LMFDB - Embedded newform 38.4.e.b.5.1

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			5.1
Root			$-4.21239 + 7.29608i$ of defining polynomial
Character	$\chi$	$=$	38.5
Dual form			38.4.e.b.23.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.87939 - 0.684040i) q^{2} +(-1.31024 + 7.43077i) q^{3} +(3.06418 - 2.57115i) q^{4} +(3.45478 + 2.89891i) q^{5} +(2.62049 + 14.8615i) q^{6} +(4.21085 + 7.29340i) q^{7} +(4.00000 - 6.92820i) q^{8} +(-28.1279 - 10.2377i) q^{9} +O(q^{10})$	\(q+(1.87939 - 0.684040i) q^{2} +(-1.31024 + 7.43077i) q^{3} +(3.06418 - 2.57115i) q^{4} +(3.45478 + 2.89891i) q^{5} +(2.62049 + 14.8615i) q^{6} +(4.21085 + 7.29340i) q^{7} +(4.00000 - 6.92820i) q^{8} +(-28.1279 - 10.2377i) q^{9} +(8.47584 + 3.08495i) q^{10} +(19.9270 - 34.5147i) q^{11} +(15.0908 + 26.1380i) q^{12} +(-12.5243 - 71.0287i) q^{13} +(12.9028 + 10.8267i) q^{14} +(-26.0677 + 21.8734i) q^{15} +(2.77837 - 15.7569i) q^{16} +(-83.5662 + 30.4156i) q^{17} -59.8661 q^{18} +(34.2213 + 75.4182i) q^{19} +18.0396 q^{20} +(-59.7128 + 21.7337i) q^{21} +(13.8412 - 78.4973i) q^{22} +(68.3271 - 57.3332i) q^{23} +(46.2409 + 38.8007i) q^{24} +(-18.1742 - 103.071i) q^{25} +(-72.1244 - 124.923i) q^{26} +(11.0655 - 19.1661i) q^{27} +(31.6552 + 11.5216i) q^{28} +(163.711 + 59.5858i) q^{29} +(-34.0290 + 58.9399i) q^{30} +(27.1416 + 47.0106i) q^{31} +(-5.55674 - 31.5138i) q^{32} +(230.361 + 193.296i) q^{33} +(-136.248 + 114.325i) q^{34} +(-6.59533 + 37.4040i) q^{35} +(-112.511 + 40.9508i) q^{36} -342.543 q^{37} +(115.904 + 118.331i) q^{38} +544.207 q^{39} +(33.9033 - 12.3398i) q^{40} +(-55.4266 + 314.340i) q^{41} +(-97.3567 + 81.6919i) q^{42} +(-155.259 - 130.278i) q^{43} +(-27.6824 - 156.995i) q^{44} +(-67.4975 - 116.909i) q^{45} +(89.1947 - 154.490i) q^{46} +(91.4185 + 33.2736i) q^{47} +(113.446 + 41.2909i) q^{48} +(136.038 - 235.624i) q^{49} +(-104.661 - 181.278i) q^{50} +(-116.519 - 660.813i) q^{51} +(-221.002 - 185.443i) q^{52} +(-324.180 + 272.019i) q^{53} +(7.68604 - 43.5897i) q^{54} +(168.898 - 61.4740i) q^{55} +67.3736 q^{56} +(-605.253 + 155.475i) q^{57} +348.434 q^{58} +(-285.926 + 104.069i) q^{59} +(-23.6363 + 134.048i) q^{60} +(-253.870 + 213.022i) q^{61} +(83.1667 + 69.7851i) q^{62} +(-43.7745 - 248.257i) q^{63} +(-32.0000 - 55.4256i) q^{64} +(162.637 - 281.695i) q^{65} +(565.160 + 205.701i) q^{66} +(-878.531 - 319.759i) q^{67} +(-177.859 + 308.060i) q^{68} +(336.505 + 582.843i) q^{69} +(13.1907 + 74.8079i) q^{70} +(818.667 + 686.944i) q^{71} +(-183.440 + 153.925i) q^{72} +(179.899 - 1020.26i) q^{73} +(-643.770 + 234.313i) q^{74} +789.708 q^{75} +(298.772 + 143.106i) q^{76} +335.639 q^{77} +(1022.78 - 372.260i) q^{78} +(18.3231 - 103.915i) q^{79} +(55.2765 - 46.3825i) q^{80} +(-491.191 - 412.158i) q^{81} +(110.853 + 628.679i) q^{82} +(436.673 + 756.340i) q^{83} +(-127.090 + 220.126i) q^{84} +(-376.875 - 137.171i) q^{85} +(-380.908 - 138.639i) q^{86} +(-657.269 + 1138.42i) q^{87} +(-159.416 - 276.117i) q^{88} +(27.6387 + 156.747i) q^{89} +(-206.824 - 173.546i) q^{90} +(465.303 - 390.435i) q^{91} +(61.9540 - 351.358i) q^{92} +(-384.887 + 140.087i) q^{93} +194.571 q^{94} +(-100.403 + 359.758i) q^{95} +241.453 q^{96} +(926.508 - 337.221i) q^{97} +(94.4907 - 535.883i) q^{98} +(-913.857 + 766.817i) 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 $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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 $

$2$	1.87939	−	0.684040i	0.664463	−	0.241845i
$2$	1.87939	−	0.684040i	0.664463	−	0.241845i
$3$	−1.31024	+	7.43077i	−0.252157	+	1.43005i	0.551110	+	0.834433i	$0.314204\pi$
$3$	−1.31024	+	7.43077i	−0.252157	+	1.43005i	−0.803267	+	0.595619i	$0.796907\pi$
$4$	3.06418	−	2.57115i	0.383022	−	0.321394i
$5$	3.45478	+	2.89891i	0.309005	+	0.259286i	0.784081	−	0.620659i	$-0.213135\pi$
$5$	3.45478	+	2.89891i	0.309005	+	0.259286i	−0.475076	+	0.879945i	$0.657579\pi$
$6$	2.62049	+	14.8615i	0.178302	+	1.01120i
$7$	4.21085	+	7.29340i	0.227364	+	0.393807i	0.957026	−	0.290002i	$-0.0936558\pi$
$7$	4.21085	+	7.29340i	0.227364	+	0.393807i	−0.729662	+	0.683808i	$0.760322\pi$
$8$	4.00000	−	6.92820i	0.176777	−	0.306186i
$9$	−28.1279	−	10.2377i	−1.04177	−	0.379174i
$10$	8.47584	+	3.08495i	0.268029	+	0.0975548i
$11$	19.9270	−	34.5147i	0.546203	−	0.946051i	−0.452327	−	0.891852i	$-0.649406\pi$
$11$	19.9270	−	34.5147i	0.546203	−	0.946051i	0.998530	−	0.0541991i	$-0.0172606\pi$
$12$	15.0908	+	26.1380i	0.363028	+	0.628783i
$13$	−12.5243	−	71.0287i	−0.267201	−	1.51537i	−0.762695	−	0.646759i	$-0.776124\pi$
$13$	−12.5243	−	71.0287i	−0.267201	−	1.51537i	0.495494	−	0.868611i	$-0.334987\pi$
$14$	12.9028	+	10.8267i	0.246315	+	0.206683i
$15$	−26.0677	+	21.8734i	−0.448710	+	0.376513i
$16$	2.77837	−	15.7569i	0.0434120	−	0.246202i
$17$	−83.5662	+	30.4156i	−1.19222	+	0.433934i	−0.860504	−	0.509445i	$-0.829851\pi$
$17$	−83.5662	+	30.4156i	−1.19222	+	0.433934i	−0.331719	+	0.943378i	$0.607629\pi$
$18$	−59.8661			−0.783921
$19$	34.2213	+	75.4182i	0.413206	+	0.910638i
$19$	34.2213	+	75.4182i	0.413206	+	0.910638i
$20$	18.0396			0.201689
$21$	−59.7128	+	21.7337i	−0.620495	+	0.225842i
$22$	13.8412	−	78.4973i	0.134134	−	0.760712i
$23$	68.3271	−	57.3332i	0.619443	−	0.519774i	−0.278186	−	0.960527i	$-0.589733\pi$
$23$	68.3271	−	57.3332i	0.619443	−	0.519774i	0.897628	+	0.440753i	$0.145289\pi$
$24$	46.2409	+	38.8007i	0.393287	+	0.330007i
$25$	−18.1742	−	103.071i	−0.145393	−	0.824566i
$26$	−72.1244	−	124.923i	−0.544029	−	0.942286i
$27$	11.0655	−	19.1661i	0.0788727	−	0.136612i
$28$	31.6552	+	11.5216i	0.213653	+	0.0777632i
$29$	163.711	+	59.5858i	1.04829	+	0.381545i	0.808016	−	0.589161i	$-0.200542\pi$
$29$	163.711	+	59.5858i	1.04829	+	0.381545i	0.240270	+	0.970706i	$0.422764\pi$
$30$	−34.0290	+	58.9399i	−0.207094	+	0.358697i
$31$	27.1416	+	47.0106i	0.157251	+	0.272366i	0.933876	−	0.357596i	$-0.116404\pi$
$31$	27.1416	+	47.0106i	0.157251	+	0.272366i	−0.776626	+	0.629963i	$0.783070\pi$
$32$	−5.55674	−	31.5138i	−0.0306970	−	0.174091i
$33$	230.361	+	193.296i	1.21517	+	1.01965i
$34$	−136.248	+	114.325i	−0.687243	+	0.576666i
$35$	−6.59533	+	37.4040i	−0.0318518	+	0.180641i
$36$	−112.511	+	40.9508i	−0.520887	+	0.189587i
$37$	−342.543			−1.52199			−0.760996	−	0.648756i	$-0.775290\pi$
$37$	−342.543			−1.52199			−0.760996	+	0.648756i	$0.775290\pi$
$38$	115.904	+	118.331i	0.494793	+	0.505153i
$39$	544.207			2.23443
$40$	33.9033	−	12.3398i	0.134015	−	0.0487774i
$41$	−55.4266	+	314.340i	−0.211126	+	1.19736i	0.676377	+	0.736555i	$0.263549\pi$
$41$	−55.4266	+	314.340i	−0.211126	+	1.19736i	−0.887503	+	0.460801i	$0.847562\pi$
$42$	−97.3567	+	81.6919i	−0.357678	+	0.300127i
$43$	−155.259	−	130.278i	−0.550624	−	0.462028i	0.324528	−	0.945876i	$-0.394794\pi$
$43$	−155.259	−	130.278i	−0.550624	−	0.462028i	−0.875152	+	0.483848i	$0.839239\pi$
$44$	−27.6824	−	156.995i	−0.0948471	−	0.537905i
$45$	−67.4975	−	116.909i	−0.223599	−	0.387284i
$46$	89.1947	−	154.490i	0.285892	−	0.495180i
$47$	91.4185	+	33.2736i	0.283718	+	0.103265i	0.479960	−	0.877291i	$-0.340651\pi$
$47$	91.4185	+	33.2736i	0.283718	+	0.103265i	−0.196241	+	0.980556i	$0.562874\pi$
$48$	113.446	+	41.2909i	0.341135	+	0.124163i
$49$	136.038	−	235.624i	0.396611	−	0.686950i
$50$	−104.661	−	181.278i	−0.296025	−	0.512731i
$51$	−116.519	−	660.813i	−0.319921	−	1.81436i
$52$	−221.002	−	185.443i	−0.589374	−	0.494544i
$53$	−324.180	+	272.019i	−0.840180	+	0.704995i	−0.957604	−	0.288087i	$-0.906981\pi$
$53$	−324.180	+	272.019i	−0.840180	+	0.704995i	0.117424	+	0.993082i	$0.462536\pi$
$54$	7.68604	−	43.5897i	0.0193692	−	0.109848i
$55$	168.898	−	61.4740i	0.414077	−	0.150712i
$56$	67.3736			0.160771
$57$	−605.253	+	155.475i	−1.40645	+	0.361283i
$58$	348.434			0.788822
$59$	−285.926	+	104.069i	−0.630923	+	0.229637i	−0.637633	−	0.770340i	$-0.720086\pi$
$59$	−285.926	+	104.069i	−0.630923	+	0.229637i	0.00671005	+	0.999977i	$0.497864\pi$
$60$	−23.6363	+	134.048i	−0.0508572	+	0.288425i
