LMFDB - Embedded newform 1710.2.p.c.37.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(37,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1710.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.p (of order $4$, degree $2$, 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:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 108x^{16} + 1318x^{12} + 4652x^{8} + 5057x^{4} + 256 $ x^20 + 108x^16 + 1318x^12 + 4652x^8 + 5057x^4 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	no (minimal twist has level 570)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.8
Root			$-1.20277 + 1.20277i$ of defining polynomial
Character	$\chi$	$=$	1710.37
Dual form			1710.2.p.c.1063.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.528178 - 2.17279i) q^{5} +(0.904140 + 0.904140i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.528178 - 2.17279i) q^{5} +(0.904140 + 0.904140i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.90987 - 1.16292i) q^{10} -2.66147 q^{11} +(-0.143663 - 0.143663i) q^{13} +1.27865 q^{14} -1.00000 q^{16} +(-3.29524 - 3.29524i) q^{17} +(-4.05688 - 1.59427i) q^{19} +(-2.17279 + 0.528178i) q^{20} +(-1.88194 + 1.88194i) q^{22} +(-1.75733 + 1.75733i) q^{23} +(-4.44206 + 2.29524i) q^{25} -0.203169 q^{26} +(0.904140 - 0.904140i) q^{28} +2.17494 q^{29} +2.62167i q^{31} +(-0.707107 + 0.707107i) q^{32} -4.66018 q^{34} +(1.48696 - 2.44206i) q^{35} +(0.984090 - 0.984090i) q^{37} +(-3.99597 + 1.74133i) q^{38} +(-1.16292 + 1.90987i) q^{40} -3.74005i q^{41} +(-2.01084 + 2.01084i) q^{43} +2.66147i q^{44} +2.48524i q^{46} +(-3.24973 - 3.24973i) q^{47} -5.36506i q^{49} +(-1.51803 + 4.76399i) q^{50} +(-0.143663 + 0.143663i) q^{52} +(-2.54197 - 2.54197i) q^{53} +(1.40573 + 5.78282i) q^{55} -1.27865i q^{56} +(1.53792 - 1.53792i) q^{58} +2.19877 q^{59} -8.90579 q^{61} +(1.85380 + 1.85380i) q^{62} +1.00000i q^{64} +(-0.236270 + 0.388028i) q^{65} +(4.50928 - 4.50928i) q^{67} +(-3.29524 + 3.29524i) q^{68} +(-0.675353 - 2.77824i) q^{70} +2.55729i q^{71} +(-5.25513 + 5.25513i) q^{73} -1.39171i q^{74} +(-1.59427 + 4.05688i) q^{76} +(-2.40634 - 2.40634i) q^{77} -4.22731 q^{79} +(0.528178 + 2.17279i) q^{80} +(-2.64461 - 2.64461i) q^{82} +(-6.55477 + 6.55477i) q^{83} +(-5.41940 + 8.90035i) q^{85} +2.84376i q^{86} +(1.88194 + 1.88194i) q^{88} +4.94664 q^{89} -0.259782i q^{91} +(1.75733 + 1.75733i) q^{92} -4.59581 q^{94} +(-1.32127 + 9.65682i) q^{95} +(11.8481 - 11.8481i) q^{97} +(-3.79367 - 3.79367i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 12 q^{5} - 4 q^{7}+O(q^{10}) $ 20 * q - 12 * q^5 - 4 * q^7	$ 20 q - 12 q^{5} - 4 q^{7} + 8 q^{11} - 20 q^{16} + 12 q^{17} + 4 q^{23} - 28 q^{25} - 24 q^{26} - 4 q^{28} - 4 q^{35} + 12 q^{38} - 12 q^{43} + 44 q^{47} + 64 q^{55} - 8 q^{58} + 24 q^{62} + 12 q^{68} - 4 q^{73} + 4 q^{76} - 88 q^{77} + 12 q^{80} - 8 q^{82} - 76 q^{83} - 12 q^{85} - 4 q^{92} + 24 q^{95}+O(q^{100}) $ 20 * q - 12 * q^5 - 4 * q^7 + 8 * q^11 - 20 * q^16 + 12 * q^17 + 4 * q^23 - 28 * q^25 - 24 * q^26 - 4 * q^28 - 4 * q^35 + 12 * q^38 - 12 * q^43 + 44 * q^47 + 64 * q^55 - 8 * q^58 + 24 * q^62 + 12 * q^68 - 4 * q^73 + 4 * q^76 - 88 * q^77 + 12 * q^80 - 8 * q^82 - 76 * q^83 - 12 * q^85 - 4 * q^92 + 24 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	−0.528178	−	2.17279i	−0.236208	−	0.971702i
$5$	−0.528178	−	2.17279i	−0.236208	−	0.971702i
$6$		0			0
$7$	0.904140	+	0.904140i	0.341733	+	0.341733i	0.857018	−	0.515286i	$-0.172314\pi$
$7$	0.904140	+	0.904140i	0.341733	+	0.341733i	−0.515286	+	0.857018i	$0.672314\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	−1.90987	−	1.16292i	−0.603955	−	0.367747i
$11$	−2.66147			−0.802462			−0.401231	−	0.915977i	$-0.631418\pi$
$11$	−2.66147			−0.802462			−0.401231	+	0.915977i	$0.631418\pi$
$12$		0			0
$13$	−0.143663	−	0.143663i	−0.0398448	−	0.0398448i	0.686904	−	0.726748i	$-0.258969\pi$
$13$	−0.143663	−	0.143663i	−0.0398448	−	0.0398448i	−0.726748	+	0.686904i	$0.758969\pi$
$14$	1.27865			0.341733
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−3.29524	−	3.29524i	−0.799214	−	0.799214i	0.183758	−	0.982972i	$-0.441174\pi$
$17$	−3.29524	−	3.29524i	−0.799214	−	0.799214i	−0.982972	+	0.183758i	$0.941174\pi$
$18$		0			0
$19$	−4.05688	−	1.59427i	−0.930713	−	0.365751i
$19$	−4.05688	−	1.59427i	−0.930713	−	0.365751i
$20$	−2.17279	+	0.528178i	−0.485851	+	0.118104i
$21$		0			0
$22$	−1.88194	+	1.88194i	−0.401231	+	0.401231i
$23$	−1.75733	+	1.75733i	−0.366428	+	0.366428i	−0.866173	−	0.499745i	$-0.833427\pi$
$23$	−1.75733	+	1.75733i	−0.366428	+	0.366428i	0.499745	+	0.866173i	$0.333427\pi$
$24$		0			0
$25$	−4.44206	+	2.29524i	−0.888411	+	0.459049i
$26$	−0.203169			−0.0398448
$27$		0			0
$28$	0.904140	−	0.904140i	0.170866	−	0.170866i
$29$	2.17494			0.403876			0.201938	−	0.979398i	$-0.435276\pi$
$29$	2.17494			0.403876			0.201938	+	0.979398i	$0.435276\pi$
$30$		0			0
$31$			2.62167i			0.470865i	0.971891	+	0.235432i	$0.0756507\pi$
$31$			2.62167i			0.470865i	−0.971891	+	0.235432i	$0.924349\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$	−4.66018			−0.799214
$35$	1.48696	−	2.44206i	0.251342	−	0.412783i
$36$		0			0
$37$	0.984090	−	0.984090i	0.161783	−	0.161783i	−0.621573	−	0.783356i	$-0.713506\pi$
$37$	0.984090	−	0.984090i	0.161783	−	0.161783i	0.783356	+	0.621573i	$0.213506\pi$
$38$	−3.99597	+	1.74133i	−0.648232	+	0.282481i
$39$		0			0
$40$	−1.16292	+	1.90987i	−0.183874	+	0.301978i
$41$		−	3.74005i		−	0.584098i	−0.956403	−	0.292049i	$-0.905663\pi$
$41$		−	3.74005i		−	0.584098i	0.956403	−	0.292049i	$-0.0943370\pi$
$42$		0			0
$43$	−2.01084	+	2.01084i	−0.306650	+	0.306650i	−0.843609	−	0.536959i	$-0.819573\pi$
$43$	−2.01084	+	2.01084i	−0.306650	+	0.306650i	0.536959	+	0.843609i	$0.319573\pi$
$44$			2.66147i			0.401231i
$45$		0			0
$46$			2.48524i			0.366428i
$47$	−3.24973	−	3.24973i	−0.474021	−	0.474021i	0.429192	−	0.903213i	$-0.358798\pi$
$47$	−3.24973	−	3.24973i	−0.474021	−	0.474021i	−0.903213	+	0.429192i	$0.858798\pi$
$48$		0			0
$49$		−	5.36506i		−	0.766437i
$50$	−1.51803	+	4.76399i	−0.214681	+	0.673730i
$51$		0			0
$52$	−0.143663	+	0.143663i	−0.0199224	+	0.0199224i
$53$	−2.54197	−	2.54197i	−0.349166	−	0.349166i	0.510633	−	0.859799i	$-0.329411\pi$
$53$	−2.54197	−	2.54197i	−0.349166	−	0.349166i	−0.859799	+	0.510633i	$0.829411\pi$
$54$		0			0
$55$	1.40573	+	5.78282i	0.189548	+	0.779755i
$56$		−	1.27865i		−	0.170866i
$57$		0			0
$58$	1.53792	−	1.53792i	0.201938	−	0.201938i
$59$	2.19877			0.286256			0.143128	−	0.989704i	$-0.454284\pi$
$59$	2.19877			0.286256			0.143128	+	0.989704i	$0.454284\pi$
$60$		0			0
$61$	−8.90579			−1.14027			−0.570135	−	0.821551i	$-0.693109\pi$
$61$	−8.90579			−1.14027			−0.570135	+	0.821551i	$0.693109\pi$
$62$	1.85380	+	1.85380i	0.235432	+	0.235432i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−0.236270	+	0.388028i	−0.0293056	+	0.0481290i
$66$		0			0
$67$	4.50928	−	4.50928i	0.550896	−	0.550896i	−0.375803	−	0.926700i	$-0.622633\pi$
$67$	4.50928	−	4.50928i	0.550896	−	0.550896i	0.926700	+	0.375803i	$0.122633\pi$
$68$	−3.29524	+	3.29524i	−0.399607	+	0.399607i
