LMFDB - Embedded newform 225.4.h.a.46.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(46,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("225.46");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.h (of order $5$, degree $4$, 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:	$13.2754297513$
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			46.6
Character	$\chi$	$=$	225.46
Dual form			225.4.h.a.181.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.907834 - 2.79403i) q^{2} +(-0.510282 - 0.370741i) q^{4} +(-10.7234 + 3.16365i) q^{5} +18.9115 q^{7} +(17.5148 - 12.7253i) q^{8} +O(q^{10})$	\(q+(0.907834 - 2.79403i) q^{2} +(-0.510282 - 0.370741i) q^{4} +(-10.7234 + 3.16365i) q^{5} +18.9115 q^{7} +(17.5148 - 12.7253i) q^{8} +(-0.895733 + 32.8335i) q^{10} +(1.87505 - 5.77082i) q^{11} +(24.1805 + 74.4201i) q^{13} +(17.1685 - 52.8393i) q^{14} +(-21.2134 - 65.2882i) q^{16} +(31.0670 - 22.5715i) q^{17} +(75.2030 - 54.6382i) q^{19} +(6.64485 + 2.36125i) q^{20} +(-14.4216 - 10.4779i) q^{22} +(25.0398 - 77.0645i) q^{23} +(104.983 - 67.8503i) q^{25} +229.884 q^{26} +(-9.65021 - 7.01128i) q^{28} +(-9.02201 - 6.55487i) q^{29} +(181.125 - 131.595i) q^{31} -28.4793 q^{32} +(-34.8617 - 107.293i) q^{34} +(-202.796 + 59.8295i) q^{35} +(-33.2987 - 102.483i) q^{37} +(-84.3887 - 259.722i) q^{38} +(-147.560 + 191.869i) q^{40} +(108.379 + 333.556i) q^{41} -356.550 q^{43} +(-3.09629 + 2.24959i) q^{44} +(-192.588 - 139.924i) q^{46} +(-236.019 - 171.478i) q^{47} +14.6457 q^{49} +(-94.2687 - 354.921i) q^{50} +(15.2517 - 46.9399i) q^{52} +(554.021 + 402.520i) q^{53} +(-1.85006 + 67.8149i) q^{55} +(331.232 - 240.654i) q^{56} +(-26.5050 + 19.2570i) q^{58} +(69.2082 + 213.001i) q^{59} +(-215.599 + 663.544i) q^{61} +(-203.249 - 625.535i) q^{62} +(143.853 - 442.734i) q^{64} +(-494.737 - 721.537i) q^{65} +(735.443 - 534.330i) q^{67} -24.2211 q^{68} +(-16.9397 + 620.932i) q^{70} +(163.274 + 118.625i) q^{71} +(-90.2156 + 277.655i) q^{73} -316.570 q^{74} -58.6314 q^{76} +(35.4601 - 109.135i) q^{77} +(-573.822 - 416.906i) q^{79} +(434.030 + 633.000i) q^{80} +1030.36 q^{82} +(-897.021 + 651.724i) q^{83} +(-261.736 + 340.329i) q^{85} +(-323.688 + 996.211i) q^{86} +(-40.5940 - 124.935i) q^{88} +(-1.16808 + 3.59497i) q^{89} +(457.291 + 1407.40i) q^{91} +(-41.3483 + 30.0413i) q^{92} +(-693.380 + 503.770i) q^{94} +(-633.576 + 823.824i) q^{95} +(-14.9369 - 10.8523i) q^{97} +(13.2959 - 40.9205i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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	−0.652260	−	0.757995i	$-0.726179\pi$
$2$	0.907834	−	2.79403i	0.320968	−	0.987837i	0.973228	−	0.229842i	$-0.0738210\pi$
$3$		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	−0.922065	−	0.387036i	$-0.873499\pi$
$11$	1.87505	−	5.77082i	0.0513955	−	0.158179i	0.973460	+	0.228857i	$0.0734989\pi$
$12$		0			0
$13$	24.1805	+	74.4201i	0.515883	+	1.58772i	0.781670	+	0.623692i	$0.214368\pi$
$13$	24.1805	+	74.4201i	0.515883	+	1.58772i	−0.265787	+	0.964032i	$0.585632\pi$
$14$	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	−0.343689	−	0.939084i	$-0.611676\pi$
$17$	31.0670	−	22.5715i	0.443227	−	0.322023i	0.786916	+	0.617060i	$0.211676\pi$
$18$		0			0
$19$	75.2030	−	54.6382i	0.908040	−	0.659730i	−0.0324785	−	0.999472i	$-0.510340\pi$
$19$	75.2030	−	54.6382i	0.908040	−	0.659730i	0.940518	+	0.339743i	$0.110340\pi$
$20$	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	−0.771075	−	0.636744i	$-0.780281\pi$
$23$	25.0398	−	77.0645i	0.227007	−	0.698655i	0.998082	−	0.0619104i	$-0.0197193\pi$
$24$		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	0.558525	−	0.829488i	$-0.311367\pi$
$29$	−9.02201	−	6.55487i	−0.0577705	−	0.0419727i	−0.616296	+	0.787515i	$0.711367\pi$
$30$		0			0
$31$	181.125	−	131.595i	1.04939	−	0.762425i	0.0772923	−	0.997008i	$-0.475373\pi$
$31$	181.125	−	131.595i	1.04939	−	0.762425i	0.972096	+	0.234583i	$0.0753725\pi$
$32$	−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	0.849425	−	0.527709i	$-0.176949\pi$
$37$	−33.2987	−	102.483i	−0.147954	−	0.455354i	−0.997379	+	0.0723545i	$0.976949\pi$
$38$	−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	0.914179	+	0.405311i	$0.132837\pi$