$61$	−253.870	+	213.022i	−0.532865	+	0.447127i	−0.869089	−	0.494655i	$-0.835294\pi$
$61$	−253.870	+	213.022i	−0.532865	+	0.447127i	0.336224	+	0.941782i	$0.390850\pi$
$62$	83.1667	+	69.7851i	0.170358	+	0.142947i
$63$	−43.7745	−	248.257i	−0.0875407	−	0.496468i
$64$	−32.0000	−	55.4256i	−0.0625000	−	0.108253i
$65$	162.637	−	281.695i	0.310348	−	0.537538i
$66$	565.160	+	205.701i	1.05404	+	0.383637i
$67$	−878.531	−	319.759i	−1.60194	−	0.583057i	−0.622113	−	0.782927i	$-0.713726\pi$
$67$	−878.531	−	319.759i	−1.60194	−	0.583057i	−0.979822	+	0.199870i	$0.935948\pi$
$68$	−177.859	+	308.060i	−0.317184	+	0.549379i
$69$	336.505	+	582.843i	0.587107	+	1.01690i
$70$	13.1907	+	74.8079i	0.0225226	+	0.127732i
$71$	818.667	+	686.944i	1.36842	+	1.14824i	0.973280	+	0.229622i	$0.0737490\pi$
$71$	818.667	+	686.944i	1.36842	+	1.14824i	0.395142	+	0.918620i	$0.370695\pi$
$72$	−183.440	+	153.925i	−0.300259	+	0.251947i
$73$	179.899	−	1020.26i	0.288433	−	1.63578i	−0.404327	−	0.914615i	$-0.632494\pi$
$73$	179.899	−	1020.26i	0.288433	−	1.63578i	0.692759	−	0.721169i	$-0.256395\pi$
$74$	−643.770	+	234.313i	−1.01131	+	0.368086i
$75$	789.708			1.21583
$76$	298.772	+	143.106i	0.450940	+	0.215993i
$77$	335.639			0.496748
$78$	1022.78	−	372.260i	1.48470	−	0.540386i
$79$	18.3231	−	103.915i	0.0260951	−	0.147992i	−0.968976	−	0.247154i	$-0.920505\pi$
$79$	18.3231	−	103.915i	0.0260951	−	0.147992i	0.995071	+	0.0991611i	$0.0316159\pi$
$80$	55.2765	−	46.3825i	0.0772513	−	0.0648215i
$81$	−491.191	−	412.158i	−0.673788	−	0.565375i
$82$	110.853	+	628.679i	0.149289	+	0.846659i
$83$	436.673	+	756.340i	0.577483	+	1.00023i	0.995767	+	0.0919137i	$0.0292984\pi$
$83$	436.673	+	756.340i	0.577483	+	1.00023i	−0.418284	+	0.908316i	$0.637368\pi$
$84$	−127.090	+	220.126i	−0.165079	+	0.285926i
$85$	−376.875	−	137.171i	−0.480916	−	0.175039i
$86$	−380.908	−	138.639i	−0.477608	−	0.173835i
$87$	−657.269	+	1138.42i	−0.809961	+	1.40289i
$88$	−159.416	−	276.117i	−0.193112	−	0.334480i
$89$	27.6387	+	156.747i	0.0329180	+	0.186687i	0.996833	−	0.0795228i	$-0.0253397\pi$
$89$	27.6387	+	156.747i	0.0329180	+	0.186687i	−0.963915	+	0.266210i	$0.914229\pi$
$90$	−206.824	−	173.546i	−0.242236	−	0.203260i
$91$	465.303	−	390.435i	0.536011	−	0.449766i
$92$	61.9540	−	351.358i	0.0702081	−	0.398170i
$93$	−384.887	+	140.087i	−0.429150	+	0.156198i
$94$	194.571			0.213494
$95$	−100.403	+	359.758i	−0.108433	+	0.388530i
$96$	241.453			0.256700
$97$	926.508	−	337.221i	0.969821	−	0.352986i	0.191946	−	0.981405i	$-0.438520\pi$
$97$	926.508	−	337.221i	0.969821	−	0.352986i	0.777875	+	0.628420i	$0.216298\pi$
$98$	94.4907	−	535.883i	0.0973980	−	0.552371i
$99$	−913.857	+	766.817i	−0.927738	+	0.778464i
$100$	−320.699	−	269.099i	−0.320699	−	0.269099i
$101$	−128.986	−	731.516i	−0.127075	−	0.720679i	−0.980054	−	0.198733i	$-0.936317\pi$
$101$	−128.986	−	731.516i	−0.127075	−	0.720679i	0.852978	−	0.521946i	$-0.174794\pi$
$102$	−671.007	−	1162.22i	−0.651369	−	1.12820i
$103$	−89.2997	+	154.672i	−0.0854268	+	0.147964i	−0.905573	−	0.424190i	$-0.860559\pi$
$103$	−89.2997	+	154.672i	−0.0854268	+	0.147964i	0.820146	+	0.572154i	$0.193892\pi$
$104$	−542.198	−	197.344i	−0.511220	−	0.186069i
$105$	−269.299	−	98.0167i	−0.250294	−	0.0910995i
$106$	−423.187	+	732.981i	−0.387769	+	0.671636i
$107$	−30.1938	−	52.2971i	−0.0272798	−	0.0472500i	0.852063	−	0.523439i	$-0.175351\pi$
$107$	−30.1938	−	52.2971i	−0.0272798	−	0.0472500i	−0.879343	+	0.476189i	$0.842018\pi$
$108$	−15.3721	−	87.1794i	−0.0136961	−	0.0776745i
$109$	249.955	+	209.737i	0.219645	+	0.184304i	0.745970	−	0.665979i	$-0.231986\pi$
$109$	249.955	+	209.737i	0.219645	+	0.184304i	−0.526325	+	0.850283i	$0.676430\pi$
$110$	275.374	−	231.067i	0.238690	−	0.200285i
$111$	448.815	−	2545.36i	0.383781	−	2.17653i
$112$	126.621	−	46.0862i	0.106826	−	0.0388816i
$113$	1991.15			1.65762			0.828811	−	0.559528i	$-0.189018\pi$
$113$	1991.15			1.65762			0.828811	+	0.559528i	$0.189018\pi$
$114$	−1031.15	+	706.214i	−0.847161	+	0.580202i
$115$	402.259			0.326181
$116$	654.842	−	238.343i	0.524143	−	0.190772i
$117$	−374.890	+	2126.11i	−0.296227	+	1.67999i
$118$	−466.179	+	391.170i	−0.363688	+	0.305171i
$119$	−573.718	−	481.406i	−0.441955	−	0.370844i
$120$	47.2726	+	268.096i	0.0359615	+	0.203948i
$121$	−128.675	−	222.871i	−0.0966752	−	0.167446i
$122$	−331.404	+	574.009i	−0.245934	+	0.425970i
$123$	−2263.16	−	823.724i	−1.65905	−	0.603843i
$124$	204.038	+	74.2638i	0.147767	+	0.0537829i
$125$	517.873	−	896.983i	0.370560	−	0.641829i
$126$	−252.087	−	436.628i	−0.178236	−	0.308713i
$127$	423.699	+	2402.92i	0.296041	+	1.67893i	0.662942	+	0.748671i	$0.269308\pi$
$127$	423.699	+	2402.92i	0.296041	+	1.67893i	−0.366901	+	0.930260i	$0.619581\pi$
$128$	−98.0537	−	82.2768i	−0.0677094	−	0.0568149i
$129$	1171.49	−	983.000i	0.799568	−	0.670917i
$130$	112.966	−	640.664i	0.0762139	−	0.432230i
$131$	433.656	−	157.838i	0.289227	−	0.105270i	−0.193332	−	0.981133i	$-0.561930\pi$
$131$	433.656	−	157.838i	0.289227	−	0.105270i	0.482559	+	0.875863i	$0.339707\pi$
$132$	1202.86			0.793148
$133$	−405.954	+	567.164i	−0.264667	+	0.369770i
$134$	−1869.83			−1.20544
$135$	93.7897	−	34.1367i	0.0597936	−	0.0217631i
$136$	−123.539	+	700.626i	−0.0778927	+	0.441752i
$137$	−118.978	+	99.8341i	−0.0741967	+	0.0622584i	−0.679132	−	0.734016i	$-0.737644\pi$
$137$	−118.978	+	99.8341i	−0.0741967	+	0.0622584i	0.604935	+	0.796275i	$0.293199\pi$
$138$	1031.11	+	865.204i	0.636043	+	0.533703i
$139$	3.20544	+	18.1790i	0.00195599	+	0.0110929i	0.985770	−	0.168099i	$-0.0537628\pi$
$139$	3.20544	+	18.1790i	0.00195599	+	0.0110929i	−0.983814	+	0.179192i	$0.942652\pi$
$140$	75.9620	+	131.570i	0.0458568	+	0.0794264i
$141$	−367.029	+	635.713i	−0.219216	+	0.379693i
$142$	2008.49	+	731.030i	1.18696	+	0.432019i
$143$	−2701.10	−	983.121i	−1.57956	−	0.574914i
$144$	−239.464	+	414.765i	−0.138579	+	0.240026i
$145$	392.851	+	680.438i	0.224996	+	0.389705i
$146$	−359.798	−	2040.52i	−0.203953	−	1.15667i
$147$	1572.62	+	1319.59i	0.882366	+	0.740393i
$148$	−1049.61	+	880.730i	−0.582957	+	0.489159i
$149$	137.443	−	779.478i	0.0755690	−	0.428573i	−0.923427	−	0.383774i	$-0.874624\pi$
$149$	137.443	−	779.478i	0.0755690	−	0.428573i	0.998996	−	0.0447989i	$-0.0142647\pi$
$150$	1484.16	−	540.192i	0.807877	−	0.294043i
$151$	−447.674			−0.241266			−0.120633	−	0.992697i	$-0.538492\pi$
$151$	−447.674			−0.241266			−0.120633	+	0.992697i	$0.538492\pi$
$152$	659.398	+	64.5802i	0.351870	+	0.0344615i
$153$	2661.93			1.40656
$154$	630.795	−	229.591i	0.330071	−	0.120136i
$155$	−42.5111	+	241.092i	−0.0220295	+	0.124936i
$156$	1667.55	−	1399.24i	0.855838	−	0.718133i
$157$	1513.38	+	1269.87i	0.769304	+	0.645523i	0.940531	−	0.339709i	$-0.110329\pi$
$157$	1513.38	+	1269.87i	0.769304	+	0.645523i	−0.171227	+	0.985232i	$0.554773\pi$
$158$	−36.6462	−	207.831i	−0.0184520	−	0.104646i
$159$	−1596.56	−	2765.32i	−0.796322	−	1.37927i
$160$	72.1584	−	124.982i	0.0356539	−	0.0617543i
$161$	705.869	+	256.915i	0.345530	+	0.125763i
$162$	−1205.07	−	438.610i	−0.584440	−	0.212719i
$163$	−544.393	+	942.917i	−0.261596	+	0.453098i	−0.966666	−	0.256040i	$-0.917582\pi$
$163$	−544.393	+	942.917i	−0.261596	+	0.453098i	0.705070	+	0.709138i	$0.250916\pi$
$164$	638.378	+	1105.70i	0.303957	+	0.526469i
$165$	235.501	+	1335.59i	0.111113	+	0.630155i
$166$	1338.04	+	1122.75i	0.625617	+	0.524955i
$167$	−2066.64	+	1734.12i	−0.957613	+	0.803533i	−0.980563	−	0.196204i	$-0.937139\pi$
$167$	−2066.64	+	1734.12i	−0.957613	+	0.803533i	0.0229499	+	0.999737i	$0.492694\pi$
$168$	−88.2759	+	500.637i	−0.0405395	+	0.229911i
$169$	−2823.71	+	1027.75i	−1.28526	+	0.467795i
$170$	−802.124			−0.361883
$171$	−190.465	−	2471.70i	−0.0851765	−	1.10535i
$172$	−810.707			−0.359394
$173$	−1336.67	+	486.510i	−0.587431	+	0.213807i	−0.618599	−	0.785707i	$-0.712299\pi$
$173$	−1336.67	+	486.510i	−0.587431	+	0.213807i	0.0311684	+	0.999514i	$0.490077\pi$
$174$	−456.534	+	2589.13i	−0.198907	+	1.12806i
$175$	675.208	−	566.567i	0.291662	−	0.244734i
