LMFDB - Embedded newform 704.2.m.g.641.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [704,2,Mod(257,704)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("704.257"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(704, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 704 = 2^{6} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	704.m (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,3,0,-3,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.62146830230$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			641.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	704.641
Dual form			704.2.m.g.257.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.190983 + 0.587785i) q^{3} +(-1.30902 - 0.951057i) q^{5} +(0.190983 - 0.587785i) q^{7} +(2.11803 - 1.53884i) q^{9} +(-3.23607 - 0.726543i) q^{11} +(0.690983 - 0.502029i) q^{13} +(0.309017 - 0.951057i) q^{15} +(-3.92705 - 2.85317i) q^{17} +(-0.572949 - 1.76336i) q^{19} +0.381966 q^{21} +4.00000 q^{23} +(-0.736068 - 2.26538i) q^{25} +(2.80902 + 2.04087i) q^{27} +(2.57295 - 7.91872i) q^{29} +(-8.16312 + 5.93085i) q^{31} +(-0.190983 - 2.04087i) q^{33} +(-0.809017 + 0.587785i) q^{35} +(2.28115 - 7.02067i) q^{37} +(0.427051 + 0.310271i) q^{39} +(-2.28115 - 7.02067i) q^{41} +10.4721 q^{43} -4.23607 q^{45} +(-2.95492 - 9.09429i) q^{47} +(5.35410 + 3.88998i) q^{49} +(0.927051 - 2.85317i) q^{51} +(-1.30902 + 0.951057i) q^{53} +(3.54508 + 4.02874i) q^{55} +(0.927051 - 0.673542i) q^{57} +(-1.42705 + 4.39201i) q^{59} +(3.92705 + 2.85317i) q^{61} +(-0.500000 - 1.53884i) q^{63} -1.38197 q^{65} -5.52786 q^{67} +(0.763932 + 2.35114i) q^{69} +(4.92705 + 3.57971i) q^{71} +(-3.04508 + 9.37181i) q^{73} +(1.19098 - 0.865300i) q^{75} +(-1.04508 + 1.76336i) q^{77} +(2.30902 - 1.67760i) q^{79} +(1.76393 - 5.42882i) q^{81} +(-9.39919 - 6.82891i) q^{83} +(2.42705 + 7.46969i) q^{85} +5.14590 q^{87} +4.47214 q^{89} +(-0.163119 - 0.502029i) q^{91} +(-5.04508 - 3.66547i) q^{93} +(-0.927051 + 2.85317i) q^{95} +(-2.69098 + 1.95511i) q^{97} +(-7.97214 + 3.44095i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{3} - 3 q^{5} + 3 q^{7} + 4 q^{9} - 4 q^{11} + 5 q^{13} - q^{15} - 9 q^{17} - 9 q^{19} + 6 q^{21} + 16 q^{23} + 6 q^{25} + 9 q^{27} + 17 q^{29} - 17 q^{31} - 3 q^{33} - q^{35} - 11 q^{37} - 5 q^{39}+ \cdots - 14 q^{99}+O(q^{100}) $ 4 * q + 3 * q^3 - 3 * q^5 + 3 * q^7 + 4 * q^9 - 4 * q^11 + 5 * q^13 - q^15 - 9 * q^17 - 9 * q^19 + 6 * q^21 + 16 * q^23 + 6 * q^25 + 9 * q^27 + 17 * q^29 - 17 * q^31 - 3 * q^33 - q^35 - 11 * q^37 - 5 * q^39 + 11 * q^41 + 24 * q^43 - 8 * q^45 - 23 * q^47 + 8 * q^49 - 3 * q^51 - 3 * q^53 + 3 * q^55 - 3 * q^57 + q^59 + 9 * q^61 - 2 * q^63 - 10 * q^65 - 40 * q^67 + 12 * q^69 + 13 * q^71 - q^73 + 7 * q^75 + 7 * q^77 + 7 * q^79 + 16 * q^81 - 13 * q^83 + 3 * q^85 + 34 * q^87 + 15 * q^91 - 9 * q^93 + 3 * q^95 - 13 * q^97 - 14 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/704\mathbb{Z}\right)^\times$.

$n$	$133$	$321$	$639$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$

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
$3$	0.190983	+	0.587785i	0.110264	+	0.339358i	0.990930	−	0.134380i	$-0.0429043\pi$
$3$	0.190983	+	0.587785i	0.110264	+	0.339358i	−0.880666	+	0.473738i	$0.842904\pi$
$4$		0			0
$5$	−1.30902	−	0.951057i	−0.585410	−	0.425325i	0.255260	−	0.966872i	$-0.417839\pi$
$5$	−1.30902	−	0.951057i	−0.585410	−	0.425325i	−0.840670	+	0.541547i	$0.817839\pi$
$6$		0			0
$7$	0.190983	−	0.587785i	0.0721848	−	0.222162i	−0.908455	−	0.417983i	$-0.862737\pi$
$7$	0.190983	−	0.587785i	0.0721848	−	0.222162i	0.980640	+	0.195821i	$0.0627372\pi$
$8$		0			0
$9$	2.11803	−	1.53884i	0.706011	−	0.512947i
$10$		0			0
$11$	−3.23607	−	0.726543i	−0.975711	−	0.219061i
$11$	−3.23607	−	0.726543i	−0.975711	−	0.219061i
$12$		0			0
$13$	0.690983	−	0.502029i	0.191644	−	0.139238i	−0.487826	−	0.872941i	$-0.662210\pi$
$13$	0.690983	−	0.502029i	0.191644	−	0.139238i	0.679470	+	0.733703i	$0.262210\pi$
$14$		0			0
$15$	0.309017	−	0.951057i	0.0797878	−	0.245562i
$16$		0			0
$17$	−3.92705	−	2.85317i	−0.952450	−	0.691995i	−0.00106476	−	0.999999i	$-0.500339\pi$
$17$	−3.92705	−	2.85317i	−0.952450	−	0.691995i	−0.951385	+	0.308004i	$0.900339\pi$
$18$		0			0
$19$	−0.572949	−	1.76336i	−0.131444	−	0.404542i	0.863576	−	0.504218i	$-0.168219\pi$
$19$	−0.572949	−	1.76336i	−0.131444	−	0.404542i	−0.995020	+	0.0996765i	$0.968219\pi$
$20$		0			0
$21$	0.381966			0.0833518
$22$		0			0
$23$	4.00000			0.834058			0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000			0.834058			0.417029	+	0.908893i	$0.363071\pi$
$24$		0			0
$25$	−0.736068	−	2.26538i	−0.147214	−	0.453077i
$26$		0			0
$27$	2.80902	+	2.04087i	0.540596	+	0.392766i
$28$		0			0
$29$	2.57295	−	7.91872i	0.477785	−	1.47047i	−0.364380	−	0.931250i	$-0.618719\pi$
$29$	2.57295	−	7.91872i	0.477785	−	1.47047i	0.842165	−	0.539220i	$-0.181281\pi$
$30$		0			0
$31$	−8.16312	+	5.93085i	−1.46614	+	1.06521i	−0.484429	+	0.874830i	$0.660973\pi$
$31$	−8.16312	+	5.93085i	−1.46614	+	1.06521i	−0.981710	+	0.190382i	$0.939027\pi$
$32$		0			0
$33$	−0.190983	−	2.04087i	−0.0332459	−	0.355270i
$34$		0			0
$35$	−0.809017	+	0.587785i	−0.136749	+	0.0993538i
$36$		0			0
$37$	2.28115	−	7.02067i	0.375019	−	1.15419i	−0.568446	−	0.822720i	$-0.692455\pi$
$37$	2.28115	−	7.02067i	0.375019	−	1.15419i	0.943466	−	0.331470i	$-0.107545\pi$
$38$		0			0
$39$	0.427051	+	0.310271i	0.0683829	+	0.0496831i
$40$		0			0
$41$	−2.28115	−	7.02067i	−0.356256	−	1.09644i	−0.955277	−	0.295711i	$-0.904444\pi$
$41$	−2.28115	−	7.02067i	−0.356256	−	1.09644i	0.599021	−	0.800733i	$-0.295556\pi$
$42$		0			0
$43$	10.4721			1.59699			0.798493	−	0.602004i	$-0.205631\pi$
$43$	10.4721			1.59699			0.798493	+	0.602004i	$0.205631\pi$
$44$		0			0
$45$	−4.23607			−0.631476
$46$		0			0
$47$	−2.95492	−	9.09429i	−0.431019	−	1.32654i	−0.897112	−	0.441803i	$-0.854339\pi$
$47$	−2.95492	−	9.09429i	−0.431019	−	1.32654i	0.466093	−	0.884736i	$-0.345661\pi$
$48$		0			0
$49$	5.35410	+	3.88998i	0.764872	+	0.555712i
$50$		0			0
$51$	0.927051	−	2.85317i	0.129813	−	0.399524i
$52$		0			0
$53$	−1.30902	+	0.951057i	−0.179807	+	0.130638i	−0.674048	−	0.738687i	$-0.735446\pi$
$53$	−1.30902	+	0.951057i	−0.179807	+	0.130638i	0.494241	+	0.869325i	$0.335446\pi$
$54$		0			0
$55$	3.54508	+	4.02874i	0.478019	+	0.543235i
$56$		0			0
$57$	0.927051	−	0.673542i	0.122791	−	0.0892128i
$58$		0			0
$59$	−1.42705	+	4.39201i	−0.185786	+	0.571791i	−0.999961	−	0.00882865i	$-0.997190\pi$
$59$	−1.42705	+	4.39201i	−0.185786	+	0.571791i	0.814175	+	0.580620i	$0.197190\pi$
$60$		0			0
$61$	3.92705	+	2.85317i	0.502807	+	0.365311i	0.810088	−	0.586308i	$-0.199419\pi$
$61$	3.92705	+	2.85317i	0.502807	+	0.365311i	−0.307281	+	0.951619i	$0.599419\pi$
$62$		0			0
$63$	−0.500000	−	1.53884i	−0.0629941	−	0.193876i
$64$		0			0
$65$	−1.38197			−0.171412
$66$		0			0
$67$	−5.52786			−0.675336			−0.337668	−	0.941265i	$-0.609638\pi$
