LMFDB - Embedded newform 354.5.d.a.235.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,5,Mod(235,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("354.235");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	354.d (of order $2$, degree $1$, 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:	$36.5929669317$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			235.2
Character	$\chi$	$=$	354.235
Dual form			354.5.d.a.235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.82843i q^{2} +5.19615 q^{3} -8.00000 q^{4} -10.0054 q^{5} +14.6969i q^{6} +10.1747 q^{7} -22.6274i q^{8} +27.0000 q^{9} +O(q^{10})$	\(q+2.82843i q^{2} +5.19615 q^{3} -8.00000 q^{4} -10.0054 q^{5} +14.6969i q^{6} +10.1747 q^{7} -22.6274i q^{8} +27.0000 q^{9} -28.2996i q^{10} +214.809i q^{11} -41.5692 q^{12} -161.876i q^{13} +28.7784i q^{14} -51.9897 q^{15} +64.0000 q^{16} -0.829921 q^{17} +76.3675i q^{18} +254.188 q^{19} +80.0433 q^{20} +52.8693 q^{21} -607.573 q^{22} +470.095i q^{23} -117.576i q^{24} -524.892 q^{25} +457.855 q^{26} +140.296 q^{27} -81.3977 q^{28} -322.556 q^{29} -147.049i q^{30} -247.138i q^{31} +181.019i q^{32} +1116.18i q^{33} -2.34737i q^{34} -101.802 q^{35} -216.000 q^{36} +1175.47i q^{37} +718.952i q^{38} -841.134i q^{39} +226.397i q^{40} -2680.79 q^{41} +149.537i q^{42} +1045.13i q^{43} -1718.47i q^{44} -270.146 q^{45} -1329.63 q^{46} +3466.36i q^{47} +332.554 q^{48} -2297.48 q^{49} -1484.62i q^{50} -4.31240 q^{51} +1295.01i q^{52} -5159.71 q^{53} +396.817i q^{54} -2149.26i q^{55} -230.227i q^{56} +1320.80 q^{57} -912.325i q^{58} +(423.034 - 3455.20i) q^{59} +415.917 q^{60} +441.526i q^{61} +699.012 q^{62} +274.717 q^{63} -512.000 q^{64} +1619.64i q^{65} -3157.04 q^{66} +8215.23i q^{67} +6.63937 q^{68} +2442.68i q^{69} -287.940i q^{70} +9394.94 q^{71} -610.940i q^{72} -3859.68i q^{73} -3324.72 q^{74} -2727.42 q^{75} -2033.50 q^{76} +2185.62i q^{77} +2379.09 q^{78} -7332.48 q^{79} -640.347 q^{80} +729.000 q^{81} -7582.41i q^{82} +2016.11i q^{83} -422.955 q^{84} +8.30370 q^{85} -2956.08 q^{86} -1676.05 q^{87} +4860.58 q^{88} +13542.5i q^{89} -764.089i q^{90} -1647.04i q^{91} -3760.76i q^{92} -1284.17i q^{93} -9804.34 q^{94} -2543.26 q^{95} +940.604i q^{96} -14364.0i q^{97} -6498.24i q^{98} +5799.85i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 320 q^{4} - 80 q^{7} + 1080 q^{9}+O(q^{10}) $ 40 * q - 320 * q^4 - 80 * q^7 + 1080 * q^9	$ 40 q - 320 q^{4} - 80 q^{7} + 1080 q^{9} - 144 q^{15} + 2560 q^{16} + 480 q^{17} - 792 q^{19} - 1024 q^{22} + 3400 q^{25} + 768 q^{26} + 640 q^{28} + 1608 q^{29} - 5760 q^{35} - 8640 q^{36} + 6264 q^{41} + 7040 q^{46} + 17912 q^{49} + 1296 q^{51} - 1104 q^{53} + 5040 q^{57} + 13584 q^{59} + 1152 q^{60} - 12288 q^{62} - 2160 q^{63} - 20480 q^{64} + 1152 q^{66} - 3840 q^{68} + 35352 q^{71} + 4608 q^{74} + 3168 q^{75} + 6336 q^{76} - 12672 q^{78} - 15720 q^{79} + 29160 q^{81} - 26872 q^{85} + 18432 q^{86} + 7776 q^{87} + 8192 q^{88} - 18432 q^{94} - 19128 q^{95}+O(q^{100}) $ 40 * q - 320 * q^4 - 80 * q^7 + 1080 * q^9 - 144 * q^15 + 2560 * q^16 + 480 * q^17 - 792 * q^19 - 1024 * q^22 + 3400 * q^25 + 768 * q^26 + 640 * q^28 + 1608 * q^29 - 5760 * q^35 - 8640 * q^36 + 6264 * q^41 + 7040 * q^46 + 17912 * q^49 + 1296 * q^51 - 1104 * q^53 + 5040 * q^57 + 13584 * q^59 + 1152 * q^60 - 12288 * q^62 - 2160 * q^63 - 20480 * q^64 + 1152 * q^66 - 3840 * q^68 + 35352 * q^71 + 4608 * q^74 + 3168 * q^75 + 6336 * q^76 - 12672 * q^78 - 15720 * q^79 + 29160 * q^81 - 26872 * q^85 + 18432 * q^86 + 7776 * q^87 + 8192 * q^88 - 18432 * q^94 - 19128 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$1$

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 $

$2$			2.82843i			0.707107i
$2$			2.82843i			0.707107i
$3$	5.19615			0.577350
$3$	5.19615			0.577350
$4$	−8.00000			−0.500000
$5$	−10.0054			−0.400217			−0.200108	−	0.979774i	$-0.564129\pi$
$5$	−10.0054			−0.400217			−0.200108	+	0.979774i	$0.564129\pi$
$6$			14.6969i			0.408248i
$7$	10.1747			0.207647			0.103824	−	0.994596i	$-0.466892\pi$
$7$	10.1747			0.207647			0.103824	+	0.994596i	$0.466892\pi$
$8$		−	22.6274i		−	0.353553i
$9$	27.0000			0.333333
$10$		−	28.2996i		−	0.282996i
$11$			214.809i			1.77528i	0.460534	+	0.887642i	$0.347658\pi$
$11$			214.809i			1.77528i	−0.460534	+	0.887642i	$0.652342\pi$
$12$	−41.5692			−0.288675
$13$		−	161.876i		−	0.957848i	−0.877856	−	0.478924i	$-0.841027\pi$
$13$		−	161.876i		−	0.957848i	0.877856	−	0.478924i	$-0.158973\pi$
$14$			28.7784i			0.146829i
$15$	−51.9897			−0.231065
$16$	64.0000			0.250000
$17$	−0.829921			−0.00287170			−0.00143585	−	0.999999i	$-0.500457\pi$
$17$	−0.829921			−0.00287170			−0.00143585	+	0.999999i	$0.500457\pi$
$18$			76.3675i			0.235702i
$19$	254.188			0.704122			0.352061	−	0.935977i	$-0.385481\pi$
$19$	254.188			0.704122			0.352061	+	0.935977i	$0.385481\pi$
$20$	80.0433			0.200108
$21$	52.8693			0.119885
$22$	−607.573			−1.25532
$23$			470.095i			0.888648i	0.895866	+	0.444324i	$0.146556\pi$
$23$			470.095i			0.888648i	−0.895866	+	0.444324i	$0.853444\pi$
$24$		−	117.576i		−	0.204124i
$25$	−524.892			−0.839827
$26$	457.855			0.677301
$27$	140.296			0.192450
$28$	−81.3977			−0.103824
$29$	−322.556			−0.383538			−0.191769	−	0.981440i	$-0.561423\pi$
$29$	−322.556			−0.383538			−0.191769	+	0.981440i	$0.561423\pi$
$30$		−	147.049i		−	0.163388i
$31$		−	247.138i		−	0.257168i	−0.991699	−	0.128584i	$-0.958957\pi$
$31$		−	247.138i		−	0.257168i	0.991699	−	0.128584i	$-0.0410431\pi$
$32$			181.019i			0.176777i
$33$			1116.18i			1.02496i
$34$		−	2.34737i		−	0.00203060i
$35$	−101.802			−0.0831038
$36$	−216.000			−0.166667
$37$			1175.47i			0.858632i	0.903154	+	0.429316i	$0.141245\pi$
$37$			1175.47i			0.858632i	−0.903154	+	0.429316i	$0.858755\pi$
$38$			718.952i			0.497889i
$39$		−	841.134i		−	0.553014i
$40$			226.397i			0.141498i
$41$	−2680.79			−1.59476			−0.797378	−	0.603480i	$-0.793780\pi$
$41$	−2680.79			−1.59476			−0.797378	+	0.603480i	$0.793780\pi$
$42$			149.537i			0.0847716i
$43$			1045.13i			0.565241i	0.959232	+	0.282621i	$0.0912038\pi$
$43$			1045.13i			0.565241i	−0.959232	+	0.282621i	$0.908796\pi$
$44$		−	1718.47i		−	0.887642i
$45$	−270.146			−0.133406
$46$	−1329.63			−0.628369
$47$			3466.36i			1.56920i	0.620004	+	0.784599i	$0.287131\pi$
$47$			3466.36i			1.56920i	−0.620004	+	0.784599i	$0.712869\pi$
$48$	332.554			0.144338
$49$	−2297.48			−0.956883
$50$		−	1484.62i		−	0.593847i
$51$	−4.31240			−0.00165798
$52$			1295.01i			0.478924i
$53$	−5159.71			−1.83685			−0.918424	−	0.395597i	$-0.870538\pi$
$53$	−5159.71			−1.83685			−0.918424	+	0.395597i	$0.870538\pi$
$54$			396.817i			0.136083i
$55$		−	2149.26i		−	0.710498i
$56$		−	230.227i		−	0.0734144i
