LMFDB - Embedded newform 74.5.d.b.31.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,5,Mod(31,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("74.31");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	74.d (of order $4$, degree $2$, 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:	$7.64937726820$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 727 x^{12} + 207381 x^{10} + 29788577 x^{8} + 2302194203 x^{6} + 92916575085 x^{4} + \cdots + 6531254919424 $ x^14 + 727x^12 + 207381x^10 + 29788577x^8 + 2302194203x^6 + 92916575085x^4 + 1658451585508x^2 + 6531254919424
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.5
Root			$6.93683i$ of defining polynomial
Character	$\chi$	$=$	74.31
Dual form			74.5.d.b.43.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 + 2.00000i) q^{2} +5.93683i q^{3} +8.00000i q^{4} +(34.8311 - 34.8311i) q^{5} +(-11.8737 + 11.8737i) q^{6} +33.1642 q^{7} +(-16.0000 + 16.0000i) q^{8} +45.7541 q^{9} +O(q^{10})$	\(q+(2.00000 + 2.00000i) q^{2} +5.93683i q^{3} +8.00000i q^{4} +(34.8311 - 34.8311i) q^{5} +(-11.8737 + 11.8737i) q^{6} +33.1642 q^{7} +(-16.0000 + 16.0000i) q^{8} +45.7541 q^{9} +139.324 q^{10} +4.42515i q^{11} -47.4946 q^{12} +(-155.523 + 155.523i) q^{13} +(66.3284 + 66.3284i) q^{14} +(206.786 + 206.786i) q^{15} -64.0000 q^{16} +(29.7847 - 29.7847i) q^{17} +(91.5081 + 91.5081i) q^{18} +(-367.142 + 367.142i) q^{19} +(278.649 + 278.649i) q^{20} +196.890i q^{21} +(-8.85031 + 8.85031i) q^{22} +(647.183 - 647.183i) q^{23} +(-94.9893 - 94.9893i) q^{24} -1801.41i q^{25} -622.093 q^{26} +752.517i q^{27} +265.314i q^{28} +(-558.837 - 558.837i) q^{29} +827.145i q^{30} +(928.228 + 928.228i) q^{31} +(-128.000 - 128.000i) q^{32} -26.2714 q^{33} +119.139 q^{34} +(1155.15 - 1155.15i) q^{35} +366.033i q^{36} +(-1012.61 + 921.290i) q^{37} -1468.57 q^{38} +(-923.315 - 923.315i) q^{39} +1114.60i q^{40} -1994.29i q^{41} +(-393.780 + 393.780i) q^{42} +(-223.022 + 223.022i) q^{43} -35.4012 q^{44} +(1593.66 - 1593.66i) q^{45} +2588.73 q^{46} -3142.01 q^{47} -379.957i q^{48} -1301.14 q^{49} +(3602.82 - 3602.82i) q^{50} +(176.827 + 176.827i) q^{51} +(-1244.19 - 1244.19i) q^{52} -1011.94 q^{53} +(-1505.03 + 1505.03i) q^{54} +(154.133 + 154.133i) q^{55} +(-530.627 + 530.627i) q^{56} +(-2179.66 - 2179.66i) q^{57} -2235.35i q^{58} +(550.662 - 550.662i) q^{59} +(-1654.29 + 1654.29i) q^{60} +(-1174.38 - 1174.38i) q^{61} +3712.91i q^{62} +1517.40 q^{63} -512.000i q^{64} +10834.1i q^{65} +(-52.5428 - 52.5428i) q^{66} -2319.11i q^{67} +(238.278 + 238.278i) q^{68} +(3842.21 + 3842.21i) q^{69} +4620.58 q^{70} -3068.87 q^{71} +(-732.065 + 732.065i) q^{72} -11.2597i q^{73} +(-3867.81 - 182.645i) q^{74} +10694.7 q^{75} +(-2937.13 - 2937.13i) q^{76} +146.757i q^{77} -3693.26i q^{78} +(-2103.45 + 2103.45i) q^{79} +(-2229.19 + 2229.19i) q^{80} -761.486 q^{81} +(3988.58 - 3988.58i) q^{82} +9140.45 q^{83} -1575.12 q^{84} -2074.87i q^{85} -892.087 q^{86} +(3317.72 - 3317.72i) q^{87} +(-70.8025 - 70.8025i) q^{88} +(2126.17 + 2126.17i) q^{89} +6374.66 q^{90} +(-5157.81 + 5157.81i) q^{91} +(5177.46 + 5177.46i) q^{92} +(-5510.73 + 5510.73i) q^{93} +(-6284.02 - 6284.02i) q^{94} +25575.9i q^{95} +(759.914 - 759.914i) q^{96} +(6567.54 - 6567.54i) q^{97} +(-2602.27 - 2602.27i) q^{98} +202.469i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 28 q^{2} + 36 q^{5} + 40 q^{6} - 48 q^{7} - 224 q^{8} - 346 q^{9}+O(q^{10}) $ 14 * q + 28 * q^2 + 36 * q^5 + 40 * q^6 - 48 * q^7 - 224 * q^8 - 346 * q^9	\( 14 q + 28 q^{2} + 36 q^{5} + 40 q^{6} - 48 q^{7} - 224 q^{8} - 346 q^{9} + 144 q^{10} + 160 q^{12} - 104 q^{13} - 96 q^{14} - 378 q^{15} - 896 q^{16} + 516 q^{17} - 692 q^{18} - 328 q^{19} + 288 q^{20} - 320 q^{22} + 154 q^{23} + 320 q^{24} - 416 q^{26} + 1686 q^{29} + 3834 q^{31} - 1792 q^{32} + 2104 q^{33} + 2064 q^{34} - 1502 q^{35} + 2640 q^{37} - 1312 q^{38} - 4526 q^{39} - 5984 q^{42} + 3616 q^{43} - 1280 q^{44} - 2238 q^{45} + 616 q^{46} - 6892 q^{47} + 12854 q^{49} + 7516 q^{50} - 6742 q^{51} - 832 q^{52} + 12572 q^{53} - 1072 q^{54} + 5510 q^{55} + 768 q^{56} - 6302 q^{57} - 8422 q^{59} + 3024 q^{60} - 6386 q^{61} + 22244 q^{63} + 4208 q^{66} + 4128 q^{68} + 1728 q^{69} - 6008 q^{70} + 8680 q^{71} + 5536 q^{72} + 1316 q^{74} - 37980 q^{75} - 2624 q^{76} - 28520 q^{79} - 2304 q^{80} - 33962 q^{81} + 9136 q^{82} - 22688 q^{83} - 23936 q^{84} + 14464 q^{86} + 1828 q^{87} - 2560 q^{88} + 18344 q^{89} - 8952 q^{90} - 4918 q^{91} + 1232 q^{92} + 24 q^{93} - 13784 q^{94} - 2560 q^{96} + 23246 q^{97} + 25708 q^{98}+O(q^{100}) \) 14 * q + 28 * q^2 + 36 * q^5 + 40 * q^6 - 48 * q^7 - 224 * q^8 - 346 * q^9 + 144 * q^10 + 160 * q^12 - 104 * q^13 - 96 * q^14 - 378 * q^15 - 896 * q^16 + 516 * q^17 - 692 * q^18 - 328 * q^19 + 288 * q^20 - 320 * q^22 + 154 * q^23 + 320 * q^24 - 416 * q^26 + 1686 * q^29 + 3834 * q^31 - 1792 * q^32 + 2104 * q^33 + 2064 * q^34 - 1502 * q^35 + 2640 * q^37 - 1312 * q^38 - 4526 * q^39 - 5984 * q^42 + 3616 * q^43 - 1280 * q^44 - 2238 * q^45 + 616 * q^46 - 6892 * q^47 + 12854 * q^49 + 7516 * q^50 - 6742 * q^51 - 832 * q^52 + 12572 * q^53 - 1072 * q^54 + 5510 * q^55 + 768 * q^56 - 6302 * q^57 - 8422 * q^59 + 3024 * q^60 - 6386 * q^61 + 22244 * q^63 + 4208 * q^66 + 4128 * q^68 + 1728 * q^69 - 6008 * q^70 + 8680 * q^71 + 5536 * q^72 + 1316 * q^74 - 37980 * q^75 - 2624 * q^76 - 28520 * q^79 - 2304 * q^80 - 33962 * q^81 + 9136 * q^82 - 22688 * q^83 - 23936 * q^84 + 14464 * q^86 + 1828 * q^87 - 2560 * q^88 + 18344 * q^89 - 8952 * q^90 - 4918 * q^91 + 1232 * q^92 + 24 * q^93 - 13784 * q^94 - 2560 * q^96 + 23246 * q^97 + 25708 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	2.00000	+	2.00000i	0.500000	+	0.500000i
$2$	2.00000	+	2.00000i	0.500000	+	0.500000i
$3$			5.93683i			0.659648i	0.944043	+	0.329824i	$0.106989\pi$
$3$			5.93683i			0.659648i	−0.944043	+	0.329824i	$0.893011\pi$
$4$			8.00000i			0.500000i
$5$	34.8311	−	34.8311i	1.39324	−	1.39324i	0.575306	−	0.817938i	$-0.304883\pi$
$5$	34.8311	−	34.8311i	1.39324	−	1.39324i	0.817938	−	0.575306i	$-0.195117\pi$
$6$	−11.8737	+	11.8737i	−0.329824	+	0.329824i
$7$	33.1642			0.676821			0.338410	−	0.940999i	$-0.390111\pi$
$7$	33.1642			0.676821			0.338410	+	0.940999i	$0.390111\pi$
$8$	−16.0000	+	16.0000i	−0.250000	+	0.250000i
$9$	45.7541			0.564865
$10$	139.324			1.39324
$11$			4.42515i			0.0365715i	0.999833	+	0.0182858i	$0.00582086\pi$
$11$			4.42515i			0.0365715i	−0.999833	+	0.0182858i	$0.994179\pi$
$12$	−47.4946			−0.329824
$13$	−155.523	+	155.523i	−0.920256	+	0.920256i	−0.997047	−	0.0767912i	$-0.975533\pi$
$13$	−155.523	+	155.523i	−0.920256	+	0.920256i	0.0767912	+	0.997047i	$0.475533\pi$
$14$	66.3284	+	66.3284i	0.338410	+	0.338410i
$15$	206.786	+	206.786i	0.919050	+	0.919050i
$16$	−64.0000			−0.250000
$17$	29.7847	−	29.7847i	0.103061	−	0.103061i	−0.653696	−	0.756757i	$-0.726782\pi$
$17$	29.7847	−	29.7847i	0.103061	−	0.103061i	0.756757	+	0.653696i	$0.226782\pi$
$18$	91.5081	+	91.5081i	0.282432	+	0.282432i
$19$	−367.142	+	367.142i	−1.01701	+	1.01701i	−0.0171600	+	0.999853i	$0.505462\pi$
$19$	−367.142	+	367.142i	−1.01701	+	1.01701i	−0.999853	+	0.0171600i	$0.994538\pi$
$20$	278.649	+	278.649i	0.696622	+	0.696622i
$21$			196.890i			0.446463i
$22$	−8.85031	+	8.85031i	−0.0182858	+	0.0182858i
$23$	647.183	−	647.183i	1.22341	−	1.22341i	0.256995	−	0.966413i	$-0.417268\pi$
$23$	647.183	−	647.183i	1.22341	−	1.22341i	0.966413	−	0.256995i	$-0.0827323\pi$
$24$	−94.9893	−	94.9893i	−0.164912	−	0.164912i
$25$		−	1801.41i		−	2.88226i
$26$	−622.093			−0.920256
$27$			752.517i			1.03226i
$28$			265.314i			0.338410i
$29$	−558.837	−	558.837i	−0.664492	−	0.664492i	0.291944	−	0.956435i	$-0.405698\pi$
$29$	−558.837	−	558.837i	−0.664492	−	0.664492i	−0.956435	+	0.291944i	$0.905698\pi$
$30$			827.145i			0.919050i
$31$	928.228	+	928.228i	0.965898	+	0.965898i	0.999437	−	0.0335395i	$-0.0106780\pi$
$31$	928.228	+	928.228i	0.965898	+	0.965898i	−0.0335395	+	0.999437i	$0.510678\pi$
$32$	−128.000	−	128.000i	−0.125000	−	0.125000i
$33$	−26.2714			−0.0241243
$34$	119.139			0.103061
$35$	1155.15	−	1155.15i	0.942976	−	0.942976i
$36$			366.033i			0.282432i
$37$	−1012.61	+	921.290i	−0.739673	+	0.672966i
$37$	−1012.61	+	921.290i	−0.739673	+	0.672966i
$38$	−1468.57			−1.01701
$39$	−923.315	−	923.315i	−0.607045	−	0.607045i
$40$			1114.60i			0.696622i
$41$		−	1994.29i		−	1.18637i	−0.805066	−	0.593186i	$-0.797870\pi$
$41$		−	1994.29i		−	1.18637i	0.805066	−	0.593186i	$-0.202130\pi$
$42$	−393.780	+	393.780i	−0.223232	+	0.223232i
