LMFDB - Embedded newform 875.2.f.b.307.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [875,2,Mod(307,875)] 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("875.307"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(875, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([1, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,0,0,0,0,24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 36x^{14} + 456x^{12} + 2616x^{10} + 7596x^{8} + 11600x^{6} + 9040x^{4} + 3200x^{2} + 400 $ x^16 + 36x^14 + 456x^12 + 2616x^10 + 7596x^8 + 11600x^6 + 9040x^4 + 3200*x^2 + 400
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.8
Root			$1.33102i$ of defining polynomial
Character	$\chi$	$=$	875.307
Dual form			875.2.f.b.818.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.67601 + 1.67601i) q^{2} +(2.17625 + 2.17625i) q^{3} +3.61803i q^{4} +7.29485i q^{6} +(-0.844758 - 2.50727i) q^{7} +(-2.71184 + 2.71184i) q^{8} +6.47214i q^{9} +2.61803 q^{11} +(-7.87375 + 7.87375i) q^{12} +(-1.02749 - 1.02749i) q^{13} +(2.78638 - 5.61803i) q^{14} -1.85410 q^{16} +(-0.831254 + 0.831254i) q^{17} +(-10.8474 + 10.8474i) q^{18} -7.29485 q^{19} +(3.61803 - 7.29485i) q^{21} +(4.38786 + 4.38786i) q^{22} +(5.02804 - 5.02804i) q^{23} -11.8033 q^{24} -3.44416i q^{26} +(-7.55624 + 7.55624i) q^{27} +(9.07137 - 3.05636i) q^{28} -8.70820i q^{29} +1.06430i q^{31} +(2.31619 + 2.31619i) q^{32} +(5.69750 + 5.69750i) q^{33} -2.78638 q^{34} -23.4164 q^{36} +(3.10750 + 3.10750i) q^{37} +(-12.2263 - 12.2263i) q^{38} -4.47214i q^{39} -5.57277i q^{41} +(18.2901 - 6.16238i) q^{42} +(-1.03583 + 1.03583i) q^{43} +9.47214i q^{44} +16.8541 q^{46} +(-5.37999 + 5.37999i) q^{47} +(-4.03499 - 4.03499i) q^{48} +(-5.57277 + 4.23607i) q^{49} -3.61803 q^{51} +(3.71748 - 3.71748i) q^{52} +(-3.99220 + 3.99220i) q^{53} -25.3287 q^{54} +(9.09017 + 4.50846i) q^{56} +(-15.8754 - 15.8754i) q^{57} +(14.5951 - 14.5951i) q^{58} +10.7390 q^{59} -7.95262i q^{61} +(-1.78379 + 1.78379i) q^{62} +(16.2274 - 5.46739i) q^{63} +11.4721i q^{64} +19.0982i q^{66} +(-0.640180 - 0.640180i) q^{67} +(-3.00750 - 3.00750i) q^{68} +21.8845 q^{69} +1.76393 q^{71} +(-17.5514 - 17.5514i) q^{72} +(10.4425 + 10.4425i) q^{73} +10.4164i q^{74} -26.3930i q^{76} +(-2.21161 - 6.56411i) q^{77} +(7.49535 - 7.49535i) q^{78} -3.70820i q^{79} -13.4721 q^{81} +(9.34003 - 9.34003i) q^{82} +(-3.20374 - 3.20374i) q^{83} +(26.3930 + 13.0902i) q^{84} -3.47214 q^{86} +(18.9512 - 18.9512i) q^{87} +(-7.09970 + 7.09970i) q^{88} -11.8033 q^{89} +(-1.70820 + 3.44416i) q^{91} +(18.1916 + 18.1916i) q^{92} +(-2.31619 + 2.31619i) q^{93} -18.0339 q^{94} +10.0812i q^{96} +(-1.02749 + 1.02749i) q^{97} +(-16.4397 - 2.24032i) q^{98} +16.9443i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 24 q^{11} + 24 q^{16} + 40 q^{21} - 160 q^{36} + 216 q^{46} - 40 q^{51} + 56 q^{56} + 64 q^{71} - 144 q^{81} + 16 q^{86} + 80 q^{91}+O(q^{100}) $ 16 * q + 24 * q^11 + 24 * q^16 + 40 * q^21 - 160 * q^36 + 216 * q^46 - 40 * q^51 + 56 * q^56 + 64 * q^71 - 144 * q^81 + 16 * q^86 + 80 * q^91

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	1.67601	+	1.67601i	1.18512	+	1.18512i	0.978400	+	0.206719i	$0.0662787\pi$
$2$	1.67601	+	1.67601i	1.18512	+	1.18512i	0.206719	+	0.978400i	$0.433721\pi$
$3$	2.17625	+	2.17625i	1.25646	+	1.25646i	0.952772	+	0.303687i	$0.0982178\pi$
$3$	2.17625	+	2.17625i	1.25646	+	1.25646i	0.303687	+	0.952772i	$0.401782\pi$
$4$			3.61803i			1.80902i
$5$		0			0
$5$		0			0
$6$			7.29485i			2.97811i
$7$	−0.844758	−	2.50727i	−0.319289	−	0.947658i
$7$	−0.844758	−	2.50727i	−0.319289	−	0.947658i
$8$	−2.71184	+	2.71184i	−0.958782	+	0.958782i
$9$			6.47214i			2.15738i
$10$		0			0
$11$	2.61803			0.789367			0.394683	−	0.918817i	$-0.370854\pi$
$11$	2.61803			0.789367			0.394683	+	0.918817i	$0.370854\pi$
$12$	−7.87375	+	7.87375i	−2.27296	+	2.27296i
$13$	−1.02749	−	1.02749i	−0.284973	−	0.284973i	0.550115	−	0.835089i	$-0.314584\pi$
$13$	−1.02749	−	1.02749i	−0.284973	−	0.284973i	−0.835089	+	0.550115i	$0.814584\pi$
$14$	2.78638	−	5.61803i	0.744692	−	1.50148i
$15$		0			0
$16$	−1.85410			−0.463525
$17$	−0.831254	+	0.831254i	−0.201609	+	0.201609i	−0.800689	−	0.599080i	$-0.795533\pi$
$17$	−0.831254	+	0.831254i	−0.201609	+	0.201609i	0.599080	+	0.800689i	$0.295533\pi$
$18$	−10.8474	+	10.8474i	−2.55675	+	2.55675i
$19$	−7.29485			−1.67355			−0.836776	−	0.547545i	$-0.815562\pi$
$19$	−7.29485			−1.67355			−0.836776	+	0.547545i	$0.815562\pi$
$20$		0			0
$21$	3.61803	−	7.29485i	0.789520	−	1.59187i
$22$	4.38786	+	4.38786i	0.935494	+	0.935494i
$23$	5.02804	−	5.02804i	1.04842	−	1.04842i	0.0496515	−	0.998767i	$-0.484189\pi$
$23$	5.02804	−	5.02804i	1.04842	−	1.04842i	0.998767	−	0.0496515i	$-0.0158111\pi$
$24$	−11.8033			−2.40934
$25$		0			0
$26$		−	3.44416i		−	0.675455i
$27$	−7.55624	+	7.55624i	−1.45420	+	1.45420i
$28$	9.07137	−	3.05636i	1.71433	−	0.577599i
$29$		−	8.70820i		−	1.61707i	−0.588446	−	0.808536i	$-0.700260\pi$
$29$		−	8.70820i		−	1.61707i	0.588446	−	0.808536i	$-0.299740\pi$
$30$		0			0
$31$			1.06430i			0.191155i	0.995422	+	0.0955773i	$0.0304697\pi$
$31$			1.06430i			0.191155i	−0.995422	+	0.0955773i	$0.969530\pi$
$32$	2.31619	+	2.31619i	0.409449	+	0.409449i
$33$	5.69750	+	5.69750i	0.991807	+	0.991807i
$34$	−2.78638			−0.477861
$35$		0			0
$36$	−23.4164			−3.90273
$37$	3.10750	+	3.10750i	0.510869	+	0.510869i	0.914793	−	0.403923i	$-0.132354\pi$
$37$	3.10750	+	3.10750i	0.510869	+	0.510869i	−0.403923	+	0.914793i	$0.632354\pi$
$38$	−12.2263	−	12.2263i	−1.98336	−	1.98336i
$39$		−	4.47214i		−	0.716115i
$40$		0			0
$41$		−	5.57277i		−	0.870320i	−0.900353	−	0.435160i	$-0.856692\pi$
$41$		−	5.57277i		−	0.870320i	0.900353	−	0.435160i	$-0.143308\pi$
$42$	18.2901	−	6.16238i	2.82223	−	0.950876i
$43$	−1.03583	+	1.03583i	−0.157963	+	0.157963i	−0.781663	−	0.623700i	$-0.785629\pi$
$43$	−1.03583	+	1.03583i	−0.157963	+	0.157963i	0.623700	+	0.781663i	$0.285629\pi$
$44$			9.47214i			1.42798i
$45$		0			0
$46$	16.8541			2.48500
$47$	−5.37999	+	5.37999i	−0.784752	+	0.784752i	−0.980629	−	0.195877i	$-0.937245\pi$
$47$	−5.37999	+	5.37999i	−0.784752	+	0.784752i	0.195877	+	0.980629i	$0.437245\pi$
$48$	−4.03499	−	4.03499i	−0.582401	−	0.582401i
$49$	−5.57277	+	4.23607i	−0.796110	+	0.605153i
$50$		0			0
$51$	−3.61803			−0.506626
$52$	3.71748	−	3.71748i	0.515522	−	0.515522i
$53$	−3.99220	+	3.99220i	−0.548371	+	0.548371i	−0.925970	−	0.377598i	$-0.876750\pi$
$53$	−3.99220	+	3.99220i	−0.548371	+	0.548371i	0.377598	+	0.925970i	$0.376750\pi$
$54$	−25.3287			−3.44680
$55$		0			0
$56$	9.09017	+	4.50846i	1.21473	+	0.602469i
$57$	−15.8754	−	15.8754i	−2.10275	−	2.10275i
$58$	14.5951	−	14.5951i	1.91642	−	1.91642i
$59$	10.7390			1.39810			0.699050	−	0.715073i	$-0.253607\pi$
$59$	10.7390			1.39810			0.699050	+	0.715073i	$0.253607\pi$
$60$		0			0
$61$		−	7.95262i		−	1.01823i	−0.860699	−	0.509114i	$-0.829973\pi$
$61$		−	7.95262i		−	1.01823i	0.860699	−	0.509114i	$-0.170027\pi$
$62$	−1.78379	+	1.78379i	−0.226541	+	0.226541i
$63$	16.2274	−	5.46739i	2.04446	−	0.688827i
$64$			11.4721i			1.43402i
$65$		0			0
$66$			19.0982i			2.35082i
$67$	−0.640180	−	0.640180i	−0.0782104	−	0.0782104i	0.666919	−	0.745130i	$-0.267613\pi$
$67$	−0.640180	−	0.640180i	−0.0782104	−	0.0782104i	−0.745130	+	0.666919i	$0.767613\pi$
$68$	−3.00750	−	3.00750i	−0.364714	−	0.364714i