$69$		0			0
$70$	−0.675353	−	2.77824i	−0.0807202	−	0.332063i
$71$			2.55729i			0.303495i	0.988419	+	0.151748i	$0.0484901\pi$
$71$			2.55729i			0.303495i	−0.988419	+	0.151748i	$0.951510\pi$
$72$		0			0
$73$	−5.25513	+	5.25513i	−0.615066	+	0.615066i	−0.944262	−	0.329196i	$-0.893222\pi$
$73$	−5.25513	+	5.25513i	−0.615066	+	0.615066i	0.329196	+	0.944262i	$0.393222\pi$
$74$		−	1.39171i		−	0.161783i
$75$		0			0
$76$	−1.59427	+	4.05688i	−0.182876	+	0.465356i
$77$	−2.40634	−	2.40634i	−0.274228	−	0.274228i
$78$		0			0
$79$	−4.22731			−0.475610			−0.237805	−	0.971313i	$-0.576428\pi$
$79$	−4.22731			−0.475610			−0.237805	+	0.971313i	$0.576428\pi$
$80$	0.528178	+	2.17279i	0.0590521	+	0.242926i
$81$		0			0
$82$	−2.64461	−	2.64461i	−0.292049	−	0.292049i
$83$	−6.55477	+	6.55477i	−0.719479	+	0.719479i	−0.968499	−	0.249019i	$-0.919892\pi$
$83$	−6.55477	+	6.55477i	−0.719479	+	0.719479i	0.249019	+	0.968499i	$0.419892\pi$
$84$		0			0
$85$	−5.41940	+	8.90035i	−0.587817	+	0.965379i
$86$			2.84376i			0.306650i
$87$		0			0
$88$	1.88194	+	1.88194i	0.200616	+	0.200616i
$89$	4.94664			0.524343			0.262171	−	0.965021i	$-0.415561\pi$
$89$	4.94664			0.524343			0.262171	+	0.965021i	$0.415561\pi$
$90$		0			0
$91$		−	0.259782i		−	0.0272326i
$92$	1.75733	+	1.75733i	0.183214	+	0.183214i
$93$		0			0
$94$	−4.59581			−0.474021
$95$	−1.32127	+	9.65682i	−0.135559	+	0.990769i
$96$		0			0
$97$	11.8481	−	11.8481i	1.20300	−	1.20300i	0.229746	−	0.973251i	$-0.426211\pi$
$97$	11.8481	−	11.8481i	1.20300	−	1.20300i	0.973251	−	0.229746i	$-0.0737894\pi$
$98$	−3.79367	−	3.79367i	−0.383219	−	0.383219i
$99$		0			0
$100$	2.29524	+	4.44206i	0.229524	+	0.444206i
$101$	−3.64684			−0.362874			−0.181437	−	0.983403i	$-0.558075\pi$
$101$	−3.64684			−0.362874			−0.181437	+	0.983403i	$0.558075\pi$
$102$		0			0
$103$	4.27174	+	4.27174i	0.420907	+	0.420907i	0.885516	−	0.464609i	$-0.153805\pi$
$103$	4.27174	+	4.27174i	0.420907	+	0.420907i	−0.464609	+	0.885516i	$0.653805\pi$
$104$			0.203169i			0.0199224i
$105$		0			0
$106$	−3.59488			−0.349166
$107$	−9.39155	+	9.39155i	−0.907915	+	0.907915i	−0.996104	−	0.0881885i	$-0.971892\pi$
$107$	−9.39155	+	9.39155i	−0.907915	+	0.907915i	0.0881885	+	0.996104i	$0.471892\pi$
$108$		0			0
$109$	12.0254			1.15182			0.575912	−	0.817512i	$-0.304647\pi$
$109$	12.0254			1.15182			0.575912	+	0.817512i	$0.304647\pi$
$110$	5.08307	+	3.09507i	0.484652	+	0.295103i
$111$		0			0
$112$	−0.904140	−	0.904140i	−0.0854332	−	0.0854332i
$113$	1.99650	+	1.99650i	0.187815	+	0.187815i	0.794751	−	0.606936i	$-0.207601\pi$
$113$	1.99650	+	1.99650i	0.187815	+	0.187815i	−0.606936	+	0.794751i	$0.707601\pi$
$114$		0			0
$115$	4.74649	+	2.89013i	0.442612	+	0.269506i
$116$		−	2.17494i		−	0.201938i
$117$		0			0
$118$	1.55477	−	1.55477i	0.143128	−	0.143128i
$119$		−	5.95872i		−	0.546235i
$120$		0			0
$121$	−3.91659			−0.356054
$122$	−6.29734	+	6.29734i	−0.570135	+	0.570135i
$123$		0			0
$124$	2.62167			0.235432
$125$	7.33328	+	8.43937i	0.655909	+	0.754840i
$126$		0			0
$127$	12.5449	−	12.5449i	1.11318	−	1.11318i	0.120462	−	0.992718i	$-0.461562\pi$
$127$	12.5449	−	12.5449i	1.11318	−	1.11318i	0.992718	−	0.120462i	$-0.0384377\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$	0.107310	+	0.441445i	0.00941168	+	0.0387173i
$131$	−20.6202			−1.80159			−0.900797	−	0.434240i	$-0.857017\pi$
$131$	−20.6202			−1.80159			−0.900797	+	0.434240i	$0.857017\pi$
$132$		0			0
$133$	−2.22655	−	5.10944i	−0.193066	−	0.443044i
$134$		−	6.37709i		−	0.550896i
$135$		0			0
$136$			4.66018i			0.399607i
$137$	2.44206	+	2.44206i	0.208639	+	0.208639i	0.803689	−	0.595050i	$-0.202868\pi$
$137$	2.44206	+	2.44206i	0.208639	+	0.208639i	−0.595050	+	0.803689i	$0.702868\pi$
$138$		0			0
$139$		−	16.1995i		−	1.37402i	−0.726647	−	0.687011i	$-0.758923\pi$
$139$		−	16.1995i		−	1.37402i	0.726647	−	0.687011i	$-0.241077\pi$
$140$	−2.44206	−	1.48696i	−0.206391	−	0.125671i
$141$		0			0
$142$	1.80828	+	1.80828i	0.151748	+	0.151748i
$143$	0.382353	+	0.382353i	0.0319740	+	0.0319740i
$144$		0			0
$145$	−1.14876	−	4.72570i	−0.0953990	−	0.392448i
$146$			7.43187i			0.615066i
$147$		0			0
$148$	−0.984090	−	0.984090i	−0.0808917	−	0.0808917i
$149$		−	2.85261i		−	0.233695i	−0.993150	−	0.116847i	$-0.962721\pi$
$149$		−	2.85261i		−	0.233695i	0.993150	−	0.116847i	$-0.0372789\pi$
$150$		0			0
$151$			18.6146i			1.51483i	0.652932	+	0.757417i	$0.273539\pi$
$151$			18.6146i			1.51483i	−0.652932	+	0.757417i	$0.726461\pi$
$152$	1.74133	+	3.99597i	0.141240	+	0.324116i
$153$		0			0
$154$	−3.40308			−0.274228
$155$	5.69634	−	1.38471i	0.457541	−	0.111222i
$156$		0			0
$157$	−10.0694	−	10.0694i	−0.803627	−	0.803627i	0.180033	−	0.983661i	$-0.442379\pi$
$157$	−10.0694	−	10.0694i	−0.803627	−	0.803627i	−0.983661	+	0.180033i	$0.942379\pi$
$158$	−2.98916	+	2.98916i	−0.237805	+	0.237805i
$159$		0			0
$160$	1.90987	+	1.16292i	0.150989	+	0.0919368i
$161$	−3.17774			−0.250441
$162$		0			0
$163$	16.5520	−	16.5520i	1.29645	−	1.29645i	0.365735	−	0.930719i	$-0.380818\pi$
$163$	16.5520	−	16.5520i	1.29645	−	1.29645i	0.930719	−	0.365735i	$-0.119182\pi$
$164$	−3.74005			−0.292049
$165$		0			0
$166$			9.26984i			0.719479i
$167$	−7.05038	+	7.05038i	−0.545575	+	0.545575i	−0.925158	−	0.379583i	$-0.876068\pi$
$167$	−7.05038	+	7.05038i	−0.545575	+	0.545575i	0.379583	+	0.925158i	$0.376068\pi$
$168$		0			0
$169$		−	12.9587i		−	0.996825i
$170$	2.46140	+	10.1256i	0.188781	+	0.776598i
$171$		0			0
$172$	2.01084	+	2.01084i	0.153325	+	0.153325i
$173$	−14.7696	−	14.7696i	−1.12291	−	1.12291i	−0.991302	−	0.131609i	$-0.957986\pi$
$173$	−14.7696	−	14.7696i	−1.12291	−	1.12291i	−0.131609	−	0.991302i	$-0.542014\pi$
$174$		0			0
$175$	−6.09146	−	1.94102i	−0.460471	−	0.146727i
$176$	2.66147			0.200616
$177$		0			0
$178$	3.49780	−	3.49780i	0.262171	−	0.262171i
$179$	−6.48791			−0.484929			−0.242465	−	0.970160i	$-0.577956\pi$
$179$	−6.48791			−0.484929			−0.242465	+	0.970160i	$0.577956\pi$
$180$		0			0
$181$			0.122571i			0.00911063i	0.999990	+	0.00455531i	$0.00145001\pi$
$181$			0.122571i			0.00911063i	−0.999990	+	0.00455531i	$0.998550\pi$
$182$	−0.183694	−	0.183694i	−0.0136163	−	0.0136163i
$183$		0			0
$184$	2.48524			0.183214
$185$	−2.65800	−	1.61845i	−0.195420	−	0.118991i
$186$		0			0
$187$	8.77018	+	8.77018i	0.641339	+	0.641339i
$188$	−3.24973	+	3.24973i	−0.237011	+	0.237011i
$189$		0			0
$190$	5.89413	+	7.76268i	0.427605	+	0.563164i
$191$	0.473897			0.0342900			0.0171450	−	0.999853i	$-0.494542\pi$
$191$	0.473897			0.0342900			0.0171450	+	0.999853i	$0.494542\pi$
$192$		0			0
$193$	−8.37158	−	8.37158i	−0.602600	−	0.602600i	0.338402	−	0.941002i	$-0.390114\pi$
$193$	−8.37158	−	8.37158i	−0.602600	−	0.602600i	−0.941002	+	0.338402i	$0.890114\pi$
$194$		−	16.7558i		−	1.20300i
$195$		0			0
$196$	−5.36506			−0.383219
$197$	9.45290	+	9.45290i	0.673491	+	0.673491i	0.958519	−	0.285028i	$-0.0920030\pi$
$197$	9.45290	+	9.45290i	0.673491	+	0.673491i	−0.285028	+	0.958519i	$0.592003\pi$
$198$		0			0
$199$			3.17530i			0.225091i	0.993647	+	0.112545i	$0.0359004\pi$
