LMFDB - Embedded newform 1120.2.bz.f.271.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1120,2,Mod(271,1120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1120, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

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

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

chi := DirichletCharacter("1120.271");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1120 = 2^{5} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1120.bz (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:	$8.94324502638$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			271.11
Character	$\chi$	$=$	1120.271
Dual form			1120.2.bz.f.591.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.84104 - 1.06293i) q^{3} +(0.500000 - 0.866025i) q^{5} +(2.17552 + 1.50569i) q^{7} +(0.759621 - 1.31570i) q^{9} +O(q^{10})$	\(q+(1.84104 - 1.06293i) q^{3} +(0.500000 - 0.866025i) q^{5} +(2.17552 + 1.50569i) q^{7} +(0.759621 - 1.31570i) q^{9} +(-2.04422 - 3.54069i) q^{11} +4.95585 q^{13} -2.12585i q^{15} +(2.09103 - 1.20726i) q^{17} +(-5.22809 - 3.01844i) q^{19} +(5.60566 + 0.459619i) q^{21} +(0.443005 + 0.255769i) q^{23} +(-0.500000 - 0.866025i) q^{25} +3.14787i q^{27} +3.08127i q^{29} +(-2.30669 - 3.99530i) q^{31} +(-7.52697 - 4.34570i) q^{33} +(2.39173 - 1.13121i) q^{35} +(8.64910 + 4.99356i) q^{37} +(9.12392 - 5.26770i) q^{39} -5.81092i q^{41} +10.7069 q^{43} +(-0.759621 - 1.31570i) q^{45} +(-0.698912 + 1.21055i) q^{47} +(2.46579 + 6.55133i) q^{49} +(2.56645 - 4.44522i) q^{51} +(-6.79325 + 3.92208i) q^{53} -4.08843 q^{55} -12.8335 q^{57} +(-8.82516 + 5.09521i) q^{59} +(-1.33141 + 2.30607i) q^{61} +(3.63361 - 1.71859i) q^{63} +(2.47792 - 4.29189i) q^{65} +(-3.46437 - 6.00046i) q^{67} +1.08745 q^{69} -1.54183i q^{71} +(6.99634 - 4.03934i) q^{73} +(-1.84104 - 1.06293i) q^{75} +(0.883939 - 10.7808i) q^{77} +(-3.21095 - 1.85384i) q^{79} +(5.62481 + 9.74247i) q^{81} -9.94035i q^{83} -2.41452i q^{85} +(3.27516 + 5.67274i) q^{87} +(-3.81064 - 2.20007i) q^{89} +(10.7816 + 7.46197i) q^{91} +(-8.49342 - 4.90368i) q^{93} +(-5.22809 + 3.01844i) q^{95} +5.67803i q^{97} -6.21132 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{3} + 12 q^{5} + 10 q^{7} + 12 q^{9}+O(q^{10}) $ 24 * q - 12 * q^3 + 12 * q^5 + 10 * q^7 + 12 * q^9	$ 24 q - 12 q^{3} + 12 q^{5} + 10 q^{7} + 12 q^{9} - 8 q^{11} - 20 q^{13} + 6 q^{17} - 18 q^{19} + 26 q^{21} + 18 q^{23} - 12 q^{25} - 6 q^{31} + 12 q^{33} + 8 q^{35} - 18 q^{39} - 32 q^{43} - 12 q^{45} + 8 q^{49} + 22 q^{51} - 30 q^{53} - 16 q^{55} - 44 q^{57} + 18 q^{59} - 22 q^{61} - 12 q^{63} - 10 q^{65} + 8 q^{67} + 12 q^{69} + 30 q^{73} + 12 q^{75} + 32 q^{77} + 6 q^{79} - 4 q^{81} + 14 q^{87} - 60 q^{89} - 18 q^{91} + 18 q^{93} - 18 q^{95} + 56 q^{99}+O(q^{100}) $ 24 * q - 12 * q^3 + 12 * q^5 + 10 * q^7 + 12 * q^9 - 8 * q^11 - 20 * q^13 + 6 * q^17 - 18 * q^19 + 26 * q^21 + 18 * q^23 - 12 * q^25 - 6 * q^31 + 12 * q^33 + 8 * q^35 - 18 * q^39 - 32 * q^43 - 12 * q^45 + 8 * q^49 + 22 * q^51 - 30 * q^53 - 16 * q^55 - 44 * q^57 + 18 * q^59 - 22 * q^61 - 12 * q^63 - 10 * q^65 + 8 * q^67 + 12 * q^69 + 30 * q^73 + 12 * q^75 + 32 * q^77 + 6 * q^79 - 4 * q^81 + 14 * q^87 - 60 * q^89 - 18 * q^91 + 18 * q^93 - 18 * q^95 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times$.

$n$	$351$	$421$	$801$	$897$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.84104	−	1.06293i	1.06293	−	0.613680i	0.136685	−	0.990615i	$-0.456355\pi$
$3$	1.84104	−	1.06293i	1.06293	−	0.613680i	0.926240	+	0.376934i	$0.123022\pi$
$4$		0			0
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	2.17552	+	1.50569i	0.822270	+	0.569097i
$7$	2.17552	+	1.50569i	0.822270	+	0.569097i
$8$		0			0
$9$	0.759621	−	1.31570i	0.253207	−	0.438567i
$10$		0			0
$11$	−2.04422	−	3.54069i	−0.616354	−	1.06756i	−0.990145	−	0.140044i	$-0.955276\pi$
$11$	−2.04422	−	3.54069i	−0.616354	−	1.06756i	0.373791	−	0.927513i	$-0.378058\pi$
$12$		0			0
$13$	4.95585			1.37450			0.687252	−	0.726419i	$-0.258817\pi$
$13$	4.95585			1.37450			0.687252	+	0.726419i	$0.258817\pi$
$14$		0			0
$15$		−	2.12585i		−	0.548892i
$16$		0			0
$17$	2.09103	−	1.20726i	0.507150	−	0.292803i	−0.224511	−	0.974471i	$-0.572079\pi$
$17$	2.09103	−	1.20726i	0.507150	−	0.292803i	0.731661	+	0.681668i	$0.238745\pi$
$18$		0			0
$19$	−5.22809	−	3.01844i	−1.19941	−	0.692478i	−0.238984	−	0.971024i	$-0.576814\pi$
$19$	−5.22809	−	3.01844i	−1.19941	−	0.692478i	−0.960423	+	0.278546i	$0.910148\pi$
$20$		0			0
$21$	5.60566	+	0.459619i	1.22326	+	0.100297i
$22$		0			0
$23$	0.443005	+	0.255769i	0.0923730	+	0.0533316i	0.545475	−	0.838127i	$-0.316349\pi$
$23$	0.443005	+	0.255769i	0.0923730	+	0.0533316i	−0.453102	+	0.891459i	$0.649683\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$			3.14787i			0.605808i
$28$		0			0
$29$			3.08127i			0.572177i	0.958203	+	0.286088i	$0.0923551\pi$
$29$			3.08127i			0.572177i	−0.958203	+	0.286088i	$0.907645\pi$
$30$		0			0
$31$	−2.30669	−	3.99530i	−0.414294	−	0.717578i	0.581060	−	0.813861i	$-0.302638\pi$
$31$	−2.30669	−	3.99530i	−0.414294	−	0.717578i	−0.995354	+	0.0962826i	$0.969305\pi$
$32$		0			0
$33$	−7.52697	−	4.34570i	−1.31028	−	0.756489i
$34$		0			0
$35$	2.39173	−	1.13121i	0.404276	−	0.191210i
$36$		0			0
$37$	8.64910	+	4.99356i	1.42190	+	0.820937i	0.996462	−	0.0840489i	$-0.0267852\pi$
$37$	8.64910	+	4.99356i	1.42190	+	0.820937i	0.425442	+	0.904986i	$0.360119\pi$
$38$		0			0
$39$	9.12392	−	5.26770i	1.46100	−	0.843507i
$40$		0			0
$41$		−	5.81092i		−	0.907514i	−0.891126	−	0.453757i	$-0.850083\pi$
$41$		−	5.81092i		−	0.907514i	0.891126	−	0.453757i	$-0.149917\pi$
$42$		0			0
$43$	10.7069			1.63278			0.816390	−	0.577501i	$-0.195972\pi$
$43$	10.7069			1.63278			0.816390	+	0.577501i	$0.195972\pi$
$44$		0			0
$45$	−0.759621	−	1.31570i	−0.113238	−	0.196133i
$46$		0			0
$47$	−0.698912	+	1.21055i	−0.101947	+	0.176577i	−0.912487	−	0.409106i	$-0.865840\pi$
$47$	−0.698912	+	1.21055i	−0.101947	+	0.176577i	0.810540	+	0.585683i	$0.199174\pi$
$48$		0			0
$49$	2.46579	+	6.55133i	0.352256	+	0.935904i
$50$		0			0
$51$	2.56645	−	4.44522i	0.359375	−	0.622456i
$52$		0			0
$53$	−6.79325	+	3.92208i	−0.933124	+	0.538739i	−0.887798	−	0.460233i	$-0.847766\pi$
$53$	−6.79325	+	3.92208i	−0.933124	+	0.538739i	−0.0453258	+	0.998972i	$0.514433\pi$
$54$		0			0
$55$	−4.08843			−0.551284
$56$		0			0
$57$	−12.8335			−1.69984
$58$		0			0
$59$	−8.82516	+	5.09521i	−1.14894	+	0.663339i	−0.948628	−	0.316393i	$-0.897528\pi$
$59$	−8.82516	+	5.09521i	−1.14894	+	0.663339i	−0.200310	+	0.979733i	$0.564195\pi$
$60$		0			0
$61$	−1.33141	+	2.30607i	−0.170469	+	0.295262i	−0.938584	−	0.345051i	$-0.887862\pi$