$176$	−488.480	−	409.884i	−0.209208	−	0.175546i
$177$	−398.677	−	2261.01i	−0.169302	−	0.960157i
$178$	159.165	+	275.682i	0.0670221	+	0.116086i
$179$	492.061	−	852.275i	0.205466	−	0.355877i	−0.744815	−	0.667271i	$-0.767462\pi$
$179$	492.061	−	852.275i	0.205466	−	0.355877i	0.950281	+	0.311393i	$0.100796\pi$
$180$	−507.415	−	184.684i	−0.210114	−	0.0764752i
$181$	−678.112	−	246.813i	−0.278473	−	0.101356i	0.199008	−	0.979998i	$-0.436228\pi$
$181$	−678.112	−	246.813i	−0.278473	−	0.101356i	−0.477481	+	0.878642i	$0.658450\pi$
$182$	607.410	−	1052.06i	0.247386	−	0.428485i
$183$	−1250.29	−	2165.56i	−0.505049	−	0.874771i
$184$	−123.908	−	702.717i	−0.0496446	−	0.281549i
$185$	−1183.41	−	993.000i	−0.470304	−	0.394632i
$186$	−627.526	+	526.557i	−0.247379	+	0.207575i
$187$	−615.444	+	3490.35i	−0.240672	+	1.36492i
$188$	365.674	−	133.094i	0.141859	−	0.0516325i
$189$	186.381			0.0717314
$190$	57.3931	+	744.803i	0.0219144	+	0.284388i
$191$	2072.90			0.785287			0.392643	−	0.919691i	$-0.371561\pi$
$191$	2072.90			0.785287			0.392643	+	0.919691i	$0.371561\pi$
$192$	453.783	−	165.163i	0.170567	−	0.0620815i
$193$	804.129	−	4560.44i	0.299909	−	1.70087i	−0.346640	−	0.937998i	$-0.612677\pi$
$193$	804.129	−	4560.44i	0.299909	−	1.70087i	0.646549	−	0.762872i	$-0.276211\pi$
$194$	1510.59	−	1267.54i	0.559042	−	0.469092i
$195$	1880.12	+	1577.61i	0.690452	+	0.579358i
$196$	−188.981	−	1071.77i	−0.0688708	−	0.390585i
$197$	−1282.87	−	2222.00i	−0.463964	−	0.803609i	0.535190	−	0.844732i	$-0.320240\pi$
$197$	−1282.87	−	2222.00i	−0.463964	−	0.803609i	−0.999154	+	0.0411225i	$0.986907\pi$
$198$	−1192.95	+	2066.26i	−0.428180	+	0.741629i
$199$	−957.254	−	348.412i	−0.340995	−	0.124112i	0.165846	−	0.986152i	$-0.446965\pi$
$199$	−957.254	−	348.412i	−0.340995	−	0.124112i	−0.506841	+	0.862040i	$0.669187\pi$
$200$	−786.792	−	286.369i	−0.278173	−	0.101247i
$201$	3527.15	−	6109.20i	1.23774	−	2.14383i
$202$	−742.801	−	1286.57i	−0.258729	−	0.448132i
$203$	254.777	+	1444.91i	0.0880880	+	0.499572i
$204$	−2056.09	−	1725.26i	−0.705661	−	0.592120i
$205$	−1102.73	+	925.299i	−0.375697	+	0.315247i
$206$	−62.0269	+	351.772i	−0.0209787	+	0.118976i
$207$	−2508.86	+	913.149i	−0.842404	+	0.306610i
$208$	−1153.99			−0.384687
$209$	3284.96	+	321.723i	1.08720	+	0.106479i
$210$	−573.163			−0.188343
$211$	2075.58	−	755.449i	0.677198	−	0.246480i	0.0195538	−	0.999809i	$-0.493775\pi$
$211$	2075.58	−	755.449i	0.677198	−	0.246480i	0.657644	+	0.753329i	$0.271553\pi$
$212$	−293.943	+	1667.03i	−0.0952267	+	0.540057i
$213$	−6177.17	+	5183.26i	−1.98710	+	1.66738i
$214$	−92.5190	−	77.6327i	−0.0295536	−	0.0247984i
$215$	−158.723	−	900.165i	−0.0503481	−	0.285538i
$216$	−88.5243	−	153.329i	−0.0278857	−	0.0482995i
$217$	−228.578	+	395.909i	−0.0715065	+	0.123853i
$218$	613.230	+	223.198i	0.190519	+	0.0693433i
$219$	7345.59	+	2673.58i	2.26652	+	0.824948i
$220$	359.476	−	622.630i	0.110163	−	0.190808i
$221$	3206.99	+	5554.66i	0.976133	+	1.69071i
$222$	−897.631	−	5090.72i	−0.271374	−	1.53904i
$223$	4420.26	+	3709.04i	1.32737	+	1.11379i	0.984685	+	0.174341i	$0.0557794\pi$
$223$	4420.26	+	3709.04i	1.32737	+	1.11379i	0.342681	+	0.939452i	$0.388665\pi$
$224$	206.445	−	173.228i	0.0615788	−	0.0516708i
$225$	−544.008	+	3085.22i	−0.161188	+	0.914140i
$226$	3742.13	−	1362.03i	1.10143	−	0.400887i
$227$	−4429.23			−1.29506			−0.647529	−	0.762041i	$-0.724198\pi$
$227$	−4429.23			−1.29506			−0.647529	+	0.762041i	$0.724198\pi$
$228$	−1454.85	+	2032.60i	−0.422588	+	0.590404i
$229$	−880.027			−0.253947			−0.126973	−	0.991906i	$-0.540526\pi$
$229$	−880.027			−0.253947			−0.126973	+	0.991906i	$0.540526\pi$
$230$	755.999	−	275.161i	0.216735	−	0.0788852i
$231$	−439.769	+	2494.06i	−0.125258	+	0.710376i
$232$	1067.66	−	895.877i	0.302136	−	0.253522i
$233$	−293.030	−	245.881i	−0.0823906	−	0.0691339i	0.600662	−	0.799503i	$-0.294904\pi$
$233$	−293.030	−	245.881i	−0.0823906	−	0.0691339i	−0.683053	+	0.730369i	$0.739348\pi$
$234$	749.779	+	4252.21i	0.209464	+	1.18793i
$235$	219.374	+	379.967i	0.0608952	+	0.105474i
$236$	−608.553	+	1054.04i	−0.167854	+	0.290731i
$237$	748.164	+	272.309i	0.205057	+	0.0746346i
$238$	−1407.54	−	512.302i	−0.383349	−	0.139528i
$239$	−1527.57	+	2645.82i	−0.413431	+	0.716084i	−0.995262	−	0.0972259i	$-0.969003\pi$
$239$	−1527.57	+	2645.82i	−0.413431	+	0.716084i	0.581831	+	0.813310i	$0.302336\pi$
$240$	272.232	+	471.519i	0.0732187	+	0.126819i
$241$	−9.38097	−	53.2021i	−0.00250739	−	0.0142201i	0.983528	−	0.180754i	$-0.0578537\pi$
$241$	−9.38097	−	53.2021i	−0.00250739	−	0.0142201i	−0.986036	+	0.166534i	$0.946743\pi$
$242$	−394.282	−	330.842i	−0.104733	−	0.0878815i
$243$	4163.98	−	3493.99i	1.09926	−	0.922385i
$244$	−230.191	+	1305.48i	−0.0603953	+	0.342519i
$245$	1153.03	−	419.669i	0.300671	−	0.109435i
$246$	−4816.82			−1.24841
$247$	4928.25	−	3375.25i	1.26954	−	0.869483i
$248$	434.266			0.111193
$249$	−6192.34	+	2253.83i	−1.57600	+	0.573616i
$250$	359.711	−	2040.02i	0.0910005	−	0.516090i
$251$	3375.11	−	2832.05i	0.848745	−	0.712182i	−0.110768	−	0.993846i	$-0.535331\pi$
$251$	3375.11	−	2832.05i	0.848745	−	0.712182i	0.959513	+	0.281665i	$0.0908866\pi$
$252$	−772.439	−	648.154i	−0.193092	−	0.162023i
$253$	−617.280	−	3500.77i	−0.153392	−	0.869927i
$254$	2439.98	+	4226.18i	0.602749	+	1.04399i
$255$	1513.09	−	2620.74i	0.371581	−	0.643598i
$256$	−240.561	−	87.5572i	−0.0587308	−	0.0213763i
$257$	1340.44	+	487.880i	0.325347	+	0.118417i	0.499530	−	0.866297i	$-0.333506\pi$
$257$	1340.44	+	487.880i	0.325347	+	0.118417i	−0.174183	+	0.984713i	$0.555728\pi$
$258$	1529.28	−	2648.79i	0.369026	−	0.639171i
$259$	−1442.40	−	2498.30i	−0.346047	−	0.599371i
$260$	−225.933	−	1281.33i	−0.0538914	−	0.305633i
$261$	−3994.81	−	3352.04i	−0.947404	−	0.794966i
$262$	707.040	−	593.277i	0.166722	−	0.139896i
$263$	79.1222	−	448.724i	0.0185509	−	0.105207i	−0.974126	−	0.226004i	$-0.927434\pi$
$263$	79.1222	−	448.724i	0.0185509	−	0.105207i	0.992677	+	0.120797i	$0.0385449\pi$
$264$	2260.64	−	822.805i	0.527018	−	0.191819i
$265$	−1908.53			−0.442415
$266$	−374.981	+	1343.61i	−0.0864344	+	0.309707i
$267$	−1200.96			−0.275273
$268$	−3514.13	+	1279.04i	−0.800968	+	0.291528i
$269$	1357.59	−	7699.26i	0.307708	−	1.74510i	−0.302765	−	0.953065i	$-0.597910\pi$
$269$	1357.59	−	7699.26i	0.307708	−	1.74510i	0.610474	−	0.792036i	$-0.290979\pi$
$270$	152.916	−	128.312i	0.0344673	−	0.0289215i
$271$	−3252.94	−	2729.54i	−0.729159	−	0.611837i	0.200743	−	0.979644i	$-0.435664\pi$
$271$	−3252.94	−	2729.54i	−0.729159	−	0.611837i	−0.929902	+	0.367807i	$0.880109\pi$
$272$	247.079	+	1401.25i	0.0550785	+	0.312366i
$273$	2291.57	+	3969.12i	0.508031	+	0.879935i
$274$	−155.314	+	269.012i	−0.0342441	+	0.0593125i
$275$	−3919.61	−	1426.62i	−0.859496	−	0.312831i
$276$	2529.69	+	920.731i	0.551700	+	0.200803i
$277$	−2907.49	+	5035.92i	−0.630665	+	1.09234i	0.356751	+	0.934199i	$0.383884\pi$
$277$	−2907.49	+	5035.92i	−0.630665	+	1.09234i	−0.987416	+	0.158144i	$0.949449\pi$
$278$	18.4594	+	31.9726i	0.00398245	+	0.00689781i
$279$	−282.154	−	1600.18i	−0.0605453	−	0.343369i
$280$	232.761	+	195.310i	0.0496790	+	0.0416857i
$281$	−2636.30	+	2212.12i	−0.559675	+	0.469623i	−0.878201	−	0.478291i	$-0.841256\pi$
$281$	−2636.30	+	2212.12i	−0.559675	+	0.469623i	0.318527	+	0.947914i	$0.396812\pi$
$282$	−254.936	+	1445.81i	−0.0538341	+	0.305308i
$283$	−3156.25	+	1148.78i	−0.662966	+	0.241300i	−0.651516	−	0.758635i	$-0.725867\pi$
$283$	−3156.25	+	1148.78i	−0.662966	+	0.241300i	−0.0114497	+	0.999934i	$0.503645\pi$
$284$	4274.78			0.893174
$285$	−2541.72	−	1217.44i	−0.528276	−	0.253035i
$286$	−5748.91			−1.18860
$287$	−2526.00	+	919.388i	−0.519530	+	0.189093i
$288$	−166.330	+	943.306i	−0.0340316	+	0.193003i
$289$	2294.63	−	1925.42i	0.467052	−	0.391904i
$290$	1203.76	+	1010.08i	0.243750	+	0.204531i
$291$	1291.86	+	7326.51i	0.260241	+	1.47590i
$292$	−2071.99	−	3588.80i	−0.415254	−	0.719242i
$293$	−1038.40	+	1798.56i	−0.207044	+	0.358611i	−0.950782	−	0.309860i	$-0.899718\pi$