$69$	21.8845			2.63459
$70$		0			0
$71$	1.76393			0.209340			0.104670	−	0.994507i	$-0.466621\pi$
$71$	1.76393			0.209340			0.104670	+	0.994507i	$0.466621\pi$
$72$	−17.5514	−	17.5514i	−2.06846	−	2.06846i
$73$	10.4425	+	10.4425i	1.22220	+	1.22220i	0.966849	+	0.255349i	$0.0821905\pi$
$73$	10.4425	+	10.4425i	1.22220	+	1.22220i	0.255349	+	0.966849i	$0.417810\pi$
$74$			10.4164i			1.21088i
$75$		0			0
$76$		−	26.3930i		−	3.02748i
$77$	−2.21161	−	6.56411i	−0.252036	−	0.748050i
$78$	7.49535	−	7.49535i	0.848682	−	0.848682i
$79$		−	3.70820i		−	0.417206i	−0.978000	−	0.208603i	$-0.933108\pi$
$79$		−	3.70820i		−	0.417206i	0.978000	−	0.208603i	$-0.0668916\pi$
$80$		0			0
$81$	−13.4721			−1.49690
$82$	9.34003	−	9.34003i	1.03143	−	1.03143i
$83$	−3.20374	−	3.20374i	−0.351656	−	0.351656i	0.509070	−	0.860725i	$-0.329990\pi$
$83$	−3.20374	−	3.20374i	−0.351656	−	0.351656i	−0.860725	+	0.509070i	$0.829990\pi$
$84$	26.3930	+	13.0902i	2.87971	+	1.42825i
$85$		0			0
$86$	−3.47214			−0.374410
$87$	18.9512	−	18.9512i	2.03179	−	2.03179i
$88$	−7.09970	+	7.09970i	−0.756831	+	0.756831i
$89$	−11.8033			−1.25115			−0.625574	−	0.780165i	$-0.715135\pi$
$89$	−11.8033			−1.25115			−0.625574	+	0.780165i	$0.715135\pi$
$90$		0			0
$91$	−1.70820	+	3.44416i	−0.179068	+	0.361046i
$92$	18.1916	+	18.1916i	1.89661	+	1.89661i
$93$	−2.31619	+	2.31619i	−0.240178	+	0.240178i
$94$	−18.0339			−1.86005
$95$		0			0
$96$			10.0812i			1.02891i
$97$	−1.02749	+	1.02749i	−0.104325	+	0.104325i	−0.757343	−	0.653017i	$-0.773503\pi$
$97$	−1.02749	+	1.02749i	−0.104325	+	0.104325i	0.653017	+	0.757343i	$0.273503\pi$
$98$	−16.4397	−	2.24032i	−1.66066	−	0.226307i
$99$			16.9443i			1.70296i
$100$		0			0
$101$		−	7.29485i		−	0.725864i	−0.931816	−	0.362932i	$-0.881776\pi$
$101$		−	7.29485i		−	0.725864i	0.931816	−	0.362932i	$-0.118224\pi$
$102$	−6.06387	−	6.06387i	−0.600413	−	0.600413i
$103$	−6.52875	−	6.52875i	−0.643297	−	0.643297i	0.308067	−	0.951365i	$-0.400318\pi$
$103$	−6.52875	−	6.52875i	−0.643297	−	0.643297i	−0.951365	+	0.308067i	$0.900318\pi$
$104$	5.57277			0.546455
$105$		0			0
$106$	−13.3820			−1.29977
$107$	7.34423	+	7.34423i	0.709993	+	0.709993i	0.966534	−	0.256540i	$-0.0825826\pi$
$107$	7.34423	+	7.34423i	0.709993	+	0.709993i	−0.256540	+	0.966534i	$0.582583\pi$
$108$	−27.3387	−	27.3387i	−2.63067	−	2.63067i
$109$		−	7.00000i		−	0.670478i	−0.942133	−	0.335239i	$-0.891183\pi$
$109$		−	7.00000i		−	0.670478i	0.942133	−	0.335239i	$-0.108817\pi$
$110$		0			0
$111$			13.5254i			1.28377i
$112$	1.56627	+	4.64873i	0.147998	+	0.439263i
$113$	−9.41589	+	9.41589i	−0.885773	+	0.885773i	−0.994114	−	0.108341i	$-0.965446\pi$
$113$	−9.41589	+	9.41589i	−0.885773	+	0.885773i	0.108341	+	0.994114i	$0.465446\pi$
$114$		−	53.2148i		−	4.98402i
$115$		0			0
$116$	31.5066			2.92531
$117$	6.65003	−	6.65003i	0.614796	−	0.614796i
$118$	17.9987	+	17.9987i	1.65692	+	1.65692i
$119$	2.78638	+	1.38197i	0.255427	+	0.126685i
$120$		0			0
$121$	−4.14590			−0.376900
$122$	13.3287	−	13.3287i	1.20672	−	1.20672i
$123$	12.1277	−	12.1277i	1.09352	−	1.09352i
$124$	−3.85069			−0.345802
$125$		0			0
$126$	36.3607	+	18.0339i	3.23927	+	1.60658i
$127$	3.10750	+	3.10750i	0.275746	+	0.275746i	0.831408	−	0.555662i	$-0.187535\pi$
$127$	3.10750	+	3.10750i	0.275746	+	0.275746i	−0.555662	+	0.831408i	$0.687535\pi$
$128$	−14.5951	+	14.5951i	−1.29003	+	1.29003i
$129$	−4.50846			−0.396948
$130$		0			0
$131$			13.9319i			1.21724i	0.793463	+	0.608619i	$0.208276\pi$
$131$			13.9319i			1.21724i	−0.793463	+	0.608619i	$0.791724\pi$
$132$	−20.6137	+	20.6137i	−1.79420	+	1.79420i
$133$	6.16238	+	18.2901i	0.534346	+	1.58595i
$134$		−	2.14590i		−	0.185377i
$135$		0			0
$136$		−	4.50846i		−	0.386598i
$137$	−4.78351	−	4.78351i	−0.408683	−	0.408683i	0.472596	−	0.881279i	$-0.343317\pi$
$137$	−4.78351	−	4.78351i	−0.408683	−	0.408683i	−0.881279	+	0.472596i	$0.843317\pi$
$138$	36.6788	+	36.6788i	3.12230	+	3.12230i
$139$	−2.78638			−0.236338			−0.118169	−	0.992994i	$-0.537702\pi$
$139$	−2.78638			−0.236338			−0.118169	+	0.992994i	$0.537702\pi$
$140$		0			0
$141$	−23.4164			−1.97202
$142$	2.95637	+	2.95637i	0.248093	+	0.248093i
$143$	−2.68999	−	2.68999i	−0.224949	−	0.224949i
$144$		−	12.0000i		−	1.00000i
$145$		0			0
$146$			35.0034i			2.89690i
$147$	−21.3465	−	2.90899i	−1.76063	−	0.239930i
$148$	−11.2430	+	11.2430i	−0.924172	+	0.924172i
$149$		−	7.32624i		−	0.600189i	−0.953910	−	0.300094i	$-0.902982\pi$
$149$		−	7.32624i		−	0.600189i	0.953910	−	0.300094i	$-0.0970182\pi$
$150$		0			0
$151$	4.85410			0.395021			0.197511	−	0.980301i	$-0.436714\pi$
$151$	4.85410			0.395021			0.197511	+	0.980301i	$0.436714\pi$
$152$	19.7825	−	19.7825i	1.60457	−	1.60457i
$153$	−5.37999	−	5.37999i	−0.434946	−	0.434946i
$154$	7.29485	−	14.7082i	0.587835	−	1.18522i
$155$		0			0
$156$	16.1803			1.29546
$157$	−8.19126	+	8.19126i	−0.653734	+	0.653734i	−0.953890	−	0.300156i	$-0.902961\pi$
$157$	−8.19126	+	8.19126i	−0.653734	+	0.653734i	0.300156	+	0.953890i	$0.402961\pi$
$158$	6.21500	−	6.21500i	0.494438	−	0.494438i
$159$	−17.3761			−1.37801
$160$		0			0
$161$	−16.8541	−	8.35915i	−1.32829	−	0.658793i
$162$	−22.5795	−	22.5795i	−1.77401	−	1.77401i
$163$	−1.67601	+	1.67601i	−0.131275	+	0.131275i	−0.769691	−	0.638416i	$-0.779590\pi$
$163$	−1.67601	+	1.67601i	−0.131275	+	0.131275i	0.638416	+	0.769691i	$0.279590\pi$
$164$	20.1625			1.57442
$165$		0			0
$166$		−	10.7390i		−	0.833508i
$167$	−6.52875	+	6.52875i	−0.505210	+	0.505210i	−0.913052	−	0.407842i	$-0.866281\pi$
$167$	−6.52875	+	6.52875i	−0.505210	+	0.505210i	0.407842	+	0.913052i	$0.366281\pi$
$168$	9.97094	+	29.5940i	0.769275	+	2.28323i
$169$		−	10.8885i		−	0.837580i
$170$		0			0
$171$		−	47.2132i		−	3.61049i
$172$	−3.74768	−	3.74768i	−0.285758	−	0.285758i
$173$	6.52875	+	6.52875i	0.496372	+	0.496372i	0.910307	−	0.413935i	$-0.135846\pi$
$173$	6.52875	+	6.52875i	0.496372	+	0.496372i	−0.413935	+	0.910307i	$0.635846\pi$
$174$	63.5250			4.81582
$175$		0			0
$176$	−4.85410			−0.365892
$177$	23.3708	+	23.3708i	1.75665	+	1.75665i
$178$	−19.7825	−	19.7825i	−1.48276	−	1.48276i
$179$		−	13.0344i		−	0.974240i	−0.873335	−	0.487120i	$-0.838047\pi$
$179$		−	13.0344i		−	0.974240i	0.873335	−	0.487120i	$-0.161953\pi$
$180$		0			0
$181$			14.1832i			1.05423i	0.849795	+	0.527113i	$0.176726\pi$
$181$			14.1832i			1.05423i	−0.849795	+	0.527113i	$0.823274\pi$
$182$	−8.63542	+	2.90948i	−0.640100	+	0.215665i
$183$	17.3069	−	17.3069i	1.27936	−	1.27936i
$184$			27.2705i			2.01041i
$185$		0			0
$186$	−7.76393			−0.569279
$187$	−2.17625	+	2.17625i	−0.159143	+	0.159143i
$188$	−19.4650	−	19.4650i	−1.41963	−	1.41963i
$189$	25.3287	+	12.5623i	1.84239	+	0.913773i
$190$		0			0
$191$	−14.7082			−1.06425			−0.532124	−	0.846666i	$-0.678606\pi$
$191$	−14.7082			−1.06425			−0.532124	+	0.846666i	$0.678606\pi$
$192$	−24.9662	+	24.9662i	−1.80178	+	1.80178i
$193$	−0.151126	+	0.151126i	−0.0108783	+	0.0108783i	−0.712525	−	0.701647i	$-0.752448\pi$
$193$	−0.151126	+	0.151126i	−0.0108783	+	0.0108783i	0.701647	+	0.712525i	$0.252448\pi$
$194$	−3.44416			−0.247276
$195$		0			0
$196$	−15.3262	−	20.1625i	−1.09473	−	1.44018i
$197$	3.99220	+	3.99220i	0.284433	+	0.284433i	0.834874	−	0.550441i	$-0.185540\pi$
$197$	3.99220	+	3.99220i	0.284433	+	0.284433i	−0.550441	+	0.834874i	$0.685540\pi$
$198$	−28.3988	+	28.3988i	−2.01822	+	2.01822i
