LMFDB - Embedded newform 880.2.bd.c.417.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [880,2,Mod(417,880)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(880, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))

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

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

chi := DirichletCharacter("880.417");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.bd (of order $4$, 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:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 110)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			417.1
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	880.417
Dual form			880.2.bd.c.593.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.70711 + 1.70711i) q^{3} +(-0.707107 + 2.12132i) q^{5} +(-2.12132 + 2.12132i) q^{7} -2.82843i q^{9} +(1.41421 + 3.00000i) q^{11} +(3.00000 + 3.00000i) q^{13} +(-2.41421 - 4.82843i) q^{15} +(-5.12132 + 5.12132i) q^{17} +3.00000 q^{19} -7.24264i q^{21} +(0.171573 - 0.171573i) q^{23} +(-4.00000 - 3.00000i) q^{25} +(-0.292893 - 0.292893i) q^{27} -1.24264 q^{29} +7.24264 q^{31} +(-7.53553 - 2.70711i) q^{33} +(-3.00000 - 6.00000i) q^{35} +(0.121320 + 0.121320i) q^{37} -10.2426 q^{39} -1.75736i q^{41} +(-1.24264 - 1.24264i) q^{43} +(6.00000 + 2.00000i) q^{45} +(-4.41421 - 4.41421i) q^{47} -2.00000i q^{49} -17.4853i q^{51} +(9.53553 - 9.53553i) q^{53} +(-7.36396 + 0.878680i) q^{55} +(-5.12132 + 5.12132i) q^{57} -1.41421i q^{59} -7.24264i q^{61} +(6.00000 + 6.00000i) q^{63} +(-8.48528 + 4.24264i) q^{65} +(4.00000 + 4.00000i) q^{67} +0.585786i q^{69} +1.24264 q^{71} +(6.00000 + 6.00000i) q^{73} +(11.9497 - 1.70711i) q^{75} +(-9.36396 - 3.36396i) q^{77} -10.2426 q^{79} +9.48528 q^{81} +(7.24264 + 7.24264i) q^{83} +(-7.24264 - 14.4853i) q^{85} +(2.12132 - 2.12132i) q^{87} +5.48528i q^{89} -12.7279 q^{91} +(-12.3640 + 12.3640i) q^{93} +(-2.12132 + 6.36396i) q^{95} +(-2.24264 - 2.24264i) q^{97} +(8.48528 - 4.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} + 12 q^{13} - 4 q^{15} - 12 q^{17} + 12 q^{19} + 12 q^{23} - 16 q^{25} - 4 q^{27} + 12 q^{29} + 12 q^{31} - 16 q^{33} - 12 q^{35} - 8 q^{37} - 24 q^{39} + 12 q^{43} + 24 q^{45} - 12 q^{47}+ \cdots + 8 q^{97}+O(q^{100}) $ 4 * q - 4 * q^3 + 12 * q^13 - 4 * q^15 - 12 * q^17 + 12 * q^19 + 12 * q^23 - 16 * q^25 - 4 * q^27 + 12 * q^29 + 12 * q^31 - 16 * q^33 - 12 * q^35 - 8 * q^37 - 24 * q^39 + 12 * q^43 + 24 * q^45 - 12 * q^47 + 24 * q^53 - 4 * q^55 - 12 * q^57 + 24 * q^63 + 16 * q^67 - 12 * q^71 + 24 * q^73 + 28 * q^75 - 12 * q^77 - 24 * q^79 + 4 * q^81 + 12 * q^83 - 12 * q^85 - 24 * q^93 + 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.70711	+	1.70711i	−0.985599	+	0.985599i	−0.999898	−	0.0142992i	$-0.995448\pi$
$3$	−1.70711	+	1.70711i	−0.985599	+	0.985599i	0.0142992	+	0.999898i	$0.495448\pi$
$4$		0			0
$5$	−0.707107	+	2.12132i	−0.316228	+	0.948683i
$5$	−0.707107	+	2.12132i	−0.316228	+	0.948683i
$6$		0			0
$7$	−2.12132	+	2.12132i	−0.801784	+	0.801784i	−0.983374	−	0.181591i	$-0.941875\pi$
$7$	−2.12132	+	2.12132i	−0.801784	+	0.801784i	0.181591	+	0.983374i	$0.441875\pi$
$8$		0			0
$9$		−	2.82843i		−	0.942809i
$10$		0			0
$11$	1.41421	+	3.00000i	0.426401	+	0.904534i
$11$	1.41421	+	3.00000i	0.426401	+	0.904534i
$12$		0			0
$13$	3.00000	+	3.00000i	0.832050	+	0.832050i	0.987797	−	0.155747i	$-0.0497784\pi$
$13$	3.00000	+	3.00000i	0.832050	+	0.832050i	−0.155747	+	0.987797i	$0.549778\pi$
$14$		0			0
$15$	−2.41421	−	4.82843i	−0.623347	−	1.24669i
$16$		0			0
$17$	−5.12132	+	5.12132i	−1.24210	+	1.24210i	−0.282975	+	0.959127i	$0.591322\pi$
$17$	−5.12132	+	5.12132i	−1.24210	+	1.24210i	−0.959127	+	0.282975i	$0.908678\pi$
$18$		0			0
$19$	3.00000			0.688247			0.344124	−	0.938924i	$-0.388176\pi$
$19$	3.00000			0.688247			0.344124	+	0.938924i	$0.388176\pi$
$20$		0			0
$21$		−	7.24264i		−	1.58047i
$22$		0			0
$23$	0.171573	−	0.171573i	0.0357754	−	0.0357754i	−0.688993	−	0.724768i	$-0.741947\pi$
$23$	0.171573	−	0.171573i	0.0357754	−	0.0357754i	0.724768	+	0.688993i	$0.241947\pi$
$24$		0			0
$25$	−4.00000	−	3.00000i	−0.800000	−	0.600000i
$26$		0			0
$27$	−0.292893	−	0.292893i	−0.0563673	−	0.0563673i
$28$		0			0
$29$	−1.24264			−0.230753			−0.115376	−	0.993322i	$-0.536807\pi$
$29$	−1.24264			−0.230753			−0.115376	+	0.993322i	$0.536807\pi$
$30$		0			0
$31$	7.24264			1.30082			0.650408	−	0.759585i	$-0.274598\pi$
$31$	7.24264			1.30082			0.650408	+	0.759585i	$0.274598\pi$
$32$		0			0
$33$	−7.53553	−	2.70711i	−1.31177	−	0.471247i
$34$		0			0
$35$	−3.00000	−	6.00000i	−0.507093	−	1.01419i
$36$		0			0
$37$	0.121320	+	0.121320i	0.0199449	+	0.0199449i	0.717009	−	0.697064i	$-0.245511\pi$
$37$	0.121320	+	0.121320i	0.0199449	+	0.0199449i	−0.697064	+	0.717009i	$0.745511\pi$
$38$		0			0
$39$	−10.2426			−1.64014
$40$		0			0
$41$		−	1.75736i		−	0.274453i	−0.990540	−	0.137227i	$-0.956181\pi$
$41$		−	1.75736i		−	0.274453i	0.990540	−	0.137227i	$-0.0438189\pi$
$42$		0			0
$43$	−1.24264	−	1.24264i	−0.189501	−	0.189501i	0.605979	−	0.795480i	$-0.292781\pi$
$43$	−1.24264	−	1.24264i	−0.189501	−	0.189501i	−0.795480	+	0.605979i	$0.792781\pi$
$44$		0			0
$45$	6.00000	+	2.00000i	0.894427	+	0.298142i
$46$		0			0
$47$	−4.41421	−	4.41421i	−0.643879	−	0.643879i	0.307628	−	0.951507i	$-0.400465\pi$
$47$	−4.41421	−	4.41421i	−0.643879	−	0.643879i	−0.951507	+	0.307628i	$0.900465\pi$
$48$		0			0
$49$		−	2.00000i		−	0.285714i
$50$		0			0
$51$		−	17.4853i		−	2.44843i
$52$		0			0
$53$	9.53553	−	9.53553i	1.30981	−	1.30981i	0.388254	−	0.921552i	$-0.373078\pi$
$53$	9.53553	−	9.53553i	1.30981	−	1.30981i	0.921552	−	0.388254i	$-0.126922\pi$
$54$		0			0
$55$	−7.36396	+	0.878680i	−0.992956	+	0.118481i
$56$		0			0
$57$	−5.12132	+	5.12132i	−0.678335	+	0.678335i
$58$		0			0
$59$		−	1.41421i		−	0.184115i	−0.995754	−	0.0920575i	$-0.970656\pi$
$59$		−	1.41421i		−	0.184115i	0.995754	−	0.0920575i	$-0.0293443\pi$
$60$		0			0
$61$		−	7.24264i		−	0.927325i	−0.886012	−	0.463663i	$-0.846535\pi$
$61$		−	7.24264i		−	0.927325i	0.886012	−	0.463663i	$-0.153465\pi$
$62$		0			0
$63$	6.00000	+	6.00000i	0.755929	+	0.755929i
$64$		0			0
$65$	−8.48528	+	4.24264i	−1.05247	+	0.526235i
$66$		0			0
$67$	4.00000	+	4.00000i	0.488678	+	0.488678i	0.907889	−	0.419211i	$-0.137693\pi$
$67$	4.00000	+	4.00000i	0.488678	+	0.488678i	−0.419211	+	0.907889i	$0.637693\pi$
$68$		0			0
$69$			0.585786i			0.0705204i
$70$		0			0
