LMFDB - Embedded newform 74.5.d.a.31.7

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} + 198453 x^{10} + 24875201 x^{8} + 1392846203 x^{6} + 29089700589 x^{4} + \cdots + 446074380544 $ x^14 + 727x^12 + 198453x^10 + 24875201x^8 + 1392846203x^6 + 29089700589x^4 + 220261242916x^2 + 446074380544
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.7
Root			$14.0996i$ of defining polynomial
Character	$\chi$	$=$	74.31
Dual form			74.5.d.a.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 - 2.00000i) q^{2} +13.0996i q^{3} +8.00000i q^{4} +(-23.5442 + 23.5442i) q^{5} +(26.1992 - 26.1992i) q^{6} -19.7742 q^{7} +(16.0000 - 16.0000i) q^{8} -90.5991 q^{9} +O(q^{10})$	\(q+(-2.00000 - 2.00000i) q^{2} +13.0996i q^{3} +8.00000i q^{4} +(-23.5442 + 23.5442i) q^{5} +(26.1992 - 26.1992i) q^{6} -19.7742 q^{7} +(16.0000 - 16.0000i) q^{8} -90.5991 q^{9} +94.1766 q^{10} -152.071i q^{11} -104.797 q^{12} +(144.158 - 144.158i) q^{13} +(39.5484 + 39.5484i) q^{14} +(-308.419 - 308.419i) q^{15} -64.0000 q^{16} +(-104.714 + 104.714i) q^{17} +(181.198 + 181.198i) q^{18} +(-227.423 + 227.423i) q^{19} +(-188.353 - 188.353i) q^{20} -259.034i q^{21} +(-304.142 + 304.142i) q^{22} +(-346.188 + 346.188i) q^{23} +(209.593 + 209.593i) q^{24} -483.655i q^{25} -576.631 q^{26} -125.744i q^{27} -158.194i q^{28} +(-831.151 - 831.151i) q^{29} +1233.67i q^{30} +(237.857 + 237.857i) q^{31} +(128.000 + 128.000i) q^{32} +1992.07 q^{33} +418.857 q^{34} +(465.567 - 465.567i) q^{35} -724.792i q^{36} +(-1250.02 + 558.226i) q^{37} +909.692 q^{38} +(1888.41 + 1888.41i) q^{39} +753.413i q^{40} +316.672i q^{41} +(-518.068 + 518.068i) q^{42} +(2172.28 - 2172.28i) q^{43} +1216.57 q^{44} +(2133.08 - 2133.08i) q^{45} +1384.75 q^{46} -613.021 q^{47} -838.373i q^{48} -2009.98 q^{49} +(-967.310 + 967.310i) q^{50} +(-1371.71 - 1371.71i) q^{51} +(1153.26 + 1153.26i) q^{52} -2538.56 q^{53} +(-251.487 + 251.487i) q^{54} +(3580.38 + 3580.38i) q^{55} +(-316.387 + 316.387i) q^{56} +(-2979.15 - 2979.15i) q^{57} +3324.60i q^{58} +(-2732.58 + 2732.58i) q^{59} +(2467.35 - 2467.35i) q^{60} +(1632.21 + 1632.21i) q^{61} -951.430i q^{62} +1791.52 q^{63} -512.000i q^{64} +6788.14i q^{65} +(-3984.13 - 3984.13i) q^{66} +6634.72i q^{67} +(-837.714 - 837.714i) q^{68} +(-4534.92 - 4534.92i) q^{69} -1862.27 q^{70} -9616.78 q^{71} +(-1449.58 + 1449.58i) q^{72} -5989.19i q^{73} +(3616.49 + 1383.58i) q^{74} +6335.68 q^{75} +(-1819.38 - 1819.38i) q^{76} +3007.08i q^{77} -7553.62i q^{78} +(7624.90 - 7624.90i) q^{79} +(1506.83 - 1506.83i) q^{80} -5691.33 q^{81} +(633.345 - 633.345i) q^{82} -2358.53 q^{83} +2072.27 q^{84} -4930.82i q^{85} -8689.13 q^{86} +(10887.7 - 10887.7i) q^{87} +(-2433.13 - 2433.13i) q^{88} +(4769.82 + 4769.82i) q^{89} -8532.31 q^{90} +(-2850.60 + 2850.60i) q^{91} +(-2769.51 - 2769.51i) q^{92} +(-3115.83 + 3115.83i) q^{93} +(1226.04 + 1226.04i) q^{94} -10709.0i q^{95} +(-1676.75 + 1676.75i) q^{96} +(113.114 - 113.114i) q^{97} +(4019.96 + 4019.96i) q^{98} +13777.5i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 28 q^{2} - 12 q^{5} - 40 q^{6} + 48 q^{7} + 224 q^{8} - 346 q^{9}+O(q^{10}) $ 14 * q - 28 * q^2 - 12 * q^5 - 40 * q^6 + 48 * q^7 + 224 * q^8 - 346 * q^9	\( 14 q - 28 q^{2} - 12 q^{5} - 40 q^{6} + 48 q^{7} + 224 q^{8} - 346 q^{9} + 48 q^{10} + 160 q^{12} - 56 q^{13} - 96 q^{14} - 378 q^{15} - 896 q^{16} - 348 q^{17} + 692 q^{18} - 184 q^{19} - 96 q^{20} - 320 q^{22} - 502 q^{23} - 320 q^{24} + 224 q^{26} - 474 q^{29} - 630 q^{31} + 1792 q^{32} + 632 q^{33} + 1392 q^{34} + 1826 q^{35} - 2544 q^{37} + 736 q^{38} - 798 q^{39} - 224 q^{42} + 1936 q^{43} + 1280 q^{44} + 6162 q^{45} + 2008 q^{46} + 5716 q^{47} + 7862 q^{49} - 1372 q^{50} - 2422 q^{51} - 448 q^{52} - 20228 q^{53} - 656 q^{54} + 14006 q^{55} + 768 q^{56} - 2270 q^{57} - 4502 q^{59} + 3024 q^{60} - 11906 q^{61} - 2588 q^{63} - 1264 q^{66} - 2784 q^{68} + 21440 q^{69} - 7304 q^{70} - 11224 q^{71} - 5536 q^{72} + 4924 q^{74} - 18652 q^{75} - 1472 q^{76} + 20488 q^{79} + 768 q^{80} - 1706 q^{81} + 9808 q^{82} - 20224 q^{83} + 896 q^{84} - 7744 q^{86} + 19636 q^{87} - 2560 q^{88} + 13864 q^{89} - 24648 q^{90} - 6070 q^{91} - 4016 q^{92} - 13800 q^{93} - 11432 q^{94} + 2560 q^{96} + 16622 q^{97} - 15724 q^{98}+O(q^{100}) \) 14 * q - 28 * q^2 - 12 * q^5 - 40 * q^6 + 48 * q^7 + 224 * q^8 - 346 * q^9 + 48 * q^10 + 160 * q^12 - 56 * q^13 - 96 * q^14 - 378 * q^15 - 896 * q^16 - 348 * q^17 + 692 * q^18 - 184 * q^19 - 96 * q^20 - 320 * q^22 - 502 * q^23 - 320 * q^24 + 224 * q^26 - 474 * q^29 - 630 * q^31 + 1792 * q^32 + 632 * q^33 + 1392 * q^34 + 1826 * q^35 - 2544 * q^37 + 736 * q^38 - 798 * q^39 - 224 * q^42 + 1936 * q^43 + 1280 * q^44 + 6162 * q^45 + 2008 * q^46 + 5716 * q^47 + 7862 * q^49 - 1372 * q^50 - 2422 * q^51 - 448 * q^52 - 20228 * q^53 - 656 * q^54 + 14006 * q^55 + 768 * q^56 - 2270 * q^57 - 4502 * q^59 + 3024 * q^60 - 11906 * q^61 - 2588 * q^63 - 1264 * q^66 - 2784 * q^68 + 21440 * q^69 - 7304 * q^70 - 11224 * q^71 - 5536 * q^72 + 4924 * q^74 - 18652 * q^75 - 1472 * q^76 + 20488 * q^79 + 768 * q^80 - 1706 * q^81 + 9808 * q^82 - 20224 * q^83 + 896 * q^84 - 7744 * q^86 + 19636 * q^87 - 2560 * q^88 + 13864 * q^89 - 24648 * q^90 - 6070 * q^91 - 4016 * q^92 - 13800 * q^93 - 11432 * q^94 + 2560 * q^96 + 16622 * q^97 - 15724 * 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
$3$			13.0996i			1.45551i	0.685838	+	0.727755i	$0.259436\pi$
$3$			13.0996i			1.45551i	−0.685838	+	0.727755i	$0.740564\pi$
$4$			8.00000i			0.500000i
$5$	−23.5442	+	23.5442i	−0.941766	+	0.941766i	−0.998395	−	0.0566289i	$-0.981965\pi$
$5$	−23.5442	+	23.5442i	−0.941766	+	0.941766i	0.0566289	+	0.998395i	$0.481965\pi$
$6$	26.1992	−	26.1992i	0.727755	−	0.727755i
$7$	−19.7742			−0.403555			−0.201778	−	0.979431i	$-0.564672\pi$
$7$	−19.7742			−0.403555			−0.201778	+	0.979431i	$0.564672\pi$
$8$	16.0000	−	16.0000i	0.250000	−	0.250000i
$9$	−90.5991			−1.11851
$10$	94.1766			0.941766
$11$		−	152.071i		−	1.25678i	−0.777897	−	0.628392i	$-0.783713\pi$
$11$		−	152.071i		−	1.25678i	0.777897	−	0.628392i	$-0.216287\pi$
$12$	−104.797			−0.727755
$13$	144.158	−	144.158i	0.853004	−	0.853004i	−0.137498	−	0.990502i	$-0.543906\pi$
$13$	144.158	−	144.158i	0.853004	−	0.853004i	0.990502	+	0.137498i	$0.0439061\pi$
$14$	39.5484	+	39.5484i	0.201778	+	0.201778i
$15$	−308.419	−	308.419i	−1.37075	−	1.37075i
$16$	−64.0000			−0.250000
$17$	−104.714	+	104.714i	−0.362333	+	0.362333i	−0.864671	−	0.502338i	$-0.832473\pi$
$17$	−104.714	+	104.714i	−0.362333	+	0.362333i	0.502338	+	0.864671i	$0.332473\pi$
$18$	181.198	+	181.198i	0.559253	+	0.559253i
$19$	−227.423	+	227.423i	−0.629980	+	0.629980i	−0.948063	−	0.318083i	$-0.896961\pi$
$19$	−227.423	+	227.423i	−0.629980	+	0.629980i	0.318083	+	0.948063i	$0.396961\pi$
$20$	−188.353	−	188.353i	−0.470883	−	0.470883i
$21$		−	259.034i		−	0.587378i
$22$	−304.142	+	304.142i	−0.628392	+	0.628392i
$23$	−346.188	+	346.188i	−0.654420	+	0.654420i	−0.954054	−	0.299634i	$-0.903135\pi$
$23$	−346.188	+	346.188i	−0.654420	+	0.654420i	0.299634	+	0.954054i	$0.403135\pi$
$24$	209.593	+	209.593i	0.363877	+	0.363877i
$25$		−	483.655i		−	0.773848i
$26$	−576.631			−0.853004
$27$		−	125.744i		−	0.172488i
$28$		−	158.194i		−	0.201778i
$29$	−831.151	−	831.151i	−0.988289	−	0.988289i	0.0116431	−	0.999932i	$-0.496294\pi$
$29$	−831.151	−	831.151i	−0.988289	−	0.988289i	−0.999932	+	0.0116431i	$0.996294\pi$
$30$			1233.67i			1.37075i
$31$	237.857	+	237.857i	0.247510	+	0.247510i	0.819948	−	0.572438i	$-0.194002\pi$
$31$	237.857	+	237.857i	0.247510	+	0.247510i	−0.572438	+	0.819948i	$0.694002\pi$
$32$	128.000	+	128.000i	0.125000	+	0.125000i
$33$	1992.07			1.82926
$34$	418.857			0.362333
$35$	465.567	−	465.567i	0.380055	−	0.380055i
$36$		−	724.792i		−	0.559253i
$37$	−1250.02	+	558.226i	−0.913088	+	0.407762i
$37$	−1250.02	+	558.226i	−0.913088	+	0.407762i
$38$	909.692			0.629980
$39$	1888.41	+	1888.41i	1.24156	+	1.24156i
$40$			753.413i			0.470883i
$41$			316.672i			0.188383i	0.995554	+	0.0941916i	$0.0300266\pi$
$41$			316.672i			0.188383i	−0.995554	+	0.0941916i	$0.969973\pi$
$42$	−518.068	+	518.068i	−0.293689	+	0.293689i
$43$	2172.28	−	2172.28i	1.17484	−	1.17484i	0.193801	−	0.981041i	$-0.437919\pi$
$43$	2172.28	−	2172.28i	1.17484	−	1.17484i	0.981041	−	0.193801i	$-0.0620815\pi$
$44$	1216.57			0.628392
$45$	2133.08	−	2133.08i	1.05337	−	1.05337i
$46$	1384.75			0.654420
$47$	−613.021			−0.277511			−0.138755	−	0.990327i	$-0.544310\pi$
