LMFDB - Embedded newform 605.2.e.b.362.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(362,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("605.362");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			362.11
Character	$\chi$	$=$	605.362
Dual form			605.2.e.b.483.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.738792 - 0.738792i) q^{2} +(1.99135 - 1.99135i) q^{3} +0.908372i q^{4} +(0.742178 - 2.10931i) q^{5} -2.94239i q^{6} +(0.388787 - 0.388787i) q^{7} +(2.14868 + 2.14868i) q^{8} -4.93096i q^{9} +O(q^{10})$	\(q+(0.738792 - 0.738792i) q^{2} +(1.99135 - 1.99135i) q^{3} +0.908372i q^{4} +(0.742178 - 2.10931i) q^{5} -2.94239i q^{6} +(0.388787 - 0.388787i) q^{7} +(2.14868 + 2.14868i) q^{8} -4.93096i q^{9} +(-1.01002 - 2.10665i) q^{10} +(1.80889 + 1.80889i) q^{12} +(2.29427 + 2.29427i) q^{13} -0.574465i q^{14} +(-2.72243 - 5.67831i) q^{15} +1.35812 q^{16} +(-4.00409 + 4.00409i) q^{17} +(-3.64296 - 3.64296i) q^{18} -1.55652 q^{19} +(1.91603 + 0.674174i) q^{20} -1.54842i q^{21} +(-0.803543 + 0.803543i) q^{23} +8.55757 q^{24} +(-3.89834 - 3.13096i) q^{25} +3.38998 q^{26} +(-3.84523 - 3.84523i) q^{27} +(0.353163 + 0.353163i) q^{28} -4.25677 q^{29} +(-6.20640 - 2.18378i) q^{30} -1.64783 q^{31} +(-3.29400 + 3.29400i) q^{32} +5.91638i q^{34} +(-0.531521 - 1.10862i) q^{35} +4.47915 q^{36} +(0.676632 + 0.676632i) q^{37} +(-1.14995 + 1.14995i) q^{38} +9.13740 q^{39} +(6.12693 - 2.93752i) q^{40} -8.94662i q^{41} +(-1.14396 - 1.14396i) q^{42} +(2.55312 + 2.55312i) q^{43} +(-10.4009 - 3.65965i) q^{45} +1.18730i q^{46} +(-2.87915 - 2.87915i) q^{47} +(2.70449 - 2.70449i) q^{48} +6.69769i q^{49} +(-5.19320 + 0.566936i) q^{50} +15.9471i q^{51} +(-2.08405 + 2.08405i) q^{52} +(4.98134 - 4.98134i) q^{53} -5.68165 q^{54} +1.67076 q^{56} +(-3.09959 + 3.09959i) q^{57} +(-3.14487 + 3.14487i) q^{58} +6.76710i q^{59} +(5.15801 - 2.47298i) q^{60} +9.20114i q^{61} +(-1.21741 + 1.21741i) q^{62} +(-1.91709 - 1.91709i) q^{63} +7.58340i q^{64} +(6.54208 - 3.13656i) q^{65} +(-2.62254 - 2.62254i) q^{67} +(-3.63720 - 3.63720i) q^{68} +3.20027i q^{69} +(-1.21172 - 0.426355i) q^{70} +6.85404 q^{71} +(10.5951 - 10.5951i) q^{72} +(-7.13445 - 7.13445i) q^{73} +0.999781 q^{74} +(-13.9978 + 1.52813i) q^{75} -1.41390i q^{76} +(6.75064 - 6.75064i) q^{78} +4.16632 q^{79} +(1.00796 - 2.86468i) q^{80} -0.521516 q^{81} +(-6.60969 - 6.60969i) q^{82} +(-8.01121 - 8.01121i) q^{83} +1.40654 q^{84} +(5.47411 + 11.4176i) q^{85} +3.77246 q^{86} +(-8.47673 + 8.47673i) q^{87} -3.64860i q^{89} +(-10.3878 + 4.98039i) q^{90} +1.78396 q^{91} +(-0.729916 - 0.729916i) q^{92} +(-3.28142 + 3.28142i) q^{93} -4.25419 q^{94} +(-1.15522 + 3.28319i) q^{95} +13.1190i q^{96} +(11.7862 + 11.7862i) q^{97} +(4.94820 + 4.94820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{3} + 8 q^{5}+O(q^{10}) $ 32 * q - 4 * q^3 + 8 * q^5	$ 32 q - 4 q^{3} + 8 q^{5} + 12 q^{12} - 36 q^{15} - 8 q^{16} - 64 q^{20} - 24 q^{23} + 16 q^{25} - 16 q^{27} - 8 q^{31} + 24 q^{36} + 32 q^{37} - 40 q^{38} + 60 q^{42} - 28 q^{45} - 28 q^{47} + 56 q^{48} + 116 q^{53} - 80 q^{56} - 80 q^{58} + 104 q^{60} - 8 q^{67} - 80 q^{70} + 24 q^{71} - 76 q^{75} + 60 q^{78} + 8 q^{80} + 8 q^{81} - 20 q^{82} - 40 q^{86} + 80 q^{91} + 52 q^{92} + 32 q^{93} + 92 q^{97}+O(q^{100}) $ 32 * q - 4 * q^3 + 8 * q^5 + 12 * q^12 - 36 * q^15 - 8 * q^16 - 64 * q^20 - 24 * q^23 + 16 * q^25 - 16 * q^27 - 8 * q^31 + 24 * q^36 + 32 * q^37 - 40 * q^38 + 60 * q^42 - 28 * q^45 - 28 * q^47 + 56 * q^48 + 116 * q^53 - 80 * q^56 - 80 * q^58 + 104 * q^60 - 8 * q^67 - 80 * q^70 + 24 * q^71 - 76 * q^75 + 60 * q^78 + 8 * q^80 + 8 * q^81 - 20 * q^82 - 40 * q^86 + 80 * q^91 + 52 * q^92 + 32 * q^93 + 92 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	0.738792	−	0.738792i	0.522405	−	0.522405i	−0.395892	−	0.918297i	$-0.629565\pi$
$2$	0.738792	−	0.738792i	0.522405	−	0.522405i	0.918297	+	0.395892i	$0.129565\pi$
$3$	1.99135	−	1.99135i	1.14971	−	1.14971i	0.163098	−	0.986610i	$-0.447851\pi$
$3$	1.99135	−	1.99135i	1.14971	−	1.14971i	0.986610	−	0.163098i	$-0.0521485\pi$
$4$			0.908372i			0.454186i
$5$	0.742178	−	2.10931i	0.331912	−	0.943310i
$5$	0.742178	−	2.10931i	0.331912	−	0.943310i
$6$		−	2.94239i		−	1.20123i
$7$	0.388787	−	0.388787i	0.146948	−	0.146948i	−0.629805	−	0.776753i	$-0.716865\pi$
$7$	0.388787	−	0.388787i	0.146948	−	0.146948i	0.776753	+	0.629805i	$0.216865\pi$
$8$	2.14868	+	2.14868i	0.759674	+	0.759674i
$9$		−	4.93096i		−	1.64365i
$10$	−1.01002	−	2.10665i	−0.319398	−	0.666183i
$11$		0			0
$11$		0			0
$12$	1.80889	+	1.80889i	0.522181	+	0.522181i
$13$	2.29427	+	2.29427i	0.636316	+	0.636316i	0.949645	−	0.313329i	$-0.101444\pi$
$13$	2.29427	+	2.29427i	0.636316	+	0.636316i	−0.313329	+	0.949645i	$0.601444\pi$
$14$		−	0.574465i		−	0.153532i
$15$	−2.72243	−	5.67831i	−0.702929	−	1.46613i
$16$	1.35812			0.339529
$17$	−4.00409	+	4.00409i	−0.971135	+	0.971135i	−0.999595	−	0.0284600i	$-0.990940\pi$
$17$	−4.00409	+	4.00409i	−0.971135	+	0.971135i	0.0284600	+	0.999595i	$0.490940\pi$
$18$	−3.64296	−	3.64296i	−0.858654	−	0.858654i
$19$	−1.55652			−0.357091			−0.178546	−	0.983932i	$-0.557139\pi$
$19$	−1.55652			−0.357091			−0.178546	+	0.983932i	$0.557139\pi$
$20$	1.91603	+	0.674174i	0.428438	+	0.150750i
$21$		−	1.54842i		−	0.337893i
$22$		0			0
$23$	−0.803543	+	0.803543i	−0.167550	+	0.167550i	−0.785902	−	0.618351i	$-0.787801\pi$
$23$	−0.803543	+	0.803543i	−0.167550	+	0.167550i	0.618351	+	0.785902i	$0.287801\pi$
$24$	8.55757			1.74681
$25$	−3.89834	−	3.13096i	−0.779669	−	0.626192i
$26$	3.38998			0.664830
$27$	−3.84523	−	3.84523i	−0.740015	−	0.740015i
$28$	0.353163	+	0.353163i	0.0667415	+	0.0667415i
$29$	−4.25677			−0.790463			−0.395232	−	0.918582i	$-0.629336\pi$
$29$	−4.25677			−0.790463			−0.395232	+	0.918582i	$0.629336\pi$
$30$	−6.20640	−	2.18378i	−1.13313	−	0.398701i
$31$	−1.64783			−0.295960			−0.147980	−	0.988990i	$-0.547277\pi$
$31$	−1.64783			−0.295960			−0.147980	+	0.988990i	$0.547277\pi$
$32$	−3.29400	+	3.29400i	−0.582302	+	0.582302i
$33$		0			0
$34$			5.91638i			1.01465i
$35$	−0.531521	−	1.10862i	−0.0898434	−	0.187391i
$36$	4.47915			0.746525
$37$	0.676632	+	0.676632i	0.111238	+	0.111238i	0.760535	−	0.649297i	$-0.224937\pi$
$37$	0.676632	+	0.676632i	0.111238	+	0.111238i	−0.649297	+	0.760535i	$0.724937\pi$
$38$	−1.14995	+	1.14995i	−0.186546	+	0.186546i
$39$	9.13740			1.46315
$40$	6.12693	−	2.93752i	0.968753	−	0.464463i
$41$		−	8.94662i		−	1.39723i	−0.715499	−	0.698614i	$-0.753801\pi$
$41$		−	8.94662i		−	1.39723i	0.715499	−	0.698614i	$-0.246199\pi$
$42$	−1.14396	−	1.14396i	−0.176517	−	0.176517i
$43$	2.55312	+	2.55312i	0.389348	+	0.389348i	0.874455	−	0.485107i	$-0.161219\pi$
$43$	2.55312	+	2.55312i	0.389348	+	0.389348i	−0.485107	+	0.874455i	$0.661219\pi$
$44$		0			0
$45$	−10.4009	−	3.65965i	−1.55048	−	0.545549i
$46$			1.18730i			0.175058i
$47$	−2.87915	−	2.87915i	−0.419967	−	0.419967i	0.465225	−	0.885192i	$-0.345973\pi$
$47$	−2.87915	−	2.87915i	−0.419967	−	0.419967i	−0.885192	+	0.465225i	$0.845973\pi$
$48$	2.70449	−	2.70449i	0.390359	−	0.390359i
$49$			6.69769i			0.956813i
$50$	−5.19320	+	0.566936i	−0.734429	+	0.0801769i
$51$			15.9471i			2.23304i
$52$	−2.08405	+	2.08405i	−0.289006	+	0.289006i
$53$	4.98134	−	4.98134i	0.684239	−	0.684239i	−0.276713	−	0.960953i	$-0.589245\pi$
$53$	4.98134	−	4.98134i	0.684239	−	0.684239i	0.960953	+	0.276713i	$0.0892452\pi$
$54$	−5.68165			−0.773175
$55$		0			0
$56$	1.67076			0.223264
$57$	−3.09959	+	3.09959i	−0.410550	+	0.410550i
$58$	−3.14487	+	3.14487i	−0.412942	+	0.412942i
$59$			6.76710i			0.881001i	0.897752	+	0.440500i	$0.145199\pi$
$59$			6.76710i			0.881001i	−0.897752	+	0.440500i	$0.854801\pi$
$60$	5.15801	−	2.47298i	0.665897	−	0.319260i
$61$			9.20114i			1.17809i	0.808102	+	0.589043i	$0.200495\pi$
$61$			9.20114i			1.17809i	−0.808102	+	0.589043i	$0.799505\pi$
$62$	−1.21741	+	1.21741i	−0.154611	+	0.154611i
$63$	−1.91709	−	1.91709i	−0.241531	−	0.241531i
$64$			7.58340i			0.947925i
$65$	6.54208	−	3.13656i	0.811445	−	0.389043i
$66$		0			0
$67$	−2.62254	−	2.62254i	−0.320394	−	0.320394i	0.528524	−	0.848918i	$-0.322746\pi$
$67$	−2.62254	−	2.62254i	−0.320394	−	0.320394i	−0.848918	+	0.528524i	$0.822746\pi$
$68$	−3.63720	−	3.63720i	−0.441076	−	0.441076i