$41$	108.379	+	333.556i	0.412828	+	1.27056i	−0.501350	+	0.865244i	$0.667163\pi$
$42$		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	0.157861	−	0.987461i	$-0.449540\pi$
$47$	−236.019	−	171.478i	−0.732488	−	0.532184i	−0.890350	+	0.455277i	$0.849540\pi$
$48$		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	0.988887	+	0.148669i	$0.0474988\pi$
$53$	554.021	+	402.520i	1.43586	+	1.04322i	0.446975	+	0.894546i	$0.352501\pi$
$54$		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	0.997922	−	0.0644317i	$-0.0205235\pi$
$59$	69.2082	+	213.001i	0.152714	+	0.470006i	−0.845208	+	0.534438i	$0.820523\pi$
$60$		0			0
$61$	−215.599	+	663.544i	−0.452534	+	1.39276i	0.421472	+	0.906842i	$0.361514\pi$
$61$	−215.599	+	663.544i	−0.452534	+	1.39276i	−0.874006	+	0.485915i	$0.838486\pi$
$62$	−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	0.341618	−	0.939839i	$-0.389025\pi$
$67$	735.443	−	534.330i	1.34102	−	0.974311i	0.999406	−	0.0344723i	$-0.0109750\pi$
$68$	−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	0.715822	−	0.698283i	$-0.246052\pi$
$71$	163.274	+	118.625i	0.272916	+	0.198285i	−0.442906	+	0.896568i	$0.646052\pi$
$72$		0			0
$73$	−90.2156	+	277.655i	−0.144643	+	0.445165i	−0.996965	−	0.0778521i	$-0.975194\pi$
$73$	−90.2156	+	277.655i	−0.144643	+	0.445165i	0.852322	+	0.523018i	$0.175194\pi$
$74$	−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	0.0986978	−	0.995117i	$-0.468532\pi$
$79$	−573.822	−	416.906i	−0.817216	−	0.593742i	−0.915914	+	0.401375i	$0.868532\pi$
$80$	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	−0.992866	−	0.119238i	$-0.961955\pi$
$83$	−897.021	+	651.724i	−1.18628	+	0.861880i	−0.193410	+	0.981118i	$0.561955\pi$
$84$		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	−0.951750	−	0.306875i	$-0.900717\pi$
$89$	−1.16808	+	3.59497i	−0.00139119	+	0.00428165i	0.950359	+	0.311157i	$0.100717\pi$
$90$		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	0.579940	−	0.814659i	$-0.303076\pi$
$97$	−14.9369	−	10.8523i	−0.0156351	−	0.0113596i	−0.595575	+	0.803299i	$0.703076\pi$
$98$	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	−0.299206	−	0.954188i	$-0.596722\pi$
$103$	−1358.05	−	986.682i	−1.29915	−	0.943890i	−0.999947	+	0.0102985i	$0.996722\pi$
$104$	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	0.993224	−	0.116218i	$-0.0370772\pi$
$109$	138.127	+	425.111i	0.121378	+	0.373562i	−0.871846	+	0.489780i	$0.837077\pi$
$110$	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	0.998630	−	0.0523321i	$-0.0166654\pi$
$113$	192.146	+	591.366i	0.159961	+	0.492310i	−0.838668	+	0.544642i	$0.816665\pi$
$114$		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	−0.997752	−	0.0670095i	$-0.978654\pi$
$127$	−216.352	+	665.864i	−0.151167	+	0.465243i	0.846586	+	0.532252i	$0.178654\pi$
$128$	−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	−0.733600	−	0.679581i	$-0.762161\pi$
$131$	−470.763	+	342.029i	−0.313975	+	0.228116i	0.419625	+	0.907697i	$0.362161\pi$
$132$		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	0.876144	−	0.482050i	$-0.160108\pi$
$137$	−186.032	−	572.548i	−0.116013	−	0.357051i	−0.992157	+	0.124998i	$0.960108\pi$
$138$		0			0
$139$	−57.3812	+	176.601i	−0.0350145	+	0.107763i	−0.967036	−	0.254639i	$-0.918043\pi$
$139$	−57.3812	+	176.601i	−0.0350145	+	0.107763i	0.932022	+	0.362402i	$0.118043\pi$
$140$	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	0.873583	−	0.486676i	$-0.161791\pi$
$163$	−248.105	−	763.589i	−0.119221	−	0.366926i	−0.992804	+	0.119750i	$0.961791\pi$
$164$	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	0.0869544	−	0.996212i	$-0.472287\pi$
$167$	2290.36	−	1664.05i	1.06128	−	0.771064i	0.974325	+	0.225148i	$0.0722865\pi$
$168$		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	−0.123560	−	0.992337i	$-0.539431\pi$
$173$	1273.54	−	3919.54i	0.559683	−	1.72253i	0.683243	−	0.730191i	$-0.260569\pi$
$174$		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	0.248457	−	0.968643i	$-0.420076\pi$
$179$	−1427.33	−	1037.02i	−0.595999	−	0.433019i	−0.844457	+	0.535624i	$0.820076\pi$
$180$		0			0
$181$	1207.80	−	877.516i	0.495994	−	0.360361i	−0.311491	−	0.950249i	$-0.600828\pi$