$293$	−1038.40	+	1798.56i	−0.207044	+	0.358611i	0.743738	+	0.668471i	$0.233051\pi$
$294$	3858.22	+	1404.28i	0.765360	+	0.278568i
$295$	−1289.50	−	469.339i	−0.254500	−	0.0926305i
$296$	−1370.17	+	2373.21i	−0.269053	+	0.466013i
$297$	−441.007	−	763.847i	−0.0861610	−	0.149235i
$298$	−274.886	−	1558.96i	−0.0534353	−	0.303047i
$299$	−4928.05	−	4135.12i	−0.953166	−	0.799801i
$300$	2419.80	−	2030.46i	0.465692	−	0.390762i
$301$	296.397	−	1680.95i	0.0567576	−	0.321888i
$302$	−841.353	+	306.227i	−0.160313	+	0.0583490i
$303$	5604.73			1.06265
$304$	1283.44	−	329.684i	0.242139	−	0.0621995i
$305$	−1494.60			−0.280592
$306$	5002.79	−	1820.86i	0.934608	−	0.340170i
$307$	1088.00	−	6170.38i	0.202266	−	1.14711i	−0.699418	−	0.714713i	$-0.746557\pi$
$307$	1088.00	−	6170.38i	0.202266	−	1.14711i	0.901684	−	0.432395i	$-0.142331\pi$
$308$	1028.46	−	862.978i	0.190266	−	0.159652i
$309$	−1032.32	−	866.223i	−0.190055	−	0.159475i
$310$	85.0222	+	482.185i	0.0155772	+	0.0883428i
$311$	5034.62	+	8720.21i	0.917964	+	1.58996i	0.802502	+	0.596649i	$0.203501\pi$
$311$	5034.62	+	8720.21i	0.917964	+	1.58996i	0.115462	+	0.993312i	$0.463165\pi$
$312$	2176.83	−	3770.38i	0.394996	−	0.684153i
$313$	4244.92	+	1545.03i	0.766572	+	0.279010i	0.695562	−	0.718466i	$-0.255155\pi$
$313$	4244.92	+	1545.03i	0.766572	+	0.279010i	0.0710104	+	0.997476i	$0.477378\pi$
$314$	3712.87	+	1351.37i	0.667290	+	0.242874i
$315$	568.443	−	984.573i	0.101677	−	0.176109i
$316$	−211.037	−	365.527i	−0.0375689	−	0.0650712i
$317$	1809.86	+	10264.2i	0.320669	+	1.81860i	0.538510	+	0.842619i	$0.318987\pi$
$317$	1809.86	+	10264.2i	0.320669	+	1.81860i	−0.217841	+	0.975984i	$0.569901\pi$
$318$	−4892.13	−	4104.99i	−0.862696	−	0.723888i
$319$	5318.85	−	4463.05i	0.933538	−	0.783331i
$320$	50.1207	−	284.248i	0.00875572	−	0.0496562i
$321$	428.169	−	155.841i	0.0744488	−	0.0270971i
$322$	1502.34			0.260007
$323$	−5153.64	−	5261.55i	−0.887790	−	0.906379i
$324$	−2564.82			−0.439784
$325$	−7093.36	+	2581.77i	−1.21067	+	0.440649i
$326$	−378.132	+	2144.49i	−0.0642417	+	0.364333i
$327$	−1886.01	+	1582.55i	−0.318950	+	0.267631i
$328$	1956.10	+	1641.37i	0.329292	+	0.276309i
$329$	142.272	+	806.862i	0.0238410	+	0.135209i
$330$	1356.19	+	2349.00i	0.226230	+	0.391843i
$331$	4107.72	−	7114.78i	0.682117	−	1.18146i	−0.292217	−	0.956352i	$-0.594393\pi$
$331$	4107.72	−	7114.78i	0.682117	−	1.18146i	0.974334	−	0.225109i	$-0.0722737\pi$
$332$	3282.71	+	1194.81i	0.542657	+	0.197511i
$333$	9635.01	+	3506.86i	1.58557	+	0.577101i
$334$	−2697.81	+	4672.74i	−0.441968	+	0.765512i
$335$	−2108.18	−	3651.48i	−0.343828	−	0.595527i
$336$	176.552	+	1001.27i	0.0286657	+	0.162571i
$337$	−5782.41	−	4852.02i	−0.934683	−	0.784292i	0.0419693	−	0.999119i	$-0.486637\pi$
$337$	−5782.41	−	4852.02i	−0.934683	−	0.784292i	−0.976652	+	0.214827i	$0.931081\pi$
$338$	−4603.82	+	3863.06i	−0.740872	+	0.621665i
$339$	−2608.89	+	14795.8i	−0.417981	+	2.37049i
$340$	−1507.50	+	548.685i	−0.240458	+	0.0875195i
$341$	2163.41			0.343563
$342$	−2048.70	−	4514.99i	−0.323921	−	0.713868i
$343$	5179.97			0.815429
$344$	−1523.63	+	554.556i	−0.238804	+	0.0869176i
$345$	−527.058	+	2989.09i	−0.0822488	+	0.466456i
$346$	−2179.33	+	1828.68i	−0.338618	+	0.284134i
$347$	−2487.27	−	2087.06i	−0.384794	−	0.322880i	0.429787	−	0.902930i	$-0.358589\pi$
$347$	−2487.27	−	2087.06i	−0.384794	−	0.322880i	−0.814581	+	0.580050i	$0.803033\pi$
$348$	913.068	+	5178.27i	0.140648	+	0.797656i
$349$	2064.43	+	3575.69i	0.316637	+	0.548431i	0.979784	−	0.200058i	$-0.0641131\pi$
$349$	2064.43	+	3575.69i	0.316637	+	0.548431i	−0.663147	+	0.748489i	$0.730780\pi$
$350$	881.421	−	1526.67i	0.134611	−	0.233154i
$351$	−1499.93	−	545.929i	−0.228092	−	0.0830187i
$352$	−1198.42	−	436.189i	−0.181466	−	0.0660482i
$353$	3001.83	−	5199.32i	0.452610	−	0.783943i	−0.545937	−	0.837826i	$-0.683826\pi$
$353$	3001.83	−	5199.32i	0.452610	−	0.783943i	0.998547	+	0.0538825i	$0.0171597\pi$
$354$	−2295.89	−	3976.59i	−0.344704	−	0.597044i
$355$	836.933	+	4746.48i	0.125126	+	0.709625i
$356$	487.710	+	409.238i	0.0726084	+	0.0609257i
$357$	4328.93	−	3632.40i	0.641768	−	0.538508i
$358$	341.782	−	1938.34i	0.0504574	−	0.286158i
$359$	7598.99	−	2765.81i	1.11716	−	0.406612i	0.283543	−	0.958959i	$-0.408490\pi$
$359$	7598.99	−	2765.81i	1.11716	−	0.406612i	0.833614	+	0.552347i	$0.186268\pi$
$360$	−1079.96			−0.158108
$361$	−4516.80	+	5161.82i	−0.658521	+	0.752562i
$362$	−1443.26			−0.209548
$363$	1824.70	−	664.136i	0.263834	−	0.0960278i
$364$	421.902	−	2392.73i	0.0607519	−	0.344541i
$365$	3579.15	−	3003.26i	0.513263	−	0.430679i
$366$	−3831.11	−	3214.68i	−0.547145	−	0.459109i
$367$	1211.10	+	6868.52i	0.172259	+	0.976931i	0.941260	+	0.337683i	$0.109643\pi$
$367$	1211.10	+	6868.52i	0.172259	+	0.976931i	−0.769001	+	0.639248i	$0.779246\pi$
$368$	−713.557	−	1235.92i	−0.101078	−	0.175072i
$369$	4777.15	−	8274.27i	0.673953	−	1.16732i
$370$	−2903.34	−	1056.73i	−0.407939	−	0.148478i
$371$	−3349.02	−	1218.94i	−0.468659	−	0.170578i
$372$	−819.177	+	1418.86i	−0.114173	+	0.197753i
$373$	−503.952	−	872.870i	−0.0699561	−	0.121168i	0.828926	−	0.559359i	$-0.188953\pi$
$373$	−503.952	−	872.870i	−0.0699561	−	0.121168i	−0.898882	+	0.438191i	$0.855619\pi$
$374$	1230.89	+	6980.71i	0.170181	+	0.965144i
$375$	5986.73	+	5023.47i	0.824409	+	0.691762i
$376$	596.201	−	500.272i	0.0817731	−	0.0686158i
$377$	2181.94	−	12374.4i	0.298079	−	1.69049i
$378$	350.282	−	127.492i	0.0476629	−	0.0173479i
$379$	−8901.68			−1.20646			−0.603230	−	0.797567i	$-0.706120\pi$
$379$	−8901.68			−1.20646			−0.603230	+	0.797567i	$0.706120\pi$
$380$	617.339	+	1360.51i	0.0833390	+	0.183665i
$381$	−18410.7			−2.47561
$382$	3895.78	−	1417.95i	0.521794	−	0.189918i
$383$	114.417	−	648.888i	0.0152648	−	0.0865709i	−0.976224	−	0.216766i	$-0.930449\pi$
$383$	114.417	−	648.888i	0.0152648	−	0.0865709i	0.991488	+	0.130195i	$0.0415603\pi$
$384$	739.854	−	620.811i	0.0983217	−	0.0825017i
$385$	1159.56	+	972.986i	0.153498	+	0.128800i
$386$	−1608.26	−	9120.89i	−0.212068	−	1.20270i
$387$	3033.37	+	5253.95i	0.398436	+	0.690111i
$388$	1971.94	−	3415.50i	0.258015	−	0.446896i
$389$	1658.98	+	603.821i	0.216231	+	0.0787016i	0.447864	−	0.894102i	$-0.352185\pi$
$389$	1658.98	+	603.821i	0.216231	+	0.0787016i	−0.231633	+	0.972803i	$0.574407\pi$
$390$	4612.61	+	1678.85i	0.598894	+	0.217980i
$391$	−3966.01	+	6869.33i	−0.512966	+	0.888484i
$392$	−1088.30	−	1884.99i	−0.140223	−	0.242874i
$393$	604.662	+	3429.21i	0.0776111	+	0.440154i
$394$	−3930.95	−	3298.46i	−0.502636	−	0.421761i
$395$	364.544	−	305.888i	0.0464359	−	0.0389643i
$396$	−828.618	+	4699.33i	−0.105151	+	0.596338i
$397$	14003.2	−	5096.74i	1.77028	−	0.644327i	0.770297	−	0.637685i	$-0.220108\pi$
$397$	14003.2	−	5096.74i	1.77028	−	0.644327i	0.999978	−	0.00664239i	$-0.00211436\pi$
$398$	−2037.38			−0.256594
$399$	−3682.57	−	3759.67i	−0.462053	−	0.471727i
$400$	−1674.57			−0.209322
$401$	−3369.54	+	1226.41i	−0.419618	+	0.152729i	−0.543195	−	0.839606i	$-0.682786\pi$
$401$	−3369.54	+	1226.41i	−0.419618	+	0.152729i	0.123577	+	0.992335i	$0.460563\pi$
$402$	2449.93	−	13894.3i	0.303959	−	1.72384i
$403$	2999.17	−	2516.61i	0.370718	−	0.311070i
$404$	−2276.07	−	1909.85i	−0.280294	−	0.235195i
$405$	−502.150	−	2847.84i	−0.0616100	−	0.349408i
$406$	1467.20	+	2541.27i	0.179350	+	0.310643i
$407$	−6825.87	+	11822.8i	−0.831317	+	1.43988i
$408$	−5044.32	−	1835.98i	−0.612087	−	0.222781i
$409$	−3749.86	−	1364.84i	−0.453347	−	0.165005i	0.105247	−	0.994446i	$-0.466437\pi$
$409$	−3749.86	−	1364.84i	−0.453347	−	0.165005i	−0.558594	+	0.829441i	$0.688659\pi$
$410$	−1439.51	+	2493.30i	−0.173396	+	0.300330i
$411$	−585.954	−	1014.90i	−0.0703236	−	0.121804i
$412$	124.054	+	703.545i	0.0148342	+	0.0841290i
$413$	−1963.01	−	1647.16i	−0.233882	−	0.196250i
$414$	−4090.48	+	3432.32i	−0.485594	+	0.407462i
$415$	−683.948	+	3878.86i	−0.0809005	+	0.458810i
$416$	−2168.79	+	789.376i	−0.255610	+	0.0930345i
$417$	−139.284			−0.0163567