$57$	1320.80			0.406525
$58$		−	912.325i		−	0.271203i
$59$	423.034	−	3455.20i	0.121526	−	0.992588i
$59$	423.034	−	3455.20i	0.121526	−	0.992588i
$60$	415.917			0.115533
$61$			441.526i			0.118658i	0.998238	+	0.0593290i	$0.0188961\pi$
$61$			441.526i			0.118658i	−0.998238	+	0.0593290i	$0.981104\pi$
$62$	699.012			0.181845
$63$	274.717			0.0692157
$64$	−512.000			−0.125000
$65$			1619.64i			0.383347i
$66$	−3157.04			−0.724757
$67$			8215.23i			1.83008i	0.403362	+	0.915040i	$0.367842\pi$
$67$			8215.23i			1.83008i	−0.403362	+	0.915040i	$0.632158\pi$
$68$	6.63937			0.00143585
$69$			2442.68i			0.513061i
$70$		−	287.940i		−	0.0587633i
$71$	9394.94			1.86371			0.931853	−	0.362836i	$-0.118191\pi$
$71$	9394.94			1.86371			0.931853	+	0.362836i	$0.118191\pi$
$72$		−	610.940i		−	0.117851i
$73$		−	3859.68i		−	0.724278i	−0.932124	−	0.362139i	$-0.882047\pi$
$73$		−	3859.68i		−	0.724278i	0.932124	−	0.362139i	$-0.117953\pi$
$74$	−3324.72			−0.607145
$75$	−2727.42			−0.484874
$76$	−2033.50			−0.352061
$77$			2185.62i			0.368633i
$78$	2379.09			0.391040
$79$	−7332.48			−1.17489			−0.587445	−	0.809264i	$-0.699866\pi$
$79$	−7332.48			−1.17489			−0.587445	+	0.809264i	$0.699866\pi$
$80$	−640.347			−0.100054
$81$	729.000			0.111111
$82$		−	7582.41i		−	1.12766i
$83$			2016.11i			0.292656i	0.989236	+	0.146328i	$0.0467455\pi$
$83$			2016.11i			0.292656i	−0.989236	+	0.146328i	$0.953254\pi$
$84$	−422.955			−0.0599426
$85$	8.30370			0.00114930
$86$	−2956.08			−0.399686
$87$	−1676.05			−0.221436
$88$	4860.58			0.627658
$89$			13542.5i			1.70970i	0.518874	+	0.854851i	$0.326352\pi$
$89$			13542.5i			1.70970i	−0.518874	+	0.854851i	$0.673648\pi$
$90$		−	764.089i		−	0.0943320i
$91$		−	1647.04i		−	0.198894i
$92$		−	3760.76i		−	0.444324i
$93$		−	1284.17i		−	0.148476i
$94$	−9804.34			−1.10959
$95$	−2543.26			−0.281801
$96$			940.604i			0.102062i
$97$		−	14364.0i		−	1.52662i	−0.646031	−	0.763311i	$-0.723572\pi$
$97$		−	14364.0i		−	1.52662i	0.646031	−	0.763311i	$-0.276428\pi$
$98$		−	6498.24i		−	0.676618i
$99$			5799.85i			0.591761i
$100$	4199.13			0.419913
$101$			5621.97i			0.551119i	0.961284	+	0.275560i	$0.0888631\pi$
$101$			5621.97i			0.551119i	−0.961284	+	0.275560i	$0.911137\pi$
$102$		−	12.1973i		−	0.00117237i
$103$		−	8704.61i		−	0.820493i	−0.911975	−	0.410247i	$-0.865443\pi$
$103$		−	8704.61i		−	0.820493i	0.911975	−	0.410247i	$-0.134557\pi$
$104$	−3662.84			−0.338650
$105$	−528.980			−0.0479800
$106$		−	14593.9i		−	1.29885i
$107$	−14770.5			−1.29011			−0.645054	−	0.764137i	$-0.723165\pi$
$107$	−14770.5			−1.29011			−0.645054	+	0.764137i	$0.723165\pi$
$108$	−1122.37			−0.0962250
$109$		−	3068.24i		−	0.258248i	−0.991628	−	0.129124i	$-0.958783\pi$
$109$		−	3068.24i		−	0.258248i	0.991628	−	0.129124i	$-0.0412165\pi$
$110$	6079.02			0.502398
$111$			6107.91i			0.495732i
$112$	651.182			0.0519118
$113$		−	17760.0i		−	1.39087i	−0.718591	−	0.695433i	$-0.755213\pi$
$113$		−	17760.0i		−	1.39087i	0.718591	−	0.695433i	$-0.244787\pi$
$114$			3735.79i			0.287457i
$115$		−	4703.49i		−	0.355652i
$116$	2580.45			0.191769
$117$		−	4370.66i		−	0.319283i
$118$	9772.78	+	1196.52i	0.701866	+	0.0859322i
$119$	−8.44420			−0.000596300
$120$			1176.39i			0.0816939i
$121$	−31502.1			−2.15163
$122$	−1248.82			−0.0839038
$123$	−13929.8			−0.920733
$124$			1977.11i			0.128584i
$125$	11505.1			0.736329
$126$			777.018i			0.0489429i
$127$	−21918.0			−1.35892			−0.679459	−	0.733714i	$-0.737785\pi$
$127$	−21918.0			−1.35892			−0.679459	+	0.733714i	$0.737785\pi$
$128$		−	1448.15i		−	0.0883883i
$129$			5430.66i			0.326342i
$130$	−4581.03			−0.271067
$131$			28861.1i			1.68179i	0.541202	+	0.840893i	$0.317970\pi$
$131$			28861.1i			1.68179i	−0.541202	+	0.840893i	$0.682030\pi$
$132$		−	8929.46i		−	0.512480i
$133$	2586.29			0.146209
$134$	−23236.2			−1.29406
$135$	−1403.72			−0.0770217
$136$			18.7790i			0.00101530i
$137$	16609.6			0.884950			0.442475	−	0.896781i	$-0.354101\pi$
$137$	16609.6			0.884950			0.442475	+	0.896781i	$0.354101\pi$
$138$	−6908.96			−0.362789
$139$	18096.7			0.936632			0.468316	−	0.883561i	$-0.344861\pi$
$139$	18096.7			0.936632			0.468316	+	0.883561i	$0.344861\pi$
$140$	814.418			0.0415519
$141$			18011.7i			0.905977i
$142$			26572.9i			1.31784i
$143$	34772.5			1.70045
$144$	1728.00			0.0833333
$145$	3227.30			0.153498
$146$	10916.8			0.512142
$147$	−11938.0			−0.552456
$148$		−	9403.74i		−	0.429316i
$149$		−	14995.2i		−	0.675427i	−0.941249	−	0.337713i	$-0.890347\pi$
$149$		−	14995.2i		−	0.675427i	0.941249	−	0.337713i	$-0.109653\pi$
$150$		−	7714.30i		−	0.342858i
$151$			37752.7i			1.65575i	0.560916	+	0.827873i	$0.310449\pi$
$151$			37752.7i			1.65575i	−0.560916	+	0.827873i	$0.689551\pi$
$152$		−	5751.62i		−	0.248945i
$153$	−22.4079			−0.000957233
$154$	−6181.88			−0.260663
$155$			2472.72i			0.102923i
$156$			6729.07i			0.276507i
$157$		−	505.595i		−	0.0205118i	−0.999947	−	0.0102559i	$-0.996735\pi$
$157$		−	505.595i		−	0.0205118i	0.999947	−	0.0102559i	$-0.00326461\pi$
$158$		−	20739.4i		−	0.830772i
$159$	−26810.6			−1.06050
$160$		−	1811.17i		−	0.0707490i
$161$			4783.08i			0.184525i
$162$			2061.92i			0.0785674i
$163$	−7951.79			−0.299288			−0.149644	−	0.988740i	$-0.547813\pi$
$163$	−7951.79			−0.299288			−0.149644	+	0.988740i	$0.547813\pi$
$164$	21446.3			0.797378
$165$		−	11167.9i		−	0.410206i
$166$	−5702.42			−0.206939
$167$	53639.0			1.92330			0.961652	−	0.274273i	$-0.0884372\pi$
$167$	53639.0			1.92330			0.961652	+	0.274273i	$0.0884372\pi$
$168$		−	1196.30i		−	0.0423858i
$169$	2357.07			0.0825277
$170$			23.4864i			0.000812679i
$171$	6863.08			0.234707
$172$		−	8361.05i		−	0.282621i
$173$			16064.4i			0.536752i	0.963314	+	0.268376i	$0.0864869\pi$
$173$			16064.4i			0.536752i	−0.963314	+	0.268376i	$0.913513\pi$
$174$		−	4740.58i		−	0.156579i
$175$	−5340.62			−0.174388
$176$			13747.8i			0.443821i
$177$	2198.15	−	17953.7i	0.0701633	−	0.573071i
$178$	−38304.1			−1.20894
$179$		−	49040.9i		−	1.53057i	−0.643693	−	0.765284i	$-0.722599\pi$
$179$		−	49040.9i		−	1.53057i	0.643693	−	0.765284i	$-0.277401\pi$
$180$	2161.17			0.0667028
$181$	39633.6			1.20978			0.604889	−	0.796310i	$-0.293217\pi$
$181$	39633.6			1.20978			0.604889	+	0.796310i	$0.293217\pi$
$182$	4658.54			0.140640
$183$			2294.24i			0.0685072i
$184$	10637.0			0.314185
$185$		−	11761.0i		−	0.343639i
$186$	3632.17			0.104988
$187$		−	178.275i		−	0.00509808i
$188$		−	27730.9i		−	0.784599i
$189$	1427.47			0.0399617
$190$		−	7193.42i		−	0.199264i
$191$			55669.7i			1.52599i	0.646403	+	0.762996i	$0.276272\pi$
$191$			55669.7i			1.52599i	−0.646403	+	0.762996i	$0.723728\pi$
$192$	−2660.43			−0.0721688
$193$	25059.0			0.672743			0.336371	−	0.941729i	$-0.390800\pi$
