$
$48$		0			0
$49$	−9.38245	+	1.99430i	−1.34035	+	0.284900i
$50$	0.651896	−	0.138565i	0.0921920	−	0.0195960i
$51$		0			0
$52$	−6.75000	+	3.00529i	−0.936056	+	0.416759i
$53$	0.485721	+	1.49489i	0.0667189	+	0.205340i	0.978858	−	0.204541i	$-0.0655703\pi$
$53$	0.485721	+	1.49489i	0.0667189	+	0.205340i	−0.912139	+	0.409881i	$0.865570\pi$
$54$		0			0
$55$	8.65855	−	2.39567i	1.16752	−	0.323032i
$56$	2.27579	−	3.94178i	0.304115	−	0.526743i
$57$		0			0
$58$	−0.105911	+	1.00768i	−0.0139069	+	0.132315i
$59$	−10.3802	−	4.62154i	−1.35138	−	0.601674i	−0.401954	−	0.915660i	$-0.631669\pi$
$59$	−10.3802	−	4.62154i	−1.35138	−	0.601674i	−0.949427	+	0.313986i	$0.898335\pi$
$60$		0			0
$61$	−5.75953	−	6.39660i	−0.737432	−	0.819001i	0.251424	−	0.967877i	$-0.419101\pi$
$61$	−5.75953	−	6.39660i	−0.737432	−	0.819001i	−0.988856	+	0.148876i	$0.952434\pi$
$62$	−1.12221	+	0.815335i	−0.142521	+	0.103548i
$63$		0			0
$64$	−1.88937	−	5.81490i	−0.236172	−	0.726862i
$65$	5.21561	−	9.03370i	0.646916	−	1.12049i
$66$		0			0
$67$	0.870282	+	1.50737i	0.106322	+	0.184155i	0.914277	−	0.405088i	$-0.132759\pi$
$67$	0.870282	+	1.50737i	0.106322	+	0.184155i	−0.807956	+	0.589243i	$0.799426\pi$
$68$	−5.54651	+	6.16003i	−0.672614	+	0.747013i
$69$		0			0
$70$	0.328868	+	3.12897i	0.0393073	+	0.373984i
$71$	1.77418	−	5.46036i	0.210556	−	0.648026i	−0.788883	−	0.614543i	$-0.789340\pi$
$71$	1.77418	−	5.46036i	0.210556	−	0.648026i	0.999439	−	0.0334822i	$-0.0106597\pi$
$72$		0			0
$73$	3.27379	−	2.37855i	0.383168	−	0.278388i	−0.379482	−	0.925199i	$-0.623898\pi$
$73$	3.27379	−	2.37855i	0.383168	−	0.278388i	0.762650	+	0.646811i	$0.223898\pi$
$74$	−2.01741	+	0.898208i	−0.234519	+	0.104415i
$75$		0			0
$76$	−1.55634	−	2.69566i	−0.178524	−	0.309213i
$77$	2.22180	+	13.3258i	0.253198	+	1.51861i
$78$		0			0
$79$	4.18662	+	0.889893i	0.471031	+	0.100121i	0.437311	−	0.899311i	$-0.355931\pi$
$79$	4.18662	+	0.889893i	0.471031	+	0.100121i	0.0337205	+	0.999431i	$0.489264\pi$
$80$	7.71104	+	5.60240i	0.862120	+	0.626367i
$81$		0			0
$82$	0.605544	−	1.86367i	0.0668711	−	0.205808i
$83$	4.34947	+	4.83058i	0.477417	+	0.530225i	0.932956	−	0.359991i	$-0.117220\pi$
$83$	4.34947	+	4.83058i	0.477417	+	0.530225i	−0.455539	+	0.890216i	$0.650554\pi$
$84$		0			0
$85$	1.22322	−	11.6382i	0.132677	−	1.26234i
$86$	−0.187938	+	0.208726i	−0.0202659	+	0.0225075i
$87$		0			0
$88$	−3.12444	−	1.99311i	−0.333066	−	0.212466i
$89$	−9.26243			−0.981816			−0.490908	−	0.871211i	$-0.663335\pi$
$89$	−9.26243			−0.981816			−0.490908	+	0.871211i	$0.663335\pi$
$90$		0			0
$91$	12.6904	+	9.22014i	1.33032	+	0.966533i
$92$	0.373887	+	3.55729i	0.0389804	+	0.370874i
$93$		0			0
$94$	−1.63623	+	0.347790i	−0.168764	+	0.0358718i
$95$	4.01445	+	1.78735i	0.411874	+	0.183378i
$96$		0			0
$97$	7.25070	+	1.54118i	0.736197	+	0.156483i	0.560726	−	0.828001i	$-0.310522\pi$
$97$	7.25070	+	1.54118i	0.736197	+	0.156483i	0.175470	+	0.984485i	$0.443855\pi$
$98$	−2.73516			−0.276293
$99$		0			0
$100$	−4.48444			−0.448444
$101$	−13.4178	−	2.85205i	−1.33513	−	0.283790i	−0.515598	−	0.856830i	$-0.672430\pi$
$101$	−13.4178	−	2.85205i	−1.33513	−	0.283790i	−0.819527	+	0.573041i	$0.805764\pi$
$102$		0			0
$103$	4.63647	+	2.06429i	0.456845	+	0.203400i	0.622239	−	0.782827i	$-0.286223\pi$
$103$	4.63647	+	2.06429i	0.456845	+	0.203400i	−0.165395	+	0.986227i	$0.552890\pi$
$104$	−4.20906	+	0.894663i	−0.412732	+	0.0877289i
$105$		0			0
$106$	0.0468500	+	0.445748i	0.00455048	+	0.0432949i
$107$	−2.24824	−	1.63344i	−0.217346	−	0.157911i	0.473785	−	0.880640i	$-0.342887\pi$
$107$	−2.24824	−	1.63344i	−0.217346	−	0.157911i	−0.691131	+	0.722730i	$0.742887\pi$
$108$		0			0
$109$	−17.3573			−1.66253			−0.831263	−	0.555879i	$-0.812382\pi$
$109$	−17.3573			−1.66253			−0.831263	+	0.555879i	$0.812382\pi$
$110$	2.55705	−	0.154865i	0.243805	−	0.0147658i
$111$		0			0
$112$	−9.59069	+	10.6515i	−0.906235	+	1.00648i
$113$	0.0986387	−	0.938485i	0.00927915	−	0.0882852i	−0.988902	−	0.148568i	$-0.952534\pi$
$113$	0.0986387	−	0.938485i	0.00927915	−	0.0882852i	0.998181	+	0.0602828i	$0.0192003\pi$
$114$		0			0
$115$	−3.37892	−	3.75267i	−0.315086	−	0.349938i
$116$	2.10681	−	6.48408i	0.195612	−	0.602032i
$117$		0			0
$118$	−2.62121	−	1.90442i	−0.241302	−	0.175316i
$119$	17.2131	+	3.65876i	1.57792	+	0.335398i
$120$		0			0
$121$	10.9196	−	1.32754i	0.992691	−	0.120685i
$122$	−1.22720	−	2.12558i	−0.111106	−	0.192441i
$123$		0			0
$124$	8.52671	−	3.79633i	0.765721	−	0.340921i
$125$	−5.83521	+	4.23953i	−0.521917	+	0.379195i
$126$		0			0
$127$	0.757216	−	2.33047i	0.0671920	−	0.206796i	−0.911823	−	0.410583i	$-0.865325\pi$
$127$	0.757216	−	2.33047i	0.0671920	−	0.206796i	0.979015	+	0.203787i	$0.0653251\pi$
$128$	−0.859204	−	8.17478i	−0.0759436	−	0.722555i
$129$		0			0
$130$	1.99029	−	2.21044i	0.174560	−	0.193869i
$131$	1.99869	+	3.46183i	0.174626	+	0.302461i	0.940032	−	0.341087i	$-0.110795\pi$
$131$	1.99869	+	3.46183i	0.174626	+	0.302461i	−0.765406	+	0.643548i	$0.777462\pi$
$132$		0			0
$133$	−3.30407	+	5.72282i	−0.286500	+	0.496232i
$134$	0.153371	+	0.472027i	0.0132492	+	0.0407769i
$135$		0			0
$136$	−3.90547	+	2.83749i	−0.334892	+	0.243313i
$137$	−0.728855	−	0.809475i	−0.0622703	−	0.0691581i	0.711205	−	0.702985i	$-0.248150\pi$
$137$	−0.728855	−	0.809475i	−0.0622703	−	0.0691581i	−0.773475	+	0.633827i	$0.781483\pi$
$138$		0			0
$139$	2.63551	+	1.17340i	0.223541	+	0.0995269i	0.515451	−	0.856919i	$-0.327624\pi$
$139$	2.63551	+	1.17340i	0.223541	+	0.0995269i	−0.291910	+	0.956446i	$0.594291\pi$
$140$	2.21287	−	21.0541i	0.187022	−	1.77939i
$141$		0			0
$142$	0.818570	−	1.41780i	0.0686929	−	0.118980i
$143$	7.95683	−	9.99087i	0.665383	−	0.835478i
$144$		0			0
$145$	2.97431	+	9.15398i	0.247003	+	0.760197i
$146$	1.05413	−	0.469329i	0.0872404	−	0.0388419i
$147$		0			0
$148$	14.5346	−	3.08942i	1.19473	−	0.253948i
$149$	19.7339	−	4.19458i	1.61667	−	0.343633i	0.691260	−	0.722606i	$-0.257056\pi$
$149$	19.7339	−	4.19458i	1.61667	−	0.343633i	0.925408	+	0.378973i	$0.123723\pi$
$150$		0			0
$151$	−10.1206	+	4.50597i	−0.823601	+	0.366691i	−0.774870	−	0.632121i	$-0.782185\pi$
$151$	−10.1206	+	4.50597i	−0.823601	+	0.366691i	−0.0487316	+	0.998812i	$0.515518\pi$
$152$	−0.560175	−	1.72404i	−0.0454362	−	0.139838i
$153$		0			0
$154$	−0.170330	+	3.84851i	−0.0137255	+	0.310122i
$155$	−6.58844	+	11.4115i	−0.529196	+	0.916595i
$156$		0			0
$157$	−0.0347854	+	0.330961i	−0.00277618	+	0.0264136i	−0.995822	−	0.0913125i	$-0.970894\pi$
$157$	−0.0347854	+	0.330961i	−0.00277618	+	0.0264136i	0.993046	+	0.117726i	$0.0375605\pi$
$158$	1.11496	+	0.496413i	0.0887016	+	0.0394925i
$159$		0			0
$160$	5.86920	+	6.51840i	0.464001	+	0.515325i
$161$	6.14339	−	4.46344i	0.484167	−	0.351768i
$162$		0			0
$163$	4.12168	+	12.6852i	0.322835	+	0.993584i	0.972408	+	0.233285i	$0.0749475\pi$
$163$	4.12168	+	12.6852i	0.322835	+	0.993584i	−0.649574	+	0.760299i	$0.725053\pi$
$164$	−6.59276	+	11.4190i	−0.514808	+	0.891674i
$165$		0			0
$166$	0.926759	+	1.60519i	0.0719304	+	0.124587i
$167$	12.6567	−	14.0567i	0.979405	−	1.08774i	−0.0167258	−	0.999860i	$-0.505324\pi$
$167$	12.6567	−	14.0567i	0.979405	−	1.08774i	0.996131	−	0.0878797i	$-0.0280091\pi$
$168$		0			0
$169$	−0.191273	−	1.81984i	−0.0147133	−	0.139988i
