LMFDB - Embedded newform 38.4.e.b.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,4,Mod(5,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("38.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	38.e (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.24207258022$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 165 x^{16} - 56 x^{15} + 18435 x^{14} - 11748 x^{13} + 1092662 x^{12} - 1833567 x^{11} + \cdots + 3892796082289 $ x^18 + 165x^16 - 56x^15 + 18435x^14 - 11748x^13 + 1092662x^12 - 1833567x^11 + 46842546x^10 - 93643115x^9 + 1273086000x^8 - 3159018183x^7 + 24752942108x^6 - 51265274250x^5 + 247917053361x^4 - 421854393530x^3 + 1634375353605x^2 - 2066139456366x + 3892796082289
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.1
Root			$2.89395 + 5.01246i$ of defining polynomial
Character	$\chi$	$=$	38.25
Dual form			38.4.e.b.35.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.53209 + 1.28558i) q^{2} +(-3.05945 - 1.11355i) q^{3} +(0.694593 - 3.93923i) q^{4} +(-1.91957 - 10.8864i) q^{5} +(6.11891 - 2.22710i) q^{6} +(9.80910 - 16.9899i) q^{7} +(4.00000 + 6.92820i) q^{8} +(-12.5629 - 10.5416i) q^{9} +O(q^{10})$	\(q+(-1.53209 + 1.28558i) q^{2} +(-3.05945 - 1.11355i) q^{3} +(0.694593 - 3.93923i) q^{4} +(-1.91957 - 10.8864i) q^{5} +(6.11891 - 2.22710i) q^{6} +(9.80910 - 16.9899i) q^{7} +(4.00000 + 6.92820i) q^{8} +(-12.5629 - 10.5416i) q^{9} +(16.9363 + 14.2112i) q^{10} +(-6.14803 - 10.6487i) q^{11} +(-6.51160 + 11.2784i) q^{12} +(-6.72390 + 2.44730i) q^{13} +(6.81333 + 38.6403i) q^{14} +(-6.24975 + 35.4441i) q^{15} +(-15.0351 - 5.47232i) q^{16} +(-69.7004 + 58.4856i) q^{17} +32.7995 q^{18} +(82.6923 + 4.58044i) q^{19} -44.2176 q^{20} +(-48.9295 + 41.0567i) q^{21} +(23.1090 + 8.41100i) q^{22} +(16.6886 - 94.6457i) q^{23} +(-4.52291 - 25.6507i) q^{24} +(2.63162 - 0.957832i) q^{25} +(7.15543 - 12.3936i) q^{26} +(70.6505 + 122.370i) q^{27} +(-60.1136 - 50.4413i) q^{28} +(34.5111 + 28.9583i) q^{29} +(-35.9909 - 62.3381i) q^{30} +(146.443 - 253.646i) q^{31} +(30.0702 - 10.9446i) q^{32} +(6.95175 + 39.4253i) q^{33} +(31.5996 - 179.210i) q^{34} +(-203.788 - 74.1729i) q^{35} +(-50.2518 + 42.1662i) q^{36} +161.550 q^{37} +(-132.580 + 99.2896i) q^{38} +23.2967 q^{39} +(67.7452 - 56.8450i) q^{40} +(-307.571 - 111.947i) q^{41} +(22.1828 - 125.805i) q^{42} +(40.5783 + 230.131i) q^{43} +(-46.2181 + 16.8220i) q^{44} +(-90.6446 + 157.001i) q^{45} +(96.1058 + 166.460i) q^{46} +(242.311 + 203.323i) q^{47} +(39.9054 + 33.4846i) q^{48} +(-20.9368 - 36.2636i) q^{49} +(-2.80051 + 4.85063i) q^{50} +(278.372 - 101.319i) q^{51} +(4.97011 + 28.1869i) q^{52} +(-92.6474 + 525.430i) q^{53} +(-265.559 - 96.6556i) q^{54} +(-104.125 + 87.3712i) q^{55} +156.946 q^{56} +(-247.893 - 106.096i) q^{57} -90.1021 q^{58} +(226.705 - 190.228i) q^{59} +(135.282 + 49.2384i) q^{60} +(147.622 - 837.205i) q^{61} +(101.718 + 576.872i) q^{62} +(-302.331 + 110.039i) q^{63} +(-32.0000 + 55.4256i) q^{64} +(39.5494 + 68.5016i) q^{65} +(-61.3349 - 51.4661i) q^{66} +(246.069 + 206.477i) q^{67} +(181.975 + 315.189i) q^{68} +(-156.451 + 270.980i) q^{69} +(407.577 - 148.346i) q^{70} +(-91.0318 - 516.267i) q^{71} +(22.7823 - 129.205i) q^{72} +(-900.416 - 327.725i) q^{73} +(-247.510 + 207.685i) q^{74} -9.11792 q^{75} +(75.4809 - 322.563i) q^{76} -241.227 q^{77} +(-35.6925 + 29.9496i) q^{78} +(-428.051 - 155.798i) q^{79} +(-30.7132 + 174.183i) q^{80} +(-2.99623 - 16.9924i) q^{81} +(615.141 - 223.893i) q^{82} +(567.312 - 982.613i) q^{83} +(127.746 + 221.262i) q^{84} +(770.495 + 646.522i) q^{85} +(-358.020 - 300.414i) q^{86} +(-73.3386 - 127.026i) q^{87} +(49.1842 - 85.1896i) q^{88} +(1317.78 - 479.631i) q^{89} +(-62.9611 - 357.070i) q^{90} +(-24.3761 + 138.244i) q^{91} +(-361.240 - 131.480i) q^{92} +(-730.483 + 612.948i) q^{93} -632.630 q^{94} +(-108.869 - 909.018i) q^{95} -104.186 q^{96} +(391.024 - 328.108i) q^{97} +(78.6966 + 28.6432i) q^{98} +(-35.0166 + 198.589i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 6 q^{3} - 12 q^{6} - 33 q^{7} + 72 q^{8} + 42 q^{9}+O(q^{10}) $ 18 * q + 6 * q^3 - 12 * q^6 - 33 * q^7 + 72 * q^8 + 42 * q^9	\( 18 q + 6 q^{3} - 12 q^{6} - 33 q^{7} + 72 q^{8} + 42 q^{9} - 75 q^{11} + 36 q^{12} + 99 q^{13} + 162 q^{14} - 183 q^{15} - 111 q^{17} - 408 q^{18} - 372 q^{19} + 24 q^{20} - 207 q^{21} - 180 q^{22} + 198 q^{23} - 48 q^{24} + 534 q^{25} + 180 q^{26} + 678 q^{27} + 216 q^{28} + 669 q^{29} - 42 q^{31} + 315 q^{33} - 48 q^{34} - 1995 q^{35} + 168 q^{36} - 1056 q^{37} - 180 q^{38} + 1812 q^{39} - 210 q^{41} - 342 q^{42} - 399 q^{43} + 360 q^{44} + 1494 q^{45} + 672 q^{46} + 1149 q^{47} - 192 q^{48} - 858 q^{49} + 1068 q^{50} + 2646 q^{51} - 468 q^{52} - 633 q^{53} - 2898 q^{54} - 3483 q^{55} - 528 q^{56} - 2814 q^{57} + 636 q^{58} + 51 q^{59} - 84 q^{60} - 4104 q^{61} - 1326 q^{62} + 1215 q^{63} - 576 q^{64} + 1755 q^{65} + 2340 q^{66} - 675 q^{67} - 948 q^{68} + 3693 q^{69} + 3990 q^{70} + 2964 q^{71} + 672 q^{72} - 2004 q^{73} - 486 q^{74} - 4446 q^{75} - 408 q^{76} + 5820 q^{77} + 4992 q^{78} + 543 q^{79} + 1722 q^{81} + 420 q^{82} + 381 q^{83} + 1092 q^{84} + 1266 q^{85} - 3396 q^{86} - 4506 q^{87} + 600 q^{88} + 4386 q^{89} - 2148 q^{90} - 1356 q^{91} - 2628 q^{92} - 8604 q^{93} - 3264 q^{94} + 921 q^{95} + 576 q^{96} + 7599 q^{97} - 954 q^{98} - 5055 q^{99}+O(q^{100}) \) 18 * q + 6 * q^3 - 12 * q^6 - 33 * q^7 + 72 * q^8 + 42 * q^9 - 75 * q^11 + 36 * q^12 + 99 * q^13 + 162 * q^14 - 183 * q^15 - 111 * q^17 - 408 * q^18 - 372 * q^19 + 24 * q^20 - 207 * q^21 - 180 * q^22 + 198 * q^23 - 48 * q^24 + 534 * q^25 + 180 * q^26 + 678 * q^27 + 216 * q^28 + 669 * q^29 - 42 * q^31 + 315 * q^33 - 48 * q^34 - 1995 * q^35 + 168 * q^36 - 1056 * q^37 - 180 * q^38 + 1812 * q^39 - 210 * q^41 - 342 * q^42 - 399 * q^43 + 360 * q^44 + 1494 * q^45 + 672 * q^46 + 1149 * q^47 - 192 * q^48 - 858 * q^49 + 1068 * q^50 + 2646 * q^51 - 468 * q^52 - 633 * q^53 - 2898 * q^54 - 3483 * q^55 - 528 * q^56 - 2814 * q^57 + 636 * q^58 + 51 * q^59 - 84 * q^60 - 4104 * q^61 - 1326 * q^62 + 1215 * q^63 - 576 * q^64 + 1755 * q^65 + 2340 * q^66 - 675 * q^67 - 948 * q^68 + 3693 * q^69 + 3990 * q^70 + 2964 * q^71 + 672 * q^72 - 2004 * q^73 - 486 * q^74 - 4446 * q^75 - 408 * q^76 + 5820 * q^77 + 4992 * q^78 + 543 * q^79 + 1722 * q^81 + 420 * q^82 + 381 * q^83 + 1092 * q^84 + 1266 * q^85 - 3396 * q^86 - 4506 * q^87 + 600 * q^88 + 4386 * q^89 - 2148 * q^90 - 1356 * q^91 - 2628 * q^92 - 8604 * q^93 - 3264 * q^94 + 921 * q^95 + 576 * q^96 + 7599 * q^97 - 954 * q^98 - 5055 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

Coefficient data

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

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

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

$2$	−1.53209	+	1.28558i	−0.541675	+	0.454519i
$2$	−1.53209	+	1.28558i	−0.541675	+	0.454519i
$3$	−3.05945	−	1.11355i	−0.588792	−	0.214303i	0.0304061	−	0.999538i	$-0.490320\pi$
$3$	−3.05945	−	1.11355i	−0.588792	−	0.214303i	−0.619198	+	0.785235i	$0.712542\pi$
$4$	0.694593	−	3.93923i	0.0868241	−	0.492404i
$5$	−1.91957	−	10.8864i	−0.171692	−	0.973713i	−0.941893	−	0.335912i	$-0.890955\pi$
$5$	−1.91957	−	10.8864i	−0.171692	−	0.973713i	0.770201	−	0.637801i	$-0.220156\pi$
$6$	6.11891	−	2.22710i	0.416339	−	0.151535i
$7$	9.80910	−	16.9899i	0.529641	−	0.917366i	−0.469761	−	0.882794i	$-0.655660\pi$
$7$	9.80910	−	16.9899i	0.529641	−	0.917366i	0.999402	−	0.0345722i	$-0.0110069\pi$
$8$	4.00000	+	6.92820i	0.176777	+	0.306186i
$9$	−12.5629	−	10.5416i	−0.465294	−	0.390428i
$10$	16.9363	+	14.2112i	0.535573	+	0.449399i
$11$	−6.14803	−	10.6487i	−0.168518	−	0.291882i	0.769381	−	0.638790i	$-0.220565\pi$
$11$	−6.14803	−	10.6487i	−0.168518	−	0.291882i	−0.937899	+	0.346908i	$0.887232\pi$
$12$	−6.51160	+	11.2784i	−0.156645	+	0.271317i
$13$	−6.72390	+	2.44730i	−0.143452	+	0.0522122i	−0.412748	−	0.910845i	$-0.635431\pi$
$13$	−6.72390	+	2.44730i	−0.143452	+	0.0522122i	0.269296	+	0.963057i	$0.413209\pi$
$14$	6.81333	+	38.6403i	0.130067	+	0.737647i
$15$	−6.24975	+	35.4441i	−0.107579	+	0.610109i
$16$	−15.0351	−	5.47232i	−0.234923	−	0.0855050i
$17$	−69.7004	+	58.4856i	−0.994401	+	0.834402i	−0.986199	−	0.165565i	$-0.947055\pi$
$17$	−69.7004	+	58.4856i	−0.994401	+	0.834402i	−0.00820237	+	0.999966i	$0.502611\pi$
$18$	32.7995			0.429496
$19$	82.6923	+	4.58044i	0.998469	+	0.0553066i
$19$	82.6923	+	4.58044i	0.998469	+	0.0553066i
$20$	−44.2176			−0.494367
$21$	−48.9295	+	41.0567i	−0.508443	+	0.426634i
$22$	23.1090	+	8.41100i	0.223948	+	0.0815105i
$23$	16.6886	−	94.6457i	0.151296	−	0.858043i	−0.810798	−	0.585326i	$-0.800967\pi$
$23$	16.6886	−	94.6457i	0.151296	−	0.858043i	0.962094	−	0.272717i	$-0.0879223\pi$
$24$	−4.52291	−	25.6507i	−0.0384681	−	0.218164i
$25$	2.63162	−	0.957832i	0.0210530	−	0.00766266i
$26$	7.15543	−	12.3936i	0.0539729	−	0.0934838i
$27$	70.6505	+	122.370i	0.503581	+	0.872228i
$28$	−60.1136	−	50.4413i	−0.405729	−	0.340447i
$29$	34.5111	+	28.9583i	0.220985	+	0.185428i	0.746558	−	0.665320i	$-0.231705\pi$
$29$	34.5111	+	28.9583i	0.220985	+	0.185428i	−0.525574	+	0.850748i	$0.676149\pi$
$30$	−35.9909	−	62.3381i	−0.219034	−	0.379377i
$31$	146.443	−	253.646i	0.848448	−	1.46956i	−0.0341443	−	0.999417i	$-0.510871\pi$
$31$	146.443	−	253.646i	0.848448	−	1.46956i	0.882593	−	0.470139i	$-0.155796\pi$
$32$	30.0702	−	10.9446i	0.166116	−	0.0604612i
$33$	6.95175	+	39.4253i	0.0366710	+	0.207972i
$34$	31.5996	−	179.210i	0.159391	−	0.903950i
$35$	−203.788	−	74.1729i	−0.984187	−	0.358215i
$36$	−50.2518	+	42.1662i	−0.232647	+	0.195214i
$37$	161.550			0.717803			0.358902	−	0.933375i	$-0.383151\pi$
$37$	161.550			0.717803			0.358902	+	0.933375i	$0.383151\pi$
$38$	−132.580	+	99.2896i	−0.565984	+	0.423866i
$39$	23.2967			0.0956526
$40$	67.7452	−	56.8450i	0.267786	−	0.224700i