$69$			3.20027i			0.385268i
$70$	−1.21172	−	0.426355i	−0.144829	−	0.0509592i
$71$	6.85404			0.813425			0.406713	−	0.913556i	$-0.366675\pi$
$71$	6.85404			0.813425			0.406713	+	0.913556i	$0.366675\pi$
$72$	10.5951	−	10.5951i	1.24864	−	1.24864i
$73$	−7.13445	−	7.13445i	−0.835024	−	0.835024i	0.153175	−	0.988199i	$-0.451050\pi$
$73$	−7.13445	−	7.13445i	−0.835024	−	0.835024i	−0.988199	+	0.153175i	$0.951050\pi$
$74$	0.999781			0.116222
$75$	−13.9978	+	1.52813i	−1.61633	+	0.176453i
$76$		−	1.41390i		−	0.162186i
$77$		0			0
$78$	6.75064	−	6.75064i	0.764360	−	0.764360i
$79$	4.16632			0.468748			0.234374	−	0.972147i	$-0.424696\pi$
$79$	4.16632			0.468748			0.234374	+	0.972147i	$0.424696\pi$
$80$	1.00796	−	2.86468i	0.112694	−	0.320281i
$81$	−0.521516			−0.0579462
$82$	−6.60969	−	6.60969i	−0.729919	−	0.729919i
$83$	−8.01121	−	8.01121i	−0.879345	−	0.879345i	0.114122	−	0.993467i	$-0.463595\pi$
$83$	−8.01121	−	8.01121i	−0.879345	−	0.879345i	−0.993467	+	0.114122i	$0.963595\pi$
$84$	1.40654			0.153466
$85$	5.47411	+	11.4176i	0.593750	+	1.23841i
$86$	3.77246			0.406794
$87$	−8.47673	+	8.47673i	−0.908801	+	0.908801i
$88$		0			0
$89$		−	3.64860i		−	0.386750i	−0.981125	−	0.193375i	$-0.938057\pi$
$89$		−	3.64860i		−	0.386750i	0.981125	−	0.193375i	$-0.0619435\pi$
$90$	−10.3878	+	4.98039i	−1.09497	+	0.524979i
$91$	1.78396			0.187010
$92$	−0.729916	−	0.729916i	−0.0760990	−	0.0760990i
$93$	−3.28142	+	3.28142i	−0.340267	+	0.340267i
$94$	−4.25419			−0.438786
$95$	−1.15522	+	3.28319i	−0.118523	+	0.336848i
$96$			13.1190i			1.33895i
$97$	11.7862	+	11.7862i	1.19671	+	1.19671i	0.975146	+	0.221564i	$0.0711162\pi$
$97$	11.7862	+	11.7862i	1.19671	+	1.19671i	0.221564	+	0.975146i	$0.428884\pi$
$98$	4.94820	+	4.94820i	0.499844	+	0.499844i
$99$		0			0
$100$	2.84408	−	3.54115i	0.284408	−	0.354115i
$101$		−	0.640188i		−	0.0637011i	−0.999493	−	0.0318506i	$-0.989860\pi$
$101$		−	0.640188i		−	0.0637011i	0.999493	−	0.0318506i	$-0.0101401\pi$
$102$	11.7816	+	11.7816i	1.16655	+	1.16655i
$103$	1.46091	−	1.46091i	0.143947	−	0.143947i	−0.631461	−	0.775408i	$-0.717544\pi$
$103$	1.46091	−	1.46091i	0.143947	−	0.143947i	0.775408	+	0.631461i	$0.217544\pi$
$104$			9.85932i			0.966786i
$105$	−3.26610	−	1.14920i	−0.318738	−	0.112151i
$106$		−	7.36035i		−	0.714900i
$107$	6.32008	−	6.32008i	0.610985	−	0.610985i	−0.332218	−	0.943203i	$-0.607797\pi$
$107$	6.32008	−	6.32008i	0.610985	−	0.610985i	0.943203	+	0.332218i	$0.107797\pi$
$108$	3.49290	−	3.49290i	0.336104	−	0.336104i
$109$	−4.48044			−0.429148			−0.214574	−	0.976708i	$-0.568836\pi$
$109$	−4.48044			−0.429148			−0.214574	+	0.976708i	$0.568836\pi$
$110$		0			0
$111$	2.69482			0.255781
$112$	0.528018	−	0.528018i	0.0498930	−	0.0498930i
$113$	1.01522	−	1.01522i	0.0955041	−	0.0955041i	−0.657741	−	0.753245i	$-0.728488\pi$
$113$	1.01522	−	1.01522i	0.0955041	−	0.0955041i	0.753245	+	0.657741i	$0.228488\pi$
$114$			4.57990i			0.428947i
$115$	1.09855	+	2.29129i	0.102440	+	0.213664i
$116$		−	3.86673i		−	0.359017i
$117$	11.3130	−	11.3130i	1.04588	−	1.04588i
$118$	4.99948	+	4.99948i	0.460239	+	0.460239i
$119$			3.11347i			0.285412i
$120$	6.35124	−	18.0505i	0.579786	−	1.64778i
$121$		0			0
$122$	6.79773	+	6.79773i	0.615438	+	0.615438i
$123$	−17.8159	−	17.8159i	−1.60640	−	1.60640i
$124$		−	1.49685i		−	0.134421i
$125$	−9.49742	+	5.89907i	−0.849475	+	0.527629i
$126$	−2.83267			−0.252354
$127$	−8.36069	+	8.36069i	−0.741891	+	0.741891i	−0.972942	−	0.231050i	$-0.925784\pi$
$127$	−8.36069	+	8.36069i	−0.741891	+	0.741891i	0.231050	+	0.972942i	$0.425784\pi$
$128$	−0.985443	−	0.985443i	−0.0871016	−	0.0871016i
$129$	10.1683			0.895272
$130$	2.51597	−	7.15050i	0.220665	−	0.627141i
$131$		−	7.94436i		−	0.694102i	−0.937846	−	0.347051i	$-0.887183\pi$
$131$		−	7.94436i		−	0.694102i	0.937846	−	0.347051i	$-0.112817\pi$
$132$		0			0
$133$	−0.605156	+	0.605156i	−0.0524737	+	0.0524737i
$134$	−3.87502			−0.334751
$135$	−10.9646	+	5.25692i	−0.943683	+	0.452444i
$136$	−17.2070			−1.47549
$137$	3.16421	+	3.16421i	0.270337	+	0.270337i	0.829236	−	0.558899i	$-0.188776\pi$
$137$	3.16421	+	3.16421i	0.270337	+	0.270337i	−0.558899	+	0.829236i	$0.688776\pi$
$138$	2.36434	+	2.36434i	0.201266	+	0.201266i
$139$	22.6161			1.91827			0.959137	−	0.282941i	$-0.0913101\pi$
$139$	22.6161			1.91827			0.959137	+	0.282941i	$0.0913101\pi$
$140$	1.00704	−	0.482819i	0.0851102	−	0.0408056i
$141$	−11.4668			−0.965679
$142$	5.06371	−	5.06371i	0.424937	−	0.424937i
$143$		0			0
$144$		−	6.69683i		−	0.558069i
$145$	−3.15928	+	8.97884i	−0.262364	+	0.745652i
$146$	−10.5418			−0.872441
$147$	13.3375	+	13.3375i	1.10005	+	1.10005i
$148$	−0.614633	+	0.614633i	−0.0505225	+	0.0505225i
$149$	14.7853			1.21126			0.605631	−	0.795745i	$-0.292921\pi$
$149$	14.7853			1.21126			0.605631	+	0.795745i	$0.292921\pi$
$150$	−9.21251	+	11.4705i	−0.752198	+	0.936558i
$151$		−	6.64532i		−	0.540788i	−0.962750	−	0.270394i	$-0.912846\pi$
$151$		−	6.64532i		−	0.540788i	0.962750	−	0.270394i	$-0.0871540\pi$
$152$	−3.34448	−	3.34448i	−0.271273	−	0.271273i
$153$	19.7440	+	19.7440i	1.59621	+	1.59621i
$154$		0			0
$155$	−1.22299	+	3.47579i	−0.0982327	+	0.279182i
$156$			8.30016i			0.664544i
$157$	−1.14150	−	1.14150i	−0.0911015	−	0.0911015i	0.660087	−	0.751189i	$-0.270519\pi$
$157$	−1.14150	−	1.14150i	−0.0911015	−	0.0911015i	−0.751189	+	0.660087i	$0.770519\pi$
$158$	3.07805	−	3.07805i	0.244876	−	0.244876i
$159$		−	19.8392i		−	1.57335i
$160$	4.50332	+	9.39279i	0.356019	+	0.742565i
$161$			0.624813i			0.0492422i
$162$	−0.385292	+	0.385292i	−0.0302714	+	0.0302714i
$163$	−7.16266	+	7.16266i	−0.561023	+	0.561023i	−0.929598	−	0.368575i	$-0.879846\pi$
$163$	−7.16266	+	7.16266i	−0.561023	+	0.561023i	0.368575	+	0.929598i	$0.379846\pi$
$164$	8.12686			0.634601
$165$		0			0
$166$	−11.8372			−0.918749
$167$	10.1243	−	10.1243i	0.783443	−	0.783443i	−0.196967	−	0.980410i	$-0.563109\pi$
$167$	10.1243	−	10.1243i	0.783443	−	0.783443i	0.980410	+	0.196967i	$0.0631093\pi$
$168$	3.32707	−	3.32707i	0.256689	−	0.256689i
$169$		−	2.47265i		−	0.190204i
$170$	12.4795	+	4.39101i	0.957131	+	0.336775i
$171$			7.67517i			0.586935i
$172$	−2.31919	+	2.31919i	−0.176836	+	0.176836i
$173$	−11.7162	−	11.7162i	−0.890766	−	0.890766i	0.103829	−	0.994595i	$-0.466890\pi$
$173$	−11.7162	−	11.7162i	−0.890766	−	0.890766i	−0.994595	+	0.103829i	$0.966890\pi$
$174$			12.5251i			0.949525i
$175$	−2.73290	+	0.298348i	−0.206588	+	0.0225530i
$176$		0			0
$177$	13.4757	+	13.4757i	1.01289	+	1.01289i
$178$	−2.69555	−	2.69555i	−0.202040	−	0.202040i
$179$			19.9864i			1.49386i	0.664905	+	0.746928i	$0.268472\pi$
$179$			19.9864i			1.49386i	−0.664905	+	0.746928i	$0.731528\pi$
$180$	3.32433	−	9.44790i	0.247781	−	0.704205i
$181$	−26.8748			−1.99758			−0.998792	−	0.0491306i	$-0.984355\pi$
$181$	−26.8748			−1.99758			−0.998792	+	0.0491306i	$0.984355\pi$
$182$	1.31798	−	1.31798i	0.0976950	−	0.0976950i
$183$	18.3227	+	18.3227i	1.35445	+	1.35445i
$184$	−3.45312			−0.254567
$185$	1.92940	−	0.925042i	0.141853	−	0.0680105i
$186$			4.84857i			0.355515i
$187$		0			0
$188$	2.61534	−	2.61534i	0.190743	−	0.190743i
$189$	−2.98995			−0.217487
$190$	1.57213	+	3.27906i	0.114054	+	0.237888i
$191$	12.9405			0.936345			0.468172	−	0.883637i	$-0.344913\pi$
$191$	12.9405			0.936345			0.468172	+	0.883637i	$0.344913\pi$
$192$	15.1012	+	15.1012i	1.08984	+	1.08984i
$193$	−5.30182	−	5.30182i	−0.381633	−	0.381633i	0.490057	−	0.871690i	$-0.336976\pi$
$193$	−5.30182	−	5.30182i	−0.381633	−	0.381633i	−0.871690	+	0.490057i	$0.836976\pi$
$194$	17.4151			1.25033
$195$	6.78158	−	19.2736i	0.485639	−	1.38021i
$196$	−6.08399			−0.434571
$197$	−2.73095	+	2.73095i	−0.194572	+	0.194572i	−0.797668	−	0.603096i	$-0.793933\pi$
$197$	−2.73095	+	2.73095i	−0.194572	+	0.194572i	0.603096	+	0.797668i	$0.293933\pi$
$198$		0			0
$199$			12.3835i			0.877842i	0.898526	+	0.438921i	$0.144639\pi$
$199$			12.3835i			0.877842i	−0.898526	+	0.438921i	$0.855361\pi$
$200$	−1.64886	−	15.1037i	−0.116592	−	1.06800i
$201$	−10.4448			−0.736719
$202$	−0.472966	−	0.472966i	−0.0332778	−	0.0332778i
$203$	−1.65498	+	1.65498i	−0.116157	+	0.116157i
$204$	−14.4859			−1.01422
$205$	−18.8712	−	6.63999i	−1.31802	−	0.463757i
$206$		−	2.15861i		−	0.150398i
$207$	3.96224	+	3.96224i	0.275395	+	0.275395i