$199$	−18.4404			−1.30720			−0.653602	−	0.756839i	$-0.726743\pi$
$199$	−18.4404			−1.30720			−0.653602	+	0.756839i	$0.726743\pi$
$200$		0			0
$201$		−	2.78638i		−	0.196536i
$202$	12.2263	−	12.2263i	0.860236	−	0.860236i
$203$	−21.8338	+	7.35633i	−1.53243	+	0.516313i
$204$		−	13.0902i		−	0.916495i
$205$		0			0
$206$		−	21.8845i		−	1.52477i
$207$	32.5421	+	32.5421i	2.26183	+	2.26183i
$208$	1.90506	+	1.90506i	0.132092	+	0.132092i
$209$	−19.0982			−1.32105
$210$		0			0
$211$	−3.52786			−0.242868			−0.121434	−	0.992599i	$-0.538749\pi$
$211$	−3.52786			−0.242868			−0.121434	+	0.992599i	$0.538749\pi$
$212$	−14.4439	−	14.4439i	−0.992013	−	0.992013i
$213$	3.83876	+	3.83876i	0.263027	+	0.263027i
$214$			24.6180i			1.68285i
$215$		0			0
$216$		−	40.9827i		−	2.78852i
$217$	2.66849	−	0.899079i	0.181149	−	0.0610335i
$218$	11.7321	−	11.7321i	0.794597	−	0.794597i
$219$			45.4508i			3.07128i
$220$		0			0
$221$	1.70820			0.114906
$222$	−22.6687	+	22.6687i	−1.52142	+	1.52142i
$223$	1.54123	+	1.54123i	0.103208	+	0.103208i	0.756825	−	0.653617i	$-0.226749\pi$
$223$	1.54123	+	1.54123i	0.103208	+	0.103208i	−0.653617	+	0.756825i	$0.726749\pi$
$224$	3.85069	−	7.76393i	0.257285	−	0.518750i
$225$		0			0
$226$	−31.5623			−2.09949
$227$	−1.90506	+	1.90506i	−0.126444	+	0.126444i	−0.767497	−	0.641053i	$-0.778498\pi$
$227$	−1.90506	+	1.90506i	−0.126444	+	0.126444i	0.641053	+	0.767497i	$0.278498\pi$
$228$	57.4378	−	57.4378i	3.80391	−	3.80391i
$229$	22.5423			1.48964			0.744819	−	0.667267i	$-0.232536\pi$
$229$	22.5423			1.48964			0.744819	+	0.667267i	$0.232536\pi$
$230$		0			0
$231$	9.47214	−	19.0982i	0.623221	−	1.25657i
$232$	23.6153	+	23.6153i	1.55042	+	1.55042i
$233$	−12.2789	+	12.2789i	−0.804415	+	0.804415i	−0.983782	−	0.179367i	$-0.942595\pi$
$233$	−12.2789	+	12.2789i	−0.804415	+	0.804415i	0.179367	+	0.983782i	$0.442595\pi$
$234$	22.2911			1.45721
$235$		0			0
$236$			38.8541i			2.52919i
$237$	8.06998	−	8.06998i	0.524202	−	0.524202i
$238$	2.35382	+	6.98620i	0.152576	+	0.452848i
$239$		−	2.05573i		−	0.132974i	−0.997787	−	0.0664870i	$-0.978821\pi$
$239$		−	2.05573i		−	0.132974i	0.997787	−	0.0664870i	$-0.0211791\pi$
$240$		0			0
$241$		−	2.12861i		−	0.137116i	−0.997647	−	0.0685578i	$-0.978160\pi$
$241$		−	2.12861i		−	0.137116i	0.997647	−	0.0685578i	$-0.0218398\pi$
$242$	−6.94858	−	6.94858i	−0.446671	−	0.446671i
$243$	−6.65003	−	6.65003i	−0.426600	−	0.426600i
$244$	28.7729			1.84199
$245$		0			0
$246$	40.6525			2.59191
$247$	7.49535	+	7.49535i	0.476918	+	0.476918i
$248$	−2.88623	−	2.88623i	−0.183276	−	0.183276i
$249$		−	13.9443i		−	0.883682i
$250$		0			0
$251$		−	13.5254i		−	0.853715i	−0.904319	−	0.426857i	$-0.859621\pi$
$251$		−	13.5254i		−	0.853715i	0.904319	−	0.426857i	$-0.140379\pi$
$252$	19.7812	+	58.7112i	1.24610	+	3.69846i
$253$	13.1636	−	13.1636i	0.827587	−	0.827587i
$254$			10.4164i			0.653584i
$255$		0			0
$256$	−25.9787			−1.62367
$257$	17.4100	−	17.4100i	1.08601	−	1.08601i	0.0900711	−	0.995935i	$-0.471291\pi$
$257$	17.4100	−	17.4100i	1.08601	−	1.08601i	0.995935	−	0.0900711i	$-0.0287094\pi$
$258$	−7.55624	−	7.55624i	−0.470431	−	0.470431i
$259$	5.16624	−	10.4164i	0.321014	−	0.647244i
$260$		0			0
$261$	56.3607			3.48864
$262$	−23.3501	+	23.3501i	−1.44257	+	1.44257i
$263$	5.91274	−	5.91274i	0.364595	−	0.364595i	−0.500906	−	0.865502i	$-0.667000\pi$
$263$	5.91274	−	5.91274i	0.364595	−	0.364595i	0.865502	+	0.500906i	$0.167000\pi$
$264$	−30.9015			−1.90185
$265$		0			0
$266$	−20.3262	+	40.9827i	−1.24628	+	2.51281i
$267$	−25.6870	−	25.6870i	−1.57202	−	1.57202i
$268$	2.31619	−	2.31619i	0.141484	−	0.141484i
$269$	9.67470			0.589877			0.294938	−	0.955516i	$-0.404701\pi$
$269$	9.67470			0.589877			0.294938	+	0.955516i	$0.404701\pi$
$270$		0			0
$271$		−	15.2475i		−	0.926218i	−0.886301	−	0.463109i	$-0.846734\pi$
$271$		−	15.2475i		−	0.926218i	0.886301	−	0.463109i	$-0.153266\pi$
$272$	1.54123	−	1.54123i	0.0934508	−	0.0934508i
$273$	−11.2128	+	3.77787i	−0.678632	+	0.228647i
$274$		−	16.0344i		−	0.968676i
$275$		0			0
$276$			79.1790i			4.76602i
$277$	−9.41589	−	9.41589i	−0.565746	−	0.565746i	0.365188	−	0.930934i	$-0.381005\pi$
$277$	−9.41589	−	9.41589i	−0.565746	−	0.565746i	−0.930934	+	0.365188i	$0.881005\pi$
$278$	−4.67001	−	4.67001i	−0.280089	−	0.280089i
$279$	−6.88832			−0.412393
$280$		0			0
$281$	19.1246			1.14088			0.570439	−	0.821340i	$-0.306773\pi$
$281$	19.1246			1.14088			0.570439	+	0.821340i	$0.306773\pi$
$282$	−39.2462	−	39.2462i	−2.33708	−	2.33708i
$283$	−4.94120	−	4.94120i	−0.293724	−	0.293724i	0.544826	−	0.838549i	$-0.316596\pi$
$283$	−4.94120	−	4.94120i	−0.293724	−	0.293724i	−0.838549	+	0.544826i	$0.816596\pi$
$284$			6.38197i			0.378700i
$285$		0			0
$286$		−	9.01693i		−	0.533182i
$287$	−13.9724	+	4.70764i	−0.824765	+	0.277883i
$288$	−14.9907	+	14.9907i	−0.883336	+	0.883336i
$289$			15.6180i			0.918708i
$290$		0			0
$291$	−4.47214			−0.262161
$292$	−37.7812	+	37.7812i	−2.21098	+	2.21098i
$293$	−9.73249	−	9.73249i	−0.568578	−	0.568578i	0.363152	−	0.931730i	$-0.381701\pi$
$293$	−9.73249	−	9.73249i	−0.568578	−	0.568578i	−0.931730	+	0.363152i	$0.881701\pi$
$294$	−30.9015	−	40.6525i	−1.80221	−	2.37090i
$295$		0			0
$296$	−16.8541			−0.979625
$297$	−19.7825	+	19.7825i	−1.14790	+	1.14790i
$298$	12.2789	−	12.2789i	0.711296	−	0.711296i
$299$	−10.3325			−0.597543
$300$		0			0
$301$	3.47214	+	1.72208i	0.200131	+	0.0992590i
$302$	8.13553	+	8.13553i	0.468147	+	0.468147i
$303$	15.8754	−	15.8754i	0.912019	−	0.912019i
$304$	13.5254			0.775734
$305$		0			0
$306$		−	18.0339i		−	1.03093i
$307$	17.0925	−	17.0925i	0.975520	−	0.975520i	−0.0241871	−	0.999707i	$-0.507700\pi$
$307$	17.0925	−	17.0925i	0.975520	−	0.975520i	0.999707	+	0.0241871i	$0.00769976\pi$
$308$	23.7492	−	8.00167i	1.35323	−	0.455937i
$309$		−	28.4164i		−	1.61655i
$310$		0			0
$311$			5.57277i			0.316003i	0.987439	+	0.158001i	$0.0505050\pi$
$311$			5.57277i			0.316003i	−0.987439	+	0.158001i	$0.949495\pi$
$312$	12.1277	+	12.1277i	0.686598	+	0.686598i
$313$	−12.1513	−	12.1513i	−0.686832	−	0.686832i	0.274698	−	0.961530i	$-0.411422\pi$
$313$	−12.1513	−	12.1513i	−0.686832	−	0.686832i	−0.961530	+	0.274698i	$0.911422\pi$
$314$	−27.4573			−1.54951
$315$		0			0
$316$	13.4164			0.754732
$317$	23.0685	+	23.0685i	1.29566	+	1.29566i	0.931233	+	0.364424i	$0.118734\pi$
$317$	23.0685	+	23.0685i	1.29566	+	1.29566i	0.364424	+	0.931233i	$0.381266\pi$
$318$	−29.1225	−	29.1225i	−1.63311	−	1.63311i
$319$		−	22.7984i		−	1.27646i
$320$		0			0
$321$			31.9658i			1.78416i
$322$	−14.2376	−	42.2577i	−0.793433	−	2.35493i
$323$	6.06387	−	6.06387i	0.337403	−	0.337403i
$324$		−	48.7426i		−	2.70792i
$325$		0			0
$326$	−5.61803			−0.311154
$327$	15.2338	−	15.2338i	0.842429	−	0.842429i
$328$	15.1125	+	15.1125i	0.834447	+	0.834447i
$329$	18.0339	+	8.94427i	0.994238	+	0.493114i
$330$		0			0
$331$	−30.0689			−1.65274			−0.826368	−	0.563131i	$-0.809597\pi$
$331$	−30.0689			−1.65274			−0.826368	+	0.563131i	$0.809597\pi$
$332$	11.5912	−	11.5912i	0.636151	−	0.636151i
$333$	−20.1121	+	20.1121i	−1.10214	+	1.10214i
$334$	−21.8845			−1.19747
$335$		0			0
$336$	−6.70820	+	13.5254i	−0.365963	+	0.737870i
$337$	18.5873	+	18.5873i	1.01251	+	1.01251i	0.999921	+	0.0125919i	$0.00400822\pi$
$337$	18.5873	+	18.5873i	1.01251	+	1.01251i	0.0125919	+	0.999921i	$0.495992\pi$
$338$	18.2493	−	18.2493i	0.992633	−	0.992633i
$339$	−40.9827			−2.22587