$41$	−307.571	−	111.947i	−1.17157	−	0.426417i	−0.318354	−	0.947972i	$-0.603130\pi$
$41$	−307.571	−	111.947i	−1.17157	−	0.426417i	−0.853218	+	0.521554i	$0.825352\pi$
$42$	22.1828	−	125.805i	0.0814973	−	0.462194i
$43$	40.5783	+	230.131i	0.143910	+	0.816154i	0.968236	+	0.250039i	$0.0804433\pi$
$43$	40.5783	+	230.131i	0.143910	+	0.816154i	−0.824326	+	0.566116i	$0.808446\pi$
$44$	−46.2181	+	16.8220i	−0.158355	+	0.0576366i
$45$	−90.6446	+	157.001i	−0.300278	+	0.520097i
$46$	96.1058	+	166.460i	0.308044	+	0.533548i
$47$	242.311	+	203.323i	0.752016	+	0.631016i	0.936035	−	0.351907i	$-0.114467\pi$
$47$	242.311	+	203.323i	0.752016	+	0.631016i	−0.184020	+	0.982923i	$0.558911\pi$
$48$	39.9054	+	33.4846i	0.119997	+	0.100689i
$49$	−20.9368	−	36.2636i	−0.0610402	−	0.105725i
$50$	−2.80051	+	4.85063i	−0.00792105	+	0.0137197i
$51$	278.372	−	101.319i	0.764310	−	0.278186i
$52$	4.97011	+	28.1869i	0.0132544	+	0.0751696i
$53$	−92.6474	+	525.430i	−0.240115	+	1.36176i	0.591454	+	0.806339i	$0.298554\pi$
$53$	−92.6474	+	525.430i	−0.240115	+	1.36176i	−0.831569	+	0.555422i	$0.812557\pi$
$54$	−265.559	−	96.6556i	−0.669222	−	0.243577i
$55$	−104.125	+	87.3712i	−0.255276	+	0.214202i
$56$	156.946			0.374513
$57$	−247.893	−	106.096i	−0.576038	−	0.246539i
$58$	−90.1021			−0.203982
$59$	226.705	−	190.228i	0.500246	−	0.419757i	−0.357435	−	0.933938i	$-0.616349\pi$
$59$	226.705	−	190.228i	0.500246	−	0.419757i	0.857681	+	0.514181i	$0.171904\pi$
$60$	135.282	+	49.2384i	0.291079	+	0.105944i
$61$	147.622	−	837.205i	0.309853	−	1.75726i	−0.289880	−	0.957063i	$-0.593615\pi$
$61$	147.622	−	837.205i	0.309853	−	1.75726i	0.599733	−	0.800200i	$-0.295274\pi$
$62$	101.718	+	576.872i	0.208358	+	1.18166i
$63$	−302.331	+	110.039i	−0.604605	+	0.220058i
$64$	−32.0000	+	55.4256i	−0.0625000	+	0.108253i
$65$	39.5494	+	68.5016i	0.0754693	+	0.130717i
$66$	−61.3349	−	51.4661i	−0.114391	−	0.0959855i
$67$	246.069	+	206.477i	0.448689	+	0.376494i	0.838949	−	0.544210i	$-0.183171\pi$
$67$	246.069	+	206.477i	0.448689	+	0.376494i	−0.390260	+	0.920705i	$0.627615\pi$
$68$	181.975	+	315.189i	0.324525	+	0.562093i
$69$	−156.451	+	270.980i	−0.272963	+	0.472786i
$70$	407.577	−	148.346i	0.695925	−	0.253296i
$71$	−91.0318	−	516.267i	−0.152162	−	0.862952i	−0.961335	−	0.275382i	$-0.911196\pi$
$71$	−91.0318	−	516.267i	−0.152162	−	0.862952i	0.809173	−	0.587570i	$-0.199915\pi$
$72$	22.7823	−	129.205i	0.0372906	−	0.211485i
$73$	−900.416	−	327.725i	−1.44364	−	0.525442i	−0.502833	−	0.864384i	$-0.667709\pi$
$73$	−900.416	−	327.725i	−1.44364	−	0.525442i	−0.940807	+	0.338942i	$0.889931\pi$
$74$	−247.510	+	207.685i	−0.388816	+	0.326256i
$75$	−9.11792			−0.0140379
$76$	75.4809	−	322.563i	0.113924	−	0.486848i
$77$	−241.227			−0.357017
$78$	−35.6925	+	29.9496i	−0.0518126	+	0.0434760i
$79$	−428.051	−	155.798i	−0.609614	−	0.221882i	0.0187201	−	0.999825i	$-0.494041\pi$
$79$	−428.051	−	155.798i	−0.609614	−	0.221882i	−0.628335	+	0.777943i	$0.716263\pi$
$80$	−30.7132	+	174.183i	−0.0429230	+	0.243428i
$81$	−2.99623	−	16.9924i	−0.00411005	−	0.0233092i
$82$	615.141	−	223.893i	0.828427	−	0.301523i
$83$	567.312	−	982.613i	0.750248	−	1.29947i	−0.197455	−	0.980312i	$-0.563268\pi$
$83$	567.312	−	982.613i	0.750248	−	1.29947i	0.947702	−	0.319155i	$-0.103399\pi$
$84$	127.746	+	221.262i	0.165931	+	0.287401i
$85$	770.495	+	646.522i	0.983199	+	0.825002i
$86$	−358.020	−	300.414i	−0.448910	−	0.376681i
$87$	−73.3386	−	127.026i	−0.0903762	−	0.156536i
$88$	49.1842	−	85.1896i	0.0595802	−	0.103196i
$89$	1317.78	−	479.631i	1.56948	−	0.571245i	0.596598	−	0.802540i	$-0.296519\pi$
$89$	1317.78	−	479.631i	1.56948	−	0.571245i	0.972884	+	0.231295i	$0.0742963\pi$
$90$	−62.9611	−	357.070i	−0.0737409	−	0.418206i
$91$	−24.3761	+	138.244i	−0.0280804	+	0.159252i
$92$	−361.240	−	131.480i	−0.409368	−	0.148998i
$93$	−730.483	+	612.948i	−0.814489	+	0.683438i
$94$	−632.630			−0.694157
$95$	−108.869	−	909.018i	−0.117576	−	0.981719i
$96$	−104.186			−0.110765
$97$	391.024	−	328.108i	0.409304	−	0.343446i	−0.414773	−	0.909925i	$-0.636139\pi$
$97$	391.024	−	328.108i	0.409304	−	0.343446i	0.824077	+	0.566478i	$0.191695\pi$
$98$	78.6966	+	28.6432i	0.0811179	+	0.0295245i
$99$	−35.0166	+	198.589i	−0.0355485	+	0.201605i
$100$	−1.94522	−	11.0319i	−0.00194522	−	0.0110319i
$101$	−361.611	+	131.616i	−0.356254	+	0.129666i	−0.513946	−	0.857822i	$-0.671817\pi$
$101$	−361.611	+	131.616i	−0.356254	+	0.129666i	0.157692	+	0.987488i	$0.449595\pi$
$102$	−296.237	+	513.097i	−0.287567	+	0.498080i
$103$	730.022	+	1264.44i	0.698362	+	1.20960i	0.969034	+	0.246926i	$0.0794206\pi$
$103$	730.022	+	1264.44i	0.698362	+	1.20960i	−0.270673	+	0.962671i	$0.587246\pi$
$104$	−43.8510	−	36.7954i	−0.0413456	−	0.0346931i
$105$	540.886	+	453.857i	0.502715	+	0.421828i
$106$	−533.535	−	924.110i	−0.488882	−	0.846769i
$107$	−703.303	+	1218.16i	−0.635429	+	1.10059i	0.350995	+	0.936377i	$0.385843\pi$
$107$	−703.303	+	1218.16i	−0.635429	+	1.10059i	−0.986424	+	0.164218i	$0.947490\pi$
$108$	531.118	−	193.311i	0.473212	−	0.172235i
$109$	373.866	+	2120.30i	0.328531	+	1.86319i	0.483602	+	0.875288i	$0.339328\pi$
$109$	373.866	+	2120.30i	0.328531	+	1.86319i	−0.155071	+	0.987903i	$0.549561\pi$
$110$	47.2064	−	267.721i	0.0409178	−	0.232056i
$111$	−494.256	−	179.894i	−0.422637	−	0.153827i
$112$	−240.455	+	201.765i	−0.202864	+	0.170223i
$113$	−292.836			−0.243785			−0.121892	−	0.992543i	$-0.538896\pi$
$113$	−292.836			−0.243785			−0.121892	+	0.992543i	$0.538896\pi$
$114$	516.188	−	156.137i	0.424082	−	0.128277i
$115$	−1062.39			−0.861464
$116$	138.044	−	115.833i	0.110492	−	0.0927140i
$117$	110.270	+	40.1351i	0.0871325	+	0.0317136i
$118$	−102.780	+	582.894i	−0.0801835	+	0.454743i
$119$	309.963	+	1757.89i	0.238776	+	1.35416i
$120$	−270.563	+	98.4769i	−0.205824	+	0.0749139i
$121$	589.903	−	1021.74i	0.443203	−	0.767650i
$122$	850.120	+	1472.45i	0.630871	+	1.09270i
$123$	816.340	+	684.990i	0.598430	+	0.502142i
$124$	−897.453	−	753.053i	−0.649949	−	0.545372i
$125$	−706.378	−	1223.48i	−0.505443	−	0.875453i
$126$	321.734	−	557.259i	0.227479	−	0.394005i
$127$	−1334.93	+	485.876i	−0.932725	+	0.339484i	−0.763289	−	0.646057i	$-0.776417\pi$
$127$	−1334.93	+	485.876i	−0.932725	+	0.339484i	−0.169436	+	0.985541i	$0.554195\pi$
$128$	−22.2270	−	126.055i	−0.0153485	−	0.0870455i
$129$	132.115	−	749.260i	0.0901710	−	0.511385i
$130$	−148.657	−	54.1068i	−0.100293	−	0.0365037i
$131$	556.894	−	467.289i	0.371420	−	0.311658i	−0.437903	−	0.899022i	$-0.644279\pi$
$131$	556.894	−	467.289i	0.371420	−	0.311658i	0.809323	+	0.587364i	$0.199834\pi$
$132$	160.134			0.105590
$133$	888.958	−	1360.00i	0.579567	−	0.886669i
$134$	−642.441			−0.414167
$135$	1196.56	−	1004.03i	0.762840	−	0.640098i
$136$	−684.001	−	248.956i	−0.431269	−	0.156969i
$137$	432.290	−	2451.64i	0.269584	−	1.52889i	−0.486072	−	0.873919i	$-0.661571\pi$
$137$	432.290	−	2451.64i	0.269584	−	1.52889i	0.755656	−	0.654968i	$-0.227318\pi$
$138$	−108.669	−	616.295i	−0.0670330	−	0.380163i
$139$	−1746.44	+	635.652i	−1.06569	+	0.387880i	−0.814564	−	0.580074i	$-0.803024\pi$
$139$	−1746.44	+	635.652i	−1.06569	+	0.387880i	−0.251128	+	0.967954i	$0.580801\pi$
$140$	−433.734	+	751.250i	−0.261837	+	0.453516i
$141$	−514.929	−	891.884i	−0.307552	−	0.532696i
$142$	803.168	+	673.938i	0.474651	+	0.398279i
$143$	67.3993	+	56.5548i	0.0394141	+	0.0330724i
$144$	131.198	+	227.242i	0.0759248	+	0.131506i
$145$	249.006	−	431.291i	0.142613	−	0.247012i
$146$	1800.83	−	655.449i	1.02081	−	0.371544i
$147$	23.6738	+	134.261i	0.0132829	+	0.0753310i
$148$	112.212	−	636.384i	0.0623226	−	0.353449i
$149$	2496.03	+	908.482i	1.37237	+	0.499502i	0.919856	−	0.392256i	$-0.128305\pi$
$149$	2496.03	+	908.482i	1.37237	+	0.499502i	0.452513	+	0.891758i	$0.350527\pi$
$150$	13.9695	−	11.7218i	0.00760401	−	0.00638052i
$151$	−1464.59			−0.789314			−0.394657	−	0.918828i	$-0.629137\pi$
$151$	−1464.59			−0.789314			−0.394657	+	0.918828i	$0.629137\pi$
$152$	299.035	+	591.231i	0.159572	+	0.315494i
$153$	1492.17			0.788463
$154$	369.581	−	310.115i	0.193387	−	0.162271i
$155$	−3042.41	−	1107.35i	−1.57660	−	0.573835i
$156$	16.1817	−	91.7709i	0.00830495	−	0.0470997i
$157$	456.344	+	2588.06i	0.231976	+	1.31560i	0.848889	+	0.528571i	$0.177272\pi$
$157$	456.344	+	2588.06i	0.231976	+	1.31560i	−0.616913	+	0.787031i	$0.711617\pi$
$158$	856.103	−	311.596i	0.431063	−	0.156894i
$159$	868.543	−	1504.36i	0.433207	−	0.750336i
$160$	−176.870	−	306.348i	−0.0873926	−	0.151368i
$161$	−1444.32	−	1211.93i	−0.707007	−	0.593249i
$162$	26.4355	+	22.1821i	0.0128208	+	0.0107579i
$163$	−447.193	−	774.561i	−0.214889	−	0.372198i	0.738349	−	0.674418i	$-0.235606\pi$
$163$	−447.193	−	774.561i	−0.214889	−	0.372198i	−0.953238	+	0.302220i	$0.902272\pi$
$164$	−654.620	+	1133.83i	−0.311690	+	0.539863i
$165$	415.857	−	151.360i	0.196209	−	0.0714142i
$166$	394.051	+	2234.77i	0.184243	+	1.04489i
$167$	−31.1075	+	176.419i	−0.0144142	+	0.0817469i	−0.991166	−	0.132625i	$-0.957659\pi$
$167$	−31.1075	+	176.419i	−0.0144142	+	0.0817469i	0.976752	+	0.214372i	$0.0687705\pi$
$168$	−480.168	−	174.767i	−0.220510	−	0.0802592i
$169$	−1643.78	+	1379.29i	−0.748192	+	0.627808i
$170$	−2011.62			−0.907554
$171$	−990.574	−	929.250i	−0.442989	−	0.415564i
$172$	934.724			0.414372
$173$	−336.235	+	282.135i	−0.147766	+	0.123990i	−0.713674	−	0.700478i	$-0.752970\pi$
$173$	−336.235	+	282.135i	−0.147766	+	0.123990i	0.565908	+	0.824468i	$0.308526\pi$
$174$	275.663	+	100.333i	0.120103	+	0.0437140i
$175$	9.54041	−	54.1063i	0.00412107	−	0.0233717i
$176$	34.1630	+	193.748i	0.0146314	+	0.0829791i
$177$	−905.424	+	329.547i	−0.384496	+	0.139945i
$178$	−1402.35	+	2428.94i	−0.590508	+	1.02279i
$179$	431.404	+	747.214i	0.180138	+	0.312008i	0.941927	−	0.335817i	$-0.109012\pi$
$179$	431.404	+	747.214i	0.180138	+	0.312008i	−0.761790	+	0.647825i	$0.775679\pi$
$180$	555.503	+	466.122i	0.230026	+	0.193015i
$181$	952.904	+	799.581i	0.391319	+	0.328356i	0.817127	−	0.576458i	$-0.195566\pi$