$43$	−223.022	+	223.022i	−0.120618	+	0.120618i	−0.764839	−	0.644221i	$-0.777182\pi$
$43$	−223.022	+	223.022i	−0.120618	+	0.120618i	0.644221	+	0.764839i	$0.277182\pi$
$44$	−35.4012			−0.0182858
$45$	1593.66	−	1593.66i	0.786995	−	0.786995i
$46$	2588.73			1.22341
$47$	−3142.01			−1.42237			−0.711183	−	0.703007i	$-0.751840\pi$
$47$	−3142.01			−1.42237			−0.711183	+	0.703007i	$0.751840\pi$
$48$		−	379.957i		−	0.164912i
$49$	−1301.14			−0.541914
$50$	3602.82	−	3602.82i	1.44113	−	1.44113i
$51$	176.827	+	176.827i	0.0679842	+	0.0679842i
$52$	−1244.19	−	1244.19i	−0.460128	−	0.460128i
$53$	−1011.94			−0.360248			−0.180124	−	0.983644i	$-0.557650\pi$
$53$	−1011.94			−0.360248			−0.180124	+	0.983644i	$0.557650\pi$
$54$	−1505.03	+	1505.03i	−0.516130	+	0.516130i
$55$	154.133	+	154.133i	0.0509531	+	0.0509531i
$56$	−530.627	+	530.627i	−0.169205	+	0.169205i
$57$	−2179.66	−	2179.66i	−0.670870	−	0.670870i
$58$		−	2235.35i		−	0.664492i
$59$	550.662	−	550.662i	0.158191	−	0.158191i	−0.623574	−	0.781765i	$-0.714320\pi$
$59$	550.662	−	550.662i	0.158191	−	0.158191i	0.781765	+	0.623574i	$0.214320\pi$
$60$	−1654.29	+	1654.29i	−0.459525	+	0.459525i
$61$	−1174.38	−	1174.38i	−0.315608	−	0.315608i	0.531469	−	0.847078i	$-0.321640\pi$
$61$	−1174.38	−	1174.38i	−0.315608	−	0.315608i	−0.847078	+	0.531469i	$0.821640\pi$
$62$			3712.91i			0.965898i
$63$	1517.40			0.382312
$64$		−	512.000i		−	0.125000i
$65$			10834.1i			2.56428i
$66$	−52.5428	−	52.5428i	−0.0120622	−	0.0120622i
$67$		−	2319.11i		−	0.516620i	−0.966062	−	0.258310i	$-0.916834\pi$
$67$		−	2319.11i		−	0.516620i	0.966062	−	0.258310i	$-0.0831657\pi$
$68$	238.278	+	238.278i	0.0515307	+	0.0515307i
$69$	3842.21	+	3842.21i	0.807018	+	0.807018i
$70$	4620.58			0.942976
$71$	−3068.87			−0.608782			−0.304391	−	0.952547i	$-0.598453\pi$
$71$	−3068.87			−0.608782			−0.304391	+	0.952547i	$0.598453\pi$
$72$	−732.065	+	732.065i	−0.141216	+	0.141216i
$73$		−	11.2597i		−	0.00211290i	−0.999999	−	0.00105645i	$-0.999664\pi$
$73$		−	11.2597i		−	0.00211290i	0.999999	−	0.00105645i	$-0.000336279\pi$
$74$	−3867.81	−	182.645i	−0.706320	−	0.0333537i
$75$	10694.7			1.90128
$76$	−2937.13	−	2937.13i	−0.508506	−	0.508506i
$77$			146.757i			0.0247524i
$78$		−	3693.26i		−	0.607045i
$79$	−2103.45	+	2103.45i	−0.337038	+	0.337038i	−0.855251	−	0.518214i	$-0.826597\pi$
$79$	−2103.45	+	2103.45i	−0.337038	+	0.337038i	0.518214	+	0.855251i	$0.326597\pi$
$80$	−2229.19	+	2229.19i	−0.348311	+	0.348311i
$81$	−761.486			−0.116063
$82$	3988.58	−	3988.58i	0.593186	−	0.593186i
$83$	9140.45			1.32682			0.663409	−	0.748257i	$-0.269109\pi$
$83$	9140.45			1.32682			0.663409	+	0.748257i	$0.269109\pi$
$84$	−1575.12			−0.223232
$85$		−	2074.87i		−	0.287179i
$86$	−892.087			−0.120618
$87$	3317.72	−	3317.72i	0.438330	−	0.438330i
$88$	−70.8025	−	70.8025i	−0.00914288	−	0.00914288i
$89$	2126.17	+	2126.17i	0.268422	+	0.268422i	0.828464	−	0.560042i	$-0.189215\pi$
$89$	2126.17	+	2126.17i	0.268422	+	0.268422i	−0.560042	+	0.828464i	$0.689215\pi$
$90$	6374.66			0.786995
$91$	−5157.81	+	5157.81i	−0.622848	+	0.622848i
$92$	5177.46	+	5177.46i	0.611704	+	0.611704i
$93$	−5510.73	+	5510.73i	−0.637152	+	0.637152i
$94$	−6284.02	−	6284.02i	−0.711183	−	0.711183i
$95$			25575.9i			2.83389i
$96$	759.914	−	759.914i	0.0824560	−	0.0824560i
$97$	6567.54	−	6567.54i	0.698006	−	0.698006i	−0.265974	−	0.963980i	$-0.585693\pi$
$97$	6567.54	−	6567.54i	0.698006	−	0.698006i	0.963980	+	0.265974i	$0.0856935\pi$
$98$	−2602.27	−	2602.27i	−0.270957	−	0.270957i
$99$			202.469i			0.0206580i
$100$	14411.3			1.44113
$101$			6127.82i			0.600708i	0.953828	+	0.300354i	$0.0971048\pi$
$101$			6127.82i			0.600708i	−0.953828	+	0.300354i	$0.902895\pi$
$102$			707.307i			0.0679842i
$103$	−4941.22	−	4941.22i	−0.465758	−	0.465758i	0.434779	−	0.900537i	$-0.356826\pi$
$103$	−4941.22	−	4941.22i	−0.465758	−	0.465758i	−0.900537	+	0.434779i	$0.856826\pi$
$104$		−	4976.74i		−	0.460128i
$105$	6857.90	+	6857.90i	0.622032	+	0.622032i
$106$	−2023.87	−	2023.87i	−0.180124	−	0.180124i
$107$	4211.19			0.367822			0.183911	−	0.982943i	$-0.441124\pi$
$107$	4211.19			0.367822			0.183911	+	0.982943i	$0.441124\pi$
$108$	−6020.14			−0.516130
$109$	−12057.3	+	12057.3i	−1.01484	+	1.01484i	−0.0149486	+	0.999888i	$0.504758\pi$
$109$	−12057.3	+	12057.3i	−1.01484	+	1.01484i	−0.999888	+	0.0149486i	$0.995242\pi$
$110$			616.532i			0.0509531i
$111$	−5469.54	−	6011.71i	−0.443920	−	0.487924i
$112$	−2122.51			−0.169205
$113$	−13317.2	−	13317.2i	−1.04293	−	1.04293i	−0.999036	−	0.0438926i	$-0.986024\pi$
$113$	−13317.2	−	13317.2i	−1.04293	−	1.04293i	−0.0438926	−	0.999036i	$-0.513976\pi$
$114$		−	8718.63i		−	0.670870i
$115$		−	45084.2i		−	3.40901i
$116$	4470.70	−	4470.70i	0.332246	−	0.332246i
$117$	−7115.82	+	7115.82i	−0.519820	+	0.519820i
$118$	2202.65			0.158191
$119$	987.787	−	987.787i	0.0697541	−	0.0697541i
$120$	−6617.16			−0.459525
$121$	14621.4			0.998663
$122$		−	4697.52i		−	0.315608i
$123$	11839.8			0.782587
$124$	−7425.82	+	7425.82i	−0.482949	+	0.482949i
$125$	−40975.7	−	40975.7i	−2.62245	−	2.62245i
$126$	3034.79	+	3034.79i	0.191156	+	0.191156i
$127$	−4034.55			−0.250143			−0.125071	−	0.992148i	$-0.539916\pi$
$127$	−4034.55			−0.250143			−0.125071	+	0.992148i	$0.539916\pi$
$128$	1024.00	−	1024.00i	0.0625000	−	0.0625000i
$129$	−1324.04	−	1324.04i	−0.0795651	−	0.0795651i
$130$	−21668.2	+	21668.2i	−1.28214	+	1.28214i
$131$	15101.0	+	15101.0i	0.879963	+	0.879963i	0.993530	−	0.113568i	$-0.0362279\pi$
$131$	15101.0	+	15101.0i	0.879963	+	0.879963i	−0.113568	+	0.993530i	$0.536228\pi$
$132$		−	210.171i		−	0.0120622i
$133$	−12176.0	+	12176.0i	−0.688335	+	0.688335i
$134$	4638.22	−	4638.22i	0.258310	−	0.258310i
$135$	26211.0	+	26211.0i	1.43819	+	1.43819i
$136$			953.112i			0.0515307i
$137$	−13171.6			−0.701772			−0.350886	−	0.936418i	$-0.614120\pi$
$137$	−13171.6			−0.701772			−0.350886	+	0.936418i	$0.614120\pi$
$138$			15368.8i			0.807018i
$139$			941.634i			0.0487363i	0.999703	+	0.0243681i	$0.00775739\pi$
$139$			941.634i			0.0487363i	−0.999703	+	0.0243681i	$0.992243\pi$
$140$	9241.17	+	9241.17i	0.471488	+	0.471488i
$141$		−	18653.6i		−	0.938261i
$142$	−6137.74	−	6137.74i	−0.304391	−	0.304391i
$143$	−688.214	−	688.214i	−0.0336552	−	0.0336552i
$144$	−2928.26			−0.141216
$145$	−38929.9			−1.85160
$146$	22.5193	−	22.5193i	0.00105645	−	0.00105645i
$147$		−	7724.62i		−	0.357472i
$148$	−7370.32	−	8100.90i	−0.336483	−	0.369837i
$149$	−3780.31			−0.170277			−0.0851383	−	0.996369i	$-0.527133\pi$
$149$	−3780.31			−0.170277			−0.0851383	+	0.996369i	$0.527133\pi$
$150$	21389.4	+	21389.4i	0.950638	+	0.950638i
$151$			5043.24i			0.221185i	0.993866	+	0.110593i	$0.0352749\pi$
$151$			5043.24i			0.221185i	−0.993866	+	0.110593i	$0.964725\pi$
$152$		−	11748.5i		−	0.508506i
$153$	1362.77	−	1362.77i	0.0582158	−	0.0582158i
$154$	−293.513	+	293.513i	−0.0123762	+	0.0123762i
$155$	64662.4			2.69146
$156$	7386.52	−	7386.52i	0.303522	−	0.303522i
$157$	16703.7			0.677661			0.338830	−	0.940847i	$-0.389969\pi$
$157$	16703.7			0.677661			0.338830	+	0.940847i	$0.389969\pi$
$158$	−8413.81			−0.337038
$159$		−	6007.69i		−	0.237637i
$160$	−8916.76			−0.348311
$161$	21463.3	−	21463.3i	0.828027	−	0.828027i
$162$	−1522.97	−	1522.97i	−0.0580313	−	0.0580313i
$163$	−14378.1	−	14378.1i	−0.541160	−	0.541160i	0.382709	−	0.923869i	$-0.374991\pi$
$163$	−14378.1	−	14378.1i	−0.541160	−	0.541160i	−0.923869	+	0.382709i	$0.874991\pi$
$164$	15954.3			0.593186
$165$	−915.061	+	915.061i	−0.0336111	+	0.0336111i
$166$	18280.9	+	18280.9i	0.663409	+	0.663409i
$167$	−8767.98	+	8767.98i	−0.314389	+	0.314389i	−0.846607	−	0.532218i	$-0.821358\pi$
$167$	−8767.98	+	8767.98i	−0.314389	+	0.314389i	0.532218	+	0.846607i	$0.321358\pi$
$168$	−3150.24	−	3150.24i	−0.111616	−	0.111616i
$169$		−	19814.0i		−	0.693742i
$170$	4149.74	−	4149.74i	0.143590	−	0.143590i
$171$	−16798.2	+	16798.2i	−0.574475	+	0.574475i
$172$	−1784.17	−	1784.17i	−0.0603088	−	0.0603088i
$173$			24278.1i			0.811188i	0.914053	+	0.405594i	$0.132935\pi$
$173$			24278.1i			0.811188i	−0.914053	+	0.405594i	$0.867065\pi$
$174$	13270.9			0.438330
$175$		−	59742.4i		−	1.95077i
$176$		−	283.210i		−	0.00914288i
$177$	3269.19	+	3269.19i	0.104350	+	0.104350i
$178$			8504.67i			0.268422i
$179$	42787.2	+	42787.2i	1.33539	+	1.33539i	0.900468	+	0.434922i	$0.143224\pi$
$179$	42787.2	+	42787.2i	1.33539	+	1.33539i	0.434922	+	0.900468i	$0.356776\pi$
$180$	12749.3	+	12749.3i	0.393497	+	0.393497i
$181$	62865.8			1.91892			0.959461	−	0.281841i	$-0.0909450\pi$
$181$	62865.8			1.91892			0.959461	+	0.281841i	$0.0909450\pi$