$61$	−1.33141	+	2.30607i	−0.170469	+	0.295262i	0.768115	+	0.640312i	$0.221195\pi$
$62$		0			0
$63$	3.63361	−	1.71859i	0.457792	−	0.216521i
$64$		0			0
$65$	2.47792	−	4.29189i	0.307349	−	0.532343i
$66$		0			0
$67$	−3.46437	−	6.00046i	−0.423240	−	0.733073i	0.573014	−	0.819545i	$-0.305774\pi$
$67$	−3.46437	−	6.00046i	−0.423240	−	0.733073i	−0.996254	+	0.0864725i	$0.972441\pi$
$68$		0			0
$69$	1.08745			0.130914
$70$		0			0
$71$		−	1.54183i		−	0.182981i	−0.995806	−	0.0914906i	$-0.970837\pi$
$71$		−	1.54183i		−	0.182981i	0.995806	−	0.0914906i	$-0.0291631\pi$
$72$		0			0
$73$	6.99634	−	4.03934i	0.818859	−	0.472769i	−0.0311636	−	0.999514i	$-0.509921\pi$
$73$	6.99634	−	4.03934i	0.818859	−	0.472769i	0.850023	+	0.526746i	$0.176588\pi$
$74$		0			0
$75$	−1.84104	−	1.06293i	−0.212585	−	0.122736i
$76$		0			0
$77$	0.883939	−	10.7808i	0.100734	−	1.22859i
$78$		0			0
$79$	−3.21095	−	1.85384i	−0.361260	−	0.208574i	0.308373	−	0.951265i	$-0.400215\pi$
$79$	−3.21095	−	1.85384i	−0.361260	−	0.208574i	−0.669633	+	0.742692i	$0.733549\pi$
$80$		0			0
$81$	5.62481	+	9.74247i	0.624979	+	1.08250i
$82$		0			0
$83$		−	9.94035i		−	1.09109i	−0.838080	−	0.545547i	$-0.816322\pi$
$83$		−	9.94035i		−	1.09109i	0.838080	−	0.545547i	$-0.183678\pi$
$84$		0			0
$85$		−	2.41452i		−	0.261891i
$86$		0			0
$87$	3.27516	+	5.67274i	0.351134	+	0.608181i
$88$		0			0
$89$	−3.81064	−	2.20007i	−0.403927	−	0.233207i	0.284250	−	0.958750i	$-0.408255\pi$
$89$	−3.81064	−	2.20007i	−0.403927	−	0.233207i	−0.688177	+	0.725543i	$0.741589\pi$
$90$		0			0
$91$	10.7816	+	7.46197i	1.13021	+	0.782227i
$92$		0			0
$93$	−8.49342	−	4.90368i	−0.880727	−	0.508488i
$94$		0			0
$95$	−5.22809	+	3.01844i	−0.536391	+	0.309685i
$96$		0			0
$97$			5.67803i			0.576517i	0.957553	+	0.288258i	$0.0930762\pi$
$97$			5.67803i			0.576517i	−0.957553	+	0.288258i	$0.906924\pi$
$98$		0			0
$99$	−6.21132			−0.624261
$100$		0			0
$101$	−7.38908	−	12.7983i	−0.735241	−	1.27348i	−0.954617	−	0.297835i	$-0.903735\pi$
$101$	−7.38908	−	12.7983i	−0.735241	−	1.27348i	0.219376	−	0.975640i	$-0.429598\pi$
$102$		0			0
$103$	−4.73633	+	8.20356i	−0.466684	+	0.808321i	−0.999276	−	0.0380514i	$-0.987885\pi$
$103$	−4.73633	+	8.20356i	−0.466684	+	0.808321i	0.532591	+	0.846373i	$0.321218\pi$
$104$		0			0
$105$	3.20087	−	4.62484i	0.312373	−	0.451338i
$106$		0			0
$107$	−9.53855	+	16.5212i	−0.922126	+	1.59717i	−0.126007	+	0.992029i	$0.540216\pi$
$107$	−9.53855	+	16.5212i	−0.922126	+	1.59717i	−0.796119	+	0.605140i	$0.793117\pi$
$108$		0			0
$109$	−0.554540	+	0.320164i	−0.0531153	+	0.0306662i	−0.526323	−	0.850285i	$-0.676430\pi$
$109$	−0.554540	+	0.320164i	−0.0531153	+	0.0306662i	0.473207	+	0.880951i	$0.343096\pi$
$110$		0			0
$111$	21.2311			2.01517
$112$		0			0
$113$	−14.8422			−1.39623			−0.698117	−	0.715984i	$-0.745978\pi$
$113$	−14.8422			−1.39623			−0.698117	+	0.715984i	$0.745978\pi$
$114$		0			0
$115$	0.443005	−	0.255769i	0.0413105	−	0.0238506i
$116$		0			0
$117$	3.76457	−	6.52042i	0.348034	−	0.602813i
$118$		0			0
$119$	6.36685	+	0.522030i	0.583648	+	0.0478544i
$120$		0			0
$121$	−2.85764	+	4.94958i	−0.259786	+	0.449962i
$122$		0			0
$123$	−6.17658	−	10.6981i	−0.556923	−	0.964619i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$			7.19222i			0.638207i	0.947720	+	0.319103i	$0.103382\pi$
$127$			7.19222i			0.638207i	−0.947720	+	0.319103i	$0.896618\pi$
$128$		0			0
$129$	19.7118	−	11.3806i	1.73552	−	1.00201i
$130$		0			0
$131$	6.50864	+	3.75777i	0.568663	+	0.328318i	0.756615	−	0.653860i	$-0.226852\pi$
$131$	6.50864	+	3.75777i	0.568663	+	0.328318i	−0.187952	+	0.982178i	$0.560185\pi$
$132$		0			0
$133$	−6.82899	−	14.4386i	−0.592149	−	1.25198i
$134$		0			0
$135$	2.72614	+	1.57394i	0.234628	+	0.135463i
$136$		0			0
$137$	1.70968	+	2.96124i	0.146067	+	0.252996i	0.929771	−	0.368139i	$-0.120005\pi$
$137$	1.70968	+	2.96124i	0.146067	+	0.252996i	−0.783703	+	0.621135i	$0.786672\pi$
$138$		0			0
$139$			11.0468i			0.936981i	0.883468	+	0.468491i	$0.155202\pi$
$139$			11.0468i			0.936981i	−0.883468	+	0.468491i	$0.844798\pi$
$140$		0			0
$141$			2.97156i			0.250251i
$142$		0			0
$143$	−10.1308	−	17.5471i	−0.847182	−	1.46736i
$144$		0			0
$145$	2.66845	+	1.54063i	0.221603	+	0.127943i
$146$		0			0
$147$	11.5032	+	9.44030i	0.948768	+	0.778623i
$148$		0			0
$149$	8.88620	+	5.13045i	0.727986	+	0.420303i	0.817685	−	0.575666i	$-0.195257\pi$
$149$	8.88620	+	5.13045i	0.727986	+	0.420303i	−0.0896992	+	0.995969i	$0.528591\pi$
$150$		0			0
$151$	−14.2514	+	8.22804i	−1.15976	+	0.669588i	−0.951247	−	0.308431i	$-0.900196\pi$
$151$	−14.2514	+	8.22804i	−1.15976	+	0.669588i	−0.208514	+	0.978019i	$0.566863\pi$
$152$		0			0
$153$		−	3.66824i		−	0.296559i
$154$		0			0
$155$	−4.61338			−0.370556
$156$		0			0
$157$	11.1196	+	19.2597i	0.887441	+	1.53709i	0.842890	+	0.538087i	$0.180853\pi$
$157$	11.1196	+	19.2597i	0.887441	+	1.53709i	0.0445519	+	0.999007i	$0.485814\pi$
$158$		0			0
$159$	−8.33776	+	14.4414i	−0.661227	+	1.14528i
$160$		0			0
$161$	0.578659	+	1.22346i	0.0456047	+	0.0964222i
$162$		0			0
$163$	6.48712	−	11.2360i	0.508111	−	0.880073i	−0.491845	−	0.870683i	$-0.663677\pi$
$163$	6.48712	−	11.2360i	0.508111	−	0.880073i	0.999956	−	0.00939084i	$-0.00298924\pi$
$164$		0			0
$165$	−7.52697	+	4.34570i	−0.585974	+	0.338312i
$166$		0			0
$167$	11.9246			0.922755			0.461377	−	0.887204i	$-0.347355\pi$
$167$	11.9246			0.922755			0.461377	+	0.887204i	$0.347355\pi$
$168$		0			0
$169$	11.5604			0.889264
$170$		0			0
$171$	−7.94273	+	4.58574i	−0.607396	+	0.350680i
$172$		0			0
$173$	−5.55929	+	9.62897i	−0.422665	+	0.732077i	−0.996199	−	0.0871047i	$-0.972239\pi$
$173$	−5.55929	+	9.62897i	−0.422665	+	0.732077i	0.573534	+	0.819181i	$0.305572\pi$
$174$		0			0
$175$	0.216205	−	2.63690i	0.0163436	−	0.199331i
$176$		0			0
$177$	−10.8317	+	18.7610i	−0.814157	+	1.41016i
$178$		0			0
$179$	−4.27641	−	7.40695i	−0.319634	−	0.553622i	0.660778	−	0.750581i	$-0.270227\pi$
$179$	−4.27641	−	7.40695i	−0.319634	−	0.553622i	−0.980412	+	0.196960i	$0.936893\pi$
$180$		0			0
$181$	0.821960			0.0610958			0.0305479	−	0.999533i	$-0.490275\pi$
$181$	0.821960			0.0610958			0.0305479	+	0.999533i	$0.490275\pi$
$182$		0			0
$183$			5.66075i			0.418455i
$184$		0			0
$185$	8.64910	−	4.99356i	0.635895	−	0.367134i
$186$		0			0
$187$	−8.54905	−	4.93580i	−0.625168	−	0.360941i
$188$		0			0
$189$	−4.73972	+	6.84826i	−0.344764	+	0.498138i
$190$		0			0
$191$	19.4375	+	11.2222i	1.40645	+	0.812012i	0.995043	−	0.0994420i	$-0.0317058\pi$
$191$	19.4375	+	11.2222i	1.40645	+	0.812012i	0.411402	+	0.911454i	$0.365039\pi$
$192$		0			0
$193$	2.15591	+	3.73414i	0.155186	+	0.268789i	0.933127	−	0.359548i	$-0.117069\pi$
$193$	2.15591	+	3.73414i	0.155186	+	0.268789i	−0.777941	+	0.628337i	$0.783736\pi$
