LMFDB - Embedded newform 297.2.n.b.64.5

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			64.5
Character	$\chi$	$=$	297.64
Dual form			297.2.n.b.181.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Character values

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

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{5}\right)$

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	−0.108240	−	0.994125i	$-0.534522\pi$
$2$	0.278917	−	0.0592857i	0.197224	−	0.0419213i	0.305465	+	0.952203i	$0.401188\pi$
$3$		0			0
$3$		0			0
$4$	−1.75281	+	0.780402i	−0.876405	+	0.390201i
$5$	2.64954	+	0.563177i	1.18491	+	0.251861i	0.757891	−	0.652381i	$-0.226230\pi$
$5$	2.64954	+	0.563177i	1.18491	+	0.251861i	0.427020	+	0.904242i	$0.359563\pi$
$6$		0			0
$7$	0.425779	−	4.05102i	0.160930	−	1.53114i	−0.554338	−	0.832291i	$-0.687029\pi$
$7$	0.425779	−	4.05102i	0.160930	−	1.53114i	0.715268	−	0.698851i	$-0.246305\pi$
$8$	−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	0.985639	−	0.168863i	$-0.0540097\pi$
$13$	2.57679	+	2.86182i	0.714674	+	0.793726i	−0.270966	+	0.962589i	$0.587343\pi$
$14$	−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	0.971984	+	0.235046i	$0.0755241\pi$
$17$	1.33502	+	4.10876i	0.323789	+	0.996520i	−0.648195	+	0.761474i	$0.724476\pi$
$18$		0			0
$19$	1.31246	−	0.953561i	0.301100	−	0.218762i	−0.426968	−	0.904267i	$-0.640418\pi$
$19$	1.31246	−	0.953561i	0.301100	−	0.218762i	0.728068	+	0.685505i	$0.240418\pi$
$20$	−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	−0.946691	−	0.322145i	$-0.895596\pi$
$23$	−0.932117	+	1.61447i	−0.194360	+	0.336641i	0.752331	+	0.658786i	$0.228930\pi$
$24$		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	−0.904352	−	0.426788i	$-0.859645\pi$
$29$	0.371426	−	3.53388i	0.0689720	−	0.656225i	0.973324	−	0.229437i	$-0.0736884\pi$
$30$		0			0
$31$	−3.25505	−	3.61509i	−0.584624	−	0.649290i	0.376171	−	0.926550i	$-0.377240\pi$
$31$	−3.25505	−	3.61509i	−0.584624	−	0.649290i	−0.960795	+	0.277260i	$0.910574\pi$
$32$	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	−0.0617145	−	0.998094i	$-0.519657\pi$
$37$	−6.26542	−	4.55210i	−1.03003	−	0.748360i	−0.968314	+	0.249734i	$0.919657\pi$
$38$	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	0.895291	+	0.445481i	$0.146967\pi$
$41$	0.718335	+	6.83450i	0.112185	+	1.06737i	−0.783106	+	0.621888i	$0.786366\pi$
$42$		0			0
$43$	−0.492496	−	0.853027i	−0.0751049	−	0.130085i	0.826027	−	0.563631i	$-0.190596\pi$
$43$	−0.492496	−	0.853027i	−0.0751049	−	0.130085i	−0.901132	+	0.433545i	$0.857262\pi$
$44$	−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	−0.0232288	−	0.999730i	$-0.507395\pi$
$47$	−5.35918	−	2.38606i	−0.781716	−	0.348042i	−0.758487	+	0.651688i	$0.774061\pi$
$48$		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	−0.912139	−	0.409881i	$-0.865570\pi$
$53$	0.485721	−	1.49489i	0.0667189	−	0.205340i	0.978858	+	0.204541i	$0.0655703\pi$
$54$		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	−0.949427	−	0.313986i	$-0.898335\pi$
$59$	−10.3802	+	4.62154i	−1.35138	+	0.601674i	−0.401954	+	0.915660i	$0.631669\pi$
$60$		0			0
$61$	−5.75953	+	6.39660i	−0.737432	+	0.819001i	−0.988856	−	0.148876i	$-0.952434\pi$
$61$	−5.75953	+	6.39660i	−0.737432	+	0.819001i	0.251424	+	0.967877i	$0.419101\pi$
$62$	−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	−0.807956	−	0.589243i	$-0.799426\pi$
$67$	0.870282	−	1.50737i	0.106322	−	0.184155i	0.914277	+	0.405088i	$0.132759\pi$
$68$	−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	0.999439	+	0.0334822i	$0.0106597\pi$
$71$	1.77418	+	5.46036i	0.210556	+	0.648026i	−0.788883	+	0.614543i	$0.789340\pi$
$72$		0			0
$73$	3.27379	+	2.37855i	0.383168	+	0.278388i	0.762650	−	0.646811i	$-0.223898\pi$
$73$	3.27379	+	2.37855i	0.383168	+	0.278388i	−0.379482	+	0.925199i	$0.623898\pi$
