LMFDB - Embedded newform 198.6.f.g.37.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [198,6,Mod(37,198)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(198, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("198.37");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 198 = 2 \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	198.f (of order $5$, degree $4$, 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:	$31.7559963230$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} - 32717 x^{18} - 175765 x^{17} + 429989344 x^{16} + 5846276963 x^{15} + \cdots + 29\!\cdots\!01 $ x^20 - 3x^19 - 32717x^18 - 175765x^17 + 429989344x^16 + 5846276963x^15 - 2895568160445x^14 - 61486624057387x^13 + 10571261221333419x^12 + 294539949044070726x^11 - 20572959391661926036x^10 - 692661753702996624264x^9 + 20344799403272690812036x^8 + 835601227125892021783426x^7 - 8238304884590821296664394x^6 - 499725651021814750309330328x^5 - 404520969181668980873288047x^4 + 120964284575575042907998183609x^3 + 816183701186375238030969243281x^2 - 2633638927157539958891566472415*x + 2936565356795086268881959852401
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{8}\cdot 11^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			37.4
Root			$-20.8963 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	198.37
Dual form			198.6.f.g.91.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.23607 - 2.35114i) q^{2} +(4.94427 + 15.2169i) q^{4} +(5.56531 - 4.04343i) q^{5} +(-20.6422 - 63.5301i) q^{7} +(19.7771 - 60.8676i) q^{8} +O(q^{10})$	\(q+(-3.23607 - 2.35114i) q^{2} +(4.94427 + 15.2169i) q^{4} +(5.56531 - 4.04343i) q^{5} +(-20.6422 - 63.5301i) q^{7} +(19.7771 - 60.8676i) q^{8} -27.5164 q^{10} +(-138.325 + 376.719i) q^{11} +(291.608 + 211.866i) q^{13} +(-82.5688 + 254.121i) q^{14} +(-207.108 + 150.473i) q^{16} +(429.972 - 312.393i) q^{17} +(819.802 - 2523.09i) q^{19} +(89.0450 + 64.6949i) q^{20} +(1333.35 - 893.865i) q^{22} -4816.31 q^{23} +(-951.055 + 2927.05i) q^{25} +(-445.538 - 1371.22i) q^{26} +(864.672 - 628.221i) q^{28} +(1956.27 + 6020.77i) q^{29} +(6217.90 + 4517.57i) q^{31} +1024.00 q^{32} -2125.90 q^{34} +(-371.760 - 270.100i) q^{35} +(-591.449 - 1820.29i) q^{37} +(-8585.08 + 6237.42i) q^{38} +(-136.049 - 418.715i) q^{40} +(-828.887 + 2551.05i) q^{41} +16310.2 q^{43} +(-6416.41 - 242.284i) q^{44} +(15585.9 + 11323.8i) q^{46} +(4330.52 - 13328.0i) q^{47} +(9987.17 - 7256.10i) q^{49} +(9959.58 - 7236.05i) q^{50} +(-1782.15 + 5484.90i) q^{52} +(1780.21 + 1293.40i) q^{53} +(753.414 + 2655.87i) q^{55} -4275.17 q^{56} +(7825.07 - 24083.1i) q^{58} +(10833.9 + 33343.2i) q^{59} +(32896.7 - 23900.9i) q^{61} +(-9500.11 - 29238.3i) q^{62} +(-3313.73 - 2407.57i) q^{64} +2479.56 q^{65} +57363.8 q^{67} +(6879.56 + 4998.29i) q^{68} +(567.999 + 1748.12i) q^{70} +(41338.5 - 30034.2i) q^{71} +(15987.1 + 49203.1i) q^{73} +(-2365.80 + 7281.17i) q^{74} +42447.0 q^{76} +(26788.3 + 1011.53i) q^{77} +(-23909.3 - 17371.1i) q^{79} +(-544.194 + 1674.86i) q^{80} +(8680.22 - 6306.55i) q^{82} +(-1245.40 + 904.838i) q^{83} +(1129.79 - 3477.13i) q^{85} +(-52781.0 - 38347.6i) q^{86} +(20194.3 + 15869.9i) q^{88} +49841.6 q^{89} +(7440.43 - 22899.3i) q^{91} +(-23813.1 - 73289.3i) q^{92} +(-45349.8 + 32948.6i) q^{94} +(-5639.50 - 17356.6i) q^{95} +(55324.2 + 40195.4i) q^{97} -49379.3 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{2} - 80 q^{4} - 112 q^{5} - 392 q^{7} - 320 q^{8}+O(q^{10}) $ 20 * q - 20 * q^2 - 80 * q^4 - 112 * q^5 - 392 * q^7 - 320 * q^8	$ 20 q - 20 q^{2} - 80 q^{4} - 112 q^{5} - 392 q^{7} - 320 q^{8} + 552 q^{10} + 60 q^{11} - 420 q^{13} - 1568 q^{14} - 1280 q^{16} + 712 q^{17} - 898 q^{19} - 1792 q^{20} + 2020 q^{22} + 1180 q^{23} - 1079 q^{25} - 2880 q^{26} + 4688 q^{28} + 517 q^{29} - 5551 q^{31} + 20480 q^{32} - 6992 q^{34} + 14325 q^{35} - 7584 q^{37} - 1832 q^{38} + 2752 q^{40} - 16868 q^{41} - 704 q^{43} + 8080 q^{44} - 11400 q^{46} - 38866 q^{47} - 22573 q^{49} - 5416 q^{50} - 11520 q^{52} - 97517 q^{53} + 14404 q^{55} + 12672 q^{56} + 2068 q^{58} - 52682 q^{59} + 73874 q^{61} + 21136 q^{62} - 20480 q^{64} + 236352 q^{65} - 267432 q^{67} + 11392 q^{68} - 67660 q^{70} + 20588 q^{71} + 97257 q^{73} - 30336 q^{74} + 43392 q^{76} + 100582 q^{77} + 37498 q^{79} + 11008 q^{80} - 3672 q^{82} - 140952 q^{83} - 158376 q^{85} - 75136 q^{86} - 63040 q^{88} + 168796 q^{89} + 173196 q^{91} + 36160 q^{92} + 45376 q^{94} - 518002 q^{95} - 225802 q^{97} + 396808 q^{98}+O(q^{100}) $ 20 * q - 20 * q^2 - 80 * q^4 - 112 * q^5 - 392 * q^7 - 320 * q^8 + 552 * q^10 + 60 * q^11 - 420 * q^13 - 1568 * q^14 - 1280 * q^16 + 712 * q^17 - 898 * q^19 - 1792 * q^20 + 2020 * q^22 + 1180 * q^23 - 1079 * q^25 - 2880 * q^26 + 4688 * q^28 + 517 * q^29 - 5551 * q^31 + 20480 * q^32 - 6992 * q^34 + 14325 * q^35 - 7584 * q^37 - 1832 * q^38 + 2752 * q^40 - 16868 * q^41 - 704 * q^43 + 8080 * q^44 - 11400 * q^46 - 38866 * q^47 - 22573 * q^49 - 5416 * q^50 - 11520 * q^52 - 97517 * q^53 + 14404 * q^55 + 12672 * q^56 + 2068 * q^58 - 52682 * q^59 + 73874 * q^61 + 21136 * q^62 - 20480 * q^64 + 236352 * q^65 - 267432 * q^67 + 11392 * q^68 - 67660 * q^70 + 20588 * q^71 + 97257 * q^73 - 30336 * q^74 + 43392 * q^76 + 100582 * q^77 + 37498 * q^79 + 11008 * q^80 - 3672 * q^82 - 140952 * q^83 - 158376 * q^85 - 75136 * q^86 - 63040 * q^88 + 168796 * q^89 + 173196 * q^91 + 36160 * q^92 + 45376 * q^94 - 518002 * q^95 - 225802 * q^97 + 396808 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/198\mathbb{Z}\right)^\times$.

$n$	$145$	$155$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

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 $

$2$	−3.23607	−	2.35114i	−0.572061	−	0.415627i
$2$	−3.23607	−	2.35114i	−0.572061	−	0.415627i
$3$		0			0
$3$		0			0
$4$	4.94427	+	15.2169i	0.154508	+	0.475528i
$5$	5.56531	−	4.04343i	0.0995553	−	0.0723312i	−0.536894	−	0.843650i	$-0.680402\pi$
$5$	5.56531	−	4.04343i	0.0995553	−	0.0723312i	0.636449	+	0.771319i	$0.280402\pi$
$6$		0			0
$7$	−20.6422	−	63.5301i	−0.159225	−	0.490044i	0.839340	−	0.543607i	$-0.182942\pi$
$7$	−20.6422	−	63.5301i	−0.159225	−	0.490044i	−0.998564	+	0.0535638i	$0.982942\pi$
$8$	19.7771	−	60.8676i	0.109254	−	0.336249i
$9$		0			0
$10$	−27.5164			−0.0870145
$11$	−138.325	+	376.719i	−0.344683	+	0.938719i
$11$	−138.325	+	376.719i	−0.344683	+	0.938719i
$12$		0			0
$13$	291.608	+	211.866i	0.478566	+	0.347698i	0.800770	−	0.598972i	$-0.204424\pi$
$13$	291.608	+	211.866i	0.478566	+	0.347698i	−0.322205	+	0.946670i	$0.604424\pi$
$14$	−82.5688	+	254.121i	−0.112589	+	0.346513i
$15$		0			0
$16$	−207.108	+	150.473i	−0.202254	+	0.146946i
$17$	429.972	−	312.393i	0.360843	−	0.262168i	−0.392561	−	0.919726i	$-0.628411\pi$
$17$	429.972	−	312.393i	0.360843	−	0.262168i	0.753404	+	0.657558i	$0.228411\pi$
$18$		0			0
$19$	819.802	−	2523.09i	0.520985	−	1.60343i	−0.251137	−	0.967952i	$-0.580804\pi$
$19$	819.802	−	2523.09i	0.520985	−	1.60343i	0.772122	−	0.635475i	$-0.219196\pi$
$20$	89.0450	+	64.6949i	0.0497776	+	0.0361656i
$21$		0			0
$22$	1333.35	−	893.865i	0.587337	−	0.393745i
$23$	−4816.31			−1.89843			−0.949215	−	0.314629i	$-0.898120\pi$
$23$	−4816.31			−1.89843			−0.949215	+	0.314629i	$0.898120\pi$
$24$		0			0
$25$	−951.055	+	2927.05i	−0.304338	+	0.936655i
$26$	−445.538	−	1371.22i	−0.129256	−	0.397809i
$27$		0			0
$28$	864.672	−	628.221i	0.208428	−	0.151432i
$29$	1956.27	+	6020.77i	0.431950	+	1.32940i	0.896180	+	0.443690i	$0.146331\pi$
$29$	1956.27	+	6020.77i	0.431950	+	1.32940i	−0.464231	+	0.885714i	$0.653669\pi$
$30$		0			0
$31$	6217.90	+	4517.57i	1.16209	+	0.844308i	0.990041	−	0.140781i	$-0.0449612\pi$
$31$	6217.90	+	4517.57i	1.16209	+	0.844308i	0.172049	+	0.985088i	$0.444961\pi$
$32$	1024.00			0.176777
$33$		0			0
$34$	−2125.90			−0.315388
$35$	−371.760	−	270.100i	−0.0512971	−	0.0372695i
$36$		0			0
$37$	−591.449	−	1820.29i	−0.0710253	−	0.218593i	0.909243	−	0.416266i	$-0.136662\pi$
$37$	−591.449	−	1820.29i	−0.0710253	−	0.218593i	−0.980268	+	0.197673i	$0.936662\pi$
$38$	−8585.08	+	6237.42i	−0.964462	+	0.700723i
$39$		0			0
$40$	−136.049	−	418.715i	−0.0134445	−	0.0413779i