$71$	1.24264			0.147474			0.0737372	−	0.997278i	$-0.476507\pi$
$71$	1.24264			0.147474			0.0737372	+	0.997278i	$0.476507\pi$
$72$		0			0
$73$	6.00000	+	6.00000i	0.702247	+	0.702247i	0.964892	−	0.262646i	$-0.0845950\pi$
$73$	6.00000	+	6.00000i	0.702247	+	0.702247i	−0.262646	+	0.964892i	$0.584595\pi$
$74$		0			0
$75$	11.9497	−	1.70711i	1.37984	−	0.197120i
$76$		0			0
$77$	−9.36396	−	3.36396i	−1.06712	−	0.383359i
$78$		0			0
$79$	−10.2426			−1.15239			−0.576194	−	0.817313i	$-0.695463\pi$
$79$	−10.2426			−1.15239			−0.576194	+	0.817313i	$0.695463\pi$
$80$		0			0
$81$	9.48528			1.05392
$82$		0			0
$83$	7.24264	+	7.24264i	0.794983	+	0.794983i	0.982300	−	0.187317i	$-0.0599790\pi$
$83$	7.24264	+	7.24264i	0.794983	+	0.794983i	−0.187317	+	0.982300i	$0.559979\pi$
$84$		0			0
$85$	−7.24264	−	14.4853i	−0.785575	−	1.57115i
$86$		0			0
$87$	2.12132	−	2.12132i	0.227429	−	0.227429i
$88$		0			0
$89$			5.48528i			0.581439i	0.956808	+	0.290719i	$0.0938946\pi$
$89$			5.48528i			0.581439i	−0.956808	+	0.290719i	$0.906105\pi$
$90$		0			0
$91$	−12.7279			−1.33425
$92$		0			0
$93$	−12.3640	+	12.3640i	−1.28208	+	1.28208i
$94$		0			0
$95$	−2.12132	+	6.36396i	−0.217643	+	0.652929i
$96$		0			0
$97$	−2.24264	−	2.24264i	−0.227706	−	0.227706i	0.584028	−	0.811734i	$-0.301476\pi$
$97$	−2.24264	−	2.24264i	−0.227706	−	0.227706i	−0.811734	+	0.584028i	$0.801476\pi$
$98$		0			0
$99$	8.48528	−	4.00000i	0.852803	−	0.402015i
$100$		0			0
$101$		−	2.48528i		−	0.247295i	−0.992326	−	0.123647i	$-0.960541\pi$
$101$		−	2.48528i		−	0.247295i	0.992326	−	0.123647i	$-0.0394592\pi$
$102$		0			0
$103$	−6.24264	+	6.24264i	−0.615106	+	0.615106i	−0.944272	−	0.329166i	$-0.893232\pi$
$103$	−6.24264	+	6.24264i	−0.615106	+	0.615106i	0.329166	+	0.944272i	$0.393232\pi$
$104$		0			0
$105$	15.3640	+	5.12132i	1.49937	+	0.499790i
$106$		0			0
$107$	−10.2426	+	10.2426i	−0.990193	+	0.990193i	−0.999952	−	0.00975893i	$-0.996894\pi$
$107$	−10.2426	+	10.2426i	−0.990193	+	0.990193i	0.00975893	+	0.999952i	$0.496894\pi$
$108$		0			0
$109$	2.48528			0.238047			0.119023	−	0.992891i	$-0.462024\pi$
$109$	2.48528			0.238047			0.119023	+	0.992891i	$0.462024\pi$
$110$		0			0
$111$	−0.414214			−0.0393154
$112$		0			0
$113$	−4.41421	+	4.41421i	−0.415254	+	0.415254i	−0.883564	−	0.468310i	$-0.844863\pi$
$113$	−4.41421	+	4.41421i	−0.415254	+	0.415254i	0.468310	+	0.883564i	$0.344863\pi$
$114$		0			0
$115$	0.242641	+	0.485281i	0.0226264	+	0.0452527i
$116$		0			0
$117$	8.48528	−	8.48528i	0.784465	−	0.784465i
$118$		0			0
$119$		−	21.7279i		−	1.99180i
$120$		0			0
$121$	−7.00000	+	8.48528i	−0.636364	+	0.771389i
$122$		0			0
$123$	3.00000	+	3.00000i	0.270501	+	0.270501i
$124$		0			0
$125$	9.19239	−	6.36396i	0.822192	−	0.569210i
$126$		0			0
$127$	4.24264	−	4.24264i	0.376473	−	0.376473i	−0.493355	−	0.869828i	$-0.664230\pi$
$127$	4.24264	−	4.24264i	0.376473	−	0.376473i	0.869828	+	0.493355i	$0.164230\pi$
$128$		0			0
$129$	4.24264			0.373544
$130$		0			0
$131$			13.9706i			1.22061i	0.792165	+	0.610307i	$0.208954\pi$
$131$			13.9706i			1.22061i	−0.792165	+	0.610307i	$0.791046\pi$
$132$		0			0
$133$	−6.36396	+	6.36396i	−0.551825	+	0.551825i
$134$		0			0
$135$	0.828427	−	0.414214i	0.0712997	−	0.0356498i
$136$		0			0
$137$	−11.6569	−	11.6569i	−0.995912	−	0.995912i	0.00407941	−	0.999992i	$-0.498701\pi$
$137$	−11.6569	−	11.6569i	−0.995912	−	0.995912i	−0.999992	+	0.00407941i	$0.998701\pi$
$138$		0			0
$139$	14.4853			1.22863			0.614313	−	0.789063i	$-0.289433\pi$
$139$	14.4853			1.22863			0.614313	+	0.789063i	$0.289433\pi$
$140$		0			0
$141$	15.0711			1.26921
$142$		0			0
$143$	−4.75736	+	13.2426i	−0.397830	+	1.10741i
$144$		0			0
$145$	0.878680	−	2.63604i	0.0729704	−	0.218911i
$146$		0			0
$147$	3.41421	+	3.41421i	0.281600	+	0.281600i
$148$		0			0
$149$	−19.2426			−1.57642			−0.788209	−	0.615407i	$-0.788992\pi$
$149$	−19.2426			−1.57642			−0.788209	+	0.615407i	$0.788992\pi$
$150$		0			0
$151$		−	12.0000i		−	0.976546i	−0.872691	−	0.488273i	$-0.837627\pi$
$151$		−	12.0000i		−	0.976546i	0.872691	−	0.488273i	$-0.162373\pi$
$152$		0			0
$153$	14.4853	+	14.4853i	1.17107	+	1.17107i
$154$		0			0
$155$	−5.12132	+	15.3640i	−0.411354	+	1.23406i
$156$		0			0
$157$	16.3640	+	16.3640i	1.30599	+	1.30599i	0.924286	+	0.381700i	$0.124661\pi$
$157$	16.3640	+	16.3640i	1.30599	+	1.30599i	0.381700	+	0.924286i	$0.375339\pi$
$158$		0			0
$159$			32.5563i			2.58189i
$160$		0			0
$161$			0.727922i			0.0573683i
$162$		0			0
$163$	13.8492	−	13.8492i	1.08476	−	1.08476i	0.0886978	−	0.996059i	$-0.471729\pi$
$163$	13.8492	−	13.8492i	1.08476	−	1.08476i	0.996059	−	0.0886978i	$-0.0282705\pi$
$164$		0			0
$165$	11.0711	−	14.0711i	0.861881	−	1.09543i
$166$		0			0
$167$	6.36396	−	6.36396i	0.492458	−	0.492458i	−0.416622	−	0.909080i	$-0.636786\pi$
$167$	6.36396	−	6.36396i	0.492458	−	0.492458i	0.909080	+	0.416622i	$0.136786\pi$
$168$		0			0
$169$			5.00000i			0.384615i
$170$		0			0
$171$		−	8.48528i		−	0.648886i
$172$		0			0
$173$	16.2426	+	16.2426i	1.23491	+	1.23491i	0.962057	+	0.272848i	$0.0879656\pi$
$173$	16.2426	+	16.2426i	1.23491	+	1.23491i	0.272848	+	0.962057i	$0.412034\pi$
$174$		0			0
$175$	14.8492	−	2.12132i	1.12250	−	0.160357i
$176$		0			0
$177$	2.41421	+	2.41421i	0.181463	+	0.181463i
$178$		0			0
$179$			13.7574i			1.02827i	0.857708	+	0.514137i	$0.171888\pi$
$179$			13.7574i			1.02827i	−0.857708	+	0.514137i	$0.828112\pi$
$180$		0			0
$181$	12.0000			0.891953			0.445976	−	0.895045i	$-0.352856\pi$
$181$	12.0000			0.891953			0.445976	+	0.895045i	$0.352856\pi$
$182$		0			0
$183$	12.3640	+	12.3640i	0.913970	+	0.913970i
$184$		0			0
$185$	−0.343146	+	0.171573i	−0.0252286	+	0.0126143i
$186$		0			0
$187$	−22.6066	−	8.12132i	−1.65316	−	0.593890i
$188$		0			0
$189$	1.24264			0.0903888
$190$		0			0
$191$	−2.82843			−0.204658			−0.102329	−	0.994751i	$-0.532629\pi$
$191$	−2.82843			−0.204658			−0.102329	+	0.994751i	$0.532629\pi$
$192$		0			0
$193$	0.878680	+	0.878680i	0.0632487	+	0.0632487i	0.738024	−	0.674775i	$-0.235759\pi$
$193$	0.878680	+	0.878680i	0.0632487	+	0.0632487i	−0.674775	+	0.738024i	$0.735759\pi$
$194$		0			0
$195$	7.24264	−	21.7279i	0.518656	−	1.55597i
$196$		0			0
$197$	−1.24264	+	1.24264i	−0.0885345	+	0.0885345i	−0.749987	−	0.661453i	$-0.769940\pi$
$197$	−1.24264	+	1.24264i	−0.0885345	+	0.0885345i	0.661453	+	0.749987i	$0.269940\pi$
$198$		0			0
$199$		−	4.75736i		−	0.337240i	−0.985681	−	0.168620i	$-0.946069\pi$
$199$		−	4.75736i		−	0.337240i	0.985681	−	0.168620i	$-0.0539311\pi$
