LMFDB - Embedded newform 680.2.bo.a.161.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(121,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 0, 0, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.121"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.bo (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			161.8
Character	$\chi$	$=$	680.161
Dual form			680.2.bo.a.321.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.01006 - 2.43851i) q^{3} +(-0.923880 - 0.382683i) q^{5} +(1.54095 - 0.638280i) q^{7} +(-2.80479 - 2.80479i) q^{9} +(0.182074 + 0.439567i) q^{11} -3.35467i q^{13} +(-1.86636 + 1.86636i) q^{15} +(1.41138 - 3.87402i) q^{17} +(-2.12053 + 2.12053i) q^{19} -4.40232i q^{21} +(-1.73771 - 4.19521i) q^{23} +(0.707107 + 0.707107i) q^{25} +(-2.35700 + 0.976300i) q^{27} +(-2.49368 - 1.03292i) q^{29} +(-2.29919 + 5.55072i) q^{31} +1.25580 q^{33} -1.66791 q^{35} +(-1.54978 + 3.74150i) q^{37} +(-8.18040 - 3.38843i) q^{39} +(10.8493 - 4.49395i) q^{41} +(-2.89197 - 2.89197i) q^{43} +(1.51794 + 3.66463i) q^{45} +3.77940i q^{47} +(-2.98264 + 2.98264i) q^{49} +(-8.02126 - 7.35467i) q^{51} +(1.24438 - 1.24438i) q^{53} -0.475783i q^{55} +(3.02906 + 7.31280i) q^{57} +(2.74570 + 2.74570i) q^{59} +(-2.91336 + 1.20675i) q^{61} +(-6.11227 - 2.53179i) q^{63} +(-1.28378 + 3.09931i) q^{65} -2.24565 q^{67} -11.9853 q^{69} +(-1.34638 + 3.25044i) q^{71} +(12.5824 + 5.21180i) q^{73} +(2.43851 - 1.01006i) q^{75} +(0.561134 + 0.561134i) q^{77} +(1.81391 + 4.37916i) q^{79} -5.16602i q^{81} +(11.1510 - 11.1510i) q^{83} +(-2.78647 + 3.03901i) q^{85} +(-5.03757 + 5.03757i) q^{87} -11.4569i q^{89} +(-2.14122 - 5.16936i) q^{91} +(11.2132 + 11.2132i) q^{93} +(2.77060 - 1.14762i) q^{95} +(12.7036 + 5.26200i) q^{97} +(0.722211 - 1.74357i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{9} + 8 q^{11} - 8 q^{17} + 8 q^{19} + 8 q^{23} - 24 q^{27} - 32 q^{29} + 32 q^{31} + 16 q^{33} + 16 q^{35} + 16 q^{37} - 24 q^{39} - 16 q^{41} - 8 q^{49} + 16 q^{51} + 16 q^{53} + 48 q^{57}+ \cdots + 48 q^{99}+O(q^{100}) $ 32 * q + 16 * q^9 + 8 * q^11 - 8 * q^17 + 8 * q^19 + 8 * q^23 - 24 * q^27 - 32 * q^29 + 32 * q^31 + 16 * q^33 + 16 * q^35 + 16 * q^37 - 24 * q^39 - 16 * q^41 - 8 * q^49 + 16 * q^51 + 16 * q^53 + 48 * q^57 + 24 * q^59 - 24 * q^61 - 48 * q^63 - 16 * q^67 - 80 * q^69 - 64 * q^71 + 16 * q^73 - 8 * q^79 - 56 * q^83 + 16 * q^85 + 96 * q^87 - 48 * q^91 + 32 * q^93 + 24 * q^97 + 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$	$1$	$1$

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
$3$	1.01006	−	2.43851i	0.583161	−	1.40788i	−0.306771	−	0.951783i	$-0.599249\pi$
$3$	1.01006	−	2.43851i	0.583161	−	1.40788i	0.889932	−	0.456092i	$-0.150751\pi$
$4$		0			0
$5$	−0.923880	−	0.382683i	−0.413171	−	0.171141i
$5$	−0.923880	−	0.382683i	−0.413171	−	0.171141i
$6$		0			0
$7$	1.54095	−	0.638280i	0.582423	−	0.241247i	−0.0719644	−	0.997407i	$-0.522927\pi$
$7$	1.54095	−	0.638280i	0.582423	−	0.241247i	0.654387	+	0.756160i	$0.272927\pi$
$8$		0			0
$9$	−2.80479	−	2.80479i	−0.934930	−	0.934930i
$10$		0			0
$11$	0.182074	+	0.439567i	0.0548975	+	0.132534i	0.948949	−	0.315431i	$-0.102149\pi$
$11$	0.182074	+	0.439567i	0.0548975	+	0.132534i	−0.894051	+	0.447965i	$0.852149\pi$
$12$		0			0
$13$		−	3.35467i		−	0.930418i	−0.885201	−	0.465209i	$-0.845979\pi$
$13$		−	3.35467i		−	0.930418i	0.885201	−	0.465209i	$-0.154021\pi$
$14$		0			0
$15$	−1.86636	+	1.86636i	−0.481891	+	0.481891i
$16$		0			0
$17$	1.41138	−	3.87402i	0.342309	−	0.939587i
$17$	1.41138	−	3.87402i	0.342309	−	0.939587i
$18$		0			0
$19$	−2.12053	+	2.12053i	−0.486482	+	0.486482i	−0.907194	−	0.420712i	$-0.861780\pi$
$19$	−2.12053	+	2.12053i	−0.486482	+	0.486482i	0.420712	+	0.907194i	$0.361780\pi$
$20$		0			0
$21$		−	4.40232i		−	0.960665i
$22$		0			0
$23$	−1.73771	−	4.19521i	−0.362338	−	0.874761i	−0.994957	−	0.100298i	$-0.968020\pi$
$23$	−1.73771	−	4.19521i	−0.362338	−	0.874761i	0.632619	−	0.774463i	$-0.281980\pi$
$24$		0			0
$25$	0.707107	+	0.707107i	0.141421	+	0.141421i
$26$		0			0
$27$	−2.35700	+	0.976300i	−0.453604	+	0.187889i
$28$		0			0
$29$	−2.49368	−	1.03292i	−0.463066	−	0.191808i	0.138939	−	0.990301i	$-0.455631\pi$
$29$	−2.49368	−	1.03292i	−0.463066	−	0.191808i	−0.602004	+	0.798493i	$0.705631\pi$
$30$		0			0
$31$	−2.29919	+	5.55072i	−0.412946	+	0.996940i	0.571397	+	0.820674i	$0.306402\pi$
$31$	−2.29919	+	5.55072i	−0.412946	+	0.996940i	−0.984343	+	0.176266i	$0.943598\pi$
$32$		0			0
$33$	1.25580			0.218606
$34$		0			0
$35$	−1.66791			−0.281928
$36$		0			0
$37$	−1.54978	+	3.74150i	−0.254782	+	0.615099i	−0.998578	−	0.0533081i	$-0.983023\pi$
$37$	−1.54978	+	3.74150i	−0.254782	+	0.615099i	0.743796	+	0.668407i	$0.233023\pi$
$38$		0			0
$39$	−8.18040	−	3.38843i	−1.30991	−	0.542584i
$40$		0			0
$41$	10.8493	−	4.49395i	1.69438	−	0.701837i	0.694539	−	0.719455i	$-0.255608\pi$
$41$	10.8493	−	4.49395i	1.69438	−	0.701837i	0.999845	+	0.0176186i	$0.00560848\pi$
$42$		0			0
$43$	−2.89197	−	2.89197i	−0.441021	−	0.441021i	0.451334	−	0.892355i	$-0.350948\pi$
$43$	−2.89197	−	2.89197i	−0.441021	−	0.441021i	−0.892355	+	0.451334i	$0.850948\pi$
$44$		0			0
$45$	1.51794	+	3.66463i	0.226281	+	0.546291i
$46$		0			0
$47$			3.77940i			0.551282i	0.961261	+	0.275641i	$0.0888901\pi$
$47$			3.77940i			0.551282i	−0.961261	+	0.275641i	$0.911110\pi$
$48$		0			0
$49$	−2.98264	+	2.98264i	−0.426091	+	0.426091i
$50$		0			0
$51$	−8.02126	−	7.35467i	−1.12320	−	1.02986i
$52$		0			0
$53$	1.24438	−	1.24438i	0.170929	−	0.170929i	−0.616459	−	0.787387i	$-0.711433\pi$
$53$	1.24438	−	1.24438i	0.170929	−	0.170929i	0.787387	+	0.616459i	$0.211433\pi$
$54$		0			0
$55$		−	0.475783i		−	0.0641546i
$56$		0			0
$57$	3.02906	+	7.31280i	0.401209	+	0.968604i
$58$		0			0
$59$	2.74570	+	2.74570i	0.357459	+	0.357459i	0.862876	−	0.505416i	$-0.168661\pi$
$59$	2.74570	+	2.74570i	0.357459	+	0.357459i	−0.505416	+	0.862876i	$0.668661\pi$
$60$		0			0
$61$	−2.91336	+	1.20675i	−0.373017	+	0.154509i	−0.561313	−	0.827603i	$-0.689704\pi$
$61$	−2.91336	+	1.20675i	−0.373017	+	0.154509i	0.188296	+	0.982112i	$0.439704\pi$
$62$		0			0
$63$	−6.11227	−	2.53179i	−0.770074	−	0.318975i
$64$		0			0
$65$	−1.28378	+	3.09931i	−0.159233	+	0.384422i
$66$		0			0
$67$	−2.24565			−0.274350			−0.137175	−	0.990547i	$-0.543802\pi$
$67$	−2.24565			−0.274350			−0.137175	+	0.990547i	$0.543802\pi$
$68$		0			0
$69$	−11.9853			−1.44286
$70$		0			0
$71$	−1.34638	+	3.25044i	−0.159786	+	0.385757i	−0.983414	−	0.181373i	$-0.941946\pi$
$71$	−1.34638	+	3.25044i	−0.159786	+	0.385757i	0.823629	+	0.567129i	$0.191946\pi$
$72$		0			0