$74$	−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	0.0337205	−	0.999431i	$-0.489264\pi$
$79$	4.18662	−	0.889893i	0.471031	−	0.100121i	0.437311	+	0.899311i	$0.355931\pi$
$80$	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	−0.455539	−	0.890216i	$-0.650554\pi$
$83$	4.34947	−	4.83058i	0.477417	−	0.530225i	0.932956	+	0.359991i	$0.117220\pi$
$84$		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	0.175470	−	0.984485i	$-0.443855\pi$
$97$	7.25070	−	1.54118i	0.736197	−	0.156483i	0.560726	+	0.828001i	$0.310522\pi$
$98$	−2.73516			−0.276293
$99$		0			0
$100$	−4.48444			−0.448444
$101$	−13.4178	+	2.85205i	−1.33513	+	0.283790i	−0.819527	−	0.573041i	$-0.805764\pi$
$101$	−13.4178	+	2.85205i	−1.33513	+	0.283790i	−0.515598	+	0.856830i	$0.672430\pi$
$102$		0			0
$103$	4.63647	−	2.06429i	0.456845	−	0.203400i	−0.165395	−	0.986227i	$-0.552890\pi$
$103$	4.63647	−	2.06429i	0.456845	−	0.203400i	0.622239	+	0.782827i	$0.286223\pi$
$104$	−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	−0.691131	−	0.722730i	$-0.742887\pi$
$107$	−2.24824	+	1.63344i	−0.217346	+	0.157911i	0.473785	+	0.880640i	$0.342887\pi$
$108$		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	0.998181	−	0.0602828i	$-0.0192003\pi$
$113$	0.0986387	+	0.938485i	0.00927915	+	0.0882852i	−0.988902	+	0.148568i	$0.952534\pi$
$114$		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	0.979015	−	0.203787i	$-0.0653251\pi$
$127$	0.757216	+	2.33047i	0.0671920	+	0.206796i	−0.911823	+	0.410583i	$0.865325\pi$
$128$	−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	−0.765406	−	0.643548i	$-0.777462\pi$
$131$	1.99869	−	3.46183i	0.174626	−	0.302461i	0.940032	+	0.341087i	$0.110795\pi$
$132$		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	−0.773475	−	0.633827i	$-0.781483\pi$
$137$	−0.728855	+	0.809475i	−0.0622703	+	0.0691581i	0.711205	+	0.702985i	$0.248150\pi$
$138$		0			0
$139$	2.63551	−	1.17340i	0.223541	−	0.0995269i	−0.291910	−	0.956446i	$-0.594291\pi$
$139$	2.63551	−	1.17340i	0.223541	−	0.0995269i	0.515451	+	0.856919i	$0.327624\pi$
$140$	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	0.925408	−	0.378973i	$-0.123723\pi$
$149$	19.7339	+	4.19458i	1.61667	+	0.343633i	0.691260	+	0.722606i	$0.257056\pi$
$150$		0			0
$151$	−10.1206	−	4.50597i	−0.823601	−	0.366691i	−0.0487316	−	0.998812i	$-0.515518\pi$
$151$	−10.1206	−	4.50597i	−0.823601	−	0.366691i	−0.774870	+	0.632121i	$0.782185\pi$
$152$	−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	0.993046	−	0.117726i	$-0.0375605\pi$
$157$	−0.0347854	−	0.330961i	−0.00277618	−	0.0264136i	−0.995822	+	0.0913125i	$0.970894\pi$
$158$	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	−0.649574	−	0.760299i	$-0.725053\pi$
$163$	4.12168	−	12.6852i	0.322835	−	0.993584i	0.972408	−	0.233285i	$-0.0749475\pi$
$164$	−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	0.996131	+	0.0878797i	$0.0280091\pi$
$167$	12.6567	+	14.0567i	0.979405	+	1.08774i	−0.0167258	+	0.999860i	$0.505324\pi$
$168$		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	0.458643	−	0.888620i	$-0.348336\pi$
$173$	1.38319	+	0.615835i	0.105162	+	0.0468211i	−0.353481	+	0.935442i	$0.615002\pi$
$174$		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	−0.112653	−	0.993634i	$-0.535935\pi$
$179$	10.6703	−	7.75244i	0.797537	−	0.579445i	0.910191	+	0.414190i	$0.135935\pi$
$180$		0			0
$181$	0.864886	+	2.66185i	0.0642865	+	0.197853i	0.978041	−	0.208414i	$-0.0668301\pi$
$181$	0.864886	+	2.66185i	0.0642865	+	0.197853i	−0.913754	+	0.406267i	$0.866830\pi$
$182$	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	0.728032	+	0.685544i	$0.240435\pi$
$191$	−1.74997	+	16.6498i	−0.126623	+	1.20474i	−0.854655	+	0.519197i	$0.826231\pi$
$192$		0			0
$193$	21.5578	+	4.58224i	1.55176	+	0.329837i	0.902487	−	0.430717i	$-0.141739\pi$