$182$	−20631.2			−0.622848
$183$	6972.09	−	6972.09i	0.208190	−	0.208190i
$184$			20709.8i			0.611704i
$185$	−3180.86	+	67360.0i	−0.0929397	+	1.96815i
$186$	−22042.9			−0.637152
$187$	131.802	+	131.802i	0.00376911	+	0.00376911i
$188$		−	25136.1i		−	0.711183i
$189$			24956.6i			0.698654i
$190$	−51151.8	+	51151.8i	−1.41695	+	1.41695i
$191$	−12310.7	+	12310.7i	−0.337456	+	0.337456i	−0.855409	−	0.517953i	$-0.826694\pi$
$191$	−12310.7	+	12310.7i	−0.337456	+	0.337456i	0.517953	+	0.855409i	$0.326694\pi$
$192$	3039.66			0.0824560
$193$	−18731.8	+	18731.8i	−0.502879	+	0.502879i	−0.912332	−	0.409452i	$-0.865720\pi$
$193$	−18731.8	+	18731.8i	−0.502879	+	0.502879i	0.409452	+	0.912332i	$0.365720\pi$
$194$	26270.2			0.698006
$195$	−64320.2			−1.69152
$196$		−	10409.1i		−	0.270957i
$197$	21741.1			0.560209			0.280104	−	0.959970i	$-0.409631\pi$
$197$	21741.1			0.560209			0.280104	+	0.959970i	$0.409631\pi$
$198$	−404.938	+	404.938i	−0.0103290	+	0.0103290i
$199$	−12770.0	−	12770.0i	−0.322467	−	0.322467i	0.527246	−	0.849713i	$-0.323225\pi$
$199$	−12770.0	−	12770.0i	−0.322467	−	0.322467i	−0.849713	+	0.527246i	$0.823225\pi$
$200$	28822.6	+	28822.6i	0.720565	+	0.720565i
$201$	13768.2			0.340787
$202$	−12255.6	+	12255.6i	−0.300354	+	0.300354i
$203$	−18533.4	−	18533.4i	−0.449742	−	0.449742i
$204$	−1414.61	+	1414.61i	−0.0339921	+	0.0339921i
$205$	−69463.4	−	69463.4i	−1.65291	−	1.65291i
$206$		−	19764.9i		−	0.465758i
$207$	29611.2	−	29611.2i	0.691060	−	0.691060i
$208$	9953.49	−	9953.49i	0.230064	−	0.230064i
$209$	−1624.66	−	1624.66i	−0.0371937	−	0.0371937i
$210$			27431.6i			0.622032i
$211$	−14514.0			−0.326004			−0.163002	−	0.986626i	$-0.552118\pi$
$211$	−14514.0			−0.326004			−0.163002	+	0.986626i	$0.552118\pi$
$212$		−	8095.49i		−	0.180124i
$213$		−	18219.4i		−	0.401582i
$214$	8422.38	+	8422.38i	0.183911	+	0.183911i
$215$			15536.2i			0.336099i
$216$	−12040.3	−	12040.3i	−0.258065	−	0.258065i
$217$	30783.9	+	30783.9i	0.653740	+	0.653740i
$218$	−48229.1			−1.01484
$219$	66.8466			0.00139377
$220$	−1233.06	+	1233.06i	−0.0254765	+	0.0254765i
$221$			9264.44i			0.189686i
$222$	1084.33	−	22962.5i	0.0220017	−	0.465922i
$223$	38969.2			0.783631			0.391815	−	0.920044i	$-0.371847\pi$
$223$	38969.2			0.783631			0.391815	+	0.920044i	$0.371847\pi$
$224$	−4245.02	−	4245.02i	−0.0846026	−	0.0846026i
$225$		−	82421.9i		−	1.62809i
$226$		−	53268.6i		−	1.04293i
$227$	−1533.11	+	1533.11i	−0.0297523	+	0.0297523i	−0.721826	−	0.692074i	$-0.756697\pi$
$227$	−1533.11	+	1533.11i	−0.0297523	+	0.0297523i	0.692074	+	0.721826i	$0.256697\pi$
$228$	17437.3	−	17437.3i	0.335435	−	0.335435i
$229$	−18827.0			−0.359013			−0.179507	−	0.983757i	$-0.557450\pi$
$229$	−18827.0			−0.359013			−0.179507	+	0.983757i	$0.557450\pi$
$230$	90168.3	−	90168.3i	1.70451	−	1.70451i
$231$	−871.270			−0.0163278
$232$	17882.8			0.332246
$233$			92498.5i			1.70382i	0.523691	+	0.851909i	$0.324555\pi$
$233$			92498.5i			1.70382i	−0.523691	+	0.851909i	$0.675445\pi$
$234$	−28463.3			−0.519820
$235$	−109440.	+	109440.i	−1.98170	+	1.98170i
$236$	4405.30	+	4405.30i	0.0790954	+	0.0790954i
$237$	−12487.8	−	12487.8i	−0.222326	−	0.222326i
$238$	3951.15			0.0697541
$239$	6432.82	−	6432.82i	0.112617	−	0.112617i	−0.648553	−	0.761170i	$-0.724625\pi$
$239$	6432.82	−	6432.82i	0.112617	−	0.112617i	0.761170	+	0.648553i	$0.224625\pi$
$240$	−13234.3	−	13234.3i	−0.229763	−	0.229763i
$241$	80856.3	−	80856.3i	1.39213	−	1.39213i	0.571594	−	0.820537i	$-0.306325\pi$
$241$	80856.3	−	80856.3i	1.39213	−	1.39213i	0.820537	−	0.571594i	$-0.193675\pi$
$242$	29242.8	+	29242.8i	0.499331	+	0.499331i
$243$			56433.1i			0.955699i
$244$	9395.03	−	9395.03i	0.157804	−	0.157804i
$245$	−45320.0	+	45320.0i	−0.755019	+	0.755019i
$246$	23679.5	+	23679.5i	0.391294	+	0.391294i
$247$		−	114198.i		−	1.87182i
$248$	−29703.3			−0.482949
$249$			54265.3i			0.875233i
$250$		−	163903.i		−	2.62245i
$251$	2524.56	+	2524.56i	0.0400718	+	0.0400718i	0.726859	−	0.686787i	$-0.240979\pi$
$251$	2524.56	+	2524.56i	0.0400718	+	0.0400718i	−0.686787	+	0.726859i	$0.740979\pi$
$252$			12139.2i			0.191156i
$253$	2863.88	+	2863.88i	0.0447419	+	0.0447419i
$254$	−8069.10	−	8069.10i	−0.125071	−	0.125071i
$255$	12318.2			0.189437
$256$	4096.00			0.0625000
$257$	26770.5	−	26770.5i	0.405312	−	0.405312i	−0.474788	−	0.880100i	$-0.657475\pi$
$257$	26770.5	−	26770.5i	0.405312	−	0.405312i	0.880100	+	0.474788i	$0.157475\pi$
$258$		−	5296.17i		−	0.0795651i
$259$	−33582.5	+	30553.9i	−0.500626	+	0.455477i
$260$	−86672.8			−1.28214
$261$	−25569.1	−	25569.1i	−0.375348	−	0.375348i
$262$			60404.2i			0.879963i
$263$			259.616i			0.00375336i	0.999998	+	0.00187668i	$0.000597367\pi$
$263$			259.616i			0.00375336i	−0.999998	+	0.00187668i	$0.999403\pi$
$264$	420.342	−	420.342i	0.00603108	−	0.00603108i
$265$	−35246.9	+	35246.9i	−0.501913	+	0.501913i
$266$	−48703.8			−0.688335
$267$	−12622.7	+	12622.7i	−0.177064	+	0.177064i
$268$	18552.9			0.258310
$269$	55811.7			0.771295			0.385647	−	0.922646i	$-0.373978\pi$
$269$	55811.7			0.771295			0.385647	+	0.922646i	$0.373978\pi$
$270$			104844.i			1.43819i
$271$	115383.			1.57110			0.785552	−	0.618796i	$-0.212379\pi$
$271$	115383.			1.57110			0.785552	+	0.618796i	$0.212379\pi$
$272$	−1906.22	+	1906.22i	−0.0257653	+	0.0257653i
$273$	−30621.0	−	30621.0i	−0.410860	−	0.410860i
$274$	−26343.1	−	26343.1i	−0.350886	−	0.350886i
$275$	7971.53			0.105409
$276$	−30737.7	+	30737.7i	−0.403509	+	0.403509i
$277$	−51689.2	−	51689.2i	−0.673659	−	0.673659i	0.284898	−	0.958558i	$-0.408040\pi$
$277$	−51689.2	−	51689.2i	−0.673659	−	0.673659i	−0.958558	+	0.284898i	$0.908040\pi$
$278$	−1883.27	+	1883.27i	−0.0243681	+	0.0243681i
$279$	42470.2	+	42470.2i	0.545602	+	0.545602i
$280$			36964.7i			0.471488i
$281$	80464.7	−	80464.7i	1.01904	−	1.01904i	0.0192283	−	0.999815i	$-0.493879\pi$
$281$	80464.7	−	80464.7i	1.01904	−	1.01904i	0.999815	−	0.0192283i	$-0.00612092\pi$
$282$	37307.1	−	37307.1i	0.469130	−	0.469130i
$283$	−48024.8	−	48024.8i	−0.599643	−	0.599643i	0.340574	−	0.940218i	$-0.389378\pi$
$283$	−48024.8	−	48024.8i	−0.599643	−	0.599643i	−0.940218	+	0.340574i	$0.889378\pi$
$284$		−	24551.0i		−	0.304391i
$285$	−151840.			−1.86937
$286$		−	2752.86i		−	0.0336552i
$287$		−	66139.1i		−	0.802961i
$288$	−5856.52	−	5856.52i	−0.0706081	−	0.0706081i
$289$			81746.7i			0.978757i
$290$	−77859.7	−	77859.7i	−0.925799	−	0.925799i
$291$	38990.4	+	38990.4i	0.460438	+	0.460438i
$292$	90.0772			0.00105645
$293$	105263.			1.22615			0.613073	−	0.790026i	$-0.289933\pi$
$293$	105263.			1.22615			0.613073	+	0.790026i	$0.289933\pi$
$294$	15449.2	−	15449.2i	0.178736	−	0.178736i
$295$		−	38360.3i		−	0.440797i
$296$	1461.16	−	30942.5i	0.0166769	−	0.353160i
$297$	−3330.00			−0.0377513
$298$	−7560.62	−	7560.62i	−0.0851383	−	0.0851383i
$299$			201304.i			2.25170i
$300$			85557.4i			0.950638i
$301$	−7396.34	+	7396.34i	−0.0816364	+	0.0816364i
$302$	−10086.5	+	10086.5i	−0.110593	+	0.110593i
$303$	−36379.8			−0.396256
$304$	23497.1	−	23497.1i	0.254253	−	0.254253i
$305$	−81809.8			−0.879439
$306$	5451.09			0.0582158
$307$			175738.i			1.86462i	0.361665	+	0.932308i	$0.382208\pi$
$307$			175738.i			1.86462i	−0.361665	+	0.932308i	$0.617792\pi$
$308$	−1174.05			−0.0123762
$309$	29335.2	−	29335.2i	0.307236	−	0.307236i
$310$	129325.	+	129325.i	1.34573	+	1.34573i
$311$	−22500.1	−	22500.1i	−0.232628	−	0.232628i	0.581161	−	0.813789i	$-0.302599\pi$
$311$	−22500.1	−	22500.1i	−0.232628	−	0.232628i	−0.813789	+	0.581161i	$0.802599\pi$
$312$	29546.1			0.303522
$313$	27113.8	−	27113.8i	0.276759	−	0.276759i	−0.555055	−	0.831814i	$-0.687303\pi$
$313$	27113.8	−	27113.8i	0.276759	−	0.276759i	0.831814	+	0.555055i	$0.187303\pi$
$314$	33407.3	+	33407.3i	0.338830	+	0.338830i
$315$	52852.6	−	52852.6i	0.532654	−	0.532654i
$316$	−16827.6	−	16827.6i	−0.168519	−	0.168519i
$317$		−	82559.3i		−	0.821575i	−0.911731	−	0.410788i	$-0.865254\pi$
$317$		−	82559.3i		−	0.821575i	0.911731	−	0.410788i	$-0.134746\pi$
$318$	12015.4	−	12015.4i	0.118818	−	0.118818i
$319$	2472.94	−	2472.94i	0.0243015	−	0.0243015i
$320$	−17833.5	−	17833.5i	−0.174156	−	0.174156i
$321$			25001.1i			0.242633i
$322$	85853.2			0.828027
$323$			21870.4i			0.209629i
$324$		−	6091.89i		−	0.0580313i
$325$	280162.	+	280162.i	2.65242	+	2.65242i
$326$		−	57512.4i		−	0.541160i
$327$	−71582.0	−	71582.0i	−0.669435	−	0.669435i
$328$	31908.7	+	31908.7i	0.296593	+	0.296593i
$329$	−104202.			−0.962687
$330$	−3660.25			−0.0336111
$331$	96948.7	−	96948.7i	0.884883	−	0.884883i	−0.109143	−	0.994026i	$-0.534811\pi$