$73$	12.5824	+	5.21180i	1.47266	+	0.609995i	0.967464	−	0.253010i	$-0.0814206\pi$
$73$	12.5824	+	5.21180i	1.47266	+	0.609995i	0.505195	+	0.863005i	$0.331421\pi$
$74$		0			0
$75$	2.43851	−	1.01006i	0.281575	−	0.116632i
$76$		0			0
$77$	0.561134	+	0.561134i	0.0639471	+	0.0639471i
$78$		0			0
$79$	1.81391	+	4.37916i	0.204080	+	0.492694i	0.992471	−	0.122481i	$-0.0390852\pi$
$79$	1.81391	+	4.37916i	0.204080	+	0.492694i	−0.788390	+	0.615175i	$0.789085\pi$
$80$		0			0
$81$		−	5.16602i		−	0.574003i
$82$		0			0
$83$	11.1510	−	11.1510i	1.22398	−	1.22398i	0.257774	−	0.966205i	$-0.417011\pi$
$83$	11.1510	−	11.1510i	1.22398	−	1.22398i	0.966205	−	0.257774i	$-0.0829889\pi$
$84$		0			0
$85$	−2.78647	+	3.03901i	−0.302235	+	0.329627i
$86$		0			0
$87$	−5.03757	+	5.03757i	−0.540084	+	0.540084i
$88$		0			0
$89$		−	11.4569i		−	1.21443i	−0.794538	−	0.607214i	$-0.792287\pi$
$89$		−	11.4569i		−	1.21443i	0.794538	−	0.607214i	$-0.207713\pi$
$90$		0			0
$91$	−2.14122	−	5.16936i	−0.224461	−	0.541896i
$92$		0			0
$93$	11.2132	+	11.2132i	1.16275	+	1.16275i
$94$		0			0
$95$	2.77060	−	1.14762i	0.284258	−	0.117743i
$96$		0			0
$97$	12.7036	+	5.26200i	1.28985	+	0.534275i	0.918942	−	0.394393i	$-0.129045\pi$
$97$	12.7036	+	5.26200i	1.28985	+	0.534275i	0.370912	+	0.928668i	$0.379045\pi$
$98$		0			0
$99$	0.722211	−	1.74357i	0.0725850	−	0.175236i
$100$		0			0
$101$	−2.61803			−0.260503			−0.130252	−	0.991481i	$-0.541579\pi$
$101$	−2.61803			−0.260503			−0.130252	+	0.991481i	$0.541579\pi$
$102$		0			0
$103$	0.229263			0.0225900			0.0112950	−	0.999936i	$-0.496405\pi$
$103$	0.229263			0.0225900			0.0112950	+	0.999936i	$0.496405\pi$
$104$		0			0
$105$	−1.68469	+	4.06721i	−0.164409	+	0.396919i
$106$		0			0
$107$	−4.70864	−	1.95038i	−0.455202	−	0.188551i	0.143288	−	0.989681i	$-0.454232\pi$
$107$	−4.70864	−	1.95038i	−0.455202	−	0.188551i	−0.598490	+	0.801130i	$0.704232\pi$
$108$		0			0
$109$	14.2079	−	5.88512i	1.36087	−	0.563692i	0.421575	−	0.906793i	$-0.361477\pi$
$109$	14.2079	−	5.88512i	1.36087	−	0.563692i	0.939299	+	0.343101i	$0.111477\pi$
$110$		0			0
$111$	7.55831	+	7.55831i	0.717403	+	0.717403i
$112$		0			0
$113$	1.25141	+	3.02117i	0.117723	+	0.284208i	0.971747	−	0.236026i	$-0.0758449\pi$
$113$	1.25141	+	3.02117i	0.117723	+	0.284208i	−0.854024	+	0.520233i	$0.825845\pi$
$114$		0			0
$115$			4.54086i			0.423437i
$116$		0			0
$117$	−9.40914	+	9.40914i	−0.869875	+	0.869875i
$118$		0			0
$119$	−0.297854	−	6.87050i	−0.0273042	−	0.629818i
$120$		0			0
$121$	7.61811	−	7.61811i	0.692555	−	0.692555i
$122$		0			0
$123$		−	30.9954i		−	2.79477i
$124$		0			0
$125$	−0.382683	−	0.923880i	−0.0342282	−	0.0826343i
$126$		0			0
$127$	14.9971	+	14.9971i	1.33078	+	1.33078i	0.904671	+	0.426110i	$0.140116\pi$
$127$	14.9971	+	14.9971i	1.33078	+	1.33078i	0.426110	+	0.904671i	$0.359884\pi$
$128$		0			0
$129$	−9.97318	+	4.13102i	−0.878089	+	0.363716i
$130$		0			0
$131$	−7.51053	−	3.11096i	−0.656198	−	0.271806i	0.0296397	−	0.999561i	$-0.490564\pi$
$131$	−7.51053	−	3.11096i	−0.656198	−	0.271806i	−0.685838	+	0.727755i	$0.740564\pi$
$132$		0			0
$133$	−1.91412	+	4.62111i	−0.165976	+	0.400701i
$134$		0			0
$135$	2.55120			0.219572
$136$		0			0
$137$	19.9300			1.70274			0.851368	−	0.524568i	$-0.175773\pi$
$137$	19.9300			1.70274			0.851368	+	0.524568i	$0.175773\pi$
$138$		0			0
$139$	0.0703616	−	0.169868i	0.00596799	−	0.0144080i	−0.920867	−	0.389876i	$-0.872518\pi$
$139$	0.0703616	−	0.169868i	0.00596799	−	0.0144080i	0.926835	+	0.375468i	$0.122518\pi$
$140$		0			0
$141$	9.21611	+	3.81744i	0.776137	+	0.321486i
$142$		0			0
$143$	1.47460	−	0.610800i	0.123312	−	0.0510776i
$144$		0			0
$145$	1.90858	+	1.90858i	0.158499	+	0.158499i
$146$		0			0
$147$	4.26054	+	10.2859i	0.351403	+	0.848363i
$148$		0			0
$149$		−	13.7969i		−	1.13029i	−0.824992	−	0.565144i	$-0.808821\pi$
$149$		−	13.7969i		−	1.13029i	0.824992	−	0.565144i	$-0.191179\pi$
$150$		0			0
$151$	−2.16549	+	2.16549i	−0.176225	+	0.176225i	−0.789708	−	0.613483i	$-0.789768\pi$
$151$	−2.16549	+	2.16549i	−0.176225	+	0.176225i	0.613483	+	0.789708i	$0.289768\pi$
$152$		0			0
$153$	−14.8244	+	6.90719i	−1.19848	+	0.558413i
$154$		0			0
$155$	4.24834	−	4.24834i	0.341235	−	0.341235i
$156$		0			0
$157$		−	3.46705i		−	0.276700i	−0.990383	−	0.138350i	$-0.955820\pi$
$157$		−	3.46705i		−	0.276700i	0.990383	−	0.138350i	$-0.0441800\pi$
$158$		0			0
$159$	−1.77753	−	4.29134i	−0.140968	−	0.340326i
$160$		0			0
$161$	−5.35544	−	5.35544i	−0.422068	−	0.422068i
$162$		0			0
$163$	−20.9015	+	8.65767i	−1.63713	+	0.678121i	−0.996003	−	0.0893152i	$-0.971532\pi$
$163$	−20.9015	+	8.65767i	−1.63713	+	0.678121i	−0.641125	+	0.767436i	$0.721532\pi$
$164$		0			0
$165$	−1.16020	−	0.480572i	−0.0903217	−	0.0374125i
$166$		0			0
$167$	−2.95221	+	7.12726i	−0.228449	+	0.551524i	−0.995989	−	0.0894771i	$-0.971480\pi$
$167$	−2.95221	+	7.12726i	−0.228449	+	0.551524i	0.767540	+	0.641001i	$0.221480\pi$
$168$		0			0
$169$	1.74620			0.134323
$170$		0			0
$171$	11.8953			0.909654
$172$		0			0
$173$	−3.43634	+	8.29606i	−0.261260	+	0.630738i	−0.999017	−	0.0443289i	$-0.985885\pi$
$173$	−3.43634	+	8.29606i	−0.261260	+	0.630738i	0.737757	+	0.675066i	$0.235885\pi$
$174$		0			0
$175$	1.54095	+	0.638280i	0.116485	+	0.0482495i
$176$		0			0
$177$	9.46874	−	3.92208i	0.711714	−	0.294802i
$178$		0			0
$179$	10.7789	+	10.7789i	0.805654	+	0.805654i	0.983973	−	0.178319i	$-0.0570660\pi$
$179$	10.7789	+	10.7789i	0.805654	+	0.805654i	−0.178319	+	0.983973i	$0.557066\pi$
$180$		0			0
$181$	2.70511	+	6.53072i	0.201069	+	0.485425i	0.991963	−	0.126529i	$-0.0403838\pi$
$181$	2.70511	+	6.53072i	0.201069	+	0.485425i	−0.790893	+	0.611954i	$0.790384\pi$
$182$		0			0
$183$			8.32316i			0.615266i
$184$		0			0
$185$	2.86362	−	2.86362i	0.210538	−	0.210538i
$186$		0			0
$187$	1.95986	−	0.0849650i	0.143319	−	0.00621326i
$188$		0			0
$189$	−3.00885	+	3.00885i	−0.218862	+	0.218862i
$190$		0			0
$191$			22.1540i			1.60301i	0.597989	+	0.801505i	$0.295967\pi$
$191$			22.1540i			1.60301i	−0.597989	+	0.801505i	$0.704033\pi$
$192$		0			0
$193$	−1.12868	−	2.72488i	−0.0812443	−	0.196141i	0.878038	−	0.478592i	$-0.158853\pi$
$193$	−1.12868	−	2.72488i	−0.0812443	−	0.196141i	−0.959282	+	0.282451i	$0.908853\pi$
$194$		0			0
$195$	6.26101	+	6.26101i	0.448360	+	0.448360i
$196$		0			0
$197$	−21.8410	+	9.04683i	−1.55611	+	0.644560i	−0.984407	−	0.175904i	$-0.943715\pi$
$197$	−21.8410	+	9.04683i	−1.55611	+	0.644560i	−0.571698	+	0.820464i	$0.693715\pi$
$198$		0			0
$199$	−1.83100	−	0.758424i	−0.129796	−	0.0537633i	0.316840	−	0.948479i	$-0.397378\pi$
$199$	−1.83100	−	0.758424i	−0.129796	−	0.0537633i	−0.446636	+	0.894716i	$0.647378\pi$
