LMFDB - Embedded newform 225.4.h.a.181.6

Newspace parameters

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.h (of order $5$, degree $4$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			181.6
Character	$\chi$	$=$	225.181
Dual form			225.4.h.a.46.6

$q$-expansion

$f(q)$	$=$	$q+(0.907834 + 2.79403i) q^{2} +(-0.510282 + 0.370741i) q^{4} +(-10.7234 - 3.16365i) q^{5} +18.9115 q^{7} +(17.5148 + 12.7253i) q^{8} +O(q^{10})$	\(q+(0.907834 + 2.79403i) q^{2} +(-0.510282 + 0.370741i) q^{4} +(-10.7234 - 3.16365i) q^{5} +18.9115 q^{7} +(17.5148 + 12.7253i) q^{8} +(-0.895733 - 32.8335i) q^{10} +(1.87505 + 5.77082i) q^{11} +(24.1805 - 74.4201i) q^{13} +(17.1685 + 52.8393i) q^{14} +(-21.2134 + 65.2882i) q^{16} +(31.0670 + 22.5715i) q^{17} +(75.2030 + 54.6382i) q^{19} +(6.64485 - 2.36125i) q^{20} +(-14.4216 + 10.4779i) q^{22} +(25.0398 + 77.0645i) q^{23} +(104.983 + 67.8503i) q^{25} +229.884 q^{26} +(-9.65021 + 7.01128i) q^{28} +(-9.02201 + 6.55487i) q^{29} +(181.125 + 131.595i) q^{31} -28.4793 q^{32} +(-34.8617 + 107.293i) q^{34} +(-202.796 - 59.8295i) q^{35} +(-33.2987 + 102.483i) q^{37} +(-84.3887 + 259.722i) q^{38} +(-147.560 - 191.869i) q^{40} +(108.379 - 333.556i) q^{41} -356.550 q^{43} +(-3.09629 - 2.24959i) q^{44} +(-192.588 + 139.924i) q^{46} +(-236.019 + 171.478i) q^{47} +14.6457 q^{49} +(-94.2687 + 354.921i) q^{50} +(15.2517 + 46.9399i) q^{52} +(554.021 - 402.520i) q^{53} +(-1.85006 - 67.8149i) q^{55} +(331.232 + 240.654i) q^{56} +(-26.5050 - 19.2570i) q^{58} +(69.2082 - 213.001i) q^{59} +(-215.599 - 663.544i) q^{61} +(-203.249 + 625.535i) q^{62} +(143.853 + 442.734i) q^{64} +(-494.737 + 721.537i) q^{65} +(735.443 + 534.330i) q^{67} -24.2211 q^{68} +(-16.9397 - 620.932i) q^{70} +(163.274 - 118.625i) q^{71} +(-90.2156 - 277.655i) q^{73} -316.570 q^{74} -58.6314 q^{76} +(35.4601 + 109.135i) q^{77} +(-573.822 + 416.906i) q^{79} +(434.030 - 633.000i) q^{80} +1030.36 q^{82} +(-897.021 - 651.724i) q^{83} +(-261.736 - 340.329i) q^{85} +(-323.688 - 996.211i) q^{86} +(-40.5940 + 124.935i) q^{88} +(-1.16808 - 3.59497i) q^{89} +(457.291 - 1407.40i) q^{91} +(-41.3483 - 30.0413i) q^{92} +(-693.380 - 503.770i) q^{94} +(-633.576 - 823.824i) q^{95} +(-14.9369 + 10.8523i) q^{97} +(13.2959 + 40.9205i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8}+O(q^{10}) $ 28 * q - 30 * q^4 + 15 * q^5 - 54 * q^7 + 63 * q^8	$ 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8} + 165 q^{10} - 19 q^{11} + 4 q^{13} + 24 q^{14} - 66 q^{16} - 208 q^{17} + 42 q^{19} - 295 q^{20} - 89 q^{22} - 32 q^{23} + 95 q^{25} - 206 q^{26} - 482 q^{28} + 716 q^{29} + 637 q^{31} + 844 q^{32} - 90 q^{34} - 430 q^{35} + 216 q^{37} - 2314 q^{38} - 500 q^{40} + 38 q^{41} - 1392 q^{43} - 603 q^{44} + 1622 q^{46} + 536 q^{47} + 162 q^{49} + 2265 q^{50} - 1922 q^{52} - 1672 q^{53} - 1000 q^{55} - 3000 q^{56} - 827 q^{58} - 973 q^{59} - 2712 q^{61} - 1057 q^{62} + 4439 q^{64} + 4360 q^{65} + 2768 q^{67} + 1370 q^{68} + 3230 q^{70} + 1074 q^{71} - 1018 q^{73} + 1414 q^{74} - 11408 q^{76} - 1607 q^{77} - 1820 q^{79} + 1290 q^{80} + 1772 q^{82} - 4045 q^{83} + 1850 q^{85} + 3986 q^{86} + 2407 q^{88} - 4542 q^{89} + 4412 q^{91} + 1089 q^{92} + 5137 q^{94} + 720 q^{95} - 5977 q^{97} + 10689 q^{98}+O(q^{100}) $ 28 * q - 30 * q^4 + 15 * q^5 - 54 * q^7 + 63 * q^8 + 165 * q^10 - 19 * q^11 + 4 * q^13 + 24 * q^14 - 66 * q^16 - 208 * q^17 + 42 * q^19 - 295 * q^20 - 89 * q^22 - 32 * q^23 + 95 * q^25 - 206 * q^26 - 482 * q^28 + 716 * q^29 + 637 * q^31 + 844 * q^32 - 90 * q^34 - 430 * q^35 + 216 * q^37 - 2314 * q^38 - 500 * q^40 + 38 * q^41 - 1392 * q^43 - 603 * q^44 + 1622 * q^46 + 536 * q^47 + 162 * q^49 + 2265 * q^50 - 1922 * q^52 - 1672 * q^53 - 1000 * q^55 - 3000 * q^56 - 827 * q^58 - 973 * q^59 - 2712 * q^61 - 1057 * q^62 + 4439 * q^64 + 4360 * q^65 + 2768 * q^67 + 1370 * q^68 + 3230 * q^70 + 1074 * q^71 - 1018 * q^73 + 1414 * q^74 - 11408 * q^76 - 1607 * q^77 - 1820 * q^79 + 1290 * q^80 + 1772 * q^82 - 4045 * q^83 + 1850 * q^85 + 3986 * q^86 + 2407 * q^88 - 4542 * q^89 + 4412 * q^91 + 1089 * q^92 + 5137 * q^94 + 720 * q^95 - 5977 * q^97 + 10689 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.907834	+	2.79403i	0.320968	+	0.987837i	0.973228	+	0.229842i	$0.0738210\pi$
$2$	0.907834	+	2.79403i	0.320968	+	0.987837i	−0.652260	+	0.757995i	$0.726179\pi$
$3$		0			0
$3$		0			0
$4$	−0.510282	+	0.370741i	−0.0637852	+	0.0463427i
$5$	−10.7234	−	3.16365i	−0.959130	−	0.282966i
$5$	−10.7234	−	3.16365i	−0.959130	−	0.282966i
$6$		0			0
$7$	18.9115			1.02113			0.510563	−	0.859840i	$-0.329437\pi$
$7$	18.9115			1.02113			0.510563	+	0.859840i	$0.329437\pi$
$8$	17.5148	+	12.7253i	0.774053	+	0.562382i
$9$		0			0
$10$	−0.895733	−	32.8335i	−0.0283256	−	1.03829i
$11$	1.87505	+	5.77082i	0.0513955	+	0.158179i	0.973460	−	0.228857i	$-0.0734989\pi$
$11$	1.87505	+	5.77082i	0.0513955	+	0.158179i	−0.922065	+	0.387036i	$0.873499\pi$
$12$		0			0
$13$	24.1805	−	74.4201i	0.515883	−	1.58772i	−0.265787	−	0.964032i	$-0.585632\pi$
$13$	24.1805	−	74.4201i	0.515883	−	1.58772i	0.781670	−	0.623692i	$-0.214368\pi$
$14$	17.1685	+	52.8393i	0.327749	+	1.00871i
$15$		0			0
$16$	−21.2134	+	65.2882i	−0.331460	+	1.02013i
$17$	31.0670	+	22.5715i	0.443227	+	0.322023i	0.786916	−	0.617060i	$-0.211676\pi$
$17$	31.0670	+	22.5715i	0.443227	+	0.322023i	−0.343689	+	0.939084i	$0.611676\pi$
$18$		0			0
$19$	75.2030	+	54.6382i	0.908040	+	0.659730i	0.940518	−	0.339743i	$-0.110340\pi$
$19$	75.2030	+	54.6382i	0.908040	+	0.659730i	−0.0324785	+	0.999472i	$0.510340\pi$
$20$	6.64485	−	2.36125i	0.0742917	−	0.0263996i
$21$		0			0
$22$	−14.4216	+	10.4779i	−0.139759	+	0.101541i
$23$	25.0398	+	77.0645i	0.227007	+	0.698655i	0.998082	+	0.0619104i	$0.0197193\pi$
$23$	25.0398	+	77.0645i	0.227007	+	0.698655i	−0.771075	+	0.636744i	$0.780281\pi$
$24$		0			0
$25$	104.983	+	67.8503i	0.839861	+	0.542802i
$26$	229.884			1.73399
$27$		0			0
$28$	−9.65021	+	7.01128i	−0.0651328	+	0.0473217i
$29$	−9.02201	+	6.55487i	−0.0577705	+	0.0419727i	−0.616296	−	0.787515i	$-0.711367\pi$
$29$	−9.02201	+	6.55487i	−0.0577705	+	0.0419727i	0.558525	+	0.829488i	$0.311367\pi$
$30$		0			0
$31$	181.125	+	131.595i	1.04939	+	0.762425i	0.972096	−	0.234583i	$-0.0753725\pi$
$31$	181.125	+	131.595i	1.04939	+	0.762425i	0.0772923	+	0.997008i	$0.475373\pi$
$32$	−28.4793			−0.157327