$193$	21.5578	+	4.58224i	1.55176	+	0.329837i	0.649275	+	0.760554i	$0.275073\pi$
$194$	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	0.902877	−	0.429899i	$-0.141451\pi$
$211$	5.53373	+	6.14582i	0.380957	+	0.423096i	−0.521920	+	0.852995i	$0.674784\pi$
$212$	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	0.169337	−	0.985558i	$-0.445837\pi$
$223$	−6.71646	−	2.99036i	−0.449768	−	0.200249i	−0.619104	+	0.785309i	$0.712504\pi$
$224$	−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	0.707775	+	0.706438i	$0.249699\pi$
$227$	−1.97989	+	18.8374i	−0.131410	+	1.25028i	−0.839185	+	0.543846i	$0.816968\pi$
$228$		0			0
$229$	−5.25900	−	5.84071i	−0.347524	−	0.385965i	0.543888	−	0.839158i	$-0.316952\pi$
$229$	−5.25900	−	5.84071i	−0.347524	−	0.385965i	−0.891412	+	0.453193i	$0.850285\pi$
$230$	−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	−0.862279	−	0.506434i	$-0.830963\pi$
$233$	2.03006	−	6.24789i	0.132994	−	0.409313i	0.995273	+	0.0971212i	$0.0309634\pi$
$234$		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	−0.646617	−	0.762815i	$-0.723817\pi$
$239$	−2.67031	−	25.4063i	−0.172728	−	1.64340i	0.473889	−	0.880585i	$-0.342850\pi$
$240$		0			0
$241$	1.49099	+	2.58247i	0.0960432	+	0.166352i	0.910044	−	0.414513i	$-0.136048\pi$
$241$	1.49099	+	2.58247i	0.0960432	+	0.166352i	−0.814000	+	0.580864i	$0.802715\pi$
$242$	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	0.770424	+	0.637532i	$0.220045\pi$
$251$	−3.60577	+	11.0974i	−0.227594	+	0.700463i	−0.998018	+	0.0629308i	$0.979955\pi$
$252$		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	−0.900843	−	0.434146i	$-0.857050\pi$
$257$	−18.9327	+	8.42939i	−1.18099	+	0.525811i	−0.280148	+	0.959957i	$0.590384\pi$
$258$		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	0.971413	−	0.237395i	$-0.0762936\pi$
$263$	4.54273	+	7.86823i	0.280117	+	0.485176i	−0.691297	+	0.722571i	$0.742960\pi$
$264$		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	0.847954	−	0.530070i	$-0.177834\pi$
$269$	−2.45399	−	7.55261i	−0.149623	−	0.460491i	−0.997576	+	0.0695792i	$0.977834\pi$
$270$		0			0
$271$	−3.01249	−	2.18870i	−0.182995	−	0.132954i	0.492516	−	0.870303i	$-0.336077\pi$
$271$	−3.01249	−	2.18870i	−0.182995	−	0.132954i	−0.675512	+	0.737349i	$0.736077\pi$
$272$	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	−0.0918567	−	0.995772i	$-0.529280\pi$
$277$	3.81540	−	0.810988i	0.229245	−	0.0487275i	0.321102	+	0.947045i	$0.395947\pi$
$278$	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	−0.743935	−	0.668252i	$-0.767043\pi$
$281$	−0.0265130	+	0.0294457i	−0.00158163	+	0.00175658i	0.742353	+	0.670008i	$0.233710\pi$
$282$		0			0
$283$	−0.668341	−	6.35884i	−0.0397288	−	0.377994i	−0.996263	−	0.0863734i	$-0.972472\pi$
$283$	−0.668341	−	6.35884i	−0.0397288	−	0.377994i	0.956534	−	0.291621i	$-0.0941945\pi$
$284$	−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	0.327819	−	0.944741i	$-0.393686\pi$
$293$	21.3837	−	9.52066i	1.24925	−	0.556203i	0.921433	+	0.388538i	$0.127020\pi$
$294$		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	−0.883224	−	0.468952i	$-0.844632\pi$
$311$	−2.05981	−	19.5978i	−0.116801	−	1.11129i	0.766423	−	0.642337i	$-0.222035\pi$
$312$		0			0
$313$	0.895549	−	0.994608i	0.0506194	−	0.0562185i	−0.717303	−	0.696761i	$-0.754624\pi$
$313$	0.895549	−	0.994608i	0.0506194	−	0.0562185i	0.767923	+	0.640542i	$0.221290\pi$
$314$	−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	−0.0966942	−	0.995314i	$-0.530827\pi$
$317$	3.91346	−	0.831832i	0.219802	−	0.0467203i	0.316496	+	0.948594i	$0.397494\pi$
$318$		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	0.819009	−	0.573780i	$-0.194524\pi$
$331$	−1.59017	−	2.75425i	−0.0874034	−	0.151387i	−0.906413	+	0.422393i	$0.861190\pi$
