LMFDB - Embedded newform 512.2.i.a.97.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(33,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 15]))

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

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

chi := DirichletCharacter("512.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.i (of order $16$, degree $8$, 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:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 64)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			97.1
Character	$\chi$	$=$	512.97
Dual form			512.2.i.a.417.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.599600 - 3.01439i) q^{3} +(1.78465 - 1.19247i) q^{5} +(-1.99271 - 0.825409i) q^{7} +(-5.95540 + 2.46681i) q^{9} +O(q^{10})$	\(q+(-0.599600 - 3.01439i) q^{3} +(1.78465 - 1.19247i) q^{5} +(-1.99271 - 0.825409i) q^{7} +(-5.95540 + 2.46681i) q^{9} +(-3.15038 - 0.626650i) q^{11} +(-0.0943077 - 0.0630144i) q^{13} +(-4.66465 - 4.66465i) q^{15} +(2.42319 - 2.42319i) q^{17} +(1.93596 - 2.89737i) q^{19} +(-1.29328 + 6.50174i) q^{21} +(1.33543 + 3.22402i) q^{23} +(-0.150405 + 0.363110i) q^{25} +(5.88424 + 8.80639i) q^{27} +(-2.01879 + 0.401561i) q^{29} +4.16617i q^{31} +9.87224i q^{33} +(-4.54058 + 0.903177i) q^{35} +(-5.48499 - 8.20886i) q^{37} +(-0.133403 + 0.322064i) q^{39} +(0.347569 + 0.839106i) q^{41} +(0.925855 - 4.65459i) q^{43} +(-7.68675 + 11.5040i) q^{45} +(8.31575 - 8.31575i) q^{47} +(-1.66014 - 1.66014i) q^{49} +(-8.75739 - 5.85150i) q^{51} +(-0.565279 - 0.112441i) q^{53} +(-6.36961 + 2.63838i) q^{55} +(-9.89462 - 4.09848i) q^{57} +(-0.649771 + 0.434163i) q^{59} +(0.528753 + 2.65822i) q^{61} +13.9035 q^{63} -0.243449 q^{65} +(0.971210 + 4.88260i) q^{67} +(8.91774 - 5.95864i) q^{69} +(-9.38522 - 3.88748i) q^{71} +(12.6303 - 5.23165i) q^{73} +(1.18474 + 0.235659i) q^{75} +(5.76057 + 3.84909i) q^{77} +(3.50532 + 3.50532i) q^{79} +(9.34353 - 9.34353i) q^{81} +(-8.25513 + 12.3547i) q^{83} +(1.43498 - 7.21413i) q^{85} +(2.42093 + 5.84464i) q^{87} +(4.98881 - 12.0441i) q^{89} +(0.135916 + 0.203412i) q^{91} +(12.5585 - 2.49803i) q^{93} -7.47938i q^{95} -4.06140i q^{97} +(20.3076 - 4.03944i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{3} + 8 q^{5} + 8 q^{7} - 8 q^{9}+O(q^{10}) $ 56 * q - 8 * q^3 + 8 * q^5 + 8 * q^7 - 8 * q^9	$ 56 q - 8 q^{3} + 8 q^{5} + 8 q^{7} - 8 q^{9} - 8 q^{11} + 8 q^{13} + 8 q^{15} - 8 q^{17} - 8 q^{19} + 8 q^{21} + 8 q^{23} - 8 q^{25} - 8 q^{27} + 8 q^{29} - 8 q^{35} + 8 q^{37} + 8 q^{39} - 8 q^{41} - 8 q^{43} + 8 q^{45} + 8 q^{47} - 8 q^{49} + 24 q^{51} + 8 q^{53} - 56 q^{55} - 8 q^{57} + 56 q^{59} + 8 q^{61} - 64 q^{63} - 16 q^{65} + 72 q^{67} + 8 q^{69} - 56 q^{71} - 8 q^{73} + 56 q^{75} + 8 q^{77} - 24 q^{79} - 8 q^{81} - 8 q^{83} + 8 q^{85} + 8 q^{87} - 8 q^{89} - 8 q^{91} - 16 q^{93} + 16 q^{99}+O(q^{100}) $ 56 * q - 8 * q^3 + 8 * q^5 + 8 * q^7 - 8 * q^9 - 8 * q^11 + 8 * q^13 + 8 * q^15 - 8 * q^17 - 8 * q^19 + 8 * q^21 + 8 * q^23 - 8 * q^25 - 8 * q^27 + 8 * q^29 - 8 * q^35 + 8 * q^37 + 8 * q^39 - 8 * q^41 - 8 * q^43 + 8 * q^45 + 8 * q^47 - 8 * q^49 + 24 * q^51 + 8 * q^53 - 56 * q^55 - 8 * q^57 + 56 * q^59 + 8 * q^61 - 64 * q^63 - 16 * q^65 + 72 * q^67 + 8 * q^69 - 56 * q^71 - 8 * q^73 + 56 * q^75 + 8 * q^77 - 24 * q^79 - 8 * q^81 - 8 * q^83 + 8 * q^85 + 8 * q^87 - 8 * q^89 - 8 * q^91 - 16 * q^93 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{13}{16}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.599600	−	3.01439i	−0.346179	−	1.74036i	−0.625556	−	0.780179i	$-0.715128\pi$
$3$	−0.599600	−	3.01439i	−0.346179	−	1.74036i	0.279377	−	0.960181i	$-0.409872\pi$
$4$		0			0
$5$	1.78465	−	1.19247i	0.798122	−	0.533288i	−0.0883396	−	0.996090i	$-0.528156\pi$
$5$	1.78465	−	1.19247i	0.798122	−	0.533288i	0.886461	+	0.462802i	$0.153156\pi$
$6$		0			0
$7$	−1.99271	−	0.825409i	−0.753175	−	0.311975i	−0.0271386	−	0.999632i	$-0.508640\pi$
$7$	−1.99271	−	0.825409i	−0.753175	−	0.311975i	−0.726036	+	0.687656i	$0.758640\pi$
$8$		0			0
$9$	−5.95540	+	2.46681i	−1.98513	+	0.822270i
$10$		0			0
$11$	−3.15038	−	0.626650i	−0.949877	−	0.188942i	−0.304247	−	0.952593i	$-0.598405\pi$
$11$	−3.15038	−	0.626650i	−0.949877	−	0.188942i	−0.645629	+	0.763651i	$0.723405\pi$
$12$		0			0
$13$	−0.0943077	−	0.0630144i	−0.0261563	−	0.0174770i	0.542423	−	0.840105i	$-0.317507\pi$
$13$	−0.0943077	−	0.0630144i	−0.0261563	−	0.0174770i	−0.568580	+	0.822628i	$0.692507\pi$
$14$		0			0
$15$	−4.66465	−	4.66465i	−1.20441	−	1.20441i
$16$		0			0
$17$	2.42319	−	2.42319i	0.587710	−	0.587710i	−0.349301	−	0.937011i	$-0.613581\pi$
$17$	2.42319	−	2.42319i	0.587710	−	0.587710i	0.937011	+	0.349301i	$0.113581\pi$
$18$		0			0
$19$	1.93596	−	2.89737i	0.444140	−	0.664702i	−0.540088	−	0.841609i	$-0.681609\pi$
$19$	1.93596	−	2.89737i	0.444140	−	0.664702i	0.984228	+	0.176906i	$0.0566089\pi$
$20$		0			0
$21$	−1.29328	+	6.50174i	−0.282216	+	1.41879i
$22$		0			0
$23$	1.33543	+	3.22402i	0.278457	+	0.672255i	0.999793	−	0.0203301i	$-0.00647173\pi$
$23$	1.33543	+	3.22402i	0.278457	+	0.672255i	−0.721336	+	0.692585i	$0.756472\pi$
$24$		0			0
$25$	−0.150405	+	0.363110i	−0.0300810	+	0.0726220i
$26$		0			0
$27$	5.88424	+	8.80639i	1.13242	+	1.69479i
$28$		0			0
$29$	−2.01879	+	0.401561i	−0.374879	+	0.0745681i	−0.378934	−	0.925424i	$-0.623709\pi$
$29$	−2.01879	+	0.401561i	−0.374879	+	0.0745681i	0.00405495	+	0.999992i	$0.498709\pi$
$30$		0			0
$31$			4.16617i			0.748266i	0.927375	+	0.374133i	$0.122060\pi$
$31$			4.16617i			0.748266i	−0.927375	+	0.374133i	$0.877940\pi$
$32$		0			0
$33$			9.87224i			1.71854i
$34$		0			0
$35$	−4.54058	+	0.903177i	−0.767498	+	0.152665i
$36$		0			0
$37$	−5.48499	−	8.20886i	−0.901726	−	1.34953i	−0.936697	−	0.350140i	$-0.886134\pi$
$37$	−5.48499	−	8.20886i	−0.901726	−	1.34953i	0.0349711	−	0.999388i	$-0.488866\pi$
$38$		0			0
$39$	−0.133403	+	0.322064i	−0.0213616	+	0.0515715i
$40$		0			0
$41$	0.347569	+	0.839106i	0.0542812	+	0.131046i	0.948694	−	0.316197i	$-0.102406\pi$
$41$	0.347569	+	0.839106i	0.0542812	+	0.131046i	−0.894413	+	0.447243i	$0.852406\pi$
$42$		0			0
$43$	0.925855	−	4.65459i	0.141192	−	0.709818i	−0.843723	−	0.536778i	$-0.819641\pi$
$43$	0.925855	−	4.65459i	0.141192	−	0.709818i	0.984915	−	0.173039i	$-0.0553588\pi$
$44$		0			0
$45$	−7.68675	+	11.5040i	−1.14587	+	1.71492i
$46$		0			0
$47$	8.31575	−	8.31575i	1.21298	−	1.21298i	0.242935	−	0.970043i	$-0.421890\pi$
$47$	8.31575	−	8.31575i	1.21298	−	1.21298i	0.970043	−	0.242935i	$-0.0781101\pi$
$48$		0			0
$49$	−1.66014	−	1.66014i	−0.237163	−	0.237163i
$50$		0			0
$51$	−8.75739	−	5.85150i	−1.22628	−	0.819374i
$52$		0			0
$53$	−0.565279	−	0.112441i	−0.0776470	−	0.0154450i	0.156114	−	0.987739i	$-0.450103\pi$
$53$	−0.565279	−	0.112441i	−0.0776470	−	0.0154450i	−0.233761	+	0.972294i	$0.575103\pi$
$54$		0			0
$55$	−6.36961	+	2.63838i	−0.858878	+	0.355759i
$56$		0			0
$57$	−9.89462	−	4.09848i	−1.31057	−	0.542857i
$58$		0			0
$59$	−0.649771	+	0.434163i	−0.0845930	+	0.0565232i	−0.597147	−	0.802132i	$-0.703699\pi$