$418$	6393.78	−	1642.41i	0.748158	−	0.192183i
$419$	−7662.91			−0.893455			−0.446728	−	0.894670i	$-0.647411\pi$
$419$	−7662.91			−0.893455			−0.446728	+	0.894670i	$0.647411\pi$
$420$	−1077.19	+	392.067i	−0.125147	+	0.0455498i
$421$	−1167.98	+	6623.97i	−0.135212	+	0.766823i	0.839501	+	0.543359i	$0.182848\pi$
$421$	−1167.98	+	6623.97i	−0.135212	+	0.766823i	−0.974712	+	0.223464i	$0.928263\pi$
$422$	3384.05	−	2839.56i	0.390363	−	0.327553i
$423$	−2230.76	−	1871.83i	−0.256415	−	0.215157i
$424$	587.885	+	3334.06i	0.0673354	+	0.381878i
$425$	4653.71	+	8060.46i	0.531148	+	0.919976i
$426$	−8063.73	+	13966.8i	−0.917110	+	1.58848i
$427$	−2622.67	−	954.573i	−0.297236	−	0.108185i
$428$	−226.983	−	82.6150i	−0.0256346	−	0.00933025i
$429$	10844.4	−	18783.1i	1.22045	−	2.11389i
$430$	−914.051	−	1583.18i	−0.102510	−	0.177553i
$431$	−2854.31	−	16187.6i	−0.318996	−	1.80912i	−0.548884	−	0.835898i	$-0.684947\pi$
$431$	−2854.31	−	16187.6i	−0.318996	−	1.80912i	0.229889	−	0.973217i	$-0.426164\pi$
$432$	−271.254	−	227.609i	−0.0302100	−	0.0253492i
$433$	2205.35	−	1850.51i	0.244763	−	0.205381i	−0.512150	−	0.858896i	$-0.671151\pi$
$433$	2205.35	−	1850.51i	0.244763	−	0.205381i	0.756913	+	0.653515i	$0.226706\pi$
$434$	−158.769	+	900.422i	−0.0175602	+	0.0995891i
$435$	−5570.90	+	2027.64i	−0.614033	+	0.223490i
$436$	1305.17			0.143363
$437$	6662.21	+	3191.08i	0.729283	+	0.349314i
$438$	15634.0			1.70553
$439$	−4098.23	+	1491.63i	−0.445553	+	0.162168i	−0.555046	−	0.831819i	$-0.687299\pi$
$439$	−4098.23	+	1491.63i	−0.445553	+	0.162168i	0.109493	+	0.993988i	$0.465077\pi$
$440$	249.689	−	1416.06i	0.0270533	−	0.153427i
$441$	−6238.70	+	5234.89i	−0.673652	+	0.565262i
$442$	9826.78	+	8245.65i	1.05749	+	0.887343i
$443$	−2563.65	−	14539.2i	−0.274949	−	1.55932i	−0.739122	−	0.673571i	$-0.764759\pi$
$443$	−2563.65	−	14539.2i	−0.274949	−	1.55932i	0.464173	−	0.885745i	$-0.346352\pi$
$444$	−5169.25	−	8953.40i	−0.552526	−	0.957004i
$445$	−358.909	+	621.649i	−0.0382336	+	0.0662225i
$446$	10844.5	+	3947.08i	1.15135	+	0.419057i
$447$	5612.04	+	2042.62i	0.593826	+	0.216135i
$448$	269.494	−	466.778i	0.0284205	−	0.0492258i
$449$	4094.23	+	7091.41i	0.430331	+	0.745355i	0.996902	−	0.0786581i	$-0.0250635\pi$
$449$	4094.23	+	7091.41i	0.430331	+	0.745355i	−0.566571	+	0.824013i	$0.691730\pi$
$450$	1088.02	+	6170.45i	0.113977	+	0.646395i
$451$	9744.84	+	8176.89i	1.01744	+	0.853736i
$452$	6101.23	−	5119.54i	0.634906	−	0.532750i
$453$	586.563	−	3326.56i	0.0608369	−	0.345023i
$454$	−8324.22	+	3029.77i	−0.860518	+	0.313203i
$455$	2739.36			0.282248
$456$	−1343.85	+	4815.22i	−0.138008	+	0.494503i
$457$	7478.89			0.765531			0.382766	−	0.923845i	$-0.374972\pi$
$457$	7478.89			0.765531			0.382766	+	0.923845i	$0.374972\pi$
$458$	−1653.91	+	601.974i	−0.168738	+	0.0614157i
$459$	−341.757	+	1938.20i	−0.0347535	+	0.197097i
$460$	1232.59	−	1034.27i	0.124935	−	0.104833i
$461$	4474.16	+	3754.27i	0.452023	+	0.379292i	0.840186	−	0.542299i	$-0.182446\pi$
$461$	4474.16	+	3754.27i	0.452023	+	0.379292i	−0.388163	+	0.921591i	$0.626890\pi$
$462$	879.539	+	4988.11i	0.0885711	+	0.502312i
$463$	−5781.86	−	10014.5i	−0.580358	−	1.00521i	−0.995437	−	0.0954239i	$-0.969579\pi$
$463$	−5781.86	−	10014.5i	−0.580358	−	1.00521i	0.415079	−	0.909785i	$-0.363754\pi$
$464$	1393.74	−	2414.02i	0.139445	−	0.241526i
$465$	−1735.80	−	631.780i	−0.173109	−	0.0630067i
$466$	−718.908	−	261.661i	−0.0714652	−	0.0260112i
$467$	−3611.87	+	6255.94i	−0.357896	+	0.619894i	−0.987609	−	0.156934i	$-0.949839\pi$
$467$	−3611.87	+	6255.94i	−0.357896	+	0.619894i	0.629713	+	0.776828i	$0.283172\pi$
$468$	4317.81	+	7478.66i	0.426476	+	0.738678i
$469$	−1367.23	−	7753.94i	−0.134611	−	0.763419i
$470$	672.201	+	564.044i	0.0659709	+	0.0553562i
$471$	−11419.0	+	9581.71i	−1.11712	+	0.937372i
$472$	−422.697	+	2397.23i	−0.0412207	+	0.233774i
$473$	−7590.37	+	2762.67i	−0.737855	+	0.268557i
$474$	1592.36			0.154303
$475$	7151.47	−	4897.88i	0.690804	−	0.473116i
$476$	−2995.74			−0.288466
$477$	11903.3	−	4332.46i	1.14259	−	0.415870i
$478$	−1061.04	+	6017.44i	−0.101529	+	0.575797i
$479$	3395.13	−	2848.86i	0.323857	−	0.271749i	−0.466334	−	0.884609i	$-0.654426\pi$
$479$	3395.13	−	2848.86i	0.323857	−	0.271749i	0.790191	+	0.612860i	$0.209981\pi$
$480$	834.167	+	699.949i	0.0793215	+	0.0665587i
$481$	4290.10	+	24330.4i	0.406677	+	2.30638i
$482$	−54.0229	−	93.5703i	−0.00510513	−	0.00884235i
$483$	−2833.94	+	4908.53i	−0.266975	+	0.462414i
$484$	−967.317	−	352.075i	−0.0908449	−	0.0330648i
$485$	4178.46	+	1520.83i	0.391204	+	0.142387i
$486$	5435.68	−	9414.88i	0.507341	−	0.878740i
$487$	307.423	+	532.473i	0.0286051	+	0.0495455i	0.879974	−	0.475023i	$-0.157560\pi$
$487$	307.423	+	532.473i	0.0286051	+	0.0495455i	−0.851368	+	0.524568i	$0.824227\pi$
$488$	460.382	+	2610.95i	0.0427060	+	0.242197i
$489$	−6293.31	−	5280.71i	−0.581990	−	0.488348i
$490$	1879.92	−	1577.44i	0.173319	−	0.145432i
$491$	−1520.38	+	8622.53i	−0.139743	+	0.792524i	0.831695	+	0.555232i	$0.187371\pi$
$491$	−1520.38	+	8622.53i	−0.139743	+	0.792524i	−0.971439	+	0.237291i	$0.923740\pi$
$492$	−9052.65	+	3294.90i	−0.829523	+	0.301922i
$493$	−15493.0			−1.41536
$494$	6953.28	−	9714.53i	0.633285	−	0.884772i
$495$	−5380.11			−0.488521
$496$	816.152	−	297.055i	0.0738837	−	0.0268915i
$497$	−1562.87	+	8863.48i	−0.141055	+	0.799963i
$498$	−10096.1	+	8471.61i	−0.908466	+	0.762293i
$499$	9102.01	+	7637.49i	0.816557	+	0.685172i	0.952163	−	0.305590i	$-0.0988538\pi$
$499$	9102.01	+	7637.49i	0.816557	+	0.685172i	−0.135606	+	0.990763i	$0.543298\pi$
$500$	−719.422	−	4080.05i	−0.0643471	−	0.364930i
$501$	−10178.0	−	17628.8i	−0.907625	−	1.57205i
$502$	4405.89	−	7631.23i	0.391722	−	0.678483i
$503$	−8898.72	−	3238.87i	−0.788816	−	0.287106i	−0.0839722	−	0.996468i	$-0.526761\pi$
$503$	−8898.72	−	3238.87i	−0.788816	−	0.287106i	−0.704844	+	0.709363i	$0.748983\pi$
$504$	−1895.07	−	689.751i	−0.167487	−	0.0609602i
$505$	1674.98	−	2901.15i	0.147595	−	0.255642i
$506$	−3554.77	−	6157.05i	−0.312310	−	0.540937i
$507$	−3937.19	−	22328.9i	−0.344885	−	1.95594i
$508$	7476.55	+	6273.57i	0.652988	+	0.547922i
$509$	−1561.50	+	1310.25i	−0.135977	+	0.114098i	−0.708239	−	0.705972i	$-0.750510\pi$
$509$	−1561.50	+	1310.25i	−0.135977	+	0.114098i	0.572263	+	0.820070i	$0.306066\pi$
$510$	1050.98	−	5960.40i	0.0912513	−	0.517512i
$511$	8198.68	−	2984.08i	0.709762	−	0.258332i
$512$	−512.000			−0.0441942
$513$	1824.15	+	178.654i	0.156994	+	0.0153757i
$514$	2852.93			0.244820
$515$	−756.890	+	275.485i	−0.0647622	+	0.0235715i
$516$	1062.22	−	6024.18i	0.0906237	−	0.513953i
$517$	2970.13	−	2492.23i	0.252662	−	0.212008i
$518$	−4419.76	−	3708.62i	−0.374890	−	0.314570i
$519$	−1863.77	−	10570.0i	−0.157631	−	0.893969i
$520$	−1301.09	−	2253.56i	−0.109725	−	0.190049i
$521$	−4264.50	+	7386.33i	−0.358601	+	0.621115i	−0.987727	−	0.156188i	$-0.950079\pi$
$521$	−4264.50	+	7386.33i	−0.358601	+	0.621115i	0.629127	+	0.777303i	$0.283413\pi$
$522$	−9800.71	−	3567.17i	−0.821773	−	0.299101i
$523$	−17329.0	−	6307.25i	−1.44884	−	0.527336i	−0.506576	−	0.862195i	$-0.669089\pi$
$523$	−17329.0	−	6307.25i	−1.44884	−	0.527336i	−0.942268	+	0.334859i	$0.891311\pi$
$524$	922.975	−	1598.64i	0.0769472	−	0.133277i
$525$	3325.34	+	5759.65i	0.276437	+	0.478804i
$526$	−158.244	−	897.448i	−0.0131175	−	0.0743928i
$527$	−3697.98	−	3102.97i	−0.305667	−	0.256485i
$528$	3685.78	−	3092.74i	0.303793	−	0.254913i
$529$	−731.286	+	4147.33i	−0.0601041	+	0.340867i
$530$	−3586.86	+	1305.51i	−0.293969	+	0.106996i
$531$	9107.93			0.744351
$532$	214.349	+	2781.66i	0.0174685	+	0.226692i
$533$	23021.3			1.87085
$534$	−2257.08	+	821.508i	−0.182909	+	0.0665733i
$535$	47.2916	−	268.204i	0.00382167	−	0.0216738i
$536$	−5729.48	+	4807.61i	−0.461709	+	0.387420i
$537$	5688.34	+	4773.08i	0.457113	+	0.383564i
$538$	−2715.18	−	15398.5i	−0.217583	−	1.23397i
$539$	−5421.65	−	9390.58i	−0.433260	−	0.750428i
$540$	199.618	−	345.748i	0.0159077	−	0.0275530i