$41$	−828.887	+	2551.05i	−0.0770080	+	0.237006i	−0.982149	−	0.188106i	$-0.939765\pi$
$41$	−828.887	+	2551.05i	−0.0770080	+	0.237006i	0.905141	+	0.425112i	$0.139765\pi$
$42$		0			0
$43$	16310.2			1.34521			0.672603	−	0.740004i	$-0.265176\pi$
$43$	16310.2			1.34521			0.672603	+	0.740004i	$0.265176\pi$
$44$	−6416.41	−	242.284i	−0.499644	−	0.0188666i
$45$		0			0
$46$	15585.9	+	11323.8i	1.08602	+	0.789038i
$47$	4330.52	−	13328.0i	0.285954	−	0.880075i	−0.700158	−	0.713988i	$-0.746887\pi$
$47$	4330.52	−	13328.0i	0.285954	−	0.880075i	0.986111	−	0.166086i	$-0.0531131\pi$
$48$		0			0
$49$	9987.17	−	7256.10i	0.594227	−	0.431731i
$50$	9959.58	−	7236.05i	0.563399	−	0.409333i
$51$		0			0
$52$	−1782.15	+	5484.90i	−0.0913979	+	0.281294i
$53$	1780.21	+	1293.40i	0.0870526	+	0.0632474i	0.630460	−	0.776222i	$-0.282866\pi$
$53$	1780.21	+	1293.40i	0.0870526	+	0.0632474i	−0.543408	+	0.839469i	$0.682866\pi$
$54$		0			0
$55$	753.414	+	2655.87i	0.0335836	+	0.118386i
$56$	−4275.17			−0.182173
$57$		0			0
$58$	7825.07	−	24083.1i	0.305434	−	0.940031i
$59$	10833.9	+	33343.2i	0.405185	+	1.24703i	0.920741	+	0.390175i	$0.127585\pi$
$59$	10833.9	+	33343.2i	0.405185	+	1.24703i	−0.515556	+	0.856856i	$0.672415\pi$
$60$		0			0
$61$	32896.7	−	23900.9i	1.13195	−	0.822412i	0.145975	−	0.989288i	$-0.453368\pi$
$61$	32896.7	−	23900.9i	1.13195	−	0.822412i	0.985978	+	0.166877i	$0.0533682\pi$
$62$	−9500.11	−	29238.3i	−0.313870	−	0.965992i
$63$		0			0
$64$	−3313.73	−	2407.57i	−0.101127	−	0.0734732i
$65$	2479.56			0.0727931
$66$		0			0
$67$	57363.8			1.56117			0.780586	−	0.625048i	$-0.214921\pi$
$67$	57363.8			1.56117			0.780586	+	0.625048i	$0.214921\pi$
$68$	6879.56	+	4998.29i	0.180421	+	0.131084i
$69$		0			0
$70$	567.999	+	1748.12i	0.0138549	+	0.0426409i
$71$	41338.5	−	30034.2i	0.973215	−	0.707082i	0.0170329	−	0.999855i	$-0.494578\pi$
$71$	41338.5	−	30034.2i	0.973215	−	0.707082i	0.956182	+	0.292773i	$0.0945780\pi$
$72$		0			0
$73$	15987.1	+	49203.1i	0.351125	+	1.08065i	0.958223	+	0.286024i	$0.0923336\pi$
$73$	15987.1	+	49203.1i	0.351125	+	1.08065i	−0.607098	+	0.794627i	$0.707666\pi$
$74$	−2365.80	+	7281.17i	−0.0502225	+	0.154569i
$75$		0			0
$76$	42447.0			0.842971
$77$	26788.3	+	1011.53i	0.514895	+	0.0194425i
$78$		0			0
$79$	−23909.3	−	17371.1i	−0.431021	−	0.313155i	0.351036	−	0.936362i	$-0.385829\pi$
$79$	−23909.3	−	17371.1i	−0.431021	−	0.313155i	−0.782057	+	0.623207i	$0.785829\pi$
$80$	−544.194	+	1674.86i	−0.00950668	+	0.0292586i
$81$		0			0
$82$	8680.22	−	6306.55i	0.142559	−	0.103575i
$83$	−1245.40	+	904.838i	−0.0198433	+	0.0144170i	−0.597663	−	0.801748i	$-0.703904\pi$
$83$	−1245.40	+	904.838i	−0.0198433	+	0.0144170i	0.577819	+	0.816165i	$0.303904\pi$
$84$		0			0
$85$	1129.79	−	3477.13i	0.0169609	−	0.0522004i
$86$	−52781.0	−	38347.6i	−0.769540	−	0.559104i
$87$		0			0
$88$	20194.3	+	15869.9i	0.277986	+	0.218458i
$89$	49841.6			0.666986			0.333493	−	0.942753i	$-0.391773\pi$
$89$	49841.6			0.666986			0.333493	+	0.942753i	$0.391773\pi$
$90$		0			0
$91$	7440.43	−	22899.3i	0.0941878	−	0.289880i
$92$	−23813.1	−	73289.3i	−0.293323	−	0.902757i
$93$		0			0
$94$	−45349.8	+	32948.6i	−0.529366	+	0.384607i
$95$	−5639.50	−	17356.6i	−0.0641109	−	0.197313i
$96$		0			0
$97$	55324.2	+	40195.4i	0.597016	+	0.433757i	0.844818	−	0.535053i	$-0.179708\pi$
$97$	55324.2	+	40195.4i	0.597016	+	0.433757i	−0.247803	+	0.968811i	$0.579708\pi$
$98$	−49379.3			−0.519373
$99$		0			0
$100$	−49242.8			−0.492428
$101$	114673.	+	83314.8i	1.11856	+	0.812678i	0.983989	−	0.178227i	$-0.0570360\pi$
$101$	114673.	+	83314.8i	1.11856	+	0.812678i	0.134566	+	0.990905i	$0.457036\pi$
$102$		0			0
$103$	−1780.75	−	5480.58i	−0.0165390	−	0.0509019i	0.942446	−	0.334357i	$-0.108519\pi$
$103$	−1780.75	−	5480.58i	−0.0165390	−	0.0509019i	−0.958985	+	0.283455i	$0.908519\pi$
$104$	18662.9	−	13559.4i	0.169198	−	0.122930i
$105$		0			0
$106$	−2719.92	−	8371.05i	−0.0235121	−	0.0723628i
$107$	−44652.5	+	137426.i	−0.377039	+	1.16041i	0.565054	+	0.825054i	$0.308855\pi$
$107$	−44652.5	+	137426.i	−0.377039	+	1.16041i	−0.942093	+	0.335353i	$0.891145\pi$
$108$		0			0
$109$	−18289.8			−0.147449			−0.0737246	−	0.997279i	$-0.523489\pi$
$109$	−18289.8			−0.147449			−0.0737246	+	0.997279i	$0.523489\pi$
$110$	3806.22	−	10365.9i	0.0299925	−	0.0816822i
$111$		0			0
$112$	13834.7	+	10051.5i	0.104214	+	0.0757159i
$113$	3559.68	−	10955.6i	0.0262249	−	0.0807120i	−0.937087	−	0.349095i	$-0.886489\pi$
$113$	3559.68	−	10955.6i	0.0262249	−	0.0807120i	0.963312	+	0.268383i	$0.0864892\pi$
$114$		0			0
$115$	−26804.2	+	19474.4i	−0.188999	+	0.137316i
$116$	−81945.2	+	59536.6i	−0.565429	+	0.410808i
$117$		0			0
$118$	43335.4	−	133373.i	0.286509	−	0.881784i
$119$	−28722.0	−	20867.7i	−0.185929	−	0.135085i
$120$		0			0
$121$	−122783.	−	104220.i	−0.762387	−	0.647122i
$122$	−162650.			−0.989363
$123$		0			0
$124$	−38000.4	+	116953.i	−0.221939	+	0.683059i
$125$	13185.4	+	40580.5i	0.0754776	+	0.232296i
$126$		0			0
$127$	−179158.	+	130166.i	−0.985660	+	0.716124i	−0.958966	−	0.283520i	$-0.908498\pi$
$127$	−179158.	+	130166.i	−0.985660	+	0.716124i	−0.0266934	+	0.999644i	$0.508498\pi$
$128$	5062.93	+	15582.1i	0.0273135	+	0.0840623i
$129$		0			0
$130$	−8024.01	−	5829.79i	−0.0416421	−	0.0302548i
$131$	321828.			1.63850			0.819248	−	0.573439i	$-0.194391\pi$
$131$	321828.			1.63850			0.819248	+	0.573439i	$0.194391\pi$
$132$		0			0
$133$	−177215.			−0.868702
$134$	−185633.	−	134870.i	−0.893087	−	0.648865i
$135$		0			0
$136$	−10511.0	−	32349.6i	−0.0487302	−	0.149976i
$137$	−227194.	+	165066.i	−1.03418	+	0.751376i	−0.969141	−	0.246507i	$-0.920717\pi$
$137$	−227194.	+	165066.i	−1.03418	+	0.751376i	−0.0650388	+	0.997883i	$0.520717\pi$
$138$		0			0
$139$	−46267.7	−	142397.i	−0.203114	−	0.625122i	−0.999786	−	0.0207090i	$-0.993408\pi$
$139$	−46267.7	−	142397.i	−0.203114	−	0.625122i	0.796671	−	0.604413i	$-0.206592\pi$
$140$	2272.00	−	6992.49i	0.00979687	−	0.0301517i
$141$		0			0
$142$	−204389.			−0.850621
$143$	−120151.	+	80547.9i	−0.491345	+	0.329393i
$144$		0			0
$145$	35231.8	+	25597.4i	0.139160	+	0.101106i
$146$	63948.2	−	196812.i	0.248283	−	0.764135i
$147$		0			0
$148$	24774.9	−	18000.1i	0.0929734	−	0.0675491i
$149$	−11232.3	+	8160.72i	−0.0414478	+	0.0301136i	−0.608316	−	0.793695i	$-0.708155\pi$
$149$	−11232.3	+	8160.72i	−0.0414478	+	0.0301136i	0.566868	+	0.823808i	$0.308155\pi$
$150$		0			0
$151$	−79983.7	+	246165.i	−0.285469	+	0.878584i	0.700788	+	0.713369i	$0.252832\pi$
$151$	−79983.7	+	246165.i	−0.285469	+	0.878584i	−0.986258	+	0.165215i	$0.947168\pi$
$152$	−137361.	−	99798.8i	−0.482231	−	0.350361i
$153$		0			0
$154$	−84310.6	−	66256.6i	−0.286471	−	0.225127i
$155$	52871.1			0.176762
$156$		0			0
$157$	−5400.41	+	16620.8i	−0.0174855	+	0.0538148i	−0.959419	−	0.281986i	$-0.909007\pi$
$157$	−5400.41	+	16620.8i	−0.0174855	+	0.0538148i	0.941933	+	0.335801i	$0.109007\pi$
$158$	36530.1	+	112428.i	0.116415	+	0.358288i
$159$		0			0
$160$	5698.88	−	4140.48i	0.0175991	−	0.0127865i
$161$	99419.1	+	305981.i	0.302277	+	0.930313i
$162$		0			0
$163$	−545381.	−	396242.i	−1.60780	−	1.16813i	−0.869917	−	0.493198i	$-0.835828\pi$
$163$	−545381.	−	396242.i	−1.60780	−	1.16813i	−0.737879	−	0.674933i	$-0.764172\pi$
$164$	−42917.3			−0.124601
$165$		0			0
$166$	6157.61			0.0173437
$167$	295648.	+	214801.i	0.820321	+	0.595998i	0.916805	−	0.399336i	$-0.130759\pi$
$167$	295648.	+	214801.i	0.820321	+	0.595998i	−0.0964832	+	0.995335i	$0.530759\pi$
$168$		0			0
$169$	−74587.6	−	229557.i	−0.200886	−	0.618264i
$170$	−11831.3	+	8595.94i	−0.0313986	+	0.0228124i
$171$		0			0
$172$	80642.2	+	248191.i	0.207846	+	0.639683i
$173$	98348.7	−	302686.i	0.249835	−	0.768913i	−0.744968	−	0.667100i	$-0.767535\pi$
$173$	98348.7	−	302686.i	0.249835	−	0.768913i	0.994803	−	0.101814i	$-0.0324646\pi$
$174$		0			0
$175$	205588.			0.507460
$176$	−28037.7	−	98835.9i	−0.0682276	−	0.240510i
$177$		0			0
$178$	−161291.	−	117185.i	−0.381557	−	0.277217i
$179$	133958.	−	412280.i	0.312490	−	0.961746i	−0.664285	−	0.747479i	$-0.731264\pi$
$179$	133958.	−	412280.i	0.312490	−	0.961746i	0.976775	−	0.214266i	$-0.0687360\pi$
$180$		0			0
$181$	−396526.	+	288093.i	−0.899654	+	0.653637i	−0.938377	−	0.345613i	$-0.887671\pi$