$340$		0			0
$341$			2.78638i			0.150891i
$342$	79.1300	−	79.1300i	4.27886	−	4.27886i
$343$	15.3286	+	10.3940i	0.827666	+	0.561221i
$344$		−	5.61803i		−	0.302904i
$345$		0			0
$346$			21.8845i			1.17652i
$347$	−4.93464	−	4.93464i	−0.264905	−	0.264905i	0.562138	−	0.827043i	$-0.309979\pi$
$347$	−4.93464	−	4.93464i	−0.264905	−	0.264905i	−0.827043	+	0.562138i	$0.809979\pi$
$348$	68.5662	+	68.5662i	3.67554	+	3.67554i
$349$	20.5690			1.10103			0.550516	−	0.834824i	$-0.314431\pi$
$349$	20.5690			1.10103			0.550516	+	0.834824i	$0.314431\pi$
$350$		0			0
$351$	15.5279			0.828816
$352$	6.06387	+	6.06387i	0.323205	+	0.323205i
$353$	−8.19126	−	8.19126i	−0.435977	−	0.435977i	0.454679	−	0.890656i	$-0.349754\pi$
$353$	−8.19126	−	8.19126i	−0.435977	−	0.435977i	−0.890656	+	0.454679i	$0.849754\pi$
$354$			78.3394i			4.16369i
$355$		0			0
$356$		−	42.7048i		−	2.26335i
$357$	3.05636	+	9.07137i	0.161760	+	0.480108i
$358$	21.8459	−	21.8459i	1.15459	−	1.15459i
$359$			4.70820i			0.248489i	0.992252	+	0.124245i	$0.0396508\pi$
$359$			4.70820i			0.248489i	−0.992252	+	0.124245i	$0.960349\pi$
$360$		0			0
$361$	34.2148			1.80078
$362$	−23.7712	+	23.7712i	−1.24938	+	1.24938i
$363$	−9.02251	−	9.02251i	−0.473559	−	0.473559i
$364$	−12.4611	−	6.18034i	−0.653138	−	0.323938i
$365$		0			0
$366$	58.0132			3.03240
$367$	19.1475	−	19.1475i	0.999490	−	0.999490i	−0.000510121	−	1.00000i	$-0.500162\pi$
$367$	19.1475	−	19.1475i	0.999490	−	0.999490i	1.00000		0.000510121i	$0.000162376\pi$
$368$	−9.32249	+	9.32249i	−0.485969	+	0.485969i
$369$	36.0677			1.87761
$370$		0			0
$371$	13.3820	+	6.63707i	0.694757	+	0.344580i
$372$	−8.38006	−	8.38006i	−0.434486	−	0.434486i
$373$	−22.0904	+	22.0904i	−1.14380	+	1.14380i	−0.156049	+	0.987749i	$0.549876\pi$
$373$	−22.0904	+	22.0904i	−1.14380	+	1.14380i	−0.987749	+	0.156049i	$0.950124\pi$
$374$	−7.29485			−0.377208
$375$		0			0
$376$		−	29.1794i		−	1.50481i
$377$	−8.94756	+	8.94756i	−0.460823	+	0.460823i
$378$	21.3966	+	63.5058i	1.10052	+	3.26639i
$379$		−	10.2918i		−	0.528654i	−0.964433	−	0.264327i	$-0.914850\pi$
$379$		−	10.2918i		−	0.528654i	0.964433	−	0.264327i	$-0.0851498\pi$
$380$		0			0
$381$			13.5254i			0.692927i
$382$	−24.6511	−	24.6511i	−1.26126	−	1.26126i
$383$	−1.58755	−	1.58755i	−0.0811202	−	0.0811202i	0.665382	−	0.746503i	$-0.268268\pi$
$383$	−1.58755	−	1.58755i	−0.0811202	−	0.0811202i	−0.746503	+	0.665382i	$0.768268\pi$
$384$	−63.5250			−3.24175
$385$		0			0
$386$	−0.506578			−0.0257841
$387$	−6.70405	−	6.70405i	−0.340786	−	0.340786i
$388$	−3.71748	−	3.71748i	−0.188726	−	0.188726i
$389$		−	16.1459i		−	0.818630i	−0.912393	−	0.409315i	$-0.865768\pi$
$389$		−	16.1459i		−	0.818630i	0.912393	−	0.409315i	$-0.134232\pi$
$390$		0			0
$391$			8.35915i			0.422740i
$392$	3.62492	−	26.6000i	0.183086	−	1.34350i
$393$	−30.3193	+	30.3193i	−1.52941	+	1.52941i
$394$			13.3820i			0.674174i
$395$		0			0
$396$	−61.3050			−3.08069
$397$	23.1825	−	23.1825i	1.16349	−	1.16349i	0.179789	−	0.983705i	$-0.442458\pi$
$397$	23.1825	−	23.1825i	1.16349	−	1.16349i	0.983705	−	0.179789i	$-0.0575415\pi$
$398$	−30.9063	−	30.9063i	−1.54919	−	1.54919i
$399$	−26.3930	+	53.2148i	−1.32130	+	2.66407i
$400$		0			0
$401$	−8.03444			−0.401221			−0.200610	−	0.979671i	$-0.564293\pi$
$401$	−8.03444			−0.401221			−0.200610	+	0.979671i	$0.564293\pi$
$402$	4.67001	−	4.67001i	0.232919	−	0.232919i
$403$	1.09356	−	1.09356i	0.0544740	−	0.0544740i
$404$	26.3930			1.31310
$405$		0			0
$406$	−48.9230	−	24.2644i	−2.42801	−	1.20422i
$407$	8.13553	+	8.13553i	0.403263	+	0.403263i
$408$	9.81155	−	9.81155i	0.485744	−	0.485744i
$409$	15.2475			0.753939			0.376969	−	0.926226i	$-0.376966\pi$
$409$	15.2475			0.753939			0.376969	+	0.926226i	$0.376966\pi$
$410$		0			0
$411$		−	20.8202i		−	1.02699i
$412$	23.6212	−	23.6212i	1.16374	−	1.16374i
$413$	−9.07186	−	26.9255i	−0.446397	−	1.32492i
$414$			109.082i			5.36109i
$415$		0			0
$416$		−	4.75971i		−	0.233364i
$417$	−6.06387	−	6.06387i	−0.296949	−	0.296949i
$418$	−32.0087	−	32.0087i	−1.56560	−	1.56560i
$419$	−6.23054			−0.304382			−0.152191	−	0.988351i	$-0.548633\pi$
$419$	−6.23054			−0.304382			−0.152191	+	0.988351i	$0.548633\pi$
$420$		0			0
$421$	−9.29180			−0.452854			−0.226427	−	0.974028i	$-0.572705\pi$
$421$	−9.29180			−0.452854			−0.226427	+	0.974028i	$0.572705\pi$
$422$	−5.91274	−	5.91274i	−0.287828	−	0.287828i
$423$	−34.8200	−	34.8200i	−1.69301	−	1.69301i
$424$		−	21.6525i		−	1.05154i
$425$		0			0
$426$			12.8676i			0.623438i
$427$	−19.9393	+	6.71804i	−0.964932	+	0.325109i
$428$	−26.5717	+	26.5717i	−1.28439	+	1.28439i
$429$		−	11.7082i		−	0.565277i
$430$		0			0
$431$	−14.8328			−0.714472			−0.357236	−	0.934014i	$-0.616281\pi$
$431$	−14.8328			−0.714472			−0.357236	+	0.934014i	$0.616281\pi$
$432$	14.0100	−	14.0100i	0.674058	−	0.674058i
$433$	11.4700	+	11.4700i	0.551211	+	0.551211i	0.926790	−	0.375579i	$-0.122556\pi$
$433$	11.4700	+	11.4700i	0.551211	+	0.551211i	−0.375579	+	0.926790i	$0.622556\pi$
$434$	5.97929	+	2.96556i	0.287015	+	0.142351i
$435$		0			0
$436$	25.3262			1.21291
$437$	−36.6788	+	36.6788i	−1.75458	+	1.75458i
$438$	−76.1762	+	76.1762i	−3.63984	+	3.63984i
$439$	31.5592			1.50624			0.753120	−	0.657883i	$-0.228548\pi$
$439$	31.5592			1.50624			0.753120	+	0.657883i	$0.228548\pi$
$440$		0			0
$441$	−27.4164	−	36.0677i	−1.30554	−	1.71751i
$442$	2.86297	+	2.86297i	0.136178	+	0.136178i
$443$	−8.62459	+	8.62459i	−0.409767	+	0.409767i	−0.881657	−	0.471891i	$-0.843572\pi$
$443$	−8.62459	+	8.62459i	−0.409767	+	0.409767i	0.471891	+	0.881657i	$0.343572\pi$
$444$	−48.9353			−2.32237
$445$		0			0
$446$			5.16624i			0.244628i
$447$	15.9437	−	15.9437i	0.754113	−	0.754113i
$448$	28.7637	−	9.69118i	1.35896	−	0.457865i
$449$			25.7639i			1.21588i	0.793985	+	0.607938i	$0.208003\pi$
$449$			25.7639i			1.21588i	−0.793985	+	0.607938i	$0.791997\pi$
$450$		0			0
$451$		−	14.5897i		−	0.687002i
$452$	−34.0670	−	34.0670i	−1.60238	−	1.60238i
$453$	10.5637	+	10.5637i	0.496328	+	0.496328i
$454$	−6.38582			−0.299701
$455$		0			0
$456$	86.1033			4.03216
$457$	−24.0109	−	24.0109i	−1.12318	−	1.12318i	−0.991260	−	0.131925i	$-0.957884\pi$
$457$	−24.0109	−	24.0109i	−1.12318	−	1.12318i	−0.131925	−	0.991260i	$-0.542116\pi$
$458$	37.7812	+	37.7812i	1.76540	+	1.76540i
$459$		−	12.5623i		−	0.586358i
$460$		0			0
$461$			31.9658i			1.48879i	0.667737	+	0.744397i	$0.267263\pi$
$461$			31.9658i			1.48879i	−0.667737	+	0.744397i	$0.732737\pi$
$462$	47.8842	−	16.1333i	2.22777	−	0.750590i
$463$	−18.9829	+	18.9829i	−0.882211	+	0.882211i	−0.993759	−	0.111548i	$-0.964419\pi$
$463$	−18.9829	+	18.9829i	−0.882211	+	0.882211i	0.111548	+	0.993759i	$0.464419\pi$
$464$			16.1459i			0.749554i
$465$		0			0
$466$	−41.1591			−1.90666
$467$	−19.6612	+	19.6612i	−0.909812	+	0.909812i	−0.996257	−	0.0864443i	$-0.972450\pi$
$467$	−19.6612	+	19.6612i	−0.909812	+	0.909812i	0.0864443	+	0.996257i	$0.472450\pi$
$468$	24.0600	+	24.0600i	1.11218	+	1.11218i
$469$	−1.06430	+	2.14590i	−0.0491450	+	0.0990884i
$470$		0			0
$471$	−35.6525			−1.64278
$472$	−29.1225	+	29.1225i	−1.34047	+	1.34047i
$473$	−2.71184	+	2.71184i	−0.124691	+	0.124691i
$474$	27.0508			1.24248
$475$		0			0
$476$	−5.00000	+	10.0812i	−0.229175	+	0.462072i
$477$	−25.8381	−	25.8381i	−1.18304	−	1.18304i
$478$	3.44543	−	3.44543i	0.157590	−	0.157590i
$479$	−25.7352			−1.17587			−0.587936	−	0.808907i	$-0.700059\pi$