$200$		0			0
$201$	−2.26825	+	5.47605i	−0.159990	+	0.386251i
$202$		0			0
$203$	−4.50192			−0.315973
$204$		0			0
$205$	−11.7433			−0.820184
$206$		0			0
$207$	−6.89276	+	16.6406i	−0.479080	+	1.15660i
$208$		0			0
$209$	−1.31821	−	0.546019i	−0.0911822	−	0.0377689i
$210$		0			0
$211$	13.0733	−	5.41513i	0.900002	−	0.372793i	0.115781	−	0.993275i	$-0.463063\pi$
$211$	13.0733	−	5.41513i	0.900002	−	0.372793i	0.784221	+	0.620482i	$0.213063\pi$
$212$		0			0
$213$	6.56632	+	6.56632i	0.449917	+	0.449917i
$214$		0			0
$215$	1.56512	+	3.77854i	0.106740	+	0.257694i
$216$		0			0
$217$			10.0209i			0.680262i
$218$		0			0
$219$	25.4181	−	25.4181i	1.71759	−	1.71759i
$220$		0			0
$221$	−12.9960	−	4.73471i	−0.874209	−	0.318491i
$222$		0			0
$223$	−7.06005	+	7.06005i	−0.472776	+	0.472776i	−0.902812	−	0.430036i	$-0.858501\pi$
$223$	−7.06005	+	7.06005i	−0.472776	+	0.472776i	0.430036	+	0.902812i	$0.358501\pi$
$224$		0			0
$225$		−	3.96657i		−	0.264438i
$226$		0			0
$227$	7.99688	+	19.3062i	0.530772	+	1.28140i	0.931013	+	0.364986i	$0.118926\pi$
$227$	7.99688	+	19.3062i	0.530772	+	1.28140i	−0.400241	+	0.916410i	$0.631074\pi$
$228$		0			0
$229$	3.86070	+	3.86070i	0.255122	+	0.255122i	0.823067	−	0.567945i	$-0.192261\pi$
$229$	3.86070	+	3.86070i	0.255122	+	0.255122i	−0.567945	+	0.823067i	$0.692261\pi$
$230$		0			0
$231$	1.93511	−	0.801550i	0.127321	−	0.0527381i
$232$		0			0
$233$	−3.02131	−	1.25147i	−0.197933	−	0.0819865i	0.281515	−	0.959557i	$-0.409163\pi$
$233$	−3.02131	−	1.25147i	−0.197933	−	0.0819865i	−0.479448	+	0.877570i	$0.659163\pi$
$234$		0			0
$235$	1.44631	−	3.49171i	0.0943471	−	0.227774i
$236$		0			0
$237$	12.5108			0.812663
$238$		0			0
$239$	22.9110			1.48199			0.740994	−	0.671512i	$-0.234355\pi$
$239$	22.9110			1.48199			0.740994	+	0.671512i	$0.234355\pi$
$240$		0			0
$241$	−8.48341	+	20.4808i	−0.546464	+	1.31928i	0.373627	+	0.927579i	$0.378114\pi$
$241$	−8.48341	+	20.4808i	−0.546464	+	1.31928i	−0.920092	+	0.391703i	$0.871886\pi$
$242$		0			0
$243$	−19.6684	−	8.14692i	−1.26173	−	0.522625i
$244$		0			0
$245$	3.89700	−	1.61419i	0.248970	−	0.103127i
$246$		0			0
$247$	7.11366	+	7.11366i	0.452632	+	0.452632i
$248$		0			0
$249$	−15.9286	−	38.4550i	−1.00943	−	2.43699i
$250$		0			0
$251$			21.1263i			1.33348i	0.745291	+	0.666739i	$0.232310\pi$
$251$			21.1263i			1.33348i	−0.745291	+	0.666739i	$0.767690\pi$
$252$		0			0
$253$	1.52768	−	1.52768i	0.0960444	−	0.0960444i
$254$		0			0
$255$	4.59616	+	9.86443i	0.287823	+	0.617735i
$256$		0			0
$257$	0.957887	−	0.957887i	0.0597514	−	0.0597514i	−0.676600	−	0.736351i	$-0.736547\pi$
$257$	0.957887	−	0.957887i	0.0597514	−	0.0597514i	0.736351	+	0.676600i	$0.236547\pi$
$258$		0			0
$259$			6.75464i			0.419713i
$260$		0			0
$261$	4.09714	+	9.89138i	0.253607	+	0.612261i
$262$		0			0
$263$	−5.90271	−	5.90271i	−0.363977	−	0.363977i	0.501298	−	0.865275i	$-0.332856\pi$
$263$	−5.90271	−	5.90271i	−0.363977	−	0.363977i	−0.865275	+	0.501298i	$0.832856\pi$
$264$		0			0
$265$	−1.62586	+	0.673454i	−0.0998759	+	0.0413700i
$266$		0			0
$267$	−27.9378	−	11.5722i	−1.70976	−	0.708208i
$268$		0			0
$269$	9.02791	−	21.7953i	0.550441	−	1.32888i	−0.366707	−	0.930337i	$-0.619515\pi$
$269$	9.02791	−	21.7953i	0.550441	−	1.32888i	0.917148	−	0.398546i	$-0.130485\pi$
$270$		0			0
$271$	−27.6280			−1.67828			−0.839142	−	0.543912i	$-0.816943\pi$
$271$	−27.6280			−1.67828			−0.839142	+	0.543912i	$0.816943\pi$
$272$		0			0
$273$	−14.7683			−0.893819
$274$		0			0
$275$	−0.182074	+	0.439567i	−0.0109795	+	0.0265069i
$276$		0			0
$277$	−23.3087	−	9.65477i	−1.40048	−	0.580099i	−0.450605	−	0.892723i	$-0.648792\pi$
$277$	−23.3087	−	9.65477i	−1.40048	−	0.580099i	−0.949877	+	0.312624i	$0.898792\pi$
$278$		0			0
$279$	22.0173	−	9.11988i	1.31814	−	0.545993i
$280$		0			0
$281$	−13.5384	−	13.5384i	−0.807633	−	0.807633i	0.176642	−	0.984275i	$-0.443476\pi$
$281$	−13.5384	−	13.5384i	−0.807633	−	0.807633i	−0.984275	+	0.176642i	$0.943476\pi$
$282$		0			0
$283$	4.95000	+	11.9504i	0.294247	+	0.710375i	0.999998	+	0.00191510i	$0.000609594\pi$
$283$	4.95000	+	11.9504i	0.294247	+	0.710375i	−0.705751	+	0.708460i	$0.749390\pi$
$284$		0			0
$285$		−	7.91532i		−	0.468863i
$286$		0			0
$287$	13.8499	−	13.8499i	0.817531	−	0.817531i
$288$		0			0
$289$	−13.0160	−	10.9354i	−0.765649	−	0.643259i
$290$		0			0
$291$	25.6629	−	25.6629i	1.50439	−	1.50439i
$292$		0			0
$293$		−	30.5043i		−	1.78208i	−0.453926	−	0.891039i	$-0.649977\pi$
$293$		−	30.5043i		−	1.78208i	0.453926	−	0.891039i	$-0.350023\pi$
$294$		0			0
$295$	−1.48596	−	3.58742i	−0.0865159	−	0.208868i
$296$		0			0
$297$	−0.858298	−	0.858298i	−0.0498035	−	0.0498035i
$298$		0			0
$299$	−14.0735	+	5.82945i	−0.813893	+	0.337126i
$300$		0			0
$301$	−6.30225	−	2.61048i	−0.363256	−	0.150465i
$302$		0			0
$303$	−2.64438	+	6.38409i	−0.151915	+	0.366756i
$304$		0			0
$305$	3.15340			0.180563
$306$		0			0
$307$	12.3694			0.705959			0.352979	−	0.935631i	$-0.385169\pi$
$307$	12.3694			0.705959			0.352979	+	0.935631i	$0.385169\pi$
$308$		0			0
$309$	0.231571	−	0.559061i	0.0131736	−	0.0318039i
$310$		0			0
$311$	−22.0008	−	9.11302i	−1.24755	−	0.516752i	−0.341483	−	0.939888i	$-0.610929\pi$
$311$	−22.0008	−	9.11302i	−1.24755	−	0.516752i	−0.906066	+	0.423136i	$0.860929\pi$
$312$		0			0
$313$	−8.16498	+	3.38205i	−0.461512	+	0.191165i	−0.601311	−	0.799015i	$-0.705355\pi$
$313$	−8.16498	+	3.38205i	−0.461512	+	0.191165i	0.139798	+	0.990180i	$0.455355\pi$
$314$		0			0
$315$	4.67813	+	4.67813i	0.263583	+	0.263583i
$316$		0			0
$317$	−5.67759	−	13.7069i	−0.318885	−	0.769857i	−0.999314	−	0.0370424i	$-0.988206\pi$
$317$	−5.67759	−	13.7069i	−0.318885	−	0.769857i	0.680429	−	0.732814i	$-0.261794\pi$
$318$		0			0
$319$		−	1.28421i		−	0.0719019i
$320$		0			0
$321$	−9.51207	+	9.51207i	−0.530912	+	0.530912i
$322$		0			0
$323$	5.22209	+	11.2078i	0.290565	+	0.623620i
$324$		0			0
$325$	2.37211	−	2.37211i	0.131581	−	0.131581i
$326$		0			0
$327$		−	40.5906i		−	2.24466i
$328$		0			0
$329$	2.41232	+	5.82385i	0.132995	+	0.321079i
$330$		0			0
$331$	−24.8908	−	24.8908i	−1.36812	−	1.36812i	−0.863118	−	0.505002i	$-0.831492\pi$
$331$	−24.8908	−	24.8908i	−1.36812	−	1.36812i	−0.505002	−	0.863118i	$-0.668508\pi$
$332$		0			0
$333$	14.8409	−	6.14731i	0.813278	−	0.336871i
$334$		0			0
$335$	2.07471	+	0.859374i	0.113354	+	0.0469526i
$336$		0			0
$337$	−2.80793	+	6.77895i	−0.152958	+	0.369273i	−0.981721	−	0.190327i	$-0.939045\pi$
$337$	−2.80793	+	6.77895i	−0.152958	+	0.369273i	0.828763	+	0.559600i	$0.189045\pi$
$338$		0			0
$339$	8.63116			0.468780
$340$		0			0