$200$		0			0
$201$	−13.6569			−0.963280
$202$		0			0
$203$	2.63604	−	2.63604i	0.185014	−	0.185014i
$204$		0			0
$205$	3.72792	+	1.24264i	0.260369	+	0.0867898i
$206$		0			0
$207$	−0.485281	−	0.485281i	−0.0337294	−	0.0337294i
$208$		0			0
$209$	4.24264	+	9.00000i	0.293470	+	0.622543i
$210$		0			0
$211$			17.4853i			1.20374i	0.798595	+	0.601868i	$0.205577\pi$
$211$			17.4853i			1.20374i	−0.798595	+	0.601868i	$0.794423\pi$
$212$		0			0
$213$	−2.12132	+	2.12132i	−0.145350	+	0.145350i
$214$		0			0
$215$	3.51472	−	1.75736i	0.239702	−	0.119851i
$216$		0			0
$217$	−15.3640	+	15.3640i	−1.04297	+	1.04297i
$218$		0			0
$219$	−20.4853			−1.38427
$220$		0			0
$221$	−30.7279			−2.06698
$222$		0			0
$223$	3.75736	−	3.75736i	0.251611	−	0.251611i	−0.570020	−	0.821631i	$-0.693064\pi$
$223$	3.75736	−	3.75736i	0.251611	−	0.251611i	0.821631	+	0.570020i	$0.193064\pi$
$224$		0			0
$225$	−8.48528	+	11.3137i	−0.565685	+	0.754247i
$226$		0			0
$227$	−15.0000	+	15.0000i	−0.995585	+	0.995585i	−0.999990	−	0.00440533i	$-0.998598\pi$
$227$	−15.0000	+	15.0000i	−0.995585	+	0.995585i	0.00440533	+	0.999990i	$0.498598\pi$
$228$		0			0
$229$		−	15.2132i		−	1.00532i	−0.864485	−	0.502658i	$-0.832355\pi$
$229$		−	15.2132i		−	1.00532i	0.864485	−	0.502658i	$-0.167645\pi$
$230$		0			0
$231$	21.7279	−	10.2426i	1.42959	−	0.673916i
$232$		0			0
$233$	1.60660	+	1.60660i	0.105252	+	0.105252i	0.757772	−	0.652520i	$-0.226288\pi$
$233$	1.60660	+	1.60660i	0.105252	+	0.105252i	−0.652520	+	0.757772i	$0.726288\pi$
$234$		0			0
$235$	12.4853	−	6.24264i	0.814450	−	0.407225i
$236$		0			0
$237$	17.4853	−	17.4853i	1.13579	−	1.13579i
$238$		0			0
$239$	0.727922			0.0470854			0.0235427	−	0.999723i	$-0.492505\pi$
$239$	0.727922			0.0470854			0.0235427	+	0.999723i	$0.492505\pi$
$240$		0			0
$241$		−	6.72792i		−	0.433384i	−0.976240	−	0.216692i	$-0.930473\pi$
$241$		−	6.72792i		−	0.433384i	0.976240	−	0.216692i	$-0.0695267\pi$
$242$		0			0
$243$	−15.3137	+	15.3137i	−0.982375	+	0.982375i
$244$		0			0
$245$	4.24264	+	1.41421i	0.271052	+	0.0903508i
$246$		0			0
$247$	9.00000	+	9.00000i	0.572656	+	0.572656i
$248$		0			0
$249$	−24.7279			−1.56707
$250$		0			0
$251$	−3.51472			−0.221847			−0.110924	−	0.993829i	$-0.535381\pi$
$251$	−3.51472			−0.221847			−0.110924	+	0.993829i	$0.535381\pi$
$252$		0			0
$253$	0.757359	+	0.272078i	0.0476148	+	0.0171054i
$254$		0			0
$255$	37.0919	+	12.3640i	2.32278	+	0.774261i
$256$		0			0
$257$	−1.92893	−	1.92893i	−0.120323	−	0.120323i	0.644381	−	0.764705i	$-0.277115\pi$
$257$	−1.92893	−	1.92893i	−0.120323	−	0.120323i	−0.764705	+	0.644381i	$0.777115\pi$
$258$		0			0
$259$	−0.514719			−0.0319831
$260$		0			0
$261$			3.51472i			0.217556i
$262$		0			0
$263$	−6.36396	−	6.36396i	−0.392419	−	0.392419i	0.483130	−	0.875549i	$-0.339500\pi$
$263$	−6.36396	−	6.36396i	−0.392419	−	0.392419i	−0.875549	+	0.483130i	$0.839500\pi$
$264$		0			0
$265$	13.4853	+	26.9706i	0.828394	+	1.65679i
$266$		0			0
$267$	−9.36396	−	9.36396i	−0.573065	−	0.573065i
$268$		0			0
$269$			19.7990i			1.20717i	0.797300	+	0.603583i	$0.206261\pi$
$269$			19.7990i			1.20717i	−0.797300	+	0.603583i	$0.793739\pi$
$270$		0			0
$271$		−	6.72792i		−	0.408692i	−0.978899	−	0.204346i	$-0.934493\pi$
$271$		−	6.72792i		−	0.408692i	0.978899	−	0.204346i	$-0.0655068\pi$
$272$		0			0
$273$	21.7279	−	21.7279i	1.31503	−	1.31503i
$274$		0			0
$275$	3.34315	−	16.2426i	0.201599	−	0.979468i
$276$		0			0
$277$	10.2426	−	10.2426i	0.615421	−	0.615421i	−0.328933	−	0.944353i	$-0.606689\pi$
$277$	10.2426	−	10.2426i	0.615421	−	0.615421i	0.944353	+	0.328933i	$0.106689\pi$
$278$		0			0
$279$		−	20.4853i		−	1.22642i
$280$		0			0
$281$			22.9706i			1.37031i	0.728398	+	0.685154i	$0.240265\pi$
$281$			22.9706i			1.37031i	−0.728398	+	0.685154i	$0.759735\pi$
$282$		0			0
$283$	−13.2426	−	13.2426i	−0.787193	−	0.787193i	0.193840	−	0.981033i	$-0.437906\pi$
$283$	−13.2426	−	13.2426i	−0.787193	−	0.787193i	−0.981033	+	0.193840i	$0.937906\pi$
$284$		0			0
$285$	−7.24264	−	14.4853i	−0.429017	−	0.858034i
$286$		0			0
$287$	3.72792	+	3.72792i	0.220052	+	0.220052i
$288$		0			0
$289$		−	35.4558i		−	2.08564i
$290$		0			0
$291$	7.65685			0.448853
$292$		0			0
$293$	−15.7279	−	15.7279i	−0.918835	−	0.918835i	0.0781097	−	0.996945i	$-0.475112\pi$
$293$	−15.7279	−	15.7279i	−0.918835	−	0.918835i	−0.996945	+	0.0781097i	$0.975112\pi$
$294$		0			0
$295$	3.00000	+	1.00000i	0.174667	+	0.0582223i
$296$		0			0
$297$	0.464466	−	1.29289i	0.0269511	−	0.0750213i
$298$		0			0
$299$	1.02944			0.0595339
$300$		0			0
$301$	5.27208			0.303878
$302$		0			0
$303$	4.24264	+	4.24264i	0.243733	+	0.243733i
$304$		0			0
$305$	15.3640	+	5.12132i	0.879738	+	0.293246i
$306$		0			0
$307$	11.4853	−	11.4853i	0.655500	−	0.655500i	−0.298812	−	0.954312i	$-0.596590\pi$
$307$	11.4853	−	11.4853i	0.655500	−	0.655500i	0.954312	+	0.298812i	$0.0965904\pi$
$308$		0			0
$309$		−	21.3137i		−	1.21249i
$310$		0			0
$311$	9.72792			0.551620			0.275810	−	0.961212i	$-0.411054\pi$
$311$	9.72792			0.551620			0.275810	+	0.961212i	$0.411054\pi$
$312$		0			0
$313$	3.75736	−	3.75736i	0.212379	−	0.212379i	−0.592899	−	0.805277i	$-0.702017\pi$
$313$	3.75736	−	3.75736i	0.212379	−	0.212379i	0.805277	+	0.592899i	$0.202017\pi$
$314$		0			0
$315$	−16.9706	+	8.48528i	−0.956183	+	0.478091i
$316$		0			0
$317$	−9.53553	−	9.53553i	−0.535569	−	0.535569i	0.386655	−	0.922224i	$-0.373630\pi$
$317$	−9.53553	−	9.53553i	−0.535569	−	0.535569i	−0.922224	+	0.386655i	$0.873630\pi$
$318$		0			0
$319$	−1.75736	−	3.72792i	−0.0983932	−	0.208724i
$320$		0			0
$321$		−	34.9706i		−	1.95187i
$322$		0			0
$323$	−15.3640	+	15.3640i	−0.854874	+	0.854874i
$324$		0			0
$325$	−3.00000	−	21.0000i	−0.166410	−	1.16487i
$326$		0			0
$327$	−4.24264	+	4.24264i	−0.234619	+	0.234619i
$328$		0			0
$329$	18.7279			1.03250
$330$		0			0
$331$	−24.7279			−1.35917			−0.679585	−	0.733597i	$-0.737840\pi$
$331$	−24.7279			−1.35917			−0.679585	+	0.733597i	$0.737840\pi$
$332$		0			0
$333$	0.343146	−	0.343146i	0.0188043	−	0.0188043i
$334$		0			0
$335$	−11.3137	+	5.65685i	−0.618134	+	0.309067i
$336$		0			0
$337$	−12.8787	+	12.8787i	−0.701546	+	0.701546i	−0.964742	−	0.263196i	$-0.915223\pi$
$337$	−12.8787	+	12.8787i	−0.701546	+	0.701546i	0.263196	+	0.964742i	$0.415223\pi$
$338$		0			0
$339$		−	15.0711i		−	0.818548i
$340$		0			0
$341$	10.2426	+	21.7279i	0.554670	+	1.17663i
$342$		0			0
$343$	−10.6066	−	10.6066i	−0.572703	−	0.572703i
$344$		0			0