$59$	−0.649771	+	0.434163i	−0.0845930	+	0.0565232i	0.512554	+	0.858655i	$0.328699\pi$
$60$		0			0
$61$	0.528753	+	2.65822i	0.0676999	+	0.340350i	0.999759	−	0.0219561i	$-0.00698941\pi$
$61$	0.528753	+	2.65822i	0.0676999	+	0.340350i	−0.932059	+	0.362306i	$0.881989\pi$
$62$		0			0
$63$	13.9035			1.75168
$64$		0			0
$65$	−0.243449			−0.0301962
$66$		0			0
$67$	0.971210	+	4.88260i	0.118652	+	0.596505i	0.993663	+	0.112401i	$0.0358542\pi$
$67$	0.971210	+	4.88260i	0.118652	+	0.596505i	−0.875011	+	0.484104i	$0.839146\pi$
$68$		0			0
$69$	8.91774	−	5.95864i	1.07357	−	0.717336i
$70$		0			0
$71$	−9.38522	−	3.88748i	−1.11382	−	0.461360i	−0.251569	−	0.967839i	$-0.580946\pi$
$71$	−9.38522	−	3.88748i	−1.11382	−	0.461360i	−0.862252	+	0.506480i	$0.830946\pi$
$72$		0			0
$73$	12.6303	−	5.23165i	1.47827	−	0.612318i	0.509539	−	0.860447i	$-0.329816\pi$
$73$	12.6303	−	5.23165i	1.47827	−	0.612318i	0.968727	+	0.248129i	$0.0798158\pi$
$74$		0			0
$75$	1.18474	+	0.235659i	0.136802	+	0.0272116i
$76$		0			0
$77$	5.76057	+	3.84909i	0.656478	+	0.438645i
$78$		0			0
$79$	3.50532	+	3.50532i	0.394379	+	0.394379i	0.876245	−	0.481866i	$-0.160041\pi$
$79$	3.50532	+	3.50532i	0.394379	+	0.394379i	−0.481866	+	0.876245i	$0.660041\pi$
$80$		0			0
$81$	9.34353	−	9.34353i	1.03817	−	1.03817i
$82$		0			0
$83$	−8.25513	+	12.3547i	−0.906118	+	1.35610i	0.0281778	+	0.999603i	$0.491030\pi$
$83$	−8.25513	+	12.3547i	−0.906118	+	1.35610i	−0.934296	+	0.356499i	$0.883970\pi$
$84$		0			0
$85$	1.43498	−	7.21413i	0.155645	−	0.782483i
$86$		0			0
$87$	2.42093	+	5.84464i	0.259551	+	0.626611i
$88$		0			0
$89$	4.98881	−	12.0441i	0.528813	−	1.27667i	−0.403488	−	0.914985i	$-0.632202\pi$
$89$	4.98881	−	12.0441i	0.528813	−	1.27667i	0.932301	−	0.361683i	$-0.117798\pi$
$90$		0			0
$91$	0.135916	+	0.203412i	0.0142478	+	0.0213234i
$92$		0			0
$93$	12.5585	−	2.49803i	1.30225	−	0.259034i
$94$		0			0
$95$		−	7.47938i		−	0.767368i
$96$		0			0
$97$		−	4.06140i		−	0.412373i	−0.978513	−	0.206187i	$-0.933895\pi$
$97$		−	4.06140i		−	0.412373i	0.978513	−	0.206187i	$-0.0661054\pi$
$98$		0			0
$99$	20.3076	−	4.03944i	2.04099	−	0.405979i
$100$		0			0
$101$	−3.05636	−	4.57417i	−0.304119	−	0.455147i	0.647660	−	0.761929i	$-0.275748\pi$
$101$	−3.05636	−	4.57417i	−0.304119	−	0.455147i	−0.951780	+	0.306782i	$0.900748\pi$
$102$		0			0
$103$	5.12950	−	12.3837i	0.505425	−	1.22020i	−0.441066	−	0.897475i	$-0.645400\pi$
$103$	5.12950	−	12.3837i	0.505425	−	1.22020i	0.946491	−	0.322730i	$-0.104600\pi$
$104$		0			0
$105$	5.44506	+	13.1455i	0.531384	+	1.28287i
$106$		0			0
$107$	1.35370	−	6.80550i	0.130867	−	0.657913i	−0.858540	−	0.512746i	$-0.828628\pi$
$107$	1.35370	−	6.80550i	0.130867	−	0.657913i	0.989407	−	0.145167i	$-0.0463718\pi$
$108$		0			0
$109$	11.0688	−	16.5656i	1.06020	−	1.58670i	0.281225	−	0.959642i	$-0.409259\pi$
$109$	11.0688	−	16.5656i	1.06020	−	1.58670i	0.778973	−	0.627057i	$-0.215741\pi$
$110$		0			0
$111$	−21.4559	+	21.4559i	−2.03651	+	2.03651i
$112$		0			0
$113$	6.43123	+	6.43123i	0.605000	+	0.605000i	0.941635	−	0.336635i	$-0.109289\pi$
$113$	6.43123	+	6.43123i	0.605000	+	0.605000i	−0.336635	+	0.941635i	$0.609289\pi$
$114$		0			0
$115$	6.22783	+	4.16130i	0.580748	+	0.388044i
$116$		0			0
$117$	0.717085	+	0.142637i	0.0662945	+	0.0131868i
$118$		0			0
$119$	−6.82884	+	2.82860i	−0.625999	+	0.259297i
$120$		0			0
$121$	−0.630442	−	0.261137i	−0.0573129	−	0.0237398i
$122$		0			0
$123$	2.32099	−	1.55084i	0.209277	−	0.139834i
$124$		0			0
$125$	2.25827	+	11.3531i	0.201986	+	1.01545i
$126$		0			0
$127$	5.12090			0.454406			0.227203	−	0.973847i	$-0.427042\pi$
$127$	5.12090			0.454406			0.227203	+	0.973847i	$0.427042\pi$
$128$		0			0
$129$	−14.5859			−1.28422
$130$		0			0
$131$	−2.39632	−	12.0471i	−0.209368	−	1.05256i	−0.932312	−	0.361656i	$-0.882211\pi$
$131$	−2.39632	−	12.0471i	−0.209368	−	1.05256i	0.722944	−	0.690907i	$-0.242789\pi$
$132$		0			0
$133$	−6.24933	+	4.17567i	−0.541886	+	0.362076i
$134$		0			0
$135$	21.0027	+	8.69960i	1.80762	+	0.748742i
$136$		0			0
$137$	−1.03177	+	0.427371i	−0.0881496	+	0.0365128i	−0.426323	−	0.904571i	$-0.640191\pi$
$137$	−1.03177	+	0.427371i	−0.0881496	+	0.0365128i	0.338173	+	0.941084i	$0.390191\pi$
$138$		0			0
$139$	3.00073	+	0.596882i	0.254518	+	0.0506269i	0.320700	−	0.947181i	$-0.396082\pi$
$139$	3.00073	+	0.596882i	0.254518	+	0.0506269i	−0.0661819	+	0.997808i	$0.521082\pi$
$140$		0			0
$141$	−30.0531	−	20.0808i	−2.53093	−	1.69111i
$142$		0			0
$143$	0.257618	+	0.257618i	0.0215431	+	0.0215431i
$144$		0			0
$145$	−3.12399	+	3.12399i	−0.259433	+	0.259433i
$146$		0			0
$147$	−4.00890	+	5.99974i	−0.330648	+	0.494850i
$148$		0			0
$149$	0.649276	−	3.26413i	0.0531907	−	0.267408i	−0.945034	−	0.326973i	$-0.893971\pi$
$149$	0.649276	−	3.26413i	0.0531907	−	0.267408i	0.998224	+	0.0595651i	$0.0189714\pi$
$150$		0			0
$151$	1.38074	+	3.33339i	0.112363	+	0.271268i	0.970051	−	0.242903i	$-0.0780998\pi$
$151$	1.38074	+	3.33339i	0.112363	+	0.271268i	−0.857688	+	0.514171i	$0.828100\pi$
$152$		0			0
$153$	−8.45353	+	20.4086i	−0.683427	+	1.64994i
$154$		0			0
$155$	4.96802	+	7.43517i	0.399041	+	0.597207i
$156$		0			0
$157$	14.8431	−	2.95247i	1.18460	−	0.235633i	0.436805	−	0.899556i	$-0.356110\pi$
$157$	14.8431	−	2.95247i	1.18460	−	0.235633i	0.747800	+	0.663924i	$0.231110\pi$
$158$		0			0
$159$			1.77139i			0.140481i
$160$		0			0
$161$		−	7.52683i		−	0.593197i
$162$		0			0
$163$	14.0586	−	2.79643i	1.10115	−	0.219033i	0.389126	−	0.921185i	$-0.372777\pi$
$163$	14.0586	−	2.79643i	1.10115	−	0.219033i	0.712027	+	0.702152i	$0.247777\pi$
$164$		0			0
$165$	11.7723	+	17.6185i	0.916474	+	1.37160i
$166$		0			0
$167$	−2.52271	+	6.09036i	−0.195213	+	0.471286i	−0.990929	−	0.134383i	$-0.957095\pi$
$167$	−2.52271	+	6.09036i	−0.195213	+	0.471286i	0.795716	+	0.605670i	$0.207095\pi$
$168$		0			0
$169$	−4.96996	−	11.9985i	−0.382305	−	0.922965i
$170$		0			0
$171$	−4.38217	+	22.0307i	−0.335113	+	1.68473i
$172$		0			0
$173$	−10.9283	+	16.3554i	−0.830866	+	1.24348i	0.136637	+	0.990621i	$0.456371\pi$
$173$	−10.9283	+	16.3554i	−0.830866	+	1.24348i	−0.967503	+	0.252858i	$0.918629\pi$
$174$		0			0
$175$	0.599428	−	0.599428i	0.0453125	−	0.0453125i
$176$		0			0
$177$	1.69834	+	1.69834i	0.127655	+	0.127655i
$178$		0			0
$179$	1.59347	+	1.06472i	0.119102	+	0.0795812i	0.613694	−	0.789544i	$-0.289683\pi$
$179$	1.59347	+	1.06472i	0.119102	+	0.0795812i	−0.494593	+	0.869125i	$0.664683\pi$
$180$		0			0
$181$	19.2000	+	3.81912i	1.42713	+	0.283873i	0.847408	−	0.530943i	$-0.178162\pi$
$181$	19.2000	+	3.81912i	1.42713	+	0.283873i	0.579720	+	0.814816i	$0.303162\pi$
$182$		0			0
$183$	7.69588	−	3.18774i	0.568896	−	0.235644i
$184$		0			0
$185$	−19.5776	−	8.10931i	−1.43937	−	0.596209i
$186$		0			0
$187$	−9.15247	+	6.11549i	−0.669295	+	0.447209i
$188$		0			0
$189$	−4.45674	−	22.4055i	−0.324180	−	1.62976i
$190$		0			0
$191$	−12.6604			−0.916073			−0.458037	−	0.888933i	$-0.651447\pi$
$191$	−12.6604			−0.916073			−0.458037	+	0.888933i	$0.651447\pi$
$192$		0			0
$193$	6.31378			0.454476			0.227238	−	0.973839i	$-0.427030\pi$