$341$	−2.85854			−0.154798
$342$		0			0
$343$	−7.16028	+	17.2865i	−0.386619	+	0.933381i
$344$		0			0
$345$	11.0729	+	4.58656i	0.596147	+	0.246932i
$346$		0			0
$347$	19.4483	−	8.05575i	1.04404	−	0.432455i	0.206279	−	0.978493i	$-0.433864\pi$
$347$	19.4483	−	8.05575i	1.04404	−	0.432455i	0.837761	+	0.546038i	$0.183864\pi$
$348$		0			0
$349$	15.7676	+	15.7676i	0.844019	+	0.844019i	0.989379	−	0.145359i	$-0.0464339\pi$
$349$	15.7676	+	15.7676i	0.844019	+	0.844019i	−0.145359	+	0.989379i	$0.546434\pi$
$350$		0			0
$351$	3.27516	+	7.90695i	0.174815	+	0.422042i
$352$		0			0
$353$		−	9.09412i		−	0.484031i	−0.970272	−	0.242016i	$-0.922191\pi$
$353$		−	9.09412i		−	0.484031i	0.970272	−	0.242016i	$-0.0778085\pi$
$354$		0			0
$355$	2.48778	−	2.48778i	0.132038	−	0.132038i
$356$		0			0
$357$	−17.0547	−	6.21333i	−0.902628	−	0.328845i
$358$		0			0
$359$	12.0595	−	12.0595i	0.636477	−	0.636477i	−0.313208	−	0.949685i	$-0.601404\pi$
$359$	12.0595	−	12.0595i	0.636477	−	0.636477i	0.949685	+	0.313208i	$0.101404\pi$
$360$		0			0
$361$			10.0067i			0.526670i
$362$		0			0
$363$	−10.8821	−	26.2716i	−0.571160	−	1.37890i
$364$		0			0
$365$	−9.63015	−	9.63015i	−0.504065	−	0.504065i
$366$		0			0
$367$	12.0621	−	4.99628i	0.629635	−	0.260803i	−0.0449628	−	0.998989i	$-0.514317\pi$
$367$	12.0621	−	4.99628i	0.629635	−	0.260803i	0.674598	+	0.738185i	$0.264317\pi$
$368$		0			0
$369$	−43.0347	−	17.8256i	−2.24030	−	0.927962i
$370$		0			0
$371$	1.12326	−	2.71179i	0.0583167	−	0.140789i
$372$		0			0
$373$	35.9919			1.86359			0.931795	−	0.362984i	$-0.118242\pi$
$373$	35.9919			1.86359			0.931795	+	0.362984i	$0.118242\pi$
$374$		0			0
$375$	−2.63943			−0.136299
$376$		0			0
$377$	−3.46510	+	8.36549i	−0.178462	+	0.430844i
$378$		0			0
$379$	−2.10828	−	0.873279i	−0.108295	−	0.0448574i	0.327878	−	0.944720i	$-0.393667\pi$
$379$	−2.10828	−	0.873279i	−0.108295	−	0.0448574i	−0.436173	+	0.899863i	$0.643667\pi$
$380$		0			0
$381$	51.7188	−	21.4226i	2.64963	−	1.09751i
$382$		0			0
$383$	4.18834	+	4.18834i	0.214014	+	0.214014i	0.805970	−	0.591956i	$-0.201644\pi$
$383$	4.18834	+	4.18834i	0.214014	+	0.214014i	−0.591956	+	0.805970i	$0.701644\pi$
$384$		0			0
$385$	−0.303683	−	0.733156i	−0.0154771	−	0.0373651i
$386$		0			0
$387$			16.2227i			0.824648i
$388$		0			0
$389$	−7.30073	+	7.30073i	−0.370162	+	0.370162i	−0.867536	−	0.497374i	$-0.834298\pi$
$389$	−7.30073	+	7.30073i	−0.370162	+	0.370162i	0.497374	+	0.867536i	$0.334298\pi$
$390$		0			0
$391$	−18.7049	+	0.810903i	−0.945946	+	0.0410091i
$392$		0			0
$393$	−15.1722	+	15.1722i	−0.765338	+	0.765338i
$394$		0			0
$395$		−	4.73997i		−	0.238494i
$396$		0			0
$397$	5.66013	+	13.6648i	0.284074	+	0.685814i	0.999923	−	0.0124407i	$-0.00396010\pi$
$397$	5.66013	+	13.6648i	0.284074	+	0.685814i	−0.715849	+	0.698255i	$0.753960\pi$
$398$		0			0
$399$	9.33523	+	9.33523i	0.467346	+	0.467346i
$400$		0			0
$401$	−4.46990	+	1.85149i	−0.223216	+	0.0924592i	−0.491489	−	0.870884i	$-0.663547\pi$
$401$	−4.46990	+	1.85149i	−0.223216	+	0.0924592i	0.268273	+	0.963343i	$0.413547\pi$
$402$		0			0
$403$	18.6208	+	7.71301i	0.927570	+	0.384212i
$404$		0			0
$405$	−1.97695	+	4.77278i	−0.0982355	+	0.237161i
$406$		0			0
$407$	−1.92681			−0.0955086
$408$		0			0
$409$	−22.3384			−1.10456			−0.552281	−	0.833658i	$-0.686243\pi$
$409$	−22.3384			−1.10456			−0.552281	+	0.833658i	$0.686243\pi$
$410$		0			0
$411$	20.1306	−	48.5996i	0.992970	−	2.39724i
$412$		0			0
$413$	5.98349	+	2.47844i	0.294428	+	0.121956i
$414$		0			0
$415$	−14.5695	+	6.03487i	−0.715186	+	0.296240i
$416$		0			0
$417$	−0.343155	−	0.343155i	−0.0168044	−	0.0168044i
$418$		0			0
$419$	−8.56138	−	20.6690i	−0.418251	−	1.00975i	−0.982854	−	0.184384i	$-0.940971\pi$
$419$	−8.56138	−	20.6690i	−0.418251	−	1.00975i	0.564604	−	0.825362i	$-0.309029\pi$
$420$		0			0
$421$		−	7.56788i		−	0.368836i	−0.982848	−	0.184418i	$-0.940960\pi$
$421$		−	7.56788i		−	0.368836i	0.982848	−	0.184418i	$-0.0590400\pi$
$422$		0			0
$423$	10.6004	−	10.6004i	0.515410	−	0.515410i
$424$		0			0
$425$	3.73734	−	1.74135i	0.181288	−	0.0844678i
$426$		0			0
$427$	−3.71908	+	3.71908i	−0.179979	+	0.179979i
$428$		0			0
$429$		−	4.21278i		−	0.203395i
$430$		0			0
$431$	−1.67473	−	4.04317i	−0.0806691	−	0.194752i	0.878399	−	0.477928i	$-0.158612\pi$
$431$	−1.67473	−	4.04317i	−0.0806691	−	0.194752i	−0.959068	+	0.283176i	$0.908612\pi$
$432$		0			0
$433$	−0.531408	−	0.531408i	−0.0255378	−	0.0255378i	0.694223	−	0.719760i	$-0.255748\pi$
$433$	−0.531408	−	0.531408i	−0.0255378	−	0.0255378i	−0.719760	+	0.694223i	$0.755748\pi$
$434$		0			0
$435$	6.58190	−	2.72631i	0.315578	−	0.130717i
$436$		0			0
$437$	12.5809	+	5.21118i	0.601827	+	0.249285i
$438$		0			0
$439$	−8.69220	+	20.9848i	−0.414856	+	1.00155i	0.568959	+	0.822366i	$0.307346\pi$
$439$	−8.69220	+	20.9848i	−0.414856	+	1.00155i	−0.983815	+	0.179186i	$0.942654\pi$
$440$		0			0
$441$	16.7313			0.796731
$442$		0			0
$443$	3.12017			0.148244			0.0741219	−	0.997249i	$-0.476385\pi$
$443$	3.12017			0.148244			0.0741219	+	0.997249i	$0.476385\pi$
$444$		0			0
$445$	−4.38436	+	10.5848i	−0.207839	+	0.501767i
$446$		0			0
$447$	−33.6440	−	13.9358i	−1.59131	−	0.659140i
$448$		0			0
$449$	−14.1828	+	5.87470i	−0.669327	+	0.277244i	−0.691357	−	0.722513i	$-0.742987\pi$
$449$	−14.1828	+	5.87470i	−0.669327	+	0.277244i	0.0220306	+	0.999757i	$0.492987\pi$
$450$		0			0
$451$	3.95078	+	3.95078i	0.186035	+	0.186035i
$452$		0			0
$453$	3.09329	+	7.46785i	0.145335	+	0.350870i
$454$		0			0
$455$			5.59528i			0.262311i
$456$		0			0
$457$	−22.9717	+	22.9717i	−1.07457	+	1.07457i	−0.0775856	+	0.996986i	$0.524721\pi$
$457$	−22.9717	+	22.9717i	−1.07457	+	1.07457i	−0.996986	+	0.0775856i	$0.975279\pi$
$458$		0			0
$459$	0.455591	+	10.5090i	0.0212651	+	0.490517i
$460$		0			0
$461$	−28.3979	+	28.3979i	−1.32262	+	1.32262i	−0.410974	+	0.911647i	$0.634811\pi$
$461$	−28.3979	+	28.3979i	−1.32262	+	1.32262i	−0.911647	+	0.410974i	$0.865189\pi$
$462$		0			0
$463$		−	14.4135i		−	0.669851i	−0.942245	−	0.334926i	$-0.891289\pi$
$463$		−	14.4135i		−	0.669851i	0.942245	−	0.334926i	$-0.108711\pi$
$464$		0			0
$465$	−6.06853	−	14.6507i	−0.281421	−	0.679411i
$466$		0			0
$467$	−20.1364	−	20.1364i	−0.931800	−	0.931800i	0.0660184	−	0.997818i	$-0.478970\pi$
$467$	−20.1364	−	20.1364i	−0.931800	−	0.931800i	−0.997818	+	0.0660184i	$0.978970\pi$
$468$		0			0
$469$	−3.46043	+	1.43336i	−0.159788	+	0.0661862i
$470$		0			0
$471$	−8.45444	−	3.50194i	−0.389560	−	0.161361i
$472$		0			0
$473$	0.744659	−	1.79777i	0.0342395	−	0.0826614i
$474$		0			0
$475$	−2.99888			−0.137598
$476$		0			0
$477$	−6.98045			−0.319613