$67$	−5.52786			−0.675336			−0.337668	+	0.941265i	$0.609638\pi$
$68$		0			0
$69$	0.763932	+	2.35114i	0.0919666	+	0.283044i
$70$		0			0
$71$	4.92705	+	3.57971i	0.584733	+	0.424834i	0.840427	−	0.541924i	$-0.182304\pi$
$71$	4.92705	+	3.57971i	0.584733	+	0.424834i	−0.255694	+	0.966758i	$0.582304\pi$
$72$		0			0
$73$	−3.04508	+	9.37181i	−0.356400	+	1.09689i	0.598793	+	0.800904i	$0.295647\pi$
$73$	−3.04508	+	9.37181i	−0.356400	+	1.09689i	−0.955193	+	0.295983i	$0.904353\pi$
$74$		0			0
$75$	1.19098	−	0.865300i	0.137523	−	0.0999162i
$76$		0			0
$77$	−1.04508	+	1.76336i	−0.119098	+	0.200953i
$78$		0			0
$79$	2.30902	−	1.67760i	0.259785	−	0.188745i	−0.450267	−	0.892894i	$-0.648671\pi$
$79$	2.30902	−	1.67760i	0.259785	−	0.188745i	0.710052	+	0.704149i	$0.248671\pi$
$80$		0			0
$81$	1.76393	−	5.42882i	0.195992	−	0.603203i
$82$		0			0
$83$	−9.39919	−	6.82891i	−1.03169	−	0.749570i	−0.0630476	−	0.998011i	$-0.520082\pi$
$83$	−9.39919	−	6.82891i	−1.03169	−	0.749570i	−0.968647	+	0.248440i	$0.920082\pi$
$84$		0			0
$85$	2.42705	+	7.46969i	0.263251	+	0.810202i
$86$		0			0
$87$	5.14590			0.551698
$88$		0			0
$89$	4.47214			0.474045			0.237023	−	0.971504i	$-0.423828\pi$
$89$	4.47214			0.474045			0.237023	+	0.971504i	$0.423828\pi$
$90$		0			0
$91$	−0.163119	−	0.502029i	−0.0170995	−	0.0526269i
$92$		0			0
$93$	−5.04508	−	3.66547i	−0.523151	−	0.380091i
$94$		0			0
$95$	−0.927051	+	2.85317i	−0.0951134	+	0.292729i
$96$		0			0
$97$	−2.69098	+	1.95511i	−0.273228	+	0.198512i	−0.715958	−	0.698143i	$-0.754010\pi$
$97$	−2.69098	+	1.95511i	−0.273228	+	0.198512i	0.442730	+	0.896655i	$0.354010\pi$
$98$		0			0
$99$	−7.97214	+	3.44095i	−0.801230	+	0.345829i
$100$		0			0
$101$	−6.54508	+	4.75528i	−0.651260	+	0.473168i	−0.863700	−	0.504006i	$-0.831859\pi$
$101$	−6.54508	+	4.75528i	−0.651260	+	0.473168i	0.212440	+	0.977174i	$0.431859\pi$
$102$		0			0
$103$	−0.281153	+	0.865300i	−0.0277028	+	0.0852605i	−0.963952	−	0.266076i	$-0.914273\pi$
$103$	−0.281153	+	0.865300i	−0.0277028	+	0.0852605i	0.936249	+	0.351337i	$0.114273\pi$
$104$		0			0
$105$	−0.500000	−	0.363271i	−0.0487950	−	0.0354516i
$106$		0			0
$107$	4.66312	+	14.3516i	0.450801	+	1.38742i	0.875995	+	0.482320i	$0.160206\pi$
$107$	4.66312	+	14.3516i	0.450801	+	1.38742i	−0.425194	+	0.905102i	$0.639794\pi$
$108$		0			0
$109$	2.94427			0.282010			0.141005	−	0.990009i	$-0.454967\pi$
$109$	2.94427			0.282010			0.141005	+	0.990009i	$0.454967\pi$
$110$		0			0
$111$	4.56231			0.433035
$112$		0			0
$113$	0.663119	+	2.04087i	0.0623810	+	0.191989i	0.977390	−	0.211444i	$-0.0678167\pi$
$113$	0.663119	+	2.04087i	0.0623810	+	0.191989i	−0.915009	+	0.403433i	$0.867817\pi$
$114$		0			0
$115$	−5.23607	−	3.80423i	−0.488266	−	0.354746i
$116$		0			0
$117$	0.690983	−	2.12663i	0.0638814	−	0.196607i
$118$		0			0
$119$	−2.42705	+	1.76336i	−0.222487	+	0.161647i
$120$		0			0
$121$	9.94427	+	4.70228i	0.904025	+	0.427480i
$122$		0			0
$123$	3.69098	−	2.68166i	0.332805	−	0.241797i
$124$		0			0
$125$	−3.69098	+	11.3597i	−0.330132	+	1.01604i
$126$		0			0
$127$	−17.2533	−	12.5352i	−1.53098	−	1.11232i	−0.955690	−	0.294375i	$-0.904888\pi$
$127$	−17.2533	−	12.5352i	−1.53098	−	1.11232i	−0.575292	−	0.817948i	$-0.695112\pi$
$128$		0			0
$129$	2.00000	+	6.15537i	0.176090	+	0.541950i
$130$		0			0
$131$	8.00000			0.698963			0.349482	−	0.936943i	$-0.386358\pi$
$131$	8.00000			0.698963			0.349482	+	0.936943i	$0.386358\pi$
$132$		0			0
$133$	−1.14590			−0.0993620
$134$		0			0
$135$	−1.73607	−	5.34307i	−0.149417	−	0.459858i
$136$		0			0
$137$	2.07295	+	1.50609i	0.177104	+	0.128674i	0.672806	−	0.739819i	$-0.265089\pi$
$137$	2.07295	+	1.50609i	0.177104	+	0.128674i	−0.495702	+	0.868493i	$0.665089\pi$
$138$		0			0
$139$	5.33688	−	16.4252i	0.452668	−	1.39317i	−0.421183	−	0.906976i	$-0.638385\pi$
$139$	5.33688	−	16.4252i	0.452668	−	1.39317i	0.873851	−	0.486194i	$-0.161615\pi$
$140$		0			0
$141$	4.78115	−	3.47371i	0.402646	−	0.292539i
$142$		0			0
$143$	−2.60081	+	1.12257i	−0.217491	+	0.0938740i
$144$		0			0
$145$	−10.8992	+	7.91872i	−0.905128	+	0.657614i
$146$		0			0
$147$	−1.26393	+	3.88998i	−0.104247	+	0.320840i
$148$		0			0
$149$	−9.01722	−	6.55139i	−0.738720	−	0.536711i	0.153590	−	0.988135i	$-0.450916\pi$
$149$	−9.01722	−	6.55139i	−0.738720	−	0.536711i	−0.892310	+	0.451423i	$0.850916\pi$
$150$		0			0
$151$	2.57295	+	7.91872i	0.209384	+	0.644417i	0.999505	+	0.0314659i	$0.0100176\pi$
$151$	2.57295	+	7.91872i	0.209384	+	0.644417i	−0.790121	+	0.612951i	$0.789982\pi$
$152$		0			0
$153$	−12.7082			−1.02740
$154$		0			0
$155$	16.3262			1.31135
$156$		0			0
$157$	5.04508	+	15.5272i	0.402642	+	1.23920i	0.922848	+	0.385163i	$0.125855\pi$
$157$	5.04508	+	15.5272i	0.402642	+	1.23920i	−0.520207	+	0.854040i	$0.674145\pi$
$158$		0			0
$159$	−0.809017	−	0.587785i	−0.0641592	−	0.0466144i
$160$		0			0
$161$	0.763932	−	2.35114i	0.0602063	−	0.185296i
$162$		0			0
$163$	−12.7812	+	9.28605i	−1.00110	+	0.727340i	−0.962323	−	0.271908i	$-0.912345\pi$
$163$	−12.7812	+	9.28605i	−1.00110	+	0.727340i	−0.0387740	+	0.999248i	$0.512345\pi$
$164$		0			0
$165$	−1.69098	+	2.85317i	−0.131643	+	0.222119i
$166$		0			0
$167$	1.07295	−	0.779543i	0.0830273	−	0.0603229i	−0.545497	−	0.838113i	$-0.683659\pi$
$167$	1.07295	−	0.779543i	0.0830273	−	0.0603229i	0.628525	+	0.777790i	$0.283659\pi$
$168$		0			0
$169$	−3.79180	+	11.6699i	−0.291677	+	0.897688i
$170$		0			0
$171$	−3.92705	−	2.85317i	−0.300309	−	0.218187i
$172$		0			0
$173$	−0.663119	−	2.04087i	−0.0504160	−	0.155164i	0.922679	−	0.385569i	$-0.125995\pi$
$173$	−0.663119	−	2.04087i	−0.0504160	−	0.155164i	−0.973095	+	0.230405i	$0.925995\pi$
$174$		0			0
$175$	−1.47214			−0.111283
$176$		0			0
$177$	−2.85410			−0.214527
$178$		0			0
$179$	−2.86475	−	8.81678i	−0.214121	−	0.658997i	−0.999215	−	0.0396200i	$-0.987385\pi$
$179$	−2.86475	−	8.81678i	−0.214121	−	0.658997i	0.785094	−	0.619377i	$-0.212615\pi$
$180$		0			0
$181$	19.6353	+	14.2658i	1.45948	+	1.06037i	0.983499	+	0.180915i	$0.0579059\pi$
$181$	19.6353	+	14.2658i	1.45948	+	1.06037i	0.475978	+	0.879457i	$0.342094\pi$
$182$		0			0
$183$	−0.927051	+	2.85317i	−0.0685296	+	0.210912i
$184$		0			0
$185$	−9.66312	+	7.02067i	−0.710447	+	0.516170i
$186$		0			0
$187$	10.6353	+	12.0862i	0.777727	+	0.883832i
$188$		0			0
$189$	1.73607	−	1.26133i	0.126280	−	0.0917481i
$190$		0			0
$191$	−6.75329	+	20.7845i	−0.488651	+	1.50391i	0.337972	+	0.941156i	$0.390259\pi$
$191$	−6.75329	+	20.7845i	−0.488651	+	1.50391i	−0.826623	+	0.562756i	$0.809741\pi$
$192$		0			0
$193$	7.78115	+	5.65334i	0.560100	+	0.406936i	0.831495	−	0.555532i	$-0.187485\pi$
$193$	7.78115	+	5.65334i	0.560100	+	0.406936i	−0.271396	+	0.962468i	$0.587485\pi$
$194$		0			0
$195$	−0.263932	−	0.812299i	−0.0189006	−	0.0581700i
$196$		0			0
$197$	8.47214			0.603615			0.301807	−	0.953369i	$-0.402410\pi$
$197$	8.47214			0.603615			0.301807	+	0.953369i	$0.402410\pi$
$198$		0			0
$199$	24.3607			1.72688			0.863441	−	0.504449i	$-0.168304\pi$
$199$	24.3607			1.72688			0.863441	+	0.504449i	$0.168304\pi$