$33$		0			0
$34$	−34.8617	+	107.293i	−0.175845	+	0.541196i
$35$	−202.796	−	59.8295i	−0.979393	−	0.288944i
$36$		0			0
$37$	−33.2987	+	102.483i	−0.147954	+	0.455354i	−0.997379	−	0.0723545i	$-0.976949\pi$
$37$	−33.2987	+	102.483i	−0.147954	+	0.455354i	0.849425	+	0.527709i	$0.176949\pi$
$38$	−84.3887	+	259.722i	−0.360254	+	1.10875i
$39$		0			0
$40$	−147.560	−	191.869i	−0.583282	−	0.758428i
$41$	108.379	−	333.556i	0.412828	−	1.27056i	−0.501350	−	0.865244i	$-0.667163\pi$
$41$	108.379	−	333.556i	0.412828	−	1.27056i	0.914179	−	0.405311i	$-0.132837\pi$
$42$		0			0
$43$	−356.550			−1.26450			−0.632249	−	0.774765i	$-0.717868\pi$
$43$	−356.550			−1.26450			−0.632249	+	0.774765i	$0.717868\pi$
$44$	−3.09629	−	2.24959i	−0.0106087	−	0.00770768i
$45$		0			0
$46$	−192.588	+	139.924i	−0.617295	+	0.448491i
$47$	−236.019	+	171.478i	−0.732488	+	0.532184i	−0.890350	−	0.455277i	$-0.849540\pi$
$47$	−236.019	+	171.478i	−0.732488	+	0.532184i	0.157861	+	0.987461i	$0.449540\pi$
$48$		0			0
$49$	14.6457			0.0426989
$50$	−94.2687	+	354.921i	−0.266632	+	1.00387i
$51$		0			0
$52$	15.2517	+	46.9399i	0.0406737	+	0.125181i
$53$	554.021	−	402.520i	1.43586	−	1.04322i	0.446975	−	0.894546i	$-0.352501\pi$
$53$	554.021	−	402.520i	1.43586	−	1.04322i	0.988887	−	0.148669i	$-0.0474988\pi$
$54$		0			0
$55$	−1.85006	−	67.8149i	−0.00453568	−	0.166257i
$56$	331.232	+	240.654i	0.790405	+	0.574263i
$57$		0			0
$58$	−26.5050	−	19.2570i	−0.0600047	−	0.0435960i
$59$	69.2082	−	213.001i	0.152714	−	0.470006i	−0.845208	−	0.534438i	$-0.820523\pi$
$59$	69.2082	−	213.001i	0.152714	−	0.470006i	0.997922	+	0.0644317i	$0.0205235\pi$
$60$		0			0
$61$	−215.599	−	663.544i	−0.452534	−	1.39276i	−0.874006	−	0.485915i	$-0.838486\pi$
$61$	−215.599	−	663.544i	−0.452534	−	1.39276i	0.421472	−	0.906842i	$-0.361514\pi$
$62$	−203.249	+	625.535i	−0.416332	+	1.28134i
$63$		0			0
$64$	143.853	+	442.734i	0.280963	+	0.864715i
$65$	−494.737	+	721.537i	−0.944070	+	1.37686i
$66$		0			0
$67$	735.443	+	534.330i	1.34102	+	0.974311i	0.999406	+	0.0344723i	$0.0109750\pi$
$67$	735.443	+	534.330i	1.34102	+	0.974311i	0.341618	+	0.939839i	$0.389025\pi$
$68$	−24.2211			−0.0431948
$69$		0			0
$70$	−16.9397	−	620.932i	−0.0289240	−	1.06022i
$71$	163.274	−	118.625i	0.272916	−	0.198285i	−0.442906	−	0.896568i	$-0.646052\pi$
$71$	163.274	−	118.625i	0.272916	−	0.198285i	0.715822	+	0.698283i	$0.246052\pi$
$72$		0			0
$73$	−90.2156	−	277.655i	−0.144643	−	0.445165i	0.852322	−	0.523018i	$-0.175194\pi$
$73$	−90.2156	−	277.655i	−0.144643	−	0.445165i	−0.996965	+	0.0778521i	$0.975194\pi$
$74$	−316.570			−0.497304
$75$		0			0
$76$	−58.6314			−0.0884932
$77$	35.4601	+	109.135i	0.0524813	+	0.161521i
$78$		0			0
$79$	−573.822	+	416.906i	−0.817216	+	0.593742i	−0.915914	−	0.401375i	$-0.868532\pi$
$79$	−573.822	+	416.906i	−0.817216	+	0.593742i	0.0986978	+	0.995117i	$0.468532\pi$
$80$	434.030	−	633.000i	0.606575	−	0.884644i
$81$		0			0
$82$	1030.36			1.38761
$83$	−897.021	−	651.724i	−1.18628	−	0.861880i	−0.193410	−	0.981118i	$-0.561955\pi$
$83$	−897.021	−	651.724i	−1.18628	−	0.861880i	−0.992866	+	0.119238i	$0.961955\pi$
$84$		0			0
$85$	−261.736	−	340.329i	−0.333991	−	0.434281i
$86$	−323.688	−	996.211i	−0.405863	−	1.24912i
$87$		0			0
$88$	−40.5940	+	124.935i	−0.0491742	+	0.151343i
$89$	−1.16808	−	3.59497i	−0.00139119	−	0.00428165i	0.950359	−	0.311157i	$-0.100717\pi$
$89$	−1.16808	−	3.59497i	−0.00139119	−	0.00428165i	−0.951750	+	0.306875i	$0.900717\pi$
$90$		0			0
$91$	457.291	−	1407.40i	0.526782	−	1.62127i
$92$	−41.3483	−	30.0413i	−0.0468572	−	0.0340438i
$93$		0			0
$94$	−693.380	−	503.770i	−0.760816	−	0.552765i
$95$	−633.576	−	823.824i	−0.684247	−	0.889711i
$96$		0			0
$97$	−14.9369	+	10.8523i	−0.0156351	+	0.0113596i	−0.595575	−	0.803299i	$-0.703076\pi$
$97$	−14.9369	+	10.8523i	−0.0156351	+	0.0113596i	0.579940	+	0.814659i	$0.303076\pi$
$98$	13.2959	+	40.9205i	0.0137050	+	0.0421795i
$99$		0			0
$100$	−78.7256	+	4.29863i	−0.0787256	+	0.00429863i
$101$	1332.50			1.31276			0.656381	−	0.754430i	$-0.272087\pi$
$101$	1332.50			1.31276			0.656381	+	0.754430i	$0.272087\pi$
$102$		0			0
$103$	−1358.05	+	986.682i	−1.29915	+	0.943890i	−0.999947	−	0.0102985i	$-0.996722\pi$
$103$	−1358.05	+	986.682i	−1.29915	+	0.943890i	−0.299206	+	0.954188i	$0.596722\pi$
$104$	1370.53	−	995.750i	1.29223	−	0.938859i
$105$		0			0
$106$	1627.61	+	1182.53i	1.49139	+	1.08356i
$107$	−1550.64			−1.40099			−0.700496	−	0.713657i	$-0.747038\pi$
$107$	−1550.64			−1.40099			−0.700496	+	0.713657i	$0.747038\pi$
$108$		0			0
$109$	138.127	−	425.111i	0.121378	−	0.373562i	−0.871846	−	0.489780i	$-0.837077\pi$
$109$	138.127	−	425.111i	0.121378	−	0.373562i	0.993224	+	0.116218i	$0.0370772\pi$
$110$	187.797	−	66.7338i	0.162779	−	0.0578438i
$111$		0			0
$112$	−401.178	+	1234.70i	−0.338462	+	1.04168i
$113$	192.146	−	591.366i	0.159961	−	0.492310i	−0.838668	−	0.544642i	$-0.816665\pi$
$113$	192.146	−	591.366i	0.159961	−	0.492310i	0.998630	+	0.0523321i	$0.0166654\pi$
$114$		0			0
$115$	−24.7060	−	905.611i	−0.0200334	−	0.734336i
$116$	2.17360	−	6.68966i	0.00173978	−	0.00535448i
$117$		0			0
$118$	657.959			0.513306
$119$	587.525	+	426.862i	0.452591	+	0.328827i
$120$		0			0
$121$	1047.02	−	760.701i	0.786638	−	0.571526i
$122$	1658.23	−	1204.78i	1.23057	−	0.894060i
$123$		0			0
$124$	−141.213			−0.102268
$125$	−911.115	−	1059.71i	−0.651941	−	0.758270i
$126$		0			0
$127$	−216.352	−	665.864i	−0.151167	−	0.465243i	0.846586	−	0.532252i	$-0.178654\pi$
$127$	−216.352	−	665.864i	−0.151167	−	0.465243i	−0.997752	+	0.0670095i	$0.978654\pi$
$128$	−1290.74	+	937.776i	−0.891298	+	0.647566i
$129$		0			0
$130$	−2465.13	−	727.272i	−1.66313	−	0.490661i
$131$	−470.763	−	342.029i	−0.313975	−	0.228116i	0.419625	−	0.907697i	$-0.362161\pi$
$131$	−470.763	−	342.029i	−0.313975	−	0.228116i	−0.733600	+	0.679581i	$0.762161\pi$
$132$		0			0
$133$	1422.20	+	1033.29i	0.927223	+	0.673667i
$134$	−825.273	+	2539.93i	−0.532035	+	1.63744i
$135$		0			0
$136$	256.905	+	790.672i	0.161981	+	0.498526i
$137$	−186.032	+	572.548i	−0.116013	+	0.357051i	−0.992157	−	0.124998i	$-0.960108\pi$
$137$	−186.032	+	572.548i	−0.116013	+	0.357051i	0.876144	+	0.482050i	$0.160108\pi$
$138$		0			0
$139$	−57.3812	−	176.601i	−0.0350145	−	0.107763i	0.932022	−	0.362402i	$-0.118043\pi$
$139$	−57.3812	−	176.601i	−0.0350145	−	0.107763i	−0.967036	+	0.254639i	$0.918043\pi$