$199$			3.17530i			0.225091i	−0.993647	+	0.112545i	$0.964100\pi$
$200$	4.76399	+	1.51803i	0.336865	+	0.107341i
$201$		0			0
$202$	−2.57871	+	2.57871i	−0.181437	+	0.181437i
$203$	1.96645	+	1.96645i	0.138018	+	0.138018i
$204$		0			0
$205$	−8.12635	+	1.97541i	−0.567569	+	0.137969i
$206$	6.04115			0.420907
$207$		0			0
$208$	0.143663	+	0.143663i	0.00996120	+	0.00996120i
$209$	10.7973	+	4.24310i	0.746862	+	0.293501i
$210$		0			0
$211$		−	14.4553i		−	0.995142i	−0.867423	−	0.497571i	$-0.834225\pi$
$211$		−	14.4553i		−	0.995142i	0.867423	−	0.497571i	$-0.165775\pi$
$212$	−2.54197	+	2.54197i	−0.174583	+	0.174583i
$213$		0			0
$214$			13.2817i			0.907915i
$215$	5.43122	+	3.30706i	0.370406	+	0.225539i
$216$		0			0
$217$	−2.37035	+	2.37035i	−0.160910	+	0.160910i
$218$	8.50324	−	8.50324i	0.575912	−	0.575912i
$219$		0			0
$220$	5.78282	−	1.40573i	0.389877	−	0.0947742i
$221$			0.946806i			0.0636890i
$222$		0			0
$223$	13.3101	+	13.3101i	0.891312	+	0.891312i	0.994647	−	0.103335i	$-0.0329513\pi$
$223$	13.3101	+	13.3101i	0.891312	+	0.891312i	−0.103335	+	0.994647i	$0.532951\pi$
$224$	−1.27865			−0.0854332
$225$		0			0
$226$	2.82348			0.187815
$227$	21.0661	−	21.0661i	1.39820	−	1.39820i	0.593005	−	0.805199i	$-0.297942\pi$
$227$	21.0661	−	21.0661i	1.39820	−	1.39820i	0.805199	−	0.593005i	$-0.202058\pi$
$228$		0			0
$229$		−	18.2167i		−	1.20379i	−0.798574	−	0.601897i	$-0.794412\pi$
$229$		−	18.2167i		−	1.20379i	0.798574	−	0.601897i	$-0.205588\pi$
$230$	5.39990	−	1.31265i	0.356059	−	0.0865533i
$231$		0			0
$232$	−1.53792	−	1.53792i	−0.100969	−	0.100969i
$233$	20.6479	−	20.6479i	1.35269	−	1.35269i	0.470045	−	0.882642i	$-0.344238\pi$
$233$	20.6479	−	20.6479i	1.35269	−	1.35269i	0.882642	−	0.470045i	$-0.155762\pi$
$234$		0			0
$235$	−5.34455	+	8.77741i	−0.348640	+	0.572575i
$236$		−	2.19877i		−	0.143128i
$237$		0			0
$238$	−4.21345	−	4.21345i	−0.273118	−	0.273118i
$239$			1.78480i			0.115449i	0.998333	+	0.0577247i	$0.0183846\pi$
$239$			1.78480i			0.115449i	−0.998333	+	0.0577247i	$0.981615\pi$
$240$		0			0
$241$			6.17706i			0.397899i	0.980010	+	0.198950i	$0.0637530\pi$
$241$			6.17706i			0.397899i	−0.980010	+	0.198950i	$0.936247\pi$
$242$	−2.76945	+	2.76945i	−0.178027	+	0.178027i
$243$		0			0
$244$			8.90579i			0.570135i
$245$	−11.6572	+	2.83371i	−0.744749	+	0.181039i
$246$		0			0
$247$	0.353785	+	0.811859i	0.0225108	+	0.0516574i
$248$	1.85380	−	1.85380i	0.117716	−	0.117716i
$249$		0			0
$250$	11.1529	+	0.782122i	0.705374	+	0.0494658i
$251$	3.89007			0.245539			0.122769	−	0.992435i	$-0.460822\pi$
$251$	3.89007			0.245539			0.122769	+	0.992435i	$0.460822\pi$
$252$		0			0
$253$	4.67707	−	4.67707i	0.294045	−	0.294045i
$254$		−	17.7412i		−	1.11318i
$255$		0			0
$256$	1.00000			0.0625000
$257$	13.9017	−	13.9017i	0.867164	−	0.867164i	−0.124994	−	0.992158i	$-0.539891\pi$
$257$	13.9017	−	13.9017i	0.867164	−	0.867164i	0.992158	+	0.124994i	$0.0398911\pi$
$258$		0			0
$259$	1.77951			0.110573
$260$	0.388028	+	0.236270i	0.0240645	+	0.0146528i
$261$		0			0
$262$	−14.5807	+	14.5807i	−0.900797	+	0.900797i
$263$	12.6517	−	12.6517i	0.780135	−	0.780135i	−0.199718	−	0.979853i	$-0.564003\pi$
$263$	12.6517	−	12.6517i	0.780135	−	0.780135i	0.979853	+	0.199718i	$0.0640027\pi$
$264$		0			0
$265$	−4.18055	+	6.86578i	−0.256809	+	0.421761i
$266$	−5.18732	−	2.03851i	−0.318055	−	0.124989i
$267$		0			0
$268$	−4.50928	−	4.50928i	−0.275448	−	0.275448i
$269$	23.7972			1.45094			0.725470	−	0.688254i	$-0.241623\pi$
$269$	23.7972			1.45094			0.725470	+	0.688254i	$0.241623\pi$
$270$		0			0
$271$	−13.5524			−0.823249			−0.411624	−	0.911354i	$-0.635038\pi$
$271$	−13.5524			−0.823249			−0.411624	+	0.911354i	$0.635038\pi$
$272$	3.29524	+	3.29524i	0.199803	+	0.199803i
$273$		0			0
$274$	3.45359			0.208639
$275$	11.8224	−	6.10871i	0.712917	−	0.368369i
$276$		0			0
$277$	11.8777	+	11.8777i	0.713662	+	0.713662i	0.967299	−	0.253637i	$-0.0816270\pi$
$277$	11.8777	+	11.8777i	0.713662	+	0.713662i	−0.253637	+	0.967299i	$0.581627\pi$
$278$	−11.4548	−	11.4548i	−0.687011	−	0.687011i
$279$		0			0
$280$	−2.77824	+	0.675353i	−0.166031	+	0.0403601i
$281$			16.4158i			0.979285i	0.871923	+	0.489643i	$0.162873\pi$
$281$			16.4158i			0.979285i	−0.871923	+	0.489643i	$0.837127\pi$
$282$		0			0
$283$	15.5488	−	15.5488i	0.924283	−	0.924283i	−0.0730457	−	0.997329i	$-0.523272\pi$
$283$	15.5488	−	15.5488i	0.924283	−	0.924283i	0.997329	+	0.0730457i	$0.0232719\pi$
$284$	2.55729			0.151748
$285$		0			0
$286$	0.540729			0.0319740
$287$	3.38153	−	3.38153i	0.199605	−	0.199605i
$288$		0			0
$289$			4.71725i			0.277485i
$290$	−4.15387	−	2.52928i	−0.243923	−	0.148524i
$291$		0			0
$292$	5.25513	+	5.25513i	0.307533	+	0.307533i
$293$	−19.2031	−	19.2031i	−1.12186	−	1.12186i	−0.991462	−	0.130398i	$-0.958375\pi$
$293$	−19.2031	−	19.2031i	−1.12186	−	1.12186i	−0.130398	−	0.991462i	$-0.541625\pi$
$294$		0			0
$295$	−1.16134	−	4.77748i	−0.0676161	−	0.278156i
$296$	−1.39171			−0.0808917
$297$		0			0
$298$	−2.01710	−	2.01710i	−0.116847	−	0.116847i
$299$	0.504924			0.0292005
$300$		0			0
$301$	−3.63616			−0.209585
$302$	13.1625	+	13.1625i	0.757417	+	0.757417i
$303$		0			0
$304$	4.05688	+	1.59427i	0.232678	+	0.0914378i
$305$	4.70384	+	19.3504i	0.269341	+	1.10800i
$306$		0			0
$307$	15.2483	−	15.2483i	0.870269	−	0.870269i	−0.122233	−	0.992501i	$-0.539005\pi$
$307$	15.2483	−	15.2483i	0.870269	−	0.870269i	0.992501	+	0.122233i	$0.0390054\pi$
$308$	−2.40634	+	2.40634i	−0.137114	+	0.137114i
$309$		0			0
$310$	3.04878	−	5.00705i	0.173159	−	0.284381i
$311$	−0.213974			−0.0121334			−0.00606668	−	0.999982i	$-0.501931\pi$
$311$	−0.213974			−0.0121334			−0.00606668	+	0.999982i	$0.501931\pi$
$312$		0			0
$313$	−18.2399	+	18.2399i	−1.03098	+	1.03098i	−0.0314771	+	0.999504i	$0.510021\pi$
$313$	−18.2399	+	18.2399i	−1.03098	+	1.03098i	−0.999504	+	0.0314771i	$0.989979\pi$
$314$	−14.2403			−0.803627
$315$		0			0
$316$			4.22731i			0.237805i
$317$	12.5740	−	12.5740i	0.706226	−	0.706226i	−0.259513	−	0.965740i	$-0.583562\pi$
$317$	12.5740	−	12.5740i	0.706226	−	0.706226i	0.965740	+	0.259513i	$0.0835621\pi$
$318$		0			0
$319$	−5.78853			−0.324096
$320$	2.17279	−	0.528178i	0.121463	−	0.0295260i
$321$		0			0
$322$	−2.24700	+	2.24700i	−0.125220	+	0.125220i
$323$	8.11490	+	18.6219i	0.451525	+	1.03615i
$324$		0			0
$325$	0.967897	+	0.308417i	0.0536893	+	0.0171079i
$326$		−	23.4081i		−	1.29645i
$327$		0			0
$328$	−2.64461	+	2.64461i	−0.146024	+	0.146024i
$329$		−	5.87641i		−	0.323977i
$330$		0			0
$331$			12.5316i			0.688802i	0.938823	+	0.344401i	$0.111918\pi$
$331$			12.5316i			0.688802i	−0.938823	+	0.344401i	$0.888082\pi$
$332$	6.55477	+	6.55477i	0.359740	+	0.359740i
$333$		0			0
$334$			9.97075i			0.545575i
$335$	−12.1794	−	7.41603i	−0.665434	−	0.405181i
$336$		0			0
$337$	−10.1843	+	10.1843i	−0.554774	+	0.554774i	−0.927815	−	0.373041i	$-0.878315\pi$
$337$	−10.1843	+	10.1843i	−0.554774	+	0.554774i	0.373041	+	0.927815i	$0.378315\pi$
$338$	−9.16320	−	9.16320i	−0.498412	−	0.498412i
$339$		0			0
$340$	8.90035	+	5.41940i	0.482689	+	0.293908i
$341$		−	6.97748i		−	0.377851i
$342$		0			0
