LMFDB - Embedded newform 63.7.m.d.10.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,7,Mod(10,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("63.10");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	63.m (of order $6$, 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:	$14.4934072681$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 212x^{6} + 473x^{5} + 39800x^{4} + 36821x^{3} + 985651x^{2} - 601290x + 21068100 $ x^8 - x^7 + 212x^6 + 473x^5 + 39800x^4 + 36821x^3 + 985651x^2 - 601290x + 21068100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3\cdot 7 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			10.1
Root			$-6.30797 - 10.9257i$ of defining polynomial
Character	$\chi$	$=$	63.10
Dual form			63.7.m.d.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.80797 - 10.0597i) q^{2} +(-35.4650 + 61.4271i) q^{4} +(165.302 - 95.4373i) q^{5} +(-103.254 + 327.089i) q^{7} +80.4975 q^{8} +O(q^{10})$	\(q+(-5.80797 - 10.0597i) q^{2} +(-35.4650 + 61.4271i) q^{4} +(165.302 - 95.4373i) q^{5} +(-103.254 + 327.089i) q^{7} +80.4975 q^{8} +(-1920.14 - 1108.59i) q^{10} +(-1027.55 + 1779.77i) q^{11} +3059.97i q^{13} +(3890.12 - 861.018i) q^{14} +(1802.23 + 3121.55i) q^{16} +(-2468.38 - 1425.12i) q^{17} +(-3420.04 + 1974.56i) q^{19} +13538.7i q^{20} +23872.0 q^{22} +(330.272 + 572.047i) q^{23} +(10404.0 - 18020.3i) q^{25} +(30782.3 - 17772.2i) q^{26} +(-16430.3 - 17942.8i) q^{28} +9282.66 q^{29} +(2426.36 + 1400.86i) q^{31} +(23510.5 - 40721.4i) q^{32} +33108.2i q^{34} +(14148.4 + 63922.9i) q^{35} +(18466.2 + 31984.5i) q^{37} +(39727.0 + 22936.4i) q^{38} +(13306.4 - 7682.46i) q^{40} +67941.3i q^{41} +12336.3 q^{43} +(-72884.2 - 126239. i) q^{44} +(3836.41 - 6644.86i) q^{46} +(-127836. + 73806.3i) q^{47} +(-96326.1 - 67546.8i) q^{49} -241705. q^{50} +(-187965. - 108522. i) q^{52} +(109818. - 190210. i) q^{53} +392267. i q^{55} +(-8311.72 + 26329.9i) q^{56} +(-53913.4 - 93380.8i) q^{58} +(-166725. - 96258.8i) q^{59} +(288244. - 166418. i) q^{61} -32544.5i q^{62} -315508. q^{64} +(292035. + 505819. i) q^{65} +(-174592. + 302402. i) q^{67} +(175082. - 101084. i) q^{68} +(560872. - 513590. i) q^{70} -305650. q^{71} +(-204814. - 118249. i) q^{73} +(214503. - 371529. i) q^{74} -280111. i q^{76} +(-476046. - 519871. i) q^{77} +(293218. + 507869. i) q^{79} +(595825. + 344000. i) q^{80} +(683468. - 394601. i) q^{82} -106377. i q^{83} -544039. q^{85} +(-71648.8 - 124099. i) q^{86} +(-82715.4 + 143267. i) q^{88} +(-11308.5 + 6528.95i) q^{89} +(-1.00088e6 - 315955. i) q^{91} -46852.3 q^{92} +(1.48494e6 + 857329. i) q^{94} +(-376894. + 652799. i) q^{95} +205209. i q^{97} +(-120042. + 1.36132e6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 5 q^{2} - 173 q^{4} + 294 q^{5} - 656 q^{7} - 3326 q^{8}+O(q^{10}) $ 8 * q + 5 * q^2 - 173 * q^4 + 294 * q^5 - 656 * q^7 - 3326 * q^8	$ 8 q + 5 q^{2} - 173 q^{4} + 294 q^{5} - 656 q^{7} - 3326 q^{8} - 3411 q^{10} + 314 q^{11} + 5360 q^{14} - 12721 q^{16} + 5532 q^{17} - 18234 q^{19} + 86106 q^{22} - 3928 q^{23} - 17038 q^{25} - 12366 q^{26} + 85037 q^{28} + 8300 q^{29} - 89508 q^{31} + 186207 q^{32} + 25860 q^{35} + 64706 q^{37} + 77136 q^{38} + 221823 q^{40} + 45740 q^{43} - 92529 q^{44} - 111504 q^{46} - 483276 q^{47} - 310684 q^{49} - 967216 q^{50} - 1673988 q^{52} + 540974 q^{53} + 241885 q^{56} + 539799 q^{58} + 181770 q^{59} + 418224 q^{61} + 2378626 q^{64} + 414204 q^{65} - 1158902 q^{67} + 821250 q^{68} + 1087917 q^{70} - 1442344 q^{71} - 378666 q^{73} + 432940 q^{74} - 1065994 q^{77} + 611452 q^{79} + 2094945 q^{80} - 1561266 q^{82} - 275112 q^{85} - 816224 q^{86} - 366441 q^{88} + 989196 q^{89} + 304446 q^{91} - 678720 q^{92} - 716148 q^{94} + 591792 q^{95} - 3509629 q^{98}+O(q^{100}) $ 8 * q + 5 * q^2 - 173 * q^4 + 294 * q^5 - 656 * q^7 - 3326 * q^8 - 3411 * q^10 + 314 * q^11 + 5360 * q^14 - 12721 * q^16 + 5532 * q^17 - 18234 * q^19 + 86106 * q^22 - 3928 * q^23 - 17038 * q^25 - 12366 * q^26 + 85037 * q^28 + 8300 * q^29 - 89508 * q^31 + 186207 * q^32 + 25860 * q^35 + 64706 * q^37 + 77136 * q^38 + 221823 * q^40 + 45740 * q^43 - 92529 * q^44 - 111504 * q^46 - 483276 * q^47 - 310684 * q^49 - 967216 * q^50 - 1673988 * q^52 + 540974 * q^53 + 241885 * q^56 + 539799 * q^58 + 181770 * q^59 + 418224 * q^61 + 2378626 * q^64 + 414204 * q^65 - 1158902 * q^67 + 821250 * q^68 + 1087917 * q^70 - 1442344 * q^71 - 378666 * q^73 + 432940 * q^74 - 1065994 * q^77 + 611452 * q^79 + 2094945 * q^80 - 1561266 * q^82 - 275112 * q^85 - 816224 * q^86 - 366441 * q^88 + 989196 * q^89 + 304446 * q^91 - 678720 * q^92 - 716148 * q^94 + 591792 * q^95 - 3509629 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−5.80797	−	10.0597i	−0.725996	−	1.25746i	−0.958563	−	0.284881i	$-0.908046\pi$
$2$	−5.80797	−	10.0597i	−0.725996	−	1.25746i	0.232567	−	0.972580i	$-0.425288\pi$
$3$		0			0
$3$		0			0
$4$	−35.4650	+	61.4271i	−0.554140	+	0.959799i
$5$	165.302	−	95.4373i	1.32242	−	0.763498i	0.338304	−	0.941037i	$-0.390147\pi$
$5$	165.302	−	95.4373i	1.32242	−	0.763498i	0.984114	+	0.177539i	$0.0568136\pi$
$6$		0			0
$7$	−103.254	+	327.089i	−0.301033	+	0.953614i
$7$	−103.254	+	327.089i	−0.301033	+	0.953614i
$8$	80.4975			0.157222
$9$		0			0
$10$	−1920.14	−	1108.59i	−1.92014	−	1.10859i
$11$	−1027.55	+	1779.77i	−0.772015	+	1.33717i	0.164442	+	0.986387i	$0.447418\pi$
$11$	−1027.55	+	1779.77i	−0.772015	+	1.33717i	−0.936457	+	0.350783i	$0.885916\pi$
$12$		0			0
$13$			3059.97i			1.39279i	0.717657	+	0.696396i	$0.245214\pi$
$13$			3059.97i			1.39279i	−0.717657	+	0.696396i	$0.754786\pi$
$14$	3890.12	−	861.018i	1.41768	−	0.313782i
$15$		0			0
$16$	1802.23	+	3121.55i	0.439998	+	0.762098i
$17$	−2468.38	−	1425.12i	−0.502419	−	0.290072i	0.227293	−	0.973826i	$-0.427012\pi$
$17$	−2468.38	−	1425.12i	−0.502419	−	0.290072i	−0.729712	+	0.683755i	$0.760346\pi$
$18$		0			0
$19$	−3420.04	+	1974.56i	−0.498622	+	0.287879i	−0.728144	−	0.685424i	$-0.759617\pi$
$19$	−3420.04	+	1974.56i	−0.498622	+	0.287879i	0.229523	+	0.973303i	$0.426284\pi$
$20$			13538.7i			1.69234i
$21$		0			0
$22$	23872.0			2.24192
$23$	330.272	+	572.047i	0.0271449	+	0.0470163i	0.879279	−	0.476308i	$-0.158025\pi$
$23$	330.272	+	572.047i	0.0271449	+	0.0470163i	−0.852134	+	0.523324i	$0.824692\pi$
$24$		0			0
$25$	10404.0	−	18020.3i	0.665859	−	1.15330i
$26$	30782.3	−	17772.2i	1.75138	−	1.01116i
$27$		0			0
$28$	−16430.3	−	17942.8i	−0.748463	−	0.817367i
$29$	9282.66			0.380609			0.190304	−	0.981725i	$-0.439053\pi$
$29$	9282.66			0.380609			0.190304	+	0.981725i	$0.439053\pi$
$30$		0			0
$31$	2426.36	+	1400.86i	0.0814460	+	0.0470229i	0.540170	−	0.841556i	$-0.318360\pi$
$31$	2426.36	+	1400.86i	0.0814460	+	0.0470229i	−0.458724	+	0.888579i	$0.651693\pi$
$32$	23510.5	−	40721.4i	0.717484	−	1.24272i
$33$		0			0
$34$			33108.2i			0.842363i
$35$	14148.4	+	63922.9i	0.329991	+	1.49091i
$36$		0			0
$37$	18466.2	+	31984.5i	0.364563	+	0.631442i	0.988706	−	0.149868i	$-0.0478849\pi$
$37$	18466.2	+	31984.5i	0.364563	+	0.631442i	−0.624143	+	0.781310i	$0.714552\pi$
$38$	39727.0	+	22936.4i	0.723994	+	0.417998i
$39$		0			0
$40$	13306.4	−	7682.46i	0.207913	−	0.120039i
$41$			67941.3i			0.985785i	0.870090	+	0.492892i	$0.164060\pi$
$41$			67941.3i			0.985785i	−0.870090	+	0.492892i	$0.835940\pi$
$42$		0			0
$43$	12336.3			0.155160			0.0775799	−	0.996986i	$-0.475281\pi$
$43$	12336.3			0.155160			0.0775799	+	0.996986i	$0.475281\pi$
$44$	−72884.2	−	126239.i	−0.855609	−	1.48196i
$45$		0			0
$46$	3836.41	−	6644.86i	0.0394141	−	0.0682673i
$47$	−127836.	+	73806.3i	−1.23129	+	0.710886i	−0.967299	−	0.253639i	$-0.918372\pi$
$47$	−127836.	+	73806.3i	−1.23129	+	0.710886i	−0.263991	+	0.964525i	$0.585039\pi$
$48$		0			0
$49$	−96326.1	−	67546.8i	−0.818758	−	0.574139i
$50$	−241705.			−1.93364
$51$		0			0
$52$	−187965.	−	108522.i	−1.33680	−	0.771802i
$53$	109818.	−	190210.i	0.737641	−	1.27763i	−0.215914	−	0.976412i	$-0.569273\pi$