$208$	3.11589	+	3.11589i	0.216048	+	0.216048i
$209$		0			0
$210$	−3.26199	+	1.56394i	−0.225099	+	0.107922i
$211$			13.5566i			0.933276i	0.884448	+	0.466638i	$0.154535\pi$
$211$			13.5566i			0.933276i	−0.884448	+	0.466638i	$0.845465\pi$
$212$	4.52491	+	4.52491i	0.310772	+	0.310772i
$213$	13.6488	−	13.6488i	0.935201	−	0.935201i
$214$		−	9.33845i		−	0.638363i
$215$	7.28019	−	3.49045i	0.496505	−	0.238046i
$216$		−	16.5244i		−	1.12434i
$217$	−0.640656	+	0.640656i	−0.0434906	+	0.0434906i
$218$	−3.31011	+	3.31011i	−0.224189	+	0.224189i
$219$	−28.4144			−1.92007
$220$		0			0
$221$	−18.3729			−1.23590
$222$	1.99092	−	1.99092i	0.133621	−	0.133621i
$223$	3.70555	−	3.70555i	0.248142	−	0.248142i	−0.572066	−	0.820208i	$-0.693858\pi$
$223$	3.70555	−	3.70555i	0.248142	−	0.248142i	0.820208	+	0.572066i	$0.193858\pi$
$224$			2.56133i			0.171136i
$225$	−15.4387	+	19.2226i	−1.02924	+	1.28151i
$226$		−	1.50008i		−	0.0997836i
$227$	−10.6568	+	10.6568i	−0.707319	+	0.707319i	−0.965971	−	0.258652i	$-0.916722\pi$
$227$	−10.6568	+	10.6568i	−0.707319	+	0.707319i	0.258652	+	0.965971i	$0.416722\pi$
$228$	−2.81558	−	2.81558i	−0.186466	−	0.186466i
$229$		−	14.8673i		−	0.982456i	−0.871031	−	0.491228i	$-0.836548\pi$
$229$		−	14.8673i		−	0.982456i	0.871031	−	0.491228i	$-0.163452\pi$
$230$	2.50438	+	0.881190i	0.165134	+	0.0581040i
$231$		0			0
$232$	−9.14646	−	9.14646i	−0.600494	−	0.600494i
$233$	3.91668	+	3.91668i	0.256590	+	0.256590i	0.823666	−	0.567076i	$-0.191925\pi$
$233$	3.91668	+	3.91668i	0.256590	+	0.256590i	−0.567076	+	0.823666i	$0.691925\pi$
$234$		−	16.7159i		−	1.09275i
$235$	−8.20985	+	3.93617i	−0.535552	+	0.256767i
$236$	−6.14704			−0.400138
$237$	8.29662	−	8.29662i	0.538923	−	0.538923i
$238$	2.30021	+	2.30021i	0.149101	+	0.149101i
$239$	−24.7194			−1.59897			−0.799484	−	0.600687i	$-0.794894\pi$
$239$	−24.7194			−1.59897			−0.799484	+	0.600687i	$0.794894\pi$
$240$	−3.69738	−	7.71181i	−0.238665	−	0.497795i
$241$		−	5.19700i		−	0.334768i	−0.985892	−	0.167384i	$-0.946468\pi$
$241$		−	5.19700i		−	0.334768i	0.985892	−	0.167384i	$-0.0535320\pi$
$242$		0			0
$243$	10.4972	−	10.4972i	0.673394	−	0.673394i
$244$	−8.35806			−0.535070
$245$	14.1275	+	4.97088i	0.902571	+	0.317578i
$246$	−26.3245			−1.67839
$247$	−3.57109	−	3.57109i	−0.227223	−	0.227223i
$248$	−3.54067	−	3.54067i	−0.224833	−	0.224833i
$249$	−31.9063			−2.02198
$250$	−2.65843	+	11.3748i	−0.168134	+	0.719406i
$251$	12.4867			0.788153			0.394076	−	0.919078i	$-0.371065\pi$
$251$	12.4867			0.788153			0.394076	+	0.919078i	$0.371065\pi$
$252$	1.74143	−	1.74143i	0.109700	−	0.109700i
$253$		0			0
$254$			12.3536i			0.775136i
$255$	33.6373	+	11.8356i	2.10645	+	0.741174i
$256$	−16.6229			−1.03893
$257$	−9.01937	−	9.01937i	−0.562613	−	0.562613i	0.367436	−	0.930049i	$-0.380236\pi$
$257$	−9.01937	−	9.01937i	−0.562613	−	0.562613i	−0.930049	+	0.367436i	$0.880236\pi$
$258$	7.51229	−	7.51229i	0.467695	−	0.467695i
$259$	0.526131			0.0326922
$260$	2.84916	+	5.94264i	0.176698	+	0.368547i
$261$			20.9900i			1.29925i
$262$	−5.86923	−	5.86923i	−0.362602	−	0.362602i
$263$	−13.6161	−	13.6161i	−0.839605	−	0.839605i	0.149202	−	0.988807i	$-0.452330\pi$
$263$	−13.6161	−	13.6161i	−0.839605	−	0.839605i	−0.988807	+	0.149202i	$0.952330\pi$
$264$		0			0
$265$	−6.81012	−	14.2042i	−0.418343	−	0.872557i
$266$			0.894169i			0.0548250i
$267$	−7.26564	−	7.26564i	−0.444650	−	0.444650i
$268$	2.38224	−	2.38224i	0.145519	−	0.145519i
$269$		−	17.3960i		−	1.06065i	−0.847794	−	0.530326i	$-0.822070\pi$
$269$		−	17.3960i		−	1.06065i	0.847794	−	0.530326i	$-0.177930\pi$
$270$	−4.21680	+	11.9843i	−0.256626	+	0.729344i
$271$		−	31.7726i		−	1.93005i	−0.262162	−	0.965024i	$-0.584436\pi$
$271$		−	31.7726i		−	1.93005i	0.262162	−	0.965024i	$-0.415564\pi$
$272$	−5.43803	+	5.43803i	−0.329729	+	0.329729i
$273$	3.55250	−	3.55250i	0.215007	−	0.215007i
$274$	4.67539			0.282451
$275$		0			0
$276$	−2.90704			−0.174983
$277$	−5.13335	+	5.13335i	−0.308433	+	0.308433i	−0.844302	−	0.535868i	$-0.819984\pi$
$277$	−5.13335	+	5.13335i	−0.308433	+	0.308433i	0.535868	+	0.844302i	$0.319984\pi$
$278$	16.7086	−	16.7086i	1.00212	−	1.00212i
$279$			8.12542i			0.486456i
$280$	1.24000	−	3.52414i	0.0741042	−	0.210608i
$281$			5.54437i			0.330749i	0.986231	+	0.165375i	$0.0528833\pi$
$281$			5.54437i			0.330749i	−0.986231	+	0.165375i	$0.947117\pi$
$282$	−8.47158	+	8.47158i	−0.504476	+	0.504476i
$283$	9.77253	+	9.77253i	0.580916	+	0.580916i	0.935155	−	0.354239i	$-0.115260\pi$
$283$	9.77253	+	9.77253i	0.580916	+	0.580916i	−0.354239	+	0.935155i	$0.615260\pi$
$284$			6.22602i			0.369446i
$285$	4.23753	+	8.83842i	0.251010	+	0.523543i
$286$		0			0
$287$	−3.47833	−	3.47833i	−0.205319	−	0.205319i
$288$	16.2426	+	16.2426i	0.957104	+	0.957104i
$289$		−	15.0655i		−	0.886206i
$290$	4.29944	+	8.96755i	0.252472	+	0.526593i
$291$	46.9410			2.75173
$292$	6.48073	−	6.48073i	0.379256	−	0.379256i
$293$	−4.80792	−	4.80792i	−0.280882	−	0.280882i	0.552579	−	0.833461i	$-0.313644\pi$
$293$	−4.80792	−	4.80792i	−0.280882	−	0.280882i	−0.833461	+	0.552579i	$0.813644\pi$
$294$	19.7072			1.14935
$295$	14.2739	+	5.02239i	0.831057	+	0.292415i
$296$			2.90773i			0.169009i
$297$		0			0
$298$	10.9233	−	10.9233i	0.632770	−	0.632770i
$299$	−3.68709			−0.213230
$300$	−1.38811	−	12.7152i	−0.0801425	−	0.734114i
$301$	1.98524			0.114427
$302$	−4.90951	−	4.90951i	−0.282511	−	0.282511i
$303$	−1.27484	−	1.27484i	−0.0732376	−	0.0732376i
$304$	−2.11394			−0.121243
$305$	19.4080	+	6.82888i	1.11130	+	0.391021i
$306$	29.1735			1.66774
$307$	−5.54209	+	5.54209i	−0.316304	+	0.316304i	−0.847346	−	0.531042i	$-0.821801\pi$
$307$	−5.54209	+	5.54209i	−0.316304	+	0.316304i	0.531042	+	0.847346i	$0.321801\pi$
$308$		0			0
$309$		−	5.81836i		−	0.330995i
$310$	1.66435	+	3.47142i	0.0945289	+	0.197163i
$311$	16.5909			0.940781			0.470391	−	0.882458i	$-0.344113\pi$
$311$	16.5909			0.940781			0.470391	+	0.882458i	$0.344113\pi$
$312$	19.6334	+	19.6334i	1.11152	+	1.11152i
$313$	6.73408	−	6.73408i	0.380633	−	0.380633i	−0.490697	−	0.871330i	$-0.663258\pi$
$313$	6.73408	−	6.73408i	0.380633	−	0.380633i	0.871330	+	0.490697i	$0.163258\pi$
$314$	−1.68666			−0.0951838
$315$	−5.46656	+	2.62091i	−0.308006	+	0.147672i
$316$			3.78457i			0.212899i
$317$	−17.0535	−	17.0535i	−0.957822	−	0.957822i	0.0413235	−	0.999146i	$-0.486843\pi$
$317$	−17.0535	−	17.0535i	−0.957822	−	0.957822i	−0.999146	+	0.0413235i	$0.986843\pi$
$318$	−14.6570	−	14.6570i	−0.821926	−	0.821926i
$319$		0			0
$320$	15.9957	+	5.62823i	0.894187	+	0.314628i
$321$		−	25.1710i		−	1.40491i
$322$	0.461607	+	0.461607i	0.0257244	+	0.0257244i
$323$	6.23247	−	6.23247i	0.346784	−	0.346784i
$324$		−	0.473730i		−	0.0263183i
$325$	−1.76058	−	16.1271i	−0.0976595	−	0.894572i
$326$			10.5834i			0.586163i
$327$	−8.92213	+	8.92213i	−0.493395	+	0.493395i
$328$	19.2234	−	19.2234i	1.06144	−	1.06144i
$329$	−2.23875			−0.123426
$330$		0			0
$331$	12.5641			0.690587			0.345294	−	0.938495i	$-0.387779\pi$
$331$	12.5641			0.690587			0.345294	+	0.938495i	$0.387779\pi$
$332$	7.27716	−	7.27716i	0.399386	−	0.399386i
$333$	3.33645	−	3.33645i	0.182836	−	0.182836i
$334$		−	14.9595i		−	0.818549i
$335$	−7.47813	+	3.58535i	−0.408574	+	0.195888i
$336$		−	2.10294i		−	0.114725i
$337$	11.6500	−	11.6500i	0.634614	−	0.634614i	−0.314608	−	0.949222i	$-0.601873\pi$
$337$	11.6500	−	11.6500i	0.634614	−	0.634614i	0.949222	+	0.314608i	$0.101873\pi$
$338$	−1.82677	−	1.82677i	−0.0993633	−	0.0993633i
$339$		−	4.04333i		−	0.219604i
$340$	−10.3714	+	4.97252i	−0.562470	+	0.269673i
$341$		0			0
$342$	5.67035	+	5.67035i	0.306618	+	0.306618i
$343$	5.32548	+	5.32548i	0.287549	+	0.287549i
$344$			10.9717i			0.591555i
$345$	6.75036	+	2.37517i	0.363427	+	0.127875i
$346$	−17.3117			−0.930681
$347$	10.0692	−	10.0692i	0.540541	−	0.540541i	−0.383147	−	0.923687i	$-0.625160\pi$
$347$	10.0692	−	10.0692i	0.540541	−	0.540541i	0.923687	+	0.383147i	$0.125160\pi$
$348$	−7.70003	−	7.70003i	−0.412765	−	0.412765i
$349$	−16.6137			−0.889311			−0.444655	−	0.895702i	$-0.646674\pi$
$349$	−16.6137			−0.889311			−0.444655	+	0.895702i	$0.646674\pi$
$350$	−1.79863	+	2.23946i	−0.0961407	+	0.119704i
$351$		−	17.6440i		−	0.941767i
$352$		0			0
