LMFDB - Embedded newform 702.2.t.a.415.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [702,2,Mod(181,702)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(702, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("702.181");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.t (of order $6$, degree $2$, 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:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 234)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			415.6
Character	$\chi$	$=$	702.415
Dual form			702.2.t.a.181.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.53992 + 1.46642i) q^{5} +(1.90832 - 1.10177i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.53992 + 1.46642i) q^{5} +(1.90832 - 1.10177i) q^{7} +1.00000i q^{8} -2.93284 q^{10} +(4.47678 - 2.58467i) q^{11} +(0.680923 - 3.54067i) q^{13} +(-1.10177 + 1.90832i) q^{14} +(-0.500000 - 0.866025i) q^{16} -2.31124 q^{17} -5.16934i q^{19} +(2.53992 - 1.46642i) q^{20} +(-2.58467 + 4.47678i) q^{22} +(-4.19626 + 7.26814i) q^{23} +(1.80079 + 3.11906i) q^{25} +(1.18064 + 3.40677i) q^{26} -2.20354i q^{28} +(-4.72655 - 8.18662i) q^{29} +(5.38944 + 3.11159i) q^{31} +(0.866025 + 0.500000i) q^{32} +(2.00159 - 1.15562i) q^{34} +6.46263 q^{35} +0.646136i q^{37} +(2.58467 + 4.47678i) q^{38} +(-1.46642 + 2.53992i) q^{40} +(-0.674934 - 0.389673i) q^{41} +(-1.74579 - 3.02379i) q^{43} -5.16934i q^{44} -8.39252i q^{46} +(-4.79295 + 2.76721i) q^{47} +(-1.07221 + 1.85713i) q^{49} +(-3.11906 - 1.80079i) q^{50} +(-2.72585 - 2.36003i) q^{52} +8.68475 q^{53} +15.1609 q^{55} +(1.10177 + 1.90832i) q^{56} +(8.18662 + 4.72655i) q^{58} +(2.59002 + 1.49535i) q^{59} +(0.432428 + 0.748988i) q^{61} -6.22318 q^{62} -1.00000 q^{64} +(6.92161 - 7.99449i) q^{65} +(9.68023 + 5.58888i) q^{67} +(-1.15562 + 2.00159i) q^{68} +(-5.59680 + 3.23131i) q^{70} +12.9489i q^{71} +4.27533i q^{73} +(-0.323068 - 0.559571i) q^{74} +(-4.47678 - 2.58467i) q^{76} +(5.69541 - 9.86475i) q^{77} +(1.52175 + 2.63575i) q^{79} -2.93284i q^{80} +0.779346 q^{82} +(-3.19308 + 1.84352i) q^{83} +(-5.87036 - 3.38925i) q^{85} +(3.02379 + 1.74579i) q^{86} +(2.58467 + 4.47678i) q^{88} -3.34650i q^{89} +(-2.60158 - 7.50694i) q^{91} +(4.19626 + 7.26814i) q^{92} +(2.76721 - 4.79295i) q^{94} +(7.58044 - 13.1297i) q^{95} +(1.29119 - 0.745470i) q^{97} -2.14443i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 14 q^{4}+O(q^{10}) $ 28 * q + 14 * q^4	$ 28 q + 14 q^{4} + 2 q^{13} - 8 q^{14} - 14 q^{16} - 16 q^{17} + 8 q^{23} + 14 q^{25} - 8 q^{26} + 16 q^{29} + 68 q^{35} - 4 q^{43} + 10 q^{49} - 2 q^{52} + 120 q^{53} + 8 q^{56} + 28 q^{61} - 68 q^{62} - 28 q^{64} + 8 q^{65} - 8 q^{68} - 16 q^{74} + 24 q^{77} + 28 q^{79} - 48 q^{82} - 8 q^{92}+O(q^{100}) $ 28 * q + 14 * q^4 + 2 * q^13 - 8 * q^14 - 14 * q^16 - 16 * q^17 + 8 * q^23 + 14 * q^25 - 8 * q^26 + 16 * q^29 + 68 * q^35 - 4 * q^43 + 10 * q^49 - 2 * q^52 + 120 * q^53 + 8 * q^56 + 28 * q^61 - 68 * q^62 - 28 * q^64 + 8 * q^65 - 8 * q^68 - 16 * q^74 + 24 * q^77 + 28 * q^79 - 48 * q^82 - 8 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	2.53992	+	1.46642i	1.13589	+	0.655804i	0.945409	−	0.325888i	$-0.105663\pi$
$5$	2.53992	+	1.46642i	1.13589	+	0.655804i	0.190477	+	0.981692i	$0.438996\pi$
$6$		0			0
$7$	1.90832	−	1.10177i	0.721276	−	0.416429i	−0.0939459	−	0.995577i	$-0.529948\pi$
$7$	1.90832	−	1.10177i	0.721276	−	0.416429i	0.815222	+	0.579148i	$0.196615\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−2.93284			−0.927447
$11$	4.47678	−	2.58467i	1.34980	−	0.779307i	0.361579	−	0.932341i	$-0.382238\pi$
$11$	4.47678	−	2.58467i	1.34980	−	0.779307i	0.988221	+	0.153034i	$0.0489044\pi$
$12$		0			0
$13$	0.680923	−	3.54067i	0.188854	−	0.982005i
$13$	0.680923	−	3.54067i	0.188854	−	0.982005i
$14$	−1.10177	+	1.90832i	−0.294460	+	0.510019i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.31124			−0.560558			−0.280279	−	0.959919i	$-0.590427\pi$
$17$	−2.31124			−0.560558			−0.280279	+	0.959919i	$0.590427\pi$
$18$		0			0
$19$		−	5.16934i		−	1.18593i	−0.805229	−	0.592964i	$-0.797958\pi$
$19$		−	5.16934i		−	1.18593i	0.805229	−	0.592964i	$-0.202042\pi$
$20$	2.53992	−	1.46642i	0.567943	−	0.327902i
$21$		0			0
$22$	−2.58467	+	4.47678i	−0.551054	+	0.954453i
$23$	−4.19626	+	7.26814i	−0.874981	+	1.51551i	−0.0181984	+	0.999834i	$0.505793\pi$
$23$	−4.19626	+	7.26814i	−0.874981	+	1.51551i	−0.856783	+	0.515677i	$0.827540\pi$
$24$		0			0
$25$	1.80079	+	3.11906i	0.360158	+	0.623812i
$26$	1.18064	+	3.40677i	0.231542	+	0.668123i
$27$		0			0
$28$		−	2.20354i		−	0.416429i
$29$	−4.72655	−	8.18662i	−0.877698	−	1.52022i	−0.853860	−	0.520502i	$-0.825745\pi$
$29$	−4.72655	−	8.18662i	−0.877698	−	1.52022i	−0.0238379	−	0.999716i	$-0.507589\pi$
$30$		0			0
$31$	5.38944	+	3.11159i	0.967971	+	0.558858i	0.898617	−	0.438734i	$-0.144573\pi$
$31$	5.38944	+	3.11159i	0.967971	+	0.558858i	0.0693541	+	0.997592i	$0.477906\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$	2.00159	−	1.15562i	0.343270	−	0.198187i
$35$	6.46263			1.09238
$36$		0			0
$37$			0.646136i			0.106224i	0.998589	+	0.0531121i	$0.0169141\pi$
$37$			0.646136i			0.106224i	−0.998589	+	0.0531121i	$0.983086\pi$
$38$	2.58467	+	4.47678i	0.419289	+	0.726230i
$39$		0			0
$40$	−1.46642	+	2.53992i	−0.231862	+	0.401596i
$41$	−0.674934	−	0.389673i	−0.105407	−	0.0608567i	0.446370	−	0.894849i	$-0.352717\pi$
$41$	−0.674934	−	0.389673i	−0.105407	−	0.0608567i	−0.551777	+	0.833992i	$0.686050\pi$
$42$		0			0
$43$	−1.74579	−	3.02379i	−0.266230	−	0.461124i	0.701655	−	0.712517i	$-0.252445\pi$
$43$	−1.74579	−	3.02379i	−0.266230	−	0.461124i	−0.967885	+	0.251393i	$0.919111\pi$
$44$		−	5.16934i		−	0.779307i
$45$		0			0
$46$		−	8.39252i		−	1.23741i
$47$	−4.79295	+	2.76721i	−0.699124	+	0.403639i	−0.807021	−	0.590523i	$-0.798922\pi$
$47$	−4.79295	+	2.76721i	−0.699124	+	0.403639i	0.107897	+	0.994162i	$0.465588\pi$
$48$		0			0
$49$	−1.07221	+	1.85713i	−0.153174	+	0.265304i
$50$	−3.11906	−	1.80079i	−0.441102	−	0.254670i
$51$		0			0
$52$	−2.72585	−	2.36003i	−0.378007	−	0.327278i
$53$	8.68475			1.19294			0.596471	−	0.802635i	$-0.296569\pi$
$53$	8.68475			1.19294			0.596471	+	0.802635i	$0.296569\pi$
$54$		0			0
$55$	15.1609			2.04429
$56$	1.10177	+	1.90832i	0.147230	+	0.255010i
$57$		0			0
$58$	8.18662	+	4.72655i	1.07496	+	0.620626i
$59$	2.59002	+	1.49535i	0.337192	+	0.194678i	0.659030	−	0.752117i	$-0.270967\pi$
$59$	2.59002	+	1.49535i	0.337192	+	0.194678i	−0.321838	+	0.946795i	$0.604300\pi$
$60$		0			0
$61$	0.432428	+	0.748988i	0.0553668	+	0.0958981i	0.892380	−	0.451284i	$-0.149034\pi$
$61$	0.432428	+	0.748988i	0.0553668	+	0.0958981i	−0.837014	+	0.547182i	$0.815701\pi$
$62$	−6.22318			−0.790345
$63$		0			0
$64$	−1.00000			−0.125000
$65$	6.92161	−	7.99449i	0.858520	−	0.991595i
$66$		0			0
$67$	9.68023	+	5.58888i	1.18263	+	0.682791i	0.956621	−	0.291335i	$-0.0940993\pi$
$67$	9.68023	+	5.58888i	1.18263	+	0.682791i	0.226007	+	0.974126i	$0.427433\pi$
$68$	−1.15562	+	2.00159i	−0.140139	+	0.242729i
$69$		0			0
$70$	−5.59680	+	3.23131i	−0.668946	+	0.386216i
$71$			12.9489i			1.53675i	0.639998	+	0.768376i	$0.278935\pi$
$71$			12.9489i			1.53675i	−0.639998	+	0.768376i	$0.721065\pi$
$72$		0			0
$73$			4.27533i			0.500390i	0.968196	+	0.250195i	$0.0804947\pi$