$478$		0			0
$479$	−13.5460	+	32.7030i	−0.618934	+	1.49424i	0.234009	+	0.972235i	$0.424816\pi$
$479$	−13.5460	+	32.7030i	−0.618934	+	1.49424i	−0.852943	+	0.522005i	$0.825184\pi$
$480$		0			0
$481$	12.5515	+	5.19900i	0.572299	+	0.237054i
$482$		0			0
$483$	−18.4686	+	7.64996i	−0.840352	+	0.348085i
$484$		0			0
$485$	−9.72290	−	9.72290i	−0.441494	−	0.441494i
$486$		0			0
$487$	−7.74631	−	18.7012i	−0.351019	−	0.847434i	−0.996495	−	0.0836537i	$-0.973341\pi$
$487$	−7.74631	−	18.7012i	−0.351019	−	0.847434i	0.645476	−	0.763780i	$-0.276659\pi$
$488$		0			0
$489$			59.7133i			2.70033i
$490$		0			0
$491$	−16.8962	+	16.8962i	−0.762516	+	0.762516i	−0.976777	−	0.214260i	$-0.931266\pi$
$491$	−16.8962	+	16.8962i	−0.762516	+	0.762516i	0.214260	+	0.976777i	$0.431266\pi$
$492$		0			0
$493$	−7.52107	+	8.20274i	−0.338732	+	0.369433i
$494$		0			0
$495$	−1.33447	+	1.33447i	−0.0599801	+	0.0599801i
$496$		0			0
$497$			5.86812i			0.263221i
$498$		0			0
$499$	4.14442	+	10.0055i	0.185530	+	0.447908i	0.989090	−	0.147316i	$-0.0470634\pi$
$499$	4.14442	+	10.0055i	0.185530	+	0.447908i	−0.803560	+	0.595224i	$0.797063\pi$
$500$		0			0
$501$	14.3980	+	14.3980i	0.643254	+	0.643254i
$502$		0			0
$503$	−1.21382	+	0.502781i	−0.0541216	+	0.0224179i	−0.409580	−	0.912274i	$-0.634325\pi$
$503$	−1.21382	+	0.502781i	−0.0541216	+	0.0224179i	0.355458	+	0.934692i	$0.384325\pi$
$504$		0			0
$505$	2.41874	+	1.00188i	0.107633	+	0.0445829i
$506$		0			0
$507$	1.76377	−	4.25812i	0.0783318	−	0.189110i
$508$		0			0
$509$	3.74569			0.166025			0.0830123	−	0.996549i	$-0.473546\pi$
$509$	3.74569			0.166025			0.0830123	+	0.996549i	$0.473546\pi$
$510$		0			0
$511$	22.7154			1.00487
$512$		0			0
$513$	2.92781	−	7.06835i	0.129266	−	0.312075i
$514$		0			0
$515$	−0.211811	−	0.0877352i	−0.00933353	−	0.00386607i
$516$		0			0
$517$	−1.66130	+	0.688132i	−0.0730638	+	0.0302640i
$518$		0			0
$519$	16.7591	+	16.7591i	0.735643	+	0.735643i
$520$		0			0
$521$	−0.863917	−	2.08568i	−0.0378489	−	0.0913753i	0.903825	−	0.427903i	$-0.140747\pi$
$521$	−0.863917	−	2.08568i	−0.0378489	−	0.0913753i	−0.941674	+	0.336528i	$0.890747\pi$
$522$		0			0
$523$			6.55839i			0.286779i	0.989666	+	0.143389i	$0.0458001\pi$
$523$			6.55839i			0.286779i	−0.989666	+	0.143389i	$0.954200\pi$
$524$		0			0
$525$	3.11291	−	3.11291i	0.135858	−	0.135858i
$526$		0			0
$527$	18.2586	+	16.7413i	0.795356	+	0.729260i
$528$		0			0
$529$	1.68333	−	1.68333i	0.0731884	−	0.0731884i
$530$		0			0
$531$		−	15.4022i		−	0.668398i
$532$		0			0
$533$	−15.0757	−	36.3960i	−0.653001	−	1.57648i
$534$		0			0
$535$	3.60384	+	3.60384i	0.155807	+	0.155807i
$536$		0			0
$537$	37.1719	−	15.3971i	1.60409	−	0.664434i
$538$		0			0
$539$	−1.85413	−	0.768006i	−0.0798630	−	0.0330803i
$540$		0			0
$541$	−4.46676	+	10.7837i	−0.192041	+	0.463628i	−0.990345	−	0.138627i	$-0.955731\pi$
$541$	−4.46676	+	10.7837i	−0.192041	+	0.463628i	0.798304	+	0.602255i	$0.205731\pi$
$542$		0			0
$543$	18.6576			0.800673
$544$		0			0
$545$	−15.3786			−0.658745
$546$		0			0
$547$	6.34994	−	15.3301i	0.271504	−	0.655468i	−0.728044	−	0.685530i	$-0.759571\pi$
$547$	6.34994	−	15.3301i	0.271504	−	0.655468i	0.999548	+	0.0300621i	$0.00957051\pi$
$548$		0			0
$549$	11.5561	+	4.78667i	0.493200	+	0.204290i
$550$		0			0
$551$	7.47825	−	3.09759i	0.318584	−	0.131962i
$552$		0			0
$553$	5.59026	+	5.59026i	0.237722	+	0.237722i
$554$		0			0
$555$	−4.09053	−	9.87541i	−0.173633	−	0.419188i
$556$		0			0
$557$		−	14.1014i		−	0.597495i	−0.954332	−	0.298747i	$-0.903431\pi$
$557$		−	14.1014i		−	0.597495i	0.954332	−	0.298747i	$-0.0965688\pi$
$558$		0			0
$559$	−9.70160	+	9.70160i	−0.410334	+	0.410334i
$560$		0			0
$561$	1.77240	−	4.86497i	0.0748309	−	0.205399i
$562$		0			0
$563$	−18.4740	+	18.4740i	−0.778588	+	0.778588i	−0.979591	−	0.201003i	$-0.935580\pi$
$563$	−18.4740	+	18.4740i	−0.778588	+	0.778588i	0.201003	+	0.979591i	$0.435580\pi$
$564$		0			0
$565$		−	3.27009i		−	0.137574i
$566$		0			0
$567$	−3.29737	−	7.96056i	−0.138477	−	0.334312i
$568$		0			0
$569$	9.55488	+	9.55488i	0.400562	+	0.400562i	0.878431	−	0.477869i	$-0.158591\pi$
$569$	9.55488	+	9.55488i	0.400562	+	0.400562i	−0.477869	+	0.878431i	$0.658591\pi$
$570$		0			0
$571$	−6.39557	+	2.64913i	−0.267646	+	0.110863i	−0.512471	−	0.858705i	$-0.671270\pi$
$571$	−6.39557	+	2.64913i	−0.267646	+	0.110863i	0.244825	+	0.969567i	$0.421270\pi$
$572$		0			0
$573$	54.0229	+	22.3770i	2.25684	+	0.934813i
$574$		0			0
$575$	1.73771	−	4.19521i	0.0724676	−	0.174952i
$576$		0			0
$577$	46.8463			1.95024			0.975119	−	0.221682i	$-0.0711548\pi$
$577$	46.8463			1.95024			0.975119	+	0.221682i	$0.0711548\pi$
$578$		0			0
$579$	−7.78469			−0.323521
$580$		0			0
$581$	10.0656	−	24.3005i	0.417591	−	1.00815i
$582$		0			0
$583$	0.773558	+	0.320418i	0.0320375	+	0.0132704i
$584$		0			0
$585$	12.2936	−	5.09219i	0.508279	−	0.210536i
$586$		0			0
$587$	4.07081	+	4.07081i	0.168020	+	0.168020i	0.786109	−	0.618088i	$-0.212093\pi$
$587$	4.07081	+	4.07081i	0.168020	+	0.168020i	−0.618088	+	0.786109i	$0.712093\pi$
$588$		0			0
$589$	−6.89498	−	16.6459i	−0.284103	−	0.685884i
$590$		0			0
$591$			62.3974i			2.56668i
$592$		0			0
$593$	17.3535	−	17.3535i	0.712622	−	0.712622i	−0.254461	−	0.967083i	$-0.581898\pi$
$593$	17.3535	−	17.3535i	0.712622	−	0.712622i	0.967083	+	0.254461i	$0.0818980\pi$
$594$		0			0
$595$	−2.35405	+	6.46150i	−0.0965065	+	0.264896i
$596$		0			0
$597$	−3.69885	+	3.69885i	−0.151384	+	0.151384i
$598$		0			0
$599$			35.8315i			1.46404i	0.681285	+	0.732018i	$0.261421\pi$
$599$			35.8315i			1.46404i	−0.681285	+	0.732018i	$0.738579\pi$
$600$		0			0
$601$	12.9042	+	31.1535i	0.526373	+	1.27078i	0.933884	+	0.357577i	$0.116397\pi$
$601$	12.9042	+	31.1535i	0.526373	+	1.27078i	−0.407510	+	0.913201i	$0.633603\pi$
$602$		0			0
$603$	6.29858	+	6.29858i	0.256498	+	0.256498i
$604$		0			0
$605$	−9.95354	+	4.12289i	−0.404669	+	0.167619i
$606$		0			0
$607$	−30.6884	−	12.7115i	−1.24560	−	0.515945i	−0.340141	−	0.940374i	$-0.610475\pi$
$607$	−30.6884	−	12.7115i	−1.24560	−	0.515945i	−0.905461	+	0.424429i	$0.860475\pi$
$608$		0			0
$609$	−4.54723	+	10.9780i	−0.184263	+	0.444851i
$610$		0			0
$611$	12.6786			0.512923
$612$		0			0
$613$	−36.6432			−1.48001			−0.740003	−	0.672604i	$-0.765176\pi$
$613$	−36.6432			−1.48001			−0.740003	+	0.672604i	$0.765176\pi$
$614$		0			0
$615$	−11.8614	+	28.6361i	−0.478300	+	1.15472i
$616$		0			0
$617$	6.22729	+	2.57943i	0.250701	+	0.103844i	0.504495	−	0.863414i	$-0.331679\pi$
$617$	6.22729	+	2.57943i	0.250701	+	0.103844i	−0.253794	+	0.967258i	$0.581679\pi$
$618$		0			0