$181$	1207.80	−	877.516i	0.495994	−	0.360361i	0.807485	+	0.589888i	$0.200828\pi$
$182$	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	−0.899786	−	0.436332i	$-0.856277\pi$
$191$	−1130.61	−	3479.65i	−0.428313	−	1.31821i	0.471473	−	0.881881i	$-0.343723\pi$
$192$		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	0.656024	−	0.754740i	$-0.272237\pi$
$197$	389.722	+	283.150i	0.140947	+	0.102404i	−0.515077	+	0.857144i	$0.672237\pi$
$198$		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	−0.924328	−	0.381599i	$-0.875373\pi$
$211$	146.406	−	450.590i	0.0477676	−	0.147014i	0.972095	+	0.234586i	$0.0753734\pi$
$212$	−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	−0.382394	−	0.923999i	$-0.624900\pi$
$223$	1565.42	−	4817.87i	0.470082	−	1.44676i	0.852477	−	0.522766i	$-0.175100\pi$
$224$	−538.587			−0.160651
$225$		0			0
$226$	1826.73			0.537665
$227$	−1635.48	+	5033.48i	−0.478196	+	1.47174i	0.363403	+	0.931632i	$0.381615\pi$
$227$	−1635.48	+	5033.48i	−0.478196	+	1.47174i	−0.841599	+	0.540103i	$0.818385\pi$
$228$		0			0
$229$	−396.216	−	287.868i	−0.114335	−	0.0830692i	0.529148	−	0.848529i	$-0.322511\pi$
$229$	−396.216	−	287.868i	−0.114335	−	0.0830692i	−0.643483	+	0.765460i	$0.722511\pi$
$230$	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	−0.807430	−	0.589964i	$-0.799142\pi$
$233$	−1763.54	+	1281.28i	−0.495850	+	0.360256i	0.311579	+	0.950220i	$0.399142\pi$
$234$		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	0.575203	+	0.818011i	$0.304923\pi$
$239$	−1370.65	+	4218.41i	−0.370961	+	1.14170i	−0.946163	+	0.323689i	$0.895077\pi$
$240$		0			0
$241$	742.522	+	2285.25i	0.198465	+	0.610812i	0.999919	+	0.0127554i	$0.00406027\pi$
$241$	742.522	+	2285.25i	0.198465	+	0.610812i	−0.801454	+	0.598057i	$0.795940\pi$
$242$	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	−0.979922	−	0.199383i	$-0.936106\pi$
$263$	−1298.07	−	3995.04i	−0.304343	−	0.936671i	0.675579	−	0.737288i	$-0.263894\pi$
$264$		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	−0.776069	−	0.630648i	$-0.782789\pi$
$269$	−1835.82	+	1333.80i	−0.416105	+	0.302318i	0.359964	+	0.932966i	$0.382789\pi$
$270$		0			0
$271$	630.472	+	458.065i	0.141323	+	0.102677i	0.656200	−	0.754587i	$-0.272163\pi$
$271$	630.472	+	458.065i	0.141323	+	0.102677i	−0.514878	+	0.857264i	$0.672163\pi$
$272$	−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	0.625945	+	0.779867i	$0.284713\pi$
$277$	−1562.16	+	4807.84i	−0.338849	+	1.04287i	−0.964795	+	0.263004i	$0.915287\pi$
$278$	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	−0.779281	−	0.626675i	$-0.784416\pi$
$281$	−1997.64	+	1451.37i	−0.424089	+	0.308119i	0.355192	+	0.934793i	$0.384416\pi$
$282$		0			0
$283$	−1534.87	+	1115.15i	−0.322398	+	0.234236i	−0.737198	−	0.675677i	$-0.763851\pi$
$283$	−1534.87	+	1115.15i	−0.322398	+	0.234236i	0.414800	+	0.909913i	$0.363851\pi$
$284$	−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	−0.927200	−	0.374567i	$-0.877792\pi$
$311$	236.303	−	727.265i	0.0430852	−	0.132603i	0.970285	+	0.241964i	$0.0777915\pi$
$312$		0			0
$313$	−1734.95	−	5339.63i	−0.313307	−	0.964261i	−0.976446	−	0.215764i	$-0.930776\pi$
$313$	−1734.95	−	5339.63i	−0.313307	−	0.964261i	0.663138	−	0.748497i	$-0.269224\pi$
$314$	−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	−0.995932	−	0.0901049i	$-0.971280\pi$
$317$	−6874.41	+	4994.55i	−1.21800	+	0.884927i	−0.222065	+	0.975032i	$0.571280\pi$
$318$		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	−0.347922	−	0.937523i	$-0.613113\pi$
$331$	2626.81	−	1908.49i	0.436202	−	0.316919i	0.784124	+	0.620604i	$0.213113\pi$
$332$	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	−0.946514	−	0.322664i	$-0.895422\pi$
$337$	−2291.63	−	7052.92i	−0.370425	−	1.14005i	0.576089	−	0.817387i	$-0.304578\pi$
$338$	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	0.626108	−	0.779736i	$-0.284647\pi$
$347$	504.270	+	366.374i	0.0780133	+	0.0566800i	−0.548095	+	0.836416i	$0.684647\pi$
$348$		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	0.662146	−	0.749375i	$-0.269646\pi$
$353$	1021.78	+	742.368i	0.154062	+	0.111933i	−0.508084	+	0.861308i	$0.669646\pi$
$354$		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	0.954563	−	0.298009i	$-0.0963227\pi$