$331$	96948.7	−	96948.7i	0.884883	−	0.884883i	0.994026	+	0.109143i	$0.0348105\pi$
$332$			73123.6i			0.663409i
$333$	−46331.2	+	42152.8i	−0.417816	+	0.380135i
$334$	−35071.9			−0.314389
$335$	−80777.1	−	80777.1i	−0.719779	−	0.719779i
$336$		−	12601.0i		−	0.111616i
$337$			93100.9i			0.819774i	0.912136	+	0.409887i	$0.134432\pi$
$337$			93100.9i			0.819774i	−0.912136	+	0.409887i	$0.865568\pi$
$338$	39628.0	−	39628.0i	0.346871	−	0.346871i
$339$	79061.7	−	79061.7i	0.687966	−	0.687966i
$340$	16599.0			0.143590
$341$	−4107.55	+	4107.55i	−0.0353244	+	0.0353244i
$342$	−67192.9			−0.574475
$343$	−122778.			−1.04360
$344$		−	7136.70i		−	0.0603088i
$345$	267657.			2.24875
$346$	−48556.1	+	48556.1i	−0.405594	+	0.405594i
$347$	−141764.	−	141764.i	−1.17735	−	1.17735i	−0.980416	−	0.196937i	$-0.936901\pi$
$347$	−141764.	−	141764.i	−1.17735	−	1.17735i	−0.196937	−	0.980416i	$-0.563099\pi$
$348$	26541.8	+	26541.8i	0.219165	+	0.219165i
$349$	145687.			1.19611			0.598054	−	0.801456i	$-0.295941\pi$
$349$	145687.			1.19611			0.598054	+	0.801456i	$0.295941\pi$
$350$	119485.	−	119485.i	0.975386	−	0.975386i
$351$	−117034.	−	117034.i	−0.949943	−	0.949943i
$352$	566.420	−	566.420i	0.00457144	−	0.00457144i
$353$	−76108.8	−	76108.8i	−0.610781	−	0.610781i	0.332368	−	0.943150i	$-0.392152\pi$
$353$	−76108.8	−	76108.8i	−0.610781	−	0.610781i	−0.943150	+	0.332368i	$0.892152\pi$
$354$			13076.7i			0.104350i
$355$	−106892.	+	106892.i	−0.848182	+	0.848182i
$356$	−17009.3	+	17009.3i	−0.134211	+	0.134211i
$357$	5864.32	+	5864.32i	0.0460131	+	0.0460131i
$358$			171149.i			1.33539i
$359$	−137351.			−1.06572			−0.532859	−	0.846204i	$-0.678882\pi$
$359$	−137351.			−1.06572			−0.532859	+	0.846204i	$0.678882\pi$
$360$			50997.3i			0.393497i
$361$		−	139265.i		−	1.06863i
$362$	125732.	+	125732.i	0.959461	+	0.959461i
$363$			86804.9i			0.658765i
$364$	−41262.4	−	41262.4i	−0.311424	−	0.311424i
$365$	−392.186	−	392.186i	−0.00294379	−	0.00294379i
$366$	27888.3			0.208190
$367$	141257.			1.04876			0.524381	−	0.851484i	$-0.324297\pi$
$367$	141257.			1.04876			0.524381	+	0.851484i	$0.324297\pi$
$368$	−41419.7	+	41419.7i	−0.305852	+	0.305852i
$369$		−	91246.9i		−	0.670140i
$370$	−141082.	+	128358.i	−1.03055	+	0.937606i
$371$	−33560.1			−0.243823
$372$	−44085.8	−	44085.8i	−0.318576	−	0.318576i
$373$			135481.i			0.973778i	0.873464	+	0.486889i	$0.161868\pi$
$373$			135481.i			0.973778i	−0.873464	+	0.486889i	$0.838132\pi$
$374$			527.208i			0.00376911i
$375$	243266.	−	243266.i	1.72989	−	1.72989i
$376$	50272.1	−	50272.1i	0.355592	−	0.355592i
$377$	173824.			1.22300
$378$	−49913.3	+	49913.3i	−0.349327	+	0.349327i
$379$	−93988.6			−0.654330			−0.327165	−	0.944967i	$-0.606093\pi$
$379$	−93988.6			−0.654330			−0.327165	+	0.944967i	$0.606093\pi$
$380$	−204607.			−1.41695
$381$		−	23952.4i		−	0.165006i
$382$	−49242.9			−0.337456
$383$	−119229.	+	119229.i	−0.812800	+	0.812800i	−0.985053	−	0.172253i	$-0.944895\pi$
$383$	−119229.	+	119229.i	−0.812800	+	0.812800i	0.172253	+	0.985053i	$0.444895\pi$
$384$	6079.31	+	6079.31i	0.0412280	+	0.0412280i
$385$	5111.70	+	5111.70i	0.0344861	+	0.0344861i
$386$	−74927.0			−0.502879
$387$	−10204.2	+	10204.2i	−0.0681326	+	0.0681326i
$388$	52540.3	+	52540.3i	0.349003	+	0.349003i
$389$	125692.	−	125692.i	0.830632	−	0.830632i	−0.156971	−	0.987603i	$-0.550173\pi$
$389$	125692.	−	125692.i	0.830632	−	0.830632i	0.987603	+	0.156971i	$0.0501730\pi$
$390$	−128640.	−	128640.i	−0.845762	−	0.845762i
$391$		−	38552.3i		−	0.252172i
$392$	20818.2	−	20818.2i	0.135478	−	0.135478i
$393$	−89652.3	+	89652.3i	−0.580465	+	0.580465i
$394$	43482.3	+	43482.3i	0.280104	+	0.280104i
$395$			146531.i			0.939152i
$396$	−1619.75			−0.0103290
$397$		−	273617.i		−	1.73605i	−0.496522	−	0.868024i	$-0.665390\pi$
$397$		−	273617.i		−	1.73605i	0.496522	−	0.868024i	$-0.334610\pi$
$398$		−	51080.1i		−	0.322467i
$399$	−72286.6	−	72286.6i	−0.454059	−	0.454059i
$400$			115290.i			0.720565i
$401$	−42057.3	−	42057.3i	−0.261548	−	0.261548i	0.564134	−	0.825683i	$-0.309210\pi$
$401$	−42057.3	−	42057.3i	−0.261548	−	0.261548i	−0.825683	+	0.564134i	$0.809210\pi$
$402$	27536.3	+	27536.3i	0.170394	+	0.170394i
$403$	−288722.			−1.77775
$404$	−49022.6			−0.300354
$405$	−26523.4	+	26523.4i	−0.161703	+	0.161703i
$406$		−	74133.6i		−	0.449742i
$407$	−4076.85	−	4480.97i	−0.0246114	−	0.0270510i
$408$	−5658.46			−0.0339921
$409$	48879.1	+	48879.1i	0.292197	+	0.292197i	0.837948	−	0.545750i	$-0.183755\pi$
$409$	48879.1	+	48879.1i	0.292197	+	0.292197i	−0.545750	+	0.837948i	$0.683755\pi$
$410$		−	277853.i		−	1.65291i
$411$		−	78197.3i		−	0.462922i
$412$	39529.8	−	39529.8i	0.232879	−	0.232879i
$413$	18262.3	−	18262.3i	0.107067	−	0.107067i
$414$	118445.			0.691060
$415$	318372.	−	318372.i	1.84858	−	1.84858i
$416$	39814.0			0.230064
$417$	−5590.32			−0.0321488
$418$		−	6498.63i		−	0.0371937i
$419$	−330719.			−1.88378			−0.941892	−	0.335916i	$-0.890954\pi$
$419$	−330719.			−1.88378			−0.941892	+	0.335916i	$0.890954\pi$
$420$	−54863.2	+	54863.2i	−0.311016	+	0.311016i
$421$	70515.5	+	70515.5i	0.397851	+	0.397851i	0.877474	−	0.479624i	$-0.159227\pi$
$421$	70515.5	+	70515.5i	0.397851	+	0.397851i	−0.479624	+	0.877474i	$0.659227\pi$
$422$	−29028.1	−	29028.1i	−0.163002	−	0.163002i
$423$	−143760.			−0.803445
$424$	16191.0	−	16191.0i	0.0900620	−	0.0900620i
$425$	−53654.6	−	53654.6i	−0.297050	−	0.297050i
$426$	36438.7	−	36438.7i	0.200791	−	0.200791i
$427$	−38947.4	−	38947.4i	−0.213610	−	0.213610i
$428$			33689.5i			0.183911i
$429$	4085.81	−	4085.81i	0.0222005	−	0.0222005i
$430$	−31072.4	+	31072.4i	−0.168050	+	0.168050i
$431$	95292.9	+	95292.9i	0.512986	+	0.512986i	0.915440	−	0.402454i	$-0.131843\pi$
$431$	95292.9	+	95292.9i	0.512986	+	0.512986i	−0.402454	+	0.915440i	$0.631843\pi$
$432$		−	48161.1i		−	0.258065i
$433$	−142331.			−0.759142			−0.379571	−	0.925163i	$-0.623928\pi$
$433$	−142331.			−0.759142			−0.379571	+	0.925163i	$0.623928\pi$
$434$			123136.i			0.653740i
$435$		−	231120.i		−	1.22140i
$436$	−96458.2	−	96458.2i	−0.507418	−	0.507418i
$437$			475215.i			2.48844i
$438$	133.693	+	133.693i	0.000696885	+	0.000696885i
$439$	−145482.	−	145482.i	−0.754886	−	0.754886i	0.220501	−	0.975387i	$-0.429231\pi$
$439$	−145482.	−	145482.i	−0.754886	−	0.754886i	−0.975387	+	0.220501i	$0.929231\pi$
$440$	−4932.26			−0.0254765
$441$	−59532.2			−0.306108
$442$	−18528.9	+	18528.9i	−0.0948428	+	0.0948428i
$443$			224281.i			1.14284i	0.820658	+	0.571420i	$0.193607\pi$
$443$			224281.i			1.14284i	−0.820658	+	0.571420i	$0.806393\pi$
$444$	48093.7	−	43756.3i	0.243962	−	0.221960i
$445$	148114.			0.747954
$446$	77938.3	+	77938.3i	0.391815	+	0.391815i
$447$		−	22443.0i		−	0.112322i
$448$		−	16980.1i		−	0.0846026i
$449$	−16003.6	+	16003.6i	−0.0793823	+	0.0793823i	−0.745683	−	0.666301i	$-0.767877\pi$
$449$	−16003.6	+	16003.6i	−0.0793823	+	0.0793823i	0.666301	+	0.745683i	$0.267877\pi$
$450$	164844.	−	164844.i	0.814044	−	0.814044i
$451$	8825.04			0.0433874
$452$	106537.	−	106537.i	0.521464	−	0.521464i
$453$	−29940.9			−0.145904
$454$	−6132.43			−0.0297523
$455$			359304.i			1.73556i
$456$	69749.0			0.335435
$457$	−45786.0	+	45786.0i	−0.219230	+	0.219230i	−0.808174	−	0.588944i	$-0.799544\pi$
$457$	−45786.0	+	45786.0i	−0.219230	+	0.219230i	0.588944	+	0.808174i	$0.299544\pi$
$458$	−37654.0	−	37654.0i	−0.179507	−	0.179507i
$459$	22413.5	+	22413.5i	0.106386	+	0.106386i
$460$	360673.			1.70451
$461$	−57659.4	+	57659.4i	−0.271312	+	0.271312i	−0.829628	−	0.558316i	$-0.811447\pi$
$461$	−57659.4	+	57659.4i	−0.271312	+	0.271312i	0.558316	+	0.829628i	$0.311447\pi$
$462$	−1742.54	−	1742.54i	−0.00816392	−	0.00816392i
$463$	−53466.5	+	53466.5i	−0.249413	+	0.249413i	−0.820730	−	0.571316i	$-0.806433\pi$
$463$	−53466.5	+	53466.5i	−0.249413	+	0.249413i	0.571316	+	0.820730i	$0.306433\pi$
$464$	35765.6	+	35765.6i	0.166123	+	0.166123i
$465$			383890.i			1.77542i
$466$	−184997.	+	184997.i	−0.851909	+	0.851909i
$467$	208667.	−	208667.i	0.956795	−	0.956795i	−0.0423091	−	0.999105i	$-0.513471\pi$
$467$	208667.	−	208667.i	0.956795	−	0.956795i	0.999105	+	0.0423091i	$0.0134714\pi$
$468$	−56926.6	−	56926.6i	−0.259910	−	0.259910i
$469$		−	76911.4i		−	0.349659i
$470$	−437759.			−1.98170
$471$			99166.8i			0.447017i
$472$			17621.2i			0.0790954i
$473$	−986.906	−	986.906i	−0.00441117	−	0.00441117i
$474$		−	49951.3i		−	0.222326i
$475$	661373.	+	661373.i	2.93129	+	2.93129i
$476$	7902.30	+	7902.30i	0.0348770	+	0.0348770i
$477$	−46300.2			−0.203491
$478$	25731.3			0.112617