$181$	952.904	+	799.581i	0.391319	+	0.328356i	−0.425808	+	0.904814i	$0.640010\pi$
$182$	−140.377	−	243.139i	−0.0571726	−	0.0990258i
$183$	−1383.91	+	2397.00i	−0.559025	+	0.968260i
$184$	722.479	−	262.961i	0.289467	−	0.105357i
$185$	−310.108	−	1758.71i	−0.123241	−	0.698935i
$186$	331.174	−	1878.18i	0.130553	−	0.740403i
$187$	1051.32	+	382.647i	0.411122	+	0.149636i
$188$	969.245	−	813.293i	0.376008	−	0.315508i
$189$	2772.07			1.06687
$190$	1335.41	+	1252.74i	0.509899	+	0.478332i
$191$	2765.73			1.04775			0.523877	−	0.851794i	$-0.324485\pi$
$191$	2765.73			1.04775			0.523877	+	0.851794i	$0.324485\pi$
$192$	159.622	−	133.938i	0.0599984	−	0.0503447i
$193$	382.098	+	139.072i	0.142508	+	0.0518686i	0.412289	−	0.911053i	$-0.364729\pi$
$193$	382.098	+	139.072i	0.142508	+	0.0518686i	−0.269782	+	0.962922i	$0.586951\pi$
$194$	−177.276	+	1005.38i	−0.0656065	+	0.372073i
$195$	−44.7197	−	253.618i	−0.0164228	−	0.0931382i
$196$	−157.393	+	57.2864i	−0.0573590	+	0.0208770i
$197$	−1648.82	+	2855.83i	−0.596311	+	1.03284i	0.397049	+	0.917797i	$0.370034\pi$
$197$	−1648.82	+	2855.83i	−0.596311	+	1.03284i	−0.993360	+	0.115044i	$0.963299\pi$
$198$	−201.652	−	349.272i	−0.0723778	−	0.125362i
$199$	−363.185	−	304.748i	−0.129374	−	0.108558i	0.575805	−	0.817587i	$-0.304689\pi$
$199$	−363.185	−	304.748i	−0.129374	−	0.108558i	−0.705179	+	0.709029i	$0.749133\pi$
$200$	17.1625	+	14.4011i	0.00606787	+	0.00509155i
$201$	−522.915	−	905.715i	−0.183500	−	0.317832i
$202$	384.819	−	666.525i	0.134038	−	0.232161i
$203$	830.519	−	302.284i	0.287148	−	0.104513i
$204$	−205.764	−	1166.95i	−0.0706194	−	0.400503i
$205$	−628.295	+	3563.24i	−0.214059	+	1.21399i
$206$	−2743.99	−	998.730i	−0.928071	−	0.337790i
$207$	−1207.37	+	1013.10i	−0.405401	+	0.340172i
$208$	114.487			0.0381646
$209$	−459.619	−	908.727i	−0.152117	−	0.300756i
$210$	−1412.15			−0.464037
$211$	111.558	−	93.6087i	0.0363981	−	0.0305416i	−0.624407	−	0.781099i	$-0.714659\pi$
$211$	111.558	−	93.6087i	0.0363981	−	0.0305416i	0.660805	+	0.750557i	$0.270215\pi$
$212$	2005.44	+	729.919i	0.649689	+	0.236467i
$213$	−296.381	+	1680.86i	−0.0953414	+	0.540708i
$214$	−488.509	−	2770.47i	−0.156046	−	0.884980i
$215$	2427.41	−	883.507i	0.769992	−	0.280254i
$216$	−565.204	+	978.962i	−0.178043	+	0.308379i
$217$	−2872.94	−	4976.08i	−0.898747	−	1.55668i
$218$	−3298.60	−	2767.85i	−1.02481	−	0.859921i
$219$	2389.84	+	2005.32i	0.737400	+	0.618752i
$220$	271.851	+	470.860i	0.0833099	+	0.144297i
$221$	325.527	−	563.829i	0.0990828	−	0.171616i
$222$	988.512	−	359.789i	0.298849	−	0.108772i
$223$	−216.285	−	1226.61i	−0.0649484	−	0.368341i	−0.999908	−	0.0135857i	$-0.995675\pi$
$223$	−216.285	−	1226.61i	−0.0649484	−	0.368341i	0.934959	−	0.354755i	$-0.115436\pi$
$224$	109.013	−	618.245i	0.0325168	−	0.184412i
$225$	−43.1580	−	15.7082i	−0.0127875	−	0.00465428i
$226$	448.651	−	376.463i	0.132052	−	0.110805i
$227$	1377.67			0.402815			0.201408	−	0.979508i	$-0.435448\pi$
$227$	1377.67			0.402815			0.201408	+	0.979508i	$0.435448\pi$
$228$	−590.120	+	902.813i	−0.171411	+	0.262238i
$229$	1561.79			0.450680			0.225340	−	0.974280i	$-0.427651\pi$
$229$	1561.79			0.450680			0.225340	+	0.974280i	$0.427651\pi$
$230$	1627.68	−	1365.78i	0.466634	−	0.391552i
$231$	738.021	+	268.618i	0.210209	+	0.0765097i
$232$	−62.5843	+	354.933i	−0.0177106	+	0.100442i
$233$	−351.013	−	1990.69i	−0.0986936	−	0.559719i	−0.993553	−	0.113371i	$-0.963835\pi$
$233$	−351.013	−	1990.69i	−0.0986936	−	0.559719i	0.894859	−	0.446349i	$-0.147276\pi$
$234$	−220.541	+	80.2703i	−0.0616120	+	0.0224249i
$235$	1748.33	−	3028.20i	0.485314	−	0.840588i
$236$	−591.886	−	1025.18i	−0.163256	−	0.282768i
$237$	1136.11	+	953.313i	0.311386	+	0.261284i
$238$	−2734.79	−	2294.76i	−0.744833	−	0.624989i
$239$	2077.06	+	3597.58i	0.562151	+	0.973674i	0.997308	+	0.0733198i	$0.0233594\pi$
$239$	2077.06	+	3597.58i	0.562151	+	0.973674i	−0.435157	+	0.900354i	$0.643307\pi$
$240$	287.927	−	498.704i	0.0774401	−	0.134130i
$241$	−4271.89	+	1554.84i	−1.14181	+	0.415586i	−0.842568	−	0.538590i	$-0.818957\pi$
$241$	−4271.89	+	1554.84i	−1.14181	+	0.415586i	−0.299245	+	0.954176i	$0.596735\pi$
$242$	409.743	+	2323.77i	0.108840	+	0.617262i
$243$	652.735	−	3701.84i	0.172317	−	0.977256i
$244$	−3195.41	−	1163.03i	−0.838381	−	0.305146i
$245$	−354.592	+	297.538i	−0.0924655	+	0.0775878i
$246$	−2131.31			−0.552388
$247$	−567.225	+	171.575i	−0.146120	+	0.0441985i
$248$	2343.08			0.599944
$249$	−2829.85	+	2374.53i	−0.720219	+	0.604336i
$250$	2655.11	+	966.382i	0.671697	+	0.244478i
$251$	−433.801	+	2460.21i	−0.109089	+	0.618673i	0.880419	+	0.474196i	$0.157261\pi$
$251$	−433.801	+	2460.21i	−0.109089	+	0.618673i	−0.989508	+	0.144477i	$0.953850\pi$
$252$	223.474	+	1267.38i	0.0558632	+	0.316816i
$253$	−1110.46	+	404.173i	−0.275944	+	0.100435i
$254$	1420.61	−	2460.56i	0.350932	−	0.607832i
$255$	−1637.36	−	2835.99i	−0.402099	−	0.696457i
$256$	196.107	+	164.554i	0.0478778	+	0.0401742i
$257$	383.423	+	321.730i	0.0930634	+	0.0780894i	0.688132	−	0.725585i	$-0.258431\pi$
$257$	383.423	+	321.730i	0.0930634	+	0.0780894i	−0.595069	+	0.803675i	$0.702875\pi$
$258$	760.819	+	1317.78i	0.183591	+	0.317989i
$259$	1584.66	−	2744.72i	0.380178	−	0.658488i
$260$	297.315	−	108.214i	0.0709179	−	0.0258120i
$261$	−128.296	−	727.602i	−0.0304265	−	0.172557i
$262$	−252.475	+	1431.86i	−0.0595342	+	0.337635i
$263$	5753.26	+	2094.02i	1.34890	+	0.490961i	0.912605	−	0.408842i	$-0.134067\pi$
$263$	5753.26	+	2094.02i	1.34890	+	0.490961i	0.436298	+	0.899802i	$0.356289\pi$
$264$	−245.340	+	205.864i	−0.0571955	+	0.0479927i
$265$	5897.91			1.36719
$266$	386.420	+	3226.46i	0.0890712	+	0.743711i
$267$	−4565.76			−1.04652
$268$	984.277	−	825.906i	0.224344	−	0.188247i
$269$	−4403.97	−	1602.91i	−0.998196	−	0.363314i	−0.209307	−	0.977850i	$-0.567121\pi$
$269$	−4403.97	−	1602.91i	−0.998196	−	0.363314i	−0.788889	+	0.614536i	$0.789343\pi$
$270$	−542.476	+	3076.53i	−0.122274	+	0.693451i
$271$	−483.581	−	2742.53i	−0.108397	−	0.614747i	−0.989809	−	0.142400i	$-0.954518\pi$
$271$	−483.581	−	2742.53i	−0.108397	−	0.614747i	0.881413	−	0.472347i	$-0.156593\pi$
$272$	1368.00	−	497.912i	0.304953	−	0.110994i
$273$	228.519	−	395.807i	0.0506616	−	0.0877484i
$274$	2489.46	+	4311.87i	0.548882	+	0.950691i
$275$	−26.3790	−	22.1346i	−0.00578440	−	0.00485369i
$276$	958.785	+	804.516i	0.209102	+	0.175457i
$277$	−264.169	−	457.554i	−0.0573009	−	0.0992482i	0.835952	−	0.548803i	$-0.184916\pi$
$277$	−264.169	−	457.554i	−0.0573009	−	0.0992482i	−0.893253	+	0.449554i	$0.851583\pi$
$278$	1858.52	−	3219.06i	0.400960	−	0.694483i
$279$	−4513.58	+	1642.81i	−0.968534	+	0.352518i
$280$	−301.269	−	1708.58i	−0.0643009	−	0.364668i
$281$	−1486.24	+	8428.91i	−0.315523	+	1.78942i	0.253750	+	0.967270i	$0.418336\pi$
$281$	−1486.24	+	8428.91i	−0.315523	+	1.78942i	−0.569273	+	0.822149i	$0.692775\pi$
$282$	1935.50	+	704.465i	0.408714	+	0.148760i
$283$	4034.26	−	3385.14i	0.847391	−	0.711045i	−0.111823	−	0.993728i	$-0.535669\pi$
$283$	4034.26	−	3385.14i	0.847391	−	0.711045i	0.959213	+	0.282683i	$0.0912244\pi$
$284$	−2096.92			−0.438132
$285$	−679.156	+	2902.33i	−0.141157	+	0.603225i
$286$	−175.967			−0.0363817
$287$	−4918.95	+	4127.49i	−1.01169	+	0.848912i
$288$	−493.143	−	179.490i	−0.100898	−	0.0367240i
$289$	584.448	−	3314.57i	0.118959	−	0.674653i
$290$	172.958	+	980.892i	0.0350222	+	0.198620i
$291$	−1561.68	+	568.406i	−0.314596	+	0.114504i
$292$	−1916.41	+	3319.31i	−0.384072	+	0.665233i
$293$	57.8884	+	100.266i	0.0115422	+	0.0199918i	0.871739	−	0.489971i	$-0.162993\pi$
$293$	57.8884	+	100.266i	0.0115422	+	0.0199918i	−0.860197	+	0.509963i	$0.829659\pi$
$294$	−208.873	−	175.265i	−0.0414344	−	0.0347676i
$295$	−2506.09	−	2102.86i	−0.494611	−	0.415028i
$296$	646.202	+	1119.25i	0.126891	+	0.219781i
$297$	868.723	−	1504.67i	0.169725	−	0.293973i
$298$	−4992.07	+	1816.96i	−0.970412	+	0.353201i
$299$	119.414	+	677.230i	0.0230966	+	0.130987i
$300$	−6.33324	+	35.9176i	−0.00121883	+	0.00691234i
$301$	4307.93	+	1567.96i	0.824933	+	0.300251i
$302$	2243.88	−	1882.84i	0.427552	−	0.358759i
$303$	1252.89			0.237547
$304$	−1218.22	−	521.386i	−0.229835	−	0.0983670i
$305$	−9397.55			−1.76427
$306$	−2286.14	+	1918.30i	−0.427091	+	0.358372i
$307$	8518.10	+	3100.34i	1.58356	+	0.576370i	0.975975	−	0.217883i	$-0.0699151\pi$
$307$	8518.10	+	3100.34i	1.58356	+	0.576370i	0.607588	+	0.794253i	$0.292137\pi$
$308$	−167.554	+	950.247i	−0.0309977	+	0.175797i
$309$	−825.457	−	4681.40i	−0.151970	−	0.861862i
$310$	6084.83	−	2214.70i	1.11482	−	0.405762i
$311$	3174.24	−	5497.94i	0.578760	−	1.00244i	−0.416862	−	0.908970i	$-0.636870\pi$
$311$	3174.24	−	5497.94i	0.578760	−	1.00244i	0.995622	−	0.0934722i	$-0.0297966\pi$
$312$	93.1866	+	161.404i	0.0169091	+	0.0292875i
$313$	670.299	+	562.448i	0.121046	+	0.101570i	0.701301	−	0.712865i	$-0.252603\pi$
$313$	670.299	+	562.448i	0.121046	+	0.101570i	−0.580255	+	0.814435i	$0.697047\pi$
$314$	−4026.30	−	3378.47i	−0.723622	−	0.607191i
$315$	1778.28	+	3080.08i	0.318079	+	0.550929i
$316$	−911.046	+	1577.98i	−0.162185	+	0.280912i
$317$	−5266.65	+	1916.90i	−0.933137	+	0.339634i	−0.763452	−	0.645864i	$-0.776497\pi$
$317$	−5266.65	+	1916.90i	−0.933137	+	0.339634i	−0.169685	+	0.985498i	$0.554275\pi$
$318$	603.283	+	3421.39i	0.106385	+	0.603340i
$319$	96.1925	−	545.535i	0.0168832	−	0.0957495i
$320$	664.814	+	241.973i	0.116138	+	0.0422709i
$321$	3508.20	−	2943.73i	0.609996	−	0.511847i
$322$	3770.84			0.652611
$323$	−6031.57	+	4517.05i	−1.03903	+	0.778128i
$324$	−69.0183			−0.0118344
$325$	−15.3507	+	12.8807i	−0.00262001	+	0.00219845i
$326$	1680.90	+	611.796i	0.285571	+	0.103939i
$327$	1217.23	−	6903.27i	0.205851	−	1.16744i
$328$	−454.694	−	2578.70i	−0.0765435	−	0.434100i
$329$	5831.29	−	2122.42i	0.977171	−	0.355661i
$330$	−442.546	+	766.513i	−0.0738223	+	0.127864i
