LMFDB - Embedded newform 105.4.b.a.41.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,4,Mod(41,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("105.41");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	105.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.19520055060$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 96 x^{14} + 3618 x^{12} + 68560 x^{10} + 697017 x^{8} + 3791184 x^{6} + 10461796 x^{4} + \cdots + 5760000 $ x^16 + 96x^14 + 3618x^12 + 68560x^10 + 697017x^8 + 3791184x^6 + 10461796x^4 + 13209792*x^2 + 5760000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			41.14
Root			$4.47752i$ of defining polynomial
Character	$\chi$	$=$	105.41
Dual form			105.4.b.a.41.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.47752i q^{2} +(0.787490 - 5.13613i) q^{3} -12.0482 q^{4} -5.00000 q^{5} +(22.9971 + 3.52600i) q^{6} +(-18.2591 + 3.09943i) q^{7} -18.1258i q^{8} +(-25.7597 - 8.08931i) q^{9} +O(q^{10})$	\(q+4.47752i q^{2} +(0.787490 - 5.13613i) q^{3} -12.0482 q^{4} -5.00000 q^{5} +(22.9971 + 3.52600i) q^{6} +(-18.2591 + 3.09943i) q^{7} -18.1258i q^{8} +(-25.7597 - 8.08931i) q^{9} -22.3876i q^{10} -29.0020i q^{11} +(-9.48783 + 61.8811i) q^{12} -71.4934i q^{13} +(-13.8777 - 81.7553i) q^{14} +(-3.93745 + 25.6807i) q^{15} -15.2267 q^{16} -55.3352 q^{17} +(36.2201 - 115.340i) q^{18} +3.58869i q^{19} +60.2409 q^{20} +(1.54023 + 96.2218i) q^{21} +129.857 q^{22} +80.1966i q^{23} +(-93.0968 - 14.2739i) q^{24} +25.0000 q^{25} +320.113 q^{26} +(-61.8333 + 125.935i) q^{27} +(219.989 - 37.3425i) q^{28} +177.133i q^{29} +(-114.986 - 17.6300i) q^{30} -66.1424i q^{31} -213.184i q^{32} +(-148.958 - 22.8388i) q^{33} -247.765i q^{34} +(91.2953 - 15.4971i) q^{35} +(310.358 + 97.4615i) q^{36} -353.486 q^{37} -16.0684 q^{38} +(-367.200 - 56.3004i) q^{39} +90.6292i q^{40} +329.421 q^{41} +(-430.835 + 6.89639i) q^{42} -70.6784 q^{43} +349.422i q^{44} +(128.799 + 40.4466i) q^{45} -359.082 q^{46} -199.561 q^{47} +(-11.9908 + 78.2061i) q^{48} +(323.787 - 113.185i) q^{49} +111.938i q^{50} +(-43.5760 + 284.209i) q^{51} +861.366i q^{52} +504.068i q^{53} +(-563.877 - 276.860i) q^{54} +145.010i q^{55} +(56.1797 + 330.961i) q^{56} +(18.4320 + 2.82606i) q^{57} -793.119 q^{58} -392.306 q^{59} +(47.4392 - 309.405i) q^{60} -724.390i q^{61} +296.154 q^{62} +(495.421 + 67.8629i) q^{63} +832.724 q^{64} +357.467i q^{65} +(102.261 - 666.963i) q^{66} +411.384 q^{67} +666.689 q^{68} +(411.900 + 63.1541i) q^{69} +(69.3887 + 408.777i) q^{70} -1009.00i q^{71} +(-146.626 + 466.917i) q^{72} +341.301i q^{73} -1582.74i q^{74} +(19.6873 - 128.403i) q^{75} -43.2372i q^{76} +(89.8896 + 529.550i) q^{77} +(252.086 - 1644.14i) q^{78} +184.513 q^{79} +76.1333 q^{80} +(598.126 + 416.757i) q^{81} +1474.99i q^{82} -1338.92 q^{83} +(-18.5569 - 1159.30i) q^{84} +276.676 q^{85} -316.464i q^{86} +(909.781 + 139.491i) q^{87} -525.686 q^{88} +1515.32 q^{89} +(-181.100 + 576.698i) q^{90} +(221.589 + 1305.40i) q^{91} -966.224i q^{92} +(-339.716 - 52.0865i) q^{93} -893.538i q^{94} -17.9435i q^{95} +(-1094.94 - 167.881i) q^{96} -689.426i q^{97} +(506.789 + 1449.76i) q^{98} +(-234.606 + 747.084i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{3} - 64 q^{4} - 80 q^{5} - 28 q^{6} - 4 q^{7} - 22 q^{9}+O(q^{10}) $ 16 * q - 2 * q^3 - 64 * q^4 - 80 * q^5 - 28 * q^6 - 4 * q^7 - 22 * q^9	$ 16 q - 2 q^{3} - 64 q^{4} - 80 q^{5} - 28 q^{6} - 4 q^{7} - 22 q^{9} - 66 q^{12} - 90 q^{14} + 10 q^{15} + 376 q^{16} - 72 q^{17} - 182 q^{18} + 320 q^{20} - 74 q^{21} - 276 q^{22} + 526 q^{24} + 400 q^{25} + 696 q^{26} - 128 q^{27} + 10 q^{28} + 140 q^{30} - 502 q^{33} + 20 q^{35} + 996 q^{36} - 812 q^{37} - 1200 q^{38} - 594 q^{39} - 936 q^{41} - 1834 q^{42} - 548 q^{43} + 110 q^{45} + 1224 q^{46} + 912 q^{47} + 1850 q^{48} + 328 q^{49} + 750 q^{51} - 2950 q^{54} + 1254 q^{56} + 432 q^{57} + 576 q^{58} - 552 q^{59} + 330 q^{60} - 1860 q^{62} - 898 q^{63} - 4000 q^{64} + 1378 q^{66} + 1004 q^{67} + 3828 q^{68} + 1988 q^{69} + 450 q^{70} + 1988 q^{72} - 50 q^{75} + 1152 q^{77} + 1446 q^{78} + 1292 q^{79} - 1880 q^{80} - 2950 q^{81} - 1752 q^{83} + 1068 q^{84} + 360 q^{85} + 1910 q^{87} - 912 q^{88} + 6096 q^{89} + 910 q^{90} - 552 q^{91} - 1080 q^{93} - 9546 q^{96} - 4824 q^{98} + 2530 q^{99}+O(q^{100}) $ 16 * q - 2 * q^3 - 64 * q^4 - 80 * q^5 - 28 * q^6 - 4 * q^7 - 22 * q^9 - 66 * q^12 - 90 * q^14 + 10 * q^15 + 376 * q^16 - 72 * q^17 - 182 * q^18 + 320 * q^20 - 74 * q^21 - 276 * q^22 + 526 * q^24 + 400 * q^25 + 696 * q^26 - 128 * q^27 + 10 * q^28 + 140 * q^30 - 502 * q^33 + 20 * q^35 + 996 * q^36 - 812 * q^37 - 1200 * q^38 - 594 * q^39 - 936 * q^41 - 1834 * q^42 - 548 * q^43 + 110 * q^45 + 1224 * q^46 + 912 * q^47 + 1850 * q^48 + 328 * q^49 + 750 * q^51 - 2950 * q^54 + 1254 * q^56 + 432 * q^57 + 576 * q^58 - 552 * q^59 + 330 * q^60 - 1860 * q^62 - 898 * q^63 - 4000 * q^64 + 1378 * q^66 + 1004 * q^67 + 3828 * q^68 + 1988 * q^69 + 450 * q^70 + 1988 * q^72 - 50 * q^75 + 1152 * q^77 + 1446 * q^78 + 1292 * q^79 - 1880 * q^80 - 2950 * q^81 - 1752 * q^83 + 1068 * q^84 + 360 * q^85 + 1910 * q^87 - 912 * q^88 + 6096 * q^89 + 910 * q^90 - 552 * q^91 - 1080 * q^93 - 9546 * q^96 - 4824 * q^98 + 2530 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			4.47752i			1.58304i	0.611142	+	0.791521i	$0.290711\pi$
$2$			4.47752i			1.58304i	−0.611142	+	0.791521i	$0.709289\pi$
$3$	0.787490	−	5.13613i	0.151553	−	0.988449i
$3$	0.787490	−	5.13613i	0.151553	−	0.988449i
$4$	−12.0482			−1.50602
$5$	−5.00000			−0.447214
$5$	−5.00000			−0.447214
$6$	22.9971	+	3.52600i	1.56476	+	0.239914i
$7$	−18.2591	+	3.09943i	−0.985897	+	0.167353i
$7$	−18.2591	+	3.09943i	−0.985897	+	0.167353i
$8$		−	18.1258i		−	0.801057i
$9$	−25.7597	−	8.08931i	−0.954064	−	0.299604i
$10$		−	22.3876i		−	0.707958i
$11$		−	29.0020i		−	0.794949i	−0.917613	−	0.397474i	$-0.869887\pi$
$11$		−	29.0020i		−	0.794949i	0.917613	−	0.397474i	$-0.130113\pi$
$12$	−9.48783	+	61.8811i	−0.228242	+	1.48863i
$13$		−	71.4934i		−	1.52529i	−0.646820	−	0.762643i	$-0.723901\pi$
$13$		−	71.4934i		−	1.52529i	0.646820	−	0.762643i	$-0.276099\pi$
$14$	−13.8777	−	81.7553i	−0.264927	−	1.56072i
$15$	−3.93745	+	25.6807i	−0.0677764	+	0.442048i
$16$	−15.2267			−0.237916
$17$	−55.3352			−0.789457			−0.394728	−	0.918798i	$-0.629161\pi$
$17$	−55.3352			−0.789457			−0.394728	+	0.918798i	$0.629161\pi$
$18$	36.2201	−	115.340i	0.474286	−	1.51032i
$19$			3.58869i			0.0433317i	0.999765	+	0.0216658i	$0.00689699\pi$
$19$			3.58869i			0.0433317i	−0.999765	+	0.0216658i	$0.993103\pi$
$20$	60.2409			0.673514
$21$	1.54023	+	96.2218i	0.0160050	+	0.999872i
$22$	129.857			1.25844
$23$			80.1966i			0.727050i	0.931584	+	0.363525i	$0.118427\pi$
$23$			80.1966i			0.727050i	−0.931584	+	0.363525i	$0.881573\pi$
$24$	−93.0968	−	14.2739i	−0.791804	−	0.121402i
$25$	25.0000			0.200000
$26$	320.113			2.41459
$27$	−61.8333	+	125.935i	−0.440734	+	0.897638i
$28$	219.989	−	37.3425i	1.48478	−	0.252038i
$29$			177.133i			1.13424i	0.823636	+	0.567118i	$0.191942\pi$
$29$			177.133i			1.13424i	−0.823636	+	0.567118i	$0.808058\pi$
$30$	−114.986	−	17.6300i	−0.699781	−	0.107293i
$31$		−	66.1424i		−	0.383211i	−0.981472	−	0.191605i	$-0.938631\pi$
$31$		−	66.1424i		−	0.383211i	0.981472	−	0.191605i	$-0.0613694\pi$
$32$		−	213.184i		−	1.17769i
$33$	−148.958	−	22.8388i	−0.785766	−	0.120477i
$34$		−	247.765i		−	1.24974i
$35$	91.2953	−	15.4971i	0.440907	−	0.0748427i
$36$	310.358	+	97.4615i	1.43684	+	0.451211i
$37$	−353.486			−1.57061			−0.785306	−	0.619107i	$-0.787495\pi$
$37$	−353.486			−1.57061			−0.785306	+	0.619107i	$0.787495\pi$
$38$	−16.0684			−0.0685959
$39$	−367.200	−	56.3004i	−1.50767	−	0.231161i
$40$			90.6292i			0.358244i
$41$	329.421			1.25480			0.627401	−	0.778696i	$-0.284119\pi$
$41$	329.421			1.25480			0.627401	+	0.778696i	$0.284119\pi$
$42$	−430.835	+	6.89639i	−1.58284	+	0.0253366i
$43$	−70.6784			−0.250660			−0.125330	−	0.992115i	$-0.539999\pi$
$43$	−70.6784			−0.250660			−0.125330	+	0.992115i	$0.539999\pi$