$343$	11.1797	−	11.1797i	0.603650	−	0.603650i
$344$	2.84376			0.153325
$345$		0			0
$346$	−20.8873			−1.12291
$347$	−3.39715	−	3.39715i	−0.182369	−	0.182369i	0.610019	−	0.792387i	$-0.291162\pi$
$347$	−3.39715	−	3.39715i	−0.182369	−	0.182369i	−0.792387	+	0.610019i	$0.791162\pi$
$348$		0			0
$349$			18.4982i			0.990188i	0.868840	+	0.495094i	$0.164866\pi$
$349$			18.4982i			0.990188i	−0.868840	+	0.495094i	$0.835134\pi$
$350$	−5.67982	+	2.93481i	−0.303599	+	0.156872i
$351$		0			0
$352$	1.88194	−	1.88194i	0.100308	−	0.100308i
$353$	2.03694	−	2.03694i	0.108415	−	0.108415i	−0.650818	−	0.759234i	$-0.725574\pi$
$353$	2.03694	−	2.03694i	0.108415	−	0.108415i	0.759234	+	0.650818i	$0.225574\pi$
$354$		0			0
$355$	5.55647	−	1.35071i	0.294907	−	0.0716881i
$356$		−	4.94664i		−	0.262171i
$357$		0			0
$358$	−4.58765	+	4.58765i	−0.242465	+	0.242465i
$359$			20.9321i			1.10475i	0.833595	+	0.552376i	$0.186279\pi$
$359$			20.9321i			1.10475i	−0.833595	+	0.552376i	$0.813721\pi$
$360$		0			0
$361$	13.9166	+	12.9355i	0.732452	+	0.680818i
$362$	0.0866707	+	0.0866707i	0.00455531	+	0.00455531i
$363$		0			0
$364$	−0.259782			−0.0136163
$365$	14.1939	+	8.64266i	0.742945	+	0.452378i
$366$		0			0
$367$	20.7061	+	20.7061i	1.08085	+	1.08085i	0.996430	+	0.0844175i	$0.0269029\pi$
$367$	20.7061	+	20.7061i	1.08085	+	1.08085i	0.0844175	+	0.996430i	$0.473097\pi$
$368$	1.75733	−	1.75733i	0.0916070	−	0.0916070i
$369$		0			0
$370$	−3.02390	+	0.735072i	−0.157205	+	0.0382146i
$371$		−	4.59659i		−	0.238643i
$372$		0			0
$373$	−7.00175	−	7.00175i	−0.362537	−	0.362537i	0.502209	−	0.864746i	$-0.332521\pi$
$373$	−7.00175	−	7.00175i	−0.362537	−	0.362537i	−0.864746	+	0.502209i	$0.832521\pi$
$374$	12.4029			0.641339
$375$		0			0
$376$			4.59581i			0.237011i
$377$	−0.312458	−	0.312458i	−0.0160924	−	0.0160924i
$378$		0			0
$379$	−8.60331			−0.441922			−0.220961	−	0.975283i	$-0.570919\pi$
$379$	−8.60331			−0.441922			−0.220961	+	0.975283i	$0.570919\pi$
$380$	9.65682	+	1.32127i	0.495385	+	0.0677795i
$381$		0			0
$382$	0.335096	−	0.335096i	0.0171450	−	0.0171450i
$383$	1.41335	+	1.41335i	0.0722188	+	0.0722188i	0.742294	−	0.670075i	$-0.233738\pi$
$383$	1.41335	+	1.41335i	0.0722188	+	0.0722188i	−0.670075	+	0.742294i	$0.733738\pi$
$384$		0			0
$385$	−3.95750	+	6.49945i	−0.201693	+	0.331243i
$386$	−11.8392			−0.602600
$387$		0			0
$388$	−11.8481	−	11.8481i	−0.601498	−	0.601498i
$389$		−	14.9165i		−	0.756295i	−0.925745	−	0.378148i	$-0.876561\pi$
$389$		−	14.9165i		−	0.756295i	0.925745	−	0.378148i	$-0.123439\pi$
$390$		0			0
$391$	11.5816			0.585708
$392$	−3.79367	+	3.79367i	−0.191609	+	0.191609i
$393$		0			0
$394$	13.3684			0.673491
$395$	2.23277	+	9.18507i	0.112343	+	0.462151i
$396$		0			0
$397$	−20.0161	−	20.0161i	−1.00458	−	1.00458i	−0.999989	−	0.00459066i	$-0.998539\pi$
$397$	−20.0161	−	20.0161i	−1.00458	−	1.00458i	−0.00459066	−	0.999989i	$-0.501461\pi$
$398$	2.24527	+	2.24527i	0.112545	+	0.112545i
$399$		0			0
$400$	4.44206	−	2.29524i	0.222103	−	0.114762i
$401$			9.55630i			0.477219i	0.971116	+	0.238609i	$0.0766916\pi$
$401$			9.55630i			0.477219i	−0.971116	+	0.238609i	$0.923308\pi$
$402$		0			0
$403$	0.376635	−	0.376635i	0.0187615	−	0.0187615i
$404$			3.64684i			0.181437i
$405$		0			0
$406$	2.78098			0.138018
$407$	−2.61912	+	2.61912i	−0.129825	+	0.129825i
$408$		0			0
$409$	−37.3114			−1.84493			−0.922466	−	0.386079i	$-0.873829\pi$
$409$	−37.3114			−1.84493			−0.922466	+	0.386079i	$0.873829\pi$
$410$	−4.34937	+	7.14303i	−0.214800	+	0.352769i
$411$		0			0
$412$	4.27174	−	4.27174i	0.210454	−	0.210454i
$413$	1.98800	+	1.98800i	0.0978231	+	0.0978231i
$414$		0			0
$415$	17.7042	+	10.7801i	0.869067	+	0.529173i
$416$	0.203169			0.00996120
$417$		0			0
$418$	10.6351	−	4.63449i	0.520182	−	0.226680i
$419$			33.2272i			1.62326i	0.584175	+	0.811628i	$0.301418\pi$
$419$			33.2272i			1.62326i	−0.584175	+	0.811628i	$0.698582\pi$
$420$		0			0
$421$		−	38.3380i		−	1.86848i	−0.356646	−	0.934240i	$-0.616080\pi$
$421$		−	38.3380i		−	1.86848i	0.356646	−	0.934240i	$-0.383920\pi$
$422$	−10.2214	−	10.2214i	−0.497571	−	0.497571i
$423$		0			0
$424$			3.59488i			0.174583i
$425$	22.2010	+	7.07427i	1.07691	+	0.343153i
$426$		0			0
$427$	−8.05208	−	8.05208i	−0.389668	−	0.389668i
$428$	9.39155	+	9.39155i	0.453958	+	0.453958i
$429$		0			0
$430$	6.17889	−	1.50201i	0.297973	−	0.0724333i
$431$			21.2257i			1.02241i	0.859460	+	0.511203i	$0.170800\pi$
$431$			21.2257i			1.02241i	−0.859460	+	0.511203i	$0.829200\pi$
$432$		0			0
$433$	−10.9862	−	10.9862i	−0.527961	−	0.527961i	0.392003	−	0.919964i	$-0.371782\pi$
$433$	−10.9862	−	10.9862i	−0.527961	−	0.527961i	−0.919964	+	0.392003i	$0.871782\pi$
$434$			3.35219i			0.160910i
$435$		0			0
$436$		−	12.0254i		−	0.575912i
$437$	9.93092	−	4.32761i	0.475061	−	0.207018i
$438$		0			0
$439$	−1.43541			−0.0685084			−0.0342542	−	0.999413i	$-0.510906\pi$
$439$	−1.43541			−0.0685084			−0.0342542	+	0.999413i	$0.510906\pi$
$440$	3.09507	−	5.08307i	0.147552	−	0.242326i
$441$		0			0
$442$	0.669493	+	0.669493i	0.0318445	+	0.0318445i
$443$	−9.49661	+	9.49661i	−0.451198	+	0.451198i	−0.895752	−	0.444554i	$-0.853362\pi$
$443$	−9.49661	+	9.49661i	−0.451198	+	0.451198i	0.444554	+	0.895752i	$0.353362\pi$
$444$		0			0
$445$	−2.61271	−	10.7480i	−0.123854	−	0.509505i
$446$	18.8234			0.891312
$447$		0			0
$448$	−0.904140	+	0.904140i	−0.0427166	+	0.0427166i
$449$	−17.7665			−0.838454			−0.419227	−	0.907881i	$-0.637699\pi$
$449$	−17.7665			−0.838454			−0.419227	+	0.907881i	$0.637699\pi$
$450$		0			0
$451$			9.95402i			0.468716i
$452$	1.99650	−	1.99650i	0.0939076	−	0.0939076i
$453$		0			0
$454$		−	29.7919i		−	1.39820i
$455$	−0.564453	+	0.137211i	−0.0264620	+	0.00643256i
$456$		0			0
$457$	6.74008	+	6.74008i	0.315288	+	0.315288i	0.846954	−	0.531666i	$-0.178434\pi$
$457$	6.74008	+	6.74008i	0.315288	+	0.315288i	−0.531666	+	0.846954i	$0.678434\pi$
$458$	−12.8812	−	12.8812i	−0.601897	−	0.601897i
$459$		0			0
$460$	2.89013	−	4.74649i	0.134753	−	0.221306i
$461$	4.22763			0.196900			0.0984501	−	0.995142i	$-0.468612\pi$
$461$	4.22763			0.196900			0.0984501	+	0.995142i	$0.468612\pi$
$462$		0			0
$463$	12.2736	−	12.2736i	0.570403	−	0.570403i	−0.361838	−	0.932241i	$-0.617851\pi$
$463$	12.2736	−	12.2736i	0.570403	−	0.570403i	0.932241	+	0.361838i	$0.117851\pi$
$464$	−2.17494			−0.100969
$465$		0			0
$466$		−	29.2005i		−	1.35269i
$467$	−9.12358	−	9.12358i	−0.422189	−	0.422189i	0.463768	−	0.885957i	$-0.346497\pi$
$467$	−9.12358	−	9.12358i	−0.422189	−	0.422189i	−0.885957	+	0.463768i	$0.846497\pi$
$468$		0			0
$469$	8.15405			0.376519
$470$	2.42740	+	9.98573i	0.111968	+	0.460608i
$471$		0			0
$472$	−1.55477	−	1.55477i	−0.0715640	−	0.0715640i
$473$	5.35178	−	5.35178i	0.246075	−	0.246075i
$474$		0			0
$475$	21.6801	−	2.22968i	0.994753	−	0.102305i
$476$	−5.95872			−0.273118
$477$		0			0
$478$	1.26205	+	1.26205i	0.0577247	+	0.0577247i
$479$		−	36.9313i		−	1.68744i	−0.536787	−	0.843718i	$-0.680362\pi$
$479$		−	36.9313i		−	1.68744i	0.536787	−	0.843718i	$-0.319638\pi$
$480$		0			0
$481$	−0.282754			−0.0128925