$53$	109818.	−	190210.i	0.737641	−	1.27763i	0.953555	−	0.301219i	$-0.0973934\pi$
$54$		0			0
$55$			392267.i			2.35773i
$56$	−8311.72	+	26329.9i	−0.0473290	+	0.149929i
$57$		0			0
$58$	−53913.4	−	93380.8i	−0.276320	−	0.478601i
$59$	−166725.	−	96258.8i	−0.811792	−	0.468689i	0.0357855	−	0.999359i	$-0.488607\pi$
$59$	−166725.	−	96258.8i	−0.811792	−	0.468689i	−0.847578	+	0.530671i	$0.821940\pi$
$60$		0			0
$61$	288244.	−	166418.i	1.26990	−	0.733180i	0.294935	−	0.955517i	$-0.404702\pi$
$61$	288244.	−	166418.i	1.26990	−	0.733180i	0.974970	+	0.222338i	$0.0713688\pi$
$62$		−	32544.5i		−	0.136554i
$63$		0			0
$64$	−315508.			−1.20357
$65$	292035.	+	505819.i	1.06339	+	1.84185i
$66$		0			0
$67$	−174592.	+	302402.i	−0.580496	+	1.00545i	0.414924	+	0.909856i	$0.363808\pi$
$67$	−174592.	+	302402.i	−0.580496	+	1.00545i	−0.995420	+	0.0955931i	$0.969525\pi$
$68$	175082.	−	101084.i	0.556821	−	0.321481i
$69$		0			0
$70$	560872.	−	513590.i	1.63519	−	1.49735i
$71$	−305650.			−0.853984			−0.426992	−	0.904255i	$-0.640427\pi$
$71$	−305650.			−0.853984			−0.426992	+	0.904255i	$0.640427\pi$
$72$		0			0
$73$	−204814.	−	118249.i	−0.526490	−	0.303969i	0.213096	−	0.977031i	$-0.431645\pi$
$73$	−204814.	−	118249.i	−0.526490	−	0.303969i	−0.739586	+	0.673062i	$0.764979\pi$
$74$	214503.	−	371529.i	0.529343	−	0.916849i
$75$		0			0
$76$		−	280111.i		−	0.638102i
$77$	−476046.	−	519871.i	−1.04274	−	1.13874i
$78$		0			0
$79$	293218.	+	507869.i	0.594716	+	1.03008i	0.993587	+	0.113072i	$0.0360690\pi$
$79$	293218.	+	507869.i	0.594716	+	1.03008i	−0.398871	+	0.917007i	$0.630598\pi$
$80$	595825.	+	344000.i	1.16372	+	0.671875i
$81$		0			0
$82$	683468.	−	394601.i	1.23959	−	0.715675i
$83$		−	106377.i		−	0.186044i	−0.995664	−	0.0930218i	$-0.970347\pi$
$83$		−	106377.i		−	0.186044i	0.995664	−	0.0930218i	$-0.0296526\pi$
$84$		0			0
$85$	−544039.			−0.885876
$86$	−71648.8	−	124099.i	−0.112645	−	0.195108i
$87$		0			0
$88$	−82715.4	+	143267.i	−0.121378	+	0.210232i
$89$	−11308.5	+	6528.95i	−0.0160411	+	0.00926134i	−0.507999	−	0.861358i	$-0.669615\pi$
$89$	−11308.5	+	6528.95i	−0.0160411	+	0.00926134i	0.491958	+	0.870619i	$0.336281\pi$
$90$		0			0
$91$	−1.00088e6	−	315955.i	−1.32819	−	0.419277i
$92$	−46852.3			−0.0601682
$93$		0			0
$94$	1.48494e6	+	857329.i	1.78782	+	1.03220i
$95$	−376894.	+	652799.i	−0.439591	+	0.761393i
$96$		0			0
$97$			205209.i			0.224844i	0.993661	+	0.112422i	$0.0358609\pi$
$97$			205209.i			0.224844i	−0.993661	+	0.112422i	$0.964139\pi$
$98$	−120042.	+	1.36132e6i	−0.127542	+	1.44638i
$99$		0			0
$100$	737958.	+	1.27818e6i	0.737958	+	1.27818i
$101$	1.21339e6	+	700549.i	1.17770	+	0.679946i	0.955482	−	0.295050i	$-0.0953364\pi$
$101$	1.21339e6	+	700549.i	1.17770	+	0.679946i	0.222220	+	0.974997i	$0.428670\pi$
$102$		0			0
$103$	448291.	−	258821.i	0.410250	−	0.236858i	−0.280647	−	0.959811i	$-0.590549\pi$
$103$	448291.	−	258821.i	0.410250	−	0.236858i	0.690897	+	0.722953i	$0.257216\pi$
$104$			246320.i			0.218977i
$105$		0			0
$106$	−2.55127e6			−2.14210
$107$	323372.	+	560097.i	0.263968	+	0.457206i	0.967293	−	0.253663i	$-0.0816354\pi$
$107$	323372.	+	560097.i	0.263968	+	0.457206i	−0.703325	+	0.710869i	$0.748302\pi$
$108$		0			0
$109$	343631.	−	595186.i	0.265346	−	0.459593i	−0.702308	−	0.711873i	$-0.747847\pi$
$109$	343631.	−	595186.i	0.265346	−	0.459593i	0.967654	+	0.252280i	$0.0811805\pi$
$110$	3.94609e6	−	2.27827e6i	2.96475	−	1.71170i
$111$		0			0
$112$	−1.20712e6	+	267177.i	−0.859201	+	0.190171i
$113$	−2.11668e6			−1.46697			−0.733483	−	0.679708i	$-0.762107\pi$
$113$	−2.11668e6			−1.46697			−0.733483	+	0.679708i	$0.762107\pi$
$114$		0			0
$115$	109189.	+	63040.4i	0.0717937	+	0.0414501i
$116$	−329209.	+	570207.i	−0.210910	+	0.365308i
$117$		0			0
$118$			2.23627e6i			1.36106i
$119$	721014.	−	660232.i	0.427861	−	0.391792i
$120$		0			0
$121$	−1.22595e6	−	2.12340e6i	−0.692015	−	1.19860i
$122$	−3.34823e6	−	1.93310e6i	−1.84389	−	1.06457i
$123$		0			0
$124$	−172101.	+	99362.7i	−0.0902649	+	0.0521145i
$125$		−	989318.i		−	0.506531i
$126$		0			0
$127$	3.29012e6			1.60620			0.803102	−	0.595841i	$-0.203181\pi$
$127$	3.29012e6			1.60620			0.803102	+	0.595841i	$0.203181\pi$
$128$	327785.	+	567740.i	0.156300	+	0.270720i
$129$		0			0
$130$	3.39226e6	−	5.87556e6i	1.54404	−	2.67436i
$131$	−193424.	+	111674.i	−0.0860394	+	0.0496748i	−0.542402	−	0.840119i	$-0.682485\pi$
$131$	−193424.	+	111674.i	−0.0860394	+	0.0496748i	0.456363	+	0.889794i	$0.349152\pi$
$132$		0			0
$133$	−292725.	−	1.32254e6i	−0.124424	−	0.562153i
$134$	4.05609e6			1.68575
$135$		0			0
$136$	−198699.	−	114719.i	−0.0789912	−	0.0456056i
$137$	−1.58525e6	+	2.74573e6i	−0.616504	+	1.06782i	0.373615	+	0.927584i	$0.378118\pi$
$137$	−1.58525e6	+	2.74573e6i	−0.616504	+	1.06782i	−0.990119	+	0.140232i	$0.955215\pi$
$138$		0			0
$139$			774740.i			0.288477i	0.989543	+	0.144239i	$0.0460733\pi$
$139$			774740.i			0.288477i	−0.989543	+	0.144239i	$0.953927\pi$
$140$	−4.42837e6	−	1.39793e6i	−1.61384	−	0.509450i
$141$		0			0
$142$	1.77521e6	+	3.07475e6i	0.619989	+	1.07385i
$143$	−5.44604e6	−	3.14427e6i	−1.86240	−	1.07526i
$144$		0			0
$145$	1.53444e6	−	885912.i	0.503323	−	0.290594i
$146$			2.74715e6i			0.882722i
$147$		0			0
$148$	−2.61962e6			−0.808077
$149$	1.75461e6	+	3.03907e6i	0.530421	+	0.918716i	0.999370	+	0.0354908i	$0.0112995\pi$
$149$	1.75461e6	+	3.03907e6i	0.530421	+	0.918716i	−0.468949	+	0.883225i	$0.655367\pi$
$150$		0			0
$151$	−3.22601e6	+	5.58761e6i	−0.936989	+	1.62291i	−0.165940	+	0.986136i	$0.553066\pi$
$151$	−3.22601e6	+	5.58761e6i	−0.936989	+	1.62291i	−0.771049	+	0.636776i	$0.780268\pi$
$152$	−275305.	+	158948.i	−0.0783942	+	0.0452609i
$153$		0			0
$154$	−2.46488e6	+	7.80827e6i	−0.674892	+	2.13792i
$155$	534776.			0.143607
$156$		0			0
$157$	−4.05557e6	−	2.34148e6i	−1.04798	−	0.605051i	−0.125896	−	0.992043i	$-0.540181\pi$
$157$	−4.05557e6	−	2.34148e6i	−1.04798	−	0.605051i	−0.922083	+	0.386992i	$0.873514\pi$
$158$	3.40600e6	−	5.89937e6i	0.863523	−	1.49567i
$159$		0			0
$160$		−	8.97512e6i		−	2.19119i
$161$	−221213.	+	48962.0i	−0.0530069	+	0.0117323i
$162$		0			0
$163$	−2.59116e6	−	4.48803e6i	−0.598318	−	1.03632i	−0.993069	−	0.117529i	$-0.962503\pi$
$163$	−2.59116e6	−	4.48803e6i	−0.598318	−	1.03632i	0.394752	−	0.918788i	$-0.370831\pi$
$164$	−4.17344e6	−	2.40953e6i	−0.946155	−	0.546263i
$165$		0			0
$166$	−1.07012e6	+	617836.i	−0.233943	+	0.135067i
$167$		−	1.56630e6i		−	0.336298i	−0.985762	−	0.168149i	$-0.946221\pi$
$167$		−	1.56630e6i		−	0.336298i	0.985762	−	0.168149i	$-0.0537790\pi$
$168$		0			0
$169$	−4.53658e6			−0.939871
$170$	3.15976e6	+	5.47286e6i	0.643143	+	1.11396i
$171$		0			0
$172$	−437506.	+	757783.i	−0.0859803	+	0.148922i
$173$	1.07788e6	−	622312.i	0.208176	−	0.120190i	−0.392287	−	0.919843i	$-0.628316\pi$
$173$	1.07788e6	−	622312.i	0.208176	−	0.120190i	0.600463	+	0.799652i	$0.294983\pi$
$174$		0			0
$175$	4.82000e6	+	5.26373e6i	0.899358	+	0.982154i
$176$	−7.40754e6			−1.35874
$177$		0			0
$178$	131359.	+	75839.9i	0.0232916	+	0.0134474i
$179$	1.12800e6	−	1.95375e6i	0.196675	−	0.340651i	−0.750773	−	0.660560i	$-0.770319\pi$
$179$	1.12800e6	−	1.95375e6i	0.196675	−	0.340651i	0.947448	+	0.319909i	$0.103652\pi$
$180$		0			0
$181$			7.97198e6i			1.34441i	0.740367	+	0.672203i	$0.234652\pi$
$181$			7.97198e6i			1.34441i	−0.740367	+	0.672203i	$0.765348\pi$
$182$	2.63468e6	+	1.19036e7i	0.437033	+	1.97454i
$183$		0			0
$184$	26586.1	+	46048.4i	0.00426776	+	0.00739199i
$185$	6.10502e6	+	3.52473e6i	0.964210	+	0.556687i
$186$		0			0
$187$	5.07278e6	−	2.92877e6i	0.775750	−	0.447879i
$188$		−	1.04701e7i		−	1.57572i
$189$		0			0
$190$	8.75595e6			1.27656
$191$	2.13087e6	+	3.69078e6i	0.305814	+	0.529685i	0.977442	−	0.211203i	$-0.0677382\pi$
$191$	2.13087e6	+	3.69078e6i	0.305814	+	0.529685i	−0.671628	+	0.740888i	$0.734405\pi$
$192$		0			0
$193$	72886.7	−	126243.i	0.0101386	−	0.0175605i	−0.860912	−	0.508755i	$-0.830106\pi$
$193$	72886.7	−	126243.i	0.0101386	−	0.0175605i	0.871050	+	0.491194i	$0.163439\pi$
