LMFDB - Embedded newform 20.5.b.a.11.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [20,5,Mod(11,20)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(20, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("20.11");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	20.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:	$2.06739926168$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.246034965625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 7x^{6} - 21x^{5} + 49x^{4} - 84x^{3} + 112x^{2} - 192x + 256 $ x^8 - 3x^7 + 7x^6 - 21x^5 + 49x^4 - 84x^3 + 112x^2 - 192*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{14}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.8
Root			$1.95003 + 0.444269i$ of defining polynomial
Character	$\chi$	$=$	20.11
Dual form			20.5.b.a.11.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.90006 + 0.888538i) q^{2} -12.9912i q^{3} +(14.4210 + 6.93071i) q^{4} -11.1803 q^{5} +(11.5432 - 50.6665i) q^{6} +78.0345i q^{7} +(50.0846 + 39.8438i) q^{8} -87.7712 q^{9} +O(q^{10})$	\(q+(3.90006 + 0.888538i) q^{2} -12.9912i q^{3} +(14.4210 + 6.93071i) q^{4} -11.1803 q^{5} +(11.5432 - 50.6665i) q^{6} +78.0345i q^{7} +(50.0846 + 39.8438i) q^{8} -87.7712 q^{9} +(-43.6040 - 9.93415i) q^{10} -95.6447i q^{11} +(90.0382 - 187.346i) q^{12} -159.654 q^{13} +(-69.3366 + 304.340i) q^{14} +145.246i q^{15} +(159.931 + 199.896i) q^{16} +22.5103 q^{17} +(-342.313 - 77.9881i) q^{18} -324.934i q^{19} +(-161.232 - 77.4877i) q^{20} +1013.76 q^{21} +(84.9839 - 373.020i) q^{22} +204.951i q^{23} +(517.619 - 650.659i) q^{24} +125.000 q^{25} +(-622.661 - 141.859i) q^{26} +87.9664i q^{27} +(-540.835 + 1125.34i) q^{28} +295.747 q^{29} +(-129.057 + 566.469i) q^{30} -407.262i q^{31} +(446.125 + 921.710i) q^{32} -1242.54 q^{33} +(87.7916 + 20.0012i) q^{34} -872.453i q^{35} +(-1265.75 - 608.317i) q^{36} -2156.28 q^{37} +(288.716 - 1267.26i) q^{38} +2074.10i q^{39} +(-559.963 - 445.467i) q^{40} +1368.98 q^{41} +(3953.74 + 900.766i) q^{42} +1234.22i q^{43} +(662.885 - 1379.29i) q^{44} +981.312 q^{45} +(-182.107 + 799.321i) q^{46} -1983.43i q^{47} +(2596.88 - 2077.69i) q^{48} -3688.39 q^{49} +(487.508 + 111.067i) q^{50} -292.436i q^{51} +(-2302.37 - 1106.52i) q^{52} +4595.72 q^{53} +(-78.1615 + 343.075i) q^{54} +1069.34i q^{55} +(-3109.19 + 3908.33i) q^{56} -4221.28 q^{57} +(1153.43 + 262.783i) q^{58} -1389.15i q^{59} +(-1006.66 + 2094.59i) q^{60} +2651.94 q^{61} +(361.867 - 1588.35i) q^{62} -6849.19i q^{63} +(920.941 + 3991.13i) q^{64} +1784.99 q^{65} +(-4845.98 - 1104.04i) q^{66} +8936.51i q^{67} +(324.621 + 156.012i) q^{68} +2662.56 q^{69} +(775.207 - 3402.62i) q^{70} +3375.13i q^{71} +(-4395.99 - 3497.14i) q^{72} -1467.63 q^{73} +(-8409.65 - 1915.94i) q^{74} -1623.90i q^{75} +(2252.02 - 4685.87i) q^{76} +7463.59 q^{77} +(-1842.91 + 8089.11i) q^{78} -6306.01i q^{79} +(-1788.08 - 2234.90i) q^{80} -5966.68 q^{81} +(5339.10 + 1216.39i) q^{82} +6104.16i q^{83} +(14619.5 + 7026.09i) q^{84} -251.673 q^{85} +(-1096.65 + 4813.54i) q^{86} -3842.11i q^{87} +(3810.85 - 4790.33i) q^{88} +1708.55 q^{89} +(3827.18 + 871.933i) q^{90} -12458.5i q^{91} +(-1420.45 + 2955.60i) q^{92} -5290.82 q^{93} +(1762.35 - 7735.51i) q^{94} +3632.87i q^{95} +(11974.1 - 5795.69i) q^{96} -1988.16 q^{97} +(-14385.0 - 3277.27i) q^{98} +8394.85i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{2} - 20 q^{4} + 48 q^{6} + 216 q^{8} - 328 q^{9}+O(q^{10}) $ 8 * q + 6 * q^2 - 20 * q^4 + 48 * q^6 + 216 * q^8 - 328 * q^9	$ 8 q + 6 q^{2} - 20 q^{4} + 48 q^{6} + 216 q^{8} - 328 q^{9} - 50 q^{10} - 200 q^{12} + 352 q^{13} - 168 q^{14} - 272 q^{16} - 48 q^{17} + 286 q^{18} - 300 q^{20} + 16 q^{21} + 800 q^{22} + 1552 q^{24} + 1000 q^{25} - 2172 q^{26} + 40 q^{28} + 1200 q^{29} + 1400 q^{30} - 2304 q^{32} - 1120 q^{33} - 2132 q^{34} - 1044 q^{36} - 5728 q^{37} - 3360 q^{38} - 2200 q^{40} + 4896 q^{41} + 12120 q^{42} + 7920 q^{44} - 400 q^{45} + 728 q^{46} + 8640 q^{48} - 5768 q^{49} + 750 q^{50} - 12488 q^{52} + 2592 q^{53} - 17776 q^{54} + 48 q^{56} + 3840 q^{57} - 7428 q^{58} - 9800 q^{60} + 7936 q^{61} + 25680 q^{62} + 18880 q^{64} - 1200 q^{65} - 8080 q^{66} + 2712 q^{68} - 2256 q^{69} + 12000 q^{70} - 36264 q^{72} - 14448 q^{73} - 18492 q^{74} + 12000 q^{76} + 2400 q^{77} - 14480 q^{78} - 13200 q^{80} - 936 q^{81} + 27412 q^{82} + 50464 q^{84} + 11200 q^{85} - 7392 q^{86} + 18080 q^{88} + 23760 q^{89} + 19350 q^{90} - 52680 q^{92} + 11360 q^{93} - 43368 q^{94} + 2688 q^{96} - 4368 q^{97} - 21474 q^{98}+O(q^{100}) $ 8 * q + 6 * q^2 - 20 * q^4 + 48 * q^6 + 216 * q^8 - 328 * q^9 - 50 * q^10 - 200 * q^12 + 352 * q^13 - 168 * q^14 - 272 * q^16 - 48 * q^17 + 286 * q^18 - 300 * q^20 + 16 * q^21 + 800 * q^22 + 1552 * q^24 + 1000 * q^25 - 2172 * q^26 + 40 * q^28 + 1200 * q^29 + 1400 * q^30 - 2304 * q^32 - 1120 * q^33 - 2132 * q^34 - 1044 * q^36 - 5728 * q^37 - 3360 * q^38 - 2200 * q^40 + 4896 * q^41 + 12120 * q^42 + 7920 * q^44 - 400 * q^45 + 728 * q^46 + 8640 * q^48 - 5768 * q^49 + 750 * q^50 - 12488 * q^52 + 2592 * q^53 - 17776 * q^54 + 48 * q^56 + 3840 * q^57 - 7428 * q^58 - 9800 * q^60 + 7936 * q^61 + 25680 * q^62 + 18880 * q^64 - 1200 * q^65 - 8080 * q^66 + 2712 * q^68 - 2256 * q^69 + 12000 * q^70 - 36264 * q^72 - 14448 * q^73 - 18492 * q^74 + 12000 * q^76 + 2400 * q^77 - 14480 * q^78 - 13200 * q^80 - 936 * q^81 + 27412 * q^82 + 50464 * q^84 + 11200 * q^85 - 7392 * q^86 + 18080 * q^88 + 23760 * q^89 + 19350 * q^90 - 52680 * q^92 + 11360 * q^93 - 43368 * q^94 + 2688 * q^96 - 4368 * q^97 - 21474 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/20\mathbb{Z}\right)^\times$.

$n$	$11$	$17$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$	3.90006	+	0.888538i	0.975016	+	0.222134i
$2$	3.90006	+	0.888538i	0.975016	+	0.222134i
$3$		−	12.9912i		−	1.44347i	−0.692171	−	0.721733i	$-0.743346\pi$
$3$		−	12.9912i		−	1.44347i	0.692171	−	0.721733i	$-0.256654\pi$
$4$	14.4210	+	6.93071i	0.901313	+	0.433169i
$5$	−11.1803			−0.447214
$5$	−11.1803			−0.447214
$6$	11.5432	−	50.6665i	0.320644	−	1.40740i
$7$			78.0345i			1.59254i	0.604940	+	0.796271i	$0.293197\pi$
$7$			78.0345i			1.59254i	−0.604940	+	0.796271i	$0.706803\pi$
$8$	50.0846	+	39.8438i	0.782572	+	0.622560i
$9$	−87.7712			−1.08360
$10$	−43.6040	−	9.93415i	−0.436040	−	0.0993415i
$11$		−	95.6447i		−	0.790452i	−0.918584	−	0.395226i	$-0.870666\pi$
$11$		−	95.6447i		−	0.790452i	0.918584	−	0.395226i	$-0.129334\pi$
$12$	90.0382	−	187.346i	0.625265	−	1.30101i
$13$	−159.654			−0.944698			−0.472349	−	0.881412i	$-0.656594\pi$
$13$	−159.654			−0.944698			−0.472349	+	0.881412i	$0.656594\pi$
$14$	−69.3366	+	304.340i	−0.353758	+	1.55275i
$15$			145.246i			0.645538i
$16$	159.931	+	199.896i	0.624729	+	0.780842i
$17$	22.5103			0.0778903			0.0389451	−	0.999241i	$-0.487600\pi$
$17$	22.5103			0.0778903			0.0389451	+	0.999241i	$0.487600\pi$
$18$	−342.313	−	77.9881i	−1.05652	−	0.240704i
$19$		−	324.934i		−	0.900094i	−0.893005	−	0.450047i	$-0.851407\pi$
$19$		−	324.934i		−	0.900094i	0.893005	−	0.450047i	$-0.148593\pi$
$20$	−161.232	−	77.4877i	−0.403079	−	0.193719i
$21$	1013.76			2.29878
$22$	84.9839	−	373.020i	0.175587	−	0.770703i
$23$			204.951i			0.387431i	0.981058	+	0.193715i	$0.0620538\pi$
$23$			204.951i			0.387431i	−0.981058	+	0.193715i	$0.937946\pi$
$24$	517.619	−	650.659i	0.898644	−	1.12962i
$25$	125.000			0.200000
$26$	−622.661	−	141.859i	−0.921096	−	0.209850i
$27$			87.9664i			0.120667i
$28$	−540.835	+	1125.34i	−0.689840	+	1.43538i
$29$	295.747			0.351662			0.175831	−	0.984420i	$-0.443739\pi$
$29$	295.747			0.351662			0.175831	+	0.984420i	$0.443739\pi$
$30$	−129.057	+	566.469i	−0.143396	+	0.629410i
$31$		−	407.262i		−	0.423789i	−0.977293	−	0.211895i	$-0.932037\pi$
$31$		−	407.262i		−	0.423789i	0.977293	−	0.211895i	$-0.0679634\pi$
$32$	446.125	+	921.710i	0.435669	+	0.900107i
$33$	−1242.54			−1.14099
$34$	87.7916	+	20.0012i	0.0759443	+	0.0173021i
$35$		−	872.453i		−	0.712206i
$36$	−1265.75	−	608.317i	−0.976658	−	0.469380i
$37$	−2156.28			−1.57508			−0.787540	−	0.616263i	$-0.788646\pi$
$37$	−2156.28			−1.57508			−0.787540	+	0.616263i	$0.788646\pi$
$38$	288.716	−	1267.26i	0.199942	−	0.877606i
$39$			2074.10i			1.36364i
$40$	−559.963	−	445.467i	−0.349977	−	0.278417i
$41$	1368.98			0.814383			0.407191	−	0.913343i	$-0.366508\pi$