$359$	48.5654	+	149.469i	0.00713979	+	0.0219740i	−0.947423	+	0.319983i	$0.896323\pi$
$360$		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	−0.908835	−	0.417156i	$-0.863027\pi$
$367$	−5574.94	+	4050.43i	−0.792941	+	0.576106i	0.115894	+	0.993262i	$0.463027\pi$
$368$	−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	−0.999074	−	0.0430178i	$-0.986303\pi$
$373$	−1192.38	+	3669.78i	−0.165521	+	0.509421i	0.833553	+	0.552439i	$0.186303\pi$
$374$	−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	0.827686	−	0.561192i	$-0.189657\pi$
$379$	4056.09	+	2946.92i	0.549730	+	0.399402i	−0.277956	+	0.960594i	$0.589657\pi$
$380$	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	0.548218	−	0.836335i	$-0.315306\pi$
$383$	11340.8	−	8239.61i	1.51303	−	1.09928i	0.964811	−	0.262944i	$-0.0846936\pi$
$384$		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	−0.949083	−	0.315027i	$-0.897987\pi$
$389$	29.9938	−	92.3116i	0.00390938	−	0.0120318i	0.952992	+	0.302995i	$0.0979865\pi$
$390$		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	0.822338	−	0.569000i	$-0.192669\pi$
$397$	4234.34	+	3076.43i	0.535303	+	0.388921i	−0.287034	+	0.957920i	$0.592669\pi$
$398$	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	−0.939553	−	0.342403i	$-0.888759\pi$
$409$	−3148.95	−	9691.47i	−0.380698	−	1.17167i	0.558855	−	0.829265i	$-0.311241\pi$
$410$	−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	0.0216796	−	0.999765i	$-0.493099\pi$
$419$	8398.42	−	6101.81i	0.979212	−	0.711439i	0.957532	+	0.288326i	$0.0930986\pi$
$420$		0			0
$421$	7922.06	+	5755.72i	0.917097	+	0.666310i	0.942800	−	0.333360i	$-0.108182\pi$
$421$	7922.06	+	5755.72i	0.917097	+	0.666310i	−0.0257029	+	0.999670i	$0.508182\pi$
$422$	−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	−0.393951	−	0.919131i	$-0.628892\pi$
$431$	3207.40	−	2330.31i	0.358457	−	0.260434i	0.752408	+	0.658697i	$0.228892\pi$
$432$		0			0
$433$	−3610.83	+	2623.42i	−0.400752	+	0.291163i	−0.769847	−	0.638228i	$-0.779668\pi$
$433$	−3610.83	+	2623.42i	−0.400752	+	0.291163i	0.369095	+	0.929391i	$0.379668\pi$
$434$	−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	0.132997	+	0.991116i	$0.457540\pi$
$439$	−5124.83	+	15772.6i	−0.557164	+	1.71477i	−0.690160	+	0.723657i	$0.742460\pi$
$440$	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	−0.973043	−	0.230624i	$-0.925923\pi$
$461$	−497.651	+	1531.61i	−0.0502775	+	0.154738i	0.922766	+	0.385362i	$0.125923\pi$
$462$		0			0
$463$	606.515	+	1866.66i	0.0608793	+	0.187367i	0.976871	−	0.213830i	$-0.0685940\pi$
$463$	606.515	+	1866.66i	0.0608793	+	0.187367i	−0.915991	+	0.401198i	$0.868594\pi$
$464$	−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	−0.522863	−	0.852417i	$-0.675136\pi$
$467$	1274.21	−	925.764i	0.126260	−	0.0917329i	0.649123	+	0.760684i	$0.275136\pi$
$468$		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	0.897902	−	0.440195i	$-0.145091\pi$
$479$	7933.01	+	5763.67i	0.756719	+	0.549789i	−0.141183	+	0.989983i	$0.545091\pi$
$480$		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	−0.998330	−	0.0577737i	$-0.981600\pi$
$487$	−2414.05	−	7429.69i	−0.224623	−	0.691317i	0.773707	−	0.633543i	$-0.218400\pi$
$488$	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	0.854142	−	0.520040i	$-0.174083\pi$
$491$	−1550.87	−	4773.07i	−0.142545	−	0.438708i	−0.996687	+	0.0813313i	$0.974083\pi$
$492$		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	0.591740	−	0.806129i	$-0.298441\pi$
$503$	89.3910	+	64.9464i	0.00792395	+	0.00575709i	−0.583816	+	0.811886i	$0.698441\pi$
$504$		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	−0.925067	−	0.379804i	$-0.875992\pi$
$509$	−4592.45	−	14134.1i	−0.399915	−	1.23081i	0.525152	−	0.851008i	$-0.324008\pi$
$510$		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	0.293213	−	0.956047i	$-0.405275\pi$
$521$	−6248.48	−	4539.79i	−0.525433	−	0.381750i	−0.818647	+	0.574297i	$0.805275\pi$
$522$		0			0
$523$	−1432.62	+	4409.15i	−0.119778	+	0.368640i	−0.992914	−	0.118838i	$-0.962083\pi$
$523$	−1432.62	+	4409.15i	−0.119778	+	0.368640i	0.873135	+	0.487478i	$0.162083\pi$
$524$	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	−0.999731	−	0.0232123i	$-0.992611\pi$
