LMFDB - Embedded newform 720.2.cu.b.497.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(113,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 10, 9]))

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

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

chi := DirichletCharacter("720.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.cu (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.9349208943630483456.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 $ x^16 - 8x^15 + 48x^14 - 196x^13 + 642x^12 - 1668x^11 + 3580x^10 - 6328x^9 + 9297x^8 - 11276x^7 + 11224x^6 - 9024x^5 + 5736x^4 - 2780x^3 + 972x^2 - 220*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			497.2
Root			$0.500000 - 1.74530i$ of defining polynomial
Character	$\chi$	$=$	720.497
Dual form			720.2.cu.b.113.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0795432 + 1.73022i) q^{3} +(-2.00265 - 0.994679i) q^{5} +(-2.32238 + 0.622279i) q^{7} +(-2.98735 - 0.275255i) q^{9} +O(q^{10})$	\(q+(-0.0795432 + 1.73022i) q^{3} +(-2.00265 - 0.994679i) q^{5} +(-2.32238 + 0.622279i) q^{7} +(-2.98735 - 0.275255i) q^{9} +(-0.991757 - 0.572591i) q^{11} +(2.38971 + 0.640322i) q^{13} +(1.88031 - 3.38591i) q^{15} +(4.99855 - 4.99855i) q^{17} -2.78390i q^{19} +(-0.891952 - 4.06773i) q^{21} +(1.59630 - 5.95746i) q^{23} +(3.02123 + 3.98399i) q^{25} +(0.713876 - 5.14688i) q^{27} +(-0.672250 + 1.16437i) q^{29} +(-1.25223 - 2.16892i) q^{31} +(1.06960 - 1.67042i) q^{33} +(5.26988 + 1.06381i) q^{35} +(-8.16761 - 8.16761i) q^{37} +(-1.29799 + 4.08381i) q^{39} +(-1.70826 + 0.986264i) q^{41} +(2.32713 + 8.68498i) q^{43} +(5.70882 + 3.52269i) q^{45} +(-3.19175 - 11.9118i) q^{47} +(-1.05598 + 0.609669i) q^{49} +(8.25101 + 9.04622i) q^{51} +(-1.84828 - 1.84828i) q^{53} +(1.41660 + 2.13318i) q^{55} +(4.81678 + 0.221441i) q^{57} +(1.31456 + 2.27688i) q^{59} +(-3.54275 + 6.13623i) q^{61} +(7.10903 - 1.21972i) q^{63} +(-4.14885 - 3.65934i) q^{65} +(0.0146109 - 0.0545285i) q^{67} +(10.1808 + 3.23582i) q^{69} -9.10005i q^{71} +(7.82779 - 7.82779i) q^{73} +(-7.13351 + 4.91050i) q^{75} +(2.65955 + 0.712623i) q^{77} +(-8.46375 - 4.88655i) q^{79} +(8.84847 + 1.64456i) q^{81} +(-2.70497 + 0.724794i) q^{83} +(-14.9823 + 5.03840i) q^{85} +(-1.96115 - 1.25576i) q^{87} +4.87832 q^{89} -5.94827 q^{91} +(3.85233 - 1.99411i) q^{93} +(-2.76909 + 5.57519i) q^{95} +(-7.79929 + 2.08981i) q^{97} +(2.80511 + 1.98351i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{5} - 8 q^{7}+O(q^{10}) $ 16 * q - 12 * q^5 - 8 * q^7	$ 16 q - 12 q^{5} - 8 q^{7} + 24 q^{15} + 24 q^{21} + 24 q^{23} - 16 q^{25} + 8 q^{31} + 24 q^{41} + 36 q^{45} - 48 q^{47} + 48 q^{51} - 24 q^{55} + 24 q^{57} - 24 q^{61} + 48 q^{63} + 16 q^{67} + 16 q^{73} - 72 q^{77} + 24 q^{81} - 48 q^{83} - 4 q^{85} + 48 q^{87} + 72 q^{93} - 84 q^{95} - 48 q^{97}+O(q^{100}) $ 16 * q - 12 * q^5 - 8 * q^7 + 24 * q^15 + 24 * q^21 + 24 * q^23 - 16 * q^25 + 8 * q^31 + 24 * q^41 + 36 * q^45 - 48 * q^47 + 48 * q^51 - 24 * q^55 + 24 * q^57 - 24 * q^61 + 48 * q^63 + 16 * q^67 + 16 * q^73 - 72 * q^77 + 24 * q^81 - 48 * q^83 - 4 * q^85 + 48 * q^87 + 72 * q^93 - 84 * q^95 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.0795432	+	1.73022i	−0.0459243	+	0.998945i
$3$	−0.0795432	+	1.73022i	−0.0459243	+	0.998945i
$4$		0			0
$5$	−2.00265	−	0.994679i	−0.895613	−	0.444834i
$5$	−2.00265	−	0.994679i	−0.895613	−	0.444834i
$6$		0			0
$7$	−2.32238	+	0.622279i	−0.877776	+	0.235199i	−0.669447	−	0.742860i	$-0.733469\pi$
$7$	−2.32238	+	0.622279i	−0.877776	+	0.235199i	−0.208328	+	0.978059i	$0.566802\pi$
$8$		0			0
$9$	−2.98735	−	0.275255i	−0.995782	−	0.0917517i
$10$		0			0
$11$	−0.991757	−	0.572591i	−0.299026	−	0.172643i	0.342979	−	0.939343i	$-0.388564\pi$
$11$	−0.991757	−	0.572591i	−0.299026	−	0.172643i	−0.642005	+	0.766700i	$0.721897\pi$
$12$		0			0
$13$	2.38971	+	0.640322i	0.662788	+	0.177593i	0.574504	−	0.818502i	$-0.305195\pi$
$13$	2.38971	+	0.640322i	0.662788	+	0.177593i	0.0882838	+	0.996095i	$0.471862\pi$
$14$		0			0
$15$	1.88031	−	3.38591i	0.485495	−	0.874239i
$16$		0			0
$17$	4.99855	−	4.99855i	1.21233	−	1.21233i	0.242068	−	0.970259i	$-0.422174\pi$
$17$	4.99855	−	4.99855i	1.21233	−	1.21233i	0.970259	−	0.242068i	$-0.0778258\pi$
$18$		0			0
$19$		−	2.78390i		−	0.638671i	−0.947642	−	0.319336i	$-0.896540\pi$
$19$		−	2.78390i		−	0.638671i	0.947642	−	0.319336i	$-0.103460\pi$
$20$		0			0
$21$	−0.891952	−	4.06773i	−0.194640	−	0.887651i
$22$		0			0
$23$	1.59630	−	5.95746i	0.332851	−	1.24222i	−0.573330	−	0.819325i	$-0.694349\pi$
$23$	1.59630	−	5.95746i	0.332851	−	1.24222i	0.906181	−	0.422891i	$-0.138985\pi$
$24$		0			0
$25$	3.02123	+	3.98399i	0.604245	+	0.796798i
$26$		0			0
$27$	0.713876	−	5.14688i	0.137386	−	0.990518i
$28$		0			0
$29$	−0.672250	+	1.16437i	−0.124834	+	0.216218i	−0.921668	−	0.387980i	$-0.873173\pi$
$29$	−0.672250	+	1.16437i	−0.124834	+	0.216218i	0.796834	+	0.604198i	$0.206506\pi$
$30$		0			0
$31$	−1.25223	−	2.16892i	−0.224907	−	0.389550i	0.731385	−	0.681965i	$-0.238874\pi$
$31$	−1.25223	−	2.16892i	−0.224907	−	0.389550i	−0.956292	+	0.292415i	$0.905541\pi$
$32$		0			0
$33$	1.06960	−	1.67042i	0.186193	−	0.290782i
$34$		0			0
$35$	5.26988	+	1.06381i	0.890772	+	0.179817i
$36$		0			0
$37$	−8.16761	−	8.16761i	−1.34275	−	1.34275i	−0.893314	−	0.449434i	$-0.851626\pi$
$37$	−8.16761	−	8.16761i	−1.34275	−	1.34275i	−0.449434	−	0.893314i	$-0.648374\pi$
$38$		0			0
$39$	−1.29799	+	4.08381i	−0.207844	+	0.653932i
$40$		0			0
$41$	−1.70826	+	0.986264i	−0.266785	+	0.154029i	−0.627426	−	0.778676i	$-0.715891\pi$
$41$	−1.70826	+	0.986264i	−0.266785	+	0.154029i	0.360641	+	0.932705i	$0.382558\pi$
$42$		0			0
$43$	2.32713	+	8.68498i	0.354885	+	1.32445i	0.880630	+	0.473805i	$0.157120\pi$
$43$	2.32713	+	8.68498i	0.354885	+	1.32445i	−0.525745	+	0.850642i	$0.676213\pi$
$44$		0			0
$45$	5.70882	+	3.52269i	0.851021	+	0.525132i
$46$		0			0
$47$	−3.19175	−	11.9118i	−0.465565	−	1.73751i	−0.655010	−	0.755621i	$-0.727335\pi$
$47$	−3.19175	−	11.9118i	−0.465565	−	1.73751i	0.189445	−	0.981891i	$-0.439331\pi$
$48$		0			0
$49$	−1.05598	+	0.609669i	−0.150854	+	0.0870956i
$50$		0			0
$51$	8.25101	+	9.04622i	1.15537	+	1.26672i
$52$		0			0
$53$	−1.84828	−	1.84828i	−0.253881	−	0.253881i	0.568679	−	0.822560i	$-0.307455\pi$
$53$	−1.84828	−	1.84828i	−0.253881	−	0.253881i	−0.822560	+	0.568679i	$0.807455\pi$
$54$		0			0
$55$	1.41660	+	2.13318i	0.191014	+	0.287638i
$56$		0			0
$57$	4.81678	+	0.221441i	0.637998	+	0.0293305i
$58$		0			0
$59$	1.31456	+	2.27688i	0.171141	+	0.296424i	0.938819	−	0.344411i	$-0.111921\pi$
$59$	1.31456	+	2.27688i	0.171141	+	0.296424i	−0.767678	+	0.640835i	$0.778588\pi$
$60$		0			0
$61$	−3.54275	+	6.13623i	−0.453603	+	0.785664i	−0.998607	−	0.0527700i	$-0.983195\pi$
$61$	−3.54275	+	6.13623i	−0.453603	+	0.785664i	0.545004	+	0.838434i	$0.316528\pi$
$62$		0			0
$63$	7.10903	−	1.21972i	0.895653	−	0.153670i
$64$		0			0
$65$	−4.14885	−	3.65934i	−0.514602	−	0.453886i
$66$		0			0
$67$	0.0146109	−	0.0545285i	0.00178500	−	0.00666172i	−0.965028	−	0.262148i	$-0.915569\pi$