$345$	−1.24264	−	0.414214i	−0.0669015	−	0.0223005i
$346$		0			0
$347$	−6.72792	+	6.72792i	−0.361174	+	0.361174i	−0.864245	−	0.503071i	$-0.832203\pi$
$347$	−6.72792	+	6.72792i	−0.361174	+	0.361174i	0.503071	+	0.864245i	$0.332203\pi$
$348$		0			0
$349$	10.9706			0.587241			0.293620	−	0.955922i	$-0.405140\pi$
$349$	10.9706			0.587241			0.293620	+	0.955922i	$0.405140\pi$
$350$		0			0
$351$		−	1.75736i		−	0.0938009i
$352$		0			0
$353$	−14.8284	+	14.8284i	−0.789238	+	0.789238i	−0.981369	−	0.192132i	$-0.938460\pi$
$353$	−14.8284	+	14.8284i	−0.789238	+	0.789238i	0.192132	+	0.981369i	$0.438460\pi$
$354$		0			0
$355$	−0.878680	+	2.63604i	−0.0466355	+	0.139906i
$356$		0			0
$357$	37.0919	+	37.0919i	1.96311	+	1.96311i
$358$		0			0
$359$	−34.9706			−1.84568			−0.922838	−	0.385189i	$-0.874136\pi$
$359$	−34.9706			−1.84568			−0.922838	+	0.385189i	$0.874136\pi$
$360$		0			0
$361$	−10.0000			−0.526316
$362$		0			0
$363$	−2.53553	−	26.4350i	−0.133081	−	1.38748i
$364$		0			0
$365$	−16.9706	+	8.48528i	−0.888280	+	0.444140i
$366$		0			0
$367$	2.00000	+	2.00000i	0.104399	+	0.104399i	0.757377	−	0.652978i	$-0.226481\pi$
$367$	2.00000	+	2.00000i	0.104399	+	0.104399i	−0.652978	+	0.757377i	$0.726481\pi$
$368$		0			0
$369$	−4.97056			−0.258757
$370$		0			0
$371$			40.4558i			2.10036i
$372$		0			0
$373$	−1.24264	−	1.24264i	−0.0643415	−	0.0643415i	0.674204	−	0.738545i	$-0.264487\pi$
$373$	−1.24264	−	1.24264i	−0.0643415	−	0.0643415i	−0.738545	+	0.674204i	$0.764487\pi$
$374$		0			0
$375$	−4.82843	+	26.5563i	−0.249339	+	1.37136i
$376$		0			0
$377$	−3.72792	−	3.72792i	−0.191998	−	0.191998i
$378$		0			0
$379$			4.97056i			0.255321i	0.991818	+	0.127660i	$0.0407467\pi$
$379$			4.97056i			0.255321i	−0.991818	+	0.127660i	$0.959253\pi$
$380$		0			0
$381$			14.4853i			0.742103i
$382$		0			0
$383$	1.41421	−	1.41421i	0.0722629	−	0.0722629i	−0.670052	−	0.742315i	$-0.733728\pi$
$383$	1.41421	−	1.41421i	0.0722629	−	0.0722629i	0.742315	+	0.670052i	$0.233728\pi$
$384$		0			0
$385$	13.7574	−	17.4853i	0.701140	−	0.891132i
$386$		0			0
$387$	−3.51472	+	3.51472i	−0.178663	+	0.178663i
$388$		0			0
$389$			2.82843i			0.143407i	0.997426	+	0.0717035i	$0.0228435\pi$
$389$			2.82843i			0.143407i	−0.997426	+	0.0717035i	$0.977156\pi$
$390$		0			0
$391$			1.75736i			0.0888735i
$392$		0			0
$393$	−23.8492	−	23.8492i	−1.20304	−	1.20304i
$394$		0			0
$395$	7.24264	−	21.7279i	0.364417	−	1.09325i
$396$		0			0
$397$	−1.51472	−	1.51472i	−0.0760215	−	0.0760215i	0.668074	−	0.744095i	$-0.267119\pi$
$397$	−1.51472	−	1.51472i	−0.0760215	−	0.0760215i	−0.744095	+	0.668074i	$0.767119\pi$
$398$		0			0
$399$		−	21.7279i		−	1.08776i
$400$		0			0
$401$	2.31371			0.115541			0.0577705	−	0.998330i	$-0.481601\pi$
$401$	2.31371			0.115541			0.0577705	+	0.998330i	$0.481601\pi$
$402$		0			0
$403$	21.7279	+	21.7279i	1.08234	+	1.08234i
$404$		0			0
$405$	−6.70711	+	20.1213i	−0.333279	+	0.999836i
$406$		0			0
$407$	−0.192388	+	0.535534i	−0.00953633	+	0.0265454i
$408$		0			0
$409$	−22.9706			−1.13582			−0.567911	−	0.823090i	$-0.692248\pi$
$409$	−22.9706			−1.13582			−0.567911	+	0.823090i	$0.692248\pi$
$410$		0			0
$411$	39.7990			1.96314
$412$		0			0
$413$	3.00000	+	3.00000i	0.147620	+	0.147620i
$414$		0			0
$415$	−20.4853	+	10.2426i	−1.00558	+	0.502791i
$416$		0			0
$417$	−24.7279	+	24.7279i	−1.21093	+	1.21093i
$418$		0			0
$419$		−	6.00000i		−	0.293119i	−0.989202	−	0.146560i	$-0.953180\pi$
$419$		−	6.00000i		−	0.293119i	0.989202	−	0.146560i	$-0.0468200\pi$
$420$		0			0
$421$	−9.51472			−0.463719			−0.231860	−	0.972749i	$-0.574481\pi$
$421$	−9.51472			−0.463719			−0.231860	+	0.972749i	$0.574481\pi$
$422$		0			0
$423$	−12.4853	+	12.4853i	−0.607055	+	0.607055i
$424$		0			0
$425$	35.8492	−	5.12132i	1.73894	−	0.248421i
$426$		0			0
$427$	15.3640	+	15.3640i	0.743514	+	0.743514i
$428$		0			0
$429$	−14.4853	−	30.7279i	−0.699356	−	1.48356i
$430$		0			0
$431$		−	3.51472i		−	0.169298i	−0.996411	−	0.0846490i	$-0.973023\pi$
$431$		−	3.51472i		−	0.169298i	0.996411	−	0.0846490i	$-0.0269769\pi$
$432$		0			0
$433$	−21.9706	+	21.9706i	−1.05584	+	1.05584i	−0.0574919	+	0.998346i	$0.518310\pi$
$433$	−21.9706	+	21.9706i	−1.05584	+	1.05584i	−0.998346	+	0.0574919i	$0.981690\pi$
$434$		0			0
$435$	3.00000	+	6.00000i	0.143839	+	0.287678i
$436$		0			0
$437$	0.514719	−	0.514719i	0.0246223	−	0.0246223i
$438$		0			0
$439$	−0.727922			−0.0347418			−0.0173709	−	0.999849i	$-0.505530\pi$
$439$	−0.727922			−0.0347418			−0.0173709	+	0.999849i	$0.505530\pi$
$440$		0			0
$441$	−5.65685			−0.269374
$442$		0			0
$443$	19.0711	−	19.0711i	0.906094	−	0.906094i	−0.0898606	−	0.995954i	$-0.528642\pi$
$443$	19.0711	−	19.0711i	0.906094	−	0.906094i	0.995954	+	0.0898606i	$0.0286421\pi$
$444$		0			0
$445$	−11.6360	−	3.87868i	−0.551601	−	0.183867i
$446$		0			0
$447$	32.8492	−	32.8492i	1.55372	−	1.55372i
$448$		0			0
$449$		−	20.4853i		−	0.966760i	−0.875411	−	0.483380i	$-0.839409\pi$
$449$		−	20.4853i		−	0.966760i	0.875411	−	0.483380i	$-0.160591\pi$
$450$		0			0
$451$	5.27208	−	2.48528i	0.248252	−	0.117027i
$452$		0			0
$453$	20.4853	+	20.4853i	0.962482	+	0.962482i
$454$		0			0
$455$	9.00000	−	27.0000i	0.421927	−	1.26578i
$456$		0			0
$457$	7.60660	−	7.60660i	0.355822	−	0.355822i	−0.506448	−	0.862270i	$-0.669042\pi$
$457$	7.60660	−	7.60660i	0.355822	−	0.355822i	0.862270	+	0.506448i	$0.169042\pi$
$458$		0			0
$459$	3.00000			0.140028
$460$		0			0
$461$			1.24264i			0.0578755i	0.999581	+	0.0289378i	$0.00921247\pi$
$461$			1.24264i			0.0578755i	−0.999581	+	0.0289378i	$0.990788\pi$
$462$		0			0
$463$	15.9706	−	15.9706i	0.742215	−	0.742215i	−0.230789	−	0.973004i	$-0.574131\pi$
$463$	15.9706	−	15.9706i	0.742215	−	0.742215i	0.973004	+	0.230789i	$0.0741307\pi$
$464$		0			0
$465$	−17.4853	−	34.9706i	−0.810861	−	1.62172i
$466$		0			0
$467$	−16.7782	−	16.7782i	−0.776401	−	0.776401i	0.202816	−	0.979217i	$-0.434991\pi$
$467$	−16.7782	−	16.7782i	−0.776401	−	0.776401i	−0.979217	+	0.202816i	$0.934991\pi$
$468$		0			0
$469$	−16.9706			−0.783628
$470$		0			0
$471$	−55.8701			−2.57436
$472$		0			0
$473$	1.97056	−	5.48528i	0.0906066	−	0.252214i
$474$		0			0
$475$	−12.0000	−	9.00000i	−0.550598	−	0.412948i
$476$		0			0
$477$	−26.9706	−	26.9706i	−1.23490	−	1.23490i
$478$		0			0
$479$	36.7279			1.67814			0.839071	−	0.544022i	$-0.183099\pi$
$479$	36.7279			1.67814			0.839071	+	0.544022i	$0.183099\pi$
$480$		0			0
$481$			0.727922i			0.0331904i
$482$		0			0
$483$	−1.24264	−	1.24264i	−0.0565421	−	0.0565421i