$140$	125.664	−	44.6549i	0.0758612	−	0.0269573i
$141$		0			0
$142$	479.668	+	348.499i	0.283471	+	0.205953i
$143$	474.805			0.277659
$144$		0			0
$145$	117.484	−	41.7480i	0.0672863	−	0.0239102i
$146$	693.875	−	504.130i	0.393325	−	0.285768i
$147$		0			0
$148$	−21.0029	−	64.6404i	−0.0116651	−	0.0359014i
$149$	−2586.71			−1.42223			−0.711113	−	0.703078i	$-0.751808\pi$
$149$	−2586.71			−1.42223			−0.711113	+	0.703078i	$0.751808\pi$
$150$		0			0
$151$	−276.537			−0.149035			−0.0745175	−	0.997220i	$-0.523742\pi$
$151$	−276.537			−0.149035			−0.0745175	+	0.997220i	$0.523742\pi$
$152$	621.882	+	1913.96i	0.331850	+	1.02133i
$153$		0			0
$154$	−272.734	+	198.153i	−0.142711	+	0.103686i
$155$	−1525.96	−	1984.16i	−0.790759	−	1.02821i
$156$		0			0
$157$	−3052.85			−1.55187			−0.775937	−	0.630810i	$-0.782723\pi$
$157$	−3052.85			−1.55187			−0.775937	+	0.630810i	$0.782723\pi$
$158$	−1685.78	−	1224.79i	−0.848821	−	0.616704i
$159$		0			0
$160$	305.395	+	90.0987i	0.150897	+	0.0445183i
$161$	473.540	+	1457.41i	0.231802	+	0.713415i
$162$		0			0
$163$	−248.105	+	763.589i	−0.119221	+	0.366926i	−0.992804	−	0.119750i	$-0.961791\pi$
$163$	−248.105	+	763.589i	−0.119221	+	0.366926i	0.873583	+	0.486676i	$0.161791\pi$
$164$	68.3593	+	210.388i	0.0325486	+	0.100174i
$165$		0			0
$166$	1006.59	−	3097.96i	0.470641	−	1.44848i
$167$	2290.36	+	1664.05i	1.06128	+	0.771064i	0.974325	−	0.225148i	$-0.0722865\pi$
$167$	2290.36	+	1664.05i	1.06128	+	0.771064i	0.0869544	+	0.996212i	$0.472287\pi$
$168$		0			0
$169$	−3176.24	−	2307.67i	−1.44572	−	1.05037i
$170$	713.275	−	1040.26i	0.321798	−	0.469319i
$171$		0			0
$172$	181.941	−	132.188i	0.0806563	−	0.0586002i
$173$	1273.54	+	3919.54i	0.559683	+	1.72253i	0.683243	+	0.730191i	$0.260569\pi$
$173$	1273.54	+	3919.54i	0.559683	+	1.72253i	−0.123560	+	0.992337i	$0.539431\pi$
$174$		0			0
$175$	1985.38	+	1283.15i	0.857604	+	0.554270i
$176$	−416.543			−0.178398
$177$		0			0
$178$	8.98403	−	6.52728i	0.00378304	−	0.00274854i
$179$	−1427.33	+	1037.02i	−0.595999	+	0.433019i	−0.844457	−	0.535624i	$-0.820076\pi$
$179$	−1427.33	+	1037.02i	−0.595999	+	0.433019i	0.248457	+	0.968643i	$0.420076\pi$
$180$		0			0
$181$	1207.80	+	877.516i	0.495994	+	0.360361i	0.807485	−	0.589888i	$-0.200828\pi$
$181$	1207.80	+	877.516i	0.495994	+	0.360361i	−0.311491	+	0.950249i	$0.600828\pi$
$182$	4347.45			1.77063
$183$		0			0
$184$	−542.099	+	1668.41i	−0.217196	+	0.668460i
$185$	681.297	−	993.620i	0.270756	−	0.394878i
$186$		0			0
$187$	−72.0039	+	221.605i	−0.0281575	+	0.0866598i
$188$	56.8623	−	175.004i	0.0220591	−	0.0678909i
$189$		0			0
$190$	1726.60	−	2518.12i	0.659268	−	0.961493i
$191$	−1130.61	+	3479.65i	−0.428313	+	1.31821i	0.471473	+	0.881881i	$0.343723\pi$
$191$	−1130.61	+	3479.65i	−0.428313	+	1.31821i	−0.899786	+	0.436332i	$0.856277\pi$
$192$		0			0
$193$	−4695.92			−1.75140			−0.875699	−	0.482858i	$-0.839599\pi$
$193$	−4695.92			−1.75140			−0.875699	+	0.482858i	$0.839599\pi$
$194$	−43.8817	−	31.8819i	−0.0162398	−	0.0117989i
$195$		0			0
$196$	−7.47344	+	5.42977i	−0.00272356	+	0.00197878i
$197$	389.722	−	283.150i	0.140947	−	0.102404i	−0.515077	−	0.857144i	$-0.672237\pi$
$197$	389.722	−	283.150i	0.140947	−	0.102404i	0.656024	+	0.754740i	$0.272237\pi$
$198$		0			0
$199$	494.959			0.176315			0.0881575	−	0.996107i	$-0.471902\pi$
$199$	494.959			0.176315			0.0881575	+	0.996107i	$0.471902\pi$
$200$	975.338	+	2524.31i	0.344834	+	0.892480i
$201$		0			0
$202$	1209.69	+	3723.05i	0.421354	+	1.29679i
$203$	−170.620	+	123.963i	−0.0589910	+	0.0428595i
$204$		0			0
$205$	−2217.45	+	3233.99i	−0.755480	+	1.10181i
$206$	−3989.70	−	2898.69i	−1.34940	−	0.980394i
$207$		0			0
$208$	4345.80	+	3157.41i	1.44869	+	1.05253i
$209$	−174.298	+	536.433i	−0.0576862	+	0.177540i
$210$		0			0
$211$	146.406	+	450.590i	0.0477676	+	0.147014i	0.972095	−	0.234586i	$-0.0753734\pi$
$211$	146.406	+	450.590i	0.0477676	+	0.147014i	−0.924328	+	0.381599i	$0.875373\pi$
$212$	−133.476	+	410.797i	−0.0432414	+	0.133083i
$213$		0			0
$214$	−1407.72	−	4332.53i	−0.449673	−	1.38395i
$215$	3823.43	+	1128.00i	1.21282	+	0.357810i
$216$		0			0
$217$	3425.35	+	2488.66i	1.07156	+	0.778532i
$218$	1313.17			0.407976
$219$		0			0
$220$	26.0858	+	33.9188i	0.00799412	+	0.0103946i
$221$	2430.99	−	1766.22i	0.739938	−	0.537596i
$222$		0			0
$223$	1565.42	+	4817.87i	0.470082	+	1.44676i	0.852477	+	0.522766i	$0.175100\pi$
$223$	1565.42	+	4817.87i	0.470082	+	1.44676i	−0.382394	+	0.923999i	$0.624900\pi$
$224$	−538.587			−0.160651
$225$		0			0
$226$	1826.73			0.537665
$227$	−1635.48	−	5033.48i	−0.478196	−	1.47174i	−0.841599	−	0.540103i	$-0.818385\pi$
$227$	−1635.48	−	5033.48i	−0.478196	−	1.47174i	0.363403	−	0.931632i	$-0.381615\pi$
$228$		0			0
$229$	−396.216	+	287.868i	−0.114335	+	0.0830692i	−0.643483	−	0.765460i	$-0.722511\pi$
$229$	−396.216	+	287.868i	−0.114335	+	0.0830692i	0.529148	+	0.848529i	$0.322511\pi$
$230$	2507.87	−	891.173i	0.718974	−	0.255488i
$231$		0			0
$232$	−241.431			−0.0683221
$233$	−1763.54	−	1281.28i	−0.495850	−	0.360256i	0.311579	−	0.950220i	$-0.399142\pi$
$233$	−1763.54	−	1281.28i	−0.495850	−	0.360256i	−0.807430	+	0.589964i	$0.799142\pi$
$234$		0			0
$235$	3073.43	−	1092.14i	0.853141	−	0.303164i
$236$	43.6526	+	134.349i	0.0120404	+	0.0370566i
$237$		0			0
$238$	−659.288	+	2029.08i	−0.179560	+	0.552629i
$239$	−1370.65	−	4218.41i	−0.370961	−	1.14170i	−0.946163	−	0.323689i	$-0.895077\pi$
$239$	−1370.65	−	4218.41i	−0.370961	−	1.14170i	0.575203	−	0.818011i	$-0.304923\pi$
$240$		0			0
$241$	742.522	−	2285.25i	0.198465	−	0.610812i	−0.801454	−	0.598057i	$-0.795940\pi$
$241$	742.522	−	2285.25i	0.198465	−	0.610812i	0.999919	−	0.0127554i	$-0.00406027\pi$
$242$	3075.93	+	2234.80i	0.817060	+	0.593629i
$243$		0			0
$244$	356.019	+	258.663i	0.0934091	+	0.0678657i
$245$	−157.052	−	46.3340i	−0.0409538	−	0.0120823i
$246$		0			0
$247$	5884.63	−	4275.43i	1.51591	−	1.10137i
$248$	1497.79	+	4609.73i	0.383507	+	1.18031i
$249$		0			0
$250$	2133.73	−	3507.72i	0.539795	−	0.887392i
$251$	3459.69			0.870014			0.435007	−	0.900427i	$-0.356746\pi$
$251$	3459.69			0.870014			0.435007	+	0.900427i	$0.356746\pi$
$252$		0			0
$253$	−397.775	+	289.000i	−0.0988454	+	0.0718154i
$254$	1664.03	−	1208.99i	0.411065	−	0.298656i
$255$		0			0
$256$	−779.049	−	566.012i	−0.190197	−	0.138187i
$257$	−4772.57			−1.15838			−0.579192	−	0.815191i	$-0.696632\pi$