$193$	6.31378			0.454476			0.227238	+	0.973839i	$0.427030\pi$
$194$		0			0
$195$	0.145972	+	0.733852i	0.0104533	+	0.0525522i
$196$		0			0
$197$	−19.2658	+	12.8730i	−1.37263	+	0.917163i	−0.999942	−	0.0107926i	$-0.996565\pi$
$197$	−19.2658	+	12.8730i	−1.37263	+	0.917163i	−0.372690	+	0.927956i	$0.621565\pi$
$198$		0			0
$199$	13.5609	+	5.61712i	0.961309	+	0.398187i	0.807470	−	0.589909i	$-0.200836\pi$
$199$	13.5609	+	5.61712i	0.961309	+	0.398187i	0.153839	+	0.988096i	$0.450836\pi$
$200$		0			0
$201$	14.1357	−	5.85522i	0.997059	−	0.412995i
$202$		0			0
$203$	4.35431	+	0.866127i	0.305613	+	0.0607902i
$204$		0			0
$205$	1.62090	+	1.08305i	0.113208	+	0.0756434i
$206$		0			0
$207$	−15.9061	−	15.9061i	−1.10555	−	1.10555i
$208$		0			0
$209$	−7.91466	+	7.91466i	−0.547469	+	0.547469i
$210$		0			0
$211$	1.35601	−	2.02941i	0.0933516	−	0.139711i	−0.781854	−	0.623461i	$-0.785726\pi$
$211$	1.35601	−	2.02941i	0.0933516	−	0.139711i	0.875206	+	0.483751i	$0.160726\pi$
$212$		0			0
$213$	−6.09103	+	30.6217i	−0.417350	+	2.09816i
$214$		0			0
$215$	−3.89811	−	9.41088i	−0.265849	−	0.641817i
$216$		0			0
$217$	3.43879	−	8.30198i	0.233440	−	0.563575i
$218$		0			0
$219$	−23.3434	−	34.9358i	−1.57740	−	2.36074i
$220$		0			0
$221$	−0.381221	+	0.0758296i	−0.0256437	+	0.00510085i
$222$		0			0
$223$			7.01617i			0.469838i	0.972015	+	0.234919i	$0.0754824\pi$
$223$			7.01617i			0.469838i	−0.972015	+	0.234919i	$0.924518\pi$
$224$		0			0
$225$		−	2.53349i		−	0.168899i
$226$		0			0
$227$	−16.9611	+	3.37378i	−1.12575	+	0.223925i	−0.722638	−	0.691226i	$-0.757071\pi$
$227$	−16.9611	+	3.37378i	−1.12575	+	0.223925i	−0.403110	+	0.915151i	$0.632071\pi$
$228$		0			0
$229$	−1.93254	−	2.89225i	−0.127706	−	0.191126i	0.762107	−	0.647451i	$-0.224165\pi$
$229$	−1.93254	−	2.89225i	−0.127706	−	0.191126i	−0.889813	+	0.456326i	$0.849165\pi$
$230$		0			0
$231$	8.14863	−	19.6725i	0.536141	−	1.29436i
$232$		0			0
$233$	10.0866	+	24.3511i	0.660794	+	1.59530i	0.796563	+	0.604556i	$0.206650\pi$
$233$	10.0866	+	24.3511i	0.660794	+	1.59530i	−0.135769	+	0.990741i	$0.543350\pi$
$234$		0			0
$235$	4.92448	−	24.7570i	0.321238	−	1.61497i
$236$		0			0
$237$	8.46462	−	12.6682i	0.549836	−	0.822888i
$238$		0			0
$239$	11.2250	−	11.2250i	0.726085	−	0.726085i	−0.243752	−	0.969838i	$-0.578378\pi$
$239$	11.2250	−	11.2250i	0.726085	−	0.726085i	0.969838	+	0.243752i	$0.0783783\pi$
$240$		0			0
$241$	−15.1085	−	15.1085i	−0.973222	−	0.973222i	0.0264284	−	0.999651i	$-0.491587\pi$
$241$	−15.1085	−	15.1085i	−0.973222	−	0.973222i	−0.999651	+	0.0264284i	$0.991587\pi$
$242$		0			0
$243$	−7.34826	−	4.90995i	−0.471391	−	0.314973i
$244$		0			0
$245$	−4.94245	−	0.983113i	−0.315761	−	0.0628088i
$246$		0			0
$247$	−0.365152	+	0.151251i	−0.0232341	+	0.00962387i
$248$		0			0
$249$	42.1916	+	17.4763i	2.67378	+	1.10752i
$250$		0			0
$251$	−0.246229	+	0.164525i	−0.0155419	+	0.0103847i	−0.563317	−	0.826241i	$-0.690475\pi$
$251$	−0.246229	+	0.164525i	−0.0155419	+	0.0103847i	0.547775	+	0.836626i	$0.315475\pi$
$252$		0			0
$253$	−2.18679	−	10.9938i	−0.137483	−	0.691172i
$254$		0			0
$255$	−22.6066			−1.41568
$256$		0			0
$257$	0.958734			0.0598042			0.0299021	−	0.999553i	$-0.490480\pi$
$257$	0.958734			0.0598042			0.0299021	+	0.999553i	$0.490480\pi$
$258$		0			0
$259$	4.15434	+	20.8853i	0.258138	+	1.29775i
$260$		0			0
$261$	11.0321	−	7.37142i	0.682870	−	0.456279i
$262$		0			0
$263$	−4.44089	−	1.83948i	−0.273837	−	0.113427i	0.241539	−	0.970391i	$-0.422348\pi$
$263$	−4.44089	−	1.83948i	−0.273837	−	0.113427i	−0.515376	+	0.856964i	$0.672348\pi$
$264$		0			0
$265$	−1.14291	+	0.473409i	−0.0702084	+	0.0290813i
$266$		0			0
$267$	−39.2968	−	7.81663i	−2.40493	−	0.478370i
$268$		0			0
$269$	3.61121	+	2.41293i	0.220179	+	0.147119i	0.660769	−	0.750590i	$-0.270230\pi$
$269$	3.61121	+	2.41293i	0.220179	+	0.147119i	−0.440589	+	0.897709i	$0.645230\pi$
$270$		0			0
$271$	10.6599	+	10.6599i	0.647540	+	0.647540i	0.952398	−	0.304858i	$-0.0986089\pi$
$271$	10.6599	+	10.6599i	0.647540	+	0.647540i	−0.304858	+	0.952398i	$0.598609\pi$
$272$		0			0
$273$	0.531669	−	0.531669i	0.0321781	−	0.0321781i
$274$		0			0
$275$	0.701377	−	1.04968i	0.0422946	−	0.0632984i
$276$		0			0
$277$	−0.0750905	+	0.377506i	−0.00451175	+	0.0226821i	−0.982976	−	0.183736i	$-0.941181\pi$
$277$	−0.0750905	+	0.377506i	−0.00451175	+	0.0226821i	0.978464	+	0.206418i	$0.0661808\pi$
$278$		0			0
$279$	−10.2771	−	24.8112i	−0.615276	−	1.48541i
$280$		0			0
$281$	−1.58445	+	3.82519i	−0.0945201	+	0.228192i	−0.964067	−	0.265658i	$-0.914411\pi$
$281$	−1.58445	+	3.82519i	−0.0945201	+	0.228192i	0.869547	+	0.493850i	$0.164411\pi$
$282$		0			0
$283$	5.06218	+	7.57609i	0.300915	+	0.450352i	0.950856	−	0.309633i	$-0.100206\pi$
$283$	5.06218	+	7.57609i	0.300915	+	0.450352i	−0.649941	+	0.759985i	$0.725206\pi$
$284$		0			0
$285$	−22.5458	+	4.48464i	−1.33550	+	0.265647i
$286$		0			0
$287$		−	1.95898i		−	0.115635i
$288$		0			0
$289$			5.25630i			0.309194i
$290$		0			0
$291$	−12.2427	+	2.43522i	−0.717678	+	0.142755i
$292$		0			0
$293$	−9.97915	−	14.9349i	−0.582988	−	0.872504i	0.416338	−	0.909210i	$-0.363313\pi$
$293$	−9.97915	−	14.9349i	−0.582988	−	0.872504i	−0.999326	+	0.0367064i	$0.988313\pi$
$294$		0			0
$295$	−0.641891	+	1.54966i	−0.0373723	+	0.0902248i
$296$		0			0
$297$	−13.0191	−	31.4309i	−0.755445	−	1.82381i
$298$		0			0
$299$	0.0772181	−	0.388202i	0.00446564	−	0.0224503i
$300$		0			0
$301$	−5.68690	+	8.51105i	−0.327787	+	0.490568i
$302$		0			0
$303$	−11.9557	+	11.9557i	−0.686840	+	0.686840i
$304$		0			0
$305$	4.11348	+	4.11348i	0.235537	+	0.235537i
$306$		0			0
$307$	19.6650	+	13.1398i	1.12234	+	0.749925i	0.971124	−	0.238575i	$-0.0766803\pi$
$307$	19.6650	+	13.1398i	1.12234	+	0.749925i	0.151219	+	0.988500i	$0.451680\pi$
$308$		0			0
$309$	−40.4050	−	8.03706i	−2.29856	−	0.457213i
$310$		0			0
$311$	5.33022	−	2.20785i	0.302249	−	0.125196i	−0.226404	−	0.974033i	$-0.572697\pi$
$311$	5.33022	−	2.20785i	0.302249	−	0.125196i	0.528654	+	0.848838i	$0.322697\pi$
$312$		0			0
$313$	6.66540	+	2.76090i	0.376751	+	0.156055i	0.563020	−	0.826444i	$-0.309640\pi$
$313$	6.66540	+	2.76090i	0.376751	+	0.156055i	−0.186269	+	0.982499i	$0.559640\pi$
$314$		0			0
$315$	24.8130	−	16.5795i	1.39806	−	0.934151i
$316$		0			0
$317$	6.63635	+	33.3632i	0.372734	+	1.87386i	0.476366	+	0.879247i	$0.341954\pi$
$317$	6.63635	+	33.3632i	0.372734	+	1.87386i	−0.103632	+	0.994616i	$0.533046\pi$
$318$		0			0
$319$	6.61159			0.370178
$320$		0			0
$321$	−21.3261			−1.19031
$322$		0			0
$323$	−2.32968	−	11.7121i	−0.129627	−	0.651678i
$324$		0			0
$325$	0.0370655	−	0.0247664i	0.00205603	−	0.00137379i
$326$		0			0
$327$	−56.5721	−	23.4330i	−3.12845	−	1.29585i
$328$		0			0
$329$	−23.4348	+	9.70702i	−1.29200	+	0.535165i
$330$		0			0
$331$	14.2233	+	2.82918i	0.781781	+	0.155506i	0.569817	−	0.821772i	$-0.307014\pi$
$331$	14.2233	+	2.82918i	0.781781	+	0.155506i	0.211964	+	0.977277i	$0.432014\pi$
$332$		0			0
$333$	52.9150	+	35.3567i	2.89972	+	1.93753i
$334$		0			0
$335$	7.55562	+	7.55562i	0.412808	+	0.412808i
$336$		0			0