$181$	−396526.	+	288093.i	−0.899654	+	0.653637i	0.0387234	+	0.999250i	$0.487671\pi$
$182$	−77917.2	+	56610.2i	−0.174363	+	0.126682i
$183$		0			0
$184$	−95252.5	+	293157.i	−0.207411	+	0.638346i
$185$	−10651.8	−	7739.01i	−0.0228821	−	0.0166248i
$186$		0			0
$187$	58208.3	+	205191.i	0.121725	+	0.429095i
$188$	224222.			0.462683
$189$		0			0
$190$	−22558.0	+	69426.4i	−0.0453332	+	0.139521i
$191$	−57114.1	−	175779.i	−0.113282	−	0.348645i	0.878303	−	0.478104i	$-0.158676\pi$
$191$	−57114.1	−	175779.i	−0.113282	−	0.348645i	−0.991585	+	0.129459i	$0.958676\pi$
$192$		0			0
$193$	−426310.	+	309733.i	−0.823820	+	0.598541i	−0.917804	−	0.397033i	$-0.870040\pi$
$193$	−426310.	+	309733.i	−0.823820	+	0.598541i	0.0939838	+	0.995574i	$0.470040\pi$
$194$	−84527.8	−	260150.i	−0.161248	−	0.496272i
$195$		0			0
$196$	159795.	+	116098.i	0.297113	+	0.215866i
$197$	−337252.			−0.619141			−0.309570	−	0.950877i	$-0.600185\pi$
$197$	−337252.			−0.619141			−0.309570	+	0.950877i	$0.600185\pi$
$198$		0			0
$199$	936713.			1.67677			0.838386	−	0.545078i	$-0.183500\pi$
$199$	936713.			1.67677			0.838386	+	0.545078i	$0.183500\pi$
$200$	159353.	+	115777.i	0.281699	+	0.204667i
$201$		0			0
$202$	−175205.	−	539224.i	−0.302111	−	0.929803i
$203$	342119.	−	248564.i	0.582689	−	0.423348i
$204$		0			0
$205$	5702.00	+	17548.9i	0.00947638	+	0.0291653i
$206$	−7123.00	+	21922.3i	−0.0116949	+	0.0359931i
$207$		0			0
$208$	−92274.6			−0.147885
$209$	837097.	+	657843.i	1.32559	+	1.04173i
$210$		0			0
$211$	−114630.	−	83283.5i	−0.177252	−	0.128781i	0.495622	−	0.868539i	$-0.334940\pi$
$211$	−114630.	−	83283.5i	−0.177252	−	0.128781i	−0.672874	+	0.739757i	$0.734940\pi$
$212$	−10879.7	+	33484.2i	−0.0166256	+	0.0511682i
$213$		0			0
$214$	467607.	−	339736.i	0.697986	−	0.507116i
$215$	90771.4	−	65949.3i	0.133922	−	0.0973003i
$216$		0			0
$217$	158651.	−	488277.i	0.228714	−	0.703910i
$218$	59187.0	+	43001.9i	0.0843500	+	0.0612838i
$219$		0			0
$220$	−36689.0	+	24596.0i	−0.0511068	+	0.0342616i
$221$	191569.			0.263842
$222$		0			0
$223$	−97195.1	+	299136.i	−0.130883	+	0.402815i	−0.994927	−	0.100600i	$-0.967924\pi$
$223$	−97195.1	+	299136.i	−0.130883	+	0.402815i	0.864044	+	0.503416i	$0.167924\pi$
$224$	−21137.6	−	65054.9i	−0.0281472	−	0.0866283i
$225$		0			0
$226$	−37277.4	+	27083.6i	−0.0485484	+	0.0352725i
$227$	−240931.	−	741509.i	−0.310333	−	0.955106i	−0.977633	−	0.210318i	$-0.932550\pi$
$227$	−240931.	−	741509.i	−0.310333	−	0.955106i	0.667300	−	0.744789i	$-0.267450\pi$
$228$		0			0
$229$	692980.	+	503479.i	0.873236	+	0.634443i	0.931453	−	0.363861i	$-0.118542\pi$
$229$	692980.	+	503479.i	0.873236	+	0.634443i	−0.0582172	+	0.998304i	$0.518542\pi$
$230$	132527.			0.165191
$231$		0			0
$232$	405159.			0.494203
$233$	−1.11890e6	−	812925.i	−1.35021	−	0.980982i	−0.999001	−	0.0446827i	$-0.985772\pi$
$233$	−1.11890e6	−	812925.i	−1.35021	−	0.980982i	−0.351204	−	0.936299i	$-0.614228\pi$
$234$		0			0
$235$	−29790.1	−	91684.5i	−0.0351886	−	0.108299i
$236$	−453815.	+	329716.i	−0.530394	+	0.385354i
$237$		0			0
$238$	43883.3	+	135059.i	0.0502177	+	0.154554i
$239$	−293168.	+	902278.i	−0.331987	+	1.02175i	0.636200	+	0.771525i	$0.280505\pi$
$239$	−293168.	+	902278.i	−0.331987	+	1.02175i	−0.968187	+	0.250228i	$0.919495\pi$
$240$		0			0
$241$	1.01093e6			1.12119			0.560595	−	0.828090i	$-0.310572\pi$
$241$	1.01093e6			1.12119			0.560595	+	0.828090i	$0.310572\pi$
$242$	152300.	+	625942.i	0.167171	+	0.687062i
$243$		0			0
$244$	526348.	+	382414.i	0.565976	+	0.411206i
$245$	26242.1	−	80764.9i	0.0279308	−	0.0859622i
$246$		0			0
$247$	773618.	−	562066.i	0.806834	−	0.586199i
$248$	397946.	−	289125.i	0.410861	−	0.298508i
$249$		0			0
$250$	52741.6	−	162322.i	0.0533707	−	0.164258i
$251$	−543273.	−	394711.i	−0.544294	−	0.395453i	0.281383	−	0.959595i	$-0.409207\pi$
$251$	−543273.	−	394711.i	−0.544294	−	0.395453i	−0.825677	+	0.564143i	$0.809207\pi$
$252$		0			0
$253$	666218.	−	1.81439e6i	0.654357	−	1.78209i
$254$	885806.			0.861498
$255$		0			0
$256$	20251.7	−	62328.4i	0.0193136	−	0.0594410i
$257$	741.118	+	2280.93i	0.000699930	+	0.00215416i	0.951406	−	0.307940i	$-0.0996395\pi$
$257$	741.118	+	2280.93i	0.000699930	+	0.00215416i	−0.950706	+	0.310094i	$0.899640\pi$
$258$		0			0
$259$	−103435.	+	75149.7i	−0.0958113	+	0.0696110i
$260$	12259.6	+	37731.2i	0.0112472	+	0.0346152i
$261$		0			0
$262$	−1.04146e6	−	756663.i	−0.937320	−	0.681003i
$263$	−16689.9			−0.0148787			−0.00743935	−	0.999972i	$-0.502368\pi$
$263$	−16689.9			−0.0148787			−0.00743935	+	0.999972i	$0.502368\pi$
$264$		0			0
$265$	15137.2			0.0132413
$266$	573479.	+	416657.i	0.496951	+	0.361056i
$267$		0			0
$268$	283622.	+	872899.i	0.241214	+	0.742382i
$269$	−1.11242e6	+	808222.i	−0.937323	+	0.681005i	−0.947775	−	0.318941i	$-0.896673\pi$
$269$	−1.11242e6	+	808222.i	−0.937323	+	0.681005i	0.0104520	+	0.999945i	$0.496673\pi$
$270$		0			0
$271$	298183.	+	917714.i	0.246638	+	0.759074i	0.995363	+	0.0961927i	$0.0306665\pi$
$271$	298183.	+	917714.i	0.246638	+	0.759074i	−0.748725	+	0.662881i	$0.769334\pi$
$272$	−42044.1	+	129398.i	−0.0344574	+	0.106049i
$273$		0			0
$274$	1.12331e6			0.903906
$275$	−971118.	−	763165.i	−0.774355	−	0.608537i
$276$		0			0
$277$	1.66598e6	+	1.21040e6i	1.30458	+	0.947830i	0.999989	−	0.00465418i	$-0.00148148\pi$
$277$	1.66598e6	+	1.21040e6i	1.30458	+	0.947830i	0.304587	+	0.952484i	$0.401481\pi$
$278$	−185071.	+	569589.i	−0.143624	+	0.442028i
$279$		0			0
$280$	−23792.7	+	17286.4i	−0.0181363	+	0.0131768i
$281$	−1.21031e6	+	879341.i	−0.914388	+	0.664341i	−0.942121	−	0.335274i	$-0.891171\pi$
$281$	−1.21031e6	+	879341.i	−0.914388	+	0.664341i	0.0277332	+	0.999615i	$0.491171\pi$
$282$		0			0
$283$	59275.9	−	182432.i	0.0439959	−	0.135405i	−0.926646	−	0.375936i	$-0.877321\pi$
$283$	59275.9	−	182432.i	0.0439959	−	0.135405i	0.970642	+	0.240530i	$0.0773214\pi$
$284$	661416.	+	480547.i	0.486607	+	0.353541i
$285$		0			0
$286$	578195.	+	21832.7i	0.417984	+	0.0157831i
$287$	179179.			0.128405
$288$		0			0
$289$	−351473.	+	1.08172e6i	−0.247541	+	0.761854i
$290$	−53829.4	−	165670.i	−0.0375859	−	0.115677i
$291$		0			0
$292$	−669674.	+	486547.i	−0.459628	+	0.333939i
$293$	547655.	+	1.68551e6i	0.372682	+	1.14700i	0.945029	+	0.326985i	$0.106033\pi$
$293$	547655.	+	1.68551e6i	0.372682	+	1.14700i	−0.572348	+	0.820011i	$0.693967\pi$
$294$		0			0
$295$	195115.	+	141759.i	0.130537	+	0.0948410i
$296$	−122494.			−0.0812617
$297$		0			0
$298$	55535.4			0.0362267
$299$	−1.40447e6	−	1.02041e6i	−0.908523	−	0.660081i
$300$		0			0
$301$	−336679.	−	1.03619e6i	−0.214190	−	0.659209i
$302$	837601.	−	608552.i	0.528469	−	0.383955i
$303$		0			0
$304$	209869.	+	645911.i	0.130246	+	0.400857i
$305$	86438.9	−	266032.i	0.0532059	−	0.163751i
$306$		0			0
$307$	83226.1			0.0503980			0.0251990	−	0.999682i	$-0.491978\pi$
$307$	83226.1			0.0503980			0.0251990	+	0.999682i	$0.491978\pi$
$308$	117056.	+	412637.i	0.0703103	+	0.247851i
$309$		0			0
$310$	−171094.	−	124307.i	−0.101119	−	0.0734670i
$311$	803450.	−	2.47277e6i	0.471040	−	1.44971i	−0.380184	−	0.924911i	$-0.624139\pi$
$311$	803450.	−	2.47277e6i	0.471040	−	1.44971i	0.851224	−	0.524802i	$-0.175861\pi$
$312$		0			0
$313$	199851.	−	145200.i	0.115304	−	0.0837733i	−0.528639	−	0.848847i	$-0.677297\pi$
$313$	199851.	−	145200.i	0.115304	−	0.0837733i	0.643943	+	0.765074i	$0.277297\pi$
$314$	56553.9	−	41088.8i	0.0323697	−	0.0235179i
$315$		0			0
$316$	146120.	−	449713.i	0.0823177	−	0.253348i
$317$	−245521.	−	178381.i	−0.137227	−	0.0997014i	0.517054	−	0.855953i	$-0.327029\pi$
$317$	−245521.	−	178381.i	−0.137227	−	0.0997014i	−0.654281	+	0.756251i	$0.727029\pi$
$318$		0			0
$319$	−2.53874e6	−	95863.0i	−1.39682	−	0.0527442i
$320$	−28176.8			−0.0153821
$321$		0			0
$322$	397677.	−	1.22392e6i	0.213742	−	0.657831i
$323$	−435704.	−	1.34096e6i	−0.232373	−	0.715170i
$324$		0			0
$325$	−897476.	+	652055.i	−0.471319	+	0.342433i
$326$	833268.	+	2.56453e6i	0.434251	+	1.33649i
$327$		0			0
$328$	138883.	+	100905.i	0.0712797	+	0.0517877i
$329$	−936120.			−0.476806
$330$		0			0
$331$	3.44923e6			1.73042			0.865211	−	0.501409i	$-0.167185\pi$
$331$	3.44923e6			1.73042			0.865211	+	0.501409i	$0.167185\pi$