$194$		0			0
$195$		−	10.5354i		−	0.754455i
$196$		0			0
$197$			6.67148i			0.475323i	0.971348	+	0.237662i	$0.0763809\pi$
$197$			6.67148i			0.475323i	−0.971348	+	0.237662i	$0.923619\pi$
$198$		0			0
$199$	−4.68875	−	8.12116i	−0.332377	−	0.575693i	0.650601	−	0.759420i	$-0.274517\pi$
$199$	−4.68875	−	8.12116i	−0.332377	−	0.575693i	−0.982977	+	0.183727i	$0.941184\pi$
$200$		0			0
$201$	−12.7561	−	7.36473i	−0.899745	−	0.519468i
$202$		0			0
$203$	−4.63943	+	6.70336i	−0.325624	+	0.470484i
$204$		0			0
$205$	−5.03241	−	2.90546i	−0.351479	−	0.202926i
$206$		0			0
$207$	0.673032	−	0.388575i	0.0467790	−	0.0270079i
$208$		0			0
$209$			24.6814i			1.70725i
$210$		0			0
$211$	−6.08038			−0.418590			−0.209295	−	0.977852i	$-0.567117\pi$
$211$	−6.08038			−0.418590			−0.209295	+	0.977852i	$0.567117\pi$
$212$		0			0
$213$	−1.63885	−	2.83857i	−0.112292	−	0.194495i
$214$		0			0
$215$	5.35343	−	9.27241i	0.365101	−	0.632373i
$216$		0			0
$217$	0.997435	−	12.1650i	0.0677103	−	0.825816i
$218$		0			0
$219$	8.58703	−	14.8732i	0.580258	−	1.00504i
$220$		0			0
$221$	10.3628	−	5.98299i	0.697080	−	0.402459i
$222$		0			0
$223$	−15.1265			−1.01295			−0.506474	−	0.862255i	$-0.669051\pi$
$223$	−15.1265			−1.01295			−0.506474	+	0.862255i	$0.669051\pi$
$224$		0			0
$225$	−1.51924			−0.101283
$226$		0			0
$227$	19.6959	−	11.3714i	1.30726	−	0.754747i	0.325622	−	0.945500i	$-0.394426\pi$
$227$	19.6959	−	11.3714i	1.30726	−	0.754747i	0.981638	+	0.190753i	$0.0610929\pi$
$228$		0			0
$229$	1.35800	−	2.35213i	0.0897393	−	0.155433i	−0.817662	−	0.575699i	$-0.804730\pi$
$229$	1.35800	−	2.35213i	0.0897393	−	0.155433i	0.907401	+	0.420266i	$0.138063\pi$
$230$		0			0
$231$	−9.83182	−	20.7875i	−0.646886	−	1.36771i
$232$		0			0
$233$	8.54513	−	14.8006i	0.559810	−	0.969620i	−0.437702	−	0.899120i	$-0.644207\pi$
$233$	8.54513	−	14.8006i	0.559810	−	0.969620i	0.997512	−	0.0704994i	$-0.0224593\pi$
$234$		0			0
$235$	0.698912	+	1.21055i	0.0455920	+	0.0789676i
$236$		0			0
$237$	−7.88199			−0.511990
$238$		0			0
$239$			14.8013i			0.957416i	0.877974	+	0.478708i	$0.158895\pi$
$239$			14.8013i			0.957416i	−0.877974	+	0.478708i	$0.841105\pi$
$240$		0			0
$241$	−15.4371	+	8.91260i	−0.994389	+	0.574111i	−0.906583	−	0.422027i	$-0.861319\pi$
$241$	−15.4371	+	8.91260i	−0.994389	+	0.574111i	−0.0878059	+	0.996138i	$0.527986\pi$
$242$		0			0
$243$	12.5326	+	7.23571i	0.803968	+	0.464171i
$244$		0			0
$245$	6.90651	+	1.14022i	0.441241	+	0.0728461i
$246$		0			0
$247$	−25.9096	−	14.9589i	−1.64859	−	0.951814i
$248$		0			0
$249$	−10.5658	−	18.3006i	−0.669583	−	1.15975i
$250$		0			0
$251$			25.9720i			1.63934i	0.572837	+	0.819669i	$0.305843\pi$
$251$			25.9720i			1.63934i	−0.572837	+	0.819669i	$0.694157\pi$
$252$		0			0
$253$		−	2.09139i		−	0.131485i
$254$		0			0
$255$	−2.56645	−	4.44522i	−0.160717	−	0.278371i
$256$		0			0
$257$	8.43972	+	4.87268i	0.526455	+	0.303949i	0.739572	−	0.673078i	$-0.235028\pi$
$257$	8.43972	+	4.87268i	0.526455	+	0.303949i	−0.213116	+	0.977027i	$0.568361\pi$
$258$		0			0
$259$	11.2976	+	23.8865i	0.701996	+	1.48423i
$260$		0			0
$261$	4.05403	+	2.34059i	0.250938	+	0.144879i
$262$		0			0
$263$	−5.12532	+	2.95910i	−0.316041	+	0.182466i	−0.649626	−	0.760254i	$-0.725075\pi$
$263$	−5.12532	+	2.95910i	−0.316041	+	0.182466i	0.333586	+	0.942720i	$0.391741\pi$
$264$		0			0
$265$			7.84416i			0.481863i
$266$		0			0
$267$	−9.35405			−0.572459
$268$		0			0
$269$	−10.3914	−	17.9984i	−0.633572	−	1.09738i	−0.986816	−	0.161848i	$-0.948255\pi$
$269$	−10.3914	−	17.9984i	−0.633572	−	1.09738i	0.353244	−	0.935531i	$-0.385079\pi$
$270$		0			0
$271$	−5.73115	+	9.92664i	−0.348143	+	0.603001i	−0.985920	−	0.167221i	$-0.946521\pi$
$271$	−5.73115	+	9.92664i	−0.348143	+	0.603001i	0.637777	+	0.770221i	$0.279854\pi$
$272$		0			0
$273$	27.7808	+	2.27780i	1.68137	+	0.137859i
$274$		0			0
$275$	−2.04422	+	3.54069i	−0.123271	+	0.213511i
$276$		0			0
$277$	−28.4995	+	16.4542i	−1.71237	+	0.988638i	−0.781029	+	0.624495i	$0.785305\pi$
$277$	−28.4995	+	16.4542i	−1.71237	+	0.988638i	−0.931343	+	0.364143i	$0.881362\pi$
$278$		0			0
$279$	−7.00884			−0.419608
$280$		0			0
$281$	−23.6717			−1.41214			−0.706068	−	0.708144i	$-0.749533\pi$
$281$	−23.6717			−1.41214			−0.706068	+	0.708144i	$0.749533\pi$
$282$		0			0
$283$	17.3451	−	10.0142i	1.03106	−	0.595283i	0.113772	−	0.993507i	$-0.463707\pi$
$283$	17.3451	−	10.0142i	1.03106	−	0.595283i	0.917288	+	0.398224i	$0.130373\pi$
$284$		0			0
$285$	−6.41675	+	11.1141i	−0.380096	+	0.658345i
$286$		0			0
$287$	8.74945	−	12.6418i	0.516464	−	0.746221i
$288$		0			0
$289$	−5.58505	+	9.67360i	−0.328533	+	0.569035i
$290$		0			0
$291$	6.03532	+	10.4535i	0.353797	+	0.612794i
$292$		0			0
$293$	−4.76771			−0.278533			−0.139266	−	0.990255i	$-0.544474\pi$
$293$	−4.76771			−0.278533			−0.139266	+	0.990255i	$0.544474\pi$
$294$		0			0
$295$			10.1904i			0.593309i
$296$		0			0
$297$	11.1456	−	6.43493i	0.646735	−	0.373393i
$298$		0			0
$299$	2.19547	+	1.26755i	0.126967	+	0.0733045i
$300$		0			0
$301$	23.2930	+	16.1212i	1.34259	+	0.929211i
$302$		0			0
$303$	−27.2072	−	15.7081i	−1.56301	−	0.902406i
$304$		0			0
$305$	1.33141	+	2.30607i	0.0762362	+	0.132045i
$306$		0			0
$307$			14.4066i			0.822231i	0.911583	+	0.411115i	$0.134861\pi$
$307$			14.4066i			0.822231i	−0.911583	+	0.411115i	$0.865139\pi$
$308$		0			0
$309$			20.1375i			1.14558i
$310$		0			0
$311$	0.00739749	+	0.0128128i	0.000419473	+	0.000726549i	0.866235	−	0.499637i	$-0.166533\pi$
$311$	0.00739749	+	0.0128128i	0.000419473	+	0.000726549i	−0.865816	+	0.500363i	$0.833200\pi$
$312$		0			0
$313$	−12.0601	−	6.96291i	−0.681678	−	0.393567i	0.118809	−	0.992917i	$-0.462092\pi$
$313$	−12.0601	−	6.96291i	−0.681678	−	0.393567i	−0.800487	+	0.599350i	$0.795426\pi$
$314$		0			0
$315$	0.328467	−	4.00609i	0.0185070	−	0.225718i
$316$		0			0
$317$	−20.7904	−	12.0034i	−1.16771	−	0.674176i	−0.214568	−	0.976709i	$-0.568834\pi$
$317$	−20.7904	−	12.0034i	−1.16771	−	0.674176i	−0.953139	+	0.302533i	$0.902168\pi$
$318$		0			0
$319$	10.9098	−	6.29878i	0.610831	−	0.352664i
$320$		0			0
$321$			40.5550i			2.26356i
$322$		0			0
$323$	−14.5762			−0.811039
$324$		0			0
$325$	−2.47792	−	4.29189i	−0.137450	−	0.238071i
$326$		0			0
$327$	−0.680621	+	1.17887i	−0.0376384	+	0.0651917i
$328$		0			0
$329$	−3.34321	+	1.58124i	−0.184317	+	0.0871763i
$330$		0			0
$331$	0.783208	−	1.35656i	0.0430490	−	0.0745630i	−0.843698	−	0.536818i	$-0.819626\pi$
$331$	0.783208	−	1.35656i	0.0430490	−	0.0745630i	0.886747	+	0.462255i	$0.152960\pi$
$332$		0			0
$333$	13.1401	−	7.58643i	0.720072	−	0.415734i
$334$		0			0
$335$	−6.92873			−0.378557
$336$		0			0
$337$	0.0592518			0.00322765			0.00161383	−	0.999999i	$-0.499486\pi$