$257$	−4772.57			−1.15838			−0.579192	+	0.815191i	$0.696632\pi$
$258$		0			0
$259$	−629.730	+	1938.11i	−0.151079	+	0.464974i
$260$	−15.0484	−	551.607i	−0.00358947	−	0.131574i
$261$		0			0
$262$	528.264	−	1625.83i	0.124566	−	0.383374i
$263$	−1298.07	+	3995.04i	−0.304343	+	0.936671i	0.675579	+	0.737288i	$0.263894\pi$
$263$	−1298.07	+	3995.04i	−0.304343	+	0.936671i	−0.979922	+	0.199383i	$0.936106\pi$
$264$		0			0
$265$	−7214.43	+	2563.65i	−1.67237	+	0.594279i
$266$	−1595.92	+	4911.73i	−0.367865	+	1.13217i
$267$		0			0
$268$	−573.381			−0.130690
$269$	−1835.82	−	1333.80i	−0.416105	−	0.302318i	0.359964	−	0.932966i	$-0.382789\pi$
$269$	−1835.82	−	1333.80i	−0.416105	−	0.302318i	−0.776069	+	0.630648i	$0.782789\pi$
$270$		0			0
$271$	630.472	−	458.065i	0.141323	−	0.102677i	−0.514878	−	0.857264i	$-0.672163\pi$
$271$	630.472	−	458.065i	0.141323	−	0.102677i	0.656200	+	0.754587i	$0.272163\pi$
$272$	−2132.69	+	1549.49i	−0.475417	+	0.345411i
$273$		0			0
$274$	−1768.60			−0.389945
$275$	−194.704	+	733.059i	−0.0426949	+	0.160746i
$276$		0			0
$277$	−1562.16	−	4807.84i	−0.338849	−	1.04287i	−0.964795	−	0.263004i	$-0.915287\pi$
$277$	−1562.16	−	4807.84i	−0.338849	−	1.04287i	0.625945	−	0.779867i	$-0.284713\pi$
$278$	441.336	−	320.649i	0.0952142	−	0.0691772i
$279$		0			0
$280$	−2790.58	−	3628.53i	−0.595605	−	0.774451i
$281$	−1997.64	−	1451.37i	−0.424089	−	0.308119i	0.355192	−	0.934793i	$-0.384416\pi$
$281$	−1997.64	−	1451.37i	−0.424089	−	0.308119i	−0.779281	+	0.626675i	$0.784416\pi$
$282$		0			0
$283$	−1534.87	−	1115.15i	−0.322398	−	0.234236i	0.414800	−	0.909913i	$-0.363851\pi$
$283$	−1534.87	−	1115.15i	−0.322398	−	0.234236i	−0.737198	+	0.675677i	$0.763851\pi$
$284$	−39.3363	+	121.065i	−0.00821895	+	0.0252953i
$285$		0			0
$286$	431.044	+	1326.62i	0.0891195	+	0.274282i
$287$	2049.61	−	6308.06i	0.421550	−	1.29740i
$288$		0			0
$289$	−1062.51	−	3270.08i	−0.216266	−	0.665597i
$290$	223.301	+	290.353i	0.0452161	+	0.0587935i
$291$		0			0
$292$	148.974	+	108.236i	0.0298562	+	0.0216918i
$293$	−1090.95			−0.217522			−0.108761	−	0.994068i	$-0.534688\pi$
$293$	−1090.95			−0.217522			−0.108761	+	0.994068i	$0.534688\pi$
$294$		0			0
$295$	−1416.01	+	2065.14i	−0.279468	+	0.407584i
$296$	−1887.34	+	1371.24i	−0.370607	+	0.269262i
$297$		0			0
$298$	−2348.30	−	7227.34i	−0.456489	−	1.40493i
$299$	6340.62			1.22638
$300$		0			0
$301$	−6742.91			−1.29121
$302$	−251.050	−	772.652i	−0.0478354	−	0.147222i
$303$		0			0
$304$	−5162.55	+	3750.81i	−0.973988	+	0.707644i
$305$	212.725	+	7797.53i	0.0399364	+	1.46389i
$306$		0			0
$307$	8283.37			1.53992			0.769962	−	0.638090i	$-0.220275\pi$
$307$	8283.37			1.53992			0.769962	+	0.638090i	$0.220275\pi$
$308$	−58.5556	−	42.5431i	−0.0108328	−	0.00787051i
$309$		0			0
$310$	4158.49	−	6064.85i	0.761892	−	1.11116i
$311$	236.303	+	727.265i	0.0430852	+	0.132603i	0.970285	−	0.241964i	$-0.0777915\pi$
$311$	236.303	+	727.265i	0.0430852	+	0.132603i	−0.927200	+	0.374567i	$0.877792\pi$
$312$		0			0
$313$	−1734.95	+	5339.63i	−0.313307	+	0.964261i	0.663138	+	0.748497i	$0.269224\pi$
$313$	−1734.95	+	5339.63i	−0.313307	+	0.964261i	−0.976446	+	0.215764i	$0.930776\pi$
$314$	−2771.48	−	8529.75i	−0.498102	−	1.53300i
$315$		0			0
$316$	138.247	−	425.479i	0.0246107	−	0.0757439i
$317$	−6874.41	−	4994.55i	−1.21800	−	0.884927i	−0.222065	−	0.975032i	$-0.571280\pi$
$317$	−6874.41	−	4994.55i	−1.21800	−	0.884927i	−0.995932	+	0.0901049i	$0.971280\pi$
$318$		0			0
$319$	−54.7438	−	39.7737i	−0.00960835	−	0.00698087i
$320$	−141.935	−	5202.71i	−0.0247951	−	0.908877i
$321$		0			0
$322$	−3642.14	+	2646.17i	−0.630337	+	0.457966i
$323$	1103.07	+	3394.89i	0.190020	+	0.584820i
$324$		0			0
$325$	7587.96	−	6172.15i	1.29509	−	1.05344i
$326$	−2358.72			−0.400729
$327$		0			0
$328$	6142.83	−	4463.03i	1.03409	−	0.751309i
$329$	−4463.48	+	3242.91i	−0.747963	+	0.543427i
$330$		0			0
$331$	2626.81	+	1908.49i	0.436202	+	0.316919i	0.784124	−	0.620604i	$-0.213113\pi$
$331$	2626.81	+	1908.49i	0.436202	+	0.316919i	−0.347922	+	0.937523i	$0.613113\pi$
$332$	699.355			0.115609
$333$		0			0
$334$	−2570.12	+	7910.01i	−0.421050	+	1.29586i
$335$	−6196.01	−	8056.52i	−1.01052	−	1.31396i
$336$		0			0
$337$	−2291.63	+	7052.92i	−0.370425	+	1.14005i	0.576089	+	0.817387i	$0.304578\pi$
$337$	−2291.63	+	7052.92i	−0.370425	+	1.14005i	−0.946514	+	0.322664i	$0.895422\pi$
$338$	3564.20	−	10969.5i	0.573570	−	1.76527i
$339$		0			0
$340$	259.733	+	76.6273i	0.0414294	+	0.0122226i
$341$	−419.793	+	1291.99i	−0.0666659	+	0.205176i
$342$		0			0
$343$	−6209.68			−0.977525
$344$	−6244.91	−	4537.19i	−0.978788	−	0.711131i
$345$		0			0
$346$	−9795.14	+	7116.59i	−1.52194	+	1.10575i
$347$	504.270	−	366.374i	0.0780133	−	0.0566800i	−0.548095	−	0.836416i	$-0.684647\pi$
$347$	504.270	−	366.374i	0.0780133	−	0.0566800i	0.626108	+	0.779736i	$0.284647\pi$
$348$		0			0
$349$	12079.4			1.85271			0.926356	−	0.376649i	$-0.122924\pi$
$349$	12079.4			1.85271			0.926356	+	0.376649i	$0.122924\pi$
$350$	−1782.76	+	6712.09i	−0.272265	+	1.02508i
$351$		0			0
$352$	−53.4003	−	164.349i	−0.00808592	−	0.0248859i
$353$	1021.78	−	742.368i	0.154062	−	0.111933i	−0.508084	−	0.861308i	$-0.669646\pi$
$353$	1021.78	−	742.368i	0.154062	−	0.111933i	0.662146	+	0.749375i	$0.269646\pi$
$354$		0			0
$355$	−2126.14	+	755.525i	−0.317870	+	0.112955i
$356$	1.92886	+	1.40140i	0.000287160	+	0.000208634i
$357$		0			0
$358$	−4193.24	−	3046.56i	−0.619049	−	0.449765i
$359$	48.5654	−	149.469i	0.00713979	−	0.0219740i	−0.947423	−	0.319983i	$-0.896323\pi$
$359$	48.5654	−	149.469i	0.00713979	−	0.0219740i	0.954563	+	0.298009i	$0.0963227\pi$
$360$		0			0
$361$	550.615	+	1694.62i	0.0802763	+	0.247065i
$362$	−1355.32	+	4171.26i	−0.196780	+	0.605625i
$363$		0			0
$364$	288.433	+	887.706i	0.0415330	+	0.127825i
$365$	89.0131	+	3262.82i	0.0127648	+	0.467901i
$366$		0			0
$367$	−5574.94	−	4050.43i	−0.792941	−	0.576106i	0.115894	−	0.993262i	$-0.463027\pi$
$367$	−5574.94	−	4050.43i	−0.792941	−	0.576106i	−0.908835	+	0.417156i	$0.863027\pi$
$368$	−5562.58			−0.787961
$369$		0			0
$370$	3394.71	+	1001.52i	0.476979	+	0.140720i
$371$	10477.4	−	7612.27i	1.46620	−	1.06525i
$372$		0			0
$373$	−1192.38	−	3669.78i	−0.165521	−	0.509421i	0.833553	−	0.552439i	$-0.186303\pi$
$373$	−1192.38	−	3669.78i	−0.165521	−	0.509421i	−0.999074	+	0.0430178i	$0.986303\pi$