$479$	−25.7352			−1.17587			−0.587936	+	0.808907i	$0.700059\pi$
$480$		0			0
$481$		−	6.38582i		−	0.291168i
$482$	3.56757	−	3.56757i	0.162498	−	0.162498i
$483$	−18.4871	−	54.8704i	−0.841194	−	2.49669i
$484$		−	15.0000i		−	0.681818i
$485$		0			0
$486$		−	22.2911i		−	1.01114i
$487$	1.12923	+	1.12923i	0.0511705	+	0.0511705i	0.732229	−	0.681059i	$-0.238480\pi$
$487$	1.12923	+	1.12923i	0.0511705	+	0.0511705i	−0.681059	+	0.732229i	$0.738480\pi$
$488$	21.5663	+	21.5663i	0.976259	+	0.976259i
$489$	−7.29485			−0.329884
$490$		0			0
$491$	16.2361			0.732723			0.366362	−	0.930472i	$-0.380603\pi$
$491$	16.2361			0.732723			0.366362	+	0.930472i	$0.380603\pi$
$492$	43.8786	+	43.8786i	1.97820	+	1.97820i
$493$	7.23873	+	7.23873i	0.326016	+	0.326016i
$494$			25.1246i			1.13041i
$495$		0			0
$496$		−	1.97333i		−	0.0886050i
$497$	−1.49010	−	4.42265i	−0.0668400	−	0.198383i
$498$	23.3708	−	23.3708i	1.04727	−	1.04727i
$499$		−	26.9787i		−	1.20773i	−0.797085	−	0.603867i	$-0.793626\pi$
$499$		−	26.9787i		−	1.20773i	0.797085	−	0.603867i	$-0.206374\pi$
$500$		0			0
$501$	−28.4164			−1.26955
$502$	22.6687	−	22.6687i	1.01175	−	1.01175i
$503$	29.3651	+	29.3651i	1.30932	+	1.30932i	0.921903	+	0.387421i	$0.126634\pi$
$503$	29.3651	+	29.3651i	1.30932	+	1.30932i	0.387421	+	0.921903i	$0.373366\pi$
$504$	−29.1794	+	58.8328i	−1.29975	+	2.62062i
$505$		0			0
$506$	44.1246			1.96158
$507$	23.6962	−	23.6962i	1.05239	−	1.05239i
$508$	−11.2430	+	11.2430i	−0.498829	+	0.498829i
$509$	−38.4476			−1.70416			−0.852079	−	0.523413i	$-0.824658\pi$
$509$	−38.4476			−1.70416			−0.852079	+	0.523413i	$0.824658\pi$
$510$		0			0
$511$	17.3607	−	35.0034i	0.767991	−	1.54846i
$512$	−14.3505	−	14.3505i	−0.634210	−	0.634210i
$513$	55.1216	−	55.1216i	2.43368	−	2.43368i
$514$	58.3588			2.57409
$515$		0			0
$516$		−	16.3118i		−	0.718086i
$517$	−14.0850	+	14.0850i	−0.619457	+	0.619457i
$518$	26.1167	−	8.79935i	1.14750	−	0.386621i
$519$			28.4164i			1.24734i
$520$		0			0
$521$		−	37.1320i		−	1.62678i	−0.581717	−	0.813391i	$-0.697619\pi$
$521$		−	37.1320i		−	1.62678i	0.581717	−	0.813391i	$-0.302381\pi$
$522$	94.4612	+	94.4612i	4.13445	+	4.13445i
$523$	−7.79880	−	7.79880i	−0.341018	−	0.341018i	0.515732	−	0.856750i	$-0.327520\pi$
$523$	−7.79880	−	7.79880i	−0.341018	−	0.341018i	−0.856750	+	0.515732i	$0.827520\pi$
$524$	−50.4061			−2.20200
$525$		0			0
$526$	19.8197			0.864178
$527$	−0.884707	−	0.884707i	−0.0385384	−	0.0385384i
$528$	−10.5637	−	10.5637i	−0.459728	−	0.459728i
$529$		−	27.5623i		−	1.19836i
$530$		0			0
$531$			69.5043i			3.01623i
$532$	−66.1743	+	22.2957i	−2.86902	+	0.966642i
$533$	−5.72594	+	5.72594i	−0.248018	+	0.248018i
$534$		−	86.1033i		−	3.72606i
$535$		0			0
$536$	3.47214			0.149973
$537$	28.3662	−	28.3662i	1.22409	−	1.22409i
$538$	16.2149	+	16.2149i	0.699075	+	0.699075i
$539$	−14.5897	+	11.0902i	−0.628423	+	0.477687i
$540$		0			0
$541$	13.2705			0.570544			0.285272	−	0.958447i	$-0.407916\pi$
$541$	13.2705			0.570544			0.285272	+	0.958447i	$0.407916\pi$
$542$	25.5549	−	25.5549i	1.09768	−	1.09768i
$543$	−30.8661	+	30.8661i	−1.32459	+	1.32459i
$544$	−3.85069			−0.165097
$545$		0			0
$546$	−25.1246	−	12.4611i	−1.07523	−	0.533285i
$547$	−14.7462	−	14.7462i	−0.630501	−	0.630501i	0.317693	−	0.948194i	$-0.397092\pi$
$547$	−14.7462	−	14.7462i	−0.630501	−	0.630501i	−0.948194	+	0.317693i	$0.897092\pi$
$548$	17.3069	−	17.3069i	0.739314	−	0.739314i
$549$	51.4705			2.19671
$550$		0			0
$551$			63.5250i			2.70626i
$552$	−59.3475	+	59.3475i	−2.52600	+	2.52600i
$553$	−9.29745	+	3.13254i	−0.395368	+	0.133209i
$554$		−	31.5623i		−	1.34095i
$555$		0			0
$556$		−	10.0812i		−	0.427539i
$557$	16.6667	+	16.6667i	0.706192	+	0.706192i	0.965732	−	0.259541i	$-0.0835711\pi$
$557$	16.6667	+	16.6667i	0.706192	+	0.706192i	−0.259541	+	0.965732i	$0.583571\pi$
$558$	−11.5449	−	11.5449i	−0.488735	−	0.488735i
$559$	2.12861			0.0900305
$560$		0			0
$561$	−9.47214			−0.399914
$562$	32.0531	+	32.0531i	1.35208	+	1.35208i
$563$	0.317511	+	0.317511i	0.0133815	+	0.0133815i	0.713766	−	0.700384i	$-0.246988\pi$
$563$	0.317511	+	0.317511i	0.0133815	+	0.0133815i	−0.700384	+	0.713766i	$0.746988\pi$
$564$		−	84.7214i		−	3.56741i
$565$		0			0
$566$		−	16.5630i		−	0.696196i
$567$	11.3807	+	33.7782i	0.477944	+	1.41855i
$568$	−4.78351	+	4.78351i	−0.200712	+	0.200712i
$569$			7.59675i			0.318472i	0.987241	+	0.159236i	$0.0509031\pi$
$569$			7.59675i			0.318472i	−0.987241	+	0.159236i	$0.949097\pi$
$570$		0			0
$571$	−35.4721			−1.48446			−0.742231	−	0.670144i	$-0.766232\pi$
$571$	−35.4721			−1.48446			−0.742231	+	0.670144i	$0.766232\pi$
$572$	9.73249	−	9.73249i	0.406936	−	0.406936i
$573$	−32.0087	−	32.0087i	−1.33718	−	1.33718i
$574$	−31.3080	−	15.5279i	−1.30677	−	0.648121i
$575$		0			0
$576$	−74.2492			−3.09372
$577$	12.5438	−	12.5438i	0.522204	−	0.522204i	−0.396033	−	0.918236i	$-0.629613\pi$
$577$	12.5438	−	12.5438i	0.522204	−	0.522204i	0.918236	+	0.396033i	$0.129613\pi$
$578$	−26.1760	+	26.1760i	−1.08878	+	1.08878i
$579$	−0.657776			−0.0273362
$580$		0			0
$581$	−5.32624	+	10.7390i	−0.220970	+	0.445529i
$582$	−7.49535	−	7.49535i	−0.310692	−	0.310692i
$583$	−10.4517	+	10.4517i	−0.432866	+	0.432866i
$584$	−56.6367			−2.34364
$585$		0			0
$586$		−	32.6235i		−	1.34767i
$587$	−20.1750	+	20.1750i	−0.832710	+	0.832710i	−0.987887	−	0.155177i	$-0.950405\pi$
$587$	−20.1750	+	20.1750i	−0.832710	+	0.832710i	0.155177	+	0.987887i	$0.450405\pi$
$588$	10.5248	−	77.2323i	0.434037	−	3.18501i
$589$		−	7.76393i		−	0.319907i
$590$		0			0
$591$			17.3761i			0.714756i
$592$	−5.76162	−	5.76162i	−0.236801	−	0.236801i
$593$	31.7376	+	31.7376i	1.30331	+	1.30331i	0.926150	+	0.377155i	$0.123098\pi$
$593$	31.7376	+	31.7376i	1.30331	+	1.30331i	0.377155	+	0.926150i	$0.376902\pi$
$594$	−66.3114			−2.72079
$595$		0			0
$596$	26.5066			1.08575
$597$	−40.1309	−	40.1309i	−1.64245	−	1.64245i
$598$	−17.3174	−	17.3174i	−0.708159	−	0.708159i
$599$			22.7984i			0.931516i	0.884912	+	0.465758i	$0.154218\pi$
$599$			22.7984i			0.931516i	−0.884912	+	0.465758i	$0.845782\pi$
$600$		0			0
$601$		−	5.57277i		−	0.227318i	−0.993520	−	0.113659i	$-0.963743\pi$
$601$		−	5.57277i		−	0.227318i	0.993520	−	0.113659i	$-0.0362571\pi$
$602$	2.93312	+	8.70557i	0.119545	+	0.354812i
$603$	4.14333	−	4.14333i	0.168729	−	0.168729i
$604$			17.5623i			0.714600i
$605$		0			0
$606$	53.2148			2.16170
$607$	−9.77881	+	9.77881i	−0.396910	+	0.396910i	−0.877142	−	0.480232i	$-0.840553\pi$
$607$	−9.77881	+	9.77881i	−0.396910	+	0.396910i	0.480232	+	0.877142i	$0.340553\pi$
$608$	−16.8963	−	16.8963i	−0.685234	−	0.685234i
$609$	−63.5250	−	31.5066i	−2.57416	−	1.27671i
$610$		0			0
$611$	11.0557			0.447267
$612$	19.4650	−	19.4650i	0.786825	−	0.786825i
$613$	5.91274	−	5.91274i	0.238813	−	0.238813i	−0.577545	−	0.816359i	$-0.695989\pi$
$613$	5.91274	−	5.91274i	0.238813	−	0.238813i	0.816359	+	0.577545i	$0.195989\pi$
$614$	57.2945			2.31222
$615$		0			0
$616$	23.7984	+	11.8033i	0.958864	+	0.475569i
$617$	14.3505	+	14.3505i	0.577731	+	0.577731i	0.934277	−	0.356547i	$-0.116046\pi$
$617$	14.3505	+	14.3505i	0.577731	+	0.577731i	−0.356547	+	0.934277i	$0.616046\pi$
$618$	47.6262	−	47.6262i	1.91581	−	1.91581i
$619$	19.5047			0.783959			0.391980	−	0.919974i	$-0.371790\pi$
$619$	19.5047			0.783959			0.391980	+	0.919974i	$0.371790\pi$
$620$		0			0