$200$		0			0
$201$	−1.05573	−	3.24920i	−0.0744653	−	0.229181i
$202$		0			0
$203$	−4.16312	−	3.02468i	−0.292194	−	0.212291i
$204$		0			0
$205$	−3.69098	+	11.3597i	−0.257789	+	0.793394i
$206$		0			0
$207$	8.47214	−	6.15537i	0.588854	−	0.427828i
$208$		0			0
$209$	0.572949	+	6.12261i	0.0396317	+	0.423510i
$210$		0			0
$211$	−1.54508	+	1.12257i	−0.106368	+	0.0772809i	−0.639698	−	0.768627i	$-0.720940\pi$
$211$	−1.54508	+	1.12257i	−0.106368	+	0.0772809i	0.533330	+	0.845907i	$0.320940\pi$
$212$		0			0
$213$	−1.16312	+	3.57971i	−0.0796956	+	0.245278i
$214$		0			0
$215$	−13.7082	−	9.95959i	−0.934892	−	0.679239i
$216$		0			0
$217$	1.92705	+	5.93085i	0.130817	+	0.402613i
$218$		0			0
$219$	−6.09017			−0.411536
$220$		0			0
$221$	−4.14590			−0.278883
$222$		0			0
$223$	2.28115	+	7.02067i	0.152757	+	0.470139i	0.997927	−	0.0643598i	$-0.0205005\pi$
$223$	2.28115	+	7.02067i	0.152757	+	0.470139i	−0.845169	+	0.534498i	$0.820501\pi$
$224$		0			0
$225$	−5.04508	−	3.66547i	−0.336339	−	0.244365i
$226$		0			0
$227$	4.28115	−	13.1760i	0.284150	−	0.874524i	−0.702502	−	0.711682i	$-0.747934\pi$
$227$	4.28115	−	13.1760i	0.284150	−	0.874524i	0.986652	−	0.162842i	$-0.0520662\pi$
$228$		0			0
$229$	−0.545085	+	0.396027i	−0.0360202	+	0.0261702i	−0.605650	−	0.795731i	$-0.707087\pi$
$229$	−0.545085	+	0.396027i	−0.0360202	+	0.0261702i	0.569629	+	0.821902i	$0.307087\pi$
$230$		0			0
$231$	−1.23607	−	0.277515i	−0.0813273	−	0.0182591i
$232$		0			0
$233$	10.5451	−	7.66145i	0.690831	−	0.501918i	−0.186102	−	0.982530i	$-0.559585\pi$
$233$	10.5451	−	7.66145i	0.690831	−	0.501918i	0.876933	+	0.480612i	$0.159585\pi$
$234$		0			0
$235$	−4.78115	+	14.7149i	−0.311888	+	0.959893i
$236$		0			0
$237$	1.42705	+	1.03681i	0.0926969	+	0.0673483i
$238$		0			0
$239$	−4.48278	−	13.7966i	−0.289967	−	0.892426i	−0.984866	−	0.173319i	$-0.944551\pi$
$239$	−4.48278	−	13.7966i	−0.289967	−	0.892426i	0.694899	−	0.719107i	$-0.255449\pi$
$240$		0			0
$241$	18.9443			1.22031			0.610154	−	0.792283i	$-0.291108\pi$
$241$	18.9443			1.22031			0.610154	+	0.792283i	$0.291108\pi$
$242$		0			0
$243$	13.9443			0.894525
$244$		0			0
$245$	−3.30902	−	10.1841i	−0.211405	−	0.650639i
$246$		0			0
$247$	−1.28115	−	0.930812i	−0.0815178	−	0.0592262i
$248$		0			0
$249$	2.21885	−	6.82891i	0.140614	−	0.432765i
$250$		0			0
$251$	−6.78115	+	4.92680i	−0.428023	+	0.310977i	−0.780858	−	0.624709i	$-0.785218\pi$
$251$	−6.78115	+	4.92680i	−0.428023	+	0.310977i	0.352835	+	0.935685i	$0.385218\pi$
$252$		0			0
$253$	−12.9443	−	2.90617i	−0.813799	−	0.182709i
$254$		0			0
$255$	−3.92705	+	2.85317i	−0.245921	+	0.178672i
$256$		0			0
$257$	5.42705	−	16.7027i	0.338530	−	1.04189i	−0.626427	−	0.779480i	$-0.715483\pi$
$257$	5.42705	−	16.7027i	0.338530	−	1.04189i	0.964957	−	0.262408i	$-0.0845167\pi$
$258$		0			0
$259$	−3.69098	−	2.68166i	−0.229347	−	0.166630i
$260$		0			0
$261$	−6.73607	−	20.7315i	−0.416952	−	1.28325i
$262$		0			0
$263$	19.4164			1.19727			0.598633	−	0.801023i	$-0.295711\pi$
$263$	19.4164			1.19727			0.598633	+	0.801023i	$0.295711\pi$
$264$		0			0
$265$	2.61803			0.160825
$266$		0			0
$267$	0.854102	+	2.62866i	0.0522702	+	0.160871i
$268$		0			0
$269$	−9.78115	−	7.10642i	−0.596367	−	0.433286i	0.248220	−	0.968704i	$-0.420154\pi$
$269$	−9.78115	−	7.10642i	−0.596367	−	0.433286i	−0.844588	+	0.535417i	$0.820154\pi$
$270$		0			0
$271$	8.84346	−	27.2174i	0.537202	−	1.65334i	−0.201641	−	0.979460i	$-0.564627\pi$
$271$	8.84346	−	27.2174i	0.537202	−	1.65334i	0.738843	−	0.673878i	$-0.235373\pi$
$272$		0			0
$273$	0.263932	−	0.191758i	0.0159739	−	0.0116057i
$274$		0			0
$275$	0.736068	+	7.86572i	0.0443866	+	0.474321i
$276$		0			0
$277$	−4.54508	+	3.30220i	−0.273088	+	0.198410i	−0.715897	−	0.698206i	$-0.753982\pi$
$277$	−4.54508	+	3.30220i	−0.273088	+	0.198410i	0.442809	+	0.896616i	$0.353982\pi$
$278$		0			0
$279$	−8.16312	+	25.1235i	−0.488713	+	1.50410i
$280$		0			0
$281$	5.30902	+	3.85723i	0.316709	+	0.230103i	0.734770	−	0.678316i	$-0.237290\pi$
$281$	5.30902	+	3.85723i	0.316709	+	0.230103i	−0.418061	+	0.908419i	$0.637290\pi$
$282$		0			0
$283$	−3.33688	−	10.2699i	−0.198357	−	0.610480i	−0.999921	−	0.0125710i	$-0.995998\pi$
$283$	−3.33688	−	10.2699i	−0.198357	−	0.610480i	0.801564	−	0.597909i	$-0.204002\pi$
$284$		0			0
$285$	−1.85410			−0.109828
$286$		0			0
$287$	−4.56231			−0.269304
$288$		0			0
$289$	2.02786	+	6.24112i	0.119286	+	0.367125i
$290$		0			0
$291$	−1.66312	−	1.20833i	−0.0974938	−	0.0708334i
$292$		0			0
$293$	−2.95492	+	9.09429i	−0.172628	+	0.531294i	−0.999517	−	0.0310706i	$-0.990108\pi$
$293$	−2.95492	+	9.09429i	−0.172628	+	0.531294i	0.826889	+	0.562365i	$0.190108\pi$
$294$		0			0
$295$	6.04508	−	4.39201i	0.351958	−	0.255713i
$296$		0			0
$297$	−7.60739	−	8.64527i	−0.441426	−	0.501649i
$298$		0			0
$299$	2.76393	−	2.00811i	0.159842	−	0.116132i
$300$		0			0
$301$	2.00000	−	6.15537i	0.115278	−	0.354789i
$302$		0			0
$303$	−4.04508	−	2.93893i	−0.232384	−	0.168837i
$304$		0			0
$305$	−2.42705	−	7.46969i	−0.138973	−	0.427713i
$306$		0			0
$307$	−1.88854			−0.107785			−0.0538924	−	0.998547i	$-0.517163\pi$
$307$	−1.88854			−0.107785			−0.0538924	+	0.998547i	$0.517163\pi$
$308$		0			0
$309$	−0.562306			−0.0319885
$310$		0			0
$311$	0.392609	+	1.20833i	0.0222628	+	0.0685179i	0.961571	−	0.274557i	$-0.0885314\pi$
$311$	0.392609	+	1.20833i	0.0222628	+	0.0685179i	−0.939308	+	0.343075i	$0.888531\pi$
$312$		0			0
$313$	−11.9271	−	8.66551i	−0.674157	−	0.489804i	0.197257	−	0.980352i	$-0.436797\pi$
$313$	−11.9271	−	8.66551i	−0.674157	−	0.489804i	−0.871414	+	0.490548i	$0.836797\pi$
$314$		0			0
$315$	−0.809017	+	2.48990i	−0.0455829	+	0.140290i
$316$		0			0
$317$	12.3992	−	9.00854i	0.696408	−	0.505970i	−0.182353	−	0.983233i	$-0.558371\pi$
$317$	12.3992	−	9.00854i	0.696408	−	0.505970i	0.878760	+	0.477263i	$0.158371\pi$
$318$		0			0
$319$	−14.0795	+	23.7562i	−0.788302	+	1.33009i
$320$		0			0
$321$	−7.54508	+	5.48183i	−0.421126	+	0.305966i
$322$		0			0
$323$	−2.78115	+	8.55951i	−0.154747	+	0.476264i
$324$		0			0
$325$	−1.64590	−	1.19581i	−0.0912980	−	0.0663319i
$326$		0			0
$327$	0.562306	+	1.73060i	0.0310956	+	0.0957024i
$328$		0			0
$329$	−5.90983			−0.325819
$330$		0			0
$331$	8.94427			0.491622			0.245811	−	0.969318i	$-0.420946\pi$
$331$	8.94427			0.491622			0.245811	+	0.969318i	$0.420946\pi$
$332$		0			0
$333$	−5.97214	−	18.3803i	−0.327271	−	1.00724i
$334$		0			0
$335$	7.23607	+	5.25731i	0.395349	+	0.287238i
$336$		0			0
$337$	8.84346	−	27.2174i	0.481734	−	1.48262i	−0.354922	−	0.934896i	$-0.615493\pi$
$337$	8.84346	−	27.2174i	0.481734	−	1.48262i	0.836656	−	0.547729i	$-0.184507\pi$
$338$		0			0
$339$	−1.07295	+	0.779543i	−0.0582746	+	0.0423390i
$340$		0			0
$341$	30.7254	−	13.2618i	1.66388	−	0.718166i
$342$		0			0
$343$	6.80902	−	4.94704i	0.367652	−	0.267115i
$344$		0			0
$345$	1.23607	−	3.80423i	0.0665477	−	0.204813i
$346$		0			0
$347$	−23.8713	−	17.3435i	−1.28148	−	0.931050i	−0.281883	−	0.959449i	$-0.590959\pi$