$337$	0.0592518			0.00322765			0.00161383	+	0.999999i	$0.499486\pi$
$338$		0			0
$339$	−27.3250	+	15.7761i	−1.48409	+	0.856841i
$340$		0			0
$341$	−9.43075	+	16.3345i	−0.510704	+	0.884565i
$342$		0			0
$343$	−4.49988	+	17.9653i	−0.242970	+	0.970034i
$344$		0			0
$345$	0.543727	−	0.941763i	0.0292733	−	0.0507028i
$346$		0			0
$347$	0.0461825	+	0.0799904i	0.00247921	+	0.00429411i	0.867262	−	0.497851i	$-0.165878\pi$
$347$	0.0461825	+	0.0799904i	0.00247921	+	0.00429411i	−0.864783	+	0.502146i	$0.832544\pi$
$348$		0			0
$349$	15.4400			0.826483			0.413241	−	0.910622i	$-0.364397\pi$
$349$	15.4400			0.826483			0.413241	+	0.910622i	$0.364397\pi$
$350$		0			0
$351$			15.6004i			0.832686i
$352$		0			0
$353$	−8.58726	+	4.95786i	−0.457054	+	0.263880i	−0.710805	−	0.703389i	$-0.751669\pi$
$353$	−8.58726	+	4.95786i	−0.457054	+	0.263880i	0.253751	+	0.967270i	$0.418336\pi$
$354$		0			0
$355$	−1.33526	−	0.770914i	−0.0708683	−	0.0409158i
$356$		0			0
$357$	12.2765	−	5.80640i	0.649742	−	0.307307i
$358$		0			0
$359$	−9.04478	−	5.22201i	−0.477365	−	0.275607i	0.241953	−	0.970288i	$-0.422212\pi$
$359$	−9.04478	−	5.22201i	−0.477365	−	0.275607i	−0.719318	+	0.694681i	$0.755545\pi$
$360$		0			0
$361$	8.72196	+	15.1069i	0.459051	+	0.795099i
$362$		0			0
$363$			12.1498i			0.637701i
$364$		0			0
$365$		−	8.07867i		−	0.422857i
$366$		0			0
$367$	14.3708	+	24.8910i	0.750152	+	1.29930i	0.947749	+	0.319018i	$0.103353\pi$
$367$	14.3708	+	24.8910i	0.750152	+	1.29930i	−0.197596	+	0.980283i	$0.563314\pi$
$368$		0			0
$369$	−7.64544	−	4.41410i	−0.398006	−	0.229789i
$370$		0			0
$371$	−20.6843	−	1.69595i	−1.07388	−	0.0880491i
$372$		0			0
$373$	−8.93722	−	5.15991i	−0.462752	−	0.267170i	0.250449	−	0.968130i	$-0.419422\pi$
$373$	−8.93722	−	5.15991i	−0.462752	−	0.267170i	−0.713201	+	0.700960i	$0.752755\pi$
$374$		0			0
$375$	−1.84104	+	1.06293i	−0.0950709	+	0.0548892i
$376$		0			0
$377$			15.2703i			0.786460i
$378$		0			0
$379$	20.1192			1.03346			0.516728	−	0.856150i	$-0.327150\pi$
$379$	20.1192			1.03346			0.516728	+	0.856150i	$0.327150\pi$
$380$		0			0
$381$	7.64480	+	13.2412i	0.391655	+	0.678366i
$382$		0			0
$383$	15.9182	−	27.5710i	0.813380	−	1.40881i	−0.0971062	−	0.995274i	$-0.530959\pi$
$383$	15.9182	−	27.5710i	0.813380	−	1.40881i	0.910486	−	0.413541i	$-0.135708\pi$
$384$		0			0
$385$	−8.89448	−	6.15591i	−0.453304	−	0.313734i
$386$		0			0
$387$	8.13315	−	14.0870i	0.413431	−	0.716084i
$388$		0			0
$389$	11.9293	−	6.88741i	0.604842	−	0.349205i	−0.166102	−	0.986109i	$-0.553118\pi$
$389$	11.9293	−	6.88741i	0.604842	−	0.349205i	0.770944	+	0.636903i	$0.219785\pi$
$390$		0			0
$391$	1.23512			0.0624626
$392$		0			0
$393$	15.9769			0.805928
$394$		0			0
$395$	−3.21095	+	1.85384i	−0.161561	+	0.0932770i
$396$		0			0
$397$	15.3003	−	26.5009i	0.767900	−	1.33004i	−0.170800	−	0.985306i	$-0.554635\pi$
$397$	15.3003	−	26.5009i	0.767900	−	1.33004i	0.938700	−	0.344736i	$-0.112031\pi$
$398$		0			0
$399$	−27.9196	−	19.3233i	−1.39773	−	0.967374i
$400$		0			0
$401$	9.62164	−	16.6652i	0.480482	−	0.832219i	−0.519267	−	0.854612i	$-0.673795\pi$
$401$	9.62164	−	16.6652i	0.480482	−	0.832219i	0.999749	+	0.0223928i	$0.00712846\pi$
$402$		0			0
$403$	−11.4316	−	19.8001i	−0.569449	−	0.986314i
$404$		0			0
$405$	11.2496			0.558999
$406$		0			0
$407$		−	40.8317i		−	2.02395i
$408$		0			0
$409$	−4.36225	+	2.51854i	−0.215699	+	0.124534i	−0.603957	−	0.797017i	$-0.706410\pi$
$409$	−4.36225	+	2.51854i	−0.215699	+	0.124534i	0.388258	+	0.921551i	$0.373077\pi$
$410$		0			0
$411$	6.29516	+	3.63451i	0.310518	+	0.179277i
$412$		0			0
$413$	−26.8711	−	2.20322i	−1.32224	−	0.108413i
$414$		0			0
$415$	−8.60859	−	4.97017i	−0.422579	−	0.243976i
$416$		0			0
$417$	11.7420	+	20.3377i	0.575007	+	0.995941i
$418$		0			0
$419$		−	15.6895i		−	0.766483i	−0.923648	−	0.383242i	$-0.874808\pi$
$419$		−	15.6895i		−	0.766483i	0.923648	−	0.383242i	$-0.125192\pi$
$420$		0			0
$421$			17.3487i			0.845525i	0.906240	+	0.422763i	$0.138940\pi$
$421$			17.3487i			0.845525i	−0.906240	+	0.422763i	$0.861060\pi$
$422$		0			0
$423$	1.06182	+	1.83912i	0.0516273	+	0.0894210i
$424$		0			0
$425$	−2.09103	−	1.20726i	−0.101430	−	0.0585606i
$426$		0			0
$427$	−6.36873	+	3.01221i	−0.308205	+	0.145771i
$428$		0			0
$429$	−37.3025	−	21.5366i	−1.80098	−	1.03980i
$430$		0			0
$431$	−6.75727	+	3.90131i	−0.325486	+	0.187920i	−0.653835	−	0.756637i	$-0.726841\pi$
$431$	−6.75727	+	3.90131i	−0.325486	+	0.187920i	0.328349	+	0.944556i	$0.393508\pi$
$432$		0			0
$433$		−	8.76403i		−	0.421172i	−0.977575	−	0.210586i	$-0.932463\pi$
$433$		−	8.76403i		−	0.421172i	0.977575	−	0.210586i	$-0.0675372\pi$
$434$		0			0
$435$	6.55031			0.314063
$436$		0			0
$437$	−1.54405	−	2.67437i	−0.0738619	−	0.127932i
$438$		0			0
$439$	1.26642	−	2.19350i	0.0604428	−	0.104690i	−0.834221	−	0.551431i	$-0.814082\pi$
$439$	1.26642	−	2.19350i	0.0604428	−	0.104690i	0.894663	+	0.446741i	$0.147415\pi$
$440$		0			0
$441$	10.4927	+	1.73227i	0.499650	+	0.0824892i
$442$		0			0
$443$	14.7957	−	25.6269i	0.702964	−	1.21757i	−0.264458	−	0.964397i	$-0.585193\pi$
$443$	14.7957	−	25.6269i	0.702964	−	1.21757i	0.967421	−	0.253172i	$-0.0814737\pi$
$444$		0			0
$445$	−3.81064	+	2.20007i	−0.180642	+	0.104293i
$446$		0			0
$447$	21.8131			1.03173
$448$		0			0
$449$	−12.4051			−0.585434			−0.292717	−	0.956199i	$-0.594559\pi$
$449$	−12.4051			−0.585434			−0.292717	+	0.956199i	$0.594559\pi$
$450$		0			0
$451$	−20.5747	+	11.8788i	−0.968823	+	0.559350i
$452$		0			0
$453$	−17.4916	+	30.2963i	−0.821826	+	1.42344i
$454$		0			0
$455$	11.8530	−	5.60612i	0.555679	−	0.262819i
$456$		0			0
$457$	19.1981	−	33.2521i	0.898049	−	1.55547i	0.0680633	−	0.997681i	$-0.478318\pi$
$457$	19.1981	−	33.2521i	0.898049	−	1.55547i	0.829985	−	0.557785i	$-0.188349\pi$
$458$		0			0
$459$	3.80029	+	6.58230i	0.177383	+	0.307236i
$460$		0			0
$461$	19.3759			0.902426			0.451213	−	0.892416i	$-0.350992\pi$
$461$	19.3759			0.902426			0.451213	+	0.892416i	$0.350992\pi$
$462$		0			0
$463$			34.4968i			1.60320i	0.597860	+	0.801600i	$0.296018\pi$
$463$			34.4968i			1.60320i	−0.597860	+	0.801600i	$0.703982\pi$
$464$		0			0
$465$	−8.49342	+	4.90368i	−0.393873	+	0.227403i
$466$		0			0
$467$	−18.4058	−	10.6266i	−0.851720	−	0.491741i	0.00951086	−	0.999955i	$-0.496973\pi$
$467$	−18.4058	−	10.6266i	−0.851720	−	0.491741i	−0.861231	+	0.508214i	$0.830306\pi$
$468$		0			0
$469$	1.49803	−	18.2704i	0.0691724	−	0.843649i
$470$		0			0
$471$	40.9433	+	23.6386i	1.88657	+	1.08921i
$472$		0			0
$473$	−21.8871	−	37.9096i	−1.00637	−	1.74309i
$474$		0			0
$475$			6.03688i			0.276991i
$476$		0			0
$477$			11.9172i			0.545650i
$478$		0			0