$482$	4.36784	+	4.36784i	0.198950	+	0.198950i
$483$		0			0
$484$			3.91659i			0.178027i
$485$	−32.0015	−	19.4856i	−1.45311	−	0.884797i
$486$		0			0
$487$	10.3862	−	10.3862i	0.470642	−	0.470642i	−0.431481	−	0.902122i	$-0.642009\pi$
$487$	10.3862	−	10.3862i	0.470642	−	0.470642i	0.902122	+	0.431481i	$0.142009\pi$
$488$	6.29734	+	6.29734i	0.285067	+	0.285067i
$489$		0			0
$490$	−6.23913	+	10.2466i	−0.281855	+	0.462894i
$491$	31.2661			1.41102			0.705509	−	0.708701i	$-0.250719\pi$
$491$	31.2661			1.41102			0.705509	+	0.708701i	$0.250719\pi$
$492$		0			0
$493$	−7.16696	−	7.16696i	−0.322784	−	0.322784i
$494$	0.824235	+	0.323907i	0.0370841	+	0.0145733i
$495$		0			0
$496$		−	2.62167i		−	0.117716i
$497$	−2.31215	+	2.31215i	−0.103714	+	0.103714i
$498$		0			0
$499$		−	31.8064i		−	1.42385i	−0.702256	−	0.711925i	$-0.747824\pi$
$499$		−	31.8064i		−	1.42385i	0.702256	−	0.711925i	$-0.252176\pi$
$500$	8.43937	−	7.33328i	0.377420	−	0.327954i
$501$		0			0
$502$	2.75069	−	2.75069i	0.122769	−	0.122769i
$503$	30.1365	−	30.1365i	1.34372	−	1.34372i	0.451396	−	0.892324i	$-0.350926\pi$
$503$	30.1365	−	30.1365i	1.34372	−	1.34372i	0.892324	−	0.451396i	$-0.149074\pi$
$504$		0			0
$505$	1.92618	+	7.92383i	0.0857139	+	0.352606i
$506$		−	6.61437i		−	0.294045i
$507$		0			0
$508$	−12.5449	−	12.5449i	−0.556590	−	0.556590i
$509$	−39.4733			−1.74962			−0.874811	−	0.484463i	$-0.839015\pi$
$509$	−39.4733			−1.74962			−0.874811	+	0.484463i	$0.839015\pi$
$510$		0			0
$511$	−9.50274			−0.420377
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$		−	19.6600i		−	0.867164i
$515$	7.02537	−	11.5378i	0.309575	−	0.508418i
$516$		0			0
$517$	8.64904	+	8.64904i	0.380384	+	0.380384i
$518$	1.25830	−	1.25830i	0.0552867	−	0.0552867i
$519$		0			0
$520$	0.441445	−	0.107310i	0.0193587	−	0.00470584i
$521$			43.0892i			1.88777i	0.330271	+	0.943886i	$0.392860\pi$
$521$			43.0892i			1.88777i	−0.330271	+	0.943886i	$0.607140\pi$
$522$		0			0
$523$	12.0200	+	12.0200i	0.525600	+	0.525600i	0.919257	−	0.393658i	$-0.128790\pi$
$523$	12.0200	+	12.0200i	0.525600	+	0.525600i	−0.393658	+	0.919257i	$0.628790\pi$
$524$			20.6202i			0.900797i
$525$		0			0
$526$		−	17.8922i		−	0.780135i
$527$	8.63902	−	8.63902i	0.376322	−	0.376322i
$528$		0			0
$529$			16.8236i			0.731461i
$530$	1.89874	+	7.81093i	0.0824759	+	0.339285i
$531$		0			0
$532$	−5.10944	+	2.22655i	−0.221522	+	0.0965330i
$533$	−0.537305	+	0.537305i	−0.0232733	+	0.0232733i
$534$		0			0
$535$	25.3663	+	15.4455i	1.09668	+	0.667766i
$536$	−6.37709			−0.275448
$537$		0			0
$538$	16.8271	−	16.8271i	0.725470	−	0.725470i
$539$			14.2789i			0.615037i
$540$		0			0
$541$	−8.87532			−0.381580			−0.190790	−	0.981631i	$-0.561105\pi$
$541$	−8.87532			−0.381580			−0.190790	+	0.981631i	$0.561105\pi$
$542$	−9.58298	+	9.58298i	−0.411624	+	0.411624i
$543$		0			0
$544$	4.66018			0.199803
$545$	−6.35155	−	26.1287i	−0.272070	−	1.11923i
$546$		0			0
$547$	−13.9130	+	13.9130i	−0.594877	+	0.594877i	−0.938945	−	0.344068i	$-0.888195\pi$
$547$	−13.9130	+	13.9130i	−0.594877	+	0.594877i	0.344068	+	0.938945i	$0.388195\pi$
$548$	2.44206	−	2.44206i	0.104319	−	0.104319i
$549$		0			0
$550$	4.04018	−	12.6792i	0.172274	−	0.540643i
$551$	−8.82348	−	3.46745i	−0.375893	−	0.147718i
$552$		0			0
$553$	−3.82208	−	3.82208i	−0.162531	−	0.162531i
$554$	16.7976			0.713662
$555$		0			0
$556$	−16.1995			−0.687011
$557$	−14.7010	−	14.7010i	−0.622900	−	0.622900i	0.323372	−	0.946272i	$-0.395184\pi$
$557$	−14.7010	−	14.7010i	−0.622900	−	0.622900i	−0.946272	+	0.323372i	$0.895184\pi$
$558$		0			0
$559$	0.577764			0.0244368
$560$	−1.48696	+	2.44206i	−0.0628356	+	0.103196i
$561$		0			0
$562$	11.6077	+	11.6077i	0.489643	+	0.489643i
$563$	9.68060	+	9.68060i	0.407989	+	0.407989i	0.881037	−	0.473048i	$-0.156846\pi$
$563$	9.68060	+	9.68060i	0.407989	+	0.407989i	−0.473048	+	0.881037i	$0.656846\pi$
$564$		0			0
$565$	3.28348	−	5.39250i	0.138137	−	0.226864i
$566$		−	21.9894i		−	0.924283i
$567$		0			0
$568$	1.80828	−	1.80828i	0.0758738	−	0.0758738i
$569$	−36.5026			−1.53027			−0.765133	−	0.643872i	$-0.777327\pi$
$569$	−36.5026			−1.53027			−0.765133	+	0.643872i	$0.777327\pi$
$570$		0			0
$571$	−18.0651			−0.756000			−0.378000	−	0.925806i	$-0.623388\pi$
$571$	−18.0651			−0.756000			−0.378000	+	0.925806i	$0.623388\pi$
$572$	0.382353	−	0.382353i	0.0159870	−	0.0159870i
$573$		0			0
$574$		−	4.78220i		−	0.199605i
$575$	3.77265	−	11.8396i	0.157330	−	0.493747i
$576$		0			0
$577$	13.7843	+	13.7843i	0.573847	+	0.573847i	0.933201	−	0.359354i	$-0.117003\pi$
$577$	13.7843	+	13.7843i	0.573847	+	0.573847i	−0.359354	+	0.933201i	$0.617003\pi$
$578$	3.33560	+	3.33560i	0.138743	+	0.138743i
$579$		0			0
$580$	−4.72570	+	1.14876i	−0.196224	+	0.0476995i
$581$	−11.8529			−0.491739
$582$		0			0
$583$	6.76536	+	6.76536i	0.280192	+	0.280192i
$584$	7.43187			0.307533
$585$		0			0
$586$	−27.1573			−1.12186
$587$	12.9491	+	12.9491i	0.534466	+	0.534466i	0.921898	−	0.387432i	$-0.126638\pi$
$587$	12.9491	+	12.9491i	0.534466	+	0.534466i	−0.387432	+	0.921898i	$0.626638\pi$
$588$		0			0
$589$	4.17965	−	10.6358i	0.172219	−	0.438240i
$590$	−4.19938	−	2.55699i	−0.172886	−	0.105270i
$591$		0			0
$592$	−0.984090	+	0.984090i	−0.0404458	+	0.0404458i
$593$	−1.56552	+	1.56552i	−0.0642881	+	0.0642881i	−0.738520	−	0.674232i	$-0.764475\pi$
$593$	−1.56552	+	1.56552i	−0.0642881	+	0.0642881i	0.674232	+	0.738520i	$0.264475\pi$
$594$		0			0
$595$	−12.9471	+	3.14727i	−0.530778	+	0.129025i
$596$	−2.85261			−0.116847
$597$		0			0
$598$	0.357035	−	0.357035i	0.0146003	−	0.0146003i
$599$	−31.2077			−1.27511			−0.637556	−	0.770404i	$-0.720054\pi$
$599$	−31.2077			−1.27511			−0.637556	+	0.770404i	$0.720054\pi$
$600$		0			0
$601$			27.0296i			1.10256i	0.834320	+	0.551281i	$0.185861\pi$
$601$			27.0296i			1.10256i	−0.834320	+	0.551281i	$0.814139\pi$
$602$	−2.57115	+	2.57115i	−0.104792	+	0.104792i
$603$		0			0
$604$	18.6146			0.757417
$605$	2.06866	+	8.50995i	0.0841029	+	0.345979i
$606$		0			0
$607$	−10.1961	+	10.1961i	−0.413847	+	0.413847i	−0.883076	−	0.469229i	$-0.844532\pi$
$607$	−10.1961	+	10.1961i	−0.413847	+	0.413847i	0.469229	+	0.883076i	$0.344532\pi$
$608$	3.99597	−	1.74133i	0.162058	−	0.0706202i
$609$		0			0
$610$	17.0089	+	10.3567i	0.688672	+	0.419331i
$611$			0.933728i			0.0377746i
$612$		0			0
$613$	−22.4225	+	22.4225i	−0.905634	+	0.905634i	−0.995916	−	0.0902818i	$-0.971223\pi$
$613$	−22.4225	+	22.4225i	−0.905634	+	0.905634i	0.0902818	+	0.995916i	$0.471223\pi$
$614$		−	21.5644i		−	0.870269i
$615$		0			0
$616$			3.40308i			0.137114i
$617$	1.22259	+	1.22259i	0.0492195	+	0.0492195i	0.731288	−	0.682069i	$-0.238919\pi$
$617$	1.22259	+	1.22259i	0.0492195	+	0.0492195i	−0.682069	+	0.731288i	$0.738919\pi$
$618$		0			0
$619$		−	26.1462i		−	1.05090i	−0.850823	−	0.525452i	$-0.823896\pi$
$619$		−	26.1462i		−	1.05090i	0.850823	−	0.525452i	$-0.176104\pi$
$620$	−1.38471	−	5.69634i	−0.0556111	−	0.228770i
$621$		0			0
$622$	−0.151302	+	0.151302i	−0.00606668	+	0.00606668i
$623$	4.47245	+	4.47245i	0.179185	+	0.179185i
$624$		0			0
$625$	14.4637	−	20.3912i	0.578549	−	0.815648i