$337$	−22.7689	+	22.7689i	−1.24030	+	1.24030i	−0.280423	+	0.959877i	$0.590475\pi$
$337$	−22.7689	+	22.7689i	−1.24030	+	1.24030i	−0.959877	+	0.280423i	$0.909525\pi$
$338$		0			0
$339$	15.5301	−	23.2424i	0.843479	−	1.26236i
$340$		0			0
$341$	2.61073	−	13.1250i	0.141379	−	0.710760i
$342$		0			0
$343$	7.71575	+	18.6275i	0.416611	+	1.00579i
$344$		0			0
$345$	8.80959	−	21.2682i	0.474293	−	1.14504i
$346$		0			0
$347$	5.44427	+	8.14793i	0.292264	+	0.437404i	0.948323	−	0.317305i	$-0.102778\pi$
$347$	5.44427	+	8.14793i	0.292264	+	0.437404i	−0.656060	+	0.754709i	$0.727778\pi$
$348$		0			0
$349$	−33.0492	+	6.57390i	−1.76909	+	0.351893i	−0.968822	−	0.247756i	$-0.920307\pi$
$349$	−33.0492	+	6.57390i	−1.76909	+	0.351893i	−0.800263	+	0.599649i	$0.795307\pi$
$350$		0			0
$351$		−	1.20130i		−	0.0641208i
$352$		0			0
$353$			17.4677i			0.929711i	0.885387	+	0.464856i	$0.153894\pi$
$353$			17.4677i			0.929711i	−0.885387	+	0.464856i	$0.846106\pi$
$354$		0			0
$355$	−21.3851	+	4.25376i	−1.13500	+	0.225766i
$356$		0			0
$357$	12.6211	+	18.8888i	0.667979	+	0.999701i
$358$		0			0
$359$	−6.92204	+	16.7113i	−0.365331	+	0.881987i	0.629171	+	0.777267i	$0.283395\pi$
$359$	−6.92204	+	16.7113i	−0.365331	+	0.881987i	−0.994502	+	0.104720i	$0.966605\pi$
$360$		0			0
$361$	2.62417	+	6.33532i	0.138114	+	0.333438i
$362$		0			0
$363$	−0.409158	+	2.05698i	−0.0214752	+	0.107963i
$364$		0			0
$365$	16.3022	−	24.3979i	0.853295	−	1.27705i
$366$		0			0
$367$	22.7264	−	22.7264i	1.18631	−	1.18631i	0.208226	−	0.978081i	$-0.433231\pi$
$367$	22.7264	−	22.7264i	1.18631	−	1.18631i	0.978081	−	0.208226i	$-0.0667690\pi$
$368$		0			0
$369$	−4.13983	−	4.13983i	−0.215511	−	0.215511i
$370$		0			0
$371$	1.03363	+	0.690649i	0.0536633	+	0.0358567i
$372$		0			0
$373$	4.36804	+	0.868856i	0.226168	+	0.0449877i	0.306873	−	0.951750i	$-0.400717\pi$
$373$	4.36804	+	0.868856i	0.226168	+	0.0449877i	−0.0807051	+	0.996738i	$0.525717\pi$
$374$		0			0
$375$	32.8686	−	13.6146i	1.69733	−	0.703057i
$376$		0			0
$377$	0.215691	+	0.0893422i	0.0111087	+	0.00460136i
$378$		0			0
$379$	−19.0406	+	12.7225i	−0.978052	+	0.653513i	−0.938346	−	0.345698i	$-0.887642\pi$
$379$	−19.0406	+	12.7225i	−0.978052	+	0.653513i	−0.0397061	+	0.999211i	$0.512642\pi$
$380$		0			0
$381$	−3.07049	−	15.4364i	−0.157306	−	0.790830i
$382$		0			0
$383$	9.58576			0.489809			0.244905	−	0.969547i	$-0.421243\pi$
$383$	9.58576			0.489809			0.244905	+	0.969547i	$0.421243\pi$
$384$		0			0
$385$	14.8705			0.757873
$386$		0			0
$387$	5.96814	+	30.0038i	0.303377	+	1.52518i
$388$		0			0
$389$	10.2676	−	6.86062i	0.520590	−	0.347847i	−0.267349	−	0.963600i	$-0.586148\pi$
$389$	10.2676	−	6.86062i	0.520590	−	0.347847i	0.787940	+	0.615752i	$0.211148\pi$
$390$		0			0
$391$	11.0484	+	4.57641i	0.558743	+	0.231439i
$392$		0			0
$393$	−34.8779	+	14.4469i	−1.75936	+	0.728751i
$394$		0			0
$395$	10.4358	+	2.07580i	0.525081	+	0.104445i
$396$		0			0
$397$	−6.79289	−	4.53886i	−0.340925	−	0.227799i	0.373307	−	0.927708i	$-0.378224\pi$
$397$	−6.79289	−	4.53886i	−0.340925	−	0.227799i	−0.714232	+	0.699909i	$0.753224\pi$
$398$		0			0
$399$	16.3342	+	16.3342i	0.817733	+	0.817733i
$400$		0			0
$401$	6.63465	−	6.63465i	0.331319	−	0.331319i	−0.521769	−	0.853087i	$-0.674728\pi$
$401$	6.63465	−	6.63465i	0.331319	−	0.331319i	0.853087	+	0.521769i	$0.174728\pi$
$402$		0			0
$403$	0.262529	−	0.392902i	0.0130775	−	0.0195718i
$404$		0			0
$405$	5.53311	−	27.8168i	0.274943	−	1.38223i
$406$		0			0
$407$	12.1357	+	29.2982i	0.601546	+	1.45226i
$408$		0			0
$409$	−3.09518	+	7.47242i	−0.153047	+	0.369487i	−0.981743	−	0.190211i	$-0.939083\pi$
$409$	−3.09518	+	7.47242i	−0.153047	+	0.369487i	0.828697	+	0.559698i	$0.189083\pi$
$410$		0			0
$411$	1.90691	+	2.85389i	0.0940610	+	0.140772i
$412$		0			0
$413$	1.65317	−	0.328836i	0.0813471	−	0.0161809i
$414$		0			0
$415$			31.8928i			1.56556i
$416$		0			0
$417$		−	9.40326i		−	0.460480i
$418$		0			0
$419$	−2.86945	+	0.570769i	−0.140182	+	0.0278839i	−0.264682	−	0.964336i	$-0.585267\pi$
$419$	−2.86945	+	0.570769i	−0.140182	+	0.0278839i	0.124501	+	0.992220i	$0.460267\pi$
$420$		0			0
$421$	11.9038	+	17.8153i	0.580157	+	0.868266i	0.999212	−	0.0396948i	$-0.0126386\pi$
$421$	11.9038	+	17.8153i	0.580157	+	0.868266i	−0.419055	+	0.907961i	$0.637639\pi$
$422$		0			0
$423$	−29.0103	+	70.0371i	−1.41053	+	3.40532i
$424$		0			0
$425$	0.515424	+	1.24434i	0.0250018	+	0.0603596i
$426$		0			0
$427$	1.14047	−	5.73351i	0.0551910	−	0.277464i
$428$		0			0
$429$	0.622093	−	0.931028i	0.0300349	−	0.0449505i
$430$		0			0
$431$	−8.75609	+	8.75609i	−0.421766	+	0.421766i	−0.885811	−	0.464045i	$-0.846397\pi$
$431$	−8.75609	+	8.75609i	−0.421766	+	0.421766i	0.464045	+	0.885811i	$0.346397\pi$
$432$		0			0
$433$	−13.9449	−	13.9449i	−0.670149	−	0.670149i	0.287601	−	0.957750i	$-0.407142\pi$
$433$	−13.9449	−	13.9449i	−0.670149	−	0.670149i	−0.957750	+	0.287601i	$0.907142\pi$
$434$		0			0
$435$	11.2901	+	7.54378i	0.541317	+	0.361696i
$436$		0			0
$437$	11.9265	+	2.37233i	0.570523	+	0.113484i
$438$		0			0
$439$	9.84033	−	4.07600i	0.469653	−	0.194537i	−0.135289	−	0.990806i	$-0.543196\pi$
$439$	9.84033	−	4.07600i	0.469653	−	0.194537i	0.604942	+	0.796270i	$0.293196\pi$
$440$		0			0
$441$	13.9821	+	5.79156i	0.665813	+	0.275789i
$442$		0			0
$443$	16.3602	−	10.9315i	0.777294	−	0.519371i	−0.102496	−	0.994733i	$-0.532683\pi$
$443$	16.3602	−	10.9315i	0.777294	−	0.519371i	0.879790	+	0.475362i	$0.157683\pi$
$444$		0			0
$445$	−5.45885	−	27.4435i	−0.258774	−	1.30095i
$446$		0			0
$447$	−10.2287			−0.483800
$448$		0			0
$449$	30.9457			1.46042			0.730209	−	0.683224i	$-0.239423\pi$
$449$	30.9457			1.46042			0.730209	+	0.683224i	$0.239423\pi$
$450$		0			0
$451$	−0.569150	−	2.86131i	−0.0268002	−	0.134734i
$452$		0			0
$453$	9.22026	−	6.16078i	0.433206	−	0.289459i
$454$		0			0
$455$	0.485125	+	0.200945i	0.0227430	+	0.00942046i
$456$		0			0
$457$	36.3997	−	15.0773i	1.70271	−	0.705285i	0.702727	−	0.711459i	$-0.251965\pi$
$457$	36.3997	−	15.0773i	1.70271	−	0.705285i	0.999981	+	0.00617459i	$0.00196544\pi$
$458$		0			0
$459$	35.5982	+	7.08092i	1.66158	+	0.330509i
$460$		0			0
$461$	−7.22960	−	4.83066i	−0.336716	−	0.224986i	0.375704	−	0.926740i	$-0.377401\pi$
$461$	−7.22960	−	4.83066i	−0.336716	−	0.224986i	−0.712420	+	0.701753i	$0.752401\pi$
$462$		0			0
$463$	−25.2338	−	25.2338i	−1.17271	−	1.17271i	−0.981560	−	0.191154i	$-0.938777\pi$
$463$	−25.2338	−	25.2338i	−1.17271	−	1.17271i	−0.191154	−	0.981560i	$-0.561223\pi$
$464$		0			0
$465$	19.4337	−	19.4337i	0.901216	−	0.901216i
$466$		0			0
$467$	20.5128	−	30.6996i	0.949220	−	1.42061i	0.0423942	−	0.999101i	$-0.486501\pi$
$467$	20.5128	−	30.6996i	0.949220	−	1.42061i	0.906825	−	0.421507i	$-0.138499\pi$
$468$		0			0
$469$	2.09480	−	10.5313i	0.0967289	−	0.486289i
$470$		0			0
$471$	−17.7998	−	42.9725i	−0.820171	−	1.98007i
$472$		0			0
$473$	−5.83360	+	14.0835i	−0.268229	+	0.647562i
$474$		0			0
$475$	0.760886	+	1.13875i	0.0349118	+	0.0522493i
$476$		0			0
$477$	3.64383	−	0.724804i	0.166840	−	0.0331865i
$478$		0			0
$479$		−	22.3832i		−	1.02271i	−0.859368	−	0.511357i	$-0.829143\pi$