$41$	1368.98			0.814383			0.407191	+	0.913343i	$0.366508\pi$
$42$	3953.74	+	900.766i	2.24135	+	0.510638i
$43$			1234.22i			0.667507i	0.942660	+	0.333754i	$0.108315\pi$
$43$			1234.22i			0.667507i	−0.942660	+	0.333754i	$0.891685\pi$
$44$	662.885	−	1379.29i	0.342399	−	0.712444i
$45$	981.312			0.484599
$46$	−182.107	+	799.321i	−0.0860617	+	0.377751i
$47$		−	1983.43i		−	0.897887i	−0.893560	−	0.448943i	$-0.851800\pi$
$47$		−	1983.43i		−	0.897887i	0.893560	−	0.448943i	$-0.148200\pi$
$48$	2596.88	−	2077.69i	1.12712	−	0.901775i
$49$	−3688.39			−1.53619
$50$	487.508	+	111.067i	0.195003	+	0.0444269i
$51$		−	292.436i		−	0.112432i
$52$	−2302.37	−	1106.52i	−0.851468	−	0.409214i
$53$	4595.72			1.63607			0.818035	−	0.575168i	$-0.195063\pi$
$53$	4595.72			1.63607			0.818035	+	0.575168i	$0.195063\pi$
$54$	−78.1615	+	343.075i	−0.0268043	+	0.117652i
$55$			1069.34i			0.353501i
$56$	−3109.19	+	3908.33i	−0.991452	+	1.24628i
$57$	−4221.28			−1.29926
$58$	1153.43	+	262.783i	0.342876	+	0.0781161i
$59$		−	1389.15i		−	0.399068i	−0.979891	−	0.199534i	$-0.936057\pi$
$59$		−	1389.15i		−	0.399068i	0.979891	−	0.199534i	$-0.0639428\pi$
$60$	−1006.66	+	2094.59i	−0.279627	+	0.581831i
$61$	2651.94			0.712694			0.356347	−	0.934354i	$-0.384022\pi$
$61$	2651.94			0.712694			0.356347	+	0.934354i	$0.384022\pi$
$62$	361.867	−	1588.35i	0.0941382	−	0.413201i
$63$		−	6849.19i		−	1.72567i
$64$	920.941	+	3991.13i	0.224839	+	0.974396i
$65$	1784.99			0.422482
$66$	−4845.98	−	1104.04i	−1.11248	−	0.253453i
$67$			8936.51i			1.99076i	0.0960241	+	0.995379i	$0.469387\pi$
$67$			8936.51i			1.99076i	−0.0960241	+	0.995379i	$0.530613\pi$
$68$	324.621	+	156.012i	0.0702035	+	0.0337397i
$69$	2662.56			0.559243
$70$	775.207	−	3402.62i	0.158206	−	0.694413i
$71$			3375.13i			0.669535i	0.942301	+	0.334767i	$0.108658\pi$
$71$			3375.13i			0.669535i	−0.942301	+	0.334767i	$0.891342\pi$
$72$	−4395.99	−	3497.14i	−0.847992	−	0.674603i
$73$	−1467.63			−0.275404			−0.137702	−	0.990474i	$-0.543972\pi$
$73$	−1467.63			−0.275404			−0.137702	+	0.990474i	$0.543972\pi$
$74$	−8409.65	−	1915.94i	−1.53573	−	0.349880i
$75$		−	1623.90i		−	0.288693i
$76$	2252.02	−	4685.87i	0.389893	−	0.811266i
$77$	7463.59			1.25883
$78$	−1842.91	+	8089.11i	−0.302911	+	1.32957i
$79$		−	6306.01i		−	1.01042i	−0.862997	−	0.505208i	$-0.831416\pi$
$79$		−	6306.01i		−	1.01042i	0.862997	−	0.505208i	$-0.168584\pi$
$80$	−1788.08	−	2234.90i	−0.279387	−	0.349203i
$81$	−5966.68			−0.909416
$82$	5339.10	+	1216.39i	0.794036	+	0.180902i
$83$			6104.16i			0.886073i	0.896504	+	0.443037i	$0.146099\pi$
$83$			6104.16i			0.886073i	−0.896504	+	0.443037i	$0.853901\pi$
$84$	14619.5	+	7026.09i	2.07192	+	0.995761i
$85$	−251.673			−0.0348336
$86$	−1096.65	+	4813.54i	−0.148276	+	0.650830i
$87$		−	3842.11i		−	0.507612i
$88$	3810.85	−	4790.33i	0.492103	−	0.618586i
$89$	1708.55			0.215698			0.107849	−	0.994167i	$-0.465604\pi$
$89$	1708.55			0.215698			0.107849	+	0.994167i	$0.465604\pi$
$90$	3827.18	+	871.933i	0.472491	+	0.107646i
$91$		−	12458.5i		−	1.50447i
$92$	−1420.45	+	2955.60i	−0.167823	+	0.349196i
$93$	−5290.82			−0.611726
$94$	1762.35	−	7735.51i	0.199452	−	0.875454i
$95$			3632.87i			0.402534i
$96$	11974.1	−	5795.69i	1.29927	−	0.628873i
$97$	−1988.16			−0.211304			−0.105652	−	0.994403i	$-0.533693\pi$
$97$	−1988.16			−0.211304			−0.105652	+	0.994403i	$0.533693\pi$
$98$	−14385.0	−	3277.27i	−1.49781	−	0.341241i
$99$			8394.85i			0.856530i
$100$	1802.63	+	866.339i	0.180263	+	0.0866339i
$101$	−6012.56			−0.589408			−0.294704	−	0.955589i	$-0.595221\pi$
$101$	−6012.56			−0.589408			−0.294704	+	0.955589i	$0.595221\pi$
$102$	259.840	−	1140.52i	0.0249750	−	0.109623i
$103$			10161.1i			0.957780i	0.877875	+	0.478890i	$0.158961\pi$
$103$			10161.1i			0.957780i	−0.877875	+	0.478890i	$0.841039\pi$
$104$	−7996.21	−	6361.22i	−0.739295	−	0.588131i
$105$	−11334.2			−1.02805
$106$	17923.6	+	4083.47i	1.59519	+	0.363428i
$107$		−	12961.6i		−	1.13212i	−0.824364	−	0.566060i	$-0.808467\pi$
$107$		−	12961.6i		−	1.13212i	0.824364	−	0.566060i	$-0.191533\pi$
$108$	−609.670	+	1268.56i	−0.0522693	+	0.108759i
$109$	1002.18			0.0843517			0.0421758	−	0.999110i	$-0.486571\pi$
$109$	1002.18			0.0843517			0.0421758	+	0.999110i	$0.486571\pi$
$110$	−950.149	+	4170.49i	−0.0785247	+	0.344669i
$111$			28012.7i			2.27358i
$112$	−15598.8	+	12480.1i	−1.24352	+	0.994907i
$113$	−9956.56			−0.779745			−0.389872	−	0.920869i	$-0.627481\pi$
$113$	−9956.56			−0.779745			−0.389872	+	0.920869i	$0.627481\pi$
$114$	−16463.3	−	3750.77i	−1.26680	−	0.288610i
$115$		−	2291.42i		−	0.173264i
$116$	4264.97	+	2049.74i	0.316957	+	0.152329i
$117$	14013.0			1.02367
$118$	1234.32	−	5417.79i	0.0886467	−	0.389097i
$119$			1756.58i			0.124044i
$120$	−5787.16	+	7274.59i	−0.401886	+	0.505180i
$121$	5493.10			0.375186
$122$	10342.7	+	2356.35i	0.694889	+	0.158314i
$123$		−	17784.7i		−	1.17553i
$124$	2822.61	−	5873.12i	0.183573	−	0.381967i
$125$	−1397.54			−0.0894427
$126$	6085.76	−	26712.3i	0.383331	−	1.68256i
$127$		−	21746.1i		−	1.34826i	−0.738613	−	0.674130i	$-0.764519\pi$
$127$		−	21746.1i		−	1.34826i	0.738613	−	0.674130i	$-0.235481\pi$
$128$	45.4627	+	16383.9i	0.00277482	+	0.999996i
$129$	16034.0			0.963524
$130$	6961.56	+	1586.03i	0.411927	+	0.0938478i
$131$		−	26640.6i		−	1.55239i	−0.630491	−	0.776197i	$-0.717146\pi$
$131$		−	26640.6i		−	1.55239i	0.630491	−	0.776197i	$-0.282854\pi$
$132$	−17918.7	−	8611.68i	−1.02839	−	0.494242i
$133$	25356.1			1.43344
$134$	−7940.43	+	34853.0i	−0.442216	+	1.94102i
$135$		−	983.494i		−	0.0539640i
$136$	1127.42	+	896.896i	0.0609548	+	0.0484913i
$137$	34924.8			1.86077			0.930385	−	0.366584i	$-0.119473\pi$
$137$	34924.8			1.86077			0.930385	+	0.366584i	$0.119473\pi$
$138$	10384.1	+	2365.78i	0.545271	+	0.124227i
$139$			16591.6i			0.858736i	0.903130	+	0.429368i	$0.141264\pi$
$139$			16591.6i			0.858736i	−0.903130	+	0.429368i	$0.858736\pi$
$140$	6046.72	−	12581.6i	0.308506	−	0.641921i
$141$	−25767.2			−1.29607
$142$	−2998.93	+	13163.2i	−0.148727	+	0.652807i
$143$			15270.1i			0.746738i
$144$	−14037.3	−	17545.1i	−0.676953	−	0.846117i
$145$	−3306.56			−0.157268
$146$	−5723.84	−	1304.04i	−0.268523	−	0.0611767i
$147$			47916.6i			2.21744i
$148$	−31095.8	−	14944.6i	−1.41964	−	0.682276i
$149$	−10061.9			−0.453217			−0.226609	−	0.973986i	$-0.572764\pi$
$149$	−10061.9			−0.453217			−0.226609	+	0.973986i	$0.572764\pi$
$150$	1442.90	−	6333.31i	0.0641287	−	0.281481i
$151$			2823.63i			0.123838i	0.998081	+	0.0619190i	$0.0197221\pi$
$151$			2823.63i			0.123838i	−0.998081	+	0.0619190i	$0.980278\pi$
$152$	12946.6	−	16274.2i	0.560362	−	0.704389i
$153$	−1975.76			−0.0844016
$154$	29108.5	+	6631.68i	1.22738	+	0.279629i
$155$			4553.32i			0.189524i
$156$	−14375.0	+	29910.5i	−0.590687	+	1.22907i
$157$	−39136.1			−1.58774			−0.793869	−	0.608089i	$-0.791936\pi$
$157$	−39136.1			−1.58774			−0.793869	+	0.608089i	$0.791936\pi$
$158$	5603.13	−	24593.8i	0.224448	−	0.985172i
$159$		−	59703.9i		−	2.36161i
$160$	−4987.83	−	10305.0i	−0.194837	−	0.402540i
$161$	−15993.2			−0.616999
$162$	−23270.4	−	5301.62i	−0.886696	−	0.202013i
$163$		−	9169.48i		−	0.345119i	−0.984999	−	0.172560i	$-0.944796\pi$
$163$		−	9169.48i		−	0.345119i	0.984999	−	0.172560i	$-0.0552038\pi$
$164$	19742.0	+	9487.98i	0.734013	+	0.352766i
$165$	13892.0			0.510267
$166$	−5423.78	+	23806.6i	−0.196827	+	0.863936i
$167$			5446.76i			0.195301i	0.995221	+	0.0976507i	$0.0311328\pi$
$167$			5446.76i			0.195301i	−0.995221	+	0.0976507i	$0.968867\pi$
$168$	50773.9	+	40392.2i	1.79896	+	1.43113i
$169$	−3071.61			−0.107546
$170$	−981.540	−	223.621i	−0.0339633	−	0.00773774i
$171$			28519.9i			0.975338i
$172$	−8554.03	+	17798.7i	−0.289144	+	0.601633i
$173$	−16187.9			−0.540876			−0.270438	−	0.962737i	$-0.587168\pi$
$173$	−16187.9			−0.540876			−0.270438	+	0.962737i	$0.587168\pi$
$174$	3413.86	−	14984.5i	0.112758	−	0.494929i
$175$			9754.32i			0.318508i
$176$	19118.9	−	15296.5i	0.617218	−	0.493818i
$177$	−18046.8			−0.576041
$178$	6663.44	+	1518.11i	0.210309	+	0.0479140i
$179$			3484.14i			0.108740i	0.998521	+	0.0543700i	$0.0173151\pi$
$179$			3484.14i			0.108740i	−0.998521	+	0.0543700i	$0.982685\pi$
$180$	14151.5	+	6801.19i	0.436775	+	0.209913i
$181$	−12654.0			−0.386251			−0.193125	−	0.981174i	$-0.561862\pi$
$181$	−12654.0			−0.386251			−0.193125	+	0.981174i	$0.561862\pi$
$182$	11069.9	−	48589.1i	0.334195	−	1.46688i