$626$			25.7952i			1.03098i
$627$		0			0
$628$	−10.0694	+	10.0694i	−0.401814	+	0.401814i
$629$	−6.48563			−0.258599
$630$		0			0
$631$	−33.3652			−1.32825			−0.664124	−	0.747623i	$-0.731195\pi$
$631$	−33.3652			−1.32825			−0.664124	+	0.747623i	$0.731195\pi$
$632$	2.98916	+	2.98916i	0.118902	+	0.118902i
$633$		0			0
$634$		−	17.7823i		−	0.706226i
$635$	−33.8834	−	20.6315i	−1.34462	−	0.818737i
$636$		0			0
$637$	−0.770758	+	0.770758i	−0.0305386	+	0.0305386i
$638$	−4.09311	+	4.09311i	−0.162048	+	0.162048i
$639$		0			0
$640$	1.16292	−	1.90987i	0.0459684	−	0.0754944i
$641$			31.2439i			1.23406i	0.786940	+	0.617029i	$0.211664\pi$
$641$			31.2439i			1.23406i	−0.786940	+	0.617029i	$0.788336\pi$
$642$		0			0
$643$	−3.28874	+	3.28874i	−0.129695	+	0.129695i	−0.768975	−	0.639279i	$-0.779233\pi$
$643$	−3.28874	+	3.28874i	−0.129695	+	0.129695i	0.639279	+	0.768975i	$0.279233\pi$
$644$			3.17774i			0.125220i
$645$		0			0
$646$	18.9058	+	7.42959i	0.743838	+	0.292313i
$647$	−24.2688	−	24.2688i	−0.954105	−	0.954105i	0.0448869	−	0.998992i	$-0.485707\pi$
$647$	−24.2688	−	24.2688i	−0.954105	−	0.954105i	−0.998992	+	0.0448869i	$0.985707\pi$
$648$		0			0
$649$	−5.85196			−0.229710
$650$	0.902490	−	0.466323i	0.0353986	−	0.0182907i
$651$		0			0
$652$	−16.5520	−	16.5520i	−0.648227	−	0.648227i
$653$	−0.820035	+	0.820035i	−0.0320904	+	0.0320904i	−0.722970	−	0.690879i	$-0.757224\pi$
$653$	−0.820035	+	0.820035i	−0.0320904	+	0.0320904i	0.690879	+	0.722970i	$0.257224\pi$
$654$		0			0
$655$	10.8911	+	44.8034i	0.425552	+	1.75061i
$656$			3.74005i			0.146024i
$657$		0			0
$658$	−4.15525	−	4.15525i	−0.161989	−	0.161989i
$659$	42.2189			1.64461			0.822307	−	0.569044i	$-0.192687\pi$
$659$	42.2189			1.64461			0.822307	+	0.569044i	$0.192687\pi$
$660$		0			0
$661$		−	26.8163i		−	1.04303i	−0.853241	−	0.521517i	$-0.825366\pi$
$661$		−	26.8163i		−	1.04303i	0.853241	−	0.521517i	$-0.174634\pi$
$662$	8.86121	+	8.86121i	0.344401	+	0.344401i
$663$		0			0
$664$	9.26984			0.359740
$665$	−9.92573	+	7.53651i	−0.384903	+	0.292253i
$666$		0			0
$667$	−3.82208	+	3.82208i	−0.147992	+	0.147992i
$668$	7.05038	+	7.05038i	0.272788	+	0.272788i
$669$		0			0
$670$	−13.8561	+	3.36824i	−0.535307	+	0.130126i
$671$	23.7025			0.915023
$672$		0			0
$673$	−23.1618	−	23.1618i	−0.892824	−	0.892824i	0.101964	−	0.994788i	$-0.467487\pi$
$673$	−23.1618	−	23.1618i	−0.892824	−	0.892824i	−0.994788	+	0.101964i	$0.967487\pi$
$674$			14.4028i			0.554774i
$675$		0			0
$676$	−12.9587			−0.498412
$677$	18.0408	−	18.0408i	0.693364	−	0.693364i	−0.269606	−	0.962971i	$-0.586894\pi$
$677$	18.0408	−	18.0408i	0.693364	−	0.693364i	0.962971	+	0.269606i	$0.0868935\pi$
$678$		0			0
$679$	21.4248			0.822207
$680$	10.1256	−	2.46140i	0.388299	−	0.0943905i
$681$		0			0
$682$	−4.93382	−	4.93382i	−0.188926	−	0.188926i
$683$	20.2075	+	20.2075i	0.773220	+	0.773220i	0.978668	−	0.205448i	$-0.0658651\pi$
$683$	20.2075	+	20.2075i	0.773220	+	0.773220i	−0.205448	+	0.978668i	$0.565865\pi$
$684$		0			0
$685$	4.01624	−	6.59592i	0.153453	−	0.252017i
$686$		−	15.8106i		−	0.603650i
$687$		0			0
$688$	2.01084	−	2.01084i	0.0766625	−	0.0766625i
$689$			0.730371i			0.0278249i
$690$		0			0
$691$	−5.06618			−0.192727			−0.0963633	−	0.995346i	$-0.530721\pi$
$691$	−5.06618			−0.192727			−0.0963633	+	0.995346i	$0.530721\pi$
$692$	−14.7696	+	14.7696i	−0.561455	+	0.561455i
$693$		0			0
$694$	−4.80430			−0.182369
$695$	−35.1981	+	8.55620i	−1.33514	+	0.324555i
$696$		0			0
$697$	−12.3244	+	12.3244i	−0.466819	+	0.466819i
$698$	13.0802	+	13.0802i	0.495094	+	0.495094i
$699$		0			0
$700$	−1.94102	+	6.09146i	−0.0733637	+	0.230236i
$701$	−31.7812			−1.20036			−0.600180	−	0.799865i	$-0.704904\pi$
$701$	−31.7812			−1.20036			−0.600180	+	0.799865i	$0.704904\pi$
$702$		0			0
$703$	−5.56124	+	2.42343i	−0.209746	+	0.0914014i
$704$		−	2.66147i		−	0.100308i
$705$		0			0
$706$		−	2.88067i		−	0.108415i
$707$	−3.29726	−	3.29726i	−0.124006	−	0.124006i
$708$		0			0
$709$			40.1995i			1.50972i	0.655884	+	0.754861i	$0.272296\pi$
$709$			40.1995i			1.50972i	−0.655884	+	0.754861i	$0.727704\pi$
$710$	2.97392	−	4.88411i	0.111609	−	0.183297i
$711$		0			0
$712$	−3.49780	−	3.49780i	−0.131086	−	0.131086i
$713$	−4.60712	−	4.60712i	−0.172538	−	0.172538i
$714$		0			0
$715$	0.628823	−	1.03272i	0.0235167	−	0.0386217i
$716$			6.48791i			0.242465i
$717$		0			0
$718$	14.8012	+	14.8012i	0.552376	+	0.552376i
$719$		−	9.60719i		−	0.358288i	−0.983823	−	0.179144i	$-0.942667\pi$
$719$		−	9.60719i		−	0.358288i	0.983823	−	0.179144i	$-0.0573328\pi$
$720$		0			0
$721$			7.72450i			0.287676i
$722$	18.9873	−	0.693705i	0.706635	−	0.0258170i
$723$		0			0
$724$	0.122571			0.00455531
$725$	−9.66121	+	4.99202i	−0.358808	+	0.185399i
$726$		0			0
$727$	7.58566	+	7.58566i	0.281337	+	0.281337i	0.833642	−	0.552305i	$-0.186252\pi$
$727$	7.58566	+	7.58566i	0.281337	+	0.281337i	−0.552305	+	0.833642i	$0.686252\pi$
$728$	−0.183694	+	0.183694i	−0.00680814	+	0.00680814i
$729$		0			0
$730$	16.1479	−	3.92535i	0.597661	−	0.145284i
$731$	13.2524			0.490158
$732$		0			0
$733$	16.6371	−	16.6371i	0.614504	−	0.614504i	−0.329612	−	0.944116i	$-0.606918\pi$
$733$	16.6371	−	16.6371i	0.614504	−	0.614504i	0.944116	+	0.329612i	$0.106918\pi$
$734$	29.2828			1.08085
$735$		0			0
$736$		−	2.48524i		−	0.0916070i
$737$	−12.0013	+	12.0013i	−0.442074	+	0.442074i
$738$		0			0
$739$		−	18.7582i		−	0.690030i	−0.938597	−	0.345015i	$-0.887874\pi$
$739$		−	18.7582i		−	0.690030i	0.938597	−	0.345015i	$-0.112126\pi$
$740$	−1.61845	+	2.65800i	−0.0594954	+	0.0977099i
$741$		0			0
$742$	−3.25028	−	3.25028i	−0.119321	−	0.119321i
$743$	18.3052	+	18.3052i	0.671553	+	0.671553i	0.958074	−	0.286521i	$-0.0924989\pi$
$743$	18.3052	+	18.3052i	0.671553	+	0.671553i	−0.286521	+	0.958074i	$0.592499\pi$
$744$		0			0
$745$	−6.19813	+	1.50669i	−0.227082	+	0.0552007i
$746$	−9.90197			−0.362537
$747$		0			0
$748$	8.77018	−	8.77018i	0.320669	−	0.320669i
$749$	−16.9826			−0.620529
$750$		0			0
$751$			32.7384i			1.19464i	0.802002	+	0.597321i	$0.203768\pi$
$751$			32.7384i			1.19464i	−0.802002	+	0.597321i	$0.796232\pi$
$752$	3.24973	+	3.24973i	0.118505	+	0.118505i
$753$		0			0
$754$	−0.441882			−0.0160924
$755$	40.4456	−	9.83182i	1.47197	−	0.357816i
$756$		0			0
$757$	18.8701	+	18.8701i	0.685844	+	0.685844i	0.961311	−	0.275466i	$-0.0888322\pi$
$757$	18.8701	+	18.8701i	0.685844	+	0.685844i	−0.275466	+	0.961311i	$0.588832\pi$
$758$	−6.08346	+	6.08346i	−0.220961	+	0.220961i
$759$		0			0
$760$	7.76268	−	5.89413i	0.281582	−	0.213803i
$761$	−6.60459			−0.239416			−0.119708	−	0.992809i	$-0.538196\pi$
$761$	−6.60459			−0.239416			−0.119708	+	0.992809i	$0.538196\pi$
$762$		0			0
$763$	10.8726	+	10.8726i	0.393616	+	0.393616i
$764$		−	0.473897i		−	0.0171450i
$765$		0			0
$766$	1.99878			0.0722188
$767$	−0.315881	−	0.315881i	−0.0114058	−	0.0114058i
$768$		0			0
$769$		−	5.37624i		−	0.193872i	−0.995291	−	0.0969360i	$-0.969096\pi$
$769$		−	5.37624i		−	0.193872i	0.995291	−	0.0969360i	$-0.0309042\pi$
$770$	1.79743	+	7.39418i	0.0647749	+	0.266468i
$771$		0			0