$479$		−	22.3832i		−	1.02271i	0.859368	−	0.511357i	$-0.170857\pi$
$480$		0			0
$481$			1.11979i			0.0510581i
$482$		0			0
$483$	−22.6888	+	4.51309i	−1.03238	+	0.205353i
$484$		0			0
$485$	−4.84310	−	7.24821i	−0.219914	−	0.329124i
$486$		0			0
$487$	13.3025	−	32.1150i	0.602792	−	1.45527i	−0.267902	−	0.963446i	$-0.586330\pi$
$487$	13.3025	−	32.1150i	0.602792	−	1.45527i	0.870695	−	0.491824i	$-0.163670\pi$
$488$		0			0
$489$	−16.8591	−	40.7014i	−0.762393	−	1.84058i
$490$		0			0
$491$	−5.09965	+	25.6377i	−0.230144	+	1.15701i	0.676933	+	0.736045i	$0.263309\pi$
$491$	−5.09965	+	25.6377i	−0.230144	+	1.15701i	−0.907076	+	0.420966i	$0.861691\pi$
$492$		0			0
$493$	−3.91884	+	5.86496i	−0.176496	+	0.264144i
$494$		0			0
$495$	31.4252	−	31.4252i	1.41246	−	1.41246i
$496$		0			0
$497$	15.4933	+	15.4933i	0.694969	+	0.694969i
$498$		0			0
$499$	−27.9332	−	18.6644i	−1.25046	−	0.835532i	−0.258994	−	0.965879i	$-0.583391\pi$
$499$	−27.9332	−	18.6644i	−1.25046	−	0.835532i	−0.991468	+	0.130347i	$0.958391\pi$
$500$		0			0
$501$	19.8714	+	3.95266i	0.887787	+	0.176592i
$502$		0			0
$503$	−20.0549	+	8.30702i	−0.894205	+	0.370392i	−0.781989	−	0.623292i	$-0.785795\pi$
$503$	−20.0549	+	8.30702i	−0.894205	+	0.370392i	−0.112216	+	0.993684i	$0.535795\pi$
$504$		0			0
$505$	−10.9091	−	4.51870i	−0.485449	−	0.201079i
$506$		0			0
$507$	−33.1883	+	22.1757i	−1.47395	+	0.984859i
$508$		0			0
$509$	0.581805	+	2.92493i	0.0257881	+	0.129645i	0.991535	−	0.129841i	$-0.0414467\pi$
$509$	0.581805	+	2.92493i	0.0257881	+	0.129645i	−0.965747	+	0.259486i	$0.916447\pi$
$510$		0			0
$511$	−29.4868			−1.30442
$512$		0			0
$513$	36.9071			1.62949
$514$		0			0
$515$	−5.61280	−	28.2174i	−0.247329	−	1.24341i
$516$		0			0
$517$	−31.4089	+	20.9868i	−1.38136	+	0.922996i
$518$		0			0
$519$	55.8543	+	23.1356i	2.45173	+	1.01554i
$520$		0			0
$521$	−18.7789	+	7.77848i	−0.822719	+	0.340781i	−0.754016	−	0.656856i	$-0.771886\pi$
$521$	−18.7789	+	7.77848i	−0.822719	+	0.340781i	−0.0687028	+	0.997637i	$0.521886\pi$
$522$		0			0
$523$	13.4384	+	2.67306i	0.587620	+	0.116885i	0.479941	−	0.877301i	$-0.340658\pi$
$523$	13.4384	+	2.67306i	0.587620	+	0.116885i	0.107679	+	0.994186i	$0.465658\pi$
$524$		0			0
$525$	−2.16633	−	1.44750i	−0.0945464	−	0.0631739i
$526$		0			0
$527$	10.0954	+	10.0954i	0.439763	+	0.439763i
$528$		0			0
$529$	7.65252	−	7.65252i	0.332718	−	0.332718i
$530$		0			0
$531$	2.79865	−	4.18848i	0.121451	−	0.181764i
$532$		0			0
$533$	0.0200973	−	0.101036i	0.000870511	−	0.00437635i
$534$		0			0
$535$	−5.69946	−	13.7597i	−0.246409	−	0.594884i
$536$		0			0
$537$	2.25405	−	5.44176i	0.0972694	−	0.234829i
$538$		0			0
$539$	4.18976	+	6.27041i	0.180466	+	0.270086i
$540$		0			0
$541$	−7.53938	+	1.49968i	−0.324143	+	0.0644761i	−0.354480	−	0.935064i	$-0.615342\pi$
$541$	−7.53938	+	1.49968i	−0.324143	+	0.0644761i	0.0303365	+	0.999540i	$0.490342\pi$
$542$		0			0
$543$		−	60.1664i		−	2.58199i
$544$		0			0
$545$		−	42.7631i		−	1.83177i
$546$		0			0
$547$	23.2900	−	4.63267i	0.995809	−	0.198079i	0.329823	−	0.944043i	$-0.393011\pi$
$547$	23.2900	−	4.63267i	0.995809	−	0.198079i	0.665986	+	0.745964i	$0.268011\pi$
$548$		0			0
$549$	−9.70626	−	14.5264i	−0.414253	−	0.619974i
$550$		0			0
$551$	−2.74482	+	6.62658i	−0.116933	+	0.282302i
$552$		0			0
$553$	−4.09178	−	9.87842i	−0.174000	−	0.420073i
$554$		0			0
$555$	−12.7059	+	63.8770i	−0.539336	+	2.71143i
$556$		0			0
$557$	7.86803	−	11.7753i	0.333379	−	0.498937i	−0.626473	−	0.779443i	$-0.715502\pi$
$557$	7.86803	−	11.7753i	0.333379	−	0.498937i	0.959852	+	0.280506i	$0.0905023\pi$
$558$		0			0
$559$	−0.380621	+	0.380621i	−0.0160986	+	0.0160986i
$560$		0			0
$561$	23.9223	+	23.9223i	1.01000	+	1.01000i
$562$		0			0
$563$	−5.80935	−	3.88168i	−0.244835	−	0.163593i	0.427098	−	0.904205i	$-0.359536\pi$
$563$	−5.80935	−	3.88168i	−0.244835	−	0.163593i	−0.671933	+	0.740612i	$0.734536\pi$
$564$		0			0
$565$	19.1466	+	3.80849i	0.805502	+	0.160224i
$566$		0			0
$567$	−26.3312	+	10.9067i	−1.10581	+	0.458040i
$568$		0			0
$569$	−17.1266	−	7.09406i	−0.717983	−	0.297398i	−0.00637952	−	0.999980i	$-0.502031\pi$
$569$	−17.1266	−	7.09406i	−0.717983	−	0.297398i	−0.711603	+	0.702581i	$0.752031\pi$
$570$		0			0
$571$	1.16513	−	0.778514i	0.0487591	−	0.0325798i	−0.530952	−	0.847402i	$-0.678165\pi$
$571$	1.16513	−	0.778514i	0.0487591	−	0.0325798i	0.579711	+	0.814822i	$0.303165\pi$
$572$		0			0
$573$	7.59116	+	38.1634i	0.317125	+	1.59430i
$574$		0			0
$575$	−1.37153			−0.0571968
$576$		0			0
$577$	28.1108			1.17027			0.585135	−	0.810936i	$-0.301042\pi$
$577$	28.1108			1.17027			0.585135	+	0.810936i	$0.301042\pi$
$578$		0			0
$579$	−3.78574	−	19.0322i	−0.157330	−	0.790952i
$580$		0			0
$581$	26.6478	−	17.8055i	1.10554	−	0.738695i
$582$		0			0
$583$	1.71038	+	0.708464i	0.0708369	+	0.0293416i
$584$		0			0
$585$	1.44984	−	0.600543i	0.0599435	−	0.0248294i
$586$		0			0
$587$	11.1359	+	2.21507i	0.459629	+	0.0914258i	0.419473	−	0.907768i	$-0.362215\pi$
$587$	11.1359	+	2.21507i	0.459629	+	0.0914258i	0.0401553	+	0.999193i	$0.487215\pi$
$588$		0			0
$589$	12.0709	+	8.06554i	0.497374	+	0.332335i
$590$		0			0
$591$	50.3561	+	50.3561i	2.07137	+	2.07137i
$592$		0			0
$593$	5.38627	−	5.38627i	0.221188	−	0.221188i	−0.587811	−	0.808998i	$-0.700010\pi$
$593$	5.38627	−	5.38627i	0.221188	−	0.221188i	0.808998	+	0.587811i	$0.200010\pi$
$594$		0			0
$595$	−8.81411	+	13.1913i	−0.361343	+	0.540789i
$596$		0			0
$597$	8.80108	−	44.2460i	0.360204	−	1.81087i
$598$		0			0
$599$	10.9367	+	26.4036i	0.446863	+	1.07882i	0.973491	+	0.228727i	$0.0734563\pi$
$599$	10.9367	+	26.4036i	0.446863	+	1.07882i	−0.526627	+	0.850096i	$0.676544\pi$
$600$		0			0
$601$	−8.76796	+	21.1677i	−0.357653	+	0.863450i	0.637977	+	0.770056i	$0.279772\pi$
$601$	−8.76796	+	21.1677i	−0.357653	+	0.863450i	−0.995629	+	0.0933942i	$0.970228\pi$
$602$		0			0
$603$	−17.8284	−	26.6821i	−0.726029	−	1.08658i
$604$		0			0
$605$	−1.43652	+	0.285741i	−0.0584028	+	0.0116170i
$606$		0			0
$607$			27.1652i			1.10260i	0.834306	+	0.551301i	$0.185868\pi$
$607$			27.1652i			1.10260i	−0.834306	+	0.551301i	$0.814132\pi$
$608$		0			0
$609$		−	13.6449i		−	0.552921i
$610$		0			0
$611$	−1.30825	+	0.260227i	−0.0529262	+	0.0105277i
$612$		0			0
$613$	4.77987	+	7.15358i	0.193057	+	0.288930i	0.915352	−	0.402655i	$-0.131913\pi$
$613$	4.77987	+	7.15358i	0.193057	+	0.288930i	−0.722295	+	0.691585i	$0.756913\pi$
$614$		0			0
$615$	2.29285	−	5.53542i	0.0924564	−	0.223210i
$616$		0			0
$617$	−3.84308	−	9.27803i	−0.154717	−	0.373519i	0.827448	−	0.561543i	$-0.189792\pi$
$617$	−3.84308	−	9.27803i	−0.154717	−	0.373519i	−0.982165	+	0.188023i	$0.939792\pi$
$618$		0			0
$619$	−0.956021	+	4.80624i	−0.0384257	+	0.193179i	−0.995230	−	0.0975524i	$-0.968899\pi$
$619$	−0.956021	+	4.80624i	−0.0384257	+	0.193179i	0.956805	+	0.290732i	$0.0938987\pi$
$620$		0			0
$621$	−20.5340	+	30.7313i	−0.824000	+	1.23320i
$622$		0			0
$623$	−19.8826	+	19.8826i	−0.796578	+	0.796578i
$624$		0			0
$625$	16.1789	+	16.1789i	0.647155	+	0.647155i
$626$		0			0