$44$			349.422i			1.19721i
$45$	128.799	+	40.4466i	0.426670	+	0.133987i
$46$	−359.082			−1.15095
$47$	−199.561			−0.619339			−0.309670	−	0.950844i	$-0.600218\pi$
$47$	−199.561			−0.619339			−0.309670	+	0.950844i	$0.600218\pi$
$48$	−11.9908	+	78.2061i	−0.0360569	+	0.235168i
$49$	323.787	−	113.185i	0.943986	−	0.329986i
$50$			111.938i			0.316609i
$51$	−43.5760	+	284.209i	−0.119644	+	0.780338i
$52$			861.366i			2.29712i
$53$			504.068i			1.30640i	0.757186	+	0.653199i	$0.226573\pi$
$53$			504.068i			1.30640i	−0.757186	+	0.653199i	$0.773427\pi$
$54$	−563.877	−	276.860i	−1.42100	−	0.697701i
$55$			145.010i			0.355512i
$56$	56.1797	+	330.961i	0.134060	+	0.789760i
$57$	18.4320	+	2.82606i	0.0428312	+	0.00656703i
$58$	−793.119			−1.79554
$59$	−392.306			−0.865660			−0.432830	−	0.901476i	$-0.642485\pi$
$59$	−392.306			−0.865660			−0.432830	+	0.901476i	$0.642485\pi$
$60$	47.4392	−	309.405i	0.102073	−	0.665735i
$61$		−	724.390i		−	1.52047i	−0.649649	−	0.760235i	$-0.725084\pi$
$61$		−	724.390i		−	1.52047i	0.649649	−	0.760235i	$-0.274916\pi$
$62$	296.154			0.606639
$63$	495.421	+	67.8629i	0.990748	+	0.135713i
$64$	832.724			1.62641
$65$			357.467i			0.682128i
$66$	102.261	−	666.963i	0.190719	−	1.24390i
$67$	411.384			0.750128			0.375064	−	0.926999i	$-0.377621\pi$
$67$	411.384			0.750128			0.375064	+	0.926999i	$0.377621\pi$
$68$	666.689			1.18894
$69$	411.900	+	63.1541i	0.718652	+	0.110186i
$70$	69.3887	+	408.777i	0.118479	+	0.697974i
$71$		−	1009.00i		−	1.68656i	−0.537473	−	0.843281i	$-0.680621\pi$
$71$		−	1009.00i		−	1.68656i	0.537473	−	0.843281i	$-0.319379\pi$
$72$	−146.626	+	466.917i	−0.240000	+	0.764259i
$73$			341.301i			0.547208i	0.961842	+	0.273604i	$0.0882158\pi$
$73$			341.301i			0.547208i	−0.961842	+	0.273604i	$0.911784\pi$
$74$		−	1582.74i		−	2.48635i
$75$	19.6873	−	128.403i	0.0303105	−	0.197690i
$76$		−	43.2372i		−	0.0652585i
$77$	89.8896	+	529.550i	0.133037	+	0.783738i
$78$	252.086	−	1644.14i	0.365938	−	2.38670i
$79$	184.513			0.262776			0.131388	−	0.991331i	$-0.458057\pi$
$79$	184.513			0.262776			0.131388	+	0.991331i	$0.458057\pi$
$80$	76.1333			0.106399
$81$	598.126	+	416.757i	0.820475	+	0.571683i
$82$			1474.99i			1.98641i
$83$	−1338.92			−1.77067			−0.885337	−	0.464949i	$-0.846073\pi$
$83$	−1338.92			−1.77067			−0.885337	+	0.464949i	$0.846073\pi$
$84$	−18.5569	−	1159.30i	−0.0241039	−	1.50583i
$85$	276.676			0.353056
$86$		−	316.464i		−	0.396805i
$87$	909.781	+	139.491i	1.12114	+	0.171896i
$88$	−525.686			−0.636799
$89$	1515.32			1.80476			0.902378	−	0.430945i	$-0.141820\pi$
$89$	1515.32			1.80476			0.902378	+	0.430945i	$0.141820\pi$
$90$	−181.100	+	576.698i	−0.212107	+	0.675437i
$91$	221.589	+	1305.40i	0.255262	+	1.50377i
$92$		−	966.224i		−	1.09495i
$93$	−339.716	−	52.0865i	−0.378784	−	0.0580766i
$94$		−	893.538i		−	0.980441i
$95$		−	17.9435i		−	0.0193785i
$96$	−1094.94	−	167.881i	−1.16409	−	0.178482i
$97$		−	689.426i		−	0.721656i	−0.932632	−	0.360828i	$-0.882494\pi$
$97$		−	689.426i		−	0.721656i	0.932632	−	0.360828i	$-0.117506\pi$
$98$	506.789	+	1449.76i	0.522382	+	1.49437i
$99$	−234.606	+	747.084i	−0.238170	+	0.758432i
$100$	−301.205			−0.301205
$101$	−1662.22			−1.63759			−0.818797	−	0.574083i	$-0.805359\pi$
$101$	−1662.22			−1.63759			−0.818797	+	0.574083i	$0.805359\pi$
$102$	−1272.55	−	195.112i	−1.23531	−	0.189402i
$103$		−	1243.75i		−	1.18981i	−0.803797	−	0.594903i	$-0.797190\pi$
$103$		−	1243.75i		−	1.18981i	0.803797	−	0.594903i	$-0.202810\pi$
$104$	−1295.88			−1.22184
$105$	−7.70113	−	481.109i	−0.00715765	−	0.447156i
$106$	−2256.98			−2.06808
$107$			105.982i			0.0957537i	0.998853	+	0.0478768i	$0.0152455\pi$
$107$			105.982i			0.0957537i	−0.998853	+	0.0478768i	$0.984755\pi$
$108$	744.979	−	1517.29i	0.663756	−	1.35186i
$109$	567.837			0.498981			0.249490	−	0.968377i	$-0.419737\pi$
$109$	567.837			0.498981			0.249490	+	0.968377i	$0.419737\pi$
$110$	−649.286			−0.562790
$111$	−278.366	+	1815.55i	−0.238030	+	1.55247i
$112$	278.025	−	47.1939i	0.234561	−	0.0398161i
$113$		−	219.705i		−	0.182904i	−0.995809	−	0.0914520i	$-0.970849\pi$
$113$		−	219.705i		−	0.182904i	0.995809	−	0.0914520i	$-0.0291508\pi$
$114$	−12.6537	+	82.5296i	−0.0103959	+	0.0678036i
$115$		−	400.983i		−	0.325147i
$116$		−	2134.14i		−	1.70819i
$117$	−578.333	+	1841.65i	−0.456982	+	1.45522i
$118$		−	1756.56i		−	1.37038i
$119$	1010.37	−	171.507i	0.778323	−	0.132118i
$120$	465.484	+	71.3697i	0.354106	+	0.0542927i
$121$	489.883			0.368056
$122$	3243.47			2.40697
$123$	259.416	−	1691.95i	0.190169	−	1.24031i
$124$			796.897i			0.577124i
$125$	−125.000			−0.0894427
$126$	−303.858	+	2218.26i	−0.214840	+	1.56840i
$127$	−1571.54			−1.09804			−0.549021	−	0.835809i	$-0.684999\pi$
$127$	−1571.54			−1.09804			−0.549021	+	0.835809i	$0.684999\pi$
$128$			2023.07i			1.39700i
$129$	−55.6586	+	363.014i	−0.0379881	+	0.247764i
$130$	−1600.57			−1.07984
$131$	−571.633			−0.381250			−0.190625	−	0.981663i	$-0.561051\pi$
$131$	−571.633			−0.381250			−0.190625	+	0.981663i	$0.561051\pi$
$132$	1794.68	+	275.166i	1.18338	+	0.181441i
$133$	−11.1229	−	65.5261i	−0.00725170	−	0.0427206i
$134$			1841.98i			1.18748i
$135$	309.167	−	629.675i	0.197102	−	0.401436i
$136$			1003.00i			0.632400i
$137$		−	773.281i		−	0.482232i	−0.970496	−	0.241116i	$-0.922487\pi$
$137$		−	773.281i		−	0.482232i	0.970496	−	0.241116i	$-0.0775135\pi$
$138$	−282.774	+	1844.29i	−0.174430	+	1.13766i
$139$		−	2232.55i		−	1.36232i	−0.732136	−	0.681158i	$-0.761476\pi$
$139$		−	2232.55i		−	1.36232i	0.732136	−	0.681158i	$-0.238524\pi$
$140$	−1099.94	+	186.712i	−0.664016	+	0.112715i
$141$	−157.152	+	1024.97i	−0.0938625	+	0.612185i
$142$	4517.80			2.66990
$143$	−2073.45			−1.21252
$144$	392.234	+	123.173i	0.226987	+	0.0712807i
$145$		−	885.667i		−	0.507246i
$146$	−1528.18			−0.866254
$147$	−326.355	−	1752.15i	−0.183111	−	0.983092i
$148$	4258.86			2.36538
$149$			1855.42i			1.02015i	0.860131	+	0.510074i	$0.170382\pi$
$149$			1855.42i			1.02015i	−0.860131	+	0.510074i	$0.829618\pi$
$150$	574.928	+	88.1501i	0.312951	+	0.0479828i
$151$	1377.02			0.742121			0.371060	−	0.928609i	$-0.378994\pi$
$151$	1377.02			0.742121			0.371060	+	0.928609i	$0.378994\pi$
$152$	65.0481			0.0347111
$153$	1425.42	+	447.624i	0.753192	+	0.236524i
$154$	−2371.07	+	402.483i	−1.24069	+	0.210604i
$155$			330.712i			0.171377i
$156$	4424.09	+	678.318i	2.27058	+	0.348134i
$157$			103.126i			0.0524228i	0.999656	+	0.0262114i	$0.00834430\pi$
$157$			103.126i			0.0524228i	−0.999656	+	0.0262114i	$0.991656\pi$
$158$			826.161i			0.415986i
$159$	2588.96	+	396.949i	1.29131	+	0.197988i
$160$			1065.92i			0.526678i
$161$	−248.564	−	1464.32i	−0.121674	−	0.716796i
$162$	−1866.04	+	2678.12i	−0.904998	+	1.29885i
$163$	777.220			0.373476			0.186738	−	0.982410i	$-0.440208\pi$
$163$	777.220			0.373476			0.186738	+	0.982410i	$0.440208\pi$
$164$	−3968.92			−1.88976
$165$	744.791	+	114.194i	0.351405	+	0.0538788i
$166$		−	5995.06i		−	2.80305i
$167$	−1824.56			−0.845442			−0.422721	−	0.906260i	$-0.638925\pi$
$167$	−1824.56			−0.845442			−0.422721	+	0.906260i	$0.638925\pi$
$168$	1744.10	−	27.9179i	0.800954	−	0.0128209i
$169$	−2914.31			−1.32650
$170$			1238.82i			0.558902i
$171$	29.0300	−	92.4437i	0.0129824	−	0.0413412i
$172$	851.547			0.377499
$173$	−321.941			−0.141484			−0.0707420	−	0.997495i	$-0.522537\pi$
$173$	−321.941			−0.141484			−0.0707420	+	0.997495i	$0.522537\pi$
$174$	−624.573	+	4073.56i	−0.272119	+	1.77480i
$175$	−456.477	+	77.4857i	−0.197179	+	0.0334707i
$176$			441.604i			0.189131i
$177$	−308.937	+	2014.94i	−0.131193	+	0.855661i
$178$			6784.86i			2.85701i
$179$		−	3401.83i		−	1.42047i	−0.703964	−	0.710236i	$-0.748588\pi$
$179$		−	3401.83i		−	1.42047i	0.703964	−	0.710236i	$-0.251412\pi$
$180$	−1551.79	−	487.308i	−0.642575	−	0.201788i
$181$			903.626i			0.371083i	0.982636	+	0.185541i	$0.0594039\pi$
$181$			903.626i			0.371083i	−0.982636	+	0.185541i	$0.940596\pi$
$182$	−5844.97	+	992.168i	−2.38054	+	0.404090i
$183$	−3720.56	−	570.450i	−1.50291	−	0.230431i
