LMFDB - Embedded newform 280.2.bo.a.33.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(17,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))

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

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

chi := DirichletCharacter("280.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.bo (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			33.6
Character	$\chi$	$=$	280.33
Dual form			280.2.bo.a.17.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0749389 - 0.0200798i) q^{3} +(-0.965007 - 2.01712i) q^{5} +(1.45892 - 2.20716i) q^{7} +(-2.59286 - 1.49699i) q^{9} +O(q^{10})$	\(q+(-0.0749389 - 0.0200798i) q^{3} +(-0.965007 - 2.01712i) q^{5} +(1.45892 - 2.20716i) q^{7} +(-2.59286 - 1.49699i) q^{9} +(-0.390978 - 0.677193i) q^{11} +(-3.28478 + 3.28478i) q^{13} +(0.0318132 + 0.170538i) q^{15} +(1.40637 - 5.24865i) q^{17} +(2.91828 - 5.05461i) q^{19} +(-0.153649 + 0.136108i) q^{21} +(8.39046 - 2.24822i) q^{23} +(-3.13752 + 3.89306i) q^{25} +(0.328824 + 0.328824i) q^{27} +0.303774i q^{29} +(-5.04234 + 2.91120i) q^{31} +(0.0157015 + 0.0585989i) q^{33} +(-5.85997 - 0.812878i) q^{35} +(1.90872 + 7.12345i) q^{37} +(0.312116 - 0.180200i) q^{39} -4.39716i q^{41} +(7.33155 + 7.33155i) q^{43} +(-0.517475 + 6.67472i) q^{45} +(2.28130 - 0.611272i) q^{47} +(-2.74313 - 6.44013i) q^{49} +(-0.210784 + 0.365088i) q^{51} +(-1.61262 + 6.01838i) q^{53} +(-0.988682 + 1.44214i) q^{55} +(-0.320188 + 0.320188i) q^{57} +(2.56228 + 4.43800i) q^{59} +(-8.91983 - 5.14987i) q^{61} +(-7.08687 + 3.53889i) q^{63} +(9.79563 + 3.45595i) q^{65} +(-1.47788 - 0.395996i) q^{67} -0.673916 q^{69} -5.83740 q^{71} +(12.9542 + 3.47108i) q^{73} +(0.313295 - 0.228741i) q^{75} +(-2.06508 - 0.125017i) q^{77} +(8.66781 + 5.00437i) q^{79} +(4.47293 + 7.74735i) q^{81} +(2.94473 - 2.94473i) q^{83} +(-11.9443 + 2.22817i) q^{85} +(0.00609973 - 0.0227645i) q^{87} +(6.43727 - 11.1497i) q^{89} +(2.45783 + 12.0423i) q^{91} +(0.436324 - 0.116913i) q^{93} +(-13.0119 - 1.00878i) q^{95} +(-0.0900545 - 0.0900545i) q^{97} +2.34116i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{7}+O(q^{10}) $ 48 * q - 4 * q^7	$ 48 q - 4 q^{7} + 4 q^{11} + 8 q^{15} - 4 q^{21} - 4 q^{23} - 8 q^{25} - 36 q^{33} + 24 q^{35} + 8 q^{37} - 16 q^{43} + 48 q^{45} + 24 q^{51} + 16 q^{53} - 96 q^{57} - 36 q^{61} - 68 q^{63} + 12 q^{65} - 16 q^{67} - 64 q^{71} - 48 q^{73} - 48 q^{75} + 4 q^{77} - 40 q^{85} - 12 q^{87} - 80 q^{91} + 24 q^{95}+O(q^{100}) $ 48 * q - 4 * q^7 + 4 * q^11 + 8 * q^15 - 4 * q^21 - 4 * q^23 - 8 * q^25 - 36 * q^33 + 24 * q^35 + 8 * q^37 - 16 * q^43 + 48 * q^45 + 24 * q^51 + 16 * q^53 - 96 * q^57 - 36 * q^61 - 68 * q^63 + 12 * q^65 - 16 * q^67 - 64 * q^71 - 48 * q^73 - 48 * q^75 + 4 * q^77 - 40 * q^85 - 12 * q^87 - 80 * q^91 + 24 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	−0.0749389	−	0.0200798i	−0.0432660	−	0.0115931i	0.237121	−	0.971480i	$-0.423796\pi$
$3$	−0.0749389	−	0.0200798i	−0.0432660	−	0.0115931i	−0.280387	+	0.959887i	$0.590463\pi$
$4$		0			0
$5$	−0.965007	−	2.01712i	−0.431564	−	0.902082i
$5$	−0.965007	−	2.01712i	−0.431564	−	0.902082i
$6$		0			0
$7$	1.45892	−	2.20716i	0.551418	−	0.834229i
$7$	1.45892	−	2.20716i	0.551418	−	0.834229i
$8$		0			0
$9$	−2.59286	−	1.49699i	−0.864288	−	0.498997i
$10$		0			0
$11$	−0.390978	−	0.677193i	−0.117884	−	0.204181i	0.801045	−	0.598604i	$-0.204278\pi$
$11$	−0.390978	−	0.677193i	−0.117884	−	0.204181i	−0.918929	+	0.394423i	$0.870945\pi$
$12$		0			0
$13$	−3.28478	+	3.28478i	−0.911035	+	0.911035i	−0.996354	−	0.0853189i	$-0.972809\pi$
$13$	−3.28478	+	3.28478i	−0.911035	+	0.911035i	0.0853189	+	0.996354i	$0.472809\pi$
$14$		0			0
$15$	0.0318132	+	0.170538i	0.00821413	+	0.0440327i
$16$		0			0
$17$	1.40637	−	5.24865i	0.341095	−	1.27298i	−0.556013	−	0.831174i	$-0.687670\pi$
$17$	1.40637	−	5.24865i	0.341095	−	1.27298i	0.897108	−	0.441811i	$-0.145664\pi$
$18$		0			0
$19$	2.91828	−	5.05461i	0.669499	−	1.15961i	−0.308545	−	0.951210i	$-0.599842\pi$
$19$	2.91828	−	5.05461i	0.669499	−	1.15961i	0.978044	−	0.208397i	$-0.0668245\pi$
$20$		0			0
$21$	−0.153649	+	0.136108i	−0.0335290	+	0.0297011i
$22$		0			0
$23$	8.39046	−	2.24822i	1.74953	−	0.468786i	0.765006	−	0.644024i	$-0.222736\pi$
$23$	8.39046	−	2.24822i	1.74953	−	0.468786i	0.984526	+	0.175238i	$0.0560695\pi$
$24$		0			0
$25$	−3.13752	+	3.89306i	−0.627505	+	0.778613i
$26$		0			0
$27$	0.328824	+	0.328824i	0.0632823	+	0.0632823i
$28$		0			0
$29$			0.303774i			0.0564094i	0.999602	+	0.0282047i	$0.00897903\pi$
$29$			0.303774i			0.0564094i	−0.999602	+	0.0282047i	$0.991021\pi$
$30$		0			0
$31$	−5.04234	+	2.91120i	−0.905632	+	0.522867i	−0.879023	−	0.476779i	$-0.841804\pi$
$31$	−5.04234	+	2.91120i	−0.905632	+	0.522867i	−0.0266086	+	0.999646i	$0.508471\pi$
$32$		0			0
$33$	0.0157015	+	0.0585989i	0.00273328	+	0.0102008i
$34$		0			0
$35$	−5.85997	−	0.812878i	−0.990515	−	0.137401i
$36$		0			0
$37$	1.90872	+	7.12345i	0.313792	+	1.17109i	0.925109	+	0.379702i	$0.123973\pi$
$37$	1.90872	+	7.12345i	0.313792	+	1.17109i	−0.611317	+	0.791386i	$0.709360\pi$
$38$		0			0
$39$	0.312116	−	0.180200i	0.0499785	−	0.0288551i
$40$		0			0
$41$		−	4.39716i		−	0.686722i	−0.939204	−	0.343361i	$-0.888435\pi$
$41$		−	4.39716i		−	0.686722i	0.939204	−	0.343361i	$-0.111565\pi$
$42$		0			0
$43$	7.33155	+	7.33155i	1.11805	+	1.11805i	0.992027	+	0.126023i	$0.0402214\pi$
$43$	7.33155	+	7.33155i	1.11805	+	1.11805i	0.126023	+	0.992027i	$0.459779\pi$
$44$		0			0
$45$	−0.517475	+	6.67472i	−0.0771406	+	0.995008i
$46$		0			0
$47$	2.28130	−	0.611272i	0.332761	−	0.0891631i	−0.0885698	−	0.996070i	$-0.528230\pi$
$47$	2.28130	−	0.611272i	0.332761	−	0.0891631i	0.421331	+	0.906907i	$0.361563\pi$
$48$		0			0
$49$	−2.74313	−	6.44013i	−0.391876	−	0.920018i
$50$		0			0
$51$	−0.210784	+	0.365088i	−0.0295157	+	0.0511226i
$52$		0			0
$53$	−1.61262	+	6.01838i	−0.221510	+	0.826688i	0.762262	+	0.647268i	$0.224089\pi$
$53$	−1.61262	+	6.01838i	−0.221510	+	0.826688i	−0.983773	+	0.179420i	$0.942578\pi$
$54$		0			0
$55$	−0.988682	+	1.44214i	−0.133314	+	0.194459i
$56$		0			0
$57$	−0.320188	+	0.320188i	−0.0424100	+	0.0424100i
$58$		0			0
$59$	2.56228	+	4.43800i	0.333581	+	0.577779i	0.983211	−	0.182471i	$-0.0584097\pi$
$59$	2.56228	+	4.43800i	0.333581	+	0.577779i	−0.649630	+	0.760250i	$0.725076\pi$
$60$		0			0
$61$	−8.91983	−	5.14987i	−1.14207	−	0.659373i	−0.195126	−	0.980778i	$-0.562511\pi$
$61$	−8.91983	−	5.14987i	−1.14207	−	0.659373i	−0.946942	+	0.321405i	$0.895845\pi$
$62$		0			0
$63$	−7.08687	+	3.53889i	−0.892862	+	0.445858i
$64$		0			0
$65$	9.79563	+	3.45595i	1.21500	+	0.428658i
$66$		0			0
$67$	−1.47788	−	0.395996i	−0.180551	−	0.0483786i	0.167410	−	0.985887i	$-0.446459\pi$
$67$	−1.47788	−	0.395996i	−0.180551	−	0.0483786i	−0.347962	+	0.937509i	$0.613126\pi$
$68$		0			0
$69$	−0.673916			−0.0811299
$70$		0			0
$71$	−5.83740			−0.692772			−0.346386	−	0.938092i	$-0.612591\pi$