$541$	−2574.24	−	7922.70i	−0.204575	−	0.629618i	0.795155	−	0.606406i	$-0.207389\pi$
$542$	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	0.0274369	−	0.999624i	$-0.491265\pi$
$547$	−11703.1	−	8502.77i	−0.914783	−	0.664629i	−0.942220	+	0.334995i	$0.891265\pi$
$548$	−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	0.983365	+	0.181643i	$0.0581414\pi$
$563$	3935.09	+	12111.0i	0.294573	+	0.906602i	−0.688792	+	0.724959i	$0.741859\pi$
$564$		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	−0.695546	−	0.718481i	$-0.744838\pi$
$569$	−3083.27	+	2240.13i	−0.227166	+	0.165046i	0.468381	+	0.883527i	$0.344838\pi$
$570$		0			0
$571$	16776.5	+	12188.9i	1.22955	+	0.893324i	0.996857	−	0.0792254i	$-0.0252447\pi$
$571$	16776.5	+	12188.9i	1.22955	+	0.893324i	0.232698	+	0.972549i	$0.425245\pi$
$572$	−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	−0.0209185	+	0.999781i	$0.506659\pi$
$577$	−8200.30	+	25237.9i	−0.591652	+	1.82092i	−0.570733	+	0.821136i	$0.693341\pi$
$578$	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	0.892012	+	0.452011i	$0.149293\pi$
$587$	6201.38	+	19085.9i	0.436045	+	1.34201i	−0.455968	+	0.889996i	$0.650707\pi$
$588$		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	0.878454	+	0.477827i	$0.158576\pi$
$613$	6808.93	+	20955.7i	0.448630	+	1.38074i	−0.429824	+	0.902913i	$0.641424\pi$
$614$	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	−0.406850	−	0.913495i	$-0.633373\pi$
$617$	5152.77	−	3743.71i	0.336212	−	0.244272i	0.743062	+	0.669223i	$0.233373\pi$
$618$		0			0
$619$	−6709.39	+	4874.66i	−0.435659	+	0.316525i	−0.783908	−	0.620877i	$-0.786777\pi$
$619$	−6709.39	+	4874.66i	−0.435659	+	0.316525i	0.348249	+	0.937402i	$0.386777\pi$
$620$	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	−0.991600	−	0.129340i	$-0.958714\pi$
$631$	−18624.6	+	13531.5i	−1.17501	+	0.853696i	−0.183411	+	0.983036i	$0.558714\pi$
$632$	−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	0.885387	+	0.464855i	$0.153894\pi$
$641$	7178.47	+	22093.1i	0.442329	+	1.36135i	−0.443058	+	0.896493i	$0.646106\pi$
$642$		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	0.912125	−	0.409911i	$-0.134440\pi$
$647$	13233.9	+	9614.98i	0.804139	+	0.584241i	−0.107987	+	0.994152i	$0.534440\pi$
$648$		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	0.906781	−	0.421603i	$-0.138532\pi$
$653$	13116.1	+	9529.41i	0.786023	+	0.571079i	−0.120758	+	0.992682i	$0.538532\pi$
$654$		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	−0.999942	−	0.0107834i	$-0.996567\pi$
$659$	−3337.93	−	10273.1i	−0.197310	−	0.607258i	0.802632	−	0.596475i	$-0.203433\pi$
$660$		0			0
$661$	4696.20	−	14453.4i	0.276341	−	0.850489i	−0.712521	−	0.701651i	$-0.752447\pi$
$661$	4696.20	−	14453.4i	0.276341	−	0.850489i	0.988862	−	0.148838i	$-0.0475534\pi$
$662$	−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	−0.832462	−	0.554081i	$-0.813070\pi$
$673$	2910.35	−	8957.12i	0.166695	−	0.513034i	0.999157	+	0.0410478i	$0.0130696\pi$
$674$	−21786.5			−1.24508
$675$		0			0
$676$	2476.33			0.140892
$677$	4739.48	−	14586.6i	0.269059	−	0.828079i	−0.721671	−	0.692236i	$-0.756626\pi$
$677$	4739.48	−	14586.6i	0.269059	−	0.828079i	0.990730	−	0.135843i	$-0.0433743\pi$
$678$		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	−0.410347	−	0.911929i	$-0.634592\pi$
$683$	5893.00	−	4281.51i	0.330145	−	0.239865i	0.740492	+	0.672065i	$0.234592\pi$
$684$		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	0.997829	+	0.0658530i	$0.0209768\pi$
$691$	4164.62	+	12817.4i	0.229276	+	0.705639i	−0.768553	+	0.639786i	$0.779023\pi$
$692$	−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	0.987679	−	0.156494i	$-0.0500191\pi$
$709$	1824.52	+	5615.31i	0.0966452	+	0.297443i	−0.891034	+	0.453937i	$0.850019\pi$
$710$	−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	−0.678156	−	0.734918i	$-0.737221\pi$
$719$	−3639.38	+	2644.16i	−0.188770	+	0.137150i	0.489386	+	0.872067i	$0.337221\pi$
$720$		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	−0.987440	−	0.157994i	$-0.949497\pi$
$727$	−1876.26	+	5774.55i	−0.0957177	+	0.294589i	0.891722	+	0.452583i	$0.149497\pi$