$47$	−613.021			−0.277511			−0.138755	+	0.990327i	$0.544310\pi$
$48$		−	838.373i		−	0.363877i
$49$	−2009.98			−0.837143
$50$	−967.310	+	967.310i	−0.386924	+	0.386924i
$51$	−1371.71	−	1371.71i	−0.527379	−	0.527379i
$52$	1153.26	+	1153.26i	0.426502	+	0.426502i
$53$	−2538.56			−0.903723			−0.451861	−	0.892088i	$-0.649240\pi$
$53$	−2538.56			−0.903723			−0.451861	+	0.892088i	$0.649240\pi$
$54$	−251.487	+	251.487i	−0.0862439	+	0.0862439i
$55$	3580.38	+	3580.38i	1.18360	+	1.18360i
$56$	−316.387	+	316.387i	−0.100889	+	0.100889i
$57$	−2979.15	−	2979.15i	−0.916942	−	0.916942i
$58$			3324.60i			0.988289i
$59$	−2732.58	+	2732.58i	−0.784998	+	0.784998i	−0.980669	−	0.195672i	$-0.937311\pi$
$59$	−2732.58	+	2732.58i	−0.784998	+	0.784998i	0.195672	+	0.980669i	$0.437311\pi$
$60$	2467.35	−	2467.35i	0.685375	−	0.685375i
$61$	1632.21	+	1632.21i	0.438649	+	0.438649i	0.891557	−	0.452908i	$-0.149613\pi$
$61$	1632.21	+	1632.21i	0.438649	+	0.438649i	−0.452908	+	0.891557i	$0.649613\pi$
$62$		−	951.430i		−	0.247510i
$63$	1791.52			0.451379
$64$		−	512.000i		−	0.125000i
$65$			6788.14i			1.60666i
$66$	−3984.13	−	3984.13i	−0.914631	−	0.914631i
$67$			6634.72i			1.47800i	0.673708	+	0.738998i	$0.264701\pi$
$67$			6634.72i			1.47800i	−0.673708	+	0.738998i	$0.735299\pi$
$68$	−837.714	−	837.714i	−0.181167	−	0.181167i
$69$	−4534.92	−	4534.92i	−0.952514	−	0.952514i
$70$	−1862.27			−0.380055
$71$	−9616.78			−1.90771			−0.953856	−	0.300265i	$-0.902925\pi$
$71$	−9616.78			−1.90771			−0.953856	+	0.300265i	$0.902925\pi$
$72$	−1449.58	+	1449.58i	−0.279627	+	0.279627i
$73$		−	5989.19i		−	1.12389i	−0.827176	−	0.561943i	$-0.810054\pi$
$73$		−	5989.19i		−	1.12389i	0.827176	−	0.561943i	$-0.189946\pi$
$74$	3616.49	+	1383.58i	0.660425	+	0.252663i
$75$	6335.68			1.12634
$76$	−1819.38	−	1819.38i	−0.314990	−	0.314990i
$77$			3007.08i			0.507182i
$78$		−	7553.62i		−	1.24156i
$79$	7624.90	−	7624.90i	1.22174	−	1.22174i	0.254732	−	0.967012i	$-0.418013\pi$
$79$	7624.90	−	7624.90i	1.22174	−	1.22174i	0.967012	−	0.254732i	$-0.0819873\pi$
$80$	1506.83	−	1506.83i	0.235442	−	0.235442i
$81$	−5691.33			−0.867449
$82$	633.345	−	633.345i	0.0941916	−	0.0941916i
$83$	−2358.53			−0.342362			−0.171181	−	0.985240i	$-0.554758\pi$
$83$	−2358.53			−0.342362			−0.171181	+	0.985240i	$0.554758\pi$
$84$	2072.27			0.293689
$85$		−	4930.82i		−	0.682466i
$86$	−8689.13			−1.17484
$87$	10887.7	−	10887.7i	1.43846	−	1.43846i
$88$	−2433.13	−	2433.13i	−0.314196	−	0.314196i
$89$	4769.82	+	4769.82i	0.602174	+	0.602174i	0.940889	−	0.338715i	$-0.109992\pi$
$89$	4769.82	+	4769.82i	0.602174	+	0.602174i	−0.338715	+	0.940889i	$0.609992\pi$
$90$	−8532.31			−1.05337
$91$	−2850.60	+	2850.60i	−0.344234	+	0.344234i
$92$	−2769.51	−	2769.51i	−0.327210	−	0.327210i
$93$	−3115.83	+	3115.83i	−0.360254	+	0.360254i
$94$	1226.04	+	1226.04i	0.138755	+	0.138755i
$95$		−	10709.0i		−	1.18659i
$96$	−1676.75	+	1676.75i	−0.181939	+	0.181939i
$97$	113.114	−	113.114i	0.0120219	−	0.0120219i	−0.701070	−	0.713092i	$-0.747294\pi$
$97$	113.114	−	113.114i	0.0120219	−	0.0120219i	0.713092	+	0.701070i	$0.247294\pi$
$98$	4019.96	+	4019.96i	0.418572	+	0.418572i
$99$			13777.5i			1.40572i
$100$	3869.24			0.386924
$101$			13533.1i			1.32665i	0.748333	+	0.663323i	$0.230854\pi$
$101$			13533.1i			1.32665i	−0.748333	+	0.663323i	$0.769146\pi$
$102$			5486.85i			0.527379i
$103$	13459.1	+	13459.1i	1.26865	+	1.26865i	0.946784	+	0.321870i	$0.104311\pi$
$103$	13459.1	+	13459.1i	1.26865	+	1.26865i	0.321870	+	0.946784i	$0.395689\pi$
$104$		−	4613.05i		−	0.426502i
$105$	6098.73	+	6098.73i	0.553173	+	0.553173i
$106$	5077.11	+	5077.11i	0.451861	+	0.451861i
$107$	6141.07			0.536385			0.268193	−	0.963365i	$-0.413574\pi$
$107$	6141.07			0.536385			0.268193	+	0.963365i	$0.413574\pi$
$108$	1005.95			0.0862439
$109$	−14823.0	+	14823.0i	−1.24762	+	1.24762i	−0.290853	+	0.956768i	$0.593939\pi$
$109$	−14823.0	+	14823.0i	−1.24762	+	1.24762i	−0.956768	+	0.290853i	$0.906061\pi$
$110$		−	14321.5i		−	1.18360i
$111$	−7312.53	−	16374.7i	−0.593501	−	1.32901i
$112$	1265.55			0.100889
$113$	−10121.6	−	10121.6i	−0.792673	−	0.792673i	0.189255	−	0.981928i	$-0.439393\pi$
$113$	−10121.6	−	10121.6i	−0.792673	−	0.792673i	−0.981928	+	0.189255i	$0.939393\pi$
$114$			11916.6i			0.916942i
$115$		−	16301.4i		−	1.23262i
$116$	6649.21	−	6649.21i	0.494145	−	0.494145i
$117$	−13060.6	+	13060.6i	−0.954091	+	0.954091i
$118$	10930.3			0.784998
$119$	2070.64	−	2070.64i	0.146221	−	0.146221i
$120$	−9869.40			−0.685375
$121$	−8484.56			−0.579507
$122$		−	6528.86i		−	0.438649i
$123$	−4148.27			−0.274194
$124$	−1902.86	+	1902.86i	−0.123755	+	0.123755i
$125$	−3327.85	−	3327.85i	−0.212983	−	0.212983i
$126$	−3583.05	−	3583.05i	−0.225690	−	0.225690i
$127$	12910.8			0.800472			0.400236	−	0.916412i	$-0.368928\pi$
$127$	12910.8			0.800472			0.400236	+	0.916412i	$0.368928\pi$
$128$	−1024.00	+	1024.00i	−0.0625000	+	0.0625000i
$129$	28456.0	+	28456.0i	1.70999	+	1.70999i
$130$	13576.3	−	13576.3i	0.803331	−	0.803331i
$131$	−3703.95	−	3703.95i	−0.215836	−	0.215836i	0.590905	−	0.806741i	$-0.298771\pi$
$131$	−3703.95	−	3703.95i	−0.215836	−	0.215836i	−0.806741	+	0.590905i	$0.798771\pi$
$132$			15936.5i			0.914631i
$133$	4497.11	−	4497.11i	0.254232	−	0.254232i
$134$	13269.4	−	13269.4i	0.738998	−	0.738998i
$135$	2960.53	+	2960.53i	0.162443	+	0.162443i
$136$			3350.86i			0.181167i
$137$	10380.8			0.553083			0.276541	−	0.961002i	$-0.410812\pi$
$137$	10380.8			0.553083			0.276541	+	0.961002i	$0.410812\pi$
$138$			18139.7i			0.952514i
$139$			28719.5i			1.48644i	0.669049	+	0.743219i	$0.266702\pi$
$139$			28719.5i			1.48644i	−0.669049	+	0.743219i	$0.733298\pi$
$140$	3724.54	+	3724.54i	0.190027	+	0.190027i
$141$		−	8030.32i		−	0.403919i
$142$	19233.6	+	19233.6i	0.953856	+	0.953856i
$143$	−21922.2	−	21922.2i	−1.07204	−	1.07204i
$144$	5798.34			0.279627
$145$	39137.5			1.86147
$146$	−11978.4	+	11978.4i	−0.561943	+	0.561943i
$147$		−	26329.9i		−	1.21847i
$148$	−4465.81	−	10000.1i	−0.203881	−	0.456544i
$149$	−11007.7			−0.495819			−0.247909	−	0.968783i	$-0.579744\pi$
$149$	−11007.7			−0.495819			−0.247909	+	0.968783i	$0.579744\pi$
$150$	−12671.4	−	12671.4i	−0.563171	−	0.563171i
$151$		−	23264.9i		−	1.02034i	−0.860072	−	0.510172i	$-0.829582\pi$
$151$		−	23264.9i		−	1.02034i	0.860072	−	0.510172i	$-0.170418\pi$
$152$			7277.53i			0.314990i
$153$	9487.01	−	9487.01i	0.405272	−	0.405272i
$154$	6014.16	−	6014.16i	0.253591	−	0.253591i
$155$	−11200.3			−0.466194
$156$	−15107.2	+	15107.2i	−0.620778	+	0.620778i
$157$	−17848.9			−0.724123			−0.362062	−	0.932154i	$-0.617927\pi$
$157$	−17848.9			−0.724123			−0.362062	+	0.932154i	$0.617927\pi$
$158$	−30499.6			−1.22174
$159$		−	33254.0i		−	1.31538i
$160$	−6027.30			−0.235442
$161$	6845.59	−	6845.59i	0.264095	−	0.264095i
$162$	11382.7	+	11382.7i	0.433725	+	0.433725i
$163$	26691.5	+	26691.5i	1.00461	+	1.00461i	0.999989	+	0.00462291i	$0.00147152\pi$
$163$	26691.5	+	26691.5i	1.00461	+	1.00461i	0.00462291	+	0.999989i	$0.498528\pi$
$164$	−2533.38			−0.0941916
$165$	−46901.5	+	46901.5i	−1.72274	+	1.72274i
$166$	4717.07	+	4717.07i	0.171181	+	0.171181i
$167$	12387.3	−	12387.3i	0.444163	−	0.444163i	−0.449246	−	0.893408i	$-0.648307\pi$
$167$	12387.3	−	12387.3i	0.444163	−	0.444163i	0.893408	+	0.449246i	$0.148307\pi$
$168$	−4144.54	−	4144.54i	−0.146845	−	0.146845i
$169$		−	13001.9i		−	0.455232i
$170$	−9861.64	+	9861.64i	−0.341233	+	0.341233i
$171$	20604.3	−	20604.3i	0.704637	−	0.704637i
$172$	17378.3	+	17378.3i	0.587421	+	0.587421i
$173$		−	31584.6i		−	1.05532i	−0.849457	−	0.527658i	$-0.823070\pi$
$173$		−	31584.6i		−	1.05532i	0.849457	−	0.527658i	$-0.176930\pi$
$174$	−43550.9			−1.43846
$175$			9563.89i			0.312290i
$176$			9732.54i			0.314196i
$177$	−35795.6	−	35795.6i	−1.14257	−	1.14257i
$178$		−	19079.3i		−	0.602174i
$179$	33482.1	+	33482.1i	1.04498	+	1.04498i	0.998940	+	0.0460373i	$0.0146593\pi$
$179$	33482.1	+	33482.1i	1.04498	+	1.04498i	0.0460373	+	0.998940i	$0.485341\pi$
$180$	17064.6	+	17064.6i	0.526686	+	0.526686i
$181$	−47551.7			−1.45147			−0.725737	−	0.687972i	$-0.758501\pi$
$181$	−47551.7			−1.45147			−0.725737	+	0.687972i	$0.758501\pi$
$182$	11402.4			0.344234
$183$	−21381.3	+	21381.3i	−0.638458	+	0.638458i
$184$			11078.0i			0.327210i
$185$	16287.7	−	42573.6i	0.475899	−	1.24393i
$186$	12463.3			0.360254
$187$	15924.0	+	15924.0i	0.455375	+	0.455375i
$188$		−	4904.17i		−	0.138755i