$347$	−23.8713	−	17.3435i	−1.28148	−	0.931050i	−0.999597	+	0.0283992i	$0.990959\pi$
$348$		0			0
$349$	4.10081	+	12.6210i	0.219511	+	0.675587i	0.998802	+	0.0489247i	$0.0155794\pi$
$349$	4.10081	+	12.6210i	0.219511	+	0.675587i	−0.779291	+	0.626662i	$0.784421\pi$
$350$		0			0
$351$	2.96556			0.158290
$352$		0			0
$353$	−25.4164			−1.35278			−0.676389	−	0.736544i	$-0.736456\pi$
$353$	−25.4164			−1.35278			−0.676389	+	0.736544i	$0.736456\pi$
$354$		0			0
$355$	−3.04508	−	9.37181i	−0.161616	−	0.497404i
$356$		0			0
$357$	−1.50000	−	1.08981i	−0.0793884	−	0.0576791i
$358$		0			0
$359$	6.95492	−	21.4050i	0.367066	−	1.12971i	−0.581611	−	0.813467i	$-0.697577\pi$
$359$	6.95492	−	21.4050i	0.367066	−	1.12971i	0.948677	−	0.316247i	$-0.102423\pi$
$360$		0			0
$361$	12.5902	−	9.14729i	0.662641	−	0.481437i
$362$		0			0
$363$	−0.864745	+	6.74315i	−0.0453873	+	0.353924i
$364$		0			0
$365$	12.8992	−	9.37181i	0.675174	−	0.490543i
$366$		0			0
$367$	3.60739	−	11.1024i	0.188304	−	0.579541i	−0.811685	−	0.584095i	$-0.801450\pi$
$367$	3.60739	−	11.1024i	0.188304	−	0.579541i	0.999990	+	0.00455397i	$0.00144958\pi$
$368$		0			0
$369$	−15.6353	−	11.3597i	−0.813939	−	0.591361i
$370$		0			0
$371$	0.309017	+	0.951057i	0.0160434	+	0.0493764i
$372$		0			0
$373$	−21.4164			−1.10890			−0.554450	−	0.832217i	$-0.687071\pi$
$373$	−21.4164			−1.10890			−0.554450	+	0.832217i	$0.687071\pi$
$374$		0			0
$375$	−7.38197			−0.381203
$376$		0			0
$377$	−2.19756	−	6.76340i	−0.113180	−	0.348333i
$378$		0			0
$379$	11.5451	+	8.38800i	0.593031	+	0.430862i	0.843398	−	0.537289i	$-0.180551\pi$
$379$	11.5451	+	8.38800i	0.593031	+	0.430862i	−0.250367	+	0.968151i	$0.580551\pi$
$380$		0			0
$381$	4.07295	−	12.5352i	0.208663	−	0.642200i
$382$		0			0
$383$	−25.1074	+	18.2416i	−1.28293	+	0.932102i	−0.999637	−	0.0269326i	$-0.991426\pi$
$383$	−25.1074	+	18.2416i	−1.28293	+	0.932102i	−0.283290	+	0.959034i	$0.591426\pi$
$384$		0			0
$385$	3.04508	−	1.31433i	0.155192	−	0.0669843i
$386$		0			0
$387$	22.1803	−	16.1150i	1.12749	−	0.819169i
$388$		0			0
$389$	4.86475	−	14.9721i	0.246652	−	0.759118i	−0.748708	−	0.662900i	$-0.769325\pi$
$389$	4.86475	−	14.9721i	0.246652	−	0.759118i	0.995360	−	0.0962179i	$-0.0306746\pi$
$390$		0			0
$391$	−15.7082	−	11.4127i	−0.794398	−	0.577164i
$392$		0			0
$393$	1.52786	+	4.70228i	0.0770705	+	0.237199i
$394$		0			0
$395$	−4.61803			−0.232359
$396$		0			0
$397$	29.4164			1.47637			0.738184	−	0.674600i	$-0.235684\pi$
$397$	29.4164			1.47637			0.738184	+	0.674600i	$0.235684\pi$
$398$		0			0
$399$	−0.218847	−	0.673542i	−0.0109561	−	0.0337193i
$400$		0			0
$401$	3.30902	+	2.40414i	0.165244	+	0.120057i	0.667334	−	0.744758i	$-0.267435\pi$
$401$	3.30902	+	2.40414i	0.165244	+	0.120057i	−0.502090	+	0.864816i	$0.667435\pi$
$402$		0			0
$403$	−2.66312	+	8.19624i	−0.132659	+	0.408284i
$404$		0			0
$405$	−7.47214	+	5.42882i	−0.371293	+	0.269760i
$406$		0			0
$407$	−12.4828	+	21.0620i	−0.618748	+	1.04400i
$408$		0			0
$409$	15.0172	−	10.9106i	0.742554	−	0.539497i	−0.150956	−	0.988540i	$-0.548235\pi$
$409$	15.0172	−	10.9106i	0.742554	−	0.539497i	0.893510	+	0.449044i	$0.148235\pi$
$410$		0			0
$411$	−0.489357	+	1.50609i	−0.0241382	+	0.0742897i
$412$		0			0
$413$	2.30902	+	1.67760i	0.113619	+	0.0825493i
$414$		0			0
$415$	5.80902	+	17.8783i	0.285153	+	0.877612i
$416$		0			0
$417$	10.6738			0.522696
$418$		0			0
$419$	20.9443			1.02319			0.511597	−	0.859225i	$-0.329054\pi$
$419$	20.9443			1.02319			0.511597	+	0.859225i	$0.329054\pi$
$420$		0			0
$421$	−0.954915	−	2.93893i	−0.0465397	−	0.143235i	0.925086	−	0.379757i	$-0.123992\pi$
$421$	−0.954915	−	2.93893i	−0.0465397	−	0.143235i	−0.971626	+	0.236522i	$0.923992\pi$
$422$		0			0
$423$	−20.2533	−	14.7149i	−0.984749	−	0.715462i
$424$		0			0
$425$	−3.57295	+	10.9964i	−0.173313	+	0.533404i
$426$		0			0
$427$	2.42705	−	1.76336i	0.117453	−	0.0853348i
$428$		0			0
$429$	−1.15654	−	1.31433i	−0.0558383	−	0.0634563i
$430$		0			0
$431$	29.2533	−	21.2538i	1.40908	−	1.02376i	0.415626	−	0.909536i	$-0.363562\pi$
$431$	29.2533	−	21.2538i	1.40908	−	1.02376i	0.993455	−	0.114222i	$-0.0364375\pi$
$432$		0			0
$433$	−8.28115	+	25.4868i	−0.397967	+	1.22482i	0.528660	+	0.848834i	$0.322695\pi$
$433$	−8.28115	+	25.4868i	−0.397967	+	1.22482i	−0.926627	+	0.375982i	$0.877305\pi$
$434$		0			0
$435$	−6.73607	−	4.89404i	−0.322970	−	0.234651i
$436$		0			0
$437$	−2.29180	−	7.05342i	−0.109631	−	0.337411i
$438$		0			0
$439$	−16.9443			−0.808706			−0.404353	−	0.914603i	$-0.632503\pi$
$439$	−16.9443			−0.808706			−0.404353	+	0.914603i	$0.632503\pi$
$440$		0			0
$441$	17.3262			0.825059
$442$		0			0
$443$	−5.80902	−	17.8783i	−0.275995	−	0.849424i	−0.988954	−	0.148219i	$-0.952646\pi$
$443$	−5.80902	−	17.8783i	−0.275995	−	0.849424i	0.712960	−	0.701205i	$-0.247354\pi$
$444$		0			0
$445$	−5.85410	−	4.25325i	−0.277511	−	0.201624i
$446$		0			0
$447$	2.12868	−	6.55139i	0.100683	−	0.309870i
$448$		0			0
$449$	13.3090	−	9.66957i	0.628091	−	0.456335i	−0.227647	−	0.973744i	$-0.573103\pi$
$449$	13.3090	−	9.66957i	0.628091	−	0.456335i	0.855738	+	0.517409i	$0.173103\pi$
$450$		0			0
$451$	2.28115	+	24.3767i	0.107415	+	1.14785i
$452$		0			0
$453$	−4.16312	+	3.02468i	−0.195600	+	0.142112i
$454$		0			0
$455$	−0.263932	+	0.812299i	−0.0123733	+	0.0380812i
$456$		0			0
$457$	8.54508	+	6.20837i	0.399722	+	0.290415i	0.769428	−	0.638734i	$-0.220541\pi$
$457$	8.54508	+	6.20837i	0.399722	+	0.290415i	−0.369706	+	0.929149i	$0.620541\pi$
$458$		0			0
$459$	−5.20820	−	16.0292i	−0.243098	−	0.748179i
$460$		0			0
$461$	−14.3607			−0.668844			−0.334422	−	0.942424i	$-0.608541\pi$
$461$	−14.3607			−0.668844			−0.334422	+	0.942424i	$0.608541\pi$
$462$		0			0
$463$	11.4164			0.530565			0.265283	−	0.964171i	$-0.414535\pi$
$463$	11.4164			0.530565			0.265283	+	0.964171i	$0.414535\pi$
$464$		0			0
$465$	3.11803	+	9.59632i	0.144595	+	0.445019i
$466$		0			0
$467$	22.4894	+	16.3395i	1.04068	+	0.756101i	0.970419	−	0.241428i	$-0.0776157\pi$
$467$	22.4894	+	16.3395i	1.04068	+	0.756101i	0.0702645	+	0.997528i	$0.477616\pi$
$468$		0			0
$469$	−1.05573	+	3.24920i	−0.0487490	+	0.150034i
$470$		0			0
$471$	−8.16312	+	5.93085i	−0.376137	+	0.273279i
$472$		0			0
$473$	−33.8885	−	7.60845i	−1.55820	−	0.349837i
$474$		0			0
$475$	−3.57295	+	2.59590i	−0.163938	+	0.119108i
$476$		0			0
$477$	−1.30902	+	4.02874i	−0.0599358	+	0.184463i
$478$		0			0
$479$	19.3992	+	14.0943i	0.886371	+	0.643987i	0.934929	−	0.354834i	$-0.115463\pi$
$479$	19.3992	+	14.0943i	0.886371	+	0.643987i	−0.0485579	+	0.998820i	$0.515463\pi$
$480$		0			0
$481$	−1.94834	−	5.99637i	−0.0888365	−	0.273411i
$482$		0			0
$483$	1.52786			0.0695202
$484$		0			0
$485$	5.38197			0.244382
$486$		0			0
$487$	1.22542	+	3.77147i	0.0555293	+	0.170902i	0.974975	−	0.222316i	$-0.0713618\pi$
$487$	1.22542	+	3.77147i	0.0555293	+	0.170902i	−0.919445	+	0.393218i	$0.871362\pi$
$488$		0			0
$489$	−7.89919	−	5.73910i	−0.357214	−	0.259531i
$490$		0			0