$331$	−839.734	−	1454.46i	−0.139444	−	0.241524i	0.787842	−	0.615877i	$-0.211198\pi$
$331$	−839.734	−	1454.46i	−0.139444	−	0.241524i	−0.927286	+	0.374353i	$0.877865\pi$
$332$	−3476.69	−	2917.29i	−0.574723	−	0.482250i
$333$	−2029.55	−	1702.99i	−0.333990	−	0.280251i
$334$	−179.141	−	310.281i	−0.0293477	−	0.0508318i
$335$	1775.45	−	3075.17i	0.289561	−	0.501535i
$336$	960.335	−	349.533i	0.155924	−	0.0567518i
$337$	−1469.20	−	8332.26i	−0.237485	−	1.34685i	−0.837316	−	0.546719i	$-0.815876\pi$
$337$	−1469.20	−	8332.26i	−0.237485	−	1.34685i	0.599830	−	0.800127i	$-0.295235\pi$
$338$	745.228	−	4226.40i	0.119926	−	0.680136i
$339$	895.918	+	326.088i	0.143539	+	0.0522438i
$340$	3081.98	−	2586.09i	0.491599	−	0.412501i
$341$	−3601.34			−0.571916
$342$	2712.27	+	150.236i	0.428838	+	0.0237539i
$343$	5907.56			0.929965
$344$	−1432.08	+	1201.66i	−0.224455	+	0.188340i
$345$	3250.33	+	1183.02i	0.507223	+	0.184614i
$346$	152.437	−	864.512i	0.0236851	−	0.134325i
$347$	−746.481	−	4233.50i	−0.115485	−	0.654946i	−0.986509	−	0.163707i	$-0.947655\pi$
$347$	−746.481	−	4233.50i	−0.115485	−	0.654946i	0.871024	−	0.491240i	$-0.163456\pi$
$348$	−551.326	+	200.666i	−0.0849258	+	0.0309105i
$349$	−1741.91	+	3017.07i	−0.267169	+	0.462751i	−0.968130	−	0.250449i	$-0.919422\pi$
$349$	−1741.91	+	3017.07i	−0.267169	+	0.462751i	0.700960	+	0.713200i	$0.252755\pi$
$350$	54.9410	+	95.1606i	0.00839063	+	0.0145330i
$351$	−774.524	−	649.903i	−0.117781	−	0.0988297i
$352$	−301.419	−	252.920i	−0.0456411	−	0.0382974i
$353$	1036.43	+	1795.14i	0.156270	+	0.270668i	0.933521	−	0.358523i	$-0.116720\pi$
$353$	1036.43	+	1795.14i	0.156270	+	0.270668i	−0.777251	+	0.629191i	$0.783386\pi$
$354$	963.532	−	1668.89i	0.144664	−	0.250566i
$355$	−5445.57	+	1982.02i	−0.814143	+	0.296324i
$356$	−974.060	−	5524.17i	−0.145014	−	0.822417i
$357$	1009.18	−	5723.34i	0.149612	−	0.848491i
$358$	−1621.55	−	590.195i	−0.239390	−	0.0871307i
$359$	100.618	−	84.4289i	0.0147923	−	0.0124122i	−0.635361	−	0.772215i	$-0.719149\pi$
$359$	100.618	−	84.4289i	0.0147923	−	0.0124122i	0.650154	+	0.759803i	$0.274704\pi$
$360$	−1450.31			−0.212329
$361$	6817.04	+	757.534i	0.993882	+	0.110444i
$362$	−2487.86			−0.361212
$363$	−2942.54	+	2469.09i	−0.425464	+	0.357007i
$364$	527.643	+	192.046i	0.0759781	+	0.0276538i
$365$	−1839.34	+	10431.4i	−0.263769	+	1.49591i
$366$	−961.254	−	5451.54i	−0.137283	−	0.778570i
$367$	−6231.63	+	2268.13i	−0.886344	+	0.322603i	−0.744767	−	0.667324i	$-0.767439\pi$
$367$	−6231.63	+	2268.13i	−0.886344	+	0.322603i	−0.141577	+	0.989927i	$0.545217\pi$
$368$	−768.846	+	1331.68i	−0.108910	+	0.188638i
$369$	2683.90	+	4648.65i	0.378640	+	0.655824i
$370$	2736.07	+	2295.83i	0.384436	+	0.322580i
$371$	8018.19	+	6728.06i	1.12206	+	0.941519i
$372$	1907.15	+	3303.29i	0.265810	+	0.460397i
$373$	−1394.78	+	2415.82i	−0.193616	+	0.335353i	−0.946446	−	0.322862i	$-0.895355\pi$
$373$	−1394.78	+	2415.82i	−0.193616	+	0.335353i	0.752830	+	0.658215i	$0.228688\pi$
$374$	−2102.63	+	765.295i	−0.290707	+	0.105809i
$375$	798.722	+	4529.78i	0.109989	+	0.623778i
$376$	−439.420	+	2492.08i	−0.0602696	+	0.341806i
$377$	−302.919	−	110.253i	−0.0413823	−	0.0150619i
$378$	−4247.06	+	3563.71i	−0.577897	+	0.484913i
$379$	−7045.15			−0.954842			−0.477421	−	0.878675i	$-0.658428\pi$
$379$	−7045.15			−0.954842			−0.477421	+	0.878675i	$0.658428\pi$
$380$	−3656.45	−	202.536i	−0.493611	−	0.0273418i
$381$	4625.21			0.621934
$382$	−4237.34	+	3555.55i	−0.567542	+	0.476225i
$383$	2553.58	+	929.427i	0.340683	+	0.123999i	0.506696	−	0.862125i	$-0.330867\pi$
$383$	2553.58	+	929.427i	0.340683	+	0.123999i	−0.166012	+	0.986124i	$0.553089\pi$
$384$	−72.3666	+	410.411i	−0.00961704	+	0.0545409i
$385$	463.052	+	2626.10i	0.0612970	+	0.347632i
$386$	−764.196	+	278.145i	−0.100768	+	0.0366767i
$387$	1916.16	−	3318.88i	0.251689	−	0.435938i
$388$	−1020.89	−	1768.23i	−0.133577	−	0.231362i
$389$	−892.555	−	748.943i	−0.116335	−	0.0976167i	0.582764	−	0.812641i	$-0.301971\pi$
$389$	−892.555	−	748.943i	−0.116335	−	0.0976167i	−0.699099	+	0.715024i	$0.746416\pi$
$390$	394.559	+	331.074i	0.0512289	+	0.0429862i
$391$	4372.21	+	7572.88i	0.565504	+	0.979481i
$392$	167.494	−	290.109i	0.0215810	−	0.0373793i
$393$	−2224.14	+	809.520i	−0.285478	+	0.103906i
$394$	−1145.26	−	6495.07i	−0.146439	−	0.830499i
$395$	−874.410	+	4959.02i	−0.111383	+	0.631685i
$396$	757.965	+	275.877i	0.0961848	+	0.0350084i
$397$	9422.84	−	7906.70i	1.19123	−	0.999562i	0.191394	−	0.981513i	$-0.438699\pi$
$397$	9422.84	−	7906.70i	1.19123	−	0.999562i	0.999837	−	0.0180487i	$-0.00574538\pi$
$398$	948.208			0.119420
$399$	−4234.15	+	3170.96i	−0.531260	+	0.397861i
$400$	−44.8082			−0.00560103
$401$	−5702.54	+	4785.00i	−0.710153	+	0.595889i	−0.924642	−	0.380837i	$-0.875636\pi$
$401$	−5702.54	+	4785.00i	−0.710153	+	0.595889i	0.214489	+	0.976726i	$0.431191\pi$
$402$	1965.52	+	715.390i	0.243858	+	0.0887572i
$403$	−363.918	+	2063.88i	−0.0449828	+	0.255110i
$404$	267.292	+	1515.89i	0.0329165	+	0.186679i
$405$	−179.236	+	65.2365i	−0.0219909	+	0.00800402i
$406$	−883.820	+	1530.82i	−0.108038	+	0.187127i
$407$	−993.217	−	1720.30i	−0.120963	−	0.209514i
$408$	1815.44	+	1523.34i	0.220289	+	0.184844i
$409$	1029.23	+	863.628i	0.124431	+	0.104410i	0.702880	−	0.711309i	$-0.251897\pi$
$409$	1029.23	+	863.628i	0.124431	+	0.104410i	−0.578449	+	0.815719i	$0.696342\pi$
$410$	−3618.21	−	6266.92i	−0.435831	−	0.754881i
$411$	−4052.59	+	7019.29i	−0.486374	+	0.842424i
$412$	5487.97	−	1997.46i	0.656245	−	0.238854i
$413$	−1008.18	−	5717.66i	−0.120119	−	0.681230i
$414$	547.378	−	3104.33i	0.0649810	−	0.368526i
$415$	−11786.2	−	4289.81i	−1.39412	−	0.507418i
$416$	−175.404	+	147.181i	−0.0206728	+	0.0173465i
$417$	6050.98			0.710595
$418$	1872.41	+	801.375i	0.219097	+	0.0937716i
$419$	15619.7			1.82117			0.910586	−	0.413320i	$-0.135631\pi$
$419$	15619.7			1.82117			0.910586	+	0.413320i	$0.135631\pi$
$420$	2163.54	−	1815.43i	0.251357	−	0.210914i
$421$	4980.50	+	1812.75i	0.576567	+	0.209853i	0.613811	−	0.789453i	$-0.289636\pi$
$421$	4980.50	+	1812.75i	0.576567	+	0.209853i	−0.0372441	+	0.999306i	$0.511858\pi$
$422$	−50.5765	+	286.834i	−0.00583418	+	0.0330873i
$423$	−900.798	−	5108.68i	−0.103542	−	0.587216i
$424$	−4010.87	+	1459.84i	−0.459399	+	0.167208i
$425$	−127.406	+	220.673i	−0.0145414	+	0.0251864i
$426$	−1706.79	−	2956.25i	−0.194118	−	0.336223i
$427$	−12775.9	−	10720.3i	−1.44794	−	1.21497i
$428$	4310.09	+	3616.60i	0.486767	+	0.408446i
$429$	−143.229	−	248.079i	−0.0161192	−	0.0279193i
$430$	−2583.20	+	4474.23i	−0.289705	+	0.501783i
$431$	−3066.44	+	1116.09i	−0.342704	+	0.124734i	−0.507638	−	0.861571i	$-0.669481\pi$
$431$	−3066.44	+	1116.09i	−0.342704	+	0.124734i	0.164934	+	0.986305i	$0.447259\pi$
$432$	−392.587	−	2226.47i	−0.0437230	−	0.247965i
$433$	−1516.58	+	8600.95i	−0.168319	+	0.954585i	0.777257	+	0.629183i	$0.216611\pi$
$433$	−1516.58	+	8600.95i	−0.168319	+	0.954585i	−0.945576	+	0.325401i	$0.894501\pi$
$434$	10798.7	+	3930.42i	1.19437	+	0.434714i
$435$	−1242.09	+	1042.23i	−0.136904	+	0.114876i
$436$	8612.03			0.945967
$437$	1813.54	−	7750.03i	0.198520	−	0.848362i
$438$	−6239.44			−0.680666
$439$	10287.9	−	8632.61i	1.11849	−	0.938524i	0.119962	−	0.992779i	$-0.461723\pi$
$439$	10287.9	−	8632.61i	1.11849	−	0.938524i	0.998527	+	0.0542548i	$0.0172783\pi$
$440$	−1021.83	−	371.914i	−0.110713	−	0.0402961i
$441$	−119.247	+	676.284i	−0.0128763	+	0.0730249i
$442$	226.109	+	1282.33i	0.0243323	+	0.137995i
$443$	4967.60	−	1808.06i	0.532772	−	0.193913i	−0.0616036	−	0.998101i	$-0.519621\pi$
$443$	4967.60	−	1808.06i	0.532772	−	0.193913i	0.594376	+	0.804188i	$0.297399\pi$
$444$	−1051.95	+	1822.03i	−0.112440	+	0.194752i
$445$	−7751.04	−	13425.2i	−0.825696	−	1.43015i
$446$	1908.27	+	1601.23i	0.202599	+	0.170001i
$447$	−6624.86	−	5558.92i	−0.700996	−	0.588205i
$448$	627.782	+	1087.35i	0.0662052	+	0.114671i
$449$	5163.23	−	8942.98i	0.542690	−	0.939967i	−0.456058	−	0.889950i	$-0.650739\pi$
$449$	5163.23	−	8942.98i	0.542690	−	0.939967i	0.998748	−	0.0500170i	$-0.0159276\pi$
$450$	86.3159	−	31.4164i	0.00904216	−	0.00329108i
$451$	698.868	+	3963.48i	0.0729677	+	0.413820i
$452$	−203.402	+	1153.55i	−0.0211664	+	0.120041i
$453$	4480.84	+	1630.89i	0.464742	+	0.169152i
$454$	−2110.71	+	1771.10i	−0.218195	+	0.183087i
$455$	1551.78			0.159887
$456$	−256.519	−	2141.83i	−0.0263434	−	0.219957i
$457$	−9788.28			−1.00192			−0.500959	−	0.865471i	$-0.667019\pi$
$457$	−9788.28			−1.00192			−0.500959	+	0.865471i	$0.667019\pi$
$458$	−2392.80	+	2007.79i	−0.244122	+	0.204843i
$459$	−12081.3	−	4397.22i	−1.22855	−	0.447156i
$460$	−737.929	+	4185.00i	−0.0747959	+	0.424188i
$461$	−471.077	−	2671.61i	−0.0475927	−	0.269912i	0.951721	−	0.306966i	$-0.0993137\pi$
$461$	−471.077	−	2671.61i	−0.0475927	−	0.269912i	−0.999313	+	0.0370542i	$0.988203\pi$
$462$	−1476.04	+	537.236i	−0.148640	+	0.0541006i
$463$	−6435.33	+	11146.3i	−0.645951	+	1.11882i	0.338130	+	0.941099i	$0.390206\pi$
$463$	−6435.33	+	11146.3i	−0.645951	+	1.11882i	−0.984081	+	0.177720i	$0.943128\pi$
$464$	−360.408	−	624.246i	−0.0360594	−	0.0624566i
$465$	8075.04	+	6775.76i	0.805314	+	0.675738i
$466$	3096.97	+	2598.66i	0.307863	+	0.258328i
$467$	−6824.97	−	11821.2i	−0.676278	−	1.17135i	−0.976094	−	0.217351i	$-0.930258\pi$
$467$	−6824.97	−	11821.2i	−0.676278	−	1.17135i	0.299815	−	0.953997i	$-0.403075\pi$
$468$	234.695	−	406.503i	0.0231811	−	0.0401509i
$469$	5921.72	−	2155.33i	0.583027	−	0.212205i
$470$	1214.38	+	6887.09i	0.119181	+	0.675910i
$471$	1485.77	−	8426.20i	0.145351	−	0.824329i
$472$	2224.76	+	809.748i	0.216956	+	0.0789654i
$473$	2201.12	−	1846.96i	0.213969	−	0.179542i
$474$	−2966.18			−0.287429
$475$	222.002	−	67.1514i	0.0214445	−	0.00648656i
$476$	7140.03			0.687527
$477$	6702.77	−	5624.29i	0.643394	−	0.539872i
$478$	−7807.21	−	2841.59i	−0.747057	−	0.271907i
$479$	−405.827	+	2301.56i	−0.0387113	+	0.219543i	−0.998026	−	0.0627948i	$-0.979999\pi$