$189$			2486.48i			0.0696084i
$190$	−21417.9	+	21417.9i	−0.593294	+	0.593294i
$191$	4475.00	−	4475.00i	0.122666	−	0.122666i	−0.643109	−	0.765775i	$-0.722356\pi$
$191$	4475.00	−	4475.00i	0.122666	−	0.122666i	0.765775	+	0.643109i	$0.222356\pi$
$192$	6706.99			0.181939
$193$	12085.4	−	12085.4i	0.324448	−	0.324448i	−0.526023	−	0.850470i	$-0.676317\pi$
$193$	12085.4	−	12085.4i	0.324448	−	0.324448i	0.850470	+	0.526023i	$0.176317\pi$
$194$	−452.456			−0.0120219
$195$	−88921.8			−2.33851
$196$		−	16079.8i		−	0.418572i
$197$	−43196.6			−1.11306			−0.556528	−	0.830829i	$-0.687867\pi$
$197$	−43196.6			−1.11306			−0.556528	+	0.830829i	$0.687867\pi$
$198$	27555.0	−	27555.0i	0.702861	−	0.702861i
$199$	14458.4	+	14458.4i	0.365101	+	0.365101i	0.865687	−	0.500586i	$-0.166882\pi$
$199$	14458.4	+	14458.4i	0.365101	+	0.365101i	−0.500586	+	0.865687i	$0.666882\pi$
$200$	−7738.48	−	7738.48i	−0.193462	−	0.193462i
$201$	−86912.1			−2.15124
$202$	27066.2	−	27066.2i	0.663323	−	0.663323i
$203$	16435.3	+	16435.3i	0.398829	+	0.398829i
$204$	10973.7	−	10973.7i	0.263690	−	0.263690i
$205$	−7455.78	−	7455.78i	−0.177413	−	0.177413i
$206$		−	53836.6i		−	1.26865i
$207$	31364.3	−	31364.3i	0.731973	−	0.731973i
$208$	−9226.09	+	9226.09i	−0.213251	+	0.213251i
$209$	34584.4	+	34584.4i	0.791749	+	0.791749i
$210$		−	24394.9i		−	0.553173i
$211$	38389.4			0.862276			0.431138	−	0.902286i	$-0.358112\pi$
$211$	38389.4			0.862276			0.431138	+	0.902286i	$0.358112\pi$
$212$		−	20308.5i		−	0.451861i
$213$		−	125976.i		−	2.77669i
$214$	−12282.1	−	12282.1i	−0.268193	−	0.268193i
$215$			102289.i			2.21285i
$216$	−2011.90	−	2011.90i	−0.0431220	−	0.0431220i
$217$	−4703.44	−	4703.44i	−0.0998841	−	0.0998841i
$218$	59291.9			1.24762
$219$	78455.9			1.63583
$220$	−28643.1	+	28643.1i	−0.591799	+	0.591799i
$221$			30190.7i			0.618143i
$222$	−18124.4	+	47374.5i	−0.367754	+	0.961255i
$223$	−6647.07			−0.133666			−0.0668329	−	0.997764i	$-0.521289\pi$
$223$	−6647.07			−0.133666			−0.0668329	+	0.997764i	$0.521289\pi$
$224$	−2531.10	−	2531.10i	−0.0504444	−	0.0504444i
$225$			43818.7i			0.865554i
$226$			40486.5i			0.792673i
$227$	−17341.3	+	17341.3i	−0.336535	+	0.336535i	−0.855061	−	0.518527i	$-0.826481\pi$
$227$	−17341.3	+	17341.3i	−0.336535	+	0.336535i	0.518527	+	0.855061i	$0.326481\pi$
$228$	23833.2	−	23833.2i	0.458471	−	0.458471i
$229$	−74769.8			−1.42579			−0.712895	−	0.701271i	$-0.752616\pi$
$229$	−74769.8			−1.42579			−0.712895	+	0.701271i	$0.752616\pi$
$230$	−32602.8	+	32602.8i	−0.616311	+	0.616311i
$231$	−39391.5			−0.738208
$232$	−26596.8			−0.494145
$233$			85523.8i			1.57534i	0.616096	+	0.787671i	$0.288713\pi$
$233$			85523.8i			1.57534i	−0.616096	+	0.787671i	$0.711287\pi$
$234$	52242.2			0.954091
$235$	14433.1	−	14433.1i	0.261350	−	0.261350i
$236$	−21860.6	−	21860.6i	−0.392499	−	0.392499i
$237$	99883.0	+	99883.0i	1.77826	+	1.77826i
$238$	−8282.56			−0.146221
$239$	−14535.0	+	14535.0i	−0.254459	+	0.254459i	−0.822796	−	0.568337i	$-0.807587\pi$
$239$	−14535.0	+	14535.0i	−0.254459	+	0.254459i	0.568337	+	0.822796i	$0.307587\pi$
$240$	19738.8	+	19738.8i	0.342687	+	0.342687i
$241$	37780.9	−	37780.9i	0.650486	−	0.650486i	−0.302624	−	0.953110i	$-0.597863\pi$
$241$	37780.9	−	37780.9i	0.650486	−	0.650486i	0.953110	+	0.302624i	$0.0978626\pi$
$242$	16969.1	+	16969.1i	0.289753	+	0.289753i
$243$		−	84739.3i		−	1.43507i
$244$	−13057.7	+	13057.7i	−0.219325	+	0.219325i
$245$	47323.3	−	47323.3i	0.788393	−	0.788393i
$246$	8296.55	+	8296.55i	0.137097	+	0.137097i
$247$			65569.5i			1.07475i
$248$	7611.44			0.123755
$249$		−	30895.8i		−	0.498312i
$250$			13311.4i			0.212983i
$251$	40564.8	+	40564.8i	0.643876	+	0.643876i	0.951506	−	0.307630i	$-0.0995359\pi$
$251$	40564.8	+	40564.8i	0.643876	+	0.643876i	−0.307630	+	0.951506i	$0.599536\pi$
$252$			14332.2i			0.225690i
$253$	52645.1	+	52645.1i	0.822465	+	0.822465i
$254$	−25821.6	−	25821.6i	−0.400236	−	0.400236i
$255$	64591.7			0.993336
$256$	4096.00			0.0625000
$257$	15552.2	−	15552.2i	0.235464	−	0.235464i	−0.579505	−	0.814969i	$-0.696754\pi$
$257$	15552.2	−	15552.2i	0.235464	−	0.235464i	0.814969	+	0.579505i	$0.196754\pi$
$258$		−	113824.i		−	1.70999i
$259$	24718.1	−	11038.5i	0.368481	−	0.164554i
$260$	−54305.1			−0.803331
$261$	75301.5	+	75301.5i	1.10541	+	1.10541i
$262$			14815.8i			0.215836i
$263$		−	7873.27i		−	0.113827i	−0.998379	−	0.0569133i	$-0.981874\pi$
$263$		−	7873.27i		−	0.113827i	0.998379	−	0.0569133i	$-0.0181259\pi$
$264$	31873.0	−	31873.0i	0.457315	−	0.457315i
$265$	59768.2	−	59768.2i	0.851096	−	0.851096i
$266$	−17988.4			−0.254232
$267$	−62482.7	+	62482.7i	−0.876470	+	0.876470i
$268$	−53077.8			−0.738998
$269$	49063.4			0.678037			0.339018	−	0.940780i	$-0.389905\pi$
$269$	49063.4			0.678037			0.339018	+	0.940780i	$0.389905\pi$
$270$		−	11842.1i		−	0.162443i
$271$	−21218.5			−0.288919			−0.144460	−	0.989511i	$-0.546144\pi$
$271$	−21218.5			−0.288919			−0.144460	+	0.989511i	$0.546144\pi$
$272$	6701.71	−	6701.71i	0.0905833	−	0.0905833i
$273$	−37341.7	−	37341.7i	−0.501036	−	0.501036i
$274$	−20761.6	−	20761.6i	−0.276541	−	0.276541i
$275$	−73549.8			−0.972560
$276$	36279.4	−	36279.4i	0.476257	−	0.476257i
$277$	−48467.9	−	48467.9i	−0.631676	−	0.631676i	0.316812	−	0.948488i	$-0.397388\pi$
$277$	−48467.9	−	48467.9i	−0.631676	−	0.631676i	−0.948488	+	0.316812i	$0.897388\pi$
$278$	57438.9	−	57438.9i	0.743219	−	0.743219i
$279$	−21549.7	−	21549.7i	−0.276842	−	0.276842i
$280$		−	14898.1i		−	0.190027i
$281$	−4510.08	+	4510.08i	−0.0571178	+	0.0571178i	−0.735089	−	0.677971i	$-0.762860\pi$
$281$	−4510.08	+	4510.08i	−0.0571178	+	0.0571178i	0.677971	+	0.735089i	$0.262860\pi$
$282$	−16060.6	+	16060.6i	−0.201960	+	0.201960i
$283$	−72880.9	−	72880.9i	−0.909999	−	0.909999i	0.0862730	−	0.996272i	$-0.472504\pi$
$283$	−72880.9	−	72880.9i	−0.909999	−	0.909999i	−0.996272	+	0.0862730i	$0.972504\pi$
$284$		−	76934.2i		−	0.953856i
$285$	140283.			1.72709
$286$			87688.8i			1.07204i
$287$		−	6261.94i		−	0.0760230i
$288$	−11596.7	−	11596.7i	−0.139813	−	0.139813i
$289$			61590.8i			0.737429i
$290$	−78275.0	−	78275.0i	−0.930737	−	0.930737i
$291$	1481.75	+	1481.75i	0.0174980	+	0.0174980i
$292$	47913.5			0.561943
$293$	23239.5			0.270702			0.135351	−	0.990798i	$-0.456784\pi$
$293$	23239.5			0.270702			0.135351	+	0.990798i	$0.456784\pi$
$294$	−52659.8	+	52659.8i	−0.609235	+	0.609235i
$295$		−	128672.i		−	1.47857i
$296$	−11068.7	+	28931.9i	−0.126332	+	0.330213i
$297$	−19122.0			−0.216780
$298$	22015.3	+	22015.3i	0.247909	+	0.247909i
$299$			99811.4i			1.11645i
$300$			50685.4i			0.563171i
$301$	−42955.1	+	42955.1i	−0.474113	+	0.474113i
$302$	−46529.7	+	46529.7i	−0.510172	+	0.510172i
$303$	−177278.			−1.93094
$304$	14555.1	−	14555.1i	0.157495	−	0.157495i
$305$	−76858.2			−0.826211
$306$	−37948.1			−0.405272
$307$			8792.55i			0.0932907i	0.998912	+	0.0466453i	$0.0148531\pi$
$307$			8792.55i			0.0932907i	−0.998912	+	0.0466453i	$0.985147\pi$
$308$	−24056.6			−0.253591
$309$	−176309.	+	176309.i	−1.84654	+	1.84654i
$310$	22400.6	+	22400.6i	0.233097	+	0.233097i
$311$	87685.1	+	87685.1i	0.906577	+	0.906577i	0.995994	−	0.0894171i	$-0.0285004\pi$
$311$	87685.1	+	87685.1i	0.906577	+	0.906577i	−0.0894171	+	0.995994i	$0.528500\pi$
$312$	60429.0			0.620778
$313$	121488.	−	121488.i	1.24006	−	1.24006i	0.280091	−	0.959974i	$-0.409635\pi$
$313$	121488.	−	121488.i	1.24006	−	1.24006i	0.959974	−	0.280091i	$-0.0903646\pi$
$314$	35697.8	+	35697.8i	0.362062	+	0.362062i
$315$	−42179.9	+	42179.9i	−0.425094	+	0.425094i
$316$	60999.2	+	60999.2i	0.610872	+	0.610872i
$317$		−	164919.i		−	1.64116i	−0.571532	−	0.820580i	$-0.693651\pi$
$317$		−	164919.i		−	1.64116i	0.571532	−	0.820580i	$-0.306349\pi$
$318$	−66508.1	+	66508.1i	−0.657688	+	0.657688i
$319$	−126394.	+	126394.i	−1.24207	+	1.24207i
$320$	12054.6	+	12054.6i	0.117721	+	0.117721i
$321$			80445.5i			0.780714i
$322$	−27382.4			−0.264095
$323$		−	47628.8i		−	0.456525i
$324$		−	45530.7i		−	0.433725i
$325$	−69722.6	−	69722.6i	−0.660095	−	0.660095i
$326$		−	106766.i		−	1.00461i
$327$	−194175.	−	194175.i	−1.81592	−	1.81592i
$328$	5066.76	+	5066.76i	0.0470958	+	0.0470958i
$329$	12122.0			0.111991
$330$	187606.			1.72274
$331$	−125950.	+	125950.i	−1.14958	+	1.14958i	−0.162950	+	0.986634i	$0.552101\pi$
$331$	−125950.	+	125950.i	−1.14958	+	1.14958i	−0.986634	+	0.162950i	$0.947899\pi$
$332$		−	18868.3i		−	0.171181i
$333$	113250.	−	50574.8i	1.02130	−	0.456085i
$334$	−49549.0			−0.444163