$374$	−684.538			−0.0946434
$375$		0			0
$376$	−6315.93			−0.866275
$377$	269.657	+	829.919i	0.0368383	+	0.113377i
$378$		0			0
$379$	4056.09	−	2946.92i	0.549730	−	0.399402i	−0.277956	−	0.960594i	$-0.589657\pi$
$379$	4056.09	−	2946.92i	0.549730	−	0.399402i	0.827686	+	0.561192i	$0.189657\pi$
$380$	628.728	+	185.489i	0.0848764	+	0.0250405i
$381$		0			0
$382$	−10748.6			−1.43965
$383$	11340.8	+	8239.61i	1.51303	+	1.09928i	0.964811	+	0.262944i	$0.0846936\pi$
$383$	11340.8	+	8239.61i	1.51303	+	1.09928i	0.548218	+	0.836335i	$0.315306\pi$
$384$		0			0
$385$	−34.9875	−	1282.48i	−0.00463150	−	0.169770i
$386$	−4263.12	−	13120.5i	−0.562142	−	1.73010i
$387$		0			0
$388$	3.59863	−	11.0754i	0.000470857	−	0.00144915i
$389$	29.9938	+	92.3116i	0.00390938	+	0.0120318i	0.952992	−	0.302995i	$-0.0979865\pi$
$389$	29.9938	+	92.3116i	0.00390938	+	0.0120318i	−0.949083	+	0.315027i	$0.897987\pi$
$390$		0			0
$391$	−961.552	+	2959.35i	−0.124368	+	0.382764i
$392$	256.517	+	186.370i	0.0330512	+	0.0240131i
$393$		0			0
$394$	1144.93	+	831.841i	0.146398	+	0.106364i
$395$	7472.27	−	2655.28i	0.951825	−	0.338232i
$396$		0			0
$397$	4234.34	−	3076.43i	0.535303	−	0.388921i	−0.287034	−	0.957920i	$-0.592669\pi$
$397$	4234.34	−	3076.43i	0.535303	−	0.388921i	0.822338	+	0.569000i	$0.192669\pi$
$398$	449.340	+	1382.93i	0.0565915	+	0.174171i
$399$		0			0
$400$	−6656.86	+	5414.79i	−0.832108	+	0.676849i
$401$	10349.0			1.28879			0.644396	−	0.764692i	$-0.277109\pi$
$401$	10349.0			1.28879			0.644396	+	0.764692i	$0.277109\pi$
$402$		0			0
$403$	14173.0	−	10297.3i	1.75188	−	1.27282i
$404$	−679.951	+	494.014i	−0.0837348	+	0.0608369i
$405$		0			0
$406$	−501.249	−	364.179i	−0.0612724	−	0.0445170i
$407$	−653.848			−0.0796316
$408$		0			0
$409$	−3148.95	+	9691.47i	−0.380698	+	1.17167i	0.558855	+	0.829265i	$0.311241\pi$
$409$	−3148.95	+	9691.47i	−0.380698	+	1.17167i	−0.939553	+	0.342403i	$0.888759\pi$
$410$	−11048.9	−	3259.69i	−1.33090	−	0.392645i
$411$		0			0
$412$	327.185	−	1006.97i	0.0391244	−	0.120412i
$413$	1308.83	−	4028.17i	0.155940	−	0.479935i
$414$		0			0
$415$	7557.29	+	9826.56i	0.893910	+	1.16233i
$416$	−688.645	+	2119.43i	−0.0811625	+	0.249793i
$417$		0			0
$418$	−1657.04			−0.193896
$419$	8398.42	+	6101.81i	0.979212	+	0.711439i	0.957532	−	0.288326i	$-0.0930986\pi$
$419$	8398.42	+	6101.81i	0.979212	+	0.711439i	0.0216796	+	0.999765i	$0.493099\pi$
$420$		0			0
$421$	7922.06	−	5755.72i	0.917097	−	0.666310i	−0.0257029	−	0.999670i	$-0.508182\pi$
$421$	7922.06	−	5755.72i	0.917097	−	0.666310i	0.942800	+	0.333360i	$0.108182\pi$
$422$	−1126.05	+	818.122i	−0.129894	+	0.0943733i
$423$		0			0
$424$	14825.8			1.69812
$425$	1730.01	+	4477.52i	0.197454	+	0.511040i
$426$		0			0
$427$	−4077.30	−	12548.6i	−0.462094	−	1.42218i
$428$	791.264	−	574.887i	0.0893625	−	0.0649257i
$429$		0			0
$430$	319.374	+	11706.8i	0.0358176	+	1.31291i
$431$	3207.40	+	2330.31i	0.358457	+	0.260434i	0.752408	−	0.658697i	$-0.228892\pi$
$431$	3207.40	+	2330.31i	0.358457	+	0.260434i	−0.393951	+	0.919131i	$0.628892\pi$
$432$		0			0
$433$	−3610.83	−	2623.42i	−0.400752	−	0.291163i	0.369095	−	0.929391i	$-0.379668\pi$
$433$	−3610.83	−	2623.42i	−0.400752	−	0.291163i	−0.769847	+	0.638228i	$0.779668\pi$
$434$	−3843.74	+	11829.8i	−0.425128	+	1.30841i
$435$		0			0
$436$	87.1225	+	268.136i	0.00956975	+	0.0294527i
$437$	−2327.60	+	7163.61i	−0.254792	+	0.784169i
$438$		0			0
$439$	−5124.83	−	15772.6i	−0.557164	−	1.71477i	−0.690160	−	0.723657i	$-0.742460\pi$
$439$	−5124.83	−	15772.6i	−0.557164	−	1.71477i	0.132997	−	0.991116i	$-0.457540\pi$
$440$	830.558	−	1211.31i	0.0899893	−	0.131243i
$441$		0			0
$442$	7141.80	+	5188.82i	0.768554	+	0.558387i
$443$	−5664.63			−0.607528			−0.303764	−	0.952747i	$-0.598243\pi$
$443$	−5664.63			−0.607528			−0.303764	+	0.952747i	$0.598243\pi$
$444$		0			0
$445$	1.15251	+	42.2457i	0.000122773	+	0.00450032i
$446$	−12040.1	+	8747.66i	−1.27829	+	0.928730i
$447$		0			0
$448$	2720.48	+	8372.77i	0.286899	+	0.882983i
$449$	14047.7			1.47651			0.738253	−	0.674524i	$-0.235651\pi$
$449$	14047.7			1.47651			0.738253	+	0.674524i	$0.235651\pi$
$450$		0			0
$451$	2128.11			0.222193
$452$	121.195	+	373.000i	0.0126118	+	0.0388151i
$453$		0			0
$454$	12578.9	−	9139.13i	1.30035	−	0.944759i
$455$	−9356.23	+	13645.4i	−0.964015	+	1.40594i
$456$		0			0
$457$	−11501.1			−1.17724			−0.588622	−	0.808409i	$-0.700329\pi$
$457$	−11501.1			−1.17724			−0.588622	+	0.808409i	$0.700329\pi$
$458$	−1164.01	−	845.702i	−0.118757	−	0.0862817i
$459$		0			0
$460$	348.354	+	452.957i	0.0353089	+	0.0459114i
$461$	−497.651	−	1531.61i	−0.0502775	−	0.154738i	0.922766	−	0.385362i	$-0.125923\pi$
$461$	−497.651	−	1531.61i	−0.0502775	−	0.154738i	−0.973043	+	0.230624i	$0.925923\pi$
$462$		0			0
$463$	606.515	−	1866.66i	0.0608793	−	0.187367i	−0.915991	−	0.401198i	$-0.868594\pi$
$463$	606.515	−	1866.66i	0.0608793	−	0.187367i	0.976871	+	0.213830i	$0.0685940\pi$
$464$	−236.568	−	728.082i	−0.0236690	−	0.0728456i
$465$		0			0
$466$	1978.94	−	6090.56i	0.196723	−	0.605450i
$467$	1274.21	+	925.764i	0.126260	+	0.0917329i	0.649123	−	0.760684i	$-0.275136\pi$
$467$	1274.21	+	925.764i	0.126260	+	0.0917329i	−0.522863	+	0.852417i	$0.675136\pi$
$468$		0			0
$469$	13908.3	+	10105.0i	1.36935	+	0.994895i
$470$	5841.64	+	7595.75i	0.573308	+	0.745459i
$471$		0			0
$472$	3922.66	−	2849.98i	0.382532	−	0.277926i
$473$	−668.551	−	2057.59i	−0.0649895	−	0.200017i
$474$		0			0
$475$	4187.79	+	10838.6i	0.404524	+	1.04697i
$476$	−458.059			−0.0441073
$477$		0			0
$478$	10542.0	−	7659.24i	1.00875	−	0.732898i
$479$	7933.01	−	5763.67i	0.756719	−	0.549789i	−0.141183	−	0.989983i	$-0.545091\pi$
$479$	7933.01	−	5763.67i	0.756719	−	0.549789i	0.897902	+	0.440195i	$0.145091\pi$
$480$		0			0
$481$	6821.61	+	4956.19i	0.646650	+	0.469819i
$482$	7059.13			0.667084
$483$		0			0
$484$	−252.249	+	776.344i	−0.0236898	+	0.0729098i
$485$	194.507	−	69.1181i	0.0182105	−	0.00647112i
$486$		0			0
$487$	−2414.05	+	7429.69i	−0.224623	+	0.691317i	0.773707	+	0.633543i	$0.218400\pi$
$487$	−2414.05	+	7429.69i	−0.224623	+	0.691317i	−0.998330	+	0.0577737i	$0.981600\pi$
$488$	4667.60	−	14365.4i	0.432976	−	1.33256i
$489$		0			0
$490$	−13.1186	−	480.870i	−0.00120947	−	0.0443337i
$491$	−1550.87	+	4773.07i	−0.142545	+	0.438708i	−0.996687	−	0.0813313i	$-0.974083\pi$
$491$	−1550.87	+	4773.07i	−0.142545	+	0.438708i	0.854142	+	0.520040i	$0.174083\pi$