$619$	−12.1214	+	5.02083i	−0.487198	+	0.201804i	−0.612741	−	0.790284i	$-0.709933\pi$
$619$	−12.1214	+	5.02083i	−0.487198	+	0.201804i	0.125542	+	0.992088i	$0.459933\pi$
$620$		0			0
$621$	8.19156	+	8.19156i	0.328716	+	0.328716i
$622$		0			0
$623$	−7.31271	−	17.6545i	−0.292978	−	0.707311i
$624$		0			0
$625$			1.00000i			0.0400000i
$626$		0			0
$627$	−2.66295	+	2.66295i	−0.106348	+	0.106348i
$628$		0			0
$629$	12.3073	+	11.2845i	0.490725	+	0.449944i
$630$		0			0
$631$	24.4176	−	24.4176i	0.972050	−	0.972050i	−0.0275699	−	0.999620i	$-0.508777\pi$
$631$	24.4176	−	24.4176i	0.972050	−	0.972050i	0.999620	+	0.0275699i	$0.00877687\pi$
$632$		0			0
$633$		−	37.3490i		−	1.48449i
$634$		0			0
$635$	−8.11640	−	19.5947i	−0.322089	−	0.777592i
$636$		0			0
$637$	10.0058	+	10.0058i	0.396443	+	0.396443i
$638$		0			0
$639$	12.8931	−	5.34050i	0.510044	−	0.211267i
$640$		0			0
$641$	−38.7486	−	16.0502i	−1.53048	−	0.633945i	−0.550821	−	0.834624i	$-0.685685\pi$
$641$	−38.7486	−	16.0502i	−1.53048	−	0.633945i	−0.979657	+	0.200679i	$0.935685\pi$
$642$		0			0
$643$	−18.2596	+	44.0826i	−0.720090	+	1.73845i	−0.0469930	+	0.998895i	$0.514964\pi$
$643$	−18.2596	+	44.0826i	−0.720090	+	1.73845i	−0.673097	+	0.739555i	$0.735036\pi$
$644$		0			0
$645$	10.7949			0.425048
$646$		0			0
$647$	25.2762			0.993708			0.496854	−	0.867834i	$-0.334488\pi$
$647$	25.2762			0.993708			0.496854	+	0.867834i	$0.334488\pi$
$648$		0			0
$649$	−0.706995	+	1.70684i	−0.0277520	+	0.0669992i
$650$		0			0
$651$	24.4361	+	10.1217i	0.957725	+	0.396702i
$652$		0			0
$653$	43.8134	−	18.1481i	1.71455	−	0.710190i	0.714607	−	0.699526i	$-0.246605\pi$
$653$	43.8134	−	18.1481i	1.71455	−	0.710190i	0.999943	−	0.0106641i	$-0.00339455\pi$
$654$		0			0
$655$	5.74831	+	5.74831i	0.224605	+	0.224605i
$656$		0			0
$657$	−20.6730	−	49.9090i	−0.806530	−	1.94714i
$658$		0			0
$659$			16.5949i			0.646447i	0.946323	+	0.323224i	$0.104767\pi$
$659$			16.5949i			0.646447i	−0.946323	+	0.323224i	$0.895233\pi$
$660$		0			0
$661$	−10.6497	+	10.6497i	−0.414224	+	0.414224i	−0.883207	−	0.468983i	$-0.844620\pi$
$661$	−10.6497	+	10.6497i	−0.414224	+	0.414224i	0.468983	+	0.883207i	$0.344620\pi$
$662$		0			0
$663$	−24.6725	+	26.9087i	−0.958200	+	1.04505i
$664$		0			0
$665$	3.53684	−	3.53684i	0.137153	−	0.137153i
$666$		0			0
$667$			12.2564i			0.474571i
$668$		0			0
$669$	10.0849	+	24.3471i	0.389905	+	0.941314i
$670$		0			0
$671$	−1.06090	−	1.06090i	−0.0409555	−	0.0409555i
$672$		0			0
$673$	4.63205	−	1.91866i	0.178552	−	0.0739588i	−0.291616	−	0.956535i	$-0.594193\pi$
$673$	4.63205	−	1.91866i	0.178552	−	0.0739588i	0.470169	+	0.882577i	$0.344193\pi$
$674$		0			0
$675$	−2.35700	−	0.976300i	−0.0907209	−	0.0375778i
$676$		0			0
$677$	−9.85148	+	23.7836i	−0.378623	+	0.914077i	0.613601	+	0.789616i	$0.289720\pi$
$677$	−9.85148	+	23.7836i	−0.378623	+	0.914077i	−0.992224	+	0.124461i	$0.960280\pi$
$678$		0			0
$679$	22.9342			0.880132
$680$		0			0
$681$	55.1557			2.11357
$682$		0			0
$683$	13.6849	−	33.0383i	0.523638	−	1.26417i	−0.411991	−	0.911188i	$-0.635166\pi$
$683$	13.6849	−	33.0383i	0.523638	−	1.26417i	0.935629	−	0.352986i	$-0.114834\pi$
$684$		0			0
$685$	−18.4129	−	7.62689i	−0.703522	−	0.291408i
$686$		0			0
$687$	13.3139	−	5.51480i	0.507957	−	0.210403i
$688$		0			0
$689$	−4.17449	−	4.17449i	−0.159035	−	0.159035i
$690$		0			0
$691$	−18.2161	−	43.9777i	−0.692975	−	1.67299i	−0.738699	−	0.674035i	$-0.764560\pi$
$691$	−18.2161	−	43.9777i	−0.692975	−	1.67299i	0.0457245	−	0.998954i	$-0.485440\pi$
$692$		0			0
$693$		−	3.14772i		−	0.119572i
$694$		0			0
$695$	−0.130011	+	0.130011i	−0.00493161	+	0.00493161i
$696$		0			0
$697$	−2.09710	−	48.3732i	−0.0794333	−	1.83227i
$698$		0			0
$699$	−6.10345	+	6.10345i	−0.230854	+	0.230854i
$700$		0			0
$701$			28.6540i			1.08225i	0.840943	+	0.541124i	$0.182001\pi$
$701$			28.6540i			1.08225i	−0.840943	+	0.541124i	$0.817999\pi$
$702$		0			0
$703$	−4.64760	−	11.2203i	−0.175288	−	0.423182i
$704$		0			0
$705$	−7.05371	−	7.05371i	−0.265658	−	0.265658i
$706$		0			0
$707$	−4.03423	+	1.67103i	−0.151723	+	0.0628457i
$708$		0			0
$709$	28.8593	+	11.9539i	1.08383	+	0.448939i	0.851853	−	0.523782i	$-0.175479\pi$
$709$	28.8593	+	11.9539i	1.08383	+	0.448939i	0.231981	+	0.972720i	$0.425479\pi$
$710$		0			0
$711$	7.19499	−	17.3702i	0.269833	−	0.651435i
$712$		0			0
$713$	27.2818			1.02171
$714$		0			0
$715$	−1.59610			−0.0596906
$716$		0			0
$717$	23.1416	−	55.8687i	0.864238	−	2.08645i
$718$		0			0
$719$	−18.7019	−	7.74656i	−0.697461	−	0.288898i	0.00564349	−	0.999984i	$-0.498204\pi$
$719$	−18.7019	−	7.74656i	−0.697461	−	0.288898i	−0.703105	+	0.711086i	$0.748204\pi$
$720$		0			0
$721$	0.353282	−	0.146334i	0.0131569	−	0.00544977i
$722$		0			0
$723$	41.3738	+	41.3738i	1.53871	+	1.53871i
$724$		0			0
$725$	−1.03292	−	2.49368i	−0.0383616	−	0.0926131i
$726$		0			0
$727$		−	28.2598i		−	1.04810i	−0.851688	−	0.524049i	$-0.824421\pi$
$727$		−	28.2598i		−	1.04810i	0.851688	−	0.524049i	$-0.175579\pi$
$728$		0			0
$729$	−28.7739	+	28.7739i	−1.06570	+	1.06570i
$730$		0			0
$731$	−15.2852	+	7.12188i	−0.565343	+	0.263412i
$732$		0			0
$733$	−6.91684	+	6.91684i	−0.255479	+	0.255479i	−0.823213	−	0.567733i	$-0.807821\pi$
$733$	−6.91684	+	6.91684i	−0.255479	+	0.255479i	0.567733	+	0.823213i	$0.307821\pi$
$734$		0			0
$735$		−	11.1333i		−	0.410659i
$736$		0			0
$737$	−0.408876	−	0.987114i	−0.0150611	−	0.0363608i
$738$		0			0
$739$	−17.4220	−	17.4220i	−0.640880	−	0.640880i	0.309892	−	0.950772i	$-0.399707\pi$
$739$	−17.4220	−	17.4220i	−0.640880	−	0.640880i	−0.950772	+	0.309892i	$0.899707\pi$
$740$		0			0
$741$	24.5320	−	10.1615i	0.901206	−	0.373292i
$742$		0			0
$743$	42.9988	+	17.8107i	1.57747	+	0.653411i	0.988011	−	0.154384i	$-0.0493393\pi$
$743$	42.9988	+	17.8107i	1.57747	+	0.653411i	0.589463	+	0.807795i	$0.299339\pi$
$744$		0			0
$745$	−5.27986	+	12.7467i	−0.193439	+	0.467003i
$746$		0			0
$747$	−62.5523			−2.28867
$748$		0			0
$749$	−8.50065			−0.310607
$750$		0			0
$751$	5.07719	−	12.2574i	0.185269	−	0.447279i	−0.803769	−	0.594942i	$-0.797175\pi$
$751$	5.07719	−	12.2574i	0.185269	−	0.447279i	0.989038	+	0.147663i	$0.0471750\pi$
$752$		0			0
$753$	51.5166	+	21.3389i	1.87737	+	0.777632i
$754$		0			0
$755$	2.82935	−	1.17195i	0.102970	−	0.0426518i
$756$		0			0
$757$	−17.5750	−	17.5750i	−0.638773	−	0.638773i	0.311480	−	0.950253i	$-0.399175\pi$
$757$	−17.5750	−	17.5750i	−0.638773	−	0.638773i	−0.950253	+	0.311480i	$0.899175\pi$
$758$		0			0
$759$	−2.18221	−	5.26832i	−0.0792092	−	0.191228i
$760$		0			0
$761$		−	4.37844i		−	0.158718i	−0.996846	−	0.0793592i	$-0.974713\pi$
$761$		−	4.37844i		−	0.158718i	0.996846	−	0.0793592i	$-0.0252874\pi$