$621$			75.9861i			3.04922i
$622$	−9.34003	+	9.34003i	−0.374501	+	0.374501i
$623$	9.97094	+	29.5940i	0.399477	+	1.18566i
$624$			8.29180i			0.331937i
$625$		0			0
$626$		−	40.7314i		−	1.62796i
$627$	−41.5624	−	41.5624i	−1.65984	−	1.65984i
$628$	−29.6363	−	29.6363i	−1.18262	−	1.18262i
$629$	−5.16624			−0.205991
$630$		0			0
$631$	−3.23607			−0.128826			−0.0644129	−	0.997923i	$-0.520517\pi$
$631$	−3.23607			−0.128826			−0.0644129	+	0.997923i	$0.520517\pi$
$632$	10.0561	+	10.0561i	0.400009	+	0.400009i
$633$	−7.67752	−	7.67752i	−0.305154	−	0.305154i
$634$			77.3262i			3.07102i
$635$		0			0
$636$		−	62.8672i		−	2.49285i
$637$	10.0784	+	1.37344i	0.399322	+	0.0544177i
$638$	38.2104	−	38.2104i	1.51276	−	1.51276i
$639$			11.4164i			0.451626i
$640$		0			0
$641$	25.5066			1.00745			0.503725	−	0.863864i	$-0.331963\pi$
$641$	25.5066			1.00745			0.503725	+	0.863864i	$0.331963\pi$
$642$	−53.5750	+	53.5750i	−2.11444	+	2.11444i
$643$	18.2876	+	18.2876i	0.721192	+	0.721192i	0.968848	−	0.247656i	$-0.0796603\pi$
$643$	18.2876	+	18.2876i	0.721192	+	0.721192i	−0.247656	+	0.968848i	$0.579660\pi$
$644$	30.2437	−	60.9787i	1.19177	−	2.40290i
$645$		0			0
$646$	20.3262			0.799725
$647$	−5.33366	+	5.33366i	−0.209688	+	0.209688i	−0.804135	−	0.594447i	$-0.797371\pi$
$647$	−5.33366	+	5.33366i	−0.209688	+	0.209688i	0.594447	+	0.804135i	$0.297371\pi$
$648$	36.5343	−	36.5343i	1.43520	−	1.43520i
$649$	28.1151			1.10361
$650$		0			0
$651$	7.76393	+	3.85069i	0.304292	+	0.150920i
$652$	−6.06387	−	6.06387i	−0.237479	−	0.237479i
$653$	−16.6667	+	16.6667i	−0.652219	+	0.652219i	−0.953527	−	0.301308i	$-0.902577\pi$
$653$	−16.6667	+	16.6667i	−0.652219	+	0.652219i	0.301308	+	0.953527i	$0.402577\pi$
$654$	51.0639			1.99676
$655$		0			0
$656$			10.3325i			0.403415i
$657$	−67.5851	+	67.5851i	−2.63674	+	2.63674i
$658$	15.2342	+	45.2157i	0.593893	+	1.76269i
$659$		−	26.5279i		−	1.03338i	−0.856173	−	0.516689i	$-0.827164\pi$
$659$		−	26.5279i		−	1.03338i	0.856173	−	0.516689i	$-0.172836\pi$
$660$		0			0
$661$			17.3761i			0.675851i	0.941173	+	0.337926i	$0.109725\pi$
$661$			17.3761i			0.675851i	−0.941173	+	0.337926i	$0.890275\pi$
$662$	−50.3958	−	50.3958i	−1.95869	−	1.95869i
$663$	3.71748	+	3.71748i	0.144375	+	0.144375i
$664$	17.3761			0.674323
$665$		0			0
$666$	−67.4164			−2.61233
$667$	−43.7852	−	43.7852i	−1.69537	−	1.69537i
$668$	−23.6212	−	23.6212i	−0.913934	−	0.913934i
$669$			6.70820i			0.259354i
$670$		0			0
$671$		−	20.8202i		−	0.803756i
$672$	25.2763	−	8.51620i	0.975055	−	0.328520i
$673$	15.6309	−	15.6309i	0.602526	−	0.602526i	−0.338456	−	0.940982i	$-0.609905\pi$
$673$	15.6309	−	15.6309i	0.602526	−	0.602526i	0.940982	+	0.338456i	$0.109905\pi$
$674$			62.3050i			2.39990i
$675$		0			0
$676$	39.3951			1.51520
$677$	−5.25871	+	5.25871i	−0.202109	+	0.202109i	−0.800903	−	0.598794i	$-0.795647\pi$
$677$	−5.25871	+	5.25871i	−0.202109	+	0.202109i	0.598794	+	0.800903i	$0.295647\pi$
$678$	−68.6875	−	68.6875i	−2.63793	−	2.63793i
$679$	3.44416	+	1.70820i	0.132175	+	0.0655549i
$680$		0			0
$681$	−8.29180			−0.317742
$682$	−4.67001	+	4.67001i	−0.178824	+	0.178824i
$683$	−2.46732	+	2.46732i	−0.0944093	+	0.0944093i	−0.752734	−	0.658325i	$-0.771265\pi$
$683$	−2.46732	+	2.46732i	−0.0944093	+	0.0944093i	0.658325	+	0.752734i	$0.271265\pi$
$684$	170.819			6.53143
$685$		0			0
$686$	8.27051	+	43.1113i	0.315770	+	1.64600i
$687$	49.0577	+	49.0577i	1.87167	+	1.87167i
$688$	1.92054	−	1.92054i	0.0732199	−	0.0732199i
$689$	8.20387			0.312543
$690$		0			0
$691$			31.1527i			1.18511i	0.805532	+	0.592553i	$0.201880\pi$
$691$			31.1527i			1.18511i	−0.805532	+	0.592553i	$0.798120\pi$
$692$	−23.6212	+	23.6212i	−0.897945	+	0.897945i
$693$	42.4838	−	14.3138i	1.61383	−	0.543737i
$694$		−	16.5410i		−	0.627889i
$695$		0			0
$696$			102.786i			3.89608i
$697$	4.63238	+	4.63238i	0.175464	+	0.175464i
$698$	34.4739	+	34.4739i	1.30486	+	1.30486i
$699$	−53.4438			−2.02143
$700$		0			0
$701$	−25.2361			−0.953153			−0.476577	−	0.879133i	$-0.658122\pi$
$701$	−25.2361			−0.953153			−0.476577	+	0.879133i	$0.658122\pi$
$702$	26.0249	+	26.0249i	0.982246	+	0.982246i
$703$	−22.6687	−	22.6687i	−0.854967	−	0.854967i
$704$			30.0344i			1.13197i
$705$		0			0
$706$		−	27.4573i		−	1.03337i
$707$	−18.2901	+	6.16238i	−0.687871	+	0.231760i
$708$	−84.5562	+	84.5562i	−3.17782	+	3.17782i
$709$			31.6869i			1.19003i	0.803716	+	0.595014i	$0.202853\pi$
$709$			31.6869i			1.19003i	−0.803716	+	0.595014i	$0.797147\pi$
$710$		0			0
$711$	24.0000			0.900070
$712$	32.0087	−	32.0087i	1.19958	−	1.19958i
$713$	5.35136	+	5.35136i	0.200410	+	0.200410i
$714$	−10.0812	+	20.3262i	−0.377281	+	0.760690i
$715$		0			0
$716$	47.1591			1.76242
$717$	4.47378	−	4.47378i	0.167076	−	0.167076i
$718$	−7.89101	+	7.89101i	−0.294490	+	0.294490i
$719$	−28.7729			−1.07305			−0.536523	−	0.843886i	$-0.680263\pi$
$719$	−28.7729			−1.07305			−0.536523	+	0.843886i	$0.680263\pi$
$720$		0			0
$721$	−10.8541	+	21.8845i	−0.404228	+	0.815023i
$722$	57.3444	+	57.3444i	2.13414	+	2.13414i
$723$	4.63238	−	4.63238i	0.172280	−	0.172280i
$724$	−51.3152			−1.90711
$725$		0			0
$726$		−	30.2437i		−	1.12245i
$727$	−2.96118	+	2.96118i	−0.109824	+	0.109824i	−0.759883	−	0.650059i	$-0.774744\pi$
$727$	−2.96118	+	2.96118i	−0.109824	+	0.109824i	0.650059	+	0.759883i	$0.274744\pi$
$728$	−4.70764	−	13.9724i	−0.174477	−	0.517852i
$729$			11.4721i			0.424894i
$730$		0			0
$731$		−	1.72208i		−	0.0636934i
$732$	62.6170	+	62.6170i	2.31439	+	2.31439i
$733$	−29.7575	−	29.7575i	−1.09912	−	1.09912i	−0.994514	−	0.104606i	$-0.966642\pi$
$733$	−29.7575	−	29.7575i	−1.09912	−	1.09912i	−0.104606	−	0.994514i	$-0.533358\pi$
$734$	64.1828			2.36903
$735$		0			0
$736$	23.2918			0.858547
$737$	−1.67601	−	1.67601i	−0.0617367	−	0.0617367i
$738$	60.4499	+	60.4499i	2.22519	+	2.22519i
$739$			36.4164i			1.33960i	0.742542	+	0.669800i	$0.233620\pi$
$739$			36.4164i			1.33960i	−0.742542	+	0.669800i	$0.766380\pi$
$740$		0			0
$741$			32.6235i			1.19846i
$742$	11.3045	+	33.5521i	0.415002	+	1.23174i
$743$	7.58876	−	7.58876i	0.278404	−	0.278404i	−0.554067	−	0.832472i	$-0.686925\pi$
$743$	7.58876	−	7.58876i	0.278404	−	0.278404i	0.832472	+	0.554067i	$0.186925\pi$
$744$		−	12.5623i		−	0.460556i
$745$		0			0
$746$	−74.0476			−2.71108
$747$	20.7350	−	20.7350i	0.758655	−	0.758655i
$748$	−7.87375	−	7.87375i	−0.287893	−	0.287893i
$749$	12.2098	−	24.6180i	0.446138	−	0.899523i
$750$		0			0
$751$	39.0344			1.42439			0.712194	−	0.701983i	$-0.247702\pi$
$751$	39.0344			1.42439			0.712194	+	0.701983i	$0.247702\pi$
$752$	9.97505	−	9.97505i	0.363753	−	0.363753i
$753$	29.4346	−	29.4346i	1.07266	−	1.07266i
$754$	−29.9924			−1.09226
$755$		0			0
$756$	−45.4508	+	91.6401i	−1.65303	+	3.33292i
$757$	23.2774	+	23.2774i	0.846030	+	0.846030i	0.989635	−	0.143605i	$-0.0458694\pi$
$757$	23.2774	+	23.2774i	0.846030	+	0.846030i	−0.143605	+	0.989635i	$0.545869\pi$
$758$	17.2492	−	17.2492i	0.626518	−	0.626518i
$759$	57.2945			2.07966
$760$		0			0
$761$		−	19.9112i		−	0.721781i	−0.932608	−	0.360890i	$-0.882473\pi$
$761$		−	19.9112i		−	0.721781i	0.932608	−	0.360890i	$-0.117527\pi$
$762$	−22.6687	+	22.6687i	−0.821201	+	0.821201i
$763$	−17.5509	+	5.91331i	−0.635384	+	0.214076i
$764$		−	53.2148i		−	1.92524i
$765$		0			0
$766$		−	5.32152i		−	0.192274i
$767$	−11.0342	−	11.0342i	−0.398421	−	0.398421i
$768$	−56.5362	−	56.5362i	−2.04007	−	2.04007i