$353$	7.78082	−	7.78082i	0.414131	−	0.414131i	−0.469044	−	0.883175i	$-0.655401\pi$
$353$	7.78082	−	7.78082i	0.414131	−	0.414131i	0.883175	+	0.469044i	$0.155401\pi$
$354$	19.9114			1.05828
$355$	5.08692	−	14.4573i	0.269986	−	0.767312i
$356$	3.31428			0.175657
$357$	6.20002	+	6.20002i	0.328140	+	0.328140i
$358$	14.7658	+	14.7658i	0.780397	+	0.780397i
$359$	−13.1797			−0.695601			−0.347800	−	0.937569i	$-0.613071\pi$
$359$	−13.1797			−0.695601			−0.347800	+	0.937569i	$0.613071\pi$
$360$	−14.4848	−	30.2117i	−0.763417	−	1.59230i
$361$	−16.5772			−0.872486
$362$	−19.8549	+	19.8549i	−1.04355	+	1.04355i
$363$		0			0
$364$			1.62050i			0.0849374i
$365$	−20.3438	+	9.75370i	−1.06484	+	0.510532i
$366$	27.0734			1.41515
$367$	−19.6593	−	19.6593i	−1.02621	−	1.02621i	−0.999647	−	0.0265582i	$-0.991545\pi$
$367$	−19.6593	−	19.6593i	−1.02621	−	1.02621i	−0.0265582	−	0.999647i	$-0.508455\pi$
$368$	−1.09131	+	1.09131i	−0.0568882	+	0.0568882i
$369$	−44.1155			−2.29656
$370$	0.742015	−	2.10884i	0.0385755	−	0.109634i
$371$		−	3.87335i		−	0.201094i
$372$	−2.98075	−	2.98075i	−0.154545	−	0.154545i
$373$	6.02155	+	6.02155i	0.311784	+	0.311784i	0.845600	−	0.533816i	$-0.179243\pi$
$373$	6.02155	+	6.02155i	0.311784	+	0.311784i	−0.533816	+	0.845600i	$0.679243\pi$
$374$		0			0
$375$	−7.16558	+	30.6598i	−0.370029	+	1.58327i
$376$		−	12.3728i		−	0.638076i
$377$	−9.76619	−	9.76619i	−0.502984	−	0.502984i
$378$	−2.20895	+	2.20895i	−0.113616	+	0.113616i
$379$			4.35511i			0.223707i	0.993725	+	0.111853i	$0.0356787\pi$
$379$			4.35511i			0.223707i	−0.993725	+	0.111853i	$0.964321\pi$
$380$	−2.98235	−	1.04937i	−0.152992	−	0.0538314i
$381$			33.2982i			1.70592i
$382$	9.56037	−	9.56037i	0.489151	−	0.489151i
$383$	−4.79725	+	4.79725i	−0.245128	+	0.245128i	−0.818968	−	0.573840i	$-0.805453\pi$
$383$	−4.79725	+	4.79725i	−0.245128	+	0.245128i	0.573840	+	0.818968i	$0.305453\pi$
$384$	−3.92473			−0.200283
$385$		0			0
$386$	−7.83388			−0.398734
$387$	12.5894	−	12.5894i	0.639953	−	0.639953i
$388$	−10.7063	+	10.7063i	−0.543529	+	0.543529i
$389$		−	24.6225i		−	1.24841i	−0.781261	−	0.624205i	$-0.785423\pi$
$389$		−	24.6225i		−	1.24841i	0.781261	−	0.624205i	$-0.214577\pi$
$390$	−9.22899	−	19.2493i	−0.467328	−	0.974728i
$391$		−	6.43492i		−	0.325428i
$392$	−14.3912	+	14.3912i	−0.726866	+	0.726866i
$393$	−15.8200	−	15.8200i	−0.798014	−	0.798014i
$394$			4.03520i			0.203291i
$395$	3.09215	−	8.78805i	0.155583	−	0.442175i
$396$		0			0
$397$	−20.7876	−	20.7876i	−1.04330	−	1.04330i	−0.999019	−	0.0442826i	$-0.985900\pi$
$397$	−20.7876	−	20.7876i	−1.04330	−	1.04330i	−0.0442826	−	0.999019i	$-0.514100\pi$
$398$	9.14882	+	9.14882i	0.458589	+	0.458589i
$399$			2.41016i			0.120659i
$400$	−5.29441	−	4.25221i	−0.264720	−	0.212611i
$401$	24.7645			1.23668			0.618339	−	0.785911i	$-0.287806\pi$
$401$	24.7645			1.23668			0.618339	+	0.785911i	$0.287806\pi$
$402$	−7.71654	+	7.71654i	−0.384866	+	0.384866i
$403$	−3.78058	−	3.78058i	−0.188324	−	0.188324i
$404$	0.581529			0.0289321
$405$	−0.387058	+	1.10004i	−0.0192330	+	0.0546612i
$406$			2.44537i			0.121362i
$407$		0			0
$408$	−34.2653	+	34.2653i	−1.69638	+	1.69638i
$409$	10.0138			0.495149			0.247574	−	0.968869i	$-0.420367\pi$
$409$	10.0138			0.495149			0.247574	+	0.968869i	$0.420367\pi$
$410$	−18.8474	+	9.03630i	−0.930809	+	0.446271i
$411$	12.6021			0.621616
$412$	1.32705	+	1.32705i	0.0653789	+	0.0653789i
$413$	2.63096	+	2.63096i	0.129461	+	0.129461i
$414$	5.85455			0.287735
$415$	−22.8438	+	10.9524i	−1.12136	+	0.537630i
$416$	−15.1146			−0.741057
$417$	45.0367	−	45.0367i	2.20545	−	2.20545i
$418$		0			0
$419$			7.65743i			0.374090i	0.982351	+	0.187045i	$0.0598910\pi$
$419$			7.65743i			0.374090i	−0.982351	+	0.187045i	$0.940109\pi$
$420$	1.04391	−	2.96683i	0.0509374	−	0.144766i
$421$	−21.6723			−1.05624			−0.528121	−	0.849169i	$-0.677103\pi$
$421$	−21.6723			−1.05624			−0.528121	+	0.849169i	$0.677103\pi$
$422$	10.0155	+	10.0155i	0.487548	+	0.487548i
$423$	−14.1970	+	14.1970i	−0.690281	+	0.690281i
$424$	21.4066			1.03960
$425$	28.1460	−	3.07267i	1.36528	−	0.149046i
$426$		−	20.1673i		−	0.977108i
$427$	3.57728	+	3.57728i	0.173117	+	0.173117i
$428$	5.74098	+	5.74098i	0.277501	+	0.277501i
$429$		0			0
$430$	2.79983	−	7.95726i	0.135020	−	0.383733i
$431$			28.4797i			1.37182i	0.727688	+	0.685909i	$0.240595\pi$
$431$			28.4797i			1.37182i	−0.727688	+	0.685909i	$0.759405\pi$
$432$	−5.22227	−	5.22227i	−0.251257	−	0.251257i
$433$	−8.81872	+	8.81872i	−0.423801	+	0.423801i	−0.886510	−	0.462709i	$-0.846877\pi$
$433$	−8.81872	+	8.81872i	−0.423801	+	0.423801i	0.462709	+	0.886510i	$0.346877\pi$
$434$			0.946624i			0.0454394i
$435$	11.5888	+	24.1713i	0.555640	+	1.15892i
$436$		−	4.06990i		−	0.194913i
$437$	1.25073	−	1.25073i	0.0598307	−	0.0598307i
$438$	−20.9923	+	20.9923i	−1.00305	+	1.00305i
$439$	16.9147			0.807294			0.403647	−	0.914915i	$-0.367742\pi$
$439$	16.9147			0.807294			0.403647	+	0.914915i	$0.367742\pi$
$440$		0			0
$441$	33.0261			1.57267
$442$	−13.5738	+	13.5738i	−0.645639	+	0.645639i
$443$	−7.82203	+	7.82203i	−0.371636	+	0.371636i	−0.868073	−	0.496437i	$-0.834641\pi$
$443$	−7.82203	+	7.82203i	−0.371636	+	0.371636i	0.496437	+	0.868073i	$0.334641\pi$
$444$			2.44790i			0.116172i
$445$	−7.69601	−	2.70791i	−0.364826	−	0.128367i
$446$		−	5.47527i		−	0.259262i
$447$	29.4428	−	29.4428i	1.39260	−	1.39260i
$448$	2.94832	+	2.94832i	0.139295	+	0.139295i
$449$		−	4.51870i		−	0.213251i	−0.994299	−	0.106625i	$-0.965995\pi$
$449$		−	4.51870i		−	0.213251i	0.994299	−	0.106625i	$-0.0340045\pi$
$450$	2.79554	+	25.6075i	0.131783	+	1.20715i
$451$		0			0
$452$	0.922199	+	0.922199i	0.0433766	+	0.0433766i
$453$	−13.2332	−	13.2332i	−0.621748	−	0.621748i
$454$			15.7464i			0.739014i
$455$	1.32402	−	3.76292i	0.0620709	−	0.176409i
$456$	−13.3201			−0.623769
$457$	−23.0703	+	23.0703i	−1.07918	+	1.07918i	−0.0825990	+	0.996583i	$0.526322\pi$
$457$	−23.0703	+	23.0703i	−1.07918	+	1.07918i	−0.996583	+	0.0825990i	$0.973678\pi$
$458$	−10.9838	−	10.9838i	−0.513240	−	0.513240i
$459$	30.7933			1.43731
$460$	−2.08134	+	0.997888i	−0.0970431	+	0.0465268i
$461$			23.4279i			1.09114i	0.838064	+	0.545572i	$0.183688\pi$
$461$			23.4279i			1.09114i	−0.838064	+	0.545572i	$0.816312\pi$
$462$		0			0
$463$	−29.2123	+	29.2123i	−1.35761	+	1.35761i	−0.480762	+	0.876851i	$0.659640\pi$
$463$	−29.2123	+	29.2123i	−1.35761	+	1.35761i	−0.876851	+	0.480762i	$0.840360\pi$
$464$	−5.78120			−0.268385
$465$	4.48612	+	9.35691i	0.208039	+	0.433917i
$466$	5.78722			0.268088
$467$	−20.0867	−	20.0867i	−0.929502	−	0.929502i	0.0681714	−	0.997674i	$-0.478284\pi$
$467$	−20.0867	−	20.0867i	−0.929502	−	0.929502i	−0.997674	+	0.0681714i	$0.978284\pi$
$468$	10.2764	+	10.2764i	0.475026	+	0.475026i
$469$	−2.03922			−0.0941622
$470$	−3.15736	+	8.97338i	−0.145638	+	0.413911i
$471$	−4.54625			−0.209480
$472$	−14.5403	+	14.5403i	−0.669273	+	0.669273i
$473$		0			0
$474$		−	12.2590i		−	0.563072i
$475$	6.06787	+	4.87342i	0.278413	+	0.223608i
$476$	−2.82819			−0.129630
$477$	−24.5628	−	24.5628i	−1.12465	−	1.12465i
$478$	−18.2625	+	18.2625i	−0.835309	+	0.835309i
$479$	31.3752			1.43357			0.716785	−	0.697294i	$-0.245613\pi$
$479$	31.3752			1.43357			0.716785	+	0.697294i	$0.245613\pi$
$480$	27.6720	+	9.73665i	1.26305	+	0.444415i
$481$			3.10475i			0.141565i
$482$	−3.83950	−	3.83950i	−0.174885	−	0.174885i
$483$	1.24422	+	1.24422i	0.0566141	+	0.0566141i
$484$		0			0
$485$	33.6082	−	16.1133i	1.52607	−	0.731666i
$486$		−	15.5105i		−	0.703568i
$487$	4.85998	+	4.85998i	0.220227	+	0.220227i	0.808594	−	0.588367i	$-0.200229\pi$
$487$	4.85998	+	4.85998i	0.220227	+	0.220227i	−0.588367	+	0.808594i	$0.700229\pi$
$488$	−19.7703	+	19.7703i	−0.894961	+	0.894961i
$489$			28.5268i			1.29002i
$490$	14.1097	−	6.76483i	0.637412	−	0.305604i
$491$			14.7298i			0.664745i	0.943148	+	0.332373i	$0.107849\pi$
$491$			14.7298i			0.664745i	−0.943148	+	0.332373i	$0.892151\pi$
$492$	16.1834	−	16.1834i	0.729605	−	0.729605i
$493$	17.0445	−	17.0445i	0.767646	−	0.767646i
$494$	−5.27658			−0.237405
$495$		0			0
$496$	−2.23795			−0.100487
$497$	2.66476	−	2.66476i	0.119531	−	0.119531i
$498$	−23.5721	+	23.5721i	−1.05629	+	1.05629i
$499$			26.4740i			1.18514i	0.805520	+	0.592569i	$0.201886\pi$
$499$			26.4740i			1.18514i	−0.805520	+	0.592569i	$0.798114\pi$