$71$	−5.83740			−0.692772			−0.346386	+	0.938092i	$0.612591\pi$
$72$		0			0
$73$	12.9542	+	3.47108i	1.51618	+	0.406259i	0.918482	−	0.395463i	$-0.129416\pi$
$73$	12.9542	+	3.47108i	1.51618	+	0.406259i	0.597697	+	0.801722i	$0.296082\pi$
$74$		0			0
$75$	0.313295	−	0.228741i	0.0361762	−	0.0264127i
$76$		0			0
$77$	−2.06508	−	0.125017i	−0.235338	−	0.0142470i
$78$		0			0
$79$	8.66781	+	5.00437i	0.975205	+	0.563035i	0.900819	−	0.434194i	$-0.142967\pi$
$79$	8.66781	+	5.00437i	0.975205	+	0.563035i	0.0743862	+	0.997230i	$0.476300\pi$
$80$		0			0
$81$	4.47293	+	7.74735i	0.496992	+	0.860816i
$82$		0			0
$83$	2.94473	−	2.94473i	0.323226	−	0.323226i	−0.526777	−	0.850003i	$-0.676600\pi$
$83$	2.94473	−	2.94473i	0.323226	−	0.323226i	0.850003	+	0.526777i	$0.176600\pi$
$84$		0			0
$85$	−11.9443	+	2.22817i	−1.29554	+	0.241678i
$86$		0			0
$87$	0.00609973	−	0.0227645i	0.000653959	−	0.00244061i
$88$		0			0
$89$	6.43727	−	11.1497i	0.682350	−	1.18186i	−0.291912	−	0.956445i	$-0.594292\pi$
$89$	6.43727	−	11.1497i	0.682350	−	1.18186i	0.974262	−	0.225419i	$-0.0723751\pi$
$90$		0			0
$91$	2.45783	+	12.0423i	0.257650	+	1.26237i
$92$		0			0
$93$	0.436324	−	0.116913i	0.0452447	−	0.0121233i
$94$		0			0
$95$	−13.0119	−	1.00878i	−1.33499	−	0.103499i
$96$		0			0
$97$	−0.0900545	−	0.0900545i	−0.00914365	−	0.00914365i	0.702520	−	0.711664i	$-0.252058\pi$
$97$	−0.0900545	−	0.0900545i	−0.00914365	−	0.00914365i	−0.711664	+	0.702520i	$0.752058\pi$
$98$		0			0
$99$			2.34116i			0.235295i
$100$		0			0
$101$	5.24945	−	3.03077i	0.522340	−	0.301573i	−0.215551	−	0.976492i	$-0.569155\pi$
$101$	5.24945	−	3.03077i	0.522340	−	0.301573i	0.737892	+	0.674919i	$0.235822\pi$
$102$		0			0
$103$	0.666178	+	2.48621i	0.0656405	+	0.244973i	0.990948	−	0.134243i	$-0.0428602\pi$
$103$	0.666178	+	2.48621i	0.0656405	+	0.244973i	−0.925308	+	0.379216i	$0.876194\pi$
$104$		0			0
$105$	0.422817	+	0.178583i	0.0412627	+	0.0174279i
$106$		0			0
$107$	−2.20467	−	8.22792i	−0.213133	−	0.795423i	−0.986815	−	0.161850i	$-0.948254\pi$
$107$	−2.20467	−	8.22792i	−0.213133	−	0.795423i	0.773682	−	0.633574i	$-0.218413\pi$
$108$		0			0
$109$	−7.24069	+	4.18042i	−0.693533	+	0.400411i	−0.804934	−	0.593364i	$-0.797799\pi$
$109$	−7.24069	+	4.18042i	−0.693533	+	0.400411i	0.111401	+	0.993775i	$0.464466\pi$
$110$		0			0
$111$		−	0.572150i		−	0.0543061i
$112$		0			0
$113$	0.624674	+	0.624674i	0.0587644	+	0.0587644i	0.735878	−	0.677114i	$-0.236770\pi$
$113$	0.624674	+	0.624674i	0.0587644	+	0.0587644i	−0.677114	+	0.735878i	$0.736770\pi$
$114$		0			0
$115$	−12.6318	−	14.7550i	−1.17792	−	1.37591i
$116$		0			0
$117$	13.4343	−	3.59970i	1.24200	−	0.332793i
$118$		0			0
$119$	−9.53284	−	10.7614i	−0.873874	−	0.986498i
$120$		0			0
$121$	5.19427	−	8.99674i	0.472207	−	0.817886i
$122$		0			0
$123$	−0.0882943	+	0.329519i	−0.00796123	+	0.0297117i
$124$		0			0
$125$	10.8805	+	2.57192i	0.973181	+	0.230040i
$126$		0			0
$127$	9.47330	−	9.47330i	0.840620	−	0.840620i	−0.148320	−	0.988939i	$-0.547387\pi$
$127$	9.47330	−	9.47330i	0.840620	−	0.840620i	0.988939	+	0.148320i	$0.0473865\pi$
$128$		0			0
$129$	−0.402202	−	0.696634i	−0.0354119	−	0.0613352i
$130$		0			0
$131$	−5.71583	−	3.30004i	−0.499394	−	0.288326i	0.229069	−	0.973410i	$-0.426432\pi$
$131$	−5.71583	−	3.30004i	−0.499394	−	0.288326i	−0.728463	+	0.685085i	$0.759765\pi$
$132$		0			0
$133$	−6.89881	−	13.8154i	−0.598203	−	1.19794i
$134$		0			0
$135$	0.345960	−	0.980595i	0.0297755	−	0.0843962i
$136$		0			0
$137$	−0.399466	−	0.107037i	−0.0341287	−	0.00914475i	0.241714	−	0.970347i	$-0.422290\pi$
$137$	−0.399466	−	0.107037i	−0.0341287	−	0.00914475i	−0.275843	+	0.961203i	$0.588957\pi$
$138$		0			0
$139$	−16.1574			−1.37045			−0.685225	−	0.728332i	$-0.740296\pi$
$139$	−16.1574			−1.37045			−0.685225	+	0.728332i	$0.740296\pi$
$140$		0			0
$141$	−0.183232			−0.0154309
$142$		0			0
$143$	3.50871	+	0.940156i	0.293413	+	0.0786198i
$144$		0			0
$145$	0.612748	−	0.293144i	0.0508859	−	0.0243443i
$146$		0			0
$147$	0.0762506	+	0.537698i	0.00628904	+	0.0443486i
$148$		0			0
$149$	4.87017	+	2.81179i	0.398979	+	0.230351i	0.686044	−	0.727560i	$-0.259346\pi$
$149$	4.87017	+	2.81179i	0.398979	+	0.230351i	−0.287064	+	0.957911i	$0.592679\pi$
$150$		0			0
$151$	3.59720	+	6.23053i	0.292736	+	0.507033i	0.974456	−	0.224580i	$-0.0721010\pi$
$151$	3.59720	+	6.23053i	0.292736	+	0.507033i	−0.681720	+	0.731613i	$0.738768\pi$
$152$		0			0
$153$	−11.5037	+	11.5037i	−0.930020	+	0.930020i
$154$		0			0
$155$	10.7381	+	7.36167i	0.862507	+	0.591304i
$156$		0			0
$157$	−0.547542	+	2.04345i	−0.0436986	+	0.163085i	−0.984327	−	0.176352i	$-0.943570\pi$
$157$	−0.547542	+	2.04345i	−0.0436986	+	0.163085i	0.940628	+	0.339438i	$0.110237\pi$
$158$		0			0
$159$	0.241696	−	0.418630i	0.0191677	−	0.0331995i
$160$		0			0
$161$	7.27879	−	21.7991i	0.573649	−	1.71801i
$162$		0			0
$163$	0.504944	−	0.135299i	0.0395503	−	0.0105975i	−0.238990	−	0.971022i	$-0.576816\pi$
$163$	0.504944	−	0.135299i	0.0395503	−	0.0105975i	0.278540	+	0.960425i	$0.410150\pi$
$164$		0			0
$165$	0.103049	−	0.0882201i	0.00802234	−	0.00686793i
$166$		0			0
$167$	0.418275	+	0.418275i	0.0323671	+	0.0323671i	0.723105	−	0.690738i	$-0.242714\pi$
$167$	0.418275	+	0.418275i	0.0323671	+	0.0323671i	−0.690738	+	0.723105i	$0.742714\pi$
$168$		0			0
$169$		−	8.57959i		−	0.659969i
$170$		0			0
$171$	−15.1334	+	8.73727i	−1.15728	+	0.668156i
$172$		0			0
$173$	−2.64144	−	9.85798i	−0.200825	−	0.749488i	−0.990682	−	0.136197i	$-0.956512\pi$
$173$	−2.64144	−	9.85798i	−0.200825	−	0.749488i	0.789857	−	0.613291i	$-0.210155\pi$
$174$		0			0
$175$	4.01524	+	12.6047i	0.303523	+	0.952824i
$176$		0			0
$177$	−0.102900	−	0.384029i	−0.00773446	−	0.0288654i
$178$		0			0
$179$	18.6482	−	10.7666i	1.39384	−	0.804731i	0.400098	−	0.916472i	$-0.368976\pi$
$179$	18.6482	−	10.7666i	1.39384	−	0.804731i	0.993737	+	0.111741i	$0.0356427\pi$
$180$		0			0
$181$		−	3.63457i		−	0.270155i	−0.990835	−	0.135078i	$-0.956872\pi$
$181$		−	3.63457i		−	0.270155i	0.990835	−	0.135078i	$-0.0431284\pi$
$182$		0			0
$183$	0.565034	+	0.565034i	0.0417685	+	0.0417685i
$184$		0			0
$185$	12.5269	−	10.7243i	0.920996	−	0.788466i
$186$		0			0
$187$	−4.10421	+	1.09972i	−0.300130	+	0.0804195i
$188$		0			0
$189$	1.20550	−	0.246042i	0.0876869	−	0.0178969i
$190$		0			0
$191$	0.00324409	−	0.00561893i	0.000234734	−	0.000406571i	−0.865908	−	0.500203i	$-0.833259\pi$
$191$	0.00324409	−	0.00561893i	0.000234734	−	0.000406571i	0.866143	+	0.499797i	$0.166592\pi$
$192$		0			0
$193$	0.678515	−	2.53225i	0.0488406	−	0.182275i	−0.937196	−	0.348802i	$-0.886589\pi$
$193$	0.678515	−	2.53225i	0.0488406	−	0.182275i	0.986037	+	0.166527i	$0.0532552\pi$
$194$		0			0
$195$	−0.664679	−	0.455680i	−0.0475986	−	0.0326319i
$196$		0			0
$197$	−6.64991	+	6.64991i	−0.473786	+	0.473786i	−0.903138	−	0.429351i	$-0.858742\pi$
$197$	−6.64991	+	6.64991i	−0.473786	+	0.473786i	0.429351	+	0.903138i	$0.358742\pi$
$198$		0			0
$199$	0.846048	+	1.46540i	0.0599747	+	0.103879i	0.894454	−	0.447160i	$-0.147565\pi$