$479$	138990.	−	138990.i	0.605775	−	0.605775i	−0.336064	−	0.941839i	$-0.609096\pi$
$479$	138990.	−	138990.i	0.605775	−	0.605775i	0.941839	+	0.336064i	$0.109096\pi$
$480$		−	52937.3i		−	0.229763i
$481$	14202.8	−	300767.i	0.0613879	−	1.29999i
$482$	323425.			1.39213
$483$	127424.	+	127424.i	0.546206	+	0.546206i
$484$			116971.i			0.499331i
$485$		−	457510.i		−	1.94499i
$486$	−112866.	+	112866.i	−0.477850	+	0.477850i
$487$	−268161.	+	268161.i	−1.13068	+	1.13068i	−0.140610	+	0.990065i	$0.544906\pi$
$487$	−268161.	+	268161.i	−1.13068	+	1.13068i	−0.990065	+	0.140610i	$0.955094\pi$
$488$	37580.1			0.157804
$489$	85360.3	−	85360.3i	0.356975	−	0.356975i
$490$	−181280.			−0.755019
$491$	317255.			1.31597			0.657984	−	0.753032i	$-0.271410\pi$
$491$	317255.			1.31597			0.657984	+	0.753032i	$0.271410\pi$
$492$			94718.1i			0.391294i
$493$	−33289.6			−0.136967
$494$	228396.	−	228396.i	0.935912	−	0.935912i
$495$	7052.21	+	7052.21i	0.0287816	+	0.0287816i
$496$	−59406.6	−	59406.6i	−0.241474	−	0.241474i
$497$	−101777.			−0.412036
$498$	−108531.	+	108531.i	−0.437616	+	0.437616i
$499$	258204.	+	258204.i	1.03696	+	1.03696i	0.999290	+	0.0376701i	$0.0119936\pi$
$499$	258204.	+	258204.i	1.03696	+	1.03696i	0.0376701	+	0.999290i	$0.488006\pi$
$500$	327806.	−	327806.i	1.31122	−	1.31122i
$501$	−52054.0	−	52054.0i	−0.207386	−	0.207386i
$502$			10098.3i			0.0400718i
$503$	−248652.	+	248652.i	−0.982781	+	0.982781i	−0.999854	−	0.0170737i	$-0.994565\pi$
$503$	−248652.	+	248652.i	−0.982781	+	0.982781i	0.0170737	+	0.999854i	$0.494565\pi$
$504$	−24278.4	+	24278.4i	−0.0955781	+	0.0955781i
$505$	213439.	+	213439.i	0.836933	+	0.836933i
$506$			11455.5i			0.0447419i
$507$	117632.			0.457626
$508$		−	32276.4i		−	0.125071i
$509$		−	192284.i		−	0.742177i	−0.928598	−	0.371088i	$-0.878985\pi$
$509$		−	192284.i		−	0.742177i	0.928598	−	0.371088i	$-0.121015\pi$
$510$	24636.3	+	24636.3i	0.0947186	+	0.0947186i
$511$		−	373.417i		−	0.00143006i
$512$	8192.00	+	8192.00i	0.0312500	+	0.0312500i
$513$	−276280.	−	276280.i	−1.04982	−	1.04982i
$514$	107082.			0.405312
$515$	−344217.			−1.29783
$516$	10592.3	−	10592.3i	0.0397825	−	0.0397825i
$517$		−	13903.9i		−	0.0520181i
$518$	−128273.	−	6057.27i	−0.478052	−	0.0225745i
$519$	−144135.			−0.535098
$520$	−173346.	−	173346.i	−0.641071	−	0.641071i
$521$		−	231118.i		−	0.851448i	−0.904853	−	0.425724i	$-0.860019\pi$
$521$		−	231118.i		−	0.851448i	0.904853	−	0.425724i	$-0.139981\pi$
$522$		−	102276.i		−	0.375348i
$523$	85348.4	−	85348.4i	0.312027	−	0.312027i	−0.533667	−	0.845694i	$-0.679187\pi$
$523$	85348.4	−	85348.4i	0.312027	−	0.312027i	0.845694	+	0.533667i	$0.179187\pi$
$524$	−120808.	+	120808.i	−0.439981	+	0.439981i
$525$	354680.			1.28682
$526$	−519.233	+	519.233i	−0.00187668	+	0.00187668i
$527$	55294.0			0.199094
$528$	1681.37			0.00603108
$529$		−	557850.i		−	1.99345i
$530$	−140987.			−0.501913
$531$	25195.0	−	25195.0i	0.0893564	−	0.0893564i
$532$	−97407.7	−	97407.7i	−0.344168	−	0.344168i
$533$	310159.	+	310159.i	1.09177	+	1.09177i
$534$	−50490.8			−0.177064
$535$	146680.	−	146680.i	0.512465	−	0.512465i
$536$	37105.7	+	37105.7i	0.129155	+	0.129155i
$537$	−254021.	+	254021.i	−0.880887	+	0.880887i
$538$	111623.	+	111623.i	0.385647	+	0.385647i
$539$		−	5757.72i		−	0.0198186i
$540$	−209688.	+	209688.i	−0.719095	+	0.719095i
$541$	−234565.	+	234565.i	−0.801436	+	0.801436i	−0.983320	−	0.181884i	$-0.941780\pi$
$541$	−234565.	+	234565.i	−0.801436	+	0.801436i	0.181884	+	0.983320i	$0.441780\pi$
$542$	230767.	+	230767.i	0.785552	+	0.785552i
$543$			373224.i			1.26581i
$544$	−7624.89			−0.0257653
$545$			839937.i			2.82783i
$546$		−	122484.i		−	0.410860i
$547$	157826.	+	157826.i	0.527476	+	0.527476i	0.919819	−	0.392343i	$-0.128335\pi$
$547$	157826.	+	157826.i	0.527476	+	0.527476i	−0.392343	+	0.919819i	$0.628335\pi$
$548$		−	105372.i		−	0.350886i
$549$	−53732.6	−	53732.6i	−0.178276	−	0.178276i
$550$	15943.1	+	15943.1i	0.0527043	+	0.0527043i
$551$	410345.			1.35159
$552$	−122951.			−0.403509
$553$	−69759.3	+	69759.3i	−0.228114	+	0.228114i
$554$		−	206757.i		−	0.673659i
$555$	−399905.	−	18884.2i	−1.29829	−	0.0613075i
$556$	−7533.07			−0.0243681
$557$	−196118.	−	196118.i	−0.632132	−	0.632132i	0.316470	−	0.948602i	$-0.397502\pi$
$557$	−196118.	−	196118.i	−0.632132	−	0.632132i	−0.948602	+	0.316470i	$0.897502\pi$
$558$			169881.i			0.545602i
$559$		−	69370.2i		−	0.221998i
$560$	−73929.4	+	73929.4i	−0.235744	+	0.235744i
$561$	−782.486	+	782.486i	−0.00248628	+	0.00248628i
$562$	321859.			1.01904
$563$	12439.6	−	12439.6i	0.0392454	−	0.0392454i	−0.687212	−	0.726457i	$-0.741166\pi$
$563$	12439.6	−	12439.6i	0.0392454	−	0.0392454i	0.726457	+	0.687212i	$0.241166\pi$
$564$	149229.			0.469130
$565$	−927703.			−2.90611
$566$		−	192099.i		−	0.599643i
$567$	−25254.1			−0.0785535
$568$	49101.9	−	49101.9i	0.152195	−	0.152195i
$569$	−100481.	−	100481.i	−0.310357	−	0.310357i	0.534691	−	0.845048i	$-0.320428\pi$
$569$	−100481.	−	100481.i	−0.310357	−	0.310357i	−0.845048	+	0.534691i	$0.820428\pi$
$570$	−303679.	−	303679.i	−0.934686	−	0.934686i
$571$	460437.			1.41221			0.706103	−	0.708109i	$-0.250451\pi$
$571$	460437.			1.41221			0.706103	+	0.708109i	$0.250451\pi$
$572$	5505.72	−	5505.72i	0.0168276	−	0.0168276i
$573$	−73086.7	−	73086.7i	−0.222602	−	0.222602i
$574$	132278.	−	132278.i	0.401480	−	0.401480i
$575$	−1.16584e6	−	1.16584e6i	−3.52618	−	3.52618i
$576$		−	23426.1i		−	0.0706081i
$577$	244370.	−	244370.i	0.734001	−	0.734001i	−0.237409	−	0.971410i	$-0.576298\pi$
$577$	244370.	−	244370.i	0.734001	−	0.734001i	0.971410	+	0.237409i	$0.0762980\pi$
$578$	−163493.	+	163493.i	−0.489378	+	0.489378i
$579$	−111207.	−	111207.i	−0.331723	−	0.331723i
$580$		−	311439.i		−	0.925799i
$581$	303136.			0.898018
$582$			155962.i			0.460438i
$583$		−	4477.97i		−	0.0131748i
$584$	180.154	+	180.154i	0.000528225	+	0.000528225i
$585$			495704.i			1.44847i
$586$	210527.	+	210527.i	0.613073	+	0.613073i
$587$	−107059.	−	107059.i	−0.310703	−	0.310703i	0.534479	−	0.845182i	$-0.320508\pi$
$587$	−107059.	−	107059.i	−0.310703	−	0.310703i	−0.845182	+	0.534479i	$0.820508\pi$
$588$	61796.9			0.178736
$589$	−681582.			−1.96466
$590$	76720.7	−	76720.7i	0.220398	−	0.220398i
$591$			129073.i			0.369540i
$592$	64807.2	−	58962.6i	0.184918	−	0.168242i
$593$	311613.			0.886149			0.443074	−	0.896485i	$-0.353888\pi$
$593$	311613.			0.886149			0.443074	+	0.896485i	$0.353888\pi$
$594$	−6660.01	−	6660.01i	−0.0188756	−	0.0188756i
$595$		−	68811.4i		−	0.194369i
$596$		−	30242.5i		−	0.0851383i
$597$	75813.5	−	75813.5i	0.212715	−	0.212715i
$598$	−402608.	+	402608.i	−1.12585	+	1.12585i
$599$	616554.			1.71837			0.859187	−	0.511662i	$-0.170970\pi$
$599$	616554.			1.71837			0.859187	+	0.511662i	$0.170970\pi$
$600$	−171115.	+	171115.i	−0.475319	+	0.475319i
$601$	446062.			1.23494			0.617471	−	0.786594i	$-0.288157\pi$
$601$	446062.			1.23494			0.617471	+	0.786594i	$0.288157\pi$
$602$	−29585.4			−0.0816364
$603$		−	106109.i		−	0.291821i
$604$	−40345.9			−0.110593
$605$	509280.	−	509280.i	1.39138	−	1.39138i
$606$	−72759.7	−	72759.7i	−0.198128	−	0.198128i
$607$	−259551.	−	259551.i	−0.704443	−	0.704443i	0.260918	−	0.965361i	$-0.415975\pi$
$607$	−259551.	−	259551.i	−0.704443	−	0.704443i	−0.965361	+	0.260918i	$0.915975\pi$
$608$	93988.2			0.254253
$609$	110030.	−	110030.i	0.296671	−	0.296671i
$610$	−163620.	−	163620.i	−0.439720	−	0.439720i
$611$	488655.	−	488655.i	1.30894	−	1.30894i
$612$	10902.2	+	10902.2i	0.0291079	+	0.0291079i
$613$		−	325514.i		−	0.866261i	−0.901331	−	0.433130i	$-0.857409\pi$
$613$		−	325514.i		−	0.866261i	0.901331	−	0.433130i	$-0.142591\pi$
$614$	−351476.	+	351476.i	−0.932308	+	0.932308i
$615$	412392.	−	412392.i	1.09034	−	1.09034i
$616$	−2348.11	−	2348.11i	−0.00618809	−	0.00618809i
$617$		−	88330.8i		−	0.232029i	−0.993248	−	0.116014i	$-0.962988\pi$
$617$		−	88330.8i		−	0.232029i	0.993248	−	0.116014i	$-0.0370119\pi$
$618$	117341.			0.307236
$619$			601121.i			1.56885i	0.620226	+	0.784423i	$0.287041\pi$
$619$			601121.i			1.56885i	−0.620226	+	0.784423i	$0.712959\pi$
$620$			517299.i			1.34573i
$621$	487016.	+	487016.i	1.26287	+	1.26287i
$622$		−	90000.2i		−	0.232628i
$623$	70512.7	+	70512.7i	0.181673	+	0.181673i
$624$	59092.2	+	59092.2i	0.151761	+	0.151761i
$625$	−1.72858e6			−4.42516
$626$	108455.			0.276759
$627$	9645.32	−	9645.32i	0.0245347	−	0.0245347i
$628$			133629.i			0.338830i
$629$	−2720.01	+	57600.8i	−0.00687496	+	0.145589i
$630$	211411.			0.532654
$631$	−167496.	−	167496.i	−0.420673	−	0.420673i	0.464762	−	0.885436i	$-0.346140\pi$