$332$	−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	−0.806058	−	0.591837i	$-0.798403\pi$
$337$	−16.6245	+	7.40171i	−0.905595	+	0.403197i	−0.0995376	+	0.995034i	$0.531736\pi$
$338$	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	−0.578963	−	0.815354i	$-0.696543\pi$
$347$	−26.8150	−	5.69971i	−1.43951	−	0.305977i	−0.860543	+	0.509377i	$0.829876\pi$
$348$		0			0
$349$	20.9252	+	9.31652i	1.12010	+	0.498702i	0.881390	−	0.472389i	$-0.156608\pi$
$349$	20.9252	+	9.31652i	1.12010	+	0.498702i	0.238712	+	0.971090i	$0.423275\pi$
$350$	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	−0.925651	−	0.378379i	$-0.876482\pi$
$353$	−14.8524	−	25.7250i	−0.790511	−	1.36921i	0.135140	−	0.990827i	$-0.456852\pi$
$354$		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	−0.923450	−	0.383718i	$-0.874644\pi$
$359$	−29.8183	−	21.6643i	−1.57375	−	1.14340i	−0.650299	−	0.759678i	$-0.725356\pi$
$360$		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	−0.688918	−	0.724839i	$-0.741914\pi$
$367$	2.59864	−	24.7244i	0.135648	−	1.29061i	0.824566	−	0.565766i	$-0.191419\pi$
$368$	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	−0.999530	−	0.0306440i	$-0.990244\pi$
$373$	−9.13952	+	15.8301i	−0.473227	+	0.819653i	0.526304	+	0.850297i	$0.323578\pi$
$374$	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	−0.810054	−	0.586355i	$-0.800562\pi$
$379$	−9.72145	−	29.9196i	−0.499357	−	1.53686i	0.310697	−	0.950509i	$-0.399438\pi$
$380$	−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	0.917191	−	0.398447i	$-0.130451\pi$
$383$	8.31848	+	9.23861i	0.425054	+	0.472071i	−0.492137	+	0.870518i	$0.663784\pi$
$384$		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	−0.957853	−	0.287258i	$-0.907256\pi$
$389$	0.765115	−	7.27958i	0.0387929	−	0.369090i	0.996646	−	0.0818317i	$-0.0260770\pi$
$390$		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	0.386840	−	0.922147i	$-0.373567\pi$
$401$	7.31241	+	1.55430i	0.365164	+	0.0776181i	−0.0216754	+	0.999765i	$0.506900\pi$
$402$		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	0.781697	−	0.623659i	$-0.214355\pi$
$409$	1.61274	+	1.79113i	0.0797447	+	0.0885655i	−0.701952	+	0.712224i	$0.747688\pi$
$410$	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	−0.969786	−	0.243956i	$-0.921555\pi$
$419$	−5.60088	+	9.70101i	−0.273621	+	0.473925i	0.696165	+	0.717881i	$0.254888\pi$
$420$		0			0
$421$	−6.30791	−	2.80846i	−0.307429	−	0.136876i	0.247223	−	0.968959i	$-0.420482\pi$
$421$	−6.30791	−	2.80846i	−0.307429	−	0.136876i	−0.554652	+	0.832083i	$0.687149\pi$
$422$	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	−0.459406	−	0.888226i	$-0.651938\pi$
$431$	9.01729	−	27.7524i	0.434348	−	1.33678i	0.893754	−	0.448558i	$-0.148062\pi$
$432$		0			0
$433$	29.5582	+	21.4753i	1.42048	+	1.03204i	0.991693	+	0.128630i	$0.0410581\pi$
$433$	29.5582	+	21.4753i	1.42048	+	1.03204i	0.428785	+	0.903407i	$0.358942\pi$
$434$	−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	0.999886	+	0.0150869i	$0.00480250\pi$
$439$	10.7487	+	18.6173i	0.513009	+	0.888557i	−0.486877	+	0.873470i	$0.661864\pi$
$440$	−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	0.972812	−	0.231595i	$-0.0743945\pi$
$443$	30.5535	+	13.6033i	1.45164	+	0.646313i	0.478830	+	0.877908i	$0.341061\pi$
$444$		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	0.0543777	+	0.998520i	$0.482682\pi$
$449$	−12.2165	+	37.5984i	−0.576530	+	1.77438i	−0.630908	+	0.775858i	$0.717318\pi$
$450$		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	0.230516	−	0.973069i	$-0.425959\pi$
$457$	25.1006	−	27.8771i	1.17416	−	1.30404i	0.943642	−	0.330967i	$-0.107375\pi$
$458$	−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	0.998446	−	0.0557228i	$-0.0177463\pi$
$461$	9.68265	+	16.7708i	0.450966	+	0.781096i	−0.547480	+	0.836818i	$0.684413\pi$
$462$		0			0