$194$	2.06434e6	−	1.19185e6i	0.282733	−	0.163236i
$195$		0			0
$196$	7.56541e6	−	3.52149e6i	1.00476	−	0.467690i
$197$	7.21313e6			0.943463			0.471732	−	0.881742i	$-0.343629\pi$
$197$	7.21313e6			0.943463			0.471732	+	0.881742i	$0.343629\pi$
$198$		0			0
$199$	1.52836e6	+	882399.i	0.193940	+	0.111971i	0.593826	−	0.804594i	$-0.297617\pi$
$199$	1.52836e6	+	882399.i	0.193940	+	0.111971i	−0.399886	+	0.916565i	$0.630950\pi$
$200$	837500.	−	1.45059e6i	0.104687	−	0.181324i
$201$		0			0
$202$		−	1.62751e7i		−	1.97455i
$203$	−958475.	+	3.03626e6i	−0.114576	+	0.362954i
$204$		0			0
$205$	6.48413e6	+	1.12308e7i	0.752645	+	1.30362i
$206$	−5.20732e6	−	3.00645e6i	−0.595680	−	0.343916i
$207$		0			0
$208$	−9.55185e6	+	5.51476e6i	−1.06144	+	0.612825i
$209$		−	8.11587e6i		−	0.888989i
$210$		0			0
$211$	1.37033e7			1.45874			0.729369	−	0.684121i	$-0.239814\pi$
$211$	1.37033e7			1.45874			0.729369	+	0.684121i	$0.239814\pi$
$212$	7.78936e6	+	1.34916e7i	0.817512	+	1.41597i
$213$		0			0
$214$	3.75627e6	−	6.50605e6i	0.383279	−	0.663859i
$215$	2.03922e6	−	1.17734e6i	0.205186	−	0.118464i
$216$		0			0
$217$	−708738.	+	648991.i	−0.0693596	+	0.0635126i
$218$	−7.98318e6			−0.770560
$219$		0			0
$220$	−2.40958e7	−	1.39117e7i	−2.26294	−	1.30651i
$221$	4.36082e6	−	7.55317e6i	0.404010	−	0.699765i
$222$		0			0
$223$		−	2.15029e7i		−	1.93902i	−0.245055	−	0.969509i	$-0.578806\pi$
$223$		−	2.15029e7i		−	1.93902i	0.245055	−	0.969509i	$-0.421194\pi$
$224$	1.08920e7	+	1.18947e7i	0.969087	+	1.05830i
$225$		0			0
$226$	1.22936e7	+	2.12932e7i	1.06501	+	1.84465i
$227$	−3.40461e6	−	1.96565e6i	−0.291065	−	0.168046i	0.347357	−	0.937733i	$-0.387079\pi$
$227$	−3.40461e6	−	1.96565e6i	−0.291065	−	0.168046i	−0.638422	+	0.769687i	$0.720412\pi$
$228$		0			0
$229$	486988.	−	281163.i	0.0405520	−	0.0234127i	−0.479587	−	0.877494i	$-0.659213\pi$
$229$	486988.	−	281163.i	0.0405520	−	0.0234127i	0.520139	+	0.854082i	$0.325880\pi$
$230$		−	1.46455e6i		−	0.120370i
$231$		0			0
$232$	747232.			0.0598400
$233$	−8.16657e6	−	1.41449e7i	−0.645612	−	1.11823i	−0.984160	−	0.177284i	$-0.943269\pi$
$233$	−8.16657e6	−	1.41449e7i	−0.645612	−	1.11823i	0.338548	−	0.940949i	$-0.390064\pi$
$234$		0			0
$235$	−1.40877e7	+	2.44007e7i	−1.08552	+	1.88018i
$236$	1.18258e7	−	6.82763e6i	0.899693	−	0.519438i
$237$		0			0
$238$	−1.08294e7	−	3.41857e6i	−0.803289	−	0.253579i
$239$	1.96132e7			1.43666			0.718331	−	0.695702i	$-0.244906\pi$
$239$	1.96132e7			1.43666			0.718331	+	0.695702i	$0.244906\pi$
$240$		0			0
$241$	3.11683e6	+	1.79950e6i	0.222670	+	0.128559i	0.607186	−	0.794560i	$-0.292298\pi$
$241$	3.11683e6	+	1.79950e6i	0.222670	+	0.128559i	−0.384516	+	0.923118i	$0.625632\pi$
$242$	−1.42405e7	+	2.46653e7i	−1.00480	+	1.74036i
$243$		0			0
$244$			2.36080e7i			1.62514i
$245$	−2.23694e7	−	1.97254e6i	−1.52109	−	0.134131i
$246$		0			0
$247$	−6.04210e6	−	1.04652e7i	−0.400956	−	0.694476i
$248$	195316.	+	112766.i	0.0128051	+	0.00739302i
$249$		0			0
$250$	−9.95223e6	+	5.74592e6i	−0.636943	+	0.367739i
$251$			6.49855e6i			0.410956i	0.978662	+	0.205478i	$0.0658749\pi$
$251$			6.49855e6i			0.410956i	−0.978662	+	0.205478i	$0.934125\pi$
$252$		0			0
$253$	−1.35749e6			−0.0838250
$254$	−1.91089e7	−	3.30976e7i	−1.16610	−	2.01974i
$255$		0			0
$256$	−6.28871e6	+	1.08924e7i	−0.374837	+	0.649236i
$257$	−2.47506e6	+	1.42897e6i	−0.145810	+	0.0841832i	−0.571130	−	0.820860i	$-0.693495\pi$
$257$	−2.47506e6	+	1.42897e6i	−0.145810	+	0.0841832i	0.425320	+	0.905043i	$0.360161\pi$
$258$		0			0
$259$	−1.23685e7	+	2.73758e6i	−0.711898	+	0.157568i
$260$	−4.14280e7			−2.35708
$261$		0			0
$262$	2.24680e6	+	1.29719e6i	0.124928	+	0.0721275i
$263$	−2.49913e6	+	4.32862e6i	−0.137380	+	0.237948i	−0.926504	−	0.376285i	$-0.877201\pi$
$263$	−2.49913e6	+	4.32862e6i	−0.137380	+	0.237948i	0.789124	+	0.614233i	$0.210535\pi$
$264$		0			0
$265$		−	4.19228e7i		−	2.25275i
$266$	−1.16042e7	+	1.06260e7i	−0.616555	+	0.564580i
$267$		0			0
$268$	−1.23838e7	−	2.14493e7i	−0.643352	−	1.11432i
$269$	1.76842e7	+	1.02100e7i	0.908507	+	0.524527i	0.879951	−	0.475065i	$-0.157576\pi$
$269$	1.76842e7	+	1.02100e7i	0.908507	+	0.524527i	0.0285567	+	0.999592i	$0.490909\pi$
$270$		0			0
$271$	1.06885e7	−	6.17102e6i	0.537044	−	0.310062i	−0.206836	−	0.978376i	$-0.566317\pi$
$271$	1.06885e7	−	6.17102e6i	0.537044	−	0.310062i	0.743880	+	0.668313i	$0.232983\pi$
$272$		−	1.02736e7i		−	0.510523i
$273$		0			0
$274$	3.68283e7			1.79032
$275$	2.13814e7	+	3.70336e7i	1.02811	+	1.78073i
$276$		0			0
$277$	1.04151e7	−	1.80395e7i	0.490031	−	0.848758i	−0.509903	−	0.860232i	$-0.670319\pi$
$277$	1.04151e7	−	1.80395e7i	0.490031	−	0.848758i	0.999934	+	0.0114733i	$0.00365216\pi$
$278$	7.79365e6	−	4.49966e6i	0.362749	−	0.209433i
$279$		0			0
$280$	1.13891e6	+	5.14564e6i	0.0518817	+	0.234404i
$281$	−2.10143e7			−0.947100			−0.473550	−	0.880767i	$-0.657028\pi$
$281$	−2.10143e7			−0.947100			−0.473550	+	0.880767i	$0.657028\pi$
$282$		0			0
$283$	9.02737e6	+	5.21195e6i	0.398292	+	0.229954i	0.685747	−	0.727840i	$-0.259476\pi$
$283$	9.02737e6	+	5.21195e6i	0.398292	+	0.229954i	−0.287455	+	0.957794i	$0.592809\pi$
$284$	1.08399e7	−	1.87752e7i	0.473227	−	0.819653i
$285$		0			0
$286$			7.30474e7i			3.12253i
$287$	−2.22229e7	−	7.01523e6i	−0.940058	−	0.296754i
$288$		0			0
$289$	−8.00684e6	−	1.38683e7i	−0.331717	−	0.574551i
$290$	−1.78240e7	−	1.02907e7i	−0.730821	−	0.421940i
$291$		0			0
$292$	1.45274e7	−	8.38741e6i	0.583499	−	0.336883i
$293$		−	2.85328e7i		−	1.13433i	−0.823603	−	0.567167i	$-0.808039\pi$
$293$		−	2.85328e7i		−	1.13433i	0.823603	−	0.567167i	$-0.191961\pi$
$294$		0			0
$295$	−3.67467e7			−1.43137
$296$	1.48649e6	+	2.57467e6i	0.0573173	+	0.0992765i
$297$		0			0
$298$	2.03814e7	−	3.53016e7i	0.770167	−	1.33397i
$299$	−1.75044e6	+	1.01062e6i	−0.0654839	+	0.0378072i
$300$		0			0
$301$	−1.27378e6	+	4.03507e6i	−0.0467082	+	0.147963i
$302$	7.49461e7			2.72100
$303$		0			0
$304$	−1.23274e7	−	7.11724e6i	−0.438785	−	0.253332i
$305$	3.17649e7	−	5.50185e7i	1.11956	−	1.93914i
$306$		0			0
$307$			1.02269e7i			0.353450i	0.984260	+	0.176725i	$0.0565503\pi$
$307$			1.02269e7i			0.353450i	−0.984260	+	0.176725i	$0.943450\pi$
$308$	4.88171e7	−	1.08049e7i	1.67078	−	0.369802i
$309$		0			0
$310$	−3.10596e6	−	5.37968e6i	−0.104258	−	0.180581i
$311$	1.36331e7	+	7.87108e6i	0.453225	+	0.261669i	0.709191	−	0.705016i	$-0.249060\pi$
$311$	1.36331e7	+	7.87108e6i	0.453225	+	0.261669i	−0.255966	+	0.966686i	$0.582394\pi$
$312$		0			0
$313$	4.80881e7	−	2.77637e7i	1.56821	−	0.905408i	0.571834	−	0.820369i	$-0.306232\pi$
$313$	4.80881e7	−	2.77637e7i	1.56821	−	0.905408i	0.996378	−	0.0850387i	$-0.0271014\pi$
$314$			5.43970e7i			1.75706i
$315$		0			0
$316$	−4.15959e7			−1.31822
$317$	−3.01539e6	−	5.22282e6i	−0.0946600	−	0.163956i	0.814807	−	0.579733i	$-0.196843\pi$
$317$	−3.01539e6	−	5.22282e6i	−0.0946600	−	0.163956i	−0.909467	+	0.415777i	$0.863510\pi$
$318$		0			0
$319$	−9.53842e6	+	1.65210e7i	−0.293836	+	0.508938i
$320$	−5.21541e7	+	3.01112e7i	−1.59162	+	0.918920i
$321$		0			0
$322$	1.77734e6	+	1.94096e6i	0.0532357	+	0.0581366i
$323$	1.12560e7			0.334022
$324$		0			0
$325$	5.51416e7	+	3.18360e7i	1.60631	+	0.927403i
$326$	−3.00988e7	+	5.21326e7i	−0.868752	+	1.50472i
$327$		0			0
$328$			5.46910e6i			0.154987i
$329$	−1.09416e7	−	4.94347e7i	−0.307251	−	1.38818i
$330$		0			0
$331$	−4.88277e6	−	8.45720e6i	−0.134643	−	0.233208i	0.790818	−	0.612051i	$-0.209655\pi$
$331$	−4.88277e6	−	8.45720e6i	−0.134643	−	0.233208i	−0.925461	+	0.378843i	$0.876322\pi$
$332$	6.53445e6	+	3.77267e6i	0.178564	+	0.103094i
$333$		0			0
$334$	−1.57564e7	+	9.09699e6i	−0.422882	+	0.244151i
$335$			6.66502e7i			1.77283i
$336$		0			0
$337$	−5.70025e7			−1.48938			−0.744688	−	0.667412i	$-0.767402\pi$
$337$	−5.70025e7			−1.48938			−0.744688	+	0.667412i	$0.767402\pi$
$338$	2.63483e7	+	4.56366e7i	0.682343	+	1.18185i
$339$		0			0
$340$	1.92943e7	−	3.34187e7i	0.490900	−	0.850263i