$193$	25059.0			0.672743			0.336371	+	0.941729i	$0.390800\pi$
$194$	40627.5			1.07949
$195$			8415.89i			0.221325i
$196$	18379.8			0.478441
$197$	63019.9			1.62385			0.811924	−	0.583763i	$-0.198420\pi$
$197$	63019.9			1.62385			0.811924	+	0.583763i	$0.198420\pi$
$198$	−16404.5			−0.418438
$199$	21749.0			0.549204			0.274602	−	0.961558i	$-0.411454\pi$
$199$	21749.0			0.549204			0.274602	+	0.961558i	$0.411454\pi$
$200$			11876.9i			0.296924i
$201$			42687.6i			1.05660i
$202$	−15901.3			−0.389700
$203$	−3281.91			−0.0796407
$204$	34.4992			0.000828988
$205$	26822.4			0.638248
$206$	24620.4			0.580176
$207$			12692.6i			0.296216i
$208$		−	10360.1i		−	0.239462i
$209$			54602.0i			1.25002i
$210$		−	1496.18i		−	0.0339270i
$211$		−	4681.52i		−	0.105153i	−0.998617	−	0.0525765i	$-0.983257\pi$
$211$		−	4681.52i		−	0.105153i	0.998617	−	0.0525765i	$-0.0167433\pi$
$212$	41277.6			0.918424
$213$	48817.6			1.07601
$214$		−	41777.1i		−	0.912244i
$215$		−	10457.0i		−	0.226219i
$216$		−	3174.54i		−	0.0680414i
$217$		−	2514.56i		−	0.0534001i
$218$	8678.30			0.182609
$219$		−	20055.5i		−	0.418162i
$220$			17194.1i			0.355249i
$221$			134.344i			0.00275065i
$222$	−17275.8			−0.350535
$223$	−41799.6			−0.840549			−0.420274	−	0.907397i	$-0.638066\pi$
$223$	−41799.6			−0.840549			−0.420274	+	0.907397i	$0.638066\pi$
$224$			1841.82i			0.0367072i
$225$	−14172.1			−0.279942
$226$	50232.8			0.983491
$227$			84678.2i			1.64331i	0.569984	+	0.821656i	$0.306950\pi$
$227$			84678.2i			1.64331i	−0.569984	+	0.821656i	$0.693050\pi$
$228$	−10566.4			−0.203263
$229$			65177.3i			1.24287i	0.783466	+	0.621435i	$0.213450\pi$
$229$			65177.3i			1.24287i	−0.783466	+	0.621435i	$0.786550\pi$
$230$	13303.5			0.251484
$231$			11356.8i			0.212830i
$232$			7298.60i			0.135601i
$233$		−	26841.3i		−	0.494415i	−0.968963	−	0.247207i	$-0.920487\pi$
$233$		−	26841.3i		−	0.494415i	0.968963	−	0.247207i	$-0.0795129\pi$
$234$	12362.1			0.225767
$235$		−	34682.3i		−	0.628019i
$236$	−3384.27	+	27641.6i	−0.0607632	+	0.496294i
$237$	−38100.7			−0.678323
$238$		−	23.8838i		−	0.000421648i
$239$	79266.3			1.38769			0.693845	−	0.720124i	$-0.255915\pi$
$239$	79266.3			1.38769			0.693845	+	0.720124i	$0.255915\pi$
$240$	−3327.34			−0.0577663
$241$	−65983.7			−1.13606			−0.568032	−	0.823007i	$-0.692295\pi$
$241$	−65983.7			−1.13606			−0.568032	+	0.823007i	$0.692295\pi$
$242$		−	89101.3i		−	1.52143i
$243$	3788.00			0.0641500
$244$		−	3532.21i		−	0.0593290i
$245$	22987.2			0.382960
$246$		−	39399.4i		−	0.651057i
$247$		−	41147.0i		−	0.674442i
$248$	−5592.10			−0.0909225
$249$			10476.0i			0.168965i
$250$			32541.5i			0.520663i
$251$	98663.8			1.56607			0.783033	−	0.621980i	$-0.213671\pi$
$251$	98663.8			1.56607			0.783033	+	0.621980i	$0.213671\pi$
$252$	−2197.74			−0.0346079
$253$	−100981.			−1.57760
$254$		−	61993.4i		−	0.960900i
$255$	43.1473			0.000663549
$256$	4096.00			0.0625000
$257$	−29166.2			−0.441585			−0.220792	−	0.975321i	$-0.570864\pi$
$257$	−29166.2			−0.441585			−0.220792	+	0.975321i	$0.570864\pi$
$258$	−15360.2			−0.230759
$259$			11960.0i			0.178293i
$260$		−	12957.1i		−	0.191673i
$261$	−8709.01			−0.127846
$262$	−81631.6			−1.18920
$263$	35005.4			0.506086			0.253043	−	0.967455i	$-0.418569\pi$
$263$	35005.4			0.506086			0.253043	+	0.967455i	$0.418569\pi$
$264$	25256.3			0.362378
$265$	51625.0			0.735137
$266$			7315.13i			0.103385i
$267$			70369.2i			0.987097i
$268$		−	65721.9i		−	0.915040i
$269$		−	45566.0i		−	0.629704i	−0.949141	−	0.314852i	$-0.898045\pi$
$269$		−	45566.0i		−	0.629704i	0.949141	−	0.314852i	$-0.101955\pi$
$270$		−	3970.32i		−	0.0544626i
$271$	117165.			1.59536			0.797682	−	0.603079i	$-0.206060\pi$
$271$	117165.			1.59536			0.797682	+	0.603079i	$0.206060\pi$
$272$	−53.1149			−0.000717925
$273$		−	8558.29i		−	0.114832i
$274$			46979.1i			0.625754i
$275$		−	112752.i		−	1.49093i
$276$		−	19541.5i		−	0.256531i
$277$	24391.1			0.317886			0.158943	−	0.987288i	$-0.449191\pi$
$277$	24391.1			0.317886			0.158943	+	0.987288i	$0.449191\pi$
$278$			51185.1i			0.662299i
$279$		−	6672.73i		−	0.0857226i
$280$			2303.52i			0.0293816i
$281$	−67971.2			−0.860820			−0.430410	−	0.902633i	$-0.641631\pi$
$281$	−67971.2			−0.860820			−0.430410	+	0.902633i	$0.641631\pi$
$282$	−50944.8			−0.640622
$283$		−	53084.1i		−	0.662814i	−0.943488	−	0.331407i	$-0.892477\pi$
$283$		−	53084.1i		−	0.662814i	0.943488	−	0.331407i	$-0.107523\pi$
$284$	−75159.6			−0.931853
$285$	−13215.1			−0.162698
$286$			98351.6i			1.20240i
$287$	−27276.2			−0.331147
$288$			4887.52i			0.0589256i
$289$	−83520.3			−0.999992
$290$			9128.19i			0.108540i
$291$		−	74637.5i		−	0.881396i
$292$			30877.4i			0.362139i
$293$	−26421.2			−0.307764			−0.153882	−	0.988089i	$-0.549178\pi$
$293$	−26421.2			−0.307764			−0.153882	+	0.988089i	$0.549178\pi$
$294$		−	33765.9i		−	0.390646i
$295$	−4232.63	+	34570.7i	−0.0486369	+	0.397250i
$296$	26597.8			0.303572
$297$			30136.9i			0.341654i
$298$	42412.7			0.477599
$299$	76097.2			0.851190
$300$	21819.3			0.242437
$301$			10633.9i			0.117371i
$302$	−106781.			−1.17079
$303$			29212.6i			0.318189i
$304$	16268.0			0.176031
$305$		−	4417.65i		−	0.0474889i
$306$		−	63.3790i		−	0.000676866i
$307$	−64300.7			−0.682243			−0.341121	−	0.940019i	$-0.610807\pi$
$307$	−64300.7			−0.682243			−0.341121	+	0.940019i	$0.610807\pi$
$308$		−	17485.0i		−	0.184316i
$309$		−	45230.5i		−	0.473712i
$310$	−6993.91			−0.0727774
$311$	−101244.			−1.04677			−0.523384	−	0.852097i	$-0.675331\pi$
$311$	−101244.			−1.04677			−0.523384	+	0.852097i	$0.675331\pi$
$312$	−19032.7			−0.195520
$313$			46262.1i			0.472212i	0.971727	+	0.236106i	$0.0758712\pi$
$313$			46262.1i			0.472212i	−0.971727	+	0.236106i	$0.924129\pi$
$314$	1430.04			0.0145040
$315$	−2748.66			−0.0277013
$316$	58659.9			0.587445
$317$	133478.			1.32829			0.664145	−	0.747604i	$-0.268796\pi$
$317$	133478.			1.32829			0.664145	+	0.747604i	$0.268796\pi$
$318$		−	75831.9i		−	0.749890i
$319$		−	69288.0i		−	0.680890i
$320$	5122.77			0.0500271
$321$	−76749.5			−0.744844
$322$	−13528.6			−0.130479
$323$	−210.956			−0.00202203
$324$	−5832.00			−0.0555556
$325$			84967.5i			0.804426i
$326$		−	22491.0i		−	0.211629i
$327$		−	15943.1i		−	0.149099i
$328$			60659.3i			0.563832i
$329$			35269.2i			0.325839i
$330$	31587.5			0.290060
$331$	−169734.			−1.54922			−0.774609	−	0.632440i	$-0.782053\pi$
$331$	−169734.			−1.54922			−0.774609	+	0.632440i	$0.782053\pi$
$332$		−	16128.9i		−	0.146328i
$333$			31737.6i			0.286211i
$334$			151714.i			1.35998i
$335$		−	82196.8i		−	0.732429i
$336$	3383.64			0.0299713
$337$		−	13800.1i		−	0.121513i	−0.998153	−	0.0607563i	$-0.980649\pi$