$479$	−405.827	+	2301.56i	−0.0387113	+	0.219543i	0.959315	+	0.282337i	$0.0911097\pi$
$480$	199.992	+	1134.21i	0.0190174	+	0.107853i
$481$	−1086.25	+	395.362i	−0.102970	+	0.0374781i
$482$	4546.05	−	7874.00i	0.429600	−	0.744089i
$483$	3069.28	+	5316.15i	0.289145	+	0.500814i
$484$	−3615.14	−	3033.46i	−0.339513	−	0.284886i
$485$	−4322.53	−	3627.03i	−0.404693	−	0.339577i
$486$	3758.95	+	6510.69i	0.350842	+	0.607677i
$487$	−4423.84	+	7662.32i	−0.411629	+	0.712963i	−0.995068	−	0.0991941i	$-0.968374\pi$
$487$	−4423.84	+	7662.32i	−0.411629	+	0.712963i	0.583439	+	0.812157i	$0.301707\pi$
$488$	6390.81	−	2326.06i	0.592825	−	0.215771i
$489$	505.653	+	2867.70i	0.0467616	+	0.265198i
$490$	160.759	−	911.709i	0.0148211	−	0.0840547i
$491$	−311.146	−	113.248i	−0.0285984	−	0.0104090i	0.327681	−	0.944788i	$-0.393733\pi$
$491$	−311.146	−	113.248i	−0.0285984	−	0.0104090i	−0.356280	+	0.934379i	$0.615955\pi$
$492$	3265.36	−	2739.96i	0.299215	−	0.251071i
$493$	−4099.08			−0.374469
$494$	648.467	−	992.078i	0.0590605	−	0.0903556i
$495$	2229.14			0.202409
$496$	−3589.81	+	3012.21i	−0.324975	+	0.272686i
$497$	−9664.24	−	3517.49i	−0.872234	−	0.317467i
$498$	1282.95	−	7275.97i	0.115443	−	0.654707i
$499$	3254.16	+	18455.2i	0.291936	+	1.65565i	0.679402	+	0.733767i	$0.262239\pi$
$499$	3254.16	+	18455.2i	0.291936	+	1.65565i	−0.387466	+	0.921884i	$0.626649\pi$
$500$	−5310.23	+	1932.76i	−0.474961	+	0.172872i
$501$	291.623	−	505.106i	0.0260055	−	0.0450429i
$502$	−2498.16	−	4326.94i	−0.222108	−	0.384703i
$503$	−6963.30	−	5842.90i	−0.617253	−	0.517937i	0.279686	−	0.960092i	$-0.409770\pi$
$503$	−6963.30	−	5842.90i	−0.617253	−	0.517937i	−0.896939	+	0.442155i	$0.854214\pi$
$504$	−1971.70	−	1654.45i	−0.174259	−	0.146220i
$505$	2126.97	+	3684.01i	0.187423	+	0.324627i
$506$	1181.72	−	2046.80i	0.103822	−	0.179825i
$507$	6564.97	−	2389.45i	0.575070	−	0.209309i
$508$	986.742	+	5596.09i	0.0861803	+	0.488753i
$509$	1627.33	−	9229.06i	0.141710	−	0.803675i	−0.828241	−	0.560372i	$-0.810658\pi$
$509$	1627.33	−	9229.06i	0.141710	−	0.803675i	0.969950	−	0.243303i	$-0.0782309\pi$
$510$	6154.45	+	2240.04i	0.534360	+	0.194491i
$511$	−14400.3	+	12083.3i	−1.24663	+	1.04605i
$512$	−512.000			−0.0441942
$513$	5281.74	+	10442.7i	0.454571	+	0.898745i
$514$	−1001.05			−0.0859033
$515$	12363.9	−	10374.5i	1.05790	−	0.887682i
$516$	−2859.74	−	1040.86i	−0.243979	−	0.0888011i
$517$	675.392	−	3830.34i	0.0574540	−	0.325838i
$518$	1100.70	+	6242.36i	0.0933625	+	0.529485i
$519$	1342.87	−	488.764i	0.113575	−	0.0413379i
$520$	−316.395	+	548.013i	−0.0266824	+	0.0462153i
$521$	5808.19	+	10060.1i	0.488410	+	0.845951i	0.999911	−	0.0133317i	$-0.00424375\pi$
$521$	5808.19	+	10060.1i	0.488410	+	0.845951i	−0.511501	+	0.859283i	$0.670910\pi$
$522$	1131.95	+	949.817i	0.0949119	+	0.0796405i
$523$	−8625.22	−	7237.42i	−0.721137	−	0.605105i	0.206563	−	0.978433i	$-0.433772\pi$
$523$	−8625.22	−	7237.42i	−0.721137	−	0.605105i	−0.927699	+	0.373328i	$0.878217\pi$
$524$	−1453.95	−	2518.31i	−0.121214	−	0.209948i
$525$	−89.4385	+	154.912i	−0.00743508	+	0.0128779i
$526$	−11506.5	+	4188.03i	−0.953819	+	0.347162i
$527$	4627.53	+	26244.0i	0.382502	+	2.16927i
$528$	111.228	−	630.805i	0.00916776	−	0.0519930i
$529$	2753.94	+	1002.35i	0.226345	+	0.0823829i
$530$	−9036.12	+	7582.20i	−0.740573	+	0.621415i
$531$	−4853.39			−0.396647
$532$	−4739.89	−	4446.46i	−0.386279	−	0.362365i
$533$	2342.04			0.190328
$534$	6995.16	−	5869.63i	0.566873	−	0.475663i
$535$	14611.4	+	5318.13i	1.18076	+	0.429762i
$536$	−446.235	+	2530.72i	−0.0359597	+	0.203938i
$537$	−487.801	−	2766.45i	−0.0391995	−	0.222312i
$538$	8807.94	−	3205.83i	0.705831	−	0.256901i
$539$	−257.440	+	445.899i	−0.0205728	+	0.0356331i
$540$	−3123.99	−	5410.91i	−0.248954	−	0.431201i
$541$	12982.9	+	10893.9i	1.03175	+	0.865743i	0.991058	−	0.133429i	$-0.0425988\pi$
$541$	12982.9	+	10893.9i	1.03175	+	0.865743i	0.0406936	+	0.999172i	$0.487043\pi$
$542$	4266.61	+	3580.11i	0.338130	+	0.283725i
$543$	−2024.99	−	3507.39i	−0.160038	−	0.277194i
$544$	−1455.80	+	2521.52i	−0.114737	+	0.198730i
$545$	22364.9	−	8140.15i	1.75781	−	0.639790i
$546$	158.728	+	900.190i	0.0124412	+	0.0705578i
$547$	−215.539	+	1222.38i	−0.0168478	+	0.0955488i	−0.992072	−	0.125669i	$-0.959892\pi$
$547$	−215.539	+	1222.38i	−0.0168478	+	0.0955488i	0.975224	+	0.221218i	$0.0710033\pi$
$548$	−9357.30	−	3405.78i	−0.729424	−	0.265488i
$549$	−10680.0	+	8961.59i	−0.830258	+	0.696669i
$550$	68.8706			0.00533937
$551$	2721.16	+	2552.70i	0.210391	+	0.197366i
$552$	−2503.21			−0.193014
$553$	−6845.78	+	5744.29i	−0.526424	+	0.441722i
$554$	992.950	+	361.404i	0.0761487	+	0.0277159i
$555$	−1009.65	+	5726.01i	−0.0772203	+	0.437938i
$556$	1290.92	+	7321.15i	0.0984659	+	0.558428i
$557$	−7745.13	+	2819.00i	−0.589177	+	0.214443i	−0.619367	−	0.785101i	$-0.712611\pi$
$557$	−7745.13	+	2819.00i	−0.589177	+	0.214443i	0.0301904	+	0.999544i	$0.490389\pi$
$558$	4803.25	−	8319.48i	0.364405	−	0.631168i
$559$	−836.044	−	1448.07i	−0.0632574	−	0.109565i
$560$	2658.08	+	2230.39i	0.200579	+	0.168306i
$561$	−2790.35	−	2341.38i	−0.209998	−	0.176209i
$562$	−8558.94	−	14824.5i	−0.642415	−	1.11269i
$563$	7886.28	−	13659.4i	0.590350	−	1.02252i	−0.403835	−	0.914832i	$-0.632323\pi$
$563$	7886.28	−	13659.4i	0.590350	−	1.02252i	0.994185	−	0.107684i	$-0.0343435\pi$
$564$	−3871.00	+	1408.93i	−0.289005	+	0.105189i
$565$	562.121	+	3187.94i	0.0418559	+	0.237377i
$566$	−1828.98	+	10372.7i	−0.135827	+	0.770311i
$567$	−318.089	−	115.775i	−0.0235600	−	0.00857512i
$568$	3212.67	−	2695.75i	0.237325	−	0.199140i
$569$	−22799.6			−1.67981			−0.839903	−	0.542736i	$-0.817388\pi$
$569$	−22799.6			−1.67981			−0.839903	+	0.542736i	$0.817388\pi$
$570$	−2690.63	−	5319.73i	−0.197716	−	0.390911i
$571$	−13021.2			−0.954323			−0.477162	−	0.878816i	$-0.658334\pi$
$571$	−13021.2			−0.954323			−0.477162	+	0.878816i	$0.658334\pi$
$572$	269.597	−	226.219i	0.0197070	−	0.0165362i
$573$	−8461.61	−	3079.77i	−0.616909	−	0.224537i
$574$	2230.07	−	12647.3i	0.162163	−	0.919669i
$575$	−46.7366	−	265.057i	−0.00338966	−	0.0192237i
$576$	986.287	−	358.979i	0.0713460	−	0.0259678i
$577$	−9724.42	+	16843.2i	−0.701617	+	1.21524i	0.266282	+	0.963895i	$0.414205\pi$
$577$	−9724.42	+	16843.2i	−0.701617	+	1.21524i	−0.967899	+	0.251341i	$0.919129\pi$
$578$	3365.70	+	5829.57i	0.242205	+	0.419512i
$579$	−1014.15	−	850.971i	−0.0727919	−	0.0610797i
$580$	−1526.00	−	1280.46i	−0.109248	−	0.0916695i
$581$	−11129.6	−	19277.1i	−0.794725	−	1.37650i
$582$	1661.91	−	2878.51i	0.118365	−	0.205014i
$583$	6164.74	−	2243.78i	0.437938	−	0.159396i
$584$	−1331.12	−	7549.16i	−0.0943188	−	0.534909i
$585$	225.257	−	1277.49i	0.0159200	−	0.0902870i
$586$	−217.589	−	79.1960i	−0.0153388	−	0.00558286i
$587$	4222.11	−	3542.77i	0.296874	−	0.249107i	−0.482168	−	0.876079i	$-0.660150\pi$
$587$	4222.11	−	3542.77i	0.296874	−	0.249107i	0.779042	+	0.626972i	$0.215706\pi$
$588$	545.328			0.0382465
$589$	13271.5	−	20303.8i	0.928426	−	1.42038i
$590$	6542.94			0.456557
$591$	8224.59	−	6901.25i	0.572444	−	0.480337i
$592$	−2428.92	−	884.056i	−0.168629	−	0.0613758i
$593$	−1257.97	+	7134.31i	−0.0871141	+	0.494049i	0.909766	+	0.415121i	$0.136261\pi$
$593$	−1257.97	+	7134.31i	−0.0871141	+	0.494049i	−0.996880	+	0.0789278i	$0.974850\pi$
$594$	603.409	+	3422.10i	0.0416804	+	0.236381i
$595$	18542.2	−	6748.80i	1.27757	−	0.464998i
$596$	5312.45	−	9201.43i	0.365111	−	0.632391i
$597$	771.794	+	1336.79i	0.0529103	+	0.0916433i
$598$	−1053.58	−	884.062i	−0.0720472	−	0.0604548i
$599$	15437.6	+	12953.7i	1.05303	+	0.883595i	0.993409	−	0.114626i	$-0.0365670\pi$
$599$	15437.6	+	12953.7i	1.05303	+	0.883595i	0.0596190	+	0.998221i	$0.481011\pi$
$600$	−36.4717	−	63.1708i	−0.00248158	−	0.00429823i
$601$	−5802.61	+	10050.4i	−0.393833	+	0.682138i	−0.992951	−	0.118522i	$-0.962184\pi$
$601$	−5802.61	+	10050.4i	−0.393833	+	0.682138i	0.599119	+	0.800660i	$0.295518\pi$
$602$	−8615.85	+	3135.91i	−0.583315	+	0.212309i
$603$	−914.768	−	5187.91i	−0.0617781	−	0.350361i
$604$	−1017.29	+	5769.35i	−0.0685315	+	0.388661i
$605$	−12255.5	−	4460.64i	−0.823566	−	0.299753i
$606$	−1919.54	+	1610.69i	−0.128673	+	0.107970i
$607$	15678.2			1.04836			0.524182	−	0.851606i	$-0.324371\pi$
$607$	15678.2			1.04836			0.524182	+	0.851606i	$0.324371\pi$
$608$	2536.70	−	767.303i	0.169205	−	0.0511814i
$609$	−2877.54			−0.191468
$610$	14397.9	−	12081.3i	0.955661	−	0.801895i
$611$	−2126.87	−	774.118i	−0.140825	−	0.0512561i
$612$	1036.45	−	5878.01i	0.0684576	−	0.388242i
$613$	−632.555	−	3587.40i	−0.0416781	−	0.236368i	0.956852	−	0.290577i	$-0.0938473\pi$
$613$	−632.555	−	3587.40i	−0.0416781	−	0.236368i	−0.998530	+	0.0542092i	$0.982736\pi$
$614$	−17036.2	+	6200.67i	−1.11975	+	0.407555i
$615$	5890.09	−	10201.9i	0.386197	−	0.668913i
$616$	−964.906	−	1671.27i	−0.0631123	−	0.109314i
$617$	18233.9	+	15300.0i	1.18974	+	0.998309i	0.999864	+	0.0165003i	$0.00525245\pi$
$617$	18233.9	+	15300.0i	1.18974	+	0.998309i	0.189874	+	0.981808i	$0.439192\pi$
$618$	7282.96	+	6111.13i	0.474051	+	0.397776i
$619$	−5166.52	−	8948.67i	−0.335476	−	0.581062i	0.648100	−	0.761555i	$-0.275564\pi$
$619$	−5166.52	−	8948.67i	−0.335476	−	0.581062i	−0.983576	+	0.180493i	$0.942231\pi$
$620$	−6475.34	+	11215.6i	−0.419445	+	0.726500i
$621$	12760.9	−	4644.58i	0.824600	−	0.300130i
$622$	2204.80	+	12504.1i	0.142129	+	0.806056i
$623$	4777.33	−	27093.6i	0.307222	−	1.74234i
$624$	−350.267	−	127.487i	−0.0224710	−	0.00817878i
$625$	−11695.3	+	9813.50i	−0.748497	+	0.628064i
$626$	−1750.03			−0.111733
$627$	394.271	+	3292.01i	0.0251127	+	0.209682i
$628$	10511.9			0.667949
$629$	−11260.1	+	9448.36i	−0.713785	+	0.598936i
$630$	−6684.16	−	2432.84i	−0.422704	−	0.153852i
$631$	3598.39	−	20407.5i	0.227020	−	1.28750i	−0.631765	−	0.775160i	$-0.717669\pi$
$631$	3598.39	−	20407.5i	0.227020	−	1.28750i	0.858785	−	0.512336i	$-0.171220\pi$