$335$	−156209.	−	156209.i	−1.39193	−	1.39193i
$336$			16578.2i			0.146845i
$337$			7186.65i			0.0632800i	0.999499	+	0.0316400i	$0.0100730\pi$
$337$			7186.65i			0.0632800i	−0.999499	+	0.0316400i	$0.989927\pi$
$338$	−26003.8	+	26003.8i	−0.227616	+	0.227616i
$339$	132589.	−	132589.i	1.15374	−	1.15374i
$340$	39446.5			0.341233
$341$	36171.2	−	36171.2i	0.311067	−	0.311067i
$342$	−82417.2			−0.704637
$343$	87223.6			0.741389
$344$		−	69513.0i		−	0.587421i
$345$	213542.			1.79409
$346$	−63169.2	+	63169.2i	−0.527658	+	0.527658i
$347$	−43965.3	−	43965.3i	−0.365133	−	0.365133i	0.500566	−	0.865699i	$-0.333125\pi$
$347$	−43965.3	−	43965.3i	−0.365133	−	0.365133i	−0.865699	+	0.500566i	$0.833125\pi$
$348$	87101.9	+	87101.9i	0.719232	+	0.719232i
$349$	−197535.			−1.62178			−0.810891	−	0.585197i	$-0.801017\pi$
$349$	−197535.			−1.62178			−0.810891	+	0.585197i	$0.801017\pi$
$350$	19127.8	−	19127.8i	0.156145	−	0.156145i
$351$	−18126.9	−	18126.9i	−0.147133	−	0.147133i
$352$	19465.1	−	19465.1i	0.157098	−	0.157098i
$353$	140884.	+	140884.i	1.13061	+	1.13061i	0.990076	+	0.140536i	$0.0448826\pi$
$353$	140884.	+	140884.i	1.13061	+	1.13061i	0.140536	+	0.990076i	$0.455117\pi$
$354$			143182.i			1.14257i
$355$	226419.	−	226419.i	1.79662	−	1.79662i
$356$	−38158.6	+	38158.6i	−0.301087	+	0.301087i
$357$	27124.5	+	27124.5i	0.212827	+	0.212827i
$358$		−	133928.i		−	1.04498i
$359$	−36497.2			−0.283186			−0.141593	−	0.989925i	$-0.545222\pi$
$359$	−36497.2			−0.283186			−0.141593	+	0.989925i	$0.545222\pi$
$360$		−	68258.5i		−	0.526686i
$361$			26878.6i			0.206249i
$362$	95103.5	+	95103.5i	0.725737	+	0.725737i
$363$		−	111144.i		−	0.843478i
$364$	−22804.8	−	22804.8i	−0.172117	−	0.172117i
$365$	141011.	+	141011.i	1.05844	+	1.05844i
$366$	85525.3			0.638458
$367$	91669.0			0.680598			0.340299	−	0.940317i	$-0.389472\pi$
$367$	91669.0			0.680598			0.340299	+	0.940317i	$0.389472\pi$
$368$	22156.0	−	22156.0i	0.163605	−	0.163605i
$369$		−	28690.2i		−	0.210708i
$370$	−117722.	+	52571.9i	−0.859916	+	0.384016i
$371$	50197.9			0.364702
$372$	−24926.7	−	24926.7i	−0.180127	−	0.180127i
$373$		−	83737.2i		−	0.601867i	−0.953645	−	0.300934i	$-0.902702\pi$
$373$		−	83737.2i		−	0.601867i	0.953645	−	0.300934i	$-0.0972983\pi$
$374$		−	63696.0i		−	0.455375i
$375$	43593.5	−	43593.5i	0.309998	−	0.309998i
$376$	−9808.34	+	9808.34i	−0.0693777	+	0.0693777i
$377$	−239634.			−1.68603
$378$	4972.96	−	4972.96i	0.0348042	−	0.0348042i
$379$	−19315.2			−0.134469			−0.0672343	−	0.997737i	$-0.521417\pi$
$379$	−19315.2			−0.134469			−0.0672343	+	0.997737i	$0.521417\pi$
$380$	85671.7			0.593294
$381$			169126.i			1.16509i
$382$	−17900.0			−0.122666
$383$	107304.	−	107304.i	0.731505	−	0.731505i	−0.239413	−	0.970918i	$-0.576955\pi$
$383$	107304.	−	107304.i	0.731505	−	0.731505i	0.970918	+	0.239413i	$0.0769549\pi$
$384$	−13414.0	−	13414.0i	−0.0909693	−	0.0909693i
$385$	−70799.2	−	70799.2i	−0.477647	−	0.477647i
$386$	−48341.4			−0.324448
$387$	−196807.	+	196807.i	−1.31407	+	1.31407i
$388$	904.912	+	904.912i	0.00601094	+	0.00601094i
$389$	−45020.2	+	45020.2i	−0.297515	+	0.297515i	−0.840040	−	0.542525i	$-0.817468\pi$
$389$	−45020.2	+	45020.2i	−0.297515	+	0.297515i	0.542525	+	0.840040i	$0.317468\pi$
$390$	177844.	+	177844.i	1.16925	+	1.16925i
$391$		−	72501.7i		−	0.474236i
$392$	−32159.7	+	32159.7i	−0.209286	+	0.209286i
$393$	48520.2	−	48520.2i	0.314151	−	0.314151i
$394$	86393.2	+	86393.2i	0.556528	+	0.556528i
$395$			359044.i			2.30119i
$396$	−110220.			−0.702861
$397$		−	259119.i		−	1.64406i	−0.569441	−	0.822032i	$-0.692840\pi$
$397$		−	259119.i		−	1.64406i	0.569441	−	0.822032i	$-0.307160\pi$
$398$		−	57833.4i		−	0.365101i
$399$	58910.2	+	58910.2i	0.370037	+	0.370037i
$400$			30953.9i			0.193462i
$401$	193875.	+	193875.i	1.20568	+	1.20568i	0.972412	+	0.233271i	$0.0749431\pi$
$401$	193875.	+	193875.i	1.20568	+	1.20568i	0.233271	+	0.972412i	$0.425057\pi$
$402$	173824.	+	173824.i	1.07562	+	1.07562i
$403$	68578.0			0.422255
$404$	−108265.			−0.663323
$405$	133998.	−	133998.i	0.816934	−	0.816934i
$406$		−	65741.4i		−	0.398829i
$407$	84890.0	+	190091.i	0.512469	+	1.14756i
$408$	−43894.8			−0.263690
$409$	12139.7	+	12139.7i	0.0725706	+	0.0725706i	0.742460	−	0.669890i	$-0.233659\pi$
$409$	12139.7	+	12139.7i	0.0725706	+	0.0725706i	−0.669890	+	0.742460i	$0.733659\pi$
$410$			29823.1i			0.177413i
$411$			135984.i			0.805017i
$412$	−107673.	+	107673.i	−0.634327	+	0.634327i
$413$	54034.5	−	54034.5i	0.316790	−	0.316790i
$414$	−125457.			−0.731973
$415$	55529.7	−	55529.7i	0.322425	−	0.322425i
$416$	36904.4			0.213251
$417$	−376213.			−2.16352
$418$		−	138338.i		−	0.791749i
$419$	−87917.3			−0.500779			−0.250390	−	0.968145i	$-0.580559\pi$
$419$	−87917.3			−0.500779			−0.250390	+	0.968145i	$0.580559\pi$
$420$	−48789.9	+	48789.9i	−0.276586	+	0.276586i
$421$	35067.3	+	35067.3i	0.197851	+	0.197851i	0.799078	−	0.601227i	$-0.205321\pi$
$421$	35067.3	+	35067.3i	0.197851	+	0.197851i	−0.601227	+	0.799078i	$0.705321\pi$
$422$	−76778.8	−	76778.8i	−0.431138	−	0.431138i
$423$	55539.1			0.310398
$424$	−40616.9	+	40616.9i	−0.225931	+	0.225931i
$425$	50645.6	+	50645.6i	0.280391	+	0.280391i
$426$	−251951.	+	251951.i	−1.38835	+	1.38835i
$427$	−32275.7	−	32275.7i	−0.177019	−	0.177019i
$428$			49128.6i			0.268193i
$429$	287172.	−	287172.i	1.56037	−	1.56037i
$430$	204578.	−	204578.i	1.10643	−	1.10643i
$431$	−98575.3	−	98575.3i	−0.530656	−	0.530656i	0.390111	−	0.920768i	$-0.372437\pi$
$431$	−98575.3	−	98575.3i	−0.530656	−	0.530656i	−0.920768	+	0.390111i	$0.872437\pi$
$432$			8047.59i			0.0431220i
$433$	−66346.3			−0.353867			−0.176934	−	0.984223i	$-0.556618\pi$
$433$	−66346.3			−0.353867			−0.176934	+	0.984223i	$0.556618\pi$
$434$			18813.8i			0.0998841i
$435$			512685.i			2.70939i
$436$	−118584.	−	118584.i	−0.623810	−	0.623810i
$437$		−	157462.i		−	0.824543i
$438$	−156912.	−	156912.i	−0.817914	−	0.817914i
$439$	−194833.	−	194833.i	−1.01096	−	1.01096i	−0.999939	−	0.0110175i	$-0.996493\pi$
$439$	−194833.	−	194833.i	−1.01096	−	1.01096i	−0.0110175	−	0.999939i	$-0.503507\pi$
$440$	114572.			0.591799
$441$	182102.			0.936351
$442$	60381.5	−	60381.5i	0.309072	−	0.309072i
$443$			282981.i			1.44195i	0.692962	+	0.720974i	$0.256306\pi$
$443$			282981.i			1.44195i	−0.692962	+	0.720974i	$0.743694\pi$
$444$	130998.	−	58500.2i	0.664504	−	0.296751i
$445$	−224603.			−1.13422
$446$	13294.1	+	13294.1i	0.0668329	+	0.0668329i
$447$		−	144196.i		−	0.721669i
$448$			10124.4i			0.0504444i
$449$	175892.	−	175892.i	0.872475	−	0.872475i	−0.120266	−	0.992742i	$-0.538375\pi$
$449$	175892.	−	175892.i	0.872475	−	0.872475i	0.992742	+	0.120266i	$0.0383748\pi$
$450$	87637.3	−	87637.3i	0.432777	−	0.432777i
$451$	48156.6			0.236757
$452$	80973.1	−	80973.1i	0.396336	−	0.396336i
$453$	304760.			1.48512
$454$	69365.2			0.336535
$455$		−	134230.i		−	0.648376i
$456$	−95332.6			−0.458471
$457$	−116094.	+	116094.i	−0.555873	+	0.555873i	−0.928130	−	0.372257i	$-0.878584\pi$
$457$	−116094.	+	116094.i	−0.555873	+	0.555873i	0.372257	+	0.928130i	$0.378584\pi$
$458$	149540.	+	149540.i	0.712895	+	0.712895i
$459$	13167.2	+	13167.2i	0.0624981	+	0.0624981i
$460$	130411.			0.616311
$461$	−166216.	+	166216.i	−0.782116	+	0.782116i	−0.980188	−	0.198072i	$-0.936532\pi$
$461$	−166216.	+	166216.i	−0.782116	+	0.782116i	0.198072	+	0.980188i	$0.436532\pi$
$462$	78783.0	+	78783.0i	0.369104	+	0.369104i
$463$	−232696.	+	232696.i	−1.08549	+	1.08549i	−0.0895072	+	0.995986i	$0.528529\pi$
$463$	−232696.	+	232696.i	−1.08549	+	1.08549i	−0.995986	+	0.0895072i	$0.971471\pi$
$464$	53193.7	+	53193.7i	0.247072	+	0.247072i
$465$		−	146719.i		−	0.678549i
$466$	171048.	−	171048.i	0.787671	−	0.787671i
$467$	13082.1	−	13082.1i	0.0599851	−	0.0599851i	−0.676478	−	0.736463i	$-0.736495\pi$
$467$	13082.1	−	13082.1i	0.0599851	−	0.0599851i	0.736463	+	0.676478i	$0.236495\pi$
$468$	−104484.	−	104484.i	−0.477045	−	0.477045i
$469$		−	131196.i		−	0.596453i
$470$	−57732.3			−0.261350
$471$		−	233813.i		−	1.05397i
$472$			87442.5i			0.392499i
$473$	−330341.	−	330341.i	−1.47652	−	1.47652i
$474$		−	399532.i		−	1.77826i
$475$	109994.	+	109994.i	0.487509	+	0.487509i
$476$	16565.1	+	16565.1i	0.0731107	+	0.0731107i
$477$	229991.			1.01082
$478$	58139.9			0.254459
$479$	−25172.8	+	25172.8i	−0.109714	+	0.109714i	−0.759832	−	0.650119i	$-0.774719\pi$
$479$	−25172.8	+	25172.8i	−0.109714	+	0.109714i	0.650119	+	0.759832i	$0.274719\pi$
$480$		−	78955.2i		−	0.342687i