$479$	2.99806	+	5.19279i	0.136985	+	0.237265i	0.926354	−	0.376654i	$-0.122925\pi$
$479$	2.99806	+	5.19279i	0.136985	+	0.237265i	−0.789369	+	0.613919i	$0.789592\pi$
$480$		0			0
$481$	42.8636	+	24.7473i	1.95441	+	1.12838i
$482$		0			0
$483$	2.36578	+	1.63737i	0.107647	+	0.0745029i
$484$		0			0
$485$	4.91732	+	2.83902i	0.223284	+	0.128913i
$486$		0			0
$487$	−8.18300	+	4.72445i	−0.370807	+	0.214085i	−0.673811	−	0.738904i	$-0.735344\pi$
$487$	−8.18300	+	4.72445i	−0.370807	+	0.214085i	0.303004	+	0.952989i	$0.402010\pi$
$488$		0			0
$489$		−	27.5813i		−	1.24727i
$490$		0			0
$491$	−24.6604			−1.11291			−0.556454	−	0.830879i	$-0.687838\pi$
$491$	−24.6604			−1.11291			−0.556454	+	0.830879i	$0.687838\pi$
$492$		0			0
$493$	3.71989	+	6.44303i	0.167535	+	0.290179i
$494$		0			0
$495$	−3.10566	+	5.37916i	−0.139589	+	0.241775i
$496$		0			0
$497$	2.32151	−	3.35428i	0.104134	−	0.150460i
$498$		0			0
$499$	11.1699	−	19.3469i	0.500035	−	0.866086i	−0.499965	−	0.866046i	$-0.666654\pi$
$499$	11.1699	−	19.3469i	0.500035	−	0.866086i	1.00000		4.07161e-5i	$-1.29603e-5\pi$
$500$		0			0
$501$	21.9537	−	12.6750i	0.980820	−	0.566276i
$502$		0			0
$503$	7.59124			0.338477			0.169238	−	0.985575i	$-0.445869\pi$
$503$	7.59124			0.338477			0.169238	+	0.985575i	$0.445869\pi$
$504$		0			0
$505$	−14.7782			−0.657620
$506$		0			0
$507$	21.2832	−	12.2879i	0.945221	−	0.545724i
$508$		0			0
$509$	16.7288	−	28.9751i	0.741490	−	1.28430i	−0.210326	−	0.977631i	$-0.567453\pi$
$509$	16.7288	−	28.9751i	0.741490	−	1.28430i	0.951817	−	0.306668i	$-0.0992140\pi$
$510$		0			0
$511$	21.3027	+	1.74665i	0.942375	+	0.0772672i
$512$		0			0
$513$	9.50166	−	16.4574i	0.419509	−	0.726610i
$514$		0			0
$515$	4.73633	+	8.20356i	0.208708	+	0.361492i
$516$		0			0
$517$	5.71491			0.251341
$518$		0			0
$519$			23.6364i			1.03752i
$520$		0			0
$521$	−4.24541	+	2.45109i	−0.185995	+	0.107384i	−0.590106	−	0.807326i	$-0.700914\pi$
$521$	−4.24541	+	2.45109i	−0.185995	+	0.107384i	0.404111	+	0.914710i	$0.367581\pi$
$522$		0			0
$523$	−2.15135	−	1.24208i	−0.0940721	−	0.0543125i	0.452226	−	0.891903i	$-0.350630\pi$
$523$	−2.15135	−	1.24208i	−0.0940721	−	0.0543125i	−0.546298	+	0.837591i	$0.683963\pi$
$524$		0			0
$525$	−2.40479	−	5.08445i	−0.104954	−	0.221904i
$526$		0			0
$527$	−9.64673	−	5.56954i	−0.420218	−	0.242613i
$528$		0			0
$529$	−11.3692	−	19.6920i	−0.494311	−	0.856173i
$530$		0			0
$531$			15.4817i			0.671849i
$532$		0			0
$533$		−	28.7981i		−	1.24738i
$534$		0			0
$535$	9.53855	+	16.5212i	0.412387	+	0.714276i
$536$		0			0
$537$	−15.7461	−	9.09100i	−0.679493	−	0.392306i
$538$		0			0
$539$	18.1556	−	22.1229i	0.782016	−	0.952902i
$540$		0			0
$541$	−23.1290	−	13.3535i	−0.994392	−	0.574113i	−0.0878078	−	0.996137i	$-0.527986\pi$
$541$	−23.1290	−	13.3535i	−0.994392	−	0.574113i	−0.906584	+	0.422025i	$0.861319\pi$
$542$		0			0
$543$	1.51326	−	0.873682i	0.0649403	−	0.0374933i
$544$		0			0
$545$			0.640328i			0.0274286i
$546$		0			0
$547$	−21.5603			−0.921851			−0.460926	−	0.887439i	$-0.652483\pi$
$547$	−21.5603			−0.921851			−0.460926	+	0.887439i	$0.652483\pi$
$548$		0			0
$549$	2.02273	+	3.50347i	0.0863281	+	0.149525i
$550$		0			0
$551$	9.30062	−	16.1091i	0.396220	−	0.686273i
$552$		0			0
$553$	−4.19418	−	8.86778i	−0.178355	−	0.377096i
$554$		0			0
$555$	10.6156	−	18.3867i	0.450606	−	0.780472i
$556$		0			0
$557$	11.7177	−	6.76520i	0.496493	−	0.286651i	−0.230771	−	0.973008i	$-0.574125\pi$
$557$	11.7177	−	6.76520i	0.496493	−	0.286651i	0.727264	+	0.686358i	$0.240791\pi$
$558$		0			0
$559$	53.0616			2.24426
$560$		0			0
$561$	−20.9855			−0.886010
$562$		0			0
$563$	−0.290557	+	0.167753i	−0.0122455	+	0.00706994i	−0.506110	−	0.862469i	$-0.668917\pi$
$563$	−0.290557	+	0.167753i	−0.0122455	+	0.00706994i	0.493865	+	0.869539i	$0.335584\pi$
$564$		0			0
$565$	−7.42108	+	12.8537i	−0.312207	+	0.540759i
$566$		0			0
$567$	−2.43222	+	29.6642i	−0.102144	+	1.24578i
$568$		0			0
$569$	−6.01354	+	10.4158i	−0.252101	+	0.436651i	−0.964104	−	0.265525i	$-0.914455\pi$
$569$	−6.01354	+	10.4158i	−0.252101	+	0.436651i	0.712003	+	0.702176i	$0.247788\pi$
$570$		0			0
$571$	−17.2292	−	29.8419i	−0.721020	−	1.24884i	−0.960591	−	0.277965i	$-0.910340\pi$
$571$	−17.2292	−	29.8419i	−0.721020	−	1.24884i	0.239571	−	0.970879i	$-0.422993\pi$
$572$		0			0
$573$	47.7136			1.99326
$574$		0			0
$575$		−	0.511539i		−	0.0213326i
$576$		0			0
$577$	26.7684	−	15.4547i	1.11438	−	0.643389i	0.174422	−	0.984671i	$-0.444194\pi$
$577$	26.7684	−	15.4547i	1.11438	−	0.643389i	0.939961	+	0.341282i	$0.110861\pi$
$578$		0			0
$579$	7.93823	+	4.58314i	0.329901	+	0.190469i
$580$		0			0
$581$	14.9671	−	21.6254i	0.620939	−	0.897175i
$582$		0			0
$583$	27.7737	+	16.0352i	1.15027	+	0.664109i
$584$		0			0
$585$	−3.76457	−	6.52042i	−0.155646	−	0.269586i
$586$		0			0
$587$		−	11.3376i		−	0.467955i	−0.972242	−	0.233977i	$-0.924826\pi$
$587$		−	11.3376i		−	0.467955i	0.972242	−	0.233977i	$-0.0751742\pi$
$588$		0			0
$589$			27.8504i			1.14756i
$590$		0			0
$591$	7.09128	+	12.2825i	0.291696	+	0.505233i
$592$		0			0
$593$	26.3586	+	15.2182i	1.08242	+	0.624935i	0.931548	−	0.363618i	$-0.118459\pi$
$593$	26.3586	+	15.2182i	1.08242	+	0.624935i	0.150872	+	0.988553i	$0.451792\pi$
$594$		0			0
$595$	3.63551	−	5.25284i	0.149042	−	0.215345i
$596$		0			0
$597$	−17.2644	−	9.96759i	−0.706583	−	0.407946i
$598$		0			0
$599$	11.1298	−	6.42577i	0.454750	−	0.262550i	−0.255084	−	0.966919i	$-0.582103\pi$
$599$	11.1298	−	6.42577i	0.454750	−	0.262550i	0.709834	+	0.704369i	$0.248770\pi$
$600$		0			0
$601$		−	17.2953i		−	0.705489i	−0.935720	−	0.352745i	$-0.885248\pi$
$601$		−	17.2953i		−	0.705489i	0.935720	−	0.352745i	$-0.114752\pi$
$602$		0			0
$603$	−10.5264			−0.428669
$604$		0			0
$605$	2.85764	+	4.94958i	0.116180	+	0.201229i
$606$		0			0
$607$	7.03358	−	12.1825i	0.285484	−	0.494473i	−0.687242	−	0.726428i	$-0.741179\pi$
$607$	7.03358	−	12.1825i	0.285484	−	0.494473i	0.972726	+	0.231955i	$0.0745123\pi$
$608$		0			0
$609$	−1.41621	+	17.2725i	−0.0573877	+	0.699918i
$610$		0			0
$611$	−3.46370	+	5.99931i	−0.140126	+	0.242706i
$612$		0			0
$613$	−8.38938	+	4.84361i	−0.338844	+	0.195632i	−0.659761	−	0.751476i	$-0.729342\pi$
$613$	−8.38938	+	4.84361i	−0.338844	+	0.195632i	0.320917	+	0.947107i	$0.396009\pi$
$614$		0			0
$615$	−12.3532			−0.498127
$616$		0			0
$617$	−36.8175			−1.48222			−0.741108	−	0.671386i	$-0.765699\pi$
$617$	−36.8175			−1.48222			−0.741108	+	0.671386i	$0.765699\pi$
$618$		0			0
$619$	14.5742	−	8.41442i	0.585787	−	0.338204i	−0.177643	−	0.984095i	$-0.556847\pi$
$619$	14.5742	−	8.41442i	0.585787	−	0.338204i	0.763430	+	0.645891i	$0.223514\pi$
$620$		0			0
$621$	−0.805129	+	1.39452i	−0.0323087	+	0.0559603i
$622$		0			0