$73$			4.27533i			0.500390i	−0.968196	+	0.250195i	$0.919505\pi$
$74$	−0.323068	−	0.559571i	−0.0375559	−	0.0650488i
$75$		0			0
$76$	−4.47678	−	2.58467i	−0.513522	−	0.296482i
$77$	5.69541	−	9.86475i	0.649053	−	1.12419i
$78$		0			0
$79$	1.52175	+	2.63575i	0.171210	+	0.296545i	0.938843	−	0.344345i	$-0.111899\pi$
$79$	1.52175	+	2.63575i	0.171210	+	0.296545i	−0.767633	+	0.640890i	$0.778566\pi$
$80$		−	2.93284i		−	0.327902i
$81$		0			0
$82$	0.779346			0.0860644
$83$	−3.19308	+	1.84352i	−0.350486	+	0.202353i	−0.664899	−	0.746933i	$-0.731526\pi$
$83$	−3.19308	+	1.84352i	−0.350486	+	0.202353i	0.314413	+	0.949286i	$0.398192\pi$
$84$		0			0
$85$	−5.87036	−	3.38925i	−0.636730	−	0.367616i
$86$	3.02379	+	1.74579i	0.326064	+	0.188253i
$87$		0			0
$88$	2.58467	+	4.47678i	0.275527	+	0.477226i
$89$		−	3.34650i		−	0.354728i	−0.984145	−	0.177364i	$-0.943243\pi$
$89$		−	3.34650i		−	0.354728i	0.984145	−	0.177364i	$-0.0567570\pi$
$90$		0			0
$91$	−2.60158	−	7.50694i	−0.272720	−	0.786942i
$92$	4.19626	+	7.26814i	0.437491	+	0.757756i
$93$		0			0
$94$	2.76721	−	4.79295i	0.285416	−	0.494355i
$95$	7.58044	−	13.1297i	0.777736	−	1.34708i
$96$		0			0
$97$	1.29119	−	0.745470i	0.131101	−	0.0756910i	−0.433015	−	0.901387i	$-0.642550\pi$
$97$	1.29119	−	0.745470i	0.131101	−	0.0756910i	0.564116	+	0.825696i	$0.309217\pi$
$98$		−	2.14443i		−	0.216620i
$99$		0			0
$100$	3.60158			0.360158
$101$	0.203346	+	0.352206i	0.0202337	+	0.0350458i	0.875965	−	0.482375i	$-0.160226\pi$
$101$	0.203346	+	0.352206i	0.0202337	+	0.0350458i	−0.855731	+	0.517421i	$0.826892\pi$
$102$		0			0
$103$	−8.58044	+	14.8618i	−0.845456	+	1.46437i	0.0397695	+	0.999209i	$0.487338\pi$
$103$	−8.58044	+	14.8618i	−0.845456	+	1.46437i	−0.885225	+	0.465163i	$0.845996\pi$
$104$	3.54067	+	0.680923i	0.347191	+	0.0667700i
$105$		0			0
$106$	−7.52122	+	4.34238i	−0.730525	+	0.421769i
$107$	0.329555			0.0318592			0.0159296	−	0.999873i	$-0.494929\pi$
$107$	0.329555			0.0318592			0.0159296	+	0.999873i	$0.494929\pi$
$108$		0			0
$109$			9.64927i			0.924232i	0.886819	+	0.462116i	$0.152910\pi$
$109$			9.64927i			0.924232i	−0.886819	+	0.462116i	$0.847090\pi$
$110$	−13.1297	+	7.58044i	−1.25187	+	0.722766i
$111$		0			0
$112$	−1.90832	−	1.10177i	−0.180319	−	0.104107i
$113$	−1.51605	+	2.62588i	−0.142618	+	0.247022i	−0.928482	−	0.371378i	$-0.878885\pi$
$113$	−1.51605	+	2.62588i	−0.142618	+	0.247022i	0.785864	+	0.618400i	$0.212219\pi$
$114$		0			0
$115$	−21.3163	+	12.3070i	−1.98776	+	1.14763i
$116$	−9.45310			−0.877698
$117$		0			0
$118$	−2.99070			−0.275316
$119$	−4.41058	+	2.54645i	−0.404317	+	0.233433i
$120$		0			0
$121$	7.86104	−	13.6157i	0.714640	−	1.23779i
$122$	−0.748988	−	0.432428i	−0.0678102	−	0.0391502i
$123$		0			0
$124$	5.38944	−	3.11159i	0.483986	−	0.279429i
$125$		−	4.10135i		−	0.366836i
$126$		0			0
$127$	−9.03355			−0.801598			−0.400799	−	0.916166i	$-0.631267\pi$
$127$	−9.03355			−0.801598			−0.400799	+	0.916166i	$0.631267\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−1.99704	+	10.3842i	−0.175152	+	0.910758i
$131$	−8.70860	+	15.0837i	−0.760874	+	1.31787i	0.181527	+	0.983386i	$0.441896\pi$
$131$	−8.70860	+	15.0837i	−0.760874	+	1.31787i	−0.942401	+	0.334486i	$0.891437\pi$
$132$		0			0
$133$	−5.69541	−	9.86475i	−0.493855	−	0.855382i
$134$	−11.1778			−0.965612
$135$		0			0
$136$		−	2.31124i		−	0.198187i
$137$	4.20543	−	2.42800i	0.359294	−	0.207438i	−0.309477	−	0.950907i	$-0.600154\pi$
$137$	4.20543	−	2.42800i	0.359294	−	0.207438i	0.668771	+	0.743468i	$0.266821\pi$
$138$		0			0
$139$	5.82263	−	10.0851i	0.493869	−	0.855406i	−0.506106	−	0.862471i	$-0.668916\pi$
$139$	5.82263	−	10.0851i	0.493869	−	0.855406i	0.999975	+	0.00706513i	$0.00224892\pi$
$140$	3.23131	−	5.59680i	0.273096	−	0.473016i
$141$		0			0
$142$	−6.47445	−	11.2141i	−0.543324	−	0.941065i
$143$	−6.10312	−	17.6108i	−0.510369	−	1.47269i
$144$		0			0
$145$		−	27.7245i		−	2.30239i
$146$	−2.13767	−	3.70254i	−0.176914	−	0.306425i
$147$		0			0
$148$	0.559571	+	0.323068i	0.0459964	+	0.0265560i
$149$	−18.8841	−	10.9027i	−1.54704	−	0.893186i	−0.998365	−	0.0571529i	$-0.981798\pi$
$149$	−18.8841	−	10.9027i	−1.54704	−	0.893186i	−0.548679	−	0.836033i	$-0.684869\pi$
$150$		0			0
$151$	−12.6987	+	7.33161i	−1.03341	+	0.596638i	−0.917959	−	0.396676i	$-0.870164\pi$
$151$	−12.6987	+	7.33161i	−1.03341	+	0.596638i	−0.115448	+	0.993313i	$0.536830\pi$
$152$	5.16934			0.419289
$153$		0			0
$154$			11.3908i			0.917899i
$155$	9.12582	+	15.8064i	0.733003	+	1.26960i
$156$		0			0
$157$	−3.97434	+	6.88376i	−0.317187	+	0.549384i	−0.979900	−	0.199489i	$-0.936072\pi$
$157$	−3.97434	+	6.88376i	−0.317187	+	0.549384i	0.662713	+	0.748874i	$0.269405\pi$
$158$	−2.63575	−	1.52175i	−0.209689	−	0.121064i
$159$		0			0
$160$	1.46642	+	2.53992i	0.115931	+	0.200798i
$161$			18.4932i			1.45747i
$162$		0			0
$163$		−	0.222533i		−	0.0174302i	−0.999962	−	0.00871508i	$-0.997226\pi$
$163$		−	0.222533i		−	0.0174302i	0.999962	−	0.00871508i	$-0.00277413\pi$
$164$	−0.674934	+	0.389673i	−0.0527035	+	0.0304284i
$165$		0			0
$166$	1.84352	−	3.19308i	0.143085	−	0.247831i
$167$	3.26552	+	1.88535i	0.252693	+	0.145893i	0.620997	−	0.783813i	$-0.286728\pi$
$167$	3.26552	+	1.88535i	0.252693	+	0.145893i	−0.368303	+	0.929706i	$0.620061\pi$
$168$		0			0
$169$	−12.0727	−	4.82185i	−0.928668	−	0.370911i
$170$	6.77851			0.519888
$171$		0			0
$172$	−3.49158			−0.266230
$173$	−5.42672	−	9.39936i	−0.412586	−	0.714620i	0.582586	−	0.812769i	$-0.302041\pi$
$173$	−5.42672	−	9.39936i	−0.412586	−	0.714620i	−0.995172	+	0.0981495i	$0.968708\pi$
$174$		0			0
$175$	6.87296	+	3.96810i	0.519547	+	0.299960i
$176$	−4.47678	−	2.58467i	−0.337450	−	0.194827i
$177$		0			0
$178$	1.67325	+	2.89815i	0.125415	+	0.217226i
$179$	14.6400			1.09425			0.547123	−	0.837052i	$-0.315723\pi$
$179$	14.6400			1.09425			0.547123	+	0.837052i	$0.315723\pi$
$180$		0			0
$181$	−2.81354			−0.209129			−0.104565	−	0.994518i	$-0.533345\pi$
$181$	−2.81354			−0.209129			−0.104565	+	0.994518i	$0.533345\pi$
$182$	6.00651	+	5.20041i	0.445232	+	0.385480i
$183$		0			0
$184$	−7.26814	−	4.19626i	−0.535814	−	0.309353i
$185$	−0.947509	+	1.64113i	−0.0696622	+	0.120659i
$186$		0			0
$187$	−10.3469	+	5.97379i	−0.756641	+	0.436847i
$188$			5.53442i			0.403639i
$189$		0			0
$190$			15.1609i			1.09989i
$191$	−4.38820	−	7.60058i	−0.317519	−	0.549959i	0.662451	−	0.749105i	$-0.269516\pi$
$191$	−4.38820	−	7.60058i	−0.317519	−	0.549959i	−0.979970	+	0.199147i	$0.936183\pi$
$192$		0			0
$193$	13.7032	+	7.91153i	0.986376	+	0.569485i	0.904189	−	0.427132i	$-0.140476\pi$
$193$	13.7032	+	7.91153i	0.986376	+	0.569485i	0.0821872	+	0.996617i	$0.473809\pi$
$194$	−0.745470	+	1.29119i	−0.0535216	+	0.0927022i
$195$		0			0
$196$	1.07221	+	1.85713i	0.0765868	+	0.132652i
$197$			0.395717i			0.0281936i	0.999901	+	0.0140968i	$0.00448731\pi$
$197$			0.395717i			0.0281936i	−0.999901	+	0.0140968i	$0.995513\pi$
$198$		0			0
$199$	3.20316			0.227066			0.113533	−	0.993534i	$-0.463783\pi$
$199$	3.20316			0.227066			0.113533	+	0.993534i	$0.463783\pi$
$200$	−3.11906	+	1.80079i	−0.220551	+	0.127335i
$201$		0			0
$202$	−0.352206	−	0.203346i	−0.0247811	−	0.0143074i
$203$	−18.0395	−	10.4151i	−1.26613	−	0.730998i
$204$		0			0
$205$	−1.14285	−	1.97948i	−0.0798202	−	0.138253i