$481$	−99727.1	+	260672.i	−0.431045	+	1.12669i
$482$	−151124.			−0.650486
$483$	89674.4	+	89674.4i	0.384392	+	0.384392i
$484$		−	67876.5i		−	0.289753i
$485$			5326.35i			0.0226436i
$486$	−169479.	+	169479.i	−0.717534	+	0.717534i
$487$	−264887.	+	264887.i	−1.11687	+	1.11687i	−0.124672	+	0.992198i	$0.539788\pi$
$487$	−264887.	+	264887.i	−1.11687	+	1.11687i	−0.992198	+	0.124672i	$0.960212\pi$
$488$	52230.9			0.219325
$489$	−349648.	+	349648.i	−1.46222	+	1.46222i
$490$	−189293.			−0.788393
$491$	130782.			0.542483			0.271241	−	0.962511i	$-0.412566\pi$
$491$	130782.			0.542483			0.271241	+	0.962511i	$0.412566\pi$
$492$		−	33186.2i		−	0.137097i
$493$	174067.			0.716180
$494$	131139.	−	131139.i	0.537376	−	0.537376i
$495$	−324379.	−	324379.i	−1.32386	−	1.32386i
$496$	−15222.9	−	15222.9i	−0.0618776	−	0.0618776i
$497$	190164.			0.769867
$498$	−61791.6	+	61791.6i	−0.249156	+	0.249156i
$499$	−63580.0	−	63580.0i	−0.255340	−	0.255340i	0.567816	−	0.823156i	$-0.307789\pi$
$499$	−63580.0	−	63580.0i	−0.255340	−	0.255340i	−0.823156	+	0.567816i	$0.807789\pi$
$500$	26622.8	−	26622.8i	0.106491	−	0.106491i
$501$	162268.	+	162268.i	0.646483	+	0.646483i
$502$		−	162259.i		−	0.643876i
$503$	320918.	−	320918.i	1.26841	−	1.26841i	0.321497	−	0.946911i	$-0.395814\pi$
$503$	320918.	−	320918.i	1.26841	−	1.26841i	0.946911	−	0.321497i	$-0.104186\pi$
$504$	28664.4	−	28664.4i	0.112845	−	0.112845i
$505$	−318626.	−	318626.i	−1.24939	−	1.24939i
$506$		−	210581.i		−	0.822465i
$507$	170319.			0.662594
$508$			103287.i			0.400236i
$509$			293144.i			1.13148i	0.824585	+	0.565738i	$0.191409\pi$
$509$			293144.i			1.13148i	−0.824585	+	0.565738i	$0.808591\pi$
$510$	−129183.	−	129183.i	−0.496668	−	0.496668i
$511$			118432.i			0.453550i
$512$	−8192.00	−	8192.00i	−0.0312500	−	0.0312500i
$513$	28597.0	+	28597.0i	0.108664	+	0.108664i
$514$	−62208.8			−0.235464
$515$	−633769.			−2.38955
$516$	−227648.	+	227648.i	−0.854996	+	0.854996i
$517$			93222.7i			0.348771i
$518$	−71513.2	−	27359.3i	−0.266518	−	0.101964i
$519$	413745.			1.53602
$520$	108610.	+	108610.i	0.401665	+	0.401665i
$521$			215318.i			0.793242i	0.917982	+	0.396621i	$0.129817\pi$
$521$			215318.i			0.793242i	−0.917982	+	0.396621i	$0.870183\pi$
$522$		−	301206.i		−	1.10541i
$523$	−308216.	+	308216.i	−1.12681	+	1.12681i	−0.136121	+	0.990692i	$0.543464\pi$
$523$	−308216.	+	308216.i	−1.12681	+	1.12681i	−0.990692	+	0.136121i	$0.956536\pi$
$524$	29631.6	−	29631.6i	0.107918	−	0.107918i
$525$	−125283.			−0.454541
$526$	−15746.5	+	15746.5i	−0.0569133	+	0.0569133i
$527$	−49814.1			−0.179362
$528$	−127492.			−0.457315
$529$			40148.5i			0.143469i
$530$	−239073.			−0.851096
$531$	247569.	−	247569.i	0.878025	−	0.878025i
$532$	35976.8	+	35976.8i	0.127116	+	0.127116i
$533$	45650.7	+	45650.7i	0.160692	+	0.160692i
$534$	249931.			0.876470
$535$	−144586.	+	144586.i	−0.505150	+	0.505150i
$536$	106156.	+	106156.i	0.369499	+	0.369499i
$537$	−438602.	+	438602.i	−1.52097	+	1.52097i
$538$	−98126.8	−	98126.8i	−0.339018	−	0.339018i
$539$			305660.i			1.05211i
$540$	−23684.2	+	23684.2i	−0.0812216	+	0.0812216i
$541$	161345.	−	161345.i	0.551265	−	0.551265i	−0.375541	−	0.926806i	$-0.622543\pi$
$541$	161345.	−	161345.i	0.551265	−	0.551265i	0.926806	+	0.375541i	$0.122543\pi$
$542$	42437.1	+	42437.1i	0.144460	+	0.144460i
$543$		−	622908.i		−	2.11263i
$544$	−26806.9			−0.0905833
$545$		−	697989.i		−	2.34993i
$546$			149367.i			0.501036i
$547$	250164.	+	250164.i	0.836083	+	0.836083i	0.988341	−	0.152258i	$-0.0486544\pi$
$547$	250164.	+	250164.i	0.836083	+	0.836083i	−0.152258	+	0.988341i	$0.548654\pi$
$548$			83046.5i			0.276541i
$549$	−147877.	−	147877.i	−0.490632	−	0.490632i
$550$	147100.	+	147100.i	0.486280	+	0.486280i
$551$	378046.			1.24521
$552$	−145117.			−0.476257
$553$	−150776.	+	150776.i	−0.493041	+	0.493041i
$554$			193872.i			0.631676i
$555$	557696.	+	213361.i	1.81055	+	0.692676i
$556$	−229756.			−0.743219
$557$	191922.	+	191922.i	0.618606	+	0.618606i	0.945174	−	0.326567i	$-0.105892\pi$
$557$	191922.	+	191922.i	0.618606	+	0.618606i	−0.326567	+	0.945174i	$0.605892\pi$
$558$			86198.6i			0.276842i
$559$		−	626302.i		−	2.00429i
$560$	−29796.3	+	29796.3i	−0.0950137	+	0.0950137i
$561$	−208598.	+	208598.i	−0.662802	+	0.662802i
$562$	18040.3			0.0571178
$563$	−12868.7	+	12868.7i	−0.0405992	+	0.0405992i	−0.727115	−	0.686516i	$-0.759139\pi$
$563$	−12868.7	+	12868.7i	−0.0405992	+	0.0405992i	0.686516	+	0.727115i	$0.259139\pi$
$564$	64242.6			0.201960
$565$	476611.			1.49302
$566$			291523.i			0.909999i
$567$	112542.			0.350064
$568$	−153868.	+	153868.i	−0.476928	+	0.476928i
$569$	−196332.	−	196332.i	−0.606411	−	0.606411i	0.335595	−	0.942006i	$-0.391063\pi$
$569$	−196332.	−	196332.i	−0.606411	−	0.606411i	−0.942006	+	0.335595i	$0.891063\pi$
$570$	−280566.	−	280566.i	−0.863545	−	0.863545i
$571$	30220.9			0.0926906			0.0463453	−	0.998925i	$-0.485243\pi$
$571$	30220.9			0.0926906			0.0463453	+	0.998925i	$0.485243\pi$
$572$	175378.	−	175378.i	0.536021	−	0.536021i
$573$	58620.6	+	58620.6i	0.178542	+	0.178542i
$574$	−12523.9	+	12523.9i	−0.0380115	+	0.0380115i
$575$	167436.	+	167436.i	0.506421	+	0.506421i
$576$			46386.7i			0.139813i
$577$	96144.6	−	96144.6i	0.288784	−	0.288784i	−0.547815	−	0.836599i	$-0.684540\pi$
$577$	96144.6	−	96144.6i	0.288784	−	0.288784i	0.836599	+	0.547815i	$0.184540\pi$
$578$	123182.	−	123182.i	0.368715	−	0.368715i
$579$	158313.	+	158313.i	0.472237	+	0.472237i
$580$			313100.i			0.930737i
$581$	46638.1			0.138162
$582$		−	5926.98i		−	0.0174980i
$583$			386041.i			1.13578i
$584$	−95827.1	−	95827.1i	−0.280972	−	0.280972i
$585$		−	614999.i		−	1.79706i
$586$	−46479.1	−	46479.1i	−0.135351	−	0.135351i
$587$	198548.	+	198548.i	0.576222	+	0.576222i	0.933860	−	0.357638i	$-0.116418\pi$
$587$	198548.	+	198548.i	0.576222	+	0.576222i	−0.357638	+	0.933860i	$0.616418\pi$
$588$	210639.			0.609235
$589$	−108188.			−0.311853
$590$	−257345.	+	257345.i	−0.739284	+	0.739284i
$591$		−	565858.i		−	1.62006i
$592$	80001.1	−	35726.5i	0.228272	−	0.101940i
$593$	118739.			0.337664			0.168832	−	0.985645i	$-0.446000\pi$
$593$	118739.			0.337664			0.168832	+	0.985645i	$0.446000\pi$
$594$	38243.9	+	38243.9i	0.108390	+	0.108390i
$595$			97503.0i			0.275413i
$596$		−	88061.4i		−	0.247909i
$597$	−189398.	+	189398.i	−0.531407	+	0.531407i
$598$	199623.	−	199623.i	0.558223	−	0.558223i
$599$	−134637.			−0.375240			−0.187620	−	0.982242i	$-0.560077\pi$
$599$	−134637.			−0.375240			−0.187620	+	0.982242i	$0.560077\pi$
$600$	101371.	−	101371.i	0.281586	−	0.281586i
$601$	123225.			0.341154			0.170577	−	0.985344i	$-0.445437\pi$
$601$	123225.			0.341154			0.170577	+	0.985344i	$0.445437\pi$
$602$	171821.			0.474113
$603$		−	601100.i		−	1.65315i
$604$	186119.			0.510172
$605$	199762.	−	199762.i	0.545760	−	0.545760i
$606$	354556.	+	354556.i	0.965472	+	0.965472i
$607$	758.659	+	758.659i	0.00205906	+	0.00205906i	0.708136	−	0.706077i	$-0.249537\pi$
$607$	758.659	+	758.659i	0.00205906	+	0.00205906i	−0.706077	+	0.708136i	$0.749537\pi$
$608$	−58220.3			−0.157495
$609$	−215296.	+	215296.i	−0.580499	+	0.580499i
$610$	153716.	+	153716.i	0.413105	+	0.413105i
$611$	−88371.7	+	88371.7i	−0.236718	+	0.236718i
$612$	75896.1	+	75896.1i	0.202636	+	0.202636i
$613$			374042.i			0.995404i	0.867348	+	0.497702i	$0.165823\pi$
$613$			374042.i			0.995404i	−0.867348	+	0.497702i	$0.834177\pi$
$614$	17585.1	−	17585.1i	0.0466453	−	0.0466453i
$615$	97667.6	−	97667.6i	0.258226	−	0.258226i
$616$	48113.3	+	48113.3i	0.126795	+	0.126795i
$617$		−	300323.i		−	0.788894i	−0.918919	−	0.394447i	$-0.870936\pi$
$617$		−	300323.i		−	0.788894i	0.918919	−	0.394447i	$-0.129064\pi$
$618$	705237.			1.84654
$619$		−	62524.1i		−	0.163180i	−0.996666	−	0.0815898i	$-0.974000\pi$
$619$		−	62524.1i		−	0.163180i	0.996666	−	0.0815898i	$-0.0259997\pi$
$620$		−	89602.5i		−	0.233097i
$621$	43531.0	+	43531.0i	0.112880	+	0.112880i
$622$		−	350740.i		−	0.906577i
$623$	−94319.4	−	94319.4i	−0.243011	−	0.243011i
$624$	−120858.	−	120858.i	−0.310389	−	0.310389i
$625$	458987.			1.17501
$626$	−485951.			−1.24006
$627$	−453041.	+	453041.i	−1.15240	+	1.15240i
$628$		−	142791.i		−	0.362062i
$629$	72440.5	−	189349.i	0.183096	−	0.478588i
$630$	168720.			0.425094
$631$	155309.	+	155309.i	0.390065	+	0.390065i	0.874711	−	0.484645i	$-0.161051\pi$
$631$	155309.	+	155309.i	0.390065	+	0.390065i	−0.484645	+	0.874711i	$0.661051\pi$
$632$		−	243997.i		−	0.610872i
$633$			502885.i			1.25505i