$337$		−	13800.1i		−	0.121513i	0.998153	−	0.0607563i	$-0.0193512\pi$
$338$			6666.81i			0.0583559i
$339$		−	92283.5i		−	0.803017i
$340$	−66.4296			−0.000574651
$341$	53087.6			0.456546
$342$			19411.7i			0.165963i
$343$	−47805.6			−0.406341
$344$	23648.6			0.199843
$345$		−	24440.1i		−	0.205336i
$346$	−45437.1			−0.379541
$347$		−	94772.8i		−	0.787090i	−0.919305	−	0.393545i	$-0.871249\pi$
$347$		−	94772.8i		−	0.787090i	0.919305	−	0.393545i	$-0.128751\pi$
$348$	13408.4			0.110718
$349$		−	108927.i		−	0.894307i	−0.894457	−	0.447153i	$-0.852438\pi$
$349$		−	108927.i		−	0.894307i	0.894457	−	0.447153i	$-0.147562\pi$
$350$		−	15105.6i		−	0.123311i
$351$		−	22710.6i		−	0.184338i
$352$	−38884.6			−0.313829
$353$		−	94203.7i		−	0.755994i	−0.925807	−	0.377997i	$-0.876613\pi$
$353$		−	94203.7i		−	0.755994i	0.925807	−	0.377997i	$-0.123387\pi$
$354$	50780.9	+	6217.30i	0.405222	+	0.0496130i
$355$	−94000.3			−0.745886
$356$		−	108340.i		−	0.854851i
$357$	−43.8774			−0.000344274
$358$	138709.			1.08227
$359$	−209394.			−1.62471			−0.812354	−	0.583165i	$-0.801814\pi$
$359$	−209394.			−1.62471			−0.812354	+	0.583165i	$0.801814\pi$
$360$			6112.71i			0.0471660i
$361$	−65709.4			−0.504212
$362$			112101.i			0.855443i
$363$	−163689.			−1.24225
$364$			13176.4i			0.0994472i
$365$			38617.7i			0.289868i
$366$	−6489.08			−0.0484419
$367$		−	128948.i		−	0.957373i	−0.877986	−	0.478687i	$-0.841113\pi$
$367$		−	128948.i		−	0.957373i	0.877986	−	0.478687i	$-0.158887\pi$
$368$			30086.1i			0.222162i
$369$	−72381.2			−0.531586
$370$	33265.3			0.242989
$371$	−52498.5			−0.381416
$372$			10273.3i			0.0742379i
$373$	87947.6			0.632130			0.316065	−	0.948738i	$-0.397638\pi$
$373$	87947.6			0.632130			0.316065	+	0.948738i	$0.397638\pi$
$374$	504.237			0.00360489
$375$	59782.5			0.425120
$376$	78434.7			0.554795
$377$			52214.1i			0.367371i
$378$			4037.50i			0.0282572i
$379$	123649.			0.860821			0.430411	−	0.902633i	$-0.358369\pi$
$379$	123649.			0.860821			0.430411	+	0.902633i	$0.358369\pi$
$380$	20346.1			0.140901
$381$	−113889.			−0.784571
$382$	−157458.			−1.07904
$383$	158988.			1.08385			0.541924	−	0.840428i	$-0.317696\pi$
$383$	158988.			1.08385			0.541924	+	0.840428i	$0.317696\pi$
$384$		−	7524.83i		−	0.0510310i
$385$		−	21868.1i		−	0.147533i
$386$			70877.6i			0.475701i
$387$			28218.5i			0.188414i
$388$			114912.i			0.763311i
$389$	40077.7			0.264852			0.132426	−	0.991193i	$-0.457723\pi$
$389$	40077.7			0.264852			0.132426	+	0.991193i	$0.457723\pi$
$390$	−23803.7			−0.156501
$391$		−	390.142i		−	0.00255193i
$392$			51985.9i			0.338309i
$393$			149967.i			0.970979i
$394$			178247.i			1.14823i
$395$	73364.5			0.470210
$396$		−	46398.8i		−	0.295881i
$397$			17559.9i			0.111414i	0.998447	+	0.0557071i	$0.0177413\pi$
$397$			17559.9i			0.111414i	−0.998447	+	0.0557071i	$0.982259\pi$
$398$			61515.5i			0.388346i
$399$	13438.8			0.0844138
$400$	−33593.1			−0.209957
$401$			171518.i			1.06665i	0.845912	+	0.533323i	$0.179057\pi$
$401$			171518.i			1.06665i	−0.845912	+	0.533323i	$0.820943\pi$
$402$	−120739.			−0.747127
$403$	−40005.8			−0.246327
$404$		−	44975.7i		−	0.275560i
$405$	−7293.95			−0.0444685
$406$		−	9282.65i		−	0.0563144i
$407$	−252501.			−1.52432
$408$			97.5784i			0.000586183i
$409$			22250.3i			0.133011i	0.997786	+	0.0665057i	$0.0211851\pi$
$409$			22250.3i			0.133011i	−0.997786	+	0.0665057i	$0.978815\pi$
$410$			75865.1i			0.451310i
$411$	86306.1			0.510926
$412$			69636.9i			0.410247i
$413$	4304.25	−	35155.7i	0.0252346	−	0.206108i
$414$	−35900.0			−0.209456
$415$		−	20172.0i		−	0.117126i
$416$	29302.7			0.169325
$417$	94033.0			0.540765
$418$	−154438.			−0.883895
$419$			58173.2i			0.331356i	0.986180	+	0.165678i	$0.0529813\pi$
$419$			58173.2i			0.331356i	−0.986180	+	0.165678i	$0.947019\pi$
$420$	4231.84			0.0239900
$421$		−	108403.i		−	0.611613i	−0.952094	−	0.305806i	$-0.901074\pi$
$421$		−	108403.i		−	0.611613i	0.952094	−	0.305806i	$-0.0989261\pi$
$422$	13241.3			0.0743544
$423$			93591.7i			0.523066i
$424$			116751.i			0.649424i
$425$	435.619			0.00241173
$426$			138077.i			0.760855i
$427$			4492.40i			0.0246390i
$428$	118164.			0.645054
$429$	180683.			0.981756
$430$	29576.8			0.159961
$431$			82375.6i			0.443449i	0.975109	+	0.221725i	$0.0711686\pi$
$431$			82375.6i			0.443449i	−0.975109	+	0.221725i	$0.928831\pi$
$432$	8978.95			0.0481125
$433$	178319.			0.951090			0.475545	−	0.879691i	$-0.342251\pi$
$433$	178319.			0.951090			0.475545	+	0.879691i	$0.342251\pi$
$434$	7112.25			0.0377596
$435$	16769.6			0.0886224
$436$			24545.9i			0.129124i
$437$			119493.i			0.625717i
$438$	56725.5			0.295685
$439$	−254103.			−1.31850			−0.659251	−	0.751923i	$-0.729127\pi$
$439$	−254103.			−1.31850			−0.659251	+	0.751923i	$0.729127\pi$
$440$	−48632.1			−0.251199
$441$	−62031.8			−0.318961
$442$	−379.984			−0.00194500
$443$		−	287247.i		−	1.46368i	−0.681474	−	0.731842i	$-0.738661\pi$
$443$		−	287247.i		−	1.46368i	0.681474	−	0.731842i	$-0.261339\pi$
$444$		−	48863.3i		−	0.247866i
$445$		−	135499.i		−	0.684251i
$446$		−	118227.i		−	0.594358i
$447$		−	77917.1i		−	0.389958i
$448$	−5209.45			−0.0259559
$449$	129559.			0.642653			0.321326	−	0.946969i	$-0.395871\pi$
$449$	129559.			0.642653			0.321326	+	0.946969i	$0.395871\pi$
$450$		−	40084.7i		−	0.197949i
$451$		−	575858.i		−	2.83115i
$452$			142080.i			0.695433i
$453$			196169.i			0.955945i
$454$	−239506.			−1.16200
$455$			16479.4i			0.0796008i
$456$		−	29886.3i		−	0.143728i
$457$			18236.8i			0.0873203i	0.999046	+	0.0436602i	$0.0139019\pi$
$457$			18236.8i			0.0873203i	−0.999046	+	0.0436602i	$0.986098\pi$
$458$	−184349.			−0.878841
$459$	−116.435			−0.000552659
$460$			37628.0i			0.177826i
$461$	−243028.			−1.14355			−0.571773	−	0.820412i	$-0.693744\pi$
$461$	−243028.			−1.14355			−0.571773	+	0.820412i	$0.693744\pi$
$462$	−32122.0			−0.150494
$463$		−	114535.i		−	0.534289i	−0.963657	−	0.267144i	$-0.913920\pi$
$463$		−	114535.i		−	0.534289i	0.963657	−	0.267144i	$-0.0860801\pi$
$464$	−20643.6			−0.0958846
$465$			12848.6i			0.0594225i
$466$	75918.6			0.349604
$467$			60874.5i			0.279127i	0.990213	+	0.139563i	$0.0445699\pi$
$467$			60874.5i			0.279127i	−0.990213	+	0.139563i	$0.955430\pi$
$468$			34965.3i			0.159641i
$469$			83587.6i			0.380011i
$470$	98096.5			0.444076
$471$		−	2627.15i		−	0.0118425i
$472$	−78182.2	−	9572.16i	−0.350933	−	0.0429661i
$473$	−224504.			−1.00346
$474$		−	107765.i		−	0.479646i
$475$	−133421.			−0.591340
$476$	67.5536			0.000298150
$477$	−139312.			−0.612283
$478$			224199.i			0.981245i
$479$	−219233.			−0.955511			−0.477755	−	0.878493i	$-0.658549\pi$
$479$	−219233.			−0.955511			−0.477755	+	0.878493i	$0.658549\pi$
$480$		−	9411.13i		−	0.0408469i
$481$	190280.			0.822439