$183$		−	34451.8i		−	1.02875i
$184$	−8166.02	+	10264.9i	−0.241199	+	0.303192i
$185$	24108.0			0.704397
$186$	−20634.5	−	4701.09i	−0.596442	−	0.135885i
$187$		−	2152.99i		−	0.0615685i
$188$	13746.6	−	28603.1i	0.388937	−	0.809277i
$189$	−6864.42			−0.192168
$190$	−3227.95	+	14168.4i	−0.0894168	+	0.392478i
$191$			12436.5i			0.340903i	0.985366	+	0.170452i	$0.0545227\pi$
$191$			12436.5i			0.340903i	−0.985366	+	0.170452i	$0.945477\pi$
$192$	51849.5	−	11964.1i	1.40651	−	0.324548i
$193$	21537.6			0.578206			0.289103	−	0.957298i	$-0.406643\pi$
$193$	21537.6			0.578206			0.289103	+	0.957298i	$0.406643\pi$
$194$	−7753.94	−	1766.55i	−0.206025	−	0.0469379i
$195$		−	23189.1i		−	0.609838i
$196$	−53190.3	−	25563.2i	−1.38459	−	0.665430i
$197$	−30840.7			−0.794679			−0.397339	−	0.917672i	$-0.630066\pi$
$197$	−30840.7			−0.794679			−0.397339	+	0.917672i	$0.630066\pi$
$198$	−7459.14	+	32740.5i	−0.190265	+	0.835131i
$199$			57562.7i			1.45357i	0.686866	+	0.726784i	$0.258986\pi$
$199$			57562.7i			1.45357i	−0.686866	+	0.726784i	$0.741014\pi$
$200$	6260.58	+	4980.48i	0.156514	+	0.124512i
$201$	116096.			2.87359
$202$	−23449.4	−	5342.38i	−0.574683	−	0.130928i
$203$			23078.5i			0.560036i
$204$	2026.79	−	4217.22i	0.0487021	−	0.101336i
$205$	−15305.6			−0.364203
$206$	−9028.51	+	39628.9i	−0.212756	+	0.933851i
$207$		−	17988.8i		−	0.419818i
$208$	−25533.5	−	31914.1i	−0.590180	−	0.737660i
$209$	−31078.2			−0.711481
$210$	−44204.1	−	10070.9i	−1.00236	−	0.228364i
$211$		−	42485.0i		−	0.954270i	−0.878830	−	0.477135i	$-0.841675\pi$
$211$		−	42485.0i		−	0.954270i	0.878830	−	0.477135i	$-0.158325\pi$
$212$	66274.9	+	31851.6i	1.47461	+	0.708695i
$213$	43846.9			0.966451
$214$	11516.9	−	50551.2i	0.251483	−	1.10384i
$215$		−	13799.0i		−	0.298518i
$216$	−3504.92	+	4405.77i	−0.0751225	+	0.0944308i
$217$	31780.5			0.674902
$218$	3908.58	+	890.477i	0.0822443	+	0.0187374i
$219$			19066.2i			0.397536i
$220$	−7411.28	+	15421.0i	−0.153126	+	0.318615i
$221$	−3593.86			−0.0735828
$222$	−24890.4	+	109251.i	−0.505039	+	2.21677i
$223$			14687.7i			0.295354i	0.989036	+	0.147677i	$0.0471796\pi$
$223$			14687.7i			0.295354i	−0.989036	+	0.147677i	$0.952820\pi$
$224$	−71925.2	+	34813.1i	−1.43346	+	0.693820i
$225$	−10971.4			−0.216719
$226$	−38831.2	−	8846.78i	−0.760264	−	0.173208i
$227$		−	54734.7i		−	1.06221i	−0.847305	−	0.531106i	$-0.821777\pi$
$227$		−	54734.7i		−	1.06221i	0.847305	−	0.531106i	$-0.178223\pi$
$228$	−60875.1	−	29256.5i	−1.17104	−	0.562798i
$229$	−14583.3			−0.278090			−0.139045	−	0.990286i	$-0.544403\pi$
$229$	−14583.3			−0.278090			−0.139045	+	0.990286i	$0.544403\pi$
$230$	2036.01	−	8936.68i	0.0384880	−	0.168935i
$231$		−	96961.0i		−	1.81708i
$232$	14812.4	+	11783.7i	0.275201	+	0.218930i
$233$	−99275.8			−1.82865			−0.914327	−	0.404976i	$-0.867280\pi$
$233$	−99275.8			−1.82865			−0.914327	+	0.404976i	$0.867280\pi$
$234$	54651.7	+	12451.1i	0.998095	+	0.227392i
$235$			22175.4i			0.401547i
$236$	9627.83	−	20033.0i	0.172864	−	0.359685i
$237$	−81922.6			−1.45850
$238$	−1560.79	+	6850.78i	−0.0275543	+	0.120944i
$239$			61775.6i			1.08149i	0.841188	+	0.540743i	$0.181857\pi$
$239$			61775.6i			1.08149i	−0.841188	+	0.540743i	$0.818143\pi$
$240$	−29034.0	+	23229.3i	−0.504063	+	0.403286i
$241$	97702.4			1.68218			0.841088	−	0.540899i	$-0.181916\pi$
$241$	97702.4			1.68218			0.841088	+	0.540899i	$0.181916\pi$
$242$	21423.4	+	4880.82i	0.365812	+	0.0833417i
$243$			84639.6i			1.43338i
$244$	38243.6	+	18379.8i	0.642360	+	0.308717i
$245$	41237.5			0.687005
$246$	15802.3	−	69361.3i	0.261127	−	1.14616i
$247$			51877.0i			0.850317i
$248$	16226.9	−	20397.5i	0.263834	−	0.331646i
$249$	79300.3			1.27902
$250$	−5450.51	−	1241.77i	−0.0872081	−	0.0198683i
$251$			72156.2i			1.14532i	0.819794	+	0.572659i	$0.194088\pi$
$251$			72156.2i			1.14532i	−0.819794	+	0.572659i	$0.805912\pi$
$252$	47469.7	−	98772.2i	0.747508	−	1.55537i
$253$	19602.5			0.306245
$254$	19322.2	−	84811.1i	0.299495	−	1.31458i
$255$			3269.53i			0.0502811i
$256$	−14380.4	+	63938.8i	−0.219428	+	0.975629i
$257$	−1740.16			−0.0263465			−0.0131732	−	0.999913i	$-0.504193\pi$
$257$	−1740.16			−0.0263465			−0.0131732	+	0.999913i	$0.504193\pi$
$258$	62533.7	+	14246.8i	0.939452	+	0.214032i
$259$		−	168265.i		−	2.50838i
$260$	25741.3	+	12371.2i	0.380788	+	0.183006i
$261$	−25958.1			−0.381059
$262$	23671.2	−	103900.i	0.344840	−	1.51361i
$263$		−	55537.8i		−	0.802929i	−0.915875	−	0.401464i	$-0.868501\pi$
$263$		−	55537.8i		−	0.802929i	0.915875	−	0.401464i	$-0.131499\pi$
$264$	−62232.1	−	49507.5i	−0.892908	−	0.710335i
$265$	−51381.7			−0.731673
$266$	98890.3	+	22529.8i	1.39762	+	0.318416i
$267$		−	22196.1i		−	0.311353i
$268$	−61936.4	+	128873.i	−0.862335	+	1.79430i
$269$	−60126.3			−0.830922			−0.415461	−	0.909611i	$-0.636380\pi$
$269$	−60126.3			−0.830922			−0.415461	+	0.909611i	$0.636380\pi$
$270$	873.872	−	3835.69i	0.0119873	−	0.0526158i
$271$			65827.7i			0.896334i	0.893950	+	0.448167i	$0.147923\pi$
$271$			65827.7i			0.896334i	−0.893950	+	0.448167i	$0.852077\pi$
$272$	3600.08	+	4499.71i	0.0486603	+	0.0608200i
$273$	−161851.			−2.17165
$274$	136209.	+	31032.0i	1.81428	+	0.413341i
$275$		−	11955.6i		−	0.158090i
$276$	38396.7	+	18453.4i	0.504053	+	0.242247i
$277$	61361.9			0.799723			0.399861	−	0.916576i	$-0.369058\pi$
$277$	61361.9			0.799723			0.399861	+	0.916576i	$0.369058\pi$
$278$	−14742.3	+	64708.5i	−0.190755	+	0.837282i
$279$			35745.8i			0.459216i
$280$	34761.8	−	43696.5i	0.443391	−	0.557353i
$281$	−26231.4			−0.332207			−0.166104	−	0.986108i	$-0.553119\pi$
$281$	−26231.4			−0.332207			−0.166104	+	0.986108i	$0.553119\pi$
$282$	−100494.	−	22895.1i	−1.26369	−	0.287902i
$283$		−	91765.5i		−	1.14579i	−0.819627	−	0.572897i	$-0.805820\pi$
$283$		−	91765.5i		−	1.14579i	0.819627	−	0.572897i	$-0.194180\pi$
$284$	−23392.0	+	48672.7i	−0.290022	+	0.603460i
$285$	47195.4			0.581045
$286$	−13568.0	+	59554.2i	−0.165876	+	0.728082i
$287$			106828.i			1.29694i
$288$	−39156.9	−	80899.6i	−0.472089	−	0.975352i
$289$	−83014.3			−0.993933
$290$	−12895.8	−	2938.00i	−0.153339	−	0.0349346i
$291$			25828.6i			0.305010i
$292$	−21164.7	−	10171.7i	−0.248225	−	0.119297i
$293$	82014.2			0.955331			0.477665	−	0.878542i	$-0.341483\pi$
$293$	82014.2			0.955331			0.477665	+	0.878542i	$0.341483\pi$
$294$	−42575.7	+	186878.i	−0.492569	+	2.16204i
$295$			15531.2i			0.178469i
$296$	−107997.	−	85914.6i	−1.23261	−	0.980581i
$297$	8413.52			0.0953816
$298$	−39242.0	−	8940.36i	−0.441894	−	0.100675i
$299$		−	32721.2i		−	0.366005i
$300$	11254.8	−	23418.3i	0.125053	−	0.260203i
$301$	−96311.9			−1.06303
$302$	−2508.90	+	11012.3i	−0.0275087	+	0.120744i
$303$			78110.3i			0.850791i
$304$	64952.9	−	51966.9i	0.702831	−	0.562315i
$305$	−29649.5			−0.318727
$306$	−7705.58	−	1755.53i	−0.0822929	−	0.0187485i
$307$			14373.1i			0.152501i	0.997089	+	0.0762507i	$0.0242949\pi$
$307$			14373.1i			0.152501i	−0.997089	+	0.0762507i	$0.975705\pi$
$308$	107632.	+	51728.0i	1.13460	+	0.545285i
$309$	132005.			1.38252
$310$	−4045.80	+	17758.2i	−0.0420999	+	0.184789i
$311$		−	178570.i		−	1.84623i	−0.384520	−	0.923117i	$-0.625633\pi$
$311$		−	178570.i		−	1.84623i	0.384520	−	0.923117i	$-0.374367\pi$
$312$	−82639.9	+	103880.i	−0.848947	+	1.06715i
$313$	188132.			1.92032			0.960162	−	0.279444i	$-0.0901501\pi$
$313$	188132.			1.92032			0.960162	+	0.279444i	$0.0901501\pi$
$314$	−152633.	−	34773.9i	−1.54807	−	0.352691i
$315$			76576.3i			0.771744i
$316$	43705.1	−	90939.0i	0.437681	−	0.910701i
$317$	104987.			1.04477			0.522383	−	0.852711i	$-0.325043\pi$
$317$	104987.			1.04477			0.522383	+	0.852711i	$0.325043\pi$
$318$	53049.2	−	232849.i	0.524596	−	2.30261i
$319$		−	28286.7i		−	0.277971i
$320$	−10296.4	−	44622.1i	−0.100551	−	0.435763i
$321$	−168387.			−1.63418
$322$	−62374.7	−	14210.6i	−0.601584	−	0.137057i
$323$		−	7314.36i		−	0.0701086i
$324$	−86045.5	−	41353.3i	−0.819668	−	0.393931i
$325$	−19956.7			−0.188940
$326$	8147.43	−	35761.5i	0.0766629	−	0.336497i
$327$		−	13019.6i		−	0.121759i
$328$	68564.7	+	54545.3i	0.637313	+	0.507002i
$329$	154776.			1.42992
$330$	54179.7	+	12343.6i	0.497518	+	0.113348i
$331$			107333.i			0.979660i	0.871818	+	0.489830i	$0.162941\pi$
$331$			107333.i			0.979660i	−0.871818	+	0.489830i	$0.837059\pi$
$332$	−42306.1	+	88028.1i	−0.383820	+	0.798629i
$333$	189260.			1.70675