$341$	−4.98642e6	+	2.87891e6i	−0.125755	+	0.0726047i
$342$		0			0
$343$	3.20399e7	−	2.45327e7i	0.793980	−	0.607944i
$344$	993041.			0.0243945
$345$		0			0
$346$	−1.25205e7	−	7.22874e6i	−0.302270	−	0.174516i
$347$	−1.83677e7	+	3.18139e7i	−0.439610	+	0.761426i	−0.997659	−	0.0683813i	$-0.978217\pi$
$347$	−1.83677e7	+	3.18139e7i	−0.439610	+	0.761426i	0.558050	+	0.829808i	$0.311550\pi$
$348$		0			0
$349$			6.58421e7i			1.54891i	0.632626	+	0.774457i	$0.281977\pi$
$349$			6.58421e7i			1.54891i	−0.632626	+	0.774457i	$0.718023\pi$
$350$	2.49571e7	−	7.90593e7i	0.582090	−	1.84395i
$351$		0			0
$352$	4.83166e7	+	8.36867e7i	1.10782	+	1.91879i
$353$	−2.76008e7	−	1.59353e7i	−0.627476	−	0.362273i	0.152298	−	0.988335i	$-0.451333\pi$
$353$	−2.76008e7	−	1.59353e7i	−0.627476	−	0.362273i	−0.779774	+	0.626061i	$0.784666\pi$
$354$		0			0
$355$	−5.05247e7	+	2.91704e7i	−1.12932	+	0.652015i
$356$		−	926197.i		−	0.0205283i
$357$		0			0
$358$	−2.62055e7			−0.571141
$359$	−1.91128e7	−	3.31044e7i	−0.413087	−	0.715488i	0.582138	−	0.813090i	$-0.302216\pi$
$359$	−1.91128e7	−	3.31044e7i	−0.413087	−	0.715488i	−0.995226	+	0.0976018i	$0.968883\pi$
$360$		0			0
$361$	−1.57251e7	+	2.72367e7i	−0.334251	+	0.578940i
$362$	8.01957e7	−	4.63010e7i	1.69054	−	0.976033i
$363$		0			0
$364$	5.49044e7	−	5.02760e7i	1.13842	−	1.04245i
$365$	−4.51415e7			−0.928320
$366$		0			0
$367$	8.43371e7	+	4.86920e7i	1.70616	+	0.985053i	0.939206	+	0.343354i	$0.111563\pi$
$367$	8.43371e7	+	4.86920e7i	1.70616	+	0.985053i	0.766956	+	0.641699i	$0.221770\pi$
$368$	−1.19045e6	+	2.06192e6i	−0.0238874	+	0.0413741i
$369$		0			0
$370$		−	8.18861e7i		−	1.61661i
$371$	5.08765e7	+	5.55602e7i	0.996312	+	1.08803i
$372$		0			0
$373$	−1.05213e7	−	1.82235e7i	−0.202742	−	0.351160i	0.746669	−	0.665196i	$-0.231652\pi$
$373$	−1.05213e7	−	1.82235e7i	−0.202742	−	0.351160i	−0.949411	+	0.314036i	$0.898319\pi$
$374$	−5.89251e7	−	3.40204e7i	−1.12638	−	0.650317i
$375$		0			0
$376$	−1.02905e7	+	5.94122e6i	−0.193586	+	0.111767i
$377$			2.84046e7i			0.530109i
$378$		0			0
$379$	−4.11794e7			−0.756418			−0.378209	−	0.925720i	$-0.623460\pi$
$379$	−4.11794e7			−0.756418			−0.378209	+	0.925720i	$0.623460\pi$
$380$	−2.67331e7	−	4.63030e7i	−0.487189	−	0.843837i
$381$		0			0
$382$	2.47521e7	−	4.28718e7i	0.444039	−	0.769098i
$383$	1.31798e7	−	7.60939e6i	0.234592	−	0.135442i	−0.378096	−	0.925766i	$-0.623421\pi$
$383$	1.31798e7	−	7.60939e6i	0.234592	−	0.135442i	0.612689	+	0.790324i	$0.290088\pi$
$384$		0			0
$385$	−1.28306e8	−	4.05033e7i	−2.24836	−	0.709754i
$386$	−1.69329e6			−0.0294422
$387$		0			0
$388$	−1.26054e7	−	7.27774e6i	−0.215805	−	0.124595i
$389$	−3.37497e7	+	5.84563e7i	−0.573353	+	0.993076i	0.422866	+	0.906192i	$0.361024\pi$
$389$	−3.37497e7	+	5.84563e7i	−0.573353	+	0.993076i	−0.996218	+	0.0868835i	$0.972309\pi$
$390$		0			0
$391$		−	1.88271e6i		−	0.0314958i
$392$	−7.75401e6	−	5.43735e6i	−0.128727	−	0.0902671i
$393$		0			0
$394$	−4.18936e7	−	7.25619e7i	−0.684951	−	1.18637i
$395$	9.69393e7	+	5.59679e7i	1.57293	+	0.908130i
$396$		0			0
$397$	8.14198e6	−	4.70078e6i	0.130124	−	0.0751273i	−0.433525	−	0.901142i	$-0.642730\pi$
$397$	8.14198e6	−	4.70078e6i	0.130124	−	0.0751273i	0.563649	+	0.826014i	$0.309397\pi$
$398$		−	2.04998e7i		−	0.325162i
$399$		0			0
$400$	7.50019e7			1.17190
$401$	−2.77486e7	−	4.80620e7i	−0.430336	−	0.745364i	0.566566	−	0.824016i	$-0.308272\pi$
$401$	−2.77486e7	−	4.80620e7i	−0.430336	−	0.745364i	−0.996902	+	0.0786521i	$0.974938\pi$
$402$		0			0
$403$	−4.28658e6	+	7.42457e6i	−0.0654931	+	0.113437i
$404$	−8.60654e7	+	4.96899e7i	−1.30522	+	0.753571i
$405$		0			0
$406$	3.61107e7	−	7.99254e6i	0.539582	−	0.119428i
$407$	−7.59001e7			−1.12579
$408$		0			0
$409$	1.41570e7	+	8.17357e6i	0.206920	+	0.119465i	0.599879	−	0.800091i	$-0.295215\pi$
$409$	1.41570e7	+	8.17357e6i	0.206920	+	0.119465i	−0.392959	+	0.919556i	$0.628549\pi$
$410$	7.53192e7	−	1.30457e8i	1.09283	−	1.89284i
$411$		0			0
$412$			3.67163e7i			0.525010i
$413$	4.87003e7	−	4.45949e7i	0.691324	−	0.633046i
$414$		0			0
$415$	−1.01524e7	−	1.75844e7i	−0.142044	−	0.246027i
$416$	1.24606e8	+	7.19413e7i	1.73085	+	0.999306i
$417$		0			0
$418$	−8.16432e7	+	4.71367e7i	−1.11787	+	0.645402i
$419$		−	3.75022e7i		−	0.509818i	−0.966965	−	0.254909i	$-0.917955\pi$
$419$		−	3.75022e7i		−	0.509818i	0.966965	−	0.254909i	$-0.0820455\pi$
$420$		0			0
$421$	9.17501e7			1.22959			0.614795	−	0.788687i	$-0.289239\pi$
$421$	9.17501e7			1.22959			0.614795	+	0.788687i	$0.289239\pi$
$422$	−7.95882e7	−	1.37851e8i	−1.05904	−	1.83431i
$423$		0			0
$424$	8.84006e6	−	1.53114e7i	0.115973	−	0.200871i
$425$	−5.13623e7	+	2.96540e7i	−0.669080	+	0.386293i
$426$		0			0
$427$	2.46711e7	+	1.11465e8i	0.316887	+	1.43171i
$428$	−4.58735e7			−0.585101
$429$		0			0
$430$	−2.36874e7	−	1.36759e7i	−0.297928	−	0.172009i
$431$	−6.89035e7	+	1.19344e8i	−0.860616	+	1.49063i	0.0107202	+	0.999943i	$0.496588\pi$
$431$	−6.89035e7	+	1.19344e8i	−0.860616	+	1.49063i	−0.871336	+	0.490687i	$0.836746\pi$
$432$		0			0
$433$		−	2.00324e7i		−	0.246757i	−0.992360	−	0.123378i	$-0.960627\pi$
$433$		−	2.00324e7i		−	0.246757i	0.992360	−	0.123378i	$-0.0393729\pi$
$434$	1.06450e7	+	3.36037e6i	0.130219	+	0.0411071i
$435$		0			0
$436$	2.43737e7	+	4.22165e7i	0.294078	+	0.509357i
$437$	−2.25909e6	−	1.30428e6i	−0.0270700	−	0.0156289i
$438$		0			0
$439$	7.45669e7	−	4.30512e7i	0.881359	−	0.508853i	0.0102525	−	0.999947i	$-0.496736\pi$
$439$	7.45669e7	−	4.30512e7i	0.881359	−	0.508853i	0.871106	+	0.491095i	$0.163403\pi$
$440$			3.15765e7i			0.370686i
$441$		0			0
$442$	−1.01310e8			−1.17324
$443$	−4.03937e6	−	6.99640e6i	−0.0464625	−	0.0804754i	0.841859	−	0.539698i	$-0.181461\pi$
$443$	−4.03937e6	−	6.99640e6i	−0.0464625	−	0.0804754i	−0.888321	+	0.459222i	$0.848128\pi$
$444$		0			0
$445$	−1.24621e6	+	2.15850e6i	−0.0141420	+	0.0244947i
$446$	−2.16312e8	+	1.24888e8i	−2.43824	+	1.40772i
$447$		0			0
$448$	3.25775e7	−	1.03199e8i	0.362313	−	1.14774i
$449$	5.16486e7			0.570584			0.285292	−	0.958441i	$-0.407909\pi$
$449$	5.16486e7			0.570584			0.285292	+	0.958441i	$0.407909\pi$
$450$		0			0
$451$	−1.20920e8	−	6.98132e7i	−1.31816	−	0.761041i
$452$	7.50680e7	−	1.30022e8i	0.812904	−	1.40799i
$453$		0			0
$454$			4.56657e7i			0.488004i
$455$	−1.95602e8	+	4.32935e7i	−2.07653	+	0.459609i
$456$		0			0
$457$	1.99697e7	+	3.45885e7i	0.209229	+	0.362396i	0.951472	−	0.307735i	$-0.0995711\pi$
$457$	1.99697e7	+	3.45885e7i	0.209229	+	0.362396i	−0.742243	+	0.670131i	$0.766238\pi$
$458$	−5.65682e6	−	3.26597e6i	−0.0588811	−	0.0339950i
$459$		0			0
$460$	−7.74478e6	+	4.47145e6i	−0.0795675	+	0.0459383i
$461$		−	1.40914e7i		−	0.143831i	−0.997411	−	0.0719153i	$-0.977089\pi$
$461$		−	1.40914e7i		−	0.143831i	0.997411	−	0.0719153i	$-0.0229111\pi$
$462$		0			0
$463$	1.25200e8			1.26142			0.630712	−	0.776017i	$-0.282763\pi$
$463$	1.25200e8			1.26142			0.630712	+	0.776017i	$0.282763\pi$
$464$	1.67295e7	+	2.89763e7i	0.167467	+	0.290061i
$465$		0			0
$466$	−9.48623e7	+	1.64306e8i	−0.937423	+	1.62367i
$467$	8.96567e7	−	5.17633e7i	0.880303	−	0.508243i	0.00954455	−	0.999954i	$-0.496962\pi$
$467$	8.96567e7	−	5.17633e7i	0.880303	−	0.508243i	0.870758	+	0.491711i	$0.163628\pi$
$468$		0			0
$469$	−8.08851e7	−	8.83315e7i	−0.784061	−	0.856243i
$470$	3.27284e8			3.15233
$471$		0			0
$472$	−1.34210e7	−	7.74860e6i	−0.127631	−	0.0736880i
$473$	−1.26762e7	+	2.19558e7i	−0.119786	+	0.207475i
$474$		0			0
$475$			8.21738e7i			0.766747i
$476$	1.49854e7	+	6.77049e7i	0.138947	+	0.627768i
$477$		0			0
$478$	−1.13913e8	−	1.97303e8i	−1.04301	−	1.80655i
$479$	6.75301e7	+	3.89885e7i	0.614456	+	0.354757i	0.774708	−	0.632320i	$-0.217897\pi$
$479$	6.75301e7	+	3.89885e7i	0.614456	+	0.354757i	−0.160251	+	0.987076i	$0.551230\pi$
$480$		0			0
$481$	−9.78713e7	+	5.65060e7i	−0.879468	+	0.507761i
$482$		−	4.18058e7i		−	0.373333i
$483$		0			0
$484$	1.73913e8			1.53389
$485$	1.95846e7	+	3.39216e7i	0.171668	+	0.297338i
$486$		0			0