$67$	0.0146109	−	0.0545285i	0.00178500	−	0.00666172i	0.966813	+	0.255487i	$0.0822357\pi$
$68$		0			0
$69$	10.1808	+	3.23582i	1.22562	+	0.389547i
$70$		0			0
$71$		−	9.10005i		−	1.07998i	−0.841672	−	0.539989i	$-0.818429\pi$
$71$		−	9.10005i		−	1.07998i	0.841672	−	0.539989i	$-0.181571\pi$
$72$		0			0
$73$	7.82779	−	7.82779i	0.916174	−	0.916174i	−0.0805747	−	0.996749i	$-0.525676\pi$
$73$	7.82779	−	7.82779i	0.916174	−	0.916174i	0.996749	+	0.0805747i	$0.0256756\pi$
$74$		0			0
$75$	−7.13351	+	4.91050i	−0.823707	+	0.567015i
$76$		0			0
$77$	2.65955	+	0.712623i	0.303083	+	0.0812109i
$78$		0			0
$79$	−8.46375	−	4.88655i	−0.952246	−	0.549779i	−0.0584679	−	0.998289i	$-0.518622\pi$
$79$	−8.46375	−	4.88655i	−0.952246	−	0.549779i	−0.893778	+	0.448510i	$0.851955\pi$
$80$		0			0
$81$	8.84847	+	1.64456i	0.983163	+	0.182729i
$82$		0			0
$83$	−2.70497	+	0.724794i	−0.296909	+	0.0795565i	−0.404198	−	0.914671i	$-0.632449\pi$
$83$	−2.70497	+	0.724794i	−0.296909	+	0.0795565i	0.107290	+	0.994228i	$0.465783\pi$
$84$		0			0
$85$	−14.9823	+	5.03840i	−1.62506	+	0.546491i
$86$		0			0
$87$	−1.96115	−	1.25576i	−0.210257	−	0.134632i
$88$		0			0
$89$	4.87832			0.517100			0.258550	−	0.965998i	$-0.416755\pi$
$89$	4.87832			0.517100			0.258550	+	0.965998i	$0.416755\pi$
$90$		0			0
$91$	−5.94827			−0.623549
$92$		0			0
$93$	3.85233	−	1.99411i	0.399468	−	0.206780i
$94$		0			0
$95$	−2.76909	+	5.57519i	−0.284103	+	0.572002i
$96$		0			0
$97$	−7.79929	+	2.08981i	−0.791898	+	0.212188i	−0.632024	−	0.774949i	$-0.717775\pi$
$97$	−7.79929	+	2.08981i	−0.791898	+	0.212188i	−0.159874	+	0.987137i	$0.551109\pi$
$98$		0			0
$99$	2.80511	+	1.98351i	0.281925	+	0.199351i
$100$		0			0
$101$	−0.631074	−	0.364351i	−0.0627942	−	0.0362543i	0.468274	−	0.883583i	$-0.344876\pi$
$101$	−0.631074	−	0.364351i	−0.0627942	−	0.0362543i	−0.531068	+	0.847329i	$0.678209\pi$
$102$		0			0
$103$	1.31888	+	0.353393i	0.129953	+	0.0348209i	0.323209	−	0.946327i	$-0.395238\pi$
$103$	1.31888	+	0.353393i	0.129953	+	0.0348209i	−0.193256	+	0.981148i	$0.561905\pi$
$104$		0			0
$105$	−2.25982	+	9.03345i	−0.220535	+	0.881574i
$106$		0			0
$107$	−0.399208	+	0.399208i	−0.0385929	+	0.0385929i	−0.726140	−	0.687547i	$-0.758688\pi$
$107$	−0.399208	+	0.399208i	−0.0385929	+	0.0385929i	0.687547	+	0.726140i	$0.258688\pi$
$108$		0			0
$109$			13.5974i			1.30239i	0.758909	+	0.651196i	$0.225732\pi$
$109$			13.5974i			1.30239i	−0.758909	+	0.651196i	$0.774268\pi$
$110$		0			0
$111$	14.7815	−	13.4821i	1.40300	−	1.27967i
$112$		0			0
$113$	1.32472	−	4.94392i	0.124619	−	0.465084i	−0.875207	−	0.483749i	$-0.839275\pi$
$113$	1.32472	−	4.94392i	0.124619	−	0.465084i	0.999826	+	0.0186645i	$0.00594144\pi$
$114$		0			0
$115$	−9.12258	+	10.3429i	−0.850685	+	0.964481i
$116$		0			0
$117$	−6.96265	−	2.57064i	−0.643697	−	0.237656i
$118$		0			0
$119$	−8.49803	+	14.7190i	−0.779013	+	1.34929i
$120$		0			0
$121$	−4.84428	−	8.39054i	−0.440389	−	0.762776i
$122$		0			0
$123$	−1.57058	−	3.03412i	−0.141614	−	0.273578i
$124$		0			0
$125$	−2.08767	−	10.9837i	−0.186727	−	0.982412i
$126$		0			0
$127$	4.88817	+	4.88817i	0.433755	+	0.433755i	0.889904	−	0.456149i	$-0.150772\pi$
$127$	4.88817	+	4.88817i	0.433755	+	0.433755i	−0.456149	+	0.889904i	$0.650772\pi$
$128$		0			0
$129$	−15.2121	+	3.33563i	−1.33935	+	0.293686i
$130$		0			0
$131$	−4.98351	+	2.87723i	−0.435412	+	0.251385i	−0.701649	−	0.712522i	$-0.747553\pi$
$131$	−4.98351	+	2.87723i	−0.435412	+	0.251385i	0.266238	+	0.963907i	$0.414219\pi$
$132$		0			0
$133$	1.73236	+	6.46527i	0.150215	+	0.560610i
$134$		0			0
$135$	−6.54914	+	9.59733i	−0.563660	+	0.826007i
$136$		0			0
$137$	−2.69177	−	10.0458i	−0.229973	−	0.858272i	−0.980351	−	0.197262i	$-0.936795\pi$
$137$	−2.69177	−	10.0458i	−0.229973	−	0.858272i	0.750377	−	0.661010i	$-0.229872\pi$
$138$		0			0
$139$	−2.19537	+	1.26750i	−0.186209	+	0.107508i	−0.590207	−	0.807252i	$-0.700954\pi$
$139$	−2.19537	+	1.26750i	−0.186209	+	0.107508i	0.403998	+	0.914760i	$0.367620\pi$
$140$		0			0
$141$	20.8639	−	4.57494i	1.75706	−	0.385280i
$142$		0			0
$143$	−2.00337	−	2.00337i	−0.167531	−	0.167531i
$144$		0			0
$145$	2.50446	−	1.66316i	0.207984	−	0.138118i
$146$		0			0
$147$	−0.970868	−	1.87557i	−0.0800759	−	0.154695i
$148$		0			0
$149$	−6.49294	−	11.2461i	−0.531922	−	0.921316i	−0.999306	−	0.0372613i	$-0.988137\pi$
$149$	−6.49294	−	11.2461i	−0.531922	−	0.921316i	0.467384	−	0.884055i	$-0.345197\pi$
$150$		0			0
$151$	−1.58502	+	2.74534i	−0.128987	+	0.223412i	−0.923284	−	0.384117i	$-0.874506\pi$
$151$	−1.58502	+	2.74534i	−0.128987	+	0.223412i	0.794297	+	0.607529i	$0.207839\pi$
$152$		0			0
$153$	−16.3083	+	13.5565i	−1.31845	+	1.09598i
$154$		0			0
$155$	0.350394	+	5.58916i	0.0281443	+	0.448933i
$156$		0			0
$157$	−2.76487	+	10.3186i	−0.220660	+	0.823515i	0.763437	+	0.645883i	$0.223511\pi$
$157$	−2.76487	+	10.3186i	−0.220660	+	0.823515i	−0.984097	+	0.177633i	$0.943156\pi$
$158$		0			0
$159$	3.34495	−	3.05092i	0.265272	−	0.241953i
$160$		0			0
$161$			14.8288i			1.16867i
$162$		0			0
$163$	15.7354	−	15.7354i	1.23249	−	1.23249i	0.269490	−	0.963003i	$-0.413145\pi$
$163$	15.7354	−	15.7354i	1.23249	−	1.23249i	0.963003	−	0.269490i	$-0.0868552\pi$
$164$		0			0
$165$	−3.80356	+	2.28135i	−0.296107	+	0.177603i
$166$		0			0
$167$	3.92724	+	1.05230i	0.303899	+	0.0814295i	0.407546	−	0.913185i	$-0.366385\pi$
$167$	3.92724	+	1.05230i	0.303899	+	0.0814295i	−0.103647	+	0.994614i	$0.533051\pi$
$168$		0			0
$169$	−5.95761	−	3.43963i	−0.458277	−	0.264587i
$170$		0			0
$171$	−0.766284	+	8.31648i	−0.0585992	+	0.635977i
$172$		0			0
$173$	−5.37809	+	1.44105i	−0.408889	+	0.109561i	−0.457400	−	0.889261i	$-0.651219\pi$
$173$	−5.37809	+	1.44105i	−0.408889	+	0.109561i	0.0485110	+	0.998823i	$0.484552\pi$
$174$		0			0
$175$	−9.49558	−	7.37228i	−0.717798	−	0.557292i
$176$		0			0
$177$	−4.04407	+	2.09336i	−0.303971	+	0.157347i
$178$		0			0
$179$	−0.310192			−0.0231848			−0.0115924	−	0.999933i	$-0.503690\pi$
$179$	−0.310192			−0.0231848			−0.0115924	+	0.999933i	$0.503690\pi$
$180$		0			0
$181$	3.07416			0.228501			0.114250	−	0.993452i	$-0.463553\pi$
$181$	3.07416			0.228501			0.114250	+	0.993452i	$0.463553\pi$
$182$		0			0
$183$	−10.3352	−	6.61785i	−0.764003	−	0.489206i
$184$		0			0
$185$	8.23273	+	24.4810i	0.605282	+	1.79988i
$186$		0			0
$187$	−7.81948	+	2.09522i	−0.571817	+	0.153218i
$188$		0			0
$189$	1.54491	+	12.3972i	0.112375	+	0.901765i
$190$		0			0
$191$	12.3541	+	7.13262i	0.893909	+	0.516098i	0.875219	−	0.483727i	$-0.160717\pi$
$191$	12.3541	+	7.13262i	0.893909	+	0.516098i	0.0186896	+	0.999825i	$0.494051\pi$
$192$		0			0
$193$	9.27437	+	2.48506i	0.667584	+	0.178879i	0.576666	−	0.816980i	$-0.304353\pi$
$193$	9.27437	+	2.48506i	0.667584	+	0.178879i	0.0909176	+	0.995858i	$0.471020\pi$
$194$		0			0
$195$	6.66149	−	6.88736i	0.477039	−	0.493214i
$196$		0			0
$197$	−4.62495	+	4.62495i	−0.329514	+	0.329514i	−0.852402	−	0.522887i	$-0.824855\pi$
$197$	−4.62495	+	4.62495i	−0.329514	+	0.329514i	0.522887	+	0.852402i	$0.324855\pi$
$198$		0			0
$199$		−	4.07227i		−	0.288675i	−0.989528	−	0.144338i	$-0.953895\pi$
$199$		−	4.07227i		−	0.288675i	0.989528	−	0.144338i	$-0.0461051\pi$