$623$	−4.97750	−	10.5239i	−0.199419	−	0.421633i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	26.2345	+	45.4394i	1.04770	+	1.81468i
$628$		0			0
$629$	24.1141			0.961492
$630$		0			0
$631$		−	40.9250i		−	1.62920i	−0.580023	−	0.814600i	$-0.696957\pi$
$631$		−	40.9250i		−	1.62920i	0.580023	−	0.814600i	$-0.303043\pi$
$632$		0			0
$633$	−11.1942	+	6.46299i	−0.444930	+	0.256881i
$634$		0			0
$635$	6.22865	+	3.59611i	0.247176	+	0.142707i
$636$		0			0
$637$	12.2201	+	32.4674i	0.484178	+	1.28640i
$638$		0			0
$639$	−2.02858	−	1.17120i	−0.0802496	−	0.0463321i
$640$		0			0
$641$	−22.3915	−	38.7833i	−0.884413	−	1.53185i	−0.846385	−	0.532571i	$-0.821226\pi$
$641$	−22.3915	−	38.7833i	−0.884413	−	1.53185i	−0.0380272	−	0.999277i	$-0.512107\pi$
$642$		0			0
$643$			35.9649i			1.41832i	0.705049	+	0.709159i	$0.250925\pi$
$643$			35.9649i			1.41832i	−0.705049	+	0.709159i	$0.749075\pi$
$644$		0			0
$645$		−	22.7612i		−	0.896221i
$646$		0			0
$647$	10.7834	+	18.6773i	0.423937	+	0.734281i	0.996321	−	0.0857054i	$-0.0273144\pi$
$647$	10.7834	+	18.6773i	0.423937	+	0.734281i	−0.572383	+	0.819986i	$0.693981\pi$
$648$		0			0
$649$	36.0811	+	20.8314i	1.41631	+	0.817704i
$650$		0			0
$651$	−11.0942	−	23.4565i	−0.434816	−	0.919334i
$652$		0			0
$653$	26.3715	+	15.2256i	1.03200	+	0.595824i	0.917556	−	0.397606i	$-0.130159\pi$
$653$	26.3715	+	15.2256i	1.03200	+	0.595824i	0.114441	+	0.993430i	$0.463492\pi$
$654$		0			0
$655$	6.50864	−	3.75777i	0.254314	−	0.146828i
$656$		0			0
$657$		−	12.2735i		−	0.478833i
$658$		0			0
$659$	4.95909			0.193179			0.0965894	−	0.995324i	$-0.469207\pi$
$659$	4.95909			0.193179			0.0965894	+	0.995324i	$0.469207\pi$
$660$		0			0
$661$	−8.90153	−	15.4179i	−0.346230	−	0.599687i	0.639347	−	0.768918i	$-0.279205\pi$
$661$	−8.90153	−	15.4179i	−0.346230	−	0.599687i	−0.985576	+	0.169231i	$0.945871\pi$
$662$		0			0
$663$	12.7189	−	22.0299i	0.493963	−	0.855569i
$664$		0			0
$665$	−15.9187	−	1.30520i	−0.617299	−	0.0506136i
$666$		0			0
$667$	−0.788093	+	1.36502i	−0.0305151	+	0.0528537i
$668$		0			0
$669$	−27.8486	+	16.0784i	−1.07669	+	0.621626i
$670$		0			0
$671$	10.8867			0.420278
$672$		0			0
$673$	20.2860			0.781968			0.390984	−	0.920397i	$-0.372135\pi$
$673$	20.2860			0.781968			0.390984	+	0.920397i	$0.372135\pi$
$674$		0			0
$675$	2.72614	−	1.57394i	0.104929	−	0.0605808i
$676$		0			0
$677$	12.8287	−	22.2199i	0.493046	−	0.853980i	−0.506922	−	0.861992i	$-0.669217\pi$
$677$	12.8287	−	22.2199i	0.493046	−	0.853980i	0.999968	+	0.00801166i	$0.00255022\pi$
$678$		0			0
$679$	−8.54936	+	12.3527i	−0.328094	+	0.474053i
$680$		0			0
$681$	24.1739	−	41.8705i	0.926347	−	1.60448i
$682$		0			0
$683$	−11.8802	−	20.5772i	−0.454585	−	0.787365i	0.544079	−	0.839034i	$-0.316879\pi$
$683$	−11.8802	−	20.5772i	−0.454585	−	0.787365i	−0.998664	+	0.0516694i	$0.983546\pi$
$684$		0			0
$685$	3.41935			0.130647
$686$		0			0
$687$		−	5.77382i		−	0.220285i
$688$		0			0
$689$	−33.6663	+	19.4372i	−1.28258	+	0.740500i
$690$		0			0
$691$	8.25902	+	4.76835i	0.314188	+	0.181396i	0.648799	−	0.760960i	$-0.275272\pi$
$691$	8.25902	+	4.76835i	0.314188	+	0.181396i	−0.334611	+	0.942356i	$0.608605\pi$
$692$		0			0
$693$	−13.5129	−	9.35232i	−0.513311	−	0.355265i
$694$		0			0
$695$	9.56685	+	5.52342i	0.362891	+	0.209515i
$696$		0			0
$697$	−7.01529	−	12.1508i	−0.265723	−	0.460246i
$698$		0			0
$699$		−	36.3313i		−	1.37418i
$700$		0			0
$701$			19.1213i			0.722201i	0.932527	+	0.361101i	$0.117599\pi$
$701$			19.1213i			0.722201i	−0.932527	+	0.361101i	$0.882401\pi$
$702$		0			0
$703$	−30.1455	−	52.2136i	−1.13696	−	1.96927i
$704$		0			0
$705$	2.57345	+	1.48578i	0.0969217	+	0.0559578i
$706$		0			0
$707$	3.19511	−	38.9686i	0.120165	−	1.46556i
$708$		0			0
$709$	42.0444	+	24.2743i	1.57901	+	0.911642i	0.994998	+	0.0998972i	$0.0318514\pi$
$709$	42.0444	+	24.2743i	1.57901	+	0.911642i	0.584012	+	0.811745i	$0.301482\pi$
$710$		0			0
$711$	−4.87821	+	2.81644i	−0.182947	+	0.105625i
$712$		0			0
$713$		−	2.35992i		−	0.0883798i
$714$		0			0
$715$	−20.2617			−0.757743
$716$		0			0
$717$	15.7327	+	27.2498i	0.587547	+	1.01766i
$718$		0			0
$719$	14.8570	−	25.7331i	0.554073	−	0.959682i	−0.443903	−	0.896075i	$-0.646406\pi$
$719$	14.8570	−	25.7331i	0.554073	−	0.959682i	0.997975	−	0.0636067i	$-0.0202603\pi$
$720$		0			0
$721$	−22.6560	+	10.7156i	−0.843754	+	0.399069i
$722$		0			0
$723$	−18.9469	+	32.8169i	−0.704641	+	1.22047i
$724$		0			0
$725$	2.66845	−	1.54063i	0.0991039	−	0.0572177i
$726$		0			0
$727$	−3.32731			−0.123403			−0.0617015	−	0.998095i	$-0.519653\pi$
$727$	−3.32731			−0.123403			−0.0617015	+	0.998095i	$0.519653\pi$
$728$		0			0
$729$	−2.98481			−0.110548
$730$		0			0
$731$	22.3884	−	12.9259i	0.828065	−	0.478083i
$732$		0			0
$733$	16.6332	−	28.8096i	0.614362	−	1.06411i	−0.376135	−	0.926565i	$-0.622747\pi$
$733$	16.6332	−	28.8096i	0.614362	−	1.06411i	0.990496	−	0.137540i	$-0.0439197\pi$
$734$		0			0
$735$	13.9271	−	5.24191i	0.513710	−	0.193351i
$736$		0			0
$737$	−14.1638	+	24.5325i	−0.521731	+	0.903665i
$738$		0			0
$739$	8.20295	+	14.2079i	0.301750	+	0.522647i	0.976533	−	0.215370i	$-0.0690957\pi$
$739$	8.20295	+	14.2079i	0.301750	+	0.522647i	−0.674782	+	0.738017i	$0.735762\pi$
$740$		0			0
$741$	−63.6009			−2.33644
$742$		0			0
$743$			28.3857i			1.04137i	0.853749	+	0.520685i	$0.174323\pi$
$743$			28.3857i			1.04137i	−0.853749	+	0.520685i	$0.825677\pi$
$744$		0			0
$745$	8.88620	−	5.13045i	0.325565	−	0.187965i
$746$		0			0
$747$	−13.0785	−	7.55090i	−0.478519	−	0.276273i
$748$		0			0
$749$	−45.6272	+	21.5802i	−1.66718	+	0.788525i
$750$		0			0
$751$	−27.1307	−	15.6639i	−0.990014	−	0.571585i	−0.0847355	−	0.996403i	$-0.527005\pi$
$751$	−27.1307	−	15.6639i	−0.990014	−	0.571585i	−0.905278	+	0.424819i	$0.860338\pi$
$752$		0			0
$753$	27.6063	+	47.8155i	1.00603	+	1.74249i
$754$		0			0
$755$			16.4561i			0.598898i
$756$		0			0
$757$		−	12.5842i		−	0.457380i	−0.973499	−	0.228690i	$-0.926556\pi$
$757$		−	12.5842i		−	0.457380i	0.973499	−	0.228690i	$-0.0734442\pi$
$758$		0			0
$759$	−2.22299	−	3.85034i	−0.0806895	−	0.139758i
$760$		0			0
$761$	10.7941	+	6.23196i	0.391285	+	0.225908i	0.682717	−	0.730683i	$-0.260798\pi$
$761$	10.7941	+	6.23196i	0.391285	+	0.225908i	−0.291432	+	0.956592i	$0.594132\pi$
$762$		0			0
$763$	−1.68848	−	0.138442i	−0.0611272	−	0.00501194i
$764$		0			0
$765$	−3.17678	−	1.83412i	−0.114857	−	0.0663127i
$766$		0			0
$767$	−43.7361	+	25.2511i	−1.57922	+	0.911763i
$768$		0			0
$769$			31.8352i			1.14801i	0.818853	+	0.574003i	$0.194610\pi$
$769$			31.8352i			1.14801i	−0.818853	+	0.574003i	$0.805390\pi$
$770$		0			0
$771$	20.7172			0.746111
$772$		0			0
$773$	3.58420	+	6.20801i	0.128915	+	0.223287i	0.923256	−	0.384184i	$-0.125517\pi$