$627$	28.6035	+	19.1123i	1.14231	+	0.763270i
$628$		0			0
$629$	−33.1828	−	6.60047i	−1.32308	−	0.263178i
$630$		0			0
$631$	−4.21091	+	1.74421i	−0.167634	+	0.0694361i	−0.464922	−	0.885352i	$-0.653918\pi$
$631$	−4.21091	+	1.74421i	−0.167634	+	0.0694361i	0.297289	+	0.954788i	$0.403918\pi$
$632$		0			0
$633$	−6.93051	−	2.87071i	−0.275463	−	0.114101i
$634$		0			0
$635$	9.13903	−	6.10650i	0.362671	−	0.242329i
$636$		0			0
$637$	0.0519513	+	0.261177i	0.00205839	+	0.0103482i
$638$		0			0
$639$	65.4825			2.59045
$640$		0			0
$641$	−18.0849			−0.714310			−0.357155	−	0.934045i	$-0.616253\pi$
$641$	−18.0849			−0.714310			−0.357155	+	0.934045i	$0.616253\pi$
$642$		0			0
$643$	−1.42112	−	7.14443i	−0.0560433	−	0.281749i	0.942594	−	0.333942i	$-0.108379\pi$
$643$	−1.42112	−	7.14443i	−0.0560433	−	0.281749i	−0.998637	+	0.0521929i	$0.983379\pi$
$644$		0			0
$645$	−26.0308	+	17.3932i	−1.02496	+	0.684857i
$646$		0			0
$647$	−3.05247	−	1.26437i	−0.120005	−	0.0497076i	0.321873	−	0.946783i	$-0.395688\pi$
$647$	−3.05247	−	1.26437i	−0.120005	−	0.0497076i	−0.441878	+	0.897075i	$0.645688\pi$
$648$		0			0
$649$	2.31910	−	0.960601i	0.0910325	−	0.0377069i
$650$		0			0
$651$	−27.0873	−	5.38800i	−1.06164	−	0.211172i
$652$		0			0
$653$	−10.1827	−	6.80383i	−0.398478	−	0.266254i	0.340145	−	0.940373i	$-0.389524\pi$
$653$	−10.1827	−	6.80383i	−0.398478	−	0.266254i	−0.738623	+	0.674118i	$0.764524\pi$
$654$		0			0
$655$	−18.6424	−	18.6424i	−0.728420	−	0.728420i
$656$		0			0
$657$	−62.3131	+	62.3131i	−2.43107	+	2.43107i
$658$		0			0
$659$	−14.7692	+	22.1037i	−0.575328	+	0.861039i	−0.998997	−	0.0447783i	$-0.985742\pi$
$659$	−14.7692	+	22.1037i	−0.575328	+	0.861039i	0.423669	+	0.905817i	$0.360742\pi$
$660$		0			0
$661$	−2.82505	+	14.2025i	−0.109882	+	0.552412i	0.886149	+	0.463400i	$0.153371\pi$
$661$	−2.82505	+	14.2025i	−0.109882	+	0.552412i	−0.996031	+	0.0890116i	$0.971629\pi$
$662$		0			0
$663$	0.457161	+	1.10368i	0.0177546	+	0.0428635i
$664$		0			0
$665$	−6.17355	+	14.9043i	−0.239400	+	0.577962i
$666$		0			0
$667$	−3.99060	−	5.97235i	−0.154516	−	0.231250i
$668$		0			0
$669$	21.1495	−	4.20690i	0.817687	−	0.162648i
$670$		0			0
$671$		−	8.70576i		−	0.336082i
$672$		0			0
$673$		−	26.9629i		−	1.03934i	−0.854366	−	0.519671i	$-0.826054\pi$
$673$		−	26.9629i		−	1.03934i	0.854366	−	0.519671i	$-0.173946\pi$
$674$		0			0
$675$	−4.08271	+	0.812101i	−0.157144	+	0.0312578i
$676$		0			0
$677$	9.17925	+	13.7377i	0.352787	+	0.527984i	0.964842	−	0.262832i	$-0.0846566\pi$
$677$	9.17925	+	13.7377i	0.352787	+	0.527984i	−0.612054	+	0.790816i	$0.709657\pi$
$678$		0			0
$679$	−3.35232	+	8.09321i	−0.128650	+	0.310589i
$680$		0			0
$681$	20.3398	+	49.1045i	0.779422	+	1.88169i
$682$		0			0
$683$	−3.67420	+	18.4714i	−0.140589	+	0.706790i	0.844611	+	0.535381i	$0.179832\pi$
$683$	−3.67420	+	18.4714i	−0.140589	+	0.706790i	−0.985200	+	0.171409i	$0.945168\pi$
$684$		0			0
$685$	−1.33172	+	1.99306i	−0.0508823	+	0.0761508i
$686$		0			0
$687$	−7.55964	+	7.55964i	−0.288418	+	0.288418i
$688$		0			0
$689$	0.0462248	+	0.0462248i	0.00176102	+	0.00176102i
$690$		0			0
$691$	−22.5013	−	15.0349i	−0.855989	−	0.571953i	0.0483204	−	0.998832i	$-0.484613\pi$
$691$	−22.5013	−	15.0349i	−0.855989	−	0.571953i	−0.904309	+	0.426879i	$0.859613\pi$
$692$		0			0
$693$	−43.8015	−	8.71266i	−1.66388	−	0.330967i
$694$		0			0
$695$	6.06703	−	2.51304i	0.230135	−	0.0953252i
$696$		0			0
$697$	2.87554	+	1.19109i	0.108919	+	0.0451156i
$698$		0			0
$699$	67.3560	−	45.0058i	2.54764	−	1.70228i
$700$		0			0
$701$	4.62224	+	23.2376i	0.174579	+	0.877670i	0.964423	+	0.264362i	$0.0851615\pi$
$701$	4.62224	+	23.2376i	0.174579	+	0.877670i	−0.789844	+	0.613308i	$0.789838\pi$
$702$		0			0
$703$	−34.4028			−1.29753
$704$		0			0
$705$	−77.5801			−2.92184
$706$		0			0
$707$	2.31489	+	11.6378i	0.0870605	+	0.437683i
$708$		0			0
$709$	−16.3280	+	10.9100i	−0.613211	+	0.409734i	−0.823024	−	0.568007i	$-0.807715\pi$
$709$	−16.3280	+	10.9100i	−0.613211	+	0.409734i	0.209813	+	0.977742i	$0.432715\pi$
$710$		0			0
$711$	−29.5226	−	12.2286i	−1.10718	−	0.458610i
$712$		0			0
$713$	−13.4318	+	5.56364i	−0.503025	+	0.208360i
$714$		0			0
$715$	0.766959	+	0.152558i	0.0286826	+	0.00570533i
$716$		0			0
$717$	−40.5671	−	27.1061i	−1.51501	−	1.01229i
$718$		0			0
$719$	−3.45757	−	3.45757i	−0.128946	−	0.128946i	0.639689	−	0.768634i	$-0.279063\pi$
$719$	−3.45757	−	3.45757i	−0.128946	−	0.128946i	−0.768634	+	0.639689i	$0.779063\pi$
$720$		0			0
$721$	−20.4433	+	20.4433i	−0.761347	+	0.761347i
$722$		0			0
$723$	−36.4838	+	54.6019i	−1.35685	+	2.03067i
$724$		0			0
$725$	0.157825	−	0.793438i	0.00586146	−	0.0294676i
$726$		0			0
$727$	−14.0936	−	34.0251i	−0.522704	−	1.26192i	−0.936217	−	0.351421i	$-0.885698\pi$
$727$	−14.0936	−	34.0251i	−0.522704	−	1.26192i	0.413513	−	0.910498i	$-0.364302\pi$
$728$		0			0
$729$	4.77554	−	11.5292i	0.176872	−	0.427007i
$730$		0			0
$731$	−9.03542	−	13.5225i	−0.334187	−	0.500146i
$732$		0			0
$733$	9.93170	−	1.97554i	0.366836	−	0.0729681i	−0.00823071	−	0.999966i	$-0.502620\pi$
$733$	9.93170	−	1.97554i	0.366836	−	0.0729681i	0.375066	+	0.926998i	$0.377620\pi$
$734$		0			0
$735$			15.4879i			0.571281i
$736$		0			0
$737$		−	15.9907i		−	0.589025i
$738$		0			0
$739$	47.0664	−	9.36209i	1.73137	−	0.344390i	0.773982	−	0.633207i	$-0.218262\pi$
$739$	47.0664	−	9.36209i	1.73137	−	0.344390i	0.957384	+	0.288817i	$0.0932620\pi$
$740$		0			0
$741$	0.674875	+	1.01002i	0.0247922	+	0.0371041i
$742$		0			0
$743$	8.63374	−	20.8437i	0.316741	−	0.764681i	−0.682682	−	0.730716i	$-0.739186\pi$
$743$	8.63374	−	20.8437i	0.316741	−	0.764681i	0.999423	−	0.0339651i	$-0.0108135\pi$
$744$		0			0
$745$	−2.73364	−	6.59958i	−0.100153	−	0.241790i
$746$		0			0
$747$	18.6860	−	93.9409i	0.683685	−	3.43712i
$748$		0			0
$749$	−8.31486	+	12.4441i	−0.303818	+	0.454696i
$750$		0			0
$751$	−6.86892	+	6.86892i	−0.250650	+	0.250650i	−0.821237	−	0.570587i	$-0.806716\pi$
$751$	−6.86892	+	6.86892i	−0.250650	+	0.250650i	0.570587	+	0.821237i	$0.306716\pi$
$752$		0			0
$753$	0.643583	+	0.643583i	0.0234535	+	0.0234535i
$754$		0			0
$755$	6.43910	+	4.30247i	0.234343	+	0.156583i
$756$		0			0
$757$	20.6195	+	4.10147i	0.749428	+	0.149070i	0.555005	−	0.831847i	$-0.312716\pi$
$757$	20.6195	+	4.10147i	0.749428	+	0.149070i	0.194423	+	0.980918i	$0.437716\pi$
$758$		0			0
$759$	−31.8283	+	13.1837i	−1.15529	+	0.478539i
$760$		0			0
$761$	−2.27046	−	0.940453i	−0.0823039	−	0.0340914i	0.341152	−	0.940008i	$-0.389183\pi$
$761$	−2.27046	−	0.940453i	−0.0823039	−	0.0340914i	−0.423456	+	0.905917i	$0.639183\pi$
$762$		0			0
$763$	−35.7303	+	23.8743i	−1.29353	+	0.864306i
$764$		0			0
$765$	9.25000	+	46.5029i	0.334435	+	1.68132i
$766$		0			0
$767$	0.0886369			0.00320049
$768$		0			0
$769$	−3.66124			−0.132028			−0.0660139	−	0.997819i	$-0.521028\pi$
$769$	−3.66124			−0.132028			−0.0660139	+	0.997819i	$0.521028\pi$
$770$		0			0
$771$	−0.574857	−	2.89000i	−0.0207030	−	0.104081i
$772$		0			0
$773$	35.7598	−	23.8939i	1.28619	−	0.859404i	0.290938	−	0.956742i	$-0.406033\pi$
$773$	35.7598	−	23.8939i	1.28619	−	0.859404i	0.995251	+	0.0973381i	$0.0310328\pi$