$200$		0			0
$201$	0.0931843	+	0.0296174i	0.00657271	+	0.00208905i
$202$		0			0
$203$	0.836654	−	3.12243i	0.0587216	−	0.219152i
$204$		0			0
$205$	4.40207	−	0.275973i	0.307454	−	0.0192748i
$206$		0			0
$207$	−6.40851	+	17.3576i	−0.445422	+	1.20644i
$208$		0			0
$209$	−1.59404	+	2.76096i	−0.110262	+	0.190979i
$210$		0			0
$211$	7.58800	+	13.1428i	0.522379	+	0.904788i	0.999661	+	0.0260371i	$0.00828882\pi$
$211$	7.58800	+	13.1428i	0.522379	+	0.904788i	−0.477282	+	0.878750i	$0.658378\pi$
$212$		0			0
$213$	15.7451	+	0.723847i	1.07884	+	0.0495972i
$214$		0			0
$215$	3.97833	−	19.7077i	0.271320	−	1.34406i
$216$		0			0
$217$	4.25782	+	4.25782i	0.289040	+	0.289040i
$218$		0			0
$219$	12.9212	+	14.1665i	0.873133	+	0.957282i
$220$		0			0
$221$	15.1458	−	8.74443i	1.01882	−	0.588214i
$222$		0			0
$223$	2.20248	+	8.21978i	0.147489	+	0.550437i	0.999632	+	0.0271279i	$0.00863613\pi$
$223$	2.20248	+	8.21978i	0.147489	+	0.550437i	−0.852143	+	0.523309i	$0.824697\pi$
$224$		0			0
$225$	−7.92883	−	12.7332i	−0.528589	−	0.848878i
$226$		0			0
$227$	−5.27021	−	19.6687i	−0.349796	−	1.30546i	−0.886908	−	0.461946i	$-0.847151\pi$
$227$	−5.27021	−	19.6687i	−0.349796	−	1.30546i	0.537112	−	0.843511i	$-0.319515\pi$
$228$		0			0
$229$	12.2032	−	7.04551i	0.806409	−	0.465580i	−0.0392983	−	0.999228i	$-0.512512\pi$
$229$	12.2032	−	7.04551i	0.806409	−	0.465580i	0.845707	+	0.533647i	$0.179179\pi$
$230$		0			0
$231$	−1.44455	+	4.54492i	−0.0950441	+	0.299034i
$232$		0			0
$233$	−0.643009	−	0.643009i	−0.0421249	−	0.0421249i	0.685731	−	0.727855i	$-0.259483\pi$
$233$	−0.643009	−	0.643009i	−0.0421249	−	0.0421249i	−0.727855	+	0.685731i	$0.759483\pi$
$234$		0			0
$235$	−5.45644	+	27.0299i	−0.355939	+	1.76324i
$236$		0			0
$237$	9.12805	−	14.2555i	0.592931	−	0.925993i
$238$		0			0
$239$	−5.34131	−	9.25142i	−0.345501	−	0.598425i	0.639944	−	0.768422i	$-0.278958\pi$
$239$	−5.34131	−	9.25142i	−0.345501	−	0.598425i	−0.985445	+	0.169997i	$0.945624\pi$
$240$		0			0
$241$	−10.5666	+	18.3019i	−0.680654	+	1.17893i	0.294127	+	0.955766i	$0.404971\pi$
$241$	−10.5666	+	18.3019i	−0.680654	+	1.17893i	−0.974782	+	0.223161i	$0.928362\pi$
$242$		0			0
$243$	−3.54930	+	15.1790i	−0.227688	+	0.973734i
$244$		0			0
$245$	2.72118	−	0.170595i	0.173850	−	0.0108989i
$246$		0			0
$247$	1.78260	−	6.65274i	0.113424	−	0.423303i
$248$		0			0
$249$	−1.03889	−	4.73785i	−0.0658372	−	0.300249i
$250$		0			0
$251$			24.6952i			1.55874i	0.626561	+	0.779372i	$0.284462\pi$
$251$			24.6952i			1.55874i	−0.626561	+	0.779372i	$0.715538\pi$
$252$		0			0
$253$	−4.99433	+	4.99433i	−0.313991	+	0.313991i
$254$		0			0
$255$	−7.52582	−	26.3235i	−0.471285	−	1.64844i
$256$		0			0
$257$	−5.07632	−	1.36020i	−0.316652	−	0.0848467i	0.0969925	−	0.995285i	$-0.469078\pi$
$257$	−5.07632	−	1.36020i	−0.316652	−	0.0848467i	−0.413645	+	0.910438i	$0.635744\pi$
$258$		0			0
$259$	24.0508	+	13.8857i	1.49444	+	0.862818i
$260$		0			0
$261$	2.32874	−	3.29334i	0.144145	−	0.203852i
$262$		0			0
$263$	14.4263	−	3.86551i	0.889563	−	0.238358i	0.215034	−	0.976606i	$-0.431014\pi$
$263$	14.4263	−	3.86551i	0.889563	−	0.238358i	0.674529	+	0.738249i	$0.264347\pi$
$264$		0			0
$265$	1.86301	+	5.53990i	0.114444	+	0.340313i
$266$		0			0
$267$	−0.388037	+	8.44057i	−0.0237475	+	0.516555i
$268$		0			0
$269$	−20.0071			−1.21985			−0.609927	−	0.792457i	$-0.708801\pi$
$269$	−20.0071			−1.21985			−0.609927	+	0.792457i	$0.708801\pi$
$270$		0			0
$271$	3.02714			0.183886			0.0919428	−	0.995764i	$-0.470692\pi$
$271$	3.02714			0.183886			0.0919428	+	0.995764i	$0.470692\pi$
$272$		0			0
$273$	0.473145	−	10.2918i	0.0286360	−	0.622891i
$274$		0			0
$275$	−0.715123	−	5.68108i	−0.0431235	−	0.342582i
$276$		0			0
$277$	2.70178	−	0.723941i	0.162334	−	0.0434974i	−0.176736	−	0.984258i	$-0.556554\pi$
$277$	2.70178	−	0.723941i	0.162334	−	0.0434974i	0.339071	+	0.940761i	$0.389887\pi$
$278$		0			0
$279$	3.14383	+	6.82401i	0.188216	+	0.408543i
$280$		0			0
$281$	13.0998	+	7.56319i	0.781470	+	0.451182i	0.836951	−	0.547278i	$-0.184336\pi$
$281$	13.0998	+	7.56319i	0.781470	+	0.451182i	−0.0554808	+	0.998460i	$0.517669\pi$
$282$		0			0
$283$	−23.2191	−	6.22154i	−1.38023	−	0.369832i	−0.509027	−	0.860750i	$-0.669995\pi$
$283$	−23.2191	−	6.22154i	−1.38023	−	0.369832i	−0.871206	+	0.490918i	$0.836661\pi$
$284$		0			0
$285$	−9.42606	−	5.23462i	−0.558352	−	0.310072i
$286$		0			0
$287$	3.35349	−	3.35349i	0.197950	−	0.197950i
$288$		0			0
$289$		−	32.9711i		−	1.93948i
$290$		0			0
$291$	−2.99546	−	13.6607i	−0.175597	−	0.800807i
$292$		0			0
$293$	3.90805	−	14.5851i	0.228311	−	0.852068i	−0.752740	−	0.658318i	$-0.771268\pi$
$293$	3.90805	−	14.5851i	0.228311	−	0.852068i	0.981051	−	0.193750i	$-0.0620651\pi$
$294$		0			0
$295$	−0.367834	−	5.86735i	−0.0214161	−	0.341610i
$296$		0			0
$297$	−3.65505	+	4.69570i	−0.212088	+	0.272472i
$298$		0			0
$299$	7.62938	−	13.2145i	0.441219	−	0.764213i
$300$		0			0
$301$	−10.8090	−	18.7217i	−0.623018	−	1.07910i
$302$		0			0
$303$	0.680606	−	1.06292i	0.0390998	−	0.0610630i
$304$		0			0
$305$	13.1985	−	8.76483i	0.755743	−	0.501872i
$306$		0			0
$307$	−8.29531	−	8.29531i	−0.473438	−	0.473438i	0.429587	−	0.903025i	$-0.358659\pi$
$307$	−8.29531	−	8.29531i	−0.473438	−	0.473438i	−0.903025	+	0.429587i	$0.858659\pi$
$308$		0			0
$309$	−0.716358	+	2.25385i	−0.0407522	+	0.128217i
$310$		0			0
$311$	−10.8857	+	6.28488i	−0.617274	+	0.356383i	−0.775807	−	0.630971i	$-0.782657\pi$
$311$	−10.8857	+	6.28488i	−0.617274	+	0.356383i	0.158533	+	0.987354i	$0.449324\pi$
$312$		0			0
$313$	−3.08956	−	11.5304i	−0.174632	−	0.651737i	−0.996614	−	0.0822229i	$-0.973798\pi$
$313$	−3.08956	−	11.5304i	−0.174632	−	0.651737i	0.821982	−	0.569514i	$-0.192869\pi$
$314$		0			0
$315$	−15.4501	−	4.62854i	−0.870516	−	0.260788i
$316$		0			0
$317$	−0.502531	−	1.87547i	−0.0282249	−	0.105337i	0.950376	−	0.311102i	$-0.100698\pi$
$317$	−0.502531	−	1.87547i	−0.0282249	−	0.105337i	−0.978601	+	0.205766i	$0.934032\pi$
$318$		0			0
$319$	1.33342	−	0.769849i	0.0746570	−	0.0431033i
$320$		0			0
$321$	−0.658965	−	0.722473i	−0.0367798	−	0.0403245i
$322$		0			0
$323$	−13.9155	−	13.9155i	−0.774279	−	0.774279i
$324$		0			0
$325$	4.66883	+	11.4552i	0.258980	+	0.635418i
$326$		0			0
$327$	−23.5265	−	1.08158i	−1.30102	−	0.0598115i
$328$		0			0
$329$	14.8249	+	25.6775i	0.817323	+	1.41565i
$330$		0			0
$331$	10.9811	−	19.0198i	0.603575	−	1.04542i	−0.388700	−	0.921364i	$-0.627076\pi$
$331$	10.9811	−	19.0198i	0.603575	−	1.04542i	0.992275	−	0.124058i	$-0.0395909\pi$
$332$		0			0
$333$	22.1513	+	26.6477i	1.21388	+	1.46028i
$334$		0			0
$335$	−0.0834989	+	0.0946685i	−0.00456203	+	0.00517229i
$336$		0			0
$337$	6.93565	−	25.8842i	0.377809	−	1.41000i	−0.471388	−	0.881926i	$-0.656247\pi$
$337$	6.93565	−	25.8842i	0.377809	−	1.41000i	0.849197	−	0.528076i	$-0.177086\pi$
$338$		0			0
$339$	8.44871	+	2.68531i	0.458871	+	0.145846i
$340$		0			0
$341$			2.86806i			0.155314i
$342$		0			0
$343$	13.9737	−	13.9737i	0.754508	−	0.754508i
$344$		0			0
$345$	−17.1699	−	16.6068i	−0.924396	−	0.894081i
$346$		0			0
$347$	29.0619	+	7.78712i	1.56013	+	0.418035i	0.932704	−	0.360644i	$-0.117443\pi$