$773$	3.58420	+	6.20801i	0.128915	+	0.223287i	−0.794342	+	0.607471i	$0.792184\pi$
$774$		0			0
$775$	−2.30669	+	3.99530i	−0.0828588	+	0.143516i
$776$		0			0
$777$	46.1888	+	31.9675i	1.65701	+	1.14683i
$778$		0			0
$779$	−17.5399	+	30.3800i	−0.628433	+	1.08848i
$780$		0			0
$781$	−5.45913	+	3.15183i	−0.195343	+	0.112781i
$782$		0			0
$783$	−9.69943			−0.346629
$784$		0			0
$785$	22.2392			0.793752
$786$		0			0
$787$	−5.41950	+	3.12895i	−0.193184	+	0.111535i	−0.593472	−	0.804854i	$-0.702243\pi$
$787$	−5.41950	+	3.12895i	−0.193184	+	0.111535i	0.400288	+	0.916389i	$0.368910\pi$
$788$		0			0
$789$	−6.29061	+	10.8957i	−0.223952	+	0.387896i
$790$		0			0
$791$	−32.2895	−	22.3477i	−1.14808	−	0.794593i
$792$		0			0
$793$	−6.59826	+	11.4285i	−0.234311	+	0.405839i
$794$		0			0
$795$	8.33776	+	14.4414i	0.295710	+	0.512185i
$796$		0			0
$797$	22.8115			0.808024			0.404012	−	0.914754i	$-0.367615\pi$
$797$	22.8115			0.808024			0.404012	+	0.914754i	$0.367615\pi$
$798$		0			0
$799$			3.37507i			0.119401i
$800$		0			0
$801$	−5.78928	+	3.34244i	−0.204554	+	0.118099i
$802$		0			0
$803$	−28.6041	−	16.5146i	−1.00942	−	0.582786i
$804$		0			0
$805$	1.34888	+	0.110597i	0.0475417	+	0.00389804i
$806$		0			0
$807$	−38.2618	−	22.0905i	−1.34688	−	0.777621i
$808$		0			0
$809$	−21.2796	−	36.8573i	−0.748150	−	1.29583i	−0.948708	−	0.316152i	$-0.897609\pi$
$809$	−21.2796	−	36.8573i	−0.748150	−	1.29583i	0.200558	−	0.979682i	$-0.435724\pi$
$810$		0			0
$811$			18.7275i			0.657613i	0.944397	+	0.328806i	$0.106646\pi$
$811$			18.7275i			0.657613i	−0.944397	+	0.328806i	$0.893354\pi$
$812$		0			0
$813$			24.3671i			0.854593i
$814$		0			0
$815$	−6.48712	−	11.2360i	−0.227234	−	0.393581i
$816$		0			0
$817$	−55.9764	−	32.3180i	−1.95837	−	1.13066i
$818$		0			0
$819$	18.0076	−	8.51705i	0.629237	−	0.297610i
$820$		0			0
$821$	23.7690	+	13.7231i	0.829545	+	0.478938i	0.853697	−	0.520770i	$-0.174355\pi$
$821$	23.7690	+	13.7231i	0.829545	+	0.478938i	−0.0241517	+	0.999708i	$0.507688\pi$
$822$		0			0
$823$	30.6664	−	17.7052i	1.06896	−	0.617166i	0.141065	−	0.990000i	$-0.454947\pi$
$823$	30.6664	−	17.7052i	1.06896	−	0.617166i	0.927898	+	0.372834i	$0.121614\pi$
$824$		0			0
$825$			8.69140i			0.302596i
$826$		0			0
$827$	11.1678			0.388341			0.194170	−	0.980968i	$-0.437798\pi$
$827$	11.1678			0.388341			0.194170	+	0.980968i	$0.437798\pi$
$828$		0			0
$829$	−14.7123	−	25.4824i	−0.510979	−	0.885041i	−0.999919	−	0.0127241i	$-0.995950\pi$
$829$	−14.7123	−	25.4824i	−0.510979	−	0.885041i	0.488940	−	0.872317i	$-0.337384\pi$
$830$		0			0
$831$	−34.9792	+	60.5858i	−1.21342	+	2.10170i
$832$		0			0
$833$	13.0652	+	10.7222i	0.452682	+	0.371502i
$834$		0			0
$835$	5.96231	−	10.3270i	0.206334	−	0.357381i
$836$		0			0
$837$	12.5767	−	7.26116i	0.434715	−	0.250983i
$838$		0			0
$839$	−17.3994			−0.600694			−0.300347	−	0.953830i	$-0.597103\pi$
$839$	−17.3994			−0.600694			−0.300347	+	0.953830i	$0.597103\pi$
$840$		0			0
$841$	19.5058			0.672614
$842$		0			0
$843$	−43.5806	+	25.1613i	−1.50100	+	0.866600i
$844$		0			0
$845$	5.78022	−	10.0116i	0.198845	−	0.344410i
$846$		0			0
$847$	−13.6694	+	6.46520i	−0.469686	+	0.222147i
$848$		0			0
$849$	21.2887	−	36.8731i	0.730627	−	1.26548i
$850$		0			0
$851$	2.55440	+	4.42435i	0.0875637	+	0.151665i
$852$		0			0
$853$	−16.9463			−0.580229			−0.290115	−	0.956992i	$-0.593693\pi$
$853$	−16.9463			−0.580229			−0.290115	+	0.956992i	$0.593693\pi$
$854$		0			0
$855$			9.17148i			0.313658i
$856$		0			0
$857$	−15.3141	+	8.84161i	−0.523120	+	0.302024i	−0.738210	−	0.674571i	$-0.764329\pi$
$857$	−15.3141	+	8.84161i	−0.523120	+	0.302024i	0.215090	+	0.976594i	$0.430995\pi$
$858$		0			0
$859$	−4.85975	−	2.80578i	−0.165813	−	0.0957319i	0.414797	−	0.909914i	$-0.363852\pi$
$859$	−4.85975	−	2.80578i	−0.165813	−	0.0957319i	−0.580610	+	0.814182i	$0.697186\pi$
$860$		0			0
$861$	2.67081	−	32.5741i	0.0910210	−	1.11012i
$862$		0			0
$863$	−25.4111	−	14.6711i	−0.865003	−	0.499410i	0.000681370	−	1.00000i	$-0.499783\pi$
$863$	−25.4111	−	14.6711i	−0.865003	−	0.499410i	−0.865685	+	0.500590i	$0.833116\pi$
$864$		0			0
$865$	5.55929	+	9.62897i	0.189021	+	0.327395i
$866$		0			0
$867$			23.7460i			0.806456i
$868$		0			0
$869$			15.1586i			0.514221i
$870$		0			0
$871$	−17.1689	−	29.7374i	−0.581745	−	1.00761i
$872$		0			0
$873$	7.47060	+	4.31315i	0.252841	+	0.145978i
$874$		0			0
$875$	−2.17552	−	1.50569i	−0.0735461	−	0.0509016i
$876$		0			0
$877$	−37.6795	−	21.7543i	−1.27235	−	0.734589i	−0.296917	−	0.954903i	$-0.595958\pi$
$877$	−37.6795	−	21.7543i	−1.27235	−	0.734589i	−0.975429	+	0.220314i	$0.929292\pi$
$878$		0			0
$879$	−8.77756	+	5.06772i	−0.296060	+	0.170930i
$880$		0			0
$881$		−	21.3654i		−	0.719817i	−0.932988	−	0.359909i	$-0.882808\pi$
$881$		−	21.3654i		−	0.719817i	0.932988	−	0.359909i	$-0.117192\pi$
$882$		0			0
$883$	−26.9203			−0.905939			−0.452970	−	0.891526i	$-0.649635\pi$
$883$	−26.9203			−0.905939			−0.452970	+	0.891526i	$0.649635\pi$
$884$		0			0
$885$	10.8317	+	18.7610i	0.364102	+	0.630643i
$886$		0			0
$887$	−1.58078	+	2.73799i	−0.0530774	+	0.0919327i	−0.891343	−	0.453329i	$-0.850236\pi$
$887$	−1.58078	+	2.73799i	−0.0530774	+	0.0919327i	0.838266	+	0.545262i	$0.183570\pi$
$888$		0			0
$889$	−10.8293	+	15.6468i	−0.363202	+	0.524778i
$890$		0			0
$891$	22.9967	−	39.8314i	0.770418	−	1.33440i
$892$		0			0
$893$	7.30795	−	4.21925i	0.244551	−	0.141192i
$894$		0			0
$895$	−8.55281			−0.285889
$896$		0			0
$897$	5.38926			0.179942
$898$		0			0
$899$	12.3106	−	7.10753i	0.410581	−	0.237049i
$900$		0			0
$901$	−9.46993	+	16.4024i	−0.315489	+	0.546443i
$902$		0			0
$903$	60.0190	+	4.92108i	1.99731	+	0.163763i
$904$		0			0
$905$	0.410980	−	0.711839i	0.0136614	−	0.0236623i
$906$		0			0
$907$	11.6003	+	20.0923i	0.385182	+	0.667154i	0.991794	−	0.127843i	$-0.0408054\pi$
$907$	11.6003	+	20.0923i	0.385182	+	0.667154i	−0.606613	+	0.794998i	$0.707472\pi$
$908$		0			0
$909$	−22.4516			−0.744673
$910$		0			0
$911$		−	16.0632i		−	0.532197i	−0.963946	−	0.266098i	$-0.914265\pi$
$911$		−	16.0632i		−	0.532197i	0.963946	−	0.266098i	$-0.0857346\pi$
$912$		0			0
$913$	−35.1957	+	20.3202i	−1.16481	+	0.672501i
$914$		0			0
$915$	4.90236	+	2.83038i	0.162067	+	0.0935693i
$916$		0			0
$917$	8.50167	+	17.9751i	0.280750	+	0.593590i
$918$		0			0
$919$	7.06952	+	4.08159i	0.233202	+	0.134639i	0.612048	−	0.790820i	$-0.290346\pi$
$919$	7.06952	+	4.08159i	0.233202	+	0.134639i	−0.378846	+	0.925460i	$0.623679\pi$
$920$		0			0
$921$	15.3132	+	26.5232i	0.504587	+	0.873970i
$922$		0			0
$923$		−	7.64106i		−	0.251509i
$924$		0			0
$925$		−	9.98713i		−	0.328375i
$926$		0			0
$927$	7.19563	+	12.4632i	0.236335	+	0.409345i
$928$		0			0