$774$		0			0
$775$	−1.51278	−	0.626613i	−0.0543406	−	0.0225086i
$776$		0			0
$777$	60.4654	−	25.0456i	2.16919	−	0.898506i
$778$		0			0
$779$	3.10408	+	0.617440i	0.111215	+	0.0221221i
$780$		0			0
$781$	27.1310	+	18.1283i	0.970822	+	0.648682i
$782$		0			0
$783$	−15.4153	−	15.4153i	−0.550899	−	0.550899i
$784$		0			0
$785$	22.9690	−	22.9690i	0.819799	−	0.819799i
$786$		0			0
$787$	17.0932	−	25.5818i	0.609308	−	0.911894i	−0.390655	−	0.920537i	$-0.627751\pi$
$787$	17.0932	−	25.5818i	0.609308	−	0.911894i	0.999963	+	0.00864361i	$0.00275138\pi$
$788$		0			0
$789$	−2.88215	+	14.4895i	−0.102607	+	0.515842i
$790$		0			0
$791$	−7.50721	−	18.1240i	−0.266926	−	0.644415i
$792$		0			0
$793$	0.117641	−	0.284010i	0.00417754	−	0.0100855i
$794$		0			0
$795$	2.11233	+	3.16132i	0.0749166	+	0.112121i
$796$		0			0
$797$	3.59248	−	0.714589i	0.127252	−	0.0253120i	−0.131053	−	0.991375i	$-0.541836\pi$
$797$	3.59248	−	0.714589i	0.127252	−	0.0253120i	0.258306	+	0.966063i	$0.416836\pi$
$798$		0			0
$799$		−	40.3013i		−	1.42576i
$800$		0			0
$801$			84.0337i			2.96919i
$802$		0			0
$803$	−43.0688	+	8.56691i	−1.51986	+	0.302320i
$804$		0			0
$805$	−8.97550	−	13.4328i	−0.316345	−	0.473444i
$806$		0			0
$807$	5.10825	−	12.3324i	0.179819	−	0.434121i
$808$		0			0
$809$	−4.56231	−	11.0144i	−0.160402	−	0.387245i	0.823161	−	0.567808i	$-0.192208\pi$
$809$	−4.56231	−	11.0144i	−0.160402	−	0.387245i	−0.983564	+	0.180562i	$0.942208\pi$
$810$		0			0
$811$	0.413214	−	2.07737i	0.0145099	−	0.0729462i	−0.972852	−	0.231428i	$-0.925660\pi$
$811$	0.413214	−	2.07737i	0.0145099	−	0.0729462i	0.987362	+	0.158482i	$0.0506601\pi$
$812$		0			0
$813$	25.7413	−	38.5246i	0.902788	−	1.35112i
$814$		0			0
$815$	21.7551	−	21.7551i	0.762047	−	0.762047i
$816$		0			0
$817$	−11.6936	−	11.6936i	−0.409109	−	0.409109i
$818$		0			0
$819$	−1.31121	−	0.876123i	−0.0458174	−	0.0306142i
$820$		0			0
$821$	46.0479	+	9.15949i	1.60708	+	0.319668i	0.915403	−	0.402538i	$-0.131872\pi$
$821$	46.0479	+	9.15949i	1.60708	+	0.319668i	0.691678	+	0.722206i	$0.256872\pi$
$822$		0			0
$823$	−43.8242	+	18.1526i	−1.52761	+	0.632759i	−0.979099	−	0.203382i	$-0.934807\pi$
$823$	−43.8242	+	18.1526i	−1.52761	+	0.632759i	−0.548515	+	0.836141i	$0.684807\pi$
$824$		0			0
$825$	−3.58471	−	1.48483i	−0.124804	−	0.0516953i
$826$		0			0
$827$	−7.79161	+	5.20619i	−0.270941	+	0.181037i	−0.683617	−	0.729841i	$-0.739594\pi$
$827$	−7.79161	+	5.20619i	−0.270941	+	0.181037i	0.412676	+	0.910878i	$0.364594\pi$
$828$		0			0
$829$	−10.9119	−	54.8578i	−0.378986	−	1.90529i	−0.422747	−	0.906248i	$-0.638934\pi$
$829$	−10.9119	−	54.8578i	−0.378986	−	1.90529i	0.0437617	−	0.999042i	$-0.486066\pi$
$830$		0			0
$831$	1.18297			0.0410369
$832$		0			0
$833$	−8.04568			−0.278766
$834$		0			0
$835$	2.76040	+	13.8774i	0.0955274	+	0.480249i
$836$		0			0
$837$	−36.6889	+	24.5147i	−1.26815	+	0.847354i
$838$		0			0
$839$	−38.4928	−	15.9443i	−1.32892	−	0.550457i	−0.398573	−	0.917137i	$-0.630494\pi$
$839$	−38.4928	−	15.9443i	−1.32892	−	0.550457i	−0.930347	+	0.366680i	$0.880494\pi$
$840$		0			0
$841$	−22.8783	+	9.47649i	−0.788906	+	0.326775i
$842$		0			0
$843$	12.4807	+	2.48256i	0.429857	+	0.0855038i
$844$		0			0
$845$	−23.1776	−	15.4867i	−0.797332	−	0.532760i
$846$		0			0
$847$	1.04074	+	1.04074i	0.0357604	+	0.0357604i
$848$		0			0
$849$	19.8020	−	19.8020i	0.679604	−	0.679604i
$850$		0			0
$851$	19.1407	−	28.6461i	0.656135	−	0.981976i
$852$		0			0
$853$	3.22130	−	16.1946i	0.110295	−	0.554491i	−0.885636	−	0.464379i	$-0.846277\pi$
$853$	3.22130	−	16.1946i	0.110295	−	0.554491i	0.995932	−	0.0901121i	$-0.0287225\pi$
$854$		0			0
$855$	18.4502	+	44.5427i	0.630984	+	1.52333i
$856$		0			0
$857$	−3.26603	+	7.88490i	−0.111566	+	0.269343i	−0.969794	−	0.243924i	$-0.921565\pi$
$857$	−3.26603	+	7.88490i	−0.111566	+	0.269343i	0.858229	+	0.513267i	$0.171565\pi$
$858$		0			0
$859$	−3.93549	−	5.88988i	−0.134277	−	0.200960i	0.758237	−	0.651979i	$-0.226061\pi$
$859$	−3.93549	−	5.88988i	−0.134277	−	0.200960i	−0.892515	+	0.451019i	$0.851061\pi$
$860$		0			0
$861$	−5.90515	+	1.17461i	−0.201247	+	0.0400305i
$862$		0			0
$863$		−	17.7071i		−	0.602756i	−0.953505	−	0.301378i	$-0.902553\pi$
$863$		−	17.7071i		−	0.602756i	0.953505	−	0.301378i	$-0.0974466\pi$
$864$		0			0
$865$			42.2205i			1.43554i
$866$		0			0
$867$	15.8446	−	3.15168i	0.538110	−	0.107037i
$868$		0			0
$869$	−8.84650	−	13.2397i	−0.300097	−	0.449127i
$870$		0			0
$871$	0.216082	−	0.521667i	0.00732165	−	0.0176760i
$872$		0			0
$873$	10.0187	+	24.1873i	0.339082	+	0.818616i
$874$		0			0
$875$	4.87086	−	24.4875i	0.164665	−	0.827827i
$876$		0			0
$877$	−23.3455	+	34.9391i	−0.788323	+	1.17981i	0.191804	+	0.981433i	$0.438566\pi$
$877$	−23.3455	+	34.9391i	−0.788323	+	1.17981i	−0.980126	+	0.198375i	$0.936434\pi$
$878$		0			0
$879$	−39.0360	+	39.0360i	−1.31665	+	1.31665i
$880$		0			0
$881$	−22.0191	−	22.0191i	−0.741844	−	0.741844i	0.231089	−	0.972933i	$-0.425771\pi$
$881$	−22.0191	−	22.0191i	−0.741844	−	0.741844i	−0.972933	+	0.231089i	$0.925771\pi$
$882$		0			0
$883$	−37.7422	−	25.2185i	−1.27012	−	0.848670i	−0.276457	−	0.961026i	$-0.589160\pi$
$883$	−37.7422	−	25.2185i	−1.27012	−	0.848670i	−0.993668	+	0.112356i	$0.964160\pi$
$884$		0			0
$885$	5.05617	+	1.00573i	0.169961	+	0.0338074i
$886$		0			0
$887$	44.8061	−	18.5593i	1.50444	−	0.623160i	0.530040	−	0.847973i	$-0.322177\pi$
$887$	44.8061	−	18.5593i	1.50444	−	0.623160i	0.974402	+	0.224812i	$0.0721769\pi$
$888$		0			0
$889$	−10.2045	−	4.22683i	−0.342247	−	0.141763i
$890$		0			0
$891$	−35.2908	+	23.5806i	−1.18229	+	0.789979i
$892$		0			0
$893$	−7.99485	−	40.1928i	−0.267537	−	1.34500i
$894$		0			0
$895$	4.11345			0.137497
$896$		0			0
$897$	−1.21649			−0.0406175
$898$		0			0
$899$	−1.67297	−	8.41060i	−0.0557968	−	0.280509i
$900$		0			0
$901$	−1.64224	+	1.09731i	−0.0547111	+	0.0365568i
$902$		0			0
$903$	29.0655	+	12.0393i	0.967239	+	0.400644i
$904$		0			0
$905$	38.8196	−	16.0796i	1.29041	−	0.534504i
$906$		0			0
$907$	−47.1400	−	9.37673i	−1.56526	−	0.311349i	−0.665047	−	0.746802i	$-0.731588\pi$
$907$	−47.1400	−	9.37673i	−1.56526	−	0.311349i	−0.900212	+	0.435453i	$0.856588\pi$
$908$		0			0
$909$	29.4855	+	19.7016i	0.977972	+	0.653460i
$910$		0			0
$911$	−36.2741	−	36.2741i	−1.20182	−	1.20182i	−0.973614	−	0.228202i	$-0.926715\pi$
$911$	−36.2741	−	36.2741i	−1.20182	−	1.20182i	−0.228202	−	0.973614i	$-0.573285\pi$
$912$		0			0
$913$	33.7489	−	33.7489i	1.11693	−	1.11693i
$914$		0			0
$915$	9.93321	−	14.8661i	0.328382	−	0.491458i
$916$		0			0
$917$	−5.16862	+	25.9844i	−0.170683	+	0.858081i
$918$		0			0
$919$	−11.2124	−	27.0692i	−0.369864	−	0.892932i	−0.993772	−	0.111433i	$-0.964456\pi$
$919$	−11.2124	−	27.0692i	−0.369864	−	0.892932i	0.623907	−	0.781498i	$-0.285544\pi$
$920$		0			0
$921$	27.8172	−	67.1567i	0.916609	−	2.21289i
$922$		0			0
$923$	0.640131	+	0.958024i	0.0210702	+	0.0315337i
$924$		0			0
$925$	3.80569	−	0.756999i	0.125130	−	0.0248900i
$926$		0			0
$927$			86.4036i			2.83787i
$928$		0			0
$929$			42.1312i			1.38228i	0.722722	+	0.691139i	$0.242891\pi$