$332$	−19926.4	−	14477.4i	−0.00992166	−	0.00720851i
$333$		0			0
$334$	−451710.	−	1.39022e6i	−0.221561	−	0.681895i
$335$	319247.	−	231947.i	0.155423	−	0.112921i
$336$		0			0
$337$	421403.	+	1.29694e6i	0.202126	+	0.622081i	0.999819	+	0.0190169i	$0.00605362\pi$
$337$	421403.	+	1.29694e6i	0.202126	+	0.622081i	−0.797693	+	0.603064i	$0.793946\pi$
$338$	−298350.	+	918228.i	−0.142048	+	0.437178i
$339$		0			0
$340$	58497.1			0.0274434
$341$	−2.56195e6	+	1.71751e6i	−1.19312	+	0.799857i
$342$		0			0
$343$	−1.57542e6	−	1.14461e6i	−0.723039	−	0.525318i
$344$	322569.	−	992764.i	0.146969	−	0.452324i
$345$		0			0
$346$	−1.02992e6	+	748282.i	−0.462502	+	0.336028i
$347$	3.14914e6	−	2.28799e6i	1.40400	−	1.02007i	0.409845	−	0.912155i	$-0.365583\pi$
$347$	3.14914e6	−	2.28799e6i	1.40400	−	1.02007i	0.994160	−	0.107914i	$-0.0344171\pi$
$348$		0			0
$349$	19904.2	−	61258.7i	0.00874742	−	0.0269218i	−0.946588	−	0.322447i	$-0.895495\pi$
$349$	19904.2	−	61258.7i	0.00874742	−	0.0269218i	0.955335	+	0.295525i	$0.0954946\pi$
$350$	−665295.	−	483365.i	−0.290298	−	0.210914i
$351$		0			0
$352$	−141645.	+	385760.i	−0.0609320	+	0.165944i
$353$	2.61835e6			1.11838			0.559192	−	0.829038i	$-0.311112\pi$
$353$	2.61835e6			1.11838			0.559192	+	0.829038i	$0.311112\pi$
$354$		0			0
$355$	108620.	−	334299.i	0.0457446	−	0.140788i
$356$	246430.	+	758434.i	0.103055	+	0.317171i
$357$		0			0
$358$	−1.40283e6	+	1.01921e6i	−0.578491	+	0.420298i
$359$	3864.86	+	11894.8i	0.00158270	+	0.00487104i	0.951845	−	0.306580i	$-0.0991849\pi$
$359$	3864.86	+	11894.8i	0.00158270	+	0.00487104i	−0.950262	+	0.311452i	$0.899185\pi$
$360$		0			0
$361$	−3.69071e6	−	2.68146e6i	−1.49053	−	1.08294i
$362$	1.96053e6			0.786326
$363$		0			0
$364$	385244.			0.152399
$365$	287922.	+	209188.i	0.113121	+	0.0821872i
$366$		0			0
$367$	−715352.	−	2.20163e6i	−0.277239	−	0.853254i	−0.988618	−	0.150446i	$-0.951929\pi$
$367$	−715352.	−	2.20163e6i	−0.277239	−	0.853254i	0.711379	−	0.702809i	$-0.248071\pi$
$368$	997497.	−	724724.i	0.383965	−	0.278967i
$369$		0			0
$370$	16274.6	+	50087.9i	0.00618023	+	0.0190208i
$371$	45422.4	−	139796.i	0.0171331	−	0.0527301i
$372$		0			0
$373$	−255527.			−0.0950965			−0.0475483	−	0.998869i	$-0.515141\pi$
$373$	−255527.			−0.0950965			−0.0475483	+	0.998869i	$0.515141\pi$
$374$	294066.	−	800867.i	0.108709	−	0.296061i
$375$		0			0
$376$	−725597.	−	527177.i	−0.264683	−	0.192303i
$377$	−705132.	+	2.17017e6i	−0.255515	+	0.786395i
$378$		0			0
$379$	−2.37157e6	+	1.72305e6i	−0.848084	+	0.616169i	−0.924617	−	0.380898i	$-0.875615\pi$
$379$	−2.37157e6	+	1.72305e6i	−0.848084	+	0.616169i	0.0765332	+	0.997067i	$0.475615\pi$
$380$	236230.	−	171632.i	0.0839222	−	0.0609731i
$381$		0			0
$382$	−228456.	+	703117.i	−0.0801023	+	0.246530i
$383$	−3.00555e6	−	2.18366e6i	−1.04695	−	0.760656i	−0.0753226	−	0.997159i	$-0.523999\pi$
$383$	−3.00555e6	−	2.18366e6i	−1.04695	−	0.760656i	−0.971631	+	0.236503i	$0.923999\pi$
$384$		0			0
$385$	153175.	−	102687.i	0.0526669	−	0.0353074i
$386$	2.10779e6			0.720045
$387$		0			0
$388$	−338111.	+	1.04060e6i	−0.114020	+	0.350917i
$389$	−511898.	−	1.57546e6i	−0.171518	−	0.527877i	0.827940	−	0.560817i	$-0.189513\pi$
$389$	−511898.	−	1.57546e6i	−0.171518	−	0.527877i	−0.999457	+	0.0329399i	$0.989513\pi$
$390$		0			0
$391$	−2.07088e6	+	1.50458e6i	−0.685035	+	0.497707i
$392$	−244145.	−	751400.i	−0.0802476	−	0.246977i
$393$		0			0
$394$	1.09137e6	+	792928.i	0.354187	+	0.257332i
$395$	−203301.			−0.0655613
$396$		0			0
$397$	−3.43596e6			−1.09414			−0.547069	−	0.837087i	$-0.684257\pi$
$397$	−3.43596e6			−1.09414			−0.547069	+	0.837087i	$0.684257\pi$
$398$	−3.03127e6	−	2.20234e6i	−0.959216	−	0.696911i
$399$		0			0
$400$	−243470.	−	749324.i	−0.0760844	−	0.234164i
$401$	1.05355e6	−	765446.i	0.327184	−	0.237713i	−0.412051	−	0.911161i	$-0.635187\pi$
$401$	1.05355e6	−	765446.i	0.327184	−	0.237713i	0.739235	+	0.673448i	$0.235187\pi$
$402$		0			0
$403$	856073.	+	2.63472e6i	0.262572	+	0.808113i
$404$	−700819.	+	2.15690e6i	−0.213625	+	0.657470i
$405$		0			0
$406$	−1.69153e6			−0.509289
$407$	767551.	+	28982.8i	0.229679	+	0.00867271i
$408$		0			0
$409$	255153.	+	185380.i	0.0754210	+	0.0547966i	0.624857	−	0.780739i	$-0.285157\pi$
$409$	255153.	+	185380.i	0.0754210	+	0.0547966i	−0.549436	+	0.835536i	$0.685157\pi$
$410$	22808.0	−	70195.8i	0.00670081	−	0.0206230i
$411$		0			0
$412$	74593.0	−	54195.0i	0.0216499	−	0.0157295i
$413$	1.89466e6	−	1.37655e6i	0.546584	−	0.397117i
$414$		0			0
$415$	−3272.40	+	10071.4i	−0.000932709	+	0.00287058i
$416$	298607.	+	216951.i	0.0845992	+	0.0614649i
$417$		0			0
$418$	−1.16222e6	−	4.09696e6i	−0.325348	−	1.14689i
$419$	6.31123e6			1.75622			0.878110	−	0.478459i	$-0.158805\pi$
$419$	6.31123e6			1.75622			0.878110	+	0.478459i	$0.158805\pi$
$420$		0			0
$421$	−1.34617e6	+	4.14308e6i	−0.370164	+	1.13925i	0.576519	+	0.817083i	$0.304410\pi$
$421$	−1.34617e6	+	4.14308e6i	−0.370164	+	1.13925i	−0.946684	+	0.322165i	$0.895590\pi$
$422$	175139.	+	539022.i	0.0478742	+	0.147342i
$423$		0			0
$424$	113933.	−	82777.5i	0.0307777	−	0.0223613i
$425$	505462.	+	1.55565e6i	0.135743	+	0.417773i
$426$		0			0
$427$	−2.19749e6	−	1.59657e6i	−0.583253	−	0.423758i
$428$	−2.31198e6			−0.610062
$429$		0			0
$430$	−448799.			−0.117052
$431$	−3.31957e6	−	2.41181e6i	−0.860772	−	0.625387i	0.0673231	−	0.997731i	$-0.478554\pi$
$431$	−3.31957e6	−	2.41181e6i	−0.860772	−	0.625387i	−0.928095	+	0.372344i	$0.878554\pi$
$432$		0			0
$433$	−850975.	−	2.61903e6i	−0.218121	−	0.671307i	−0.998917	−	0.0465214i	$-0.985186\pi$
$433$	−850975.	−	2.61903e6i	−0.218121	−	0.671307i	0.780796	−	0.624785i	$-0.214814\pi$
$434$	−1.66141e6	+	1.20709e6i	−0.423402	+	0.307620i
$435$		0			0
$436$	−90429.7	−	278314.i	−0.0227821	−	0.0701162i
$437$	−3.94842e6	+	1.21520e7i	−0.989053	+	3.04399i
$438$		0			0
$439$	1.92421e6			0.476531			0.238266	−	0.971200i	$-0.423421\pi$
$439$	1.92421e6			0.476531			0.238266	+	0.971200i	$0.423421\pi$
$440$	176557.	+	6666.80i	0.0434763	+	0.00164167i
$441$		0			0
$442$	−619930.	−	450406.i	−0.150934	−	0.109660i
$443$	197332.	−	607324.i	0.0477735	−	0.147032i	−0.924324	−	0.381608i	$-0.875370\pi$
$443$	197332.	−	607324.i	0.0477735	−	0.147032i	0.972098	+	0.234576i	$0.0753703\pi$
$444$		0			0
$445$	277384.	−	201531.i	0.0664020	−	0.0482438i
$446$	1.01784e6	−	739504.i	0.242294	−	0.176037i
$447$		0			0
$448$	−84550.4	+	260219.i	−0.0199031	+	0.0612555i
$449$	288504.	+	209610.i	0.0675360	+	0.0490678i	0.621041	−	0.783778i	$-0.286710\pi$
$449$	288504.	+	209610.i	0.0675360	+	0.0490678i	−0.553505	+	0.832846i	$0.686710\pi$
$450$		0			0
$451$	−846373.	−	665133.i	−0.195939	−	0.153981i
$452$	184310.			0.0424328
$453$		0			0
$454$	−963723.	+	2.96604e6i	−0.219438	+	0.675362i
$455$	−51183.5	−	157527.i	−0.0115905	−	0.0356718i
$456$		0			0
$457$	−2.59738e6	+	1.88711e6i	−0.581761	+	0.422674i	−0.839359	−	0.543578i	$-0.817069\pi$
$457$	−2.59738e6	+	1.88711e6i	−0.581761	+	0.422674i	0.257597	+	0.966252i	$0.417069\pi$
$458$	−1.05878e6	−	3.25859e6i	−0.235853	−	0.725881i
$459$		0			0
$460$	−428868.	−	311591.i	−0.0944993	−	0.0686578i
$461$	−2.82005e6			−0.618023			−0.309012	−	0.951058i	$-0.599998\pi$
$461$	−2.82005e6			−0.618023			−0.309012	+	0.951058i	$0.599998\pi$
$462$		0			0
$463$	−1.92460e6			−0.417243			−0.208621	−	0.977996i	$-0.566898\pi$
$463$	−1.92460e6			−0.417243			−0.208621	+	0.977996i	$0.566898\pi$
$464$	−1.31112e6	−	952586.i	−0.282715	−	0.205404i
$465$		0			0
$466$	1.70952e6	+	5.26136e6i	0.364678	+	1.12236i
$467$	2.25307e6	−	1.63695e6i	0.478059	−	0.347330i	−0.322515	−	0.946564i	$-0.604528\pi$
$467$	2.25307e6	−	1.63695e6i	0.478059	−	0.347330i	0.800574	+	0.599234i	$0.204528\pi$
$468$		0			0
$469$	−1.18411e6	−	3.64433e6i	−0.248577	−	0.765043i
$470$	−119160.	+	366738.i	−0.0248821	+	0.0765793i
$471$		0			0
$472$	2.24378e6			0.463581
$473$	−2.25612e6	+	6.14437e6i	−0.463670	+	1.26277i
$474$		0			0
$475$	6.60553e6	+	4.79920e6i	1.34330	+	0.975965i
$476$	175533.	−	540235.i	0.0355092	−	0.109286i
$477$		0			0
$478$	3.07009e6	−	2.23055e6i	0.614585	−	0.446522i
$479$	3.03483e6	−	2.20493e6i	0.604360	−	0.439093i	−0.243064	−	0.970010i	$-0.578152\pi$