$632$	−632.806	−	3588.82i	−0.0398286	−	0.225879i
$633$	−445.546	+	162.165i	−0.0279761	+	0.0101825i
$634$	5604.65	−	9707.54i	0.351087	−	0.608100i
$635$	7851.96	+	13600.0i	0.490702	+	0.849920i
$636$	−5322.74	−	4466.31i	−0.331856	−	0.278460i
$637$	229.525	+	192.594i	0.0142765	+	0.0119794i
$638$	553.950	+	959.470i	0.0343748	+	0.0595389i
$639$	−4298.63	+	7445.45i	−0.266121	+	0.460935i
$640$	−1329.63	+	483.945i	−0.0821222	+	0.0298900i
$641$	−2901.25	−	16453.8i	−0.178771	−	1.01386i	−0.933700	−	0.358056i	$-0.883440\pi$
$641$	−2901.25	−	16453.8i	−0.178771	−	1.01386i	0.754929	−	0.655807i	$-0.227672\pi$
$642$	−1590.49	+	9020.11i	−0.0977751	+	0.554510i
$643$	−21174.9	−	7707.05i	−1.29869	−	0.472685i	−0.402121	−	0.915587i	$-0.631727\pi$
$643$	−21174.9	−	7707.05i	−1.29869	−	0.472685i	−0.896570	+	0.442902i	$0.853949\pi$
$644$	−5777.27	+	4847.70i	−0.353503	+	0.296625i
$645$	−8410.39			−0.513424
$646$	3433.90	−	14674.6i	0.209141	−	0.893751i
$647$	−2985.35			−0.181401			−0.0907004	−	0.995878i	$-0.528911\pi$
$647$	−2985.35			−0.181401			−0.0907004	+	0.995878i	$0.528911\pi$
$648$	105.742	−	88.7282i	0.00641041	−	0.00537897i
$649$	−3419.48	−	1244.59i	−0.206820	−	0.0752764i
$650$	6.95943	−	39.4689i	0.000419956	−	0.00238169i
$651$	3248.52	+	18423.3i	0.195575	+	1.10916i
$652$	−3361.79	+	1223.59i	−0.201929	+	0.0734962i
$653$	−5704.35	+	9880.23i	−0.341851	+	0.592103i	−0.984776	−	0.173826i	$-0.944387\pi$
$653$	−5704.35	+	9880.23i	−0.341851	+	0.592103i	0.642926	+	0.765929i	$0.277720\pi$
$654$	7009.77	+	12141.3i	0.419119	+	0.725935i
$655$	−6156.12	−	5165.60i	−0.367236	−	0.308147i
$656$	4011.74	+	3366.25i	0.238769	+	0.200351i
$657$	7857.15	+	13609.0i	0.466570	+	0.808123i
$658$	−6205.53	+	10748.3i	−0.367655	+	0.636796i
$659$	12383.6	−	4507.25i	0.732011	−	0.266430i	0.0509954	−	0.998699i	$-0.483761\pi$
$659$	12383.6	−	4507.25i	0.732011	−	0.266430i	0.681016	+	0.732269i	$0.261538\pi$
$660$	−307.389	−	1743.29i	−0.0181290	−	0.102814i
$661$	189.669	−	1075.66i	0.0111607	−	0.0632957i	−0.978719	−	0.205206i	$-0.934213\pi$
$661$	189.669	−	1075.66i	0.0111607	−	0.0632957i	0.989879	+	0.141911i	$0.0453246\pi$
$662$	3156.37	+	1148.82i	0.185311	+	0.0674476i
$663$	−1623.79	+	1362.52i	−0.0951170	+	0.0798127i
$664$	9076.99			0.530505
$665$	−16512.0	−	7066.97i	−0.962869	−	0.412098i
$666$	5298.77			0.308293
$667$	3316.72	−	2783.06i	0.192539	−	0.161560i
$668$	673.349	+	245.079i	0.0390010	+	0.0141952i
$669$	−704.180	+	3993.60i	−0.0406953	+	0.230795i
$670$	1233.21	+	6993.90i	0.0711092	+	0.403280i
$671$	−9822.73	+	3575.18i	−0.565130	+	0.205690i
$672$	−1021.97	+	1770.10i	−0.0586655	+	0.101612i
$673$	13544.6	+	23460.0i	0.775792	+	1.34371i	0.934348	+	0.356361i	$0.115983\pi$
$673$	13544.6	+	23460.0i	0.775792	+	1.34371i	−0.158557	+	0.987350i	$0.550684\pi$
$674$	12962.7	+	10877.0i	0.740808	+	0.621612i
$675$	303.136	+	254.361i	0.0172855	+	0.0145042i
$676$	4291.60	+	7433.27i	0.244174	+	0.422922i
$677$	−1141.85	+	1977.74i	−0.0648225	+	0.112276i	−0.896615	−	0.442810i	$-0.853981\pi$
$677$	−1141.85	+	1977.74i	−0.0648225	+	0.112276i	0.831793	+	0.555086i	$0.187315\pi$
$678$	−1791.84	+	652.175i	−0.101497	+	0.0369419i
$679$	−1738.92	−	9861.88i	−0.0982819	−	0.557385i
$680$	−1397.26	+	7924.23i	−0.0787975	+	0.446883i
$681$	−4214.91	−	1534.10i	−0.237174	−	0.0863244i
$682$	5517.57	−	4629.79i	0.309793	−	0.259947i
$683$	−13754.9			−0.770595			−0.385298	−	0.922792i	$-0.625901\pi$
$683$	−13754.9			−0.770595			−0.385298	+	0.922792i	$0.625901\pi$
$684$	−4348.58	+	3256.65i	−0.243088	+	0.182048i
$685$	−27519.4			−1.53498
$686$	−9050.90	+	7594.61i	−0.503739	+	0.422687i
$687$	−4778.21	−	1739.13i	−0.265357	−	0.0965820i
$688$	649.252	−	3682.09i	0.0359775	−	0.204039i
$689$	−662.932	−	3759.67i	−0.0366556	−	0.207884i
$690$	−6500.67	+	2366.05i	−0.358661	+	0.130542i
$691$	536.351	−	928.986i	0.0295278	−	0.0511437i	−0.850884	−	0.525354i	$-0.823933\pi$
$691$	536.351	−	928.986i	0.0295278	−	0.0511437i	0.880412	+	0.474210i	$0.157266\pi$
$692$	877.848	+	1520.48i	0.0482237	+	0.0835259i
$693$	3030.52	+	2542.90i	0.166118	+	0.139390i
$694$	6586.16	+	5526.45i	0.360241	+	0.302278i
$695$	10272.4	+	17792.4i	0.560655	+	0.971082i
$696$	586.709	−	1016.21i	0.0319528	−	0.0553439i
$697$	27985.0	−	10185.7i	1.52082	−	0.553532i
$698$	−1209.92	−	6861.77i	−0.0656103	−	0.372094i
$699$	−1142.83	+	6481.30i	−0.0618394	+	0.350709i
$700$	−206.511	−	75.1637i	−0.0111505	−	0.00405846i
$701$	−1478.18	+	1240.34i	−0.0796434	+	0.0668288i	−0.681740	−	0.731594i	$-0.738777\pi$
$701$	−1478.18	+	1240.34i	−0.0796434	+	0.0668288i	0.602097	+	0.798423i	$0.294332\pi$
$702$	2022.14			0.108719
$703$	13359.0	+	739.972i	0.716705	+	0.0396992i
$704$	786.948			0.0421296
$705$	−8721.00	+	7317.79i	−0.465889	+	0.390927i
$706$	−3895.69	−	1417.91i	−0.207672	−	0.0755863i
$707$	−1310.95	+	7434.75i	−0.0697359	+	0.395492i
$708$	669.262	+	3795.57i	0.0355260	+	0.201478i
$709$	−299.802	+	109.119i	−0.0158805	+	0.00578004i	−0.349948	−	0.936769i	$-0.613801\pi$
$709$	−299.802	+	109.119i	−0.0158805	+	0.00578004i	0.334068	+	0.942549i	$0.391579\pi$
$710$	5795.05	−	10037.3i	0.306316	−	0.530555i
$711$	3735.23	+	6469.61i	0.197021	+	0.341251i
$712$	8594.08	+	7211.29i	0.452355	+	0.379571i
$713$	−21562.6	−	18093.2i	−1.13258	−	0.950343i
$714$	5811.63	+	10066.0i	0.304615	+	0.527608i
$715$	486.302	−	842.300i	0.0254359	−	0.0440563i
$716$	3243.10	−	1180.39i	0.169274	−	0.0616107i
$717$	−2348.59	−	13319.5i	−0.122329	−	0.693762i
$718$	−45.6167	+	258.705i	−0.00237103	+	0.0134468i
$719$	−30787.6	−	11205.8i	−1.59692	−	0.581230i	−0.618123	−	0.786082i	$-0.712107\pi$
$719$	−30787.6	−	11205.8i	−1.59692	−	0.581230i	−0.978793	+	0.204852i	$0.934329\pi$
$720$	2222.01	−	1864.49i	0.115013	−	0.0965074i
$721$	28643.4			1.47953
$722$	−11418.2	+	7603.21i	−0.588560	+	0.391914i
$723$	14801.1			0.761351
$724$	3811.62	−	3198.33i	0.195660	−	0.164178i
$725$	118.557	+	43.1513i	0.00607325	+	0.00221048i
$726$	1334.04	−	7565.72i	0.0681968	−	0.386763i
$727$	5357.94	+	30386.4i	0.273335	+	1.55016i	0.744200	+	0.667957i	$0.232831\pi$
$727$	5357.94	+	30386.4i	0.273335	+	1.55016i	−0.470864	+	0.882206i	$0.656058\pi$
$728$	−1055.29	+	384.093i	−0.0537246	+	0.0195542i
$729$	−6352.13	+	11002.2i	−0.322722	+	0.558971i
$730$	−10592.3	−	18346.5i	−0.537041	−	0.930183i
$731$	−16287.7	−	13667.0i	−0.824105	−	0.691506i
$732$	8481.10	+	7116.49i	0.428238	+	0.359335i
$733$	−11906.6	−	20622.9i	−0.599976	−	1.03919i	−0.992824	−	0.119585i	$-0.961844\pi$
$733$	−11906.6	−	20622.9i	−0.599976	−	1.03919i	0.392848	−	0.919603i	$-0.371490\pi$
$734$	6631.56	−	11486.2i	0.333481	−	0.577607i
$735$	1416.18	−	515.448i	0.0710702	−	0.0258674i
$736$	−534.035	−	3028.66i	−0.0267456	−	0.151682i
$737$	685.866	−	3889.74i	0.0342798	−	0.194410i
$738$	−10088.2	−	3671.79i	−0.503185	−	0.183144i
$739$	27459.1	−	23040.9i	1.36685	−	1.14692i	0.393047	−	0.919519i	$-0.371421\pi$
$739$	27459.1	−	23040.9i	1.36685	−	1.14692i	0.973801	−	0.227403i	$-0.0730233\pi$
$740$	−7143.36			−0.354858
$741$	1926.45	+	106.709i	0.0955062	+	0.00529022i
$742$	−20934.0			−1.03573
$743$	18587.0	−	15596.3i	0.917753	−	0.770086i	−0.0558255	−	0.998441i	$-0.517779\pi$
$743$	18587.0	−	15596.3i	0.917753	−	0.770086i	0.973578	+	0.228355i	$0.0733346\pi$
$744$	−7168.56	−	2609.14i	−0.353242	−	0.128570i
$745$	5098.82	−	28916.8i	0.250747	−	1.42206i
$746$	−968.801	−	5494.34i	−0.0475473	−	0.269654i
$747$	−17485.4	+	6364.16i	−0.856434	+	0.311717i
$748$	2237.57	−	3875.59i	0.109377	−	0.189446i
$749$	13797.5	+	23898.0i	0.673099	+	1.16584i
$750$	−7047.08	−	5913.20i	−0.343097	−	0.287893i
$751$	−8912.16	−	7478.19i	−0.433035	−	0.363359i	0.400060	−	0.916489i	$-0.368989\pi$
$751$	−8912.16	−	7478.19i	−0.433035	−	0.363359i	−0.833095	+	0.553129i	$0.813434\pi$
$752$	−2530.52	−	4382.99i	−0.122711	−	0.212541i
$753$	4066.76	−	7043.84i	0.196814	−	0.340892i
$754$	605.838	−	220.507i	0.0292617	−	0.0106504i
$755$	2811.39	+	15944.2i	0.135519	+	0.768566i
$756$	1925.46	−	10919.8i	0.0926300	−	0.525331i
$757$	15948.3	+	5804.71i	0.765721	+	0.278700i	0.695206	−	0.718811i	$-0.255313\pi$
$757$	15948.3	+	5804.71i	0.765721	+	0.278700i	0.0705158	+	0.997511i	$0.477535\pi$
$758$	10793.8	−	9057.07i	0.517214	−	0.433994i
$759$	3847.45			0.183997
$760$	5862.38	−	4390.34i	0.279804	−	0.209545i
$761$	14733.7			0.701836			0.350918	−	0.936406i	$-0.385870\pi$
$761$	14733.7			0.701836			0.350918	+	0.936406i	$0.385870\pi$
$762$	−7086.23	+	5946.06i	−0.336886	+	0.282681i
$763$	39690.9	+	14446.3i	1.88323	+	0.685440i
$764$	1921.05	−	10894.8i	0.0909703	−	0.515918i
$765$	−2864.33	−	16244.4i	−0.135373	−	0.767737i
$766$	−5107.16	+	1858.85i	−0.240900	+	0.0876803i
$767$	−1058.80	+	1833.89i	−0.0498449	+	0.0863339i
$768$	−416.743	−	721.819i	−0.0195806	−	0.0339146i
$769$	−7550.14	−	6335.32i	−0.354051	−	0.297084i	0.448363	−	0.893851i	$-0.352007\pi$
$769$	−7550.14	−	6335.32i	−0.354051	−	0.297084i	−0.802414	+	0.596767i	$0.796452\pi$
$770$	−4085.49	−	3428.13i	−0.191209	−	0.160443i
$771$	−814.803	−	1411.28i	−0.0380602	−	0.0659222i
$772$	813.241	−	1408.57i	0.0379134	−	0.0656680i
$773$	9147.81	−	3329.53i	0.425645	−	0.154922i	−0.120310	−	0.992736i	$-0.538389\pi$
$773$	9147.81	−	3329.53i	0.425645	−	0.154922i	0.545956	+	0.837814i	$0.316167\pi$
$774$	1330.95	+	7548.18i	0.0618087	+	0.350535i
$775$	142.431	−	807.769i	0.00660166	−	0.0374399i
$776$	3837.29	+	1396.66i	0.177514	+	0.0646098i
$777$	−7904.58	+	6632.73i	−0.364962	+	0.306239i
$778$	2330.30			0.107385
$779$	−24921.0	−	10665.9i	−1.14620	−	0.490560i
$780$	−1030.12			−0.0472875
$781$	−4937.90	+	4143.39i	−0.226238	+	0.189836i
$782$	−16434.1	−	5981.53i	−0.751513	−	0.273528i
$783$	−1105.40	+	6269.05i	−0.0504519	+	0.286127i
$784$	116.340	+	659.799i	0.00529976	+	0.0300564i
$785$	27298.8	−	9935.94i	1.24119	−	0.451757i
$786$	2366.88	−	4099.56i	0.107409	−	0.186039i
$787$	8158.66	+	14131.2i	0.369536	+	0.640055i	0.989493	−	0.144581i	$-0.0461833\pi$