$199$	0.846048	+	1.46540i	0.0599747	+	0.103879i	−0.834479	+	0.551040i	$0.814231\pi$
$200$		0			0
$201$	0.102799	+	0.0593510i	0.00725088	+	0.00418630i
$202$		0			0
$203$	0.670478	+	0.443180i	0.0470584	+	0.0311052i
$204$		0			0
$205$	−8.86960	+	4.24329i	−0.619479	+	0.296364i
$206$		0			0
$207$	−25.1209	−	6.73112i	−1.74602	−	0.467845i
$208$		0			0
$209$	−4.56393			−0.315693
$210$		0			0
$211$	9.03597			0.622062			0.311031	−	0.950400i	$-0.399326\pi$
$211$	9.03597			0.622062			0.311031	+	0.950400i	$0.399326\pi$
$212$		0			0
$213$	0.437448	+	0.117214i	0.0299735	+	0.00803137i
$214$		0			0
$215$	7.71360	−	21.8636i	0.526063	−	1.49108i
$216$		0			0
$217$	−0.930867	+	15.3765i	−0.0631914	+	1.04382i
$218$		0			0
$219$	−0.901078	−	0.520238i	−0.0608892	−	0.0351544i
$220$		0			0
$221$	12.6210	+	21.8603i	0.848984	+	1.47048i
$222$		0			0
$223$	2.08617	−	2.08617i	0.139700	−	0.139700i	−0.633798	−	0.773499i	$-0.718505\pi$
$223$	2.08617	−	2.08617i	0.139700	−	0.139700i	0.773499	+	0.633798i	$0.218505\pi$
$224$		0			0
$225$	13.9631	−	5.39734i	0.930870	−	0.359822i
$226$		0			0
$227$	0.121724	−	0.454280i	0.00807910	−	0.0301516i	−0.961769	−	0.273863i	$-0.911698\pi$
$227$	0.121724	−	0.454280i	0.00807910	−	0.0301516i	0.969848	+	0.243712i	$0.0783651\pi$
$228$		0			0
$229$	−12.6003	+	21.8244i	−0.832651	+	1.44219i	0.0632774	+	0.997996i	$0.479845\pi$
$229$	−12.6003	+	21.8244i	−0.832651	+	1.44219i	−0.895929	+	0.444198i	$0.853489\pi$
$230$		0			0
$231$	0.152244	+	0.0508350i	0.0100170	+	0.00334470i
$232$		0			0
$233$	−15.0074	+	4.02122i	−0.983168	+	0.263439i	−0.714378	−	0.699760i	$-0.753290\pi$
$233$	−15.0074	+	4.02122i	−0.983168	+	0.263439i	−0.268790	+	0.963199i	$0.586624\pi$
$234$		0			0
$235$	−3.43447	−	4.01176i	−0.224040	−	0.261699i
$236$		0			0
$237$	−0.549070	−	0.549070i	−0.0356659	−	0.0356659i
$238$		0			0
$239$			28.2271i			1.82586i	0.408117	+	0.912930i	$0.366186\pi$
$239$			28.2271i			1.82586i	−0.408117	+	0.912930i	$0.633814\pi$
$240$		0			0
$241$	−11.8212	+	6.82500i	−0.761473	+	0.439637i	−0.829824	−	0.558025i	$-0.811559\pi$
$241$	−11.8212	+	6.82500i	−0.761473	+	0.439637i	0.0683514	+	0.997661i	$0.478226\pi$
$242$		0			0
$243$	−0.540706	−	2.01794i	−0.0346863	−	0.129451i
$244$		0			0
$245$	−10.3434	+	11.7480i	−0.660813	+	0.750551i
$246$		0			0
$247$	7.01737	+	26.1892i	0.446505	+	1.66638i
$248$		0			0
$249$	−0.279804	+	0.161545i	−0.0177319	+	0.0102375i
$250$		0			0
$251$		−	8.14470i		−	0.514089i	−0.966400	−	0.257045i	$-0.917251\pi$
$251$		−	8.14470i		−	0.514089i	0.966400	−	0.257045i	$-0.0827487\pi$
$252$		0			0
$253$	−4.80296	−	4.80296i	−0.301960	−	0.301960i
$254$		0			0
$255$	0.939834	+	0.0728631i	0.0588547	+	0.00456287i
$256$		0			0
$257$	−10.0007	+	2.67967i	−0.623823	+	0.167153i	−0.556865	−	0.830603i	$-0.687996\pi$
$257$	−10.0007	+	2.67967i	−0.623823	+	0.167153i	−0.0669581	+	0.997756i	$0.521329\pi$
$258$		0			0
$259$	18.5073	+	6.17965i	1.14999	+	0.383985i
$260$		0			0
$261$	0.454747	−	0.787644i	0.0281481	−	0.0487540i
$262$		0			0
$263$	7.62698	−	28.4643i	0.470300	−	1.75518i	−0.168391	−	0.985720i	$-0.553857\pi$
$263$	7.62698	−	28.4643i	0.470300	−	1.75518i	0.638691	−	0.769463i	$-0.279476\pi$
$264$		0			0
$265$	13.6960	−	2.55493i	0.841337	−	0.156948i
$266$		0			0
$267$	−0.706286	+	0.706286i	−0.0432240	+	0.0432240i
$268$		0			0
$269$	10.2431	+	17.7415i	0.624531	+	1.08172i	0.988631	+	0.150360i	$0.0480433\pi$
$269$	10.2431	+	17.7415i	0.624531	+	1.08172i	−0.364100	+	0.931360i	$0.618623\pi$
$270$		0			0
$271$	13.4287	+	7.75309i	0.815738	+	0.470967i	0.848945	−	0.528482i	$-0.177239\pi$
$271$	13.4287	+	7.75309i	0.815738	+	0.470967i	−0.0332065	+	0.999449i	$0.510572\pi$
$272$		0			0
$273$	0.0576197	−	0.951787i	0.00348730	−	0.0576048i
$274$		0			0
$275$	3.86306	+	0.602610i	0.232951	+	0.0363387i
$276$		0			0
$277$	−2.32259	−	0.622335i	−0.139551	−	0.0373925i	0.188368	−	0.982099i	$-0.439680\pi$
$277$	−2.32259	−	0.622335i	−0.139551	−	0.0373925i	−0.327918	+	0.944706i	$0.606347\pi$
$278$		0			0
$279$	17.4321			1.04364
$280$		0			0
$281$	−16.9059			−1.00852			−0.504261	−	0.863552i	$-0.668235\pi$
$281$	−16.9059			−1.00852			−0.504261	+	0.863552i	$0.668235\pi$
$282$		0			0
$283$	5.27738	+	1.41407i	0.313708	+	0.0840578i	0.412238	−	0.911076i	$-0.364747\pi$
$283$	5.27738	+	1.41407i	0.313708	+	0.0840578i	−0.0985299	+	0.995134i	$0.531414\pi$
$284$		0			0
$285$	0.954841	+	0.336873i	0.0565599	+	0.0199547i
$286$		0			0
$287$	−9.70525	−	6.41509i	−0.572883	−	0.378671i
$288$		0			0
$289$	−10.8480	−	6.26310i	−0.638118	−	0.368418i
$290$		0			0
$291$	0.00494031	+	0.00855687i	0.000289606	+	0.000501612i
$292$		0			0
$293$	−9.62258	+	9.62258i	−0.562157	+	0.562157i	−0.929920	−	0.367762i	$-0.880124\pi$
$293$	−9.62258	+	9.62258i	−0.562157	+	0.562157i	0.367762	+	0.929920i	$0.380124\pi$
$294$		0			0
$295$	6.47935	−	9.45113i	0.377243	−	0.550266i
$296$		0			0
$297$	0.0941146	−	0.351241i	0.00546109	−	0.0203810i
$298$		0			0
$299$	−20.1759	+	34.9457i	−1.16680	+	2.02096i
$300$		0			0
$301$	26.8780	−	5.48581i	1.54922	−	0.316197i
$302$		0			0
$303$	−0.454246	+	0.121715i	−0.0260957	+	0.00699233i
$304$		0			0
$305$	−1.78019	+	22.9620i	−0.101933	+	1.31480i
$306$		0			0
$307$	17.8381	+	17.8381i	1.01807	+	1.01807i	0.999834	+	0.0182409i	$0.00580657\pi$
$307$	17.8381	+	17.8381i	1.01807	+	1.01807i	0.0182409	+	0.999834i	$0.494193\pi$
$308$		0			0
$309$		−	0.199691i		−	0.0113600i
$310$		0			0
$311$	−10.7681	+	6.21694i	−0.610601	+	0.352530i	−0.773200	−	0.634162i	$-0.781345\pi$
$311$	−10.7681	+	6.21694i	−0.610601	+	0.352530i	0.162600	+	0.986692i	$0.448012\pi$
$312$		0			0
$313$	0.654518	+	2.44269i	0.0369955	+	0.138069i	0.981953	−	0.189123i	$-0.0605643\pi$
$313$	0.654518	+	2.44269i	0.0369955	+	0.138069i	−0.944958	+	0.327192i	$0.893898\pi$
$314$		0			0
$315$	13.9772	+	10.8800i	0.787528	+	0.613018i
$316$		0			0
$317$	−4.12570	−	15.3973i	−0.231722	−	0.864799i	−0.979599	−	0.200962i	$-0.935593\pi$
$317$	−4.12570	−	15.3973i	−0.231722	−	0.864799i	0.747877	−	0.663837i	$-0.231073\pi$
$318$		0			0
$319$	0.205714	−	0.118769i	0.0115178	−	0.00664978i
$320$		0			0
$321$			0.660861i			0.0368857i
$322$		0			0
$323$	−22.4257	−	22.4257i	−1.24780	−	1.24780i
$324$		0			0
$325$	−2.48178	−	23.0940i	−0.137664	−	1.28102i
$326$		0			0
$327$	0.626552	−	0.167884i	0.0346484	−	0.00928401i
$328$		0			0
$329$	1.97904	−	5.92699i	0.109108	−	0.326765i
$330$		0			0
$331$	12.4183	−	21.5091i	0.682572	−	1.18225i	−0.291621	−	0.956534i	$-0.594195\pi$
$331$	12.4183	−	21.5091i	0.682572	−	1.18225i	0.974193	−	0.225716i	$-0.0724721\pi$
$332$		0			0
$333$	5.71468	−	21.3275i	0.313162	−	1.16874i
$334$		0			0
$335$	0.627391	+	3.36319i	0.0342780	+	0.183751i
$336$		0			0
$337$	−20.6822	+	20.6822i	−1.12663	+	1.12663i	−0.135912	+	0.990721i	$0.543396\pi$
$337$	−20.6822	+	20.6822i	−1.12663	+	1.12663i	−0.990721	+	0.135912i	$0.956604\pi$
$338$		0			0
$339$	−0.0342690	−	0.0593557i	−0.00186124	−	0.00322376i
$340$		0			0
$341$	3.94289	+	2.27643i	0.213519	+	0.123275i