$487$	−7.13992e7	+	1.23667e8i	−0.618168	+	1.07070i	0.371651	+	0.928372i	$0.378792\pi$
$487$	−7.13992e7	+	1.23667e8i	−0.618168	+	1.07070i	−0.989820	+	0.142327i	$0.954542\pi$
$488$	2.32029e7	−	1.33962e7i	0.199657	−	0.115272i
$489$		0			0
$490$	1.10078e8	+	2.36486e8i	0.935644	+	2.01010i
$491$	−5.07818e7			−0.429006			−0.214503	−	0.976723i	$-0.568813\pi$
$491$	−5.07818e7			−0.429006			−0.214503	+	0.976723i	$0.568813\pi$
$492$		0			0
$493$	−2.29132e7	−	1.32289e7i	−0.191225	−	0.110404i
$494$	−7.01846e7	+	1.21563e8i	−0.582185	+	1.00837i
$495$		0			0
$496$			1.00987e7i			0.0827598i
$497$	3.15597e7	−	9.99750e7i	0.257078	−	0.814371i
$498$		0			0
$499$	−6.32522e7	−	1.09556e8i	−0.509065	−	0.881727i	−0.999945	−	0.0104998i	$-0.996658\pi$
$499$	−6.32522e7	−	1.09556e8i	−0.509065	−	0.881727i	0.490879	−	0.871228i	$-0.336676\pi$
$500$	6.07709e7	+	3.50861e7i	0.486167	+	0.280689i
$501$		0			0
$502$	6.53735e7	−	3.77434e7i	0.516762	−	0.298353i
$503$		−	7.36652e6i		−	0.0578840i	−0.999581	−	0.0289420i	$-0.990786\pi$
$503$		−	7.36652e6i		−	0.0578840i	0.999581	−	0.0289420i	$-0.00921381\pi$
$504$		0			0
$505$	2.67434e8			2.07655
$506$	7.88423e6	+	1.36559e7i	0.0608566	+	0.105407i
$507$		0			0
$508$	−1.16684e8	+	2.02103e8i	−0.890062	+	1.54163i
$509$	1.98695e8	−	1.14716e8i	1.50672	−	0.869906i	0.506753	−	0.862092i	$-0.330846\pi$
$509$	1.98695e8	−	1.14716e8i	1.50672	−	0.869906i	0.999969	−	0.00781491i	$-0.00248759\pi$
$510$		0			0
$511$	5.98260e7	−	5.47826e7i	0.448360	−	0.410563i
$512$	1.88055e8			1.40112
$513$		0			0
$514$	2.87501e7	+	1.65989e7i	0.211714	+	0.122233i
$515$	4.94024e7	−	8.55674e7i	0.361681	−	0.626450i
$516$		0			0
$517$		−	3.03359e8i		−	2.19526i
$518$	9.93750e7	+	1.08524e8i	0.714970	+	0.780791i
$519$		0			0
$520$	2.35081e7	+	4.07172e7i	0.167189	+	0.289579i
$521$	9.29834e7	+	5.36840e7i	0.657495	+	0.379605i	0.791322	−	0.611400i	$-0.209393\pi$
$521$	9.29834e7	+	5.36840e7i	0.657495	+	0.379605i	−0.133827	+	0.991005i	$0.542727\pi$
$522$		0			0
$523$	1.30357e8	−	7.52614e7i	0.911230	−	0.526099i	0.0304034	−	0.999538i	$-0.490321\pi$
$523$	1.30357e8	−	7.52614e7i	0.911230	−	0.526099i	0.880827	+	0.473439i	$0.156987\pi$
$524$		−	1.58420e7i		−	0.110107i
$525$		0			0
$526$	5.80595e7			0.398948
$527$	−3.99279e6	−	6.91571e6i	−0.0272800	−	0.0472503i
$528$		0			0
$529$	7.37998e7	−	1.27825e8i	0.498526	−	0.863473i
$530$	−4.21731e8	+	2.43486e8i	−2.83275	+	1.63549i
$531$		0			0
$532$	9.16215e7	+	2.89227e7i	0.608503	+	0.192090i
$533$	−2.07898e8			−1.37299
$534$		0			0
$535$	1.06908e8	+	6.17235e7i	0.698151	+	0.403078i
$536$	−1.40542e7	+	2.43426e7i	−0.0912666	+	0.158078i
$537$		0			0
$538$		−	2.37197e8i		−	1.52322i
$539$	2.19198e8	−	1.02031e8i	1.39981	−	0.651575i
$540$		0			0
$541$	3.02874e7	+	5.24593e7i	0.191280	+	0.331307i	0.945675	−	0.325114i	$-0.105403\pi$
$541$	3.02874e7	+	5.24593e7i	0.191280	+	0.331307i	−0.754395	+	0.656421i	$0.772069\pi$
$542$	−1.24157e8	−	7.16821e7i	−0.779783	−	0.450208i
$543$		0			0
$544$	−1.16066e8	+	6.70107e7i	−0.720955	+	0.416243i
$545$		−	1.31181e8i		−	0.810365i
$546$		0			0
$547$	−2.68955e8			−1.64330			−0.821651	−	0.569992i	$-0.806946\pi$
$547$	−2.68955e8			−1.64330			−0.821651	+	0.569992i	$0.806946\pi$
$548$	−1.12442e8	−	1.94755e8i	−0.683259	−	1.18344i
$549$		0			0
$550$	2.48365e8	−	4.30180e8i	1.49280	−	2.58561i
$551$	−3.17471e7	+	1.83292e7i	−0.189780	+	0.109569i
$552$		0			0
$553$	−1.96395e8	+	4.34689e7i	−1.16133	+	0.257042i
$554$	−2.41962e8			−1.42304
$555$		0			0
$556$	−4.75900e7	−	2.74761e7i	−0.276880	−	0.159857i
$557$	1.00886e8	−	1.74739e8i	0.583800	−	1.01117i	−0.411223	−	0.911535i	$-0.634898\pi$
$557$	1.00886e8	−	1.74739e8i	0.583800	−	1.01117i	0.995024	−	0.0996375i	$-0.0317683\pi$
$558$		0			0
$559$			3.77486e7i			0.216105i
$560$	−1.74040e8	+	1.59369e8i	−0.991028	+	0.907484i
$561$		0			0
$562$	1.22050e8	+	2.11397e8i	0.687591	+	1.19094i
$563$	−1.52694e8	−	8.81577e7i	−0.855650	−	0.494010i	0.00690346	−	0.999976i	$-0.497803\pi$
$563$	−1.52694e8	−	8.81577e7i	−0.855650	−	0.494010i	−0.862553	+	0.505967i	$0.831136\pi$
$564$		0			0
$565$	−3.49892e8	+	2.02010e8i	−1.93994	+	1.12003i
$566$		−	1.21083e8i		−	0.667783i
$567$		0			0
$568$	−2.46041e7			−0.134265
$569$	1.00368e8	+	1.73843e8i	0.544828	+	0.943669i	0.998618	+	0.0525605i	$0.0167382\pi$
$569$	1.00368e8	+	1.73843e8i	0.544828	+	0.943669i	−0.453790	+	0.891109i	$0.649928\pi$
$570$		0			0
$571$	2.23204e7	−	3.86600e7i	0.119893	−	0.207660i	−0.799832	−	0.600224i	$-0.795078\pi$
$571$	2.23204e7	−	3.86600e7i	0.119893	−	0.207660i	0.919725	+	0.392563i	$0.128412\pi$
$572$	3.86287e8	−	2.23023e8i	2.06406	−	1.19169i
$573$		0			0
$574$	5.84986e7	+	2.64300e8i	0.309321	+	1.39753i
$575$	1.37446e7			0.0722986
$576$		0			0
$577$	−2.24118e8	−	1.29395e8i	−1.16668	−	0.673581i	−0.213781	−	0.976882i	$-0.568578\pi$
$577$	−2.24118e8	−	1.29395e8i	−1.16668	−	0.673581i	−0.952895	+	0.303301i	$0.901911\pi$
$578$	−9.30069e7	+	1.61093e8i	−0.481650	+	0.834243i
$579$		0			0
$580$			1.25675e8i			0.644119i
$581$	3.47949e7	+	1.09839e7i	0.177414	+	0.0560053i
$582$		0			0
$583$	2.25687e8	+	3.90901e8i	1.13894	+	1.97270i
$584$	−1.64870e7	−	9.51877e6i	−0.0827757	−	0.0477906i
$585$		0			0
$586$	−2.87031e8	+	1.65717e8i	−1.42638	+	0.823522i
$587$			3.41902e8i			1.69039i	0.534457	+	0.845196i	$0.320516\pi$
$587$			3.41902e8i			1.69039i	−0.534457	+	0.845196i	$0.679484\pi$
$588$		0			0
$589$	−1.10643e7			−0.0541476
$590$	2.13424e8	+	3.69661e8i	1.03917	+	1.79989i
$591$		0			0
$592$	−6.65608e7	+	1.15287e8i	−0.320814	+	0.555666i
$593$	−1.27791e8	+	7.37803e7i	−0.612826	+	0.353815i	−0.774071	−	0.633099i	$-0.781782\pi$
$593$	−1.27791e8	+	7.37803e7i	−0.612826	+	0.353815i	0.161245	+	0.986914i	$0.448449\pi$
$594$		0			0
$595$	5.61744e7	−	1.77949e8i	0.266678	−	0.844784i
$596$	−2.48908e8			−1.17571
$597$		0			0
$598$	2.03331e7	+	1.17393e7i	0.0950822	+	0.0548957i
$599$	−3.32461e7	+	5.75840e7i	−0.154690	+	0.267930i	−0.932946	−	0.360017i	$-0.882771\pi$
$599$	−3.32461e7	+	5.75840e7i	−0.154690	+	0.267930i	0.778256	+	0.627947i	$0.216104\pi$
$600$		0			0
$601$		−	3.71302e7i		−	0.171042i	−0.996336	−	0.0855212i	$-0.972744\pi$
$601$		−	3.71302e7i		−	0.171042i	0.996336	−	0.0855212i	$-0.0272555\pi$
$602$	4.79896e7	−	1.06218e7i	0.219967	−	0.0486864i
$603$		0			0
$604$	−2.28820e8	−	3.96328e8i	−1.03845	−	1.79864i
$605$	−4.05303e8	−	2.34002e8i	−1.83026	−	1.05670i
$606$		0			0
$607$	1.10132e8	−	6.35850e7i	0.492436	−	0.284308i	−0.233149	−	0.972441i	$-0.574903\pi$
$607$	1.10132e8	−	6.35850e7i	0.492436	−	0.284308i	0.725584	+	0.688133i	$0.241570\pi$
$608$			1.85692e8i			0.826195i
$609$		0			0
$610$	−7.37959e8			−3.25119
$611$	−2.25845e8	−	3.91174e8i	−0.990116	−	1.71493i
$612$		0			0
$613$	7.14975e7	−	1.23837e8i	0.310391	−	0.537614i	−0.668056	−	0.744111i	$-0.732873\pi$
$613$	7.14975e7	−	1.23837e8i	0.310391	−	0.537614i	0.978447	+	0.206498i	$0.0662066\pi$
$614$	1.02879e8	−	5.93974e7i	0.444450	−	0.256603i
$615$		0			0
$616$	−3.83205e7	−	4.18483e7i	−0.163942	−	0.179034i
$617$	2.96115e8			1.26068			0.630339	−	0.776320i	$-0.282916\pi$
$617$	2.96115e8			1.26068			0.630339	+	0.776320i	$0.282916\pi$
$618$		0			0
$619$	2.81343e8	+	1.62433e8i	1.18622	+	0.684862i	0.957444	−	0.288619i	$-0.0931959\pi$
$619$	2.81343e8	+	1.62433e8i	1.18622	+	0.684862i	0.228771	+	0.973480i	$0.426529\pi$
$620$	−1.89658e7	+	3.28498e7i	−0.0795786	+	0.137834i
$621$		0			0
$622$		−	1.82860e8i		−	0.759884i
$623$	−967903.	−	4.37303e6i	−0.00400283	−	0.0180850i
$624$		0			0
$625$	6.81453e7	+	1.18031e8i	0.279123	+	0.483456i
$626$	−5.58588e8	−	3.22501e8i	−2.27703	−	1.31464i
$627$		0			0
$628$	2.87661e8	−	1.66081e8i	1.16145	−	0.670566i
$629$		−	1.05267e8i		−	0.422998i
$630$		0			0
$631$	−1.40735e8			−0.560163			−0.280082	−	0.959976i	$-0.590362\pi$
$631$	−1.40735e8			−0.560163			−0.280082	+	0.959976i	$0.590362\pi$
$632$	2.36034e7	+	4.08822e7i	0.0935023	+	0.161951i
$633$		0			0
$634$	−3.50266e7	+	6.06679e7i	−0.137446	+	0.238063i
$635$	5.43864e8	−	3.14000e8i	2.12407	−	1.22633i