$479$	3.03483e6	−	2.20493e6i	0.604360	−	0.439093i	0.847424	+	0.530917i	$0.178152\pi$
$480$		0			0
$481$	213186.	−	656121.i	0.0420143	−	0.129307i
$482$	−3.27145e6	−	2.37684e6i	−0.641390	−	0.465997i
$483$		0			0
$484$	978826.	−	2.38367e6i	0.189929	−	0.462522i
$485$	470424.			0.0908102
$486$		0			0
$487$	2.23095e6	−	6.86614e6i	0.426252	−	1.31187i	−0.475538	−	0.879695i	$-0.657747\pi$
$487$	2.23095e6	−	6.86614e6i	0.426252	−	1.31187i	0.901790	−	0.432174i	$-0.142253\pi$
$488$	−804188.	−	2.47504e6i	−0.152865	−	0.470470i
$489$		0			0
$490$	−274811.	+	199662.i	−0.0517064	+	0.0375669i
$491$	1.88264e6	+	5.79418e6i	0.352423	+	1.08465i	0.957489	+	0.288471i	$0.0931469\pi$
$491$	1.88264e6	+	5.79418e6i	0.352423	+	1.08465i	−0.605065	+	0.796176i	$0.706853\pi$
$492$		0			0
$493$	2.72199e6	+	1.97764e6i	0.504393	+	0.366463i
$494$	−3.82498e6			−0.705199
$495$		0			0
$496$	−1.96755e6			−0.359106
$497$	−2.76139e6	−	2.00627e6i	−0.501461	−	0.364333i
$498$		0			0
$499$	−863939.	−	2.65893e6i	−0.155322	−	0.478031i	0.842872	−	0.538114i	$-0.180863\pi$
$499$	−863939.	−	2.65893e6i	−0.155322	−	0.478031i	−0.998193	+	0.0600839i	$0.980863\pi$
$500$	−552317.	+	401282.i	−0.0988015	+	0.0717835i
$501$		0			0
$502$	830047.	+	2.55462e6i	0.147009	+	0.452447i
$503$	1.28734e6	−	3.96203e6i	0.226868	−	0.698229i	−0.771228	−	0.636559i	$-0.780357\pi$
$503$	1.28734e6	−	3.96203e6i	0.226868	−	0.698229i	0.998097	−	0.0616704i	$-0.0196428\pi$
$504$		0			0
$505$	975068.			0.170140
$506$	−6.42182e6	+	4.30513e6i	−1.11502	+	0.747498i
$507$		0			0
$508$	−2.86653e6	−	2.08265e6i	−0.492830	−	0.358062i
$509$	1.86855e6	−	5.75081e6i	0.319677	−	0.983864i	−0.654110	−	0.756400i	$-0.726957\pi$
$509$	1.86855e6	−	5.75081e6i	0.319677	−	0.983864i	0.973786	−	0.227464i	$-0.0730434\pi$
$510$		0			0
$511$	2.79587e6	−	2.03132e6i	0.473658	−	0.344133i
$512$	−212079.	+	154084.i	−0.0357538	+	0.0259767i
$513$		0			0
$514$	2964.47	−	9123.70i	0.000494925	−	0.00152322i
$515$	−32070.8	−	23300.8i	−0.00532834	−	0.00387126i
$516$		0			0
$517$	4.42188e6	+	3.47499e6i	0.727579	+	0.571777i
$518$	511409.			0.0837422
$519$		0			0
$520$	49038.4	−	150925.i	0.00795294	−	0.0244766i
$521$	2.26420e6	+	6.96848e6i	0.365443	+	1.12472i	0.949703	+	0.313152i	$0.101385\pi$
$521$	2.26420e6	+	6.96848e6i	0.365443	+	1.12472i	−0.584260	+	0.811567i	$0.698615\pi$
$522$		0			0
$523$	−2.15505e6	+	1.56573e6i	−0.344511	+	0.250302i	−0.746563	−	0.665315i	$-0.768297\pi$
$523$	−2.15505e6	+	1.56573e6i	−0.344511	+	0.250302i	0.402052	+	0.915617i	$0.368297\pi$
$524$	1.59120e6	+	4.89722e6i	0.253162	+	0.779151i
$525$		0			0
$526$	54009.7	+	39240.4i	0.00851153	+	0.00618399i
$527$	4.08479e6			0.640682
$528$		0			0
$529$	1.67605e7			2.60403
$530$	−48985.0	−	35589.7i	−0.00757484	−	0.00550344i
$531$		0			0
$532$	−876199.	−	2.69666e6i	−0.134222	−	0.413093i
$533$	−782191.	+	568295.i	−0.119260	+	0.0866474i
$534$		0			0
$535$	307169.	+	945369.i	0.0463973	+	0.142796i
$536$	1.13449e6	−	3.49160e6i	0.170564	−	0.524943i
$537$		0			0
$538$	5.50012e6			0.819250
$539$	1.35203e6	+	4.76606e6i	0.200454	+	0.706622i
$540$		0			0
$541$	−2.98777e6	−	2.17075e6i	−0.438889	−	0.318872i	0.346304	−	0.938122i	$-0.387436\pi$
$541$	−2.98777e6	−	2.17075e6i	−0.438889	−	0.318872i	−0.785193	+	0.619251i	$0.787436\pi$
$542$	1.19273e6	−	3.67085e6i	0.174399	−	0.536746i
$543$		0			0
$544$	440292.	−	319891.i	0.0637886	−	0.0463452i
$545$	−101788.	+	73953.5i	−0.0146793	+	0.0106652i
$546$		0			0
$547$	229301.	−	705715.i	0.0327670	−	0.100846i	−0.933335	−	0.359006i	$-0.883116\pi$
$547$	229301.	−	705715.i	0.0327670	−	0.100846i	0.966102	+	0.258159i	$0.0831159\pi$
$548$	−3.63511e6	−	2.64106e6i	−0.517090	−	0.375688i
$549$		0			0
$550$	1.34830e6	+	4.75289e6i	0.190055	+	0.669963i
$551$	1.67947e7			2.35664
$552$		0			0
$553$	−610049.	+	1.87754e6i	−0.0848304	+	0.261081i
$554$	−2.54539e6	−	7.83389e6i	−0.352354	−	1.08443i
$555$		0			0
$556$	1.93809e6	−	1.40810e6i	0.265880	−	0.193173i
$557$	3.87833e6	+	1.19363e7i	0.529672	+	1.63016i	0.754888	+	0.655854i	$0.227691\pi$
$557$	3.87833e6	+	1.19363e7i	0.529672	+	1.63016i	−0.225216	+	0.974309i	$0.572309\pi$
$558$		0			0
$559$	4.75619e6	+	3.45558e6i	0.643769	+	0.467726i
$560$	117637.			0.0158517
$561$		0			0
$562$	5.98409e6			0.799204
$563$	−1.01301e7	−	7.35994e6i	−1.34692	−	0.978595i	−0.999159	−	0.0410123i	$-0.986942\pi$
$563$	−1.01301e7	−	7.35994e6i	−1.34692	−	0.978595i	−0.347762	−	0.937583i	$-0.613058\pi$
$564$		0			0
$565$	−24487.4	−	75364.4i	−0.00322716	−	0.00993219i
$566$	−620745.	+	450998.i	−0.0814464	+	0.0591743i
$567$		0			0
$568$	−1.01055e6	−	3.11016e6i	−0.131428	−	0.404494i
$569$	−4.13450e6	+	1.27247e7i	−0.535355	+	1.64765i	0.207524	+	0.978230i	$0.433459\pi$
$569$	−4.13450e6	+	1.27247e7i	−0.535355	+	1.64765i	−0.742880	+	0.669425i	$0.766541\pi$
$570$		0			0
$571$	−5.41642e6			−0.695220			−0.347610	−	0.937639i	$-0.613007\pi$
$571$	−5.41642e6			−0.695220			−0.347610	+	0.937639i	$0.613007\pi$
$572$	−1.81975e6	−	1.43007e6i	−0.232552	−	0.182754i
$573$		0			0
$574$	−579834.	−	421274.i	−0.0734555	−	0.0533685i
$575$	4.58057e6	−	1.40975e7i	0.577763	−	1.77817i
$576$		0			0
$577$	−1.43257e6	+	1.04083e6i	−0.179134	+	0.130148i	−0.673739	−	0.738970i	$-0.735313\pi$
$577$	−1.43257e6	+	1.04083e6i	−0.179134	+	0.130148i	0.494605	+	0.869118i	$0.335313\pi$
$578$	3.68068e6	−	2.67417e6i	0.458256	−	0.332942i
$579$		0			0
$580$	−215318.	+	662680.i	−0.0265772	+	0.0817963i
$581$	83192.3	+	60442.8i	0.0102245	+	0.00742855i
$582$		0			0
$583$	−733496.	+	491729.i	−0.0893771	+	0.0599176i
$584$	3.31105e6			0.401730
$585$		0			0
$586$	2.19062e6	−	6.74204e6i	0.263526	−	0.811049i
$587$	−4.21096e6	−	1.29600e7i	−0.504412	−	1.55242i	−0.801757	−	0.597651i	$-0.796101\pi$
$587$	−4.21096e6	−	1.29600e7i	−0.504412	−	1.55242i	0.297345	−	0.954770i	$-0.403899\pi$
$588$		0			0
$589$	1.64957e7	−	1.19848e7i	1.95922	−	1.42345i
$590$	−298109.	−	917485.i	−0.0352570	−	0.108510i
$591$		0			0
$592$	396399.	+	288001.i	0.0464867	+	0.0337745i
$593$	8.94020e6			1.04402			0.522012	−	0.852938i	$-0.325182\pi$
$593$	8.94020e6			1.04402			0.522012	+	0.852938i	$0.325182\pi$
$594$		0			0
$595$	−244224.			−0.0282811
$596$	−179716.	−	130572.i	−0.0207239	−	0.0150568i
$597$		0			0
$598$	2.14585e6	+	6.60424e6i	0.245384	+	0.755213i
$599$	−7.61260e6	+	5.53088e6i	−0.866894	+	0.629835i	−0.929752	−	0.368187i	$-0.879979\pi$
$599$	−7.61260e6	+	5.53088e6i	−0.866894	+	0.629835i	0.0628579	+	0.998022i	$0.479979\pi$
$600$		0			0
$601$	2.40849e6	+	7.41256e6i	0.271993	+	0.837109i	0.989999	+	0.141072i	$0.0450550\pi$
$601$	2.40849e6	+	7.41256e6i	0.271993	+	0.837109i	−0.718006	+	0.696037i	$0.754945\pi$
$602$	−1.34671e6	+	4.14476e6i	−0.151455	+	0.466131i
$603$		0			0
$604$	−4.14132e6			−0.461899
$605$	−1.10473e6	−	83548.7i	−0.122707	−	0.00928007i
$606$		0			0
$607$	8.49231e6	+	6.17002e6i	0.935522	+	0.679697i	0.947339	−	0.320234i	$-0.103761\pi$
$607$	8.49231e6	+	6.17002e6i	0.935522	+	0.679697i	−0.0118164	+	0.999930i	$0.503761\pi$
$608$	839477.	−	2.58365e6i	0.0920980	−	0.283448i
$609$		0			0
$610$	−905200.	+	657666.i	−0.0984963	+	0.0715617i
$611$	4.08656e6	−	2.96906e6i	0.442848	−	0.321748i
$612$		0			0
$613$	63184.4	−	194462.i	0.00679139	−	0.0209017i	−0.947603	−	0.319449i	$-0.896502\pi$
$613$	63184.4	−	194462.i	0.00679139	−	0.0209017i	0.954395	+	0.298547i	$0.0965021\pi$
$614$	−269325.	−	195676.i	−0.0288308	−	0.0209468i
$615$		0			0
$616$	591365.	−	1.61054e6i	0.0627919	−	0.171009i
$617$	1.53007e7			1.61808			0.809038	−	0.587757i	$-0.199989\pi$
$617$	1.53007e7			1.61808			0.809038	+	0.587757i	$0.199989\pi$
$618$		0			0
$619$	−3.54313e6	+	1.09046e7i	−0.371672	+	1.14389i	0.574024	+	0.818838i	$0.305382\pi$
$619$	−3.54313e6	+	1.09046e7i	−0.371672	+	1.14389i	−0.945696	+	0.325051i	$0.894618\pi$
$620$	261409.	+	804534.i	0.0273112	+	0.0840553i
$621$		0			0
$622$	−8.41384e6	+	6.11301e6i	−0.872004	+	0.633548i
$623$	−1.02884e6	−	3.16644e6i	−0.106201	−	0.326852i
$624$		0			0
$625$	−7.54345e6	−	5.48064e6i	−0.772450	−	0.561217i
$626$	−988116.			−0.100779
$627$		0			0
$628$	−279618.			−0.0282921
$629$	−822954.	−	597911.i	−0.0829371	−	0.0602574i
$630$		0			0
$631$	1.05674e6	+	3.25230e6i	0.105656	+	0.325175i	0.989884	−	0.141880i	$-0.0453148\pi$