$347$	29.0619	+	7.78712i	1.56013	+	0.418035i	0.627423	+	0.778679i	$0.284110\pi$
$348$		0			0
$349$	22.2846	+	12.8660i	1.19287	+	0.688702i	0.958956	−	0.283556i	$-0.0915143\pi$
$349$	22.2846	+	12.8660i	1.19287	+	0.688702i	0.233911	+	0.972258i	$0.424848\pi$
$350$		0			0
$351$	5.00162	−	11.8425i	0.266967	−	0.632104i
$352$		0			0
$353$	−15.0636	+	4.03627i	−0.801752	+	0.214829i	−0.636353	−	0.771398i	$-0.719558\pi$
$353$	−15.0636	+	4.03627i	−0.801752	+	0.214829i	−0.165399	+	0.986227i	$0.552891\pi$
$354$		0			0
$355$	−9.05163	+	18.2242i	−0.480411	+	0.967241i
$356$		0			0
$357$	−24.7912	−	15.8743i	−1.31209	−	0.840156i
$358$		0			0
$359$	−22.9830			−1.21300			−0.606498	−	0.795085i	$-0.707426\pi$
$359$	−22.9830			−1.21300			−0.606498	+	0.795085i	$0.707426\pi$
$360$		0			0
$361$	11.2499			0.592099
$362$		0			0
$363$	14.9028	−	7.71427i	0.782196	−	0.404894i
$364$		0			0
$365$	−23.4625	+	7.89020i	−1.22808	+	0.412992i
$366$		0			0
$367$	−3.36526	+	0.901720i	−0.175665	+	0.0470694i	−0.345580	−	0.938389i	$-0.612318\pi$
$367$	−3.36526	+	0.901720i	−0.175665	+	0.0470694i	0.169914	+	0.985459i	$0.445651\pi$
$368$		0			0
$369$	5.37464	−	2.47611i	0.279792	−	0.128901i
$370$		0			0
$371$	5.44254	+	3.14225i	0.282563	+	0.163138i
$372$		0			0
$373$	−22.0898	−	5.91894i	−1.14377	−	0.306471i	−0.363302	−	0.931671i	$-0.618351\pi$
$373$	−22.0898	−	5.91894i	−1.14377	−	0.306471i	−0.780464	+	0.625200i	$0.785017\pi$
$374$		0			0
$375$	19.1703	−	2.73845i	0.989951	−	0.141413i
$376$		0			0
$377$	−2.35206	+	2.35206i	−0.121137	+	0.121137i
$378$		0			0
$379$		−	36.3113i		−	1.86519i	−0.360927	−	0.932594i	$-0.617540\pi$
$379$		−	36.3113i		−	1.86519i	0.360927	−	0.932594i	$-0.382460\pi$
$380$		0			0
$381$	−8.84644	+	8.06880i	−0.453217	+	0.413377i
$382$		0			0
$383$	−4.29635	+	16.0342i	−0.219533	+	0.819308i	0.764988	+	0.644044i	$0.222745\pi$
$383$	−4.29635	+	16.0342i	−0.219533	+	0.819308i	−0.984521	+	0.175264i	$0.943922\pi$
$384$		0			0
$385$	−4.61731	−	4.07253i	−0.235320	−	0.207555i
$386$		0			0
$387$	−4.56137	−	26.5856i	−0.231867	−	1.35142i
$388$		0			0
$389$	11.7878	−	20.4171i	0.597667	−	1.03519i	−0.395497	−	0.918467i	$-0.629428\pi$
$389$	11.7878	−	20.4171i	0.597667	−	1.03519i	0.993164	−	0.116723i	$-0.0372390\pi$
$390$		0			0
$391$	−21.7995	−	37.7578i	−1.10245	−	1.90950i
$392$		0			0
$393$	−4.58185	−	8.85146i	−0.231124	−	0.446497i
$394$		0			0
$395$	12.0894	+	18.2048i	0.608283	+	0.915981i
$396$		0			0
$397$	27.6509	+	27.6509i	1.38776	+	1.38776i	0.830011	+	0.557748i	$0.188334\pi$
$397$	27.6509	+	27.6509i	1.38776	+	1.38776i	0.557748	+	0.830011i	$0.311666\pi$
$398$		0			0
$399$	−11.3242	+	2.48311i	−0.566917	+	0.124311i
$400$		0			0
$401$	−26.4658	+	15.2801i	−1.32164	+	0.763050i	−0.983990	−	0.178222i	$-0.942966\pi$
$401$	−26.4658	+	15.2801i	−1.32164	+	0.763050i	−0.337651	+	0.941272i	$0.609632\pi$
$402$		0			0
$403$	−1.60366	−	5.98494i	−0.0798840	−	0.298131i
$404$		0			0
$405$	−16.0846	−	12.0949i	−0.799249	−	0.600999i
$406$		0			0
$407$	3.42359	+	12.7770i	0.169701	+	0.633332i
$408$		0			0
$409$	2.43668	−	1.40682i	0.120486	−	0.0695626i	−0.438546	−	0.898709i	$-0.644506\pi$
$409$	2.43668	−	1.40682i	0.120486	−	0.0695626i	0.559032	+	0.829146i	$0.311173\pi$
$410$		0			0
$411$	17.5956	−	3.85828i	0.867928	−	0.190315i
$412$		0			0
$413$	−4.46974	−	4.46974i	−0.219942	−	0.219942i
$414$		0			0
$415$	6.13805	+	1.23907i	0.301305	+	0.0608234i
$416$		0			0
$417$	−2.01843	−	3.89931i	−0.0988429	−	0.190950i
$418$		0			0
$419$	−2.23812	−	3.87654i	−0.109339	−	0.189381i	0.806163	−	0.591693i	$-0.201540\pi$
$419$	−2.23812	−	3.87654i	−0.109339	−	0.189381i	−0.915503	+	0.402311i	$0.868207\pi$
$420$		0			0
$421$	2.85177	−	4.93941i	0.138987	−	0.240732i	−0.788127	−	0.615513i	$-0.788949\pi$
$421$	2.85177	−	4.93941i	0.138987	−	0.240732i	0.927113	+	0.374781i	$0.122282\pi$
$422$		0			0
$423$	6.25609	+	36.4632i	0.304181	+	1.77290i
$424$		0			0
$425$	35.0160	+	4.81244i	1.69852	+	0.233438i
$426$		0			0
$427$	4.40916	−	16.4552i	0.213374	−	0.796324i
$428$		0			0
$429$	3.62564	−	3.30693i	0.175048	−	0.159660i
$430$		0			0
$431$			28.4120i			1.36856i	0.729221	+	0.684278i	$0.239883\pi$
$431$			28.4120i			1.36856i	−0.729221	+	0.684278i	$0.760117\pi$
$432$		0			0
$433$	20.2290	−	20.2290i	0.972142	−	0.972142i	−0.0274806	−	0.999622i	$-0.508748\pi$
$433$	20.2290	−	20.2290i	0.972142	−	0.972142i	0.999622	+	0.0274806i	$0.00874844\pi$
$434$		0			0
$435$	2.67842	+	4.46556i	0.128420	+	0.214107i
$436$		0			0
$437$	−16.5850	−	4.44393i	−0.793368	−	0.212582i
$438$		0			0
$439$	12.4785	+	7.20447i	0.595567	+	0.343851i	0.767296	−	0.641293i	$-0.221602\pi$
$439$	12.4785	+	7.20447i	0.595567	+	0.343851i	−0.171729	+	0.985144i	$0.554935\pi$
$440$		0			0
$441$	3.32239	−	1.53063i	0.158209	−	0.0728871i
$442$		0			0
$443$	−25.9195	+	6.94511i	−1.23147	+	0.329972i	−0.815153	−	0.579246i	$-0.803347\pi$
$443$	−25.9195	+	6.94511i	−1.23147	+	0.329972i	−0.416320	+	0.909218i	$0.636680\pi$
$444$		0			0
$445$	−9.76956	−	4.85236i	−0.463122	−	0.230024i
$446$		0			0
$447$	19.9747	−	10.3397i	0.944772	−	0.489050i
$448$		0			0
$449$	1.72288			0.0813077			0.0406538	−	0.999173i	$-0.487056\pi$
$449$	1.72288			0.0813077			0.0406538	+	0.999173i	$0.487056\pi$
$450$		0			0
$451$	2.25891			0.106368
$452$		0			0
$453$	−4.62397	−	2.96081i	−0.217253	−	0.139111i
$454$		0			0
$455$	11.9123	+	5.91663i	0.558458	+	0.277376i
$456$		0			0
$457$	12.3215	−	3.30155i	0.576377	−	0.154440i	0.0411576	−	0.999153i	$-0.486895\pi$
$457$	12.3215	−	3.30155i	0.576377	−	0.154440i	0.535220	+	0.844713i	$0.320229\pi$
$458$		0			0
$459$	−22.1586	−	29.2953i	−1.03428	−	1.36739i
$460$		0			0
$461$	8.72418	+	5.03691i	0.406326	+	0.234592i	0.689210	−	0.724562i	$-0.257958\pi$
$461$	8.72418	+	5.03691i	0.406326	+	0.234592i	−0.282884	+	0.959154i	$0.591291\pi$
$462$		0			0
$463$	36.9737	+	9.90706i	1.71831	+	0.460420i	0.977438	−	0.211224i	$-0.0677450\pi$
$463$	36.9737	+	9.90706i	1.71831	+	0.460420i	0.740874	+	0.671644i	$0.234412\pi$
$464$		0			0
$465$	−9.69838	+	0.161679i	−0.449751	+	0.00749769i
$466$		0			0
$467$	−14.5094	+	14.5094i	−0.671413	+	0.671413i	−0.958042	−	0.286629i	$-0.907465\pi$
$467$	−14.5094	+	14.5094i	−0.671413	+	0.671413i	0.286629	+	0.958042i	$0.407465\pi$
$468$		0			0
$469$			0.135728i			0.00626733i
$470$		0			0
$471$	−17.6336	−	5.60461i	−0.812513	−	0.258247i
$472$		0			0
$473$	2.66499	−	9.94589i	0.122537	−	0.457313i
$474$		0			0
$475$	11.0911	−	8.41080i	0.508892	−	0.385914i
$476$		0			0
$477$	5.01270	+	6.03020i	0.229516	+	0.276104i
$478$		0			0
$479$	2.27813	−	3.94584i	0.104091	−	0.180290i	−0.809276	−	0.587429i	$-0.800140\pi$
$479$	2.27813	−	3.94584i	0.104091	−	0.180290i	0.913366	+	0.407139i	$0.133473\pi$
$480$		0			0
$481$	−14.2884	−	24.7482i	−0.651493	−	1.12842i
$482$		0			0
$483$	−25.6571	−	1.17953i	−1.16744	−	0.0536705i
$484$		0			0
$485$	17.6979	+	3.57262i	0.803622	+	0.162225i
$486$		0			0
$487$	18.4889	+	18.4889i	0.837814	+	0.837814i	0.988571	−	0.150757i	$-0.0481710\pi$
$487$	18.4889	+	18.4889i	0.837814	+	0.837814i	−0.150757	+	0.988571i	$0.548171\pi$
$488$		0			0
$489$	25.9741	+	28.4774i	1.17459	+	1.28779i