$631$	−167496.	−	167496.i	−0.420673	−	0.420673i	−0.885436	+	0.464762i	$0.846140\pi$
$632$		−	67310.5i		−	0.168519i
$633$		−	86167.4i		−	0.215048i
$634$	165119.	−	165119.i	0.410788	−	0.410788i
$635$	−140528.	+	140528.i	−0.348510	+	0.348510i
$636$	48061.5			0.118818
$637$	202357.	−	202357.i	0.498700	−	0.498700i
$638$	9891.77			0.0243015
$639$	−140413.			−0.343880
$640$		−	71334.1i		−	0.174156i
$641$	119109.			0.289887			0.144943	−	0.989440i	$-0.453700\pi$
$641$	119109.			0.289887			0.144943	+	0.989440i	$0.453700\pi$
$642$	−50002.2	+	50002.2i	−0.121316	+	0.121316i
$643$	−122318.	−	122318.i	−0.295847	−	0.295847i	0.543538	−	0.839385i	$-0.317084\pi$
$643$	−122318.	−	122318.i	−0.295847	−	0.295847i	−0.839385	+	0.543538i	$0.817084\pi$
$644$	171706.	+	171706.i	0.414014	+	0.414014i
$645$	−92235.7			−0.221707
$646$	−43740.9	+	43740.9i	−0.104815	+	0.104815i
$647$	−51581.0	−	51581.0i	−0.123220	−	0.123220i	0.642808	−	0.766028i	$-0.277769\pi$
$647$	−51581.0	−	51581.0i	−0.123220	−	0.123220i	−0.766028	+	0.642808i	$0.777769\pi$
$648$	12183.8	−	12183.8i	0.0290156	−	0.0290156i
$649$	2436.76	+	2436.76i	0.00578528	+	0.00578528i
$650$			1.12065e6i			2.65242i
$651$	−182759.	+	182759.i	−0.431238	+	0.431238i
$652$	115025.	−	115025.i	0.270580	−	0.270580i
$653$	−54714.1	−	54714.1i	−0.128314	−	0.128314i	0.640033	−	0.768347i	$-0.278921\pi$
$653$	−54714.1	−	54714.1i	−0.128314	−	0.128314i	−0.768347	+	0.640033i	$0.778921\pi$
$654$		−	286328.i		−	0.669435i
$655$	1.05197e6			2.45201
$656$			127635.i			0.296593i
$657$		−	515.175i		−	0.00119350i
$658$	−208404.	−	208404.i	−0.481344	−	0.481344i
$659$		−	650669.i		−	1.49827i	−0.662418	−	0.749134i	$-0.730470\pi$
$659$		−	650669.i		−	1.49827i	0.662418	−	0.749134i	$-0.269530\pi$
$660$	−7320.49	−	7320.49i	−0.0168055	−	0.0168055i
$661$	45310.1	+	45310.1i	0.103703	+	0.103703i	0.757055	−	0.653352i	$-0.226638\pi$
$661$	45310.1	+	45310.1i	0.103703	+	0.103703i	−0.653352	+	0.757055i	$0.726638\pi$
$662$	387795.			0.884883
$663$	−55001.4			−0.125126
$664$	−146247.	+	146247.i	−0.331705	+	0.331705i
$665$			848204.i			1.91804i
$666$	−176968.	−	8356.75i	−0.398975	−	0.0188403i
$667$	−723340.			−1.62589
$668$	−70143.9	−	70143.9i	−0.157194	−	0.157194i
$669$			231353.i			0.516920i
$670$		−	323109.i		−	0.719779i
$671$	5196.81	−	5196.81i	0.0115423	−	0.0115423i
$672$	25201.9	−	25201.9i	0.0558079	−	0.0558079i
$673$	−145711.			−0.321708			−0.160854	−	0.986978i	$-0.551425\pi$
$673$	−145711.			−0.321708			−0.160854	+	0.986978i	$0.551425\pi$
$674$	−186202.	+	186202.i	−0.409887	+	0.409887i
$675$	1.35559e6			2.97524
$676$	158512.			0.346871
$677$			94182.3i			0.205491i	0.994708	+	0.102745i	$0.0327627\pi$
$677$			94182.3i			0.205491i	−0.994708	+	0.102745i	$0.967237\pi$
$678$	316247.			0.687966
$679$	217807.	−	217807.i	0.472425	−	0.472425i
$680$	33197.9	+	33197.9i	0.0717948	+	0.0717948i
$681$	−9101.80	−	9101.80i	−0.0196261	−	0.0196261i
$682$	−16430.2			−0.0353244
$683$	−377950.	+	377950.i	−0.810201	+	0.810201i	−0.984664	−	0.174463i	$-0.944181\pi$
$683$	−377950.	+	377950.i	−0.810201	+	0.810201i	0.174463	+	0.984664i	$0.444181\pi$
$684$	−134386.	−	134386.i	−0.287237	−	0.287237i
$685$	−458780.	+	458780.i	−0.977740	+	0.977740i
$686$	−245557.	−	245557.i	−0.521800	−	0.521800i
$687$		−	111773.i		−	0.236822i
$688$	14273.4	−	14273.4i	0.0301544	−	0.0301544i
$689$	157380.	−	157380.i	0.331520	−	0.331520i
$690$	535314.	+	535314.i	1.12437	+	1.12437i
$691$			572040.i			1.19804i	0.800735	+	0.599019i	$0.204443\pi$
$691$			572040.i			1.19804i	−0.800735	+	0.599019i	$0.795557\pi$
$692$	−194224.			−0.405594
$693$			6714.72i			0.0139817i
$694$		−	567056.i		−	1.17735i
$695$	32798.2	+	32798.2i	0.0679016	+	0.0679016i
$696$			106167.i			0.219165i
$697$	−59399.4	−	59399.4i	−0.122269	−	0.122269i
$698$	291374.	+	291374.i	0.598054	+	0.598054i
$699$	−549148.			−1.12392
$700$	477939.			0.975386
$701$	135953.	−	135953.i	0.276664	−	0.276664i	−0.555112	−	0.831776i	$-0.687324\pi$
$701$	135953.	−	135953.i	0.276664	−	0.276664i	0.831776	+	0.555112i	$0.187324\pi$
$702$		−	468136.i		−	0.949943i
$703$	33528.3	−	710016.i	0.0678423	−	1.43667i
$704$	2265.68			0.00457144
$705$	−649724.	−	649724.i	−1.30723	−	1.30723i
$706$		−	304435.i		−	0.610781i
$707$			203224.i			0.406572i
$708$	−26153.5	+	26153.5i	−0.0521751	+	0.0521751i
$709$	152643.	−	152643.i	0.303658	−	0.303658i	−0.538785	−	0.842443i	$-0.681117\pi$
$709$	152643.	−	152643.i	0.303658	−	0.303658i	0.842443	+	0.538785i	$0.181117\pi$
$710$	−427569.			−0.848182
$711$	−96241.5	+	96241.5i	−0.190381	+	0.190381i
$712$	−68037.4			−0.134211
$713$	1.20147e6			2.36337
$714$			23457.3i			0.0460131i
$715$	−47942.5			−0.0937797
$716$	−342298.	+	342298.i	−0.667695	+	0.667695i
$717$	38190.5	+	38190.5i	0.0742878	+	0.0742878i
$718$	−274702.	−	274702.i	−0.532859	−	0.532859i
$719$	46120.6			0.0892149			0.0446075	−	0.999005i	$-0.485796\pi$
$719$	46120.6			0.0892149			0.0446075	+	0.999005i	$0.485796\pi$
$720$	−101995.	+	101995.i	−0.196749	+	0.196749i
$721$	−163872.	−	163872.i	−0.315234	−	0.315234i
$722$	278530.	−	278530.i	0.534315	−	0.534315i
$723$	480030.	+	480030.i	0.918316	+	0.918316i
$724$			502927.i			0.959461i
$725$	−1.00670e6	+	1.00670e6i	−1.91524	+	1.91524i
$726$	−173610.	+	173610.i	−0.329383	+	0.329383i
$727$	504839.	+	504839.i	0.955178	+	0.955178i	0.999038	−	0.0438596i	$-0.0139654\pi$
$727$	504839.	+	504839.i	0.955178	+	0.955178i	−0.0438596	+	0.999038i	$0.513965\pi$
$728$		−	165050.i		−	0.311424i
$729$	−396714.			−0.746487
$730$		−	1568.74i		−	0.00294379i
$731$			13285.3i			0.0248620i
$732$	55776.7	+	55776.7i	0.104095	+	0.104095i
$733$			524436.i			0.976079i	0.872822	+	0.488039i	$0.162288\pi$
$733$			524436.i			0.976079i	−0.872822	+	0.488039i	$0.837712\pi$
$734$	282513.	+	282513.i	0.524381	+	0.524381i
$735$	−269057.	−	269057.i	−0.498046	−	0.498046i
$736$	−165679.			−0.305852
$737$	10262.4			0.0188936
$738$	182494.	−	182494.i	0.335070	−	0.335070i
$739$			523967.i			0.959435i	0.877423	+	0.479717i	$0.159261\pi$
$739$			523967.i			0.959435i	−0.877423	+	0.479717i	$0.840739\pi$
$740$	−538880.	−	25446.9i	−0.984076	−	0.0464699i
$741$	677975.			1.23474
$742$	−67120.1	−	67120.1i	−0.121912	−	0.121912i
$743$		−	91675.0i		−	0.166063i	−0.996547	−	0.0830316i	$-0.973540\pi$
$743$		−	91675.0i		−	0.166063i	0.996547	−	0.0830316i	$-0.0264602\pi$
$744$		−	176343.i		−	0.318576i
$745$	−131672.	+	131672.i	−0.237237	+	0.237237i
$746$	−270962.	+	270962.i	−0.486889	+	0.486889i
$747$	418213.			0.749473
$748$	−1054.42	+	1054.42i	−0.00188456	+	0.00188456i
$749$	139661.			0.248949
$750$	973064.			1.72989
$751$			483848.i			0.857885i	0.903332	+	0.428943i	$0.141114\pi$
$751$			483848.i			0.857885i	−0.903332	+	0.428943i	$0.858886\pi$
$752$	201089.			0.355592
$753$	−14987.9	+	14987.9i	−0.0264333	+	0.0264333i
$754$	347649.	+	347649.i	0.611502	+	0.611502i
$755$	175662.	+	175662.i	0.308165	+	0.308165i
$756$	−199653.			−0.349327
$757$	151529.	−	151529.i	0.264426	−	0.264426i	−0.562423	−	0.826849i	$-0.690131\pi$
$757$	151529.	−	151529.i	0.264426	−	0.264426i	0.826849	+	0.562423i	$0.190131\pi$
$758$	−187977.	−	187977.i	−0.327165	−	0.327165i
$759$	−17002.4	+	17002.4i	−0.0295139	+	0.0295139i
$760$	−409214.	−	409214.i	−0.708474	−	0.708474i
$761$		−	191135.i		−	0.330044i	−0.986290	−	0.165022i	$-0.947230\pi$
$761$		−	191135.i		−	0.330044i	0.986290	−	0.165022i	$-0.0527695\pi$
$762$	47904.9	−	47904.9i	0.0825030	−	0.0825030i
$763$	−399870.	+	399870.i	−0.686862	+	0.686862i
$764$	−98485.8	−	98485.8i	−0.168728	−	0.168728i
$765$		−	94933.8i		−	0.162218i
$766$	−476915.			−0.812800
$767$			171282.i			0.291152i
$768$			24317.3i			0.0412280i
$769$	−95194.7	−	95194.7i	−0.160976	−	0.160976i	0.622023	−	0.782999i	$-0.286311\pi$
$769$	−95194.7	−	95194.7i	−0.160976	−	0.160976i	−0.782999	+	0.622023i	$0.786311\pi$
$770$			20446.8i			0.0344861i
$771$	158932.	+	158932.i	0.267363	+	0.267363i
$772$	−149854.	−	149854.i	−0.251440	−	0.251440i
$773$	−153875.			−0.257519			−0.128760	−	0.991676i	$-0.541100\pi$
$773$	−153875.			−0.257519			−0.128760	+	0.991676i	$0.541100\pi$
$774$	−40816.6			−0.0681326
$775$	1.67212e6	−	1.67212e6i	2.78397	−	2.78397i
$776$			210161.i			0.349003i
$777$	−181393.	−	199374.i	−0.300454	−	0.330237i
$778$	502768.			0.830632
$779$	732187.	+	732187.i	1.20656	+	1.20656i
$780$		−	514561.i		−	0.845762i
$781$		−	13580.2i		−	0.0222641i
$782$	77104.6	−	77104.6i	0.126086	−	0.126086i
$783$	420535.	−	420535.i	0.685928	−	0.685928i
$784$	83272.7			0.135478
$785$	581807.	−	581807.i	0.944147	−	0.944147i
$786$	−358609.			−0.580465