$728$	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	−0.974151	−	0.225897i	$-0.927469\pi$
$733$	−21042.7	+	15288.4i	−1.06034	+	0.770382i	−0.0861888	+	0.996279i	$0.527469\pi$
$734$	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	−0.374265	−	0.927322i	$-0.622105\pi$
$739$	9514.09	−	29281.4i	0.473588	−	1.45755i	0.847853	−	0.530232i	$-0.177895\pi$
$740$	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	0.753222	+	0.657767i	$0.228499\pi$
$761$	−5096.57	+	15685.6i	−0.242773	+	0.747179i	−0.995995	+	0.0894121i	$0.971501\pi$
$762$		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	−0.632156	−	0.774841i	$-0.717830\pi$
$769$	−1931.73	+	1403.49i	−0.0905853	+	0.0658140i	0.541571	+	0.840655i	$0.317830\pi$
$770$	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	−0.136068	−	0.990699i	$-0.543447\pi$
$773$	11956.5	−	36798.2i	0.556332	−	1.71221i	0.692400	−	0.721514i	$-0.256553\pi$
$774$		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
$785$	32737.0	−	9658.18i	1.48845	−	0.439128i
$786$		0			0
$787$	−1420.04	−	4370.44i	−0.0643189	−	0.197953i	0.913733	−	0.406316i	$-0.133187\pi$
$787$	−1420.04	−	4370.44i	−0.0643189	−	0.197953i	−0.978052	+	0.208362i	$0.933187\pi$
$788$	−93.8928	−	288.972i	−0.00424466	−	0.0130637i
$789$		0			0
$790$	14202.5	−	18467.2i	0.639623	−	0.831687i
$791$	3633.78	+	11183.6i	0.163341	+	0.502711i
$792$		0			0
$793$	−54594.3			−2.44477
$794$	12439.7	−	9037.97i	0.556006	−	0.403962i
$795$		0			0
$796$	−252.568	−	183.502i	−0.0112463	−	0.00817091i
$797$	2673.62	+	1942.50i	0.118826	+	0.0863322i	0.645611	−	0.763666i	$-0.276603\pi$
$797$	2673.62	+	1942.50i	0.118826	+	0.0863322i	−0.526785	+	0.849999i	$0.676603\pi$
$798$		0			0
$799$	−11202.9			−0.496034
$800$	−2989.83	+	1932.33i	−0.132133	+	0.0853977i
$801$		0			0
$802$	9395.19	−	28915.4i	0.413661	−	1.27312i
$803$	1433.14	+	1041.24i	0.0629818	+	0.0457590i
$804$		0			0
$805$	−467.228	+	17126.5i	−0.0204567	+	0.749850i
$806$	41637.7	−	30251.5i	1.81963	−	1.32204i
$807$		0			0
$808$	23338.5	−	16956.4i	1.01615	−	0.738274i
$809$	−10925.2	−	33624.2i	−0.474794	−	1.46127i	−0.846235	−	0.532809i	$-0.821136\pi$
$809$	−10925.2	−	33624.2i	−0.474794	−	1.46127i	0.371442	−	0.928456i	$-0.378864\pi$
$810$		0			0
$811$	−5705.38	+	17559.4i	−0.247032	+	0.760287i	0.748263	+	0.663402i	$0.230888\pi$
$811$	−5705.38	+	17559.4i	−0.247032	+	0.760287i	−0.995296	+	0.0968851i	$0.969112\pi$
$812$	41.1062	+	126.512i	0.00177653	+	0.00546760i
$813$		0			0
$814$	−593.586	+	1826.87i	−0.0255592	+	0.0786631i
$815$	5076.26	+	7403.35i	0.218176	+	0.318194i
$816$		0			0
$817$	−26813.7	+	19481.3i	−1.14821	+	0.834227i
$818$	−29936.9			−1.27961
$819$		0			0
$820$	−67.4481	+	2472.34i	−0.00287243	+	0.105290i
$821$	−21329.3	−	15496.6i	−0.906695	−	0.658752i	0.0334822	−	0.999439i	$-0.489340\pi$
$821$	−21329.3	−	15496.6i	−0.906695	−	0.658752i	−0.940177	+	0.340687i	$0.889340\pi$
$822$		0			0
$823$	6176.50	−	19009.3i	0.261603	−	0.805131i	−0.730854	−	0.682534i	$-0.760878\pi$
$823$	6176.50	−	19009.3i	0.261603	−	0.805131i	0.992457	−	0.122597i	$-0.0391222\pi$
$824$	−36341.8			−1.53644
$825$		0			0
$826$	12443.0			0.524150
$827$	−7502.35	+	23089.9i	−0.315456	+	0.970875i	0.660110	+	0.751169i	$0.270510\pi$
$827$	−7502.35	+	23089.9i	−0.315456	+	0.970875i	−0.975566	+	0.219706i	$0.929490\pi$
$828$		0			0
$829$	−17447.0	−	12676.0i	−0.730953	−	0.531068i	0.158912	−	0.987293i	$-0.449201\pi$
$829$	−17447.0	−	12676.0i	−0.730953	−	0.531068i	−0.889865	+	0.456225i	$0.849201\pi$
$830$	−20594.9	−	30036.1i	−0.861277	−	1.25611i
$831$		0			0
$832$	36426.7			1.51787
$833$	454.999	−	330.576i	0.0189253	−	0.0137500i
$834$		0			0
$835$	−19296.0	+	25090.1i	−0.799720	+	1.03986i
$836$	−109.937	+	338.351i	−0.00454815	+	0.0139978i
$837$		0			0
$838$	−9424.24	−	29004.8i	−0.388491	−	1.19565i
$839$	738.292	−	2272.23i	0.0303798	−	0.0934994i	−0.934717	−	0.355393i	$-0.884347\pi$
$839$	738.292	−	2272.23i	0.0303798	−	0.0934994i	0.965097	+	0.261894i	$0.0843470\pi$
$840$		0			0
$841$	−7498.19	−	23077.0i	−0.307441	−	0.946207i
$842$	23273.5	−	16909.2i	0.952564	−	0.692078i
$843$		0			0
$844$	−241.760	+	175.649i	−0.00985988	+	0.00716362i
$845$	26759.4	−	34794.6i	1.08941	−	1.41653i
$846$		0			0
$847$	19800.6	+	14386.0i	0.803257	+	0.583600i