$490$		0			0
$491$	0.730071	−	0.421507i	0.0329476	−	0.0190223i	−0.483436	−	0.875380i	$-0.660611\pi$
$491$	0.730071	−	0.421507i	0.0329476	−	0.0190223i	0.516383	+	0.856358i	$0.327278\pi$
$492$		0			0
$493$	2.45989	+	9.18045i	0.110788	+	0.413467i
$494$		0			0
$495$	−3.64470	−	6.76248i	−0.163817	−	0.303951i
$496$		0			0
$497$	5.66277	+	21.1337i	0.254010	+	0.947978i
$498$		0			0
$499$	−8.45869	+	4.88363i	−0.378663	+	0.218621i	−0.677236	−	0.735765i	$-0.736823\pi$
$499$	−8.45869	+	4.88363i	−0.378663	+	0.218621i	0.298573	+	0.954387i	$0.403489\pi$
$500$		0			0
$501$	−2.13310	+	6.71130i	−0.0953000	+	0.299839i
$502$		0			0
$503$	22.3161	+	22.3161i	0.995025	+	0.995025i	0.999988	−	0.00496279i	$-0.00157971\pi$
$503$	22.3161	+	22.3161i	0.995025	+	0.995025i	−0.00496279	+	0.999988i	$0.501580\pi$
$504$		0			0
$505$	0.901410	+	1.35738i	0.0401122	+	0.0604028i
$506$		0			0
$507$	6.42521	−	10.0344i	0.285354	−	0.445643i
$508$		0			0
$509$	−3.83647	−	6.64497i	−0.170049	−	0.294533i	0.768388	−	0.639984i	$-0.221059\pi$
$509$	−3.83647	−	6.64497i	−0.170049	−	0.294533i	−0.938437	+	0.345451i	$0.887726\pi$
$510$		0			0
$511$	−13.3080	+	23.0501i	−0.588712	+	1.01968i
$512$		0			0
$513$	−14.3284	−	1.98736i	−0.632615	−	0.0877442i
$514$		0			0
$515$	−2.28975	−	2.01959i	−0.100898	−	0.0889937i
$516$		0			0
$517$	−3.65514	+	13.6412i	−0.160753	+	0.599938i
$518$		0			0
$519$	−2.06556	−	9.41992i	−0.0906678	−	0.413489i
$520$		0			0
$521$			23.2333i			1.01787i	0.860805	+	0.508934i	$0.169960\pi$
$521$			23.2333i			1.01787i	−0.860805	+	0.508934i	$0.830040\pi$
$522$		0			0
$523$	3.86103	−	3.86103i	0.168831	−	0.168831i	−0.617634	−	0.786465i	$-0.711909\pi$
$523$	3.86103	−	3.86103i	0.168831	−	0.168831i	0.786465	+	0.617634i	$0.211909\pi$
$524$		0			0
$525$	13.5110	−	15.8431i	0.589669	−	0.691447i
$526$		0			0
$527$	−17.1008	−	4.58215i	−0.744923	−	0.199602i
$528$		0			0
$529$	−13.0246	−	7.51973i	−0.566285	−	0.326945i
$530$		0			0
$531$	−3.30031	−	7.16366i	−0.143221	−	0.310876i
$532$		0			0
$533$	−4.71378	+	1.26305i	−0.204176	+	0.0547089i
$534$		0			0
$535$	1.19656	−	0.402390i	0.0517317	−	0.0173969i
$536$		0			0
$537$	0.0246737	−	0.536701i	0.00106475	−	0.0231604i
$538$		0			0
$539$	1.39637			0.0601457
$540$		0			0
$541$	−21.3692			−0.918732			−0.459366	−	0.888247i	$-0.651923\pi$
$541$	−21.3692			−0.918732			−0.459366	+	0.888247i	$0.651923\pi$
$542$		0			0
$543$	−0.244529	+	5.31899i	−0.0104937	+	0.228260i
$544$		0			0
$545$	13.5250	−	27.2308i	0.579349	−	1.16644i
$546$		0			0
$547$	26.5343	−	7.10984i	1.13452	−	0.303995i	0.357777	−	0.933807i	$-0.383535\pi$
$547$	26.5343	−	7.10984i	1.13452	−	0.303995i	0.776747	+	0.629812i	$0.216868\pi$
$548$		0			0
$549$	12.2725	−	17.3559i	0.523776	−	0.740731i
$550$		0			0
$551$	3.24150	+	1.87148i	0.138092	+	0.0797277i
$552$		0			0
$553$	22.6968	+	6.08159i	0.965166	+	0.258615i
$554$		0			0
$555$	−43.0125	+	12.2972i	−1.82578	+	0.521985i
$556$		0			0
$557$	13.7347	−	13.7347i	0.581958	−	0.581958i	−0.353483	−	0.935441i	$-0.615003\pi$
$557$	13.7347	−	13.7347i	0.581958	−	0.581958i	0.935441	+	0.353483i	$0.115003\pi$
$558$		0			0
$559$			22.2447i			0.940852i
$560$		0			0
$561$	−3.00322	−	13.6961i	−0.126796	−	0.578250i
$562$		0			0
$563$	3.85201	−	14.3759i	0.162343	−	0.605872i	−0.836021	−	0.548697i	$-0.815124\pi$
$563$	3.85201	−	14.3759i	0.162343	−	0.605872i	0.998364	−	0.0571749i	$-0.0182093\pi$
$564$		0			0
$565$	−7.57056	+	8.58327i	−0.318496	+	0.361101i
$566$		0			0
$567$	−21.5729	+	1.68692i	−0.905975	+	0.0708439i
$568$		0			0
$569$	−14.7082	+	25.4753i	−0.616599	+	1.06798i	0.373503	+	0.927629i	$0.378157\pi$
$569$	−14.7082	+	25.4753i	−0.616599	+	1.06798i	−0.990102	+	0.140351i	$0.955177\pi$
$570$		0			0
$571$	−15.2909	−	26.4847i	−0.639906	−	1.10835i	−0.985453	−	0.169948i	$-0.945640\pi$
$571$	−15.2909	−	26.4847i	−0.639906	−	1.10835i	0.345548	−	0.938401i	$-0.387693\pi$
$572$		0			0
$573$	−13.3237	+	20.8079i	−0.556606	+	0.869264i
$574$		0			0
$575$	28.5572	−	11.6392i	1.19092	−	0.485388i
$576$		0			0
$577$	−2.75877	−	2.75877i	−0.114849	−	0.114849i	0.647347	−	0.762196i	$-0.275879\pi$
$577$	−2.75877	−	2.75877i	−0.114849	−	0.114849i	−0.762196	+	0.647347i	$0.775879\pi$
$578$		0			0
$579$	−5.03742	+	15.8491i	−0.209348	+	0.658665i
$580$		0			0
$581$	5.83093	−	3.36649i	0.241908	−	0.139665i
$582$		0			0
$583$	0.774736	+	2.89135i	0.0320863	+	0.119748i
$584$		0			0
$585$	11.3868	+	12.0737i	0.470786	+	0.499187i
$586$		0			0
$587$	4.16617	+	15.5484i	0.171956	+	0.641750i	0.997050	+	0.0767539i	$0.0244556\pi$
$587$	4.16617	+	15.5484i	0.171956	+	0.641750i	−0.825094	+	0.564996i	$0.808878\pi$
$588$		0			0
$589$	−6.03808	+	3.48608i	−0.248795	+	0.143642i
$590$		0			0
$591$	−7.63432	−	8.37008i	−0.314034	−	0.344299i
$592$		0			0
$593$	31.4829	+	31.4829i	1.29285	+	1.29285i	0.933018	+	0.359830i	$0.117165\pi$
$593$	31.4829	+	31.4829i	1.29285	+	1.29285i	0.359830	+	0.933018i	$0.382835\pi$
$594$		0			0
$595$	31.6593	−	21.0242i	1.29790	−	0.861910i
$596$		0			0
$597$	7.04593	+	0.323921i	0.288371	+	0.0132572i
$598$		0			0
$599$	−0.0708577	−	0.122729i	−0.00289517	−	0.00501457i	0.864574	−	0.502505i	$-0.167588\pi$
$599$	−0.0708577	−	0.122729i	−0.00289517	−	0.00501457i	−0.867469	+	0.497491i	$0.834255\pi$
$600$		0			0
$601$	21.9425	−	38.0055i	0.895052	−	1.55028i	0.0613115	−	0.998119i	$-0.480472\pi$
$601$	21.9425	−	38.0055i	0.895052	−	1.55028i	0.833740	−	0.552157i	$-0.186195\pi$
$602$		0			0
$603$	−0.0586570	+	0.158874i	−0.00238870	+	0.00646984i
$604$		0			0
$605$	1.35551	+	21.6218i	0.0551092	+	0.879052i
$606$		0			0
$607$	−8.65049	+	32.2841i	−0.351113	+	1.31037i	0.534194	+	0.845362i	$0.320615\pi$
$607$	−8.65049	+	32.2841i	−0.351113	+	1.31037i	−0.885306	+	0.465008i	$0.846051\pi$
$608$		0			0
$609$	5.33596	+	1.69597i	0.216224	+	0.0687240i
$610$		0			0
$611$		−	30.5095i		−	1.23428i
$612$		0			0
$613$	6.75021	−	6.75021i	0.272638	−	0.272638i	−0.557523	−	0.830161i	$-0.688248\pi$
$613$	6.75021	−	6.75021i	0.272638	−	0.272638i	0.830161	+	0.557523i	$0.188248\pi$
$614$		0			0
$615$	0.127340	+	7.63851i	0.00513483	+	0.308014i
$616$		0			0
$617$	31.8700	+	8.53953i	1.28304	+	0.343789i	0.835012	−	0.550232i	$-0.185461\pi$
$617$	31.8700	+	8.53953i	1.28304	+	0.343789i	0.448025	+	0.894021i	$0.352128\pi$
$618$		0			0
$619$	13.2360	+	7.64183i	0.532001	+	0.307151i	0.741831	−	0.670587i	$-0.233958\pi$
$619$	13.2360	+	7.64183i	0.532001	+	0.307151i	−0.209830	+	0.977738i	$0.567291\pi$
$620$		0			0
$621$	−29.5228	−	12.4688i	−1.18471	−	0.500357i
$622$		0			0
$623$	−11.3293	+	3.03567i	−0.453898	+	0.121622i
$624$		0			0
$625$	−6.74439	+	24.0731i	−0.269776	+	0.962923i
$626$		0			0
$627$	−4.65028	−	2.97766i	−0.185714	−	0.118916i
$628$		0			0
$629$	−81.6525			−3.25570
$630$		0			0
$631$	−10.8347			−0.431321			−0.215660	−	0.976468i	$-0.569190\pi$
$631$	−10.8347			−0.431321			−0.215660	+	0.976468i	$0.569190\pi$
$632$		0			0
$633$	−23.3435	+	12.0835i	−0.927823	+	0.480276i
$634$		0			0
$635$	−4.92714	−	14.6515i	−0.195527	−	0.581425i
$636$		0			0
$637$	−2.91387	+	0.780770i	−0.115452	+	0.0309352i
$638$		0			0
$639$	−2.50484	+	27.1850i	−0.0990897	+	1.07542i