$929$	3.96274	+	2.28789i	0.130013	+	0.0750633i	0.563596	−	0.826051i	$-0.309417\pi$
$929$	3.96274	+	2.28789i	0.130013	+	0.0750633i	−0.433583	+	0.901114i	$0.642751\pi$
$930$		0			0
$931$	6.88339	−	41.6938i	0.225594	−	1.36646i
$932$		0			0
$933$	0.0272382	+	0.0157260i	0.000891737	+	0.000514845i
$934$		0			0
$935$	−8.54905	+	4.93580i	−0.279584	+	0.161418i
$936$		0			0
$937$		−	15.7959i		−	0.516028i	−0.966141	−	0.258014i	$-0.916932\pi$
$937$		−	15.7959i		−	0.516028i	0.966141	−	0.258014i	$-0.0830681\pi$
$938$		0			0
$939$	−29.6042			−0.966097
$940$		0			0
$941$	−20.9789	−	36.3366i	−0.683894	−	1.18454i	−0.973783	−	0.227479i	$-0.926952\pi$
$941$	−20.9789	−	36.3366i	−0.683894	−	1.18454i	0.289889	−	0.957060i	$-0.406381\pi$
$942$		0			0
$943$	1.48626	−	2.57427i	0.0483991	−	0.0838298i
$944$		0			0
$945$	3.56091	+	7.52885i	0.115836	+	0.244913i
$946$		0			0
$947$	−26.3811	+	45.6935i	−0.857272	+	1.48484i	0.0172491	+	0.999851i	$0.494509\pi$
$947$	−26.3811	+	45.6935i	−0.857272	+	1.48484i	−0.874521	+	0.484987i	$0.838824\pi$
$948$		0			0
$949$	34.6728	−	20.0183i	1.12553	−	0.649823i
$950$		0			0
$951$	−51.0347			−1.65491
$952$		0			0
$953$	13.4387			0.435323			0.217661	−	0.976024i	$-0.430157\pi$
$953$	13.4387			0.435323			0.217661	+	0.976024i	$0.430157\pi$
$954$		0			0
$955$	19.4375	−	11.2222i	0.628982	−	0.363143i
$956$		0			0
$957$	13.3903	−	23.1926i	0.432846	−	0.749710i
$958$		0			0
$959$	−0.739280	+	9.01650i	−0.0238726	+	0.291158i
$960$		0			0
$961$	4.85836	−	8.41493i	0.156721	−	0.271449i
$962$		0			0
$963$	14.4914	+	25.0998i	0.466977	+	0.808829i
$964$		0			0
$965$	4.31181			0.138802
$966$		0			0
$967$		−	0.422493i		−	0.0135865i	−0.999977	−	0.00679323i	$-0.997838\pi$
$967$		−	0.422493i		−	0.0135865i	0.999977	−	0.00679323i	$-0.00216237\pi$
$968$		0			0
$969$	−26.8353	+	15.4934i	−0.862074	+	0.497718i
$970$		0			0
$971$	21.7350	+	12.5487i	0.697511	+	0.402708i	0.806420	−	0.591344i	$-0.201402\pi$
$971$	21.7350	+	12.5487i	0.697511	+	0.402708i	−0.108909	+	0.994052i	$0.534736\pi$
$972$		0			0
$973$	−16.6331	+	24.0327i	−0.533234	+	0.770452i
$974$		0			0
$975$	−9.12392	−	5.26770i	−0.292199	−	0.168701i
$976$		0			0
$977$	16.5269	+	28.6254i	0.528743	+	0.915809i	0.999438	+	0.0335135i	$0.0106697\pi$
$977$	16.5269	+	28.6254i	0.528743	+	0.915809i	−0.470696	+	0.882296i	$0.655997\pi$
$978$		0			0
$979$			17.9897i			0.574953i
$980$		0			0
$981$			0.972813i			0.0310595i
$982$		0			0
$983$	16.6386	+	28.8188i	0.530688	+	0.919178i	0.999359	+	0.0358054i	$0.0113997\pi$
$983$	16.6386	+	28.8188i	0.530688	+	0.919178i	−0.468671	+	0.883373i	$0.655267\pi$
$984$		0			0
$985$	5.77767	+	3.33574i	0.184092	+	0.106285i
$986$		0			0
$987$	−4.47426	+	6.46470i	−0.142417	+	0.205774i
$988$		0			0
$989$	4.74320	+	2.73849i	0.150825	+	0.0870788i
$990$		0			0
$991$	27.1291	−	15.6630i	0.861785	−	0.497552i	−0.00282457	−	0.999996i	$-0.500899\pi$
$991$	27.1291	−	15.6630i	0.861785	−	0.497552i	0.864610	+	0.502444i	$0.167566\pi$
$992$		0			0
$993$		−	3.32996i		−	0.105673i
$994$		0			0
$995$	−9.37750			−0.297287
$996$		0			0
$997$	0.280864	+	0.486471i	0.00889505	+	0.0154067i	0.870439	−	0.492277i	$-0.163835\pi$
$997$	0.280864	+	0.486471i	0.00889505	+	0.0154067i	−0.861544	+	0.507684i	$0.830502\pi$
$998$		0			0
$999$	−15.7191	+	27.2263i	−0.497330	+	0.861401i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1120.2.bz.f.271.11		24
4.3	odd	2		280.2.bj.e.131.5	✓	24
7.3	odd	6		1120.2.bz.e.591.11		24
8.3	odd	2		1120.2.bz.e.271.11		24
8.5	even	2		280.2.bj.f.131.12	yes	24
28.3	even	6		280.2.bj.f.171.12	yes	24
56.3	even	6	inner	1120.2.bz.f.591.11		24
56.45	odd	6		280.2.bj.e.171.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bj.e.131.5	✓	24	4.3	odd	2
280.2.bj.e.171.5	yes	24	56.45	odd	6
280.2.bj.f.131.12	yes	24	8.5	even	2
280.2.bj.f.171.12	yes	24	28.3	even	6
1120.2.bz.e.271.11		24	8.3	odd	2
1120.2.bz.e.591.11		24	7.3	odd	6
1120.2.bz.f.271.11		24	1.1	even	1	trivial
1120.2.bz.f.591.11		24	56.3	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1120.bz (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.84104 - 1.06293i) q^{3} +(0.500000 - 0.866025i) q^{5} +(2.17552 + 1.50569i) q^{7} +(0.759621 - 1.31570i) q^{9} +O(q^{10})\)	\(q+(1.84104 - 1.06293i) q^{3} +(0.500000 - 0.866025i) q^{5} +(2.17552 + 1.50569i) q^{7} +(0.759621 - 1.31570i) q^{9} +(-2.04422 - 3.54069i) q^{11} +4.95585 q^{13} -2.12585i q^{15} +(2.09103 - 1.20726i) q^{17} +(-5.22809 - 3.01844i) q^{19} +(5.60566 + 0.459619i) q^{21} +(0.443005 + 0.255769i) q^{23} +(-0.500000 - 0.866025i) q^{25} +3.14787i q^{27} +3.08127i q^{29} +(-2.30669 - 3.99530i) q^{31} +(-7.52697 - 4.34570i) q^{33} +(2.39173 - 1.13121i) q^{35} +(8.64910 + 4.99356i) q^{37} +(9.12392 - 5.26770i) q^{39} -5.81092i q^{41} +10.7069 q^{43} +(-0.759621 - 1.31570i) q^{45} +(-0.698912 + 1.21055i) q^{47} +(2.46579 + 6.55133i) q^{49} +(2.56645 - 4.44522i) q^{51} +(-6.79325 + 3.92208i) q^{53} -4.08843 q^{55} -12.8335 q^{57} +(-8.82516 + 5.09521i) q^{59} +(-1.33141 + 2.30607i) q^{61} +(3.63361 - 1.71859i) q^{63} +(2.47792 - 4.29189i) q^{65} +(-3.46437 - 6.00046i) q^{67} +1.08745 q^{69} -1.54183i q^{71} +(6.99634 - 4.03934i) q^{73} +(-1.84104 - 1.06293i) q^{75} +(0.883939 - 10.7808i) q^{77} +(-3.21095 - 1.85384i) q^{79} +(5.62481 + 9.74247i) q^{81} -9.94035i q^{83} -2.41452i q^{85} +(3.27516 + 5.67274i) q^{87} +(-3.81064 - 2.20007i) q^{89} +(10.7816 + 7.46197i) q^{91} +(-8.49342 - 4.90368i) q^{93} +(-5.22809 + 3.01844i) q^{95} +5.67803i q^{97} -6.21132 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{3} + 12 q^{5} + 10 q^{7} + 12 q^{9}+O(q^{10}) \) 24 * q - 12 * q^3 + 12 * q^5 + 10 * q^7 + 12 * q^9	\( 24 q - 12 q^{3} + 12 q^{5} + 10 q^{7} + 12 q^{9} - 8 q^{11} - 20 q^{13} + 6 q^{17} - 18 q^{19} + 26 q^{21} + 18 q^{23} - 12 q^{25} - 6 q^{31} + 12 q^{33} + 8 q^{35} - 18 q^{39} - 32 q^{43} - 12 q^{45} + 8 q^{49} + 22 q^{51} - 30 q^{53} - 16 q^{55} - 44 q^{57} + 18 q^{59} - 22 q^{61} - 12 q^{63} - 10 q^{65} + 8 q^{67} + 12 q^{69} + 30 q^{73} + 12 q^{75} + 32 q^{77} + 6 q^{79} - 4 q^{81} + 14 q^{87} - 60 q^{89} - 18 q^{91} + 18 q^{93} - 18 q^{95} + 56 q^{99}+O(q^{100}) \) 24 * q - 12 * q^3 + 12 * q^5 + 10 * q^7 + 12 * q^9 - 8 * q^11 - 20 * q^13 + 6 * q^17 - 18 * q^19 + 26 * q^21 + 18 * q^23 - 12 * q^25 - 6 * q^31 + 12 * q^33 + 8 * q^35 - 18 * q^39 - 32 * q^43 - 12 * q^45 + 8 * q^49 + 22 * q^51 - 30 * q^53 - 16 * q^55 - 44 * q^57 + 18 * q^59 - 22 * q^61 - 12 * q^63 - 10 * q^65 + 8 * q^67 + 12 * q^69 + 30 * q^73 + 12 * q^75 + 32 * q^77 + 6 * q^79 - 4 * q^81 + 14 * q^87 - 60 * q^89 - 18 * q^91 + 18 * q^93 - 18 * q^95 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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