$463$	7.17464	−	12.4268i	0.333434	−	0.577524i	−0.649749	−	0.760149i	$-0.725126\pi$
$463$	7.17464	−	12.4268i	0.333434	−	0.577524i	0.983183	+	0.182625i	$0.0584594\pi$
$464$	−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	0.973999	+	0.226551i	$0.0727449\pi$
$467$	6.89755	+	21.2285i	0.319180	+	0.982336i	−0.654819	+	0.755786i	$0.727255\pi$
$468$		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	−0.273929	−	0.961750i	$-0.588323\pi$
$479$	15.5651	−	17.2868i	0.711186	−	0.789852i	0.985115	+	0.171898i	$0.0549898\pi$
$480$		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	−0.592738	−	0.805395i	$-0.701953\pi$
$487$	−0.219083	+	0.159173i	−0.00992760	+	0.00721282i	0.582810	+	0.812608i	$0.301953\pi$
$488$	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	−0.318187	−	0.948028i	$-0.603074\pi$
$491$	3.84288	−	1.71096i	0.173427	−	0.0772146i	0.491614	+	0.870813i	$0.336407\pi$
$492$		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	−0.696096	−	0.717949i	$-0.745081\pi$
$499$	−14.0359	+	6.24920i	−0.628334	+	0.279752i	0.0677612	+	0.997702i	$0.478414\pi$
$500$	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	−0.514917	−	0.857240i	$-0.672177\pi$
$503$	3.16786	−	2.30159i	0.141248	−	0.102623i	0.656165	+	0.754617i	$0.272177\pi$
$504$		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	0.836280	+	0.548303i	$0.184726\pi$
$509$	2.98422	+	28.3930i	0.132273	+	1.25850i	−0.704006	+	0.710194i	$0.748607\pi$
$510$		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	0.305335	−	0.952245i	$-0.401232\pi$
$521$	−11.5485	−	8.39049i	−0.505950	−	0.367594i	−0.811285	+	0.584651i	$0.801232\pi$
$522$		0			0
$523$	−10.2462	−	31.5345i	−0.448034	−	1.37891i	−0.879122	−	0.476597i	$-0.841870\pi$
$523$	−10.2462	−	31.5345i	−0.448034	−	1.37891i	0.431088	−	0.902310i	$-0.358130\pi$
$524$	−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	0.563226	+	0.826303i	$0.309560\pi$
$541$	−8.79490	+	27.0679i	−0.378122	+	1.16374i	−0.941348	+	0.337437i	$0.890440\pi$
$542$	−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	−0.293965	−	0.955816i	$-0.594975\pi$
$547$	−28.0884	−	12.5058i	−1.20098	−	0.534709i	−0.907011	+	0.421108i	$0.861641\pi$
$548$	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	0.455698	−	0.890135i	$-0.349390\pi$
$557$	−5.90145	−	4.28765i	−0.250052	−	0.181674i	−0.705750	+	0.708461i	$0.749390\pi$
$558$		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	0.989231	+	0.146363i	$0.0467567\pi$
$563$	24.4724	+	27.1794i	1.03139	+	1.14547i	0.0421581	+	0.999111i	$0.486577\pi$
$564$		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	0.403834	−	0.914832i	$-0.367677\pi$
$569$	−0.138387	−	0.0616140i	−0.00580150	−	0.00258299i	−0.409635	+	0.912249i	$0.634344\pi$
$570$		0			0
$571$	−21.6127	+	37.4343i	−0.904463	+	1.56658i	−0.0828262	+	0.996564i	$0.526395\pi$
$571$	−21.6127	+	37.4343i	−0.904463	+	1.56658i	−0.821637	+	0.570012i	$0.806939\pi$
$572$	−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	0.943693	+	0.330822i	$0.107326\pi$
$577$	9.00017	+	27.6997i	0.374682	+	1.15315i	−0.569011	+	0.822330i	$0.692674\pi$
$578$	−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	0.829741	+	0.558148i	$0.188488\pi$
$587$	−2.37226	+	22.5706i	−0.0979137	+	0.931586i	−0.927655	+	0.373438i	$0.878179\pi$
$588$		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	−0.0487841	−	0.998809i	$-0.515535\pi$
$599$	−12.2275	−	2.59904i	−0.499603	−	0.106194i	−0.450819	+	0.892615i	$0.648868\pi$
$600$		0			0
$601$	−2.34968	+	22.3557i	−0.0958453	+	0.911907i	0.835921	+	0.548849i	$0.184934\pi$
$601$	−2.34968	+	22.3557i	−0.0958453	+	0.911907i	−0.931767	+	0.363058i	$0.881733\pi$
$602$	−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	0.987183	−	0.159590i	$-0.0510173\pi$
$607$	17.8690	+	19.8455i	0.725279	+	0.805504i	−0.261905	+	0.965094i	$0.584351\pi$