$640$		0			0
$641$	−23.0771	−	13.3236i	−0.911491	−	0.526250i	−0.0305804	−	0.999532i	$-0.509736\pi$
$641$	−23.0771	−	13.3236i	−0.911491	−	0.526250i	−0.880911	+	0.473283i	$0.843069\pi$
$642$		0			0
$643$	−13.6969	−	3.67008i	−0.540153	−	0.144734i	−0.0215806	−	0.999767i	$-0.506870\pi$
$643$	−13.6969	−	3.67008i	−0.540153	−	0.144734i	−0.518573	+	0.855033i	$0.673537\pi$
$644$		0			0
$645$	33.7823	+	8.45102i	1.33018	+	0.332759i
$646$		0			0
$647$	−22.3507	+	22.3507i	−0.878698	+	0.878698i	−0.993400	−	0.114702i	$-0.963409\pi$
$647$	−22.3507	+	22.3507i	−0.878698	+	0.878698i	0.114702	+	0.993400i	$0.463409\pi$
$648$		0			0
$649$		−	3.01081i		−	0.118185i
$650$		0			0
$651$	−7.70566	+	7.02830i	−0.302009	+	0.275461i
$652$		0			0
$653$	6.60293	−	24.6425i	0.258393	−	0.964334i	−0.707779	−	0.706434i	$-0.750303\pi$
$653$	6.60293	−	24.6425i	0.258393	−	0.964334i	0.966172	−	0.257900i	$-0.0830306\pi$
$654$		0			0
$655$	12.8422	−	0.805096i	0.501785	−	0.0314577i
$656$		0			0
$657$	−25.5390	+	21.2297i	−0.996370	+	0.828249i
$658$		0			0
$659$	−10.2346	+	17.7269i	−0.398684	+	0.690540i	−0.993564	−	0.113274i	$-0.963866\pi$
$659$	−10.2346	+	17.7269i	−0.398684	+	0.690540i	0.594880	+	0.803814i	$0.297200\pi$
$660$		0			0
$661$	−0.883223	−	1.52979i	−0.0343534	−	0.0595018i	0.848338	−	0.529456i	$-0.177604\pi$
$661$	−0.883223	−	1.52979i	−0.0343534	−	0.0595018i	−0.882691	+	0.469954i	$0.844271\pi$
$662$		0			0
$663$	13.9251	+	26.9012i	0.540805	+	1.04476i
$664$		0			0
$665$	2.96155	−	14.6708i	0.114844	−	0.568911i
$666$		0			0
$667$	5.86358	+	5.86358i	0.227039	+	0.227039i
$668$		0			0
$669$	−14.3973	+	3.15696i	−0.556630	+	0.122055i
$670$		0			0
$671$	7.02711	−	4.05710i	0.271278	−	0.156623i
$672$		0			0
$673$	3.61246	+	13.4819i	0.139250	+	0.519688i	0.999944	+	0.0105656i	$0.00336320\pi$
$673$	3.61246	+	13.4819i	0.139250	+	0.519688i	−0.860694	+	0.509122i	$0.829970\pi$
$674$		0			0
$675$	22.6619	−	12.7058i	0.872257	−	0.489047i
$676$		0			0
$677$	−0.458071	−	1.70954i	−0.0176051	−	0.0657031i	0.956564	−	0.291521i	$-0.0941613\pi$
$677$	−0.458071	−	1.70954i	−0.0176051	−	0.0657031i	−0.974170	+	0.225818i	$0.927495\pi$
$678$		0			0
$679$	16.8124	−	9.70666i	0.645202	−	0.372508i
$680$		0			0
$681$	34.4504	−	7.55413i	1.32014	−	0.289475i
$682$		0			0
$683$	−22.8964	−	22.8964i	−0.876105	−	0.876105i	0.117024	−	0.993129i	$-0.462665\pi$
$683$	−22.8964	−	22.8964i	−0.876105	−	0.876105i	−0.993129	+	0.117024i	$0.962665\pi$
$684$		0			0
$685$	−4.60169	+	22.7957i	−0.175822	+	0.870980i
$686$		0			0
$687$	11.2196	+	21.6747i	0.428055	+	0.826940i
$688$		0			0
$689$	−3.23336	−	5.60035i	−0.123181	−	0.213356i
$690$		0			0
$691$	−11.3908	+	19.7295i	−0.433327	+	0.750545i	−0.997157	−	0.0753461i	$-0.975994\pi$
$691$	−11.3908	+	19.7295i	−0.433327	+	0.750545i	0.563830	+	0.825891i	$0.309327\pi$
$692$		0			0
$693$	−7.74883	−	2.86090i	−0.294354	−	0.108677i
$694$		0			0
$695$	5.65732	−	0.354667i	0.214594	−	0.0134533i
$696$		0			0
$697$	−3.60893	+	13.4687i	−0.136698	+	0.510164i
$698$		0			0
$699$	1.16370	−	1.06140i	0.0440150	−	0.0401459i
$700$		0			0
$701$			26.0321i			0.983220i	0.870816	+	0.491610i	$0.163591\pi$
$701$			26.0321i			0.983220i	−0.870816	+	0.491610i	$0.836409\pi$
$702$		0			0
$703$	−22.7379	+	22.7379i	−0.857574	+	0.857574i
$704$		0			0
$705$	−46.3338	−	11.5909i	−1.74503	−	0.436539i
$706$		0			0
$707$	1.69232	+	0.453456i	0.0636462	+	0.0170540i
$708$		0			0
$709$	2.58254	+	1.49103i	0.0969892	+	0.0559968i	0.547710	−	0.836668i	$-0.315500\pi$
$709$	2.58254	+	1.49103i	0.0969892	+	0.0559968i	−0.450721	+	0.892665i	$0.648833\pi$
$710$		0			0
$711$	23.9391	+	16.9275i	0.897786	+	0.634831i
$712$		0			0
$713$	−14.9202	+	3.99786i	−0.558766	+	0.149721i
$714$		0			0
$715$	2.01935	+	6.00478i	0.0755192	+	0.224566i
$716$		0			0
$717$	16.4319	−	8.50577i	0.613660	−	0.317654i
$718$		0			0
$719$	−7.38853			−0.275546			−0.137773	−	0.990464i	$-0.543994\pi$
$719$	−7.38853			−0.275546			−0.137773	+	0.990464i	$0.543994\pi$
$720$		0			0
$721$	−3.28285			−0.122260
$722$		0			0
$723$	−30.8258	−	19.7384i	−1.14643	−	0.734077i
$724$		0			0
$725$	−6.66986	+	0.839589i	−0.247712	+	0.0311815i
$726$		0			0
$727$	−20.8204	+	5.57881i	−0.772185	+	0.206906i	−0.623337	−	0.781954i	$-0.714223\pi$
$727$	−20.8204	+	5.57881i	−0.772185	+	0.206906i	−0.148849	+	0.988860i	$0.547557\pi$
$728$		0			0
$729$	−25.9808	−	7.34847i	−0.962250	−	0.272166i
$730$		0			0
$731$	55.0446	+	31.7800i	2.03590	+	1.17543i
$732$		0			0
$733$	6.52116	+	1.74734i	0.240865	+	0.0645395i	0.377232	−	0.926119i	$-0.376876\pi$
$733$	6.52116	+	1.74734i	0.240865	+	0.0645395i	−0.136367	+	0.990658i	$0.543543\pi$
$734$		0			0
$735$	0.0787163	+	4.72182i	0.00290350	+	0.174167i
$736$		0			0
$737$	−0.0457130	+	0.0457130i	−0.00168386	+	0.00168386i
$738$		0			0
$739$			12.8637i			0.473200i	0.971607	+	0.236600i	$0.0760331\pi$
$739$			12.8637i			0.473200i	−0.971607	+	0.236600i	$0.923967\pi$
$740$		0			0
$741$	11.3689	+	3.61347i	0.417648	+	0.132744i
$742$		0			0
$743$	8.77270	−	32.7401i	0.321839	−	1.20112i	−0.595613	−	0.803272i	$-0.703091\pi$
$743$	8.77270	−	32.7401i	0.321839	−	1.20112i	0.917452	−	0.397848i	$-0.130243\pi$
$744$		0			0
$745$	1.81683	+	28.9804i	0.0665634	+	1.06176i
$746$		0			0
$747$	8.28018	−	1.42065i	0.302956	−	0.0519790i
$748$		0			0
$749$	0.678692	−	1.17553i	0.0247989	−	0.0429529i
$750$		0			0
$751$	−6.70415	−	11.6119i	−0.244638	−	0.423725i	0.717392	−	0.696670i	$-0.245336\pi$
$751$	−6.70415	−	11.6119i	−0.244638	−	0.423725i	−0.962030	+	0.272945i	$0.912002\pi$
$752$		0			0
$753$	−42.7281	−	1.96433i	−1.55710	−	0.0715843i
$754$		0			0
$755$	5.90498	−	3.92137i	0.214904	−	0.142713i
$756$		0			0
$757$	−1.11492	−	1.11492i	−0.0405223	−	0.0405223i	0.686555	−	0.727078i	$-0.259122\pi$
$757$	−1.11492	−	1.11492i	−0.0405223	−	0.0405223i	−0.727078	+	0.686555i	$0.759122\pi$
$758$		0			0
$759$	−8.24404	−	9.03857i	−0.299240	−	0.328079i
$760$		0			0
$761$	−29.7531	+	17.1780i	−1.07855	+	0.622702i	−0.930505	−	0.366279i	$-0.880632\pi$
$761$	−29.7531	+	17.1780i	−1.07855	+	0.622702i	−0.148046	+	0.988981i	$0.547298\pi$
$762$		0			0
$763$	−8.46136	−	31.5782i	−0.306322	−	1.14321i
$764$		0			0
$765$	46.1442	−	10.9275i	1.66835	−	0.395084i
$766$		0			0
$767$	1.68348	+	6.28282i	0.0607869	+	0.226860i
$768$		0			0
$769$	−14.4890	+	8.36522i	−0.522486	+	0.301658i	−0.737951	−	0.674854i	$-0.764207\pi$
$769$	−14.4890	+	8.36522i	−0.522486	+	0.301658i	0.215465	+	0.976512i	$0.430873\pi$
$770$		0			0
$771$	2.75723	−	8.67497i	0.0992992	−	0.312421i
$772$		0			0
$773$	−5.20827	−	5.20827i	−0.187328	−	0.187328i	0.607212	−	0.794540i	$-0.292288\pi$
$773$	−5.20827	−	5.20827i	−0.187328	−	0.187328i	−0.794540	+	0.607212i	$0.792288\pi$
$774$		0			0
$775$	4.85771	−	11.5417i	0.174494	−	0.414589i
$776$		0			0
$777$	−25.9385	+	40.5087i	−0.930539	+	1.45324i
$778$		0			0
$779$	2.74567	+	4.75563i	0.0983737	+	0.170388i
$780$		0			0
$781$	−5.21061	+	9.02504i	−0.186450	+	0.322941i
$782$		0			0
$783$	5.51297	+	4.29121i	0.197018	+	0.153355i
$784$		0			0
$785$	15.8008	−	17.9144i	0.563954	−	0.639394i
$786$		0			0
$787$	−11.9724	+	44.6815i	−0.426769	+	1.59272i	0.333262	+	0.942834i	$0.391851\pi$