$206$		−	17.1609i		−	1.19565i
$207$		0			0
$208$	−3.40677	+	1.18064i	−0.236217	+	0.0818625i
$209$	−13.3610	−	23.1420i	−0.924202	−	1.60077i
$210$		0			0
$211$	−4.13986	+	7.17045i	−0.285000	+	0.493634i	−0.972609	−	0.232447i	$-0.925327\pi$
$211$	−4.13986	+	7.17045i	−0.285000	+	0.493634i	0.687609	+	0.726081i	$0.258660\pi$
$212$	4.34238	−	7.52122i	0.298236	−	0.516559i
$213$		0			0
$214$	−0.285403	+	0.164777i	−0.0195097	+	0.0112639i
$215$		−	10.2403i		−	0.698380i
$216$		0			0
$217$	13.7130			0.930900
$218$	−4.82463	−	8.35651i	−0.326765	−	0.565974i
$219$		0			0
$220$	7.58044	−	13.1297i	0.511073	−	0.885204i
$221$	−1.57378	+	8.18334i	−0.105864	+	0.550471i
$222$		0			0
$223$	12.4014	−	7.15993i	0.830456	−	0.479464i	−0.0235526	−	0.999723i	$-0.507498\pi$
$223$	12.4014	−	7.15993i	0.830456	−	0.479464i	0.854009	+	0.520258i	$0.174164\pi$
$224$	2.20354			0.147230
$225$		0			0
$226$		−	3.03210i		−	0.201692i
$227$	−17.3351	+	10.0084i	−1.15057	+	0.664284i	−0.949027	−	0.315195i	$-0.897930\pi$
$227$	−17.3351	+	10.0084i	−1.15057	+	0.664284i	−0.201546	+	0.979479i	$0.564597\pi$
$228$		0			0
$229$	−2.23215	−	1.28873i	−0.147505	−	0.0851619i	0.424431	−	0.905460i	$-0.360474\pi$
$229$	−2.23215	−	1.28873i	−0.147505	−	0.0851619i	−0.571936	+	0.820298i	$0.693807\pi$
$230$	12.3070	−	21.3163i	0.811499	−	1.40556i
$231$		0			0
$232$	8.18662	−	4.72655i	0.537478	−	0.310313i
$233$	−14.0412			−0.919866			−0.459933	−	0.887954i	$-0.652127\pi$
$233$	−14.0412			−0.919866			−0.459933	+	0.887954i	$0.652127\pi$
$234$		0			0
$235$	−16.2316			−1.05883
$236$	2.59002	−	1.49535i	0.168596	−	0.0973390i
$237$		0			0
$238$	2.54645	−	4.41058i	0.165062	−	0.285895i
$239$	−4.07262	−	2.35133i	−0.263436	−	0.152095i	0.362465	−	0.931997i	$-0.381935\pi$
$239$	−4.07262	−	2.35133i	−0.263436	−	0.152095i	−0.625901	+	0.779903i	$0.715269\pi$
$240$		0			0
$241$	19.5733	−	11.3007i	1.26083	−	0.727939i	0.287593	−	0.957753i	$-0.407145\pi$
$241$	19.5733	−	11.3007i	1.26083	−	0.727939i	0.973235	+	0.229814i	$0.0738116\pi$
$242$			15.7221i			1.01065i
$243$		0			0
$244$	0.864857			0.0553668
$245$	−5.44668	+	3.14464i	−0.347975	+	0.200904i
$246$		0			0
$247$	−18.3029	−	3.51992i	−1.16459	−	0.223967i
$248$	−3.11159	+	5.38944i	−0.197586	+	0.342230i
$249$		0			0
$250$	2.05068	+	3.55188i	0.129696	+	0.224640i
$251$	−3.40669			−0.215028			−0.107514	−	0.994204i	$-0.534289\pi$
$251$	−3.40669			−0.215028			−0.107514	+	0.994204i	$0.534289\pi$
$252$		0			0
$253$			43.3838i			2.72752i
$254$	7.82328	−	4.51677i	0.490876	−	0.283408i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−10.9148	+	18.9049i	−0.680844	+	1.17926i	0.293880	+	0.955842i	$0.405053\pi$
$257$	−10.9148	+	18.9049i	−0.680844	+	1.17926i	−0.974724	+	0.223414i	$0.928280\pi$
$258$		0			0
$259$	0.711892	+	1.23303i	0.0442348	+	0.0766170i
$260$	−3.46263	−	9.99153i	−0.214743	−	0.619649i
$261$		0			0
$262$		−	17.4172i		−	1.07604i
$263$	2.95513	+	5.11843i	0.182221	+	0.315616i	0.942637	−	0.333821i	$-0.108338\pi$
$263$	2.95513	+	5.11843i	0.182221	+	0.315616i	−0.760416	+	0.649437i	$0.775005\pi$
$264$		0			0
$265$	22.0586	+	12.7355i	1.35505	+	0.782336i
$266$	9.86475	+	5.69541i	0.604846	+	0.349208i
$267$		0			0
$268$	9.68023	−	5.58888i	0.591314	−	0.341395i
$269$	−1.05911			−0.0645751			−0.0322875	−	0.999479i	$-0.510279\pi$
$269$	−1.05911			−0.0645751			−0.0322875	+	0.999479i	$0.510279\pi$
$270$		0			0
$271$		−	21.8135i		−	1.32508i	−0.749027	−	0.662539i	$-0.769479\pi$
$271$		−	21.8135i		−	1.32508i	0.749027	−	0.662539i	$-0.230521\pi$
$272$	1.15562	+	2.00159i	0.0700697	+	0.121364i
$273$		0			0
$274$	−2.42800	+	4.20543i	−0.146681	+	0.254059i
$275$	16.1235	+	9.30889i	0.972282	+	0.561347i
$276$		0			0
$277$	8.83826	+	15.3083i	0.531040	+	0.919788i	0.999344	+	0.0362206i	$0.0115319\pi$
$277$	8.83826	+	15.3083i	0.531040	+	0.919788i	−0.468304	+	0.883567i	$0.655135\pi$
$278$			11.6453i			0.698436i
$279$		0			0
$280$			6.46263i			0.386216i
$281$	11.5370	−	6.66092i	0.688243	−	0.397357i	−0.114711	−	0.993399i	$-0.536594\pi$
$281$	11.5370	−	6.66092i	0.688243	−	0.397357i	0.802953	+	0.596042i	$0.203261\pi$
$282$		0			0
$283$	−2.64908	+	4.58833i	−0.157471	+	0.272748i	−0.933956	−	0.357388i	$-0.883667\pi$
$283$	−2.64908	+	4.58833i	−0.157471	+	0.272748i	0.776485	+	0.630136i	$0.217001\pi$
$284$	11.2141	+	6.47445i	0.665433	+	0.384188i
$285$		0			0
$286$	14.0908	+	12.1998i	0.833209	+	0.721390i
$287$	−1.71732			−0.101370
$288$		0			0
$289$	−11.6582			−0.685775
$290$	13.8622	+	24.0101i	0.814019	+	1.40992i
$291$		0			0
$292$	3.70254	+	2.13767i	0.216675	+	0.125097i
$293$	12.7124	+	7.33950i	0.742666	+	0.428778i	0.823038	−	0.567987i	$-0.192278\pi$
$293$	12.7124	+	7.33950i	0.742666	+	0.428778i	−0.0803721	+	0.996765i	$0.525611\pi$
$294$		0			0
$295$	4.38563	+	7.59613i	0.255341	+	0.442264i
$296$	−0.646136			−0.0375559
$297$		0			0
$298$	21.8055			1.26316
$299$	22.8768	+	19.8066i	1.32300	+	1.14545i
$300$		0			0
$301$	−6.66304	−	3.84691i	−0.384051	−	0.221732i
$302$	7.33161	−	12.6987i	0.421887	−	0.730729i
$303$		0			0
$304$	−4.47678	+	2.58467i	−0.256761	+	0.148241i
$305$			2.53649i			0.145239i
$306$		0			0
$307$			3.41724i			0.195032i	0.995234	+	0.0975160i	$0.0310897\pi$
$307$			3.41724i			0.195032i	−0.995234	+	0.0975160i	$0.968910\pi$
$308$	−5.69541	−	9.86475i	−0.324526	−	0.562096i
$309$		0			0
$310$	−15.8064	−	9.12582i	−0.897742	−	0.518312i
$311$	5.41458	−	9.37832i	0.307033	−	0.531796i	−0.670679	−	0.741747i	$-0.733997\pi$
$311$	5.41458	−	9.37832i	0.307033	−	0.531796i	0.977712	+	0.209952i	$0.0673306\pi$
$312$		0			0
$313$	−9.67596	−	16.7593i	−0.546918	−	0.947289i	−0.998484	−	0.0550515i	$-0.982468\pi$
$313$	−9.67596	−	16.7593i	−0.546918	−	0.947289i	0.451566	−	0.892238i	$-0.350866\pi$
$314$		−	7.94869i		−	0.448570i
$315$		0			0
$316$	3.04350			0.171210
$317$	−13.7615	+	7.94519i	−0.772922	+	0.446247i	−0.833916	−	0.551892i	$-0.813906\pi$
$317$	−13.7615	+	7.94519i	−0.772922	+	0.446247i	0.0609942	+	0.998138i	$0.480573\pi$
$318$		0			0
$319$	−42.3194	−	24.4331i	−2.36943	−	1.36799i
$320$	−2.53992	−	1.46642i	−0.141986	−	0.0819755i
$321$		0			0
$322$	−9.24661	−	16.0156i	−0.515294	−	0.892515i
$323$			11.9476i			0.664781i
$324$		0			0
$325$	12.2698	−	4.25216i	0.680604	−	0.235867i
$326$	0.111267	+	0.192720i	0.00616249	+	0.0106737i
$327$		0			0
$328$	0.389673	−	0.674934i	0.0215161	−	0.0372670i
$329$	−6.09765	+	10.5614i	−0.336174	+	0.582271i
$330$		0			0
$331$	24.7786	−	14.3059i	1.36195	−	0.786325i	0.372070	−	0.928204i	$-0.378648\pi$
$331$	24.7786	−	14.3059i	1.36195	−	0.786325i	0.989884	+	0.141880i	$0.0453146\pi$
$332$			3.68705i			0.202353i
$333$		0			0
$334$	−3.77070			−0.206323
$335$	16.3913	+	28.3906i	0.895554	+	1.55115i
$336$		0			0
$337$	2.75329	−	4.76884i	0.149981	−	0.259775i	−0.781239	−	0.624232i	$-0.785412\pi$
$337$	2.75329	−	4.76884i	0.149981	−	0.259775i	0.931220	+	0.364457i	$0.118745\pi$
$338$	12.8662	−	1.86050i	0.699828	−	0.101198i
$339$		0			0
$340$	−5.87036	+	3.38925i	−0.318365	+	0.183808i
$341$	32.1698			1.74209
$342$		0			0
$343$			20.1501i			1.08800i
$344$	3.02379	−	1.74579i	0.163032	−	0.0941266i
$345$		0			0
$346$	9.39936	+	5.42672i	0.505312	+	0.291742i
$347$	−1.32309	+	2.29165i	−0.0710271	+	0.123022i	−0.899352	−	0.437226i	$-0.855961\pi$