$491$	−5.71885	+	17.6008i	−0.258088	+	0.794313i	0.735118	+	0.677940i	$0.237127\pi$
$491$	−5.71885	+	17.6008i	−0.258088	+	0.794313i	−0.993206	+	0.116373i	$0.962873\pi$
$492$		0			0
$493$	−32.6976	+	23.7562i	−1.47262	+	1.06992i
$494$		0			0
$495$	13.7082	+	3.07768i	0.616138	+	0.138332i
$496$		0			0
$497$	3.04508	−	2.21238i	0.136591	−	0.0992390i
$498$		0			0
$499$	−7.13525	+	21.9601i	−0.319418	+	0.983067i	0.654480	+	0.756080i	$0.272888\pi$
$499$	−7.13525	+	21.9601i	−0.319418	+	0.983067i	−0.973898	+	0.226988i	$0.927112\pi$
$500$		0			0
$501$	0.663119	+	0.481784i	0.0296260	+	0.0215245i
$502$		0			0
$503$	−0.954915	−	2.93893i	−0.0425776	−	0.131040i	0.927508	−	0.373803i	$-0.121946\pi$
$503$	−0.954915	−	2.93893i	−0.0425776	−	0.131040i	−0.970086	+	0.242763i	$0.921946\pi$
$504$		0			0
$505$	13.0902			0.582505
$506$		0			0
$507$	−7.58359			−0.336799
$508$		0			0
$509$	−5.71885	−	17.6008i	−0.253483	−	0.780142i	−0.994125	−	0.108241i	$-0.965478\pi$
$509$	−5.71885	−	17.6008i	−0.253483	−	0.780142i	0.740641	−	0.671901i	$-0.234522\pi$
$510$		0			0
$511$	4.92705	+	3.57971i	0.217960	+	0.158357i
$512$		0			0
$513$	1.98936	−	6.12261i	0.0878323	−	0.270320i
$514$		0			0
$515$	1.19098	−	0.865300i	0.0524810	−	0.0381297i
$516$		0			0
$517$	2.95492	+	31.5766i	0.129957	+	1.38874i
$518$		0			0
$519$	1.07295	−	0.779543i	0.0470972	−	0.0342181i
$520$		0			0
$521$	1.24671	−	3.83698i	0.0546194	−	0.168101i	−0.920026	−	0.391858i	$-0.871832\pi$
$521$	1.24671	−	3.83698i	0.0546194	−	0.168101i	0.974645	+	0.223757i	$0.0718323\pi$
$522$		0			0
$523$	−20.6353	−	14.9924i	−0.902317	−	0.655571i	0.0367433	−	0.999325i	$-0.488302\pi$
$523$	−20.6353	−	14.9924i	−0.902317	−	0.655571i	−0.939060	+	0.343753i	$0.888302\pi$
$524$		0			0
$525$	−0.281153	−	0.865300i	−0.0122705	−	0.0377648i
$526$		0			0
$527$	48.9787			2.13355
$528$		0			0
$529$	−7.00000			−0.304348
$530$		0			0
$531$	3.73607	+	11.4984i	0.162132	+	0.498990i
$532$		0			0
$533$	−5.10081	−	3.70596i	−0.220941	−	0.160523i
$534$		0			0
$535$	7.54508	−	23.2214i	0.326202	−	1.00395i
$536$		0			0
$537$	4.63525	−	3.36771i	0.200026	−	0.145327i
$538$		0			0
$539$	−14.5000	−	16.4782i	−0.624559	−	0.709768i
$540$		0			0
$541$	29.3435	−	21.3193i	1.26157	−	0.916587i	0.262740	−	0.964867i	$-0.415374\pi$
$541$	29.3435	−	21.3193i	1.26157	−	0.916587i	0.998834	+	0.0482796i	$0.0153739\pi$
$542$		0			0
$543$	−4.63525	+	14.2658i	−0.198918	+	0.612206i
$544$		0			0
$545$	−3.85410	−	2.80017i	−0.165092	−	0.119946i
$546$		0			0
$547$	−10.7533	−	33.0952i	−0.459777	−	1.41505i	−0.865434	−	0.501024i	$-0.832957\pi$
$547$	−10.7533	−	33.0952i	−0.459777	−	1.41505i	0.405656	−	0.914026i	$-0.367043\pi$
$548$		0			0
$549$	12.7082			0.542373
$550$		0			0
$551$	−15.4377			−0.657668
$552$		0			0
$553$	−0.545085	−	1.67760i	−0.0231794	−	0.0713388i
$554$		0			0
$555$	−5.97214	−	4.33901i	−0.253503	−	0.184181i
$556$		0			0
$557$	−8.07953	+	24.8662i	−0.342341	+	1.05362i	0.620652	+	0.784086i	$0.286868\pi$
$557$	−8.07953	+	24.8662i	−0.342341	+	1.05362i	−0.962992	+	0.269529i	$0.913132\pi$
$558$		0			0
$559$	7.23607	−	5.25731i	0.306053	−	0.222361i
$560$		0			0
$561$	−5.07295	+	8.55951i	−0.214180	+	0.361383i
$562$		0			0
$563$	3.69098	−	2.68166i	0.155556	−	0.113018i	−0.507284	−	0.861779i	$-0.669351\pi$
$563$	3.69098	−	2.68166i	0.155556	−	0.113018i	0.662841	+	0.748760i	$0.269351\pi$
$564$		0			0
$565$	1.07295	−	3.30220i	0.0451393	−	0.138924i
$566$		0			0
$567$	−2.85410	−	2.07363i	−0.119861	−	0.0870841i
$568$		0			0
$569$	0.371323	+	1.14281i	0.0155667	+	0.0479093i	0.958538	−	0.284964i	$-0.0919818\pi$
$569$	0.371323	+	1.14281i	0.0155667	+	0.0479093i	−0.942971	+	0.332874i	$0.891982\pi$
$570$		0			0
$571$	22.8328			0.955524			0.477762	−	0.878489i	$-0.341448\pi$
$571$	22.8328			0.955524			0.477762	+	0.878489i	$0.341448\pi$
$572$		0			0
$573$	−13.5066			−0.564245
$574$		0			0
$575$	−2.94427	−	9.06154i	−0.122785	−	0.377892i
$576$		0			0
$577$	17.4894	+	12.7068i	0.728091	+	0.528989i	0.888959	−	0.457987i	$-0.151429\pi$
$577$	17.4894	+	12.7068i	0.728091	+	0.528989i	−0.160868	+	0.986976i	$0.551429\pi$
$578$		0			0
$579$	−1.83688	+	5.65334i	−0.0763382	+	0.234945i
$580$		0			0
$581$	−5.80902	+	4.22050i	−0.240999	+	0.175096i
$582$		0			0
$583$	4.92705	−	2.12663i	0.204058	−	0.0880759i
$584$		0			0
$585$	−2.92705	+	2.12663i	−0.121019	+	0.0879252i
$586$		0			0
$587$	−3.42705	+	10.5474i	−0.141450	+	0.435337i	−0.996537	−	0.0831463i	$-0.973503\pi$
$587$	−3.42705	+	10.5474i	−0.141450	+	0.435337i	0.855088	+	0.518483i	$0.173503\pi$
$588$		0			0
$589$	15.1353	+	10.9964i	0.623637	+	0.453099i
$590$		0			0
$591$	1.61803	+	4.97980i	0.0665570	+	0.204841i
$592$		0			0
$593$	−8.47214			−0.347909			−0.173954	−	0.984754i	$-0.555655\pi$
$593$	−8.47214			−0.347909			−0.173954	+	0.984754i	$0.555655\pi$
$594$		0			0
$595$	4.85410			0.198999
$596$		0			0
$597$	4.65248	+	14.3188i	0.190413	+	0.586031i
$598$		0			0
$599$	−11.2533	−	8.17599i	−0.459797	−	0.334062i	0.333655	−	0.942695i	$-0.391718\pi$
$599$	−11.2533	−	8.17599i	−0.459797	−	0.334062i	−0.793452	+	0.608633i	$0.791718\pi$
$600$		0			0
$601$	−11.6976	+	36.0014i	−0.477153	+	1.46853i	0.365878	+	0.930663i	$0.380769\pi$
$601$	−11.6976	+	36.0014i	−0.477153	+	1.46853i	−0.843031	+	0.537864i	$0.819231\pi$
$602$		0			0
$603$	−11.7082	+	8.50651i	−0.476795	+	0.346412i
$604$		0			0
$605$	−8.54508	−	15.6129i	−0.347407	−	0.634756i
$606$		0			0
$607$	−25.5795	+	18.5846i	−1.03824	+	0.754326i	−0.969941	−	0.243339i	$-0.921757\pi$
$607$	−25.5795	+	18.5846i	−1.03824	+	0.754326i	−0.0682996	+	0.997665i	$0.521757\pi$
$608$		0			0
$609$	0.982779	−	3.02468i	0.0398242	−	0.122566i
$610$		0			0
$611$	−6.60739	−	4.80055i	−0.267306	−	0.194209i
$612$		0			0
$613$	−1.53851	−	4.73504i	−0.0621397	−	0.191246i	0.915167	−	0.403074i	$-0.132058\pi$
$613$	−1.53851	−	4.73504i	−0.0621397	−	0.191246i	−0.977307	+	0.211828i	$0.932058\pi$
$614$		0			0
$615$	−7.38197			−0.297670
$616$		0			0
$617$	1.41641			0.0570224			0.0285112	−	0.999593i	$-0.490923\pi$
$617$	1.41641			0.0570224			0.0285112	+	0.999593i	$0.490923\pi$
$618$		0			0
$619$	−4.28115	−	13.1760i	−0.172074	−	0.529590i	0.827414	−	0.561593i	$-0.189811\pi$
$619$	−4.28115	−	13.1760i	−0.172074	−	0.529590i	−0.999488	+	0.0320034i	$0.989811\pi$
$620$		0			0
$621$	11.2361	+	8.16348i	0.450888	+	0.327589i
$622$		0			0
$623$	0.854102	−	2.62866i	0.0342189	−	0.105315i
$624$		0			0
$625$	6.00000	−	4.35926i	0.240000	−	0.174370i
$626$		0			0
$627$	−3.48936	+	1.50609i	−0.139351	+	0.0601473i
$628$		0			0
$629$	−28.9894	+	21.0620i	−1.15588	+	0.839797i
$630$		0			0
$631$	−0.281153	+	0.865300i	−0.0111925	+	0.0344470i	−0.956497	−	0.291743i	$-0.905765\pi$
$631$	−0.281153	+	0.865300i	−0.0111925	+	0.0344470i	0.945304	+	0.326190i	$0.105765\pi$
$632$		0			0
$633$	−0.954915	−	0.693786i	−0.0379545	−	0.0275755i
$634$		0			0
$635$	10.6631	+	32.8177i	0.423153	+	1.30233i
$636$		0			0
$637$	5.65248			0.223959
$638$		0			0
$639$	15.9443			0.630746
$640$		0			0