$636$		0			0
$637$	2.06691e8	−	2.94754e8i	0.799656	−	1.14036i
$638$	2.21595e8			0.853294
$639$		0			0
$640$	1.08367e8	+	6.25658e7i	0.413388	+	0.238670i
$641$	−1.08339e8	+	1.87648e8i	−0.411348	+	0.712476i	−0.995037	−	0.0995014i	$-0.968275\pi$
$641$	−1.08339e8	+	1.87648e8i	−0.411348	+	0.712476i	0.583689	+	0.811977i	$0.301609\pi$
$642$		0			0
$643$			2.61645e8i			0.984192i	0.870541	+	0.492096i	$0.163769\pi$
$643$			2.61645e8i			0.984192i	−0.870541	+	0.492096i	$0.836231\pi$
$644$	4.83770e6	−	1.53249e7i	0.0181126	−	0.0573773i
$645$		0			0
$646$	−6.53743e7	−	1.13232e8i	−0.242499	−	0.420020i
$647$	9.29409e7	+	5.36595e7i	0.343158	+	0.198122i	0.661668	−	0.749797i	$-0.269849\pi$
$647$	9.29409e7	+	5.36595e7i	0.343158	+	0.198122i	−0.318510	+	0.947920i	$0.603182\pi$
$648$		0			0
$649$	3.42637e8	−	1.97822e8i	1.25343	−	0.723669i
$650$		−	7.39610e8i		−	2.69316i
$651$		0			0
$652$	3.67582e8			1.32621
$653$	2.21977e8	+	3.84475e8i	0.797200	+	1.38079i	0.921432	+	0.388539i	$0.127020\pi$
$653$	2.21977e8	+	3.84475e8i	0.797200	+	1.38079i	−0.124232	+	0.992253i	$0.539647\pi$
$654$		0			0
$655$	−2.13156e7	+	3.69198e7i	−0.0758533	+	0.131382i
$656$	−2.12082e8	+	1.22446e8i	−0.751265	+	0.433743i
$657$		0			0
$658$	−4.33750e8	+	3.97184e8i	−1.52251	+	1.39417i
$659$	1.87037e7			0.0653538			0.0326769	−	0.999466i	$-0.489597\pi$
$659$	1.87037e7			0.0653538			0.0326769	+	0.999466i	$0.489597\pi$
$660$		0			0
$661$	−1.85577e7	−	1.07143e7i	−0.0642570	−	0.0370988i	0.467527	−	0.883979i	$-0.345145\pi$
$661$	−1.85577e7	−	1.07143e7i	−0.0642570	−	0.0370988i	−0.531784	+	0.846880i	$0.678478\pi$
$662$	−5.67179e7	+	9.82383e7i	−0.195500	+	0.338616i
$663$		0			0
$664$		−	8.56311e6i		−	0.0292501i
$665$	−1.74608e8	−	1.90682e8i	−0.593744	−	0.648404i
$666$		0			0
$667$	3.06580e6	+	5.31012e6i	0.0103316	+	0.0178948i
$668$	9.62130e7	+	5.55486e7i	0.322778	+	0.186356i
$669$		0			0
$670$	6.70481e8	−	3.87102e8i	2.22927	−	1.28707i
$671$			6.84012e8i			2.26410i
$672$		0			0
$673$	2.29593e8			0.753205			0.376603	−	0.926375i	$-0.377092\pi$
$673$	2.29593e8			0.753205			0.376603	+	0.926375i	$0.377092\pi$
$674$	3.31069e8	+	5.73428e8i	1.08128	+	1.87283i
$675$		0			0
$676$	1.60890e8	−	2.78669e8i	0.520820	−	0.902087i
$677$	−1.96110e7	+	1.13224e7i	−0.0632024	+	0.0364899i	−0.531268	−	0.847204i	$-0.678284\pi$
$677$	−1.96110e7	+	1.13224e7i	−0.0632024	+	0.0364899i	0.468066	+	0.883694i	$0.344951\pi$
$678$		0			0
$679$	−6.71218e7	−	2.11888e7i	−0.214415	−	0.0676856i
$680$	−4.37938e7			−0.139279
$681$		0			0
$682$	5.79219e7	+	3.34412e7i	0.182595	+	0.105421i
$683$	1.12310e8	−	1.94527e8i	0.352499	−	0.610546i	−0.634188	−	0.773179i	$-0.718665\pi$
$683$	1.12310e8	−	1.94527e8i	0.352499	−	0.610546i	0.986687	+	0.162633i	$0.0519986\pi$
$684$		0			0
$685$			6.05167e8i			1.88280i
$686$	−4.32879e8	−	1.79827e8i	−1.34089	−	0.557034i
$687$		0			0
$688$	2.22328e7	+	3.85084e7i	0.0682700	+	0.118247i
$689$	5.82036e8	+	3.36038e8i	1.77947	+	1.02738i
$690$		0			0
$691$	2.19279e8	−	1.26601e8i	0.664603	−	0.383709i	−0.129426	−	0.991589i	$-0.541313\pi$
$691$	2.19279e8	−	1.26601e8i	0.664603	−	0.383709i	0.794029	+	0.607880i	$0.207980\pi$
$692$			8.82811e7i			0.266409i
$693$		0			0
$694$	4.26717e8			1.27662
$695$	7.39390e7	+	1.28066e8i	0.220252	+	0.381487i
$696$		0			0
$697$	9.68246e7	−	1.67705e8i	0.285948	−	0.495277i
$698$	6.62351e8	−	3.82409e8i	1.94770	−	1.12451i
$699$		0			0
$700$	−4.94277e8	+	1.09401e8i	−1.44104	+	0.318952i
$701$	−3.18180e8			−0.923674			−0.461837	−	0.886965i	$-0.652809\pi$
$701$	−3.18180e8			−0.923674			−0.461837	+	0.886965i	$0.652809\pi$
$702$		0			0
$703$	−1.26311e8	−	7.29255e7i	−0.363558	−	0.209900i
$704$	3.24201e8	−	5.61532e8i	0.929171	−	1.60937i
$705$		0			0
$706$			3.70207e8i			1.05204i
$707$	−3.54430e8	+	3.24551e8i	−1.00293	+	0.918386i
$708$		0			0
$709$	−1.35142e8	−	2.34072e8i	−0.379185	−	0.656767i	0.611759	−	0.791044i	$-0.290462\pi$
$709$	−1.35142e8	−	2.34072e8i	−0.379185	−	0.656767i	−0.990944	+	0.134277i	$0.957129\pi$
$710$	5.86891e8	+	3.38842e8i	1.63977	+	0.946721i
$711$		0			0
$712$	−910305.	+	525565.i	−0.00252201	+	0.00145608i
$713$			1.85065e6i			0.00510572i
$714$		0			0
$715$	−1.20032e9			−3.28383
$716$	8.00089e7	+	1.38579e8i	0.217971	+	0.377537i
$717$		0			0
$718$	−2.22013e8	+	3.84538e8i	−0.599799	+	1.03888i
$719$	−9.13702e7	+	5.27526e7i	−0.245820	+	0.141924i	−0.617849	−	0.786297i	$-0.711996\pi$
$719$	−9.13702e7	+	5.27526e7i	−0.245820	+	0.141924i	0.372029	+	0.928221i	$0.378662\pi$
$720$		0			0
$721$	3.83697e7	+	1.73356e8i	0.102372	+	0.462522i
$722$	3.65324e8			0.970660
$723$		0			0
$724$	−4.89696e8	−	2.82726e8i	−1.29036	−	0.744989i
$725$	9.65772e7	−	1.67277e8i	0.253431	−	0.438956i
$726$		0			0
$727$		−	3.47133e8i		−	0.903425i	−0.892164	−	0.451713i	$-0.850813\pi$
$727$		−	3.47133e8i		−	0.903425i	0.892164	−	0.451713i	$-0.149187\pi$
$728$	−8.05686e7	−	2.54336e7i	−0.208820	−	0.0659194i
$729$		0			0
$730$	2.62180e8	+	4.54110e8i	0.673956	+	1.16733i
$731$	−3.04507e7	−	1.75807e7i	−0.0779552	−	0.0450074i
$732$		0			0
$733$	−4.04599e8	+	2.33596e8i	−1.02734	+	0.593134i	−0.916221	−	0.400673i	$-0.868776\pi$
$733$	−4.04599e8	+	2.33596e8i	−1.02734	+	0.593134i	−0.111117	+	0.993807i	$0.535443\pi$
$734$		−	1.13121e9i		−	2.86058i
$735$		0			0
$736$	3.10594e7			0.0779040
$737$	−3.58804e8	−	6.21467e8i	−0.896304	−	1.55244i
$738$		0			0
$739$	−1.98814e8	+	3.44356e8i	−0.492623	+	0.853247i	−0.999964	−	0.00849788i	$-0.997295\pi$
$739$	−1.98814e8	+	3.44356e8i	−0.492623	+	0.853247i	0.507341	+	0.861745i	$0.330628\pi$
$740$	−4.33028e8	+	2.50009e8i	−1.06861	+	0.616965i
$741$		0			0
$742$	2.63430e8	−	8.34494e8i	0.644842	−	2.04273i
$743$	−6.88913e8			−1.67957			−0.839784	−	0.542920i	$-0.817319\pi$
$743$	−6.88913e8			−1.67957			−0.839784	+	0.542920i	$0.817319\pi$
$744$		0			0
$745$	5.80080e8	+	3.34909e8i	1.40288	+	0.809951i
$746$	−1.22215e8	+	2.11683e8i	−0.294380	+	0.509881i
$747$		0			0
$748$			4.15475e8i			0.992751i
$749$	−2.16591e8	+	4.79392e7i	−0.515461	+	0.114089i
$750$		0			0
$751$	−1.83282e8	−	3.17453e8i	−0.432712	−	0.749480i	0.564393	−	0.825506i	$-0.309110\pi$
$751$	−1.83282e8	−	3.17453e8i	−0.432712	−	0.749480i	−0.997106	+	0.0760260i	$0.975777\pi$
$752$	−4.60781e8	−	2.66032e8i	−1.08353	−	0.625576i
$753$		0			0
$754$	2.85742e8	−	1.64973e8i	0.666592	−	0.384857i
$755$			1.23152e9i			2.86156i
$756$		0			0
$757$	−2.07241e8			−0.477735			−0.238868	−	0.971052i	$-0.576776\pi$
$757$	−2.07241e8			−0.477735			−0.238868	+	0.971052i	$0.576776\pi$
$758$	2.39168e8	+	4.14252e8i	0.549157	+	0.951167i
$759$		0			0
$760$	−3.03390e7	+	5.25487e7i	−0.0691132	+	0.119708i
$761$	5.86021e8	−	3.38339e8i	1.32972	−	0.767712i	0.344461	−	0.938801i	$-0.388062\pi$
$761$	5.86021e8	−	3.38339e8i	1.32972	−	0.767712i	0.985256	+	0.171088i	$0.0547283\pi$
$762$		0			0
$763$	1.59198e8	+	1.73854e8i	0.358396	+	0.391390i
$764$	−3.02285e8			−0.677854
$765$		0			0
$766$	−1.53096e8	−	8.83901e7i	−0.340626	−	0.196661i
$767$	2.94549e8	−	5.10173e8i	0.652786	−	1.13066i
$768$		0			0
$769$			5.58023e8i			1.22708i	0.789663	+	0.613540i	$0.210255\pi$
$769$			5.58023e8i			1.22708i	−0.789663	+	0.613540i	$0.789745\pi$
$770$	3.37749e8	+	1.52596e9i	0.739813	+	3.34251i
$771$		0			0
$772$	5.16985e6	+	8.95443e6i	0.0112364	+	0.0194619i
$773$	−7.17689e7	−	4.14358e7i	−0.155381	−	0.0897093i	0.420293	−	0.907388i	$-0.361927\pi$
$773$	−7.17689e7	−	4.14358e7i	−0.155381	−	0.0897093i	−0.575675	+	0.817679i	$0.695260\pi$
$774$		0			0
$775$	5.04878e7	−	2.91492e7i	0.108463	−	0.0626211i
$776$			1.65188e7i			0.0353504i
$777$		0			0
$778$	7.84070e8			1.66501
$779$	−1.34154e8	−	2.32362e8i	−0.283787	−	0.491533i
$780$		0			0
$781$	3.14072e8	−	5.43988e8i	0.659289	−	1.14192i
$782$	−1.89395e7	+	1.09347e7i	−0.0396048	+	0.0228658i
$783$		0			0
$784$	3.72493e7	−	4.22422e8i	0.0772984	−	0.876594i
$785$	−8.93859e8			−1.84782
$786$		0			0
$787$	−4.59435e8	−	2.65255e8i	−0.942541	−	0.544176i	−0.0517851	−	0.998658i	$-0.516491\pi$