$608$	−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	0.429269	−	0.903176i	$-0.358771\pi$
$613$	35.1797	−	25.5595i	1.42089	−	1.03234i	0.991623	−	0.129163i	$-0.0412289\pi$
$614$	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	−0.0610871	−	0.998132i	$-0.519457\pi$
$617$	20.7128	−	35.8756i	0.833864	−	1.44430i	0.894952	−	0.446163i	$-0.147210\pi$
$618$		0			0
$619$	8.14129	+	3.62474i	0.327226	+	0.145690i	0.563773	−	0.825930i	$-0.309349\pi$
$619$	8.14129	+	3.62474i	0.327226	+	0.145690i	−0.236547	+	0.971620i	$0.576016\pi$
$620$	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	0.675342	−	0.737504i	$-0.263996\pi$
$631$	4.58752	+	3.33303i	0.182626	+	0.132686i	−0.492716	+	0.870190i	$0.663996\pi$
$632$	−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	−0.138833	−	0.990316i	$-0.544335\pi$
$641$	−24.4996	−	10.9079i	−0.967678	−	0.430838i	−0.828845	+	0.559478i	$0.811002\pi$
$642$		0			0
$643$	−13.8295	−	2.93955i	−0.545382	−	0.115925i	−0.0730222	−	0.997330i	$-0.523264\pi$
$643$	−13.8295	−	2.93955i	−0.545382	−	0.115925i	−0.472360	+	0.881406i	$0.656598\pi$
$644$	−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	−0.943019	−	0.332738i	$-0.892027\pi$
$647$	0.393698	−	1.21168i	0.0154779	−	0.0476360i	0.958497	+	0.285102i	$0.0920275\pi$
$648$		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	−0.318612	−	0.947885i	$-0.603217\pi$
$653$	4.41090	−	1.96386i	0.172612	−	0.0768517i	0.491223	+	0.871034i	$0.336550\pi$
$654$		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	0.565082	−	0.825035i	$-0.308845\pi$
$659$	−11.0889	−	19.2065i	−0.431961	−	0.748178i	−0.997042	+	0.0768574i	$0.975511\pi$
$660$		0			0
$661$	13.6987	−	23.7269i	0.532820	−	0.922871i	−0.466446	−	0.884550i	$-0.654466\pi$
$661$	13.6987	−	23.7269i	0.532820	−	0.922871i	0.999265	−	0.0383209i	$-0.0122009\pi$
$662$	−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	−0.817010	−	0.576624i	$-0.804370\pi$
$673$	−34.4734	+	7.32754i	−1.32885	+	0.282456i	−0.511842	+	0.859080i	$0.671037\pi$
$674$	−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	0.170757	−	0.985313i	$-0.445379\pi$
$677$	29.4752	−	32.7355i	1.13282	−	1.25813i	0.962067	−	0.272815i	$-0.0879546\pi$
$678$		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	−0.0476694	−	0.998863i	$-0.515179\pi$
$691$	8.28186	−	1.76036i	0.315057	−	0.0669674i	0.362726	+	0.931896i	$0.381846\pi$
$692$	−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	0.331046	−	0.943615i	$-0.392599\pi$
$701$	35.2342	−	25.5991i	1.33078	−	0.966865i	0.999730	−	0.0232503i	$-0.00740148\pi$
$702$		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	−0.814102	−	0.580722i	$-0.802770\pi$
$709$	−4.03304	+	4.47915i	−0.151464	+	0.168218i	0.662638	+	0.748940i	$0.269437\pi$
$710$	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	0.996027	−	0.0890560i	$-0.0283850\pi$
$719$	32.6897	+	23.7504i	1.21912	+	0.885741i	0.223092	+	0.974797i	$0.428385\pi$
$720$		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	0.638588	−	0.769549i	$-0.279519\pi$
$727$	−9.36031	−	16.2125i	−0.347155	−	0.601290i	−0.985743	+	0.168259i	$0.946185\pi$
$728$	−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	−0.397196	−	0.917734i	$-0.630017\pi$
$733$	0.515414	−	0.229477i	0.0190373	−	0.00847594i	0.416233	+	0.909258i	$0.363350\pi$
$734$	−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	−0.939373	−	0.342896i	$-0.888592\pi$
$739$	0.602004	−	1.85278i	0.0221451	−	0.0681555i	0.961518	+	0.274741i	$0.0885921\pi$
$740$	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	−0.309111	−	0.951026i	$-0.600032\pi$
$743$	−26.6669	−	5.66823i	−0.978315	−	0.207947i	−0.669204	+	0.743079i	$0.733365\pi$
$744$		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	−0.886451	−	0.462822i	$-0.846837\pi$
$751$	−3.16787	−	30.1402i	−0.115597	−	1.09983i	0.770854	−	0.637011i	$-0.219830\pi$