$170$	1.03115	−	3.17357i	0.0790860	−	0.243402i
$171$		0			0
$172$	1.52896	−	1.11085i	0.116582	−	0.0847016i
$173$	1.38319	−	0.615835i	0.105162	−	0.0468211i	−0.353481	−	0.935442i	$-0.615002\pi$
$173$	1.38319	−	0.615835i	0.105162	−	0.0468211i	0.458643	+	0.888620i	$0.348336\pi$
$174$		0			0
$175$	4.76018	+	8.24487i	0.359836	+	0.623254i
$176$	8.31903	+	8.18485i	0.627070	+	0.616956i
$177$		0			0
$178$	−2.58345	−	0.549130i	−0.193638	−	0.0411590i
$179$	10.6703	+	7.75244i	0.797537	+	0.579445i	0.910191	−	0.414190i	$-0.135935\pi$
$179$	10.6703	+	7.75244i	0.797537	+	0.579445i	−0.112653	+	0.993634i	$0.535935\pi$
$180$		0			0
$181$	0.864886	−	2.66185i	0.0642865	−	0.197853i	−0.913754	−	0.406267i	$-0.866830\pi$
$181$	0.864886	−	2.66185i	0.0642865	−	0.197853i	0.978041	+	0.208414i	$0.0668301\pi$
$182$	2.99296	+	3.32402i	0.221853	+	0.246392i
$183$		0			0
$184$	−0.217744	+	2.07170i	−0.0160523	+	0.152728i
$185$	−14.0369	+	15.5895i	−1.03201	+	1.14616i
$186$		0			0
$187$	3.59584	−	13.8700i	0.262954	−	1.01427i
$188$	11.2557			0.820907
$189$		0			0
$190$	1.01374	+	0.736522i	0.0735441	+	0.0534329i
$191$	−1.74997	−	16.6498i	−0.126623	−	1.20474i	−0.854655	−	0.519197i	$-0.826231\pi$
$191$	−1.74997	−	16.6498i	−0.126623	−	1.20474i	0.728032	−	0.685544i	$-0.240435\pi$
$192$		0			0
$193$	21.5578	−	4.58224i	1.55176	−	0.329837i	0.649275	−	0.760554i	$-0.275073\pi$
$193$	21.5578	−	4.58224i	1.55176	−	0.329837i	0.902487	+	0.430717i	$0.141739\pi$
$194$	1.93097	+	0.859725i	0.138636	+	0.0617247i
$195$		0			0
$196$	18.0020	+	3.82645i	1.28586	+	0.273318i
$197$	−18.2247			−1.29845			−0.649227	−	0.760595i	$-0.724907\pi$
$197$	−18.2247			−1.29845			−0.649227	+	0.760595i	$0.724907\pi$
$198$		0			0
$199$	−25.0958			−1.77899			−0.889497	−	0.456942i	$-0.848945\pi$
$199$	−25.0958			−1.77899			−0.889497	+	0.456942i	$0.848945\pi$
$200$	−2.55458	−	0.542993i	−0.180636	−	0.0383954i
$201$		0			0
$202$	−3.57338	−	1.59097i	−0.251422	−	0.111940i
$203$	−14.1577	+	3.00931i	−0.993674	+	0.211212i
$204$		0			0
$205$	−1.94578	−	18.5128i	−0.135899	−	1.29299i
$206$	1.17081	+	0.850642i	0.0815741	+	0.0592670i
$207$		0			0
$208$	13.5506			0.939563
$209$	4.53618	+	2.89367i	0.313774	+	0.200159i
$210$		0			0
$211$	5.53373	−	6.14582i	0.380957	−	0.423096i	−0.521920	−	0.852995i	$-0.674784\pi$
$211$	5.53373	−	6.14582i	0.380957	−	0.423096i	0.902877	+	0.429899i	$0.141451\pi$
$212$	0.315242	−	2.99933i	0.0216509	−	0.205995i
$213$		0			0
$214$	−0.530233	−	0.588884i	−0.0362460	−	0.0402552i
$215$	−0.824482	+	2.53749i	−0.0562292	+	0.173056i
$216$		0			0
$217$	−16.0308	−	11.6470i	−1.08824	−	0.790652i
$218$	−4.84125	−	1.02904i	−0.327891	−	0.0696953i
$219$		0			0
$220$	−17.0464	−	2.55799i	−1.14927	−	0.172460i
$221$	−8.31846	−	14.4080i	−0.559560	−	0.969187i
$222$		0			0
$223$	−6.71646	+	2.99036i	−0.449768	+	0.200249i	−0.619104	−	0.785309i	$-0.712504\pi$
$223$	−6.71646	+	2.99036i	−0.449768	+	0.200249i	0.169337	+	0.985558i	$0.445837\pi$
$224$	−10.6711	+	7.75301i	−0.712993	+	0.518020i
$225$		0			0
$226$	0.0831507	−	0.255912i	0.00553110	−	0.0170230i
$227$	−1.97989	−	18.8374i	−0.131410	−	1.25028i	−0.839185	−	0.543846i	$-0.816968\pi$
$227$	−1.97989	−	18.8374i	−0.131410	−	1.25028i	0.707775	−	0.706438i	$-0.249699\pi$
$228$		0			0
$229$	−5.25900	+	5.84071i	−0.347524	+	0.385965i	−0.891412	−	0.453193i	$-0.850285\pi$
$229$	−5.25900	+	5.84071i	−0.347524	+	0.385965i	0.543888	+	0.839158i	$0.316952\pi$
$230$	−0.719959	−	1.24701i	−0.0474727	−	0.0822251i
$231$		0			0
$232$	1.98527	−	3.43859i	0.130339	−	0.225754i
$233$	2.03006	+	6.24789i	0.132994	+	0.409313i	0.995273	−	0.0971212i	$-0.0309634\pi$
$233$	2.03006	+	6.24789i	0.132994	+	0.409313i	−0.862279	+	0.506434i	$0.830963\pi$
$234$		0			0
$235$	−12.8556	+	9.34013i	−0.838606	+	0.609283i
$236$	14.5878	+	16.2014i	0.949584	+	1.05462i
$237$		0			0
$238$	4.58412	+	2.04098i	0.297144	+	0.132297i
$239$	−2.67031	+	25.4063i	−0.172728	+	1.64340i	0.473889	+	0.880585i	$0.342850\pi$
$239$	−2.67031	+	25.4063i	−0.172728	+	1.64340i	−0.646617	+	0.762815i	$0.723817\pi$
$240$		0			0
$241$	1.49099	−	2.58247i	0.0960432	−	0.166352i	−0.814000	−	0.580864i	$-0.802715\pi$
$241$	1.49099	−	2.58247i	0.0960432	−	0.166352i	0.910044	+	0.414513i	$0.136048\pi$
$242$	3.12437	+	0.277103i	0.200842	+	0.0178129i
$243$		0			0
$244$	5.10344	+	15.7068i	0.326714	+	1.00552i
$245$	−23.7360	+	10.5680i	−1.51644	+	0.675163i
$246$		0			0
$247$	6.11086	−	1.29890i	0.388825	−	0.0826473i
$248$	5.31695	−	1.13015i	0.337627	−	0.0717647i
$249$		0			0
$250$	−1.87888	+	0.836532i	−0.118831	+	0.0529070i
$251$	−3.60577	−	11.0974i	−0.227594	−	0.700463i	−0.998018	−	0.0629308i	$-0.979955\pi$
$251$	−3.60577	−	11.0974i	−0.227594	−	0.700463i	0.770424	−	0.637532i	$-0.220045\pi$
$252$		0			0
$253$	−3.40953	−	5.15792i	−0.214355	−	0.324276i
$254$	0.349364	−	0.605116i	0.0219211	−	0.0379684i
$255$		0			0
$256$	−1.03320	+	9.83028i	−0.0645752	+	0.614392i
$257$	−18.9327	−	8.42939i	−1.18099	−	0.525811i	−0.280148	−	0.959957i	$-0.590384\pi$
$257$	−18.9327	−	8.42939i	−1.18099	−	0.525811i	−0.900843	+	0.434146i	$0.857050\pi$
$258$		0			0
$259$	−21.1083	−	23.4432i	−1.31161	−	1.45669i
$260$	−16.1919	+	11.7641i	−1.00418	+	0.729578i
$261$		0			0
$262$	0.352231	+	1.08406i	0.0217609	+	0.0669732i
$263$	4.54273	−	7.86823i	0.280117	−	0.485176i	−0.691297	−	0.722571i	$-0.742960\pi$
$263$	4.54273	−	7.86823i	0.280117	−	0.485176i	0.971413	+	0.237395i	$0.0762936\pi$
$264$		0			0
$265$	2.12883	+	3.68724i	0.130773	+	0.226505i
$266$	−1.26084	+	1.40031i	−0.0773073	+	0.0858585i
$267$		0			0
$268$	−0.349083	−	3.32131i	−0.0213237	−	0.202881i
$269$	−2.45399	+	7.55261i	−0.149623	+	0.460491i	−0.997576	−	0.0695792i	$-0.977834\pi$
$269$	−2.45399	+	7.55261i	−0.149623	+	0.460491i	0.847954	+	0.530070i	$0.177834\pi$
$270$		0			0
$271$	−3.01249	+	2.18870i	−0.182995	+	0.132954i	−0.675512	−	0.737349i	$-0.736077\pi$
$271$	−3.01249	+	2.18870i	−0.182995	+	0.132954i	0.492516	+	0.870303i	$0.336077\pi$
$272$	13.8875	−	6.18310i	0.842052	−	0.374906i
$273$		0			0
$274$	−0.155300	−	0.268987i	−0.00938201	−	0.0162501i
$275$	6.87801	−	3.57526i	0.414760	−	0.215596i
$276$		0			0
$277$	3.81540	+	0.810988i	0.229245	+	0.0487275i	0.321102	−	0.947045i	$-0.395947\pi$
$277$	3.81540	+	0.810988i	0.229245	+	0.0487275i	−0.0918567	+	0.995772i	$0.529280\pi$
$278$	0.665523	+	0.483531i	0.0399154	+	0.0290003i
$279$		0			0
$280$	3.80987	−	11.7256i	0.227684	−	0.700738i
$281$	−0.0265130	−	0.0294457i	−0.00158163	−	0.00175658i	0.742353	−	0.670008i	$-0.233710\pi$
$281$	−0.0265130	−	0.0294457i	−0.00158163	−	0.00175658i	−0.743935	+	0.668252i	$0.767043\pi$
$282$		0			0
$283$	−0.668341	+	6.35884i	−0.0397288	+	0.377994i	0.956534	+	0.291621i	$0.0941945\pi$
$283$	−0.668341	+	6.35884i	−0.0397288	+	0.377994i	−0.996263	+	0.0863734i	$0.972472\pi$
$284$	−7.37107	+	8.18641i	−0.437393	+	0.485774i
$285$		0			0
$286$	2.81161	−	2.31490i	0.166254	−	0.136883i
$287$	27.9925			1.65235
$288$		0			0
$289$	−1.34634	−	0.978174i	−0.0791965	−	0.0575397i
$290$	0.286886	+	2.72954i	0.0168465	+	0.160284i
$291$		0			0
$292$	−7.59455	+	1.61427i	−0.444438	+	0.0944681i
$293$	21.3837	+	9.52066i	1.24925	+	0.556203i	0.921433	−	0.388538i	$-0.127020\pi$
$293$	21.3837	+	9.52066i	1.24925	+	0.556203i	0.327819	+	0.944741i	$0.393686\pi$