$631$	1.05674e6	+	3.25230e6i	0.105656	+	0.325175i	−0.884228	+	0.467055i	$0.845315\pi$
$632$	−1.53019e6	+	1.11175e6i	−0.152389	+	0.110717i
$633$		0			0
$634$	375122.	+	1.15451e6i	0.0370638	+	0.114071i
$635$	−470753.	+	1.44883e6i	−0.0463296	+	0.142588i
$636$		0			0
$637$	4.44966e6			0.434489
$638$	7.99014e6	+	6.27915e6i	0.777146	+	0.610730i
$639$		0			0
$640$	91182.0	+	66247.6i	0.00879953	+	0.00639323i
$641$	−982394.	+	3.02350e6i	−0.0944367	+	0.290646i	−0.987106	−	0.160065i	$-0.948830\pi$
$641$	−982394.	+	3.02350e6i	−0.0944367	+	0.290646i	0.892670	+	0.450711i	$0.148830\pi$
$642$		0			0
$643$	5.10791e6	−	3.71111e6i	0.487209	−	0.353978i	−0.316901	−	0.948459i	$-0.602642\pi$
$643$	5.10791e6	−	3.71111e6i	0.487209	−	0.353978i	0.804110	+	0.594480i	$0.202642\pi$
$644$	−4.16452e6	+	3.02570e6i	−0.395686	+	0.287483i
$645$		0			0
$646$	−1.74282e6	+	5.36384e6i	−0.164313	+	0.505702i
$647$	−8.78380e6	−	6.38180e6i	−0.824939	−	0.599353i	0.0931840	−	0.995649i	$-0.470296\pi$
$647$	−8.78380e6	−	6.38180e6i	−0.824939	−	0.599353i	−0.918123	+	0.396296i	$0.870296\pi$
$648$		0			0
$649$	−1.40596e7	−	530892.i	−1.31027	−	0.0494760i
$650$	4.43737e6			0.411948
$651$		0			0
$652$	3.33307e6	−	1.02581e7i	0.307062	−	0.945038i
$653$	−206829.	−	636554.i	−0.0189814	−	0.0584188i	0.941117	−	0.338081i	$-0.109778\pi$
$653$	−206829.	−	636554.i	−0.0189814	−	0.0584188i	−0.960099	+	0.279662i	$0.909778\pi$
$654$		0			0
$655$	1.79107e6	−	1.30129e6i	0.163121	−	0.118514i
$656$	−212195.	−	653069.i	−0.0192520	−	0.0592515i
$657$		0			0
$658$	3.02935e6	+	2.20095e6i	0.272762	+	0.198173i
$659$	−1.07470e7			−0.963996			−0.481998	−	0.876172i	$-0.660089\pi$
$659$	−1.07470e7			−0.963996			−0.481998	+	0.876172i	$0.660089\pi$
$660$		0			0
$661$	−1.85537e7			−1.65169			−0.825843	−	0.563901i	$-0.809300\pi$
$661$	−1.85537e7			−1.65169			−0.825843	+	0.563901i	$0.809300\pi$
$662$	−1.11619e7	−	8.10962e6i	−0.989907	−	0.719210i
$663$		0			0
$664$	30444.9	+	93699.8i	0.00267975	+	0.00824742i
$665$	−986256.	+	716557.i	−0.0864839	+	0.0628343i
$666$		0			0
$667$	−9.42198e6	−	2.89979e7i	−0.820026	−	2.52378i
$668$	−1.80684e6	+	5.56088e6i	−0.156667	+	0.482173i
$669$		0			0
$670$	−1.57845e6			−0.135845
$671$	4.45346e6	+	1.56989e7i	0.381848	+	1.34606i
$672$		0			0
$673$	804725.	+	584667.i	0.0684873	+	0.0497589i	0.621502	−	0.783412i	$-0.286523\pi$
$673$	804725.	+	584667.i	0.0684873	+	0.0497589i	−0.553015	+	0.833171i	$0.686523\pi$
$674$	1.68561e6	−	5.18778e6i	0.142925	−	0.439878i
$675$		0			0
$676$	3.12437e6	−	2.26998e6i	0.262963	−	0.191054i
$677$	−1.99525e6	+	1.44963e6i	−0.167311	+	0.121559i	−0.668290	−	0.743901i	$-0.732973\pi$
$677$	−1.99525e6	+	1.44963e6i	−0.167311	+	0.121559i	0.500979	+	0.865460i	$0.332973\pi$
$678$		0			0
$679$	1.41161e6	−	4.34447e6i	0.117500	−	0.361629i
$680$	−189301.	−	137535.i	−0.0156993	−	0.0114062i
$681$		0			0
$682$	1.23287e7	+	465534.i	1.01498	+	0.0383258i
$683$	1.38596e7			1.13684			0.568418	−	0.822740i	$-0.307556\pi$
$683$	1.38596e7			1.13684			0.568418	+	0.822740i	$0.307556\pi$
$684$		0			0
$685$	−596972.	+	1.83729e6i	−0.0486102	+	0.149607i
$686$	2.40703e6	+	7.40808e6i	0.195286	+	0.601029i
$687$		0			0
$688$	−3.37798e6	+	2.45425e6i	−0.272074	+	0.197673i
$689$	245097.	+	754331.i	0.0196694	+	0.0605361i
$690$		0			0
$691$	1.54074e7	+	1.11941e7i	1.22754	+	0.891858i	0.996703	−	0.0811355i	$-0.0258547\pi$
$691$	1.54074e7	+	1.11941e7i	1.22754	+	0.891858i	0.230834	+	0.972993i	$0.425855\pi$
$692$	5.09221e6			0.404242
$693$		0			0
$694$	−1.55702e7			−1.22715
$695$	−833268.	−	605405.i	−0.0654369	−	0.0475427i
$696$		0			0
$697$	440533.	+	1.35582e6i	0.0343476	+	0.105711i
$698$	−208439.	+	151440.i	−0.0161935	+	0.0117653i
$699$		0			0
$700$	1.01648e6	+	3.12841e6i	0.0784068	+	0.241311i
$701$	−4.41686e6	+	1.35937e7i	−0.339484	+	1.04482i	0.624987	+	0.780635i	$0.285104\pi$
$701$	−4.41686e6	+	1.35937e7i	−0.339484	+	1.04482i	−0.964471	+	0.264188i	$0.914896\pi$
$702$		0			0
$703$	−5.07764e6			−0.387502
$704$	1.36535e6	−	915318.i	0.103827	−	0.0696050i
$705$		0			0
$706$	−8.47315e6	−	6.15611e6i	−0.639784	−	0.464830i
$707$	2.92590e6	−	9.00499e6i	0.220146	−	0.677539i
$708$		0			0
$709$	−1.39194e7	+	1.01130e7i	−1.03993	+	0.755553i	−0.970272	−	0.242018i	$-0.922191\pi$
$709$	−1.39194e7	+	1.01130e7i	−1.03993	+	0.755553i	−0.0696578	+	0.997571i	$0.522191\pi$
$710$	−1.13749e6	+	826432.i	−0.0846838	+	0.0615264i
$711$		0			0
$712$	985721.	−	3.03374e6i	0.0728709	−	0.224273i
$713$	−2.99473e7	−	2.17580e7i	−2.20615	−	1.60286i
$714$		0			0
$715$	−342986.	+	934095.i	−0.0250906	+	0.0683323i
$716$	6.93596e6			0.505620
$717$		0			0
$718$	15459.4	−	47579.3i	0.00111914	−	0.00344434i
$719$	−4.48948e6	−	1.38172e7i	−0.323872	−	0.996776i	−0.971947	−	0.235199i	$-0.924426\pi$
$719$	−4.48948e6	−	1.38172e7i	−0.323872	−	0.996776i	0.648075	−	0.761576i	$-0.275574\pi$
$720$		0			0
$721$	−311424.	+	226263.i	−0.0223107	+	0.0162097i
$722$	5.63890e6	+	1.73547e7i	0.402579	+	1.23901i
$723$		0			0
$724$	−6.34442e6	−	4.60949e6i	−0.449827	−	0.326818i
$725$	−1.94836e7			−1.37665
$726$		0			0
$727$	−2.08172e7			−1.46078			−0.730392	−	0.683028i	$-0.760663\pi$
$727$	−2.08172e7			−1.46078			−0.730392	+	0.683028i	$0.760663\pi$
$728$	−1.24668e6	−	905763.i	−0.0871816	−	0.0633411i
$729$		0			0
$730$	−439906.	−	1.35389e6i	−0.0305529	−	0.0940323i
$731$	7.01294e6	−	5.09520e6i	0.485408	−	0.352670i
$732$		0			0
$733$	373128.	+	1.14837e6i	0.0256506	+	0.0789446i	0.963062	−	0.269278i	$-0.0867852\pi$
$733$	373128.	+	1.14837e6i	0.0256506	+	0.0789446i	−0.937412	+	0.348223i	$0.886785\pi$
$734$	−2.86141e6	+	8.80651e6i	−0.196038	+	0.603342i
$735$		0			0
$736$	−4.93190e6			−0.335598
$737$	−7.93487e6	+	2.16100e7i	−0.538110	+	1.46550i
$738$		0			0
$739$	−1.10354e7	−	8.01767e6i	−0.743320	−	0.540054i	0.150429	−	0.988621i	$-0.451934\pi$
$739$	−1.10354e7	−	8.01767e6i	−0.743320	−	0.540054i	−0.893749	+	0.448567i	$0.851934\pi$
$740$	65098.2	−	200352.i	0.00437009	−	0.0134497i
$741$		0			0
$742$	−475669.	+	345594.i	−0.0317172	+	0.0230439i
$743$	−6.51870e6	+	4.73611e6i	−0.433201	+	0.314739i	−0.782927	−	0.622113i	$-0.786274\pi$
$743$	−6.51870e6	+	4.73611e6i	−0.433201	+	0.314739i	0.349727	+	0.936852i	$0.386274\pi$
$744$		0			0
$745$	−29513.7	+	90833.9i	−0.00194820	+	0.00599594i
$746$	826903.	+	600780.i	0.0544011	+	0.0395247i
$747$		0			0
$748$	−2.83457e6	+	1.90027e6i	−0.185239	+	0.124183i
$749$	9.65244e6			0.628684
$750$		0			0
$751$	−2.94882e6	+	9.07552e6i	−0.190787	+	0.587181i	−1.00000		0.000334069i	$-0.999894\pi$
$751$	−2.94882e6	+	9.07552e6i	−0.190787	+	0.587181i	0.809213	+	0.587515i	$0.199894\pi$
$752$	1.10861e6	+	3.41196e6i	0.0714884	+	0.220019i
$753$		0			0
$754$	7.38423e6	−	5.36496e6i	0.473017	−	0.343667i
$755$	550216.	+	1.69339e6i	0.0351290	+	0.108116i
$756$		0			0
$757$	−7.89285e6	−	5.73449e6i	−0.500604	−	0.363710i	0.308644	−	0.951178i	$-0.400125\pi$
$757$	−7.89285e6	−	5.73449e6i	−0.500604	−	0.363710i	−0.809248	+	0.587468i	$0.800125\pi$
$758$	1.17257e7			0.741252
$759$		0			0
$760$	−1.16799e6			−0.0733507
$761$	−9.13048e6	−	6.63368e6i	−0.571521	−	0.415234i	0.264137	−	0.964485i	$-0.414913\pi$
$761$	−9.13048e6	−	6.63368e6i	−0.571521	−	0.415234i	−0.835657	+	0.549251i	$0.814913\pi$
$762$		0			0
$763$	377541.	+	1.16195e6i	0.0234776	+	0.0722565i
$764$	2.39243e6	−	1.73820e6i	0.148288	−	0.107737i
$765$		0			0
$766$	4.59207e6	+	1.41330e7i	0.282772	+	0.870284i
$767$	−3.90504e6	+	1.20185e7i	−0.239683	+	0.737668i
$768$		0			0
$769$	−1.93388e7			−1.17927			−0.589634	−	0.807670i	$-0.700728\pi$
$769$	−1.93388e7			−1.17927			−0.589634	+	0.807670i	$0.700728\pi$
$770$	−737119.	−	27833.7i	−0.0448034	−	0.00169178i
$771$		0			0
$772$	−6.82096e6	−	4.95572e6i	−0.411910	−	0.299270i
$773$	8.17300e6	−	2.51539e7i	0.491963	−	1.51411i	−0.329673	−	0.944095i	$-0.606938\pi$
$773$	8.17300e6	−	2.51539e7i	0.491963	−	1.51411i	0.821636	−	0.570012i	$-0.193062\pi$
$774$		0			0
$775$	−1.91367e7	+	1.39036e7i	−1.14449	+	0.831522i
$776$	3.54075e6	−	2.57250e6i	0.211077	−	0.153356i
$777$		0			0
$778$	−2.04759e6	+	6.30184e6i	−0.121281	+	0.373266i
$779$	5.75701e6	+	4.18271e6i	0.339902	+	0.246953i
$780$		0			0