$634$	−329837.	+	329837.i	−0.820580	+	0.820580i
$635$	−303974.	+	303974.i	−0.753858	+	0.753858i
$636$	266032.			0.657688
$637$	−289754.	+	289754.i	−0.714087	+	0.714087i
$638$	505576.			1.24207
$639$	871271.			2.13379
$640$		−	48218.4i		−	0.117721i
$641$	−602346.			−1.46599			−0.732993	−	0.680236i	$-0.761877\pi$
$641$	−602346.			−1.46599			−0.732993	+	0.680236i	$0.761877\pi$
$642$	160891.	−	160891.i	0.390357	−	0.390357i
$643$	−203681.	−	203681.i	−0.492640	−	0.492640i	0.416497	−	0.909137i	$-0.363258\pi$
$643$	−203681.	−	203681.i	−0.492640	−	0.492640i	−0.909137	+	0.416497i	$0.863258\pi$
$644$	54764.7	+	54764.7i	0.132047	+	0.132047i
$645$	−1.33994e6			−3.22083
$646$	−95257.7	+	95257.7i	−0.228263	+	0.228263i
$647$	108538.	+	108538.i	0.259282	+	0.259282i	0.824762	−	0.565480i	$-0.191309\pi$
$647$	108538.	+	108538.i	0.259282	+	0.259282i	−0.565480	+	0.824762i	$0.691309\pi$
$648$	−91061.3	+	91061.3i	−0.216862	+	0.216862i
$649$	415545.	+	415545.i	0.986573	+	0.986573i
$650$			278890.i			0.660095i
$651$	61613.1	−	61613.1i	0.145382	−	0.145382i
$652$	−213532.	+	213532.i	−0.502306	+	0.502306i
$653$	−329684.	−	329684.i	−0.773165	−	0.773165i	0.205494	−	0.978658i	$-0.434120\pi$
$653$	−329684.	−	329684.i	−0.773165	−	0.773165i	−0.978658	+	0.205494i	$0.934120\pi$
$654$			776700.i			1.81592i
$655$	174413.			0.406533
$656$		−	20267.0i		−	0.0470958i
$657$			542615.i			1.25708i
$658$	−24244.0	−	24244.0i	−0.0559954	−	0.0559954i
$659$		−	685736.i		−	1.57901i	−0.613741	−	0.789507i	$-0.710336\pi$
$659$		−	685736.i		−	1.57901i	0.613741	−	0.789507i	$-0.289664\pi$
$660$	−375212.	−	375212.i	−0.861368	−	0.861368i
$661$	−487186.	−	487186.i	−1.11504	−	1.11504i	−0.992458	−	0.122585i	$-0.960882\pi$
$661$	−487186.	−	487186.i	−1.11504	−	1.11504i	−0.122585	−	0.992458i	$-0.539118\pi$
$662$	503798.			1.14958
$663$	−395486.			−0.899713
$664$	−37736.6	+	37736.6i	−0.0855906	+	0.0855906i
$665$			211761.i			0.478854i
$666$	−327650.	−	125351.i	−0.738690	−	0.282605i
$667$	575469.			1.29351
$668$	99098.0	+	99098.0i	0.222081	+	0.222081i
$669$		−	87073.8i		−	0.194552i
$670$			624836.i			1.39193i
$671$	248212.	−	248212.i	0.551288	−	0.551288i
$672$	33156.3	−	33156.3i	0.0734223	−	0.0734223i
$673$	644106.			1.42209			0.711045	−	0.703146i	$-0.248222\pi$
$673$	644106.			1.42209			0.711045	+	0.703146i	$0.248222\pi$
$674$	14373.3	−	14373.3i	0.0316400	−	0.0316400i
$675$	−60816.5			−0.133479
$676$	104015.			0.227616
$677$			380512.i			0.830215i	0.909772	+	0.415107i	$0.136256\pi$
$677$			380512.i			0.830215i	−0.909772	+	0.415107i	$0.863744\pi$
$678$	−530357.			−1.15374
$679$	−2236.74	+	2236.74i	−0.00485149	+	0.00485149i
$680$	−78893.1	−	78893.1i	−0.170617	−	0.170617i
$681$	−227164.	−	227164.i	−0.489829	−	0.489829i
$682$	−144685.			−0.311067
$683$	290940.	−	290940.i	0.623680	−	0.623680i	−0.322791	−	0.946470i	$-0.604621\pi$
$683$	290940.	−	290940.i	0.623680	−	0.623680i	0.946470	+	0.322791i	$0.104621\pi$
$684$	164834.	+	164834.i	0.352319	+	0.352319i
$685$	−244407.	+	244407.i	−0.520875	+	0.520875i
$686$	−174447.	−	174447.i	−0.370694	−	0.370694i
$687$		−	979453.i		−	2.07525i
$688$	−139026.	+	139026.i	−0.293710	+	0.293710i
$689$	−365952.	+	365952.i	−0.770879	+	0.770879i
$690$	−427084.	−	427084.i	−0.897046	−	0.897046i
$691$		−	676751.i		−	1.41734i	−0.705542	−	0.708668i	$-0.749296\pi$
$691$		−	676751.i		−	1.41734i	0.705542	−	0.708668i	$-0.250704\pi$
$692$	252677.			0.527658
$693$		−	272439.i		−	0.567286i
$694$			175861.i			0.365133i
$695$	−676175.	−	676175.i	−1.39988	−	1.39988i
$696$		−	348407.i		−	0.719232i
$697$	−33160.1	−	33160.1i	−0.0682575	−	0.0682575i
$698$	395069.	+	395069.i	0.810891	+	0.810891i
$699$	−1.12033e6			−2.29293
$700$	−76511.1			−0.156145
$701$	358626.	−	358626.i	0.729802	−	0.729802i	−0.240778	−	0.970580i	$-0.577403\pi$
$701$	358626.	−	358626.i	0.729802	−	0.729802i	0.970580	+	0.240778i	$0.0774026\pi$
$702$			72507.7i			0.147133i
$703$	157329.	−	411236.i	0.318346	−	0.832110i
$704$	−77860.3			−0.157098
$705$	189067.	+	189067.i	0.380398	+	0.380398i
$706$		−	563538.i		−	1.13061i
$707$		−	267606.i		−	0.535375i
$708$	286365.	−	286365.i	0.571286	−	0.571286i
$709$	395349.	−	395349.i	0.786481	−	0.786481i	−0.194434	−	0.980916i	$-0.562287\pi$
$709$	395349.	−	395349.i	0.786481	−	0.786481i	0.980916	+	0.194434i	$0.0622871\pi$
$710$	−905676.			−1.79662
$711$	−690809.	+	690809.i	−1.36653	+	1.36653i
$712$	152634.			0.301087
$713$	−164687.			−0.323951
$714$		−	108498.i		−	0.212827i
$715$	1.03228e6			2.01923
$716$	−267857.	+	267857.i	−0.522489	+	0.522489i
$717$	−190402.	−	190402.i	−0.370368	−	0.370368i
$718$	72994.5	+	72994.5i	0.141593	+	0.141593i
$719$	−623995.			−1.20705			−0.603523	−	0.797346i	$-0.706237\pi$
$719$	−623995.			−1.20705			−0.603523	+	0.797346i	$0.706237\pi$
$720$	−136517.	+	136517.i	−0.263343	+	0.263343i
$721$	−266144.	−	266144.i	−0.511972	−	0.511972i
$722$	53757.3	−	53757.3i	0.103125	−	0.103125i
$723$	494914.	+	494914.i	0.946788	+	0.946788i
$724$		−	380414.i		−	0.725737i
$725$	−401990.	+	401990.i	−0.764785	+	0.764785i
$726$	−222288.	+	222288.i	−0.421739	+	0.421739i
$727$	−13044.1	−	13044.1i	−0.0246800	−	0.0246800i	0.694659	−	0.719339i	$-0.255555\pi$
$727$	−13044.1	−	13044.1i	−0.0246800	−	0.0246800i	−0.719339	+	0.694659i	$0.755555\pi$
$728$			91219.3i			0.172117i
$729$	649052.			1.22131
$730$		−	564042.i		−	1.05844i
$731$			454938.i			0.851368i
$732$	−171051.	−	171051.i	−0.319229	−	0.319229i
$733$			324175.i			0.603354i	0.953410	+	0.301677i	$0.0975464\pi$
$733$			324175.i			0.603354i	−0.953410	+	0.301677i	$0.902454\pi$
$734$	−183338.	−	183338.i	−0.340299	−	0.340299i
$735$	619916.	+	619916.i	1.14751	+	1.14751i
$736$	−88624.2			−0.163605
$737$	1.00895e6			1.85752
$738$	−57380.4	+	57380.4i	−0.105354	+	0.105354i
$739$		−	412435.i		−	0.755207i	−0.925967	−	0.377604i	$-0.876748\pi$
$739$		−	412435.i		−	0.755207i	0.925967	−	0.377604i	$-0.123252\pi$
$740$	340589.	+	130301.i	0.621966	+	0.237950i
$741$	−858933.			−1.56431
$742$	−100396.	−	100396.i	−0.182351	−	0.182351i
$743$		−	65043.9i		−	0.117823i	−0.998263	−	0.0589114i	$-0.981237\pi$
$743$		−	65043.9i		−	0.117823i	0.998263	−	0.0589114i	$-0.0187629\pi$
$744$			99706.7i			0.180127i
$745$	259166.	−	259166.i	0.466945	−	0.466945i
$746$	−167474.	+	167474.i	−0.300934	+	0.300934i
$747$	213681.			0.382935
$748$	−127392.	+	127392.i	−0.227687	+	0.227687i
$749$	−121435.			−0.216461
$750$	−174374.			−0.309998
$751$		−	53025.2i		−	0.0940161i	−0.998895	−	0.0470081i	$-0.985031\pi$
$751$		−	53025.2i		−	0.0940161i	0.998895	−	0.0470081i	$-0.0149687\pi$
$752$	39233.4			0.0693777
$753$	−531382.	+	531382.i	−0.937167	+	0.937167i
$754$	479267.	+	479267.i	0.843015	+	0.843015i
$755$	547752.	+	547752.i	0.960925	+	0.960925i
$756$	−19891.8			−0.0348042
$757$	139987.	−	139987.i	0.244285	−	0.244285i	−0.574335	−	0.818620i	$-0.694739\pi$
$757$	139987.	−	139987.i	0.244285	−	0.244285i	0.818620	+	0.574335i	$0.194739\pi$
$758$	38630.4	+	38630.4i	0.0672343	+	0.0672343i
$759$	−689629.	+	689629.i	−1.19710	+	1.19710i
$760$	−171343.	−	171343.i	−0.296647	−	0.296647i
$761$		−	996640.i		−	1.72095i	−0.509490	−	0.860477i	$-0.670166\pi$
$761$		−	996640.i		−	1.72095i	0.509490	−	0.860477i	$-0.329834\pi$
$762$	338253.	−	338253.i	0.582547	−	0.582547i
$763$	293113.	−	293113.i	0.503484	−	0.503484i
$764$	35800.0	+	35800.0i	0.0613332	+	0.0613332i
$765$			446728.i			0.763343i
$766$	−429215.			−0.731505
$767$			787844.i			1.33921i
$768$			53655.9i			0.0909693i
$769$	−401157.	−	401157.i	−0.678362	−	0.678362i	0.281267	−	0.959630i	$-0.409245\pi$
$769$	−401157.	−	401157.i	−0.678362	−	0.678362i	−0.959630	+	0.281267i	$0.909245\pi$
$770$			283197.i			0.477647i
$771$	203727.	+	203727.i	0.342721	+	0.342721i
$772$	96682.8	+	96682.8i	0.162224	+	0.162224i
$773$	176385.			0.295191			0.147595	−	0.989048i	$-0.452847\pi$
$773$	176385.			0.295191			0.147595	+	0.989048i	$0.452847\pi$
$774$	787227.			1.31407
$775$	115041.	−	115041.i	0.191535	−	0.191535i
$776$		−	3619.65i		−	0.00601094i
$777$	144599.	+	323797.i	0.239510	+	0.536328i
$778$	180081.			0.297515
$779$	−72018.5	−	72018.5i	−0.118678	−	0.118678i
$780$		−	711375.i		−	1.16925i
$781$			1.46243e6i			2.39758i
$782$	−145003.	+	145003.i	−0.237118	+	0.237118i
$783$	−104512.	+	104512.i	−0.170468	+	0.170468i
$784$	128639.			0.209286
$785$	420238.	−	420238.i	0.681955	−	0.681955i
$786$	−194081.			−0.314151
$787$	99310.4			0.160341			0.0801706	−	0.996781i	$-0.474453\pi$