$294$		0			0
$295$	−30.1054	−	6.39910i	−1.75280	−	0.372570i
$296$	8.65375			0.502989
$297$		0			0
$298$	5.75282			0.333252
$299$	−7.02221	−	1.49262i	−0.406105	−	0.0863202i
$300$		0			0
$301$	−3.66533	−	1.63191i	−0.211266	−	0.0940616i
$302$	−3.08994	+	0.656788i	−0.177806	+	0.0377939i
$303$		0			0
$304$	0.596696	+	5.67718i	0.0342229	+	0.325609i
$305$	−18.8625	−	13.7044i	−1.08007	−	0.784713i
$306$		0			0
$307$	29.1494			1.66365			0.831823	−	0.555042i	$-0.187298\pi$
$307$	29.1494			1.66365			0.831823	+	0.555042i	$0.187298\pi$
$308$	6.50506	−	25.0915i	0.370660	−	1.42972i
$309$		0			0
$310$	−2.51417	+	2.79227i	−0.142795	+	0.158590i
$311$	−2.05981	+	19.5978i	−0.116801	+	1.11129i	0.766423	+	0.642337i	$0.222035\pi$
$311$	−2.05981	+	19.5978i	−0.116801	+	1.11129i	−0.883224	+	0.468952i	$0.844632\pi$
$312$		0			0
$313$	0.895549	+	0.994608i	0.0506194	+	0.0562185i	0.767923	−	0.640542i	$-0.221290\pi$
$313$	0.895549	+	0.994608i	0.0506194	+	0.0562185i	−0.717303	+	0.696761i	$0.754624\pi$
$314$	−0.0293235	+	0.0902485i	−0.00165482	+	0.00509302i
$315$		0			0
$316$	−6.64387	−	4.82706i	−0.373747	−	0.271543i
$317$	3.91346	+	0.831832i	0.219802	+	0.0467203i	0.316496	−	0.948594i	$-0.397494\pi$
$317$	3.91346	+	0.831832i	0.219802	+	0.0467203i	−0.0966942	+	0.995314i	$0.530827\pi$
$318$		0			0
$319$	1.93817	+	11.6246i	0.108517	+	0.650855i
$320$	−8.28080	−	14.3428i	−0.462911	−	0.801785i
$321$		0			0
$322$	1.97812	−	0.880714i	0.110236	−	0.0490803i
$323$	5.67011	−	4.11958i	0.315493	−	0.229219i
$324$		0			0
$325$	2.78134	−	8.56008i	0.154281	−	0.474828i
$326$	0.397555	+	3.78248i	0.0220185	+	0.209492i
$327$		0			0
$328$	−5.13825	+	5.70660i	−0.283712	+	0.315094i
$329$	−11.9478	−	20.6942i	−0.658704	−	1.14091i
$330$		0			0
$331$	−1.59017	+	2.75425i	−0.0874034	+	0.151387i	−0.906413	−	0.422393i	$-0.861190\pi$
$331$	−1.59017	+	2.75425i	−0.0874034	+	0.151387i	0.819009	+	0.573780i	$0.194524\pi$
$332$	−3.85401	−	11.8614i	−0.211516	−	0.650980i
$333$		0			0
$334$	4.36353	−	3.17029i	0.238762	−	0.173471i
$335$	3.15477	+	3.50372i	0.172363	+	0.191429i
$336$		0			0
$337$	−16.6245	−	7.40171i	−0.905595	−	0.403197i	−0.0995376	−	0.995034i	$-0.531736\pi$
$337$	−16.6245	−	7.40171i	−0.905595	−	0.403197i	−0.806058	+	0.591837i	$0.798403\pi$
$338$	0.0545411	−	0.518924i	0.00296665	−	0.0282258i
$339$		0			0
$340$	−11.2265	+	19.4449i	−0.608844	+	1.05455i
$341$	−10.0512	+	12.6206i	−0.544303	+	0.683445i
$342$		0			0
$343$	−3.26270	−	10.0416i	−0.176169	−	0.542193i
$344$	1.00548	−	0.447669i	0.0542120	−	0.0241367i
$345$		0			0
$346$	0.422305	−	0.0897637i	0.0227033	−	0.00482573i
$347$	−26.8150	+	5.69971i	−1.43951	+	0.305977i	−0.860543	−	0.509377i	$-0.829876\pi$
$347$	−26.8150	+	5.69971i	−1.43951	+	0.305977i	−0.578963	+	0.815354i	$0.696543\pi$
$348$		0			0
$349$	20.9252	−	9.31652i	1.12010	−	0.498702i	0.238712	−	0.971090i	$-0.423275\pi$
$349$	20.9252	−	9.31652i	1.12010	−	0.498702i	0.881390	+	0.472389i	$0.156608\pi$
$350$	0.838893	+	2.58185i	0.0448407	+	0.138006i
$351$		0			0
$352$	5.92237	+	8.95933i	0.315663	+	0.477534i
$353$	−14.8524	+	25.7250i	−0.790511	+	1.36921i	0.135140	+	0.990827i	$0.456852\pi$
$353$	−14.8524	+	25.7250i	−0.790511	+	1.36921i	−0.925651	+	0.378379i	$0.876482\pi$
$354$		0			0
$355$	1.62561	−	15.4666i	0.0862783	−	0.820883i
$356$	16.2353	+	7.22842i	0.860469	+	0.383105i
$357$		0			0
$358$	2.51653	+	2.79489i	0.133003	+	0.147714i
$359$	−29.8183	+	21.6643i	−1.57375	+	1.14340i	−0.650299	+	0.759678i	$0.725356\pi$
$359$	−29.8183	+	21.6643i	−1.57375	+	1.14340i	−0.923450	+	0.383718i	$0.874644\pi$
$360$		0			0
$361$	−5.05804	−	15.5670i	−0.266213	−	0.819318i
$362$	0.399041	−	0.691159i	0.0209731	−	0.0363265i
$363$		0			0
$364$	−15.0485	−	26.0648i	−0.788756	−	1.36617i
$365$	7.33449	−	8.14578i	0.383905	−	0.426370i
$366$		0			0
$367$	2.59864	+	24.7244i	0.135648	+	1.29061i	0.824566	+	0.565766i	$0.191419\pi$
$367$	2.59864	+	24.7244i	0.135648	+	1.29061i	−0.688918	+	0.724839i	$0.741914\pi$
$368$	2.02708	−	6.23872i	0.105669	−	0.325216i
$369$		0			0
$370$	−4.83936	+	3.51600i	−0.251586	+	0.182788i
$371$	−5.84904	+	2.60416i	−0.303667	+	0.135201i
$372$		0			0
$373$	−9.13952	−	15.8301i	−0.473227	−	0.819653i	0.526304	−	0.850297i	$-0.323578\pi$
$373$	−9.13952	−	15.8301i	−0.473227	−	0.819653i	−0.999530	+	0.0306440i	$0.990244\pi$
$374$	1.82523	−	3.65539i	0.0943805	−	0.189016i
$375$		0			0
$376$	6.41186	+	1.36288i	0.330667	+	0.0702853i
$377$	11.0704	+	8.04312i	0.570155	+	0.414242i
$378$		0			0
$379$	−9.72145	+	29.9196i	−0.499357	+	1.53686i	0.310697	+	0.950509i	$0.399438\pi$
$379$	−9.72145	+	29.9196i	−0.499357	+	1.53686i	−0.810054	+	0.586355i	$0.800562\pi$
$380$	−5.64172	−	6.26577i	−0.289414	−	0.321427i
$381$		0			0
$382$	0.499001	−	4.74767i	0.0255311	−	0.242912i
$383$	8.31848	−	9.23861i	0.425054	−	0.472071i	−0.492137	−	0.870518i	$-0.663784\pi$
$383$	8.31848	−	9.23861i	0.425054	−	0.472071i	0.917191	+	0.398447i	$0.130451\pi$
$384$		0			0
$385$	13.3915	+	34.0559i	0.682495	+	1.73565i
$386$	6.28449			0.319872
$387$		0			0
$388$	−11.5064	−	8.35986i	−0.584147	−	0.424408i
$389$	0.765115	+	7.27958i	0.0387929	+	0.369090i	0.996646	+	0.0818317i	$0.0260770\pi$
$389$	0.765115	+	7.27958i	0.0387929	+	0.369090i	−0.957853	+	0.287258i	$0.907256\pi$
$390$		0			0
$391$	−7.87788	+	1.67449i	−0.398401	+	0.0846829i
$392$	9.79160	+	4.35950i	0.494551	+	0.220188i
$393$		0			0
$394$	−5.08317	−	1.08046i	−0.256087	−	0.0544329i
$395$	11.5938			0.583346
$396$		0			0
$397$	34.2087			1.71688			0.858442	−	0.512911i	$-0.171433\pi$
$397$	34.2087			1.71688			0.858442	+	0.512911i	$0.171433\pi$
$398$	−6.99965	−	1.48782i	−0.350861	−	0.0745777i
$399$		0			0
$400$	7.51315	+	3.34507i	0.375658	+	0.167254i
$401$	7.31241	−	1.55430i	0.365164	−	0.0776181i	−0.0216754	−	0.999765i	$-0.506900\pi$
$401$	7.31241	−	1.55430i	0.365164	−	0.0776181i	0.386840	+	0.922147i	$0.373567\pi$
$402$		0			0
$403$	1.95817	+	18.6307i	0.0975432	+	0.928061i
$404$	21.2932	+	15.4704i	1.05938	+	0.769682i
$405$		0			0
$406$	−4.12723			−0.204831
$407$	−19.8294	+	16.3262i	−0.982904	+	0.809260i
$408$		0			0
$409$	1.61274	−	1.79113i	0.0797447	−	0.0885655i	−0.701952	−	0.712224i	$-0.747688\pi$
$409$	1.61274	−	1.79113i	0.0797447	−	0.0885655i	0.781697	+	0.623659i	$0.214355\pi$
$410$	0.554835	−	5.27891i	0.0274014	−	0.260707i
$411$		0			0
$412$	−6.51588	−	7.23662i	−0.321014	−	0.356522i
$413$	14.3023	−	44.0180i	0.703771	−	2.16598i
$414$		0			0
$415$	14.2446	+	10.3493i	0.699239	+	0.508027i
$416$	12.1976	+	2.59268i	0.598037	+	0.127117i
$417$		0			0
$418$	1.09366	+	1.07602i	0.0534929	+	0.0526301i
$419$	−5.60088	−	9.70101i	−0.273621	−	0.473925i	0.696165	−	0.717881i	$-0.254888\pi$
$419$	−5.60088	−	9.70101i	−0.273621	−	0.473925i	−0.969786	+	0.243956i	$0.921555\pi$
$420$		0			0
$421$	−6.30791	+	2.80846i	−0.307429	+	0.136876i	−0.554652	−	0.832083i	$-0.687149\pi$
$421$	−6.30791	+	2.80846i	−0.307429	+	0.136876i	0.247223	+	0.968959i	$0.420482\pi$
$422$	1.90781	−	1.38611i	0.0928708	−	0.0674746i
$423$		0			0
$424$	0.542748	−	1.67041i	0.0263582	−	0.0811222i
$425$	−1.05546	−	10.0420i	−0.0511974	−	0.487110i
$426$		0			0
$427$	23.4605	−	26.0555i	1.13533	−	1.26091i
$428$	2.66600	+	4.61765i	0.128866	+	0.223202i
$429$		0			0
$430$	−0.380399	+	0.658871i	−0.0183445	+	0.0317736i