$334$	−4839.65	+	21242.7i	−0.0433832	+	0.190422i
$335$		−	99913.2i		−	0.890294i
$336$	162132.	+	202647.i	1.43611	+	1.79498i
$337$	48193.1			0.424351			0.212176	−	0.977232i	$-0.431945\pi$
$337$	48193.1			0.424351			0.212176	+	0.977232i	$0.431945\pi$
$338$	−11979.5	−	2729.24i	−0.104859	−	0.0238896i
$339$			129348.i			1.12554i
$340$	−3629.37	−	1744.27i	−0.0313960	−	0.0150888i
$341$	−38952.4			−0.334985
$342$	−25341.0	+	111229.i	−0.216656	+	0.950970i
$343$		−	100461.i		−	0.853904i
$344$	−49176.1	+	61815.5i	−0.415563	+	0.522373i
$345$	−29768.3			−0.250101
$346$	−63133.7	−	14383.5i	−0.527362	−	0.120147i
$347$		−	158887.i		−	1.31956i	−0.751460	−	0.659778i	$-0.770650\pi$
$347$		−	158887.i		−	1.31956i	0.751460	−	0.659778i	$-0.229350\pi$
$348$	26628.6	−	55407.1i	0.219882	−	0.457517i
$349$	−155827.			−1.27935			−0.639677	−	0.768643i	$-0.720932\pi$
$349$	−155827.			−1.27935			−0.639677	+	0.768643i	$0.720932\pi$
$350$	−8667.08	+	38042.5i	−0.0707517	+	0.310551i
$351$		−	14044.2i		−	0.113994i
$352$	88156.6	−	42669.4i	0.711491	−	0.344375i
$353$	−197430.			−1.58439			−0.792197	−	0.610265i	$-0.791063\pi$
$353$	−197430.			−1.58439			−0.792197	+	0.610265i	$0.791063\pi$
$354$	−70383.6	−	16035.3i	−0.561649	−	0.127959i
$355$		−	37735.0i		−	0.299425i
$356$	24638.9	+	11841.4i	0.194412	+	0.0934339i
$357$	22820.1			0.179053
$358$	−3095.79	+	13588.4i	−0.0241549	+	0.106023i
$359$			12434.1i			0.0964774i	0.998836	+	0.0482387i	$0.0153608\pi$
$359$			12434.1i			0.0964774i	−0.998836	+	0.0482387i	$0.984639\pi$
$360$	49148.7	+	39099.2i	0.379233	+	0.301692i
$361$	24738.9			0.189830
$362$	−49351.2	−	11243.5i	−0.376601	−	0.0857996i
$363$		−	71361.9i		−	0.541568i
$364$	86346.4	−	179664.i	0.651691	−	1.35600i
$365$	16408.6			0.123164
$366$	30611.8	−	134364.i	0.228521	−	1.00305i
$367$		−	112753.i		−	0.837136i	−0.908185	−	0.418568i	$-0.862532\pi$
$367$		−	112753.i		−	0.837136i	0.908185	−	0.418568i	$-0.137468\pi$
$368$	−40968.7	+	32777.9i	−0.302522	+	0.242039i
$369$	−120157.			−0.882461
$370$	94022.7	+	21420.9i	0.686799	+	0.156471i
$371$			358625.i			2.60551i
$372$	−76298.9	−	36669.1i	−0.551356	−	0.264981i
$373$	129467.			0.930552			0.465276	−	0.885166i	$-0.345955\pi$
$373$	129467.			0.930552			0.465276	+	0.885166i	$0.345955\pi$
$374$	1913.01	−	8396.80i	0.0136765	−	0.0600303i
$375$			18155.8i			0.129108i
$376$	79027.5	−	99339.5i	0.558988	−	0.702661i
$377$	−47217.2			−0.332214
$378$	−26771.7	−	6099.30i	−0.187366	−	0.0426870i
$379$			259093.i			1.80376i	0.431990	+	0.901878i	$0.357812\pi$
$379$			259093.i			1.80376i	−0.431990	+	0.901878i	$0.642188\pi$
$380$	−25178.4	+	52389.7i	−0.174366	+	0.362809i
$381$	−282508.			−1.94617
$382$	−11050.3	+	48503.1i	−0.0757264	+	0.332386i
$383$			191511.i			1.30556i	0.757548	+	0.652780i	$0.226397\pi$
$383$			191511.i			1.30556i	−0.757548	+	0.652780i	$0.773603\pi$
$384$	212847.	−	590.615i	1.44346	−	0.00400536i
$385$	−83445.5			−0.562965
$386$	83998.1	+	19137.0i	0.563761	+	0.128440i
$387$		−	108329.i		−	0.723308i
$388$	−28671.2	−	13779.3i	−0.190451	−	0.0915303i
$389$	255416.			1.68791			0.843954	−	0.536415i	$-0.180222\pi$
$389$	255416.			1.68791			0.843954	+	0.536415i	$0.180222\pi$
$390$	20604.4	−	90439.0i	0.135466	−	0.594602i
$391$			4613.50i			0.0301771i
$392$	−184732.	−	146960.i	−1.20218	−	0.956369i
$393$	−346094.			−2.24083
$394$	−120281.	−	27403.1i	−0.774825	−	0.176526i
$395$			70503.3i			0.451872i
$396$	−58182.3	+	121062.i	−0.371023	+	0.772001i
$397$	−142760.			−0.905789			−0.452894	−	0.891564i	$-0.649609\pi$
$397$	−142760.			−0.905789			−0.452894	+	0.891564i	$0.649609\pi$
$398$	−51146.7	+	224498.i	−0.322887	+	1.41725i
$399$		−	329406.i		−	2.06912i
$400$	19991.3	+	24986.9i	0.124946	+	0.156168i
$401$	194681.			1.21070			0.605348	−	0.795961i	$-0.293034\pi$
$401$	194681.			1.21070			0.605348	+	0.795961i	$0.293034\pi$
$402$	452782.	+	103156.i	2.80180	+	0.638324i
$403$			65020.9i			0.400353i
$404$	−86707.1	−	41671.3i	−0.531241	−	0.255314i
$405$	66709.5			0.406703
$406$	−20506.1	+	90007.7i	−0.124403	+	0.546044i
$407$			206237.i			1.24503i
$408$	11651.8	−	14646.5i	0.0699956	−	0.0879862i
$409$	−89149.0			−0.532930			−0.266465	−	0.963845i	$-0.585856\pi$
$409$	−89149.0			−0.532930			−0.266465	+	0.963845i	$0.585856\pi$
$410$	−59692.9	−	13599.6i	−0.355104	−	0.0809020i
$411$		−	453715.i		−	2.68596i
$412$	−70423.6	+	146533.i	−0.414881	+	0.863259i
$413$	108402.			0.635532
$414$	15983.7	−	70157.4i	0.0932560	−	0.409329i
$415$		−	68246.6i		−	0.396264i
$416$	−71225.6	−	147155.i	−0.411575	−	0.850329i
$417$	215545.			1.23956
$418$	−121207.	−	27614.2i	−0.693706	−	0.158044i
$419$		−	316683.i		−	1.80384i	−0.431906	−	0.901918i	$-0.642159\pi$
$419$		−	316683.i		−	1.80384i	0.431906	−	0.901918i	$-0.357841\pi$
$420$	−163451.	−	78554.1i	−0.926591	−	0.445318i
$421$	107801.			0.608217			0.304109	−	0.952637i	$-0.401641\pi$
$421$	107801.			0.608217			0.304109	+	0.952637i	$0.401641\pi$
$422$	37749.6	−	165694.i	0.211976	−	0.930428i
$423$			174088.i			0.972946i
$424$	230175.	+	183111.i	1.28034	+	1.01855i
$425$	2813.79			0.0155781
$426$	171006.	+	38959.6i	0.942305	+	0.214682i
$427$			206943.i			1.13500i
$428$	89833.4	−	186920.i	0.490400	−	1.02039i
$429$	198376.			1.07789
$430$	12260.9	−	53817.0i	0.0663112	−	0.291060i
$431$		−	122818.i		−	0.661160i	−0.943778	−	0.330580i	$-0.892756\pi$
$431$		−	122818.i		−	0.661160i	0.943778	−	0.330580i	$-0.107244\pi$
$432$	−17584.1	+	14068.5i	−0.0942220	+	0.0753843i
$433$	−182503.			−0.973406			−0.486703	−	0.873567i	$-0.661801\pi$
$433$	−182503.			−0.973406			−0.486703	+	0.873567i	$0.661801\pi$
$434$	123946.	+	28238.1i	0.658040	+	0.149919i
$435$			42956.1i			0.227011i
$436$	14452.5	+	6945.84i	0.0760272	+	0.0365386i
$437$	66595.5			0.348724
$438$	−16941.1	+	74359.6i	−0.0883065	+	0.387604i
$439$			284219.i			1.47477i	0.675473	+	0.737385i	$0.263940\pi$
$439$			284219.i			1.47477i	−0.675473	+	0.737385i	$0.736060\pi$
$440$	−42606.6	+	53557.5i	−0.220075	+	0.276640i
$441$	323735.			1.66461
$442$	−14016.3	−	3193.28i	−0.0717444	−	0.0163453i
$443$		−	290002.i		−	1.47772i	−0.673858	−	0.738861i	$-0.735364\pi$
$443$		−	290002.i		−	1.47772i	0.673858	−	0.738861i	$-0.264636\pi$
$444$	−194148.	+	403972.i	−0.984843	+	2.04920i
$445$	−19102.1			−0.0964632
$446$	−13050.5	+	57282.8i	−0.0656083	+	0.287975i
$447$			130716.i			0.654204i
$448$	−311446.	+	71865.2i	−1.55177	+	0.358066i
$449$	53644.3			0.266091			0.133046	−	0.991110i	$-0.457524\pi$
$449$	53644.3			0.266091			0.133046	+	0.991110i	$0.457524\pi$
$450$	−42789.2	−	9748.51i	−0.211305	−	0.0481408i
$451$		−	130935.i		−	0.643730i
$452$	−143584.	−	69006.0i	−0.702794	−	0.337761i
$453$	36682.4			0.178756
$454$	48633.9	−	213469.i	0.235954	−	1.03567i
$455$			139291.i			0.672820i
$456$	−211421.	−	168192.i	−1.01676	−	0.808864i
$457$	51320.3			0.245729			0.122865	−	0.992423i	$-0.460792\pi$
$457$	51320.3			0.245729			0.122865	+	0.992423i	$0.460792\pi$
$458$	−56876.0	−	12957.8i	−0.271143	−	0.0617735i
$459$			1980.15i			0.00939881i
$460$	15881.2	−	33044.6i	0.0750527	−	0.156165i
$461$	71282.3			0.335413			0.167706	−	0.985837i	$-0.446364\pi$
$461$	71282.3			0.335413			0.167706	+	0.985837i	$0.446364\pi$
$462$	86153.5	−	378154.i	0.403635	−	1.77168i
$463$		−	107296.i		−	0.500519i	−0.968179	−	0.250260i	$-0.919484\pi$
$463$		−	107296.i		−	0.500519i	0.968179	−	0.250260i	$-0.0805160\pi$
$464$	47299.0	+	59118.6i	0.219693	+	0.274592i
$465$	59153.1			0.273572
$466$	−387182.	−	88210.3i	−1.78297	−	0.406207i
$467$			32462.5i			0.148850i	0.997227	+	0.0744248i	$0.0237121\pi$
$467$			32462.5i			0.148850i	−0.997227	+	0.0744248i	$0.976288\pi$
$468$	202082.	+	97120.2i	0.922647	+	0.443423i
$469$	−697357.			−3.17037
$470$	−19703.7	+	86485.7i	−0.0891975	+	0.391515i
$471$			508425.i			2.29185i
$472$	55349.2	−	69575.3i	0.248443	−	0.312299i
$473$	118047.			0.527632
$474$	−319503.	−	72791.3i	−1.42206	−	0.323984i
$475$		−	40616.8i		−	0.180019i
$476$	−12174.3	+	25331.7i	−0.0537319	+	0.111802i
$477$	−403372.			−1.77284
$478$	−54890.0	+	240929.i	−0.240235	+	1.05447i
$479$		−	33919.3i		−	0.147835i	−0.997264	−	0.0739173i	$-0.976450\pi$
$479$		−	33919.3i		−	0.147835i	0.997264	−	0.0739173i	$-0.0235501\pi$
$480$	−133875.	+	64797.8i	−0.581053	+	0.281241i
$481$	344259.			1.48798
$482$	381046.	+	86812.3i	1.64015	+	0.373669i
$483$			207771.i			0.890618i
$484$	79216.0	+	38071.1i	0.338160	+	0.162519i