$641$	10.3713	+	31.9196i	0.409643	+	1.26075i	0.916956	+	0.398989i	$0.130639\pi$
$641$	10.3713	+	31.9196i	0.409643	+	1.26075i	−0.507313	+	0.861762i	$0.669361\pi$
$642$		0			0
$643$	19.7254	+	14.3314i	0.777895	+	0.565174i	0.904346	−	0.426799i	$-0.140359\pi$
$643$	19.7254	+	14.3314i	0.777895	+	0.565174i	−0.126452	+	0.991973i	$0.540359\pi$
$644$		0			0
$645$	3.23607	−	9.95959i	0.127420	−	0.392159i
$646$		0			0
$647$	−26.3435	+	19.1396i	−1.03567	+	0.752457i	−0.969435	−	0.245347i	$-0.921098\pi$
$647$	−26.3435	+	19.1396i	−1.03567	+	0.752457i	−0.0662330	+	0.997804i	$0.521098\pi$
$648$		0			0
$649$	7.80902	−	13.1760i	0.306531	−	0.517205i
$650$		0			0
$651$	−3.11803	+	2.26538i	−0.122205	+	0.0887874i
$652$		0			0
$653$	−8.01064	+	24.6542i	−0.313481	+	0.964794i	0.662895	+	0.748713i	$0.269328\pi$
$653$	−8.01064	+	24.6542i	−0.313481	+	0.964794i	−0.976375	+	0.216082i	$0.930672\pi$
$654$		0			0
$655$	−10.4721	−	7.60845i	−0.409180	−	0.297287i
$656$		0			0
$657$	7.97214	+	24.5357i	0.311023	+	0.957229i
$658$		0			0
$659$	32.0000			1.24654			0.623272	−	0.782006i	$-0.285803\pi$
$659$	32.0000			1.24654			0.623272	+	0.782006i	$0.285803\pi$
$660$		0			0
$661$	10.9443			0.425683			0.212841	−	0.977087i	$-0.431728\pi$
$661$	10.9443			0.425683			0.212841	+	0.977087i	$0.431728\pi$
$662$		0			0
$663$	−0.791796	−	2.43690i	−0.0307508	−	0.0946413i
$664$		0			0
$665$	1.50000	+	1.08981i	0.0581675	+	0.0422612i
$666$		0			0
$667$	10.2918	−	31.6749i	0.398500	−	1.22646i
$668$		0			0
$669$	−3.69098	+	2.68166i	−0.142702	+	0.103679i
$670$		0			0
$671$	−10.6353	−	12.0862i	−0.410569	−	0.466583i
$672$		0			0
$673$	−28.1074	+	20.4212i	−1.08346	+	0.787180i	−0.978283	−	0.207274i	$-0.933541\pi$
$673$	−28.1074	+	20.4212i	−1.08346	+	0.787180i	−0.105177	+	0.994453i	$0.533541\pi$
$674$		0			0
$675$	2.55573	−	7.86572i	0.0983700	−	0.302752i
$676$		0			0
$677$	−3.78115	−	2.74717i	−0.145322	−	0.105582i	0.512749	−	0.858539i	$-0.328627\pi$
$677$	−3.78115	−	2.74717i	−0.145322	−	0.105582i	−0.658071	+	0.752956i	$0.728627\pi$
$678$		0			0
$679$	0.635255	+	1.95511i	0.0243788	+	0.0750304i
$680$		0			0
$681$	8.56231			0.328108
$682$		0			0
$683$	16.9443			0.648355			0.324177	−	0.945996i	$-0.394913\pi$
$683$	16.9443			0.648355			0.324177	+	0.945996i	$0.394913\pi$
$684$		0			0
$685$	−1.28115	−	3.94298i	−0.0489503	−	0.150654i
$686$		0			0
$687$	−0.336881	−	0.244758i	−0.0128528	−	0.00933812i
$688$		0			0
$689$	−0.427051	+	1.31433i	−0.0162693	+	0.0500719i
$690$		0			0
$691$	−2.78115	+	2.02063i	−0.105800	+	0.0768682i	−0.639427	−	0.768852i	$-0.720829\pi$
$691$	−2.78115	+	2.02063i	−0.105800	+	0.0768682i	0.533627	+	0.845720i	$0.320829\pi$
$692$		0			0
$693$	0.500000	+	5.34307i	0.0189934	+	0.202966i
$694$		0			0
$695$	−22.6074	+	16.4252i	−0.857547	+	0.623045i
$696$		0			0
$697$	−11.0729	+	34.0790i	−0.419418	+	1.29084i
$698$		0			0
$699$	6.51722	+	4.73504i	0.246504	+	0.179096i
$700$		0			0
$701$	15.2254	+	46.8590i	0.575056	+	1.76984i	0.635987	+	0.771700i	$0.280593\pi$
$701$	15.2254	+	46.8590i	0.575056	+	1.76984i	−0.0609310	+	0.998142i	$0.519407\pi$
$702$		0			0
$703$	−13.6869			−0.516212
$704$		0			0
$705$	−9.56231			−0.360137
$706$		0			0
$707$	1.54508	+	4.75528i	0.0581089	+	0.178841i
$708$		0			0
$709$	18.3992	+	13.3678i	0.690996	+	0.502038i	0.876987	−	0.480513i	$-0.159550\pi$
$709$	18.3992	+	13.3678i	0.690996	+	0.502038i	−0.185991	+	0.982551i	$0.559550\pi$
$710$		0			0
$711$	2.30902	−	7.10642i	0.0865949	−	0.266512i
$712$		0			0
$713$	−32.6525	+	23.7234i	−1.22284	+	0.888449i
$714$		0			0
$715$	4.47214	+	1.00406i	0.167248	+	0.0375496i
$716$		0			0
$717$	7.25329	−	5.26982i	0.270879	−	0.196805i
$718$		0			0
$719$	3.42705	−	10.5474i	0.127807	−	0.393351i	−0.866595	−	0.499013i	$-0.833696\pi$
$719$	3.42705	−	10.5474i	0.127807	−	0.393351i	0.994402	+	0.105662i	$0.0336961\pi$
$720$		0			0
$721$	0.454915	+	0.330515i	0.0169419	+	0.0123090i
$722$		0			0
$723$	3.61803	+	11.1352i	0.134556	+	0.414121i
$724$		0			0
$725$	−19.8328			−0.736572
$726$		0			0
$727$	11.0557			0.410034			0.205017	−	0.978758i	$-0.434275\pi$
$727$	11.0557			0.410034			0.205017	+	0.978758i	$0.434275\pi$
$728$		0			0
$729$	−2.62868	−	8.09024i	−0.0973584	−	0.299638i
$730$		0			0
$731$	−41.1246	−	29.8788i	−1.52105	−	1.10511i
$732$		0			0
$733$	−4.95492	+	15.2497i	−0.183014	+	0.563259i	−0.999908	−	0.0135280i	$-0.995694\pi$
$733$	−4.95492	+	15.2497i	−0.183014	+	0.563259i	0.816895	+	0.576787i	$0.195694\pi$
$734$		0			0
$735$	5.35410	−	3.88998i	0.197489	−	0.143484i
$736$		0			0
$737$	17.8885	+	4.01623i	0.658933	+	0.147940i
$738$		0			0
$739$	−12.0172	+	8.73102i	−0.442061	+	0.321176i	−0.786453	−	0.617650i	$-0.788085\pi$
$739$	−12.0172	+	8.73102i	−0.442061	+	0.321176i	0.344393	+	0.938826i	$0.388085\pi$
$740$		0			0
$741$	0.302439	−	0.930812i	0.0111104	−	0.0341942i
$742$		0			0
$743$	−11.0729	−	8.04497i	−0.406227	−	0.295141i	0.365846	−	0.930676i	$-0.380780\pi$
$743$	−11.0729	−	8.04497i	−0.406227	−	0.295141i	−0.772073	+	0.635534i	$0.780780\pi$
$744$		0			0
$745$	5.57295	+	17.1518i	0.204177	+	0.628392i
$746$		0			0
$747$	−30.4164			−1.11288
$748$		0			0
$749$	9.32624			0.340773
$750$		0			0
$751$	3.80902	+	11.7229i	0.138993	+	0.427776i	0.996190	−	0.0872126i	$-0.0277960\pi$
$751$	3.80902	+	11.7229i	0.138993	+	0.427776i	−0.857197	+	0.514989i	$0.827796\pi$
$752$		0			0
$753$	−4.19098	−	3.04493i	−0.152728	−	0.110963i
$754$		0			0
$755$	4.16312	−	12.8128i	0.151511	−	0.466304i
$756$		0			0
$757$	34.1074	−	24.7805i	1.23965	−	0.900662i	0.242079	−	0.970257i	$-0.422171\pi$
$757$	34.1074	−	24.7805i	1.23965	−	0.900662i	0.997575	+	0.0695951i	$0.0221707\pi$
$758$		0			0
$759$	−0.763932	−	8.16348i	−0.0277290	−	0.296316i
$760$		0			0
$761$	25.4894	−	18.5191i	0.923988	−	0.671317i	−0.0205251	−	0.999789i	$-0.506534\pi$
$761$	25.4894	−	18.5191i	0.923988	−	0.671317i	0.944514	+	0.328472i	$0.106534\pi$
$762$		0			0
$763$	0.562306	−	1.73060i	0.0203568	−	0.0626519i
$764$		0			0
$765$	16.6353	+	12.0862i	0.601449	+	0.436978i
$766$		0			0
$767$	1.21885	+	3.75123i	0.0440100	+	0.135449i
$768$		0			0
$769$	−44.2492			−1.59567			−0.797834	−	0.602877i	$-0.794021\pi$
$769$	−44.2492			−1.59567			−0.797834	+	0.602877i	$0.794021\pi$
$770$		0			0
$771$	10.8541			0.390901
$772$		0			0
$773$	11.6287	+	35.7894i	0.418254	+	1.28725i	0.909307	+	0.416125i	$0.136612\pi$
$773$	11.6287	+	35.7894i	0.418254	+	1.28725i	−0.491053	+	0.871130i	$0.663388\pi$
$774$		0			0
$775$	19.4443	+	14.1271i	0.698459	+	0.507460i
$776$		0			0
$777$	0.871323	−	2.68166i	0.0312585	−	0.0962039i
$778$		0			0
$779$	−11.0729	+	8.04497i	−0.396730	+	0.288241i
$780$		0			0
$781$	−13.3435	−	15.1639i	−0.477466	−	0.542607i
$782$		0			0
$783$	23.3885	−	16.9928i	0.835838	−	0.607272i
$784$		0			0
$785$	8.16312	−	25.1235i	0.291354	−	0.896696i
$786$		0			0
$787$	2.78115	+	2.02063i	0.0991374	+	0.0720275i	0.636250	−	0.771483i	$-0.280485\pi$
$787$	2.78115	+	2.02063i	0.0991374	+	0.0720275i	−0.537112	+	0.843511i	$0.680485\pi$
$788$		0			0
$789$	3.70820	+	11.4127i	0.132016	+	0.406302i