$431$	9.01729	+	27.7524i	0.434348	+	1.33678i	0.893754	+	0.448558i	$0.148062\pi$
$431$	9.01729	+	27.7524i	0.434348	+	1.33678i	−0.459406	+	0.888226i	$0.651938\pi$
$432$		0			0
$433$	29.5582	−	21.4753i	1.42048	−	1.03204i	0.428785	−	0.903407i	$-0.358942\pi$
$433$	29.5582	−	21.4753i	1.42048	−	1.03204i	0.991693	−	0.128630i	$-0.0410581\pi$
$434$	−3.78075	−	4.19895i	−0.181482	−	0.201556i
$435$		0			0
$436$	30.4240	+	13.5457i	1.45705	+	0.648719i
$437$	0.316129	−	3.00777i	0.0151225	−	0.143881i
$438$		0			0
$439$	10.7487	−	18.6173i	0.513009	−	0.888557i	−0.486877	−	0.873470i	$-0.661864\pi$
$439$	10.7487	−	18.6173i	0.513009	−	0.888557i	0.999886	−	0.0150869i	$-0.00480250\pi$
$440$	−9.40081	−	3.52121i	−0.448166	−	0.167867i
$441$		0			0
$442$	−1.46597	−	4.51180i	−0.0697293	−	0.214605i
$443$	30.5535	−	13.6033i	1.45164	−	0.646313i	0.478830	−	0.877908i	$-0.341061\pi$
$443$	30.5535	−	13.6033i	1.45164	−	0.646313i	0.972812	+	0.231595i	$0.0743945\pi$
$444$		0			0
$445$	−24.5412	+	5.21639i	−1.16336	+	0.247281i
$446$	−2.05062	+	0.435873i	−0.0970998	+	0.0206392i
$447$		0			0
$448$	22.7518	−	10.1298i	1.07492	−	0.478586i
$449$	−12.2165	−	37.5984i	−0.576530	−	1.77438i	−0.630908	−	0.775858i	$-0.717318\pi$
$449$	−12.2165	−	37.5984i	−0.576530	−	1.77438i	0.0543777	−	0.998520i	$-0.482682\pi$
$450$		0			0
$451$	1.00777	−	22.7700i	0.0474540	−	1.07220i
$452$	−0.905290	+	1.56801i	−0.0425813	+	0.0737529i
$453$		0			0
$454$	0.564564	−	5.37146i	0.0264963	−	0.252095i
$455$	38.8164	+	17.2822i	1.81974	+	0.810201i
$456$		0			0
$457$	25.1006	+	27.8771i	1.17416	+	1.30404i	0.943642	+	0.330967i	$0.107375\pi$
$457$	25.1006	+	27.8771i	1.17416	+	1.30404i	0.230516	+	0.973069i	$0.425959\pi$
$458$	−1.81309	+	1.31729i	−0.0847204	+	0.0615529i
$459$		0			0
$460$	2.99402	+	9.21464i	0.139597	+	0.429635i
$461$	9.68265	−	16.7708i	0.450966	−	0.781096i	−0.547480	−	0.836818i	$-0.684413\pi$
$461$	9.68265	−	16.7708i	0.450966	−	0.781096i	0.998446	+	0.0557228i	$0.0177463\pi$
$462$		0			0
$463$	7.17464	+	12.4268i	0.333434	+	0.577524i	0.983183	−	0.182625i	$-0.0584594\pi$
$463$	7.17464	+	12.4268i	0.333434	+	0.577524i	−0.649749	+	0.760149i	$0.725126\pi$
$464$	−8.36637	+	9.29180i	−0.388399	+	0.431361i
$465$		0			0
$466$	0.195809	+	1.86300i	0.00907067	+	0.0863017i
$467$	6.89755	−	21.2285i	0.319180	−	0.982336i	−0.654819	−	0.755786i	$-0.727255\pi$
$467$	6.89755	−	21.2285i	0.319180	−	0.982336i	0.973999	−	0.226551i	$-0.0727449\pi$
$468$		0			0
$469$	−5.73585	+	4.16734i	−0.264857	+	0.192430i
$470$	−4.13938	+	1.84297i	−0.190935	+	0.0850099i
$471$		0			0
$472$	6.34827	+	10.9955i	0.292203	+	0.506110i
$473$	−1.45940	+	2.92274i	−0.0671034	+	0.134388i
$474$		0			0
$475$	3.70883	+	0.788336i	0.170173	+	0.0361714i
$476$	−27.3160	−	19.8462i	−1.25203	−	0.909651i
$477$		0			0
$478$	−2.25103	+	6.92795i	−0.102960	+	0.316877i
$479$	15.5651	+	17.2868i	0.711186	+	0.789852i	0.985115	−	0.171898i	$-0.0549898\pi$
$479$	15.5651	+	17.2868i	0.711186	+	0.789852i	−0.273929	+	0.961750i	$0.588323\pi$
$480$		0			0
$481$	−3.11742	+	29.6603i	−0.142142	+	1.35239i
$482$	0.568967	−	0.631902i	0.0259157	−	0.0287823i
$483$		0			0
$484$	−20.1760	−	6.19475i	−0.917091	−	0.281580i
$485$	20.0790			0.911740
$486$		0			0
$487$	−0.219083	−	0.159173i	−0.00992760	−	0.00721282i	0.582810	−	0.812608i	$-0.301953\pi$
$487$	−0.219083	−	0.159173i	−0.00992760	−	0.00721282i	−0.592738	+	0.805395i	$0.701953\pi$
$488$	1.00536	+	9.56538i	0.0455106	+	0.433004i
$489$		0			0
$490$	−7.24692	+	1.54038i	−0.327382	+	0.0695873i
$491$	3.84288	+	1.71096i	0.173427	+	0.0772146i	0.491614	−	0.870813i	$-0.336407\pi$
$491$	3.84288	+	1.71096i	0.173427	+	0.0772146i	−0.318187	+	0.948028i	$0.603074\pi$
$492$		0			0
$493$	15.0157	+	3.19169i	0.676274	+	0.143746i
$494$	1.78143			0.0801504
$495$		0			0
$496$	−17.1173			−0.768589
$497$	22.8754	+	4.86233i	1.02610	+	0.218105i
$498$		0			0
$499$	−14.0359	−	6.24920i	−0.628334	−	0.279752i	0.0677612	−	0.997702i	$-0.478414\pi$
$499$	−14.0359	−	6.24920i	−0.628334	−	0.279752i	−0.696096	+	0.717949i	$0.745081\pi$
$500$	13.5365	−	2.87728i	0.605373	−	0.128676i
$501$		0			0
$502$	−0.347793	−	3.30903i	−0.0155228	−	0.147689i
$503$	3.16786	+	2.30159i	0.141248	+	0.102623i	0.656165	−	0.754617i	$-0.272177\pi$
$503$	3.16786	+	2.30159i	0.141248	+	0.102623i	−0.514917	+	0.857240i	$0.672177\pi$
$504$		0			0
$505$	−37.1573			−1.65348
$506$	−0.645186	−	1.64077i	−0.0286820	−	0.0729411i
$507$		0			0
$508$	−3.14596	+	3.49394i	−0.139579	+	0.155019i
$509$	2.98422	−	28.3930i	0.132273	−	1.25850i	−0.704006	−	0.710194i	$-0.748607\pi$
$509$	2.98422	−	28.3930i	0.132273	−	1.25850i	0.836280	−	0.548303i	$-0.184726\pi$
$510$		0			0
$511$	11.0295	+	12.2494i	0.487914	+	0.541884i
$512$	−5.95109	+	18.3156i	−0.263004	+	0.809442i
$513$		0			0
$514$	−4.78092	−	3.47354i	−0.210877	−	0.153211i
$515$	13.4471	+	2.85826i	0.592549	+	0.125950i
$516$		0			0
$517$	−17.2635	+	8.97371i	−0.759246	+	0.394663i
$518$	−4.49763	−	7.79012i	−0.197615	−	0.342278i
$519$		0			0
$520$	−10.6482	+	4.74089i	−0.466955	+	0.207902i
$521$	−11.5485	+	8.39049i	−0.505950	+	0.367594i	−0.811285	−	0.584651i	$-0.801232\pi$
$521$	−11.5485	+	8.39049i	−0.505950	+	0.367594i	0.305335	+	0.952245i	$0.401232\pi$
$522$		0			0
$523$	−10.2462	+	31.5345i	−0.448034	+	1.37891i	0.431088	+	0.902310i	$0.358130\pi$
$523$	−10.2462	+	31.5345i	−0.448034	+	1.37891i	−0.879122	+	0.476597i	$0.841870\pi$
$524$	−0.801704	−	7.62771i	−0.0350226	−	0.333218i
$525$		0			0
$526$	1.73352	−	1.92527i	0.0755850	−	0.0839456i
$527$	10.5080	+	18.2004i	0.457736	+	0.792822i
$528$		0			0
$529$	9.76231	−	16.9088i	0.424448	−	0.735166i
$530$	0.375166	+	1.15464i	0.0162962	+	0.0501545i
$531$		0			0
$532$	10.2575	−	7.45252i	0.444720	−	0.323108i
$533$	−17.7081	−	19.6668i	−0.767023	−	0.851865i
$534$		0			0
$535$	−6.87672	−	3.06171i	−0.297307	−	0.132369i
$536$	0.203299	−	1.93427i	0.00878120	−	0.0835475i
$537$		0			0
$538$	−1.13222	+	1.96107i	−0.0488136	+	0.0845476i
$539$	−30.6613	+	8.48344i	−1.32068	+	0.365407i
$540$		0			0
$541$	−8.79490	−	27.0679i	−0.378122	−	1.16374i	−0.941348	−	0.337437i	$-0.890440\pi$
$541$	−8.79490	−	27.0679i	−0.378122	−	1.16374i	0.563226	−	0.826303i	$-0.309560\pi$
$542$	−0.969992	+	0.431868i	−0.0416647	+	0.0185503i
$543$		0			0
$544$	13.6839	−	2.90860i	0.586693	−	0.124705i
$545$	−45.9888	+	9.77523i	−1.96995	+	0.418725i
$546$		0			0
$547$	−28.0884	+	12.5058i	−1.20098	+	0.534709i	−0.907011	−	0.421108i	$-0.861641\pi$
$547$	−28.0884	+	12.5058i	−1.20098	+	0.534709i	−0.293965	+	0.955816i	$0.594975\pi$
$548$	0.645829	+	1.98766i	0.0275884	+	0.0849085i
$549$		0			0
$550$	2.13036	−	0.589432i	0.0908388	−	0.0251335i
$551$	−2.88228	+	4.99226i	−0.122789	+	0.212678i
$552$		0			0
$553$	−1.82240	+	17.3390i	−0.0774963	+	0.737328i
$554$	1.01610	+	0.452397i	0.0431700	+	0.0192205i
$555$		0			0
$556$	−3.70382	−	4.11351i	−0.157077	−	0.174452i
$557$	−5.90145	+	4.28765i	−0.250052	+	0.181674i	−0.705750	−	0.708461i	$-0.749390\pi$
$557$	−5.90145	+	4.28765i	−0.250052	+	0.181674i	0.455698	+	0.890135i	$0.349390\pi$
$558$		0			0
$559$	1.17215	+	3.60751i	0.0495767	+	0.152581i
$560$	−19.4122	+	33.6230i	−0.820316	+	1.42083i
$561$		0			0
$562$	−0.00564923	−	0.00978475i	−0.000238298	−	0.000412745i