$485$	22228.3			0.0944980
$486$	−75205.5	+	330100.i	−0.318403	+	1.39757i
$487$		−	324548.i		−	1.36843i	−0.729282	−	0.684213i	$-0.760146\pi$
$487$		−	324548.i		−	1.36843i	0.729282	−	0.684213i	$-0.239854\pi$
$488$	132821.	+	105663.i	0.557735	+	0.443695i
$489$	−119122.			−0.498168
$490$	160829.	+	36641.0i	0.669841	+	0.152607i
$491$		−	119081.i		−	0.493946i	−0.969022	−	0.246973i	$-0.920564\pi$
$491$		−	119081.i		−	0.493946i	0.969022	−	0.246973i	$-0.0794358\pi$
$492$	123260.	−	256473.i	0.509205	−	1.05952i
$493$	6657.36			0.0273910
$494$	−46094.7	+	202324.i	−0.188885	+	0.829073i
$495$		−	93857.3i		−	0.383052i
$496$	81409.8	−	65133.6i	0.330912	−	0.264753i
$497$	−263376.			−1.06626
$498$	309276.	+	70461.3i	1.24706	+	0.284114i
$499$		−	8360.30i		−	0.0335754i	−0.999859	−	0.0167877i	$-0.994656\pi$
$499$		−	8360.30i		−	0.0335754i	0.999859	−	0.0167877i	$-0.00534394\pi$
$500$	−20154.0	−	9685.96i	−0.0806158	−	0.0387438i
$501$	70759.9			0.281911
$502$	−64113.5	+	281414.i	−0.254415	+	1.11670i
$503$		−	400265.i		−	1.58202i	−0.611805	−	0.791009i	$-0.709556\pi$
$503$		−	400265.i		−	1.58202i	0.611805	−	0.791009i	$-0.290444\pi$
$504$	272898.	−	343039.i	1.07433	−	1.35046i
$505$	67222.4			0.263591
$506$	76450.8	+	17417.5i	0.298594	+	0.0680276i
$507$			39903.9i			0.155238i
$508$	150716.	−	313600.i	0.584025	−	1.21520i
$509$	271797.			1.04908			0.524541	−	0.851385i	$-0.324237\pi$
$509$	271797.			1.04908			0.524541	+	0.851385i	$0.324237\pi$
$510$	−2905.10	+	12751.4i	−0.0111692	+	0.0490249i
$511$		−	114526.i		−	0.438592i
$512$	−112897.	+	236588.i	−0.430667	+	0.902511i
$513$	28583.3			0.108612
$514$	−6786.73	−	1546.20i	−0.0256882	−	0.00585246i
$515$		−	113604.i		−	0.428332i
$516$	231226.	+	111127.i	0.868437	+	0.417369i
$517$	−189705.			−0.709736
$518$	149510.	−	656243.i	0.557198	−	2.44571i
$519$			210300.i			0.780736i
$520$	89400.4	+	71120.6i	0.330623	+	0.263020i
$521$	−347896.			−1.28166			−0.640832	−	0.767681i	$-0.721410\pi$
$521$	−347896.			−1.28166			−0.640832	+	0.767681i	$0.721410\pi$
$522$	−101238.	−	23064.8i	−0.371538	−	0.0846463i
$523$			275580.i			1.00750i	0.863850	+	0.503750i	$0.168047\pi$
$523$			275580.i			1.00750i	−0.863850	+	0.503750i	$0.831953\pi$
$524$	184638.	−	384184.i	0.672449	−	1.39919i
$525$	126720.			0.459756
$526$	49347.4	−	216601.i	0.178358	−	0.782868i
$527$		−	9167.58i		−	0.0330091i
$528$	−198720.	−	248378.i	−0.712810	−	0.890933i
$529$	237836.			0.849898
$530$	−200392.	−	45654.6i	−0.713393	−	0.162530i
$531$			121928.i			0.432428i
$532$	365660.	+	175736.i	1.29198	+	0.620921i
$533$	−218563.			−0.769346
$534$	19722.0	−	86566.1i	0.0691623	−	0.303574i
$535$			144916.i			0.506299i
$536$	−356065.	+	447582.i	−1.23937	+	1.55791i
$537$	45263.2			0.156963
$538$	−234497.	−	53424.5i	−0.810162	−	0.184576i
$539$			352775.i			1.21428i
$540$	6816.31	−	14183.0i	0.0233756	−	0.0486385i
$541$	−96023.1			−0.328081			−0.164041	−	0.986454i	$-0.552453\pi$
$541$	−96023.1			−0.328081			−0.164041	+	0.986454i	$0.552453\pi$
$542$	−58490.4	+	256732.i	−0.199107	+	0.873940i
$543$			164390.i			0.557540i
$544$	10042.4	+	20748.0i	0.0339344	+	0.0701096i
$545$	−11204.7			−0.0377232
$546$	−631230.	−	143811.i	−2.11740	−	0.482399i
$547$			102032.i			0.341007i	0.985357	+	0.170503i	$0.0545394\pi$
$547$			102032.i			0.341007i	−0.985357	+	0.170503i	$0.945461\pi$
$548$	503650.	+	242054.i	1.67714	+	0.806028i
$549$	−232764.			−0.772272
$550$	10623.0	−	46627.5i	0.0351173	−	0.154141i
$551$		−	96098.4i		−	0.316529i
$552$	133353.	+	106086.i	0.437648	+	0.348162i
$553$	492087.			1.60913
$554$	239315.	+	54522.4i	0.779743	+	0.177646i
$555$		−	313192.i		−	1.01677i
$556$	−114992.	+	239268.i	−0.371978	+	0.773990i
$557$	−423559.			−1.36522			−0.682612	−	0.730781i	$-0.739156\pi$
$557$	−423559.			−1.36522			−0.682612	+	0.730781i	$0.739156\pi$
$558$	−31761.5	+	139411.i	−0.102008	+	0.447743i
$559$		−	197048.i		−	0.630593i
$560$	174399.	−	139532.i	0.556121	−	0.444936i
$561$	−27969.9			−0.0888721
$562$	−102304.	−	23307.6i	−0.323907	−	0.0737946i
$563$			498724.i			1.57342i	0.617325	+	0.786708i	$0.288216\pi$
$563$			498724.i			1.57342i	−0.617325	+	0.786708i	$0.711784\pi$
$564$	−371588.	−	178585.i	−1.16816	−	0.561418i
$565$	111318.			0.348712
$566$	81537.1	−	357891.i	0.254520	−	1.11717i
$567$		−	465607.i		−	1.44828i
$568$	−134478.	+	169042.i	−0.416825	+	0.523960i
$569$	237219.			0.732697			0.366349	−	0.930478i	$-0.380608\pi$
$569$	237219.			0.732697			0.366349	+	0.930478i	$0.380608\pi$
$570$	184065.	+	41934.9i	0.566528	+	0.129070i
$571$		−	281100.i		−	0.862161i	−0.902314	−	0.431080i	$-0.858133\pi$
$571$		−	281100.i		−	0.862161i	0.902314	−	0.431080i	$-0.141867\pi$
$572$	−105832.	+	220209.i	−0.323464	+	0.673045i
$573$	161565.			0.492083
$574$	−94920.3	+	416634.i	−0.288095	+	1.26454i
$575$			25618.8i			0.0774861i
$576$	−80832.1	−	350306.i	−0.243635	−	1.05585i
$577$	404501.			1.21498			0.607489	−	0.794328i	$-0.292177\pi$
$577$	404501.			1.21498			0.607489	+	0.794328i	$0.292177\pi$
$578$	−323761.	−	73761.3i	−0.969101	−	0.220787i
$579$		−	279799.i		−	0.834622i
$580$	−47683.8	−	22916.8i	−0.141747	−	0.0681236i
$581$	−476335.			−1.41111
$582$	−22949.6	+	100733.i	−0.0677532	+	0.297390i
$583$		−	439556.i		−	1.29323i
$584$	−73505.6	−	58475.9i	−0.215524	−	0.171455i
$585$	−156670.			−0.457799
$586$	319861.	+	72872.7i	0.931463	+	0.212212i
$587$			335843.i			0.974675i	0.873214	+	0.487337i	$0.162032\pi$
$587$			335843.i			0.974675i	−0.873214	+	0.487337i	$0.837968\pi$
$588$	−332096.	+	691006.i	−0.960526	+	1.99860i
$589$	−132333.			−0.381450
$590$	−13800.1	+	60572.8i	−0.0396440	+	0.174010i
$591$			400658.i			1.14709i
$592$	−344856.	−	431032.i	−0.983998	−	1.22989i
$593$	−139571.			−0.396905			−0.198452	−	0.980111i	$-0.563592\pi$
$593$	−139571.			−0.396905			−0.198452	+	0.980111i	$0.563592\pi$
$594$	32813.3	+	7475.73i	0.0929986	+	0.0211875i
$595$		−	19639.2i		−	0.0554740i
$596$	−145102.	−	69735.9i	−0.408490	−	0.196320i
$597$	747809.			2.09818
$598$	29074.0	−	127615.i	0.0813023	−	0.356861i
$599$			71633.1i			0.199646i	0.995005	+	0.0998228i	$0.0318276\pi$
$599$			71633.1i			0.199646i	−0.995005	+	0.0998228i	$0.968172\pi$
$600$	64702.4	−	81332.4i	0.179729	−	0.225923i
$601$	524251.			1.45141			0.725706	−	0.688005i	$-0.241514\pi$
$601$	524251.			1.45141			0.725706	+	0.688005i	$0.241514\pi$
$602$	−375623.	−	85576.8i	−1.03647	−	0.236136i
$603$		−	784369.i		−	2.15718i
$604$	−19569.8	+	40719.6i	−0.0536428	+	0.111617i
$605$	−61414.7			−0.167788
$606$	−69404.0	+	304635.i	−0.188990	+	0.829535i
$607$			89856.9i			0.243879i	0.992538	+	0.121939i	$0.0389114\pi$
$607$			89856.9i			0.243879i	−0.992538	+	0.121939i	$0.961089\pi$
$608$	299495.	−	144961.i	0.810181	−	0.392143i
$609$	299817.			0.808393
$610$	−115635.	−	26344.7i	−0.310764	−	0.0708002i
$611$			316663.i			0.848232i
$612$	−28492.4	−	13693.4i	−0.0760722	−	0.0365602i
$613$	58041.7			0.154461			0.0772305	−	0.997013i	$-0.475392\pi$
$613$	58041.7			0.154461			0.0772305	+	0.997013i	$0.475392\pi$
$614$	−12771.0	+	56056.0i	−0.0338758	+	0.148691i
$615$			198839.i			0.525715i
$616$	373811.	+	297378.i	0.985124	+	0.783695i
$617$	−251038.			−0.659431			−0.329716	−	0.944080i	$-0.606953\pi$
$617$	−251038.			−0.659431			−0.329716	+	0.944080i	$0.606953\pi$
$618$	514827.	+	117291.i	1.34798	+	0.307106i
$619$			37372.0i			0.0975360i	0.998810	+	0.0487680i	$0.0155295\pi$
$619$			37372.0i			0.0975360i	−0.998810	+	0.0487680i	$0.984470\pi$
$620$	−31557.8	+	65663.5i	−0.0820961	+	0.170821i
$621$	−18028.8			−0.0467502
$622$	158666.	−	696433.i	0.410112	−	1.80011i
$623$			133326.i			0.343509i
$624$	−414603.	+	331711.i	−1.06479	+	0.851905i
$625$	15625.0			0.0400000
$626$	733728.	+	167163.i	1.87235	+	0.426570i
$627$			403743.i			1.02700i
$628$	−564382.	−	271241.i	−1.43105	−	0.687759i
$629$	−48538.6			−0.122683
$630$	−68040.9	+	298652.i	−0.171431	+	0.752462i
$631$			81639.6i			0.205042i	0.994731	+	0.102521i	$0.0326908\pi$
$631$			81639.6i			0.205042i	−0.994731	+	0.102521i	$0.967309\pi$
$632$	251255.	−	315834.i	0.629044	−	0.790724i
$633$	−551932.			−1.37746
$634$	409458.	+	93285.3i	1.01866	+	0.232078i
$635$			243129.i			0.602960i
$636$	413791.	−	860990.i	1.02298	−	2.12855i
$637$	588866.			1.45124
$638$	25133.8	−	110320.i	0.0617470	−	0.271027i
$639$		−	296239.i		−	0.725505i
$640$	−508.288	−	183178.i	−0.00124094	−	0.447212i