$762$		0			0
$763$	18.1373	−	18.1373i	0.656614	−	0.656614i
$764$		0			0
$765$	16.3392	−	0.708347i	0.590747	−	0.0256104i
$766$		0			0
$767$	9.21090	−	9.21090i	0.332586	−	0.332586i
$768$		0			0
$769$		−	6.31606i		−	0.227763i	−0.993494	−	0.113882i	$-0.963672\pi$
$769$		−	6.31606i		−	0.227763i	0.993494	−	0.113882i	$-0.0363284\pi$
$770$		0			0
$771$	−1.36829	−	3.30335i	−0.0492778	−	0.118967i
$772$		0			0
$773$	−10.8659	−	10.8659i	−0.390820	−	0.390820i	0.484160	−	0.874980i	$-0.339125\pi$
$773$	−10.8659	−	10.8659i	−0.390820	−	0.390820i	−0.874980	+	0.484160i	$0.839125\pi$
$774$		0			0
$775$	−5.55072	+	2.29919i	−0.199388	+	0.0825892i
$776$		0			0
$777$	16.4713	+	6.82262i	0.590904	+	0.244760i
$778$		0			0
$779$	−13.4768	+	32.5359i	−0.482856	+	1.16572i
$780$		0			0
$781$	−1.67393			−0.0598978
$782$		0			0
$783$	6.88605			0.246087
$784$		0			0
$785$	−1.32678	+	3.20313i	−0.0473549	+	0.114325i
$786$		0			0
$787$	26.7805	+	11.0928i	0.954620	+	0.395417i	0.804966	−	0.593322i	$-0.202184\pi$
$787$	26.7805	+	11.0928i	0.954620	+	0.395417i	0.149655	+	0.988738i	$0.452184\pi$
$788$		0			0
$789$	−20.3560	+	8.43171i	−0.724691	+	0.300177i
$790$		0			0
$791$	3.85671	+	3.85671i	0.137129	+	0.137129i
$792$		0			0
$793$	4.04826	+	9.77336i	0.143758	+	0.347062i
$794$		0			0
$795$			4.64492i			0.164738i
$796$		0			0
$797$	−22.7218	+	22.7218i	−0.804846	+	0.804846i	−0.983849	−	0.179003i	$-0.942713\pi$
$797$	−22.7218	+	22.7218i	−0.804846	+	0.804846i	0.179003	+	0.983849i	$0.442713\pi$
$798$		0			0
$799$	14.6415	+	5.33416i	0.517978	+	0.188709i
$800$		0			0
$801$	−32.1342	+	32.1342i	−1.13541	+	1.13541i
$802$		0			0
$803$			6.47974i			0.228665i
$804$		0			0
$805$	2.89834	+	6.99722i	0.102153	+	0.246619i
$806$		0			0
$807$	−44.0293	−	44.0293i	−1.54991	−	1.54991i
$808$		0			0
$809$	34.3505	−	14.2285i	1.20770	−	0.500246i	0.314221	−	0.949350i	$-0.398257\pi$
$809$	34.3505	−	14.2285i	1.20770	−	0.500246i	0.893480	+	0.449104i	$0.148257\pi$
$810$		0			0
$811$	24.5592	+	10.1728i	0.862390	+	0.357214i	0.769642	−	0.638476i	$-0.220435\pi$
$811$	24.5592	+	10.1728i	0.862390	+	0.357214i	0.0927484	+	0.995690i	$0.470435\pi$
$812$		0			0
$813$	−27.9061	+	67.3713i	−0.978710	+	2.36282i
$814$		0			0
$815$	22.6236			0.792469
$816$		0			0
$817$	12.2650			0.429098
$818$		0			0
$819$	−8.49330	+	20.5046i	−0.296780	+	0.716490i
$820$		0			0
$821$	−17.7400	−	7.34816i	−0.619131	−	0.256453i	0.0509960	−	0.998699i	$-0.483760\pi$
$821$	−17.7400	−	7.34816i	−0.619131	−	0.256453i	−0.670127	+	0.742246i	$0.733760\pi$
$822$		0			0
$823$	−33.3906	+	13.8308i	−1.16392	+	0.482112i	−0.879179	−	0.476492i	$-0.841908\pi$
$823$	−33.3906	+	13.8308i	−1.16392	+	0.482112i	−0.284743	+	0.958604i	$0.591908\pi$
$824$		0			0
$825$	0.887982	+	0.887982i	0.0309155	+	0.0309155i
$826$		0			0
$827$	14.7966	+	35.7222i	0.514530	+	1.24218i	0.941222	+	0.337788i	$0.109679\pi$
$827$	14.7966	+	35.7222i	0.514530	+	1.24218i	−0.426693	+	0.904397i	$0.640321\pi$
$828$		0			0
$829$			12.7121i			0.441509i	0.975329	+	0.220754i	$0.0708520\pi$
$829$			12.7121i			0.441509i	−0.975329	+	0.220754i	$0.929148\pi$
$830$		0			0
$831$	−47.0865	+	47.0865i	−1.63341	+	1.63341i
$832$		0			0
$833$	7.34516	+	15.7644i	0.254495	+	0.546205i
$834$		0			0
$835$	5.45496	−	5.45496i	0.188777	−	0.188777i
$836$		0			0
$837$		−	15.3277i		−	0.529804i
$838$		0			0
$839$	−2.38363	−	5.75459i	−0.0822920	−	0.198670i	0.877378	−	0.479800i	$-0.159291\pi$
$839$	−2.38363	−	5.75459i	−0.0822920	−	0.198670i	−0.959670	+	0.281130i	$0.909291\pi$
$840$		0			0
$841$	−15.3546	−	15.3546i	−0.529467	−	0.529467i
$842$		0			0
$843$	−46.6882	+	19.3389i	−1.60803	+	0.666066i
$844$		0			0
$845$	−1.61328	−	0.668240i	−0.0554984	−	0.0229882i
$846$		0			0
$847$	6.87660	−	16.6016i	0.236283	−	0.570437i
$848$		0			0
$849$	34.1409			1.17171
$850$		0			0
$851$	18.3894			0.630382
$852$		0			0
$853$	−0.0874574	+	0.211141i	−0.00299448	+	0.00722933i	−0.925370	−	0.379066i	$-0.876245\pi$
$853$	−0.0874574	+	0.211141i	−0.00299448	+	0.00722933i	0.922375	+	0.386295i	$0.126245\pi$
$854$		0			0
$855$	−10.9898	−	4.55212i	−0.375843	−	0.155679i
$856$		0			0
$857$	−26.6526	+	11.0399i	−0.910436	+	0.377115i	−0.788223	−	0.615389i	$-0.788999\pi$
$857$	−26.6526	+	11.0399i	−0.910436	+	0.377115i	−0.122212	+	0.992504i	$0.538999\pi$
$858$		0			0
$859$	8.20750	+	8.20750i	0.280036	+	0.280036i	0.833123	−	0.553087i	$-0.186550\pi$
$859$	8.20750	+	8.20750i	0.280036	+	0.280036i	−0.553087	+	0.833123i	$0.686550\pi$
$860$		0			0
$861$	−19.7838	−	47.7623i	−0.674230	−	1.62773i
$862$		0			0
$863$		−	52.8959i		−	1.80060i	−0.435272	−	0.900299i	$-0.643348\pi$
$863$		−	52.8959i		−	1.80060i	0.435272	−	0.900299i	$-0.356652\pi$
$864$		0			0
$865$	6.34953	−	6.34953i	0.215890	−	0.215890i
$866$		0			0
$867$	−39.8131	+	20.6943i	−1.35213	+	0.702814i
$868$		0			0
$869$	−1.59467	+	1.59467i	−0.0540953	+	0.0540953i
$870$		0			0
$871$			7.53342i			0.255260i
$872$		0			0
$873$	−20.8721	−	50.3897i	−0.706413	−	1.70543i
$874$		0			0
$875$	−1.17939	−	1.17939i	−0.0398706	−	0.0398706i
$876$		0			0
$877$	−13.7095	+	5.67865i	−0.462936	+	0.191754i	−0.601946	−	0.798537i	$-0.705608\pi$
$877$	−13.7095	+	5.67865i	−0.462936	+	0.191754i	0.139010	+	0.990291i	$0.455608\pi$
$878$		0			0
$879$	−74.3850	−	30.8113i	−2.50894	−	1.03924i
$880$		0			0
$881$	−17.9469	+	43.3276i	−0.604646	+	1.45974i	0.264104	+	0.964494i	$0.414924\pi$
$881$	−17.9469	+	43.3276i	−0.604646	+	1.45974i	−0.868750	+	0.495250i	$0.835076\pi$
$882$		0			0
$883$	26.6804			0.897867			0.448934	−	0.893565i	$-0.351804\pi$
$883$	26.6804			0.897867			0.448934	+	0.893565i	$0.351804\pi$
$884$		0			0
$885$	−10.2489			−0.344513
$886$		0			0
$887$	19.3108	−	46.6204i	0.648394	−	1.56536i	−0.166685	−	0.986010i	$-0.553306\pi$
$887$	19.3108	−	46.6204i	0.648394	−	1.56536i	0.815079	−	0.579350i	$-0.196694\pi$
$888$		0			0
$889$	32.6822	+	13.5374i	1.09612	+	0.454030i
$890$		0			0
$891$	2.27081	−	0.940601i	0.0760750	−	0.0315113i
$892$		0			0
$893$	−8.01432	−	8.01432i	−0.268189	−	0.268189i
$894$		0			0
$895$	−5.83350	−	14.0833i	−0.194993	−	0.470754i
$896$		0			0
$897$			40.2066i			1.34246i
$898$		0			0
$899$	11.4669	−	11.4669i	0.382442	−	0.382442i
$900$		0			0
$901$	−3.06446	−	6.57705i	−0.102092	−	0.219113i
$902$		0			0
$903$	−12.7314	+	12.7314i	−0.423673	+	0.423673i
$904$		0			0
$905$		−	7.06880i		−	0.234975i
$906$		0			0
$907$	7.21610	+	17.4212i	0.239607	+	0.578462i	0.997242	−	0.0742162i	$-0.0236455\pi$
$907$	7.21610	+	17.4212i	0.239607	+	0.578462i	−0.757636	+	0.652678i	$0.773645\pi$
$908$		0			0
$909$	7.34301	+	7.34301i	0.243552	+	0.243552i
$910$		0			0