$563$	24.4724	−	27.1794i	1.03139	−	1.14547i	0.0421581	−	0.999111i	$-0.486577\pi$
$563$	24.4724	−	27.1794i	1.03139	−	1.14547i	0.989231	−	0.146363i	$-0.0467567\pi$
$564$		0			0
$565$	−0.267186	−	2.54211i	−0.0112406	−	0.106947i
$566$	−0.563400	+	1.73397i	−0.0236815	+	0.0728841i
$567$		0			0
$568$	−5.19020	+	3.77090i	−0.217776	+	0.158224i
$569$	−0.138387	+	0.0616140i	−0.00580150	+	0.00258299i	−0.409635	−	0.912249i	$-0.634344\pi$
$569$	−0.138387	+	0.0616140i	−0.00580150	+	0.00258299i	0.403834	+	0.914832i	$0.367677\pi$
$570$		0			0
$571$	−21.6127	−	37.4343i	−0.904463	−	1.56658i	−0.821637	−	0.570012i	$-0.806939\pi$
$571$	−21.6127	−	37.4343i	−0.904463	−	1.56658i	−0.0828262	−	0.996564i	$-0.526395\pi$
$572$	−21.7437	+	11.3026i	−0.909150	+	0.472584i
$573$		0			0
$574$	7.80760	+	1.65956i	0.325883	+	0.0692686i
$575$	−3.52502	−	2.56108i	−0.147003	−	0.106804i
$576$		0			0
$577$	9.00017	−	27.6997i	0.374682	−	1.15315i	−0.569011	−	0.822330i	$-0.692674\pi$
$577$	9.00017	−	27.6997i	0.374682	−	1.15315i	0.943693	−	0.330822i	$-0.107326\pi$
$578$	−0.317526	−	0.352648i	−0.0132073	−	0.0146682i
$579$		0			0
$580$	1.93038	−	18.3664i	0.0801547	−	0.762621i
$581$	−17.7169	+	19.6766i	−0.735019	+	0.816322i
$582$		0			0
$583$	1.90773	+	4.85155i	0.0790103	+	0.200931i
$584$	−4.52173			−0.187111
$585$		0			0
$586$	5.39985	+	3.92322i	0.223066	+	0.162067i
$587$	−2.37226	−	22.5706i	−0.0979137	−	0.931586i	−0.927655	−	0.373438i	$-0.878179\pi$
$587$	−2.37226	−	22.5706i	−0.0979137	−	0.931586i	0.829741	−	0.558148i	$-0.188488\pi$
$588$		0			0
$589$	−7.71934	+	1.64080i	−0.318070	+	0.0676078i
$590$	−8.01754	−	3.56964i	−0.330077	−	0.146960i
$591$		0			0
$592$	−26.6554	−	5.66579i	−1.09553	−	0.232863i
$593$	22.9308			0.941656			0.470828	−	0.882225i	$-0.343955\pi$
$593$	22.9308			0.941656			0.470828	+	0.882225i	$0.343955\pi$
$594$		0			0
$595$	47.6673			1.95417
$596$	−37.8633	−	8.04810i	−1.55094	−	0.329663i
$597$		0			0
$598$	−1.87012	−	0.832633i	−0.0764750	−	0.0340489i
$599$	−12.2275	+	2.59904i	−0.499603	+	0.106194i	−0.450819	−	0.892615i	$-0.648868\pi$
$599$	−12.2275	+	2.59904i	−0.499603	+	0.106194i	−0.0487841	+	0.998809i	$0.515535\pi$
$600$		0			0
$601$	−2.34968	−	22.3557i	−0.0958453	−	0.911907i	−0.931767	−	0.363058i	$-0.881733\pi$
$601$	−2.34968	−	22.3557i	−0.0958453	−	0.911907i	0.835921	−	0.548849i	$-0.184934\pi$
$602$	−0.925574	−	0.672469i	−0.0377236	−	0.0274078i
$603$		0			0
$604$	21.2559			0.864892
$605$	28.1843	−	9.66704i	1.14585	−	0.393021i
$606$		0			0
$607$	17.8690	−	19.8455i	0.725279	−	0.805504i	−0.261905	−	0.965094i	$-0.584351\pi$
$607$	17.8690	−	19.8455i	0.725279	−	0.805504i	0.987183	+	0.159590i	$0.0510173\pi$
$608$	−0.549118	+	5.22451i	−0.0222697	+	0.211882i
$609$		0			0
$610$	−4.44861	−	4.94068i	−0.180119	−	0.200042i
$611$	−6.98102	+	21.4854i	−0.282422	+	0.869205i
$612$		0			0
$613$	35.1797	+	25.5595i	1.42089	+	1.03234i	0.991623	+	0.129163i	$0.0412289\pi$
$613$	35.1797	+	25.5595i	1.42089	+	1.03234i	0.429269	+	0.903176i	$0.358771\pi$
$614$	8.13027	+	1.72814i	0.328111	+	0.0697422i
$615$		0			0
$616$	6.74380	−	13.5058i	0.271716	−	0.544164i
$617$	20.7128	+	35.8756i	0.833864	+	1.44430i	0.894952	+	0.446163i	$0.147210\pi$
$617$	20.7128	+	35.8756i	0.833864	+	1.44430i	−0.0610871	+	0.998132i	$0.519457\pi$
$618$		0			0
$619$	8.14129	−	3.62474i	0.327226	−	0.145690i	−0.236547	−	0.971620i	$-0.576016\pi$
$619$	8.14129	−	3.62474i	0.327226	−	0.145690i	0.563773	+	0.825930i	$0.309349\pi$
$620$	20.4539	−	14.8606i	0.821446	−	0.596816i
$621$		0			0
$622$	−1.73638	+	5.34404i	−0.0696227	+	0.214277i
$623$	−3.94375	−	37.5223i	−0.158003	−	1.50330i
$624$		0			0
$625$	−20.8926	+	23.2036i	−0.835704	+	0.928144i
$626$	0.190818	+	0.330506i	0.00762662	+	0.0132097i
$627$		0			0
$628$	0.319255	−	0.552966i	0.0127397	−	0.0220657i
$629$	10.3390	+	31.8202i	0.412244	+	1.26876i
$630$		0			0
$631$	4.58752	−	3.33303i	0.182626	−	0.132686i	−0.492716	−	0.870190i	$-0.663996\pi$
$631$	4.58752	−	3.33303i	0.182626	−	0.132686i	0.675342	+	0.737504i	$0.263996\pi$
$632$	−3.20023	−	3.55422i	−0.127298	−	0.141379i
$633$		0			0
$634$	1.04222	+	0.464025i	0.0413917	+	0.0184288i
$635$	0.693806	−	6.60113i	0.0275329	−	0.261958i
$636$		0			0
$637$	−18.4693	+	31.9898i	−0.731780	+	1.26748i
$638$	−0.148586	+	3.35722i	−0.00588257	+	0.132914i
$639$		0			0
$640$	−6.88034	−	21.1755i	−0.271970	−	0.837036i
$641$	−24.4996	+	10.9079i	−0.967678	+	0.430838i	−0.828845	−	0.559478i	$-0.811002\pi$
$641$	−24.4996	+	10.9079i	−0.967678	+	0.430838i	−0.138833	+	0.990316i	$0.544335\pi$
$642$		0			0
$643$	−13.8295	+	2.93955i	−0.545382	+	0.115925i	−0.472360	−	0.881406i	$-0.656598\pi$
$643$	−13.8295	+	2.93955i	−0.545382	+	0.115925i	−0.0730222	+	0.997330i	$0.523264\pi$
$644$	−14.2515	+	3.02925i	−0.561587	+	0.119369i
$645$		0			0
$646$	1.82572	−	0.812864i	0.0718321	−	0.0319817i
$647$	0.393698	+	1.21168i	0.0154779	+	0.0476360i	0.958497	−	0.285102i	$-0.0920275\pi$
$647$	0.393698	+	1.21168i	0.0154779	+	0.0476360i	−0.943019	+	0.332738i	$0.892027\pi$
$648$		0			0
$649$	−35.2907	−	13.2187i	−1.38528	−	0.518878i
$650$	1.28325	−	2.22266i	0.0503334	−	0.0871799i
$651$		0			0
$652$	2.67505	−	25.4514i	0.104763	−	0.996753i
$653$	4.41090	+	1.96386i	0.172612	+	0.0768517i	0.491223	−	0.871034i	$-0.336550\pi$
$653$	4.41090	+	1.96386i	0.172612	+	0.0768517i	−0.318612	+	0.947885i	$0.603217\pi$
$654$		0			0
$655$	7.24523	+	8.04664i	0.283094	+	0.314408i
$656$	19.5632	−	14.2135i	0.763813	−	0.554942i
$657$		0			0
$658$	−2.10558	−	6.48030i	−0.0820840	−	0.252628i
$659$	−11.0889	+	19.2065i	−0.431961	+	0.748178i	−0.997042	−	0.0768574i	$-0.975511\pi$
$659$	−11.0889	+	19.2065i	−0.431961	+	0.748178i	0.565082	+	0.825035i	$0.308845\pi$
$660$		0			0
$661$	13.6987	+	23.7269i	0.532820	+	0.922871i	0.999265	+	0.0383209i	$0.0122009\pi$
$661$	13.6987	+	23.7269i	0.532820	+	0.922871i	−0.466446	+	0.884550i	$0.654466\pi$
$662$	−0.606812	+	0.673933i	−0.0235844	+	0.0261931i
$663$		0			0
$664$	−0.759228	−	7.22357i	−0.0294638	−	0.280329i
$665$	−5.53132	+	17.0236i	−0.214495	+	0.660148i
$666$		0			0
$667$	5.35915	−	3.89365i	0.207507	−	0.150763i
$668$	−33.1547	+	14.7614i	−1.28279	+	0.571136i
$669$		0			0
$670$	0.672198	+	1.16428i	0.0259693	+	0.0449801i
$671$	−20.3498	−	20.0215i	−0.785594	−	0.772923i
$672$		0			0
$673$	−34.4734	−	7.32754i	−1.32885	−	0.282456i	−0.511842	−	0.859080i	$-0.671037\pi$
$673$	−34.4734	−	7.32754i	−1.32885	−	0.282456i	−0.817010	+	0.576624i	$0.804370\pi$
$674$	−4.19805	−	3.05006i	−0.161703	−	0.117484i
$675$		0			0
$676$	−1.08494	+	3.33910i	−0.0417285	+	0.128427i
$677$	29.4752	+	32.7355i	1.13282	+	1.25813i	0.962067	+	0.272815i	$0.0879546\pi$
$677$	29.4752	+	32.7355i	1.13282	+	1.25813i	0.170757	+	0.985313i	$0.445379\pi$
$678$		0			0
$679$	−3.15617	+	30.0289i	−0.121123	+	1.15240i
$680$	−8.74970	+	9.71753i	−0.335536	+	0.372650i
$681$		0			0
$682$	−3.55167	+	2.92422i	−0.136001	+	0.111974i
$683$	−42.2845			−1.61797			−0.808985	−	0.587829i	$-0.799983\pi$
$683$	−42.2845			−1.61797			−0.808985	+	0.587829i	$0.799983\pi$
$684$		0			0
$685$	−2.38701	−	1.73426i	−0.0912029	−	0.0662628i
$686$	−0.314703	−	2.99420i	−0.0120154	−	0.114319i
$687$		0			0
$688$	−3.39020	+	0.720610i	−0.129250	+	0.0274730i
$689$	5.52972	+	2.46199i	0.210666	+	0.0937943i
$690$		0			0