$342$		0			0
$343$	−18.2164	−	3.34107i	−0.983593	−	0.180401i
$344$		0			0
$345$	0.650333	+	1.35937i	0.0350128	+	0.0731859i
$346$		0			0
$347$	20.6497	+	5.53308i	1.10854	+	0.297031i	0.766236	−	0.642560i	$-0.222128\pi$
$347$	20.6497	+	5.53308i	1.10854	+	0.297031i	0.342300	+	0.939591i	$0.388794\pi$
$348$		0			0
$349$	−14.6661			−0.785056			−0.392528	−	0.919740i	$-0.628399\pi$
$349$	−14.6661			−0.785056			−0.392528	+	0.919740i	$0.628399\pi$
$350$		0			0
$351$	−2.16023			−0.115305
$352$		0			0
$353$	−1.18700	−	0.318055i	−0.0631775	−	0.0169284i	0.227092	−	0.973873i	$-0.427078\pi$
$353$	−1.18700	−	0.318055i	−0.0631775	−	0.0169284i	−0.290269	+	0.956945i	$0.593745\pi$
$354$		0			0
$355$	5.63313	+	11.7747i	0.298975	+	0.624937i
$356$		0			0
$357$	0.498293	+	0.997868i	0.0263725	+	0.0528127i
$358$		0			0
$359$	−15.3588	−	8.86741i	−0.810607	−	0.468004i	0.0365599	−	0.999331i	$-0.488360\pi$
$359$	−15.3588	−	8.86741i	−0.810607	−	0.468004i	−0.847166	+	0.531328i	$0.821693\pi$
$360$		0			0
$361$	−7.53269	−	13.0470i	−0.396458	−	0.686685i
$362$		0			0
$363$	−0.569906	+	0.569906i	−0.0299123	+	0.0299123i
$364$		0			0
$365$	−5.49936	−	29.4798i	−0.287849	−	1.54305i
$366$		0			0
$367$	−2.40926	+	8.99149i	−0.125762	+	0.469352i	−0.999866	−	0.0163883i	$-0.994783\pi$
$367$	−2.40926	+	8.99149i	−0.125762	+	0.469352i	0.874103	+	0.485740i	$0.161450\pi$
$368$		0			0
$369$	−6.58251	+	11.4012i	−0.342672	+	0.593525i
$370$		0			0
$371$	10.9309	+	12.3396i	0.567502	+	0.640641i
$372$		0			0
$373$	−14.5351	+	3.89467i	−0.752600	+	0.201659i	−0.614671	−	0.788784i	$-0.710711\pi$
$373$	−14.5351	+	3.89467i	−0.752600	+	0.201659i	−0.137929	+	0.990442i	$0.544045\pi$
$374$		0			0
$375$	−0.763729	−	0.411216i	−0.0394388	−	0.0212351i
$376$		0			0
$377$	−0.997831	−	0.997831i	−0.0513909	−	0.0513909i
$378$		0			0
$379$		−	16.5827i		−	0.851794i	−0.904772	−	0.425897i	$-0.859959\pi$
$379$		−	16.5827i		−	0.851794i	0.904772	−	0.425897i	$-0.140041\pi$
$380$		0			0
$381$	−0.900141	+	0.519697i	−0.0461156	+	0.0266249i
$382$		0			0
$383$	7.35797	+	27.4603i	0.375975	+	1.40316i	0.851916	+	0.523679i	$0.175441\pi$
$383$	7.35797	+	27.4603i	0.375975	+	1.40316i	−0.475941	+	0.879477i	$0.657892\pi$
$384$		0			0
$385$	1.74064	+	4.28615i	0.0887113	+	0.218442i
$386$		0			0
$387$	−8.03445	−	29.9850i	−0.408414	−	1.52422i
$388$		0			0
$389$	17.2501	−	9.95935i	0.874614	−	0.504959i	0.00573552	−	0.999984i	$-0.498174\pi$
$389$	17.2501	−	9.95935i	0.874614	−	0.504959i	0.868879	+	0.495025i	$0.164841\pi$
$390$		0			0
$391$		−	47.2004i		−	2.38703i
$392$		0			0
$393$	0.362074	+	0.362074i	0.0182642	+	0.0182642i
$394$		0			0
$395$	1.72989	−	22.3132i	0.0870404	−	1.12270i
$396$		0			0
$397$	10.4715	−	2.80583i	0.525549	−	0.140821i	0.0137171	−	0.999906i	$-0.495634\pi$
$397$	10.4715	−	2.80583i	0.525549	−	0.140821i	0.511832	+	0.859085i	$0.328967\pi$
$398$		0			0
$399$	0.239580	+	1.17383i	0.0119940	+	0.0587652i
$400$		0			0
$401$	−16.8238	+	29.1397i	−0.840142	+	1.45517i	0.0496323	+	0.998768i	$0.484195\pi$
$401$	−16.8238	+	29.1397i	−0.840142	+	1.45517i	−0.889774	+	0.456401i	$0.849138\pi$
$402$		0			0
$403$	7.00035	−	26.1257i	0.348712	−	1.30141i
$404$		0			0
$405$	11.3109	−	16.4987i	0.562043	−	0.819825i
$406$		0			0
$407$	4.07768	−	4.07768i	0.202123	−	0.202123i
$408$		0			0
$409$	5.99488	+	10.3834i	0.296428	+	0.513428i	0.975316	−	0.220814i	$-0.0708712\pi$
$409$	5.99488	+	10.3834i	0.296428	+	0.513428i	−0.678888	+	0.734242i	$0.737538\pi$
$410$		0			0
$411$	0.0277863	+	0.0160424i	0.00137059	+	0.000791313i
$412$		0			0
$413$	13.5335	+	0.819300i	0.665942	+	0.0403151i
$414$		0			0
$415$	−8.78155	−	3.09818i	−0.431069	−	0.152084i
$416$		0			0
$417$	1.21081	+	0.324437i	0.0592939	+	0.0158877i
$418$		0			0
$419$	−1.15873			−0.0566075			−0.0283037	−	0.999599i	$-0.509011\pi$
$419$	−1.15873			−0.0566075			−0.0283037	+	0.999599i	$0.509011\pi$
$420$		0			0
$421$	30.6438			1.49349			0.746744	−	0.665111i	$-0.231616\pi$
$421$	30.6438			1.49349			0.746744	+	0.665111i	$0.231616\pi$
$422$		0			0
$423$	−6.83016	−	1.83014i	−0.332094	−	0.0889843i
$424$		0			0
$425$	16.0208	+	21.9429i	0.777123	+	1.06439i
$426$		0			0
$427$	−24.3799	+	12.1743i	−1.17982	+	0.589155i
$428$		0			0
$429$	−0.244061	−	0.140909i	−0.0117834	−	0.00680313i
$430$		0			0
$431$	20.2975	+	35.1563i	0.977697	+	1.69342i	0.670731	+	0.741701i	$0.265981\pi$
$431$	20.2975	+	35.1563i	0.977697	+	1.69342i	0.306967	+	0.951720i	$0.400686\pi$
$432$		0			0
$433$	19.1716	−	19.1716i	0.921327	−	0.921327i	−0.0757959	−	0.997123i	$-0.524150\pi$
$433$	19.1716	−	19.1716i	0.921327	−	0.921327i	0.997123	+	0.0757959i	$0.0241498\pi$
$434$		0			0
$435$	−0.0518049	+	0.00966402i	−0.00248386	+	0.000463354i
$436$		0			0
$437$	13.1218	−	48.9714i	0.627703	−	2.34262i
$438$		0			0
$439$	15.1874	−	26.3053i	0.724854	−	1.25548i	−0.234179	−	0.972193i	$-0.575240\pi$
$439$	15.1874	−	26.3053i	0.724854	−	1.25548i	0.959034	−	0.283291i	$-0.0914263\pi$
$440$		0			0
$441$	−2.52825	+	20.8048i	−0.120393	+	0.990705i
$442$		0			0
$443$	−35.8429	+	9.60409i	−1.70295	+	0.456304i	−0.973679	−	0.227922i	$-0.926807\pi$
$443$	−35.8429	+	9.60409i	−1.70295	+	0.456304i	−0.729270	+	0.684226i	$0.760140\pi$
$444$		0			0
$445$	−28.7022	−	2.22522i	−1.36062	−	0.105485i
$446$		0			0
$447$	−0.308505	−	0.308505i	−0.0145918	−	0.0145918i
$448$		0			0
$449$		−	16.8567i		−	0.795516i	−0.917490	−	0.397758i	$-0.869788\pi$
$449$		−	16.8567i		−	0.795516i	0.917490	−	0.397758i	$-0.130212\pi$
$450$		0			0
$451$	−2.97773	+	1.71919i	−0.140216	+	0.0809536i
$452$		0			0
$453$	−0.144462	−	0.539140i	−0.00678742	−	0.0253310i
$454$		0			0
$455$	21.9188	−	16.5786i	1.02757	−	0.777217i
$456$		0			0
$457$	1.78496	+	6.66157i	0.0834971	+	0.311615i	0.995025	−	0.0996221i	$-0.0317634\pi$
$457$	1.78496	+	6.66157i	0.0834971	+	0.311615i	−0.911528	+	0.411237i	$0.865097\pi$
$458$		0			0
$459$	2.18833	−	1.26343i	0.102143	−	0.0589721i
$460$		0			0
$461$		−	0.948800i		−	0.0441900i	−0.999756	−	0.0220950i	$-0.992966\pi$
$461$		−	0.948800i		−	0.0441900i	0.999756	−	0.0220950i	$-0.00703363\pi$
$462$		0			0
$463$	4.74202	+	4.74202i	0.220380	+	0.220380i	0.808659	−	0.588278i	$-0.200194\pi$
$463$	4.74202	+	4.74202i	0.220380	+	0.220380i	−0.588278	+	0.808659i	$0.700194\pi$
$464$		0			0
$465$	−0.656882	−	0.767295i	−0.0304622	−	0.0355825i
$466$		0			0
$467$	−26.6857	+	7.15041i	−1.23487	+	0.330882i	−0.816473	−	0.577384i	$-0.804074\pi$
$467$	−26.6857	+	7.15041i	−1.23487	+	0.330882i	−0.418394	+	0.908266i	$0.637407\pi$
$468$		0			0
$469$	−3.03013	+	2.68419i	−0.139918	+	0.123944i
$470$		0			0
$471$	0.0820644	−	0.142140i	0.00378133	−	0.00654945i
$472$		0			0
$473$	2.09840	−	7.83135i	0.0964847	−	0.360086i
$474$		0			0
$475$	10.5217	+	27.2200i	0.482770	+	1.24894i
$476$		0			0
$477$	13.1908	−	13.1908i	0.603964	−	0.603964i
$478$		0			0
$479$	−2.54289	−	4.40442i	−0.116188	−	0.201243i	0.802066	−	0.597235i	$-0.203734\pi$
$479$	−2.54289	−	4.40442i	−0.116188	−	0.201243i	−0.918254	+	0.395992i	$0.870401\pi$