$482$		−	186630.i		−	0.803318i
$483$			24853.6i			0.106536i
$484$	252016.			1.07582
$485$			143718.i			0.610980i
$486$			10714.1i			0.0453609i
$487$	199792.			0.842404			0.421202	−	0.906967i	$-0.361608\pi$
$487$	199792.			0.842404			0.421202	+	0.906967i	$0.361608\pi$
$488$	9990.59			0.0419519
$489$	−41318.7			−0.172794
$490$			65017.6i			0.270794i
$491$	−132707.			−0.550468			−0.275234	−	0.961377i	$-0.588755\pi$
$491$	−132707.			−0.550468			−0.275234	+	0.961377i	$0.588755\pi$
$492$	111438.			0.460367
$493$	267.696			0.00110141
$494$	116381.			0.476902
$495$		−	58029.9i		−	0.236833i
$496$		−	15816.8i		−	0.0642919i
$497$	95590.8			0.386993
$498$	−29630.6			−0.119476
$499$	−146596.			−0.588735			−0.294368	−	0.955692i	$-0.595109\pi$
$499$	−146596.			−0.588735			−0.294368	+	0.955692i	$0.595109\pi$
$500$	−92041.1			−0.368165
$501$	278717.			1.11042
$502$			279063.i			1.10738i
$503$			393072.i			1.55359i	0.629753	+	0.776795i	$0.283156\pi$
$503$			393072.i			1.55359i	−0.629753	+	0.776795i	$0.716844\pi$
$504$		−	6216.14i		−	0.0244715i
$505$		−	56250.1i		−	0.220567i
$506$		−	285617.i		−	1.11553i
$507$	12247.7			0.0476474
$508$	175344.			0.679459
$509$		−	265286.i		−	1.02395i	−0.859001	−	0.511974i	$-0.828914\pi$
$509$		−	265286.i		−	1.02395i	0.859001	−	0.511974i	$-0.171086\pi$
$510$			122.039i			0.000469200i
$511$		−	39271.1i		−	0.150394i
$512$			11585.2i			0.0441942i
$513$	35661.6			0.135508
$514$		−	82494.5i		−	0.312248i
$515$			87093.2i			0.328375i
$516$		−	43445.3i		−	0.163171i
$517$	−744606.			−2.78577
$518$	−33828.1			−0.126072
$519$			83473.3i			0.309894i
$520$	36648.2			0.135533
$521$	360993.			1.32991			0.664957	−	0.746882i	$-0.268450\pi$
$521$	360993.			1.32991			0.664957	+	0.746882i	$0.268450\pi$
$522$		−	24632.8i		−	0.0904009i
$523$	120641.			0.441055			0.220528	−	0.975381i	$-0.429222\pi$
$523$	120641.			0.441055			0.220528	+	0.975381i	$0.429222\pi$
$524$		−	230889.i		−	0.840893i
$525$	−27750.7			−0.100683
$526$			99010.3i			0.357857i
$527$			205.105i			0.000738508i
$528$			71435.7i			0.256240i
$529$	58851.8			0.210304
$530$			146018.i			0.519820i
$531$	11421.9	−	93290.4i	0.0405088	−	0.330863i
$532$	−20690.3			−0.0731045
$533$			433956.i			1.52753i
$534$	−199034.			−0.697983
$535$	147784.			0.516323
$536$	185890.			0.647031
$537$		−	254824.i		−	0.883673i
$538$	128880.			0.445268
$539$		−	493519.i		−	1.69874i
$540$	11229.8			0.0385109
$541$			471472.i			1.61087i	0.592682	+	0.805437i	$0.298069\pi$
$541$			471472.i			1.61087i	−0.592682	+	0.805437i	$0.701931\pi$
$542$			331393.i			1.12809i
$543$	205942.			0.698466
$544$		−	150.232i		−	0.000507649i
$545$			30699.0i			0.103355i
$546$	24206.5			0.0811983
$547$	273884.			0.915359			0.457679	−	0.889117i	$-0.348681\pi$
$547$	273884.			0.915359			0.457679	+	0.889117i	$0.348681\pi$
$548$	−132877.			−0.442475
$549$			11921.2i			0.0395526i
$550$	318910.			1.05425
$551$	−81989.8			−0.270058
$552$	55271.6			0.181395
$553$	−74605.9			−0.243962
$554$			68988.4i			0.224780i
$555$		−	61112.2i		−	0.198400i
$556$	−144773.			−0.468316
$557$	−375768.			−1.21118			−0.605591	−	0.795776i	$-0.707063\pi$
$557$	−375768.			−1.21118			−0.605591	+	0.795776i	$0.707063\pi$
$558$	18873.3			0.0606150
$559$	169182.			0.541415
$560$	−6515.34			−0.0207760
$561$		−	926.343i		−	0.00294338i
$562$		−	192252.i		−	0.608692i
$563$			292458.i			0.922671i	0.887226	+	0.461336i	$0.152630\pi$
$563$			292458.i			0.922671i	−0.887226	+	0.461336i	$0.847370\pi$
$564$		−	144094.i		−	0.452988i
$565$			177696.i			0.556648i
$566$	150145.			0.468680
$567$	7417.36			0.0230719
$568$		−	212583.i		−	0.658920i
$569$			108309.i			0.334535i	0.985912	+	0.167268i	$0.0534944\pi$
$569$			108309.i			0.334535i	−0.985912	+	0.167268i	$0.946506\pi$
$570$		−	37378.1i		−	0.115045i
$571$		−	355763.i		−	1.09116i	−0.838059	−	0.545580i	$-0.816309\pi$
$571$		−	355763.i		−	1.09116i	0.838059	−	0.545580i	$-0.183691\pi$
$572$	−278180.			−0.850226
$573$			289268.i			0.881032i
$574$		−	77148.8i		−	0.234156i
$575$		−	246749.i		−	0.746311i
$576$	−13824.0			−0.0416667
$577$	352591.			1.05906			0.529529	−	0.848292i	$-0.322369\pi$
$577$	352591.			1.05906			0.529529	+	0.848292i	$0.322369\pi$
$578$		−	236231.i		−	0.707101i
$579$	130210.			0.388408
$580$	−25818.4			−0.0767492
$581$			20513.3i			0.0607692i
$582$	211107.			0.623241
$583$		−	1.10835e6i		−	3.26093i
$584$	−87334.6			−0.256071
$585$			43730.3i			0.127782i
$586$		−	74730.5i		−	0.217622i
$587$		−	507027.i		−	1.47148i	−0.677263	−	0.735741i	$-0.736834\pi$
$587$		−	507027.i		−	1.47148i	0.677263	−	0.735741i	$-0.263166\pi$
$588$	95504.3			0.276228
$589$		−	62819.6i		−	0.181077i
$590$	−97780.7	−	11971.7i	−0.280898	−	0.0343915i
$591$	327461.			0.937529
$592$			75229.9i			0.214658i
$593$	323321.			0.919441			0.459721	−	0.888064i	$-0.347950\pi$
$593$	323321.			0.919441			0.459721	+	0.888064i	$0.347950\pi$
$594$	−85240.1			−0.241586
$595$	84.4878			0.000238649
$596$			119961.i			0.337713i
$597$	113011.			0.317083
$598$			215235.i			0.601882i
$599$	−400344.			−1.11578			−0.557891	−	0.829914i	$-0.688389\pi$
$599$	−400344.			−1.11578			−0.557891	+	0.829914i	$0.688389\pi$
$600$			61714.4i			0.171429i
$601$		−	441544.i		−	1.22243i	−0.791463	−	0.611217i	$-0.790680\pi$
$601$		−	441544.i		−	1.22243i	0.791463	−	0.611217i	$-0.209320\pi$
$602$	−30077.2			−0.0829937
$603$			221811.i			0.610027i
$604$		−	302021.i		−	0.827873i
$605$	315191.			0.861119
$606$	−82625.7			−0.224993
$607$	536879.			1.45713			0.728566	−	0.684975i	$-0.240187\pi$
$607$	536879.			1.45713			0.728566	+	0.684975i	$0.240187\pi$
$608$			46013.0i			0.124472i
$609$	−17053.3			−0.0459806
$610$	12495.0			0.0335797
$611$	561121.			1.50305
$612$	179.263			0.000478616
$613$		−	9295.08i		−	0.0247362i	−0.999924	−	0.0123681i	$-0.996063\pi$
$613$		−	9295.08i		−	0.0247362i	0.999924	−	0.0123681i	$-0.00393698\pi$
$614$		−	181870.i		−	0.482418i
$615$	139373.			0.368493
$616$	49455.0			0.130331
$617$	−225032.			−0.591117			−0.295559	−	0.955325i	$-0.595506\pi$
$617$	−225032.			−0.591117			−0.295559	+	0.955325i	$0.595506\pi$
$618$	127931.			0.334965
$619$	533323.			1.39190			0.695952	−	0.718088i	$-0.254983\pi$
$619$	533323.			1.39190			0.695952	+	0.718088i	$0.254983\pi$
$620$		−	19781.8i		−	0.0514614i
$621$			65952.5i			0.171020i
$622$		−	286363.i		−	0.740177i
$623$			137792.i			0.355015i
$624$		−	53832.6i		−	0.138253i
$625$	212944.			0.545136
$626$	−130849.			−0.333904
$627$			283720.i			0.721697i
$628$			4044.76i			0.0102559i
$629$		−	975.545i		−	0.00246573i
$630$		−	7774.38i		−	0.0195878i
$631$	−347880.			−0.873716			−0.436858	−	0.899530i	$-0.643909\pi$
$631$	−347880.			−0.873716			−0.436858	+	0.899530i	$0.643909\pi$