$787$	−4.59435e8	−	2.65255e8i	−0.942541	−	0.544176i	−0.890756	+	0.454482i	$0.849824\pi$
$788$	−2.55813e8	+	4.43082e8i	−0.522811	+	0.905535i
$789$		0			0
$790$		−	1.30024e9i		−	2.63719i
$791$	2.18556e8	−	6.92344e8i	0.441605	−	1.39892i
$792$		0			0
$793$	5.09233e8	+	8.82017e8i	1.02117	+	1.76871i
$794$	−9.45767e7	−	5.46039e7i	−0.188939	−	0.109084i
$795$		0			0
$796$	−1.08406e8	+	6.25885e7i	−0.214939	+	0.124095i
$797$		−	4.96880e8i		−	0.981469i	−0.871309	−	0.490735i	$-0.836728\pi$
$797$		−	4.96880e8i		−	0.981469i	0.871309	−	0.490735i	$-0.163272\pi$
$798$		0			0
$799$	4.20732e8			0.824831
$800$	−4.89209e8	−	8.47334e8i	−0.955486	−	1.65495i
$801$		0			0
$802$	−3.22326e8	+	5.58285e8i	−0.624845	+	1.08226i
$803$	4.20913e8	−	2.43014e8i	0.812917	−	0.469338i
$804$		0			0
$805$	−3.18941e7	+	2.92055e7i	−0.0611397	+	0.0559856i
$806$	9.95852e7			0.190191
$807$		0			0
$808$	9.76747e7	+	5.63925e7i	0.185160	+	0.106902i
$809$	−2.10152e8	+	3.63994e8i	−0.396906	+	0.687461i	−0.993342	−	0.115199i	$-0.963249\pi$
$809$	−2.10152e8	+	3.63994e8i	−0.396906	+	0.687461i	0.596437	+	0.802660i	$0.296583\pi$
$810$		0			0
$811$		−	4.27809e8i		−	0.802025i	−0.916073	−	0.401012i	$-0.868658\pi$
$811$		−	4.27809e8i		−	0.802025i	0.916073	−	0.401012i	$-0.131342\pi$
$812$	−1.52517e8	−	1.66557e8i	−0.284871	−	0.311097i
$813$		0			0
$814$	4.40825e8	+	7.63531e8i	0.817322	+	1.41564i
$815$	−8.56650e8	−	4.94587e8i	−1.58245	−	0.913629i
$816$		0			0
$817$	−4.21907e7	+	2.43588e7i	−0.0773660	+	0.0446673i
$818$		−	1.89887e8i		−	0.346925i
$819$		0			0
$820$	−9.19837e8			−1.66828
$821$	4.76401e8	+	8.25152e8i	0.860882	+	1.49109i	0.871079	+	0.491143i	$0.163421\pi$
$821$	4.76401e8	+	8.25152e8i	0.860882	+	1.49109i	−0.0101968	+	0.999948i	$0.503246\pi$
$822$		0			0
$823$	3.70614e8	−	6.41923e8i	0.664848	−	1.15155i	−0.314478	−	0.949265i	$-0.601829\pi$
$823$	3.70614e8	−	6.41923e8i	0.664848	−	1.15155i	0.979326	−	0.202287i	$-0.0648372\pi$
$824$	3.60864e7	−	2.08345e7i	0.0645003	−	0.0372392i
$825$		0			0
$826$	−7.31461e8	−	2.30905e8i	−1.29793	−	0.409725i
$827$	7.61072e8			1.34558			0.672790	−	0.739834i	$-0.265096\pi$
$827$	7.61072e8			1.34558			0.672790	+	0.739834i	$0.265096\pi$
$828$		0			0
$829$	−7.06469e8	−	4.07880e8i	−1.24002	−	0.715928i	−0.270924	−	0.962601i	$-0.587329\pi$
$829$	−7.06469e8	−	4.07880e8i	−1.24002	−	0.715928i	−0.969099	+	0.246673i	$0.920663\pi$
$830$	−1.17929e8	+	2.04259e8i	−0.206247	+	0.357230i
$831$		0			0
$832$		−	9.65442e8i		−	1.67632i
$833$	1.41507e8	+	3.04008e8i	0.244818	+	0.525956i
$834$		0			0
$835$	−1.49483e8	−	2.58912e8i	−0.256763	−	0.444726i
$836$	4.98534e8	+	2.87829e8i	0.853250	+	0.492624i
$837$		0			0
$838$	−3.77261e8	+	2.17812e8i	−0.641076	+	0.370126i
$839$		−	1.07654e9i		−	1.82283i	−0.411491	−	0.911414i	$-0.634992\pi$
$839$		−	1.07654e9i		−	1.82283i	0.411491	−	0.911414i	$-0.365008\pi$
$840$		0			0
$841$	−5.08655e8			−0.855137
$842$	−5.32881e8	−	9.22978e8i	−0.892677	−	1.54616i
$843$		0			0
$844$	−4.85986e8	+	8.41753e8i	−0.808345	+	1.40009i
$845$	−7.49906e8	+	4.32959e8i	−1.24290	+	0.717590i
$846$		0			0
$847$	8.21126e8	−	1.81744e8i	1.35132	−	0.299095i
$848$	7.91667e8			1.29824
$849$		0			0
$850$	5.96621e8	+	3.44459e8i	0.971498	+	0.560895i
$851$	−1.21977e7	+	2.11271e7i	−0.0197921	+	0.0342808i
$852$		0			0
$853$			9.74565e8i			1.57023i	0.619349	+	0.785116i	$0.287397\pi$
$853$			9.74565e8i			1.57023i	−0.619349	+	0.785116i	$0.712603\pi$
$854$	9.78015e8	−	8.95568e8i	1.57026	−	1.43789i
$855$		0			0
$856$	2.60307e7	+	4.50864e7i	0.0415015	+	0.0718827i
$857$	8.31953e8	+	4.80328e8i	1.32177	+	0.763125i	0.984011	−	0.178107i	$-0.0569974\pi$
$857$	8.31953e8	+	4.80328e8i	1.32177	+	0.763125i	0.337760	+	0.941232i	$0.390331\pi$
$858$		0			0
$859$	4.22688e8	−	2.44039e8i	0.666869	−	0.385017i	−0.128020	−	0.991772i	$-0.540862\pi$
$859$	4.22688e8	−	2.44039e8i	0.666869	−	0.385017i	0.794889	+	0.606755i	$0.207529\pi$
$860$			1.67018e8i			0.262583i
$861$		0			0
$862$	1.60076e9			2.49921
$863$	1.61373e8	+	2.79507e8i	0.251073	+	0.434871i	0.963821	−	0.266549i	$-0.0858833\pi$
$863$	1.61373e8	+	2.79507e8i	0.251073	+	0.434871i	−0.712749	+	0.701420i	$0.752550\pi$
$864$		0			0
$865$	1.18784e8	−	2.05739e8i	0.183530	−	0.317884i
$866$	−2.01520e8	+	1.16348e8i	−0.310287	+	0.179144i
$867$		0			0
$868$	−1.47303e7	−	6.65522e7i	−0.0225244	−	0.101766i
$869$	−1.20519e9			−1.83652
$870$		0			0
$871$	−9.25339e8	−	5.34245e8i	−1.40038	−	0.808511i
$872$	2.76614e7	−	4.79110e7i	0.0417182	−	0.0722580i
$873$		0			0
$874$			3.03010e7i			0.0453860i
$875$	3.23595e8	+	1.02151e8i	0.483035	+	0.152482i
$876$		0			0
$877$	−4.68948e8	−	8.12242e8i	−0.695226	−	1.20417i	−0.970104	−	0.242688i	$-0.921971\pi$
$877$	−4.68948e8	−	8.12242e8i	−0.695226	−	1.20417i	0.274878	−	0.961479i	$-0.411362\pi$
$878$	−8.66164e8	−	5.00080e8i	−1.27973	−	0.738850i
$879$		0			0
$880$	−1.22448e9	+	7.06956e8i	−1.79682	+	1.03739i
$881$			9.47337e8i			1.38540i	0.721224	+	0.692702i	$0.243580\pi$
$881$			9.47337e8i			1.38540i	−0.721224	+	0.692702i	$0.756420\pi$
$882$		0			0
$883$	1.52054e8			0.220860			0.110430	−	0.993884i	$-0.464777\pi$
$883$	1.52054e8			0.220860			0.110430	+	0.993884i	$0.464777\pi$
$884$	3.09313e8	+	5.35746e8i	0.447756	+	0.775536i
$885$		0			0
$886$	−4.69211e7	+	8.12697e7i	−0.0674632	+	0.116850i
$887$	−1.02528e9	+	5.91948e8i	−1.46917	+	0.848228i	−0.999403	−	0.0345605i	$-0.988997\pi$
$887$	−1.02528e9	+	5.91948e8i	−1.46917	+	0.848228i	−0.469771	+	0.882788i	$0.655664\pi$
$888$		0			0
$889$	−3.39719e8	+	1.07616e9i	−0.483521	+	1.53170i
$890$	2.89518e7			0.0410682
$891$		0			0
$892$	1.32086e9	+	7.62599e8i	1.86107	+	1.07449i
$893$	2.91470e8	−	5.04842e8i	0.409298	−	0.708926i
$894$		0			0
$895$		−	4.30612e8i		−	0.600644i
$896$	−2.19547e8	+	4.85934e7i	−0.305213	+	0.0675543i
$897$		0			0
$898$	−2.99974e8	−	5.19569e8i	−0.414242	−	0.717488i
$899$	2.25231e7	+	1.30037e7i	0.0309990	+	0.0178973i
$900$		0			0
$901$	−5.42144e8	+	3.13007e8i	−0.741209	+	0.427937i
$902$			1.62189e9i			2.21005i
$903$		0			0
$904$	−1.70388e8			−0.230639
$905$	7.60824e8	+	1.31779e9i	1.02645	+	1.77787i
$906$		0			0
$907$	−1.69886e8	+	2.94252e8i	−0.227686	+	0.394364i	−0.957122	−	0.289685i	$-0.906449\pi$
$907$	−1.69886e8	+	2.94252e8i	−0.227686	+	0.394364i	0.729436	+	0.684049i	$0.239783\pi$
$908$	2.41489e8	−	1.39423e8i	0.322581	−	0.186242i
$909$		0			0
$910$	1.57157e9	+	1.71625e9i	2.08549	+	2.27749i
$911$	9.44286e8			1.24896			0.624480	−	0.781041i	$-0.285311\pi$
$911$	9.44286e8			1.24896			0.624480	+	0.781041i	$0.285311\pi$
$912$		0			0
$913$	1.89327e8	+	1.09308e8i	0.248772	+	0.143628i
$914$	2.31967e8	−	4.01778e8i	0.303799	−	0.526196i
$915$		0			0
$916$			3.98857e7i			0.0518956i
$917$	−1.65554e7	−	7.47978e7i	−0.0214699	−	0.0970021i
$918$		0			0
$919$	1.87277e8	+	3.24374e8i	0.241290	+	0.417926i	0.961082	−	0.276264i	$-0.0890963\pi$
$919$	1.87277e8	+	3.24374e8i	0.241290	+	0.417926i	−0.719792	+	0.694189i	$0.755763\pi$
$920$	8.78947e6	+	5.07460e6i	0.0112875	+	0.00651686i
$921$		0			0
$922$	−1.41755e8	+	8.18424e7i	−0.180862	+	0.104420i
$923$		−	9.35280e8i		−	1.18942i
$924$		0			0
$925$	7.68494e8			0.970991
$926$	−7.27157e8	−	1.25947e9i	−0.915788	−	1.58619i
$927$		0			0
$928$	2.18240e8	−	3.78003e8i	0.273081	−	0.472989i
$929$	−7.89503e8	+	4.55820e8i	−0.984707	+	0.568521i	−0.903688	−	0.428192i	$-0.859151\pi$
$929$	−7.89503e8	+	4.55820e8i	−0.984707	+	0.568521i	−0.0810189	+	0.996713i	$0.525817\pi$
$930$		0			0
$931$	4.62815e8	+	4.08112e7i	0.573533	+	0.0505743i
$932$	1.15851e9			1.43104
$933$		0			0
$934$	−1.04145e9	−	6.01279e8i	−1.27819	−	0.737965i
$935$	5.59028e8	−	9.68265e8i	0.683910	−	1.18457i
$936$		0			0
$937$			3.76597e8i			0.457781i	0.973452	+	0.228890i	$0.0735097\pi$
$937$			3.76597e8i			0.457781i	−0.973452	+	0.228890i	$0.926490\pi$
$938$	−4.18809e8	+	1.32671e9i	−0.507467	+	1.60756i
$939$		0			0
$940$	−9.99242e8	−	1.73074e9i	−1.20306	−	2.08376i
$941$	−2.17999e8	−	1.25862e8i	−0.261629	−	0.151051i	0.363449	−	0.931614i	$-0.381599\pi$