$781$	5.59627e6	+	1.97275e7i	0.328300	+	1.15729i
$782$	1.02390e7			0.598743
$783$		0			0
$784$	−976578.	+	3.00560e6i	−0.0567436	+	0.174639i
$785$	37150.0	+	114336.i	0.00215171	+	0.00662230i
$786$		0			0
$787$	6.42805e6	−	4.67025e6i	0.369950	−	0.268784i	−0.387240	−	0.921979i	$-0.626572\pi$
$787$	6.42805e6	−	4.67025e6i	0.369950	−	0.268784i	0.757190	+	0.653195i	$0.226572\pi$
$788$	−1.66747e6	−	5.13194e6i	−0.0956625	−	0.294419i
$789$		0			0
$790$	657897.	+	477990.i	0.0375051	+	0.0272490i
$791$	−769488.			−0.0437281
$792$		0			0
$793$	1.46567e7			0.827665
$794$	1.11190e7	+	8.07844e6i	0.625914	+	0.454753i
$795$		0			0
$796$	4.63136e6	+	1.42539e7i	0.259075	+	0.797352i
$797$	−2.56765e7	+	1.86551e7i	−1.43183	+	1.04028i	−0.442153	+	0.896940i	$0.645785\pi$
$797$	−2.56765e7	+	1.86551e7i	−1.43183	+	1.04028i	−0.989673	+	0.143343i	$0.954215\pi$
$798$		0			0
$799$	−2.30156e6	−	7.08349e6i	−0.127543	−	0.392537i
$800$	−973880.	+	2.99729e6i	−0.0537998	+	0.165579i
$801$		0			0
$802$	−5.20902e6			−0.285969
$803$	−2.07471e7	−	783414.i	−1.13545	−	0.0428749i
$804$		0			0
$805$	1.79051e6	+	1.30088e6i	0.0973839	+	0.0707536i
$806$	3.42429e6	−	1.05389e7i	0.185666	−	0.571422i
$807$		0			0
$808$	7.33907e6	−	5.33214e6i	0.395469	−	0.287325i
$809$	2.54480e7	−	1.84890e7i	1.36704	−	0.993214i	0.369080	−	0.929398i	$-0.379673\pi$
$809$	2.54480e7	−	1.84890e7i	1.36704	−	0.993214i	0.997962	−	0.0638165i	$-0.0203272\pi$
$810$		0			0
$811$	−1.69224e6	+	5.20818e6i	−0.0903462	+	0.278057i	−0.986013	−	0.166669i	$-0.946699\pi$
$811$	−1.69224e6	+	5.20818e6i	−0.0903462	+	0.278057i	0.895667	+	0.444726i	$0.146699\pi$
$812$	5.47390e6	+	3.97702e6i	0.291344	+	0.211674i
$813$		0			0
$814$	−2.41571e6	−	1.89841e6i	−0.127786	−	0.100422i
$815$	−4.63739e6			−0.244557
$816$		0			0
$817$	1.33712e7	−	4.11522e7i	0.700832	−	2.15694i
$818$	−389839.	−	1.19980e6i	−0.0203705	−	0.0626940i
$819$		0			0
$820$	−238848.	+	173533.i	−0.0124047	+	0.00901257i
$821$	785065.	+	2.41618e6i	0.0406488	+	0.125104i	0.969322	−	0.245796i	$-0.0790493\pi$
$821$	785065.	+	2.41618e6i	0.0406488	+	0.125104i	−0.928673	+	0.370900i	$0.879049\pi$
$822$		0			0
$823$	−1.42504e6	−	1.03535e6i	−0.0733378	−	0.0532830i	0.550512	−	0.834827i	$-0.314432\pi$
$823$	−1.42504e6	−	1.03535e6i	−0.0733378	−	0.0532830i	−0.623850	+	0.781544i	$0.714432\pi$
$824$	−368808.			−0.0189227
$825$		0			0
$826$	−9.36773e6			−0.477732
$827$	−1.74710e7	−	1.26934e7i	−0.888288	−	0.645379i	0.0471433	−	0.998888i	$-0.484988\pi$
$827$	−1.74710e7	−	1.26934e7i	−0.888288	−	0.645379i	−0.935431	+	0.353509i	$0.884988\pi$
$828$		0			0
$829$	−937574.	−	2.88556e6i	−0.0473826	−	0.145829i	0.924566	−	0.381022i	$-0.124428\pi$
$829$	−937574.	−	2.88556e6i	−0.0473826	−	0.145829i	−0.971949	+	0.235193i	$0.924428\pi$
$830$	34269.0	−	24897.9i	0.00172666	−	0.00125449i
$831$		0			0
$832$	−456231.	−	1.40413e6i	−0.0228495	−	0.0703234i
$833$	2.02745e6	−	6.23985e6i	0.101237	−	0.311574i
$834$		0			0
$835$	2.51391e6			0.124777
$836$	−5.87149e6	+	1.59906e7i	−0.290558	+	0.791313i
$837$		0			0
$838$	−2.04236e7	−	1.48386e7i	−1.00467	−	0.729932i
$839$	1.01969e7	−	3.13829e7i	0.500109	−	1.53918i	−0.308731	−	0.951149i	$-0.599904\pi$
$839$	1.01969e7	−	3.13829e7i	0.500109	−	1.53918i	0.808840	−	0.588028i	$-0.200096\pi$
$840$		0			0
$841$	−1.58288e7	+	1.15003e7i	−0.771718	+	0.560686i
$842$	1.40973e7	−	1.02423e7i	0.685259	−	0.497870i
$843$		0			0
$844$	700556.	−	2.15609e6i	0.0338522	−	0.104186i
$845$	−1.34330e6	−	975966.i	−0.0647190	−	0.0470211i
$846$		0			0
$847$	−4.08657e6	+	9.95175e6i	−0.195727	+	0.476641i
$848$	−563318.			−0.0269007
$849$		0			0
$850$	2.02185e6	−	6.22261e6i	0.0959845	−	0.295410i
$851$	2.84860e6	+	8.76709e6i	0.134837	+	0.414984i
$852$		0			0
$853$	2.65154e7	−	1.92646e7i	1.24774	−	0.906539i	0.249655	−	0.968335i	$-0.419683\pi$
$853$	2.65154e7	−	1.92646e7i	1.24774	−	0.906539i	0.998089	+	0.0617958i	$0.0196828\pi$
$854$	3.35746e6	+	1.03332e7i	0.157531	+	0.484831i
$855$		0			0
$856$	7.48171e6	+	5.43578e6i	0.348993	+	0.253558i
$857$	3.26099e7			1.51669			0.758346	−	0.651853i	$-0.226008\pi$
$857$	3.26099e7			1.51669			0.758346	+	0.651853i	$0.226008\pi$
$858$		0			0
$859$	9.66224e6			0.446781			0.223391	−	0.974729i	$-0.428287\pi$
$859$	9.66224e6			0.446781			0.223391	+	0.974729i	$0.428287\pi$
$860$	1.45234e6	+	1.05519e6i	0.0669612	+	0.0486501i
$861$		0			0
$862$	5.07184e6	+	1.56095e7i	0.232486	+	0.715520i
$863$	1.44480e7	−	1.04971e7i	0.660359	−	0.479779i	−0.206425	−	0.978462i	$-0.566183\pi$
$863$	1.44480e7	−	1.04971e7i	0.660359	−	0.479779i	0.866784	+	0.498683i	$0.166183\pi$
$864$		0			0
$865$	−676551.	−	2.08221e6i	−0.0307440	−	0.0946203i
$866$	−3.40390e6	+	1.04761e7i	−0.154235	+	0.474686i
$867$		0			0
$868$	8.21448e6			0.370067
$869$	9.85128e6	−	6.60421e6i	0.442531	−	0.296668i
$870$		0			0
$871$	1.67278e7	+	1.21534e7i	0.747123	+	0.542817i
$872$	−361719.	+	1.11326e6i	−0.0161094	+	0.0495797i
$873$		0			0
$874$	4.13484e7	−	3.00413e7i	1.83096	−	1.33027i
$875$	2.30591e6	−	1.67534e6i	0.101817	−	0.0739747i
$876$		0			0
$877$	−1.18059e6	+	3.63349e6i	−0.0518323	+	0.159524i	−0.973622	−	0.228167i	$-0.926727\pi$
$877$	−1.18059e6	+	3.63349e6i	−0.0518323	+	0.159524i	0.921790	+	0.387690i	$0.126727\pi$
$878$	−6.22688e6	−	4.52409e6i	−0.272605	−	0.198059i
$879$		0			0
$880$	−555675.	−	436684.i	−0.0241888	−	0.0190090i
$881$	1.26160e7			0.547625			0.273813	−	0.961783i	$-0.411715\pi$
$881$	1.26160e7			0.547625			0.273813	+	0.961783i	$0.411715\pi$
$882$		0			0
$883$	−3.14873e6	+	9.69080e6i	−0.135904	+	0.418271i	−0.995730	−	0.0923176i	$-0.970572\pi$
$883$	−3.14873e6	+	9.69080e6i	−0.135904	+	0.418271i	0.859825	+	0.510589i	$0.170572\pi$
$884$	947169.	+	2.91509e6i	0.0407659	+	0.125464i
$885$		0			0
$886$	−2.06648e6	+	1.50139e6i	−0.0884398	+	0.0642553i
$887$	5.71818e6	+	1.75987e7i	0.244033	+	0.751057i	0.995794	+	0.0916209i	$0.0292048\pi$
$887$	5.71818e6	+	1.75987e7i	0.244033	+	0.751057i	−0.751761	+	0.659436i	$0.770795\pi$
$888$		0			0
$889$	1.19677e7	+	8.69503e6i	0.507873	+	0.368992i
$890$	−1.37146e6			−0.0580374
$891$		0			0
$892$	−5.03248e6			−0.211773
$893$	−3.00775e7	−	2.18526e7i	−1.26216	−	0.917011i
$894$		0			0
$895$	−921511.	−	2.83612e6i	−0.0384541	−	0.118350i
$896$	885424.	−	643298.i	0.0368452	−	0.0267696i
$897$		0			0
$898$	−440795.	−	1.35663e6i	−0.0182409	−	0.0561396i
$899$	−1.50354e7	+	4.62741e7i	−0.620462	+	1.90959i
$900$		0			0
$901$	1.16949e6			0.0479937
$902$	1.17510e6	+	4.14236e6i	0.0480904	+	0.169524i
$903$		0			0
$904$	−596439.	−	433338.i	−0.0242742	−	0.0176362i
$905$	−1.04191e6	+	3.20665e6i	−0.0422870	+	0.130146i
$906$		0			0
$907$	4.46127e6	−	3.24130e6i	0.180070	−	0.130828i	−0.494099	−	0.869406i	$-0.664502\pi$
$907$	4.46127e6	−	3.24130e6i	0.180070	−	0.130828i	0.674169	+	0.738577i	$0.264502\pi$
$908$	1.00922e7	−	7.33244e6i	0.406231	−	0.295144i
$909$		0			0
$910$	−204734.	+	630106.i	−0.00819570	+	0.0252238i
$911$	−3.49175e7	−	2.53691e7i	−1.39395	−	1.01276i	−0.995419	−	0.0956101i	$-0.969520\pi$
$911$	−3.49175e7	−	2.53691e7i	−1.39395	−	1.01276i	−0.398532	−	0.917154i	$-0.630480\pi$
$912$		0			0
$913$	−168599.	−	594329.i	−0.00669387	−	0.0235966i
$914$	1.28421e7			0.508478
$915$		0			0
$916$	−4.23511e6	+	1.30343e7i	−0.166773	+	0.513275i
$917$	−6.64323e6	−	2.04458e7i	−0.260889	−	0.802935i
$918$		0			0
$919$	3.46445e7	−	2.51707e7i	1.35315	−	0.983119i	0.354300	−	0.935132i	$-0.384719\pi$
$919$	3.46445e7	−	2.51707e7i	1.35315	−	0.983119i	0.998848	−	0.0479873i	$-0.0152807\pi$
$920$	655252.	+	2.01666e6i	0.0255234	+	0.0785530i
$921$		0			0
$922$	9.12588e6	+	6.63034e6i	0.353547	+	0.256867i
$923$	1.84179e7			0.711598
$924$		0			0
$925$	5.89058e6			0.226362
$926$	6.22815e6	+	4.52501e6i	0.238688	+	0.173417i
$927$		0			0
$928$	2.00322e6	+	6.16527e6i	0.0763586	+	0.235008i
$929$	1.54104e7	−	1.11963e7i	0.585834	−	0.425633i	−0.254989	−	0.966944i	$-0.582072\pi$
$929$	1.54104e7	−	1.11963e7i	0.585834	−	0.425633i	0.840822	+	0.541311i	$0.182072\pi$
$930$		0			0
$931$	−1.01203e7	−	3.11471e7i	−0.382666	−	1.17772i
$932$	6.83808e6	−	2.10455e7i	0.257866	−	0.793631i
$933$		0			0
$934$	−1.11398e7			−0.417839
$935$	1.15362e6	+	906588.i	0.0431553	+	0.0339141i
$936$		0			0