$632$			165915.i			0.415386i
$633$		−	24325.9i		−	0.0607101i
$634$			377534.i			0.939243i
$635$	219298.			0.543861
$636$	214485.			0.530252
$637$			371907.i			0.916548i
$638$	195976.			0.481462
$639$	253663.			0.621235
$640$			14489.4i			0.0353745i
$641$	107469.			0.261558			0.130779	−	0.991412i	$-0.458252\pi$
$641$	107469.			0.261558			0.130779	+	0.991412i	$0.458252\pi$
$642$		−	217080.i		−	0.526685i
$643$	42640.9			0.103134			0.0515672	−	0.998670i	$-0.483578\pi$
$643$	42640.9			0.103134			0.0515672	+	0.998670i	$0.483578\pi$
$644$		−	38264.6i		−	0.0922626i
$645$		−	54336.0i		−	0.130608i
$646$		−	596.674i		−	0.00142979i
$647$	−526778.			−1.25840			−0.629200	−	0.777243i	$-0.716618\pi$
$647$	−526778.			−1.25840			−0.629200	+	0.777243i	$0.716618\pi$
$648$		−	16495.4i		−	0.0392837i
$649$	742209.	+	90871.6i	1.76213	+	0.215744i
$650$	−240324.			−0.568815
$651$		−	13066.0i		−	0.0308306i
$652$	63614.3			0.149644
$653$	99132.6			0.232482			0.116241	−	0.993221i	$-0.462915\pi$
$653$	99132.6			0.232482			0.116241	+	0.993221i	$0.462915\pi$
$654$	45093.8			0.105429
$655$		−	288768.i		−	0.673079i
$656$	−171570.			−0.398689
$657$		−	104211.i		−	0.241426i
$658$	−99756.3			−0.230403
$659$			349222.i			0.804138i	0.915609	+	0.402069i	$0.131709\pi$
$659$			349222.i			0.804138i	−0.915609	+	0.402069i	$0.868291\pi$
$660$			89342.9i			0.205103i
$661$	−168568.			−0.385810			−0.192905	−	0.981217i	$-0.561791\pi$
$661$	−168568.			−0.385810			−0.192905	+	0.981217i	$0.561791\pi$
$662$		−	480080.i		−	1.09546i
$663$			698.074i			0.00158809i
$664$	45619.3			0.103470
$665$	−25876.9			−0.0585152
$666$	−89767.6			−0.202382
$667$		−	151632.i		−	0.340831i
$668$	−429112.			−0.961652
$669$	−217197.			−0.485291
$670$	232488.			0.517905
$671$	−94843.9			−0.210651
$672$			9570.37i			0.0211929i
$673$		−	44064.7i		−	0.0972883i	−0.998816	−	0.0486442i	$-0.984510\pi$
$673$		−	44064.7i		−	0.0972883i	0.998816	−	0.0486442i	$-0.0154900\pi$
$674$	39032.5			0.0859223
$675$	−73640.3			−0.161625
$676$	−18856.6			−0.0412639
$677$	−340517.			−0.742953			−0.371476	−	0.928442i	$-0.621148\pi$
$677$	−340517.			−0.742953			−0.371476	+	0.928442i	$0.621148\pi$
$678$	261017.			0.567819
$679$		−	146149.i		−	0.316999i
$680$		−	187.891i		−	0.000406339i
$681$			440001.i			0.948767i
$682$			150154.i			0.322827i
$683$			549841.i			1.17868i	0.807885	+	0.589340i	$0.200612\pi$
$683$			549841.i			1.17868i	−0.807885	+	0.589340i	$0.799388\pi$
$684$	−54904.6			−0.117354
$685$	−166186.			−0.354172
$686$		−	135215.i		−	0.287327i
$687$			338671.i			0.717571i
$688$			66888.4i			0.141310i
$689$			835234.i			1.75942i
$690$	69127.0			0.145194
$691$			57804.6i			0.121062i	0.998166	+	0.0605308i	$0.0192793\pi$
$691$			57804.6i			0.121062i	−0.998166	+	0.0605308i	$0.980721\pi$
$692$		−	128516.i		−	0.268376i
$693$			59011.8i			0.122878i
$694$	268058.			0.556557
$695$	−181065.			−0.374856
$696$			37924.7i			0.0782894i
$697$	2224.84			0.00457966
$698$	308093.			0.632370
$699$		−	139471.i		−	0.285450i
$700$	42725.0			0.0871938
$701$			221070.i			0.449876i	0.974373	+	0.224938i	$0.0722180\pi$
$701$			221070.i			0.449876i	−0.974373	+	0.224938i	$0.927782\pi$
$702$	64235.3			0.130347
$703$			298790.i			0.604582i
$704$		−	109982.i		−	0.221910i
$705$		−	180215.i		−	0.362587i
$706$	266448.			0.534569
$707$			57201.9i			0.114438i
$708$	−17585.2	+	143630.i	−0.0350817	+	0.286536i
$709$	526978.			1.04834			0.524168	−	0.851615i	$-0.324377\pi$
$709$	526978.			1.04834			0.524168	+	0.851615i	$0.324377\pi$
$710$		−	265873.i		−	0.527421i
$711$	−197977.			−0.391630
$712$	306433.			0.604471
$713$	116178.			0.228532
$714$		−	124.104i		−	0.000243438i
$715$	−347914.			−0.680549
$716$			392327.i			0.765284i
$717$	411880.			0.801183
$718$		−	592256.i		−	1.14884i
$719$		−	298121.i		−	0.576680i	−0.957528	−	0.288340i	$-0.906897\pi$
$719$		−	298121.i		−	0.576680i	0.957528	−	0.288340i	$-0.0931033\pi$
$720$	−17289.4			−0.0333514
$721$		−	88566.9i		−	0.170373i
$722$		−	185854.i		−	0.356532i
$723$	−342861.			−0.655906
$724$	−317068.			−0.604889
$725$	169307.			0.322106
$726$		−	462984.i		−	0.878400i
$727$	−192109.			−0.363478			−0.181739	−	0.983347i	$-0.558173\pi$
$727$	−192109.			−0.363478			−0.181739	+	0.983347i	$0.558173\pi$
$728$	−37268.4			−0.0703198
$729$	19683.0			0.0370370
$730$	−109227.			−0.204968
$731$		−	867.376i		−	0.00162320i
$732$		−	18353.9i		−	0.0342536i
$733$	−68995.4			−0.128414			−0.0642069	−	0.997937i	$-0.520452\pi$
$733$	−68995.4			−0.128414			−0.0642069	+	0.997937i	$0.520452\pi$
$734$	364719.			0.676965
$735$	119445.			0.221102
$736$	−85096.3			−0.157092
$737$	−1.76471e6			−3.24891
$738$		−	204725.i		−	0.375888i
$739$		−	856470.i		−	1.56828i	−0.620585	−	0.784139i	$-0.713105\pi$
$739$		−	856470.i		−	1.56828i	0.620585	−	0.784139i	$-0.286895\pi$
$740$			94088.3i			0.171819i
$741$		−	213806.i		−	0.389389i
$742$		−	148488.i		−	0.269702i
$743$	681139.			1.23384			0.616919	−	0.787027i	$-0.288381\pi$
$743$	681139.			1.23384			0.616919	+	0.787027i	$0.288381\pi$
$744$	−29057.4			−0.0524941
$745$			150033.i			0.270317i
$746$			248753.i			0.446983i
$747$			54434.9i			0.0975520i
$748$			1426.20i			0.00254904i
$749$	−150285.			−0.267887
$750$			169090.i			0.300605i
$751$			563018.i			0.998258i	0.866528	+	0.499129i	$0.166347\pi$
$751$			563018.i			0.998258i	−0.866528	+	0.499129i	$0.833653\pi$
$752$			221847.i			0.392299i
$753$	512672.			0.904169
$754$	−147684.			−0.259771
$755$		−	377731.i		−	0.662657i
$756$	−11419.8			−0.0199809
$757$	−83064.2			−0.144951			−0.0724756	−	0.997370i	$-0.523090\pi$
$757$	−83064.2			−0.144951			−0.0724756	+	0.997370i	$0.523090\pi$
$758$			349733.i			0.608693i
$759$	−524712.			−0.910829
$760$			57547.3i			0.0996318i
$761$	−2625.62			−0.00453381			−0.00226690	−	0.999997i	$-0.500722\pi$
$761$	−2625.62			−0.00453381			−0.00226690	+	0.999997i	$0.500722\pi$
$762$		−	322127.i		−	0.554776i
$763$		−	31218.5i		−	0.0536244i
$764$		−	445358.i		−	0.762996i
$765$	224.200			0.000383100
$766$			449687.i			0.766396i
$767$	−559315.	−	68479.1i	−0.950748	−	0.116404i
$768$	21283.4			0.0360844
$769$			858356.i			1.45149i	0.687962	+	0.725747i	$0.258505\pi$
$769$			858356.i			1.45149i	−0.687962	+	0.725747i	$0.741495\pi$
$770$	61852.2			0.104322
$771$	−151552.			−0.254949
$772$	−200472.			−0.336371
$773$		−	108381.i		−	0.181383i	−0.995879	−	0.0906913i	$-0.971092\pi$
$773$		−	108381.i		−	0.181383i	0.995879	−	0.0906913i	$-0.0289077\pi$
$774$	−79814.1			−0.133229
$775$			129721.i			0.215976i
$776$	−325020.			−0.539743
$777$			62146.2i			0.102937i
$778$			113357.i			0.187279i
$779$	−681424.			−1.12290
$780$		−	67327.1i		−	0.110663i
$781$			2.01812e6i			3.30861i