$911$	−0.492513	+	0.204006i	−0.0163177	+	0.00675901i	−0.390827	−	0.920464i	$-0.627811\pi$
$911$	−0.492513	+	0.204006i	−0.0163177	+	0.00675901i	0.374510	+	0.927223i	$0.377811\pi$
$912$		0			0
$913$	6.93191	+	2.87129i	0.229413	+	0.0950258i
$914$		0			0
$915$	3.18514	−	7.68960i	0.105297	−	0.254210i
$916$		0			0
$917$	−13.5590			−0.447757
$918$		0			0
$919$	5.46242			0.180188			0.0900942	−	0.995933i	$-0.471283\pi$
$919$	5.46242			0.180188			0.0900942	+	0.995933i	$0.471283\pi$
$920$		0			0
$921$	12.4939	−	30.1629i	0.411688	−	0.993902i
$922$		0			0
$923$	10.9042	+	4.51665i	0.358915	+	0.148667i
$924$		0			0
$925$	−3.74150	+	1.54978i	−0.123020	+	0.0509564i
$926$		0			0
$927$	−0.643035	−	0.643035i	−0.0211200	−	0.0211200i
$928$		0			0
$929$	−1.11742	−	2.69768i	−0.0366613	−	0.0885081i	0.904488	−	0.426498i	$-0.140253\pi$
$929$	−1.11742	−	2.69768i	−0.0366613	−	0.0885081i	−0.941150	+	0.337990i	$0.890253\pi$
$930$		0			0
$931$		−	12.6495i		−	0.414571i
$932$		0			0
$933$	−44.4444	+	44.4444i	−1.45504	+	1.45504i
$934$		0			0
$935$	−1.84319	−	0.671510i	−0.0602789	−	0.0219607i
$936$		0			0
$937$	24.5821	−	24.5821i	0.803063	−	0.803063i	−0.180510	−	0.983573i	$-0.557775\pi$
$937$	24.5821	−	24.5821i	0.803063	−	0.803063i	0.983573	+	0.180510i	$0.0577748\pi$
$938$		0			0
$939$			23.3265i			0.761231i
$940$		0			0
$941$	19.3947	+	46.8228i	0.632248	+	1.52638i	0.836790	+	0.547523i	$0.184429\pi$
$941$	19.3947	+	46.8228i	0.632248	+	1.52638i	−0.204543	+	0.978858i	$0.565571\pi$
$942$		0			0
$943$	−37.7061	−	37.7061i	−1.22788	−	1.22788i
$944$		0			0
$945$	3.93125	−	1.62838i	0.127884	−	0.0529712i
$946$		0			0
$947$	−46.6469	−	19.3218i	−1.51582	−	0.627873i	−0.539071	−	0.842260i	$-0.681225\pi$
$947$	−46.6469	−	19.3218i	−1.51582	−	0.627873i	−0.976749	+	0.214387i	$0.931225\pi$
$948$		0			0
$949$	17.4839	−	42.2098i	0.567550	−	1.37019i
$950$		0			0
$951$	−39.1592			−1.26982
$952$		0			0
$953$	30.6222			0.991949			0.495975	−	0.868337i	$-0.334811\pi$
$953$	30.6222			0.991949			0.495975	+	0.868337i	$0.334811\pi$
$954$		0			0
$955$	8.47798	−	20.4677i	0.274341	−	0.662318i
$956$		0			0
$957$	−3.13156	−	1.29713i	−0.101229	−	0.0419304i
$958$		0			0
$959$	30.7111	−	12.7209i	0.991712	−	0.410781i
$960$		0			0
$961$	−3.60398	−	3.60398i	−0.116257	−	0.116257i
$962$		0			0
$963$	7.73633	+	18.6772i	0.249300	+	0.601863i
$964$		0			0
$965$			2.94939i			0.0949442i
$966$		0			0
$967$	−6.27362	+	6.27362i	−0.201746	+	0.201746i	−0.800748	−	0.599002i	$-0.795564\pi$
$967$	−6.27362	+	6.27362i	−0.201746	+	0.201746i	0.599002	+	0.800748i	$0.295564\pi$
$968$		0			0
$969$	32.6051	−	1.41351i	1.04743	−	0.0454085i
$970$		0			0
$971$	−31.5872	+	31.5872i	−1.01368	+	1.01368i	−0.0137753	+	0.999905i	$0.504385\pi$
$971$	−31.5872	+	31.5872i	−1.01368	+	1.01368i	−0.999905	+	0.0137753i	$0.995615\pi$
$972$		0			0
$973$		−	0.306667i		−	0.00983131i
$974$		0			0
$975$	−3.38843	−	8.18040i	−0.108517	−	0.261982i
$976$		0			0
$977$	−8.23759	−	8.23759i	−0.263544	−	0.263544i	0.562948	−	0.826492i	$-0.309667\pi$
$977$	−8.23759	−	8.23759i	−0.263544	−	0.263544i	−0.826492	+	0.562948i	$0.809667\pi$
$978$		0			0
$979$	5.03607	−	2.08601i	0.160953	−	0.0666691i
$980$		0			0
$981$	−56.3568	−	23.3438i	−1.79933	−	0.745309i
$982$		0			0
$983$	−4.98044	+	12.0238i	−0.158851	+	0.383501i	−0.983187	−	0.182600i	$-0.941549\pi$
$983$	−4.98044	+	12.0238i	−0.158851	+	0.383501i	0.824336	+	0.566101i	$0.191549\pi$
$984$		0			0
$985$	23.6405			0.753249
$986$		0			0
$987$	16.6381			0.529597
$988$		0			0
$989$	−7.10700	+	17.1578i	−0.225989	+	0.545587i
$990$		0			0
$991$	−34.4622	−	14.2747i	−1.09473	−	0.453452i	−0.239075	−	0.971001i	$-0.576844\pi$
$991$	−34.4622	−	14.2747i	−1.09473	−	0.453452i	−0.855653	+	0.517549i	$0.826844\pi$
$992$		0			0
$993$	−85.8377	+	35.5551i	−2.72398	+	1.12831i
$994$		0			0
$995$	1.40139	+	1.40139i	0.0444269	+	0.0444269i
$996$		0			0
$997$	−15.1087	−	36.4756i	−0.478497	−	1.15519i	−0.960314	−	0.278921i	$-0.910023\pi$
$997$	−15.1087	−	36.4756i	−0.478497	−	1.15519i	0.481817	−	0.876272i	$-0.339977\pi$
$998$		0			0
$999$		−	10.3318i		−	0.326882i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.bo.a.161.8	✓	32
17.15	even	8	inner	680.2.bo.a.321.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.bo.a.161.8	✓	32	1.1	even	1	trivial
680.2.bo.a.321.8	yes	32	17.15	even	8	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:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.bo (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.01006 - 2.43851i) q^{3} +(-0.923880 - 0.382683i) q^{5} +(1.54095 - 0.638280i) q^{7} +(-2.80479 - 2.80479i) q^{9} +(0.182074 + 0.439567i) q^{11} -3.35467i q^{13} +(-1.86636 + 1.86636i) q^{15} +(1.41138 - 3.87402i) q^{17} +(-2.12053 + 2.12053i) q^{19} -4.40232i q^{21} +(-1.73771 - 4.19521i) q^{23} +(0.707107 + 0.707107i) q^{25} +(-2.35700 + 0.976300i) q^{27} +(-2.49368 - 1.03292i) q^{29} +(-2.29919 + 5.55072i) q^{31} +1.25580 q^{33} -1.66791 q^{35} +(-1.54978 + 3.74150i) q^{37} +(-8.18040 - 3.38843i) q^{39} +(10.8493 - 4.49395i) q^{41} +(-2.89197 - 2.89197i) q^{43} +(1.51794 + 3.66463i) q^{45} +3.77940i q^{47} +(-2.98264 + 2.98264i) q^{49} +(-8.02126 - 7.35467i) q^{51} +(1.24438 - 1.24438i) q^{53} -0.475783i q^{55} +(3.02906 + 7.31280i) q^{57} +(2.74570 + 2.74570i) q^{59} +(-2.91336 + 1.20675i) q^{61} +(-6.11227 - 2.53179i) q^{63} +(-1.28378 + 3.09931i) q^{65} -2.24565 q^{67} -11.9853 q^{69} +(-1.34638 + 3.25044i) q^{71} +(12.5824 + 5.21180i) q^{73} +(2.43851 - 1.01006i) q^{75} +(0.561134 + 0.561134i) q^{77} +(1.81391 + 4.37916i) q^{79} -5.16602i q^{81} +(11.1510 - 11.1510i) q^{83} +(-2.78647 + 3.03901i) q^{85} +(-5.03757 + 5.03757i) q^{87} -11.4569i q^{89} +(-2.14122 - 5.16936i) q^{91} +(11.2132 + 11.2132i) q^{93} +(2.77060 - 1.14762i) q^{95} +(12.7036 + 5.26200i) q^{97} +(0.722211 - 1.74357i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{9} + 8 q^{11} - 8 q^{17} + 8 q^{19} + 8 q^{23} - 24 q^{27} - 32 q^{29} + 32 q^{31} + 16 q^{33} + 16 q^{35} + 16 q^{37} - 24 q^{39} - 16 q^{41} - 8 q^{49} + 16 q^{51} + 16 q^{53} + 48 q^{57}+ \cdots + 48 q^{99}+O(q^{100}) \) 32 * q + 16 * q^9 + 8 * q^11 - 8 * q^17 + 8 * q^19 + 8 * q^23 - 24 * q^27 - 32 * q^29 + 32 * q^31 + 16 * q^33 + 16 * q^35 + 16 * q^37 - 24 * q^39 - 16 * q^41 - 8 * q^49 + 16 * q^51 + 16 * q^53 + 48 * q^57 + 24 * q^59 - 24 * q^61 - 48 * q^63 - 16 * q^67 - 80 * q^69 - 64 * q^71 + 16 * q^73 - 8 * q^79 - 56 * q^83 + 16 * q^85 + 96 * q^87 - 48 * q^91 + 32 * q^93 + 24 * q^97 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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