$480$		0			0
$481$	−29.6687	−	17.1292i	−1.35278	−	0.781026i
$482$		0			0
$483$	−0.983186	+	1.48744i	−0.0447365	+	0.0676809i
$484$		0			0
$485$	−0.0947473	+	0.268554i	−0.00430225	+	0.0121944i
$486$		0			0
$487$	−18.4260	−	4.93722i	−0.834961	−	0.223727i	−0.184084	−	0.982911i	$-0.558932\pi$
$487$	−18.4260	−	4.93722i	−0.834961	−	0.223727i	−0.650877	+	0.759184i	$0.725598\pi$
$488$		0			0
$489$	−0.0405567			−0.00183404
$490$		0			0
$491$	−21.7497			−0.981548			−0.490774	−	0.871287i	$-0.663286\pi$
$491$	−21.7497			−0.981548			−0.490774	+	0.871287i	$0.663286\pi$
$492$		0			0
$493$	1.59440	+	0.427219i	0.0718083	+	0.0192410i
$494$		0			0
$495$	4.72239	−	2.25923i	0.212256	−	0.101545i
$496$		0			0
$497$	−8.51627	+	12.8841i	−0.382007	+	0.577930i
$498$		0			0
$499$	−28.7858	−	16.6195i	−1.28863	−	0.743992i	−0.310221	−	0.950664i	$-0.600403\pi$
$499$	−28.7858	−	16.6195i	−1.28863	−	0.743992i	−0.978410	+	0.206673i	$0.933736\pi$
$500$		0			0
$501$	−0.0229462	−	0.0397440i	−0.00102516	−	0.00177563i
$502$		0			0
$503$	−25.2173	+	25.2173i	−1.12438	+	1.12438i	−0.133307	+	0.991075i	$0.542560\pi$
$503$	−25.2173	+	25.2173i	−1.12438	+	1.12438i	−0.991075	+	0.133307i	$0.957440\pi$
$504$		0			0
$505$	−11.1792	−	7.66405i	−0.497467	−	0.341046i
$506$		0			0
$507$	−0.172277	+	0.642945i	−0.00765108	+	0.0285542i
$508$		0			0
$509$	−7.44191	+	12.8898i	−0.329857	+	0.571329i	−0.982483	−	0.186351i	$-0.940334\pi$
$509$	−7.44191	+	12.8898i	−0.329857	+	0.571329i	0.652626	+	0.757680i	$0.273667\pi$
$510$		0			0
$511$	26.5604	−	23.5281i	1.17496	−	1.04082i
$512$		0			0
$513$	2.62168	−	0.702477i	0.115750	−	0.0310151i
$514$		0			0
$515$	4.37211	−	3.74297i	0.192658	−	0.164935i
$516$		0			0
$517$	−1.30589	−	1.30589i	−0.0574328	−	0.0574328i
$518$		0			0
$519$			0.791786i			0.0347555i
$520$		0			0
$521$	−23.3131	+	13.4598i	−1.02137	+	0.589686i	−0.914500	−	0.404587i	$-0.867415\pi$
$521$	−23.3131	+	13.4598i	−1.02137	+	0.589686i	−0.106867	+	0.994273i	$0.534082\pi$
$522$		0			0
$523$	7.74842	+	28.9175i	0.338815	+	1.26447i	0.899674	+	0.436563i	$0.143804\pi$
$523$	7.74842	+	28.9175i	0.338815	+	1.26447i	−0.560859	+	0.827911i	$0.689529\pi$
$524$		0			0
$525$	−0.0477979	−	1.02521i	−0.00208607	−	0.0447437i
$526$		0			0
$527$	8.18845	+	30.5597i	0.356695	+	1.33120i
$528$		0			0
$529$	45.4268	−	26.2271i	1.97508	−	1.14031i
$530$		0			0
$531$		−	15.3429i		−	0.665823i
$532$		0			0
$533$	14.4437	+	14.4437i	0.625627	+	0.625627i
$534$		0			0
$535$	−14.4692	+	12.3871i	−0.625557	+	0.535540i
$536$		0			0
$537$	−1.61367	+	0.432382i	−0.0696350	+	0.0186586i
$538$		0			0
$539$	−3.28871	+	4.37558i	−0.141655	+	0.188469i
$540$		0			0
$541$	12.1822	−	21.1003i	0.523755	−	0.907171i	−0.475862	−	0.879520i	$-0.657864\pi$
$541$	12.1822	−	21.1003i	0.523755	−	0.907171i	0.999618	−	0.0276510i	$-0.00880272\pi$
$542$		0			0
$543$	−0.0729815	+	0.272371i	−0.00313194	+	0.0116885i
$544$		0			0
$545$	15.4197	+	10.5712i	0.660508	+	0.452820i
$546$		0			0
$547$	27.6642	−	27.6642i	1.18283	−	1.18283i	0.203827	−	0.979007i	$-0.434662\pi$
$547$	27.6642	−	27.6642i	1.18283	−	1.18283i	0.979007	−	0.203827i	$-0.0653379\pi$
$548$		0			0
$549$	15.4186	+	26.7058i	0.658050	+	1.13978i
$550$		0			0
$551$	1.53546	+	0.886497i	0.0654127	+	0.0377660i
$552$		0			0
$553$	23.6911	−	11.8303i	1.00745	−	0.503077i
$554$		0			0
$555$	−1.15409	+	0.552129i	−0.0489886	+	0.0234366i
$556$		0			0
$557$	13.3251	+	3.57044i	0.564601	+	0.151284i	0.529819	−	0.848111i	$-0.322260\pi$
$557$	13.3251	+	3.57044i	0.564601	+	0.151284i	0.0347817	+	0.999395i	$0.488926\pi$
$558$		0			0
$559$	−48.1651			−2.03717
$560$		0			0
$561$	0.329647			0.0139177
$562$		0			0
$563$	19.1580	+	5.13338i	0.807415	+	0.216346i	0.638837	−	0.769342i	$-0.279416\pi$
$563$	19.1580	+	5.13338i	0.807415	+	0.216346i	0.168578	+	0.985688i	$0.446083\pi$
$564$		0			0
$565$	0.657226	−	1.86285i	0.0276497	−	0.0783709i
$566$		0			0
$567$	23.6253	+	1.43024i	0.992169	+	0.0600643i
$568$		0			0
$569$	10.4442	+	6.02994i	0.437842	+	0.252788i	0.702682	−	0.711504i	$-0.251986\pi$
$569$	10.4442	+	6.02994i	0.437842	+	0.252788i	−0.264840	+	0.964292i	$0.585319\pi$
$570$		0			0
$571$	1.69675	+	2.93885i	0.0710067	+	0.122987i	0.899343	−	0.437244i	$-0.144046\pi$
$571$	1.69675	+	2.93885i	0.0710067	+	0.122987i	−0.828336	+	0.560232i	$0.810712\pi$
$572$		0			0
$573$	−0.000355935	0	0.000355935i	−1.48694e−5	0	1.48694e-5i
$574$		0			0
$575$	−17.5728	+	39.7184i	−0.732837	+	1.65637i
$576$		0			0
$577$	−6.53624	+	24.3936i	−0.272107	+	1.01552i	0.685648	+	0.727933i	$0.259519\pi$
$577$	−6.53624	+	24.3936i	−0.272107	+	1.01552i	−0.957755	+	0.287585i	$0.907148\pi$
$578$		0			0
$579$	−0.101694	+	0.176140i	−0.00422627	+	0.00732012i
$580$		0			0
$581$	−2.20338	−	10.7956i	−0.0914117	−	0.447877i
$582$		0			0
$583$	4.70611	−	1.26100i	0.194907	−	0.0522252i
$584$		0			0
$585$	−20.2252	−	23.6248i	−0.836209	−	0.976765i
$586$		0			0
$587$	19.6875	+	19.6875i	0.812589	+	0.812589i	0.985021	−	0.172433i	$-0.0551627\pi$
$587$	19.6875	+	19.6875i	0.812589	+	0.812589i	−0.172433	+	0.985021i	$0.555163\pi$
$588$		0			0
$589$			33.9828i			1.40023i
$590$		0			0
$591$	0.631866	−	0.364808i	0.0259915	−	0.0150062i
$592$		0			0
$593$	4.42647	+	16.5198i	0.181773	+	0.678387i	0.995298	+	0.0968573i	$0.0308790\pi$
$593$	4.42647	+	16.5198i	0.181773	+	0.678387i	−0.813525	+	0.581530i	$0.802454\pi$
$594$		0			0
$595$	−12.5078	+	29.6137i	−0.512770	+	1.21404i
$596$		0			0
$597$	−0.0339770	−	0.126804i	−0.00139058	−	0.00518973i
$598$		0			0
$599$	−16.8012	+	9.70017i	−0.686478	+	0.396338i	−0.802291	−	0.596933i	$-0.796386\pi$
$599$	−16.8012	+	9.70017i	−0.686478	+	0.396338i	0.115813	+	0.993271i	$0.463053\pi$
$600$		0			0
$601$			26.7561i			1.09141i	0.837979	+	0.545703i	$0.183737\pi$
$601$			26.7561i			1.09141i	−0.837979	+	0.545703i	$0.816263\pi$
$602$		0			0
$603$	3.23913	+	3.23913i	0.131908	+	0.131908i
$604$		0			0
$605$	−23.1600	−	1.79554i	−0.941588	−	0.0729991i
$606$		0			0
$607$	−8.62113	+	2.31003i	−0.349921	+	0.0937611i	−0.429498	−	0.903068i	$-0.641310\pi$
$607$	−8.62113	+	2.31003i	−0.349921	+	0.0937611i	0.0795773	+	0.996829i	$0.474643\pi$
$608$		0			0
$609$	−0.0413459	−	0.0466745i	−0.00167542	−	0.00189135i
$610$		0			0
$611$	−5.48567	+	9.50146i	−0.221926	+	0.384388i
$612$		0			0
$613$	5.02936	−	18.7698i	0.203134	−	0.758107i	−0.786876	−	0.617111i	$-0.788303\pi$
$613$	5.02936	−	18.7698i	0.203134	−	0.758107i	0.990010	−	0.140996i	$-0.0450304\pi$
$614$		0			0
$615$	0.749882	−	0.139888i	0.0302382	−	0.00564082i
$616$		0			0
$617$	−12.8763	+	12.8763i	−0.518381	+	0.518381i	−0.917081	−	0.398700i	$-0.869461\pi$
$617$	−12.8763	+	12.8763i	−0.518381	+	0.518381i	0.398700	+	0.917081i	$0.369461\pi$
$618$		0			0
$619$	5.08338	+	8.80468i	0.204318	+	0.353890i	0.949915	−	0.312507i	$-0.101169\pi$
$619$	5.08338	+	8.80468i	0.204318	+	0.353890i	−0.745597	+	0.666397i	$0.767836\pi$
$620$		0			0
$621$	3.49826	+	2.01972i	0.140380	+	0.0810485i
$622$		0			0
$623$	−15.2177	−	30.4746i	−0.609685	−	1.22094i