$782$	1103.49			0.00180449
$783$	−45253.3			−0.0738120
$784$	−147038.			−0.239221
$785$			5058.69i			0.00820915i
$786$	−424170.			−0.686586
$787$	48333.8			0.0780371			0.0390186	−	0.999238i	$-0.487577\pi$
$787$	48333.8			0.0780371			0.0390186	+	0.999238i	$0.487577\pi$
$788$	−504159.			−0.811924
$789$	181894.			0.292189
$790$			207506.i			0.332489i
$791$		−	180703.i		−	0.288809i
$792$	131236.			0.209219
$793$	71472.6			0.113656
$794$	−49666.9			−0.0787818
$795$	268251.			0.424432
$796$	−173992.			−0.274602
$797$			801269.i			1.26143i	0.776016	+	0.630713i	$0.217238\pi$
$797$			801269.i			1.26143i	−0.776016	+	0.630713i	$0.782762\pi$
$798$			38010.5i			0.0596896i
$799$		−	2876.80i		−	0.00450626i
$800$		−	95015.5i		−	0.148462i
$801$			365649.i			0.569901i
$802$	−485125.			−0.754232
$803$	829095.			1.28580
$804$		−	341501.i		−	0.528299i
$805$		−	47856.7i		−	0.0738501i
$806$		−	113153.i		−	0.174180i
$807$		−	236768.i		−	0.363560i
$808$	127211.			0.194850
$809$		−	525531.i		−	0.802973i	−0.915865	−	0.401487i	$-0.868494\pi$
$809$		−	525531.i		−	0.802973i	0.915865	−	0.401487i	$-0.131506\pi$
$810$		−	20630.4i		−	0.0314440i
$811$		−	661679.i		−	1.00602i	−0.864281	−	0.503009i	$-0.832226\pi$
$811$		−	661679.i		−	1.00602i	0.864281	−	0.503009i	$-0.167774\pi$
$812$	26255.3			0.0398203
$813$	608808.			0.921083
$814$		−	714182.i		−	1.07785i
$815$	79560.9			0.119780
$816$	−275.993			−0.000414494
$817$			265660.i			0.397999i
$818$	−62933.3			−0.0940532
$819$		−	44470.2i		−	0.0662981i
$820$	−214579.			−0.319124
$821$			1.16994e6i			1.73571i	0.496816	+	0.867856i	$0.334502\pi$
$821$			1.16994e6i			1.73571i	−0.496816	+	0.867856i	$0.665498\pi$
$822$			244111.i			0.361279i
$823$			518659.i			0.765742i	0.923802	+	0.382871i	$0.125065\pi$
$823$			518659.i			0.765742i	−0.923802	+	0.382871i	$0.874935\pi$
$824$	−196963.			−0.290088
$825$		−	585875.i		−	0.860789i
$826$	99435.2	+	12174.2i	0.145740	+	0.0178436i
$827$	−1.00422e6			−1.46830			−0.734152	−	0.678985i	$-0.762420\pi$
$827$	−1.00422e6			−1.46830			−0.734152	+	0.678985i	$0.762420\pi$
$828$		−	101541.i		−	0.148108i
$829$	−224200.			−0.326232			−0.163116	−	0.986607i	$-0.552155\pi$
$829$	−224200.			−0.326232			−0.163116	+	0.986607i	$0.552155\pi$
$830$	57055.0			0.0828205
$831$	126740.			0.183532
$832$			82880.6i			0.119731i
$833$	1906.72			0.00274788
$834$			265966.i			0.382378i
$835$	−536681.			−0.769738
$836$		−	436816.i		−	0.625008i
$837$		−	34672.5i		−	0.0494919i
$838$	−164539.			−0.234304
$839$			769770.i			1.09355i	0.837281	+	0.546773i	$0.184144\pi$
$839$			769770.i			1.09355i	−0.837281	+	0.546773i	$0.815856\pi$
$840$			11969.4i			0.0169635i
$841$	−603239.			−0.852898
$842$	306610.			0.432476
$843$	−353189.			−0.496995
$844$			37452.2i			0.0525765i
$845$	−23583.5			−0.0330290
$846$	−264717.			−0.369863
$847$	−320524.			−0.446780
$848$	−330221.			−0.459212
$849$		−	275833.i		−	0.382676i
$850$			1232.12i			0.00170535i
$851$	−552581.			−0.763022
$852$	−390540.			−0.538006
$853$	1.03523e6			1.42279			0.711393	−	0.702795i	$-0.248065\pi$
$853$	1.03523e6			1.42279			0.711393	+	0.702795i	$0.248065\pi$
$854$	−12706.4			−0.0174224
$855$	−68667.9			−0.0939338
$856$			334217.i			0.456122i
$857$			663503.i			0.903403i	0.892169	+	0.451701i	$0.149183\pi$
$857$			663503.i			0.903403i	−0.892169	+	0.451701i	$0.850817\pi$
$858$			511050.i			0.694206i
$859$		−	152599.i		−	0.206807i	−0.994640	−	0.103403i	$-0.967027\pi$
$859$		−	152599.i		−	0.206807i	0.994640	−	0.103403i	$-0.0329732\pi$
$860$			83655.8i			0.113109i
$861$	−141731.			−0.191188
$862$	−232993.			−0.313566
$863$		−	90816.7i		−	0.121939i	−0.998140	−	0.0609697i	$-0.980581\pi$
$863$		−	90816.7i		−	0.121939i	0.998140	−	0.0609697i	$-0.0194193\pi$
$864$			25396.3i			0.0340207i
$865$		−	160731.i		−	0.214817i
$866$			504362.i			0.672522i
$867$	−433984.			−0.577346
$868$			20116.5i			0.0267001i
$869$		−	1.57509e6i		−	2.08576i
$870$			47431.5i			0.0626655i
$871$	1.32985e6			1.75294
$872$	−69426.4			−0.0913044
$873$		−	387828.i		−	0.508874i
$874$	−337976.			−0.442449
$875$	117062.			0.152897
$876$			160444.i			0.209081i
$877$	−611167.			−0.794623			−0.397311	−	0.917684i	$-0.630057\pi$
$877$	−611167.			−0.794623			−0.397311	+	0.917684i	$0.630057\pi$
$878$		−	718712.i		−	0.932322i
$879$	−137289.			−0.177688
$880$		−	137552.i		−	0.177625i
$881$		−	1.33520e6i		−	1.72026i	−0.510075	−	0.860130i	$-0.670382\pi$
$881$		−	1.33520e6i		−	1.72026i	0.510075	−	0.860130i	$-0.329618\pi$
$882$		−	175453.i		−	0.225539i
$883$	−878828.			−1.12715			−0.563576	−	0.826064i	$-0.690575\pi$
$883$	−878828.			−1.12715			−0.563576	+	0.826064i	$0.690575\pi$
$884$		−	1074.76i		−	0.00137532i
$885$	−21993.4	+	179635.i	−0.0280805	+	0.229353i
$886$	812456.			1.03498
$887$		−	1.03721e6i		−	1.31832i	−0.752002	−	0.659161i	$-0.770912\pi$
$887$		−	1.03721e6i		−	1.31832i	0.752002	−	0.659161i	$-0.229088\pi$
$888$	138206.			0.175268
$889$	−223009.			−0.282175
$890$	383249.			0.483839
$891$			156596.i			0.197254i
$892$	334397.			0.420274
$893$			881107.i			1.10491i
$894$	220383.			0.275742
$895$			490675.i			0.612558i
$896$		−	14734.6i		−	0.0183536i
$897$	395413.			0.491435
$898$			366449.i			0.454424i
$899$			79715.8i			0.0986337i
$900$	113377.			0.139971
$901$	4282.15			0.00527487
$902$	1.62877e6			2.00192
$903$			55255.4i			0.0677640i
$904$	−401862.			−0.491745
$905$	−396550.			−0.484173
$906$	−554849.			−0.675955
$907$	−276126.			−0.335655			−0.167828	−	0.985816i	$-0.553675\pi$
$907$	−276126.			−0.335655			−0.167828	+	0.985816i	$0.553675\pi$
$908$		−	677426.i		−	0.821656i
$909$			151793.i			0.183706i
$910$	−46610.7			−0.0562863
$911$	693320.			0.835405			0.417702	−	0.908584i	$-0.362835\pi$
$911$	693320.			0.835405			0.417702	+	0.908584i	$0.362835\pi$
$912$	84531.2			0.101631
$913$	−433079.			−0.519548
$914$	−51581.3			−0.0617448
$915$		−	22954.8i		−	0.0274177i
$916$		−	521419.i		−	0.621435i
$917$			293654.i			0.349218i
$918$		−	329.327i		−	0.000390789i
$919$			1.24461e6i			1.47368i	0.676067	+	0.736840i	$0.263683\pi$
$919$			1.24461e6i			1.47368i	−0.676067	+	0.736840i	$0.736317\pi$
$920$	−106428.			−0.125742
$921$	−334116.			−0.393893
$922$		−	687386.i		−	0.808610i
$923$		−	1.52082e6i		−	1.78515i
$924$		−	90854.6i		−	0.106415i
$925$		−	616993.i		−	0.721102i
$926$	323954.			0.377799
$927$		−	235024.i		−	0.273498i
$928$		−	58388.8i		−	0.0678006i
$929$		−	1.02795e6i		−	1.19108i	−0.803325	−	0.595541i	$-0.796938\pi$
$929$		−	1.02795e6i		−	1.19108i	0.803325	−	0.595541i	$-0.203062\pi$
$930$	−36341.4			−0.0420180
$931$	−583991.			−0.673762
$932$			214730.i			0.247207i
$933$	−526082.			−0.604352
$934$	−172179.			−0.197372
$935$			1783.71i			0.00204034i
$936$	−98896.7			−0.112883