$769$	22.2911			0.803836			0.401918	−	0.915676i	$-0.368344\pi$
$769$	22.2911			0.803836			0.401918	+	0.915676i	$0.368344\pi$
$770$		0			0
$771$	75.7771			2.72905
$772$	−0.546779	−	0.546779i	−0.0196790	−	0.0196790i
$773$	12.4974	+	12.4974i	0.449502	+	0.449502i	0.895189	−	0.445687i	$-0.147041\pi$
$773$	12.4974	+	12.4974i	0.449502	+	0.449502i	−0.445687	+	0.895189i	$0.647041\pi$
$774$		−	22.4721i		−	0.807744i
$775$		0			0
$776$		−	5.57277i		−	0.200051i
$777$	33.9117	−	11.4257i	1.21658	−	0.409894i
$778$	27.0607	−	27.0607i	0.970174	−	0.970174i
$779$			40.6525i			1.45653i
$780$		0			0
$781$	4.61803			0.165246
$782$	−14.0100	+	14.0100i	−0.500998	+	0.500998i
$783$	65.8013	+	65.8013i	2.35155	+	2.35155i
$784$	10.3325	−	7.85410i	0.369017	−	0.280504i
$785$		0			0
$786$	−101.631			−3.62506
$787$	−4.54873	+	4.54873i	−0.162145	+	0.162145i	−0.783516	−	0.621371i	$-0.786576\pi$
$787$	−4.54873	+	4.54873i	−0.162145	+	0.162145i	0.621371	+	0.783516i	$0.286576\pi$
$788$	−14.4439	+	14.4439i	−0.514544	+	0.514544i
$789$	25.7352			0.916198
$790$		0			0
$791$	31.5623	+	15.6540i	1.12223	+	0.556592i
$792$	−45.9502	−	45.9502i	−1.63277	−	1.63277i
$793$	−8.17121	+	8.17121i	−0.290168	+	0.290168i
$794$	77.7082			2.75776
$795$		0			0
$796$		−	66.7179i		−	2.36475i
$797$	−14.7200	+	14.7200i	−0.521410	+	0.521410i	−0.917997	−	0.396587i	$-0.870194\pi$
$797$	−14.7200	+	14.7200i	−0.521410	+	0.521410i	0.396587	+	0.917997i	$0.370194\pi$
$798$	−133.424	+	44.9536i	−4.72314	+	1.59134i
$799$		−	8.94427i		−	0.316426i
$800$		0			0
$801$		−	76.3926i		−	2.69920i
$802$	−13.4658	−	13.4658i	−0.475495	−	0.475495i
$803$	27.3387	+	27.3387i	0.964763	+	0.964763i
$804$	10.0812			0.355538
$805$		0			0
$806$	3.66563			0.129116
$807$	21.0546	+	21.0546i	0.741156	+	0.741156i
$808$	19.7825	+	19.7825i	0.695946	+	0.695946i
$809$		−	28.3050i		−	0.995149i	−0.867421	−	0.497575i	$-0.834224\pi$
$809$		−	28.3050i		−	0.995149i	0.867421	−	0.497575i	$-0.165776\pi$
$810$		0			0
$811$			7.04360i			0.247334i	0.992324	+	0.123667i	$0.0394655\pi$
$811$			7.04360i			0.247334i	−0.992324	+	0.123667i	$0.960535\pi$
$812$	−26.6154	−	78.9954i	−0.934019	−	2.77219i
$813$	33.1823	−	33.1823i	1.16375	−	1.16375i
$814$			27.2705i			0.955831i
$815$		0			0
$816$	6.70820			0.234834
$817$	7.55624	−	7.55624i	0.264359	−	0.264359i
$818$	25.5549	+	25.5549i	0.893508	+	0.893508i
$819$	−22.2911	−	11.0557i	−0.778913	−	0.386318i
$820$		0			0
$821$	51.9230			1.81212			0.906062	−	0.423144i	$-0.139074\pi$
$821$	51.9230			1.81212			0.906062	+	0.423144i	$0.139074\pi$
$822$	34.8950	−	34.8950i	1.21710	−	1.21710i
$823$	28.3988	−	28.3988i	0.989920	−	0.989920i	−0.0100295	−	0.999950i	$-0.503193\pi$
$823$	28.3988	−	28.3988i	0.989920	−	0.989920i	0.999950	+	0.0100295i	$0.00319255\pi$
$824$	35.4099			1.23356
$825$		0			0
$826$	29.9230	−	60.3321i	1.04115	−	2.09922i
$827$	−2.95637	−	2.95637i	−0.102803	−	0.102803i	0.653834	−	0.756638i	$-0.273159\pi$
$827$	−2.95637	−	2.95637i	−0.102803	−	0.102803i	−0.756638	+	0.653834i	$0.773159\pi$
$828$	−117.739	+	117.739i	−4.09170	+	4.09170i
$829$	−25.3287			−0.879702			−0.439851	−	0.898071i	$-0.644969\pi$
$829$	−25.3287			−0.879702			−0.439851	+	0.898071i	$0.644969\pi$
$830$		0			0
$831$		−	40.9827i		−	1.42167i
$832$	11.7875	−	11.7875i	0.408657	−	0.408657i
$833$	1.11114	−	8.15363i	0.0384986	−	0.282507i
$834$		−	20.3262i		−	0.703840i
$835$		0			0
$836$		−	69.0978i		−	2.38980i
$837$	−8.04213	−	8.04213i	−0.277977	−	0.277977i
$838$	−10.4425	−	10.4425i	−0.360729	−	0.360729i
$839$	4.25721			0.146975			0.0734877	−	0.997296i	$-0.476587\pi$
$839$	4.25721			0.146975			0.0734877	+	0.997296i	$0.476587\pi$
$840$		0			0
$841$	−46.8328			−1.61492
$842$	−15.5732	−	15.5732i	−0.536687	−	0.536687i
$843$	41.6200	+	41.6200i	1.43347	+	1.43347i
$844$		−	12.7639i		−	0.439353i
$845$		0			0
$846$		−	116.718i		−	4.01283i
$847$	3.50228	+	10.3949i	0.120340	+	0.357172i
$848$	7.40195	−	7.40195i	0.254184	−	0.254184i
$849$		−	21.5066i		−	0.738104i
$850$		0			0
$851$	31.2492			1.07121
$852$	−13.8888	+	13.8888i	−0.475821	+	0.475821i
$853$	37.0712	+	37.0712i	1.26929	+	1.26929i	0.946453	+	0.322841i	$0.104638\pi$
$853$	37.0712	+	37.0712i	1.26929	+	1.26929i	0.322841	+	0.946453i	$0.395362\pi$
$854$	−44.6781	−	22.1591i	−1.52885	−	0.758267i
$855$		0			0
$856$	−39.8328			−1.36146
$857$	4.59506	−	4.59506i	0.156964	−	0.156964i	−0.624256	−	0.781220i	$-0.714598\pi$
$857$	4.59506	−	4.59506i	0.156964	−	0.156964i	0.781220	+	0.624256i	$0.214598\pi$
$858$	19.6231	−	19.6231i	0.669921	−	0.669921i
$859$	5.82401			0.198713			0.0993564	−	0.995052i	$-0.468322\pi$
$859$	5.82401			0.198713			0.0993564	+	0.995052i	$0.468322\pi$
$860$		0			0
$861$	−40.6525	−	20.1625i	−1.38543	−	0.687135i
$862$	−24.8600	−	24.8600i	−0.846734	−	0.846734i
$863$	1.28036	−	1.28036i	0.0435839	−	0.0435839i	−0.684979	−	0.728563i	$-0.740189\pi$
$863$	1.28036	−	1.28036i	0.0435839	−	0.0435839i	0.728563	+	0.684979i	$0.240189\pi$
$864$	−35.0034			−1.19084
$865$		0			0
$866$			38.4476i			1.30650i
$867$	−33.9888	+	33.9888i	−1.15432	+	1.15432i
$868$	3.25290	+	9.65470i	0.110411	+	0.327702i
$869$		−	9.70820i		−	0.329328i
$870$		0			0
$871$			1.31555i			0.0445758i
$872$	18.9829	+	18.9829i	0.642843	+	0.642843i
$873$	−6.65003	−	6.65003i	−0.225069	−	0.225069i
$874$	−122.948			−4.15878
$875$		0			0
$876$	−164.443			−5.55600
$877$	2.71184	+	2.71184i	0.0915725	+	0.0915725i	0.751409	−	0.659837i	$-0.229375\pi$
$877$	2.71184	+	2.71184i	0.0915725	+	0.0915725i	−0.659837	+	0.751409i	$0.729375\pi$
$878$	52.8937	+	52.8937i	1.78508	+	1.78508i
$879$		−	42.3607i		−	1.42879i
$880$		0			0
$881$		−	36.7255i		−	1.23731i	−0.785662	−	0.618656i	$-0.787677\pi$
$881$		−	36.7255i		−	1.23731i	0.785662	−	0.618656i	$-0.212323\pi$
$882$	14.4997	−	106.400i	0.488230	−	3.58268i
$883$	−38.3038	+	38.3038i	−1.28902	+	1.28902i	−0.353644	+	0.935380i	$0.615057\pi$
$883$	−38.3038	+	38.3038i	−1.28902	+	1.28902i	−0.935380	+	0.353644i	$0.884943\pi$
$884$			6.18034i			0.207867i
$885$		0			0
$886$	−28.9098			−0.971245
$887$	8.67637	−	8.67637i	0.291324	−	0.291324i	−0.546279	−	0.837603i	$-0.683956\pi$
$887$	8.67637	−	8.67637i	0.291324	−	0.291324i	0.837603	+	0.546279i	$0.183956\pi$
$888$	−36.6788	−	36.6788i	−1.23086	−	1.23086i
$889$	5.16624	−	10.4164i	0.173270	−	0.349355i
$890$		0			0
$891$	−35.2705			−1.18161
$892$	−5.57622	+	5.57622i	−0.186706	+	0.186706i
$893$	39.2462	−	39.2462i	1.31332	−	1.31332i
$894$	53.4438			1.78743
$895$		0			0
$896$	48.9230	+	24.2644i	1.63440	+	0.810617i
$897$	−22.4861	−	22.4861i	−0.750788	−	0.750788i
$898$	−43.1807	+	43.1807i	−1.44096	+	1.44096i
$899$	9.26817			0.309111
$900$		0			0
$901$		−	6.63707i		−	0.221113i
$902$	24.4525	−	24.4525i	0.814179	−	0.814179i
$903$	3.80856	+	11.3039i	0.126741	+	0.376171i
$904$		−	51.0689i		−	1.69853i
$905$		0			0
$906$			35.4099i			1.17642i
$907$	−29.3769	−	29.3769i	−0.975444	−	0.975444i	0.0242612	−	0.999706i	$-0.492277\pi$
$907$	−29.3769	−	29.3769i	−0.975444	−	0.975444i	−0.999706	+	0.0242612i	$0.992277\pi$
$908$	−6.89259	−	6.89259i	−0.228739	−	0.228739i
$909$	47.2132			1.56596
$910$		0			0
$911$	−27.8328			−0.922142			−0.461071	−	0.887363i	$-0.652535\pi$
$911$	−27.8328			−0.922142			−0.461071	+	0.887363i	$0.652535\pi$
$912$	29.4346	+	29.4346i	0.974678	+	0.974678i
$913$	−8.38749	−	8.38749i	−0.277585	−	0.277585i
$914$		−	80.4853i		−	2.66222i
$915$		0			0