$624$		0			0
$625$	−5.31188	−	24.4292i	−0.212475	−	0.977166i
$626$		0			0
$627$	0.342016	+	0.0916428i	0.0136588	+	0.00365986i
$628$		0			0
$629$	40.0729			1.59781
$630$		0			0
$631$	−30.9143			−1.23068			−0.615339	−	0.788262i	$-0.710981\pi$
$631$	−30.9143			−1.23068			−0.615339	+	0.788262i	$0.710981\pi$
$632$		0			0
$633$	−0.677146	−	0.181441i	−0.0269141	−	0.00721162i
$634$		0			0
$635$	−28.2506	−	9.96696i	−1.12109	−	0.395527i
$636$		0			0
$637$	30.1650	+	12.1438i	1.19518	+	0.481156i
$638$		0			0
$639$	15.1356	+	8.73853i	0.598754	+	0.345691i
$640$		0			0
$641$	9.22748	+	15.9825i	0.364463	+	0.631269i	0.988690	−	0.149974i	$-0.0479191\pi$
$641$	9.22748	+	15.9825i	0.364463	+	0.631269i	−0.624226	+	0.781243i	$0.714586\pi$
$642$		0			0
$643$	15.3634	−	15.3634i	0.605874	−	0.605874i	−0.335991	−	0.941865i	$-0.609071\pi$
$643$	15.3634	−	15.3634i	0.605874	−	0.605874i	0.941865	+	0.335991i	$0.109071\pi$
$644$		0			0
$645$	−1.01707	+	1.48355i	−0.0400469	+	0.0584145i
$646$		0			0
$647$	10.5915	−	39.5282i	0.416396	−	1.55401i	−0.365626	−	0.930762i	$-0.619145\pi$
$647$	10.5915	−	39.5282i	0.416396	−	1.55401i	0.782022	−	0.623250i	$-0.214188\pi$
$648$		0			0
$649$	2.00359	−	3.47032i	0.0786478	−	0.136222i
$650$		0			0
$651$	0.378515	−	1.13360i	0.0148352	−	0.0444294i
$652$		0			0
$653$	7.32658	−	1.96315i	0.286711	−	0.0768240i	−0.112597	−	0.993641i	$-0.535917\pi$
$653$	7.32658	−	1.96315i	0.286711	−	0.0768240i	0.399308	+	0.916817i	$0.369250\pi$
$654$		0			0
$655$	−1.14075	+	14.7141i	−0.0445726	+	0.574926i
$656$		0			0
$657$	−28.3924	−	28.3924i	−1.10769	−	1.10769i
$658$		0			0
$659$		−	4.25711i		−	0.165834i	−0.996556	−	0.0829168i	$-0.973576\pi$
$659$		−	4.25711i		−	0.165834i	0.996556	−	0.0829168i	$-0.0264236\pi$
$660$		0			0
$661$	−36.1264	+	20.8576i	−1.40515	+	0.811266i	−0.994916	−	0.100713i	$-0.967888\pi$
$661$	−36.1264	+	20.8576i	−1.40515	+	0.811266i	−0.410238	+	0.911979i	$0.634554\pi$
$662$		0			0
$663$	−0.506857	−	1.89162i	−0.0196847	−	0.0734643i
$664$		0			0
$665$	−21.2098	+	27.2476i	−0.822481	+	1.05662i
$666$		0			0
$667$	0.682950	+	2.54880i	0.0264439	+	0.0986900i
$668$		0			0
$669$	−0.198225	+	0.114445i	−0.00766384	+	0.00442472i
$670$		0			0
$671$			8.05393i			0.310919i
$672$		0			0
$673$	28.2067	+	28.2067i	1.08729	+	1.08729i	0.995807	+	0.0914807i	$0.0291600\pi$
$673$	28.2067	+	28.2067i	1.08729	+	1.08729i	0.0914807	+	0.995807i	$0.470840\pi$
$674$		0			0
$675$	−2.31183	+	0.248439i	−0.0889823	+	0.00956244i
$676$		0			0
$677$	19.7132	−	5.28215i	0.757641	−	0.203009i	0.140736	−	0.990047i	$-0.455053\pi$
$677$	19.7132	−	5.28215i	0.757641	−	0.203009i	0.616905	+	0.787038i	$0.288386\pi$
$678$		0			0
$679$	−0.330147	+	0.0673830i	−0.0126699	+	0.00258592i
$680$		0			0
$681$	−0.0182437	+	0.0315990i	−0.000699100	+	0.00121088i
$682$		0			0
$683$	−11.6682	+	43.5462i	−0.446470	+	1.66625i	0.265555	+	0.964096i	$0.414445\pi$
$683$	−11.6682	+	43.5462i	−0.446470	+	1.66625i	−0.712025	+	0.702154i	$0.752222\pi$
$684$		0			0
$685$	0.169582	+	0.909060i	0.00647939	+	0.0347334i
$686$		0			0
$687$	1.38248	−	1.38248i	0.0527450	−	0.0527450i
$688$		0			0
$689$	−14.4720	−	25.0662i	−0.551338	−	0.954945i
$690$		0			0
$691$	−6.73905	−	3.89079i	−0.256366	−	0.148013i	0.366310	−	0.930493i	$-0.380621\pi$
$691$	−6.73905	−	3.89079i	−0.256366	−	0.148013i	−0.622676	+	0.782480i	$0.713954\pi$
$692$		0			0
$693$	5.16732	+	3.41555i	0.196290	+	0.129746i
$694$		0			0
$695$	15.5920	+	32.5913i	0.591437	+	1.23626i
$696$		0			0
$697$	−23.0792	−	6.18405i	−0.874186	−	0.234237i
$698$		0			0
$699$	1.20538			0.0455918
$700$		0			0
$701$	−11.0999			−0.419237			−0.209618	−	0.977783i	$-0.567222\pi$
$701$	−11.0999			−0.419237			−0.209618	+	0.977783i	$0.567222\pi$
$702$		0			0
$703$	41.5764	+	11.1404i	1.56808	+	0.420167i
$704$		0			0
$705$	0.176820	+	0.369601i	0.00665944	+	0.0139200i
$706$		0			0
$707$	0.969101	−	16.0080i	0.0364468	−	0.602044i
$708$		0			0
$709$	−34.2204	−	19.7572i	−1.28517	−	0.741996i	−0.307385	−	0.951585i	$-0.599454\pi$
$709$	−34.2204	−	19.7572i	−1.28517	−	0.741996i	−0.977790	+	0.209589i	$0.932787\pi$
$710$		0			0
$711$	−14.9830	−	25.9513i	−0.561905	−	0.973249i
$712$		0			0
$713$	−35.7626	+	35.7626i	−1.33932	+	1.33932i
$714$		0			0
$715$	−1.48952	−	7.98474i	−0.0557050	−	0.298612i
$716$		0			0
$717$	0.566795	−	2.11531i	0.0211674	−	0.0789976i
$718$		0			0
$719$	19.8400	−	34.3639i	0.739908	−	1.28156i	−0.212628	−	0.977133i	$-0.568202\pi$
$719$	19.8400	−	34.3639i	0.739908	−	1.28156i	0.952536	−	0.304425i	$-0.0984643\pi$
$720$		0			0
$721$	6.45936	+	2.15681i	0.240559	+	0.0803237i
$722$		0			0
$723$	1.02292	−	0.274089i	0.0380426	−	0.0101935i
$724$		0			0
$725$	−1.18261	−	0.953098i	−0.0439211	−	0.0353972i
$726$		0			0
$727$	23.2801	+	23.2801i	0.863410	+	0.863410i	0.991733	−	0.128322i	$-0.0409591\pi$
$727$	23.2801	+	23.2801i	0.863410	+	0.863410i	−0.128322	+	0.991733i	$0.540959\pi$
$728$		0			0
$729$		−	26.6755i		−	0.987982i
$730$		0			0
$731$	48.7916	−	28.1698i	1.80462	−	1.04190i
$732$		0			0
$733$	4.27364	+	15.9494i	0.157850	+	0.589106i	0.998844	+	0.0480612i	$0.0153043\pi$
$733$	4.27364	+	15.9494i	0.157850	+	0.589106i	−0.840994	+	0.541044i	$0.818029\pi$
$734$		0			0
$735$	1.01102	−	0.672688i	0.0372919	−	0.0248125i
$736$		0			0
$737$	0.309651	+	1.15563i	0.0114062	+	0.0425683i
$738$		0			0
$739$	37.3385	−	21.5574i	1.37352	−	0.793001i	0.382149	−	0.924101i	$-0.375184\pi$
$739$	37.3385	−	21.5574i	1.37352	−	0.793001i	0.991369	+	0.131099i	$0.0418507\pi$
$740$		0			0
$741$		−	2.10350i		−	0.0772739i
$742$		0			0
$743$	−8.79757	−	8.79757i	−0.322751	−	0.322751i	0.527070	−	0.849822i	$-0.323290\pi$
$743$	−8.79757	−	8.79757i	−0.322751	−	0.322751i	−0.849822	+	0.527070i	$0.823290\pi$
$744$		0			0
$745$	0.971971	−	12.5371i	0.0356103	−	0.459324i
$746$		0			0
$747$	−12.0435	+	3.22705i	−0.440649	+	0.118072i
$748$		0			0
$749$	−21.3768	−	7.13779i	−0.781091	−	0.260809i
$750$		0			0
$751$	−1.89233	+	3.27761i	−0.0690521	+	0.119602i	−0.898484	−	0.439006i	$-0.855331\pi$
$751$	−1.89233	+	3.27761i	−0.0690521	+	0.119602i	0.829432	+	0.558607i	$0.188664\pi$
$752$		0			0
$753$	−0.163544	+	0.610355i	−0.00595988	+	0.0222426i
$754$		0			0
$755$	9.09639	−	13.2685i	0.331051	−	0.482889i
$756$		0			0
$757$	14.6751	−	14.6751i	0.533375	−	0.533375i	−0.388200	−	0.921575i	$-0.626903\pi$
$757$	14.6751	−	14.6751i	0.533375	−	0.533375i	0.921575	+	0.388200i	$0.126903\pi$
$758$		0			0
$759$	0.263486	+	0.456371i	0.00956394	+	0.0165652i
$760$		0			0
$761$	−30.3893	−	17.5453i	−1.10161	−	0.636016i	−0.164968	−	0.986299i	$-0.552752\pi$
$761$	−30.3893	−	17.5453i	−1.10161	−	0.636016i	−0.936644	+	0.350283i	$0.886085\pi$
$762$		0			0
$763$	−1.33670	+	22.0803i	−0.0483919	+	0.799359i
$764$		0			0
$765$	34.3055	+	12.1032i	1.24032	+	0.437591i
$766$		0			0
$767$	−22.9944	−	6.16134i	−0.830280	−	0.222473i
$768$		0			0
$769$	17.2197			0.620959			0.310479	−	0.950580i	$-0.399510\pi$
$769$	17.2197			0.620959			0.310479	+	0.950580i	$0.399510\pi$
$770$		0			0