$500$	−5.35855	−	8.62719i	−0.239642	−	0.385820i
$501$		−	40.3221i		−	1.80146i
$502$	9.22507	−	9.22507i	0.411735	−	0.411735i
$503$	21.5234	+	21.5234i	0.959681	+	0.959681i	0.999218	−	0.0395367i	$-0.0125882\pi$
$503$	21.5234	+	21.5234i	0.959681	+	0.959681i	−0.0395367	+	0.999218i	$0.512588\pi$
$504$		−	8.23845i		−	0.366970i
$505$	−1.35035	−	0.475134i	−0.0600899	−	0.0211432i
$506$		0			0
$507$	−4.92391	−	4.92391i	−0.218678	−	0.218678i
$508$	−7.59462	−	7.59462i	−0.336957	−	0.336957i
$509$		−	4.05788i		−	0.179862i	−0.995948	−	0.0899312i	$-0.971335\pi$
$509$		−	4.05788i		−	0.179862i	0.995948	−	0.0899312i	$-0.0286647\pi$
$510$	33.5951	−	16.1070i	1.48761	−	0.713228i
$511$	−5.54755			−0.245409
$512$	−10.3100	+	10.3100i	−0.455640	+	0.455640i
$513$	5.98519	+	5.98519i	0.264253	+	0.264253i
$514$	−13.3269			−0.587824
$515$	−1.99725	−	4.16575i	−0.0880092	−	0.183565i
$516$			9.23663i			0.406620i
$517$		0			0
$518$	0.388701	−	0.388701i	0.0170786	−	0.0170786i
$519$	−46.6621			−2.04824
$520$	20.7963	+	7.31737i	0.911979	+	0.320888i
$521$	17.5030			0.766820			0.383410	−	0.923578i	$-0.374750\pi$
$521$	17.5030			0.766820			0.383410	+	0.923578i	$0.374750\pi$
$522$	15.5073	+	15.5073i	0.678734	+	0.678734i
$523$	−12.2865	−	12.2865i	−0.537253	−	0.537253i	0.385468	−	0.922721i	$-0.374040\pi$
$523$	−12.2865	−	12.2865i	−0.537253	−	0.537253i	−0.922721	+	0.385468i	$0.874040\pi$
$524$	7.21643			0.315251
$525$	−4.84805	+	6.03628i	−0.211586	+	0.263445i
$526$	−20.1190			−0.877228
$527$	6.59808	−	6.59808i	0.287417	−	0.287417i
$528$		0			0
$529$			21.7086i			0.943854i
$530$	−15.5252	−	5.46269i	−0.674373	−	0.237284i
$531$	33.3683			1.44806
$532$	−0.549706	−	0.549706i	−0.0238328	−	0.0238328i
$533$	20.5260	−	20.5260i	0.889078	−	0.889078i
$534$	−10.7356			−0.464575
$535$	−8.64035	−	18.0216i	−0.373555	−	0.779141i
$536$		−	11.2700i		−	0.486790i
$537$	39.8000	+	39.8000i	1.71750	+	1.71750i
$538$	−12.8520	−	12.8520i	−0.554090	−	0.554090i
$539$		0			0
$540$	−4.77524	−	9.95994i	−0.205494	−	0.428608i
$541$		−	36.8348i		−	1.58365i	−0.610748	−	0.791825i	$-0.709131\pi$
$541$		−	36.8348i		−	1.58365i	0.610748	−	0.791825i	$-0.290869\pi$
$542$	−23.4733	−	23.4733i	−1.00827	−	1.00827i
$543$	−53.5171	+	53.5171i	−2.29664	+	2.29664i
$544$		−	26.3789i		−	1.13099i
$545$	−3.32528	+	9.45062i	−0.142439	+	0.404820i
$546$		−	5.24912i		−	0.224641i
$547$	−6.12699	+	6.12699i	−0.261971	+	0.261971i	−0.825855	−	0.563883i	$-0.809307\pi$
$547$	−6.12699	+	6.12699i	−0.261971	+	0.261971i	0.563883	+	0.825855i	$0.309307\pi$
$548$	−2.87428	+	2.87428i	−0.122783	+	0.122783i
$549$	45.3705			1.93637
$550$		0			0
$551$	6.62577			0.282267
$552$	−6.87637	+	6.87637i	−0.292678	+	0.292678i
$553$	1.61981	−	1.61981i	0.0688814	−	0.0688814i
$554$			7.58496i			0.322254i
$555$	2.00004	−	5.68421i	0.0848969	−	0.241281i
$556$			20.5438i			0.871253i
$557$	−5.92322	+	5.92322i	−0.250975	+	0.250975i	−0.821370	−	0.570395i	$-0.806790\pi$
$557$	−5.92322	+	5.92322i	−0.250975	+	0.250975i	0.570395	+	0.821370i	$0.306790\pi$
$558$	6.00299	+	6.00299i	0.254127	+	0.254127i
$559$			11.7151i			0.495496i
$560$	−0.721868	−	1.50563i	−0.0305045	−	0.0636247i
$561$		0			0
$562$	4.09614	+	4.09614i	0.172785	+	0.172785i
$563$	21.3147	+	21.3147i	0.898306	+	0.898306i	0.995286	−	0.0969801i	$-0.0309183\pi$
$563$	21.3147	+	21.3147i	0.898306	+	0.898306i	−0.0969801	+	0.995286i	$0.530918\pi$
$564$		−	10.4161i		−	0.438598i
$565$	−1.38794	−	2.89489i	−0.0583910	−	0.121789i
$566$	14.4397			0.606947
$567$	−0.202758	+	0.202758i	−0.00851505	+	0.00851505i
$568$	14.7272	+	14.7272i	0.617938	+	0.617938i
$569$	27.1066			1.13637			0.568184	−	0.822902i	$-0.307646\pi$
$569$	27.1066			1.13637			0.568184	+	0.822902i	$0.307646\pi$
$570$	9.66042	+	3.39910i	0.404630	+	0.142373i
$571$		−	6.30511i		−	0.263861i	−0.991259	−	0.131930i	$-0.957883\pi$
$571$		−	6.30511i		−	0.263861i	0.991259	−	0.131930i	$-0.0421175\pi$
$572$		0			0
$573$	25.7692	−	25.7692i	1.07652	−	1.07652i
$574$	−5.13952			−0.214519
$575$	5.64835	−	0.616625i	0.235552	−	0.0257150i
$576$	37.3935			1.55806
$577$	16.8156	+	16.8156i	0.700044	+	0.700044i	0.964420	−	0.264376i	$-0.0851659\pi$
$577$	16.8156	+	16.8156i	0.700044	+	0.700044i	−0.264376	+	0.964420i	$0.585166\pi$
$578$	−11.1303	−	11.1303i	−0.462958	−	0.462958i
$579$	−21.1156			−0.877533
$580$	−8.15612	−	2.86980i	−0.338665	−	0.119162i
$581$	−6.22930			−0.258435
$582$	34.6797	−	34.6797i	1.43752	−	1.43752i
$583$		0			0
$584$		−	30.6593i		−	1.26869i
$585$	−15.4663	−	32.2587i	−0.639452	−	1.33373i
$586$	−7.10411			−0.293468
$587$	−7.71726	−	7.71726i	−0.318526	−	0.318526i	0.529675	−	0.848201i	$-0.322314\pi$
$587$	−7.71726	−	7.71726i	−0.318526	−	0.318526i	−0.848201	+	0.529675i	$0.822314\pi$
$588$	−12.1154	+	12.1154i	−0.499629	+	0.499629i
$589$	2.56490			0.105685
$590$	14.2559	−	6.83493i	0.586907	−	0.281389i
$591$			10.8765i			0.447401i
$592$	0.918945	+	0.918945i	0.0377684	+	0.0377684i
$593$	−26.5198	−	26.5198i	−1.08904	−	1.08904i	−0.995628	−	0.0934112i	$-0.970223\pi$
$593$	−26.5198	−	26.5198i	−1.08904	−	1.08904i	−0.0934112	−	0.995628i	$-0.529777\pi$
$594$		0			0
$595$	6.56727	+	2.31075i	0.269232	+	0.0947316i
$596$			13.4306i			0.550138i
$597$	24.6599	+	24.6599i	1.00926	+	1.00926i
$598$	−2.72399	+	2.72399i	−0.111392	+	0.111392i
$599$			44.1916i			1.80562i	0.430038	+	0.902811i	$0.358500\pi$
$599$			44.1916i			1.80562i	−0.430038	+	0.902811i	$0.641500\pi$
$600$	−33.3603	−	26.7934i	−1.36193	−	1.09384i
$601$			37.1505i			1.51540i	0.652602	+	0.757701i	$0.273677\pi$
$601$			37.1505i			1.51540i	−0.652602	+	0.757701i	$0.726323\pi$
$602$	1.46668	−	1.46668i	0.0597774	−	0.0597774i
$603$	−12.9316	+	12.9316i	−0.526617	+	0.526617i
$604$	6.03642			0.245618
$605$		0			0
$606$	−1.88368			−0.0765194
$607$	−31.9386	+	31.9386i	−1.29635	+	1.29635i	−0.365558	+	0.930789i	$0.619122\pi$
$607$	−31.9386	+	31.9386i	−1.29635	+	1.29635i	−0.930789	+	0.365558i	$0.880878\pi$
$608$	5.12719	−	5.12719i	0.207935	−	0.207935i
$609$			6.59128i			0.267092i
$610$	19.3836	−	9.29337i	0.784820	−	0.376278i
$611$		−	13.2111i		−	0.534464i
$612$	−17.9349	+	17.9349i	−0.724976	+	0.724976i
$613$	9.96870	+	9.96870i	0.402632	+	0.402632i	0.879159	−	0.476528i	$-0.158105\pi$
$613$	9.96870	+	9.96870i	0.402632	+	0.402632i	−0.476528	+	0.879159i	$0.658105\pi$
$614$			8.18890i			0.330477i
$615$	−50.8017	+	24.3566i	−2.04852	+	0.982152i
$616$		0			0
$617$	−17.9495	−	17.9495i	−0.722618	−	0.722618i	0.246520	−	0.969138i	$-0.420713\pi$
$617$	−17.9495	−	17.9495i	−0.722618	−	0.722618i	−0.969138	+	0.246520i	$0.920713\pi$
$618$	−4.29856	−	4.29856i	−0.172913	−	0.172913i
$619$			26.9176i			1.08191i	0.841052	+	0.540954i	$0.181937\pi$
$619$			26.9176i			1.08191i	−0.841052	+	0.540954i	$0.818063\pi$
$620$	−3.15731	−	1.11093i	−0.126801	−	0.0446159i
$621$	6.17961			0.247979
$622$	12.2572	−	12.2572i	0.491469	−	0.491469i
$623$	−1.41853	−	1.41853i	−0.0568320	−	0.0568320i
$624$	12.4097			0.496784
$625$	5.39416	+	24.4111i	0.215767	+	0.976445i
$626$		−	9.95017i		−	0.397689i
$627$		0			0
$628$	1.03690	−	1.03690i	0.0413770	−	0.0413770i
$629$	−5.41859			−0.216053
$630$	−2.10234	+	5.97496i	−0.0837594	+	0.238048i
$631$	−5.64617			−0.224771			−0.112385	−	0.993665i	$-0.535849\pi$
$631$	−5.64617			−0.224771			−0.112385	+	0.993665i	$0.535849\pi$
$632$	8.95211	+	8.95211i	0.356096	+	0.356096i
$633$	26.9960	+	26.9960i	1.07299	+	1.07299i
$634$	−25.1981			−1.00074
$635$	11.4301	+	23.8404i	0.453591	+	0.946077i
$636$	18.0214			0.714593
$637$	−15.3663	+	15.3663i	−0.608835	+	0.608835i
$638$		0			0
$639$		−	33.7970i		−	1.33699i
$640$	−2.80997	+	1.34723i	−0.111074	+	0.0532538i
$641$	34.5745			1.36561			0.682805	−	0.730600i	$-0.260760\pi$
$641$	34.5745			1.36561			0.682805	+	0.730600i	$0.260760\pi$
$642$	−18.5961	−	18.5961i	−0.733931	−	0.733931i
$643$	13.7030	−	13.7030i	0.540393	−	0.540393i	−0.383251	−	0.923644i	$-0.625196\pi$
$643$	13.7030	−	13.7030i	0.540393	−	0.540393i	0.923644	+	0.383251i	$0.125196\pi$
$644$	−0.567563			−0.0223651
$645$	7.54671	−	21.4481i	0.297152	−	0.844519i
$646$		−	9.20900i		−	0.362323i
$647$	−14.6671	−	14.6671i	−0.576622	−	0.576622i	0.357349	−	0.933971i	$-0.383681\pi$
$647$	−14.6671	−	14.6671i	−0.576622	−	0.576622i	−0.933971	+	0.357349i	$0.883681\pi$