$916$			81.5589i			2.69478i
$917$	34.9310	−	11.7691i	1.15352	−	0.388650i
$918$	21.0546	−	21.0546i	0.694905	−	0.694905i
$919$			3.72949i			0.123025i	0.998106	+	0.0615123i	$0.0195923\pi$
$919$			3.72949i			0.123025i	−0.998106	+	0.0615123i	$0.980408\pi$
$920$		0			0
$921$	74.3951			2.45140
$922$	−53.5750	+	53.5750i	−1.76440	+	1.76440i
$923$	−1.81242	−	1.81242i	−0.0596564	−	0.0596564i
$924$	69.0978	+	34.2705i	2.27315	+	1.12742i
$925$		0			0
$926$	−63.6312			−2.09105
$927$	42.2550	−	42.2550i	1.38784	−	1.38784i
$928$	20.1699	−	20.1699i	0.662108	−	0.662108i
$929$	46.9620			1.54077			0.770386	−	0.637577i	$-0.220063\pi$
$929$	46.9620			1.54077			0.770386	+	0.637577i	$0.220063\pi$
$930$		0			0
$931$	40.6525	−	30.9015i	1.33233	−	1.01275i
$932$	−44.4253	−	44.4253i	−1.45520	−	1.45520i
$933$	−12.1277	+	12.1277i	−0.397044	+	0.397044i
$934$	−65.9049			−2.15647
$935$		0			0
$936$			36.0677i			1.17891i
$937$	20.9313	−	20.9313i	0.683794	−	0.683794i	−0.277059	−	0.960853i	$-0.589360\pi$
$937$	20.9313	−	20.9313i	0.683794	−	0.683794i	0.960853	+	0.277059i	$0.0893596\pi$
$938$	−5.38034	+	1.81277i	−0.175674	+	0.0591889i
$939$		−	52.8885i		−	1.72595i
$940$		0			0
$941$		−	48.6841i		−	1.58706i	−0.608534	−	0.793528i	$-0.708242\pi$
$941$		−	48.6841i		−	1.58706i	0.608534	−	0.793528i	$-0.291758\pi$
$942$	−59.7540	−	59.7540i	−1.94689	−	1.94689i
$943$	−28.0201	−	28.0201i	−0.912459	−	0.912459i
$944$	−19.9112			−0.648055
$945$		0			0
$946$	−9.09017			−0.295547
$947$	−33.1246	−	33.1246i	−1.07640	−	1.07640i	−0.996829	−	0.0795758i	$-0.974643\pi$
$947$	−33.1246	−	33.1246i	−1.07640	−	1.07640i	−0.0795758	−	0.996829i	$-0.525357\pi$
$948$	29.1975	+	29.1975i	0.948290	+	0.948290i
$949$		−	21.4590i		−	0.696588i
$950$		0			0
$951$			100.406i			3.25588i
$952$	−11.3039	+	3.80856i	−0.366362	+	0.123436i
$953$	−8.86911	+	8.86911i	−0.287299	+	0.287299i	−0.836011	−	0.548712i	$-0.815118\pi$
$953$	−8.86911	+	8.86911i	−0.287299	+	0.287299i	0.548712	+	0.836011i	$0.315118\pi$
$954$		−	86.6099i		−	2.80410i
$955$		0			0
$956$	7.43769			0.240552
$957$	49.6150	−	49.6150i	1.60382	−	1.60382i
$958$	−43.1326	−	43.1326i	−1.39355	−	1.39355i
$959$	−7.95262	+	16.0344i	−0.256804	+	0.517779i
$960$		0			0
$961$	29.8673			0.963460
$962$	10.7027	−	10.7027i	0.345069	−	0.345069i
$963$	−47.5328	+	47.5328i	−1.53172	+	1.53172i
$964$	7.70137			0.248045
$965$		0			0
$966$	60.9787	−	122.948i	1.96196	−	3.95579i
$967$	25.5358	+	25.5358i	0.821177	+	0.821177i	0.986277	−	0.165100i	$-0.0527946\pi$
$967$	25.5358	+	25.5358i	0.821177	+	0.821177i	−0.165100	+	0.986277i	$0.552795\pi$
$968$	11.2430	−	11.2430i	0.361365	−	0.361365i
$969$	26.3930			0.847865
$970$		0			0
$971$		−	5.82401i		−	0.186902i	−0.995624	−	0.0934508i	$-0.970210\pi$
$971$		−	5.82401i		−	0.186902i	0.995624	−	0.0934508i	$-0.0297898\pi$
$972$	24.0600	−	24.0600i	0.771726	−	0.771726i
$973$	2.35382	+	6.98620i	0.0754600	+	0.223967i
$974$			3.78522i			0.121286i
$975$		0			0
$976$			14.7450i			0.471975i
$977$	35.4051	+	35.4051i	1.13271	+	1.13271i	0.989725	+	0.142985i	$0.0456700\pi$
$977$	35.4051	+	35.4051i	1.13271	+	1.13271i	0.142985	+	0.989725i	$0.454330\pi$
$978$	−12.2263	−	12.2263i	−0.390952	−	0.390952i
$979$	−30.9015			−0.987615
$980$		0			0
$981$	45.3050			1.44648
$982$	27.2118	+	27.2118i	0.868365	+	0.868365i
$983$	4.18490	+	4.18490i	0.133478	+	0.133478i	0.770689	−	0.637211i	$-0.219912\pi$
$983$	4.18490	+	4.18490i	0.133478	+	0.133478i	−0.637211	+	0.770689i	$0.719912\pi$
$984$			65.7771i			2.09690i
$985$		0			0
$986$			24.2644i			0.772736i
$987$	19.7812	+	58.7112i	0.629643	+	1.86880i
$988$	−27.1184	+	27.1184i	−0.862753	+	0.862753i
$989$			10.4164i			0.331223i
$990$		0			0
$991$	−33.1591			−1.05333			−0.526666	−	0.850072i	$-0.676558\pi$
$991$	−33.1591			−1.05333			−0.526666	+	0.850072i	$0.676558\pi$
$992$	−2.46513	+	2.46513i	−0.0782680	+	0.0782680i
$993$	−65.4374	−	65.4374i	−2.07659	−	2.07659i
$994$	4.91499	−	9.90983i	0.155894	−	0.314321i
$995$		0			0
$996$	50.4508			1.59860
$997$	29.7575	−	29.7575i	0.942431	−	0.942431i	−0.0560001	−	0.998431i	$-0.517835\pi$
$997$	29.7575	−	29.7575i	0.942431	−	0.942431i	0.998431	+	0.0560001i	$0.0178347\pi$
$998$	45.2167	−	45.2167i	1.43131	−	1.43131i
$999$	−46.9620			−1.48581

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.f.b.307.8	yes	16
5.2	odd	4	inner	875.2.f.b.818.2	yes	16
5.3	odd	4	inner	875.2.f.b.818.7	yes	16
5.4	even	2	inner	875.2.f.b.307.1	✓	16
7.6	odd	2	inner	875.2.f.b.307.7	yes	16
35.13	even	4	inner	875.2.f.b.818.8	yes	16
35.27	even	4	inner	875.2.f.b.818.1	yes	16
35.34	odd	2	inner	875.2.f.b.307.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
875.2.f.b.307.1	✓	16	5.4	even	2	inner
875.2.f.b.307.2	yes	16	35.34	odd	2	inner
875.2.f.b.307.7	yes	16	7.6	odd	2	inner
875.2.f.b.307.8	yes	16	1.1	even	1	trivial
875.2.f.b.818.1	yes	16	35.27	even	4	inner
875.2.f.b.818.2	yes	16	5.2	odd	4	inner
875.2.f.b.818.7	yes	16	5.3	odd	4	inner
875.2.f.b.818.8	yes	16	35.13	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.67601 + 1.67601i) q^{2} +(2.17625 + 2.17625i) q^{3} +3.61803i q^{4} +7.29485i q^{6} +(-0.844758 - 2.50727i) q^{7} +(-2.71184 + 2.71184i) q^{8} +6.47214i q^{9} +2.61803 q^{11} +(-7.87375 + 7.87375i) q^{12} +(-1.02749 - 1.02749i) q^{13} +(2.78638 - 5.61803i) q^{14} -1.85410 q^{16} +(-0.831254 + 0.831254i) q^{17} +(-10.8474 + 10.8474i) q^{18} -7.29485 q^{19} +(3.61803 - 7.29485i) q^{21} +(4.38786 + 4.38786i) q^{22} +(5.02804 - 5.02804i) q^{23} -11.8033 q^{24} -3.44416i q^{26} +(-7.55624 + 7.55624i) q^{27} +(9.07137 - 3.05636i) q^{28} -8.70820i q^{29} +1.06430i q^{31} +(2.31619 + 2.31619i) q^{32} +(5.69750 + 5.69750i) q^{33} -2.78638 q^{34} -23.4164 q^{36} +(3.10750 + 3.10750i) q^{37} +(-12.2263 - 12.2263i) q^{38} -4.47214i q^{39} -5.57277i q^{41} +(18.2901 - 6.16238i) q^{42} +(-1.03583 + 1.03583i) q^{43} +9.47214i q^{44} +16.8541 q^{46} +(-5.37999 + 5.37999i) q^{47} +(-4.03499 - 4.03499i) q^{48} +(-5.57277 + 4.23607i) q^{49} -3.61803 q^{51} +(3.71748 - 3.71748i) q^{52} +(-3.99220 + 3.99220i) q^{53} -25.3287 q^{54} +(9.09017 + 4.50846i) q^{56} +(-15.8754 - 15.8754i) q^{57} +(14.5951 - 14.5951i) q^{58} +10.7390 q^{59} -7.95262i q^{61} +(-1.78379 + 1.78379i) q^{62} +(16.2274 - 5.46739i) q^{63} +11.4721i q^{64} +19.0982i q^{66} +(-0.640180 - 0.640180i) q^{67} +(-3.00750 - 3.00750i) q^{68} +21.8845 q^{69} +1.76393 q^{71} +(-17.5514 - 17.5514i) q^{72} +(10.4425 + 10.4425i) q^{73} +10.4164i q^{74} -26.3930i q^{76} +(-2.21161 - 6.56411i) q^{77} +(7.49535 - 7.49535i) q^{78} -3.70820i q^{79} -13.4721 q^{81} +(9.34003 - 9.34003i) q^{82} +(-3.20374 - 3.20374i) q^{83} +(26.3930 + 13.0902i) q^{84} -3.47214 q^{86} +(18.9512 - 18.9512i) q^{87} +(-7.09970 + 7.09970i) q^{88} -11.8033 q^{89} +(-1.70820 + 3.44416i) q^{91} +(18.1916 + 18.1916i) q^{92} +(-2.31619 + 2.31619i) q^{93} -18.0339 q^{94} +10.0812i q^{96} +(-1.02749 + 1.02749i) q^{97} +(-16.4397 - 2.24032i) q^{98} +16.9443i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 24 q^{11} + 24 q^{16} + 40 q^{21} - 160 q^{36} + 216 q^{46} - 40 q^{51} + 56 q^{56} + 64 q^{71} - 144 q^{81} + 16 q^{86} + 80 q^{91}+O(q^{100}) \) 16 * q + 24 * q^11 + 24 * q^16 + 40 * q^21 - 160 * q^36 + 216 * q^46 - 40 * q^51 + 56 * q^56 + 64 * q^71 - 144 * q^81 + 16 * q^86 + 80 * q^91

Introduction

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