$492$		0			0
$493$	−428.241			−0.0391217
$494$	17287.9	+	12560.4i	1.57454	+	1.14397i
$495$		0			0
$496$	−12433.9	+	9033.76i	−1.12560	+	0.817798i
$497$	3087.76	−	2243.39i	0.278682	−	0.202474i
$498$		0			0
$499$	−16251.9			−1.45798			−0.728991	−	0.684523i	$-0.760011\pi$
$499$	−16251.9			−1.45798			−0.728991	+	0.684523i	$0.760011\pi$
$500$	857.805	+	202.965i	0.0767244	+	0.0181537i
$501$		0			0
$502$	3140.82	+	9666.45i	0.279246	+	0.859432i
$503$	89.3910	−	64.9464i	0.00792395	−	0.00575709i	−0.583816	−	0.811886i	$-0.698441\pi$
$503$	89.3910	−	64.9464i	0.00792395	−	0.00575709i	0.591740	+	0.806129i	$0.298441\pi$
$504$		0			0
$505$	−14289.0	−	4215.58i	−1.25911	−	0.371467i
$506$	−1168.59	−	849.029i	−0.102668	−	0.0745927i
$507$		0			0
$508$	357.264	+	259.567i	0.0312028	+	0.0226702i
$509$	−4592.45	+	14134.1i	−0.399915	+	1.23081i	0.525152	+	0.851008i	$0.324008\pi$
$509$	−4592.45	+	14134.1i	−0.399915	+	1.23081i	−0.925067	+	0.379804i	$0.875992\pi$
$510$		0			0
$511$	−1706.11	−	5250.88i	−0.147699	−	0.454570i
$512$	−3069.94	+	9448.29i	−0.264987	+	0.815546i
$513$		0			0
$514$	−4332.70	−	13334.7i	−0.371804	−	1.14429i
$515$	17684.4	−	6284.18i	1.51315	−	0.537697i
$516$		0			0
$517$	−1432.12	−	1040.50i	−0.121827	−	0.0885124i
$518$	−5986.82			−0.507810
$519$		0			0
$520$	−17847.0	+	6341.93i	−1.50508	+	0.534831i
$521$	−6248.48	+	4539.79i	−0.525433	+	0.381750i	−0.818647	−	0.574297i	$-0.805275\pi$
$521$	−6248.48	+	4539.79i	−0.525433	+	0.381750i	0.293213	+	0.956047i	$0.405275\pi$
$522$		0			0
$523$	−1432.62	−	4409.15i	−0.119778	−	0.368640i	0.873135	−	0.487478i	$-0.162083\pi$
$523$	−1432.62	−	4409.15i	−0.119778	−	0.368640i	−0.992914	+	0.118838i	$0.962083\pi$
$524$	367.026			0.0305985
$525$		0			0
$526$	−12340.7			−1.02296
$527$	2656.72	+	8176.54i	0.219599	+	0.675855i
$528$		0			0
$529$	4531.36	−	3292.23i	0.372431	−	0.270587i
$530$	−13712.4	−	17829.9i	−1.12383	−	1.46129i
$531$		0			0
$532$	−1108.81			−0.0903627
$533$	−22202.6	−	16131.2i	−1.80432	−	1.31092i
$534$		0			0
$535$	16628.1	+	4905.69i	1.34373	+	0.396433i
$536$	6081.65	+	18717.4i	0.490088	+	1.50834i
$537$		0			0
$538$	2060.06	−	6340.21i	0.165085	−	0.508078i
$539$	27.4615	+	84.5179i	0.00219453	+	0.00675407i
$540$		0			0
$541$	−2574.24	+	7922.70i	−0.204575	+	0.629618i	0.795155	+	0.606406i	$0.207389\pi$
$541$	−2574.24	+	7922.70i	−0.204575	+	0.629618i	−0.999731	+	0.0232123i	$0.992611\pi$
$542$	1852.21	+	1345.71i	0.146788	+	0.106648i
$543$		0			0
$544$	−884.768	−	642.821i	−0.0697318	−	0.0506631i
$545$	−2826.09	+	4121.65i	−0.222122	+	0.323948i
$546$		0			0
$547$	−11703.1	+	8502.77i	−0.914783	+	0.664629i	−0.942220	−	0.334995i	$-0.891265\pi$
$547$	−11703.1	+	8502.77i	−0.914783	+	0.664629i	0.0274369	+	0.999624i	$0.491265\pi$
$548$	−117.338	−	361.130i	−0.00914680	−	0.0281510i
$549$		0			0
$550$	−2224.94	+	121.488i	−0.172494	+	0.00941867i
$551$	−1036.63			−0.0801486
$552$		0			0
$553$	−10851.9	+	7884.33i	−0.834481	+	0.606286i
$554$	12015.1	−	8729.45i	0.921427	−	0.669456i
$555$		0			0
$556$	94.7539	+	68.8428i	0.00722745	+	0.00525105i
$557$	−21991.8			−1.67293			−0.836467	−	0.548017i	$-0.815383\pi$
$557$	−21991.8			−1.67293			−0.836467	+	0.548017i	$0.815383\pi$
$558$		0			0
$559$	−8621.58	+	26534.5i	−0.652333	+	2.00767i
$560$	8208.16	−	11971.0i	0.619389	−	0.903333i
$561$		0			0
$562$	2241.64	−	6899.05i	0.168252	−	0.517827i
$563$	3935.09	−	12111.0i	0.294573	−	0.906602i	−0.688792	−	0.724959i	$-0.741859\pi$
$563$	3935.09	−	12111.0i	0.294573	−	0.906602i	0.983365	−	0.181643i	$-0.0581414\pi$
$564$		0			0
$565$	−3931.34	+	5733.57i	−0.292731	+	0.426926i
$566$	1722.35	−	5300.84i	0.127907	−	0.393659i
$567$		0			0
$568$	4369.25			0.322763
$569$	−3083.27	−	2240.13i	−0.227166	−	0.165046i	0.468381	−	0.883527i	$-0.344838\pi$
$569$	−3083.27	−	2240.13i	−0.227166	−	0.165046i	−0.695546	+	0.718481i	$0.744838\pi$
$570$		0			0
$571$	16776.5	−	12188.9i	1.22955	−	0.893324i	0.232698	−	0.972549i	$-0.425245\pi$
$571$	16776.5	−	12188.9i	1.22955	−	0.893324i	0.996857	+	0.0792254i	$0.0252447\pi$
$572$	−242.284	+	176.030i	−0.0177105	+	0.0128674i
$573$		0			0
$574$	19485.6			1.41692
$575$	−2600.11	+	9789.39i	−0.188577	+	0.709992i
$576$		0			0
$577$	−8200.30	−	25237.9i	−0.591652	−	1.82092i	−0.570733	−	0.821136i	$-0.693341\pi$
$577$	−8200.30	−	25237.9i	−0.591652	−	1.82092i	−0.0209185	−	0.999781i	$-0.506659\pi$
$578$	8172.10	−	5937.38i	0.588088	−	0.427271i
$579$		0			0
$580$	−44.4722	+	64.8594i	−0.00318381	+	0.00464335i
$581$	−16964.0	−	12325.1i	−1.21134	−	0.880088i
$582$		0			0
$583$	3361.69	+	2442.41i	0.238812	+	0.173507i
$584$	1953.12	−	6011.09i	0.138392	−	0.425926i
$585$		0			0
$586$	−990.402	−	3048.14i	−0.0698177	−	0.214877i
$587$	6201.38	−	19085.9i	0.436045	−	1.34201i	−0.455968	−	0.889996i	$-0.650707\pi$
$587$	6201.38	−	19085.9i	0.436045	−	1.34201i	0.892012	−	0.452011i	$-0.149293\pi$
$588$		0			0
$589$	6431.04	+	19792.7i	0.449892	+	1.38462i
$590$	−7055.56	−	2081.56i	−0.492327	−	0.145248i
$591$		0			0
$592$	−5984.55	−	4348.03i	−0.415479	−	0.301863i
$593$	−5902.00			−0.408712			−0.204356	−	0.978897i	$-0.565510\pi$
$593$	−5902.00			−0.408712			−0.204356	+	0.978897i	$0.565510\pi$
$594$		0			0
$595$	−4949.82	−	6436.14i	−0.341047	−	0.443455i
$596$	1319.95	−	959.001i	0.0907170	−	0.0659097i
$597$		0			0
$598$	5756.23	+	17715.9i	0.393628	+	1.21146i
$599$	1759.46			0.120016			0.0600079	−	0.998198i	$-0.480887\pi$
$599$	1759.46			0.120016			0.0600079	+	0.998198i	$0.480887\pi$
$600$		0			0
$601$	22974.1			1.55929			0.779646	−	0.626220i	$-0.215399\pi$
$601$	22974.1			1.55929			0.779646	+	0.626220i	$0.215399\pi$
$602$	−6121.44	−	18839.9i	−0.414437	−	1.27551i
$603$		0			0
$604$	141.112	−	102.524i	0.00950623	−	0.00690668i
$605$	−13634.2	+	4844.91i	−0.916210	+	0.325576i
$606$		0			0
$607$	−18961.8			−1.26794			−0.633968	−	0.773359i	$-0.718575\pi$
$607$	−18961.8			−1.26794			−0.633968	+	0.773359i	$0.718575\pi$
$608$	−2141.73	−	1556.06i	−0.142860	−	0.103794i
$609$		0			0
$610$	−21593.4	+	7673.22i	−1.43326	+	0.509311i
$611$	7054.33	+	21711.0i	0.467083	+	1.43753i
$612$		0			0
$613$	6808.93	−	20955.7i	0.448630	−	1.38074i	−0.429824	−	0.902913i	$-0.641424\pi$
$613$	6808.93	−	20955.7i	0.448630	−	1.38074i	0.878454	−	0.477827i	$-0.158576\pi$
$614$	7519.92	+	23143.9i	0.494266	+	1.52119i
$615$		0			0
$616$	−767.694	+	2362.72i	−0.0502131	+	0.154540i