$787$	−11.9724	+	44.6815i	−0.426769	+	1.59272i	−0.760030	+	0.649888i	$0.774816\pi$
$788$		0			0
$789$	5.54069	+	25.2682i	0.197254	+	0.899571i
$790$		0			0
$791$			12.3060i			0.437550i
$792$		0			0
$793$	−12.3953	+	12.3953i	−0.440171	+	0.440171i
$794$		0			0
$795$	−9.73346	+	2.78277i	−0.345210	+	0.0986946i
$796$		0			0
$797$	49.7628	+	13.3339i	1.76269	+	0.472311i	0.987259	−	0.159123i	$-0.0508665\pi$
$797$	49.7628	+	13.3339i	1.76269	+	0.472311i	0.775430	+	0.631434i	$0.217533\pi$
$798$		0			0
$799$	−75.4958	−	43.5875i	−2.67085	−	1.54202i
$800$		0			0
$801$	−14.5732	−	1.34278i	−0.514919	−	0.0474448i
$802$		0			0
$803$	−12.2454	+	3.28114i	−0.432131	+	0.115789i
$804$		0			0
$805$	14.7499	−	29.6969i	0.519866	−	1.04668i
$806$		0			0
$807$	1.59143	−	34.6168i	0.0560210	−	1.21857i
$808$		0			0
$809$	18.0260			0.633762			0.316881	−	0.948465i	$-0.397364\pi$
$809$	18.0260			0.633762			0.316881	+	0.948465i	$0.397364\pi$
$810$		0			0
$811$	−46.7969			−1.64326			−0.821630	−	0.570021i	$-0.806935\pi$
$811$	−46.7969			−1.64326			−0.821630	+	0.570021i	$0.806935\pi$
$812$		0			0
$813$	−0.240788	+	5.23762i	−0.00844481	+	0.183691i
$814$		0			0
$815$	−47.1643	+	15.8609i	−1.65209	+	0.555582i
$816$		0			0
$817$	24.1782	−	6.47852i	0.845886	−	0.226655i
$818$		0			0
$819$	17.7696	+	1.63729i	0.620918	+	0.0572117i
$820$		0			0
$821$	5.91006	+	3.41218i	0.206263	+	0.119086i	0.599573	−	0.800320i	$-0.295337\pi$
$821$	5.91006	+	3.41218i	0.206263	+	0.119086i	−0.393311	+	0.919406i	$0.628670\pi$
$822$		0			0
$823$	19.6876	+	5.27529i	0.686268	+	0.183885i	0.585072	−	0.810982i	$-0.301066\pi$
$823$	19.6876	+	5.27529i	0.686268	+	0.183885i	0.101196	+	0.994866i	$0.467733\pi$
$824$		0			0
$825$	9.88642	−	0.785431i	0.344201	−	0.0273452i
$826$		0			0
$827$	29.8425	−	29.8425i	1.03773	−	1.03773i	0.0384654	−	0.999260i	$-0.487753\pi$
$827$	29.8425	−	29.8425i	1.03773	−	1.03773i	0.999260	−	0.0384654i	$-0.0122469\pi$
$828$		0			0
$829$		−	20.4152i		−	0.709050i	−0.935047	−	0.354525i	$-0.884643\pi$
$829$		−	20.4152i		−	0.709050i	0.935047	−	0.354525i	$-0.115357\pi$
$830$		0			0
$831$	1.03767	+	4.73227i	0.0359964	+	0.164161i
$832$		0			0
$833$	−2.23090	+	8.32583i	−0.0772961	+	0.288473i
$834$		0			0
$835$	−6.81819	−	6.01374i	−0.235953	−	0.208114i
$836$		0			0
$837$	−12.0571	+	4.89673i	−0.416755	+	0.169256i
$838$		0			0
$839$	9.70261	−	16.8054i	0.334971	−	0.580187i	−0.648508	−	0.761208i	$-0.724607\pi$
$839$	9.70261	−	16.8054i	0.334971	−	0.580187i	0.983479	+	0.181021i	$0.0579400\pi$
$840$		0			0
$841$	13.5962	+	23.5492i	0.468833	+	0.812043i
$842$		0			0
$843$	−14.1280	+	22.0640i	−0.486595	+	0.759926i
$844$		0			0
$845$	8.50968	+	12.8143i	0.292742	+	0.440825i
$846$		0			0
$847$	16.4715	+	16.4715i	0.565967	+	0.565967i
$848$		0			0
$849$	12.6116	−	39.6794i	0.432828	−	1.36179i
$850$		0			0
$851$	−61.6961	+	35.6203i	−2.11492	+	1.22105i
$852$		0			0
$853$	0.132960	+	0.496213i	0.00455246	+	0.0169900i	0.968165	−	0.250314i	$-0.0805339\pi$
$853$	0.132960	+	0.496213i	0.00455246	+	0.0169900i	−0.963612	+	0.267304i	$0.913867\pi$
$854$		0			0
$855$	9.80683	−	15.8928i	0.335387	−	0.543523i
$856$		0			0
$857$	−11.5332	−	43.0427i	−0.393968	−	1.47031i	−0.823530	−	0.567272i	$-0.807999\pi$
$857$	−11.5332	−	43.0427i	−0.393968	−	1.47031i	0.429562	−	0.903037i	$-0.358668\pi$
$858$		0			0
$859$	25.5432	−	14.7474i	0.871522	−	0.503174i	0.00366859	−	0.999993i	$-0.498832\pi$
$859$	25.5432	−	14.7474i	0.871522	−	0.503174i	0.867854	+	0.496820i	$0.165499\pi$
$860$		0			0
$861$	5.53554	+	6.06903i	0.188651	+	0.206832i
$862$		0			0
$863$	−6.17951	−	6.17951i	−0.210353	−	0.210353i	0.594064	−	0.804417i	$-0.297522\pi$
$863$	−6.17951	−	6.17951i	−0.210353	−	0.210353i	−0.804417	+	0.594064i	$0.797522\pi$
$864$		0			0
$865$	12.2038	+	2.46354i	0.414943	+	0.0837630i
$866$		0			0
$867$	57.0473	+	2.62263i	1.93743	+	0.0890691i
$868$		0			0
$869$	5.59599	+	9.69254i	0.189831	+	0.328797i
$870$		0			0
$871$	0.0698316	−	0.120952i	0.00236615	−	0.00409830i
$872$		0			0
$873$	23.8744	−	4.09620i	0.808026	−	0.138635i
$874$		0			0
$875$	11.6833	+	24.2092i	0.394967	+	0.818419i
$876$		0			0
$877$	−5.38298	+	20.0896i	−0.181770	+	0.678376i	0.813528	+	0.581525i	$0.197544\pi$
$877$	−5.38298	+	20.0896i	−0.181770	+	0.678376i	−0.995299	+	0.0968513i	$0.969123\pi$
$878$		0			0
$879$	24.9245	+	7.92195i	0.840684	+	0.267201i
$880$		0			0
$881$		−	28.3087i		−	0.953745i	−0.878972	−	0.476873i	$-0.841770\pi$
$881$		−	28.3087i		−	0.953745i	0.878972	−	0.476873i	$-0.158230\pi$
$882$		0			0
$883$	−15.1647	+	15.1647i	−0.510333	+	0.510333i	−0.914629	−	0.404295i	$-0.867517\pi$
$883$	−15.1647	+	15.1647i	−0.510333	+	0.510333i	0.404295	+	0.914629i	$0.367517\pi$
$884$		0			0
$885$	10.1811	−	0.169726i	0.342233	−	0.00570529i
$886$		0			0
$887$	46.4040	+	12.4339i	1.55809	+	0.417490i	0.932059	−	0.362306i	$-0.118011\pi$
$887$	46.4040	+	12.4339i	1.55809	+	0.417490i	0.626034	+	0.779796i	$0.284677\pi$
$888$		0			0
$889$	−14.3940	−	8.31036i	−0.482758	−	0.278721i
$890$		0			0
$891$	−7.83387	−	6.69757i	−0.262445	−	0.224377i
$892$		0			0
$893$	−33.1613	+	8.88553i	−1.10970	+	0.297343i
$894$		0			0
$895$	0.621206	+	0.308541i	0.0207646	+	0.0103134i
$896$		0			0
$897$	22.2571	+	14.2517i	0.743144	+	0.475849i
$898$		0			0
$899$	3.36724			0.112304
$900$		0			0
$901$	−18.4774			−0.615573
$902$		0			0
$903$	33.2524	−	17.2127i	1.10657	−	0.572804i
$904$		0			0
$905$	−6.15648	−	3.05781i	−0.204648	−	0.101645i
$906$		0			0
$907$	36.0516	−	9.66001i	1.19707	−	0.320755i	0.395396	−	0.918511i	$-0.370607\pi$
$907$	36.0516	−	9.66001i	1.19707	−	0.320755i	0.801679	+	0.597755i	$0.203941\pi$
$908$		0			0
$909$	1.78495	+	1.26215i	0.0592030	+	0.0418628i
$910$		0			0
$911$	−46.5957	−	26.9020i	−1.54378	−	0.891304i	−0.998595	−	0.0529906i	$-0.983125\pi$
$911$	−46.5957	−	26.9020i	−1.54378	−	0.891304i	−0.545189	−	0.838313i	$-0.683542\pi$
$912$		0			0
$913$	3.09768	+	0.830022i	0.102518	+	0.0274697i
$914$		0			0
$915$	14.1153	+	23.5335i	0.466636	+	0.777994i
$916$		0			0
$917$	9.78315	−	9.78315i	0.323068	−	0.323068i
$918$		0			0
$919$			23.1668i			0.764203i	0.924120	+	0.382101i	$0.124799\pi$
$919$			23.1668i			0.764203i	−0.924120	+	0.382101i	$0.875201\pi$
$920$		0			0
$921$	15.0126	−	13.6929i	0.494681	−	0.451196i
$922$		0			0
$923$	5.82696	−	21.7465i	0.191797	−	0.715795i
$924$		0			0
$925$	7.86351	−	57.2159i	0.258551	−	1.88125i
$926$		0			0
$927$	−3.84268	−	1.41874i	−0.126210	−	0.0465974i
$928$		0			0
$929$	6.78350	−	11.7494i	0.222559	−	0.385484i	−0.733025	−	0.680202i	$-0.761892\pi$
$929$	6.78350	−	11.7494i	0.222559	−	0.385484i	0.955584	+	0.294717i	$0.0952255\pi$
$930$		0			0
$931$	1.69726	+	2.93974i	0.0556255	+	0.0963462i
$932$		0			0
$933$	−10.0084	−	19.3347i	−0.327659	−	0.632989i
$934$		0			0
$935$	17.7438	+	3.58188i	0.580283	+	0.117140i
$936$		0			0
$937$	−6.94086	−	6.94086i	−0.226748	−	0.226748i	0.584585	−	0.811333i	$-0.301258\pi$
$937$	−6.94086	−	6.94086i	−0.226748	−	0.226748i	−0.811333	+	0.584585i	$0.801258\pi$
$938$		0			0
$939$	20.1959	−	4.42847i	0.659069	−	0.144518i
$940$		0			0
$941$	−14.5976	+	8.42791i	−0.475867	+	0.274742i	−0.718693	−	0.695328i	$-0.755259\pi$