$787$	−1.15334e6			−1.86212			−0.931060	−	0.364866i	$-0.881115\pi$
$787$	−1.15334e6			−1.86212			−0.931060	+	0.364866i	$0.881115\pi$
$788$			173929.i			0.280104i
$789$	−1541.30			−0.00247590
$790$	−293062.	+	293062.i	−0.469576	+	0.469576i
$791$	−441653.	−	441653.i	−0.705876	−	0.705876i
$792$	−3239.50	−	3239.50i	−0.00516449	−	0.00516449i
$793$	365287.			0.580881
$794$	547234.	−	547234.i	0.868024	−	0.868024i
$795$	−209255.	−	209255.i	−0.331086	−	0.331086i
$796$	102160.	−	102160.i	0.161234	−	0.161234i
$797$	−582265.	−	582265.i	−0.916651	−	0.916651i	0.0801335	−	0.996784i	$-0.474465\pi$
$797$	−582265.	−	582265.i	−0.916651	−	0.916651i	−0.996784	+	0.0801335i	$0.974465\pi$
$798$		−	289146.i		−	0.454059i
$799$	−93583.9	+	93583.9i	−0.146591	+	0.146591i
$800$	−230581.	+	230581.i	−0.360282	+	0.360282i
$801$	97280.8	+	97280.8i	0.151622	+	0.151622i
$802$		−	168229.i		−	0.261548i
$803$	49.8257			7.72720e−5
$804$			110145.i			0.170394i
$805$		−	1.49518e6i		−	2.30729i
$806$	−577444.	−	577444.i	−0.888873	−	0.888873i
$807$			331344.i			0.508783i
$808$	−98045.2	−	98045.2i	−0.150177	−	0.150177i
$809$	398584.	+	398584.i	0.609008	+	0.609008i	0.942687	−	0.333679i	$-0.108290\pi$
$809$	398584.	+	398584.i	0.609008	+	0.609008i	−0.333679	+	0.942687i	$0.608290\pi$
$810$	−106094.			−0.161703
$811$	−369426.			−0.561675			−0.280838	−	0.959755i	$-0.590612\pi$
$811$	−369426.			−0.561675			−0.280838	+	0.959755i	$0.590612\pi$
$812$	148267.	−	148267.i	0.224871	−	0.224871i
$813$			685011.i			1.03637i
$814$	808.232	−	17115.6i	0.00121980	−	0.0258312i
$815$	−1.00161e6			−1.50794
$816$	−11316.9	−	11316.9i	−0.0169960	−	0.0169960i
$817$		−	163761.i		−	0.245339i
$818$			195516.i			0.292197i
$819$	−235991.	+	235991.i	−0.351825	+	0.351825i
$820$	555707.	−	555707.i	0.826453	−	0.826453i
$821$	−912349.			−1.35355			−0.676775	−	0.736190i	$-0.736623\pi$
$821$	−912349.			−1.35355			−0.676775	+	0.736190i	$0.736623\pi$
$822$	156395.	−	156395.i	0.231461	−	0.231461i
$823$	−479257.			−0.707569			−0.353785	−	0.935327i	$-0.615105\pi$
$823$	−479257.			−0.707569			−0.353785	+	0.935327i	$0.615105\pi$
$824$	158119.			0.232879
$825$			47325.6i			0.0695325i
$826$	73049.1			0.107067
$827$	−228320.	+	228320.i	−0.333836	+	0.333836i	−0.854041	−	0.520206i	$-0.825855\pi$
$827$	−228320.	+	228320.i	−0.333836	+	0.333836i	0.520206	+	0.854041i	$0.325855\pi$
$828$	236890.	+	236890.i	0.345530	+	0.345530i
$829$	−604556.	−	604556.i	−0.879685	−	0.879685i	0.113817	−	0.993502i	$-0.463692\pi$
$829$	−604556.	−	604556.i	−0.879685	−	0.879685i	−0.993502	+	0.113817i	$0.963692\pi$
$830$	1.27349e6			1.84858
$831$	306870.	−	306870.i	0.444378	−	0.444378i
$832$	79627.9	+	79627.9i	0.115032	+	0.115032i
$833$	−38754.0	+	38754.0i	−0.0558504	+	0.0558504i
$834$	−11180.6	−	11180.6i	−0.0160744	−	0.0160744i
$835$			610797.i			0.876040i
$836$	12997.3	−	12997.3i	0.0185969	−	0.0185969i
$837$	−698507.	+	698507.i	−0.997057	+	0.997057i
$838$	−661438.	−	661438.i	−0.941892	−	0.941892i
$839$			26038.6i			0.0369909i	0.999829	+	0.0184954i	$0.00588761\pi$
$839$			26038.6i			0.0369909i	−0.999829	+	0.0184954i	$0.994112\pi$
$840$	−219453.			−0.311016
$841$		−	82682.5i		−	0.116902i
$842$			282062.i			0.397851i
$843$	477705.	+	477705.i	0.672210	+	0.672210i
$844$		−	116112.i		−	0.163002i
$845$	−690143.	−	690143.i	−0.966553	−	0.966553i
$846$	−287519.	−	287519.i	−0.401723	−	0.401723i
$847$	484908.			0.675915
$848$	64763.9			0.0900620
$849$	285115.	−	285115.i	0.395553	−	0.395553i
$850$		−	214618.i		−	0.297050i
$851$	−59102.3	+	1.25159e6i	−0.0816103	+	1.72823i
$852$	145755.			0.200791
$853$	32147.4	+	32147.4i	0.0441822	+	0.0441822i	0.728853	−	0.684671i	$-0.240054\pi$
$853$	32147.4	+	32147.4i	0.0441822	+	0.0441822i	−0.684671	+	0.728853i	$0.740054\pi$
$854$		−	155789.i		−	0.213610i
$855$			1.17020e6i			1.60077i
$856$	−67379.0	+	67379.0i	−0.0919554	+	0.0919554i
$857$	−810803.	+	810803.i	−1.10396	+	1.10396i	−0.110033	+	0.993928i	$0.535096\pi$
$857$	−810803.	+	810803.i	−1.10396	+	1.10396i	−0.993928	+	0.110033i	$0.964904\pi$
$858$	16343.2			0.0222005
$859$	−543016.	+	543016.i	−0.735913	+	0.735913i	−0.971784	−	0.235871i	$-0.924206\pi$
$859$	−543016.	+	543016.i	−0.735913	+	0.735913i	0.235871	+	0.971784i	$0.424206\pi$
$860$	−124290.			−0.168050
$861$	392656.			0.529671
$862$			381171.i			0.512986i
$863$	−827038.			−1.11046			−0.555231	−	0.831696i	$-0.687370\pi$
$863$	−827038.			−1.11046			−0.555231	+	0.831696i	$0.687370\pi$
$864$	96322.2	−	96322.2i	0.129032	−	0.129032i
$865$	845631.	+	845631.i	1.13018	+	1.13018i
$866$	−284661.	−	284661.i	−0.379571	−	0.379571i
$867$	−485316.			−0.645635
$868$	−246272.	+	246272.i	−0.326870	+	0.326870i
$869$	−9308.10	−	9308.10i	−0.0123260	−	0.0123260i
$870$	462240.	−	462240.i	0.610701	−	0.610701i
$871$	360675.	+	360675.i	0.475423	+	0.475423i
$872$		−	385833.i		−	0.507418i
$873$	300492.	−	300492.i	0.394279	−	0.394279i
$874$	−950431.	+	950431.i	−1.24422	+	1.24422i
$875$	−1.35893e6	−	1.35893e6i	−1.77493	−	1.77493i
$876$			534.773i			0.000696885i
$877$	−692104.			−0.899855			−0.449927	−	0.893065i	$-0.648550\pi$
$877$	−692104.			−0.899855			−0.449927	+	0.893065i	$0.648550\pi$
$878$		−	581930.i		−	0.754886i
$879$			624931.i			0.808824i
$880$	−9864.51	−	9864.51i	−0.0127383	−	0.0127383i
$881$			441890.i			0.569327i	0.958627	+	0.284664i	$0.0918819\pi$
$881$			441890.i			0.569327i	−0.958627	+	0.284664i	$0.908118\pi$
$882$	−119064.	−	119064.i	−0.153054	−	0.153054i
$883$	−978493.	−	978493.i	−1.25498	−	1.25498i	−0.953461	−	0.301517i	$-0.902507\pi$
$883$	−978493.	−	978493.i	−1.25498	−	1.25498i	−0.301517	−	0.953461i	$-0.597493\pi$
$884$	−74115.5			−0.0948428
$885$	227739.			0.290771
$886$	−448562.	+	448562.i	−0.571420	+	0.571420i
$887$			154949.i			0.196943i	0.995140	+	0.0984717i	$0.0313954\pi$
$887$			154949.i			0.196943i	−0.995140	+	0.0984717i	$0.968605\pi$
$888$	183700.	+	8674.65i	0.232961	+	0.0110008i
$889$	−133803.			−0.169302
$890$	296227.	+	296227.i	0.373977	+	0.373977i
$891$		−	3369.69i		−	0.00424458i
$892$			311753.i			0.391815i
$893$	1.15356e6	−	1.15356e6i	1.44657	−	1.44657i
$894$	44886.1	−	44886.1i	0.0561612	−	0.0561612i
$895$	2.98065e6			3.72105
$896$	33960.1	−	33960.1i	0.0423013	−	0.0423013i
$897$	−1.19511e6			−1.48533
$898$	−64014.2			−0.0793823
$899$		−	1.03746e6i		−	1.28366i
$900$	659375.			0.814044
$901$	−30140.3	+	30140.3i	−0.0371276	+	0.0371276i
$902$	17650.1	+	17650.1i	0.0216937	+	0.0216937i
$903$	−43910.8	−	43910.8i	−0.0538513	−	0.0538513i
$904$	426149.			0.521464
$905$	2.18969e6	−	2.18969e6i	2.67353	−	2.67353i
$906$	−59881.7	−	59881.7i	−0.0729521	−	0.0729521i
$907$	72503.8	−	72503.8i	0.0881345	−	0.0881345i	−0.661665	−	0.749800i	$-0.730150\pi$
$907$	72503.8	−	72503.8i	0.0881345	−	0.0881345i	0.749800	+	0.661665i	$0.230150\pi$
$908$	−12264.9	−	12264.9i	−0.0148762	−	0.0148762i
$909$			280373.i			0.339319i
$910$	−718608.	+	718608.i	−0.867780	+	0.867780i
$911$	385446.	−	385446.i	0.464437	−	0.464437i	−0.435670	−	0.900107i	$-0.643488\pi$
$911$	385446.	−	385446.i	0.464437	−	0.464437i	0.900107	+	0.435670i	$0.143488\pi$
$912$	139498.	+	139498.i	0.167718	+	0.167718i
$913$			40447.9i			0.0485238i
$914$	−183144.			−0.219230
$915$		−	485691.i		−	0.580120i
$916$		−	150616.i		−	0.179507i
$917$	500814.	+	500814.i	0.595577	+	0.595577i
$918$			89654.1i			0.106386i
$919$	−875288.	−	875288.i	−1.03638	−	1.03638i	−0.999313	−	0.0370691i	$-0.988198\pi$
$919$	−875288.	−	875288.i	−1.03638	−	1.03638i	−0.0370691	−	0.999313i	$-0.511802\pi$
$920$	721347.	+	721347.i	0.852253	+	0.852253i
$921$	−1.04333e6			−1.22999
$922$	−230638.			−0.271312
$923$	477281.	−	477281.i	0.560235	−	0.560235i
$924$		−	6970.16i		−	0.00816392i
$925$	1.65962e6	+	1.82413e6i	1.93966	+	2.13193i
$926$	−213866.			−0.249413
$927$	−226081.	−	226081.i	−0.263090	−	0.263090i
$928$			143062.i			0.166123i
$929$			808864.i			0.937225i	0.883404	+	0.468613i	$0.155246\pi$
$929$			808864.i			0.937225i	−0.883404	+	0.468613i	$0.844754\pi$
$930$	−767779.	+	767779.i	−0.887709	+	0.887709i
$931$	477701.	−	477701.i	0.551133	−	0.551133i
$932$	−739988.			−0.851909
$933$	133579.	−	133579.i	0.153453	−	0.153453i
$934$	834666.			0.956795
$935$	9181.62			0.0105026
$936$		−	227706.i		−	0.259910i
$937$	1.37134e6			1.56195			0.780973	−	0.624564i	$-0.214723\pi$
$937$	1.37134e6			1.56195			0.780973	+	0.624564i	$0.214723\pi$
$938$	153823.	−	153823.i	0.174830	−	0.174830i
$939$	160970.	+	160970.i	0.182563	+	0.182563i
$940$	−875517.	−	875517.i	−0.990852	−	0.990852i
$941$	843723.			0.952841			0.476421	−	0.879218i	$-0.341934\pi$