$771$	0.803245			0.0289282
$772$		0			0
$773$	19.0628	+	5.10786i	0.685641	+	0.183717i	0.584790	−	0.811185i	$-0.301177\pi$
$773$	19.0628	+	5.10786i	0.685641	+	0.183717i	0.100851	+	0.994902i	$0.467844\pi$
$774$		0			0
$775$	4.48700	−	28.7641i	0.161178	−	1.03324i
$776$		0			0
$777$	−1.26283	−	0.834719i	−0.0453037	−	0.0299454i
$778$		0			0
$779$	−22.2259	−	12.8321i	−0.796327	−	0.459759i
$780$		0			0
$781$	2.28229	+	3.95305i	0.0816669	+	0.141451i
$782$		0			0
$783$	−0.0998883	+	0.0998883i	−0.00356972	+	0.00356972i
$784$		0			0
$785$	4.65027	−	0.867490i	0.165975	−	0.0309621i
$786$		0			0
$787$	−8.85989	+	33.0656i	−0.315821	+	1.17866i	0.607402	+	0.794395i	$0.292212\pi$
$787$	−8.85989	+	33.0656i	−0.315821	+	1.17866i	−0.923223	+	0.384265i	$0.874455\pi$
$788$		0			0
$789$	−1.14312	+	1.97993i	−0.0406960	+	0.0704875i
$790$		0			0
$791$	2.29010	−	0.467410i	0.0814267	−	0.0166192i
$792$		0			0
$793$	46.2159	−	12.3835i	1.64117	−	0.439751i
$794$		0			0
$795$	−1.07766	−	0.0835487i	−0.0382208	−	0.00296317i
$796$		0			0
$797$	−26.5966	−	26.5966i	−0.942100	−	0.942100i	0.0563133	−	0.998413i	$-0.482065\pi$
$797$	−26.5966	−	26.5966i	−0.942100	−	0.942100i	−0.998413	+	0.0563133i	$0.982065\pi$
$798$		0			0
$799$		−	12.8334i		−	0.454013i
$800$		0			0
$801$	−33.3819	+	19.2731i	−1.17949	+	0.680981i
$802$		0			0
$803$	−2.71423	−	10.1296i	−0.0957830	−	0.357467i
$804$		0			0
$805$	−50.9954	+	6.35406i	−1.79735	+	0.223951i
$806$		0			0
$807$	−0.411358	−	1.53521i	−0.0144805	−	0.0540419i
$808$		0			0
$809$	−9.43671	+	5.44829i	−0.331777	+	0.191552i	−0.656630	−	0.754213i	$-0.728019\pi$
$809$	−9.43671	+	5.44829i	−0.331777	+	0.191552i	0.324853	+	0.945765i	$0.394685\pi$
$810$		0			0
$811$		−	39.7220i		−	1.39483i	−0.716668	−	0.697414i	$-0.754334\pi$
$811$		−	39.7220i		−	1.39483i	0.716668	−	0.697414i	$-0.245666\pi$
$812$		0			0
$813$	−0.850655	−	0.850655i	−0.0298338	−	0.0298338i
$814$		0			0
$815$	−0.760189	−	0.887966i	−0.0266283	−	0.0311041i
$816$		0			0
$817$	58.4536	−	15.6626i	2.04503	−	0.547965i
$818$		0			0
$819$	11.6544	−	34.9033i	0.407236	−	1.21962i
$820$		0			0
$821$	−7.63160	+	13.2183i	−0.266345	+	0.461323i	−0.967915	−	0.251278i	$-0.919149\pi$
$821$	−7.63160	+	13.2183i	−0.266345	+	0.461323i	0.701570	+	0.712600i	$0.252483\pi$
$822$		0			0
$823$	−7.97924	+	29.7789i	−0.278139	+	1.03803i	0.675570	+	0.737296i	$0.263898\pi$
$823$	−7.97924	+	29.7789i	−0.278139	+	1.03803i	−0.953709	+	0.300732i	$0.902769\pi$
$824$		0			0
$825$	−0.277393	−	0.122728i	−0.00965759	−	0.00427286i
$826$		0			0
$827$	2.11815	−	2.11815i	0.0736553	−	0.0736553i	−0.669319	−	0.742975i	$-0.733414\pi$
$827$	2.11815	−	2.11815i	0.0736553	−	0.0736553i	0.742975	+	0.669319i	$0.233414\pi$
$828$		0			0
$829$	−10.6454	−	18.4384i	−0.369730	−	0.640392i	0.619793	−	0.784765i	$-0.287217\pi$
$829$	−10.6454	−	18.4384i	−0.369730	−	0.640392i	−0.989523	+	0.144374i	$0.953883\pi$
$830$		0			0
$831$	0.161556	+	0.0932742i	0.00560431	+	0.00323565i
$832$		0			0
$833$	−37.6598	+	5.34052i	−1.30484	+	0.185038i
$834$		0			0
$835$	0.440072	−	1.24735i	0.0152293	−	0.0431663i
$836$		0			0
$837$	−2.61532	−	0.700773i	−0.0903986	−	0.0242222i
$838$		0			0
$839$	−17.0861			−0.589879			−0.294939	−	0.955516i	$-0.595299\pi$
$839$	−17.0861			−0.589879			−0.294939	+	0.955516i	$0.595299\pi$
$840$		0			0
$841$	28.9077			0.996818
$842$		0			0
$843$	1.26691	+	0.339467i	0.0436347	+	0.0116919i
$844$		0			0
$845$	−17.3060	+	8.27936i	−0.595346	+	0.284819i
$846$		0			0
$847$	−12.2793	−	24.5901i	−0.421921	−	0.844926i
$848$		0			0
$849$	−0.367087	−	0.211938i	−0.0125984	−	0.00727369i
$850$		0			0
$851$	32.0301	+	55.4778i	1.09798	+	1.90175i
$852$		0			0
$853$	−4.45830	+	4.45830i	−0.152649	+	0.152649i	−0.779300	−	0.626651i	$-0.784425\pi$
$853$	−4.45830	+	4.45830i	−0.152649	+	0.152649i	0.626651	+	0.779300i	$0.284425\pi$
$854$		0			0
$855$	32.2279	+	22.0943i	1.10217	+	0.755609i
$856$		0			0
$857$	6.97152	−	26.0181i	0.238143	−	0.888761i	−0.738564	−	0.674183i	$-0.764496\pi$
$857$	6.97152	−	26.0181i	0.238143	−	0.888761i	0.976707	−	0.214578i	$-0.0688375\pi$
$858$		0			0
$859$	−9.12384	+	15.8029i	−0.311301	+	0.539190i	−0.978644	−	0.205561i	$-0.934098\pi$
$859$	−9.12384	+	15.8029i	−0.311301	+	0.539190i	0.667343	+	0.744750i	$0.267431\pi$
$860$		0			0
$861$	0.598487	+	0.675620i	0.0203964	+	0.0230251i
$862$		0			0
$863$	3.57400	−	0.957651i	0.121660	−	0.0325988i	−0.197475	−	0.980308i	$-0.563274\pi$
$863$	3.57400	−	0.957651i	0.121660	−	0.0325988i	0.319136	+	0.947709i	$0.396607\pi$
$864$		0			0
$865$	−17.3357	+	14.8411i	−0.589431	+	0.504613i
$866$		0			0
$867$	0.687176	+	0.687176i	0.0233377	+	0.0233377i
$868$		0			0
$869$		−	7.82638i		−	0.265492i
$870$		0			0
$871$	6.15527	−	3.55375i	0.208563	−	0.120414i
$872$		0			0
$873$	0.0986883	+	0.368310i	0.00334009	+	0.0124654i
$874$		0			0
$875$	21.5504	−	20.2628i	0.728536	−	0.685008i
$876$		0			0
$877$	−10.5233	−	39.2734i	−0.355345	−	1.32617i	−0.880049	−	0.474882i	$-0.842491\pi$
$877$	−10.5233	−	39.2734i	−0.355345	−	1.32617i	0.524704	−	0.851285i	$-0.324176\pi$
$878$		0			0
$879$	0.914326	−	0.527886i	0.0308394	−	0.0178052i
$880$		0			0
$881$		−	39.2100i		−	1.32102i	−0.750818	−	0.660509i	$-0.770341\pi$
$881$		−	39.2100i		−	1.32102i	0.750818	−	0.660509i	$-0.229659\pi$
$882$		0			0
$883$	−25.5883	−	25.5883i	−0.861114	−	0.861114i	0.130353	−	0.991468i	$-0.458389\pi$
$883$	−25.5883	−	25.5883i	−0.861114	−	0.861114i	−0.991468	+	0.130353i	$0.958389\pi$
$884$		0			0
$885$	−0.675333	+	0.578153i	−0.0227011	+	0.0194344i
$886$		0			0
$887$	55.9980	−	15.0046i	1.88023	−	0.503806i	0.880683	−	0.473706i	$-0.157084\pi$
$887$	55.9980	−	15.0046i	1.88023	−	0.503806i	0.999547	−	0.0300998i	$-0.00958250\pi$
$888$		0			0
$889$	−7.08837	−	34.7299i	−0.237736	−	1.16480i
$890$		0			0
$891$	3.49763	−	6.05808i	0.117175	−	0.202953i
$892$		0			0
$893$	3.56772	−	13.3149i	0.119389	−	0.445567i
$894$		0			0
$895$	−39.7131	−	27.2259i	−1.32746	−	0.910061i
$896$		0			0
$897$	2.21367	−	2.21367i	0.0739122	−	0.0739122i
$898$		0			0
$899$	−0.884346	−	1.53173i	−0.0294946	−	0.0510861i
$900$		0			0
$901$	29.3204	+	16.9282i	0.976805	+	0.563959i
$902$		0			0
$903$	−2.12436	−	0.128606i	−0.0706944	−	0.00427973i
$904$		0			0
$905$	−7.33135	+	3.50738i	−0.243702	+	0.116589i
$906$		0			0
$907$	16.3196	+	4.37283i	0.541884	+	0.145197i	0.519371	−	0.854549i	$-0.326166\pi$
$907$	16.3196	+	4.37283i	0.541884	+	0.145197i	0.0225135	+	0.999747i	$0.492833\pi$
$908$		0			0
$909$	−18.1482			−0.601936
$910$		0			0
$911$	−29.5708			−0.979724			−0.489862	−	0.871800i	$-0.662953\pi$
$911$	−29.5708			−0.979724			−0.489862	+	0.871800i	$0.662953\pi$
$912$		0			0
$913$	−3.14547	−	0.842827i	−0.104100	−	0.0278935i
$914$		0			0
$915$	0.594478	−	1.68500i	0.0196528	−	0.0557044i
$916$		0			0
$917$	−15.6226	+	7.80129i	−0.515905	+	0.257621i
$918$		0			0
$919$	49.6782	+	28.6817i	1.63873	+	0.946123i	0.981270	+	0.192637i	$0.0617039\pi$
$919$	49.6782	+	28.6817i	1.63873	+	0.946123i	0.657463	+	0.753486i	$0.271629\pi$