$941$	−14.5976	+	8.42791i	−0.475867	+	0.274742i	0.242825	+	0.970070i	$0.421926\pi$
$942$		0			0
$943$	3.14874	+	11.7513i	0.102537	+	0.382673i
$944$		0			0
$945$	9.23735	−	26.3640i	0.300491	−	0.857621i
$946$		0			0
$947$	−9.92745	−	37.0498i	−0.322599	−	1.20396i	−0.916704	−	0.399568i	$-0.869160\pi$
$947$	−9.92745	−	37.0498i	−0.322599	−	1.20396i	0.594105	−	0.804388i	$-0.297506\pi$
$948$		0			0
$949$	23.7185	−	13.6939i	0.769935	−	0.444522i
$950$		0			0
$951$	3.28496	−	0.720309i	0.106522	−	0.0233576i
$952$		0			0
$953$	−18.8861	−	18.8861i	−0.611780	−	0.611780i	0.331630	−	0.943410i	$-0.392402\pi$
$953$	−18.8861	−	18.8861i	−0.611780	−	0.611780i	−0.943410	+	0.331630i	$0.892402\pi$
$954$		0			0
$955$	−17.6462	−	26.5725i	−0.571018	−	0.859865i
$956$		0			0
$957$	1.22595	+	2.36835i	0.0396292	+	0.0765578i
$958$		0			0
$959$	12.5026	+	21.6551i	0.403730	+	0.699281i
$960$		0			0
$961$	12.3638	−	21.4148i	0.398834	−	0.690800i
$962$		0			0
$963$	1.30246	−	1.08269i	0.0419711	−	0.0348891i
$964$		0			0
$965$	−16.1015	−	14.2017i	−0.518325	−	0.457170i
$966$		0			0
$967$	8.29288	−	30.9494i	0.266681	−	0.995267i	−0.694533	−	0.719461i	$-0.744389\pi$
$967$	8.29288	−	30.9494i	0.266681	−	0.995267i	0.961213	−	0.275805i	$-0.0889446\pi$
$968$		0			0
$969$	25.1838	−	22.9700i	0.809020	−	0.737904i
$970$		0			0
$971$		−	29.2201i		−	0.937716i	−0.883274	−	0.468858i	$-0.844666\pi$
$971$		−	29.2201i		−	0.937716i	0.883274	−	0.468858i	$-0.155334\pi$
$972$		0			0
$973$	4.30974	−	4.30974i	0.138164	−	0.138164i
$974$		0			0
$975$	−20.1914	+	7.16694i	−0.646641	+	0.229526i
$976$		0			0
$977$	−37.7399	−	10.1124i	−1.20741	−	0.323523i	−0.401662	−	0.915788i	$-0.631567\pi$
$977$	−37.7399	−	10.1124i	−1.20741	−	0.323523i	−0.805743	+	0.592265i	$0.798234\pi$
$978$		0			0
$979$	−4.83811	−	2.79328i	−0.154627	−	0.0892737i
$980$		0			0
$981$	3.74275	−	40.6201i	0.119497	−	1.29690i
$982$		0			0
$983$	−11.0660	+	2.96514i	−0.352952	+	0.0945732i	−0.430939	−	0.902381i	$-0.641818\pi$
$983$	−11.0660	+	2.96514i	−0.352952	+	0.0945732i	0.0779867	+	0.996954i	$0.475151\pi$
$984$		0			0
$985$	13.8625	−	4.66182i	0.441696	−	0.148538i
$986$		0			0
$987$	−45.6070	+	23.6079i	−1.45169	+	0.751448i
$988$		0			0
$989$	55.4552			1.76337
$990$		0			0
$991$	26.7986			0.851286			0.425643	−	0.904891i	$-0.360048\pi$
$991$	26.7986			0.851286			0.425643	+	0.904891i	$0.360048\pi$
$992$		0			0
$993$	32.0350	+	20.5126i	1.01660	+	0.650949i
$994$		0			0
$995$	−4.05060	+	8.15533i	−0.128413	+	0.258541i
$996$		0			0
$997$	−53.0819	+	14.2233i	−1.68112	+	0.450455i	−0.968075	−	0.250661i	$-0.919352\pi$
$997$	−53.0819	+	14.2233i	−1.68112	+	0.450455i	−0.713047	+	0.701116i	$0.752685\pi$
$998$		0			0
$999$	−47.8684	+	36.2071i	−1.51449	+	1.14554i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.cu.b.497.2		16
4.3	odd	2		90.2.l.b.47.2	yes	16
5.3	odd	4	inner	720.2.cu.b.353.1		16
9.5	odd	6	inner	720.2.cu.b.257.1		16
12.11	even	2		270.2.m.b.197.4		16
20.3	even	4		90.2.l.b.83.2	yes	16
20.7	even	4		450.2.p.h.443.3		16
20.19	odd	2		450.2.p.h.407.3		16
36.7	odd	6		810.2.f.c.647.3		16
36.11	even	6		810.2.f.c.647.6		16
36.23	even	6		90.2.l.b.77.2	yes	16
36.31	odd	6		270.2.m.b.17.3		16
45.23	even	12	inner	720.2.cu.b.113.2		16
60.23	odd	4		270.2.m.b.143.3		16
60.47	odd	4		1350.2.q.h.143.1		16
60.59	even	2		1350.2.q.h.1007.2		16
180.23	odd	12		90.2.l.b.23.2	✓	16
180.43	even	12		810.2.f.c.323.6		16
180.59	even	6		450.2.p.h.257.3		16
180.67	even	12		1350.2.q.h.1043.2		16
180.83	odd	12		810.2.f.c.323.3		16
180.103	even	12		270.2.m.b.233.4		16
180.139	odd	6		1350.2.q.h.557.1		16
180.167	odd	12		450.2.p.h.293.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.b.23.2	✓	16	180.23	odd	12
90.2.l.b.47.2	yes	16	4.3	odd	2
90.2.l.b.77.2	yes	16	36.23	even	6
90.2.l.b.83.2	yes	16	20.3	even	4
270.2.m.b.17.3		16	36.31	odd	6
270.2.m.b.143.3		16	60.23	odd	4
270.2.m.b.197.4		16	12.11	even	2
270.2.m.b.233.4		16	180.103	even	12
450.2.p.h.257.3		16	180.59	even	6
450.2.p.h.293.3		16	180.167	odd	12
450.2.p.h.407.3		16	20.19	odd	2
450.2.p.h.443.3		16	20.7	even	4
720.2.cu.b.113.2		16	45.23	even	12	inner
720.2.cu.b.257.1		16	9.5	odd	6	inner
720.2.cu.b.353.1		16	5.3	odd	4	inner
720.2.cu.b.497.2		16	1.1	even	1	trivial
810.2.f.c.323.3		16	180.83	odd	12
810.2.f.c.323.6		16	180.43	even	12
810.2.f.c.647.3		16	36.7	odd	6
810.2.f.c.647.6		16	36.11	even	6
1350.2.q.h.143.1		16	60.47	odd	4
1350.2.q.h.557.1		16	180.139	odd	6
1350.2.q.h.1007.2		16	60.59	even	2
1350.2.q.h.1043.2		16	180.67	even	12

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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.cu (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0795432 + 1.73022i) q^{3} +(-2.00265 - 0.994679i) q^{5} +(-2.32238 + 0.622279i) q^{7} +(-2.98735 - 0.275255i) q^{9} +O(q^{10})\)	\(q+(-0.0795432 + 1.73022i) q^{3} +(-2.00265 - 0.994679i) q^{5} +(-2.32238 + 0.622279i) q^{7} +(-2.98735 - 0.275255i) q^{9} +(-0.991757 - 0.572591i) q^{11} +(2.38971 + 0.640322i) q^{13} +(1.88031 - 3.38591i) q^{15} +(4.99855 - 4.99855i) q^{17} -2.78390i q^{19} +(-0.891952 - 4.06773i) q^{21} +(1.59630 - 5.95746i) q^{23} +(3.02123 + 3.98399i) q^{25} +(0.713876 - 5.14688i) q^{27} +(-0.672250 + 1.16437i) q^{29} +(-1.25223 - 2.16892i) q^{31} +(1.06960 - 1.67042i) q^{33} +(5.26988 + 1.06381i) q^{35} +(-8.16761 - 8.16761i) q^{37} +(-1.29799 + 4.08381i) q^{39} +(-1.70826 + 0.986264i) q^{41} +(2.32713 + 8.68498i) q^{43} +(5.70882 + 3.52269i) q^{45} +(-3.19175 - 11.9118i) q^{47} +(-1.05598 + 0.609669i) q^{49} +(8.25101 + 9.04622i) q^{51} +(-1.84828 - 1.84828i) q^{53} +(1.41660 + 2.13318i) q^{55} +(4.81678 + 0.221441i) q^{57} +(1.31456 + 2.27688i) q^{59} +(-3.54275 + 6.13623i) q^{61} +(7.10903 - 1.21972i) q^{63} +(-4.14885 - 3.65934i) q^{65} +(0.0146109 - 0.0545285i) q^{67} +(10.1808 + 3.23582i) q^{69} -9.10005i q^{71} +(7.82779 - 7.82779i) q^{73} +(-7.13351 + 4.91050i) q^{75} +(2.65955 + 0.712623i) q^{77} +(-8.46375 - 4.88655i) q^{79} +(8.84847 + 1.64456i) q^{81} +(-2.70497 + 0.724794i) q^{83} +(-14.9823 + 5.03840i) q^{85} +(-1.96115 - 1.25576i) q^{87} +4.87832 q^{89} -5.94827 q^{91} +(3.85233 - 1.99411i) q^{93} +(-2.76909 + 5.57519i) q^{95} +(-7.79929 + 2.08981i) q^{97} +(2.80511 + 1.98351i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{5} - 8 q^{7}+O(q^{10}) \) 16 * q - 12 * q^5 - 8 * q^7	\( 16 q - 12 q^{5} - 8 q^{7} + 24 q^{15} + 24 q^{21} + 24 q^{23} - 16 q^{25} + 8 q^{31} + 24 q^{41} + 36 q^{45} - 48 q^{47} + 48 q^{51} - 24 q^{55} + 24 q^{57} - 24 q^{61} + 48 q^{63} + 16 q^{67} + 16 q^{73} - 72 q^{77} + 24 q^{81} - 48 q^{83} - 4 q^{85} + 48 q^{87} + 72 q^{93} - 84 q^{95} - 48 q^{97}+O(q^{100}) \) 16 * q - 12 * q^5 - 8 * q^7 + 24 * q^15 + 24 * q^21 + 24 * q^23 - 16 * q^25 + 8 * q^31 + 24 * q^41 + 36 * q^45 - 48 * q^47 + 48 * q^51 - 24 * q^55 + 24 * q^57 - 24 * q^61 + 48 * q^63 + 16 * q^67 + 16 * q^73 - 72 * q^77 + 24 * q^81 - 48 * q^83 - 4 * q^85 + 48 * q^87 + 72 * q^93 - 84 * q^95 - 48 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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