$347$	−1.32309	+	2.29165i	−0.0710271	+	0.123022i	0.828325	+	0.560248i	$0.189294\pi$
$348$		0			0
$349$	4.83660	−	2.79241i	0.258897	−	0.149474i	−0.364934	−	0.931033i	$-0.618908\pi$
$349$	4.83660	−	2.79241i	0.258897	−	0.149474i	0.623831	+	0.781559i	$0.285575\pi$
$350$	−7.93621			−0.424208
$351$		0			0
$352$	5.16934			0.275527
$353$	22.2107	−	12.8233i	1.18216	−	0.682518i	0.225643	−	0.974210i	$-0.427552\pi$
$353$	22.2107	−	12.8233i	1.18216	−	0.682518i	0.956512	+	0.291692i	$0.0942183\pi$
$354$		0			0
$355$	−18.9886	+	32.8892i	−1.00781	+	1.74558i
$356$	−2.89815	−	1.67325i	−0.153602	−	0.0886820i
$357$		0			0
$358$	−12.6786	+	7.32001i	−0.670086	+	0.386874i
$359$		−	5.78875i		−	0.305519i	−0.988263	−	0.152759i	$-0.951184\pi$
$359$		−	5.78875i		−	0.305519i	0.988263	−	0.152759i	$-0.0488160\pi$
$360$		0			0
$361$	−7.72208			−0.406425
$362$	2.43660	−	1.40677i	0.128065	−	0.0739383i
$363$		0			0
$364$	−7.80199	−	1.50044i	−0.408936	−	0.0786443i
$365$	−6.26944	+	10.8590i	−0.328158	+	0.568386i
$366$		0			0
$367$	15.3992	+	26.6722i	0.803831	+	1.39228i	0.917078	+	0.398708i	$0.130541\pi$
$367$	15.3992	+	26.6722i	0.803831	+	1.39228i	−0.113247	+	0.993567i	$0.536125\pi$
$368$	8.39252			0.437491
$369$		0			0
$370$		−	1.89502i		−	0.0985173i
$371$	16.5733	−	9.56858i	0.860441	−	0.496776i
$372$		0			0
$373$	15.6441	−	27.0964i	0.810021	−	1.40300i	−0.102828	−	0.994699i	$-0.532789\pi$
$373$	15.6441	−	27.0964i	0.810021	−	1.40300i	0.912849	−	0.408298i	$-0.133878\pi$
$374$	5.97379	−	10.3469i	0.308897	−	0.535026i
$375$		0			0
$376$	−2.76721	−	4.79295i	−0.142708	−	0.247178i
$377$	−32.2046	+	11.1607i	−1.65862	+	0.574805i
$378$		0			0
$379$		−	5.29769i		−	0.272124i	−0.990700	−	0.136062i	$-0.956555\pi$
$379$		−	5.29769i		−	0.272124i	0.990700	−	0.136062i	$-0.0434447\pi$
$380$	−7.58044	−	13.1297i	−0.388868	−	0.673539i
$381$		0			0
$382$	7.60058	+	4.38820i	0.388880	+	0.224520i
$383$	19.2301	+	11.1025i	0.982611	+	0.567311i	0.903057	−	0.429520i	$-0.141317\pi$
$383$	19.2301	+	11.1025i	0.982611	+	0.567311i	0.0795536	+	0.996831i	$0.474651\pi$
$384$		0			0
$385$	28.9318	−	16.7038i	1.47450	−	0.851303i
$386$	−15.8231			−0.805373
$387$		0			0
$388$		−	1.49094i		−	0.0756910i
$389$	−4.38589	−	7.59658i	−0.222373	−	0.385162i	0.733155	−	0.680062i	$-0.238047\pi$
$389$	−4.38589	−	7.59658i	−0.222373	−	0.385162i	−0.955528	+	0.294900i	$0.904714\pi$
$390$		0			0
$391$	9.69857	−	16.7984i	0.490478	−	0.849532i
$392$	−1.85713	−	1.07221i	−0.0937993	−	0.0541550i
$393$		0			0
$394$	−0.197858	−	0.342701i	−0.00996796	−	0.0172650i
$395$			8.92611i			0.449121i
$396$		0			0
$397$		−	33.5447i		−	1.68356i	−0.539819	−	0.841781i	$-0.681508\pi$
$397$		−	33.5447i		−	1.68356i	0.539819	−	0.841781i	$-0.318492\pi$
$398$	−2.77402	+	1.60158i	−0.139049	+	0.0802799i
$399$		0			0
$400$	1.80079	−	3.11906i	0.0900395	−	0.155953i
$401$	−1.76682	−	1.02008i	−0.0882309	−	0.0509401i	0.455235	−	0.890371i	$-0.349555\pi$
$401$	−1.76682	−	1.02008i	−0.0882309	−	0.0509401i	−0.543466	+	0.839431i	$0.682888\pi$
$402$		0			0
$403$	14.6869	−	16.9635i	0.731607	−	0.845010i
$404$	0.406692			0.0202337
$405$		0			0
$406$	20.8302			1.03379
$407$	1.67005	+	2.89261i	0.0827813	+	0.143381i
$408$		0			0
$409$	−28.2129	−	16.2887i	−1.39504	−	0.805424i	−0.401169	−	0.916004i	$-0.631396\pi$
$409$	−28.2129	−	16.2887i	−1.39504	−	0.805424i	−0.993867	+	0.110580i	$0.964729\pi$
$410$	1.97948	+	1.14285i	0.0977593	+	0.0564414i
$411$		0			0
$412$	8.58044	+	14.8618i	0.422728	+	0.732186i
$413$	6.59011			0.324278
$414$		0			0
$415$	−10.8135			−0.530816
$416$	2.36003	−	2.72585i	0.115710	−	0.133646i
$417$		0			0
$418$	23.1420	+	13.3610i	1.13191	+	0.653510i
$419$	5.83046	−	10.0986i	0.284837	−	0.493351i	−0.687733	−	0.725964i	$-0.741394\pi$
$419$	5.83046	−	10.0986i	0.284837	−	0.493351i	0.972570	+	0.232612i	$0.0747274\pi$
$420$		0			0
$421$	−1.41549	+	0.817233i	−0.0689867	+	0.0398295i	−0.534097	−	0.845423i	$-0.679348\pi$
$421$	−1.41549	+	0.817233i	−0.0689867	+	0.0398295i	0.465110	+	0.885253i	$0.346015\pi$
$422$		−	8.27972i		−	0.403051i
$423$		0			0
$424$			8.68475i			0.421769i
$425$	−4.16206	−	7.20889i	−0.201889	−	0.349683i
$426$		0			0
$427$	1.65042	+	0.952872i	0.0798695	+	0.0461127i
$428$	0.164777	−	0.285403i	0.00796481	−	0.0137955i
$429$		0			0
$430$	5.12013	+	8.86832i	0.246914	+	0.427668i
$431$			2.92645i			0.140962i	0.997513	+	0.0704810i	$0.0224534\pi$
$431$			2.92645i			0.140962i	−0.997513	+	0.0704810i	$0.977547\pi$
$432$		0			0
$433$	−33.9770			−1.63283			−0.816414	−	0.577467i	$-0.804041\pi$
$433$	−33.9770			−1.63283			−0.816414	+	0.577467i	$0.804041\pi$
$434$	−11.8758	+	6.85651i	−0.570057	+	0.329123i
$435$		0			0
$436$	8.35651	+	4.82463i	0.400204	+	0.231058i
$437$	37.5715	+	21.6919i	1.79729	+	1.03766i
$438$		0			0
$439$	8.24661	+	14.2836i	0.393589	+	0.681717i	0.992920	−	0.118785i	$-0.0378998\pi$
$439$	8.24661	+	14.2836i	0.393589	+	0.681717i	−0.599331	+	0.800502i	$0.704566\pi$
$440$			15.1609i			0.722766i
$441$		0			0
$442$	−2.72874	−	7.87386i	−0.129793	−	0.374522i
$443$	−14.4784	−	25.0774i	−0.687891	−	1.19146i	−0.972519	−	0.232824i	$-0.925203\pi$
$443$	−14.4784	−	25.0774i	−0.687891	−	1.19146i	0.284628	−	0.958638i	$-0.408130\pi$
$444$		0			0
$445$	4.90738	−	8.49983i	0.232632	−	0.402930i
$446$	−7.15993	+	12.4014i	−0.339032	+	0.587221i
$447$		0			0
$448$	−1.90832	+	1.10177i	−0.0901596	+	0.0520536i
$449$		−	38.1292i		−	1.79943i	−0.436478	−	0.899715i	$-0.643774\pi$
$449$		−	38.1292i		−	1.79943i	0.436478	−	0.899715i	$-0.356226\pi$
$450$		0			0
$451$	−4.02871			−0.189704
$452$	1.51605	+	2.62588i	0.0713090	+	0.123511i
$453$		0			0
$454$	10.0084	−	17.3351i	0.469719	−	0.813578i
$455$	4.40055	−	22.8820i	0.206301	−	1.07273i
$456$		0			0
$457$	−27.1535	+	15.6771i	−1.27019	+	0.733343i	−0.975023	−	0.222104i	$-0.928708\pi$
$457$	−27.1535	+	15.6771i	−1.27019	+	0.733343i	−0.295164	+	0.955447i	$0.595374\pi$
$458$	2.57747			0.120437
$459$		0			0
$460$			24.6140i			1.14763i
$461$	−20.5156	+	11.8447i	−0.955507	+	0.551662i	−0.894787	−	0.446493i	$-0.852673\pi$
$461$	−20.5156	+	11.8447i	−0.955507	+	0.551662i	−0.0607196	+	0.998155i	$0.519340\pi$
$462$		0			0
$463$	−5.85941	−	3.38293i	−0.272310	−	0.157218i	0.357627	−	0.933865i	$-0.383586\pi$
$463$	−5.85941	−	3.38293i	−0.272310	−	0.157218i	−0.629937	+	0.776646i	$0.716919\pi$
$464$	−4.72655	+	8.18662i	−0.219425	+	0.380054i
$465$		0			0
$466$	12.1600	−	7.02058i	0.563301	−	0.325222i
$467$	28.8066			1.33301			0.666505	−	0.745500i	$-0.267789\pi$
$467$	28.8066			1.33301			0.666505	+	0.745500i	$0.267789\pi$
$468$		0			0
$469$	24.6306			1.13734
$470$	14.0570	−	8.11580i	0.648400	−	0.374354i
$471$		0			0
$472$	−1.49535	+	2.59002i	−0.0688291	+	0.119215i
$473$	−15.6310	−	9.02458i	−0.718715	−	0.414950i
$474$		0			0
$475$	16.1235	−	9.30889i	0.739796	−	0.427121i
$476$			5.09290i			0.233433i
$477$		0			0
$478$	4.70266			0.215095
$479$	34.9597	−	20.1840i	1.59735	−	0.922230i	0.605354	−	0.795957i	$-0.293032\pi$
$479$	34.9597	−	20.1840i	1.59735	−	0.922230i	0.991996	−	0.126273i	$-0.0403016\pi$
$480$		0			0
$481$	2.28776	+	0.439969i	0.104313	+	0.0200609i
$482$	−11.3007	+	19.5733i	−0.514731	+	0.891540i
$483$		0			0
$484$	−7.86104	−	13.6157i	−0.357320	−	0.618896i
$485$	4.37270			0.198554
$486$		0			0