$541$	−3519.32	−	1280.93i	−0.279681	−	0.101795i	0.198371	−	0.980127i	$-0.436435\pi$
$541$	−3519.32	−	1280.93i	−0.279681	−	0.101795i	−0.478052	+	0.878331i	$0.658657\pi$
$542$	−7980.65	−	2904.72i	−0.632469	−	0.230200i
$543$	2722.50	−	4715.51i	0.215163	−	0.372674i
$544$	1422.87	+	2464.48i	0.112142	+	0.194235i
$545$	255.532	+	1449.19i	0.0200840	+	0.113902i
$546$	7021.79	+	5891.98i	0.550375	+	0.461820i
$547$	−1705.45	+	1431.05i	−0.133309	+	0.111859i	−0.707004	−	0.707209i	$-0.749954\pi$
$547$	−1705.45	+	1431.05i	−0.133309	+	0.111859i	0.573695	+	0.819069i	$0.305509\pi$
$548$	−107.880	+	611.819i	−0.00840951	+	0.0476927i
$549$	9321.69	−	3392.82i	0.724663	−	0.263756i
$550$	−8342.33			−0.646760
$551$	1108.55	+	14385.9i	0.0857090	+	1.11227i
$552$	5384.08			0.415148
$553$	835.053	−	303.934i	0.0642135	−	0.0233718i
$554$	−2019.52	+	11453.3i	−0.154876	+	0.878345i
$555$	8929.31	−	7492.58i	0.682934	−	0.573050i
$556$	56.5629	+	47.4619i	0.00431439	+	0.00362020i
$557$	−3517.50	−	19948.7i	−0.267578	−	1.51751i	−0.761591	−	0.648058i	$-0.775582\pi$
$557$	−3517.50	−	19948.7i	−0.267578	−	1.51751i	0.494013	−	0.869455i	$-0.335530\pi$
$558$	−1624.86	−	2814.34i	−0.123272	−	0.213514i
$559$	−7308.97	+	12659.5i	−0.553017	+	0.957853i
$560$	571.047	+	207.844i	0.0430913	+	0.0156840i
$561$	−25129.6	−	9146.44i	−1.89122	−	0.688347i
$562$	−3441.45	+	5960.76i	−0.258307	+	0.447402i
$563$	9094.51	+	15752.2i	0.680796	+	1.17917i	0.974738	+	0.223350i	$0.0716992\pi$
$563$	9094.51	+	15752.2i	0.680796	+	1.17917i	−0.293943	+	0.955823i	$0.594967\pi$
$564$	509.872	+	2891.63i	0.0380664	+	0.215885i
$565$	6878.98	+	5772.15i	0.512214	+	0.429799i
$566$	−5145.99	+	4318.00i	−0.382159	+	0.320670i
$567$	937.705	−	5317.99i	0.0694531	−	0.393888i
$568$	8033.95	−	2924.12i	0.593481	−	0.216009i
$569$	9347.59			0.688702			0.344351	−	0.938841i	$-0.388099\pi$
$569$	9347.59			0.688702			0.344351	+	0.938841i	$0.388099\pi$
$570$	−5609.66	−	549.400i	−0.412215	−	0.0403716i
$571$	7376.50			0.540625			0.270313	−	0.962773i	$-0.412873\pi$
$571$	7376.50			0.540625			0.270313	+	0.962773i	$0.412873\pi$
$572$	−10804.4	+	3932.48i	−0.789782	+	0.287457i
$573$	−2716.01	+	15403.2i	−0.198015	+	1.12300i
$574$	−4118.43	+	3455.77i	−0.299477	+	0.251291i
$575$	−7151.17	−	6000.54i	−0.518651	−	0.435200i
$576$	332.661	+	1886.61i	0.0240640	+	0.136474i
$577$	−1562.37	−	2706.10i	−0.112725	−	0.195245i	0.804143	−	0.594436i	$-0.202625\pi$
$577$	−1562.37	−	2706.10i	−0.112725	−	0.195245i	−0.916868	+	0.399190i	$0.869291\pi$
$578$	2995.42	−	5188.23i	0.215559	−	0.373360i
$579$	32834.0	+	11950.6i	2.35671	+	0.857772i
$580$	2953.27	+	1074.90i	0.211427	+	0.0769533i
$581$	−3677.53	+	6369.66i	−0.262598	+	0.454833i
$582$	7439.53	+	12885.6i	0.529860	+	0.917744i
$583$	2928.70	+	16609.5i	0.208052	+	1.17992i
$584$	−6348.96	−	5327.41i	−0.449866	−	0.377483i
$585$	−7458.54	+	6258.46i	−0.527133	+	0.442317i
$586$	−721.264	+	4090.49i	−0.0508450	+	0.288356i
$587$	−3541.08	+	1288.85i	−0.248988	+	0.0906243i	−0.463499	−	0.886097i	$-0.653406\pi$
$587$	−3541.08	+	1288.85i	−0.248988	+	0.0906243i	0.214511	+	0.976722i	$0.431184\pi$
$588$	8211.66			0.575924
$589$	−2616.63	+	3655.74i	−0.183050	+	0.255742i
$590$	−2744.51			−0.191508
$591$	18192.0	−	6621.36i	1.26619	−	0.460857i
$592$	−951.712	+	5397.42i	−0.0660728	+	0.374718i
$593$	−9391.21	+	7880.16i	−0.650338	+	0.545699i	−0.907174	−	0.420756i	$-0.861765\pi$
$593$	−9391.21	+	7880.16i	−0.650338	+	0.545699i	0.256835	+	0.966455i	$0.417320\pi$
$594$	−1351.32	−	1133.90i	−0.0933426	−	0.0783237i
$595$	−586.518	−	3326.31i	−0.0404116	−	0.229186i
$596$	−1583.01	−	2741.85i	−0.108796	−	0.188440i
$597$	3843.21	−	6656.63i	0.263471	−	0.456344i
$598$	−12090.3	−	4400.51i	−0.826771	−	0.300920i
$599$	15096.1	+	5494.54i	1.02973	+	0.374793i	0.800980	−	0.598692i	$-0.204313\pi$
$599$	15096.1	+	5494.54i	1.02973	+	0.374793i	0.228754	+	0.973484i	$0.426535\pi$
$600$	3158.83	−	5471.26i	0.214931	−	0.372272i
$601$	−6828.80	−	11827.8i	−0.463482	−	0.802774i	0.535650	−	0.844440i	$-0.320067\pi$
$601$	−6828.80	−	11827.8i	−0.463482	−	0.802774i	−0.999132	+	0.0416663i	$0.986733\pi$
$602$	−592.794	−	3361.90i	−0.0401337	−	0.227609i
$603$	21437.6	+	17988.3i	1.44777	+	1.21483i
$604$	−1371.75	+	1151.04i	−0.0924104	+	0.0775415i
$605$	201.539	−	1142.99i	0.0135434	−	0.0768083i
$606$	10533.5	−	3833.86i	0.706093	−	0.256997i
$607$	1082.03			0.0723531			0.0361765	−	0.999345i	$-0.488482\pi$
$607$	1082.03			0.0723531			0.0361765	+	0.999345i	$0.488482\pi$
$608$	2186.56	−	1497.53i	0.145850	−	0.0998893i
$609$	−11070.6			−0.736625
$610$	−2808.93	+	1022.37i	−0.186443	+	0.0678596i
$611$	1218.43	−	6910.06i	0.0806750	−	0.457531i
$612$	8156.62	−	6844.21i	0.538745	−	0.452060i
$613$	−14039.0	−	11780.1i	−0.925009	−	0.776175i	0.0499056	−	0.998754i	$-0.484108\pi$
$613$	−14039.0	−	11780.1i	−0.925009	−	0.776175i	−0.974915	+	0.222579i	$0.928552\pi$
$614$	−2176.01	−	12340.8i	−0.143024	−	0.811128i
$615$	−5430.84	−	9406.49i	−0.356085	−	0.616758i
$616$	1342.56	−	2325.38i	0.0878135	−	0.152097i
$617$	7856.13	+	2859.40i	0.512603	+	0.186572i	0.585354	−	0.810778i	$-0.300956\pi$
$617$	7856.13	+	2859.40i	0.512603	+	0.186572i	−0.0727511	+	0.997350i	$0.523178\pi$
$618$	−2532.67	−	921.816i	−0.164852	−	0.0600014i
$619$	−5076.06	+	8792.00i	−0.329603	+	0.570889i	−0.982433	−	0.186615i	$-0.940248\pi$
$619$	−5076.06	+	8792.00i	−0.329603	+	0.570889i	0.652830	+	0.757504i	$0.273582\pi$
$620$	489.623	+	848.053i	0.0317157	+	0.0549332i
$621$	−342.777	−	1943.98i	−0.0221500	−	0.125619i
$622$	15427.0	+	12944.8i	0.994477	+	0.834465i
$623$	−1026.84	+	861.618i	−0.0660343	+	0.0554093i
$624$	1512.01	−	8575.04i	0.0970014	−	0.550122i
$625$	−7904.21	+	2876.90i	−0.505870	+	0.184122i
$626$	9034.70			0.576836
$627$	−6694.76	+	23988.3i	−0.426416	+	1.52791i
$628$	7902.30			0.502127
$629$	28625.0	−	10418.7i	1.81455	−	0.660444i
$630$	394.837	−	2239.23i	0.0249693	−	0.141608i
$631$	17327.4	−	14539.4i	1.09318	−	0.917284i	0.0962288	−	0.995359i	$-0.469322\pi$
$631$	17327.4	−	14539.4i	1.09318	−	0.917284i	0.996947	+	0.0780755i	$0.0248775\pi$
$632$	−646.655	−	542.608i	−0.0407002	−	0.0341516i
$633$	2894.05	+	16413.0i	0.181719	+	1.03058i
$634$	10422.6	+	18052.4i	0.652892	+	1.13084i
$635$	−5502.04	+	9529.81i	−0.343845	+	0.595558i
$636$	−12002.2	−	4368.44i	−0.748298	−	0.272358i
$637$	−18439.8	−	6711.55i	−1.14696	−	0.417459i
$638$	6943.27	−	12026.1i	0.430857	−	0.746266i
$639$	−15994.6	−	27703.5i	−0.990201	−	1.71508i
$640$	−100.241	−	568.497i	−0.00619123	−	0.0351122i
$641$	−21895.8	−	18372.8i	−1.34919	−	1.13211i	−0.979160	−	0.203089i	$-0.934902\pi$
$641$	−21895.8	−	18372.8i	−1.34919	−	1.13211i	−0.370033	−	0.929018i	$-0.620654\pi$
$642$	698.093	−	585.770i	0.0429152	−	0.0360101i
$643$	3385.39	−	19199.5i	0.207631	−	1.17753i	−0.685615	−	0.727965i	$-0.740466\pi$
$643$	3385.39	−	19199.5i	0.207631	−	1.17753i	0.893246	−	0.449569i	$-0.148422\pi$
$644$	2823.48	−	1027.66i	0.172765	−	0.0628813i
$645$	6896.88			0.421030
$646$	−13284.8	−	6363.18i	−0.809107	−	0.387548i
$647$	−4366.69			−0.265336			−0.132668	−	0.991161i	$-0.542354\pi$
$647$	−4366.69			−0.265336			−0.132668	+	0.991161i	$0.542354\pi$
$648$	−4820.28	+	1754.44i	−0.292220	+	0.106359i
$649$	−2105.77	+	11942.4i	−0.127363	+	0.722314i
$650$	−11565.1	+	9704.29i	−0.697879	+	0.585590i
$651$	−2642.42	−	2217.25i	−0.159085	−	0.133488i
$652$	756.263	+	4288.98i	0.0454257	+	0.257622i
$653$	−4504.04	−	7801.23i	−0.269918	−	0.467512i	0.698922	−	0.715198i	$-0.253663\pi$
$653$	−4504.04	−	7801.23i	−0.269918	−	0.467512i	−0.968841	+	0.247685i	$0.920330\pi$
$654$	−2462.01	+	4264.33i	−0.147205	+	0.254967i
$655$	1955.75	+	711.833i	0.116668	+	0.0424636i
$656$	4799.03	+	1746.70i	0.285626	+	0.103959i
$657$	−15505.3	+	26855.9i	−0.920729	+	1.59475i
$658$	819.309	+	1419.09i	0.0485410	+	0.0840755i
$659$	505.240	+	2865.36i	0.0298655	+	0.169376i	0.996092	−	0.0883171i	$-0.0281489\pi$
$659$	505.240	+	2865.36i	0.0298655	+	0.169376i	−0.966227	+	0.257693i	$0.917038\pi$