$937$	4.11850e7	+	2.99226e7i	1.53246	+	1.11340i	0.954850	+	0.297088i	$0.0960155\pi$
$937$	4.11850e7	+	2.99226e7i	1.53246	+	1.11340i	0.577612	+	0.816311i	$0.303985\pi$
$938$	−4.73646e6	+	1.45773e7i	−0.175771	+	0.540967i
$939$		0			0
$940$	1.24786e6	−	906626.i	0.0460625	−	0.0334664i
$941$	−9.18051e6	+	6.67003e6i	−0.337981	+	0.245558i	−0.743810	−	0.668392i	$-0.766983\pi$
$941$	−9.18051e6	+	6.67003e6i	−0.337981	+	0.245558i	0.405828	+	0.913949i	$0.366983\pi$
$942$		0			0
$943$	3.99217e6	−	1.22866e7i	0.146194	−	0.449939i
$944$	−7.26103e6	−	5.27545e6i	−0.265197	−	0.192677i
$945$		0			0
$946$	2.17472e7	−	1.45791e7i	0.790089	−	0.529668i
$947$	1.42330e7			0.515731			0.257865	−	0.966181i	$-0.416981\pi$
$947$	1.42330e7			0.515731			0.257865	+	0.966181i	$0.416981\pi$
$948$		0			0
$949$	−5.76250e6	+	1.77351e7i	−0.207704	+	0.639248i
$950$	−1.00923e7	−	3.10610e7i	−0.362813	−	1.11662i
$951$		0			0
$952$	−1.83821e6	+	1.33553e6i	−0.0657358	+	0.0477598i
$953$	791556.	+	2.43616e6i	0.0282325	+	0.0868907i	0.964180	−	0.265249i	$-0.0854542\pi$
$953$	791556.	+	2.43616e6i	0.0282325	+	0.0868907i	−0.935947	+	0.352140i	$0.885454\pi$
$954$		0			0
$955$	−1.02861e6	−	747328.i	−0.0364957	−	0.0265157i
$956$	−1.51794e7			−0.537167
$957$		0			0
$958$	−1.50050e7			−0.528230
$959$	1.51765e7	+	1.10264e7i	0.532874	+	0.387156i
$960$		0			0
$961$	9.40698e6	+	2.89517e7i	0.328580	+	1.01127i
$962$	−2.23252e6	+	1.62202e6i	−0.0777781	+	0.0565091i
$963$		0			0
$964$	4.99833e6	+	1.53833e7i	0.173234	+	0.533158i
$965$	−1.12017e6	+	3.44752e6i	−0.0387226	+	0.119176i
$966$		0			0
$967$	3.37425e7			1.16041			0.580205	−	0.814470i	$-0.302972\pi$
$967$	3.37425e7			1.16041			0.580205	+	0.814470i	$0.302972\pi$
$968$	−8.77189e6	+	5.41236e6i	−0.300888	+	0.185651i
$969$		0			0
$970$	−1.52232e6	−	1.10603e6i	−0.0519490	−	0.0377432i
$971$	−1.29356e7	+	3.98115e7i	−0.440288	+	1.35507i	0.447281	+	0.894393i	$0.352392\pi$
$971$	−1.29356e7	+	3.98115e7i	−0.440288	+	1.35507i	−0.887569	+	0.460674i	$0.847608\pi$
$972$		0			0
$973$	−8.09146e6	+	5.87879e6i	−0.273996	+	0.199070i
$974$	−2.33628e7	+	1.69740e7i	−0.789090	+	0.573308i
$975$		0			0
$976$	−3.21675e6	+	9.90014e6i	−0.108092	+	0.332672i
$977$	1.83195e7	+	1.33099e7i	0.614013	+	0.446107i	0.850825	−	0.525449i	$-0.176103\pi$
$977$	1.83195e7	+	1.33099e7i	0.614013	+	0.446107i	−0.236812	+	0.971555i	$0.576103\pi$
$978$		0			0
$979$	−6.89435e6	+	1.87763e7i	−0.229899	+	0.626112i
$980$	1.35874e6			0.0451930
$981$		0			0
$982$	7.53057e6	−	2.31767e7i	0.249201	−	0.766961i
$983$	2.81101e6	+	8.65139e6i	0.0927851	+	0.285563i	0.986670	−	0.162733i	$-0.0520310\pi$
$983$	2.81101e6	+	8.65139e6i	0.0927851	+	0.285563i	−0.893885	+	0.448296i	$0.852031\pi$
$984$		0			0
$985$	−1.87691e6	+	1.36366e6i	−0.0616387	+	0.0447832i
$986$	−4.15883e6	−	1.27996e7i	−0.136232	−	0.419279i
$987$		0			0
$988$	1.23779e7	+	8.99306e6i	0.403417	+	0.293100i
$989$	−7.85550e7			−2.55378
$990$		0			0
$991$	8.71166e6			0.281784			0.140892	−	0.990025i	$-0.455003\pi$
$991$	8.71166e6			0.281784			0.140892	+	0.990025i	$0.455003\pi$
$992$	6.36713e6	+	4.62599e6i	0.205430	+	0.149254i
$993$		0			0
$994$	4.21903e6	+	1.29848e7i	0.135440	+	0.416841i
$995$	5.21310e6	−	3.78754e6i	0.166931	−	0.121283i
$996$		0			0
$997$	−1.16158e7	−	3.57496e7i	−0.370092	−	1.13903i	−0.946731	−	0.322027i	$-0.895636\pi$
$997$	−1.16158e7	−	3.57496e7i	−0.370092	−	1.13903i	0.576639	−	0.816999i	$-0.304364\pi$
$998$	−3.45576e6	+	1.06357e7i	−0.109829	+	0.338019i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.6.f.g.37.4	✓	20
3.2	odd	2		198.6.f.h.37.2	yes	20
11.3	even	5	inner	198.6.f.g.91.4	yes	20
33.14	odd	10		198.6.f.h.91.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
198.6.f.g.37.4	✓	20	1.1	even	1	trivial
198.6.f.g.91.4	yes	20	11.3	even	5	inner
198.6.f.h.37.2	yes	20	3.2	odd	2
198.6.f.h.91.2	yes	20	33.14	odd	10

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:	\( N \)	\(=\)	\( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	198.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.23607 - 2.35114i) q^{2} +(4.94427 + 15.2169i) q^{4} +(5.56531 - 4.04343i) q^{5} +(-20.6422 - 63.5301i) q^{7} +(19.7771 - 60.8676i) q^{8} +O(q^{10})\)	\(q+(-3.23607 - 2.35114i) q^{2} +(4.94427 + 15.2169i) q^{4} +(5.56531 - 4.04343i) q^{5} +(-20.6422 - 63.5301i) q^{7} +(19.7771 - 60.8676i) q^{8} -27.5164 q^{10} +(-138.325 + 376.719i) q^{11} +(291.608 + 211.866i) q^{13} +(-82.5688 + 254.121i) q^{14} +(-207.108 + 150.473i) q^{16} +(429.972 - 312.393i) q^{17} +(819.802 - 2523.09i) q^{19} +(89.0450 + 64.6949i) q^{20} +(1333.35 - 893.865i) q^{22} -4816.31 q^{23} +(-951.055 + 2927.05i) q^{25} +(-445.538 - 1371.22i) q^{26} +(864.672 - 628.221i) q^{28} +(1956.27 + 6020.77i) q^{29} +(6217.90 + 4517.57i) q^{31} +1024.00 q^{32} -2125.90 q^{34} +(-371.760 - 270.100i) q^{35} +(-591.449 - 1820.29i) q^{37} +(-8585.08 + 6237.42i) q^{38} +(-136.049 - 418.715i) q^{40} +(-828.887 + 2551.05i) q^{41} +16310.2 q^{43} +(-6416.41 - 242.284i) q^{44} +(15585.9 + 11323.8i) q^{46} +(4330.52 - 13328.0i) q^{47} +(9987.17 - 7256.10i) q^{49} +(9959.58 - 7236.05i) q^{50} +(-1782.15 + 5484.90i) q^{52} +(1780.21 + 1293.40i) q^{53} +(753.414 + 2655.87i) q^{55} -4275.17 q^{56} +(7825.07 - 24083.1i) q^{58} +(10833.9 + 33343.2i) q^{59} +(32896.7 - 23900.9i) q^{61} +(-9500.11 - 29238.3i) q^{62} +(-3313.73 - 2407.57i) q^{64} +2479.56 q^{65} +57363.8 q^{67} +(6879.56 + 4998.29i) q^{68} +(567.999 + 1748.12i) q^{70} +(41338.5 - 30034.2i) q^{71} +(15987.1 + 49203.1i) q^{73} +(-2365.80 + 7281.17i) q^{74} +42447.0 q^{76} +(26788.3 + 1011.53i) q^{77} +(-23909.3 - 17371.1i) q^{79} +(-544.194 + 1674.86i) q^{80} +(8680.22 - 6306.55i) q^{82} +(-1245.40 + 904.838i) q^{83} +(1129.79 - 3477.13i) q^{85} +(-52781.0 - 38347.6i) q^{86} +(20194.3 + 15869.9i) q^{88} +49841.6 q^{89} +(7440.43 - 22899.3i) q^{91} +(-23813.1 - 73289.3i) q^{92} +(-45349.8 + 32948.6i) q^{94} +(-5639.50 - 17356.6i) q^{95} +(55324.2 + 40195.4i) q^{97} -49379.3 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} - 80 q^{4} - 112 q^{5} - 392 q^{7} - 320 q^{8}+O(q^{10}) \) 20 * q - 20 * q^2 - 80 * q^4 - 112 * q^5 - 392 * q^7 - 320 * q^8	\( 20 q - 20 q^{2} - 80 q^{4} - 112 q^{5} - 392 q^{7} - 320 q^{8} + 552 q^{10} + 60 q^{11} - 420 q^{13} - 1568 q^{14} - 1280 q^{16} + 712 q^{17} - 898 q^{19} - 1792 q^{20} + 2020 q^{22} + 1180 q^{23} - 1079 q^{25} - 2880 q^{26} + 4688 q^{28} + 517 q^{29} - 5551 q^{31} + 20480 q^{32} - 6992 q^{34} + 14325 q^{35} - 7584 q^{37} - 1832 q^{38} + 2752 q^{40} - 16868 q^{41} - 704 q^{43} + 8080 q^{44} - 11400 q^{46} - 38866 q^{47} - 22573 q^{49} - 5416 q^{50} - 11520 q^{52} - 97517 q^{53} + 14404 q^{55} + 12672 q^{56} + 2068 q^{58} - 52682 q^{59} + 73874 q^{61} + 21136 q^{62} - 20480 q^{64} + 236352 q^{65} - 267432 q^{67} + 11392 q^{68} - 67660 q^{70} + 20588 q^{71} + 97257 q^{73} - 30336 q^{74} + 43392 q^{76} + 100582 q^{77} + 37498 q^{79} + 11008 q^{80} - 3672 q^{82} - 140952 q^{83} - 158376 q^{85} - 75136 q^{86} - 63040 q^{88} + 168796 q^{89} + 173196 q^{91} + 36160 q^{92} + 45376 q^{94} - 518002 q^{95} - 225802 q^{97} + 396808 q^{98}+O(q^{100}) \) 20 * q - 20 * q^2 - 80 * q^4 - 112 * q^5 - 392 * q^7 - 320 * q^8 + 552 * q^10 + 60 * q^11 - 420 * q^13 - 1568 * q^14 - 1280 * q^16 + 712 * q^17 - 898 * q^19 - 1792 * q^20 + 2020 * q^22 + 1180 * q^23 - 1079 * q^25 - 2880 * q^26 + 4688 * q^28 + 517 * q^29 - 5551 * q^31 + 20480 * q^32 - 6992 * q^34 + 14325 * q^35 - 7584 * q^37 - 1832 * q^38 + 2752 * q^40 - 16868 * q^41 - 704 * q^43 + 8080 * q^44 - 11400 * q^46 - 38866 * q^47 - 22573 * q^49 - 5416 * q^50 - 11520 * q^52 - 97517 * q^53 + 14404 * q^55 + 12672 * q^56 + 2068 * q^58 - 52682 * q^59 + 73874 * q^61 + 21136 * q^62 - 20480 * q^64 + 236352 * q^65 - 267432 * q^67 + 11392 * q^68 - 67660 * q^70 + 20588 * q^71 + 97257 * q^73 - 30336 * q^74 + 43392 * q^76 + 100582 * q^77 + 37498 * q^79 + 11008 * q^80 - 3672 * q^82 - 140952 * q^83 - 158376 * q^85 - 75136 * q^86 - 63040 * q^88 + 168796 * q^89 + 173196 * q^91 + 36160 * q^92 + 45376 * q^94 - 518002 * q^95 - 225802 * q^97 + 396808 * q^98

Introduction

L-functions

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