$484$		0			0
$485$	6.34315	−	3.17157i	0.288027	−	0.144014i
$486$		0			0
$487$	11.9706	+	11.9706i	0.542438	+	0.542438i	0.924243	−	0.381805i	$-0.124697\pi$
$487$	11.9706	+	11.9706i	0.542438	+	0.542438i	−0.381805	+	0.924243i	$0.624697\pi$
$488$		0			0
$489$			47.2843i			2.13827i
$490$		0			0
$491$		−	5.48528i		−	0.247547i	−0.992310	−	0.123774i	$-0.960500\pi$
$491$		−	5.48528i		−	0.247547i	0.992310	−	0.123774i	$-0.0394997\pi$
$492$		0			0
$493$	6.36396	−	6.36396i	0.286618	−	0.286618i
$494$		0			0
$495$	2.48528	+	20.8284i	0.111705	+	0.936168i
$496$		0			0
$497$	−2.63604	+	2.63604i	−0.118243	+	0.118243i
$498$		0			0
$499$			34.9706i			1.56550i	0.622338	+	0.782749i	$0.286183\pi$
$499$			34.9706i			1.56550i	−0.622338	+	0.782749i	$0.713817\pi$
$500$		0			0
$501$			21.7279i			0.970732i
$502$		0			0
$503$	−0.727922	−	0.727922i	−0.0324564	−	0.0324564i	0.690692	−	0.723149i	$-0.257306\pi$
$503$	−0.727922	−	0.727922i	−0.0324564	−	0.0324564i	−0.723149	+	0.690692i	$0.757306\pi$
$504$		0			0
$505$	5.27208	+	1.75736i	0.234604	+	0.0782015i
$506$		0			0
$507$	−8.53553	−	8.53553i	−0.379076	−	0.379076i
$508$		0			0
$509$			32.1421i			1.42468i	0.701837	+	0.712338i	$0.252363\pi$
$509$			32.1421i			1.42468i	−0.701837	+	0.712338i	$0.747637\pi$
$510$		0			0
$511$	−25.4558			−1.12610
$512$		0			0
$513$	−0.878680	−	0.878680i	−0.0387947	−	0.0387947i
$514$		0			0
$515$	−8.82843	−	17.6569i	−0.389027	−	0.778054i
$516$		0			0
$517$	7.00000	−	19.4853i	0.307860	−	0.856962i
$518$		0			0
$519$	−55.4558			−2.43424
$520$		0			0
$521$	41.6569			1.82502			0.912510	−	0.409054i	$-0.134141\pi$
$521$	41.6569			1.82502			0.912510	+	0.409054i	$0.134141\pi$
$522$		0			0
$523$	−18.7279	−	18.7279i	−0.818915	−	0.818915i	0.167036	−	0.985951i	$-0.446580\pi$
$523$	−18.7279	−	18.7279i	−0.818915	−	0.818915i	−0.985951	+	0.167036i	$0.946580\pi$
$524$		0			0
$525$	−21.7279	+	28.9706i	−0.948284	+	1.26438i
$526$		0			0
$527$	−37.0919	+	37.0919i	−1.61575	+	1.61575i
$528$		0			0
$529$			22.9411i			0.997440i
$530$		0			0
$531$	−4.00000			−0.173585
$532$		0			0
$533$	5.27208	−	5.27208i	0.228359	−	0.228359i
$534$		0			0
$535$	−14.4853	−	28.9706i	−0.626253	−	1.25251i
$536$		0			0
$537$	−23.4853	−	23.4853i	−1.01346	−	1.01346i
$538$		0			0
$539$	6.00000	−	2.82843i	0.258438	−	0.121829i
$540$		0			0
$541$			10.7574i			0.462495i	0.972895	+	0.231248i	$0.0742807\pi$
$541$			10.7574i			0.462495i	−0.972895	+	0.231248i	$0.925719\pi$
$542$		0			0
$543$	−20.4853	+	20.4853i	−0.879108	+	0.879108i
$544$		0			0
$545$	−1.75736	+	5.27208i	−0.0752770	+	0.225831i
$546$		0			0
$547$	30.7279	−	30.7279i	1.31383	−	1.31383i	0.395263	−	0.918568i	$-0.370653\pi$
$547$	30.7279	−	30.7279i	1.31383	−	1.31383i	0.918568	−	0.395263i	$-0.129347\pi$
$548$		0			0
$549$	−20.4853			−0.874291
$550$		0			0
$551$	−3.72792			−0.158815
$552$		0			0
$553$	21.7279	−	21.7279i	0.923965	−	0.923965i
$554$		0			0
$555$	0.292893	−	0.878680i	0.0124326	−	0.0372979i
$556$		0			0
$557$	6.51472	−	6.51472i	0.276037	−	0.276037i	−0.555487	−	0.831525i	$-0.687468\pi$
$557$	6.51472	−	6.51472i	0.276037	−	0.276037i	0.831525	+	0.555487i	$0.187468\pi$
$558$		0			0
$559$		−	7.45584i		−	0.315349i
$560$		0			0
$561$	52.4558	−	24.7279i	2.21469	−	1.04401i
$562$		0			0
$563$	5.48528	+	5.48528i	0.231177	+	0.231177i	0.813184	−	0.582007i	$-0.197732\pi$
$563$	5.48528	+	5.48528i	0.231177	+	0.231177i	−0.582007	+	0.813184i	$0.697732\pi$
$564$		0			0
$565$	−6.24264	−	12.4853i	−0.262630	−	0.525260i
$566$		0			0
$567$	−20.1213	+	20.1213i	−0.845016	+	0.845016i
$568$		0			0
$569$	−2.48528			−0.104188			−0.0520942	−	0.998642i	$-0.516590\pi$
$569$	−2.48528			−0.104188			−0.0520942	+	0.998642i	$0.516590\pi$
$570$		0			0
$571$			29.4853i			1.23392i	0.786994	+	0.616960i	$0.211636\pi$
$571$			29.4853i			1.23392i	−0.786994	+	0.616960i	$0.788364\pi$
$572$		0			0
$573$	4.82843	−	4.82843i	0.201710	−	0.201710i
$574$		0			0
$575$	−1.20101	+	0.171573i	−0.0500856	+	0.00715508i
$576$		0			0
$577$	−19.7279	−	19.7279i	−0.821284	−	0.821284i	0.165008	−	0.986292i	$-0.447235\pi$
$577$	−19.7279	−	19.7279i	−0.821284	−	0.821284i	−0.986292	+	0.165008i	$0.947235\pi$
$578$		0			0
$579$	−3.00000			−0.124676
$580$		0			0
$581$	−30.7279			−1.27481
$582$		0			0
$583$	42.0919	+	15.1213i	1.74327	+	0.626261i
$584$		0			0
$585$	12.0000	+	24.0000i	0.496139	+	0.992278i
$586$		0			0
$587$	20.6777	+	20.6777i	0.853459	+	0.853459i	0.990557	−	0.137099i	$-0.0437777\pi$
$587$	20.6777	+	20.6777i	0.853459	+	0.853459i	−0.137099	+	0.990557i	$0.543778\pi$
$588$		0			0
$589$	21.7279			0.895283
$590$		0			0
$591$		−	4.24264i		−	0.174519i
$592$		0			0
$593$	−13.7574	−	13.7574i	−0.564947	−	0.564947i	0.365762	−	0.930709i	$-0.380809\pi$
$593$	−13.7574	−	13.7574i	−0.564947	−	0.564947i	−0.930709	+	0.365762i	$0.880809\pi$
$594$		0			0
$595$	46.0919	+	15.3640i	1.88958	+	0.629861i
$596$		0			0
$597$	8.12132	+	8.12132i	0.332384	+	0.332384i
$598$		0			0
$599$			3.72792i			0.152319i	0.997096	+	0.0761594i	$0.0242658\pi$
$599$			3.72792i			0.152319i	−0.997096	+	0.0761594i	$0.975734\pi$
$600$		0			0
$601$		−	27.9411i		−	1.13974i	−0.821734	−	0.569871i	$-0.806993\pi$
$601$		−	27.9411i		−	1.13974i	0.821734	−	0.569871i	$-0.193007\pi$
$602$		0			0
$603$	11.3137	−	11.3137i	0.460730	−	0.460730i
$604$		0			0
$605$	−13.0503	−	20.8492i	−0.530568	−	0.847642i
$606$		0			0
$607$	15.8787	−	15.8787i	0.644496	−	0.644496i	−0.307162	−	0.951657i	$-0.599379\pi$
$607$	15.8787	−	15.8787i	0.644496	−	0.644496i	0.951657	+	0.307162i	$0.0993792\pi$
$608$		0			0
$609$			9.00000i			0.364698i
$610$		0			0
$611$		−	26.4853i		−	1.07148i
$612$		0			0
$613$	−18.0000	−	18.0000i	−0.727013	−	0.727013i	0.243011	−	0.970024i	$-0.421865\pi$
$613$	−18.0000	−	18.0000i	−0.727013	−	0.727013i	−0.970024	+	0.243011i	$0.921865\pi$
$614$		0			0
$615$	−8.48528	+	4.24264i	−0.342160	+	0.171080i
$616$		0			0
$617$	31.0711	+	31.0711i	1.25087	+	1.25087i	0.955329	+	0.295545i	$0.0955014\pi$
$617$	31.0711	+	31.0711i	1.25087	+	1.25087i	0.295545	+	0.955329i	$0.404499\pi$
$618$		0			0
$619$			10.0000i			0.401934i	0.979598	+	0.200967i	$0.0644084\pi$
$619$			10.0000i			0.401934i	−0.979598	+	0.200967i	$0.935592\pi$
$620$		0			0
$621$	−0.100505			−0.00403313
$622$		0			0
$623$	−11.6360	−	11.6360i	−0.466188	−	0.466188i
$624$		0			0
$625$	7.00000	+	24.0000i	0.280000	+	0.960000i
$626$		0			0
$627$	−22.6066	−	8.12132i	−0.902821	−	0.324334i
$628$		0			0
$629$	−1.24264			−0.0495473
$630$		0			0