$648$	−1.12057	−	1.12057i	−0.0440202	−	0.0440202i
$649$		0			0
$650$	−13.2153	−	10.6139i	−0.518347	−	0.416311i
$651$			2.55154i			0.100003i
$652$	−6.50636	−	6.50636i	−0.254809	−	0.254809i
$653$	23.1943	−	23.1943i	0.907665	−	0.907665i	−0.0884186	−	0.996083i	$-0.528181\pi$
$653$	23.1943	−	23.1943i	0.907665	−	0.907665i	0.996083	+	0.0884186i	$0.0281813\pi$
$654$			13.1832i			0.515504i
$655$	−16.7571	−	5.89613i	−0.654753	−	0.230381i
$656$		−	12.1506i		−	0.474400i
$657$	−35.1797	+	35.1797i	−1.37249	+	1.37249i
$658$	−1.65397	+	1.65397i	−0.0644785	+	0.0644785i
$659$	3.99211			0.155511			0.0777553	−	0.996972i	$-0.475225\pi$
$659$	3.99211			0.155511			0.0777553	+	0.996972i	$0.475225\pi$
$660$		0			0
$661$	42.4892			1.65264			0.826318	−	0.563204i	$-0.190431\pi$
$661$	42.4892			1.65264			0.826318	+	0.563204i	$0.190431\pi$
$662$	9.28229	−	9.28229i	0.360766	−	0.360766i
$663$	−36.5870	+	36.5870i	−1.42092	+	1.42092i
$664$		−	34.4271i		−	1.33603i
$665$	0.827325	+	1.72559i	0.0320823	+	0.0669156i
$666$		−	4.92988i		−	0.191029i
$667$	3.42050	−	3.42050i	0.132442	−	0.132442i
$668$	9.19664	+	9.19664i	0.355829	+	0.355829i
$669$		−	14.7581i		−	0.570582i
$670$	−2.87596	+	8.17361i	−0.111108	+	0.315774i
$671$		0			0
$672$	5.10050	+	5.10050i	0.196756	+	0.196756i
$673$	0.447014	+	0.447014i	0.0172311	+	0.0172311i	0.715670	−	0.698439i	$-0.246122\pi$
$673$	0.447014	+	0.447014i	0.0172311	+	0.0172311i	−0.698439	+	0.715670i	$0.746122\pi$
$674$		−	17.2138i		−	0.663051i
$675$	2.95076	+	27.0293i	0.113575	+	1.04036i
$676$	2.24608			0.0863878
$677$	3.38729	−	3.38729i	0.130184	−	0.130184i	−0.639012	−	0.769196i	$-0.720657\pi$
$677$	3.38729	−	3.38729i	0.130184	−	0.130184i	0.769196	+	0.639012i	$0.220657\pi$
$678$	−2.98718	−	2.98718i	−0.114722	−	0.114722i
$679$	9.16465			0.351707
$680$	−12.7707	+	36.2949i	−0.489734	+	1.39185i
$681$			42.4430i			1.62642i
$682$		0			0
$683$	−6.48359	+	6.48359i	−0.248088	+	0.248088i	−0.820186	−	0.572098i	$-0.806130\pi$
$683$	−6.48359	+	6.48359i	−0.248088	+	0.248088i	0.572098	+	0.820186i	$0.306130\pi$
$684$	−6.97190			−0.266577
$685$	9.02270	−	4.32588i	0.344739	−	0.165283i
$686$	7.86884			0.300434
$687$	−29.6059	−	29.6059i	−1.12954	−	1.12954i
$688$	3.46744	+	3.46744i	0.132195	+	0.132195i
$689$	22.8571			0.870785
$690$	6.74187	−	3.23235i	0.256659	−	0.123054i
$691$	31.6039			1.20227			0.601134	−	0.799148i	$-0.294716\pi$
$691$	31.6039			1.20227			0.601134	+	0.799148i	$0.294716\pi$
$692$	10.6427	−	10.6427i	0.404573	−	0.404573i
$693$		0			0
$694$		−	14.8780i		−	0.564762i
$695$	16.7852	−	47.7043i	0.636699	−	1.80953i
$696$	−36.4276			−1.38079
$697$	35.8231	+	35.8231i	1.35690	+	1.35690i
$698$	−12.2741	+	12.2741i	−0.464580	+	0.464580i
$699$	15.5990			0.590007
$700$	−0.271011	−	2.48249i	−0.0102432	−	0.0938292i
$701$		−	16.3368i		−	0.617034i	−0.951219	−	0.308517i	$-0.900167\pi$
$701$		−	16.3368i		−	0.617034i	0.951219	−	0.308517i	$-0.0998326\pi$
$702$	−13.0352	−	13.0352i	−0.491984	−	0.491984i
$703$	−1.05319	−	1.05319i	−0.0397220	−	0.0397220i
$704$		0			0
$705$	−8.51041	+	24.1870i	−0.320521	+	0.910935i
$706$		−	11.4968i		−	0.432688i
$707$	−0.248897	−	0.248897i	−0.00936072	−	0.00936072i
$708$	−12.2409	+	12.2409i	−0.460042	+	0.460042i
$709$			19.1278i			0.718361i	0.933268	+	0.359180i	$0.116944\pi$
$709$			19.1278i			0.718361i	−0.933268	+	0.359180i	$0.883056\pi$
$710$	−6.92275	−	14.4391i	−0.259806	−	0.541890i
$711$		−	20.5440i		−	0.770460i
$712$	7.83968	−	7.83968i	0.293804	−	0.293804i
$713$	1.32411	−	1.32411i	0.0495882	−	0.0495882i
$714$	9.16106			0.342844
$715$		0			0
$716$	−18.1551			−0.678488
$717$	−49.2251	+	49.2251i	−1.83835	+	1.83835i
$718$	−9.73710	+	9.73710i	−0.363385	+	0.363385i
$719$			15.2209i			0.567644i	0.958877	+	0.283822i	$0.0916025\pi$
$719$			15.2209i			0.567644i	−0.958877	+	0.283822i	$0.908397\pi$
$720$	−14.1257	−	4.97024i	−0.526432	−	0.185230i
$721$		−	1.13596i		−	0.0423054i
$722$	−12.2471	+	12.2471i	−0.455791	+	0.455791i
$723$	−10.3491	−	10.3491i	−0.384885	−	0.384885i
$724$		−	24.4123i		−	0.907275i
$725$	16.5944	+	13.3278i	0.616299	+	0.494982i
$726$		0			0
$727$	5.98783	+	5.98783i	0.222076	+	0.222076i	0.809372	−	0.587296i	$-0.199808\pi$
$727$	5.98783	+	5.98783i	0.222076	+	0.222076i	−0.587296	+	0.809372i	$0.699808\pi$
$728$	3.83317	+	3.83317i	0.142067	+	0.142067i
$729$		−	43.3717i		−	1.60636i
$730$	−7.82386	+	22.2358i	−0.289574	+	0.822983i
$731$	−20.4459			−0.756218
$732$	−16.6438	+	16.6438i	−0.615174	+	0.615174i
$733$	20.6838	+	20.6838i	0.763973	+	0.763973i	0.977038	−	0.213065i	$-0.0683446\pi$
$733$	20.6838	+	20.6838i	0.763973	+	0.763973i	−0.213065	+	0.977038i	$0.568345\pi$
$734$	−29.0482			−1.07219
$735$	38.0315	−	18.2340i	1.40281	−	0.672572i
$736$		−	5.29374i		−	0.195130i
$737$		0			0
$738$	−32.5922	+	32.5922i	−1.19973	+	1.19973i
$739$	43.5904			1.60350			0.801749	−	0.597661i	$-0.203903\pi$
$739$	43.5904			1.60350			0.801749	+	0.597661i	$0.203903\pi$
$740$	0.840282	+	1.75262i	0.0308894	+	0.0644275i
$741$	−14.2226			−0.522480
$742$	−2.86160	−	2.86160i	−0.105053	−	0.105053i
$743$	32.5371	+	32.5371i	1.19367	+	1.19367i	0.976029	+	0.217642i	$0.0698364\pi$
$743$	32.5371	+	32.5371i	1.19367	+	1.19367i	0.217642	+	0.976029i	$0.430164\pi$
$744$	−14.1015			−0.516985
$745$	10.9734	−	31.1868i	0.402033	−	1.14260i
$746$	8.89735			0.325755
$747$	−39.5030	+	39.5030i	−1.44534	+	1.44534i
$748$		0			0
$749$		−	4.91432i		−	0.179565i
$750$	17.3574	+	27.9451i	0.633801	+	1.02041i
$751$	−3.27923			−0.119661			−0.0598304	−	0.998209i	$-0.519056\pi$
$751$	−3.27923			−0.119661			−0.0598304	+	0.998209i	$0.519056\pi$
$752$	−3.91022	−	3.91022i	−0.142591	−	0.142591i
$753$	24.8654	−	24.8654i	0.906145	−	0.906145i
$754$	−14.4304			−0.525523
$755$	−14.0170	−	4.93201i	−0.510131	−	0.179494i
$756$		−	2.71598i		−	0.0987794i
$757$	−13.2074	−	13.2074i	−0.480033	−	0.480033i	0.425109	−	0.905142i	$-0.360236\pi$
$757$	−13.2074	−	13.2074i	−0.480033	−	0.480033i	−0.905142	+	0.425109i	$0.860236\pi$
$758$	3.21752	+	3.21752i	0.116866	+	0.116866i
$759$		0			0
$760$	−9.53672	+	4.57233i	−0.345933	+	0.165856i
$761$		−	3.47633i		−	0.126017i	−0.998013	−	0.0630084i	$-0.979931\pi$
$761$		−	3.47633i		−	0.126017i	0.998013	−	0.0630084i	$-0.0200695\pi$
$762$	24.6004	+	24.6004i	0.891179	+	0.891179i
$763$	−1.74193	+	1.74193i	−0.0630623	+	0.0630623i
$764$			11.7548i			0.425275i
$765$	56.2998	−	26.9926i	2.03552	−	0.975920i
$766$			7.08834i			0.256112i
$767$	−15.5255	+	15.5255i	−0.560595	+	0.560595i
$768$	−33.1020	+	33.1020i	−1.19446	+	1.19446i
$769$	40.6658			1.46645			0.733223	−	0.679989i	$-0.238015\pi$
$769$	40.6658			1.46645			0.733223	+	0.679989i	$0.238015\pi$
$770$		0			0
$771$	−35.9215			−1.29368
$772$	4.81602	−	4.81602i	0.173332	−	0.173332i
$773$	30.4832	−	30.4832i	1.09640	−	1.09640i	0.101576	−	0.994828i	$-0.467611\pi$
$773$	30.4832	−	30.4832i	1.09640	−	1.09640i	0.994828	−	0.101576i	$-0.0323885\pi$
$774$		−	18.6018i		−	0.668630i
$775$	6.42383	+	5.15931i	0.230751	+	0.185328i
$776$			50.6497i			1.81822i
$777$	1.04771	−	1.04771i	0.0375864	−	0.0375864i
$778$	−18.1909	−	18.1909i	−0.652175	−	0.652175i
$779$			13.9256i			0.498938i
$780$	17.5076	+	6.16019i	0.626871	+	0.220570i
$781$		0			0
$782$	−4.75407	−	4.75407i	−0.170005	−	0.170005i
$783$	16.3683	+	16.3683i	0.584954	+	0.584954i
$784$			9.09625i			0.324866i
$785$	−3.25496	+	1.56057i	−0.116175	+	0.0556993i
$786$	−23.3754			−0.833773
$787$	18.5846	−	18.5846i	0.662468	−	0.662468i	−0.293493	−	0.955961i	$-0.594818\pi$
$787$	18.5846	−	18.5846i	0.662468	−	0.662468i	0.955961	+	0.293493i	$0.0948178\pi$
$788$	−2.48071	−	2.48071i	−0.0883718	−	0.0883718i
$789$	−54.2289			−1.93060
$790$	−4.20809	−	8.77700i	−0.149717	−	0.312272i
$791$		−	0.789410i		−	0.0280682i
$792$		0			0
$793$	−21.1099	+	21.1099i	−0.749635	+	0.749635i
$794$	−30.7155			−1.09005
$795$	−41.8469	−	14.7242i	−1.48416	−	0.522214i
$796$	−11.2488			−0.398703
$797$	−31.5680	−	31.5680i	−1.11820	−	1.11820i	−0.992006	−	0.126189i	$-0.959725\pi$
$797$	−31.5680	−	31.5680i	−1.11820	−	1.11820i	−0.126189	−	0.992006i	$-0.540275\pi$
$798$	1.78060	+	1.78060i	0.0630327	+	0.0630327i
$799$	23.0568			0.815690
$800$	23.1545	−	2.52776i	0.818636	−	0.0893697i
$801$	−17.9911			−0.635684
$802$	18.2958	−	18.2958i	0.646047	−	0.646047i
$803$		0			0