$941$	−2.17999e8	−	1.25862e8i	−0.261629	−	0.151051i	−0.625077	+	0.780563i	$0.714933\pi$
$942$		0			0
$943$	−3.88656e7	+	2.24391e7i	−0.0463479	+	0.0267590i
$944$		−	6.93922e8i		−	0.824888i
$945$		0			0
$946$	2.94491e8			0.347856
$947$	−1.32933e8	−	2.30247e8i	−0.156525	−	0.271109i	0.777088	−	0.629392i	$-0.216696\pi$
$947$	−1.32933e8	−	2.30247e8i	−0.156525	−	0.271109i	−0.933613	+	0.358282i	$0.883363\pi$
$948$		0			0
$949$	3.61838e8	−	6.26723e8i	0.423366	−	0.733292i
$950$	8.26643e8	−	4.77262e8i	0.964156	−	0.556655i
$951$		0			0
$952$	5.80398e7	−	5.31471e7i	0.0672690	−	0.0615983i
$953$	5.38039e8			0.621635			0.310817	−	0.950470i	$-0.399397\pi$
$953$	5.38039e8			0.621635			0.310817	+	0.950470i	$0.399397\pi$
$954$		0			0
$955$	7.04475e8	+	4.06729e8i	0.808827	+	0.466976i
$956$	−6.95581e8	+	1.20478e9i	−0.796112	+	1.37891i
$957$		0			0
$958$		−	9.05777e8i		−	1.03021i
$959$	−7.34416e8	−	8.02027e8i	−0.832696	−	0.909355i
$960$		0			0
$961$	−4.39827e8	−	7.61803e8i	−0.495578	−	0.858366i
$962$	1.13687e9	+	6.56370e8i	1.27698	+	0.737265i
$963$		0			0
$964$	−2.21077e8	+	1.27639e8i	−0.246781	+	0.142479i
$965$		−	2.78244e7i		−	0.0309631i
$966$		0			0
$967$	−1.16138e9			−1.28439			−0.642194	−	0.766542i	$-0.721976\pi$
$967$	−1.16138e9			−1.28439			−0.642194	+	0.766542i	$0.721976\pi$
$968$	−9.86856e7	−	1.70929e8i	−0.108800	−	0.188447i
$969$		0			0
$970$	2.27494e8	−	3.94031e8i	0.249261	−	0.431732i
$971$	−1.30640e9	+	7.54248e8i	−1.42698	+	0.823866i	−0.996881	−	0.0789166i	$-0.974854\pi$
$971$	−1.30640e9	+	7.54248e8i	−1.42698	+	0.823866i	−0.430097	+	0.902783i	$0.641521\pi$
$972$		0			0
$973$	−2.53409e8	−	7.99953e7i	−0.275096	−	0.0868412i
$974$	1.65874e9			1.79515
$975$		0			0
$976$	1.03896e9	+	5.99847e8i	1.11751	+	0.645195i
$977$	−6.03772e7	+	1.04576e8i	−0.0647425	+	0.112137i	−0.896580	−	0.442882i	$-0.853956\pi$
$977$	−6.03772e7	+	1.04576e8i	−0.0647425	+	0.112137i	0.831837	+	0.555020i	$0.187289\pi$
$978$		0			0
$979$		−	2.68354e7i		−	0.0285996i
$980$	9.14497e8	−	1.30413e9i	0.971637	−	1.38562i
$981$		0			0
$982$	2.94939e8	+	5.10849e8i	0.311457	+	0.539459i
$983$	1.86333e7	+	1.07580e7i	0.0196169	+	0.0113258i	0.509776	−	0.860307i	$-0.329728\pi$
$983$	1.86333e7	+	1.07580e7i	0.0196169	+	0.0113258i	−0.490159	+	0.871633i	$0.663061\pi$
$984$		0			0
$985$	1.19235e9	−	6.88401e8i	1.24765	−	0.720333i
$986$			3.07333e8i			0.320611i
$987$		0			0
$988$	8.57131e8			0.888743
$989$	4.07433e6	+	7.05694e6i	0.00421179	+	0.00729504i
$990$		0			0
$991$	3.07940e7	−	5.33368e7i	0.0316407	−	0.0548033i	−0.849771	−	0.527151i	$-0.823260\pi$
$991$	3.07940e7	−	5.33368e7i	0.0316407	−	0.0548033i	0.881412	+	0.472348i	$0.156593\pi$
$992$	1.14090e8	−	6.58698e7i	0.116872	−	0.0674763i
$993$		0			0
$994$	−1.18902e9	+	2.63170e8i	−1.21068	+	0.267965i
$995$	3.36855e8			0.341959
$996$		0			0
$997$	6.72319e8	+	3.88164e8i	0.678406	+	0.391678i	0.799254	−	0.600993i	$-0.205228\pi$
$997$	6.72319e8	+	3.88164e8i	0.678406	+	0.391678i	−0.120848	+	0.992671i	$0.538561\pi$
$998$	−7.34733e8	+	1.27259e9i	−0.739159	+	1.28026i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.7.m.d.10.1		8
3.2	odd	2		21.7.f.a.10.4	✓	8
7.3	odd	6		441.7.d.c.244.7		8
7.4	even	3		441.7.d.c.244.8		8
7.5	odd	6	inner	63.7.m.d.19.1		8
12.11	even	2		336.7.bh.d.241.1		8
21.2	odd	6		147.7.f.d.19.4		8
21.5	even	6		21.7.f.a.19.4	yes	8
21.11	odd	6		147.7.d.b.97.2		8
21.17	even	6		147.7.d.b.97.1		8
21.20	even	2		147.7.f.d.31.4		8
84.47	odd	6		336.7.bh.d.145.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.f.a.10.4	✓	8	3.2	odd	2
21.7.f.a.19.4	yes	8	21.5	even	6
63.7.m.d.10.1		8	1.1	even	1	trivial
63.7.m.d.19.1		8	7.5	odd	6	inner
147.7.d.b.97.1		8	21.17	even	6
147.7.d.b.97.2		8	21.11	odd	6
147.7.f.d.19.4		8	21.2	odd	6
147.7.f.d.31.4		8	21.20	even	2
336.7.bh.d.145.1		8	84.47	odd	6
336.7.bh.d.241.1		8	12.11	even	2
441.7.d.c.244.7		8	7.3	odd	6
441.7.d.c.244.8		8	7.4	even	3

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	63.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.80797 - 10.0597i) q^{2} +(-35.4650 + 61.4271i) q^{4} +(165.302 - 95.4373i) q^{5} +(-103.254 + 327.089i) q^{7} +80.4975 q^{8} +O(q^{10})\)	\(q+(-5.80797 - 10.0597i) q^{2} +(-35.4650 + 61.4271i) q^{4} +(165.302 - 95.4373i) q^{5} +(-103.254 + 327.089i) q^{7} +80.4975 q^{8} +(-1920.14 - 1108.59i) q^{10} +(-1027.55 + 1779.77i) q^{11} +3059.97i q^{13} +(3890.12 - 861.018i) q^{14} +(1802.23 + 3121.55i) q^{16} +(-2468.38 - 1425.12i) q^{17} +(-3420.04 + 1974.56i) q^{19} +13538.7i q^{20} +23872.0 q^{22} +(330.272 + 572.047i) q^{23} +(10404.0 - 18020.3i) q^{25} +(30782.3 - 17772.2i) q^{26} +(-16430.3 - 17942.8i) q^{28} +9282.66 q^{29} +(2426.36 + 1400.86i) q^{31} +(23510.5 - 40721.4i) q^{32} +33108.2i q^{34} +(14148.4 + 63922.9i) q^{35} +(18466.2 + 31984.5i) q^{37} +(39727.0 + 22936.4i) q^{38} +(13306.4 - 7682.46i) q^{40} +67941.3i q^{41} +12336.3 q^{43} +(-72884.2 - 126239. i) q^{44} +(3836.41 - 6644.86i) q^{46} +(-127836. + 73806.3i) q^{47} +(-96326.1 - 67546.8i) q^{49} -241705. q^{50} +(-187965. - 108522. i) q^{52} +(109818. - 190210. i) q^{53} +392267. i q^{55} +(-8311.72 + 26329.9i) q^{56} +(-53913.4 - 93380.8i) q^{58} +(-166725. - 96258.8i) q^{59} +(288244. - 166418. i) q^{61} -32544.5i q^{62} -315508. q^{64} +(292035. + 505819. i) q^{65} +(-174592. + 302402. i) q^{67} +(175082. - 101084. i) q^{68} +(560872. - 513590. i) q^{70} -305650. q^{71} +(-204814. - 118249. i) q^{73} +(214503. - 371529. i) q^{74} -280111. i q^{76} +(-476046. - 519871. i) q^{77} +(293218. + 507869. i) q^{79} +(595825. + 344000. i) q^{80} +(683468. - 394601. i) q^{82} -106377. i q^{83} -544039. q^{85} +(-71648.8 - 124099. i) q^{86} +(-82715.4 + 143267. i) q^{88} +(-11308.5 + 6528.95i) q^{89} +(-1.00088e6 - 315955. i) q^{91} -46852.3 q^{92} +(1.48494e6 + 857329. i) q^{94} +(-376894. + 652799. i) q^{95} +205209. i q^{97} +(-120042. + 1.36132e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 5 q^{2} - 173 q^{4} + 294 q^{5} - 656 q^{7} - 3326 q^{8}+O(q^{10}) \) 8 * q + 5 * q^2 - 173 * q^4 + 294 * q^5 - 656 * q^7 - 3326 * q^8	\( 8 q + 5 q^{2} - 173 q^{4} + 294 q^{5} - 656 q^{7} - 3326 q^{8} - 3411 q^{10} + 314 q^{11} + 5360 q^{14} - 12721 q^{16} + 5532 q^{17} - 18234 q^{19} + 86106 q^{22} - 3928 q^{23} - 17038 q^{25} - 12366 q^{26} + 85037 q^{28} + 8300 q^{29} - 89508 q^{31} + 186207 q^{32} + 25860 q^{35} + 64706 q^{37} + 77136 q^{38} + 221823 q^{40} + 45740 q^{43} - 92529 q^{44} - 111504 q^{46} - 483276 q^{47} - 310684 q^{49} - 967216 q^{50} - 1673988 q^{52} + 540974 q^{53} + 241885 q^{56} + 539799 q^{58} + 181770 q^{59} + 418224 q^{61} + 2378626 q^{64} + 414204 q^{65} - 1158902 q^{67} + 821250 q^{68} + 1087917 q^{70} - 1442344 q^{71} - 378666 q^{73} + 432940 q^{74} - 1065994 q^{77} + 611452 q^{79} + 2094945 q^{80} - 1561266 q^{82} - 275112 q^{85} - 816224 q^{86} - 366441 q^{88} + 989196 q^{89} + 304446 q^{91} - 678720 q^{92} - 716148 q^{94} + 591792 q^{95} - 3509629 q^{98}+O(q^{100}) \) 8 * q + 5 * q^2 - 173 * q^4 + 294 * q^5 - 656 * q^7 - 3326 * q^8 - 3411 * q^10 + 314 * q^11 + 5360 * q^14 - 12721 * q^16 + 5532 * q^17 - 18234 * q^19 + 86106 * q^22 - 3928 * q^23 - 17038 * q^25 - 12366 * q^26 + 85037 * q^28 + 8300 * q^29 - 89508 * q^31 + 186207 * q^32 + 25860 * q^35 + 64706 * q^37 + 77136 * q^38 + 221823 * q^40 + 45740 * q^43 - 92529 * q^44 - 111504 * q^46 - 483276 * q^47 - 310684 * q^49 - 967216 * q^50 - 1673988 * q^52 + 540974 * q^53 + 241885 * q^56 + 539799 * q^58 + 181770 * q^59 + 418224 * q^61 + 2378626 * q^64 + 414204 * q^65 - 1158902 * q^67 + 821250 * q^68 + 1087917 * q^70 - 1442344 * q^71 - 378666 * q^73 + 432940 * q^74 - 1065994 * q^77 + 611452 * q^79 + 2094945 * q^80 - 1561266 * q^82 - 275112 * q^85 - 816224 * q^86 - 366441 * q^88 + 989196 * q^89 + 304446 * q^91 - 678720 * q^92 - 716148 * q^94 + 591792 * q^95 - 3509629 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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