$937$			1.13008e6i			1.28716i	0.765380	+	0.643579i	$0.222551\pi$
$937$			1.13008e6i			1.28716i	−0.765380	+	0.643579i	$0.777449\pi$
$938$	−236422.			−0.268708
$939$			240385.i			0.272632i
$940$			277459.i			0.314009i
$941$			492063.i			0.555701i	0.960624	+	0.277851i	$0.0896220\pi$
$941$			492063.i			0.555701i	−0.960624	+	0.277851i	$0.910378\pi$
$942$	7430.70			0.00837390
$943$		−	1.26022e6i		−	1.41718i
$944$	27074.2	−	221133.i	0.0303816	−	0.248147i
$945$	−14282.5			−0.0159933
$946$		−	634993.i		−	0.709556i
$947$	818070.			0.912200			0.456100	−	0.889928i	$-0.349246\pi$
$947$	818070.			0.912200			0.456100	+	0.889928i	$0.349246\pi$
$948$	304806.			0.339161
$949$	−624790.			−0.693748
$950$		−	377372.i		−	0.418141i
$951$	693575.			0.766888
$952$			191.071i			0.000210824i
$953$	604878.			0.666011			0.333006	−	0.942925i	$-0.391937\pi$
$953$	604878.			0.666011			0.333006	+	0.942925i	$0.391937\pi$
$954$		−	394034.i		−	0.432949i
$955$		−	556998.i		−	0.610727i
$956$	−634130.			−0.693845
$957$		−	360031.i		−	0.393112i
$958$		−	620086.i		−	0.675648i
$959$	168998.			0.183757
$960$	26618.7			0.0288831
$961$	862444.			0.933865
$962$			538194.i			0.581552i
$963$	−398802.			−0.430036
$964$	527869.			0.568032
$965$	−250726.			−0.269243
$966$	−70296.6			−0.0753321
$967$		−	165331.i		−	0.176808i	−0.996085	−	0.0884040i	$-0.971823\pi$
$967$		−	165331.i		−	0.176808i	0.996085	−	0.0884040i	$-0.0281766\pi$
$968$			712810.i			0.760717i
$969$	−1096.16			−0.00116742
$970$	−406495.			−0.432028
$971$	1.71910e6			1.82332			0.911661	−	0.410944i	$-0.134801\pi$
$971$	1.71910e6			1.82332			0.911661	+	0.410944i	$0.134801\pi$
$972$	−30304.0			−0.0320750
$973$	184128.			0.194489
$974$			565097.i			0.595669i
$975$			441504.i			0.464436i
$976$			28257.7i			0.0296645i
$977$			446922.i			0.468212i	0.972211	+	0.234106i	$0.0752164\pi$
$977$			446922.i			0.468212i	−0.972211	+	0.234106i	$0.924784\pi$
$978$		−	116867.i		−	0.122184i
$979$	−2.90907e6			−3.03521
$980$	−183898.			−0.191480
$981$		−	82842.6i		−	0.0860826i
$982$		−	375353.i		−	0.389239i
$983$			1.74193e6i			1.80270i	0.433086	+	0.901352i	$0.357424\pi$
$983$			1.74193e6i			1.80270i	−0.433086	+	0.901352i	$0.642576\pi$
$984$			315195.i			0.325528i
$985$	−630540.			−0.649891
$986$			757.158i			0.000778812i
$987$			183264.i			0.188124i
$988$			329176.i			0.337221i
$989$	−491311.			−0.502301
$990$	164133.			0.167466
$991$			216550.i			0.220501i	0.993904	+	0.110251i	$0.0351653\pi$
$991$			216550.i			0.220501i	−0.993904	+	0.110251i	$0.964835\pi$
$992$	44736.8			0.0454613
$993$	−881963.			−0.894441
$994$			270372.i			0.273646i
$995$	−217608.			−0.219801
$996$		−	83808.0i		−	0.0844826i
$997$	1.04684e6			1.05315			0.526574	−	0.850129i	$-0.323476\pi$
$997$	1.04684e6			1.05315			0.526574	+	0.850129i	$0.323476\pi$
$998$		−	414635.i		−	0.416299i
$999$			164914.i			0.165244i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.5.d.a.235.2	yes	40
3.2	odd	2		1062.5.d.b.235.37		40
59.58	odd	2	inner	354.5.d.a.235.1	✓	40
177.176	even	2		1062.5.d.b.235.38		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.5.d.a.235.1	✓	40	59.58	odd	2	inner
354.5.d.a.235.2	yes	40	1.1	even	1	trivial
1062.5.d.b.235.37		40	3.2	odd	2
1062.5.d.b.235.38		40	177.176	even	2

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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	354.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.82843i q^{2} +5.19615 q^{3} -8.00000 q^{4} -10.0054 q^{5} +14.6969i q^{6} +10.1747 q^{7} -22.6274i q^{8} +27.0000 q^{9} +O(q^{10})\)	\(q+2.82843i q^{2} +5.19615 q^{3} -8.00000 q^{4} -10.0054 q^{5} +14.6969i q^{6} +10.1747 q^{7} -22.6274i q^{8} +27.0000 q^{9} -28.2996i q^{10} +214.809i q^{11} -41.5692 q^{12} -161.876i q^{13} +28.7784i q^{14} -51.9897 q^{15} +64.0000 q^{16} -0.829921 q^{17} +76.3675i q^{18} +254.188 q^{19} +80.0433 q^{20} +52.8693 q^{21} -607.573 q^{22} +470.095i q^{23} -117.576i q^{24} -524.892 q^{25} +457.855 q^{26} +140.296 q^{27} -81.3977 q^{28} -322.556 q^{29} -147.049i q^{30} -247.138i q^{31} +181.019i q^{32} +1116.18i q^{33} -2.34737i q^{34} -101.802 q^{35} -216.000 q^{36} +1175.47i q^{37} +718.952i q^{38} -841.134i q^{39} +226.397i q^{40} -2680.79 q^{41} +149.537i q^{42} +1045.13i q^{43} -1718.47i q^{44} -270.146 q^{45} -1329.63 q^{46} +3466.36i q^{47} +332.554 q^{48} -2297.48 q^{49} -1484.62i q^{50} -4.31240 q^{51} +1295.01i q^{52} -5159.71 q^{53} +396.817i q^{54} -2149.26i q^{55} -230.227i q^{56} +1320.80 q^{57} -912.325i q^{58} +(423.034 - 3455.20i) q^{59} +415.917 q^{60} +441.526i q^{61} +699.012 q^{62} +274.717 q^{63} -512.000 q^{64} +1619.64i q^{65} -3157.04 q^{66} +8215.23i q^{67} +6.63937 q^{68} +2442.68i q^{69} -287.940i q^{70} +9394.94 q^{71} -610.940i q^{72} -3859.68i q^{73} -3324.72 q^{74} -2727.42 q^{75} -2033.50 q^{76} +2185.62i q^{77} +2379.09 q^{78} -7332.48 q^{79} -640.347 q^{80} +729.000 q^{81} -7582.41i q^{82} +2016.11i q^{83} -422.955 q^{84} +8.30370 q^{85} -2956.08 q^{86} -1676.05 q^{87} +4860.58 q^{88} +13542.5i q^{89} -764.089i q^{90} -1647.04i q^{91} -3760.76i q^{92} -1284.17i q^{93} -9804.34 q^{94} -2543.26 q^{95} +940.604i q^{96} -14364.0i q^{97} -6498.24i q^{98} +5799.85i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 320 q^{4} - 80 q^{7} + 1080 q^{9}+O(q^{10}) \) 40 * q - 320 * q^4 - 80 * q^7 + 1080 * q^9	\( 40 q - 320 q^{4} - 80 q^{7} + 1080 q^{9} - 144 q^{15} + 2560 q^{16} + 480 q^{17} - 792 q^{19} - 1024 q^{22} + 3400 q^{25} + 768 q^{26} + 640 q^{28} + 1608 q^{29} - 5760 q^{35} - 8640 q^{36} + 6264 q^{41} + 7040 q^{46} + 17912 q^{49} + 1296 q^{51} - 1104 q^{53} + 5040 q^{57} + 13584 q^{59} + 1152 q^{60} - 12288 q^{62} - 2160 q^{63} - 20480 q^{64} + 1152 q^{66} - 3840 q^{68} + 35352 q^{71} + 4608 q^{74} + 3168 q^{75} + 6336 q^{76} - 12672 q^{78} - 15720 q^{79} + 29160 q^{81} - 26872 q^{85} + 18432 q^{86} + 7776 q^{87} + 8192 q^{88} - 18432 q^{94} - 19128 q^{95}+O(q^{100}) \) 40 * q - 320 * q^4 - 80 * q^7 + 1080 * q^9 - 144 * q^15 + 2560 * q^16 + 480 * q^17 - 792 * q^19 - 1024 * q^22 + 3400 * q^25 + 768 * q^26 + 640 * q^28 + 1608 * q^29 - 5760 * q^35 - 8640 * q^36 + 6264 * q^41 + 7040 * q^46 + 17912 * q^49 + 1296 * q^51 - 1104 * q^53 + 5040 * q^57 + 13584 * q^59 + 1152 * q^60 - 12288 * q^62 - 2160 * q^63 - 20480 * q^64 + 1152 * q^66 - 3840 * q^68 + 35352 * q^71 + 4608 * q^74 + 3168 * q^75 + 6336 * q^76 - 12672 * q^78 - 15720 * q^79 + 29160 * q^81 - 26872 * q^85 + 18432 * q^86 + 7776 * q^87 + 8192 * q^88 - 18432 * q^94 - 19128 * q^95

Introduction

L-functions

Modular forms

Varieties

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Database

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