$804$		−	9.48776i		−	0.334607i
$805$	1.31792	+	0.463723i	0.0464507	+	0.0163441i
$806$	−5.58613			−0.196763
$807$	−34.6415	−	34.6415i	−1.21944	−	1.21944i
$808$	1.37556	−	1.37556i	0.0483921	−	0.0483921i
$809$	−55.0895			−1.93684			−0.968421	−	0.249320i	$-0.919793\pi$
$809$	−55.0895			−1.93684			−0.968421	+	0.249320i	$0.919793\pi$
$810$	0.526743	+	1.09865i	0.0185079	+	0.0386028i
$811$		−	13.3380i		−	0.468360i	−0.972193	−	0.234180i	$-0.924759\pi$
$811$		−	13.3380i		−	0.468360i	0.972193	−	0.234180i	$-0.0752406\pi$
$812$	−1.50333	−	1.50333i	−0.0527567	−	0.0527567i
$813$	−63.2704	−	63.2704i	−2.21899	−	2.21899i
$814$		0			0
$815$	9.79228	+	20.4242i	0.343008	+	0.715429i
$816$			21.6580i			0.758183i
$817$	−3.97400	−	3.97400i	−0.139033	−	0.139033i
$818$	7.39810	−	7.39810i	0.258668	−	0.258668i
$819$		−	8.79666i		−	0.307380i
$820$	6.03158	−	17.1420i	0.210632	−	0.598626i
$821$		−	7.26138i		−	0.253424i	−0.991940	−	0.126712i	$-0.959558\pi$
$821$		−	7.26138i		−	0.253424i	0.991940	−	0.126712i	$-0.0404424\pi$
$822$	9.31034	−	9.31034i	0.324736	−	0.324736i
$823$	−34.0409	+	34.0409i	−1.18659	+	1.18659i	−0.208585	+	0.978004i	$0.566886\pi$
$823$	−34.0409	+	34.0409i	−1.18659	+	1.18659i	−0.978004	+	0.208585i	$0.933114\pi$
$824$	6.27805			0.218706
$825$		0			0
$826$	3.88746			0.135262
$827$	26.1535	−	26.1535i	0.909447	−	0.909447i	−0.0867802	−	0.996227i	$-0.527658\pi$
$827$	26.1535	−	26.1535i	0.909447	−	0.909447i	0.996227	+	0.0867802i	$0.0276578\pi$
$828$	−3.59919	+	3.59919i	−0.125080	+	0.125080i
$829$		−	21.3370i		−	0.741064i	−0.928820	−	0.370532i	$-0.879175\pi$
$829$		−	21.3370i		−	0.741064i	0.928820	−	0.370532i	$-0.120825\pi$
$830$	−8.78534	+	24.9684i	−0.304944	+	0.866665i
$831$			20.4446i			0.709216i
$832$	−17.3984	+	17.3984i	−0.603180	+	0.603180i
$833$	−26.8182	−	26.8182i	−0.929194	−	0.929194i
$834$		−	66.5455i		−	2.30428i
$835$	−13.8412	−	28.8693i	−0.478995	−	0.999064i
$836$		0			0
$837$	6.33630	+	6.33630i	0.219015	+	0.219015i
$838$	5.65725	+	5.65725i	0.195426	+	0.195426i
$839$			21.4121i			0.739228i	0.929185	+	0.369614i	$0.120510\pi$
$839$			21.4121i			0.739228i	−0.929185	+	0.369614i	$0.879490\pi$
$840$	−4.54853	−	9.48708i	−0.156939	−	0.327335i
$841$	−10.8799			−0.375168
$842$	−16.0113	+	16.0113i	−0.551786	+	0.551786i
$843$	11.0408	+	11.0408i	0.380265	+	0.380265i
$844$	−12.3145			−0.423881
$845$	−5.21557	−	1.83514i	−0.179421	−	0.0631309i
$846$			20.9772i			0.721213i
$847$		0			0
$848$	6.76524	−	6.76524i	0.232319	−	0.232319i
$849$	38.9211			1.33577
$850$	18.5240	−	23.0641i	0.635367	−	0.791092i
$851$	−1.08741			−0.0372758
$852$	12.3982	+	12.3982i	0.424755	+	0.424755i
$853$	−20.7374	−	20.7374i	−0.710035	−	0.710035i	0.256507	−	0.966542i	$-0.417428\pi$
$853$	−20.7374	−	20.7374i	−0.710035	−	0.710035i	−0.966542	+	0.256507i	$0.917428\pi$
$854$	5.28573			0.180874
$855$	16.1893	+	5.69634i	0.553661	+	0.194811i
$856$	27.1597			0.928299
$857$	14.3622	−	14.3622i	0.490604	−	0.490604i	−0.417893	−	0.908496i	$-0.637231\pi$
$857$	14.3622	−	14.3622i	0.490604	−	0.490604i	0.908496	+	0.417893i	$0.137231\pi$
$858$		0			0
$859$			21.7404i			0.741772i	0.928678	+	0.370886i	$0.120946\pi$
$859$			21.7404i			0.741772i	−0.928678	+	0.370886i	$0.879054\pi$
$860$	3.17062	+	6.61312i	0.108117	+	0.225506i
$861$	−13.8531			−0.472114
$862$	21.0406	+	21.0406i	0.716644	+	0.716644i
$863$	18.2298	−	18.2298i	0.620550	−	0.620550i	−0.325122	−	0.945672i	$-0.605405\pi$
$863$	18.2298	−	18.2298i	0.620550	−	0.620550i	0.945672	+	0.325122i	$0.105405\pi$
$864$	25.3324			0.861824
$865$	−33.4085	+	16.0175i	−1.13592	+	0.544613i
$866$			13.0304i			0.442791i
$867$	−30.0007	−	30.0007i	−1.01888	−	1.01888i
$868$	−0.581954	−	0.581954i	−0.0197528	−	0.0197528i
$869$		0			0
$870$	26.4193	+	9.29585i	0.895697	+	0.315159i
$871$		−	12.0336i		−	0.407744i
$872$	−9.62704	−	9.62704i	−0.326013	−	0.326013i
$873$	58.1175	−	58.1175i	1.96698	−	1.96698i
$874$		−	1.84807i		−	0.0625117i
$875$	−1.39899	+	5.98595i	−0.0472945	+	0.202362i
$876$		−	25.8108i		−	0.872067i
$877$	32.5728	−	32.5728i	1.09991	−	1.09991i	0.105485	−	0.994421i	$-0.466361\pi$
$877$	32.5728	−	32.5728i	1.09991	−	1.09991i	0.994421	−	0.105485i	$-0.0336395\pi$
$878$	12.4964	−	12.4964i	0.421735	−	0.421735i
$879$	−19.1485			−0.645864
$880$		0			0
$881$	3.73181			0.125728			0.0628640	−	0.998022i	$-0.479977\pi$
$881$	3.73181			0.125728			0.0628640	+	0.998022i	$0.479977\pi$
$882$	24.3994	−	24.3994i	0.821571	−	0.821571i
$883$	17.7255	−	17.7255i	0.596510	−	0.596510i	−0.342872	−	0.939382i	$-0.611400\pi$
$883$	17.7255	−	17.7255i	0.596510	−	0.596510i	0.939382	+	0.342872i	$0.111400\pi$
$884$		−	16.6895i		−	0.561327i
$885$	38.4257	−	18.4230i	1.29166	−	0.619281i
$886$			11.5577i			0.388289i
$887$	10.0574	−	10.0574i	0.337694	−	0.337694i	−0.517805	−	0.855499i	$-0.673251\pi$
$887$	10.0574	−	10.0574i	0.337694	−	0.337694i	0.855499	+	0.517805i	$0.173251\pi$
$888$	5.79032	+	5.79032i	0.194310	+	0.194310i
$889$			6.50105i			0.218038i
$890$	−7.68633	+	3.68517i	−0.257646	+	0.123527i
$891$		0			0
$892$	3.36602	+	3.36602i	0.112703	+	0.112703i
$893$	4.48147	+	4.48147i	0.149967	+	0.149967i
$894$		−	43.5043i		−	1.45500i
$895$	42.1575	+	14.8335i	1.40917	+	0.495829i
$896$	−0.766254			−0.0255987
$897$	−7.34229	+	7.34229i	−0.245152	+	0.245152i
$898$	−3.33838	−	3.33838i	−0.111403	−	0.111403i
$899$	7.01446			0.233945
$900$	−17.4613	−	14.0240i	−0.582042	−	0.467468i
$901$			39.8915i			1.32898i
$902$		0			0
$903$	3.95331	−	3.95331i	0.131558	−	0.131558i
$904$	4.36278			0.145104
$905$	−19.9459	+	56.6871i	−0.663023	+	1.88434i
$906$	−19.5531			−0.649609
$907$	34.7864	+	34.7864i	1.15506	+	1.15506i	0.985523	+	0.169540i	$0.0542283\pi$
$907$	34.7864	+	34.7864i	1.15506	+	1.15506i	0.169540	+	0.985523i	$0.445772\pi$
$908$	−9.68037	−	9.68037i	−0.321254	−	0.321254i
$909$	−3.15675			−0.104703
$910$	−1.80184	−	3.75819i	−0.0597306	−	0.124583i
$911$	43.3655			1.43676			0.718381	−	0.695650i	$-0.244883\pi$
$911$	43.3655			1.43676			0.718381	+	0.695650i	$0.244883\pi$
$912$	−4.20960	+	4.20960i	−0.139394	+	0.139394i
$913$		0			0
$914$			34.0883i			1.12754i
$915$	52.2469	−	25.0495i	1.72723	−	0.828110i
$916$	13.5050			0.446218
$917$	−3.08866	−	3.08866i	−0.101997	−	0.101997i
$918$	22.7499	−	22.7499i	0.750857	−	0.750857i
$919$	−23.4102			−0.772231			−0.386116	−	0.922450i	$-0.626183\pi$
$919$	−23.4102			−0.772231			−0.386116	+	0.922450i	$0.626183\pi$
$920$	−2.56283	+	7.28368i	−0.0844939	+	0.240136i
$921$			22.0725i			0.727313i
$922$	17.3083	+	17.3083i	0.570020	+	0.570020i
$923$	15.7250	+	15.7250i	0.517596	+	0.517596i
$924$		0			0
$925$	−0.519235	−	4.75625i	−0.0170723	−	0.156385i
$926$			43.1637i			1.41845i
$927$	−7.20368	−	7.20368i	−0.236600	−	0.236600i
$928$	14.0218	−	14.0218i	0.460288	−	0.460288i
$929$		−	12.6595i		−	0.415345i	−0.978198	−	0.207673i	$-0.933411\pi$
$929$		−	12.6595i		−	0.415345i	0.978198	−	0.207673i	$-0.0665888\pi$
$930$	10.2271	+	3.59851i	0.335361	+	0.118000i
$931$		−	10.4251i		−	0.341669i
$932$	−3.55780	+	3.55780i	−0.116540	+	0.116540i
$933$	33.0382	−	33.0382i	1.08162	−	1.08162i
$934$	−29.6798			−0.971153
$935$		0			0
$936$	48.6159			1.58906
$937$	18.8045	−	18.8045i	0.614315	−	0.614315i	−0.329753	−	0.944067i	$-0.606965\pi$
$937$	18.8045	−	18.8045i	0.614315	−	0.614315i	0.944067	+	0.329753i	$0.106965\pi$
$938$	−1.50656	+	1.50656i	−0.0491908	+	0.0491908i
$939$		−	26.8198i		−	0.875233i
$940$	−3.57550	−	7.45760i	−0.116620	−	0.243240i
$941$		−	23.8728i		−	0.778231i	−0.921189	−	0.389115i	$-0.872781\pi$
$941$		−	23.8728i		−	0.778231i	0.921189	−	0.389115i	$-0.127219\pi$
$942$	−3.35873	+	3.35873i	−0.109433	+	0.109433i
$943$	7.18899	+	7.18899i	0.234106	+	0.234106i
$944$			9.19051i			0.299126i
$945$	−2.21907	+	6.30671i	−0.0721865	+	0.205157i
$946$		0			0
$947$	38.6416	+	38.6416i	1.25568	+	1.25568i	0.953134	+	0.302548i	$0.0978374\pi$
$947$	38.6416	+	38.6416i	1.25568	+	1.25568i	0.302548	+	0.953134i	$0.402163\pi$
$948$	7.53641	+	7.53641i	0.244771	+	0.244771i
$949$		−	32.7367i		−	1.06268i
$950$	8.08334	−	0.882450i	0.262258	−	0.0286305i
$951$	−67.9192			−2.20243
$952$	−6.68987	+	6.68987i	−0.216820	+	0.216820i
$953$	−11.3115	−	11.3115i	−0.366416	−	0.366416i	0.499752	−	0.866168i	$-0.333424\pi$
$953$	−11.3115	−	11.3115i	−0.366416	−	0.366416i	−0.866168	+	0.499752i	$0.833424\pi$