$184$	1453.63			0.582408
$185$	1767.43			0.702399
$186$	233.219	−	1521.09i	0.0919377	−	0.599632i
$187$			1604.83i			0.627577i
$188$	2404.35			0.932740
$189$	738.692	−	2491.10i	0.284296	−	0.958737i
$190$	80.3422			0.0306770
$191$		−	900.665i		−	0.341203i	−0.985340	−	0.170602i	$-0.945429\pi$
$191$		−	900.665i		−	0.341203i	0.985340	−	0.170602i	$-0.0545711\pi$
$192$	655.763	−	4276.98i	0.246487	−	1.60763i
$193$	−235.479			−0.0878246			−0.0439123	−	0.999035i	$-0.513982\pi$
$193$	−235.479			−0.0878246			−0.0439123	+	0.999035i	$0.513982\pi$
$194$	3086.92			1.14241
$195$	1836.00	+	281.502i	0.674249	+	0.103378i
$196$	−3901.05	+	1363.68i	−1.42166	+	0.496967i
$197$			281.184i			0.101693i	0.998706	+	0.0508465i	$0.0161919\pi$
$197$			281.184i			0.101693i	−0.998706	+	0.0508465i	$0.983808\pi$
$198$	−3345.08	−	1050.45i	−1.20063	−	0.377033i
$199$			1533.05i			0.546107i	0.961999	+	0.273053i	$0.0880335\pi$
$199$			1533.05i			0.546107i	−0.961999	+	0.273053i	$0.911966\pi$
$200$		−	453.146i		−	0.160211i
$201$	323.961	−	2112.92i	0.113684	−	0.741463i
$202$		−	7442.62i		−	2.59238i
$203$	−549.012	−	3234.29i	−0.189818	−	1.11824i
$204$	525.011	−	3424.20i	0.180187	−	1.17521i
$205$	−1647.10			−0.561165
$206$	5568.91			1.88351
$207$	648.735	−	2065.84i	0.217827	−	0.693652i
$208$			1088.61i			0.362891i
$209$	104.079			0.0344465
$210$	2154.17	−	34.4820i	0.707867	−	0.0113309i
$211$	−5744.99			−1.87441			−0.937207	−	0.348773i	$-0.886598\pi$
$211$	−5744.99			−1.87441			−0.937207	+	0.348773i	$0.886598\pi$
$212$		−	6073.11i		−	1.96747i
$213$	−5182.34	−	794.575i	−1.66708	−	0.255603i
$214$	−474.535			−0.151582
$215$	353.392			0.112098
$216$	2282.68	+	1120.78i	0.719059	+	0.353053i
$217$	205.004	+	1207.70i	0.0641316	+	0.377806i
$218$			2542.50i			0.789908i
$219$	1752.96	+	268.771i	0.540888	+	0.0829308i
$220$		−	1747.11i		−	0.535409i
$221$			3956.10i			1.20415i
$222$	−8129.16	−	1246.39i	−2.45763	−	0.376812i
$223$		−	3116.97i		−	0.935998i	−0.883729	−	0.467999i	$-0.844975\pi$
$223$		−	3116.97i		−	0.935998i	0.883729	−	0.467999i	$-0.155025\pi$
$224$	660.750	+	3892.55i	0.197090	+	1.16108i
$225$	−643.993	−	202.233i	−0.190813	−	0.0599208i
$226$	983.735			0.289545
$227$	5446.09			1.59238			0.796188	−	0.605049i	$-0.206846\pi$
$227$	5446.09			1.59238			0.796188	+	0.605049i	$0.206846\pi$
$228$	−222.072	−	34.0489i	−0.0645048	−	0.00989010i
$229$			4734.69i			1.36628i	0.730290	+	0.683138i	$0.239385\pi$
$229$			4734.69i			1.36628i	−0.730290	+	0.683138i	$0.760615\pi$
$230$	1795.41			0.514721
$231$	2790.62	−	44.6697i	0.794847	−	0.0127232i
$232$	3210.69			0.908588
$233$			368.681i			0.103661i	0.998656	+	0.0518307i	$0.0165056\pi$
$233$			368.681i			0.103661i	−0.998656	+	0.0518307i	$0.983494\pi$
$234$	−8246.03	−	2589.50i	−2.30367	−	0.723422i
$235$	997.805			0.276977
$236$	4726.58			1.30370
$237$	145.302	−	947.683i	0.0398245	−	0.259741i
$238$	767.928	+	4523.95i	0.209149	+	1.23212i
$239$		−	4831.35i		−	1.30759i	−0.756671	−	0.653795i	$-0.773176\pi$
$239$		−	4831.35i		−	1.30759i	0.756671	−	0.653795i	$-0.226824\pi$
$240$	59.9542	−	391.031i	0.0161251	−	0.105170i
$241$			3197.65i			0.854683i	0.904090	+	0.427342i	$0.140550\pi$
$241$			3197.65i			0.854683i	−0.904090	+	0.427342i	$0.859450\pi$
$242$			2193.46i			0.582649i
$243$	2611.54	−	2743.86i	0.689424	−	0.724358i
$244$			8727.59i			2.28986i
$245$	−1618.94	+	565.926i	−0.422163	+	0.147574i
$246$	7575.74	+	1161.54i	1.96346	+	0.301045i
$247$	256.568			0.0660932
$248$	−1198.89			−0.306974
$249$	−1054.39	+	6876.89i	−0.268350	+	1.75022i
$250$		−	559.690i		−	0.141592i
$251$	2415.79			0.607504			0.303752	−	0.952751i	$-0.401761\pi$
$251$	2415.79			0.607504			0.303752	+	0.952751i	$0.401761\pi$
$252$	−5968.92	−	817.625i	−1.49209	−	0.204387i
$253$	2325.86			0.577968
$254$		−	7036.59i		−	1.73825i
$255$	217.880	−	1421.05i	0.0535065	−	0.348978i
$256$	−2396.52			−0.585088
$257$	−6260.44			−1.51952			−0.759758	−	0.650206i	$-0.774682\pi$
$257$	−6260.44			−1.51952			−0.759758	+	0.650206i	$0.774682\pi$
$258$	−1625.40	−	249.213i	−0.392221	−	0.0601368i
$259$	6454.32	−	1095.60i	1.54846	−	0.262847i
$260$		−	4306.83i		−	1.02730i
$261$	1432.89	−	4562.91i	0.339822	−	1.08213i
$262$		−	2559.50i		−	0.603535i
$263$		−	750.100i		−	0.175867i	−0.996126	−	0.0879337i	$-0.971974\pi$
$263$		−	750.100i		−	0.175867i	0.996126	−	0.0879337i	$-0.0280264\pi$
$264$	−413.973	+	2699.99i	−0.0965086	+	0.629444i
$265$		−	2520.34i		−	0.584239i
$266$	293.395	−	49.8029i	0.0676285	−	0.0114798i
$267$	1193.30	−	7782.87i	0.273516	−	1.78391i
$268$	−4956.43			−1.12971
$269$	−3613.25			−0.818974			−0.409487	−	0.912316i	$-0.634292\pi$
$269$	−3613.25			−0.818974			−0.409487	+	0.912316i	$0.634292\pi$
$270$	2819.38	+	1384.30i	0.635490	+	0.312021i
$271$			6402.12i			1.43506i	0.696528	+	0.717530i	$0.254727\pi$
$271$			6402.12i			1.43506i	−0.696528	+	0.717530i	$0.745273\pi$
$272$	842.570			0.187825
$273$	6879.22	−	110.116i	1.52509	−	0.0244122i
$274$	3462.38			0.763394
$275$		−	725.050i		−	0.158990i
$276$	−4962.65	−	760.892i	−1.08231	−	0.165943i
$277$	3511.25			0.761627			0.380813	−	0.924652i	$-0.375644\pi$
$277$	3511.25			0.761627			0.380813	+	0.924652i	$0.375644\pi$
$278$	9996.27			2.15661
$279$	−535.047	+	1703.81i	−0.114812	+	0.365607i
$280$	−280.899	−	1654.81i	−0.0599532	−	0.353191i
$281$			1109.97i			0.235641i	0.993035	+	0.117820i	$0.0375907\pi$
$281$			1109.97i			0.235641i	−0.993035	+	0.117820i	$0.962409\pi$
$282$	−4589.33	−	703.653i	−0.969116	−	0.148588i
$283$		−	4893.56i		−	1.02789i	−0.857824	−	0.513943i	$-0.828184\pi$
$283$		−	4893.56i		−	1.02789i	0.857824	−	0.513943i	$-0.171816\pi$
$284$			12156.6i			2.54000i
$285$	−92.1600	−	14.1303i	−0.0191547	−	0.00293687i
$286$		−	9283.93i		−	1.91948i
$287$	−6014.92	+	1021.02i	−1.23711	+	0.209995i
$288$	−1724.52	+	5491.57i	−0.352840	+	1.12359i
$289$	−1851.01			−0.376758
$290$	3965.59			0.802992
$291$	−3540.98	−	542.916i	−0.713320	−	0.109369i
$292$		−	4112.05i		−	0.824109i
$293$	−7461.88			−1.48781			−0.743904	−	0.668286i	$-0.767028\pi$
$293$	−7461.88			−1.48781			−0.743904	+	0.668286i	$0.767028\pi$
$294$	7845.27	−	1461.26i	1.55628	−	0.289873i
$295$	1961.53			0.387135
$296$			6407.23i			1.25815i
$297$	3652.37	+	1793.29i	0.713576	+	0.350361i
$298$	−8307.68			−1.61494
$299$	5733.53			1.10896
$300$	−237.196	+	1547.03i	−0.0456484	+	0.297726i
$301$	1290.52	−	219.063i	0.247125	−	0.0419487i
$302$			6165.63i			1.17481i
$303$	−1308.98	+	8537.38i	−0.248182	+	1.61868i
$304$		−	54.6438i		−	0.0103093i
$305$			3621.95i			0.679975i
$306$	−2004.24	+	6382.35i	−0.374428	+	1.19233i
$307$			5215.76i			0.969639i	0.874614	+	0.484820i	$0.161115\pi$
$307$			5215.76i			0.969639i	−0.874614	+	0.484820i	$0.838885\pi$
$308$	−1083.01	−	6380.12i	−0.200357	−	1.18033i
$309$	−6388.05	−	979.439i	−1.17606	−	0.180318i
$310$	−1480.77			−0.271297
$311$	−1197.00			−0.218250			−0.109125	−	0.994028i	$-0.534805\pi$
$311$	−1197.00			−0.218250			−0.109125	+	0.994028i	$0.534805\pi$
$312$	−1020.49	+	6655.81i	−0.185173	+	1.20773i
$313$		−	2534.45i		−	0.457686i	−0.973463	−	0.228843i	$-0.926506\pi$
$313$		−	2534.45i		−	0.457686i	0.973463	−	0.228843i	$-0.0734942\pi$
$314$	−461.750			−0.0829875
$315$	−2477.10	−	339.315i	−0.443076	−	0.0606927i
$316$	−2223.05			−0.395748
$317$			8725.91i			1.54604i	0.634379	+	0.773022i	$0.281256\pi$
$317$			8725.91i			1.54604i	−0.634379	+	0.773022i	$0.718744\pi$
$318$	−1777.35	+	11592.1i	−0.313423	+	2.04419i
$319$	5137.23			0.901660
$320$	−4163.62			−0.727355
$321$	544.336	+	83.4596i	0.0946476	+	0.0145117i
$322$	6556.50	−	1112.95i	1.13472	−	0.192615i
$323$		−	198.581i		−	0.0342085i
$324$	−7206.34	−	5021.16i	−1.23565	−	0.860968i
$325$		−	1787.34i		−	0.305057i
$326$			3480.02i			0.591228i
$327$	447.166	−	2916.48i	0.0756218	−	0.493217i
$328$		−	5971.03i		−	1.00517i
$329$	3643.80	−	618.524i	0.610605	−	0.103648i
$330$	−511.306	+	3334.82i	−0.0852924	+	0.556290i
$331$	−10896.5			−1.80945			−0.904724	−	0.425997i	$-0.859923\pi$
$331$	−10896.5			−1.80945			−0.904724	+	0.425997i	$0.859923\pi$