$617$	5152.77	+	3743.71i	0.336212	+	0.244272i	0.743062	−	0.669223i	$-0.233373\pi$
$617$	5152.77	+	3743.71i	0.336212	+	0.244272i	−0.406850	+	0.913495i	$0.633373\pi$
$618$		0			0
$619$	−6709.39	−	4874.66i	−0.435659	−	0.316525i	0.348249	−	0.937402i	$-0.386777\pi$
$619$	−6709.39	−	4874.66i	−0.435659	−	0.316525i	−0.783908	+	0.620877i	$0.786777\pi$
$620$	1514.28	+	446.748i	0.0980886	+	0.0289384i
$621$		0			0
$622$	−1817.47	+	1320.47i	−0.117161	+	0.0851224i
$623$	−22.0901	−	67.9865i	−0.00142058	−	0.00437210i
$624$		0			0
$625$	6417.68	+	14246.2i	0.410732	+	0.911756i
$626$	−16494.1			−1.05309
$627$		0			0
$628$	1557.82	−	1131.82i	0.0989867	−	0.0719180i
$629$	−3347.69	+	2432.24i	−0.212212	+	0.154181i
$630$		0			0
$631$	−18624.6	−	13531.5i	−1.17501	−	0.853696i	−0.183411	−	0.983036i	$-0.558714\pi$
$631$	−18624.6	−	13531.5i	−1.17501	−	0.853696i	−0.991600	+	0.129340i	$0.958714\pi$
$632$	−15355.6			−0.966478
$633$		0			0
$634$	7714.08	−	23741.5i	0.483226	−	1.48722i
$635$	213.468	+	7824.78i	0.0133405	+	0.489003i
$636$		0			0
$637$	354.141	−	1089.94i	0.0220276	−	0.0677940i
$638$	61.4304	−	189.063i	0.00381200	−	0.0117321i
$639$		0			0
$640$	16807.9	−	5972.69i	1.03811	−	0.368893i
$641$	7178.47	−	22093.1i	0.442329	−	1.36135i	−0.443058	−	0.896493i	$-0.646106\pi$
$641$	7178.47	−	22093.1i	0.442329	−	1.36135i	0.885387	−	0.464855i	$-0.153894\pi$
$642$		0			0
$643$	17439.0			1.06956			0.534780	−	0.844991i	$-0.320395\pi$
$643$	17439.0			1.06956			0.534780	+	0.844991i	$0.320395\pi$
$644$	−781.960	−	568.127i	−0.0478471	−	0.0347630i
$645$		0			0
$646$	−8484.02	+	6164.00i	−0.516717	+	0.375417i
$647$	13233.9	−	9614.98i	0.804139	−	0.584241i	−0.107987	−	0.994152i	$-0.534440\pi$
$647$	13233.9	−	9614.98i	0.804139	−	0.584241i	0.912125	+	0.409911i	$0.134440\pi$
$648$		0			0
$649$	1358.96			0.0821939
$650$	24133.8	+	15597.7i	1.45631	+	0.941216i
$651$		0			0
$652$	−156.490	−	481.628i	−0.00939975	−	0.0289295i
$653$	13116.1	−	9529.41i	0.786023	−	0.571079i	−0.120758	−	0.992682i	$-0.538532\pi$
$653$	13116.1	−	9529.41i	0.786023	−	0.571079i	0.906781	+	0.421603i	$0.138532\pi$
$654$		0			0
$655$	3966.11	+	5157.04i	0.236594	+	0.307637i
$656$	19478.2	+	14151.8i	1.15929	+	0.842276i
$657$		0			0
$658$	−13112.9	−	9527.06i	−0.776889	−	0.564443i
$659$	−3337.93	+	10273.1i	−0.197310	+	0.607258i	0.802632	+	0.596475i	$0.203433\pi$
$659$	−3337.93	+	10273.1i	−0.197310	+	0.607258i	−0.999942	+	0.0107834i	$0.996567\pi$
$660$		0			0
$661$	4696.20	+	14453.4i	0.276341	+	0.850489i	0.988862	+	0.148838i	$0.0475534\pi$
$661$	4696.20	+	14453.4i	0.276341	+	0.850489i	−0.712521	+	0.701651i	$0.752447\pi$
$662$	−2947.66	+	9071.98i	−0.173058	+	0.532617i
$663$		0			0
$664$	−7417.80	−	22829.6i	−0.433534	−	1.33428i
$665$	−11981.9	−	15579.8i	−0.698703	−	0.908507i
$666$		0			0
$667$	−731.057	−	531.144i	−0.0424387	−	0.0308336i
$668$	−1785.66			−0.103427
$669$		0			0
$670$	16885.2	−	24625.8i	0.973630	−	1.41997i
$671$	3424.94	−	2488.36i	0.197047	−	0.143163i
$672$		0			0
$673$	2910.35	+	8957.12i	0.166695	+	0.513034i	0.999157	−	0.0410478i	$-0.0130696\pi$
$673$	2910.35	+	8957.12i	0.166695	+	0.513034i	−0.832462	+	0.554081i	$0.813070\pi$
$674$	−21786.5			−1.24508
$675$		0			0
$676$	2476.33			0.140892
$677$	4739.48	+	14586.6i	0.269059	+	0.828079i	0.990730	+	0.135843i	$0.0433743\pi$
$677$	4739.48	+	14586.6i	0.269059	+	0.828079i	−0.721671	+	0.692236i	$0.756626\pi$
$678$		0			0
$679$	−282.479	+	205.233i	−0.0159655	+	0.0115996i
$680$	−253.480	−	9291.45i	−0.0142949	−	0.523986i
$681$		0			0
$682$	−3990.95			−0.224079
$683$	5893.00	+	4281.51i	0.330145	+	0.239865i	0.740492	−	0.672065i	$-0.234592\pi$
$683$	5893.00	+	4281.51i	0.330145	+	0.239865i	−0.410347	+	0.911929i	$0.634592\pi$
$684$		0			0
$685$	3806.24	−	5551.12i	0.212305	−	0.309631i
$686$	−5637.36	−	17350.0i	−0.313754	−	0.965636i
$687$		0			0
$688$	7563.65	−	23278.5i	0.419130	−	1.28995i
$689$	−16559.0	−	50963.5i	−0.915601	−	2.81793i
$690$		0			0
$691$	4164.62	−	12817.4i	0.229276	−	0.705639i	−0.768553	−	0.639786i	$-0.779023\pi$
$691$	4164.62	−	12817.4i	0.229276	−	0.705639i	0.997829	−	0.0658530i	$-0.0209768\pi$
$692$	−2103.00	−	1527.92i	−0.115526	−	0.0839346i
$693$		0			0
$694$	1481.45	+	1076.34i	0.0810304	+	0.0588720i
$695$	56.6163	+	2075.30i	0.00309004	+	0.113267i
$696$		0			0
$697$	10895.9	−	7916.33i	0.592125	−	0.430204i
$698$	10966.1	+	33750.2i	0.594661	+	1.83018i
$699$		0			0
$700$	−1488.82	+	81.2937i	−0.0803888	+	0.00438945i
$701$	−16099.1			−0.867413			−0.433706	−	0.901054i	$-0.642794\pi$
$701$	−16099.1			−0.867413			−0.433706	+	0.901054i	$0.642794\pi$
$702$		0			0
$703$	−8103.65	+	5887.65i	−0.434758	+	0.315870i
$704$	−2285.21	+	1660.30i	−0.122339	+	0.0888848i
$705$		0			0
$706$	3001.81	+	2180.94i	0.160020	+	0.116262i
$707$	25199.6			1.34050
$708$		0			0
$709$	1824.52	−	5615.31i	0.0966452	−	0.297443i	−0.891034	−	0.453937i	$-0.850019\pi$
$709$	1824.52	−	5615.31i	0.0966452	−	0.297443i	0.987679	+	0.156494i	$0.0500191\pi$
$710$	−4041.14	−	5254.60i	−0.213607	−	0.277749i
$711$		0			0
$712$	25.2883	−	77.8294i	0.00133107	−	0.00409660i
$713$	−5605.98	+	17253.4i	−0.294454	+	0.906236i
$714$		0			0
$715$	−5091.52	−	1502.12i	−0.266311	−	0.0785679i
$716$	343.876	−	1058.34i	0.0179487	−	0.0552404i
$717$		0			0
$718$	461.710			0.0239984
$719$	−3639.38	−	2644.16i	−0.188770	−	0.137150i	0.489386	−	0.872067i	$-0.337221\pi$
$719$	−3639.38	−	2644.16i	−0.188770	−	0.137150i	−0.678156	+	0.734918i	$0.737221\pi$
$720$		0			0
$721$	−25682.8	+	18659.7i	−1.32660	+	0.963831i
$722$	−4234.94	+	3076.86i	−0.218294	+	0.158600i
$723$		0			0
$724$	−941.649			−0.0483372
$725$	−1391.90	+	76.0017i	−0.0713021	+	0.00389329i
$726$		0			0
$727$	−1876.26	−	5774.55i	−0.0957177	−	0.294589i	0.891722	−	0.452583i	$-0.149497\pi$
$727$	−1876.26	−	5774.55i	−0.0957177	−	0.294589i	−0.987440	+	0.157994i	$0.949497\pi$
$728$	25918.8	−	18831.1i	1.31953	−	0.958693i
$729$		0			0
$730$	−9035.59	+	3210.80i	−0.458113	+	0.162791i
$731$	−11077.0	−	8047.88i	−0.560460	−	0.407198i
$732$		0			0
$733$	−21042.7	−	15288.4i	−1.06034	−	0.770382i	−0.0861888	−	0.996279i	$-0.527469\pi$
$733$	−21042.7	−	15288.4i	−1.06034	−	0.770382i	−0.974151	+	0.225897i	$0.927469\pi$
$734$	6255.89	−	19253.6i	0.314590	−	0.968208i
$735$		0			0
$736$	−713.115	−	2194.74i	−0.0357144	−	0.109918i
$737$	−1704.53	+	5246.01i	−0.0851930	+	0.262197i