$660$	4155.62	+	3486.98i	0.245087	+	0.205652i
$661$	4846.58	−	4066.76i	0.285189	−	0.239302i	−0.488959	−	0.872307i	$-0.662623\pi$
$661$	4846.58	−	4066.76i	0.285189	−	0.239302i	0.774148	+	0.633005i	$0.218179\pi$
$662$	2853.19	−	16181.3i	0.167511	−	0.950003i
$663$	−45477.4	+	16552.4i	−2.66394	+	0.969596i
$664$	6986.77			0.408342
$665$	−3046.64	+	782.607i	−0.177660	+	0.0456364i
$666$	20506.7			1.19312
$667$	14602.1	−	5314.73i	0.847670	−	0.308527i
$668$	−1873.88	+	10627.3i	−0.108537	+	0.615542i
$669$	−33352.6	+	27986.2i	−1.92749	+	1.61735i
$670$	−6459.85	−	5420.46i	−0.372486	−	0.312553i
$671$	2293.51	+	13007.2i	0.131952	+	0.748339i
$672$	1016.72	+	1761.01i	0.0583644	+	0.101090i
$673$	15112.3	−	26175.3i	0.865584	−	1.49924i	−0.000882392	−	1.00000i	$-0.500281\pi$
$673$	15112.3	−	26175.3i	0.865584	−	1.49924i	0.866466	−	0.499236i	$-0.166386\pi$
$674$	−14186.4	−	5163.41i	−0.810739	−	0.295085i
$675$	−2176.57	−	792.206i	−0.124113	−	0.0451734i
$676$	−6009.86	+	10409.4i	−0.341936	+	0.592250i
$677$	−9639.73	−	16696.5i	−0.547245	−	0.947856i	−0.998462	−	0.0554417i	$-0.982343\pi$
$677$	−9639.73	−	16696.5i	−0.547245	−	0.947856i	0.451217	−	0.892414i	$-0.350990\pi$
$678$	5217.78	+	29591.5i	0.295557	+	1.67619i
$679$	6360.87	+	5337.40i	0.359511	+	0.301665i
$680$	−2457.85	+	2062.38i	−0.138609	+	0.116307i
$681$	5803.37	−	32912.6i	0.326558	−	1.85200i
$682$	4065.88	−	1479.86i	0.228285	−	0.0830890i
$683$	21336.4			1.19533			0.597667	−	0.801745i	$-0.296095\pi$
$683$	21336.4			1.19533			0.597667	+	0.801745i	$0.296095\pi$
$684$	−6938.73	−	7084.02i	−0.387879	−	0.396000i
$685$	−700.452			−0.0390699
$686$	9735.17	−	3543.31i	0.541823	−	0.197207i
$687$	1153.05	−	6539.28i	0.0640344	−	0.363157i
$688$	−2484.15	+	2084.45i	−0.137656	+	0.115507i
$689$	23381.3	+	19619.2i	1.29282	+	1.08481i
$690$	1054.12	+	5978.18i	0.0581587	+	0.329834i
$691$	−5706.97	−	9884.76i	−0.314187	−	0.544188i	0.665077	−	0.746775i	$-0.268399\pi$
$691$	−5706.97	−	9884.76i	−0.314187	−	0.544188i	−0.979264	+	0.202586i	$0.935065\pi$
$692$	−2844.92	+	4927.54i	−0.156283	+	0.270689i
$693$	−9440.81	−	3436.17i	−0.517499	−	0.188354i
$694$	−6102.17	−	2221.01i	−0.333768	−	0.121482i
$695$	−41.6250	+	72.0966i	−0.00227184	+	0.00393494i
$696$	5258.15	+	9107.39i	0.286365	+	0.495998i
$697$	−4929.05	−	27954.0i	−0.267864	−	1.51913i
$698$	6325.77	+	5307.95i	0.343028	+	0.287835i
$699$	2211.03	−	1855.27i	0.119640	−	0.100390i
$700$	612.229	−	3472.12i	0.0330573	−	0.187477i
$701$	17976.4	−	6542.88i	0.968559	−	0.352527i	0.191177	−	0.981556i	$-0.438770\pi$
$701$	17976.4	−	6542.88i	0.968559	−	0.352527i	0.777382	+	0.629029i	$0.216547\pi$
$702$	−3192.38			−0.171636
$703$	−11722.3	−	25834.0i	−0.628897	−	1.38598i
$704$	−2550.66			−0.136551
$705$	−3110.88	+	1132.27i	−0.166188	+	0.0604875i
$706$	2085.05	−	11824.9i	0.111150	−	0.630363i
$707$	4792.10	−	4021.05i	0.254916	−	0.213900i
$708$	−7035.01	−	5903.07i	−0.373435	−	0.313349i
$709$	4148.24	+	23525.9i	0.219733	+	1.24617i	0.872502	+	0.488610i	$0.162496\pi$
$709$	4148.24	+	23525.9i	0.219733	+	1.24617i	−0.652770	+	0.757557i	$0.726393\pi$
$710$	4819.70	+	8347.97i	0.254761	+	0.441259i
$711$	−1579.25	+	2735.33i	−0.0833001	+	0.144280i
$712$	1196.53	+	435.501i	0.0629802	+	0.0229229i
$713$	4549.78	+	1655.98i	0.238977	+	0.0869805i
$714$	5651.02	−	9787.85i	0.296196	−	0.513027i
$715$	−6481.75	−	11226.7i	−0.339026	−	0.587210i
$716$	−683.564	−	3876.69i	−0.0356788	−	0.202344i
$717$	−17659.0	−	14817.7i	−0.919787	−	0.771793i
$718$	12389.5	−	10396.0i	0.643973	−	0.540357i
$719$	2713.73	−	15390.3i	0.140758	−	0.798278i	−0.829918	−	0.557886i	$-0.811613\pi$
$719$	2713.73	−	15390.3i	0.140758	−	0.798278i	0.970676	−	0.240392i	$-0.0772761\pi$
$720$	−2029.66	+	738.736i	−0.105057	+	0.0382376i
$721$	−1504.11			−0.0776921
$722$	−4957.91	+	12790.7i	−0.255560	+	0.659310i
$723$	407.624			0.0209678
$724$	−2712.45	+	987.250i	−0.139237	+	0.0506780i
$725$	3166.25	−	17956.7i	0.162195	−	0.919855i
$726$	2975.01	−	2496.33i	0.152084	−	0.127614i
$727$	−2128.33	−	1785.88i	−0.108577	−	0.0911069i	0.586883	−	0.809672i	$-0.300355\pi$
$727$	−2128.33	−	1785.88i	−0.108577	−	0.0911069i	−0.695460	+	0.718565i	$0.744799\pi$
$728$	−843.805	−	4785.45i	−0.0429581	−	0.243627i
$729$	11850.9	+	20526.4i	0.602090	+	1.04285i
$730$	4672.24	−	8092.56i	0.236887	−	0.410300i
$731$	16936.9	+	6164.54i	0.856956	+	0.311907i
$732$	−9399.09	−	3420.99i	−0.474591	−	0.172737i
$733$	−16469.7	+	28526.4i	−0.829908	+	1.43744i	0.0682018	+	0.997672i	$0.478274\pi$
$733$	−16469.7	+	28526.4i	−0.829908	+	1.43744i	−0.898110	+	0.439771i	$0.855059\pi$
$734$	6974.47	+	12080.1i	0.350726	+	0.607474i
$735$	1607.71	+	9117.78i	0.0806821	+	0.457571i
$736$	−2186.47	−	1834.66i	−0.109503	−	0.0918840i
$737$	−28542.9	+	23950.4i	−1.42658	+	1.19705i
$738$	3318.17	−	18818.3i	0.165506	−	0.938633i
$739$	−11380.2	+	4142.04i	−0.566476	+	0.206180i	−0.609352	−	0.792900i	$-0.708570\pi$
$739$	−11380.2	+	4142.04i	−0.566476	+	0.206180i	0.0428757	+	0.999080i	$0.486348\pi$
$740$	−6179.34			−0.306969
$741$	18623.5	+	41043.1i	0.923282	+	2.03476i
$742$	−7127.90			−0.352660
$743$	−1766.74	+	643.040i	−0.0872346	+	0.0317508i	−0.385269	−	0.922804i	$-0.625891\pi$
$743$	−1766.74	+	643.040i	−0.0872346	+	0.0317508i	0.298034	+	0.954555i	$0.403669\pi$
$744$	−568.994	+	3226.93i	−0.0280381	+	0.159012i
$745$	2734.47	−	2294.49i	0.134474	−	0.112837i
$746$	−1544.20	−	1295.74i	−0.0757870	−	0.0635928i
$747$	−4539.50	−	25744.8i	−0.222345	−	1.26098i
$748$	7088.40	+	12277.5i	0.346494	+	0.600145i
$749$	254.283	−	440.430i	0.0124049	−	0.0214859i
$750$	14687.6	+	5345.86i	0.715089	+	0.260271i
$751$	17657.1	+	6426.65i	0.857944	+	0.312266i	0.733275	−	0.679932i	$-0.237991\pi$
$751$	17657.1	+	6426.65i	0.857944	+	0.312266i	0.124669	+	0.992198i	$0.460213\pi$
$752$	778.285	−	1348.03i	0.0377408	−	0.0653691i
$753$	16622.1	+	28790.3i	0.804440	+	1.39333i
$754$	−4363.89	−	24748.8i	−0.210774	−	1.19536i
$755$	−1546.62	−	1297.77i	−0.0745525	−	0.0625570i
$756$	571.105	−	479.214i	0.0274747	−	0.0230540i
$757$	1227.29	−	6960.28i	0.0589253	−	0.334182i	−0.941067	−	0.338221i	$-0.890175\pi$
$757$	1227.29	−	6960.28i	0.0589253	−	0.334182i	0.999992	+	0.00403952i	$0.00128582\pi$
$758$	−16729.7	+	6089.11i	−0.801649	+	0.291776i
$759$	26822.2			1.28272
$760$	2090.86	+	2134.64i	0.0997942	+	0.101884i
$761$	15128.1			0.720623			0.360312	−	0.932832i	$-0.382670\pi$
$761$	15128.1			0.720623			0.360312	+	0.932832i	$0.382670\pi$
$762$	−34600.7	+	12593.6i	−1.64495	+	0.598713i
$763$	−477.175	+	2706.19i	−0.0226407	+	0.128402i
$764$	6351.73	−	5329.74i	0.300782	−	0.252386i
$765$	9196.38	+	7716.68i	0.434635	+	0.364702i
$766$	−228.833	−	1297.78i	−0.0107938	−	0.0612148i
$767$	10972.9	+	19005.6i	0.516568	+	0.894722i
$768$	965.811	−	1672.83i	0.0453785	−	0.0785979i
$769$	−35651.6	−	12976.1i	−1.67182	−	0.608493i	−0.679668	−	0.733520i	$-0.737876\pi$
$769$	−35651.6	−	12976.1i	−1.67182	−	0.608493i	−0.992153	+	0.125027i	$0.960098\pi$
$770$	2844.82	+	1035.43i	0.133143	+	0.0484602i
$771$	−5381.62	+	9321.24i	−0.251381	+	0.435404i
$772$	−9261.59	−	16041.6i	−0.431777	−	0.747860i
$773$	5331.82	+	30238.3i	0.248088	+	1.40698i	0.813210	+	0.581971i	$0.197718\pi$
$773$	5331.82	+	30238.3i	0.248088	+	1.40698i	−0.565121	+	0.825008i	$0.691171\pi$
$774$	9294.78	+	7799.24i	0.431646	+	0.362194i
$775$	4352.15	−	3651.88i	0.201721	−	0.169264i
$776$	1369.69	−	7767.92i	0.0633623	−	0.359345i
$777$	20454.2	−	7444.72i	0.944389	−	0.343730i
$778$	3530.91			0.162711
$779$	−25603.7	+	6576.96i	−1.17760	+	0.302496i
$780$	9817.28			0.450660
$781$	40023.2	−	14567.3i	1.83373	−	0.667424i
$782$	−2754.76	+	15623.0i	−0.125972	+	0.714423i
$783$	2953.57	−	2478.34i	0.134805	−	0.113114i
$784$	−3334.75	−	2798.18i	−0.151911	−	0.127468i
$785$	1547.14	+	8774.28i	0.0703438	+	0.398940i
$786$	3482.11	+	6031.19i	0.158019	+	0.273696i
$787$	−12613.2	+	21846.6i	−0.571297	+	0.989516i	0.425136	+	0.905129i	$0.360226\pi$
$787$	−12613.2	+	21846.6i	−0.571297	+	0.989516i	−0.996433	+	0.0843861i	$0.973107\pi$