$332$	16131.6			2.66668
$333$	9105.69	+	2859.45i	1.49846	+	0.470562i
$334$		−	8169.51i		−	1.33837i
$335$	−2056.92			−0.335467
$336$	−23.4525	−	1465.14i	−0.00380785	−	0.237886i
$337$	1378.20			0.222775			0.111388	−	0.993777i	$-0.464470\pi$
$337$	1378.20			0.222775			0.111388	+	0.993777i	$0.464470\pi$
$338$		−	13048.9i		−	2.09990i
$339$	−1128.44	−	173.016i	−0.180791	−	0.0277196i
$340$	−3333.45			−0.531710
$341$	−1918.26			−0.304633
$342$	413.918	+	129.983i	0.0654449	+	0.0205516i
$343$	−5561.24	+	3070.21i	−0.875448	+	0.483312i
$344$			1281.11i			0.200793i
$345$	−2059.50	−	315.770i	−0.321391	−	0.0492768i
$346$		−	1441.50i		−	0.223975i
$347$		−	203.164i		−	0.0314306i	−0.999877	−	0.0157153i	$-0.994997\pi$
$347$		−	203.164i		−	0.0314306i	0.999877	−	0.0157153i	$-0.00500254\pi$
$348$	−10961.2	−	1680.61i	−1.68846	−	0.258880i
$349$			9441.41i			1.44810i	0.689747	+	0.724050i	$0.257722\pi$
$349$			9441.41i			1.44810i	−0.689747	+	0.724050i	$0.742278\pi$
$350$	−346.944	−	2043.88i	−0.0529855	−	0.312143i
$351$	9003.53	+	4420.68i	1.36915	+	0.672246i
$352$	−6182.78			−0.936202
$353$	8690.46			1.31033			0.655165	−	0.755486i	$-0.272599\pi$
$353$	8690.46			1.31033			0.655165	+	0.755486i	$0.272599\pi$
$354$	−9021.92	−	1383.27i	−1.35455	−	0.207684i
$355$			5044.98i			0.754253i
$356$	−18256.8			−2.71801
$357$	−85.2287	−	5324.45i	−0.0126352	−	0.789355i
$358$	15231.7			2.24867
$359$			3044.44i			0.447575i	0.974638	+	0.223788i	$0.0718422\pi$
$359$			3044.44i			0.447575i	−0.974638	+	0.223788i	$0.928158\pi$
$360$	733.128	−	2334.58i	0.107331	−	0.341787i
$361$	6846.12			0.998122
$362$	−4046.00			−0.587440
$363$	385.778	−	2516.10i	0.0557799	−	0.363805i
$364$	−2669.74	−	15727.7i	−0.384430	−	2.26472i
$365$		−	1706.50i		−	0.244719i
$366$	2554.20	−	16658.9i	0.364782	−	2.37917i
$367$		−	1291.62i		−	0.183712i	−0.995772	−	0.0918559i	$-0.970720\pi$
$367$		−	1291.62i		−	0.183712i	0.995772	−	0.0918559i	$-0.0292799\pi$
$368$		−	1221.13i		−	0.172977i
$369$	−8485.79	−	2664.79i	−1.19716	−	0.375944i
$370$			7913.69i			1.11193i
$371$	−1562.32	−	9203.81i	−0.218630	−	1.28797i
$372$	4092.97	+	627.548i	0.570458	+	0.0874647i
$373$	−473.181			−0.0656846			−0.0328423	−	0.999461i	$-0.510456\pi$
$373$	−473.181			−0.0656846			−0.0328423	+	0.999461i	$0.510456\pi$
$374$	−7185.67			−0.993482
$375$	−98.4363	+	642.017i	−0.0135553	+	0.0884096i
$376$			3617.21i			0.496126i
$377$	12663.9			1.73003
$378$	11154.0	+	3307.51i	1.51772	+	0.450053i
$379$	2426.81			0.328910			0.164455	−	0.986385i	$-0.447413\pi$
$379$	2426.81			0.328910			0.164455	+	0.986385i	$0.447413\pi$
$380$			216.186i			0.0291845i
$381$	−1237.57	+	8071.62i	−0.166411	+	1.08536i
$382$	4032.74			0.540139
$383$	4880.01			0.651063			0.325531	−	0.945531i	$-0.394457\pi$
$383$	4880.01			0.651063			0.325531	+	0.945531i	$0.394457\pi$
$384$	10390.7	+	1593.14i	1.38086	+	0.211718i
$385$	−449.448	−	2647.75i	−0.0594961	−	0.350498i
$386$		−	1054.36i		−	0.139030i
$387$	1820.66	+	571.740i	0.239145	+	0.0750986i
$388$			8306.33i			1.08683i
$389$		−	6351.66i		−	0.827871i	−0.910306	−	0.413935i	$-0.864154\pi$
$389$		−	6351.66i		−	0.827871i	0.910306	−	0.413935i	$-0.135846\pi$
$390$	−1260.43	+	8220.72i	−0.163652	+	1.06737i
$391$		−	4437.70i		−	0.573974i
$392$	−2051.58	−	5868.92i	−0.264338	−	0.756186i
$393$	−450.155	+	2935.98i	−0.0577795	+	0.376846i
$394$	−1259.01			−0.160984
$395$	−922.565			−0.117517
$396$	2826.58	−	9001.01i	0.358689	−	1.14222i
$397$		−	8327.54i		−	1.05276i	−0.850248	−	0.526382i	$-0.823548\pi$
$397$		−	8327.54i		−	1.05276i	0.850248	−	0.526382i	$-0.176452\pi$
$398$	−6864.27			−0.864510
$399$	−345.310	+	5.52740i	−0.0433261	+	0.000693523i
$400$	−380.666			−0.0475833
$401$			10424.6i			1.29820i	0.760703	+	0.649100i	$0.224854\pi$
$401$			10424.6i			1.29820i	−0.760703	+	0.649100i	$0.775146\pi$
$402$	9460.65	+	1450.54i	1.17377	+	0.179966i
$403$	−4728.75			−0.584506
$404$	20026.7			2.46626
$405$	−2990.63	−	2083.78i	−0.366927	−	0.255664i
$406$	14481.6	−	2458.21i	1.77022	−	0.300490i
$407$			10251.8i			1.24856i
$408$	5151.53	+	789.851i	0.625095	+	0.0958418i
$409$		−	8044.15i		−	0.972513i	−0.873816	−	0.486256i	$-0.838362\pi$
$409$		−	8044.15i		−	0.972513i	0.873816	−	0.486256i	$-0.161638\pi$
$410$		−	7374.94i		−	0.888347i
$411$	−3971.67	−	608.951i	−0.476662	−	0.0730836i
$412$			14984.9i			1.79188i
$413$	7163.15	−	1215.92i	0.853451	−	0.144871i
$414$	9249.85	+	2904.73i	1.09808	+	0.344830i
$415$	6694.62			0.791870
$416$	−15241.3			−1.79631
$417$	−11466.7	−	1758.11i	−1.34658	−	0.206463i
$418$			466.017i			0.0545302i
$419$	−12390.6			−1.44468			−0.722341	−	0.691537i	$-0.756934\pi$
$419$	−12390.6			−1.44468			−0.722341	+	0.691537i	$0.756934\pi$
$420$	92.7847	+	5796.49i	0.0107796	+	0.673428i
$421$	−12406.3			−1.43621			−0.718105	−	0.695935i	$-0.754990\pi$
$421$	−12406.3			−1.43621			−0.718105	+	0.695935i	$0.754990\pi$
$422$		−	25723.3i		−	2.96728i
$423$	5140.63	+	1614.31i	0.590889	+	0.185557i
$424$	9136.66			1.04650
$425$	−1383.38			−0.157891
$426$	3557.73	−	23204.0i	0.404630	−	2.63906i
$427$	2245.19	+	13226.7i	0.254456	+	1.49903i
$428$		−	1276.89i		−	0.144207i
$429$	−1632.82	+	10649.5i	−0.183761	+	1.19852i
$430$			1582.32i			0.177456i
$431$			11665.4i			1.30372i	0.758338	+	0.651861i	$0.226012\pi$
$431$			11665.4i			1.30372i	−0.758338	+	0.651861i	$0.773988\pi$
$432$	941.514	−	1917.57i	0.104858	−	0.213563i
$433$		−	2203.42i		−	0.244549i	−0.992496	−	0.122275i	$-0.960981\pi$
$433$		−	2203.42i		−	0.244549i	0.992496	−	0.122275i	$-0.0390189\pi$
$434$	−5407.50	+	917.908i	−0.598084	+	0.101523i
$435$	−4548.91	−	697.455i	−0.501387	−	0.0768744i
$436$	−6841.40			−0.751477
$437$	−287.801			−0.0315043
$438$	−1203.43	+	7848.94i	−0.131283	+	0.856248i
$439$		−	8896.26i		−	0.967188i	−0.875293	−	0.483594i	$-0.839331\pi$
$439$		−	8896.26i		−	0.967188i	0.875293	−	0.483594i	$-0.160669\pi$
$440$	2628.43			0.284785
$441$	−9256.26	+	296.407i	−0.999488	+	0.0320059i
$442$	−17713.5			−1.90622
$443$		−	5300.79i		−	0.568506i	−0.958749	−	0.284253i	$-0.908254\pi$
$443$		−	5300.79i		−	0.568506i	0.958749	−	0.284253i	$-0.0917456\pi$
$444$	3353.81	−	21874.1i	0.358479	−	2.33806i
$445$	−7576.59			−0.807112
$446$	13956.3			1.48172
$447$	9529.68	+	1461.13i	1.00836	+	0.154606i
$448$	−15204.8	+	2580.97i	−1.60348	+	0.272186i
$449$			4209.52i			0.442449i	0.975223	+	0.221224i	$0.0710053\pi$
$449$			4209.52i			0.442449i	−0.975223	+	0.221224i	$0.928995\pi$
$450$	905.501	−	2883.49i	0.0948572	−	0.302065i
$451$		−	9553.87i		−	0.997503i
$452$			2647.05i			0.275458i
$453$	1084.39	−	7072.55i	0.112470	−	0.733548i
$454$			24385.0i			2.52080i
$455$	−1107.94	−	6527.02i	−0.114156	−	0.672508i
$456$	51.2247	−	334.095i	0.00526056	−	0.0343102i
$457$	11042.8			1.13032			0.565162	−	0.824980i	$-0.308814\pi$
$457$	11042.8			1.13032			0.565162	+	0.824980i	$0.308814\pi$
$458$	−21199.7			−2.16287
$459$	3421.56	−	6968.64i	0.347941	−	0.708646i
$460$			4831.12i			0.489679i
$461$	6758.46			0.682804			0.341402	−	0.939917i	$-0.389098\pi$
$461$	6758.46			0.682804			0.341402	+	0.939917i	$0.389098\pi$
$462$	200.009	+	12495.1i	0.0201413	+	1.25828i
$463$	−3605.99			−0.361953			−0.180977	−	0.983487i	$-0.557926\pi$
$463$	−3605.99			−0.361953			−0.180977	+	0.983487i	$0.557926\pi$
$464$		−	2697.15i		−	0.269854i
$465$	1698.58	+	260.433i	0.169398	+	0.0259726i
$466$	−1650.78			−0.164100
$467$	−2722.69			−0.269788			−0.134894	−	0.990860i	$-0.543069\pi$
$467$	−2722.69			−0.269788			−0.134894	+	0.990860i	$0.543069\pi$
$468$	6967.86	−	22188.6i	0.688225	−	2.19159i
$469$	−7511.49	+	1275.05i	−0.739549	+	0.125536i
$470$			4467.69i			0.438466i
$471$	529.671	+	81.2110i	0.0518173	+	0.00794481i
$472$			7110.88i			0.693443i
$473$			2049.82i			0.199262i
$474$	4243.27	+	650.594i	0.411181	+	0.0630438i
$475$			89.7173i			0.00866634i
$476$	−12173.1	+	2066.35i	−1.17217	+	0.198973i
$477$	4077.56	−	12984.7i	0.391402	−	1.24639i
$478$	21632.5			2.06997
$479$	−10406.8			−0.992692			−0.496346	−	0.868125i	$-0.665325\pi$