$848$	14527.1	−	44709.9i	0.588283	−	1.81055i
$849$		0			0
$850$	−10939.8	−	8898.55i	−0.441448	−	0.359080i
$851$	−8731.59			−0.351722
$852$		0			0
$853$	−24319.0	−	17668.8i	−0.976162	−	0.709223i	−0.0193141	−	0.999813i	$-0.506148\pi$
$853$	−24319.0	−	17668.8i	−0.976162	−	0.709223i	−0.956848	+	0.290591i	$0.906148\pi$
$854$	31359.7	+	22784.2i	1.25657	+	0.912948i
$855$		0			0
$856$	−27159.2	+	19732.3i	−1.08444	+	0.787893i
$857$	6412.98			0.255617			0.127808	−	0.991799i	$-0.459206\pi$
$857$	6412.98			0.255617			0.127808	+	0.991799i	$0.459206\pi$
$858$		0			0
$859$	−5633.81	−	17339.1i	−0.223776	−	0.688711i	−0.998414	−	0.0563056i	$-0.982068\pi$
$859$	−5633.81	−	17339.1i	−0.223776	−	0.688711i	0.774638	−	0.632405i	$-0.217932\pi$
$860$	−2369.22	−	841.905i	−0.0939417	−	0.0333822i
$861$		0			0
$862$	−3599.16	−	11077.1i	−0.142213	−	0.437688i
$863$	−10920.2	−	33608.9i	−0.430739	−	1.32568i	−0.897390	−	0.441238i	$-0.854540\pi$
$863$	−10920.2	−	33608.9i	−0.430739	−	1.32568i	0.466651	−	0.884442i	$-0.345460\pi$
$864$		0			0
$865$	−1256.56	+	46059.9i	−0.0493923	+	1.81050i
$866$	4051.87	+	12470.4i	0.158993	+	0.489331i
$867$		0			0
$868$	−2670.55			−0.104429
$869$	−3481.84	+	2529.71i	−0.135919	+	0.0987507i
$870$		0			0
$871$	57548.3	+	41811.3i	2.23875	+	1.62655i
$872$	7828.91	+	5688.03i	0.304037	+	0.220896i
$873$		0			0
$874$	−22128.4			−0.856412
$875$	−17230.6	+	20040.8i	−0.665714	+	0.774289i
$876$		0			0
$877$	−2027.80	+	6240.91i	−0.0780773	+	0.240297i	−0.982475	−	0.186393i	$-0.940320\pi$
$877$	−2027.80	+	6240.91i	−0.0780773	+	0.240297i	0.904398	+	0.426690i	$0.140320\pi$
$878$	39416.6	+	28637.8i	1.51509	+	1.10077i
$879$		0			0
$880$	4466.76	−	1317.80i	0.171107	−	0.0504807i
$881$	20779.4	−	15097.1i	0.794636	−	0.577337i	−0.114699	−	0.993400i	$-0.536590\pi$
$881$	20779.4	−	15097.1i	0.794636	−	0.577337i	0.909336	+	0.416063i	$0.136590\pi$
$882$		0			0
$883$	3035.91	−	2205.72i	0.115704	−	0.0840639i	−0.528429	−	0.848978i	$-0.677219\pi$
$883$	3035.91	−	2205.72i	0.115704	−	0.0840639i	0.644132	+	0.764914i	$0.277219\pi$
$884$	−585.680	−	1802.54i	−0.0222834	−	0.0685814i
$885$		0			0
$886$	−5142.55	+	15827.1i	−0.194997	+	0.600139i
$887$	3645.48	+	11219.6i	0.137997	+	0.424710i	0.996044	−	0.0888603i	$-0.0283225\pi$
$887$	3645.48	+	11219.6i	0.137997	+	0.424710i	−0.858047	+	0.513571i	$0.828322\pi$
$888$		0			0
$889$	−4091.55	+	12592.5i	−0.154360	+	0.475072i
$890$	−116.989	−	41.5723i	−0.00440617	−	0.00156574i
$891$		0			0
$892$	−2584.99	+	1878.11i	−0.0970313	+	0.0704973i
$893$	−27118.6			−1.01623
$894$		0			0
$895$	18586.6	+	6604.77i	0.694170	+	0.246674i
$896$	−24409.8	−	17734.8i	−0.910128	−	0.661247i
$897$		0			0
$898$	12753.0	−	39249.6i	0.473911	−	1.45855i
$899$	−2496.70			−0.0926248
$900$		0			0
$901$	26297.3			0.972353
$902$	1931.97	−	5946.00i	0.0713167	−	0.219490i
$903$		0			0
$904$	10890.7	+	7912.55i	0.400685	+	0.291115i
$905$	−10175.5	+	13231.0i	−0.373753	+	0.485982i
$906$		0			0
$907$	7027.72			0.257278			0.128639	−	0.991691i	$-0.458939\pi$
$907$	7027.72			0.257278			0.128639	+	0.991691i	$0.458939\pi$
$908$	2700.67	−	1962.15i	0.0987060	−	0.0717141i
$909$		0			0
$910$	−46619.4	+	13753.8i	−1.69826	+	0.501027i
$911$	5089.34	−	15663.4i	0.185090	−	0.569650i	−0.814859	−	0.579659i	$-0.803186\pi$
$911$	5089.34	−	15663.4i	0.185090	−	0.569650i	0.999950	+	0.0100087i	$0.00318592\pi$
$912$		0			0
$913$	2079.02	+	6398.57i	0.0753621	+	0.231941i
$914$	−10441.1	+	32134.5i	−0.377857	+	1.16292i
$915$		0			0
$916$	95.4573	+	293.787i	0.00344323	+	0.0105972i
$917$	−8902.84	+	6468.29i	−0.320608	+	0.232935i
$918$		0			0
$919$	−12998.0	+	9443.58i	−0.466554	+	0.338972i	−0.796097	−	0.605169i	$-0.793105\pi$
$919$	−12998.0	+	9443.58i	−0.466554	+	0.338972i	0.329543	+	0.944141i	$0.393105\pi$
$920$	11091.4	+	16176.0i	0.397470	+	0.579681i
$921$		0			0
$922$	3827.58	+	2780.90i	0.136719	+	0.0993319i
$923$	−4880.06	+	15019.3i	−0.174029	+	0.535607i
$924$		0			0
$925$	−10449.3	−	8499.60i	−0.371428	−	0.302124i
$926$	5766.11			0.204629
$927$		0			0
$928$	256.941	+	186.678i	0.00908889	+	0.00660346i
$929$	−4279.08	−	3108.93i	−0.151122	−	0.109796i	0.509655	−	0.860379i	$-0.329773\pi$
$929$	−4279.08	−	3108.93i	−0.151122	−	0.109796i	−0.660777	+	0.750583i	$0.729773\pi$