$929$			42.1312i			1.38228i	−0.722722	+	0.691139i	$0.757109\pi$
$930$		0			0
$931$	−8.02402	+	1.59608i	−0.262976	+	0.0523093i
$932$		0			0
$933$	−9.85133	−	14.7436i	−0.322518	−	0.482682i
$934$		0			0
$935$	−9.04148	+	21.8281i	−0.295688	+	0.713854i
$936$		0			0
$937$	11.2961	+	27.2713i	0.369028	+	0.890913i	0.993910	+	0.110194i	$0.0351472\pi$
$937$	11.2961	+	27.2713i	0.369028	+	0.890913i	−0.624882	+	0.780719i	$0.714853\pi$
$938$		0			0
$939$	4.32586	−	21.7476i	0.141169	−	0.709705i
$940$		0			0
$941$	6.97461	−	10.4382i	0.227366	−	0.340277i	−0.700193	−	0.713953i	$-0.746903\pi$
$941$	6.97461	−	10.4382i	0.227366	−	0.340277i	0.927559	+	0.373676i	$0.121903\pi$
$942$		0			0
$943$	−2.24114	+	2.24114i	−0.0729815	+	0.0729815i
$944$		0			0
$945$	−34.6716	−	34.6716i	−1.12787	−	1.12787i
$946$		0			0
$947$	−12.5016	−	8.35333i	−0.406249	−	0.271447i	0.335612	−	0.942000i	$-0.391057\pi$
$947$	−12.5016	−	8.35333i	−0.406249	−	0.271447i	−0.741861	+	0.670553i	$0.766057\pi$
$948$		0			0
$949$	−1.52080	−	0.302507i	−0.0493674	−	0.00981979i
$950$		0			0
$951$	96.5906	−	40.0091i	3.13216	−	1.29738i
$952$		0			0
$953$	42.7086	+	17.6905i	1.38347	+	0.573051i	0.945407	−	0.325893i	$-0.105665\pi$
$953$	42.7086	+	17.6905i	1.38347	+	0.573051i	0.438062	+	0.898945i	$0.355665\pi$
$954$		0			0
$955$	−22.5944	+	15.0971i	−0.731138	+	0.488531i
$956$		0			0
$957$	−3.96431	−	19.9299i	−0.128148	−	0.644243i
$958$		0			0
$959$	2.40877			0.0777832
$960$		0			0
$961$	13.6430			0.440098
$962$		0			0
$963$	8.72606	+	43.8688i	0.281193	+	1.41365i
$964$		0			0
$965$	11.2679	−	7.52898i	0.362727	−	0.242367i
$966$		0			0
$967$	35.3386	+	14.6377i	1.13641	+	0.470718i	0.869956	−	0.493129i	$-0.164147\pi$
$967$	35.3386	+	14.6377i	1.13641	+	0.470718i	0.266457	+	0.963847i	$0.414147\pi$
$968$		0			0
$969$	−33.9079	+	14.0451i	−1.08928	+	0.451194i
$970$		0			0
$971$	0.620988	+	0.123522i	0.0199285	+	0.00396402i	0.205044	−	0.978753i	$-0.434266\pi$
$971$	0.620988	+	0.123522i	0.0199285	+	0.00396402i	−0.185116	+	0.982717i	$0.559266\pi$
$972$		0			0
$973$	−5.48692	−	3.66624i	−0.175903	−	0.117534i
$974$		0			0
$975$	−0.0968801	−	0.0968801i	−0.00310265	−	0.00310265i
$976$		0			0
$977$	14.4692	−	14.4692i	0.462911	−	0.462911i	−0.436697	−	0.899608i	$-0.643852\pi$
$977$	14.4692	−	14.4692i	0.462911	−	0.462911i	0.899608	+	0.436697i	$0.143852\pi$
$978$		0			0
$979$	−23.2641	+	34.8172i	−0.743524	+	1.11276i
$980$		0			0
$981$	−25.0549	+	125.960i	−0.799942	+	4.02158i
$982$		0			0
$983$	6.41367	+	15.4840i	0.204564	+	0.493862i	0.992551	−	0.121831i	$-0.0388764\pi$
$983$	6.41367	+	15.4840i	0.204564	+	0.493862i	−0.787987	+	0.615692i	$0.788876\pi$
$984$		0			0
$985$	−19.0322	+	45.9477i	−0.606415	+	1.46402i
$986$		0			0
$987$	43.3123	+	64.8214i	1.37864	+	2.06329i
$988$		0			0
$989$	16.2429	−	3.23091i	0.516494	−	0.102737i
$990$		0			0
$991$			53.4671i			1.69844i	0.528041	+	0.849219i	$0.322927\pi$
$991$			53.4671i			1.69844i	−0.528041	+	0.849219i	$0.677073\pi$
$992$		0			0
$993$		−	44.5709i		−	1.41441i
$994$		0			0
$995$	30.8998	−	6.14636i	0.979590	−	0.194853i
$996$		0			0
$997$	17.9595	+	26.8783i	0.568783	+	0.851244i	0.998666	−	0.0516411i	$-0.0164452\pi$
$997$	17.9595	+	26.8783i	0.568783	+	0.851244i	−0.429883	+	0.902885i	$0.641445\pi$
$998$		0			0
$999$	40.0155	−	96.6059i	1.26603	−	3.05648i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.i.a.97.1		56
4.3	odd	2		512.2.i.b.97.7		56
8.3	odd	2		64.2.i.a.21.6	✓	56
8.5	even	2		256.2.i.a.177.7		56
24.11	even	2		576.2.bd.a.469.2		56
64.3	odd	16		512.2.i.b.417.7		56
64.29	even	16		256.2.i.a.81.7		56
64.35	odd	16		64.2.i.a.61.6	yes	56
64.61	even	16	inner	512.2.i.a.417.1		56
192.35	even	16		576.2.bd.a.253.2		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.21.6	✓	56	8.3	odd	2
64.2.i.a.61.6	yes	56	64.35	odd	16
256.2.i.a.81.7		56	64.29	even	16
256.2.i.a.177.7		56	8.5	even	2
512.2.i.a.97.1		56	1.1	even	1	trivial
512.2.i.a.417.1		56	64.61	even	16	inner
512.2.i.b.97.7		56	4.3	odd	2
512.2.i.b.417.7		56	64.3	odd	16
576.2.bd.a.253.2		56	192.35	even	16
576.2.bd.a.469.2		56	24.11	even	2

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:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.i (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.599600 - 3.01439i) q^{3} +(1.78465 - 1.19247i) q^{5} +(-1.99271 - 0.825409i) q^{7} +(-5.95540 + 2.46681i) q^{9} +O(q^{10})\)	\(q+(-0.599600 - 3.01439i) q^{3} +(1.78465 - 1.19247i) q^{5} +(-1.99271 - 0.825409i) q^{7} +(-5.95540 + 2.46681i) q^{9} +(-3.15038 - 0.626650i) q^{11} +(-0.0943077 - 0.0630144i) q^{13} +(-4.66465 - 4.66465i) q^{15} +(2.42319 - 2.42319i) q^{17} +(1.93596 - 2.89737i) q^{19} +(-1.29328 + 6.50174i) q^{21} +(1.33543 + 3.22402i) q^{23} +(-0.150405 + 0.363110i) q^{25} +(5.88424 + 8.80639i) q^{27} +(-2.01879 + 0.401561i) q^{29} +4.16617i q^{31} +9.87224i q^{33} +(-4.54058 + 0.903177i) q^{35} +(-5.48499 - 8.20886i) q^{37} +(-0.133403 + 0.322064i) q^{39} +(0.347569 + 0.839106i) q^{41} +(0.925855 - 4.65459i) q^{43} +(-7.68675 + 11.5040i) q^{45} +(8.31575 - 8.31575i) q^{47} +(-1.66014 - 1.66014i) q^{49} +(-8.75739 - 5.85150i) q^{51} +(-0.565279 - 0.112441i) q^{53} +(-6.36961 + 2.63838i) q^{55} +(-9.89462 - 4.09848i) q^{57} +(-0.649771 + 0.434163i) q^{59} +(0.528753 + 2.65822i) q^{61} +13.9035 q^{63} -0.243449 q^{65} +(0.971210 + 4.88260i) q^{67} +(8.91774 - 5.95864i) q^{69} +(-9.38522 - 3.88748i) q^{71} +(12.6303 - 5.23165i) q^{73} +(1.18474 + 0.235659i) q^{75} +(5.76057 + 3.84909i) q^{77} +(3.50532 + 3.50532i) q^{79} +(9.34353 - 9.34353i) q^{81} +(-8.25513 + 12.3547i) q^{83} +(1.43498 - 7.21413i) q^{85} +(2.42093 + 5.84464i) q^{87} +(4.98881 - 12.0441i) q^{89} +(0.135916 + 0.203412i) q^{91} +(12.5585 - 2.49803i) q^{93} -7.47938i q^{95} -4.06140i q^{97} +(20.3076 - 4.03944i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{3} + 8 q^{5} + 8 q^{7} - 8 q^{9}+O(q^{10}) \) 56 * q - 8 * q^3 + 8 * q^5 + 8 * q^7 - 8 * q^9	\( 56 q - 8 q^{3} + 8 q^{5} + 8 q^{7} - 8 q^{9} - 8 q^{11} + 8 q^{13} + 8 q^{15} - 8 q^{17} - 8 q^{19} + 8 q^{21} + 8 q^{23} - 8 q^{25} - 8 q^{27} + 8 q^{29} - 8 q^{35} + 8 q^{37} + 8 q^{39} - 8 q^{41} - 8 q^{43} + 8 q^{45} + 8 q^{47} - 8 q^{49} + 24 q^{51} + 8 q^{53} - 56 q^{55} - 8 q^{57} + 56 q^{59} + 8 q^{61} - 64 q^{63} - 16 q^{65} + 72 q^{67} + 8 q^{69} - 56 q^{71} - 8 q^{73} + 56 q^{75} + 8 q^{77} - 24 q^{79} - 8 q^{81} - 8 q^{83} + 8 q^{85} + 8 q^{87} - 8 q^{89} - 8 q^{91} - 16 q^{93} + 16 q^{99}+O(q^{100}) \) 56 * q - 8 * q^3 + 8 * q^5 + 8 * q^7 - 8 * q^9 - 8 * q^11 + 8 * q^13 + 8 * q^15 - 8 * q^17 - 8 * q^19 + 8 * q^21 + 8 * q^23 - 8 * q^25 - 8 * q^27 + 8 * q^29 - 8 * q^35 + 8 * q^37 + 8 * q^39 - 8 * q^41 - 8 * q^43 + 8 * q^45 + 8 * q^47 - 8 * q^49 + 24 * q^51 + 8 * q^53 - 56 * q^55 - 8 * q^57 + 56 * q^59 + 8 * q^61 - 64 * q^63 - 16 * q^65 + 72 * q^67 + 8 * q^69 - 56 * q^71 - 8 * q^73 + 56 * q^75 + 8 * q^77 - 24 * q^79 - 8 * q^81 - 8 * q^83 + 8 * q^85 + 8 * q^87 - 8 * q^89 - 8 * q^91 - 16 * q^93 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more