$631$	−1.72792			−0.0687875			−0.0343937	−	0.999408i	$-0.510950\pi$
$631$	−1.72792			−0.0687875			−0.0343937	+	0.999408i	$0.510950\pi$
$632$		0			0
$633$	−29.8492	−	29.8492i	−1.18640	−	1.18640i
$634$		0			0
$635$	6.00000	+	12.0000i	0.238103	+	0.476205i
$636$		0			0
$637$	6.00000	−	6.00000i	0.237729	−	0.237729i
$638$		0			0
$639$		−	3.51472i		−	0.139040i
$640$		0			0
$641$	−6.17157			−0.243762			−0.121881	−	0.992545i	$-0.538893\pi$
$641$	−6.17157			−0.243762			−0.121881	+	0.992545i	$0.538893\pi$
$642$		0			0
$643$	−32.5772	+	32.5772i	−1.28472	+	1.28472i	−0.346766	+	0.937952i	$0.612720\pi$
$643$	−32.5772	+	32.5772i	−1.28472	+	1.28472i	−0.937952	+	0.346766i	$0.887280\pi$
$644$		0			0
$645$	−3.00000	+	9.00000i	−0.118125	+	0.354375i
$646$		0			0
$647$	−28.1127	−	28.1127i	−1.10522	−	1.10522i	−0.993770	−	0.111455i	$-0.964449\pi$
$647$	−28.1127	−	28.1127i	−1.10522	−	1.10522i	−0.111455	−	0.993770i	$-0.535551\pi$
$648$		0			0
$649$	4.24264	−	2.00000i	0.166538	−	0.0785069i
$650$		0			0
$651$		−	52.4558i		−	2.05591i
$652$		0			0
$653$	−9.53553	+	9.53553i	−0.373154	+	0.373154i	−0.868625	−	0.495470i	$-0.834996\pi$
$653$	−9.53553	+	9.53553i	−0.373154	+	0.373154i	0.495470	+	0.868625i	$0.334996\pi$
$654$		0			0
$655$	−29.6360	−	9.87868i	−1.15798	−	0.385992i
$656$		0			0
$657$	16.9706	−	16.9706i	0.662085	−	0.662085i
$658$		0			0
$659$	28.4558			1.10848			0.554241	−	0.832356i	$-0.313009\pi$
$659$	28.4558			1.10848			0.554241	+	0.832356i	$0.313009\pi$
$660$		0			0
$661$	−16.7279			−0.650641			−0.325320	−	0.945604i	$-0.605472\pi$
$661$	−16.7279			−0.650641			−0.325320	+	0.945604i	$0.605472\pi$
$662$		0			0
$663$	52.4558	−	52.4558i	2.03722	−	2.03722i
$664$		0			0
$665$	−9.00000	−	18.0000i	−0.349005	−	0.698010i
$666$		0			0
$667$	−0.213203	+	0.213203i	−0.00825527	+	0.00825527i
$668$		0			0
$669$			12.8284i			0.495976i
$670$		0			0
$671$	21.7279	−	10.2426i	0.838797	−	0.395413i
$672$		0			0
$673$	2.63604	+	2.63604i	0.101612	+	0.101612i	0.756085	−	0.654473i	$-0.227110\pi$
$673$	2.63604	+	2.63604i	0.101612	+	0.101612i	−0.654473	+	0.756085i	$0.727110\pi$
$674$		0			0
$675$	0.292893	+	2.05025i	0.0112735	+	0.0789143i
$676$		0			0
$677$	−33.2132	+	33.2132i	−1.27649	+	1.27649i	−0.333867	+	0.942620i	$0.608354\pi$
$677$	−33.2132	+	33.2132i	−1.27649	+	1.27649i	−0.942620	+	0.333867i	$0.891646\pi$
$678$		0			0
$679$	9.51472			0.365141
$680$		0			0
$681$		−	51.2132i		−	1.96249i
$682$		0			0
$683$	−12.1924	+	12.1924i	−0.466529	+	0.466529i	−0.900788	−	0.434259i	$-0.857010\pi$
$683$	−12.1924	+	12.1924i	−0.466529	+	0.466529i	0.434259	+	0.900788i	$0.357010\pi$
$684$		0			0
$685$	32.9706	−	16.4853i	1.25974	−	0.629870i
$686$		0			0
$687$	25.9706	+	25.9706i	0.990839	+	0.990839i
$688$		0			0
$689$	57.2132			2.17965
$690$		0			0
$691$	−13.2721			−0.504894			−0.252447	−	0.967611i	$-0.581235\pi$
$691$	−13.2721			−0.504894			−0.252447	+	0.967611i	$0.581235\pi$
$692$		0			0
$693$	−9.51472	+	26.4853i	−0.361434	+	1.00609i
$694$		0			0
$695$	−10.2426	+	30.7279i	−0.388526	+	1.16558i
$696$		0			0
$697$	9.00000	+	9.00000i	0.340899	+	0.340899i
$698$		0			0
$699$	−5.48528			−0.207472
$700$		0			0
$701$		−	27.7279i		−	1.04727i	−0.851943	−	0.523635i	$-0.824576\pi$
$701$		−	27.7279i		−	1.04727i	0.851943	−	0.523635i	$-0.175424\pi$
$702$		0			0
$703$	0.363961	+	0.363961i	0.0137271	+	0.0137271i
$704$		0			0
$705$	−10.6569	+	31.9706i	−0.401360	+	1.20408i
$706$		0			0
$707$	5.27208	+	5.27208i	0.198277	+	0.198277i
$708$		0			0
$709$			10.0000i			0.375558i	0.982211	+	0.187779i	$0.0601289\pi$
$709$			10.0000i			0.375558i	−0.982211	+	0.187779i	$0.939871\pi$
$710$		0			0
$711$			28.9706i			1.08648i
$712$		0			0
$713$	1.24264	−	1.24264i	0.0465373	−	0.0465373i
$714$		0			0
$715$	−24.7279	−	19.4558i	−0.924772	−	0.727607i
$716$		0			0
$717$	−1.24264	+	1.24264i	−0.0464073	+	0.0464073i
$718$		0			0
$719$			20.6985i			0.771923i	0.922515	+	0.385962i	$0.126130\pi$
$719$			20.6985i			0.771923i	−0.922515	+	0.385962i	$0.873870\pi$
$720$		0			0
$721$		−	26.4853i		−	0.986363i
$722$		0			0
$723$	11.4853	+	11.4853i	0.427142	+	0.427142i
$724$		0			0
$725$	4.97056	+	3.72792i	0.184602	+	0.138452i
$726$		0			0
$727$	6.97056	+	6.97056i	0.258524	+	0.258524i	0.824454	−	0.565930i	$-0.191483\pi$
$727$	6.97056	+	6.97056i	0.258524	+	0.258524i	−0.565930	+	0.824454i	$0.691483\pi$
$728$		0			0
$729$		−	23.8284i		−	0.882534i
$730$		0			0
$731$	12.7279			0.470759
$732$		0			0
$733$	25.9706	+	25.9706i	0.959245	+	0.959245i	0.999201	−	0.0399568i	$-0.0127220\pi$
$733$	25.9706	+	25.9706i	0.959245	+	0.959245i	−0.0399568	+	0.999201i	$0.512722\pi$
$734$		0			0
$735$	−9.65685	+	4.82843i	−0.356198	+	0.178099i
$736$		0			0
$737$	−6.34315	+	17.6569i	−0.233653	+	0.650399i
$738$		0			0
$739$	33.9411			1.24854			0.624272	−	0.781207i	$-0.285396\pi$
$739$	33.9411			1.24854			0.624272	+	0.781207i	$0.285396\pi$
$740$		0			0
$741$	−30.7279			−1.12882
$742$		0			0
$743$	−8.12132	−	8.12132i	−0.297942	−	0.297942i	0.542265	−	0.840207i	$-0.317567\pi$
$743$	−8.12132	−	8.12132i	−0.297942	−	0.297942i	−0.840207	+	0.542265i	$0.817567\pi$
$744$		0			0
$745$	13.6066	−	40.8198i	0.498507	−	1.49552i
$746$		0			0
$747$	20.4853	−	20.4853i	0.749517	−	0.749517i
$748$		0			0
$749$		−	43.4558i		−	1.58784i
$750$		0			0
$751$	43.1838			1.57580			0.787899	−	0.615804i	$-0.211169\pi$
$751$	43.1838			1.57580			0.787899	+	0.615804i	$0.211169\pi$
$752$		0			0
$753$	6.00000	−	6.00000i	0.218652	−	0.218652i
$754$		0			0
$755$	25.4558	+	8.48528i	0.926433	+	0.308811i
$756$		0			0
$757$	13.2132	+	13.2132i	0.480242	+	0.480242i	0.905209	−	0.424967i	$-0.139714\pi$
$757$	13.2132	+	13.2132i	0.480242	+	0.480242i	−0.424967	+	0.905209i	$0.639714\pi$
$758$		0			0
$759$	−1.75736	+	0.828427i	−0.0637881	+	0.0300700i
$760$		0			0
$761$			18.7279i			0.678887i	0.940627	+	0.339443i	$0.110239\pi$
$761$			18.7279i			0.678887i	−0.940627	+	0.339443i	$0.889761\pi$
$762$		0			0
$763$	−5.27208	+	5.27208i	−0.190862	+	0.190862i
$764$		0			0
$765$	−40.9706	+	20.4853i	−1.48129	+	0.740647i
$766$		0			0
$767$	4.24264	−	4.24264i	0.153193	−	0.153193i
$768$		0			0
$769$	43.4558			1.56706			0.783529	−	0.621355i	$-0.213418\pi$
$769$	43.4558			1.56706			0.783529	+	0.621355i	$0.213418\pi$
$770$		0			0
$771$	6.58579			0.237181
$772$		0			0
$773$	16.2635	−	16.2635i	0.584956	−	0.584956i	−0.351305	−	0.936261i	$-0.614262\pi$
$773$	16.2635	−	16.2635i	0.584956	−	0.584956i	0.936261	+	0.351305i	$0.114262\pi$
$774$		0			0