$752$	−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	−0.869108	−	0.494622i	$-0.835306\pi$
$757$	3.43224	−	10.5634i	0.124747	−	0.383931i	0.993855	+	0.110691i	$0.0353064\pi$
$758$	−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	0.996462	−	0.0840467i	$-0.0267845\pi$
$761$	22.3095	+	24.7772i	0.808717	+	0.898171i	−0.187745	+	0.982218i	$0.560118\pi$
$762$		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	0.164575	−	0.986364i	$-0.447375\pi$
$769$	25.9701	−	44.9815i	0.936504	−	1.62207i	0.771929	−	0.635709i	$-0.219292\pi$
$770$	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	−0.694448	−	0.719542i	$-0.744352\pi$
$773$	−6.24784	+	4.53932i	−0.224719	+	0.163268i	0.469729	+	0.882811i	$0.344352\pi$
$774$		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	0.538218	−	0.842806i	$-0.319098\pi$
$787$	19.2757	+	4.09717i	0.687104	+	0.146048i	0.148886	+	0.988854i	$0.452431\pi$
$788$	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	0.444375	−	0.895841i	$-0.353426\pi$
$797$	13.7193	+	2.91612i	0.485961	+	0.103294i	0.0415860	+	0.999135i	$0.486759\pi$
$798$		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	0.998040	+	0.0625783i	$0.0199323\pi$
$809$	6.46767	+	19.9055i	0.227391	+	0.699839i	−0.770649	+	0.637260i	$0.780068\pi$
$810$		0			0
$811$	−1.57186	+	1.14203i	−0.0551956	+	0.0401019i	−0.615041	−	0.788495i	$-0.710861\pi$
$811$	−1.57186	+	1.14203i	−0.0551956	+	0.0401019i	0.559845	+	0.828597i	$0.310861\pi$
$812$	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	−0.956786	−	0.290794i	$-0.906080\pi$
$821$	1.13327	−	10.7824i	0.0395515	−	0.376307i	0.996337	−	0.0855130i	$-0.0272529\pi$
$822$		0			0
$823$	31.8960	+	35.4241i	1.11182	+	1.23481i	0.969528	+	0.244982i	$0.0787819\pi$
$823$	31.8960	+	35.4241i	1.11182	+	1.23481i	0.142296	+	0.989824i	$0.454551\pi$
$824$	−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	0.521291	+	0.853379i	$0.325451\pi$
$827$	−11.5619	+	35.5838i	−0.402046	+	1.23737i	−0.923337	+	0.383991i	$0.874549\pi$
$828$		0			0
$829$	−8.66207	−	6.29336i	−0.300846	−	0.218578i	0.427113	−	0.904198i	$-0.359531\pi$
$829$	−8.66207	−	6.29336i	−0.300846	−	0.218578i	−0.727959	+	0.685621i	$0.759531\pi$
$830$	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	0.149932	−	0.988696i	$-0.452094\pi$
$839$	−14.0334	−	6.24809i	−0.484488	−	0.215708i	−0.634420	+	0.772988i	$0.718761\pi$
$840$		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	−0.0484478	−	0.998826i	$-0.515427\pi$
$853$	27.7450	−	30.8139i	0.949970	−	1.05505i	0.998418	−	0.0562233i	$-0.0179059\pi$
$854$	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	0.979301	−	0.202409i	$-0.0648770\pi$
$857$	9.20273	+	15.9396i	0.314359	+	0.544486i	−0.664942	+	0.746895i	$0.731544\pi$
$858$		0			0
$859$	7.52426	−	13.0324i	0.256725	−	0.444660i	−0.708638	−	0.705572i	$-0.750690\pi$
$859$	7.52426	−	13.0324i	0.256725	−	0.444660i	0.965363	+	0.260912i	$0.0840233\pi$
$860$	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	0.997821	−	0.0659746i	$-0.0210156\pi$
$863$	4.45906	+	13.7236i	0.151788	+	0.467155i	−0.846033	+	0.533130i	$0.821016\pi$
$864$		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	0.951142	+	0.308754i	$0.0999119\pi$
$877$	2.51656	+	23.9435i	0.0849782	+	0.808514i	−0.866164	+	0.499760i	$0.833421\pi$
$878$	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	−0.384079	+	0.923300i	$0.625481\pi$
$883$	−41.0332	+	29.8124i	−1.38088	+	1.00327i	−0.996798	+	0.0799659i	$0.974519\pi$
$884$	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	−0.366900	−	0.930261i	$-0.619581\pi$
$887$	2.35029	−	1.04641i	0.0789149	−	0.0351352i	0.445815	+	0.895125i	$0.352914\pi$
$888$		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	−0.617843	−	0.786301i	$-0.711993\pi$