$738$		0			0
$739$	9514.09	+	29281.4i	0.473588	+	1.45755i	0.847853	+	0.530232i	$0.177895\pi$
$739$	9514.09	+	29281.4i	0.473588	+	1.45755i	−0.374265	+	0.927322i	$0.622105\pi$
$740$	20.7230	+	759.611i	0.00102945	+	0.0377350i
$741$		0			0
$742$	30780.6	+	22363.4i	1.52290	+	1.10645i
$743$	−29872.6			−1.47499			−0.737496	−	0.675352i	$-0.763992\pi$
$743$	−29872.6			−1.47499			−0.737496	+	0.675352i	$0.763992\pi$
$744$		0			0
$745$	27738.3	+	8183.46i	1.36410	+	0.402441i
$746$	9170.98	−	6663.11i	0.450098	−	0.327016i
$747$		0			0
$748$	−45.4160	−	139.776i	−0.00222002	−	0.00683251i
$749$	−29325.0			−1.43059
$750$		0			0
$751$	−22462.4			−1.09143			−0.545716	−	0.837970i	$-0.683742\pi$
$751$	−22462.4			−1.09143			−0.545716	+	0.837970i	$0.683742\pi$
$752$	−6188.72	−	19046.9i	−0.300106	−	0.923630i
$753$		0			0
$754$	−2074.01	+	1506.86i	−0.100174	+	0.0727805i
$755$	2965.42	+	874.869i	0.142944	+	0.0421718i
$756$		0			0
$757$	22613.9			1.08575			0.542876	−	0.839813i	$-0.317335\pi$
$757$	22613.9			1.08575			0.542876	+	0.839813i	$0.317335\pi$
$758$	11916.0	+	8657.51i	0.570990	+	0.414848i
$759$		0			0
$760$	−613.592	−	22491.5i	−0.0292860	−	1.07349i
$761$	−5096.57	−	15685.6i	−0.242773	−	0.747179i	−0.995995	−	0.0894121i	$-0.971501\pi$
$761$	−5096.57	−	15685.6i	−0.242773	−	0.747179i	0.753222	−	0.657767i	$-0.228499\pi$
$762$		0			0
$763$	2612.19	−	8039.49i	0.123942	−	0.381454i
$764$	−713.122	−	2194.76i	−0.0337694	−	0.103932i
$765$		0			0
$766$	−12726.1	+	39166.8i	−0.600276	+	1.84746i
$767$	−14178.0	−	10301.0i	−0.667457	−	0.484936i
$768$		0			0
$769$	−1931.73	−	1403.49i	−0.0905853	−	0.0658140i	0.541571	−	0.840655i	$-0.317830\pi$
$769$	−1931.73	−	1403.49i	−0.0905853	−	0.0658140i	−0.632156	+	0.774841i	$0.717830\pi$
$770$	3551.53	−	1262.04i	0.166218	−	0.0590658i
$771$		0			0
$772$	2396.24	−	1740.97i	0.111713	−	0.0811644i
$773$	11956.5	+	36798.2i	0.556332	+	1.71221i	0.692400	+	0.721514i	$0.256553\pi$
$773$	11956.5	+	36798.2i	0.556332	+	1.71221i	−0.136068	+	0.990699i	$0.543447\pi$
$774$		0			0
$775$	10086.2	+	26104.6i	0.467494	+	1.20994i
$776$	−399.714			−0.0184909
$777$		0			0
$778$	−230.691	+	167.607i	−0.0106307	+	0.00772366i
$779$	26375.4	−	19162.8i	1.21309	−	0.881360i
$780$		0			0
$781$	990.713	+	719.795i	0.0453912	+	0.0329786i
$782$	−9141.43			−0.418027
$783$		0			0
$784$	−310.686	+	956.193i	−0.0141530	+	0.0435583i

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.907834 + 2.79403i) q^{2} +(-0.510282 + 0.370741i) q^{4} +(-10.7234 - 3.16365i) q^{5} +18.9115 q^{7} +(17.5148 + 12.7253i) q^{8} +O(q^{10})\)	\(q+(0.907834 + 2.79403i) q^{2} +(-0.510282 + 0.370741i) q^{4} +(-10.7234 - 3.16365i) q^{5} +18.9115 q^{7} +(17.5148 + 12.7253i) q^{8} +(-0.895733 - 32.8335i) q^{10} +(1.87505 + 5.77082i) q^{11} +(24.1805 - 74.4201i) q^{13} +(17.1685 + 52.8393i) q^{14} +(-21.2134 + 65.2882i) q^{16} +(31.0670 + 22.5715i) q^{17} +(75.2030 + 54.6382i) q^{19} +(6.64485 - 2.36125i) q^{20} +(-14.4216 + 10.4779i) q^{22} +(25.0398 + 77.0645i) q^{23} +(104.983 + 67.8503i) q^{25} +229.884 q^{26} +(-9.65021 + 7.01128i) q^{28} +(-9.02201 + 6.55487i) q^{29} +(181.125 + 131.595i) q^{31} -28.4793 q^{32} +(-34.8617 + 107.293i) q^{34} +(-202.796 - 59.8295i) q^{35} +(-33.2987 + 102.483i) q^{37} +(-84.3887 + 259.722i) q^{38} +(-147.560 - 191.869i) q^{40} +(108.379 - 333.556i) q^{41} -356.550 q^{43} +(-3.09629 - 2.24959i) q^{44} +(-192.588 + 139.924i) q^{46} +(-236.019 + 171.478i) q^{47} +14.6457 q^{49} +(-94.2687 + 354.921i) q^{50} +(15.2517 + 46.9399i) q^{52} +(554.021 - 402.520i) q^{53} +(-1.85006 - 67.8149i) q^{55} +(331.232 + 240.654i) q^{56} +(-26.5050 - 19.2570i) q^{58} +(69.2082 - 213.001i) q^{59} +(-215.599 - 663.544i) q^{61} +(-203.249 + 625.535i) q^{62} +(143.853 + 442.734i) q^{64} +(-494.737 + 721.537i) q^{65} +(735.443 + 534.330i) q^{67} -24.2211 q^{68} +(-16.9397 - 620.932i) q^{70} +(163.274 - 118.625i) q^{71} +(-90.2156 - 277.655i) q^{73} -316.570 q^{74} -58.6314 q^{76} +(35.4601 + 109.135i) q^{77} +(-573.822 + 416.906i) q^{79} +(434.030 - 633.000i) q^{80} +1030.36 q^{82} +(-897.021 - 651.724i) q^{83} +(-261.736 - 340.329i) q^{85} +(-323.688 - 996.211i) q^{86} +(-40.5940 + 124.935i) q^{88} +(-1.16808 - 3.59497i) q^{89} +(457.291 - 1407.40i) q^{91} +(-41.3483 - 30.0413i) q^{92} +(-693.380 - 503.770i) q^{94} +(-633.576 - 823.824i) q^{95} +(-14.9369 + 10.8523i) q^{97} +(13.2959 + 40.9205i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8}+O(q^{10}) \) 28 * q - 30 * q^4 + 15 * q^5 - 54 * q^7 + 63 * q^8	\( 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8} + 165 q^{10} - 19 q^{11} + 4 q^{13} + 24 q^{14} - 66 q^{16} - 208 q^{17} + 42 q^{19} - 295 q^{20} - 89 q^{22} - 32 q^{23} + 95 q^{25} - 206 q^{26} - 482 q^{28} + 716 q^{29} + 637 q^{31} + 844 q^{32} - 90 q^{34} - 430 q^{35} + 216 q^{37} - 2314 q^{38} - 500 q^{40} + 38 q^{41} - 1392 q^{43} - 603 q^{44} + 1622 q^{46} + 536 q^{47} + 162 q^{49} + 2265 q^{50} - 1922 q^{52} - 1672 q^{53} - 1000 q^{55} - 3000 q^{56} - 827 q^{58} - 973 q^{59} - 2712 q^{61} - 1057 q^{62} + 4439 q^{64} + 4360 q^{65} + 2768 q^{67} + 1370 q^{68} + 3230 q^{70} + 1074 q^{71} - 1018 q^{73} + 1414 q^{74} - 11408 q^{76} - 1607 q^{77} - 1820 q^{79} + 1290 q^{80} + 1772 q^{82} - 4045 q^{83} + 1850 q^{85} + 3986 q^{86} + 2407 q^{88} - 4542 q^{89} + 4412 q^{91} + 1089 q^{92} + 5137 q^{94} + 720 q^{95} - 5977 q^{97} + 10689 q^{98}+O(q^{100}) \) 28 * q - 30 * q^4 + 15 * q^5 - 54 * q^7 + 63 * q^8 + 165 * q^10 - 19 * q^11 + 4 * q^13 + 24 * q^14 - 66 * q^16 - 208 * q^17 + 42 * q^19 - 295 * q^20 - 89 * q^22 - 32 * q^23 + 95 * q^25 - 206 * q^26 - 482 * q^28 + 716 * q^29 + 637 * q^31 + 844 * q^32 - 90 * q^34 - 430 * q^35 + 216 * q^37 - 2314 * q^38 - 500 * q^40 + 38 * q^41 - 1392 * q^43 - 603 * q^44 + 1622 * q^46 + 536 * q^47 + 162 * q^49 + 2265 * q^50 - 1922 * q^52 - 1672 * q^53 - 1000 * q^55 - 3000 * q^56 - 827 * q^58 - 973 * q^59 - 2712 * q^61 - 1057 * q^62 + 4439 * q^64 + 4360 * q^65 + 2768 * q^67 + 1370 * q^68 + 3230 * q^70 + 1074 * q^71 - 1018 * q^73 + 1414 * q^74 - 11408 * q^76 - 1607 * q^77 - 1820 * q^79 + 1290 * q^80 + 1772 * q^82 - 4045 * q^83 + 1850 * q^85 + 3986 * q^86 + 2407 * q^88 - 4542 * q^89 + 4412 * q^91 + 1089 * q^92 + 5137 * q^94 + 720 * q^95 - 5977 * q^97 + 10689 * q^98

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