$775$	−28.9706	−	21.7279i	−1.04065	−	0.780490i
$776$		0			0
$777$	0.878680	−	0.878680i	0.0315225	−	0.0315225i
$778$		0			0
$779$		−	5.27208i		−	0.188892i
$780$		0			0
$781$	1.75736	+	3.72792i	0.0628833	+	0.133396i
$782$		0			0
$783$	0.363961	+	0.363961i	0.0130069	+	0.0130069i
$784$		0			0
$785$	−46.2843	+	23.1421i	−1.65196	+	0.825978i
$786$		0			0
$787$	5.48528	−	5.48528i	0.195529	−	0.195529i	−0.602551	−	0.798080i	$-0.705849\pi$
$787$	5.48528	−	5.48528i	0.195529	−	0.195529i	0.798080	+	0.602551i	$0.205849\pi$
$788$		0			0
$789$	21.7279			0.773535
$790$		0			0
$791$		−	18.7279i		−	0.665888i
$792$		0			0
$793$	21.7279	−	21.7279i	0.771581	−	0.771581i
$794$		0			0
$795$	−69.0624	−	23.0208i	−2.44939	−	0.816464i
$796$		0			0
$797$	8.14214	+	8.14214i	0.288409	+	0.288409i	0.836451	−	0.548042i	$-0.184627\pi$
$797$	8.14214	+	8.14214i	0.288409	+	0.288409i	−0.548042	+	0.836451i	$0.684627\pi$
$798$		0			0
$799$	45.2132			1.59953
$800$		0			0
$801$	15.5147			0.548186
$802$		0			0
$803$	−9.51472	+	26.4853i	−0.335767	+	0.934645i
$804$		0			0
$805$	−1.54416	−	0.514719i	−0.0544243	−	0.0181414i
$806$		0			0
$807$	−33.7990	−	33.7990i	−1.18978	−	1.18978i
$808$		0			0
$809$	37.4558			1.31688			0.658439	−	0.752634i	$-0.271217\pi$
$809$	37.4558			1.31688			0.658439	+	0.752634i	$0.271217\pi$
$810$		0			0
$811$		−	4.45584i		−	0.156466i	−0.996935	−	0.0782329i	$-0.975072\pi$
$811$		−	4.45584i		−	0.156466i	0.996935	−	0.0782329i	$-0.0249278\pi$
$812$		0			0
$813$	11.4853	+	11.4853i	0.402806	+	0.402806i
$814$		0			0
$815$	19.5858	+	39.1716i	0.686060	+	1.37212i
$816$		0			0
$817$	−3.72792	−	3.72792i	−0.130423	−	0.130423i
$818$		0			0
$819$			36.0000i			1.25794i
$820$		0			0
$821$			49.4558i			1.72602i	0.505186	+	0.863010i	$0.331424\pi$
$821$			49.4558i			1.72602i	−0.505186	+	0.863010i	$0.668576\pi$
$822$		0			0
$823$	−28.6985	+	28.6985i	−1.00037	+	1.00037i	−0.000366361		1.00000i	$0.500117\pi$
$823$	−28.6985	+	28.6985i	−1.00037	+	1.00037i	−1.00000		0.000366361i	$0.999883\pi$
$824$		0			0
$825$	22.0208	+	33.4350i	0.766666	+	1.16406i
$826$		0			0
$827$	3.00000	−	3.00000i	0.104320	−	0.104320i	−0.653020	−	0.757340i	$-0.726498\pi$
$827$	3.00000	−	3.00000i	0.104320	−	0.104320i	0.757340	+	0.653020i	$0.226498\pi$
$828$		0			0
$829$			45.4558i			1.57875i	0.613913	+	0.789373i	$0.289594\pi$
$829$			45.4558i			1.57875i	−0.613913	+	0.789373i	$0.710406\pi$
$830$		0			0
$831$			34.9706i			1.21312i
$832$		0			0
$833$	10.2426	+	10.2426i	0.354886	+	0.354886i
$834$		0			0
$835$	9.00000	+	18.0000i	0.311458	+	0.622916i
$836$		0			0
$837$	−2.12132	−	2.12132i	−0.0733236	−	0.0733236i
$838$		0			0
$839$			33.1716i			1.14521i	0.819831	+	0.572605i	$0.194067\pi$
$839$			33.1716i			1.14521i	−0.819831	+	0.572605i	$0.805933\pi$
$840$		0			0
$841$	−27.4558			−0.946753
$842$		0			0
$843$	−39.2132	−	39.2132i	−1.35057	−	1.35057i
$844$		0			0
$845$	−10.6066	−	3.53553i	−0.364878	−	0.121626i
$846$		0			0
$847$	−3.15076	−	32.8492i	−0.108261	−	1.12871i
$848$		0			0
$849$	45.2132			1.55171
$850$		0			0
$851$	0.0416306			0.00142708
$852$		0			0
$853$	31.9706	+	31.9706i	1.09465	+	1.09465i	0.995025	+	0.0996263i	$0.0317647\pi$
$853$	31.9706	+	31.9706i	1.09465	+	1.09465i	0.0996263	+	0.995025i	$0.468235\pi$
$854$		0			0
$855$	18.0000	+	6.00000i	0.615587	+	0.205196i
$856$		0			0
$857$	−4.39340	+	4.39340i	−0.150076	+	0.150076i	−0.778152	−	0.628076i	$-0.783843\pi$
$857$	−4.39340	+	4.39340i	−0.150076	+	0.150076i	0.628076	+	0.778152i	$0.283843\pi$
$858$		0			0
$859$		−	32.0000i		−	1.09183i	−0.837842	−	0.545913i	$-0.816183\pi$
$859$		−	32.0000i		−	1.09183i	0.837842	−	0.545913i	$-0.183817\pi$
$860$		0			0
$861$	−12.7279			−0.433766
$862$		0			0
$863$	0.899495	−	0.899495i	0.0306192	−	0.0306192i	−0.691631	−	0.722251i	$-0.743108\pi$
$863$	0.899495	−	0.899495i	0.0306192	−	0.0306192i	0.722251	+	0.691631i	$0.243108\pi$
$864$		0			0
$865$	−45.9411	+	22.9706i	−1.56205	+	0.781023i
$866$		0			0
$867$	60.5269	+	60.5269i	2.05560	+	2.05560i
$868$		0			0
$869$	−14.4853	−	30.7279i	−0.491380	−	1.04237i
$870$		0			0
$871$			24.0000i			0.813209i
$872$		0			0
$873$	−6.34315	+	6.34315i	−0.214683	+	0.214683i
$874$		0			0
$875$	−6.00000	+	33.0000i	−0.202837	+	1.11560i
$876$		0			0
$877$	5.27208	−	5.27208i	0.178025	−	0.178025i	−0.612469	−	0.790495i	$-0.709824\pi$
$877$	5.27208	−	5.27208i	0.178025	−	0.178025i	0.790495	+	0.612469i	$0.209824\pi$
$878$		0			0
$879$	53.6985			1.81120
$880$		0			0
$881$	8.48528			0.285876			0.142938	−	0.989732i	$-0.454345\pi$
$881$	8.48528			0.285876			0.142938	+	0.989732i	$0.454345\pi$
$882$		0			0
$883$	8.39340	−	8.39340i	0.282460	−	0.282460i	−0.551629	−	0.834089i	$-0.685994\pi$
$883$	8.39340	−	8.39340i	0.282460	−	0.282460i	0.834089	+	0.551629i	$0.185994\pi$
$884$		0			0
$885$	−6.82843	+	3.41421i	−0.229535	+	0.114768i
$886$		0			0
$887$	−13.7574	+	13.7574i	−0.461927	+	0.461927i	−0.899287	−	0.437360i	$-0.855914\pi$
$887$	−13.7574	+	13.7574i	−0.461927	+	0.461927i	0.437360	+	0.899287i	$0.355914\pi$
$888$		0			0
$889$			18.0000i			0.603701i
$890$		0			0
$891$	13.4142	+	28.4558i	0.449393	+	0.953307i
$892$		0			0
$893$	−13.2426	−	13.2426i	−0.443148	−	0.443148i
$894$		0			0
$895$	−29.1838	−	9.72792i	−0.975506	−	0.325169i
$896$		0			0
$897$	−1.75736	+	1.75736i	−0.0586765	+	0.0586765i
$898$		0			0
$899$	−9.00000			−0.300167
$900$		0			0
$901$			97.6690i			3.25383i
$902$		0			0
$903$	−9.00000	+	9.00000i	−0.299501	+	0.299501i
$904$		0			0
$905$	−8.48528	+	25.4558i	−0.282060	+	0.846181i
$906$		0			0
$907$	11.3640	+	11.3640i	0.377334	+	0.377334i	0.870140	−	0.492805i	$-0.164029\pi$
$907$	11.3640	+	11.3640i	0.377334	+	0.377334i	−0.492805	+	0.870140i	$0.664029\pi$
$908$		0			0
$909$	−7.02944			−0.233152
$910$		0			0
$911$	−26.3553			−0.873191			−0.436596	−	0.899658i	$-0.643816\pi$
$911$	−26.3553			−0.873191			−0.436596	+	0.899658i	$0.643816\pi$
$912$		0			0
$913$	−11.4853	+	31.9706i	−0.380107	+	1.05807i
$914$		0			0
$915$	−34.9706	+	17.4853i	−1.15609	+	0.578046i
$916$		0			0
$917$	−29.6360	−	29.6360i	−0.978668	−	0.978668i
$918$		0			0
$919$	13.7574			0.453813			0.226907	−	0.973916i	$-0.427139\pi$
$919$	13.7574			0.453813			0.226907	+	0.973916i	$0.427139\pi$
$920$		0			0
$921$			39.2132i			1.29212i
$922$		0			0
$923$	3.72792	+	3.72792i	0.122706	+	0.122706i
$924$		0			0
$925$	−0.121320	−	0.849242i	−0.00398899	−	0.0279229i
$926$		0			0
$927$	17.6569	+	17.6569i	0.579927	+	0.579927i
$928$		0			0
$929$			42.1716i			1.38360i	0.722087	+	0.691802i	$0.243183\pi$