$487$			40.9866i			1.85728i	0.370982	+	0.928640i	$0.379021\pi$
$487$			40.9866i			1.85728i	−0.370982	+	0.928640i	$0.620979\pi$
$488$	−0.748988	+	0.432428i	−0.0339051	+	0.0195751i
$489$		0			0
$490$	3.14464	−	5.44668i	0.142060	−	0.246056i
$491$	−4.25969	+	7.37800i	−0.192237	+	0.332965i	−0.945991	−	0.324192i	$-0.894908\pi$
$491$	−4.25969	+	7.37800i	−0.192237	+	0.332965i	0.753754	+	0.657157i	$0.228241\pi$
$492$		0			0
$493$	10.9242	+	18.9212i	0.492001	+	0.852170i
$494$	17.6108	−	6.10312i	0.792346	−	0.274592i
$495$		0			0
$496$		−	6.22318i		−	0.279429i
$497$	14.2667	+	24.7106i	0.639949	+	1.10842i
$498$		0			0
$499$	18.9967	+	10.9677i	0.850408	+	0.490983i	0.860788	−	0.508963i	$-0.169971\pi$
$499$	18.9967	+	10.9677i	0.850408	+	0.490983i	−0.0103807	+	0.999946i	$0.503304\pi$
$500$	−3.55188	−	2.05068i	−0.158845	−	0.0917090i
$501$		0			0
$502$	2.95028	−	1.70335i	0.131678	−	0.0760241i
$503$	−31.5620			−1.40728			−0.703641	−	0.710556i	$-0.748444\pi$
$503$	−31.5620			−1.40728			−0.703641	+	0.710556i	$0.748444\pi$
$504$		0			0
$505$			1.19276i			0.0530773i
$506$	−21.6919	−	37.5715i	−0.964323	−	1.67026i
$507$		0			0
$508$	−4.51677	+	7.82328i	−0.200399	+	0.347102i
$509$	−32.3673	−	18.6873i	−1.43466	−	0.828299i	−0.437184	−	0.899372i	$-0.644024\pi$
$509$	−32.3673	−	18.6873i	−1.43466	−	0.828299i	−0.997471	+	0.0710731i	$0.977358\pi$
$510$		0			0
$511$	4.71042	+	8.15869i	0.208377	+	0.360919i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$		−	21.8295i		−	0.962858i
$515$	−43.5872	+	25.1651i	−1.92068	+	1.10891i
$516$		0			0
$517$	−14.3047	+	24.7764i	−0.629118	+	1.08966i
$518$	−1.23303	−	0.711892i	−0.0541764	−	0.0312788i
$519$		0			0
$520$	7.99449	+	6.92161i	0.350582	+	0.303533i
$521$	17.2949			0.757705			0.378853	−	0.925457i	$-0.376319\pi$
$521$	17.2949			0.757705			0.378853	+	0.925457i	$0.376319\pi$
$522$		0			0
$523$	−10.5189			−0.459960			−0.229980	−	0.973195i	$-0.573866\pi$
$523$	−10.5189			−0.459960			−0.229980	+	0.973195i	$0.573866\pi$
$524$	8.70860	+	15.0837i	0.380437	+	0.658936i
$525$		0			0
$526$	−5.11843	−	2.95513i	−0.223174	−	0.128850i
$527$	−12.4563	−	7.19163i	−0.542604	−	0.313273i
$528$		0			0
$529$	−23.7172	−	41.0795i	−1.03118	−	1.78606i
$530$	−25.4710			−1.10639
$531$		0			0
$532$	−11.3908			−0.493855
$533$	−1.83928	+	2.12438i	−0.0796681	+	0.0920171i
$534$		0			0
$535$	0.837042	+	0.483266i	0.0361885	+	0.0208934i
$536$	−5.58888	+	9.68023i	−0.241403	+	0.418122i
$537$		0			0
$538$	0.917216	−	0.529555i	0.0395440	−	0.0228307i
$539$			11.0853i			0.477477i
$540$		0			0
$541$			21.7436i			0.934832i	0.884038	+	0.467416i	$0.154815\pi$
$541$			21.7436i			0.934832i	−0.884038	+	0.467416i	$0.845185\pi$
$542$	10.9068	+	18.8911i	0.468486	+	0.811441i
$543$		0			0
$544$	−2.00159	−	1.15562i	−0.0858175	−	0.0495468i
$545$	−14.1499	+	24.5084i	−0.606115	+	1.04982i
$546$		0			0
$547$	−13.9964	−	24.2425i	−0.598444	−	1.03654i	−0.993051	−	0.117685i	$-0.962453\pi$
$547$	−13.9964	−	24.2425i	−0.598444	−	1.03654i	0.394607	−	0.918850i	$-0.370881\pi$
$548$		−	4.85601i		−	0.207438i
$549$		0			0
$550$	−18.6178			−0.793865
$551$	−42.3194	+	24.4331i	−1.80287	+	1.04089i
$552$		0			0
$553$	5.80796	+	3.35323i	0.246980	+	0.142594i
$554$	−15.3083	−	8.83826i	−0.650388	−	0.375502i
$555$		0			0
$556$	−5.82263	−	10.0851i	−0.246934	−	0.427703i
$557$		−	8.27318i		−	0.350546i	−0.984520	−	0.175273i	$-0.943919\pi$
$557$		−	8.27318i		−	0.350546i	0.984520	−	0.175273i	$-0.0560808\pi$
$558$		0			0
$559$	−11.8950	+	4.12229i	−0.503105	+	0.174354i
$560$	−3.23131	−	5.59680i	−0.136548	−	0.236508i
$561$		0			0
$562$	−6.66092	+	11.5370i	−0.280974	+	0.486661i
$563$	5.05976	−	8.76376i	0.213243	−	0.369349i	−0.739484	−	0.673174i	$-0.764931\pi$
$563$	5.05976	−	8.76376i	0.213243	−	0.369349i	0.952728	+	0.303825i	$0.0982639\pi$
$564$		0			0
$565$	−7.70129	+	4.44634i	−0.323996	+	0.187059i
$566$		−	5.29815i		−	0.222698i
$567$		0			0
$568$	−12.9489			−0.543324
$569$	−10.6762	−	18.4917i	−0.447568	−	0.775211i	0.550659	−	0.834730i	$-0.314376\pi$
$569$	−10.6762	−	18.4917i	−0.447568	−	0.775211i	−0.998227	+	0.0595196i	$0.981043\pi$
$570$		0			0
$571$	−5.62132	+	9.73641i	−0.235245	+	0.407456i	−0.959344	−	0.282240i	$-0.908923\pi$
$571$	−5.62132	+	9.73641i	−0.235245	+	0.407456i	0.724099	+	0.689696i	$0.242256\pi$
$572$	−18.3029	−	3.51992i	−0.765284	−	0.147175i
$573$		0			0
$574$	1.48724	−	0.858659i	0.0620762	−	0.0358397i
$575$	−30.2263			−1.26053
$576$		0			0
$577$		−	13.4761i		−	0.561018i	−0.959851	−	0.280509i	$-0.909497\pi$
$577$		−	13.4761i		−	0.561018i	0.959851	−	0.280509i	$-0.0905032\pi$
$578$	10.0963	−	5.82909i	0.419950	−	0.242458i
$579$		0			0
$580$	−24.0101	−	13.8622i	−0.996965	−	0.575598i
$581$	−4.06227	+	7.03606i	−0.168531	+	0.291905i
$582$		0			0
$583$	38.8797	−	22.4472i	1.61023	−	0.929669i
$584$	−4.27533			−0.176914
$585$		0			0
$586$	−14.6790			−0.606384
$587$	24.4663	−	14.1256i	1.00983	−	0.583027i	0.0986903	−	0.995118i	$-0.468535\pi$
$587$	24.4663	−	14.1256i	1.00983	−	0.583027i	0.911143	+	0.412091i	$0.135201\pi$
$588$		0			0
$589$	16.0849	−	27.8598i	0.662766	−	1.14794i
$590$	−7.59613	−	4.38563i	−0.312728	−	0.180554i
$591$		0			0
$592$	0.559571	−	0.323068i	0.0229982	−	0.0132780i
$593$			33.3901i			1.37117i	0.727993	+	0.685585i	$0.240453\pi$
$593$			33.3901i			1.37117i	−0.727993	+	0.685585i	$0.759547\pi$
$594$		0			0
$595$	−14.9367			−0.612344
$596$	−18.8841	+	10.9027i	−0.773522	+	0.446593i
$597$		0			0
$598$	−29.7152	−	5.71466i	−1.21514	−	0.233690i
$599$	10.0405	−	17.3907i	0.410245	−	0.710564i	−0.584672	−	0.811270i	$-0.698777\pi$
$599$	10.0405	−	17.3907i	0.410245	−	0.710564i	0.994916	+	0.100706i	$0.0321100\pi$
$600$		0			0
$601$	−5.78337	−	10.0171i	−0.235909	−	0.408606i	0.723628	−	0.690191i	$-0.242473\pi$
$601$	−5.78337	−	10.0171i	−0.235909	−	0.408606i	−0.959536	+	0.281585i	$0.909140\pi$
$602$	7.69382			0.313577
$603$		0			0
$604$			14.6632i			0.596638i
$605$	39.9328	−	23.0552i	1.62350	−	0.937328i
$606$		0			0
$607$	−12.0487	+	20.8689i	−0.489040	+	0.847042i	−0.999920	−	0.0126098i	$-0.995986\pi$
$607$	−12.0487	+	20.8689i	−0.489040	+	0.847042i	0.510881	+	0.859652i	$0.329319\pi$
$608$	2.58467	−	4.47678i	0.104822	−	0.181557i
$609$		0			0
$610$	−1.26825	−	2.19667i	−0.0513498	−	0.0889404i
$611$	6.53415	+	18.8545i	0.264344	+	0.762772i
$612$		0			0
$613$			3.75444i			0.151641i	0.997122	+	0.0758203i	$0.0241575\pi$
$613$			3.75444i			0.151641i	−0.997122	+	0.0758203i	$0.975842\pi$
$614$	−1.70862	−	2.95941i	−0.0689542	−	0.119432i
$615$		0			0
$616$	9.86475	+	5.69541i	0.397462	+	0.229475i
$617$	−12.4831	−	7.20712i	−0.502551	−	0.290148i	0.227216	−	0.973844i	$-0.427038\pi$
$617$	−12.4831	−	7.20712i	−0.502551	−	0.290148i	−0.729766	+	0.683697i	$0.760371\pi$
$618$		0			0
$619$	−7.94447	+	4.58674i	−0.319315	+	0.184357i	−0.651087	−	0.759003i	$-0.725687\pi$
$619$	−7.94447	+	4.58674i	−0.319315	+	0.184357i	0.331772	+	0.943360i	$0.392353\pi$
$620$	18.2516			0.733003
$621$		0			0
$622$			10.8292i			0.434210i
$623$	−3.68706	−	6.38618i	−0.147719	−	0.255857i
$624$		0			0
$625$	15.0183	−	26.0124i	0.600730	−	1.04050i
$626$	16.7593	+	9.67596i	0.669835	+	0.386729i
$627$		0			0
$628$	3.97434	+	6.88376i	0.158594	+	0.274692i
$629$		−	1.49338i		−	0.0595448i
$630$		0			0