$772$	−8.37158	+	8.37158i	−0.301300	+	0.301300i
$773$	1.67948	+	1.67948i	0.0604066	+	0.0604066i	0.736665	−	0.676258i	$-0.236400\pi$
$773$	1.67948	+	1.67948i	0.0604066	+	0.0604066i	−0.676258	+	0.736665i	$0.736400\pi$
$774$		0			0
$775$	−6.01736	−	11.6456i	−0.216150	−	0.418322i
$776$	−16.7558			−0.601498
$777$		0			0
$778$	−10.5475	−	10.5475i	−0.378148	−	0.378148i
$779$	−5.96266	+	15.1729i	−0.213634	+	0.543627i
$780$		0			0
$781$		−	6.80615i		−	0.243543i
$782$	8.18945	−	8.18945i	0.292854	−	0.292854i
$783$		0			0
$784$			5.36506i			0.191609i
$785$	−16.5603	+	27.1972i	−0.591063	+	0.970710i
$786$		0			0
$787$	−33.8233	+	33.8233i	−1.20567	+	1.20567i	−0.233257	+	0.972415i	$0.574938\pi$
$787$	−33.8233	+	33.8233i	−1.20567	+	1.20567i	−0.972415	+	0.233257i	$0.925062\pi$
$788$	9.45290	−	9.45290i	0.336745	−	0.336745i
$789$		0			0
$790$	8.07364	+	4.91602i	0.287247	+	0.174904i
$791$			3.61024i			0.128365i
$792$		0			0
$793$	1.27943	+	1.27943i	0.0454338	+	0.0454338i
$794$	−28.3071			−1.00458
$795$		0			0
$796$	3.17530			0.112545
$797$	19.1081	−	19.1081i	0.676844	−	0.676844i	−0.282441	−	0.959285i	$-0.591144\pi$
$797$	19.1081	−	19.1081i	0.676844	−	0.676844i	0.959285	+	0.282441i	$0.0911440\pi$
$798$		0			0
$799$			21.4173i			0.757688i
$800$	1.51803	−	4.76399i	0.0536703	−	0.168432i
$801$		0			0
$802$	6.75733	+	6.75733i	0.238609	+	0.238609i
$803$	13.9863	−	13.9863i	0.493568	−	0.493568i
$804$		0			0
$805$	1.67841	+	6.90457i	0.0591562	+	0.243354i
$806$		−	0.532642i		−	0.0187615i
$807$		0			0
$808$	2.57871	+	2.57871i	0.0907186	+	0.0907186i
$809$			9.60569i			0.337718i	0.985640	+	0.168859i	$0.0540082\pi$
$809$			9.60569i			0.337718i	−0.985640	+	0.168859i	$0.945992\pi$
$810$		0			0
$811$			28.5091i			1.00109i	0.865711	+	0.500545i	$0.166867\pi$
$811$			28.5091i			1.00109i	−0.865711	+	0.500545i	$0.833133\pi$
$812$	1.96645	−	1.96645i	0.0690089	−	0.0690089i
$813$		0			0
$814$			3.70400i			0.129825i
$815$	−44.7065	−	27.2217i	−1.56600	−	0.953534i
$816$		0			0
$817$	11.3636	−	4.95191i	0.397561	−	0.173246i
$818$	−26.3832	+	26.3832i	−0.922466	+	0.922466i
$819$		0			0
$820$	1.97541	+	8.12635i	0.0689844	+	0.283785i
$821$	−13.9024			−0.485196			−0.242598	−	0.970127i	$-0.578000\pi$
$821$	−13.9024			−0.485196			−0.242598	+	0.970127i	$0.578000\pi$
$822$		0			0
$823$	21.8340	−	21.8340i	0.761085	−	0.761085i	−0.215434	−	0.976518i	$-0.569117\pi$
$823$	21.8340	−	21.8340i	0.761085	−	0.761085i	0.976518	+	0.215434i	$0.0691165\pi$
$824$		−	6.04115i		−	0.210454i
$825$		0			0
$826$	2.81146			0.0978231
$827$	−10.5045	+	10.5045i	−0.365278	+	0.365278i	−0.865752	−	0.500473i	$-0.833159\pi$
$827$	−10.5045	+	10.5045i	−0.365278	+	0.365278i	0.500473	+	0.865752i	$0.333159\pi$
$828$		0			0
$829$	−22.5926			−0.784674			−0.392337	−	0.919822i	$-0.628333\pi$
$829$	−22.5926			−0.784674			−0.392337	+	0.919822i	$0.628333\pi$
$830$	20.1414	−	4.89613i	0.699120	−	0.169947i
$831$		0			0
$832$	0.143663	−	0.143663i	0.00498060	−	0.00498060i
$833$	−17.6792	+	17.6792i	−0.612547	+	0.612547i
$834$		0			0
$835$	19.0429	+	11.5952i	0.659006	+	0.401267i
$836$	4.24310	−	10.7973i	0.146751	−	0.373431i
$837$		0			0
$838$	23.4952	+	23.4952i	0.811628	+	0.811628i
$839$	8.89881			0.307221			0.153610	−	0.988131i	$-0.450910\pi$
$839$	8.89881			0.307221			0.153610	+	0.988131i	$0.450910\pi$
$840$		0			0
$841$	−24.2696			−0.836884
$842$	−27.1090	−	27.1090i	−0.934240	−	0.934240i
$843$		0			0
$844$	−14.4553			−0.497571
$845$	−28.1566	+	6.84451i	−0.968617	+	0.235458i
$846$		0			0
$847$	−3.54115	−	3.54115i	−0.121675	−	0.121675i
$848$	2.54197	+	2.54197i	0.0872915	+	0.0872915i
$849$		0			0
$850$	20.7008	−	10.6962i	0.710030	−	0.366878i
$851$			3.45873i			0.118564i
$852$		0			0
$853$	−4.21663	+	4.21663i	−0.144375	+	0.144375i	−0.775600	−	0.631225i	$-0.782552\pi$
$853$	−4.21663	+	4.21663i	−0.144375	+	0.144375i	0.631225	+	0.775600i	$0.282552\pi$
$854$	−11.3874			−0.389668
$855$		0			0
$856$	13.2817			0.453958
$857$	−1.84086	+	1.84086i	−0.0628825	+	0.0628825i	−0.737849	−	0.674966i	$-0.764158\pi$
$857$	−1.84086	+	1.84086i	−0.0628825	+	0.0628825i	0.674966	+	0.737849i	$0.264158\pi$
$858$		0			0
$859$		−	14.0924i		−	0.480826i	−0.970671	−	0.240413i	$-0.922717\pi$
$859$		−	14.0924i		−	0.480826i	0.970671	−	0.240413i	$-0.0772829\pi$
$860$	3.30706	−	5.43122i	0.112770	−	0.185203i
$861$		0			0
$862$	15.0089	+	15.0089i	0.511203	+	0.511203i
$863$	2.40643	+	2.40643i	0.0819160	+	0.0819160i	0.746878	−	0.664962i	$-0.231552\pi$
$863$	2.40643	+	2.40643i	0.0819160	+	0.0819160i	−0.664962	+	0.746878i	$0.731552\pi$
$864$		0			0
$865$	−24.2903	+	39.8922i	−0.825894	+	1.35638i
$866$	−15.5368			−0.527961
$867$		0			0
$868$	2.37035	+	2.37035i	0.0804550	+	0.0804550i
$869$	11.2509			0.381659
$870$		0			0
$871$	−1.29563			−0.0439007
$872$	−8.50324	−	8.50324i	−0.287956	−	0.287956i
$873$		0			0
$874$	3.96214	−	10.0823i	0.134021	−	0.341039i
$875$	−1.00006	+	14.2607i	−0.0338081	+	0.482099i
$876$		0			0
$877$	1.38678	−	1.38678i	0.0468281	−	0.0468281i	−0.683305	−	0.730133i	$-0.739458\pi$
$877$	1.38678	−	1.38678i	0.0468281	−	0.0468281i	0.730133	+	0.683305i	$0.239458\pi$
$878$	−1.01499	+	1.01499i	−0.0342542	+	0.0342542i
$879$		0			0
$880$	−1.40573	−	5.78282i	−0.0473871	−	0.194939i
$881$	−8.63628			−0.290964			−0.145482	−	0.989361i	$-0.546473\pi$
$881$	−8.63628			−0.290964			−0.145482	+	0.989361i	$0.546473\pi$
$882$		0			0
$883$	−17.5459	+	17.5459i	−0.590468	+	0.590468i	−0.937758	−	0.347290i	$-0.887102\pi$
$883$	−17.5459	+	17.5459i	−0.590468	+	0.590468i	0.347290	+	0.937758i	$0.387102\pi$
$884$	0.946806			0.0318445
$885$		0			0
$886$			13.4302i			0.451198i
$887$	19.8938	−	19.8938i	0.667970	−	0.667970i	−0.289276	−	0.957246i	$-0.593415\pi$
$887$	19.8938	−	19.8938i	0.667970	−	0.667970i	0.957246	+	0.289276i	$0.0934145\pi$
$888$		0			0
$889$	22.6847			0.760821
$890$	−9.44746	−	5.75254i	−0.316680	−	0.192825i
$891$		0			0
$892$	13.3101	−	13.3101i	0.445656	−	0.445656i
$893$	8.00281	+	18.3647i	0.267804	+	0.614551i
$894$		0			0
$895$	3.42677	+	14.0969i	0.114544	+	0.471207i
$896$			1.27865i			0.0427166i
$897$		0			0
$898$	−12.5628	+	12.5628i	−0.419227	+	0.419227i
$899$			5.70197i			0.190171i
$900$		0			0
$901$			16.7528i			0.558116i
$902$	7.03855	+	7.03855i	0.234358	+	0.234358i
$903$		0			0
$904$		−	2.82348i		−	0.0939076i
$905$	0.266321	−	0.0647393i	0.00885282	−	0.00215201i
$906$		0			0
$907$	−19.4964	+	19.4964i	−0.647367	+	0.647367i	−0.952356	−	0.304989i	$-0.901347\pi$
$907$	−19.4964	+	19.4964i	−0.647367	+	0.647367i	0.304989	+	0.952356i	$0.401347\pi$
$908$	−21.0661	−	21.0661i	−0.699102	−	0.699102i
$909$		0			0
$910$	−0.302105	+	0.496151i	−0.0100147	+	0.0164473i
$911$		−	47.2989i		−	1.56708i	−0.621341	−	0.783541i	$-0.713412\pi$
$911$		−	47.2989i		−	1.56708i	0.621341	−	0.783541i	$-0.286588\pi$
$912$		0			0
$913$	17.4453	−	17.4453i	0.577355	−	0.577355i
$914$	9.53191			0.315288
$915$		0			0
$916$	−18.2167			−0.601897
$917$	−18.6435	−	18.6435i	−0.615664	−	0.615664i
$918$		0			0
$919$			42.1995i			1.39203i	0.718026	+	0.696016i	$0.245046\pi$
$919$			42.1995i			1.39203i	−0.718026	+	0.696016i	$0.754954\pi$