$691$	8.28186	+	1.76036i	0.315057	+	0.0669674i	0.362726	−	0.931896i	$-0.381846\pi$
$691$	8.28186	+	1.76036i	0.315057	+	0.0669674i	−0.0476694	+	0.998863i	$0.515179\pi$
$692$	−2.90507			−0.110434
$693$		0			0
$694$	−7.81709			−0.296733
$695$	7.64373	+	1.62472i	0.289943	+	0.0616293i
$696$		0			0
$697$	−27.1223	−	12.0756i	−1.02733	−	0.457397i
$698$	6.38874	−	1.35797i	0.241818	−	0.0513999i
$699$		0			0
$700$	−1.90938	−	18.1666i	−0.0721678	−	0.686631i
$701$	35.2342	+	25.5991i	1.33078	+	0.966865i	0.999730	+	0.0232503i	$0.00740148\pi$
$701$	35.2342	+	25.5991i	1.33078	+	0.966865i	0.331046	+	0.943615i	$0.392599\pi$
$702$		0			0
$703$	−12.5638			−0.473854
$704$	−7.42078	−	18.8717i	−0.279681	−	0.711255i
$705$		0			0
$706$	−5.66770	+	6.29462i	−0.213307	+	0.236901i
$707$	5.84067	−	55.5703i	0.219661	−	2.08994i
$708$		0			0
$709$	−4.03304	−	4.47915i	−0.151464	−	0.168218i	0.662638	−	0.748940i	$-0.269437\pi$
$709$	−4.03304	−	4.47915i	−0.151464	−	0.168218i	−0.814102	+	0.580722i	$0.802770\pi$
$710$	1.37036	−	4.21753i	0.0514287	−	0.158281i
$711$		0			0
$712$	8.37326	+	6.08353i	0.313801	+	0.227990i
$713$	8.87056	+	1.88550i	0.332205	+	0.0706124i
$714$		0			0
$715$	15.4553	−	30.9523i	0.577996	−	1.15755i
$716$	−12.6530	−	21.9157i	−0.472866	−	0.819028i
$717$		0			0
$718$	−9.60122	+	4.27474i	−0.358314	+	0.159532i
$719$	32.6897	−	23.7504i	1.21912	−	0.885741i	0.223092	−	0.974797i	$-0.428385\pi$
$719$	32.6897	−	23.7504i	1.21912	−	0.885741i	0.996027	+	0.0890560i	$0.0283850\pi$
$720$		0			0
$721$	−6.38836	+	19.6614i	−0.237915	+	0.732227i
$722$	−0.487871	−	4.64179i	−0.0181567	−	0.172749i
$723$		0			0
$724$	−3.59329	+	3.99075i	−0.133544	+	0.148315i
$725$	4.15251	+	7.19235i	0.154220	+	0.267117i
$726$		0			0
$727$	−9.36031	+	16.2125i	−0.347155	+	0.601290i	−0.985743	−	0.168259i	$-0.946185\pi$
$727$	−9.36031	+	16.2125i	−0.347155	+	0.601290i	0.638588	+	0.769549i	$0.279519\pi$
$728$	−5.41643	−	16.6700i	−0.200746	−	0.617833i
$729$		0			0
$730$	2.52864	−	1.83717i	0.0935893	−	0.0679966i
$731$	2.84739	+	3.16235i	0.105315	+	0.116964i
$732$		0			0
$733$	0.515414	+	0.229477i	0.0190373	+	0.00847594i	0.416233	−	0.909258i	$-0.363350\pi$
$733$	0.515414	+	0.229477i	0.0190373	+	0.00847594i	−0.397196	+	0.917734i	$0.630017\pi$
$734$	−0.740999	+	7.05013i	−0.0273508	+	0.260225i
$735$		0			0
$736$	3.01837	−	5.22796i	0.111258	−	0.192705i
$737$	3.18335	+	4.81575i	0.117260	+	0.177391i
$738$		0			0
$739$	0.602004	+	1.85278i	0.0221451	+	0.0681555i	0.961518	−	0.274741i	$-0.0885921\pi$
$739$	0.602004	+	1.85278i	0.0221451	+	0.0681555i	−0.939373	+	0.342896i	$0.888592\pi$
$740$	36.7700	−	16.3711i	1.35169	−	0.601813i
$741$		0			0
$742$	−1.78579	+	0.379581i	−0.0655583	+	0.0139349i
$743$	−26.6669	+	5.66823i	−0.978315	+	0.207947i	−0.669204	−	0.743079i	$-0.733365\pi$
$743$	−26.6669	+	5.66823i	−0.978315	+	0.207947i	−0.309111	+	0.951026i	$0.600032\pi$
$744$		0			0
$745$	49.9236	−	22.2274i	1.82906	−	0.814350i
$746$	−1.61067	−	4.95714i	−0.0589709	−	0.181494i
$747$		0			0
$748$	−17.1270	+	21.5052i	−0.626224	+	0.786308i
$749$	5.65985	−	9.80315i	0.206807	−	0.358199i
$750$		0			0
$751$	−3.16787	+	30.1402i	−0.115597	+	1.09983i	0.770854	+	0.637011i	$0.219830\pi$
$751$	−3.16787	+	30.1402i	−0.115597	+	1.09983i	−0.886451	+	0.462822i	$0.846837\pi$
$752$	−18.8576	−	8.39595i	−0.687667	−	0.306169i
$753$		0			0
$754$	2.61088	+	2.89968i	0.0950828	+	0.105600i
$755$	−24.2772	+	17.6384i	−0.883539	+	0.641929i
$756$		0			0
$757$	3.43224	+	10.5634i	0.124747	+	0.383931i	0.993855	−	0.110691i	$-0.0353064\pi$
$757$	3.43224	+	10.5634i	0.124747	+	0.383931i	−0.869108	+	0.494622i	$0.835306\pi$
$758$	−4.48528	+	7.76874i	−0.162913	+	0.282173i
$759$		0			0
$760$	−2.45515	−	4.25244i	−0.0890576	−	0.154252i
$761$	22.3095	−	24.7772i	0.808717	−	0.898171i	−0.187745	−	0.982218i	$-0.560118\pi$
$761$	22.3095	−	24.7772i	0.808717	−	0.898171i	0.996462	+	0.0840467i	$0.0267845\pi$
$762$		0			0
$763$	−7.39038	−	70.3147i	−0.267550	−	2.54556i
$764$	−9.92620	+	30.5497i	−0.359117	+	1.10525i
$765$		0			0
$766$	2.86788	−	2.08364i	0.103621	−	0.0752849i
$767$	−39.9735	+	17.7974i	−1.44336	+	0.642625i
$768$		0			0
$769$	25.9701	+	44.9815i	0.936504	+	1.62207i	0.771929	+	0.635709i	$0.219292\pi$
$769$	25.9701	+	44.9815i	0.936504	+	1.62207i	0.164575	+	0.986364i	$0.447375\pi$
$770$	1.71610	+	10.2927i	0.0618439	+	0.370923i
$771$		0			0
$772$	−41.3627	−	8.79191i	−1.48868	−	0.316428i
$773$	−6.24784	−	4.53932i	−0.224719	−	0.163268i	0.469729	−	0.882811i	$-0.344352\pi$
$773$	−6.24784	−	4.53932i	−0.224719	−	0.163268i	−0.694448	+	0.719542i	$0.744352\pi$
$774$		0			0
$775$	−3.51343	+	10.8132i	−0.126206	+	0.388423i
$776$	−5.54240	−	6.15546i	−0.198961	−	0.220968i
$777$		0			0
$778$	−0.218171	+	2.07576i	−0.00782182	+	0.0744197i
$779$	7.45990	−	8.28505i	0.267279	−	0.296843i
$780$		0			0
$781$	4.77872	−	18.4326i	0.170996	−	0.659569i
$782$	−2.29655			−0.0821244
$783$		0			0
$784$	−27.3060	−	19.8390i	−0.975215	−	0.708535i
$785$	0.0942245	+	0.896486i	0.00336301	+	0.0319969i
$786$		0			0
$787$	19.2757	−	4.09717i	0.687104	−	0.146048i	0.148886	−	0.988854i	$-0.452431\pi$
$787$	19.2757	−	4.09717i	0.687104	−	0.146048i	0.538218	+	0.842806i	$0.319098\pi$
$788$	31.9444	+	14.2226i	1.13797	+	0.506658i
$789$		0			0
$790$	3.23370	+	0.687345i	0.115050	+	0.0244546i
$791$	3.84382			0.136670
$792$		0			0
$793$	−33.1470			−1.17709
$794$	9.54139	+	2.02808i	0.338611	+	0.0719740i
$795$		0			0
$796$	43.9882	+	19.5848i	1.55912	+	0.694165i
$797$	13.7193	−	2.91612i	0.485961	−	0.103294i	0.0415860	−	0.999135i	$-0.486759\pi$
$797$	13.7193	−	2.91612i	0.485961	−	0.103294i	0.444375	+	0.895841i	$0.353426\pi$
$798$		0			0
$799$	2.64915	+	25.2050i	0.0937202	+	0.891689i
$800$	6.12297	+	4.44860i	0.216480	+	0.157282i
$801$		0			0
$802$	2.13170			0.0752731
$803$	10.3612	−	8.53071i	0.365638	−	0.301042i
$804$		0			0
$805$	13.7635	−	15.2859i	0.485099	−	0.538757i
$806$	−0.558368	+	5.31251i	−0.0196677	+	0.187125i
$807$		0			0
$808$	10.2565	+	11.3910i	0.360824	+	0.400736i
$809$	6.46767	−	19.9055i	0.227391	−	0.699839i	−0.770649	−	0.637260i	$-0.780068\pi$
$809$	6.46767	−	19.9055i	0.227391	−	0.699839i	0.998040	−	0.0625783i	$-0.0199323\pi$
$810$		0			0
$811$	−1.57186	−	1.14203i	−0.0551956	−	0.0401019i	0.559845	−	0.828597i	$-0.310861\pi$
$811$	−1.57186	−	1.14203i	−0.0551956	−	0.0401019i	−0.615041	+	0.788495i	$0.710861\pi$
$812$	27.1642	+	5.77393i	0.953276	+	0.202625i
$813$		0			0
$814$	−6.49866	+	3.37806i	−0.227778	+	0.118401i
$815$	18.0646	+	31.2888i	0.632775	+	1.09600i
$816$		0			0
$817$	−1.45980	+	0.649943i	−0.0510718	+	0.0227386i
$818$	0.556008	−	0.403964i	0.0194404	−	0.0141243i
$819$		0			0
$820$	−11.0369	+	33.9680i	−0.385424	+	1.18621i
$821$	1.13327	+	10.7824i	0.0395515	+	0.376307i	0.996337	+	0.0855130i	$0.0272529\pi$
$821$	1.13327	+	10.7824i	0.0395515	+	0.376307i	−0.956786	+	0.290794i	$0.906080\pi$
$822$		0			0
$823$	31.8960	−	35.4241i	1.11182	−	1.23481i	0.142296	−	0.989824i	$-0.454551\pi$
$823$	31.8960	−	35.4241i	1.11182	−	1.23481i	0.969528	−	0.244982i	$-0.0787819\pi$
$824$	−2.83556	−	4.91134i	−0.0987815	−	0.171094i
$825$		0			0
$826$	6.59880	−	11.4295i	0.229601	−	0.397681i
$827$	−11.5619	−	35.5838i	−0.402046	−	1.23737i	−0.923337	−	0.383991i	$-0.874549\pi$