$641$	−72207.4			−0.175738			−0.0878690	−	0.996132i	$-0.528006\pi$
$641$	−72207.4			−0.175738			−0.0878690	+	0.996132i	$0.528006\pi$
$642$	−656721.	−	149618.i	−1.59335	−	0.363007i
$643$			221605.i			0.535990i	0.963420	+	0.267995i	$0.0863611\pi$
$643$			221605.i			0.535990i	−0.963420	+	0.267995i	$0.913639\pi$
$644$	−230639.	−	110845.i	−0.556109	−	0.267265i
$645$	−179266.			−0.430901
$646$	6499.09	−	28526.5i	0.0155735	−	0.0683570i
$647$		−	388806.i		−	0.928805i	−0.885624	−	0.464403i	$-0.846269\pi$
$647$		−	388806.i		−	0.928805i	0.885624	−	0.464403i	$-0.153731\pi$
$648$	−298839.	−	237735.i	−0.711684	−	0.566166i
$649$	−132865.			−0.315444
$650$	−77832.6	−	17732.3i	−0.184219	−	0.0419700i
$651$		−	412866.i		−	0.974199i
$652$	63551.0	−	132233.i	0.149495	−	0.311060i
$653$	32328.2			0.0758150			0.0379075	−	0.999281i	$-0.487931\pi$
$653$	32328.2			0.0758150			0.0379075	+	0.999281i	$0.487931\pi$
$654$	11568.4	−	50777.1i	0.0270468	−	0.118717i
$655$			297851.i			0.694252i
$656$	218941.	+	273652.i	0.508768	+	0.635904i
$657$	128816.			0.298427
$658$	603637.	+	137525.i	1.39420	+	0.317635i
$659$		−	593355.i		−	1.36629i	−0.730282	−	0.683146i	$-0.760611\pi$
$659$		−	593355.i		−	1.36629i	0.730282	−	0.683146i	$-0.239389\pi$
$660$	200337.	+	96281.5i	0.459910	+	0.221032i
$661$	−574565.			−1.31503			−0.657516	−	0.753440i	$-0.728393\pi$
$661$	−574565.			−1.31503			−0.657516	+	0.753440i	$0.728393\pi$
$662$	−95369.0	+	418604.i	−0.217616	+	0.955185i
$663$			46688.5i			0.106214i
$664$	−243213.	+	305725.i	−0.551633	+	0.693416i
$665$	−283490.			−0.641053
$666$	738125.	+	168164.i	1.66411	+	0.379128i
$667$			60613.6i			0.136244i
$668$	−37749.9	+	78547.7i	−0.0845986	+	0.176028i
$669$	190810.			0.426334
$670$	88776.7	−	389668.i	0.197765	−	0.868051i
$671$		−	253644.i		−	0.563351i
$672$	452264.	+	934395.i	1.00151	+	2.06915i
$673$	296688.			0.655043			0.327522	−	0.944844i	$-0.393787\pi$
$673$	296688.			0.655043			0.327522	+	0.944844i	$0.393787\pi$
$674$	187956.	+	42821.4i	0.413749	+	0.0942630i
$675$			10995.8i			0.0241334i
$676$	−44295.6	−	21288.4i	−0.0969321	−	0.0465854i
$677$	−348459.			−0.760282			−0.380141	−	0.924929i	$-0.624125\pi$
$677$	−348459.			−0.760282			−0.380141	+	0.924929i	$0.624125\pi$
$678$	−114930.	+	504464.i	−0.250020	+	1.09741i
$679$		−	155145.i		−	0.336510i
$680$	−12604.9	−	10027.6i	−0.0272598	−	0.0216860i
$681$	−711070.			−1.53327
$682$	−151917.	−	34610.7i	−0.326616	−	0.0744117i
$683$			555433.i			1.19067i	0.803479	+	0.595333i	$0.202980\pi$
$683$			555433.i			1.19067i	−0.803479	+	0.595333i	$0.797020\pi$
$684$	−197663.	+	411285.i	−0.422487	+	0.879085i
$685$	−390471.			−0.832162
$686$	89263.4	−	391804.i	0.189682	−	0.832570i
$687$			189455.i			0.401414i
$688$	−246715.	+	197390.i	−0.521218	+	0.417011i
$689$	−733725.			−1.54559
$690$	−116098.	−	26450.2i	−0.243853	−	0.0555561i
$691$		−	417213.i		−	0.873780i	−0.899515	−	0.436890i	$-0.856080\pi$
$691$		−	417213.i		−	0.873780i	0.899515	−	0.436890i	$-0.143920\pi$
$692$	−233445.	−	112193.i	−0.487498	−	0.234291i
$693$	−655088.			−1.36406
$694$	141177.	−	619668.i	0.293119	−	1.28659i
$695$		−	185500.i		−	0.384039i
$696$	153084.	−	192431.i	0.316018	−	0.397243i
$697$	30816.1			0.0634325
$698$	−607734.	−	138458.i	−1.24739	−	0.284189i
$699$			1.28971e6i			2.63960i
$700$	−67604.3	+	140667.i	−0.137968	+	0.287076i
$701$	752354.			1.53104			0.765519	−	0.643413i	$-0.222482\pi$
$701$	752354.			1.53104			0.765519	+	0.643413i	$0.222482\pi$
$702$	12478.8	−	54773.2i	0.0253220	−	0.111146i
$703$			700650.i			1.41772i
$704$	381730.	−	88083.1i	0.770213	−	0.177724i
$705$	288086.			0.579620
$706$	−769989.	−	175424.i	−1.54481	−	0.351949i
$707$		−	469187.i		−	0.938658i
$708$	−260253.	−	125077.i	−0.519193	−	0.249523i
$709$	480953.			0.956775			0.478388	−	0.878149i	$-0.341221\pi$
$709$	480953.			0.956775			0.478388	+	0.878149i	$0.341221\pi$
$710$	33529.0	−	147169.i	0.0665126	−	0.291944i
$711$			553486.i			1.09488i
$712$	85571.9	+	68075.0i	0.168800	+	0.134285i
$713$	83468.6			0.164189
$714$	88999.8	+	20276.5i	0.174579	+	0.0397738i
$715$		−	170724.i		−	0.333952i
$716$	−24147.6	+	50244.8i	−0.0471029	+	0.0980088i
$717$	802539.			1.56109
$718$	−11048.2	+	48493.8i	−0.0214310	+	0.0940670i
$719$			298189.i			0.576811i	0.957508	+	0.288406i	$0.0931251\pi$
$719$			298189.i			0.576811i	−0.957508	+	0.288406i	$0.906875\pi$
$720$	156942.	+	196160.i	0.302743	+	0.378395i
$721$	−792916.			−1.52531
$722$	96483.2	+	21981.4i	0.185087	+	0.0421678i
$723$		−	1.26927e6i		−	2.42816i
$724$	−182483.	−	87700.9i	−0.348133	−	0.167312i
$725$	36968.4			0.0703323
$726$	63407.8	−	278316.i	0.120301	−	0.528038i
$727$		−	104436.i		−	0.197597i	−0.995107	−	0.0987984i	$-0.968500\pi$
$727$		−	104436.i		−	0.197597i	0.995107	−	0.0987984i	$-0.0314999\pi$
$728$	496395.	−	623981.i	0.936623	−	1.17736i
$729$	616269.			1.15962
$730$	63994.5	+	14579.6i	0.120087	+	0.0273591i
$731$			27782.7i			0.0519923i
$732$	238776.	−	496830.i	0.445623	−	0.927226i
$733$	−442720.			−0.823988			−0.411994	−	0.911187i	$-0.635167\pi$
$733$	−442720.			−0.823988			−0.411994	+	0.911187i	$0.635167\pi$
$734$	100185.	−	439744.i	0.185957	−	0.816221i
$735$		−	535724.i		−	0.991668i
$736$	−188905.	+	91433.6i	−0.348729	+	0.168791i
$737$	854730.			1.57360
$738$	−468619.	−	106764.i	−0.860414	−	0.196025i
$739$		−	316611.i		−	0.579744i	−0.957065	−	0.289872i	$-0.906387\pi$
$739$		−	316611.i		−	0.579744i	0.957065	−	0.289872i	$-0.0936128\pi$
$740$	347661.	+	167086.i	0.634882	+	0.305123i
$741$	673945.			1.22740
$742$	−318652.	+	1.39866e6i	−0.578774	+	2.54041i
$743$			249871.i			0.452626i	0.974055	+	0.226313i	$0.0726671\pi$
$743$			249871.i			0.452626i	−0.974055	+	0.226313i	$0.927333\pi$
$744$	−264989.	−	210806.i	−0.478720	−	0.380836i
$745$	112495.			0.202685
$746$	504929.	+	115036.i	0.907303	+	0.206708i
$747$		−	535769.i		−	0.960145i
$748$	14921.7	−	31048.3i	0.0266696	−	0.0554925i
$749$	1.01146e6			1.80295
$750$	−16132.1	+	70808.6i	−0.0286792	+	0.125882i
$751$			745034.i			1.32098i	0.750835	+	0.660490i	$0.229651\pi$
$751$			745034.i			1.32098i	−0.750835	+	0.660490i	$0.770349\pi$
$752$	396479.	−	317211.i	0.701108	−	0.560936i
$753$	937395.			1.65323
$754$	−184150.	−	41954.3i	−0.323914	−	0.0737962i
$755$		−	31569.2i		−	0.0553821i
$756$	−98991.8	−	47575.3i	−0.173203	−	0.0832411i
$757$	−602045.			−1.05060			−0.525300	−	0.850917i	$-0.676047\pi$
$757$	−602045.			−1.05060			−0.525300	+	0.850917i	$0.676047\pi$
$758$	−230214.	+	1.01048e6i	−0.400677	+	1.75869i
$759$		−	254659.i		−	0.442055i
$760$	−144748.	+	181951.i	−0.250602	+	0.315012i
$761$	−46391.1			−0.0801061			−0.0400530	−	0.999198i	$-0.512753\pi$
$761$	−46391.1			−0.0801061			−0.0400530	+	0.999198i	$0.512753\pi$
$762$	−1.10180e6	−	251019.i	−1.89755	−	0.432311i
$763$			78204.9i			0.134334i
$764$	−86193.7	+	179347.i	−0.147669	+	0.307260i
$765$	22089.6			0.0377455
$766$	−170165.	+	746906.i	−0.290010	+	1.27294i
$767$			221784.i			0.376999i
$768$	830642.	+	186819.i	1.40829	+	0.316737i
$769$	−169035.			−0.285841			−0.142920	−	0.989734i	$-0.545649\pi$
$769$	−169035.			−0.285841			−0.142920	+	0.989734i	$0.545649\pi$
$770$	−325443.	−	74144.4i	−0.548900	−	0.125054i
$771$			22606.7i			0.0380302i
$772$	310594.	+	149271.i	0.521145	+	0.250461i
$773$	581948.			0.973924			0.486962	−	0.873423i	$-0.338105\pi$
$773$	581948.			0.973924			0.486962	+	0.873423i	$0.338105\pi$
$774$	96254.5	−	422490.i	0.160672	−	0.705237i
$775$		−	50907.7i		−	0.0847579i
$776$	−99576.2	−	79215.8i	−0.165361	−	0.131549i
$777$	−2.18596e6			−3.62076
$778$	996139.	+	226947.i	1.64574	+	0.374943i
$779$		−	444827.i		−	0.733021i
$780$	160717.	−	334410.i	0.264163	−	0.549655i
$781$	322813.			0.529235
$782$	−4099.27	+	17993.0i	−0.00670337	+	0.0294231i
$783$			26015.8i			0.0424340i
$784$	−589886.	−	737293.i	−0.959702	−	1.19952i
$785$	437555.			0.710058
$786$	−1.34979e6	−	307517.i	−2.18484	−	0.497765i
$787$		−	739795.i		−	1.19443i	−0.802080	−	0.597217i	$-0.796273\pi$
$787$		−	739795.i		−	1.19443i	0.802080	−	0.597217i	$-0.203727\pi$
$788$	−444754.	−	213748.i	−0.716254	−	0.344231i
$789$	−721502.			−1.15900
$790$	−62644.9	+	274967.i	−0.100376	+	0.440582i
$791$		−	776956.i		−	1.24178i
$792$	−334483.	+	420453.i	−0.533241	+	0.670297i
$793$	−423392.			−0.673281
$794$	−556775.	−	126848.i	−0.883159	−	0.201207i
$795$			667510.i			1.05615i