$920$	−1.31265	−	5.39990i	−0.0432767	−	0.178029i
$921$		0			0
$922$	2.98938	−	2.98938i	0.0984501	−	0.0984501i
$923$	0.367387	−	0.367387i	0.0120927	−	0.0120927i
$924$		0			0
$925$	−2.11266	+	6.63011i	−0.0694637	+	0.217997i
$926$		−	17.3575i		−	0.570403i
$927$		0			0
$928$	−1.53792	+	1.53792i	−0.0504846	+	0.0504846i
$929$		−	15.8786i		−	0.520960i	−0.965479	−	0.260480i	$-0.916119\pi$
$929$		−	15.8786i		−	0.520960i	0.965479	−	0.260480i	$-0.0838809\pi$
$930$		0			0
$931$	−8.55337	+	21.7654i	−0.280325	+	0.713333i
$932$	−20.6479	−	20.6479i	−0.676344	−	0.676344i
$933$		0			0
$934$	−12.9027			−0.422189
$935$	14.4236	−	23.6880i	0.471701	−	0.774680i
$936$		0			0
$937$	−7.52072	−	7.52072i	−0.245691	−	0.245691i	0.573508	−	0.819200i	$-0.305582\pi$
$937$	−7.52072	−	7.52072i	−0.245691	−	0.245691i	−0.819200	+	0.573508i	$0.805582\pi$
$938$	5.76578	−	5.76578i	0.188259	−	0.188259i
$939$		0			0
$940$	8.77741	+	5.34455i	0.286288	+	0.174320i
$941$		−	17.9276i		−	0.584422i	−0.956354	−	0.292211i	$-0.905609\pi$
$941$		−	17.9276i		−	0.584422i	0.956354	−	0.292211i	$-0.0943909\pi$
$942$		0			0
$943$	6.57249	+	6.57249i	0.214030	+	0.214030i
$944$	−2.19877			−0.0715640
$945$		0			0
$946$		−	7.56856i		−	0.246075i
$947$	6.90093	+	6.90093i	0.224250	+	0.224250i	0.810285	−	0.586035i	$-0.199312\pi$
$947$	6.90093	+	6.90093i	0.224250	+	0.224250i	−0.586035	+	0.810285i	$0.699312\pi$
$948$		0			0
$949$	1.50993			0.0490144
$950$	13.7535	−	16.9068i	0.446224	−	0.548529i
$951$		0			0
$952$	−4.21345	+	4.21345i	−0.136559	+	0.136559i
$953$	42.1375	+	42.1375i	1.36497	+	1.36497i	0.867458	+	0.497511i	$0.165752\pi$
$953$	42.1375	+	42.1375i	1.36497	+	1.36497i	0.497511	+	0.867458i	$0.334248\pi$
$954$		0			0
$955$	−0.250302	−	1.02968i	−0.00809958	−	0.0333197i
$956$	1.78480			0.0577247
$957$		0			0
$958$	−26.1144	−	26.1144i	−0.843718	−	0.843718i
$959$			4.41592i			0.142598i
$960$		0			0
$961$	24.1269			0.778286
$962$	−0.199937	+	0.199937i	−0.00644623	+	0.00644623i
$963$		0			0
$964$	6.17706			0.198950
$965$	−13.7680	+	22.6114i	−0.443209	+	0.727887i
$966$		0			0
$967$	−9.16729	−	9.16729i	−0.294800	−	0.294800i	0.544173	−	0.838973i	$-0.316844\pi$
$967$	−9.16729	−	9.16729i	−0.294800	−	0.294800i	−0.838973	+	0.544173i	$0.816844\pi$
$968$	2.76945	+	2.76945i	0.0890135	+	0.0890135i
$969$		0			0
$970$	−36.4069	+	8.85004i	−1.16895	+	0.284158i
$971$			47.1525i			1.51319i	0.653881	+	0.756597i	$0.273140\pi$
$971$			47.1525i			1.51319i	−0.653881	+	0.756597i	$0.726860\pi$
$972$		0			0
$973$	14.6466	−	14.6466i	0.469548	−	0.469548i
$974$		−	14.6882i		−	0.470642i
$975$		0			0
$976$	8.90579			0.285067
$977$	−26.5454	+	26.5454i	−0.849262	+	0.849262i	−0.990041	−	0.140779i	$-0.955039\pi$
$977$	−26.5454	+	26.5454i	−0.849262	+	0.849262i	0.140779	+	0.990041i	$0.455039\pi$
$978$		0			0
$979$	−13.1653			−0.420765
$980$	2.83371	+	11.6572i	0.0905195	+	0.372374i
$981$		0			0
$982$	22.1084	−	22.1084i	0.705509	−	0.705509i
$983$	30.2846	+	30.2846i	0.965928	+	0.965928i	0.999438	−	0.0335108i	$-0.0106688\pi$
$983$	30.2846	+	30.2846i	0.965928	+	0.965928i	−0.0335108	+	0.999438i	$0.510669\pi$
$984$		0			0
$985$	15.5464	−	25.5320i	0.495349	−	0.813517i
$986$	−10.1356			−0.322784
$987$		0			0
$988$	0.811859	−	0.353785i	0.0258287	−	0.0112554i
$989$		−	7.06740i		−	0.224730i
$990$		0			0
$991$			3.31607i			0.105339i	0.998612	+	0.0526693i	$0.0167729\pi$
$991$			3.31607i			0.105339i	−0.998612	+	0.0526693i	$0.983227\pi$
$992$	−1.85380	−	1.85380i	−0.0588581	−	0.0588581i
$993$		0			0
$994$			3.26988i			0.103714i
$995$	6.89926	−	1.67712i	0.218721	−	0.0531683i
$996$		0			0
$997$	−36.9548	−	36.9548i	−1.17037	−	1.17037i	−0.982122	−	0.188247i	$-0.939719\pi$
$997$	−36.9548	−	36.9548i	−1.17037	−	1.17037i	−0.188247	−	0.982122i	$-0.560281\pi$
$998$	−22.4905	−	22.4905i	−0.711925	−	0.711925i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.p.c.37.8		20
3.2	odd	2		570.2.m.b.37.3	✓	20
5.3	odd	4	inner	1710.2.p.c.1063.3		20
15.8	even	4		570.2.m.b.493.8	yes	20
19.18	odd	2	inner	1710.2.p.c.37.3		20
57.56	even	2		570.2.m.b.37.8	yes	20
95.18	even	4	inner	1710.2.p.c.1063.8		20
285.113	odd	4		570.2.m.b.493.3	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.m.b.37.3	✓	20	3.2	odd	2
570.2.m.b.37.8	yes	20	57.56	even	2
570.2.m.b.493.3	yes	20	285.113	odd	4
570.2.m.b.493.8	yes	20	15.8	even	4
1710.2.p.c.37.3		20	19.18	odd	2	inner
1710.2.p.c.37.8		20	1.1	even	1	trivial
1710.2.p.c.1063.3		20	5.3	odd	4	inner
1710.2.p.c.1063.8		20	95.18	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.528178 - 2.17279i) q^{5} +(0.904140 + 0.904140i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.528178 - 2.17279i) q^{5} +(0.904140 + 0.904140i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.90987 - 1.16292i) q^{10} -2.66147 q^{11} +(-0.143663 - 0.143663i) q^{13} +1.27865 q^{14} -1.00000 q^{16} +(-3.29524 - 3.29524i) q^{17} +(-4.05688 - 1.59427i) q^{19} +(-2.17279 + 0.528178i) q^{20} +(-1.88194 + 1.88194i) q^{22} +(-1.75733 + 1.75733i) q^{23} +(-4.44206 + 2.29524i) q^{25} -0.203169 q^{26} +(0.904140 - 0.904140i) q^{28} +2.17494 q^{29} +2.62167i q^{31} +(-0.707107 + 0.707107i) q^{32} -4.66018 q^{34} +(1.48696 - 2.44206i) q^{35} +(0.984090 - 0.984090i) q^{37} +(-3.99597 + 1.74133i) q^{38} +(-1.16292 + 1.90987i) q^{40} -3.74005i q^{41} +(-2.01084 + 2.01084i) q^{43} +2.66147i q^{44} +2.48524i q^{46} +(-3.24973 - 3.24973i) q^{47} -5.36506i q^{49} +(-1.51803 + 4.76399i) q^{50} +(-0.143663 + 0.143663i) q^{52} +(-2.54197 - 2.54197i) q^{53} +(1.40573 + 5.78282i) q^{55} -1.27865i q^{56} +(1.53792 - 1.53792i) q^{58} +2.19877 q^{59} -8.90579 q^{61} +(1.85380 + 1.85380i) q^{62} +1.00000i q^{64} +(-0.236270 + 0.388028i) q^{65} +(4.50928 - 4.50928i) q^{67} +(-3.29524 + 3.29524i) q^{68} +(-0.675353 - 2.77824i) q^{70} +2.55729i q^{71} +(-5.25513 + 5.25513i) q^{73} -1.39171i q^{74} +(-1.59427 + 4.05688i) q^{76} +(-2.40634 - 2.40634i) q^{77} -4.22731 q^{79} +(0.528178 + 2.17279i) q^{80} +(-2.64461 - 2.64461i) q^{82} +(-6.55477 + 6.55477i) q^{83} +(-5.41940 + 8.90035i) q^{85} +2.84376i q^{86} +(1.88194 + 1.88194i) q^{88} +4.94664 q^{89} -0.259782i q^{91} +(1.75733 + 1.75733i) q^{92} -4.59581 q^{94} +(-1.32127 + 9.65682i) q^{95} +(11.8481 - 11.8481i) q^{97} +(-3.79367 - 3.79367i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 12 q^{5} - 4 q^{7}+O(q^{10}) \) 20 * q - 12 * q^5 - 4 * q^7	\( 20 q - 12 q^{5} - 4 q^{7} + 8 q^{11} - 20 q^{16} + 12 q^{17} + 4 q^{23} - 28 q^{25} - 24 q^{26} - 4 q^{28} - 4 q^{35} + 12 q^{38} - 12 q^{43} + 44 q^{47} + 64 q^{55} - 8 q^{58} + 24 q^{62} + 12 q^{68} - 4 q^{73} + 4 q^{76} - 88 q^{77} + 12 q^{80} - 8 q^{82} - 76 q^{83} - 12 q^{85} - 4 q^{92} + 24 q^{95}+O(q^{100}) \) 20 * q - 12 * q^5 - 4 * q^7 + 8 * q^11 - 20 * q^16 + 12 * q^17 + 4 * q^23 - 28 * q^25 - 24 * q^26 - 4 * q^28 - 4 * q^35 + 12 * q^38 - 12 * q^43 + 44 * q^47 + 64 * q^55 - 8 * q^58 + 24 * q^62 + 12 * q^68 - 4 * q^73 + 4 * q^76 - 88 * q^77 + 12 * q^80 - 8 * q^82 - 76 * q^83 - 12 * q^85 - 4 * q^92 + 24 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more