$787$	8158.66	+	14131.2i	0.369536	+	0.640055i	−0.619957	+	0.784636i	$0.712850\pi$
$788$	10104.5	+	8478.71i	0.456801	+	0.383301i
$789$	−15270.0	−	12813.1i	−0.689009	−	0.578147i
$790$	−5035.53	−	8721.79i	−0.226780	−	0.392794i
$791$	−2872.46	+	4975.24i	−0.129119	+	0.223640i
$792$	−1515.93	+	551.754i	−0.0680129	+	0.0247547i
$793$	1056.30	+	5990.56i	0.0473016	+	0.268261i
$794$	−4271.97	+	24227.5i	−0.190940	+	1.08288i
$795$	−18044.4	−	6567.61i	−0.804991	−	0.292993i
$796$	−1452.74	+	1218.99i	−0.0646871	+	0.0542789i
$797$	−9154.08			−0.406844			−0.203422	−	0.979091i	$-0.565206\pi$
$797$	−9154.08			−0.406844			−0.203422	+	0.979091i	$0.565206\pi$
$798$	2410.59	−	10301.5i	0.106935	−	0.456979i
$799$	−28780.7			−1.27433
$800$	68.6502	−	57.6043i	0.00303394	−	0.00254578i
$801$	−21611.2	−	7865.83i	−0.953301	−	0.346973i
$802$	2585.32	−	14662.1i	0.113829	−	0.645557i
$803$	2045.94	+	11603.1i	0.0899126	+	0.509919i
$804$	−3931.04	+	1430.78i	−0.172434	+	0.0627608i
$805$	−10421.1	+	18049.9i	−0.456267	+	0.790278i
$806$	−2095.72	−	3629.90i	−0.0915864	−	0.158632i
$807$	11688.8	+	9808.08i	0.509871	+	0.427832i
$808$	−2358.30	−	1978.85i	−0.102679	−	0.0861582i
$809$	21125.8	+	36590.9i	0.918099	+	1.59019i	0.802300	+	0.596921i	$0.203609\pi$
$809$	21125.8	+	36590.9i	0.918099	+	1.59019i	0.115799	+	0.993273i	$0.463057\pi$
$810$	190.739	−	330.369i	0.00827392	−	0.0143309i
$811$	−36236.7	+	13189.1i	−1.56898	+	0.571062i	−0.972771	−	0.231767i	$-0.925549\pi$
$811$	−36236.7	+	13189.1i	−1.56898	+	0.571062i	−0.596209	+	0.802829i	$0.703327\pi$
$812$	−613.895	−	3481.57i	−0.0265314	−	0.150467i
$813$	−1574.44	+	8929.12i	−0.0679190	+	0.385188i
$814$	3733.27	+	1358.80i	0.160751	+	0.0585085i
$815$	−7573.79	+	6355.17i	−0.325520	+	0.273143i
$816$	−4739.79			−0.203340
$817$	2301.41	+	19215.9i	0.0985510	+	0.822864i
$818$	−2687.13			−0.114857
$819$	1763.54	−	1479.79i	0.0752420	−	0.0631355i
$820$	13600.0	+	4950.00i	0.579187	+	0.210807i
$821$	−3113.69	+	17658.6i	−0.132361	+	0.750657i	0.844300	+	0.535871i	$0.180017\pi$
$821$	−3113.69	+	17658.6i	−0.132361	+	0.750657i	−0.976661	+	0.214786i	$0.931095\pi$
$822$	−2814.90	−	15964.1i	−0.119441	−	0.677386i
$823$	9595.55	−	3492.50i	0.406416	−	0.147923i	−0.130720	−	0.991419i	$-0.541729\pi$
$823$	9595.55	−	3492.50i	0.406416	−	0.147923i	0.537135	+	0.843496i	$0.319507\pi$
$824$	−5840.18	+	10115.5i	−0.246908	+	0.427657i
$825$	56.0572	+	97.0940i	0.00236565	+	0.00409743i
$826$	8895.10	+	7463.88i	0.374698	+	0.314409i
$827$	24452.2	+	20517.8i	1.02816	+	0.862726i	0.990630	−	0.136570i	$-0.0436078\pi$
$827$	24452.2	+	20517.8i	1.02816	+	0.862726i	0.0375260	+	0.999296i	$0.488052\pi$
$828$	3152.22	+	5459.81i	0.132303	+	0.229156i
$829$	21246.4	−	36799.8i	0.890130	−	1.54175i	0.0504120	−	0.998729i	$-0.483947\pi$
$829$	21246.4	−	36799.8i	0.890130	−	1.54175i	0.839718	−	0.543022i	$-0.182720\pi$
$830$	23572.3	−	8579.62i	0.985792	−	0.358799i
$831$	298.703	+	1694.03i	0.0124692	+	0.0707163i
$832$	79.5217	−	450.990i	0.00331361	−	0.0187924i
$833$	3580.20	+	1303.09i	0.148915	+	0.0542008i
$834$	−9270.64	+	7778.99i	−0.384911	+	0.322979i
$835$	1980.29			0.0820728
$836$	−3898.93	+	1179.35i	−0.161301	+	0.0487903i
$837$	41385.0			1.70905
$838$	−23930.7	+	20080.3i	−0.986483	+	0.827758i
$839$	−1242.57	−	452.258i	−0.0511302	−	0.0186099i	0.316328	−	0.948650i	$-0.397550\pi$
$839$	−1242.57	−	452.258i	−0.0511302	−	0.0186099i	−0.367459	+	0.930040i	$0.619772\pi$
$840$	−980.871	+	5562.80i	−0.0402896	+	0.228494i
$841$	−3882.67	−	22019.7i	−0.159198	−	0.902854i
$842$	−9961.00	+	3625.51i	−0.407694	+	0.148389i
$843$	13933.1	−	24132.8i	0.569255	−	0.985978i
$844$	−291.258	−	504.474i	−0.0118786	−	0.0205743i
$845$	18171.0	+	15247.2i	0.739763	+	0.620735i
$846$	7947.69	+	6668.91i	0.322987	+	0.271019i
$847$	−11572.8	−	20044.7i	−0.469478	−	0.813159i
$848$	4268.28	−	7392.88i	0.172846	−	0.299378i
$849$	−16112.1	+	5864.34i	−0.651316	+	0.237060i
$850$	−88.4950	−	501.880i	−0.00357101	−	0.0202522i
$851$	2696.05	−	15290.1i	0.108601	−	0.615906i
$852$	6415.44	+	2335.03i	0.257969	+	0.0938929i
$853$	−21479.8	+	18023.7i	−0.862197	+	0.723469i	−0.962440	−	0.271494i	$-0.912482\pi$
$853$	−21479.8	+	18023.7i	−0.862197	+	0.723469i	0.100243	+	0.994963i	$0.468038\pi$
$854$	33355.6			1.33654
$855$	−8214.75	+	12567.6i	−0.328583	+	0.502693i
$856$	−11252.8			−0.449316
$857$	−2940.63	+	2467.49i	−0.117211	+	0.0983520i	−0.699509	−	0.714623i	$-0.746598\pi$
$857$	−2940.63	+	2467.49i	−0.117211	+	0.0983520i	0.582298	+	0.812975i	$0.302154\pi$
$858$	538.363	+	195.948i	0.0214212	+	0.00779669i
$859$	−888.009	+	5036.15i	−0.0352718	+	0.200036i	−0.997352	−	0.0727321i	$-0.976828\pi$
$859$	−888.009	+	5036.15i	−0.0352718	+	0.200036i	0.962080	+	0.272769i	$0.0879393\pi$
$860$	−1794.27	−	10175.8i	−0.0711444	−	0.403480i
$861$	19645.4	−	7150.36i	0.777601	−	0.283024i
$862$	3263.24	−	5652.10i	0.128940	−	0.223331i
$863$	−11459.5	−	19848.4i	−0.452010	−	0.782904i	0.546501	−	0.837458i	$-0.315959\pi$
$863$	−11459.5	−	19848.4i	−0.452010	−	0.782904i	−0.998511	+	0.0545548i	$0.982626\pi$
$864$	3463.77	+	2906.45i	0.136389	+	0.114444i
$865$	3716.88	+	3118.83i	0.146101	+	0.122594i
$866$	−8733.63	−	15127.1i	−0.342703	−	0.593579i
$867$	−5479.03	+	9489.95i	−0.214622	+	0.371737i
$868$	−21597.5	+	7860.83i	−0.844546	+	0.307390i
$869$	972.627	+	5516.04i	0.0379679	+	0.215327i
$870$	563.116	−	3193.59i	0.0219442	−	0.124451i
$871$	−2159.86	−	786.123i	−0.0840228	−	0.0305818i
$872$	−13194.4	+	11071.4i	−0.512407	+	0.429960i
$873$	−8371.18			−0.324538
$874$	7184.75	+	14205.2i	0.278064	+	0.549768i
$875$	−27715.7			−1.07081
$876$	9559.37	−	8021.26i	0.368700	−	0.309376i
$877$	11242.3	+	4091.88i	0.432870	+	0.157552i	0.549259	−	0.835652i	$-0.314910\pi$
$877$	11242.3	+	4091.88i	0.432870	+	0.157552i	−0.116389	+	0.993204i	$0.537132\pi$
$878$	−4664.17	+	26451.8i	−0.179280	+	1.01675i
$879$	−65.4561	−	371.220i	−0.00251169	−	0.0142445i
$880$	2043.65	−	743.828i	0.0782857	−	0.0284937i
$881$	22024.3	−	38147.1i	0.842243	−	1.45881i	−0.0457513	−	0.998953i	$-0.514568\pi$
$881$	22024.3	−	38147.1i	0.842243	−	1.45881i	0.887994	−	0.459855i	$-0.152098\pi$
$882$	−686.717	−	1189.43i	−0.0262165	−	0.0454083i
$883$	−20866.4	−	17509.0i	−0.795257	−	0.667299i	0.151784	−	0.988414i	$-0.451498\pi$
$883$	−20866.4	−	17509.0i	−0.795257	−	0.667299i	−0.947040	+	0.321114i	$0.895943\pi$
$884$	−1994.94	−	1673.96i	−0.0759018	−	0.0636892i
$885$	5325.63	+	9224.25i	0.202281	+	0.350362i
$886$	−5286.41	+	9156.34i	−0.200452	+	0.347193i
$887$	−32713.6	+	11906.8i	−1.23835	+	0.450722i	−0.876449	−	0.481495i	$-0.840094\pi$
$887$	−32713.6	+	11906.8i	−1.23835	+	0.450722i	−0.361900	+	0.932217i	$0.617872\pi$
$888$	−730.678	−	4143.88i	−0.0276126	−	0.156599i
$889$	−4839.53	+	27446.3i	−0.182579	+	1.03546i
$890$	29134.4	+	10604.1i	1.09729	+	0.399381i
$891$	−162.527	+	136.376i	−0.00611094	+	0.00512768i
$892$	−4982.13			−0.187011
$893$	19106.0	+	17923.2i	0.715965	+	0.671642i
$894$	17296.3			0.647063
$895$	7306.39	−	6130.79i	0.272878	−	0.228972i
$896$	−2359.69	−	858.857i	−0.0879818	−	0.0320228i
$897$	388.788	−	2204.93i	0.0144719	−	0.0820740i
$898$	3586.34	+	20339.2i	0.133271	+	0.755820i
$899$	12399.1	−	4512.89i	0.459991	−	0.167423i
$900$	−91.8555	+	159.098i	−0.00340205	+	0.00589253i
$901$	−24272.5	−	42041.2i	−0.897485	−	1.55449i
$902$	−6166.08	−	5173.95i	−0.227614	−	0.190991i
$903$	−11433.9	−	9594.18i	−0.421369	−	0.353571i
$904$	−1171.34	−	2028.83i	−0.0430955	−	0.0746436i
$905$	6875.43	−	11908.6i	0.252538	−	0.437409i
$906$	−8961.67	+	3261.78i	−0.328622	+	0.119609i
$907$	3632.55	+	20601.2i	0.132984	+	0.754193i	0.976242	+	0.216683i	$0.0695237\pi$
$907$	3632.55	+	20601.2i	0.132984	+	0.754193i	−0.843258	+	0.537510i	$0.819365\pi$
$908$	956.918	−	5426.95i	0.0349740	−	0.198348i
$909$	5930.33	+	2158.47i	0.216388	+	0.0787588i
$910$	−2377.46	+	1994.93i	−0.0866066	+	0.0726716i
$911$	757.298			0.0275416			0.0137708	−	0.999905i	$-0.495616\pi$
$911$	757.298			0.0275416			0.0137708	+	0.999905i	$0.495616\pi$
$912$	3146.50	+	2951.71i	0.114244	+	0.107172i
$913$	−13951.4			−0.505722
$914$	14996.5	−	12583.6i	0.542714	−	0.455391i
$915$	28751.4	+	10464.6i	1.03879	+	0.378088i
$916$	1084.81	−	6152.24i	0.0391299	−	0.221917i
$917$	−2476.55	−	14045.2i	−0.0891853	−	0.505795i
$918$	24162.5	−	8794.44i	0.868717	−	0.316187i
$919$	−12123.8	+	20999.1i	−0.435177	+	0.753750i	−0.997310	−	0.0732976i	$-0.976648\pi$
$919$	−12123.8	+	20999.1i	−0.435177	+	0.753750i	0.562133	+	0.827047i	$0.309981\pi$
$920$	−4249.56	−	7360.46i	−0.152287	−	0.263769i
$921$	−22608.4	−	18970.7i	−0.808871	−	0.678724i
$922$	4156.28	+	3487.54i	0.148460	+	0.124573i
$923$	1875.55	+	3248.55i	0.0668845	+	0.115847i
$924$	1570.77	−	2720.66i	0.0559249	−	0.0968647i
$925$	425.140	−	154.738i	0.0151119	−	0.00550028i
$926$	−4469.93	−	25350.3i	−0.158630	−	0.899634i
$927$	4157.90	−	23580.6i	0.147317	−	0.835479i
$928$	1354.69	+	493.068i	0.0479202	+	0.0174415i
$929$	12030.4	−	10094.7i	0.424871	−	0.356509i	−0.405141	−	0.914254i	$-0.632778\pi$
$929$	12030.4	−	10094.7i	0.424871	−	0.356509i	0.830013	+	0.557745i	$0.188333\pi$
$930$	−21082.4			−0.743355
$931$	−1565.21	−	3094.62i	−0.0550995	−	0.108939i
$932$	−8085.61			−0.284177
$933$	−15833.7	+	13286.0i	−0.555595	+	0.466200i
$934$	25653.5	+	9337.11i	0.898724	+	0.327109i
$935$	2147.59	−	12179.6i	0.0751164	−	0.426006i
$936$	163.017	+	924.516i	0.00569271	+	0.0322850i
$937$	−8791.94	+	3200.00i	−0.306532	+	0.111568i	−0.490706	−	0.871325i	$-0.663261\pi$
$937$	−8791.94	+	3200.00i	−0.306532	+	0.111568i	0.184174	+	0.982894i	$0.441039\pi$
$938$	−6301.77	+	10915.0i	−0.219360	+	0.379943i
$939$	−1424.43	−	2467.19i	−0.0495044	−	0.0857442i
$940$	−10714.4	−	8990.46i	−0.371772	−	0.311954i
$941$	29355.5	+	24632.2i	1.01696	+	0.853332i	0.989243	−	0.146284i	$-0.0467313\pi$
$941$	29355.5	+	24632.2i	1.01696	+	0.853332i	0.0277186	+	0.999616i	$0.491176\pi$
$942$	8556.19	+	14819.8i	0.295940	+	0.512584i