$796$	−398951.	+	830112.i	−0.629641	+	1.31012i
$797$	−59513.8			−0.0936917			−0.0468459	−	0.998902i	$-0.514917\pi$
$797$	−59513.8			−0.0936917			−0.0468459	+	0.998902i	$0.514917\pi$
$798$	292690.	−	1.28470e6i	0.459623	−	2.01742i
$799$		−	44647.6i		−	0.0699367i
$800$	55765.6	+	115214.i	0.0871337	+	0.180021i
$801$	−149961.			−0.233730
$802$	759269.	+	172981.i	1.18045	+	0.268937i
$803$			140371.i			0.217694i
$804$	1.67422e6	+	804628.i	2.59000	+	1.24475i
$805$	178810.			0.275931
$806$	−57773.6	+	253586.i	−0.0889322	+	0.390351i
$807$			781113.i			1.19941i
$808$	−301137.	−	239563.i	−0.461255	−	0.366942i
$809$	−1.07133e6			−1.63691			−0.818457	−	0.574568i	$-0.805170\pi$
$809$	−1.07133e6			−1.63691			−0.818457	+	0.574568i	$0.805170\pi$
$810$	260171.	+	59273.9i	0.396542	+	0.0903428i
$811$			1.12103e6i			1.70442i	0.523199	+	0.852211i	$0.324738\pi$
$811$			1.12103e6i			1.70442i	−0.523199	+	0.852211i	$0.675262\pi$
$812$	−159950.	+	332815.i	−0.242590	+	0.504767i
$813$	855181.			1.29383
$814$	−183250.	+	804338.i	−0.276563	+	1.21392i
$815$			102518.i			0.154342i
$816$	58456.6	−	46769.4i	0.0877916	−	0.0702395i
$817$	401040.			0.600820
$818$	−347687.	−	79212.3i	−0.519615	−	0.118382i
$819$			1.09350e6i			1.63024i
$820$	−220723.	−	106079.i	−0.328261	−	0.157762i
$821$	210197.			0.311846			0.155923	−	0.987769i	$-0.450165\pi$
$821$	210197.			0.311846			0.155923	+	0.987769i	$0.450165\pi$
$822$	403143.	−	1.76952e6i	0.596644	−	2.61885i
$823$		−	501270.i		−	0.740068i	−0.929018	−	0.370034i	$-0.879346\pi$
$823$		−	501270.i		−	0.740068i	0.929018	−	0.370034i	$-0.120654\pi$
$824$	−404857.	+	508915.i	−0.596275	+	0.749532i
$825$	−155317.			−0.228198
$826$	422775.	+	96319.3i	0.619654	+	0.141174i
$827$			599224.i			0.876149i	0.898939	+	0.438075i	$0.144339\pi$
$827$			599224.i			0.876149i	−0.898939	+	0.438075i	$0.855661\pi$
$828$	124675.	−	259416.i	0.181852	−	0.378387i
$829$	−92189.6			−0.134145			−0.0670723	−	0.997748i	$-0.521366\pi$
$829$	−92189.6			−0.134145			−0.0670723	+	0.997748i	$0.521366\pi$
$830$	60639.7	−	266166.i	0.0880239	−	0.386364i
$831$		−	797165.i		−	1.15437i
$832$	−147032.	−	637199.i	−0.212405	−	0.920510i
$833$	−83026.8			−0.119654
$834$	840641.	+	191520.i	1.20859	+	0.275348i
$835$		−	60896.6i		−	0.0873414i
$836$	−448179.	−	215394.i	−0.641267	−	0.308192i
$837$	35825.3			0.0511375
$838$	281385.	−	1.23509e6i	0.400694	−	1.75877i
$839$		−	16114.0i		−	0.0228918i	−0.999934	−	0.0114459i	$-0.996357\pi$
$839$		−	16114.0i		−	0.0228918i	0.999934	−	0.0114459i	$-0.00364342\pi$
$840$	−567670.	−	451598.i	−0.804520	−	0.640020i
$841$	−619815.			−0.876334
$842$	420431.	+	95785.3i	0.593022	+	0.135106i
$843$			340777.i			0.479530i
$844$	294452.	−	612677.i	0.413360	−	0.860095i
$845$	34341.6			0.0480958
$846$	−154684.	+	678955.i	−0.216125	+	0.948638i
$847$			428651.i			0.597499i
$848$	734996.	+	918664.i	1.02210	+	1.27751i
$849$	−1.19214e6			−1.65391
$850$	10973.9	+	2500.16i	0.0151889	+	0.00346042i
$851$		−	441932.i		−	0.610234i
$852$	632317.	+	303890.i	0.871075	+	0.418637i
$853$	−596015.			−0.819142			−0.409571	−	0.912278i	$-0.634322\pi$
$853$	−596015.			−0.819142			−0.409571	+	0.912278i	$0.634322\pi$
$854$	−183876.	+	807090.i	−0.252122	+	1.10664i
$855$		−	318862.i		−	0.436184i
$856$	516441.	−	649179.i	0.704812	−	0.885966i
$857$	−14006.7			−0.0190710			−0.00953550	−	0.999955i	$-0.503035\pi$
$857$	−14006.7			−0.0190710			−0.00953550	+	0.999955i	$0.503035\pi$
$858$	773680.	+	176265.i	1.05096	+	0.239437i
$859$		−	221377.i		−	0.300017i	−0.988685	−	0.150008i	$-0.952070\pi$
$859$		−	221377.i		−	0.300017i	0.988685	−	0.150008i	$-0.0479301\pi$
$860$	95636.9	−	198996.i	0.129309	−	0.269058i
$861$	1.38782e6			1.87209
$862$	109128.	−	478997.i	0.146866	−	0.644641i
$863$		−	1.44444e6i		−	1.93945i	−0.244208	−	0.969723i	$-0.578528\pi$
$863$		−	1.44444e6i		−	1.93945i	0.244208	−	0.969723i	$-0.421472\pi$
$864$	−81079.5	+	39244.0i	−0.108613	+	0.0525709i
$865$	180986.			0.241887
$866$	−711773.	−	162161.i	−0.949087	−	0.216227i
$867$			1.07846e6i			1.43471i
$868$	458306.	+	220261.i	0.608298	+	0.292347i
$869$	−603136.			−0.798686
$870$	−38168.1	+	167532.i	−0.0504269	+	0.221339i
$871$		−	1.42675e6i		−	1.88067i
$872$	50193.9	+	39930.8i	0.0660113	+	0.0525140i
$873$	174503.			0.228968
$874$	259727.	+	59172.6i	0.340012	+	0.0774636i
$875$		−	109057.i		−	0.142441i
$876$	−132143.	+	274954.i	−0.172201	+	0.358305i
$877$	−1.25884e6			−1.63671			−0.818353	−	0.574715i	$-0.805113\pi$
$877$	−1.25884e6			−1.63671			−0.818353	+	0.574715i	$0.805113\pi$
$878$	−252539.	+	1.10847e6i	−0.327597	+	1.43792i
$879$		−	1.06546e6i		−	1.37899i
$880$	−213756.	+	171020.i	−0.276028	+	0.220842i
$881$	491927.			0.633795			0.316897	−	0.948460i	$-0.397359\pi$
$881$	491927.			0.633795			0.316897	+	0.948460i	$0.397359\pi$
$882$	1.26259e6	+	287650.i	1.62302	+	0.369767i
$883$			97635.7i			0.125224i	0.998038	+	0.0626120i	$0.0199431\pi$
$883$			97635.7i			0.125224i	−0.998038	+	0.0626120i	$0.980057\pi$
$884$	−51827.0	−	24908.0i	−0.0663211	−	0.0318738i
$885$	201769.			0.257613
$886$	257677.	−	1.13102e6i	0.328253	−	1.44080i
$887$			668572.i			0.849769i	0.905248	+	0.424884i	$0.139685\pi$
$887$			668572.i			0.849769i	−0.905248	+	0.424884i	$0.860315\pi$
$888$	−1.11613e6	+	1.40301e6i	−1.41544	+	1.77924i
$889$	1.69695e6			2.14716
$890$	−74499.5	−	16973.0i	−0.0940532	−	0.0214278i
$891$			570681.i			0.718850i
$892$	−101796.	+	211811.i	−0.127938	+	0.266206i
$893$	−644485.			−0.808183
$894$	−116146.	+	509800.i	−0.145321	+	0.637859i
$895$		−	38953.9i		−	0.0486300i
$896$	−1.27851e6	+	3547.66i	−1.59254	+	0.00441902i
$897$	−425088.			−0.528316
$898$	209216.	+	47665.0i	0.259443	+	0.0591081i
$899$		−	120447.i		−	0.149030i
$900$	−158219.	−	76039.6i	−0.195332	−	0.0938761i
$901$	103451.			0.127434
$902$	116341.	−	510656.i	0.142995	−	0.627647i
$903$			1.25121e6i			1.53445i
$904$	−498671.	−	396707.i	−0.610207	−	0.485438i
$905$	141476.			0.172737
$906$	143064.	+	32593.7i	0.174290	+	0.0397079i
$907$		−	659118.i		−	0.801214i	−0.916250	−	0.400607i	$-0.868799\pi$
$907$		−	659118.i		−	0.801214i	0.916250	−	0.400607i	$-0.131201\pi$
$908$	379351.	−	789330.i	0.460118	−	0.957385i
$909$	527729.			0.638680
$910$	−123765.	+	543242.i	−0.149456	+	0.656010i
$911$			852700.i			1.02745i	0.857956	+	0.513724i	$0.171734\pi$
$911$			852700.i			1.02745i	−0.857956	+	0.513724i	$0.828266\pi$
$912$	−675112.	−	843816.i	−0.811682	−	1.01451i
$913$	583830.			0.700398
$914$	200152.	+	45600.0i	0.239590	+	0.0545849i
$915$			385183.i			0.460071i
$916$	−210306.	−	101073.i	−0.250646	−	0.120460i
$917$	2.07889e6			2.47225
$918$	−1759.44	+	7722.71i	−0.00208780	+	0.00916399i
$919$			1.11737e6i			1.32302i	0.749936	+	0.661511i	$0.230084\pi$
$919$			1.11737e6i			1.32302i	−0.749936	+	0.661511i	$0.769916\pi$
$920$	91298.9	−	114765.i	0.107867	−	0.135592i
$921$	186724.			0.220131
$922$	278005.	+	63337.0i	0.327033	+	0.0745067i
$923$		−	538852.i		−	0.632508i
$924$	672008.	−	1.39827e6i	0.787101	−	1.63775i
$925$	−269536.			−0.315016
$926$	95336.4	−	418461.i	0.111183	−	0.488014i
$927$		−	891852.i		−	1.03785i
$928$	131940.	+	272593.i	0.153208	+	0.316533i
$929$	−59813.4			−0.0693054			−0.0346527	−	0.999399i	$-0.511033\pi$
$929$	−59813.4			−0.0693054			−0.0346527	+	0.999399i	$0.511033\pi$
$930$	230701.	+	52559.8i	0.266737	+	0.0607698i
$931$			1.19848e6i			1.38272i
$932$	−1.43166e6	−	688052.i	−1.64819	−	0.792117i
$933$	−2.31983e6			−2.66498
$934$	−28844.1	+	126606.i	−0.0330646	+	0.145131i
$935$			24071.2i			0.0275343i
$936$	701837.	+	558332.i	0.801096	+	0.637296i
$937$	−981955.			−1.11844			−0.559220	−	0.829019i	$-0.688899\pi$
$937$	−981955.			−1.11844			−0.559220	+	0.829019i	$0.688899\pi$
$938$	−2.71974e6	−	619628.i	−3.09116	−	0.704247i
$939$		−	2.44406e6i		−	2.77192i
$940$	−153692.	+	319792.i	−0.173938	+	0.361920i
$941$	1.07255e6			1.21126			0.605629	−	0.795747i	$-0.292921\pi$
$941$	1.07255e6			1.21126			0.605629	+	0.795747i	$0.292921\pi$
$942$	−451755.	+	1.98289e6i	−0.509098	+	2.23459i
$943$			280573.i			0.315517i
$944$	277686.	−	222168.i	0.311609	−	0.249309i
$945$	76746.5			0.0859400
$946$	460390.	+	104889.i	0.514450	+	0.117205i
$947$		−	877745.i		−	0.978742i	−0.872076	−	0.489371i	$-0.837226\pi$
$947$		−	877745.i		−	0.978742i	0.872076	−	0.489371i	$-0.162774\pi$
$948$	−1.18141e6	−	567782.i	−1.31457	−	0.631778i
$949$	234313.			0.260174