$827$	−11.5619	−	35.5838i	−0.402046	−	1.23737i	0.521291	−	0.853379i	$-0.325451\pi$
$828$		0			0
$829$	−8.66207	+	6.29336i	−0.300846	+	0.218578i	−0.727959	−	0.685621i	$-0.759531\pi$
$829$	−8.66207	+	6.29336i	−0.300846	+	0.218578i	0.427113	+	0.904198i	$0.359531\pi$
$830$	3.35949	+	3.73110i	0.116610	+	0.129508i
$831$		0			0
$832$	−21.5097	−	9.57674i	−0.745715	−	0.332014i
$833$	−4.33162	+	41.2126i	−0.150082	+	1.42793i
$834$		0			0
$835$	25.6181	−	44.3718i	0.886549	−	1.53555i
$836$	−5.69284	−	8.61209i	−0.196891	−	0.297856i
$837$		0			0
$838$	−0.987051	−	3.03783i	−0.0340971	−	0.104940i
$839$	−14.0334	+	6.24809i	−0.484488	+	0.215708i	−0.634420	−	0.772988i	$-0.718761\pi$
$839$	−14.0334	+	6.24809i	−0.484488	+	0.215708i	0.149932	+	0.988696i	$0.452094\pi$
$840$		0			0
$841$	16.0159	−	3.40429i	0.552274	−	0.117389i
$842$	−1.92589	+	0.409360i	−0.0663704	+	0.0141075i
$843$		0			0
$844$	−14.4958	+	6.45394i	−0.498966	+	0.222154i
$845$	−1.53168	−	4.71402i	−0.0526913	−	0.162167i
$846$		0			0
$847$	10.0272	+	43.6703i	0.344539	+	1.50053i
$848$	−2.76543	+	4.78987i	−0.0949654	+	0.164485i
$849$		0			0
$850$	0.300963	−	2.86347i	0.0103229	−	0.0982162i
$851$	13.1894	+	5.87228i	0.452125	+	0.201299i
$852$		0			0
$853$	27.7450	+	30.8139i	0.949970	+	1.05505i	0.998418	+	0.0562233i	$0.0179059\pi$
$853$	27.7450	+	30.8139i	0.949970	+	1.05505i	−0.0484478	+	0.998826i	$0.515427\pi$
$854$	8.08825	−	5.87646i	0.276774	−	0.201088i
$855$		0			0
$856$	0.959576	+	2.95327i	0.0327976	+	0.100941i
$857$	9.20273	−	15.9396i	0.314359	−	0.544486i	−0.664942	−	0.746895i	$-0.731544\pi$
$857$	9.20273	−	15.9396i	0.314359	−	0.544486i	0.979301	+	0.202409i	$0.0648770\pi$
$858$		0			0
$859$	7.52426	+	13.0324i	0.256725	+	0.444660i	0.965363	−	0.260912i	$-0.0840233\pi$
$859$	7.52426	+	13.0324i	0.256725	+	0.444660i	−0.708638	+	0.705572i	$0.750690\pi$
$860$	3.42542	−	3.80432i	0.116806	−	0.129726i
$861$		0			0
$862$	0.869760	+	8.27521i	0.0296241	+	0.281855i
$863$	4.45906	−	13.7236i	0.151788	−	0.467155i	−0.846033	−	0.533130i	$-0.821016\pi$
$863$	4.45906	−	13.7236i	0.151788	−	0.467155i	0.997821	+	0.0659746i	$0.0210156\pi$
$864$		0			0
$865$	3.31799	−	2.41066i	0.112815	−	0.0819649i
$866$	9.51747	−	4.23745i	0.323417	−	0.143994i
$867$		0			0
$868$	19.0095	+	32.9255i	0.645225	+	1.11756i
$869$	14.0385	+	2.10662i	0.476222	+	0.0714623i
$870$		0			0
$871$	6.55636	+	1.39360i	0.222154	+	0.0472202i
$872$	15.6910	+	11.4002i	0.531365	+	0.386059i
$873$		0			0
$874$	0.266492	−	0.820177i	0.00901421	−	0.0277429i
$875$	−19.6589	−	21.8334i	−0.664593	−	0.738105i
$876$		0			0
$877$	2.51656	−	23.9435i	0.0849782	−	0.808514i	−0.866164	−	0.499760i	$-0.833421\pi$
$877$	2.51656	−	23.9435i	0.0849782	−	0.808514i	0.951142	−	0.308754i	$-0.0999119\pi$
$878$	4.10175	−	4.55545i	0.138427	−	0.153739i
$879$		0			0
$880$	26.6511	+	17.0010i	0.898409	+	0.573104i
$881$	10.0956			0.340129			0.170064	−	0.985433i	$-0.445602\pi$
$881$	10.0956			0.340129			0.170064	+	0.985433i	$0.445602\pi$
$882$		0			0
$883$	−41.0332	−	29.8124i	−1.38088	−	1.00327i	−0.996798	−	0.0799659i	$-0.974519\pi$
$883$	−41.0332	−	29.8124i	−1.38088	−	1.00327i	−0.384079	−	0.923300i	$-0.625481\pi$
$884$	3.33666	+	31.7462i	0.112224	+	1.06774i
$885$		0			0
$886$	9.32839	−	1.98281i	0.313393	−	0.0666138i
$887$	2.35029	+	1.04641i	0.0789149	+	0.0351352i	0.445815	−	0.895125i	$-0.352914\pi$
$887$	2.35029	+	1.04641i	0.0789149	+	0.0351352i	−0.366900	+	0.930261i	$0.619581\pi$
$888$		0			0
$889$	9.76319	+	2.07523i	0.327447	+	0.0696010i
$890$	−7.15422			−0.239810
$891$		0			0
$892$	14.1064			0.472316
$893$	−9.30898	−	1.97868i	−0.311513	−	0.0662141i
$894$		0			0
$895$	32.6375	+	14.5311i	1.09095	+	0.485722i
$896$	32.7504	−	6.96130i	1.09411	−	0.232561i
$897$		0			0
$898$	−1.17833	−	11.2111i	−0.0393215	−	0.374119i
$899$	−13.9843	−	10.1602i	−0.466403	−	0.338862i
$900$		0			0
$901$	6.79061			0.226228
$902$	1.63102	−	6.29121i	0.0543071	−	0.209474i
$903$		0			0
$904$	−0.705563	+	0.783607i	−0.0234667	+	0.0260624i
$905$	0.792460	−	7.53975i	0.0263423	−	0.250630i
$906$		0			0
$907$	6.88861	+	7.65058i	0.228733	+	0.254033i	0.846576	−	0.532268i	$-0.178660\pi$
$907$	6.88861	+	7.65058i	0.228733	+	0.254033i	−0.617843	+	0.786301i	$0.711993\pi$
$908$	−11.2304	+	34.5636i	−0.372693	+	1.14703i
$909$		0			0
$910$	9.80197	+	7.12155i	0.324932	+	0.236077i
$911$	−15.2616	−	3.24395i	−0.505639	−	0.107477i	−0.0519727	−	0.998649i	$-0.516551\pi$
$911$	−15.2616	−	3.24395i	−0.505639	−	0.107477i	−0.453666	+	0.891172i	$0.649884\pi$
$912$		0			0
$913$	15.3677	+	15.1198i	0.508597	+	0.500394i
$914$	5.34829	+	9.26351i	0.176906	+	0.306410i
$915$		0			0
$916$	13.7761	−	6.13353i	0.455176	−	0.202657i
$917$	−13.1729	+	9.57070i	−0.435009	+	0.316052i
$918$		0			0
$919$	3.46483	−	10.6637i	0.114294	−	0.351761i	−0.877505	−	0.479568i	$-0.840794\pi$
$919$	3.46483	−	10.6637i	0.114294	−	0.351761i	0.991799	+	0.127806i	$0.0407935\pi$
$920$	0.589812	+	5.61168i	0.0194455	+	0.185012i
$921$		0			0
$922$	3.69493	−	4.10363i	0.121686	−	0.135146i
$923$	−11.0549	−	19.1476i	−0.363875	−	0.630251i
$924$		0			0
$925$	−9.05036	+	15.6757i	−0.297574	+	0.515413i
$926$	1.26440	+	3.89141i	0.0415506	+	0.127880i
$927$		0			0
$928$	−9.30886	+	6.76328i	−0.305578	+	0.222016i
$929$	−15.7430	−	17.4843i	−0.516510	−	0.573643i	0.427309	−	0.904106i	$-0.359462\pi$
$929$	−15.7430	−	17.4843i	−0.516510	−	0.573643i	−0.943819	+	0.330463i	$0.892795\pi$
$930$		0			0
$931$	−14.2158	−	6.32929i	−0.465904	−	0.207434i
$932$	1.31755	−	12.5356i	0.0431577	−	0.410618i
$933$		0			0
$934$	3.18239	−	5.51206i	0.104131	−	0.180360i
$935$	1.71609	−	38.7741i	0.0561221	−	1.26805i
$936$		0			0
$937$	5.76486	+	17.7424i	0.188330	+	0.579619i	0.999990	−	0.00451068i	$-0.00143580\pi$
$937$	5.76486	+	17.7424i	0.188330	+	0.579619i	−0.811660	+	0.584130i	$0.801436\pi$
$938$	−1.84689	+	0.822288i	−0.0603031	+	0.0268487i
$939$		0			0
$940$	29.8225	−	6.33896i	0.972702	−	0.206754i
$941$	−31.7826	+	6.75560i	−1.03608	+	0.220226i	−0.694400	−	0.719589i	$-0.744330\pi$
$941$	−31.7826	+	6.75560i	−1.03608	+	0.220226i	−0.341683	+	0.939815i	$0.610997\pi$
$942$		0			0
$943$	−11.7037	+	5.21082i	−0.381125	+	0.169688i
$944$	−12.3551	−	38.0250i	−0.402123	−	1.23761i
$945$		0			0
$946$	−0.580329	+	0.728681i	−0.0188681	+	0.0236915i
$947$	−1.92137	+	3.32790i	−0.0624360	+	0.108142i	−0.895554	−	0.444953i	$-0.853220\pi$
$947$	−1.92137	+	3.32790i	−0.0624360	+	0.108142i	0.833118	+	0.553096i	$0.186554\pi$
$948$		0			0
$949$	1.62891	−	15.4980i	0.0528765	−	0.503087i
$950$	0.987720	+	0.439761i	0.0320459	+	0.0142677i
$951$		0			0
$952$	−13.1576	−	14.6130i	−0.426441	−	0.473610i
$953$	15.4434	−	11.2203i	0.500262	−	0.363461i	−0.308855	−	0.951109i	$-0.599946\pi$
$953$	15.4434	−	11.2203i	0.500262	−	0.363461i	0.809117	+	0.587648i	$0.199946\pi$
$954$		0			0
$955$	−14.0134	−	43.1289i	−0.453464	−	1.39562i
$956$	24.5077	−	42.4486i	0.792636	−	1.37289i
$957$		0			0
$958$	3.31651	+	5.74436i	0.107152	+	0.185592i
$959$	2.96887	−	3.29726i	0.0958698	−	0.106474i
$960$		0			0
$961$	0.766796	+	7.29558i	0.0247354	+	0.235341i
$962$	−2.62793	+	8.08795i	−0.0847280	+	0.260766i
$963$		0			0
$964$	−4.62879	+	3.36302i	−0.149083	+	0.108315i
$965$	54.5376	−	24.2817i	1.75563	−	0.781655i
$966$		0			0