$790$		0			0
$791$	1.32624			0.0471556
$792$		0			0
$793$	4.14590			0.147225
$794$		0			0
$795$	0.500000	+	1.53884i	0.0177332	+	0.0545771i
$796$		0			0
$797$	−35.9615	−	26.1276i	−1.27382	−	0.925485i	−0.274474	−	0.961595i	$-0.588504\pi$
$797$	−35.9615	−	26.1276i	−1.27382	−	0.925485i	−0.999348	+	0.0361092i	$0.988504\pi$
$798$		0			0
$799$	−14.3435	+	44.1446i	−0.507435	+	1.56172i
$800$		0			0
$801$	9.47214	−	6.88191i	0.334681	−	0.243160i
$802$		0			0
$803$	16.6631	−	28.1154i	0.588029	−	0.992172i
$804$		0			0
$805$	−3.23607	+	2.35114i	−0.114056	+	0.0828668i
$806$		0			0
$807$	2.30902	−	7.10642i	0.0812812	−	0.250158i
$808$		0			0
$809$	31.9615	+	23.2214i	1.12371	+	0.816420i	0.984767	−	0.173880i	$-0.0556306\pi$
$809$	31.9615	+	23.2214i	1.12371	+	0.816420i	0.138939	+	0.990301i	$0.455631\pi$
$810$		0			0
$811$	0.0795268	+	0.244758i	0.00279256	+	0.00859463i	0.952443	−	0.304717i	$-0.0985617\pi$
$811$	0.0795268	+	0.244758i	0.00279256	+	0.00859463i	−0.949651	+	0.313311i	$0.898562\pi$
$812$		0			0
$813$	17.6869			0.620307
$814$		0			0
$815$	25.5623			0.895409
$816$		0			0
$817$	−6.00000	−	18.4661i	−0.209913	−	0.646047i
$818$		0			0
$819$	−1.11803	−	0.812299i	−0.0390673	−	0.0283840i
$820$		0			0
$821$	8.16970	−	25.1437i	0.285124	−	0.877523i	−0.701237	−	0.712928i	$-0.747368\pi$
$821$	8.16970	−	25.1437i	0.285124	−	0.877523i	0.986361	−	0.164594i	$-0.0526315\pi$
$822$		0			0
$823$	23.7254	−	17.2375i	0.827016	−	0.600863i	−0.0916973	−	0.995787i	$-0.529229\pi$
$823$	23.7254	−	17.2375i	0.827016	−	0.600863i	0.918714	+	0.394924i	$0.129229\pi$
$824$		0			0
$825$	−4.48278	+	1.93487i	−0.156070	+	0.0673635i
$826$		0			0
$827$	−23.7254	+	17.2375i	−0.825014	+	0.599408i	−0.918144	−	0.396246i	$-0.870313\pi$
$827$	−23.7254	+	17.2375i	−0.825014	+	0.599408i	0.0931304	+	0.995654i	$0.470313\pi$
$828$		0			0
$829$	−3.71885	+	11.4454i	−0.129161	+	0.397516i	−0.994636	−	0.103435i	$-0.967017\pi$
$829$	−3.71885	+	11.4454i	−0.129161	+	0.397516i	0.865475	+	0.500952i	$0.167017\pi$
$830$		0			0
$831$	−2.80902	−	2.04087i	−0.0974437	−	0.0707970i
$832$		0			0
$833$	−9.92705	−	30.5523i	−0.343952	−	1.05858i
$834$		0			0
$835$	−2.14590			−0.0742619
$836$		0			0
$837$	−35.0344			−1.21097
$838$		0			0
$839$	−14.8435	−	45.6835i	−0.512453	−	1.57717i	−0.787869	−	0.615843i	$-0.788815\pi$
$839$	−14.8435	−	45.6835i	−0.512453	−	1.57717i	0.275416	−	0.961325i	$-0.411185\pi$
$840$		0			0
$841$	−32.6246	−	23.7032i	−1.12499	−	0.817351i
$842$		0			0
$843$	−1.25329	+	3.85723i	−0.0431656	+	0.132850i
$844$		0			0
$845$	16.0623	−	11.6699i	0.552560	−	0.401458i
$846$		0			0
$847$	4.66312	−	4.94704i	0.160227	−	0.169982i
$848$		0			0
$849$	5.39919	−	3.92274i	0.185300	−	0.134628i
$850$		0			0
$851$	9.12461	−	28.0827i	0.312788	−	0.962661i
$852$		0			0
$853$	−35.6697	−	25.9156i	−1.22131	−	0.887332i	−0.225099	−	0.974336i	$-0.572271\pi$
$853$	−35.6697	−	25.9156i	−1.22131	−	0.887332i	−0.996208	+	0.0870043i	$0.972271\pi$
$854$		0			0
$855$	2.42705	+	7.46969i	0.0830034	+	0.255458i
$856$		0			0
$857$	18.3607			0.627189			0.313594	−	0.949557i	$-0.398467\pi$
$857$	18.3607			0.627189			0.313594	+	0.949557i	$0.398467\pi$
$858$		0			0
$859$	−21.8885			−0.746827			−0.373414	−	0.927665i	$-0.621813\pi$
$859$	−21.8885			−0.746827			−0.373414	+	0.927665i	$0.621813\pi$
$860$		0			0
$861$	−0.871323	−	2.68166i	−0.0296946	−	0.0913906i
$862$		0			0
$863$	20.6353	+	14.9924i	0.702432	+	0.510347i	0.880723	−	0.473631i	$-0.157057\pi$
$863$	20.6353	+	14.9924i	0.702432	+	0.510347i	−0.178291	+	0.983978i	$0.557057\pi$
$864$		0			0
$865$	−1.07295	+	3.30220i	−0.0364814	+	0.112278i
$866$		0			0
$867$	−3.28115	+	2.38390i	−0.111434	+	0.0809614i
$868$		0			0
$869$	−8.69098	+	3.75123i	−0.294821	+	0.127252i
$870$		0			0
$871$	−3.81966	+	2.77515i	−0.129424	+	0.0940322i
$872$		0			0
$873$	−2.69098	+	8.28199i	−0.0910760	+	0.280303i
$874$		0			0
$875$	5.97214	+	4.33901i	0.201895	+	0.146685i
$876$		0			0
$877$	−14.8435	−	45.6835i	−0.501228	−	1.54262i	−0.807021	−	0.590523i	$-0.798921\pi$
$877$	−14.8435	−	45.6835i	−0.501228	−	1.54262i	0.305793	−	0.952098i	$-0.401079\pi$
$878$		0			0
$879$	−5.90983			−0.199334
$880$		0			0
$881$	40.4721			1.36354			0.681770	−	0.731566i	$-0.261210\pi$
$881$	40.4721			1.36354			0.681770	+	0.731566i	$0.261210\pi$
$882$		0			0
$883$	1.89919	+	5.84510i	0.0639127	+	0.196703i	0.977914	−	0.209009i	$-0.0670237\pi$
$883$	1.89919	+	5.84510i	0.0639127	+	0.196703i	−0.914001	+	0.405712i	$0.867024\pi$
$884$		0			0
$885$	3.73607	+	2.71441i	0.125587	+	0.0912440i
$886$		0			0
$887$	−14.3926	+	44.2959i	−0.483257	+	1.48731i	0.351234	+	0.936288i	$0.385762\pi$
$887$	−14.3926	+	44.2959i	−0.483257	+	1.48731i	−0.834490	+	0.551023i	$0.814238\pi$
$888$		0			0
$889$	−10.6631	+	7.74721i	−0.357630	+	0.259833i
$890$		0			0
$891$	−9.65248	+	16.2865i	−0.323370	+	0.545617i
$892$		0			0
$893$	−14.3435	+	10.4211i	−0.479986	+	0.348730i
$894$		0			0
$895$	−4.63525	+	14.2658i	−0.154939	+	0.476855i
$896$		0			0
$897$	1.70820	+	1.24108i	0.0570353	+	0.0414385i
$898$		0			0
$899$	25.9615	+	79.9013i	0.865864	+	2.66486i
$900$		0			0
$901$	7.85410			0.261658
$902$		0			0
$903$	4.00000			0.133112
$904$		0			0
$905$	−12.1353	−	37.3485i	−0.403390	−	1.24151i
$906$		0			0
$907$	5.07295	+	3.68571i	0.168445	+	0.122382i	0.668814	−	0.743430i	$-0.266802\pi$
$907$	5.07295	+	3.68571i	0.168445	+	0.122382i	−0.500369	+	0.865812i	$0.666802\pi$
$908$		0			0
$909$	−6.54508	+	20.1437i	−0.217087	+	0.668124i
$910$		0			0
$911$	0.0172209	−	0.0125117i	0.000570555	−	0.000414532i	−0.587500	−	0.809224i	$-0.699888\pi$
$911$	0.0172209	−	0.0125117i	0.000570555	−	0.000414532i	0.588070	+	0.808810i	$0.299888\pi$
$912$		0			0
$913$	25.4549	+	28.9277i	0.842435	+	0.957368i
$914$		0			0
$915$	3.92705	−	2.85317i	0.129824	−	0.0943229i
$916$		0			0
$917$	1.52786	−	4.70228i	0.0504545	−	0.155283i
$918$		0			0
$919$	−13.2533	−	9.62908i	−0.437186	−	0.317634i	0.347330	−	0.937743i	$-0.387088\pi$
$919$	−13.2533	−	9.62908i	−0.437186	−	0.317634i	−0.784516	+	0.620109i	$0.787088\pi$
$920$		0			0
$921$	−0.360680	−	1.11006i	−0.0118848	−	0.0365777i
$922$		0			0
$923$	5.20163			0.171214
$924$		0			0
$925$	−17.5836			−0.578145
$926$		0			0
$927$	0.736068	+	2.26538i	0.0241756	+	0.0744050i
$928$		0			0
$929$	27.9615	+	20.3152i	0.917387	+	0.666521i	0.942872	−	0.333155i	$-0.108113\pi$
$929$	27.9615	+	20.3152i	0.917387	+	0.666521i	−0.0254854	+	0.999675i	$0.508113\pi$
$930$		0			0
$931$	3.79180	−	11.6699i	0.124271	−	0.382467i
$932$		0			0
$933$	−0.635255	+	0.461540i	−0.0207973	+	0.0151101i
$934$		0			0
$935$	−2.42705	−	25.9358i	−0.0793731	−	0.848191i
$936$		0			0
$937$	15.0172	−	10.9106i	0.490591	−	0.356435i	−0.314820	−	0.949151i	$-0.601944\pi$
$937$	15.0172	−	10.9106i	0.490591	−	0.356435i	0.805412	+	0.592716i	$0.201944\pi$
$938$		0			0
$939$	2.81559	−	8.66551i	0.0918835	−	0.282788i
$940$		0			0
$941$	3.45492	+	2.51014i	0.112627	+	0.0818283i	0.642673	−	0.766141i	$-0.277825\pi$