$950$	36089.5	−	158408.i	0.0399884	−	0.175521i
$951$		−	1.36391e6i		−	1.50808i
$952$	−69988.9	+	87977.7i	−0.0772245	+	0.0970731i
$953$	1.25729e6			1.38436			0.692181	−	0.721724i	$-0.256650\pi$
$953$	1.25729e6			1.38436			0.692181	+	0.721724i	$0.256650\pi$
$954$	−1.57318e6	−	358411.i	−1.72855	−	0.393808i
$955$		−	139044.i		−	0.152457i
$956$	−428149.	+	890866.i	−0.468467	+	0.974758i
$957$	−367478.			−0.401243
$958$	30138.6	−	132287.i	0.0328391	−	0.144141i
$959$			2.72534e6i			2.96335i
$960$	−579695.	+	133763.i	−0.629009	+	0.145142i
$961$	757659.			0.820403
$962$	1.34263e6	+	305888.i	1.45080	+	0.330531i
$963$			1.13766e6i			1.22676i
$964$	1.40897e6	+	677147.i	1.51617	+	0.728667i
$965$	−240798.			−0.258582
$966$	−184613.	+	810322.i	−0.197837	+	0.868367i
$967$			506655.i			0.541825i	0.962604	+	0.270913i	$0.0873254\pi$
$967$			506655.i			0.541825i	−0.962604	+	0.270913i	$0.912675\pi$
$968$	275120.	+	218866.i	0.293610	+	0.233576i
$969$	−95022.3			−0.101199
$970$	86691.7	+	19750.7i	0.0921370	+	0.0209913i
$971$			424048.i			0.449755i	0.974387	+	0.224878i	$0.0721982\pi$
$971$			424048.i			0.449755i	−0.974387	+	0.224878i	$0.927802\pi$
$972$	−586613.	+	1.22059e6i	−0.620896	+	1.29192i
$973$	−1.29472e6			−1.36757
$974$	288374.	−	1.26576e6i	0.303975	−	1.33424i
$975$			259262.i			0.272728i
$976$	424126.	+	530110.i	0.445241	+	0.556502i
$977$	−269406.			−0.282240			−0.141120	−	0.989993i	$-0.545070\pi$
$977$	−269406.			−0.282240			−0.141120	+	0.989993i	$0.545070\pi$
$978$	−464585.	−	105845.i	−0.485722	−	0.110660i
$979$		−	163413.i		−	0.170499i
$980$	594685.	+	285805.i	0.619206	+	0.297589i
$981$	−87962.8			−0.0914031
$982$	105808.	−	464423.i	0.109722	−	0.481605i
$983$			758850.i			0.785325i	0.919683	+	0.392662i	$0.128446\pi$
$983$			758850.i			0.785325i	−0.919683	+	0.392662i	$0.871554\pi$
$984$	708609.	−	890738.i	0.731840	−	0.919941i
$985$	344809.			0.355391
$986$	25964.1	+	5915.32i	0.0267067	+	0.00608449i
$987$		−	2.01073e6i		−	2.06404i
$988$	−359544.	+	748118.i	−0.368331	+	0.766402i
$989$	−252955.			−0.258613
$990$	83395.7	−	366049.i	0.0850890	−	0.373482i
$991$		−	1.22397e6i		−	1.24630i	−0.782102	−	0.623150i	$-0.785853\pi$
$991$		−	1.22397e6i		−	1.24630i	0.782102	−	0.623150i	$-0.214147\pi$
$992$	375377.	−	181689.i	0.381456	−	0.184632i
$993$	1.39438e6			1.41411
$994$	−1.02718e6	−	234020.i	−1.03962	−	0.236854i
$995$		−	643571.i		−	0.650055i
$996$	1.14359e6	+	549608.i	1.15279	+	0.554031i
$997$	1.31108e6			1.31898			0.659489	−	0.751714i	$-0.270773\pi$
$997$	1.31108e6			1.31898			0.659489	+	0.751714i	$0.270773\pi$
$998$	7428.45	−	32605.7i	0.00745825	−	0.0327365i
$999$		−	189681.i		−	0.190061i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.5.b.a.11.8	yes	8
3.2	odd	2		180.5.c.a.91.1		8
4.3	odd	2	inner	20.5.b.a.11.7	✓	8
5.2	odd	4		100.5.d.c.99.8		16
5.3	odd	4		100.5.d.c.99.9		16
5.4	even	2		100.5.b.c.51.1		8
8.3	odd	2		320.5.b.d.191.2		8
8.5	even	2		320.5.b.d.191.7		8
12.11	even	2		180.5.c.a.91.2		8
20.3	even	4		100.5.d.c.99.7		16
20.7	even	4		100.5.d.c.99.10		16
20.19	odd	2		100.5.b.c.51.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.5.b.a.11.7	✓	8	4.3	odd	2	inner
20.5.b.a.11.8	yes	8	1.1	even	1	trivial
100.5.b.c.51.1		8	5.4	even	2
100.5.b.c.51.2		8	20.19	odd	2
100.5.d.c.99.7		16	20.3	even	4
100.5.d.c.99.8		16	5.2	odd	4
100.5.d.c.99.9		16	5.3	odd	4
100.5.d.c.99.10		16	20.7	even	4
180.5.c.a.91.1		8	3.2	odd	2
180.5.c.a.91.2		8	12.11	even	2
320.5.b.d.191.2		8	8.3	odd	2
320.5.b.d.191.7		8	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	20.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(3.90006 + 0.888538i) q^{2} -12.9912i q^{3} +(14.4210 + 6.93071i) q^{4} -11.1803 q^{5} +(11.5432 - 50.6665i) q^{6} +78.0345i q^{7} +(50.0846 + 39.8438i) q^{8} -87.7712 q^{9} +O(q^{10})\)	\(q+(3.90006 + 0.888538i) q^{2} -12.9912i q^{3} +(14.4210 + 6.93071i) q^{4} -11.1803 q^{5} +(11.5432 - 50.6665i) q^{6} +78.0345i q^{7} +(50.0846 + 39.8438i) q^{8} -87.7712 q^{9} +(-43.6040 - 9.93415i) q^{10} -95.6447i q^{11} +(90.0382 - 187.346i) q^{12} -159.654 q^{13} +(-69.3366 + 304.340i) q^{14} +145.246i q^{15} +(159.931 + 199.896i) q^{16} +22.5103 q^{17} +(-342.313 - 77.9881i) q^{18} -324.934i q^{19} +(-161.232 - 77.4877i) q^{20} +1013.76 q^{21} +(84.9839 - 373.020i) q^{22} +204.951i q^{23} +(517.619 - 650.659i) q^{24} +125.000 q^{25} +(-622.661 - 141.859i) q^{26} +87.9664i q^{27} +(-540.835 + 1125.34i) q^{28} +295.747 q^{29} +(-129.057 + 566.469i) q^{30} -407.262i q^{31} +(446.125 + 921.710i) q^{32} -1242.54 q^{33} +(87.7916 + 20.0012i) q^{34} -872.453i q^{35} +(-1265.75 - 608.317i) q^{36} -2156.28 q^{37} +(288.716 - 1267.26i) q^{38} +2074.10i q^{39} +(-559.963 - 445.467i) q^{40} +1368.98 q^{41} +(3953.74 + 900.766i) q^{42} +1234.22i q^{43} +(662.885 - 1379.29i) q^{44} +981.312 q^{45} +(-182.107 + 799.321i) q^{46} -1983.43i q^{47} +(2596.88 - 2077.69i) q^{48} -3688.39 q^{49} +(487.508 + 111.067i) q^{50} -292.436i q^{51} +(-2302.37 - 1106.52i) q^{52} +4595.72 q^{53} +(-78.1615 + 343.075i) q^{54} +1069.34i q^{55} +(-3109.19 + 3908.33i) q^{56} -4221.28 q^{57} +(1153.43 + 262.783i) q^{58} -1389.15i q^{59} +(-1006.66 + 2094.59i) q^{60} +2651.94 q^{61} +(361.867 - 1588.35i) q^{62} -6849.19i q^{63} +(920.941 + 3991.13i) q^{64} +1784.99 q^{65} +(-4845.98 - 1104.04i) q^{66} +8936.51i q^{67} +(324.621 + 156.012i) q^{68} +2662.56 q^{69} +(775.207 - 3402.62i) q^{70} +3375.13i q^{71} +(-4395.99 - 3497.14i) q^{72} -1467.63 q^{73} +(-8409.65 - 1915.94i) q^{74} -1623.90i q^{75} +(2252.02 - 4685.87i) q^{76} +7463.59 q^{77} +(-1842.91 + 8089.11i) q^{78} -6306.01i q^{79} +(-1788.08 - 2234.90i) q^{80} -5966.68 q^{81} +(5339.10 + 1216.39i) q^{82} +6104.16i q^{83} +(14619.5 + 7026.09i) q^{84} -251.673 q^{85} +(-1096.65 + 4813.54i) q^{86} -3842.11i q^{87} +(3810.85 - 4790.33i) q^{88} +1708.55 q^{89} +(3827.18 + 871.933i) q^{90} -12458.5i q^{91} +(-1420.45 + 2955.60i) q^{92} -5290.82 q^{93} +(1762.35 - 7735.51i) q^{94} +3632.87i q^{95} +(11974.1 - 5795.69i) q^{96} -1988.16 q^{97} +(-14385.0 - 3277.27i) q^{98} +8394.85i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{2} - 20 q^{4} + 48 q^{6} + 216 q^{8} - 328 q^{9}+O(q^{10}) \) 8 * q + 6 * q^2 - 20 * q^4 + 48 * q^6 + 216 * q^8 - 328 * q^9	\( 8 q + 6 q^{2} - 20 q^{4} + 48 q^{6} + 216 q^{8} - 328 q^{9} - 50 q^{10} - 200 q^{12} + 352 q^{13} - 168 q^{14} - 272 q^{16} - 48 q^{17} + 286 q^{18} - 300 q^{20} + 16 q^{21} + 800 q^{22} + 1552 q^{24} + 1000 q^{25} - 2172 q^{26} + 40 q^{28} + 1200 q^{29} + 1400 q^{30} - 2304 q^{32} - 1120 q^{33} - 2132 q^{34} - 1044 q^{36} - 5728 q^{37} - 3360 q^{38} - 2200 q^{40} + 4896 q^{41} + 12120 q^{42} + 7920 q^{44} - 400 q^{45} + 728 q^{46} + 8640 q^{48} - 5768 q^{49} + 750 q^{50} - 12488 q^{52} + 2592 q^{53} - 17776 q^{54} + 48 q^{56} + 3840 q^{57} - 7428 q^{58} - 9800 q^{60} + 7936 q^{61} + 25680 q^{62} + 18880 q^{64} - 1200 q^{65} - 8080 q^{66} + 2712 q^{68} - 2256 q^{69} + 12000 q^{70} - 36264 q^{72} - 14448 q^{73} - 18492 q^{74} + 12000 q^{76} + 2400 q^{77} - 14480 q^{78} - 13200 q^{80} - 936 q^{81} + 27412 q^{82} + 50464 q^{84} + 11200 q^{85} - 7392 q^{86} + 18080 q^{88} + 23760 q^{89} + 19350 q^{90} - 52680 q^{92} + 11360 q^{93} - 43368 q^{94} + 2688 q^{96} - 4368 q^{97} - 21474 q^{98}+O(q^{100}) \) 8 * q + 6 * q^2 - 20 * q^4 + 48 * q^6 + 216 * q^8 - 328 * q^9 - 50 * q^10 - 200 * q^12 + 352 * q^13 - 168 * q^14 - 272 * q^16 - 48 * q^17 + 286 * q^18 - 300 * q^20 + 16 * q^21 + 800 * q^22 + 1552 * q^24 + 1000 * q^25 - 2172 * q^26 + 40 * q^28 + 1200 * q^29 + 1400 * q^30 - 2304 * q^32 - 1120 * q^33 - 2132 * q^34 - 1044 * q^36 - 5728 * q^37 - 3360 * q^38 - 2200 * q^40 + 4896 * q^41 + 12120 * q^42 + 7920 * q^44 - 400 * q^45 + 728 * q^46 + 8640 * q^48 - 5768 * q^49 + 750 * q^50 - 12488 * q^52 + 2592 * q^53 - 17776 * q^54 + 48 * q^56 + 3840 * q^57 - 7428 * q^58 - 9800 * q^60 + 7936 * q^61 + 25680 * q^62 + 18880 * q^64 - 1200 * q^65 - 8080 * q^66 + 2712 * q^68 - 2256 * q^69 + 12000 * q^70 - 36264 * q^72 - 14448 * q^73 - 18492 * q^74 + 12000 * q^76 + 2400 * q^77 - 14480 * q^78 - 13200 * q^80 - 936 * q^81 + 27412 * q^82 + 50464 * q^84 + 11200 * q^85 - 7392 * q^86 + 18080 * q^88 + 23760 * q^89 + 19350 * q^90 - 52680 * q^92 + 11360 * q^93 - 43368 * q^94 + 2688 * q^96 - 4368 * q^97 - 21474 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more