$479$	−10406.8			−0.992692			−0.496346	+	0.868125i	$0.665325\pi$
$480$	5474.72	+	839.404i	0.520595	+	0.0798195i
$481$			25271.9i			2.39563i
$482$	−14317.5			−1.35300
$483$	−7716.66	+	123.521i	−0.726957	+	0.0116364i
$484$	−5902.20			−0.554302
$485$			3447.13i			0.322734i
$486$	12285.7	+	11693.2i	1.14669	+	1.09139i
$487$	−18125.2			−1.68651			−0.843257	−	0.537510i	$-0.819365\pi$
$487$	−18125.2			−1.68651			−0.843257	+	0.537510i	$0.819365\pi$
$488$	−13130.2			−1.21798
$489$	612.053	−	3991.91i	0.0566013	−	0.369162i
$490$	−2533.95	−	7248.82i	−0.233616	−	0.668302i
$491$		−	12930.6i		−	1.18850i	−0.804282	−	0.594248i	$-0.797450\pi$
$491$		−	12930.6i		−	1.18850i	0.804282	−	0.594248i	$-0.202550\pi$
$492$	−3125.49	+	20384.9i	−0.286398	+	1.86793i
$493$		−	9801.72i		−	0.895430i
$494$			1148.79i			0.104628i
$495$	1173.03	−	3735.42i	0.106513	−	0.339181i
$496$			1007.13i			0.0911722i
$497$	3127.31	+	18423.3i	0.282252	+	1.66278i
$498$	−30791.4	−	4721.05i	−2.77068	−	0.424810i
$499$	−9.15769			−0.000821552			−0.000410776	−	1.00000i	$-0.500131\pi$
$499$	−9.15769			−0.000821552			−0.000410776		1.00000i	$0.500131\pi$
$500$	1506.02			0.134703
$501$	−1436.82	+	9371.19i	−0.128129	+	0.835676i
$502$			10816.8i			0.961704i
$503$	1148.72			0.101827			0.0509135	−	0.998703i	$-0.483787\pi$
$503$	1148.72			0.101827			0.0509135	+	0.998703i	$0.483787\pi$
$504$	1230.07	−	8979.92i	0.108714	−	0.793646i
$505$	8311.10			0.732355
$506$			10414.1i			0.914947i
$507$	−2294.99	+	14968.3i	−0.201034	+	1.31117i
$508$	18934.2			1.65368
$509$	−9469.51			−0.824614			−0.412307	−	0.911045i	$-0.635277\pi$
$509$	−9469.51			−0.824614			−0.412307	+	0.911045i	$0.635277\pi$
$510$	6362.76	+	975.561i	0.552446	+	0.0847031i
$511$	−1057.84	−	6231.83i	−0.0915771	−	0.539491i
$512$			5454.05i			0.470776i
$513$	−451.942	−	221.901i	−0.0388962	−	0.0190978i
$514$		−	28031.2i		−	2.40546i
$515$			6218.74i			0.532098i
$516$	670.585	−	4373.66i	0.0572110	−	0.373139i
$517$			5787.67i			0.492343i
$518$	4905.58	+	28899.3i	0.416098	+	2.45128i
$519$	−253.526	+	1653.53i	−0.0214423	+	0.139850i
$520$	6479.40			0.546424
$521$	12674.3			1.06578			0.532891	−	0.846184i	$-0.321105\pi$
$521$	12674.3			1.06578			0.532891	+	0.846184i	$0.321105\pi$
$522$	20430.5	+	6415.78i	1.71306	+	0.537953i
$523$		−	8545.91i		−	0.714506i	−0.934008	−	0.357253i	$-0.883713\pi$
$523$		−	8545.91i		−	0.714506i	0.934008	−	0.357253i	$-0.116287\pi$
$524$	6887.14			0.574172
$525$	38.5057	+	2405.54i	0.00320100	+	0.199974i
$526$	3358.59			0.278406
$527$			3660.01i			0.302528i
$528$	2268.13	+	347.759i	0.186947	+	0.0286634i
$529$	5735.50			0.471398
$530$	11284.9			0.924875
$531$	10105.7	+	3173.49i	0.825894	+	0.259355i
$532$	134.011	+	789.471i	0.0109212	+	0.0643382i
$533$		−	23551.4i		−	1.91393i
$534$	34848.0	+	5343.02i	2.82401	+	0.432987i
$535$		−	529.909i		−	0.0428223i
$536$		−	7456.68i		−	0.600895i
$537$	−17472.2	−	2678.90i	−1.40406	−	0.215276i
$538$		−	16178.4i		−	1.29647i
$539$	−3282.60	−	9390.48i	−0.262322	−	0.750420i
$540$	−3724.90	+	7586.45i	−0.296841	+	0.604572i
$541$	16212.8			1.28844			0.644218	−	0.764842i	$-0.277183\pi$
$541$	16212.8			1.28844			0.644218	+	0.764842i	$0.277183\pi$
$542$	−28665.6			−2.27176
$543$	4641.14	+	711.597i	0.366796	+	0.0562386i
$544$			11796.6i			0.929734i
$545$	−2839.18			−0.223151
$546$	493.047	+	30801.9i	0.0386455	+	2.41428i
$547$	5449.59			0.425974			0.212987	−	0.977055i	$-0.431681\pi$
$547$	5449.59			0.425974			0.212987	+	0.977055i	$0.431681\pi$
$548$			9316.63i			0.726253i
$549$	−5859.81	+	18660.1i	−0.455539	+	1.45062i
$550$	3246.43			0.251688
$551$	−635.677			−0.0491484
$552$	1144.72	−	7466.05i	0.0882655	−	0.575681i
$553$	−3369.04	+	571.885i	−0.259070	+	0.0439765i
$554$			15721.7i			1.20569i
$555$	1391.83	−	9077.74i	0.106450	−	0.694286i
$556$			26898.1i			2.05168i
$557$		−	5251.61i		−	0.399493i	−0.979848	−	0.199747i	$-0.935988\pi$
$557$		−	5251.61i		−	0.399493i	0.979848	−	0.199747i	$-0.0640119\pi$
$558$	−7628.85	−	2395.68i	−0.578772	−	0.181752i
$559$			5053.05i			0.382327i
$560$	−1390.12	+	235.969i	−0.104899	+	0.0178063i
$561$	8242.63	+	1263.79i	0.620328	+	0.0951110i
$562$	−4969.90			−0.373030
$563$	13252.3			0.992040			0.496020	−	0.868311i	$-0.334794\pi$
$563$	13252.3			0.992040			0.496020	+	0.868311i	$0.334794\pi$
$564$	1893.40	−	12349.0i	0.141359	−	0.921966i
$565$			1098.53i			0.0817971i
$566$	21911.0			1.62719
$567$	−12212.9	−	5755.74i	−0.904577	−	0.426311i
$568$	−18288.9			−1.35103
$569$		−	18208.0i		−	1.34151i	−0.741677	−	0.670757i	$-0.765969\pi$
$569$		−	18208.0i		−	1.34151i	0.741677	−	0.670757i	$-0.234031\pi$
$570$	63.2687	−	412.648i	0.00464918	−	0.0303227i
$571$	7641.93			0.560079			0.280039	−	0.959989i	$-0.409652\pi$
$571$	7641.93			0.560079			0.280039	+	0.959989i	$0.409652\pi$
$572$	24981.4			1.82609
$573$	−4625.93	−	709.265i	−0.337262	−	0.0517102i
$574$	−4571.62	−	26931.9i	−0.332431	−	1.95839i
$575$			2004.92i			0.145410i
$576$	−21450.7	−	6736.17i	−1.55170	−	0.487281i
$577$		−	14924.8i		−	1.07683i	−0.842681	−	0.538413i	$-0.819024\pi$
$577$		−	14924.8i		−	1.07683i	0.842681	−	0.538413i	$-0.180976\pi$
$578$		−	8287.95i		−	0.596425i
$579$	−185.437	+	1209.45i	−0.0133100	+	0.0868101i
$580$			10670.7i			0.763924i
$581$	24447.5	−	4149.90i	1.74570	−	0.296328i
$582$	2430.92	−	15854.8i	0.173135	−	1.12922i
$583$	14619.0			1.03852
$584$	6186.36			0.438345
$585$	2891.66	−	9208.25i	0.204368	−	0.650794i
$586$		−	33410.7i		−	2.35526i
$587$	−17688.0			−1.24372			−0.621859	−	0.783130i	$-0.713622\pi$
$587$	−17688.0			−1.24372			−0.621859	+	0.783130i	$0.713622\pi$
$588$	3931.99	+	21110.2i	0.275770	+	1.48056i
$589$	237.365			0.0166052
$590$			8782.80i			0.612851i
$591$	1444.20	+	221.430i	0.100518	+	0.0154118i
$592$	5382.40			0.373675
$593$	23390.6			1.61979			0.809896	−	0.586574i	$-0.199524\pi$
$593$	23390.6			1.61979			0.809896	+	0.586574i	$0.199524\pi$
$594$	−8029.49	+	16353.6i	−0.554637	+	1.12962i
$595$	−5051.85	+	857.537i	−0.348077	+	0.0590850i
$596$		−	22354.5i		−	1.53637i
$597$	7873.96	+	1207.26i	0.539799	+	0.0827639i
$598$			25672.0i			1.75553i
$599$		−	7210.50i		−	0.491842i	−0.969290	−	0.245921i	$-0.920910\pi$
$599$		−	7210.50i		−	0.491842i	0.969290	−	0.245921i	$-0.0790903\pi$
$600$	−2327.42	−	356.848i	−0.158361	−	0.0242805i
$601$		−	20887.9i		−	1.41770i	−0.705361	−	0.708849i	$-0.749215\pi$
$601$		−	20887.9i		−	1.41770i	0.705361	−	0.708849i	$-0.250785\pi$
$602$	980.858	+	5778.34i	0.0664066	+	0.391209i
$603$	−10597.1	−	3327.81i	−0.715669	−	0.224741i
$604$	−16590.6			−1.11765
$605$	−2449.42			−0.164600
$606$	−38226.3	−	5860.99i	−2.56244	−	0.392882i
$607$			9863.20i			0.659530i	0.944063	+	0.329765i	$0.106970\pi$
$607$			9863.20i			0.659530i	−0.944063	+	0.329765i	$0.893030\pi$
$608$	765.053			0.0510312
$609$	−17044.1	+	272.826i	−1.13409	+	0.0181535i
$610$	−16217.4			−1.07643
$611$			14267.3i			0.944669i
$612$	−17173.7	−	5393.06i	−1.13432	−	0.356211i
$613$	−7785.41			−0.512968			−0.256484	−	0.966548i	$-0.582564\pi$
$613$	−7785.41			−0.512968			−0.256484	+	0.966548i	$0.582564\pi$
$614$	−23353.7			−1.53498
$615$	−1297.08	+	8459.75i	−0.0850459	+	0.554683i
$616$	9598.54	−	1629.33i	0.627818	−	0.106570i
$617$		−	13826.6i		−	0.902166i	−0.892482	−	0.451083i	$-0.851038\pi$
$617$		−	13826.6i		−	0.902166i	0.892482	−	0.451083i	$-0.148962\pi$
$618$	4385.46	−	28602.6i	0.285452	−	1.86176i
$619$		−	14770.5i		−	0.959091i	−0.877517	−	0.479545i	$-0.840802\pi$
$619$		−	14770.5i		−	0.959091i	0.877517	−	0.479545i	$-0.159198\pi$
$620$		−	3984.48i		−	0.258098i
$621$	−10099.6	−	4958.82i	−0.652628	−	0.320436i
$622$		−	5359.60i		−	0.345499i
$623$	−27668.3	+	4696.62i	−1.77930	+	0.302032i
$624$	5591.22	+	857.267i	0.358699	+	0.0549970i
$625$	625.000			0.0400000
$626$	11348.1			0.724536
$627$	81.9614	−	534.565i	0.00522045	−	0.0340486i
$628$		−	1242.49i		−	0.0789500i
$629$	19560.2			1.23993
$630$	1519.29	−	11091.3i	0.0960792	−	0.701408i
$631$	21659.8			1.36650			0.683252	−	0.730183i	$-0.260565\pi$
$631$	21659.8			1.36650			0.683252	+	0.730183i	$0.260565\pi$