$920$		0			0
$921$	−0.978582	−	1.69495i	−0.0322454	−	0.0558506i
$922$		0			0
$923$	19.1746	−	19.1746i	0.631139	−	0.631139i
$924$		0			0
$925$	−33.7207	−	14.9192i	−1.10873	−	0.490541i
$926$		0			0
$927$	1.99452	−	7.44366i	0.0655088	−	0.244482i
$928$		0			0
$929$	2.59381	−	4.49261i	0.0851001	−	0.147398i	−0.820334	−	0.571885i	$-0.806212\pi$
$929$	2.59381	−	4.49261i	0.0851001	−	0.147398i	0.905434	+	0.424487i	$0.139546\pi$
$930$		0			0
$931$	−40.5575	−	4.92864i	−1.32922	−	0.161530i
$932$		0			0
$933$	0.931782	−	0.249670i	0.0305052	−	0.00817383i
$934$		0			0
$935$	6.17885	+	7.21744i	0.202070	+	0.236035i
$936$		0			0
$937$	27.5418	+	27.5418i	0.899750	+	0.899750i	0.995414	−	0.0956634i	$-0.0304972\pi$
$937$	27.5418	+	27.5418i	0.899750	+	0.899750i	−0.0956634	+	0.995414i	$0.530497\pi$
$938$		0			0
$939$		−	0.196195i		−	0.00640260i
$940$		0			0
$941$	−11.8890	+	6.86411i	−0.387570	+	0.223763i	−0.681107	−	0.732184i	$-0.738501\pi$
$941$	−11.8890	+	6.86411i	−0.387570	+	0.223763i	0.293537	+	0.955948i	$0.405168\pi$
$942$		0			0
$943$	−9.88578	−	36.8942i	−0.321925	−	1.20144i
$944$		0			0
$945$	−1.65961	−	2.19419i	−0.0539870	−	0.0713771i
$946$		0			0
$947$	−0.258625	−	0.965201i	−0.00840418	−	0.0313648i	0.961596	−	0.274467i	$-0.0885015\pi$
$947$	−0.258625	−	0.965201i	−0.00840418	−	0.0313648i	−0.970001	+	0.243103i	$0.921835\pi$
$948$		0			0
$949$	−53.9536	+	31.1501i	−1.75141	+	1.01118i
$950$		0			0
$951$			1.23670i			0.0401028i
$952$		0			0
$953$	19.8419	+	19.8419i	0.642742	+	0.642742i	0.951229	−	0.308487i	$-0.0998225\pi$
$953$	19.8419	+	19.8419i	0.642742	+	0.642742i	−0.308487	+	0.951229i	$0.599823\pi$
$954$		0			0
$955$	−0.0144646	−	0.00112141i	−0.000468063	−	3.62878e-5i
$956$		0			0
$957$	−0.0178008	+	0.00476971i	−0.000575419	+	0.000154183i
$958$		0			0
$959$	−0.819034	+	0.725528i	−0.0264480	+	0.0234285i
$960$		0			0
$961$	1.45016	−	2.51174i	0.0467792	−	0.0810240i
$962$		0			0
$963$	−6.60073	+	24.6342i	−0.212705	+	0.793827i
$964$		0			0
$965$	−5.76262	+	1.07500i	−0.185505	+	0.0346053i
$966$		0			0
$967$	−17.7327	+	17.7327i	−0.570244	+	0.570244i	−0.932197	−	0.361952i	$-0.882110\pi$
$967$	−17.7327	+	17.7327i	−0.570244	+	0.570244i	0.361952	+	0.932197i	$0.382110\pi$
$968$		0			0
$969$	1.23025	+	2.13086i	0.0395214	+	0.0684531i
$970$		0			0
$971$	−15.3128	−	8.84086i	−0.491412	−	0.283717i	0.233748	−	0.972297i	$-0.424901\pi$
$971$	−15.3128	−	8.84086i	−0.491412	−	0.283717i	−0.725160	+	0.688581i	$0.758234\pi$
$972$		0			0
$973$	−23.5722	+	35.6619i	−0.755691	+	1.14327i
$974$		0			0
$975$	−0.277741	+	1.78047i	−0.00889482	+	0.0570207i
$976$		0			0
$977$	−5.30768	−	1.42219i	−0.169808	−	0.0454998i	0.172913	−	0.984937i	$-0.444682\pi$
$977$	−5.30768	−	1.42219i	−0.169808	−	0.0454998i	−0.342721	+	0.939437i	$0.611349\pi$
$978$		0			0
$979$	−10.0673			−0.321753
$980$		0			0
$981$	25.0322			0.799216
$982$		0			0
$983$	45.3892	+	12.1620i	1.44769	+	0.387908i	0.895220	−	0.445625i	$-0.147018\pi$
$983$	45.3892	+	12.1620i	1.44769	+	0.387908i	0.552471	+	0.833532i	$0.313685\pi$
$984$		0			0
$985$	19.8309	+	6.99644i	0.631864	+	0.222925i
$986$		0			0
$987$	−0.267320	+	0.404423i	−0.00850890	+	0.0128729i
$988$		0			0
$989$	77.9980	+	45.0321i	2.48019	+	1.43194i
$990$		0			0
$991$	−1.02005	−	1.76677i	−0.0324029	−	0.0561234i	0.849369	−	0.527799i	$-0.176983\pi$
$991$	−1.02005	−	1.76677i	−0.0324029	−	0.0561234i	−0.881772	+	0.471676i	$0.843649\pi$
$992$		0			0
$993$	−1.36251	+	1.36251i	−0.0432381	+	0.0432381i
$994$		0			0
$995$	2.13944	−	3.12070i	0.0678247	−	0.0989327i
$996$		0			0
$997$	−7.12955	+	26.6078i	−0.225795	+	0.842678i	0.756289	+	0.654237i	$0.227010\pi$
$997$	−7.12955	+	26.6078i	−0.225795	+	0.842678i	−0.982084	+	0.188441i	$0.939656\pi$
$998$		0			0
$999$	−1.71473	+	2.97000i	−0.0542516	+	0.0939666i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.bo.a.33.6	yes	48
4.3	odd	2		560.2.ci.e.33.7		48
5.2	odd	4	inner	280.2.bo.a.257.6	yes	48
7.3	odd	6	inner	280.2.bo.a.73.6	yes	48
20.7	even	4		560.2.ci.e.257.7		48
28.3	even	6		560.2.ci.e.353.7		48
35.17	even	12	inner	280.2.bo.a.17.6	✓	48
140.87	odd	12		560.2.ci.e.17.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bo.a.17.6	✓	48	35.17	even	12	inner
280.2.bo.a.33.6	yes	48	1.1	even	1	trivial
280.2.bo.a.73.6	yes	48	7.3	odd	6	inner
280.2.bo.a.257.6	yes	48	5.2	odd	4	inner
560.2.ci.e.17.7		48	140.87	odd	12
560.2.ci.e.33.7		48	4.3	odd	2
560.2.ci.e.257.7		48	20.7	even	4
560.2.ci.e.353.7		48	28.3	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.bo (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0749389 - 0.0200798i) q^{3} +(-0.965007 - 2.01712i) q^{5} +(1.45892 - 2.20716i) q^{7} +(-2.59286 - 1.49699i) q^{9} +O(q^{10})\)	\(q+(-0.0749389 - 0.0200798i) q^{3} +(-0.965007 - 2.01712i) q^{5} +(1.45892 - 2.20716i) q^{7} +(-2.59286 - 1.49699i) q^{9} +(-0.390978 - 0.677193i) q^{11} +(-3.28478 + 3.28478i) q^{13} +(0.0318132 + 0.170538i) q^{15} +(1.40637 - 5.24865i) q^{17} +(2.91828 - 5.05461i) q^{19} +(-0.153649 + 0.136108i) q^{21} +(8.39046 - 2.24822i) q^{23} +(-3.13752 + 3.89306i) q^{25} +(0.328824 + 0.328824i) q^{27} +0.303774i q^{29} +(-5.04234 + 2.91120i) q^{31} +(0.0157015 + 0.0585989i) q^{33} +(-5.85997 - 0.812878i) q^{35} +(1.90872 + 7.12345i) q^{37} +(0.312116 - 0.180200i) q^{39} -4.39716i q^{41} +(7.33155 + 7.33155i) q^{43} +(-0.517475 + 6.67472i) q^{45} +(2.28130 - 0.611272i) q^{47} +(-2.74313 - 6.44013i) q^{49} +(-0.210784 + 0.365088i) q^{51} +(-1.61262 + 6.01838i) q^{53} +(-0.988682 + 1.44214i) q^{55} +(-0.320188 + 0.320188i) q^{57} +(2.56228 + 4.43800i) q^{59} +(-8.91983 - 5.14987i) q^{61} +(-7.08687 + 3.53889i) q^{63} +(9.79563 + 3.45595i) q^{65} +(-1.47788 - 0.395996i) q^{67} -0.673916 q^{69} -5.83740 q^{71} +(12.9542 + 3.47108i) q^{73} +(0.313295 - 0.228741i) q^{75} +(-2.06508 - 0.125017i) q^{77} +(8.66781 + 5.00437i) q^{79} +(4.47293 + 7.74735i) q^{81} +(2.94473 - 2.94473i) q^{83} +(-11.9443 + 2.22817i) q^{85} +(0.00609973 - 0.0227645i) q^{87} +(6.43727 - 11.1497i) q^{89} +(2.45783 + 12.0423i) q^{91} +(0.436324 - 0.116913i) q^{93} +(-13.0119 - 1.00878i) q^{95} +(-0.0900545 - 0.0900545i) q^{97} +2.34116i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{7}+O(q^{10}) \) 48 * q - 4 * q^7	\( 48 q - 4 q^{7} + 4 q^{11} + 8 q^{15} - 4 q^{21} - 4 q^{23} - 8 q^{25} - 36 q^{33} + 24 q^{35} + 8 q^{37} - 16 q^{43} + 48 q^{45} + 24 q^{51} + 16 q^{53} - 96 q^{57} - 36 q^{61} - 68 q^{63} + 12 q^{65} - 16 q^{67} - 64 q^{71} - 48 q^{73} - 48 q^{75} + 4 q^{77} - 40 q^{85} - 12 q^{87} - 80 q^{91} + 24 q^{95}+O(q^{100}) \) 48 * q - 4 * q^7 + 4 * q^11 + 8 * q^15 - 4 * q^21 - 4 * q^23 - 8 * q^25 - 36 * q^33 + 24 * q^35 + 8 * q^37 - 16 * q^43 + 48 * q^45 + 24 * q^51 + 16 * q^53 - 96 * q^57 - 36 * q^61 - 68 * q^63 + 12 * q^65 - 16 * q^67 - 64 * q^71 - 48 * q^73 - 48 * q^75 + 4 * q^77 - 40 * q^85 - 12 * q^87 - 80 * q^91 + 24 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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