$941$	843723.			0.952841			0.476421	+	0.879218i	$0.341934\pi$
$942$	−198334.	+	198334.i	−0.223509	+	0.223509i
$943$	−1.29067e6	−	1.29067e6i	−1.45142	−	1.45142i
$944$	−35242.4	+	35242.4i	−0.0395477	+	0.0395477i
$945$	869267.	+	869267.i	0.973396	+	0.973396i
$946$		−	3947.62i		−	0.00441117i
$947$	255718.	−	255718.i	0.285142	−	0.285142i	−0.550014	−	0.835156i	$-0.685377\pi$
$947$	255718.	−	255718.i	0.285142	−	0.285142i	0.835156	+	0.550014i	$0.185377\pi$
$948$	99902.7	−	99902.7i	0.111163	−	0.111163i
$949$	1751.14	+	1751.14i	0.00194441	+	0.00194441i
$950$			2.64549e6i			2.93129i
$951$	490140.			0.541950
$952$			31609.2i			0.0348770i
$953$		−	1.56696e6i		−	1.72533i	−0.505772	−	0.862667i	$-0.668792\pi$
$953$		−	1.56696e6i		−	1.72533i	0.505772	−	0.862667i	$-0.331208\pi$
$954$	−92600.4	−	92600.4i	−0.101746	−	0.101746i
$955$			857592.i			0.940317i
$956$	51462.6	+	51462.6i	0.0563087	+	0.0563087i
$957$	14681.4	+	14681.4i	0.0160304	+	0.0160304i
$958$	555959.			0.605775
$959$	−436824.			−0.474974
$960$	105875.	−	105875.i	0.114881	−	0.114881i
$961$			799693.i			0.865917i
$962$	629939.	−	573128.i	0.680689	−	0.619301i
$963$	192679.			0.207770
$964$	646851.	+	646851.i	0.696065	+	0.696065i
$965$			1.30490e6i			1.40127i
$966$			509696.i			0.546206i
$967$	−427189.	+	427189.i	−0.456843	+	0.456843i	−0.897618	−	0.440775i	$-0.854704\pi$
$967$	−427189.	+	427189.i	−0.456843	+	0.456843i	0.440775	+	0.897618i	$0.354704\pi$
$968$	−233943.	+	233943.i	−0.249666	+	0.249666i
$969$	−129841.			−0.138282
$970$	915019.	−	915019.i	0.972494	−	0.972494i
$971$	397728.			0.421840			0.210920	−	0.977503i	$-0.432354\pi$
$971$	397728.			0.421840			0.210920	+	0.977503i	$0.432354\pi$
$972$	−451465.			−0.477850
$973$			31228.5i			0.0329857i
$974$	−1.07264e6			−1.13068
$975$	−1.66327e6	+	1.66327e6i	−1.74966	+	1.74966i
$976$	75160.3	+	75160.3i	0.0789021	+	0.0789021i
$977$	1.15077e6	+	1.15077e6i	1.20559	+	1.20559i	0.972441	+	0.233151i	$0.0749035\pi$
$977$	1.15077e6	+	1.15077e6i	1.20559	+	1.20559i	0.233151	+	0.972441i	$0.425097\pi$
$978$	341441.			0.356975
$979$	−9408.62	+	9408.62i	−0.00981659	+	0.00981659i
$980$	−362560.	−	362560.i	−0.377509	−	0.377509i
$981$	−551669.	+	551669.i	−0.573246	+	0.573246i
$982$	634510.	+	634510.i	0.657984	+	0.657984i
$983$			305549.i			0.316209i	0.987422	+	0.158104i	$0.0505383\pi$
$983$			305549.i			0.316209i	−0.987422	+	0.158104i	$0.949462\pi$
$984$	−189436.	+	189436.i	−0.195647	+	0.195647i
$985$	757268.	−	757268.i	0.780508	−	0.780508i
$986$	−66579.3	−	66579.3i	−0.0684834	−	0.0684834i
$987$		−	618631.i		−	0.635034i
$988$	913585.			0.935912
$989$			288672.i			0.295129i
$990$			28208.8i			0.0287816i
$991$	393816.	+	393816.i	0.401002	+	0.401002i	0.878586	−	0.477584i	$-0.158487\pi$
$991$	393816.	+	393816.i	0.401002	+	0.401002i	−0.477584	+	0.878586i	$0.658487\pi$
$992$		−	237626.i		−	0.241474i
$993$	575568.	+	575568.i	0.583711	+	0.583711i
$994$	−203553.	−	203553.i	−0.206018	−	0.206018i
$995$	−889589.			−0.898552
$996$	−434122.			−0.437616
$997$	−345716.	+	345716.i	−0.347800	+	0.347800i	−0.859289	−	0.511490i	$-0.829094\pi$
$997$	−345716.	+	345716.i	−0.347800	+	0.347800i	0.511490	+	0.859289i	$0.329094\pi$
$998$			1.03282e6i			1.03696i
$999$	−693287.	−	762009.i	−0.694676	−	0.763535i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.5.d.b.31.5	✓	14
37.6	odd	4	inner	74.5.d.b.43.3	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.5.d.b.31.5	✓	14	1.1	even	1	trivial
74.5.d.b.43.3	yes	14	37.6	odd	4	inner

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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	74.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 + 2.00000i) q^{2} +5.93683i q^{3} +8.00000i q^{4} +(34.8311 - 34.8311i) q^{5} +(-11.8737 + 11.8737i) q^{6} +33.1642 q^{7} +(-16.0000 + 16.0000i) q^{8} +45.7541 q^{9} +O(q^{10})\)	\(q+(2.00000 + 2.00000i) q^{2} +5.93683i q^{3} +8.00000i q^{4} +(34.8311 - 34.8311i) q^{5} +(-11.8737 + 11.8737i) q^{6} +33.1642 q^{7} +(-16.0000 + 16.0000i) q^{8} +45.7541 q^{9} +139.324 q^{10} +4.42515i q^{11} -47.4946 q^{12} +(-155.523 + 155.523i) q^{13} +(66.3284 + 66.3284i) q^{14} +(206.786 + 206.786i) q^{15} -64.0000 q^{16} +(29.7847 - 29.7847i) q^{17} +(91.5081 + 91.5081i) q^{18} +(-367.142 + 367.142i) q^{19} +(278.649 + 278.649i) q^{20} +196.890i q^{21} +(-8.85031 + 8.85031i) q^{22} +(647.183 - 647.183i) q^{23} +(-94.9893 - 94.9893i) q^{24} -1801.41i q^{25} -622.093 q^{26} +752.517i q^{27} +265.314i q^{28} +(-558.837 - 558.837i) q^{29} +827.145i q^{30} +(928.228 + 928.228i) q^{31} +(-128.000 - 128.000i) q^{32} -26.2714 q^{33} +119.139 q^{34} +(1155.15 - 1155.15i) q^{35} +366.033i q^{36} +(-1012.61 + 921.290i) q^{37} -1468.57 q^{38} +(-923.315 - 923.315i) q^{39} +1114.60i q^{40} -1994.29i q^{41} +(-393.780 + 393.780i) q^{42} +(-223.022 + 223.022i) q^{43} -35.4012 q^{44} +(1593.66 - 1593.66i) q^{45} +2588.73 q^{46} -3142.01 q^{47} -379.957i q^{48} -1301.14 q^{49} +(3602.82 - 3602.82i) q^{50} +(176.827 + 176.827i) q^{51} +(-1244.19 - 1244.19i) q^{52} -1011.94 q^{53} +(-1505.03 + 1505.03i) q^{54} +(154.133 + 154.133i) q^{55} +(-530.627 + 530.627i) q^{56} +(-2179.66 - 2179.66i) q^{57} -2235.35i q^{58} +(550.662 - 550.662i) q^{59} +(-1654.29 + 1654.29i) q^{60} +(-1174.38 - 1174.38i) q^{61} +3712.91i q^{62} +1517.40 q^{63} -512.000i q^{64} +10834.1i q^{65} +(-52.5428 - 52.5428i) q^{66} -2319.11i q^{67} +(238.278 + 238.278i) q^{68} +(3842.21 + 3842.21i) q^{69} +4620.58 q^{70} -3068.87 q^{71} +(-732.065 + 732.065i) q^{72} -11.2597i q^{73} +(-3867.81 - 182.645i) q^{74} +10694.7 q^{75} +(-2937.13 - 2937.13i) q^{76} +146.757i q^{77} -3693.26i q^{78} +(-2103.45 + 2103.45i) q^{79} +(-2229.19 + 2229.19i) q^{80} -761.486 q^{81} +(3988.58 - 3988.58i) q^{82} +9140.45 q^{83} -1575.12 q^{84} -2074.87i q^{85} -892.087 q^{86} +(3317.72 - 3317.72i) q^{87} +(-70.8025 - 70.8025i) q^{88} +(2126.17 + 2126.17i) q^{89} +6374.66 q^{90} +(-5157.81 + 5157.81i) q^{91} +(5177.46 + 5177.46i) q^{92} +(-5510.73 + 5510.73i) q^{93} +(-6284.02 - 6284.02i) q^{94} +25575.9i q^{95} +(759.914 - 759.914i) q^{96} +(6567.54 - 6567.54i) q^{97} +(-2602.27 - 2602.27i) q^{98} +202.469i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 28 q^{2} + 36 q^{5} + 40 q^{6} - 48 q^{7} - 224 q^{8} - 346 q^{9}+O(q^{10}) \) 14 * q + 28 * q^2 + 36 * q^5 + 40 * q^6 - 48 * q^7 - 224 * q^8 - 346 * q^9	\( 14 q + 28 q^{2} + 36 q^{5} + 40 q^{6} - 48 q^{7} - 224 q^{8} - 346 q^{9} + 144 q^{10} + 160 q^{12} - 104 q^{13} - 96 q^{14} - 378 q^{15} - 896 q^{16} + 516 q^{17} - 692 q^{18} - 328 q^{19} + 288 q^{20} - 320 q^{22} + 154 q^{23} + 320 q^{24} - 416 q^{26} + 1686 q^{29} + 3834 q^{31} - 1792 q^{32} + 2104 q^{33} + 2064 q^{34} - 1502 q^{35} + 2640 q^{37} - 1312 q^{38} - 4526 q^{39} - 5984 q^{42} + 3616 q^{43} - 1280 q^{44} - 2238 q^{45} + 616 q^{46} - 6892 q^{47} + 12854 q^{49} + 7516 q^{50} - 6742 q^{51} - 832 q^{52} + 12572 q^{53} - 1072 q^{54} + 5510 q^{55} + 768 q^{56} - 6302 q^{57} - 8422 q^{59} + 3024 q^{60} - 6386 q^{61} + 22244 q^{63} + 4208 q^{66} + 4128 q^{68} + 1728 q^{69} - 6008 q^{70} + 8680 q^{71} + 5536 q^{72} + 1316 q^{74} - 37980 q^{75} - 2624 q^{76} - 28520 q^{79} - 2304 q^{80} - 33962 q^{81} + 9136 q^{82} - 22688 q^{83} - 23936 q^{84} + 14464 q^{86} + 1828 q^{87} - 2560 q^{88} + 18344 q^{89} - 8952 q^{90} - 4918 q^{91} + 1232 q^{92} + 24 q^{93} - 13784 q^{94} - 2560 q^{96} + 23246 q^{97} + 25708 q^{98}+O(q^{100}) \) 14 * q + 28 * q^2 + 36 * q^5 + 40 * q^6 - 48 * q^7 - 224 * q^8 - 346 * q^9 + 144 * q^10 + 160 * q^12 - 104 * q^13 - 96 * q^14 - 378 * q^15 - 896 * q^16 + 516 * q^17 - 692 * q^18 - 328 * q^19 + 288 * q^20 - 320 * q^22 + 154 * q^23 + 320 * q^24 - 416 * q^26 + 1686 * q^29 + 3834 * q^31 - 1792 * q^32 + 2104 * q^33 + 2064 * q^34 - 1502 * q^35 + 2640 * q^37 - 1312 * q^38 - 4526 * q^39 - 5984 * q^42 + 3616 * q^43 - 1280 * q^44 - 2238 * q^45 + 616 * q^46 - 6892 * q^47 + 12854 * q^49 + 7516 * q^50 - 6742 * q^51 - 832 * q^52 + 12572 * q^53 - 1072 * q^54 + 5510 * q^55 + 768 * q^56 - 6302 * q^57 - 8422 * q^59 + 3024 * q^60 - 6386 * q^61 + 22244 * q^63 + 4208 * q^66 + 4128 * q^68 + 1728 * q^69 - 6008 * q^70 + 8680 * q^71 + 5536 * q^72 + 1316 * q^74 - 37980 * q^75 - 2624 * q^76 - 28520 * q^79 - 2304 * q^80 - 33962 * q^81 + 9136 * q^82 - 22688 * q^83 - 23936 * q^84 + 14464 * q^86 + 1828 * q^87 - 2560 * q^88 + 18344 * q^89 - 8952 * q^90 - 4918 * q^91 + 1232 * q^92 + 24 * q^93 - 13784 * q^94 - 2560 * q^96 + 23246 * q^97 + 25708 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more