$967$	−13.2813	−	23.0039i	−0.427099	−	0.739757i	0.569515	−	0.821981i	$-0.307131\pi$
$967$	−13.2813	−	23.0039i	−0.427099	−	0.739757i	−0.996614	+	0.0822239i	$0.973798\pi$
$968$	−10.7433	−	5.97185i	−0.345302	−	0.191943i
$969$		0			0
$970$	5.60037	+	1.19040i	0.179817	+	0.0382213i
$971$	−41.3472	−	30.0405i	−1.32689	−	0.964045i	−0.999819	−	0.0190472i	$-0.993937\pi$
$971$	−41.3472	−	30.0405i	−1.32689	−	0.964045i	−0.327076	−	0.944998i	$-0.606063\pi$
$972$		0			0
$973$	−3.63134	+	11.1761i	−0.116415	+	0.358290i
$974$	−0.0516693	−	0.0573846i	−0.00165559	−	0.00183872i
$975$		0			0
$976$	3.16592	−	30.1217i	0.101339	−	0.964171i
$977$	14.1686	−	15.7358i	0.453292	−	0.503432i	−0.472570	−	0.881293i	$-0.656674\pi$
$977$	14.1686	−	15.7358i	0.453292	−	0.503432i	0.925862	+	0.377861i	$0.123340\pi$
$978$		0			0
$979$	−30.6638	+	1.85712i	−0.980020	+	0.0593539i
$980$	49.8521			1.59247
$981$		0			0
$982$	0.970410	+	0.705044i	0.0309670	+	0.0224989i
$983$	5.31375	+	50.5569i	0.169482	+	1.61252i	0.666997	+	0.745061i	$0.267579\pi$
$983$	5.31375	+	50.5569i	0.169482	+	1.61252i	−0.497515	+	0.867456i	$0.665754\pi$
$984$		0			0
$985$	−48.2870	+	10.2637i	−1.53855	+	0.327029i
$986$	3.99892	+	1.78043i	0.127352	+	0.0567006i
$987$		0			0
$988$	−11.7249	−	2.49219i	−0.373017	−	0.0792873i
$989$	1.83625			0.0583895
$990$		0			0
$991$	−13.1480			−0.417662			−0.208831	−	0.977952i	$-0.566966\pi$
$991$	−13.1480			−0.417662			−0.208831	+	0.977952i	$0.566966\pi$
$992$	−15.4082	−	3.27512i	−0.489211	−	0.103985i
$993$		0			0
$994$	6.09209	+	2.71237i	0.193229	+	0.0860312i
$995$	−66.4923	+	14.1334i	−2.10795	+	0.448058i
$996$		0			0
$997$	3.88937	+	37.0048i	0.123177	+	1.17195i	0.865146	+	0.501520i	$0.167226\pi$
$997$	3.88937	+	37.0048i	0.123177	+	1.17195i	−0.741969	+	0.670435i	$0.766108\pi$
$998$	−3.54437	−	2.57514i	−0.112195	−	0.0815146i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.n.b.181.5		72
3.2	odd	2		99.2.m.b.16.5	✓	72
9.2	odd	6		891.2.f.f.82.5		36
9.4	even	3	inner	297.2.n.b.280.5		72
9.5	odd	6		99.2.m.b.49.5	yes	72
9.7	even	3		891.2.f.e.82.5		36
11.9	even	5	inner	297.2.n.b.262.5		72
33.8	even	10		1089.2.e.o.727.10		36
33.14	odd	10		1089.2.e.p.727.9		36
33.20	odd	10		99.2.m.b.97.5	yes	72
99.14	odd	30		1089.2.e.p.364.9		36
99.20	odd	30		891.2.f.f.163.5		36
99.25	even	15		9801.2.a.cp.1.9		18
99.31	even	15	inner	297.2.n.b.64.5		72
99.41	even	30		1089.2.e.o.364.10		36
99.47	odd	30		9801.2.a.cm.1.10		18
99.52	odd	30		9801.2.a.cn.1.10		18
99.74	even	30		9801.2.a.co.1.9		18
99.86	odd	30		99.2.m.b.31.5	yes	72
99.97	even	15		891.2.f.e.163.5		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.16.5	✓	72	3.2	odd	2
99.2.m.b.31.5	yes	72	99.86	odd	30
99.2.m.b.49.5	yes	72	9.5	odd	6
99.2.m.b.97.5	yes	72	33.20	odd	10
297.2.n.b.64.5		72	99.31	even	15	inner
297.2.n.b.181.5		72	1.1	even	1	trivial
297.2.n.b.262.5		72	11.9	even	5	inner
297.2.n.b.280.5		72	9.4	even	3	inner
891.2.f.e.82.5		36	9.7	even	3
891.2.f.e.163.5		36	99.97	even	15
891.2.f.f.82.5		36	9.2	odd	6
891.2.f.f.163.5		36	99.20	odd	30
1089.2.e.o.364.10		36	99.41	even	30
1089.2.e.o.727.10		36	33.8	even	10
1089.2.e.p.364.9		36	99.14	odd	30
1089.2.e.p.727.9		36	33.14	odd	10
9801.2.a.cm.1.10		18	99.47	odd	30
9801.2.a.cn.1.10		18	99.52	odd	30
9801.2.a.co.1.9		18	99.74	even	30
9801.2.a.cp.1.9		18	99.25	even	15

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:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.278917 + 0.0592857i) q^{2} +(-1.75281 - 0.780402i) q^{4} +(2.64954 - 0.563177i) q^{5} +(0.425779 + 4.05102i) q^{7} +(-0.904002 - 0.656796i) q^{8} +O(q^{10})\)	\(q+(0.278917 + 0.0592857i) q^{2} +(-1.75281 - 0.780402i) q^{4} +(2.64954 - 0.563177i) q^{5} +(0.425779 + 4.05102i) q^{7} +(-0.904002 - 0.656796i) q^{8} +0.772391 q^{10} +(3.31056 - 0.200500i) q^{11} +(2.57679 - 2.86182i) q^{13} +(-0.121410 + 1.15514i) q^{14} +(2.35451 + 2.61494i) q^{16} +(1.33502 - 4.10876i) q^{17} +(1.31246 + 0.953561i) q^{19} +(-5.08365 - 1.08056i) q^{20} +(0.935259 + 0.140346i) q^{22} +(-0.932117 - 1.61447i) q^{23} +(2.13517 - 0.950641i) q^{25} +(0.888377 - 0.645443i) q^{26} +(2.41511 - 7.43295i) q^{28} +(0.371426 + 3.53388i) q^{29} +(-3.25505 + 3.61509i) q^{31} +(1.61909 + 2.80435i) q^{32} +(0.615950 - 1.06686i) q^{34} +(3.40956 + 10.4936i) q^{35} +(-6.26542 + 4.55210i) q^{37} +(0.309536 + 0.343775i) q^{38} +(-2.76508 - 1.23109i) q^{40} +(0.718335 - 6.83450i) q^{41} +(-0.492496 + 0.853027i) q^{43} +(-5.95925 - 2.23213i) q^{44} +(-0.164268 - 0.505566i) q^{46} +(-5.35918 + 2.38606i) q^{47} +(-9.38245 + 1.99430i) q^{49} +(0.651896 - 0.138565i) q^{50} +(-6.75000 + 3.00529i) q^{52} +(0.485721 + 1.49489i) q^{53} +(8.65855 - 2.39567i) q^{55} +(2.27579 - 3.94178i) q^{56} +(-0.105911 + 1.00768i) q^{58} +(-10.3802 - 4.62154i) q^{59} +(-5.75953 - 6.39660i) q^{61} +(-1.12221 + 0.815335i) q^{62} +(-1.88937 - 5.81490i) q^{64} +(5.21561 - 9.03370i) q^{65} +(0.870282 + 1.50737i) q^{67} +(-5.54651 + 6.16003i) q^{68} +(0.328868 + 3.12897i) q^{70} +(1.77418 - 5.46036i) q^{71} +(3.27379 - 2.37855i) q^{73} +(-2.01741 + 0.898208i) q^{74} +(-1.55634 - 2.69566i) q^{76} +(2.22180 + 13.3258i) q^{77} +(4.18662 + 0.889893i) q^{79} +(7.71104 + 5.60240i) q^{80} +(0.605544 - 1.86367i) q^{82} +(4.34947 + 4.83058i) q^{83} +(1.22322 - 11.6382i) q^{85} +(-0.187938 + 0.208726i) q^{86} +(-3.12444 - 1.99311i) q^{88} -9.26243 q^{89} +(12.6904 + 9.22014i) q^{91} +(0.373887 + 3.55729i) q^{92} +(-1.63623 + 0.347790i) q^{94} +(4.01445 + 1.78735i) q^{95} +(7.25070 + 1.54118i) q^{97} -2.73516 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8}+O(q^{10}) \) 72 * q + q^2 + 11 * q^4 + 8 * q^5 - 2 * q^7 - 6 * q^8	\( 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8} - 8 q^{10} + 2 q^{11} - 11 q^{13} + 10 q^{14} - 9 q^{16} + 20 q^{17} + 8 q^{19} + 45 q^{20} - 16 q^{22} - 20 q^{23} + 11 q^{25} + 12 q^{26} - 54 q^{28} + 23 q^{29} + 3 q^{31} - 18 q^{32} + 8 q^{34} - 18 q^{35} - 42 q^{37} + q^{38} - 25 q^{40} - 10 q^{41} - 8 q^{43} - 38 q^{44} - 18 q^{46} + 34 q^{47} + q^{49} - 27 q^{52} - 4 q^{53} + 18 q^{55} - 114 q^{56} + q^{58} + 16 q^{59} - 3 q^{61} - 184 q^{62} + 26 q^{64} - 84 q^{65} + 10 q^{67} + 23 q^{68} - 46 q^{70} + 48 q^{71} - 40 q^{73} - 68 q^{74} + 16 q^{76} + 26 q^{77} + 19 q^{79} + 56 q^{80} + 94 q^{82} - 7 q^{83} + 25 q^{85} + 77 q^{86} + 18 q^{88} + 56 q^{89} + 20 q^{91} - 50 q^{92} - 63 q^{94} + 77 q^{95} - 33 q^{97} + 328 q^{98}+O(q^{100}) \) 72 * q + q^2 + 11 * q^4 + 8 * q^5 - 2 * q^7 - 6 * q^8 - 8 * q^10 + 2 * q^11 - 11 * q^13 + 10 * q^14 - 9 * q^16 + 20 * q^17 + 8 * q^19 + 45 * q^20 - 16 * q^22 - 20 * q^23 + 11 * q^25 + 12 * q^26 - 54 * q^28 + 23 * q^29 + 3 * q^31 - 18 * q^32 + 8 * q^34 - 18 * q^35 - 42 * q^37 + q^38 - 25 * q^40 - 10 * q^41 - 8 * q^43 - 38 * q^44 - 18 * q^46 + 34 * q^47 + q^49 - 27 * q^52 - 4 * q^53 + 18 * q^55 - 114 * q^56 + q^58 + 16 * q^59 - 3 * q^61 - 184 * q^62 + 26 * q^64 - 84 * q^65 + 10 * q^67 + 23 * q^68 - 46 * q^70 + 48 * q^71 - 40 * q^73 - 68 * q^74 + 16 * q^76 + 26 * q^77 + 19 * q^79 + 56 * q^80 + 94 * q^82 - 7 * q^83 + 25 * q^85 + 77 * q^86 + 18 * q^88 + 56 * q^89 + 20 * q^91 - 50 * q^92 - 63 * q^94 + 77 * q^95 - 33 * q^97 + 328 * q^98

Introduction

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