$631$			32.8572i			1.30803i	0.756483	+	0.654013i	$0.226916\pi$
$631$			32.8572i			1.30803i	−0.756483	+	0.654013i	$0.773084\pi$
$632$	−2.63575	+	1.52175i	−0.104844	+	0.0605319i
$633$		0			0
$634$	7.94519	−	13.7615i	0.315544	−	0.546538i
$635$	−22.9445	−	13.2470i	−0.910523	−	0.525691i
$636$		0			0
$637$	5.84539	+	5.06092i	0.231603	+	0.200521i
$638$	48.8663			1.93463
$639$		0			0
$640$	2.93284			0.115931
$641$	−10.6942	−	18.5230i	−0.422397	−	0.731613i	0.573776	−	0.819012i	$-0.305478\pi$
$641$	−10.6942	−	18.5230i	−0.422397	−	0.731613i	−0.996173	+	0.0873990i	$0.972145\pi$
$642$		0			0
$643$	−4.58280	−	2.64588i	−0.180728	−	0.104343i	0.406907	−	0.913470i	$-0.366607\pi$
$643$	−4.58280	−	2.64588i	−0.180728	−	0.104343i	−0.587635	+	0.809126i	$0.699941\pi$
$644$	16.0156	+	9.24661i	0.631103	+	0.364368i
$645$		0			0
$646$	−5.97379	−	10.3469i	−0.235036	−	0.407094i
$647$	−0.564603			−0.0221968			−0.0110984	−	0.999938i	$-0.503533\pi$
$647$	−0.564603			−0.0221968			−0.0110984	+	0.999938i	$0.503533\pi$
$648$		0			0
$649$	15.4599			0.606856
$650$	−8.49984	+	9.81736i	−0.333391	+	0.385068i
$651$		0			0
$652$	−0.192720	−	0.111267i	−0.00754748	−	0.00435754i
$653$	−8.01118	+	13.8758i	−0.313502	+	0.543001i	−0.979118	−	0.203293i	$-0.934835\pi$
$653$	−8.01118	+	13.8758i	−0.313502	+	0.543001i	0.665616	+	0.746294i	$0.268169\pi$
$654$		0			0
$655$	−44.2382	+	25.5410i	−1.72853	+	0.997968i
$656$			0.779346i			0.0304284i
$657$		0			0
$658$		−	12.1953i		−	0.475422i
$659$	−3.71611	−	6.43648i	−0.144759	−	0.250730i	0.784524	−	0.620098i	$-0.212907\pi$
$659$	−3.71611	−	6.43648i	−0.144759	−	0.250730i	−0.929283	+	0.369369i	$0.879574\pi$
$660$		0			0
$661$	−13.6161	−	7.86129i	−0.529607	−	0.305769i	0.211250	−	0.977432i	$-0.432247\pi$
$661$	−13.6161	−	7.86129i	−0.529607	−	0.305769i	−0.740856	+	0.671664i	$0.765580\pi$
$662$	−14.3059	+	24.7786i	−0.556016	+	0.963047i
$663$		0			0
$664$	−1.84352	−	3.19308i	−0.0715426	−	0.123915i
$665$		−	33.4075i		−	1.29549i
$666$		0			0
$667$	79.3354			3.07188
$668$	3.26552	−	1.88535i	0.126347	−	0.0729463i
$669$		0			0
$670$	−28.3906	−	16.3913i	−1.09683	−	0.633252i
$671$	3.87177	+	2.23537i	0.149468	+	0.0862955i
$672$		0			0
$673$	19.8291	+	34.3450i	0.764356	+	1.32390i	0.940586	+	0.339554i	$0.110276\pi$
$673$	19.8291	+	34.3450i	0.764356	+	1.32390i	−0.176231	+	0.984349i	$0.556390\pi$
$674$			5.50659i			0.212106i
$675$		0			0
$676$	−10.2122	+	8.04433i	−0.392776	+	0.309397i
$677$	−18.2613	−	31.6296i	−0.701840	−	1.21562i	−0.967820	−	0.251644i	$-0.919029\pi$
$677$	−18.2613	−	31.6296i	−0.701840	−	1.21562i	0.265980	−	0.963979i	$-0.414305\pi$
$678$		0			0
$679$	1.64267	−	2.84519i	0.0630399	−	0.109188i
$680$	3.38925	−	5.87036i	0.129972	−	0.225118i
$681$		0			0
$682$	−27.8598	+	16.0849i	−1.06681	+	0.615922i
$683$		−	8.46240i		−	0.323805i	−0.986807	−	0.161902i	$-0.948237\pi$
$683$		−	8.46240i		−	0.323805i	0.986807	−	0.161902i	$-0.0517630\pi$
$684$		0			0
$685$	14.2419			0.544156
$686$	−10.0750	−	17.4505i	−0.384667	−	0.666262i
$687$		0			0
$688$	−1.74579	+	3.02379i	−0.0665576	+	0.115281i
$689$	5.91365	−	30.7498i	0.225292	−	1.17148i
$690$		0			0
$691$	−42.2875	+	24.4147i	−1.60869	+	0.928779i	−0.619028	+	0.785369i	$0.712473\pi$
$691$	−42.2875	+	24.4147i	−1.60869	+	0.928779i	−0.989663	+	0.143410i	$0.954193\pi$
$692$	−10.8534			−0.412586
$693$		0			0
$694$		−	2.64618i		−	0.100447i
$695$	29.5780	−	17.0769i	1.12196	−	0.647762i
$696$		0			0
$697$	1.55993	+	0.900628i	0.0590867	+	0.0341137i
$698$	−2.79241	+	4.83660i	−0.105694	+	0.183068i
$699$		0			0
$700$	6.87296	−	3.96810i	0.259773	−	0.149980i
$701$	40.2942			1.52189			0.760946	−	0.648816i	$-0.224735\pi$
$701$	40.2942			1.52189			0.760946	+	0.648816i	$0.224735\pi$
$702$		0			0
$703$	3.34010			0.125974
$704$	−4.47678	+	2.58467i	−0.168725	+	0.0974134i
$705$		0			0
$706$	−12.8233	+	22.2107i	−0.482613	+	0.835910i
$707$	0.776098	+	0.448080i	0.0291882	+	0.0168518i
$708$		0			0
$709$	−33.3511	+	19.2553i	−1.25253	+	0.723146i	−0.971611	−	0.236586i	$-0.923971\pi$
$709$	−33.3511	+	19.2553i	−1.25253	+	0.723146i	−0.280916	+	0.959732i	$0.590638\pi$
$710$		−	37.9771i		−	1.42526i
$711$		0			0
$712$	3.34650			0.125415
$713$	−45.2310	+	26.1141i	−1.69391	+	0.977981i
$714$		0			0
$715$	10.3234	−	53.6796i	0.386073	−	2.00750i
$716$	7.32001	−	12.6786i	0.273561	−	0.473822i
$717$		0			0
$718$	2.89438	+	5.01321i	0.108017	+	0.187091i
$719$	0.951205			0.0354740			0.0177370	−	0.999843i	$-0.494354\pi$
$719$	0.951205			0.0354740			0.0177370	+	0.999843i	$0.494354\pi$
$720$		0			0
$721$			37.8146i			1.40829i
$722$	6.68752	−	3.86104i	0.248884	−	0.143693i
$723$		0			0
$724$	−1.40677	+	2.43660i	−0.0522823	+	0.0905555i
$725$	17.0230	−	29.4848i	0.632220	−	1.09504i
$726$		0			0
$727$	−0.999064	−	1.73043i	−0.0370532	−	0.0641781i	0.846904	−	0.531746i	$-0.178464\pi$
$727$	−0.999064	−	1.73043i	−0.0370532	−	0.0641781i	−0.883957	+	0.467568i	$0.845130\pi$
$728$	7.50694	−	2.60158i	0.278226	−	0.0964209i
$729$		0			0
$730$		−	12.5389i		−	0.464085i
$731$	4.03494	+	6.98871i	0.149237	+	0.258487i
$732$		0			0
$733$	13.5363	+	7.81519i	0.499975	+	0.288661i	0.728703	−	0.684830i	$-0.240123\pi$
$733$	13.5363	+	7.81519i	0.499975	+	0.288661i	−0.228728	+	0.973490i	$0.573457\pi$
$734$	−26.6722	−	15.3992i	−0.984487	−	0.568394i
$735$		0			0
$736$	−7.26814	+	4.19626i	−0.267907	+	0.154676i
$737$	57.7817			2.12842
$738$		0			0
$739$		−	20.0122i		−	0.736162i	−0.929794	−	0.368081i	$-0.880015\pi$
$739$		−	20.0122i		−	0.736162i	0.929794	−	0.368081i	$-0.119985\pi$
$740$	0.947509	+	1.64113i	0.0348311	+	0.0603293i
$741$		0			0
$742$	−9.56858	+	16.5733i	−0.351274	+	0.608424i
$743$	33.5922	+	19.3945i	1.23238	+	0.711515i	0.967526	−	0.252773i	$-0.0813427\pi$
$743$	33.5922	+	19.3945i	1.23238	+	0.711515i	0.264855	+	0.964288i	$0.414676\pi$
$744$		0			0
$745$	−31.9760	−	55.3841i	−1.17151	−	2.02912i
$746$			31.2882i			1.14554i
$747$		0			0
$748$			11.9476i			0.436847i
$749$	0.628895	−	0.363093i	0.0229793	−	0.0132671i
$750$		0			0
$751$	7.46950	−	12.9376i	0.272566	−	0.472098i	−0.696952	−	0.717118i	$-0.745461\pi$
$751$	7.46950	−	12.9376i	0.272566	−	0.472098i	0.969518	+	0.245020i	$0.0787944\pi$
$752$	4.79295	+	2.76721i	0.174781	+	0.100910i
$753$		0			0
$754$	22.3096	−	25.7677i	0.812468	−	0.938405i
$755$	−43.0049			−1.56511
$756$		0			0
$757$	−26.1383			−0.950011			−0.475006	−	0.879983i	$-0.657554\pi$
$757$	−26.1383			−0.950011			−0.475006	+	0.879983i	$0.657554\pi$
$758$	2.64885	+	4.58794i	0.0962105	+	0.166641i
$759$		0			0
$760$	13.1297	+	7.58044i	0.476264	+	0.274971i
$761$	2.64121	+	1.52490i	0.0957437	+	0.0552776i	0.547107	−	0.837062i	$-0.315729\pi$
$761$	2.64121	+	1.52490i	0.0957437	+	0.0552776i	−0.451364	+	0.892340i	$0.649062\pi$
$762$		0			0
$763$	10.6313	+	18.4139i	0.384877	+	0.666627i
$764$	−8.77640			−0.317519
$765$		0			0
$766$	−22.2050			−0.802299
$767$	7.05815	−	8.15220i	0.254855	−	0.294359i
$768$		0			0
$769$	−5.95518	−	3.43822i	−0.214749	−	0.123985i	0.388767	−	0.921336i	$-0.372901\pi$
$769$	−5.95518	−	3.43822i	−0.214749	−	0.123985i	−0.603517	+	0.797350i	$0.706234\pi$
$770$	−16.7038	+	28.9318i	−0.601962	+	1.04263i
$771$		0			0
$772$	13.7032	−	7.91153i	0.493188	−	0.284742i
$773$			18.4949i			0.665216i	0.943065	+	0.332608i	$0.107929\pi$