$787$	99310.4			0.160341			0.0801706	+	0.996781i	$0.474453\pi$
$788$		−	345573.i		−	0.556528i
$789$	103137.			0.165676
$790$	718088.	−	718088.i	1.15060	−	1.15060i
$791$	200147.	+	200147.i	0.319887	+	0.319887i
$792$	220440.	+	220440.i	0.351430	+	0.351430i
$793$	470593.			0.748340
$794$	−518239.	+	518239.i	−0.822032	+	0.822032i
$795$	782938.	+	782938.i	1.23878	+	1.23878i
$796$	−115667.	+	115667.i	−0.182550	+	0.182550i
$797$	−333443.	−	333443.i	−0.524934	−	0.524934i	0.394123	−	0.919057i	$-0.371048\pi$
$797$	−333443.	−	333443.i	−0.524934	−	0.524934i	−0.919057	+	0.394123i	$0.871048\pi$
$798$		−	235641.i		−	0.370037i
$799$	64192.1	−	64192.1i	0.100551	−	0.100551i
$800$	61907.8	−	61907.8i	0.0967310	−	0.0967310i
$801$	−432141.	−	432141.i	−0.673536	−	0.673536i
$802$		−	775500.i		−	1.20568i
$803$	−910782.			−1.41248
$804$		−	695297.i		−	1.07562i
$805$			322347.i			0.497431i
$806$	−137156.	−	137156.i	−0.211127	−	0.211127i
$807$			642710.i			0.986889i
$808$	216530.	+	216530.i	0.331661	+	0.331661i
$809$	332499.	+	332499.i	0.508035	+	0.508035i	0.913923	−	0.405888i	$-0.133038\pi$
$809$	332499.	+	332499.i	0.508035	+	0.508035i	−0.405888	+	0.913923i	$0.633038\pi$
$810$	−535991.			−0.816934
$811$	5920.83			0.00900204			0.00450102	−	0.999990i	$-0.498567\pi$
$811$	5920.83			0.00900204			0.00450102	+	0.999990i	$0.498567\pi$
$812$	−131483.	+	131483.i	−0.199415	+	0.199415i
$813$		−	277954.i		−	0.420525i
$814$	210403.	−	549963.i	0.317543	−	0.830012i
$815$	−1.25686e6			−1.89222
$816$	87789.6	+	87789.6i	0.131845	+	0.131845i
$817$			988053.i			1.48025i
$818$		−	48558.7i		−	0.0725706i
$819$	258262.	−	258262.i	0.385028	−	0.385028i
$820$	59646.3	−	59646.3i	0.0887065	−	0.0887065i
$821$	−119154.			−0.176776			−0.0883878	−	0.996086i	$-0.528171\pi$
$821$	−119154.			−0.176776			−0.0883878	+	0.996086i	$0.528171\pi$
$822$	271968.	−	271968.i	0.402508	−	0.402508i
$823$	648844.			0.957945			0.478972	−	0.877830i	$-0.341009\pi$
$823$	648844.			0.957945			0.478972	+	0.877830i	$0.341009\pi$
$824$	430693.			0.634327
$825$		−	963472.i		−	1.41557i
$826$	−216138.			−0.316790
$827$	516877.	−	516877.i	0.755747	−	0.755747i	−0.219799	−	0.975545i	$-0.570540\pi$
$827$	516877.	−	516877.i	0.755747	−	0.755747i	0.975545	+	0.219799i	$0.0705400\pi$
$828$	250915.	+	250915.i	0.365987	+	0.365987i
$829$	74845.0	+	74845.0i	0.108906	+	0.108906i	0.759460	−	0.650554i	$-0.225463\pi$
$829$	74845.0	+	74845.0i	0.108906	+	0.108906i	−0.650554	+	0.759460i	$0.725463\pi$
$830$	−222119.			−0.322425
$831$	634909.	−	634909.i	0.919410	−	0.919410i
$832$	−73808.7	−	73808.7i	−0.106626	−	0.106626i
$833$	210474.	−	210474.i	0.303325	−	0.303325i
$834$	752426.	+	752426.i	1.08176	+	1.08176i
$835$			583295.i			0.836595i
$836$	−276675.	+	276675.i	−0.395875	+	0.395875i
$837$	29909.1	−	29909.1i	0.0426925	−	0.0426925i
$838$	175835.	+	175835.i	0.250390	+	0.250390i
$839$		−	877210.i		−	1.24618i	−0.782152	−	0.623088i	$-0.785878\pi$
$839$		−	877210.i		−	1.24618i	0.782152	−	0.623088i	$-0.214122\pi$
$840$	195159.			0.276586
$841$			674343.i			0.953431i
$842$		−	140269.i		−	0.197851i
$843$	−59080.1	−	59080.1i	−0.0831354	−	0.0831354i
$844$			307115.i			0.431138i
$845$	306118.	+	306118.i	0.428722	+	0.428722i
$846$	−111078.	−	111078.i	−0.155199	−	0.155199i
$847$	167775.			0.233863
$848$	162468.			0.225931
$849$	954709.	−	954709.i	1.32451	−	1.32451i
$850$		−	202582.i		−	0.280391i
$851$	239490.	−	625993.i	0.330696	−	0.864391i
$852$	1.00781e6			1.38835
$853$	459593.	+	459593.i	0.631648	+	0.631648i	0.948481	−	0.316833i	$-0.102619\pi$
$853$	459593.	+	459593.i	0.631648	+	0.631648i	−0.316833	+	0.948481i	$0.602619\pi$
$854$			129103.i			0.177019i
$855$			970222.i			1.32721i
$856$	98257.2	−	98257.2i	0.134096	−	0.134096i
$857$	−44773.2	+	44773.2i	−0.0609616	+	0.0609616i	−0.736930	−	0.675969i	$-0.763725\pi$
$857$	−44773.2	+	44773.2i	−0.0609616	+	0.0609616i	0.675969	+	0.736930i	$0.263725\pi$
$858$	−1.14869e6			−1.56037
$859$	−884239.	+	884239.i	−1.19835	+	1.19835i	−0.223687	+	0.974661i	$0.571809\pi$
$859$	−884239.	+	884239.i	−1.19835	+	1.19835i	−0.974661	+	0.223687i	$0.928191\pi$
$860$	−818313.			−1.10643
$861$	82028.8			0.110652
$862$			394301.i			0.530656i
$863$	−861576.			−1.15684			−0.578419	−	0.815740i	$-0.696330\pi$
$863$	−861576.			−1.15684			−0.578419	+	0.815740i	$0.696330\pi$
$864$	16095.2	−	16095.2i	0.0215610	−	0.0215610i
$865$	743632.	+	743632.i	0.993862	+	0.993862i
$866$	132693.	+	132693.i	0.176934	+	0.176934i
$867$	−806814.			−1.07334
$868$	37627.5	−	37627.5i	0.0499420	−	0.0499420i
$869$	−1.15953e6	−	1.15953e6i	−1.53547	−	1.53547i
$870$	1.02537e6	−	1.02537e6i	1.35470	−	1.35470i
$871$	956446.	+	956446.i	1.26074	+	1.26074i
$872$			474335.i			0.623810i
$873$	−10248.0	+	10248.0i	−0.0134466	+	0.0134466i
$874$	−314924.	+	314924.i	−0.412272	+	0.412272i
$875$	65805.6	+	65805.6i	0.0859502	+	0.0859502i
$876$			627647.i			0.817914i
$877$	−681977.			−0.886687			−0.443343	−	0.896352i	$-0.646208\pi$
$877$	−681977.			−0.886687			−0.443343	+	0.896352i	$0.646208\pi$
$878$			779330.i			1.01096i
$879$			304428.i			0.394010i
$880$	−229144.	−	229144.i	−0.295899	−	0.295899i
$881$		−	961721.i		−	1.23907i	−0.784968	−	0.619537i	$-0.787320\pi$
$881$		−	961721.i		−	1.23907i	0.784968	−	0.619537i	$-0.212680\pi$
$882$	−364205.	−	364205.i	−0.468175	−	0.468175i
$883$	−415913.	−	415913.i	−0.533434	−	0.533434i	0.388158	−	0.921593i	$-0.373111\pi$
$883$	−415913.	−	415913.i	−0.533434	−	0.533434i	−0.921593	+	0.388158i	$0.873111\pi$
$884$	−241526.			−0.309072
$885$	1.68556e6			2.15207
$886$	565962.	−	565962.i	0.720974	−	0.720974i
$887$			886720.i			1.12704i	0.826102	+	0.563520i	$0.190553\pi$
$887$			886720.i			1.12704i	−0.826102	+	0.563520i	$0.809447\pi$
$888$	−378996.	−	144995.i	−0.480627	−	0.183877i
$889$	−255301.			−0.323035
$890$	449206.	+	449206.i	0.567108	+	0.567108i
$891$			865486.i			1.09020i
$892$		−	53176.5i		−	0.0668329i
$893$	139415.	−	139415.i	0.174826	−	0.174826i
$894$	−288392.	+	288392.i	−0.360834	+	0.360834i
$895$	−1.57662e6			−1.96825
$896$	20248.8	−	20248.8i	0.0252222	−	0.0252222i
$897$	−1.30749e6			−1.62500
$898$	−703568.			−0.872475
$899$		−	395391.i		−	0.489224i
$900$	−350549.			−0.432777
$901$	265823.	−	265823.i	0.327449	−	0.327449i
$902$	−96313.3	−	96313.3i	−0.118379	−	0.118379i
$903$	−562694.	−	562694.i	−0.690076	−	0.690076i
$904$	−323892.			−0.396336
$905$	1.11957e6	−	1.11957e6i	1.36695	−	1.36695i
$906$	−609520.	−	609520.i	−0.742560	−	0.742560i
$907$	64166.1	−	64166.1i	0.0779994	−	0.0779994i	−0.667031	−	0.745030i	$-0.732435\pi$
$907$	64166.1	−	64166.1i	0.0779994	−	0.0779994i	0.745030	+	0.667031i	$0.232435\pi$
$908$	−138730.	−	138730.i	−0.168267	−	0.168267i
$909$		−	1.22609e6i		−	1.48386i
$910$	−268460.	+	268460.i	−0.324188	+	0.324188i
$911$	938674.	−	938674.i	1.13104	−	1.13104i	0.141035	−	0.990005i	$-0.454957\pi$
$911$	938674.	−	938674.i	1.13104	−	1.13104i	0.990005	−	0.141035i	$-0.0450431\pi$
$912$	190665.	+	190665.i	0.229236	+	0.229236i
$913$			358665.i			0.430276i
$914$	464374.			0.555873
$915$		−	1.00681e6i		−	1.20256i
$916$		−	598158.i		−	0.712895i
$917$	73242.7	+	73242.7i	0.0871015	+	0.0871015i
$918$		−	52668.6i		−	0.0624981i
$919$	426749.	+	426749.i	0.505291	+	0.505291i	0.913077	−	0.407786i	$-0.133699\pi$
$919$	426749.	+	426749.i	0.505291	+	0.505291i	−0.407786	+	0.913077i	$0.633699\pi$
$920$	−260823.	−	260823.i	−0.308155	−	0.308155i
$921$	−115179.			−0.135785
$922$	664864.			0.782116
$923$	−1.38633e6	+	1.38633e6i	−1.62729	+	1.62729i
$924$		−	315132.i		−	0.369104i
$925$	269989.	+	604577.i	0.315546	+	0.706591i
$926$	930785.			1.08549
$927$	−1.21939e6	−	1.21939e6i	−1.41900	−	1.41900i
$928$		−	212775.i		−	0.247072i
$929$			1.61843e6i			1.87526i	0.347630	+	0.937632i	$0.386986\pi$
$929$			1.61843e6i			1.87526i	−0.347630	+	0.937632i	$0.613014\pi$
$930$	−293439.	+	293439.i	−0.339275	+	0.339275i
$931$	457116.	−	457116.i	0.527384	−	0.527384i
$932$	−684190.			−0.787671
$933$	−1.14864e6	+	1.14864e6i	−1.31953	+	1.31953i
$934$	−52328.3			−0.0599851
$935$	−749834.			−0.857713
$936$			417938.i			0.477045i
$937$	−1.16817e6			−1.33053			−0.665266	−	0.746607i	$-0.731682\pi$
$937$	−1.16817e6			−1.33053			−0.665266	+	0.746607i	$0.731682\pi$
$938$	−262393.	+	262393.i	−0.298226	+	0.298226i
$939$	1.59144e6	+	1.59144e6i	1.80492	+	1.80492i
$940$	115465.	+	115465.i	0.130675	+	0.130675i
$941$	938243.			1.05959			0.529793	−	0.848127i	$-0.322270\pi$
$941$	938243.			1.05959			0.529793	+	0.848127i	$0.322270\pi$