$632$		−	3344.46i		−	0.210499i
$633$	−4524.12	+	29507.0i	−0.284072	+	1.85276i
$634$	−39070.4			−2.44745
$635$	7857.68			0.491059
$636$	−31192.3	−	4782.51i	−1.94474	−	0.298175i
$637$	−8092.00	−	23148.7i	−0.503323	−	1.43985i
$638$			23002.0i			1.42737i
$639$	−8162.09	+	25991.5i	−0.505301	+	1.60909i
$640$		−	10115.3i		−	0.624755i
$641$		−	11091.0i		−	0.683413i	−0.939807	−	0.341706i	$-0.888995\pi$
$641$		−	11091.0i		−	0.683413i	0.939807	−	0.341706i	$-0.111005\pi$
$642$	−373.692	+	2437.28i	−0.0229727	+	0.149831i
$643$		−	1060.54i		−	0.0650445i	−0.999471	−	0.0325223i	$-0.989646\pi$
$643$		−	1060.54i		−	0.0650445i	0.999471	−	0.0325223i	$-0.0103540\pi$
$644$	2994.74	+	17642.4i	0.183244	+	1.07951i
$645$	278.293	−	1815.07i	0.0169888	−	0.110804i
$646$	889.150			0.0541535
$647$	1634.76			0.0993340			0.0496670	−	0.998766i	$-0.484184\pi$
$647$	1634.76			0.0993340			0.0496670	+	0.998766i	$0.484184\pi$
$648$	7554.07	−	10841.5i	0.457950	−	0.657247i
$649$			11377.7i			0.688155i
$650$	8002.83			0.482918
$651$	6364.34	−	101.874i	0.383162	−	0.00613329i
$652$	−9364.10			−0.562464
$653$			17246.1i			1.03352i	0.856129	+	0.516762i	$0.172863\pi$
$653$			17246.1i			1.03352i	−0.856129	+	0.516762i	$0.827137\pi$
$654$	13058.6	+	2002.19i	0.780784	+	0.119713i
$655$	2858.16			0.170500
$656$	−5015.98			−0.298538
$657$	2760.89	−	8791.80i	0.163946	−	0.522072i
$658$	2769.46	+	16315.2i	0.164080	+	0.966613i
$659$			1816.51i			0.107377i	0.998558	+	0.0536883i	$0.0170977\pi$
$659$			1816.51i			0.107377i	−0.998558	+	0.0536883i	$0.982902\pi$
$660$	−8973.38	−	1375.83i	−0.529225	−	0.0811427i
$661$		−	8465.60i		−	0.498145i	−0.968485	−	0.249072i	$-0.919874\pi$
$661$		−	8465.60i		−	0.498145i	0.968485	−	0.249072i	$-0.0801257\pi$
$662$		−	48789.4i		−	2.86443i
$663$	20319.1	+	3115.39i	1.19024	+	0.182492i
$664$			24269.1i			1.41841i
$665$	55.6144	+	327.631i	0.00324306	+	0.0191052i
$666$	−12803.3	+	40770.9i	−0.744920	+	2.37213i
$667$	−14205.5			−0.824647
$668$	21982.7			1.27326
$669$	−16009.2	−	2454.58i	−0.925186	−	0.141853i
$670$		−	9209.90i		−	0.531059i
$671$	−21008.8			−1.20870
$672$	20513.0	−	328.352i	1.17754	−	0.0188489i
$673$	10034.1			0.574718			0.287359	−	0.957823i	$-0.407223\pi$
$673$	10034.1			0.574718			0.287359	+	0.957823i	$0.407223\pi$
$674$			6170.91i			0.352663i
$675$	−1545.83	+	3148.38i	−0.0881468	+	0.179528i
$676$	35112.2			1.99773
$677$	12750.6			0.723850			0.361925	−	0.932207i	$-0.382120\pi$
$677$	12750.6			0.723850			0.361925	+	0.932207i	$0.382120\pi$
$678$	774.682	−	5052.60i	0.0438813	−	0.286200i
$679$	2136.82	+	12588.3i	0.120771	+	0.711478i
$680$		−	5014.99i		−	0.282818i
$681$	4288.74	−	27971.8i	0.241329	−	1.57398i
$682$		−	8589.07i		−	0.482247i
$683$			1574.02i			0.0881818i	0.999028	+	0.0440909i	$0.0140391\pi$
$683$			1574.02i			0.0881818i	−0.999028	+	0.0440909i	$0.985961\pi$
$684$	−349.759	+	1113.78i	−0.0195517	+	0.0622608i
$685$			3866.40i			0.215661i
$686$	−13746.9	−	24900.6i	−0.765103	−	1.38587i
$687$	24318.0	+	3728.52i	1.35049	+	0.207063i
$688$	1076.20			0.0596360
$689$	36037.6			1.99263
$690$	1413.87	−	9221.46i	0.0780073	−	0.508776i
$691$		−	4160.12i		−	0.229028i	−0.993422	−	0.114514i	$-0.963469\pi$
$691$		−	4160.12i		−	0.229028i	0.993422	−	0.114514i	$-0.0365311\pi$
$692$	3878.81			0.213078
$693$	1968.16	−	14368.2i	0.107885	−	0.787594i
$694$	909.671			0.0497560
$695$			11162.7i			0.609247i
$696$	2528.39	−	16490.6i	0.137699	−	0.898093i
$697$	−18228.6			−0.990612
$698$	−42274.1			−2.29241
$699$	1893.60	+	290.333i	0.102464	+	0.0157102i
$700$	5499.72	−	933.562i	0.296957	−	0.0504076i
$701$		−	34955.1i		−	1.88336i	−0.336509	−	0.941680i	$-0.609246\pi$
$701$		−	34955.1i		−	1.88336i	0.336509	−	0.941680i	$-0.390754\pi$
$702$	−19793.7	+	40313.5i	−1.06419	+	2.16743i
$703$		−	1268.55i		−	0.0680573i
$704$		−	24150.7i		−	1.29292i
$705$	785.761	−	5124.86i	0.0419766	−	0.273778i
$706$			38911.7i			2.07431i
$707$	30350.6	−	5151.93i	1.61450	−	0.274057i
$708$	3722.14	−	24276.3i	0.197580	−	1.28864i
$709$	7608.81			0.403040			0.201520	−	0.979484i	$-0.435412\pi$
$709$	7608.81			0.403040			0.201520	+	0.979484i	$0.435412\pi$
$710$	−22589.0			−1.19402
$711$	−4753.00	−	1492.58i	−0.250705	−	0.0787289i
$712$		−	27466.4i		−	1.44571i
$713$	5304.40			0.278613
$714$	23840.3	−	381.613i	1.24958	−	0.0200021i
$715$	10367.3			0.542257
$716$			40985.8i			2.13926i
$717$	−24814.5	−	3804.64i	−1.29249	−	0.198169i
$718$	−13631.6			−0.708531
$719$	−10185.5			−0.528312			−0.264156	−	0.964480i	$-0.585093\pi$
$719$	−10185.5			−0.528312			−0.264156	+	0.964480i	$0.585093\pi$
$720$	−1961.17	−	615.866i	−0.101512	−	0.0318777i
$721$	3854.90	+	22709.7i	0.199118	+	1.17303i
$722$			30653.6i			1.58007i
$723$	16423.5	+	2518.12i	0.844811	+	0.129529i
$724$		−	10887.1i		−	0.558859i
$725$			4428.34i			0.226847i
$726$	11265.9	+	1727.33i	0.575919	+	0.0883020i
$727$		−	21469.0i		−	1.09524i	−0.836727	−	0.547620i	$-0.815534\pi$
$727$		−	21469.0i		−	1.09524i	0.836727	−	0.547620i	$-0.184466\pi$
$728$	23661.5	−	4016.48i	1.20461	−	0.204479i
$729$	−12036.3	−	15574.0i	−0.611507	−	0.791239i
$730$	7640.90			0.387401
$731$	3911.01			0.197885
$732$	44826.0	+	6872.89i	2.26341	+	0.347035i
$733$			23924.9i			1.20557i	0.797902	+	0.602787i	$0.205943\pi$
$733$			23924.9i			1.20557i	−0.797902	+	0.602787i	$0.794057\pi$
$734$	5783.27			0.290824
$735$	1631.78	+	8760.73i	0.0818898	+	0.439652i
$736$	17096.7			0.856239
$737$		−	11931.0i		−	0.596313i
$738$	11931.6	−	37995.3i	0.595135	−	1.89516i
$739$	11563.9			0.575622			0.287811	−	0.957687i	$-0.407072\pi$
$739$	11563.9			0.575622			0.287811	+	0.957687i	$0.407072\pi$
$740$	−21294.3			−1.05783
$741$	202.045	−	1317.77i	0.0100166	−	0.0653298i
$742$	41210.3	−	6995.33i	2.03892	−	0.346101i
$743$			36857.6i			1.81988i	0.414735	+	0.909942i	$0.363874\pi$
$743$			36857.6i			1.81988i	−0.414735	+	0.909942i	$0.636126\pi$
$744$	−944.113	+	6157.65i	−0.0465227	+	0.303428i
$745$		−	9277.10i		−	0.456224i
$746$		−	2118.68i		−	0.103982i
$747$	34490.3	+	10831.0i	1.68934	+	0.530501i
$748$		−	19335.3i		−	0.945147i
$749$	−328.483	−	1935.13i	−0.0160247	−	0.0944032i
$750$	−2874.64	−	440.751i	−0.139956	−	0.0214586i
$751$	−27329.1			−1.32790			−0.663949	−	0.747778i	$-0.731121\pi$
$751$	−27329.1			−1.32790			−0.663949	+	0.747778i	$0.731121\pi$
$752$	3038.64			0.147351
$753$	1902.41	−	12407.8i	0.0920688	−	0.600486i
$754$			56702.8i			2.73872i
$755$	−6885.09			−0.331886
$756$	−8899.90	+	30013.3i	−0.428156	+	1.44388i
$757$	11614.3			0.557632			0.278816	−	0.960345i	$-0.410058\pi$
$757$	11614.3			0.557632			0.278816	+	0.960345i	$0.410058\pi$
$758$			10866.1i			0.520679i
$759$	1831.60	−	11945.9i	0.0875925	−	0.571292i
$760$	−325.240			−0.0155233
$761$	−37213.6			−1.77266			−0.886330	−	0.463055i	$-0.846753\pi$
$761$	−37213.6			−1.77266			−0.886330	+	0.463055i	$0.846753\pi$
$762$	−36140.9	−	5541.25i	−1.71817	−	0.263436i
$763$	−10368.2	+	1759.97i	−0.491944	+	0.0835061i
$764$			10851.4i			0.513860i
$765$	−7127.10	−	2238.12i	−0.336838	−	0.105777i
$766$			21850.4i			1.03066i
$767$			28047.3i			1.32038i
$768$	−1887.24	+	12308.8i	−0.0886716	+	0.578330i
$769$			9196.32i			0.431246i	0.976477	+	0.215623i	$0.0691782\pi$
$769$			9196.32i			0.431246i	−0.976477	+	0.215623i	$0.930822\pi$
$770$	11855.3	−	2012.41i	0.554853	−	0.0941848i
$771$	−4930.04	+	32154.4i	−0.230287	+	1.50196i
$772$	2837.09			0.132266
$773$	−12596.7			−0.586121			−0.293061	−	0.956094i	$-0.594674\pi$
$773$	−12596.7			−0.586121			−0.293061	+	0.956094i	$0.594674\pi$
$774$	−2559.98	+	8152.03i	−0.118884	+	0.378577i
$775$		−	1653.56i		−	0.0766422i
$776$	−12496.4			−0.578087
$777$	−544.448	−	34013.0i	−0.0251376	−	1.57041i
$778$	28439.7			1.31055
$779$			1182.19i			0.0543727i
$780$	−22120.5	−	3391.59i	−1.01544	−	0.155690i
$781$	−29262.9			−1.34073
$782$	19869.9			0.908626
$783$	−22307.3	−	10952.7i	−1.01813	−	0.499897i
$784$	−4930.19	+	1723.43i	−0.224590	+	0.0785092i
$785$		−	515.632i		−	0.0234442i
$786$	−13145.9	−	2015.58i	−0.596564	−	0.0914673i