$907$	6.88861	−	7.65058i	0.228733	−	0.254033i	0.846576	+	0.532268i	$0.178660\pi$
$908$	−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	−0.453666	−	0.891172i	$-0.649884\pi$
$911$	−15.2616	+	3.24395i	−0.505639	+	0.107477i	−0.0519727	+	0.998649i	$0.516551\pi$
$912$		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	0.991799	−	0.127806i	$-0.0407935\pi$
$919$	3.46483	+	10.6637i	0.114294	+	0.351761i	−0.877505	+	0.479568i	$0.840794\pi$
$920$	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	−0.943819	−	0.330463i	$-0.892795\pi$
$929$	−15.7430	+	17.4843i	−0.516510	+	0.573643i	0.427309	+	0.904106i	$0.359462\pi$
$930$		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	−0.811660	−	0.584130i	$-0.801436\pi$
$937$	5.76486	−	17.7424i	0.188330	−	0.579619i	0.999990	+	0.00451068i	$0.00143580\pi$
$938$	−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	−0.341683	−	0.939815i	$-0.610997\pi$
$941$	−31.7826	−	6.75560i	−1.03608	−	0.220226i	−0.694400	+	0.719589i	$0.744330\pi$
$942$		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	0.833118	−	0.553096i	$-0.186554\pi$
$947$	−1.92137	−	3.32790i	−0.0624360	−	0.108142i	−0.895554	+	0.444953i	$0.853220\pi$
$948$		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	0.809117	−	0.587648i	$-0.199946\pi$
$953$	15.4434	+	11.2203i	0.500262	+	0.363461i	−0.308855	+	0.951109i	$0.599946\pi$
$954$		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	−0.996614	−	0.0822239i	$-0.973798\pi$
$967$	−13.2813	+	23.0039i	−0.427099	+	0.739757i	0.569515	+	0.821981i	$0.307131\pi$
$968$	−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	−0.327076	+	0.944998i	$0.606063\pi$
$971$	−41.3472	+	30.0405i	−1.32689	+	0.964045i	−0.999819	+	0.0190472i	$0.993937\pi$
$972$		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	0.925862	−	0.377861i	$-0.123340\pi$
$977$	14.1686	+	15.7358i	0.453292	+	0.503432i	−0.472570	+	0.881293i	$0.656674\pi$
$978$		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	−0.497515	−	0.867456i	$-0.665754\pi$
$983$	5.31375	−	50.5569i	0.169482	−	1.61252i	0.666997	−	0.745061i	$-0.267579\pi$
$984$		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	−0.741969	−	0.670435i	$-0.766108\pi$
$997$	3.88937	−	37.0048i	0.123177	−	1.17195i	0.865146	−	0.501520i	$-0.167226\pi$
$998$	−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.64.5		72
3.2	odd	2		99.2.m.b.31.5	yes	72
9.2	odd	6		99.2.m.b.97.5	yes	72
9.4	even	3		891.2.f.e.163.5		36
9.5	odd	6		891.2.f.f.163.5		36
9.7	even	3	inner	297.2.n.b.262.5		72
11.5	even	5	inner	297.2.n.b.280.5		72
33.5	odd	10		99.2.m.b.49.5	yes	72
33.26	odd	10		1089.2.e.p.364.9		36
33.29	even	10		1089.2.e.o.364.10		36
99.4	even	15		9801.2.a.cp.1.9		18
99.5	odd	30		891.2.f.f.82.5		36
99.16	even	15	inner	297.2.n.b.181.5		72
99.29	even	30		1089.2.e.o.727.10		36
99.38	odd	30		99.2.m.b.16.5	✓	72
99.40	odd	30		9801.2.a.cn.1.10		18
99.49	even	15		891.2.f.e.82.5		36
99.59	odd	30		9801.2.a.cm.1.10		18
99.92	odd	30		1089.2.e.p.727.9		36
99.95	even	30		9801.2.a.co.1.9		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.16.5	✓	72	99.38	odd	30
99.2.m.b.31.5	yes	72	3.2	odd	2
99.2.m.b.49.5	yes	72	33.5	odd	10
99.2.m.b.97.5	yes	72	9.2	odd	6
297.2.n.b.64.5		72	1.1	even	1	trivial
297.2.n.b.181.5		72	99.16	even	15	inner
297.2.n.b.262.5		72	9.7	even	3	inner
297.2.n.b.280.5		72	11.5	even	5	inner
891.2.f.e.82.5		36	99.49	even	15
891.2.f.e.163.5		36	9.4	even	3
891.2.f.f.82.5		36	99.5	odd	30
891.2.f.f.163.5		36	9.5	odd	6
1089.2.e.o.364.10		36	33.29	even	10
1089.2.e.o.727.10		36	99.29	even	30
1089.2.e.p.364.9		36	33.26	odd	10
1089.2.e.p.727.9		36	99.92	odd	30
9801.2.a.cm.1.10		18	99.59	odd	30
9801.2.a.cn.1.10		18	99.40	odd	30
9801.2.a.co.1.9		18	99.95	even	30
9801.2.a.cp.1.9		18	99.4	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)

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