$942$	−467627.	+	467627.i	−0.526984	+	0.526984i
$943$	−109628.	−	109628.i	−0.123282	−	0.123282i
$944$	174885.	−	174885.i	0.196249	−	0.196249i
$945$	−58542.1	−	58542.1i	−0.0655548	−	0.0655548i
$946$			1.32136e6i			1.47652i
$947$	100085.	−	100085.i	0.111602	−	0.111602i	−0.649101	−	0.760702i	$-0.724855\pi$
$947$	100085.	−	100085.i	0.111602	−	0.111602i	0.760702	+	0.649101i	$0.224855\pi$
$948$	−799064.	+	799064.i	−0.889130	+	0.889130i
$949$	−863388.	−	863388.i	−0.958680	−	0.958680i
$950$		−	439977.i		−	0.487509i
$951$	2.16036e6			2.38872
$952$		−	66260.5i		−	0.0731107i
$953$		−	484459.i		−	0.533423i	−0.963776	−	0.266711i	$-0.914063\pi$
$953$		−	484459.i		−	0.533423i	0.963776	−	0.266711i	$-0.0859370\pi$
$954$	−459982.	−	459982.i	−0.505410	−	0.505410i
$955$			210720.i			0.231046i
$956$	−116280.	−	116280.i	−0.127230	−	0.127230i
$957$	−1.65571e6	−	1.65571e6i	−1.80784	−	1.80784i
$958$	100691.			0.109714
$959$	−205272.			−0.223199
$960$	−157910.	+	157910.i	−0.171344	+	0.171344i
$961$		−	810369.i		−	0.877477i
$962$	720799.	−	321890.i	0.778868	−	0.347823i
$963$	−556376.			−0.599951
$964$	302247.	+	302247.i	0.325243	+	0.325243i
$965$			569079.i			0.611108i
$966$		−	358698.i		−	0.384392i
$967$	−581569.	+	581569.i	−0.621940	+	0.621940i	−0.946027	−	0.324087i	$-0.894943\pi$
$967$	−581569.	+	581569.i	−0.621940	+	0.621940i	0.324087	+	0.946027i	$0.394943\pi$
$968$	−135753.	+	135753.i	−0.144877	+	0.144877i
$969$	623918.			0.664477
$970$	10652.7	−	10652.7i	0.0113218	−	0.0113218i
$971$	−376664.			−0.399499			−0.199750	−	0.979847i	$-0.564013\pi$
$971$	−376664.			−0.399499			−0.199750	+	0.979847i	$0.564013\pi$
$972$	677915.			0.717534
$973$		−	567904.i		−	0.599859i
$974$	1.05955e6			1.11687
$975$	913336.	−	913336.i	0.960775	−	0.960775i
$976$	−104462.	−	104462.i	−0.109662	−	0.109662i
$977$	597853.	+	597853.i	0.626333	+	0.626333i	0.947143	−	0.320811i	$-0.103955\pi$
$977$	597853.	+	597853.i	0.626333	+	0.626333i	−0.320811	+	0.947143i	$0.603955\pi$
$978$	1.39859e6			1.46222
$979$	725351.	−	725351.i	0.756803	−	0.756803i
$980$	378587.	+	378587.i	0.394197	+	0.394197i
$981$	1.34295e6	−	1.34295e6i	1.39547	−	1.39547i
$982$	−261564.	−	261564.i	−0.271241	−	0.271241i
$983$		−	187343.i		−	0.193878i	−0.995290	−	0.0969392i	$-0.969095\pi$
$983$		−	187343.i		−	0.193878i	0.995290	−	0.0969392i	$-0.0309052\pi$
$984$	−66372.4	+	66372.4i	−0.0685484	+	0.0685484i
$985$	1.01703e6	−	1.01703e6i	1.04824	−	1.04824i
$986$	−348134.	−	348134.i	−0.358090	−	0.358090i
$987$			158793.i			0.163004i
$988$	−524556.			−0.537376
$989$			1.50404e6i			1.53768i
$990$			1.29752e6i			1.32386i
$991$	−74918.1	−	74918.1i	−0.0762850	−	0.0762850i	0.667935	−	0.744220i	$-0.267178\pi$
$991$	−74918.1	−	74918.1i	−0.0762850	−	0.0762850i	−0.744220	+	0.667935i	$0.767178\pi$
$992$			60891.5i			0.0618776i
$993$	−1.64989e6	−	1.64989e6i	−1.67323	−	1.67323i
$994$	−380328.	−	380328.i	−0.384933	−	0.384933i
$995$	−680819.			−0.687679
$996$	247167.			0.249156
$997$	−838142.	+	838142.i	−0.843194	+	0.843194i	−0.989273	−	0.146079i	$-0.953335\pi$
$997$	−838142.	+	838142.i	−0.843194	+	0.843194i	0.146079	+	0.989273i	$0.453335\pi$
$998$			254320.i			0.255340i
$999$	70193.4	+	157182.i	0.0703340	+	0.157497i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.5.d.a.31.7	✓	14
37.6	odd	4	inner	74.5.d.a.43.1	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.5.d.a.31.7	✓	14	1.1	even	1	trivial
74.5.d.a.43.1	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)

\(f(q)\)	\(=\)	\(q+(-2.00000 - 2.00000i) q^{2} +13.0996i q^{3} +8.00000i q^{4} +(-23.5442 + 23.5442i) q^{5} +(26.1992 - 26.1992i) q^{6} -19.7742 q^{7} +(16.0000 - 16.0000i) q^{8} -90.5991 q^{9} +O(q^{10})\)	\(q+(-2.00000 - 2.00000i) q^{2} +13.0996i q^{3} +8.00000i q^{4} +(-23.5442 + 23.5442i) q^{5} +(26.1992 - 26.1992i) q^{6} -19.7742 q^{7} +(16.0000 - 16.0000i) q^{8} -90.5991 q^{9} +94.1766 q^{10} -152.071i q^{11} -104.797 q^{12} +(144.158 - 144.158i) q^{13} +(39.5484 + 39.5484i) q^{14} +(-308.419 - 308.419i) q^{15} -64.0000 q^{16} +(-104.714 + 104.714i) q^{17} +(181.198 + 181.198i) q^{18} +(-227.423 + 227.423i) q^{19} +(-188.353 - 188.353i) q^{20} -259.034i q^{21} +(-304.142 + 304.142i) q^{22} +(-346.188 + 346.188i) q^{23} +(209.593 + 209.593i) q^{24} -483.655i q^{25} -576.631 q^{26} -125.744i q^{27} -158.194i q^{28} +(-831.151 - 831.151i) q^{29} +1233.67i q^{30} +(237.857 + 237.857i) q^{31} +(128.000 + 128.000i) q^{32} +1992.07 q^{33} +418.857 q^{34} +(465.567 - 465.567i) q^{35} -724.792i q^{36} +(-1250.02 + 558.226i) q^{37} +909.692 q^{38} +(1888.41 + 1888.41i) q^{39} +753.413i q^{40} +316.672i q^{41} +(-518.068 + 518.068i) q^{42} +(2172.28 - 2172.28i) q^{43} +1216.57 q^{44} +(2133.08 - 2133.08i) q^{45} +1384.75 q^{46} -613.021 q^{47} -838.373i q^{48} -2009.98 q^{49} +(-967.310 + 967.310i) q^{50} +(-1371.71 - 1371.71i) q^{51} +(1153.26 + 1153.26i) q^{52} -2538.56 q^{53} +(-251.487 + 251.487i) q^{54} +(3580.38 + 3580.38i) q^{55} +(-316.387 + 316.387i) q^{56} +(-2979.15 - 2979.15i) q^{57} +3324.60i q^{58} +(-2732.58 + 2732.58i) q^{59} +(2467.35 - 2467.35i) q^{60} +(1632.21 + 1632.21i) q^{61} -951.430i q^{62} +1791.52 q^{63} -512.000i q^{64} +6788.14i q^{65} +(-3984.13 - 3984.13i) q^{66} +6634.72i q^{67} +(-837.714 - 837.714i) q^{68} +(-4534.92 - 4534.92i) q^{69} -1862.27 q^{70} -9616.78 q^{71} +(-1449.58 + 1449.58i) q^{72} -5989.19i q^{73} +(3616.49 + 1383.58i) q^{74} +6335.68 q^{75} +(-1819.38 - 1819.38i) q^{76} +3007.08i q^{77} -7553.62i q^{78} +(7624.90 - 7624.90i) q^{79} +(1506.83 - 1506.83i) q^{80} -5691.33 q^{81} +(633.345 - 633.345i) q^{82} -2358.53 q^{83} +2072.27 q^{84} -4930.82i q^{85} -8689.13 q^{86} +(10887.7 - 10887.7i) q^{87} +(-2433.13 - 2433.13i) q^{88} +(4769.82 + 4769.82i) q^{89} -8532.31 q^{90} +(-2850.60 + 2850.60i) q^{91} +(-2769.51 - 2769.51i) q^{92} +(-3115.83 + 3115.83i) q^{93} +(1226.04 + 1226.04i) q^{94} -10709.0i q^{95} +(-1676.75 + 1676.75i) q^{96} +(113.114 - 113.114i) q^{97} +(4019.96 + 4019.96i) q^{98} +13777.5i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 28 q^{2} - 12 q^{5} - 40 q^{6} + 48 q^{7} + 224 q^{8} - 346 q^{9}+O(q^{10}) \) 14 * q - 28 * q^2 - 12 * q^5 - 40 * q^6 + 48 * q^7 + 224 * q^8 - 346 * q^9	\( 14 q - 28 q^{2} - 12 q^{5} - 40 q^{6} + 48 q^{7} + 224 q^{8} - 346 q^{9} + 48 q^{10} + 160 q^{12} - 56 q^{13} - 96 q^{14} - 378 q^{15} - 896 q^{16} - 348 q^{17} + 692 q^{18} - 184 q^{19} - 96 q^{20} - 320 q^{22} - 502 q^{23} - 320 q^{24} + 224 q^{26} - 474 q^{29} - 630 q^{31} + 1792 q^{32} + 632 q^{33} + 1392 q^{34} + 1826 q^{35} - 2544 q^{37} + 736 q^{38} - 798 q^{39} - 224 q^{42} + 1936 q^{43} + 1280 q^{44} + 6162 q^{45} + 2008 q^{46} + 5716 q^{47} + 7862 q^{49} - 1372 q^{50} - 2422 q^{51} - 448 q^{52} - 20228 q^{53} - 656 q^{54} + 14006 q^{55} + 768 q^{56} - 2270 q^{57} - 4502 q^{59} + 3024 q^{60} - 11906 q^{61} - 2588 q^{63} - 1264 q^{66} - 2784 q^{68} + 21440 q^{69} - 7304 q^{70} - 11224 q^{71} - 5536 q^{72} + 4924 q^{74} - 18652 q^{75} - 1472 q^{76} + 20488 q^{79} + 768 q^{80} - 1706 q^{81} + 9808 q^{82} - 20224 q^{83} + 896 q^{84} - 7744 q^{86} + 19636 q^{87} - 2560 q^{88} + 13864 q^{89} - 24648 q^{90} - 6070 q^{91} - 4016 q^{92} - 13800 q^{93} - 11432 q^{94} + 2560 q^{96} + 16622 q^{97} - 15724 q^{98}+O(q^{100}) \) 14 * q - 28 * q^2 - 12 * q^5 - 40 * q^6 + 48 * q^7 + 224 * q^8 - 346 * q^9 + 48 * q^10 + 160 * q^12 - 56 * q^13 - 96 * q^14 - 378 * q^15 - 896 * q^16 - 348 * q^17 + 692 * q^18 - 184 * q^19 - 96 * q^20 - 320 * q^22 - 502 * q^23 - 320 * q^24 + 224 * q^26 - 474 * q^29 - 630 * q^31 + 1792 * q^32 + 632 * q^33 + 1392 * q^34 + 1826 * q^35 - 2544 * q^37 + 736 * q^38 - 798 * q^39 - 224 * q^42 + 1936 * q^43 + 1280 * q^44 + 6162 * q^45 + 2008 * q^46 + 5716 * q^47 + 7862 * q^49 - 1372 * q^50 - 2422 * q^51 - 448 * q^52 - 20228 * q^53 - 656 * q^54 + 14006 * q^55 + 768 * q^56 - 2270 * q^57 - 4502 * q^59 + 3024 * q^60 - 11906 * q^61 - 2588 * q^63 - 1264 * q^66 - 2784 * q^68 + 21440 * q^69 - 7304 * q^70 - 11224 * q^71 - 5536 * q^72 + 4924 * q^74 - 18652 * q^75 - 1472 * q^76 + 20488 * q^79 + 768 * q^80 - 1706 * q^81 + 9808 * q^82 - 20224 * q^83 + 896 * q^84 - 7744 * q^86 + 19636 * q^87 - 2560 * q^88 + 13864 * q^89 - 24648 * q^90 - 6070 * q^91 - 4016 * q^92 - 13800 * q^93 - 11432 * q^94 + 2560 * q^96 + 16622 * q^97 - 15724 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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