$943$	−15728.2	+	27242.0i	−0.543139	+	0.940744i
$944$	−4449.53	+	1619.50i	−0.153411	+	0.0558370i
$945$	−5321.20	−	30178.0i	−0.183173	−	1.03883i
$946$	−997.906	+	5659.41i	−0.0342967	+	0.194507i
$947$	15996.7	+	5822.32i	0.548915	+	0.199789i	0.601564	−	0.798824i	$-0.294544\pi$
$947$	15996.7	+	5822.32i	0.548915	+	0.199789i	−0.0526493	+	0.998613i	$0.516767\pi$
$948$	4544.46	−	3813.25i	0.155693	−	0.130642i
$949$	6856.35			0.234527
$950$	−253.799	+	388.282i	−0.00866771	+	0.0132606i
$951$	18247.6			0.622208
$952$	−10939.2	+	9179.05i	−0.372416	+	0.312494i
$953$	−33829.4	−	12312.9i	−1.14989	−	0.418524i	−0.304411	−	0.952541i	$-0.598460\pi$
$953$	−33829.4	−	12312.9i	−1.14989	−	0.418524i	−0.845474	+	0.534017i	$0.820682\pi$
$954$	−3038.79	+	17233.8i	−0.103128	+	0.584870i
$955$	−5309.02	−	30108.9i	−0.179891	−	1.02021i
$956$	15614.4	−	5683.18i	0.528249	−	0.192267i
$957$	−901.776	+	1561.92i	−0.0304601	+	0.0527584i
$958$	−2337.06	−	4047.91i	−0.0788174	−	0.136516i
$959$	−37412.6	−	31392.9i	−1.25977	−	1.05707i
$960$	−1764.52	−	1480.61i	−0.0593225	−	0.0497775i
$961$	−27995.5	−	48489.6i	−0.939729	−	1.62766i
$962$	1155.96	−	2002.19i	0.0387419	−	0.0671030i
$963$	21676.8	−	7889.72i	0.725365	−	0.264011i
$964$	3157.66	+	17908.0i	0.105499	+	0.598316i
$965$	780.538	−	4426.65i	0.0260377	−	0.147667i
$966$	−11536.7	−	4199.02i	−0.384252	−	0.139856i
$967$	30893.7	−	25922.9i	1.02738	−	0.862073i	0.0368420	−	0.999321i	$-0.488270\pi$
$967$	30893.7	−	25922.9i	1.02738	−	0.862073i	0.990537	+	0.137248i	$0.0438257\pi$
$968$	9438.45			0.313392
$969$	23483.3	−	7103.24i	0.778526	−	0.235489i
$970$	11285.3			0.373556
$971$	−11843.2	+	9937.64i	−0.391418	+	0.328439i	−0.817165	−	0.576403i	$-0.804456\pi$
$971$	−11843.2	+	9937.64i	−0.391418	+	0.328439i	0.425747	+	0.904842i	$0.360011\pi$
$972$	−14129.0	−	5142.55i	−0.466244	−	0.169699i
$973$	−6331.36	+	35907.0i	−0.208607	+	1.18307i
$974$	−3072.77	−	17426.5i	−0.101086	−	0.573288i
$975$	61.3080	−	22.3143i	0.00201377	−	0.000732953i
$976$	−6800.96	+	11779.6i	−0.223047	+	0.386328i
$977$	−29526.3	−	51141.1i	−0.966869	−	1.67467i	−0.704507	−	0.709697i	$-0.748832\pi$
$977$	−29526.3	−	51141.1i	−0.966869	−	1.67467i	−0.262363	−	0.964969i	$-0.584502\pi$
$978$	−4461.35	−	3743.52i	−0.145867	−	0.122397i
$979$	−13209.2	−	11083.8i	−0.431223	−	0.361839i
$980$	925.774	+	1603.49i	0.0301763	+	0.0522669i
$981$	17654.4	−	30578.3i	0.574579	−	0.995200i
$982$	622.291	−	226.496i	0.0202221	−	0.00736025i
$983$	4437.20	+	25164.6i	0.143972	+	0.816507i	0.968187	+	0.250229i	$0.0805060\pi$
$983$	4437.20	+	25164.6i	0.143972	+	0.816507i	−0.824214	+	0.566278i	$0.808383\pi$
$984$	−1480.39	+	8395.73i	−0.0479606	+	0.271998i
$985$	34254.9	+	12467.8i	1.10807	+	0.403306i
$986$	6280.15	−	5269.67i	0.202840	−	0.170203i
$987$	−20204.0			−0.651570
$988$	281.881	+	2353.60i	0.00907676	+	0.0757876i
$989$	22458.1			0.722068
$990$	−3415.25	+	2865.73i	−0.109640	+	0.0919989i
$991$	34077.8	+	12403.3i	1.09235	+	0.397582i	0.824490	−	0.565876i	$-0.191462\pi$
$991$	34077.8	+	12403.3i	1.09235	+	0.397582i	0.267858	+	0.963458i	$0.413684\pi$
$992$	1627.49	−	9229.95i	0.0520896	−	0.295415i
$993$	949.511	+	5384.94i	0.0303442	+	0.172091i
$994$	19328.5	−	7034.99i	0.616763	−	0.224483i
$995$	−2620.46	+	4538.78i	−0.0834917	+	0.144612i
$996$	7388.22	+	12796.8i	0.235045	+	0.407110i
$997$	29885.4	+	25076.8i	0.949328	+	0.796581i	0.979184	−	0.202973i	$-0.0650604\pi$
$997$	29885.4	+	25076.8i	0.949328	+	0.796581i	−0.0298559	+	0.999554i	$0.509505\pi$
$998$	−28711.2	−	24091.6i	−0.910660	−	0.764134i
$999$	11413.6	+	19769.0i	0.361472	+	0.626088i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.4.e.b.25.1	✓	18
19.4	even	9		722.4.a.t.1.7		9
19.15	odd	18		722.4.a.u.1.3		9
19.16	even	9	inner	38.4.e.b.35.1	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.4.e.b.25.1	✓	18	1.1	even	1	trivial
38.4.e.b.35.1	yes	18	19.16	even	9	inner
722.4.a.t.1.7		9	19.4	even	9
722.4.a.u.1.3		9	19.15	odd	18

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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	38.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.53209 + 1.28558i) q^{2} +(-3.05945 - 1.11355i) q^{3} +(0.694593 - 3.93923i) q^{4} +(-1.91957 - 10.8864i) q^{5} +(6.11891 - 2.22710i) q^{6} +(9.80910 - 16.9899i) q^{7} +(4.00000 + 6.92820i) q^{8} +(-12.5629 - 10.5416i) q^{9} +O(q^{10})\)	\(q+(-1.53209 + 1.28558i) q^{2} +(-3.05945 - 1.11355i) q^{3} +(0.694593 - 3.93923i) q^{4} +(-1.91957 - 10.8864i) q^{5} +(6.11891 - 2.22710i) q^{6} +(9.80910 - 16.9899i) q^{7} +(4.00000 + 6.92820i) q^{8} +(-12.5629 - 10.5416i) q^{9} +(16.9363 + 14.2112i) q^{10} +(-6.14803 - 10.6487i) q^{11} +(-6.51160 + 11.2784i) q^{12} +(-6.72390 + 2.44730i) q^{13} +(6.81333 + 38.6403i) q^{14} +(-6.24975 + 35.4441i) q^{15} +(-15.0351 - 5.47232i) q^{16} +(-69.7004 + 58.4856i) q^{17} +32.7995 q^{18} +(82.6923 + 4.58044i) q^{19} -44.2176 q^{20} +(-48.9295 + 41.0567i) q^{21} +(23.1090 + 8.41100i) q^{22} +(16.6886 - 94.6457i) q^{23} +(-4.52291 - 25.6507i) q^{24} +(2.63162 - 0.957832i) q^{25} +(7.15543 - 12.3936i) q^{26} +(70.6505 + 122.370i) q^{27} +(-60.1136 - 50.4413i) q^{28} +(34.5111 + 28.9583i) q^{29} +(-35.9909 - 62.3381i) q^{30} +(146.443 - 253.646i) q^{31} +(30.0702 - 10.9446i) q^{32} +(6.95175 + 39.4253i) q^{33} +(31.5996 - 179.210i) q^{34} +(-203.788 - 74.1729i) q^{35} +(-50.2518 + 42.1662i) q^{36} +161.550 q^{37} +(-132.580 + 99.2896i) q^{38} +23.2967 q^{39} +(67.7452 - 56.8450i) q^{40} +(-307.571 - 111.947i) q^{41} +(22.1828 - 125.805i) q^{42} +(40.5783 + 230.131i) q^{43} +(-46.2181 + 16.8220i) q^{44} +(-90.6446 + 157.001i) q^{45} +(96.1058 + 166.460i) q^{46} +(242.311 + 203.323i) q^{47} +(39.9054 + 33.4846i) q^{48} +(-20.9368 - 36.2636i) q^{49} +(-2.80051 + 4.85063i) q^{50} +(278.372 - 101.319i) q^{51} +(4.97011 + 28.1869i) q^{52} +(-92.6474 + 525.430i) q^{53} +(-265.559 - 96.6556i) q^{54} +(-104.125 + 87.3712i) q^{55} +156.946 q^{56} +(-247.893 - 106.096i) q^{57} -90.1021 q^{58} +(226.705 - 190.228i) q^{59} +(135.282 + 49.2384i) q^{60} +(147.622 - 837.205i) q^{61} +(101.718 + 576.872i) q^{62} +(-302.331 + 110.039i) q^{63} +(-32.0000 + 55.4256i) q^{64} +(39.5494 + 68.5016i) q^{65} +(-61.3349 - 51.4661i) q^{66} +(246.069 + 206.477i) q^{67} +(181.975 + 315.189i) q^{68} +(-156.451 + 270.980i) q^{69} +(407.577 - 148.346i) q^{70} +(-91.0318 - 516.267i) q^{71} +(22.7823 - 129.205i) q^{72} +(-900.416 - 327.725i) q^{73} +(-247.510 + 207.685i) q^{74} -9.11792 q^{75} +(75.4809 - 322.563i) q^{76} -241.227 q^{77} +(-35.6925 + 29.9496i) q^{78} +(-428.051 - 155.798i) q^{79} +(-30.7132 + 174.183i) q^{80} +(-2.99623 - 16.9924i) q^{81} +(615.141 - 223.893i) q^{82} +(567.312 - 982.613i) q^{83} +(127.746 + 221.262i) q^{84} +(770.495 + 646.522i) q^{85} +(-358.020 - 300.414i) q^{86} +(-73.3386 - 127.026i) q^{87} +(49.1842 - 85.1896i) q^{88} +(1317.78 - 479.631i) q^{89} +(-62.9611 - 357.070i) q^{90} +(-24.3761 + 138.244i) q^{91} +(-361.240 - 131.480i) q^{92} +(-730.483 + 612.948i) q^{93} -632.630 q^{94} +(-108.869 - 909.018i) q^{95} -104.186 q^{96} +(391.024 - 328.108i) q^{97} +(78.6966 + 28.6432i) q^{98} +(-35.0166 + 198.589i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 6 q^{3} - 12 q^{6} - 33 q^{7} + 72 q^{8} + 42 q^{9}+O(q^{10}) \) 18 * q + 6 * q^3 - 12 * q^6 - 33 * q^7 + 72 * q^8 + 42 * q^9	\( 18 q + 6 q^{3} - 12 q^{6} - 33 q^{7} + 72 q^{8} + 42 q^{9} - 75 q^{11} + 36 q^{12} + 99 q^{13} + 162 q^{14} - 183 q^{15} - 111 q^{17} - 408 q^{18} - 372 q^{19} + 24 q^{20} - 207 q^{21} - 180 q^{22} + 198 q^{23} - 48 q^{24} + 534 q^{25} + 180 q^{26} + 678 q^{27} + 216 q^{28} + 669 q^{29} - 42 q^{31} + 315 q^{33} - 48 q^{34} - 1995 q^{35} + 168 q^{36} - 1056 q^{37} - 180 q^{38} + 1812 q^{39} - 210 q^{41} - 342 q^{42} - 399 q^{43} + 360 q^{44} + 1494 q^{45} + 672 q^{46} + 1149 q^{47} - 192 q^{48} - 858 q^{49} + 1068 q^{50} + 2646 q^{51} - 468 q^{52} - 633 q^{53} - 2898 q^{54} - 3483 q^{55} - 528 q^{56} - 2814 q^{57} + 636 q^{58} + 51 q^{59} - 84 q^{60} - 4104 q^{61} - 1326 q^{62} + 1215 q^{63} - 576 q^{64} + 1755 q^{65} + 2340 q^{66} - 675 q^{67} - 948 q^{68} + 3693 q^{69} + 3990 q^{70} + 2964 q^{71} + 672 q^{72} - 2004 q^{73} - 486 q^{74} - 4446 q^{75} - 408 q^{76} + 5820 q^{77} + 4992 q^{78} + 543 q^{79} + 1722 q^{81} + 420 q^{82} + 381 q^{83} + 1092 q^{84} + 1266 q^{85} - 3396 q^{86} - 4506 q^{87} + 600 q^{88} + 4386 q^{89} - 2148 q^{90} - 1356 q^{91} - 2628 q^{92} - 8604 q^{93} - 3264 q^{94} + 921 q^{95} + 576 q^{96} + 7599 q^{97} - 954 q^{98} - 5055 q^{99}+O(q^{100}) \) 18 * q + 6 * q^3 - 12 * q^6 - 33 * q^7 + 72 * q^8 + 42 * q^9 - 75 * q^11 + 36 * q^12 + 99 * q^13 + 162 * q^14 - 183 * q^15 - 111 * q^17 - 408 * q^18 - 372 * q^19 + 24 * q^20 - 207 * q^21 - 180 * q^22 + 198 * q^23 - 48 * q^24 + 534 * q^25 + 180 * q^26 + 678 * q^27 + 216 * q^28 + 669 * q^29 - 42 * q^31 + 315 * q^33 - 48 * q^34 - 1995 * q^35 + 168 * q^36 - 1056 * q^37 - 180 * q^38 + 1812 * q^39 - 210 * q^41 - 342 * q^42 - 399 * q^43 + 360 * q^44 + 1494 * q^45 + 672 * q^46 + 1149 * q^47 - 192 * q^48 - 858 * q^49 + 1068 * q^50 + 2646 * q^51 - 468 * q^52 - 633 * q^53 - 2898 * q^54 - 3483 * q^55 - 528 * q^56 - 2814 * q^57 + 636 * q^58 + 51 * q^59 - 84 * q^60 - 4104 * q^61 - 1326 * q^62 + 1215 * q^63 - 576 * q^64 + 1755 * q^65 + 2340 * q^66 - 675 * q^67 - 948 * q^68 + 3693 * q^69 + 3990 * q^70 + 2964 * q^71 + 672 * q^72 - 2004 * q^73 - 486 * q^74 - 4446 * q^75 - 408 * q^76 + 5820 * q^77 + 4992 * q^78 + 543 * q^79 + 1722 * q^81 + 420 * q^82 + 381 * q^83 + 1092 * q^84 + 1266 * q^85 - 3396 * q^86 - 4506 * q^87 + 600 * q^88 + 4386 * q^89 - 2148 * q^90 - 1356 * q^91 - 2628 * q^92 - 8604 * q^93 - 3264 * q^94 + 921 * q^95 + 576 * q^96 + 7599 * q^97 - 954 * q^98 - 5055 * q^99

Introduction

L-functions

Modular forms

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