$787$			30667.4i			1.38904i	0.719474	+	0.694519i	$0.244383\pi$
$787$			30667.4i			1.38904i	−0.719474	+	0.694519i	$0.755617\pi$
$788$		−	3387.76i		−	0.153152i
$789$	−3852.61	−	590.696i	−0.173836	−	0.0266532i
$790$		−	4130.80i		−	0.186035i
$791$	680.961	+	4011.62i	0.0306096	+	0.180324i
$792$	13541.5	+	4252.44i	0.607547	+	0.190788i
$793$	−51789.1			−2.31915
$794$	37286.7			1.66657
$795$	−12944.8	−	1984.74i	−0.577490	−	0.0885429i
$796$		−	18470.5i		−	0.822449i
$797$	−3992.51			−0.177443			−0.0887215	−	0.996056i	$-0.528278\pi$
$797$	−3992.51			−0.177443			−0.0887215	+	0.996056i	$0.528278\pi$
$798$	−24.7490	−	1546.13i	−0.00109788	−	0.0685871i
$799$	11042.7			0.488941
$800$		−	5329.61i		−	0.235538i
$801$	−39034.1	−	12257.9i	−1.72185	−	0.540712i
$802$	−46676.2			−2.05511
$803$	9898.40			0.435003
$804$	−3903.14	+	25456.9i	−0.171210	+	1.11666i
$805$	1242.82	+	7321.58i	0.0544144	+	0.320561i
$806$		−	21173.1i		−	0.925298i
$807$	−2845.40	+	18558.1i	−0.124118	+	0.809514i
$808$			30129.1i			1.31181i
$809$			22255.7i			0.967205i	0.875288	+	0.483602i	$0.160672\pi$
$809$			22255.7i			0.967205i	−0.875288	+	0.483602i	$0.839328\pi$
$810$	9330.18	−	13390.6i	0.404727	−	0.580862i
$811$			25191.5i			1.09074i	0.838194	+	0.545372i	$0.183612\pi$
$811$			25191.5i			1.09074i	−0.838194	+	0.545372i	$0.816388\pi$
$812$	6614.60	+	38967.4i	0.285871	+	1.68410i
$813$	32882.1	+	5041.61i	1.41848	+	0.217487i
$814$	−45902.6			−1.97652
$815$	−3886.10			−0.167024
$816$	663.516	−	4327.55i	0.0284653	−	0.185655i
$817$		−	253.643i		−	0.0108615i
$818$	36017.8			1.53953
$819$	4851.75	−	35419.3i	0.207001	−	1.51117i
$820$	19844.6			0.845127
$821$			15633.3i			0.664562i	0.943180	+	0.332281i	$0.107818\pi$
$821$			15633.3i			0.664562i	−0.943180	+	0.332281i	$0.892182\pi$
$822$	2726.59	−	17783.2i	0.115694	−	0.754576i
$823$	−8116.81			−0.343784			−0.171892	−	0.985116i	$-0.554988\pi$
$823$	−8116.81			−0.343784			−0.171892	+	0.985116i	$0.554988\pi$
$824$	−22544.0			−0.953103
$825$	−3723.95	−	570.970i	−0.157153	−	0.0240953i
$826$	5444.33	+	32073.1i	0.229337	+	1.35105i
$827$			47.6466i			0.00200343i	0.999999	+	0.00100171i	$0.000318855\pi$
$827$			47.6466i			0.00200343i	−0.999999	+	0.00100171i	$0.999681\pi$
$828$	−7816.09	+	24889.7i	−0.328053	+	1.04466i
$829$			11926.0i			0.499647i	0.968291	+	0.249823i	$0.0803726\pi$
$829$			11926.0i			0.499647i	−0.968291	+	0.249823i	$0.919627\pi$
$830$			29975.3i			1.25356i
$831$	2765.08	−	18034.2i	0.115426	−	0.752829i
$832$		−	59534.3i		−	2.48075i
$833$	−17916.8	+	6263.13i	−0.745236	+	0.260510i
$834$	7871.97	−	51342.2i	0.326839	−	2.13170i
$835$	9122.81			0.378093
$836$	−1253.97			−0.0518772
$837$	8329.65	+	4089.81i	0.343984	+	0.168894i
$838$		−	55479.3i		−	2.28699i
$839$	17635.6			0.725685			0.362842	−	0.931851i	$-0.381806\pi$
$839$	17635.6			0.725685			0.362842	+	0.931851i	$0.381806\pi$
$840$	−8720.51	+	139.590i	−0.358198	+	0.00573369i
$841$	−6987.27			−0.286493
$842$		−	55549.3i		−	2.27358i
$843$	5700.94	+	874.089i	0.232919	+	0.0357120i
$844$	69216.7			2.82291
$845$	14571.6			0.593227
$846$	−7228.11	+	23017.3i	−0.293744	+	0.935403i
$847$	−8944.81	+	1518.36i	−0.362866	+	0.0615955i
$848$		−	7675.27i		−	0.310814i
$849$	−25134.0	−	3853.63i	−1.01601	−	0.155779i
$850$		−	6194.11i		−	0.249949i
$851$		−	28348.3i		−	1.14191i
$852$	62437.8	+	9573.19i	2.51066	+	0.384944i
$853$		−	1754.20i		−	0.0704134i	−0.999380	−	0.0352067i	$-0.988791\pi$
$853$		−	1754.20i		−	0.0704134i	0.999380	−	0.0352067i	$-0.0112089\pi$
$854$	−59222.7	+	10052.9i	−2.37302	+	0.402814i
$855$	−145.150	+	462.218i	−0.00580588	+	0.0184883i
$856$	1921.01			0.0767041
$857$	−34647.6			−1.38103			−0.690513	−	0.723320i	$-0.742615\pi$
$857$	−34647.6			−1.38103			−0.690513	+	0.723320i	$0.742615\pi$
$858$	−47683.5	−	7311.01i	−1.89731	−	0.290902i
$859$		−	11165.6i		−	0.443501i	−0.975103	−	0.221750i	$-0.928823\pi$
$859$		−	11165.6i		−	0.443501i	0.975103	−	0.221750i	$-0.0711770\pi$
$860$	−4257.74			−0.168823
$861$	507.383	+	31697.5i	0.0200831	+	1.25464i
$862$	−52232.2			−2.06385
$863$		−	6906.23i		−	0.272411i	−0.990681	−	0.136206i	$-0.956509\pi$
$863$		−	6906.23i		−	0.272411i	0.990681	−	0.136206i	$-0.0434908\pi$
$864$	26847.4	+	13181.9i	1.05714	+	0.519048i
$865$	1609.71			0.0632736
$866$	9865.88			0.387132
$867$	−1457.66	+	9507.05i	−0.0570987	+	0.372407i
$868$	−2469.92	−	14550.6i	−0.0965837	−	0.568985i
$869$		−	5351.25i		−	0.208894i
$870$	3122.87	−	20367.8i	0.121696	−	0.793717i
$871$		−	29411.3i		−	1.14416i
$872$		−	10292.5i		−	0.399712i
$873$	−5576.98	+	17759.4i	−0.216211	+	0.688505i
$874$		−	1288.63i		−	0.0498727i
$875$	2282.38	−	387.428i	0.0881813	−	0.0149685i
$876$	−21120.1	−	3238.20i	−0.814589	−	0.124896i
$877$	16556.6			0.637486			0.318743	−	0.947841i	$-0.396739\pi$
$877$	16556.6			0.637486			0.318743	+	0.947841i	$0.396739\pi$
$878$	39833.2			1.53110
$879$	−5876.16	+	38325.2i	−0.225481	+	1.47062i
$880$		−	2208.02i		−	0.0845821i
$881$	22919.6			0.876483			0.438241	−	0.898857i	$-0.355602\pi$
$881$	22919.6			0.876483			0.438241	+	0.898857i	$0.355602\pi$
$882$	−1327.17	−	41445.1i	−0.0506667	−	1.58223i
$883$	−20250.0			−0.771763			−0.385882	−	0.922548i	$-0.626103\pi$
$883$	−20250.0			−0.771763			−0.385882	+	0.922548i	$0.626103\pi$
$884$		−	47663.9i		−	1.81347i
$885$	1544.69	−	10074.7i	0.0586713	−	0.382663i
$886$	23734.4			0.899969
$887$	−31844.9			−1.20547			−0.602733	−	0.797943i	$-0.705921\pi$
$887$	−31844.9			−1.20547			−0.602733	+	0.797943i	$0.705921\pi$
$888$	32908.4	+	5045.63i	1.24362	+	0.190676i
$889$	28694.8	−	4870.86i	1.08256	−	0.183761i
$890$		−	33924.3i		−	1.27769i
$891$	12086.8	−	17346.9i	0.454458	−	0.652235i
$892$			37553.8i			1.40963i
$893$		−	716.162i		−	0.0268370i
$894$	−6542.22	+	42669.4i	−0.244748	+	1.59628i
$895$			17009.1i			0.635254i
$896$	−6270.34	−	36939.3i	−0.233792	−	1.37729i
$897$	4515.10	−	29448.2i	0.168066	−	1.09615i
$898$	−18848.2			−0.700415
$899$	11716.0			0.434652
$900$	7758.95	+	2436.54i	0.287368	+	0.0902422i
$901$		−	27892.7i		−	1.03134i
$902$	42777.6			1.57909
$903$	−108.861	−	6800.81i	−0.00401181	−	0.250627i
$904$	−3982.35			−0.146516
$905$		−	4518.13i		−	0.165953i
$906$	31667.5	+	4855.37i	1.16124	+	0.178045i
$907$	−16276.5			−0.595869			−0.297934	−	0.954586i	$-0.596298\pi$
$907$	−16276.5			−0.595869			−0.297934	+	0.954586i	$0.596298\pi$
$908$	−65615.5			−2.39816
$909$	42818.3	+	13446.2i	1.56237	+	0.490630i
$910$	29224.9	−	4960.84i	1.06461	−	0.180715i
$911$			26321.8i			0.957278i	0.878012	+	0.478639i	$0.158870\pi$
$911$			26321.8i			0.957278i	−0.878012	+	0.478639i	$0.841130\pi$
$912$	−280.658	−	43.0314i	−0.0101902	−	0.00156240i
$913$			38831.5i			1.40760i
$914$			49444.2i			1.78935i
$915$	18602.8	+	2852.25i	0.672120	+	0.103052i
$916$		−	57044.4i		−	2.05764i
$917$	10437.5	−	1771.73i	0.375873	−	0.0638035i
$918$	31202.2	+	15320.1i	1.12182	+	0.550805i
$919$	32057.6			1.15069			0.575344	−	0.817912i	$-0.304868\pi$
$919$	32057.6			1.15069			0.575344	+	0.817912i	$0.304868\pi$
$920$	−7268.16			−0.260461
$921$	26788.8	+	4107.36i	0.958439	+	0.146951i
$922$			30261.1i			1.08091i
$923$	−72136.6			−2.57249
$924$	−33622.0	+	538.189i	−1.19706	+	0.0191614i
$925$	−8837.14			−0.314123
$926$		−	16145.9i		−	0.572988i
$927$	−10061.1	+	32038.6i	−0.356471	+	1.13515i
$928$	37762.1			1.33578
$929$	−9274.12			−0.327528			−0.163764	−	0.986500i	$-0.552364\pi$
$929$	−9274.12			−0.327528			−0.163764	+	0.986500i	$0.552364\pi$
$930$	−1166.09	+	7605.44i	−0.0411158	+	0.268163i
$931$	406.187	+	1161.97i	0.0142989	+	0.0409045i
$932$		−	4441.94i		−	0.156117i
$933$	−942.627	+	6147.96i	−0.0330763	+	0.215729i
$934$		−	12190.9i		−	0.427085i
$935$		−	8024.16i		−	0.280661i
$936$	33381.5	+	10482.8i	1.16571	+	0.366068i
$937$		−	4933.86i		−	0.172019i	−0.996294	−	0.0860097i	$-0.972588\pi$
$937$		−	4933.86i		−	0.172019i	0.996294	−	0.0860097i	$-0.0274116\pi$
$938$	−5709.08	−	33632.8i	−0.198729	−	1.17074i
$939$	−13017.3	−	1995.86i	−0.452399	−	0.0693635i
$940$	−12021.7			−0.417134
$941$	−22852.4			−0.791675			−0.395838	−	0.918321i	$-0.629546\pi$