$941$	3.45492	+	2.51014i	0.112627	+	0.0818283i	−0.530046	+	0.847969i	$0.677825\pi$
$942$		0			0
$943$	−9.12461	−	28.0827i	−0.297138	−	0.914497i
$944$		0			0
$945$	−3.47214			−0.112949
$946$		0			0
$947$	−34.8328			−1.13191			−0.565957	−	0.824435i	$-0.691493\pi$
$947$	−34.8328			−1.13191			−0.565957	+	0.824435i	$0.691493\pi$
$948$		0			0
$949$	2.60081	+	8.00448i	0.0844260	+	0.259836i
$950$		0			0
$951$	7.66312	+	5.56758i	0.248494	+	0.180541i
$952$		0			0
$953$	5.24671	−	16.1477i	0.169958	−	0.523076i	−0.829410	−	0.558641i	$-0.811323\pi$
$953$	5.24671	−	16.1477i	0.169958	−	0.523076i	0.999367	+	0.0355649i	$0.0113231\pi$
$954$		0			0
$955$	28.6074	−	20.7845i	0.925713	−	0.672570i
$956$		0			0
$957$	−16.6525	−	3.73871i	−0.538298	−	0.120855i
$958$		0			0
$959$	1.28115	−	0.930812i	0.0413706	−	0.0300575i
$960$		0			0
$961$	21.8820	−	67.3458i	0.705870	−	2.17244i
$962$		0			0
$963$	31.9615	+	23.2214i	1.02994	+	0.748299i
$964$		0			0
$965$	−4.80902	−	14.8006i	−0.154808	−	0.476449i
$966$		0			0
$967$	29.3050			0.942384			0.471192	−	0.882031i	$-0.343824\pi$
$967$	29.3050			0.942384			0.471192	+	0.882031i	$0.343824\pi$
$968$		0			0
$969$	−5.56231			−0.178687
$970$		0			0
$971$	−5.51722	−	16.9803i	−0.177056	−	0.544922i	0.822665	−	0.568526i	$-0.192486\pi$
$971$	−5.51722	−	16.9803i	−0.177056	−	0.544922i	−0.999721	+	0.0236034i	$0.992486\pi$
$972$		0			0
$973$	−8.63525	−	6.27388i	−0.276834	−	0.201131i
$974$		0			0
$975$	0.388544	−	1.19581i	0.0124434	−	0.0382967i
$976$		0			0
$977$	−41.8156	+	30.3808i	−1.33780	+	0.971968i	−0.338278	+	0.941046i	$0.609844\pi$
$977$	−41.8156	+	30.3808i	−1.33780	+	0.971968i	−0.999522	+	0.0309218i	$0.990156\pi$
$978$		0			0
$979$	−14.4721	−	3.24920i	−0.462531	−	0.103845i
$980$		0			0
$981$	6.23607	−	4.53077i	0.199102	−	0.144656i
$982$		0			0
$983$	0.954915	−	2.93893i	0.0304571	−	0.0937372i	−0.934672	−	0.355510i	$-0.884307\pi$
$983$	0.954915	−	2.93893i	0.0304571	−	0.0937372i	0.965129	+	0.261773i	$0.0843072\pi$
$984$		0			0
$985$	−11.0902	−	8.05748i	−0.353362	−	0.256733i
$986$		0			0
$987$	−1.12868	−	3.47371i	−0.0359262	−	0.110569i
$988$		0			0
$989$	41.8885			1.33198
$990$		0			0
$991$	−44.9443			−1.42770			−0.713851	−	0.700298i	$-0.753051\pi$
$991$	−44.9443			−1.42770			−0.713851	+	0.700298i	$0.753051\pi$
$992$		0			0
$993$	1.70820	+	5.25731i	0.0542082	+	0.166836i
$994$		0			0
$995$	−31.8885	−	23.1684i	−1.01093	−	0.734487i
$996$		0			0
$997$	15.3369	−	47.2021i	0.485724	−	1.49490i	−0.345206	−	0.938527i	$-0.612191\pi$
$997$	15.3369	−	47.2021i	0.485724	−	1.49490i	0.830930	−	0.556377i	$-0.187809\pi$
$998$		0			0
$999$	20.7361	−	15.0656i	0.656060	−	0.476656i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	704.2.m.g.641.1		4
4.3	odd	2		704.2.m.b.641.1		4
8.3	odd	2		88.2.i.a.25.1	✓	4
8.5	even	2		176.2.m.a.113.1		4
11.2	odd	10		7744.2.a.cc.1.2		2
11.4	even	5	inner	704.2.m.g.257.1		4
11.9	even	5		7744.2.a.cb.1.2		2
24.11	even	2		792.2.r.b.289.1		4
44.15	odd	10		704.2.m.b.257.1		4
44.31	odd	10		7744.2.a.cr.1.1		2
44.35	even	10		7744.2.a.cq.1.1		2
88.3	odd	10		968.2.i.d.753.1		4
88.13	odd	10		1936.2.a.u.1.1		2
88.19	even	10		968.2.i.c.753.1		4
88.27	odd	10		968.2.i.d.9.1		4
88.35	even	10		968.2.a.h.1.2		2
88.37	even	10		176.2.m.a.81.1		4
88.43	even	2		968.2.i.k.729.1		4
88.51	even	10		968.2.i.k.81.1		4
88.53	even	10		1936.2.a.t.1.1		2
88.59	odd	10		88.2.i.a.81.1	yes	4
88.75	odd	10		968.2.a.i.1.2		2
88.83	even	10		968.2.i.c.9.1		4
264.35	odd	10		8712.2.a.bm.1.2		2
264.59	even	10		792.2.r.b.433.1		4
264.251	even	10		8712.2.a.bp.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.i.a.25.1	✓	4	8.3	odd	2
88.2.i.a.81.1	yes	4	88.59	odd	10
176.2.m.a.81.1		4	88.37	even	10
176.2.m.a.113.1		4	8.5	even	2
704.2.m.b.257.1		4	44.15	odd	10
704.2.m.b.641.1		4	4.3	odd	2
704.2.m.g.257.1		4	11.4	even	5	inner
704.2.m.g.641.1		4	1.1	even	1	trivial
792.2.r.b.289.1		4	24.11	even	2
792.2.r.b.433.1		4	264.59	even	10
968.2.a.h.1.2		2	88.35	even	10
968.2.a.i.1.2		2	88.75	odd	10
968.2.i.c.9.1		4	88.83	even	10
968.2.i.c.753.1		4	88.19	even	10
968.2.i.d.9.1		4	88.27	odd	10
968.2.i.d.753.1		4	88.3	odd	10
968.2.i.k.81.1		4	88.51	even	10
968.2.i.k.729.1		4	88.43	even	2
1936.2.a.t.1.1		2	88.53	even	10
1936.2.a.u.1.1		2	88.13	odd	10
7744.2.a.cb.1.2		2	11.9	even	5
7744.2.a.cc.1.2		2	11.2	odd	10
7744.2.a.cq.1.1		2	44.35	even	10
7744.2.a.cr.1.1		2	44.31	odd	10
8712.2.a.bm.1.2		2	264.35	odd	10
8712.2.a.bp.1.2		2	264.251	even	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 704 = 2^{6} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	704.m (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.190983 + 0.587785i) q^{3} +(-1.30902 - 0.951057i) q^{5} +(0.190983 - 0.587785i) q^{7} +(2.11803 - 1.53884i) q^{9} +(-3.23607 - 0.726543i) q^{11} +(0.690983 - 0.502029i) q^{13} +(0.309017 - 0.951057i) q^{15} +(-3.92705 - 2.85317i) q^{17} +(-0.572949 - 1.76336i) q^{19} +0.381966 q^{21} +4.00000 q^{23} +(-0.736068 - 2.26538i) q^{25} +(2.80902 + 2.04087i) q^{27} +(2.57295 - 7.91872i) q^{29} +(-8.16312 + 5.93085i) q^{31} +(-0.190983 - 2.04087i) q^{33} +(-0.809017 + 0.587785i) q^{35} +(2.28115 - 7.02067i) q^{37} +(0.427051 + 0.310271i) q^{39} +(-2.28115 - 7.02067i) q^{41} +10.4721 q^{43} -4.23607 q^{45} +(-2.95492 - 9.09429i) q^{47} +(5.35410 + 3.88998i) q^{49} +(0.927051 - 2.85317i) q^{51} +(-1.30902 + 0.951057i) q^{53} +(3.54508 + 4.02874i) q^{55} +(0.927051 - 0.673542i) q^{57} +(-1.42705 + 4.39201i) q^{59} +(3.92705 + 2.85317i) q^{61} +(-0.500000 - 1.53884i) q^{63} -1.38197 q^{65} -5.52786 q^{67} +(0.763932 + 2.35114i) q^{69} +(4.92705 + 3.57971i) q^{71} +(-3.04508 + 9.37181i) q^{73} +(1.19098 - 0.865300i) q^{75} +(-1.04508 + 1.76336i) q^{77} +(2.30902 - 1.67760i) q^{79} +(1.76393 - 5.42882i) q^{81} +(-9.39919 - 6.82891i) q^{83} +(2.42705 + 7.46969i) q^{85} +5.14590 q^{87} +4.47214 q^{89} +(-0.163119 - 0.502029i) q^{91} +(-5.04508 - 3.66547i) q^{93} +(-0.927051 + 2.85317i) q^{95} +(-2.69098 + 1.95511i) q^{97} +(-7.97214 + 3.44095i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{3} - 3 q^{5} + 3 q^{7} + 4 q^{9} - 4 q^{11} + 5 q^{13} - q^{15} - 9 q^{17} - 9 q^{19} + 6 q^{21} + 16 q^{23} + 6 q^{25} + 9 q^{27} + 17 q^{29} - 17 q^{31} - 3 q^{33} - q^{35} - 11 q^{37} - 5 q^{39}+ \cdots - 14 q^{99}+O(q^{100}) \) 4 * q + 3 * q^3 - 3 * q^5 + 3 * q^7 + 4 * q^9 - 4 * q^11 + 5 * q^13 - q^15 - 9 * q^17 - 9 * q^19 + 6 * q^21 + 16 * q^23 + 6 * q^25 + 9 * q^27 + 17 * q^29 - 17 * q^31 - 3 * q^33 - q^35 - 11 * q^37 - 5 * q^39 + 11 * q^41 + 24 * q^43 - 8 * q^45 - 23 * q^47 + 8 * q^49 - 3 * q^51 - 3 * q^53 + 3 * q^55 - 3 * q^57 + q^59 + 9 * q^61 - 2 * q^63 - 10 * q^65 - 40 * q^67 + 12 * q^69 + 13 * q^71 - q^73 + 7 * q^75 + 7 * q^77 + 7 * q^79 + 16 * q^81 - 13 * q^83 + 3 * q^85 + 34 * q^87 + 15 * q^91 - 9 * q^93 + 3 * q^95 - 13 * q^97 - 14 * q^99

Introduction

L-functions

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Database

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