$773$			18.4949i			0.665216i	−0.943065	+	0.332608i	$0.892071\pi$
$774$		0			0
$775$			22.4133i			0.805109i
$776$	0.745470	+	1.29119i	0.0267608	+	0.0463511i
$777$		0			0
$778$	7.59658	+	4.38589i	0.272351	+	0.157242i
$779$	−2.01435	+	3.48896i	−0.0721717	+	0.125005i
$780$		0			0
$781$	33.4687	+	57.9694i	1.19760	+	2.07431i
$782$			19.3971i			0.693640i
$783$		0			0
$784$	2.14443			0.0765868
$785$	−20.1890	+	11.6561i	−0.720577	+	0.416025i
$786$		0			0
$787$	−0.0764271	−	0.0441252i	−0.00272433	−	0.00157289i	0.498637	−	0.866811i	$-0.333834\pi$
$787$	−0.0764271	−	0.0441252i	−0.00272433	−	0.00157289i	−0.501362	+	0.865238i	$0.667167\pi$
$788$	0.342701	+	0.197858i	0.0122082	+	0.00704841i
$789$		0			0
$790$	−4.46305	−	7.73023i	−0.158788	−	0.275029i
$791$			6.68135i			0.237561i
$792$		0			0
$793$	2.94637	−	1.02108i	0.104629	−	0.0362597i
$794$	16.7724	+	29.0506i	0.595229	+	1.03097i
$795$		0			0
$796$	1.60158	−	2.77402i	0.0567665	−	0.0983224i
$797$	15.4544	−	26.7677i	0.547421	−	0.948161i	−0.451029	−	0.892509i	$-0.648943\pi$
$797$	15.4544	−	26.7677i	0.547421	−	0.948161i	0.998450	−	0.0556521i	$-0.0177238\pi$
$798$		0			0
$799$	11.0777	−	6.39569i	0.391899	−	0.226263i
$800$			3.60158i			0.127335i
$801$		0			0
$802$	2.04015			0.0720402
$803$	11.0503	+	19.1397i	0.389957	+	0.675426i
$804$		0			0
$805$	−27.1189	+	46.9713i	−0.955815	+	1.65552i
$806$	−4.23751	+	22.0342i	−0.149260	+	0.776123i
$807$		0			0
$808$	−0.352206	+	0.203346i	−0.0123905	+	0.00715369i
$809$	−45.6038			−1.60335			−0.801673	−	0.597763i	$-0.796056\pi$
$809$	−45.6038			−1.60335			−0.801673	+	0.597763i	$0.796056\pi$
$810$		0			0
$811$		−	20.3497i		−	0.714575i	−0.933994	−	0.357287i	$-0.883702\pi$
$811$		−	20.3497i		−	0.714575i	0.933994	−	0.357287i	$-0.116298\pi$
$812$	−18.0395	+	10.4151i	−0.633063	+	0.365499i
$813$		0			0
$814$	−2.89261	−	1.67005i	−0.101386	−	0.0585352i
$815$	0.326328	−	0.565216i	0.0114308	−	0.0197987i
$816$		0			0
$817$	−15.6310	+	9.02458i	−0.546860	+	0.315730i
$818$	32.5774			1.13904
$819$		0			0
$820$	−2.28570			−0.0798202
$821$	10.1101	−	5.83707i	0.352845	−	0.203715i	−0.313093	−	0.949723i	$-0.601365\pi$
$821$	10.1101	−	5.83707i	0.352845	−	0.203715i	0.665938	+	0.746007i	$0.268032\pi$
$822$		0			0
$823$	17.8000	−	30.8305i	0.620469	−	1.07468i	−0.368929	−	0.929457i	$-0.620276\pi$
$823$	17.8000	−	30.8305i	0.620469	−	1.07468i	0.989398	−	0.145227i	$-0.0463911\pi$
$824$	−14.8618	−	8.58044i	−0.517734	−	0.298914i
$825$		0			0
$826$	−5.70721	+	3.29506i	−0.198579	+	0.114650i
$827$		−	13.5478i		−	0.471103i	−0.971862	−	0.235551i	$-0.924310\pi$
$827$		−	13.5478i		−	0.471103i	0.971862	−	0.235551i	$-0.0756896\pi$
$828$		0			0
$829$	52.4752			1.82254			0.911270	−	0.411809i	$-0.135103\pi$
$829$	52.4752			1.82254			0.911270	+	0.411809i	$0.135103\pi$
$830$	9.36480	−	5.40677i	0.325057	−	0.187672i
$831$		0			0
$832$	−0.680923	+	3.54067i	−0.0236068	+	0.122751i
$833$	2.47814	−	4.29227i	0.0858626	−	0.148718i
$834$		0			0
$835$	5.52943	+	9.57726i	0.191354	+	0.331435i
$836$	−26.7221			−0.924202
$837$		0			0
$838$			11.6609i			0.402820i
$839$	−42.6368	+	24.6164i	−1.47199	+	0.849852i	−0.999504	−	0.0314877i	$-0.989976\pi$
$839$	−42.6368	+	24.6164i	−1.47199	+	0.849852i	−0.472483	+	0.881340i	$0.656642\pi$
$840$		0			0
$841$	−30.1805	+	52.2742i	−1.04071	+	1.80256i
$842$	0.817233	−	1.41549i	0.0281637	−	0.0487810i
$843$		0			0
$844$	4.13986	+	7.17045i	0.142500	+	0.246817i
$845$	−23.5928	−	29.9508i	−0.811616	−	1.03034i
$846$		0			0
$847$		−	34.6442i		−	1.19039i
$848$	−4.34238	−	7.52122i	−0.149118	−	0.258280i
$849$		0			0
$850$	7.20889	+	4.16206i	0.247263	+	0.142757i
$851$	−4.69621	−	2.71136i	−0.160984	−	0.0929442i
$852$		0			0
$853$	38.8350	−	22.4214i	1.32969	−	0.767695i	0.344436	−	0.938810i	$-0.388070\pi$
$853$	38.8350	−	22.4214i	1.32969	−	0.767695i	0.985251	+	0.171115i	$0.0547370\pi$
$854$	−1.90574			−0.0652132
$855$		0			0
$856$			0.329555i			0.0112639i
$857$	18.8779	+	32.6976i	0.644858	+	1.11693i	0.984334	+	0.176313i	$0.0564169\pi$
$857$	18.8779	+	32.6976i	0.644858	+	1.11693i	−0.339476	+	0.940615i	$0.610250\pi$
$858$		0			0
$859$	15.3522	−	26.5909i	0.523812	−	0.907269i	−0.475804	−	0.879551i	$-0.657843\pi$
$859$	15.3522	−	26.5909i	0.523812	−	0.907269i	0.999616	−	0.0277174i	$-0.00882386\pi$
$860$	−8.86832	−	5.12013i	−0.302407	−	0.174595i
$861$		0			0
$862$	−1.46322	−	2.53438i	−0.0498376	−	0.0863212i
$863$			4.16398i			0.141744i	0.997485	+	0.0708718i	$0.0225781\pi$
$863$			4.16398i			0.141744i	−0.997485	+	0.0708718i	$0.977422\pi$
$864$		0			0
$865$		−	31.8315i		−	1.08230i
$866$	29.4249	−	16.9885i	0.999899	−	0.577292i
$867$		0			0
$868$	6.85651	−	11.8758i	0.232725	−	0.403091i
$869$	13.6251	+	7.86644i	0.462199	+	0.266851i
$870$		0			0
$871$	26.3799	−	30.4689i	0.893848	−	1.03240i
$872$	−9.64927			−0.326765
$873$		0			0
$874$	−43.3838			−1.46748
$875$	−4.51874	−	7.82668i	−0.152761	−	0.264590i
$876$		0			0
$877$	1.86139	+	1.07467i	0.0628547	+	0.0362892i	0.531098	−	0.847310i	$-0.321780\pi$
$877$	1.86139	+	1.07467i	0.0628547	+	0.0362892i	−0.468243	+	0.883600i	$0.655113\pi$
$878$	−14.2836	−	8.24661i	−0.482047	−	0.278310i
$879$		0			0
$880$	−7.58044	−	13.1297i	−0.255536	−	0.442602i
$881$	5.95507			0.200632			0.100316	−	0.994956i	$-0.468015\pi$
$881$	5.95507			0.200632			0.100316	+	0.994956i	$0.468015\pi$
$882$		0			0
$883$	−27.9174			−0.939495			−0.469747	−	0.882801i	$-0.655655\pi$
$883$	−27.9174			−0.939495			−0.469747	+	0.882801i	$0.655655\pi$
$884$	6.30009	+	5.45460i	0.211895	+	0.183458i
$885$		0			0
$886$	25.0774	+	14.4784i	0.842491	+	0.486412i
$887$	24.7256	−	42.8261i	0.830206	−	1.43796i	−0.0676692	−	0.997708i	$-0.521556\pi$
$887$	24.7256	−	42.8261i	0.830206	−	1.43796i	0.897875	−	0.440251i	$-0.145110\pi$
$888$		0			0
$889$	−17.2389	+	9.95287i	−0.578173	+	0.333809i
$890$			9.81476i			0.328991i
$891$		0			0
$892$		−	14.3199i		−	0.479464i
$893$	14.3047	+	24.7764i	0.478687	+	0.829111i
$894$		0			0
$895$	37.1844	+	21.4684i	1.24294	+	0.717611i
$896$	1.10177	−	1.90832i	0.0368075	−	0.0637524i
$897$		0			0
$898$	19.0646	+	33.0209i	0.636194	+	1.10192i
$899$		−	58.8284i		−	1.96204i
$900$		0			0
$901$	−20.0725			−0.668713
$902$	3.48896	−	2.01435i	0.116170	−	0.0670706i
$903$		0			0
$904$	−2.62588	−	1.51605i	−0.0873354	−	0.0504231i
$905$	−7.14617	−	4.12584i	−0.237547	−	0.137148i
$906$		0			0
$907$	−14.8172	−	25.6642i	−0.491998	−	0.852166i	0.507959	−	0.861381i	$-0.330400\pi$
$907$	−14.8172	−	25.6642i	−0.491998	−	0.852166i	−0.999958	+	0.00921522i	$0.997067\pi$
$908$			20.0169i			0.664284i
$909$		0			0
$910$	7.63003	+	22.0167i	0.252933	+	0.729847i
$911$	29.0315	+	50.2840i	0.961855	+	1.66598i	0.717837	+	0.696211i	$0.245132\pi$
$911$	29.0315	+	50.2840i	0.961855	+	1.66598i	0.244018	+	0.969771i	$0.421534\pi$
$912$		0			0
$913$	−9.52981	+	16.5061i	−0.315391	+	0.546272i
$914$	15.6771	−	27.1535i	0.518552	−	0.898158i
$915$		0			0
$916$	−2.23215	+	1.28873i	−0.0737524	+	0.0425809i
$917$			38.3794i			1.26740i
$918$		0			0
$919$	−27.6437			−0.911882			−0.455941	−	0.890010i	$-0.650697\pi$
$919$	−27.6437			−0.911882			−0.455941	+	0.890010i	$0.650697\pi$
$920$	−12.3070	−	21.3163i	−0.405749	−	0.702778i
$921$		0			0
$922$	11.8447	−	20.5156i	0.390084	−	0.675645i
$923$	45.8478	+	8.81721i	1.50910	+	0.290222i
$924$		0			0