$941$	−22852.4			−0.791675			−0.395838	+	0.918321i	$0.629546\pi$
$942$	−363.624	+	2371.61i	−0.0125770	+	0.0820290i
$943$			26418.4i			0.912304i
$944$	5973.51			0.205955
$945$	−3693.46	+	12455.5i	−0.127141	+	0.428760i
$946$	−9178.10			−0.315439
$947$		−	14610.0i		−	0.501332i	−0.968074	−	0.250666i	$-0.919350\pi$
$947$		−	14610.0i		−	0.501332i	0.968074	−	0.250666i	$-0.0806495\pi$
$948$	−1750.63	+	11417.9i	−0.0599766	+	0.391176i
$949$	24400.7			0.834649
$950$	−401.711			−0.0137192
$951$	44817.4	+	6871.57i	1.52819	+	0.234307i
$952$	−3108.72	−	18313.8i	−0.105834	−	0.623481i
$953$		−	8952.53i		−	0.304303i	−0.988357	−	0.152152i	$-0.951380\pi$
$953$		−	8952.53i		−	0.304303i	0.988357	−	0.152152i	$-0.0486202\pi$
$954$	58139.0	+	18257.4i	1.97308	+	0.619606i
$955$			4503.32i			0.152591i
$956$			58209.1i			1.96926i
$957$	4045.52	−	26385.5i	0.136649	−	0.891245i
$958$		−	46596.7i		−	1.57147i
$959$	2396.73	+	14119.4i	0.0807032	+	0.475431i
$960$	−3278.81	+	21384.9i	−0.110233	+	0.718953i
$961$	25416.2			0.853149
$962$	−113155.			−3.79239
$963$	857.319	−	2730.06i	0.0286882	−	0.0913551i
$964$		−	38525.9i		−	1.28717i
$965$	1177.39			0.0392763
$966$	−553.067	−	34551.5i	−0.0184210	−	1.15080i
$967$	30078.9			1.00028			0.500140	−	0.865944i	$-0.333282\pi$
$967$	30078.9			1.00028			0.500140	+	0.865944i	$0.333282\pi$
$968$		−	8879.55i		−	0.294834i
$969$	−1019.94	−	156.381i	−0.0338134	−	0.00518438i
$970$	−15434.6			−0.510902
$971$	−36971.3			−1.22190			−0.610951	−	0.791668i	$-0.709213\pi$
$971$	−36971.3			−1.22190			−0.610951	+	0.791668i	$0.709213\pi$
$972$	−31464.3	+	33058.6i	−1.03829	+	1.09090i
$973$	6919.61	+	40764.2i	0.227988	+	1.34310i
$974$		−	81156.1i		−	2.66982i
$975$	−9179.99	−	1407.51i	−0.301533	−	0.0462322i
$976$			11030.0i			0.361745i
$977$			18627.5i			0.609977i	0.952356	+	0.304988i	$0.0986526\pi$
$977$			18627.5i			0.609977i	−0.952356	+	0.304988i	$0.901347\pi$
$978$	17873.8	+	2740.48i	0.584399	+	0.0896022i
$979$		−	43947.3i		−	1.43469i
$980$	19505.2	−	6818.39i	0.635788	−	0.222250i
$981$	−14627.3	−	4593.41i	−0.476059	−	0.149497i
$982$	57897.2			1.88144
$983$	18609.6			0.603820			0.301910	−	0.953336i	$-0.402376\pi$
$983$	18609.6			0.603820			0.301910	+	0.953336i	$0.402376\pi$
$984$	−30668.0	−	4702.13i	−0.993557	−	0.152336i
$985$		−	1405.92i		−	0.0454785i
$986$	43887.4			1.41750
$987$	−307.369	−	19202.1i	−0.00991252	−	0.619260i
$988$	−3091.18			−0.0995379
$989$		−	5668.17i		−	0.182242i
$990$	16725.4	+	5252.27i	0.536938	+	0.168614i
$991$	−13931.6			−0.446572			−0.223286	−	0.974753i	$-0.571678\pi$
$991$	−13931.6			−0.446572			−0.223286	+	0.974753i	$0.571678\pi$
$992$	−14100.5			−0.451303
$993$	−8580.91	+	55966.0i	−0.274227	+	1.78855i
$994$	−82490.9	+	14002.6i	−2.63225	+	0.446816i
$995$		−	7665.26i		−	0.244226i
$996$	12703.5	−	82854.1i	0.404142	−	2.63588i
$997$		−	13693.4i		−	0.434980i	−0.976063	−	0.217490i	$-0.930213\pi$
$997$		−	13693.4i		−	0.434980i	0.976063	−	0.217490i	$-0.0697870\pi$
$998$		−	41.0037i		−	0.00130055i
$999$	21857.2	−	44516.2i	0.692223	−	1.40984i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.b.a.41.14	yes	16
3.2	odd	2		105.4.b.b.41.3	yes	16
7.6	odd	2		105.4.b.b.41.14	yes	16
21.20	even	2	inner	105.4.b.a.41.3	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.b.a.41.3	✓	16	21.20	even	2	inner
105.4.b.a.41.14	yes	16	1.1	even	1	trivial
105.4.b.b.41.3	yes	16	3.2	odd	2
105.4.b.b.41.14	yes	16	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+4.47752i q^{2} +(0.787490 - 5.13613i) q^{3} -12.0482 q^{4} -5.00000 q^{5} +(22.9971 + 3.52600i) q^{6} +(-18.2591 + 3.09943i) q^{7} -18.1258i q^{8} +(-25.7597 - 8.08931i) q^{9} +O(q^{10})\)	\(q+4.47752i q^{2} +(0.787490 - 5.13613i) q^{3} -12.0482 q^{4} -5.00000 q^{5} +(22.9971 + 3.52600i) q^{6} +(-18.2591 + 3.09943i) q^{7} -18.1258i q^{8} +(-25.7597 - 8.08931i) q^{9} -22.3876i q^{10} -29.0020i q^{11} +(-9.48783 + 61.8811i) q^{12} -71.4934i q^{13} +(-13.8777 - 81.7553i) q^{14} +(-3.93745 + 25.6807i) q^{15} -15.2267 q^{16} -55.3352 q^{17} +(36.2201 - 115.340i) q^{18} +3.58869i q^{19} +60.2409 q^{20} +(1.54023 + 96.2218i) q^{21} +129.857 q^{22} +80.1966i q^{23} +(-93.0968 - 14.2739i) q^{24} +25.0000 q^{25} +320.113 q^{26} +(-61.8333 + 125.935i) q^{27} +(219.989 - 37.3425i) q^{28} +177.133i q^{29} +(-114.986 - 17.6300i) q^{30} -66.1424i q^{31} -213.184i q^{32} +(-148.958 - 22.8388i) q^{33} -247.765i q^{34} +(91.2953 - 15.4971i) q^{35} +(310.358 + 97.4615i) q^{36} -353.486 q^{37} -16.0684 q^{38} +(-367.200 - 56.3004i) q^{39} +90.6292i q^{40} +329.421 q^{41} +(-430.835 + 6.89639i) q^{42} -70.6784 q^{43} +349.422i q^{44} +(128.799 + 40.4466i) q^{45} -359.082 q^{46} -199.561 q^{47} +(-11.9908 + 78.2061i) q^{48} +(323.787 - 113.185i) q^{49} +111.938i q^{50} +(-43.5760 + 284.209i) q^{51} +861.366i q^{52} +504.068i q^{53} +(-563.877 - 276.860i) q^{54} +145.010i q^{55} +(56.1797 + 330.961i) q^{56} +(18.4320 + 2.82606i) q^{57} -793.119 q^{58} -392.306 q^{59} +(47.4392 - 309.405i) q^{60} -724.390i q^{61} +296.154 q^{62} +(495.421 + 67.8629i) q^{63} +832.724 q^{64} +357.467i q^{65} +(102.261 - 666.963i) q^{66} +411.384 q^{67} +666.689 q^{68} +(411.900 + 63.1541i) q^{69} +(69.3887 + 408.777i) q^{70} -1009.00i q^{71} +(-146.626 + 466.917i) q^{72} +341.301i q^{73} -1582.74i q^{74} +(19.6873 - 128.403i) q^{75} -43.2372i q^{76} +(89.8896 + 529.550i) q^{77} +(252.086 - 1644.14i) q^{78} +184.513 q^{79} +76.1333 q^{80} +(598.126 + 416.757i) q^{81} +1474.99i q^{82} -1338.92 q^{83} +(-18.5569 - 1159.30i) q^{84} +276.676 q^{85} -316.464i q^{86} +(909.781 + 139.491i) q^{87} -525.686 q^{88} +1515.32 q^{89} +(-181.100 + 576.698i) q^{90} +(221.589 + 1305.40i) q^{91} -966.224i q^{92} +(-339.716 - 52.0865i) q^{93} -893.538i q^{94} -17.9435i q^{95} +(-1094.94 - 167.881i) q^{96} -689.426i q^{97} +(506.789 + 1449.76i) q^{98} +(-234.606 + 747.084i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{3} - 64 q^{4} - 80 q^{5} - 28 q^{6} - 4 q^{7} - 22 q^{9}+O(q^{10}) \) 16 * q - 2 * q^3 - 64 * q^4 - 80 * q^5 - 28 * q^6 - 4 * q^7 - 22 * q^9	\( 16 q - 2 q^{3} - 64 q^{4} - 80 q^{5} - 28 q^{6} - 4 q^{7} - 22 q^{9} - 66 q^{12} - 90 q^{14} + 10 q^{15} + 376 q^{16} - 72 q^{17} - 182 q^{18} + 320 q^{20} - 74 q^{21} - 276 q^{22} + 526 q^{24} + 400 q^{25} + 696 q^{26} - 128 q^{27} + 10 q^{28} + 140 q^{30} - 502 q^{33} + 20 q^{35} + 996 q^{36} - 812 q^{37} - 1200 q^{38} - 594 q^{39} - 936 q^{41} - 1834 q^{42} - 548 q^{43} + 110 q^{45} + 1224 q^{46} + 912 q^{47} + 1850 q^{48} + 328 q^{49} + 750 q^{51} - 2950 q^{54} + 1254 q^{56} + 432 q^{57} + 576 q^{58} - 552 q^{59} + 330 q^{60} - 1860 q^{62} - 898 q^{63} - 4000 q^{64} + 1378 q^{66} + 1004 q^{67} + 3828 q^{68} + 1988 q^{69} + 450 q^{70} + 1988 q^{72} - 50 q^{75} + 1152 q^{77} + 1446 q^{78} + 1292 q^{79} - 1880 q^{80} - 2950 q^{81} - 1752 q^{83} + 1068 q^{84} + 360 q^{85} + 1910 q^{87} - 912 q^{88} + 6096 q^{89} + 910 q^{90} - 552 q^{91} - 1080 q^{93} - 9546 q^{96} - 4824 q^{98} + 2530 q^{99}+O(q^{100}) \) 16 * q - 2 * q^3 - 64 * q^4 - 80 * q^5 - 28 * q^6 - 4 * q^7 - 22 * q^9 - 66 * q^12 - 90 * q^14 + 10 * q^15 + 376 * q^16 - 72 * q^17 - 182 * q^18 + 320 * q^20 - 74 * q^21 - 276 * q^22 + 526 * q^24 + 400 * q^25 + 696 * q^26 - 128 * q^27 + 10 * q^28 + 140 * q^30 - 502 * q^33 + 20 * q^35 + 996 * q^36 - 812 * q^37 - 1200 * q^38 - 594 * q^39 - 936 * q^41 - 1834 * q^42 - 548 * q^43 + 110 * q^45 + 1224 * q^46 + 912 * q^47 + 1850 * q^48 + 328 * q^49 + 750 * q^51 - 2950 * q^54 + 1254 * q^56 + 432 * q^57 + 576 * q^58 - 552 * q^59 + 330 * q^60 - 1860 * q^62 - 898 * q^63 - 4000 * q^64 + 1378 * q^66 + 1004 * q^67 + 3828 * q^68 + 1988 * q^69 + 450 * q^70 + 1988 * q^72 - 50 * q^75 + 1152 * q^77 + 1446 * q^78 + 1292 * q^79 - 1880 * q^80 - 2950 * q^81 - 1752 * q^83 + 1068 * q^84 + 360 * q^85 + 1910 * q^87 - 912 * q^88 + 6096 * q^89 + 910 * q^90 - 552 * q^91 - 1080 * q^93 - 9546 * q^96 - 4824 * q^98 + 2530 * q^99

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