$930$		0			0
$931$	1101.40	−	800.215i	0.0387723	−	0.0281697i
$932$	1374.93			0.0483232
$933$		0			0
$934$	−1429.84	−	4400.60i	−0.0500919	−	0.154167i
$935$	1473.21	+	2148.57i	0.0515284	+	0.0751504i
$936$		0			0
$937$	−748.627	−	2304.04i	−0.0261009	−	0.0803304i	0.937158	−	0.348907i	$-0.113447\pi$
$937$	−748.627	−	2304.04i	−0.0261009	−	0.0803304i	−0.963258	+	0.268576i	$0.913447\pi$
$938$	−15607.2	−	48033.9i	−0.543275	−	1.67203i
$939$		0			0
$940$	−1163.41	−	1696.75i	−0.0403684	−	0.0588743i
$941$	−9159.00	−	28188.5i	−0.317295	−	0.976534i	−0.974799	−	0.223083i	$-0.928388\pi$
$941$	−9159.00	−	28188.5i	−0.317295	−	0.976534i	0.657504	−	0.753451i	$-0.271612\pi$
$942$		0			0
$943$	28419.2			0.981394
$944$	12438.3	−	9036.96i	0.428848	−	0.311576i
$945$		0			0
$946$	5142.02	+	3735.90i	0.176725	+	0.128398i
$947$	−31990.9	−	23242.8i	−1.09775	−	0.797559i	−0.117055	−	0.993125i	$-0.537345\pi$
$947$	−31990.9	−	23242.8i	−1.09775	−	0.797559i	−0.980690	+	0.195567i	$0.937345\pi$
$948$		0			0
$949$	−22844.6			−0.781419
$950$	−26481.5	−	21540.4i	−0.904394	−	0.735647i
$951$		0			0
$952$	4858.46	−	14952.8i	0.165403	−	0.509058i
$953$	20024.1	+	14548.3i	0.680633	+	0.494509i	0.873568	−	0.486703i	$-0.161800\pi$
$953$	20024.1	+	14548.3i	0.680633	+	0.494509i	−0.192934	+	0.981212i	$0.561800\pi$
$954$		0			0
$955$	23132.4	+	33736.8i	0.783817	+	1.14314i
$956$	2263.36	−	1644.42i	0.0765713	−	0.0556323i
$957$		0			0
$958$	23305.7	−	16932.6i	0.785984	−	0.571051i
$959$	−3518.15	−	10827.7i	−0.118464	−	0.364595i
$960$		0			0
$961$	6283.12	−	19337.4i	0.210907	−	0.649104i
$962$	−7654.83	−	23559.2i	−0.256551	−	0.789582i
$963$		0			0
$964$	468.340	−	1441.40i	0.0156475	−	0.0481582i
$965$	50356.2	−	14856.3i	1.67982	−	0.495586i
$966$		0			0
$967$	22661.2	−	16464.3i	0.753604	−	0.547526i	−0.143338	−	0.989674i	$-0.545784\pi$
$967$	22661.2	−	16464.3i	0.753604	−	0.547526i	0.896942	+	0.442148i	$0.145784\pi$
$968$	28018.4			0.930315
$969$		0			0
$970$	369.698	−	480.709i	0.0122374	−	0.0159120i
$971$	12053.9	+	8757.69i	0.398382	+	0.289442i	0.768882	−	0.639391i	$-0.220813\pi$
$971$	12053.9	+	8757.69i	0.398382	+	0.289442i	−0.370500	+	0.928833i	$0.620813\pi$
$972$		0			0
$973$	−1085.17	+	3339.80i	−0.0357542	+	0.110040i
$974$	−22950.3			−0.755005
$975$		0			0
$976$	47895.2			1.57079
$977$	13048.7	−	40159.7i	0.427292	−	1.31507i	−0.473491	−	0.880799i	$-0.657006\pi$
$977$	13048.7	−	40159.7i	0.427292	−	1.31507i	0.900783	−	0.434270i	$-0.142994\pi$
$978$		0			0
$979$	18.5558	+	13.4815i	0.000605766	+	0.000440115i
$980$	97.3186	+	34.5822i	0.00317217	+	0.00112723i
$981$		0			0
$982$	−14744.0			−0.479125
$983$	−14356.8	+	10430.8i	−0.465829	+	0.338445i	−0.795814	−	0.605542i	$-0.792957\pi$
$983$	−14356.8	+	10430.8i	−0.465829	+	0.338445i	0.329984	+	0.943986i	$0.392957\pi$
$984$		0			0
$985$	−5074.94	−	1803.38i	−0.164163	−	0.0583356i
$986$	−388.771	+	1196.52i	−0.0125568	+	0.0386458i
$987$		0			0
$988$	−1417.74	−	4363.35i	−0.0456521	−	0.140503i
$989$	−8927.94	+	27477.4i	−0.287049	+	0.883447i
$990$		0			0
$991$	−5465.34	−	16820.6i	−0.175189	−	0.539176i	0.824453	−	0.565930i	$-0.191483\pi$
$991$	−5465.34	−	16820.6i	−0.175189	−	0.539176i	−0.999642	+	0.0267544i	$0.991483\pi$
$992$	−5158.32	+	3747.74i	−0.165098	+	0.119950i
$993$		0			0
$994$	9071.25	−	6590.65i	0.289459	−	0.210305i
$995$	−5307.64	+	1565.88i	−0.169109	+	0.0498911i
$996$		0			0
$997$	7486.38	+	5439.17i	0.237809	+	0.172779i	0.700307	−	0.713842i	$-0.253047\pi$
$997$	7486.38	+	5439.17i	0.237809	+	0.172779i	−0.462497	+	0.886621i	$0.653047\pi$
$998$	−14754.0	+	45408.1i	−0.467966	+	1.44025i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.h.a.46.6		28
3.2	odd	2		75.4.g.b.46.2	yes	28
25.6	even	5	inner	225.4.h.a.181.6		28
75.41	odd	10		1875.4.a.g.1.4		14
75.56	odd	10		75.4.g.b.31.2	✓	28
75.59	odd	10		1875.4.a.f.1.11		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.4.g.b.31.2	✓	28	75.56	odd	10
75.4.g.b.46.2	yes	28	3.2	odd	2
225.4.h.a.46.6		28	1.1	even	1	trivial
225.4.h.a.181.6		28	25.6	even	5	inner
1875.4.a.f.1.11		14	75.59	odd	10
1875.4.a.g.1.4		14	75.41	odd	10

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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