$954$	−36.2936			−1.17505
$955$	9.60419	−	27.2956i	0.310784	−	0.883264i
$956$		−	22.4544i		−	0.726229i
$957$		0			0
$958$	23.1798	−	23.1798i	0.748904	−	0.748904i
$959$	2.46040			0.0794506
$960$	43.0609	−	20.6453i	1.38978	−	0.666324i
$961$	−28.2846			−0.912408
$962$	2.29377	+	2.29377i	0.0739540	+	0.0739540i
$963$	−31.1641	−	31.1641i	−1.00425	−	1.00425i
$964$	4.72081			0.152047
$965$	−15.1180	+	7.24826i	−0.486667	+	0.233330i
$966$	1.83845			0.0591510
$967$	37.1649	−	37.1649i	1.19514	−	1.19514i	0.219539	−	0.975604i	$-0.429545\pi$
$967$	37.1649	−	37.1649i	1.19514	−	1.19514i	0.975604	−	0.219539i	$-0.0704554\pi$
$968$		0			0
$969$		−	24.8221i		−	0.797400i
$970$	12.9251	−	36.7339i	0.415001	−	1.17945i
$971$	21.8915			0.702531			0.351265	−	0.936276i	$-0.385751\pi$
$971$	21.8915			0.702531			0.351265	+	0.936276i	$0.385751\pi$
$972$	9.53533	+	9.53533i	0.305846	+	0.305846i
$973$	8.79284	−	8.79284i	0.281886	−	0.281886i
$974$	7.18103			0.230095
$975$	−35.6207	−	28.6088i	−1.14078	−	0.916216i
$976$			12.4962i			0.399994i
$977$	0.0724894	+	0.0724894i	0.00231914	+	0.00231914i	0.708265	−	0.705946i	$-0.249478\pi$
$977$	0.0724894	+	0.0724894i	0.00231914	+	0.00231914i	−0.705946	+	0.708265i	$0.749478\pi$
$978$	21.0754	+	21.0754i	0.673915	+	0.673915i
$979$		0			0
$980$	−4.51541	+	12.8330i	−0.144239	+	0.409935i
$981$			22.0929i			0.705371i
$982$	10.8822	+	10.8822i	0.347266	+	0.347266i
$983$	−32.1600	+	32.1600i	−1.02574	+	1.02574i	−0.0260841	+	0.999660i	$0.508304\pi$
$983$	−32.1600	+	32.1600i	−1.02574	+	1.02574i	−0.999660	+	0.0260841i	$0.991696\pi$
$984$		−	76.5613i		−	2.44069i
$985$	3.73355	+	7.78725i	0.118961	+	0.248122i
$986$		−	25.1847i		−	0.802045i
$987$	−4.45814	+	4.45814i	−0.141904	+	0.141904i
$988$	3.24388	−	3.24388i	0.103201	−	0.103201i
$989$	−4.10309			−0.130471
$990$		0			0
$991$	−7.25030			−0.230313			−0.115157	−	0.993347i	$-0.536737\pi$
$991$	−7.25030			−0.230313			−0.115157	+	0.993347i	$0.536737\pi$
$992$	5.42797	−	5.42797i	0.172338	−	0.172338i
$993$	25.0196	−	25.0196i	0.793974	−	0.793974i
$994$		−	3.93741i		−	0.124887i
$995$	26.1205	+	9.19075i	0.828077	+	0.291366i
$996$		−	28.9828i		−	0.918354i
$997$	−19.7338	+	19.7338i	−0.624976	+	0.624976i	−0.946800	−	0.321824i	$-0.895704\pi$
$997$	−19.7338	+	19.7338i	−0.624976	+	0.624976i	0.321824	+	0.946800i	$0.395704\pi$
$998$	19.5588	+	19.5588i	0.619122	+	0.619122i
$999$		−	5.20361i		−	0.164635i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.e.b.362.11		32
5.3	odd	4	inner	605.2.e.b.483.6		32
11.2	odd	10		605.2.m.c.282.3		32
11.3	even	5		55.2.l.a.2.2	✓	32
11.4	even	5		605.2.m.e.457.3		32
11.5	even	5		605.2.m.c.602.2		32
11.6	odd	10		605.2.m.d.602.3		32
11.7	odd	10		55.2.l.a.17.2	yes	32
11.8	odd	10		605.2.m.e.112.3		32
11.9	even	5		605.2.m.d.282.2		32
11.10	odd	2	inner	605.2.e.b.362.6		32
33.14	odd	10		495.2.bj.a.442.3		32
33.29	even	10		495.2.bj.a.127.3		32
44.3	odd	10		880.2.cm.a.497.4		32
44.7	even	10		880.2.cm.a.17.4		32
55.3	odd	20		55.2.l.a.13.2	yes	32
55.7	even	20		275.2.bm.b.193.3		32
55.8	even	20		605.2.m.e.233.3		32
55.13	even	20		605.2.m.c.403.2		32
55.14	even	10		275.2.bm.b.57.3		32
55.18	even	20		55.2.l.a.28.2	yes	32
55.28	even	20		605.2.m.d.118.2		32
55.29	odd	10		275.2.bm.b.182.3		32
55.38	odd	20		605.2.m.c.118.3		32
55.43	even	4	inner	605.2.e.b.483.11		32
55.47	odd	20		275.2.bm.b.68.3		32
55.48	odd	20		605.2.m.e.578.3		32
55.53	odd	20		605.2.m.d.403.3		32
165.113	even	20		495.2.bj.a.343.3		32
165.128	odd	20		495.2.bj.a.28.3		32
220.3	even	20		880.2.cm.a.673.4		32
220.183	odd	20		880.2.cm.a.193.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.2.2	✓	32	11.3	even	5
55.2.l.a.13.2	yes	32	55.3	odd	20
55.2.l.a.17.2	yes	32	11.7	odd	10
55.2.l.a.28.2	yes	32	55.18	even	20
275.2.bm.b.57.3		32	55.14	even	10
275.2.bm.b.68.3		32	55.47	odd	20
275.2.bm.b.182.3		32	55.29	odd	10
275.2.bm.b.193.3		32	55.7	even	20
495.2.bj.a.28.3		32	165.128	odd	20
495.2.bj.a.127.3		32	33.29	even	10
495.2.bj.a.343.3		32	165.113	even	20
495.2.bj.a.442.3		32	33.14	odd	10
605.2.e.b.362.6		32	11.10	odd	2	inner
605.2.e.b.362.11		32	1.1	even	1	trivial
605.2.e.b.483.6		32	5.3	odd	4	inner
605.2.e.b.483.11		32	55.43	even	4	inner
605.2.m.c.118.3		32	55.38	odd	20
605.2.m.c.282.3		32	11.2	odd	10
605.2.m.c.403.2		32	55.13	even	20
605.2.m.c.602.2		32	11.5	even	5
605.2.m.d.118.2		32	55.28	even	20
605.2.m.d.282.2		32	11.9	even	5
605.2.m.d.403.3		32	55.53	odd	20
605.2.m.d.602.3		32	11.6	odd	10
605.2.m.e.112.3		32	11.8	odd	10
605.2.m.e.233.3		32	55.8	even	20
605.2.m.e.457.3		32	11.4	even	5
605.2.m.e.578.3		32	55.48	odd	20
880.2.cm.a.17.4		32	44.7	even	10
880.2.cm.a.193.4		32	220.183	odd	20
880.2.cm.a.497.4		32	44.3	odd	10
880.2.cm.a.673.4		32	220.3	even	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.738792 - 0.738792i) q^{2} +(1.99135 - 1.99135i) q^{3} +0.908372i q^{4} +(0.742178 - 2.10931i) q^{5} -2.94239i q^{6} +(0.388787 - 0.388787i) q^{7} +(2.14868 + 2.14868i) q^{8} -4.93096i q^{9} +O(q^{10})\)	\(q+(0.738792 - 0.738792i) q^{2} +(1.99135 - 1.99135i) q^{3} +0.908372i q^{4} +(0.742178 - 2.10931i) q^{5} -2.94239i q^{6} +(0.388787 - 0.388787i) q^{7} +(2.14868 + 2.14868i) q^{8} -4.93096i q^{9} +(-1.01002 - 2.10665i) q^{10} +(1.80889 + 1.80889i) q^{12} +(2.29427 + 2.29427i) q^{13} -0.574465i q^{14} +(-2.72243 - 5.67831i) q^{15} +1.35812 q^{16} +(-4.00409 + 4.00409i) q^{17} +(-3.64296 - 3.64296i) q^{18} -1.55652 q^{19} +(1.91603 + 0.674174i) q^{20} -1.54842i q^{21} +(-0.803543 + 0.803543i) q^{23} +8.55757 q^{24} +(-3.89834 - 3.13096i) q^{25} +3.38998 q^{26} +(-3.84523 - 3.84523i) q^{27} +(0.353163 + 0.353163i) q^{28} -4.25677 q^{29} +(-6.20640 - 2.18378i) q^{30} -1.64783 q^{31} +(-3.29400 + 3.29400i) q^{32} +5.91638i q^{34} +(-0.531521 - 1.10862i) q^{35} +4.47915 q^{36} +(0.676632 + 0.676632i) q^{37} +(-1.14995 + 1.14995i) q^{38} +9.13740 q^{39} +(6.12693 - 2.93752i) q^{40} -8.94662i q^{41} +(-1.14396 - 1.14396i) q^{42} +(2.55312 + 2.55312i) q^{43} +(-10.4009 - 3.65965i) q^{45} +1.18730i q^{46} +(-2.87915 - 2.87915i) q^{47} +(2.70449 - 2.70449i) q^{48} +6.69769i q^{49} +(-5.19320 + 0.566936i) q^{50} +15.9471i q^{51} +(-2.08405 + 2.08405i) q^{52} +(4.98134 - 4.98134i) q^{53} -5.68165 q^{54} +1.67076 q^{56} +(-3.09959 + 3.09959i) q^{57} +(-3.14487 + 3.14487i) q^{58} +6.76710i q^{59} +(5.15801 - 2.47298i) q^{60} +9.20114i q^{61} +(-1.21741 + 1.21741i) q^{62} +(-1.91709 - 1.91709i) q^{63} +7.58340i q^{64} +(6.54208 - 3.13656i) q^{65} +(-2.62254 - 2.62254i) q^{67} +(-3.63720 - 3.63720i) q^{68} +3.20027i q^{69} +(-1.21172 - 0.426355i) q^{70} +6.85404 q^{71} +(10.5951 - 10.5951i) q^{72} +(-7.13445 - 7.13445i) q^{73} +0.999781 q^{74} +(-13.9978 + 1.52813i) q^{75} -1.41390i q^{76} +(6.75064 - 6.75064i) q^{78} +4.16632 q^{79} +(1.00796 - 2.86468i) q^{80} -0.521516 q^{81} +(-6.60969 - 6.60969i) q^{82} +(-8.01121 - 8.01121i) q^{83} +1.40654 q^{84} +(5.47411 + 11.4176i) q^{85} +3.77246 q^{86} +(-8.47673 + 8.47673i) q^{87} -3.64860i q^{89} +(-10.3878 + 4.98039i) q^{90} +1.78396 q^{91} +(-0.729916 - 0.729916i) q^{92} +(-3.28142 + 3.28142i) q^{93} -4.25419 q^{94} +(-1.15522 + 3.28319i) q^{95} +13.1190i q^{96} +(11.7862 + 11.7862i) q^{97} +(4.94820 + 4.94820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{3} + 8 q^{5}+O(q^{10}) \) 32 * q - 4 * q^3 + 8 * q^5	\( 32 q - 4 q^{3} + 8 q^{5} + 12 q^{12} - 36 q^{15} - 8 q^{16} - 64 q^{20} - 24 q^{23} + 16 q^{25} - 16 q^{27} - 8 q^{31} + 24 q^{36} + 32 q^{37} - 40 q^{38} + 60 q^{42} - 28 q^{45} - 28 q^{47} + 56 q^{48} + 116 q^{53} - 80 q^{56} - 80 q^{58} + 104 q^{60} - 8 q^{67} - 80 q^{70} + 24 q^{71} - 76 q^{75} + 60 q^{78} + 8 q^{80} + 8 q^{81} - 20 q^{82} - 40 q^{86} + 80 q^{91} + 52 q^{92} + 32 q^{93} + 92 q^{97}+O(q^{100}) \) 32 * q - 4 * q^3 + 8 * q^5 + 12 * q^12 - 36 * q^15 - 8 * q^16 - 64 * q^20 - 24 * q^23 + 16 * q^25 - 16 * q^27 - 8 * q^31 + 24 * q^36 + 32 * q^37 - 40 * q^38 + 60 * q^42 - 28 * q^45 - 28 * q^47 + 56 * q^48 + 116 * q^53 - 80 * q^56 - 80 * q^58 + 104 * q^60 - 8 * q^67 - 80 * q^70 + 24 * q^71 - 76 * q^75 + 60 * q^78 + 8 * q^80 + 8 * q^81 - 20 * q^82 - 40 * q^86 + 80 * q^91 + 52 * q^92 + 32 * q^93 + 92 * q^97

Introduction

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