$929$			42.1716i			1.38360i	−0.722087	+	0.691802i	$0.756817\pi$
$930$		0			0
$931$		−	6.00000i		−	0.196642i
$932$		0			0
$933$	−16.6066	+	16.6066i	−0.543676	+	0.543676i
$934$		0			0
$935$	33.2132	−	42.2132i	1.08619	−	1.38052i
$936$		0			0
$937$	24.7279	−	24.7279i	0.807826	−	0.807826i	−0.176478	−	0.984304i	$-0.556471\pi$
$937$	24.7279	−	24.7279i	0.807826	−	0.807826i	0.984304	+	0.176478i	$0.0564706\pi$
$938$		0			0
$939$			12.8284i			0.418640i
$940$		0			0
$941$		−	43.6690i		−	1.42357i	−0.702397	−	0.711785i	$-0.747887\pi$
$941$		−	43.6690i		−	1.42357i	0.702397	−	0.711785i	$-0.252113\pi$
$942$		0			0
$943$	−0.301515	−	0.301515i	−0.00981869	−	0.00981869i
$944$		0			0
$945$	−0.878680	+	2.63604i	−0.0285835	+	0.0857504i
$946$		0			0
$947$	−22.4350	−	22.4350i	−0.729040	−	0.729040i	0.241388	−	0.970429i	$-0.422397\pi$
$947$	−22.4350	−	22.4350i	−0.729040	−	0.729040i	−0.970429	+	0.241388i	$0.922397\pi$
$948$		0			0
$949$			36.0000i			1.16861i
$950$		0			0
$951$	32.5563			1.05571
$952$		0			0
$953$	−29.1213	−	29.1213i	−0.943332	−	0.943332i	0.0551462	−	0.998478i	$-0.482438\pi$
$953$	−29.1213	−	29.1213i	−0.943332	−	0.943332i	−0.998478	+	0.0551462i	$0.982438\pi$
$954$		0			0
$955$	2.00000	−	6.00000i	0.0647185	−	0.194155i
$956$		0			0
$957$	9.36396	+	3.36396i	0.302694	+	0.108741i
$958$		0			0
$959$	49.4558			1.59701
$960$		0			0
$961$	21.4558			0.692124
$962$		0			0
$963$	28.9706	+	28.9706i	0.933563	+	0.933563i
$964$		0			0
$965$	−2.48528	+	1.24264i	−0.0800040	+	0.0400020i
$966$		0			0
$967$	8.12132	−	8.12132i	0.261164	−	0.261164i	−0.564363	−	0.825527i	$-0.690878\pi$
$967$	8.12132	−	8.12132i	0.261164	−	0.261164i	0.825527	+	0.564363i	$0.190878\pi$
$968$		0			0
$969$		−	52.4558i		−	1.68512i
$970$		0			0
$971$	−13.1127			−0.420807			−0.210403	−	0.977615i	$-0.567478\pi$
$971$	−13.1127			−0.420807			−0.210403	+	0.977615i	$0.567478\pi$
$972$		0			0
$973$	−30.7279	+	30.7279i	−0.985092	+	0.985092i
$974$		0			0
$975$	40.9706	+	30.7279i	1.31211	+	0.984081i
$976$		0			0
$977$	−3.55635	−	3.55635i	−0.113778	−	0.113778i	0.647926	−	0.761703i	$-0.275637\pi$
$977$	−3.55635	−	3.55635i	−0.113778	−	0.113778i	−0.761703	+	0.647926i	$0.775637\pi$
$978$		0			0
$979$	−16.4558	+	7.75736i	−0.525931	+	0.247926i
$980$		0			0
$981$		−	7.02944i		−	0.224433i
$982$		0			0
$983$	−9.17157	+	9.17157i	−0.292528	+	0.292528i	−0.838078	−	0.545550i	$-0.816321\pi$
$983$	−9.17157	+	9.17157i	−0.292528	+	0.292528i	0.545550	+	0.838078i	$0.316321\pi$
$984$		0			0
$985$	−1.75736	−	3.51472i	−0.0559941	−	0.111988i
$986$		0			0
$987$	−31.9706	+	31.9706i	−1.01763	+	1.01763i
$988$		0			0
$989$	−0.426407			−0.0135589
$990$		0			0
$991$	25.4558			0.808632			0.404316	−	0.914619i	$-0.367510\pi$
$991$	25.4558			0.808632			0.404316	+	0.914619i	$0.367510\pi$
$992$		0			0
$993$	42.2132	−	42.2132i	1.33960	−	1.33960i
$994$		0			0
$995$	10.0919	+	3.36396i	0.319934	+	0.106645i
$996$		0			0
$997$	41.4853	−	41.4853i	1.31385	−	1.31385i	0.395300	−	0.918552i	$-0.370641\pi$
$997$	41.4853	−	41.4853i	1.31385	−	1.31385i	0.918552	−	0.395300i	$-0.129359\pi$
$998$		0			0
$999$		−	0.0710678i		−	0.00224849i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.bd.c.417.1		4
4.3	odd	2		110.2.f.b.87.1	yes	4
5.3	odd	4		880.2.bd.b.593.1		4
11.10	odd	2		880.2.bd.b.417.1		4
12.11	even	2		990.2.m.c.307.2		4
20.3	even	4		110.2.f.c.43.2	yes	4
20.7	even	4		550.2.f.b.43.1		4
20.19	odd	2		550.2.f.a.307.2		4
44.43	even	2		110.2.f.c.87.2	yes	4
55.43	even	4	inner	880.2.bd.c.593.1		4
60.23	odd	4		990.2.m.d.703.1		4
132.131	odd	2		990.2.m.d.307.1		4
220.43	odd	4		110.2.f.b.43.1	✓	4
220.87	odd	4		550.2.f.a.43.2		4
220.219	even	2		550.2.f.b.307.1		4
660.263	even	4		990.2.m.c.703.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.f.b.43.1	✓	4	220.43	odd	4
110.2.f.b.87.1	yes	4	4.3	odd	2
110.2.f.c.43.2	yes	4	20.3	even	4
110.2.f.c.87.2	yes	4	44.43	even	2
550.2.f.a.43.2		4	220.87	odd	4
550.2.f.a.307.2		4	20.19	odd	2
550.2.f.b.43.1		4	20.7	even	4
550.2.f.b.307.1		4	220.219	even	2
880.2.bd.b.417.1		4	11.10	odd	2
880.2.bd.b.593.1		4	5.3	odd	4
880.2.bd.c.417.1		4	1.1	even	1	trivial
880.2.bd.c.593.1		4	55.43	even	4	inner
990.2.m.c.307.2		4	12.11	even	2
990.2.m.c.703.2		4	660.263	even	4
990.2.m.d.307.1		4	132.131	odd	2
990.2.m.d.703.1		4	60.23	odd	4

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:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.bd (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.70711 + 1.70711i) q^{3} +(-0.707107 + 2.12132i) q^{5} +(-2.12132 + 2.12132i) q^{7} -2.82843i q^{9} +(1.41421 + 3.00000i) q^{11} +(3.00000 + 3.00000i) q^{13} +(-2.41421 - 4.82843i) q^{15} +(-5.12132 + 5.12132i) q^{17} +3.00000 q^{19} -7.24264i q^{21} +(0.171573 - 0.171573i) q^{23} +(-4.00000 - 3.00000i) q^{25} +(-0.292893 - 0.292893i) q^{27} -1.24264 q^{29} +7.24264 q^{31} +(-7.53553 - 2.70711i) q^{33} +(-3.00000 - 6.00000i) q^{35} +(0.121320 + 0.121320i) q^{37} -10.2426 q^{39} -1.75736i q^{41} +(-1.24264 - 1.24264i) q^{43} +(6.00000 + 2.00000i) q^{45} +(-4.41421 - 4.41421i) q^{47} -2.00000i q^{49} -17.4853i q^{51} +(9.53553 - 9.53553i) q^{53} +(-7.36396 + 0.878680i) q^{55} +(-5.12132 + 5.12132i) q^{57} -1.41421i q^{59} -7.24264i q^{61} +(6.00000 + 6.00000i) q^{63} +(-8.48528 + 4.24264i) q^{65} +(4.00000 + 4.00000i) q^{67} +0.585786i q^{69} +1.24264 q^{71} +(6.00000 + 6.00000i) q^{73} +(11.9497 - 1.70711i) q^{75} +(-9.36396 - 3.36396i) q^{77} -10.2426 q^{79} +9.48528 q^{81} +(7.24264 + 7.24264i) q^{83} +(-7.24264 - 14.4853i) q^{85} +(2.12132 - 2.12132i) q^{87} +5.48528i q^{89} -12.7279 q^{91} +(-12.3640 + 12.3640i) q^{93} +(-2.12132 + 6.36396i) q^{95} +(-2.24264 - 2.24264i) q^{97} +(8.48528 - 4.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + 12 q^{13} - 4 q^{15} - 12 q^{17} + 12 q^{19} + 12 q^{23} - 16 q^{25} - 4 q^{27} + 12 q^{29} + 12 q^{31} - 16 q^{33} - 12 q^{35} - 8 q^{37} - 24 q^{39} + 12 q^{43} + 24 q^{45} - 12 q^{47}+ \cdots + 8 q^{97}+O(q^{100}) \) 4 * q - 4 * q^3 + 12 * q^13 - 4 * q^15 - 12 * q^17 + 12 * q^19 + 12 * q^23 - 16 * q^25 - 4 * q^27 + 12 * q^29 + 12 * q^31 - 16 * q^33 - 12 * q^35 - 8 * q^37 - 24 * q^39 + 12 * q^43 + 24 * q^45 - 12 * q^47 + 24 * q^53 - 4 * q^55 - 12 * q^57 + 24 * q^63 + 16 * q^67 - 12 * q^71 + 24 * q^73 + 28 * q^75 - 12 * q^77 - 24 * q^79 + 4 * q^81 + 12 * q^83 - 12 * q^85 - 24 * q^93 + 8 * q^97

Introduction

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