$925$	−2.01534	+	1.16356i	−0.0662639	+	0.0382575i
$926$	6.76587			0.222340
$927$		0			0
$928$		−	9.45310i		−	0.310313i
$929$	30.2473	−	17.4633i	0.992383	−	0.572953i	0.0863975	−	0.996261i	$-0.472464\pi$
$929$	30.2473	−	17.4633i	0.992383	−	0.572953i	0.905986	+	0.423308i	$0.139131\pi$
$930$		0			0
$931$	9.60014	+	5.54264i	0.314632	+	0.181653i
$932$	−7.02058	+	12.1600i	−0.229967	+	0.398314i
$933$		0			0
$934$	−24.9473	+	14.4033i	−0.816299	+	0.471290i
$935$	−35.0404			−1.14594
$936$		0			0
$937$	−8.39681			−0.274312			−0.137156	−	0.990549i	$-0.543796\pi$
$937$	−8.39681			−0.274312			−0.137156	+	0.990549i	$0.543796\pi$
$938$	−21.3307	+	12.3153i	−0.696473	+	0.402109i
$939$		0			0
$940$	−8.11580	+	14.0570i	−0.264708	+	0.458488i
$941$	21.9949	+	12.6987i	0.717013	+	0.413967i	0.813652	−	0.581352i	$-0.197476\pi$
$941$	21.9949	+	12.6987i	0.717013	+	0.413967i	−0.0966396	+	0.995319i	$0.530809\pi$
$942$		0			0
$943$	5.66440	−	3.27034i	0.184458	−	0.106497i
$944$		−	2.99070i		−	0.0973390i
$945$		0			0
$946$	18.0492			0.586829
$947$	−21.2779	+	12.2848i	−0.691440	+	0.399203i	−0.804151	−	0.594425i	$-0.797380\pi$
$947$	−21.2779	+	12.2848i	−0.691440	+	0.399203i	0.112711	+	0.993628i	$0.464046\pi$
$948$		0			0
$949$	15.1375	+	2.91117i	0.491385	+	0.0945006i
$950$	−9.30889	+	16.1235i	−0.302020	+	0.523115i
$951$		0			0
$952$	−2.54645	−	4.41058i	−0.0825309	−	0.142948i
$953$	−47.5723			−1.54102			−0.770509	−	0.637429i	$-0.779998\pi$
$953$	−47.5723			−1.54102			−0.770509	+	0.637429i	$0.779998\pi$
$954$		0			0
$955$		−	25.7398i		−	0.832921i
$956$	−4.07262	+	2.35133i	−0.131718	+	0.0760474i
$957$		0			0
$958$	−20.1840	+	34.9597i	−0.652115	+	1.12950i
$959$	5.35020	−	9.26681i	0.172767	−	0.299241i
$960$		0			0
$961$	3.86401	+	6.69266i	0.124646	+	0.215892i
$962$	−2.20124	+	0.762853i	−0.0709708	+	0.0245954i
$963$		0			0
$964$		−	22.6013i		−	0.727939i
$965$	23.2033	+	40.1893i	0.746941	+	1.29374i
$966$		0			0
$967$	37.3323	+	21.5538i	1.20053	+	0.693124i	0.960672	−	0.277685i	$-0.0895671\pi$
$967$	37.3323	+	21.5538i	1.20053	+	0.693124i	0.239854	+	0.970809i	$0.422900\pi$
$968$	13.6157	+	7.86104i	0.437626	+	0.252663i
$969$		0			0
$970$	−3.78687	+	2.18635i	−0.121589	+	0.0701994i
$971$	−14.7164			−0.472272			−0.236136	−	0.971720i	$-0.575881\pi$
$971$	−14.7164			−0.472272			−0.236136	+	0.971720i	$0.575881\pi$
$972$		0			0
$973$		−	25.6607i		−	0.822646i
$974$	−20.4933	−	35.4954i	−0.656648	−	1.13735i
$975$		0			0
$976$	0.432428	−	0.748988i	0.0138417	−	0.0239745i
$977$	5.12243	+	2.95743i	0.163881	+	0.0946167i	0.579697	−	0.814832i	$-0.303171\pi$
$977$	5.12243	+	2.95743i	0.163881	+	0.0946167i	−0.415816	+	0.909449i	$0.636504\pi$
$978$		0			0
$979$	−8.64959	−	14.9815i	−0.276442	−	0.478812i
$980$			6.28928i			0.200904i
$981$		0			0
$982$		−	8.51938i		−	0.271864i
$983$	12.6626	−	7.31074i	0.403873	−	0.233176i	−0.284281	−	0.958741i	$-0.591755\pi$
$983$	12.6626	−	7.31074i	0.403873	−	0.233176i	0.688154	+	0.725565i	$0.258421\pi$
$984$		0			0
$985$	−0.580288	+	1.00509i	−0.0184895	+	0.0320248i
$986$	−18.9212	−	10.9242i	−0.602575	−	0.347897i
$987$		0			0
$988$	−12.1998	+	14.0908i	−0.388128	+	0.448289i
$989$	29.3031			0.931786
$990$		0			0
$991$	35.1127			1.11539			0.557696	−	0.830045i	$-0.311685\pi$
$991$	35.1127			1.11539			0.557696	+	0.830045i	$0.311685\pi$
$992$	3.11159	+	5.38944i	0.0987932	+	0.171115i
$993$		0			0
$994$	−24.7106	−	14.2667i	−0.783774	−	0.452512i
$995$	8.13576	+	4.69718i	0.257921	+	0.148911i
$996$		0			0
$997$	17.6651	+	30.5968i	0.559459	+	0.969011i	0.997542	+	0.0700765i	$0.0223243\pi$
$997$	17.6651	+	30.5968i	0.559459	+	0.969011i	−0.438083	+	0.898935i	$0.644342\pi$
$998$	−21.9355			−0.694355
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.t.a.415.6		28
3.2	odd	2		234.2.t.a.103.9	yes	28
9.2	odd	6		234.2.t.a.25.2	✓	28
9.4	even	3		2106.2.b.d.649.2		14
9.5	odd	6		2106.2.b.c.649.13		14
9.7	even	3	inner	702.2.t.a.181.9		28
13.12	even	2	inner	702.2.t.a.415.9		28
39.38	odd	2		234.2.t.a.103.2	yes	28
117.25	even	6	inner	702.2.t.a.181.6		28
117.38	odd	6		234.2.t.a.25.9	yes	28
117.77	odd	6		2106.2.b.c.649.2		14
117.103	even	6		2106.2.b.d.649.13		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.t.a.25.2	✓	28	9.2	odd	6
234.2.t.a.25.9	yes	28	117.38	odd	6
234.2.t.a.103.2	yes	28	39.38	odd	2
234.2.t.a.103.9	yes	28	3.2	odd	2
702.2.t.a.181.6		28	117.25	even	6	inner
702.2.t.a.181.9		28	9.7	even	3	inner
702.2.t.a.415.6		28	1.1	even	1	trivial
702.2.t.a.415.9		28	13.12	even	2	inner
2106.2.b.c.649.2		14	117.77	odd	6
2106.2.b.c.649.13		14	9.5	odd	6
2106.2.b.d.649.2		14	9.4	even	3
2106.2.b.d.649.13		14	117.103	even	6

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:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.53992 + 1.46642i) q^{5} +(1.90832 - 1.10177i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.53992 + 1.46642i) q^{5} +(1.90832 - 1.10177i) q^{7} +1.00000i q^{8} -2.93284 q^{10} +(4.47678 - 2.58467i) q^{11} +(0.680923 - 3.54067i) q^{13} +(-1.10177 + 1.90832i) q^{14} +(-0.500000 - 0.866025i) q^{16} -2.31124 q^{17} -5.16934i q^{19} +(2.53992 - 1.46642i) q^{20} +(-2.58467 + 4.47678i) q^{22} +(-4.19626 + 7.26814i) q^{23} +(1.80079 + 3.11906i) q^{25} +(1.18064 + 3.40677i) q^{26} -2.20354i q^{28} +(-4.72655 - 8.18662i) q^{29} +(5.38944 + 3.11159i) q^{31} +(0.866025 + 0.500000i) q^{32} +(2.00159 - 1.15562i) q^{34} +6.46263 q^{35} +0.646136i q^{37} +(2.58467 + 4.47678i) q^{38} +(-1.46642 + 2.53992i) q^{40} +(-0.674934 - 0.389673i) q^{41} +(-1.74579 - 3.02379i) q^{43} -5.16934i q^{44} -8.39252i q^{46} +(-4.79295 + 2.76721i) q^{47} +(-1.07221 + 1.85713i) q^{49} +(-3.11906 - 1.80079i) q^{50} +(-2.72585 - 2.36003i) q^{52} +8.68475 q^{53} +15.1609 q^{55} +(1.10177 + 1.90832i) q^{56} +(8.18662 + 4.72655i) q^{58} +(2.59002 + 1.49535i) q^{59} +(0.432428 + 0.748988i) q^{61} -6.22318 q^{62} -1.00000 q^{64} +(6.92161 - 7.99449i) q^{65} +(9.68023 + 5.58888i) q^{67} +(-1.15562 + 2.00159i) q^{68} +(-5.59680 + 3.23131i) q^{70} +12.9489i q^{71} +4.27533i q^{73} +(-0.323068 - 0.559571i) q^{74} +(-4.47678 - 2.58467i) q^{76} +(5.69541 - 9.86475i) q^{77} +(1.52175 + 2.63575i) q^{79} -2.93284i q^{80} +0.779346 q^{82} +(-3.19308 + 1.84352i) q^{83} +(-5.87036 - 3.38925i) q^{85} +(3.02379 + 1.74579i) q^{86} +(2.58467 + 4.47678i) q^{88} -3.34650i q^{89} +(-2.60158 - 7.50694i) q^{91} +(4.19626 + 7.26814i) q^{92} +(2.76721 - 4.79295i) q^{94} +(7.58044 - 13.1297i) q^{95} +(1.29119 - 0.745470i) q^{97} -2.14443i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 14 q^{4}+O(q^{10}) \) 28 * q + 14 * q^4	\( 28 q + 14 q^{4} + 2 q^{13} - 8 q^{14} - 14 q^{16} - 16 q^{17} + 8 q^{23} + 14 q^{25} - 8 q^{26} + 16 q^{29} + 68 q^{35} - 4 q^{43} + 10 q^{49} - 2 q^{52} + 120 q^{53} + 8 q^{56} + 28 q^{61} - 68 q^{62} - 28 q^{64} + 8 q^{65} - 8 q^{68} - 16 q^{74} + 24 q^{77} + 28 q^{79} - 48 q^{82} - 8 q^{92}+O(q^{100}) \) 28 * q + 14 * q^4 + 2 * q^13 - 8 * q^14 - 14 * q^16 - 16 * q^17 + 8 * q^23 + 14 * q^25 - 8 * q^26 + 16 * q^29 + 68 * q^35 - 4 * q^43 + 10 * q^49 - 2 * q^52 + 120 * q^53 + 8 * q^56 + 28 * q^61 - 68 * q^62 - 28 * q^64 + 8 * q^65 - 8 * q^68 - 16 * q^74 + 24 * q^77 + 28 * q^79 - 48 * q^82 - 8 * q^92

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