$788$	−9644.05	−	3510.15i	−0.435983	−	0.158685i
$789$	3230.70	+	1175.88i	0.145774	+	0.0530574i
$790$	475.878	−	824.244i	0.0214316	−	0.0371206i
$791$	8384.42	+	14522.2i	0.376884	+	0.652783i
$792$	1657.24	+	9398.65i	0.0743527	+	0.421675i
$793$	18310.2	+	15364.1i	0.819944	+	0.688015i
$794$	22831.0	−	19157.5i	1.02046	−	0.856264i
$795$	2500.64	−	14181.8i	0.111558	−	0.632677i
$796$	−3829.02	+	1393.65i	−0.170497	+	0.0620559i
$797$	−34813.7			−1.54726			−0.773628	−	0.633640i	$-0.781560\pi$
$797$	−34813.7			−1.54726			−0.773628	+	0.633640i	$0.781560\pi$
$798$	−9492.73	−	4546.85i	−0.421102	−	0.201700i
$799$	−8651.54			−0.383066
$800$	−3147.17	+	1145.48i	−0.139086	+	0.0506233i
$801$	827.312	−	4691.92i	0.0364939	−	0.206967i
$802$	−5493.75	+	4609.81i	−0.241884	+	0.202965i
$803$	−31629.0	−	26539.9i	−1.38999	−	1.16634i
$804$	−4899.86	−	27788.5i	−0.214931	−	1.21894i
$805$	1693.85	+	2933.84i	0.0741620	+	0.128452i
$806$	3915.14	−	6781.23i	0.171098	−	0.296351i
$807$	55432.7	+	20175.8i	2.41800	+	0.880078i
$808$	−5584.04	−	2032.42i	−0.243126	−	0.0884906i
$809$	4140.95	−	7172.34i	0.179961	−	0.311701i	−0.761906	−	0.647687i	$-0.775736\pi$
$809$	4140.95	−	7172.34i	0.179961	−	0.311701i	0.941867	+	0.335987i	$0.109070\pi$
$810$	−2891.77	−	5008.69i	−0.125440	−	0.217268i
$811$	−6006.07	−	34062.1i	−0.260051	−	1.47483i	−0.782765	−	0.622317i	$-0.786191\pi$
$811$	−6006.07	−	34062.1i	−0.260051	−	1.47483i	0.522714	−	0.852508i	$-0.324920\pi$
$812$	4495.77	+	3772.40i	0.194299	+	0.163036i
$813$	24544.7	−	20595.5i	1.05882	−	0.888457i
$814$	−4741.20	+	26888.7i	−0.204151	+	1.15780i
$815$	−4614.19	+	1679.43i	−0.198317	+	0.0721813i
$816$	−10736.1			−0.460587
$817$	4512.15	−	16167.7i	0.193219	−	0.692332i
$818$	−7981.04			−0.341138
$819$	−17085.1	+	6218.48i	−0.728942	+	0.265313i
$820$	−999.873	+	5670.56i	−0.0425818	+	0.241493i
$821$	13976.3	−	11727.5i	0.594123	−	0.498528i	−0.295428	−	0.955365i	$-0.595462\pi$
$821$	13976.3	−	11727.5i	0.594123	−	0.498528i	0.889550	+	0.456837i	$0.151018\pi$
$822$	−1795.47	−	1506.58i	−0.0761851	−	0.0639269i
$823$	1638.21	+	9290.77i	0.0693858	+	0.393506i	0.999646	+	0.0266059i	$0.00846993\pi$
$823$	1638.21	+	9290.77i	0.0693858	+	0.393506i	−0.930260	+	0.366900i	$0.880419\pi$
$824$	714.398	+	1237.37i	0.0302029	+	0.0523130i
$825$	15736.5	−	27256.5i	0.664092	−	1.15024i
$826$	−4815.97	−	1752.87i	−0.202868	−	0.0738379i
$827$	16095.2	+	5858.16i	0.676764	+	0.246322i	0.657458	−	0.753492i	$-0.271632\pi$
$827$	16095.2	+	5858.16i	0.676764	+	0.246322i	0.0193066	+	0.999814i	$0.493854\pi$
$828$	−5339.74	+	9248.70i	−0.224117	+	0.388182i
$829$	−14524.7	−	25157.5i	−0.608521	−	1.05399i	−0.991484	−	0.130226i	$-0.958430\pi$
$829$	−14524.7	−	25157.5i	−0.608521	−	1.05399i	0.382963	−	0.923763i	$-0.374904\pi$
$830$	1367.90	+	7757.73i	0.0572053	+	0.324427i
$831$	−33611.2	−	28203.2i	−1.40308	−	1.17733i
$832$	−3536.03	+	2967.08i	−0.147344	+	0.123636i
$833$	−4201.50	+	23827.9i	−0.174758	+	0.991101i
$834$	−261.768	+	95.2756i	−0.0108684	+	0.00395578i
$835$	−12166.8			−0.504252
$836$	10892.9	−	7460.32i	0.450645	−	0.308637i
$837$	1201.35			0.0496112
$838$	−14401.6	+	5241.74i	−0.593668	+	0.216078i
$839$	−1713.44	+	9717.39i	−0.0705059	+	0.399859i	0.929047	+	0.369961i	$0.120629\pi$
$839$	−1713.44	+	9717.39i	−0.0705059	+	0.399859i	−0.999553	+	0.0298972i	$0.990482\pi$
$840$	−1756.27	+	1473.69i	−0.0721396	+	0.0605323i
$841$	4567.63	+	3832.69i	0.187282	+	0.157148i
$842$	2335.97	+	13247.9i	0.0956090	+	0.542226i
$843$	−12983.6	−	22488.2i	−0.530459	−	0.918783i
$844$	4417.57	−	7651.45i	0.180165	−	0.312054i
$845$	−12734.6	−	4635.03i	−0.518444	−	0.188698i
$846$	−5472.87	−	1991.96i	−0.222413	−	0.0809516i
$847$	1083.66	−	1876.95i	0.0439610	−	0.0761426i
$848$	3385.49	+	5863.85i	0.137097	+	0.237459i
$849$	−4400.86	−	24958.5i	−0.177900	−	1.00892i
$850$	14259.8	+	11965.4i	0.575420	+	0.482834i
$851$	−23405.0	+	19639.1i	−0.942787	+	0.791092i
$852$	−5601.01	+	31764.9i	−0.225220	+	1.27729i
$853$	38945.6	−	14175.0i	1.56327	−	0.568984i	0.591789	−	0.806093i	$-0.298422\pi$
$853$	38945.6	−	14175.0i	1.56327	−	0.568984i	0.971483	+	0.237109i	$0.0761997\pi$
$854$	−5581.97			−0.223666
$855$	6507.22	−	9091.33i	0.260283	−	0.363645i
$856$	−483.100			−0.0192897
$857$	−17262.3	+	6282.95i	−0.688061	+	0.250434i	−0.662305	−	0.749235i	$-0.730422\pi$
$857$	−17262.3	+	6282.95i	−0.688061	+	0.250434i	−0.0257561	+	0.999668i	$0.508199\pi$
$858$	7532.48	−	42718.8i	0.299714	−	1.69976i
$859$	−28140.6	+	23612.8i	−1.11775	+	0.937902i	−0.998489	−	0.0549607i	$-0.982497\pi$
$859$	−28140.6	+	23612.8i	−1.11775	+	0.937902i	−0.119260	+	0.992863i	$0.538052\pi$
$860$	−2800.82	−	2350.16i	−0.111055	−	0.0931860i
$861$	−3522.08	−	19974.7i	−0.139410	−	0.790635i
$862$	−16437.3	−	28470.3i	−0.649486	−	1.12494i
$863$	−4766.52	+	8255.85i	−0.188012	+	0.325646i	−0.944587	−	0.328260i	$-0.893538\pi$
$863$	−4766.52	+	8255.85i	−0.188012	+	0.325646i	0.756576	+	0.653906i	$0.226871\pi$
$864$	−665.485	−	242.217i	−0.0262040	−	0.00953748i
$865$	−6028.27	−	2194.11i	−0.236956	−	0.0862450i
$866$	2878.88	−	4986.37i	0.112966	−	0.195663i
$867$	11300.8	+	19573.6i	0.442672	+	0.766730i
$868$	317.538	+	1800.84i	0.0124170	+	0.0704201i
$869$	−3221.48	−	2703.14i	−0.125755	−	0.105521i
$870$	−9082.89	+	7621.45i	−0.353952	+	0.297001i
$871$	−11709.1	+	66405.7i	−0.455509	+	2.58332i
$872$	2452.92	−	892.790i	0.0952596	−	0.0346717i
$873$	−29513.1			−1.14418
$874$	14703.7	+	1440.05i	0.569062	+	0.0557328i
$875$	8722.74			0.337009
$876$	29382.4	−	10694.3i	1.13326	−	0.412474i
$877$	−4282.08	+	24284.9i	−0.164875	+	0.935053i	0.784318	+	0.620359i	$0.213013\pi$
$877$	−4282.08	+	24284.9i	−0.164875	+	0.935053i	−0.949193	+	0.314694i	$0.898098\pi$
$878$	−6681.82	+	5606.71i	−0.256834	+	0.215509i
$879$	−12004.1	−	10072.7i	−0.460625	−	0.386510i
$880$	−499.379	−	2832.12i	−0.0191296	−	0.108489i
$881$	−25568.5	−	44285.9i	−0.977780	−	1.69357i	−0.670437	−	0.741966i	$-0.733893\pi$
$881$	−25568.5	−	44285.9i	−0.977780	−	1.69357i	−0.307343	−	0.951599i	$-0.599440\pi$
$882$	−8144.04	+	14105.9i	−0.310912	+	0.538515i
$883$	−25695.5	−	9352.39i	−0.979300	−	0.356436i	−0.197732	−	0.980256i	$-0.563358\pi$
$883$	−25695.5	−	9352.39i	−0.979300	−	0.356436i	−0.781568	+	0.623820i	$0.785580\pi$
$884$	24108.7	+	8774.83i	0.917265	+	0.333857i
$885$	5177.11	−	8967.02i	0.196640	−	0.340591i
$886$	−14763.5	−	25571.1i	−0.559806	−	0.969613i
$887$	−4074.70	−	23108.8i	−0.154245	−	0.874766i	−0.959473	−	0.281801i	$-0.909068\pi$
$887$	−4074.70	−	23108.8i	−0.154245	−	0.874766i	0.805228	−	0.592965i	$-0.202043\pi$
$888$	−15839.5	−	13290.9i	−0.598580	−	0.502268i
$889$	−15741.3	+	13208.5i	−0.593865	+	0.498312i
$890$	−249.296	+	1413.83i	−0.00938923	+	0.0532490i
$891$	−24013.5	+	8740.20i	−0.902899	+	0.328628i
$892$	23081.0			0.866377
$893$	619.030	+	8033.29i	0.0231971	+	0.301034i
$894$	11944.4			0.446847
$895$	4170.63	−	1517.99i	0.155764	−	0.0566935i
$896$	187.189	−	1061.60i	0.00697939	−	0.0395821i
$897$	37184.1	−	31201.2i	1.38410	−	1.16140i
$898$	12545.4	+	10526.9i	0.466199	+	0.391188i
$899$	1642.20	+	9313.39i	0.0609238	+	0.345516i
$900$	6265.64	+	10852.4i	0.232061	+	0.401941i
$901$	18816.9	−	32591.8i	0.695761	−	1.20509i
$902$	23907.6	+	8701.67i	0.882525	+	0.321213i
$903$	12102.4	+	4404.91i	0.446005	+	0.162333i
$904$	7964.59	−	13795.1i	0.293029	−	0.507541i
$905$	−1627.24	−	2818.47i	−0.0597695	−	0.103524i
$906$	−1173.13	−	6653.13i	−0.0430182	−	0.243968i
$907$	9003.78	+	7555.07i	0.329620	+	0.276584i	0.792545	−	0.609813i	$-0.208756\pi$
$907$	9003.78	+	7555.07i	0.329620	+	0.276584i	−0.462925	+	0.886398i	$0.653200\pi$
$908$	−13571.9	+	11388.2i	−0.496036	+	0.416224i
$909$	−3860.95	+	21896.5i	−0.140880	+	0.798968i
$910$	5148.30	−	1873.83i	0.187544	−	0.0682603i
$911$	34914.5			1.26978			0.634891	−	0.772602i	$-0.281045\pi$
$911$	34914.5			1.26978			0.634891	+	0.772602i	$0.281045\pi$
$912$	768.184	+	9968.90i	0.0278916	+	0.361955i
$913$	34806.4			1.26169
$914$	14055.7	−	5115.86i	0.508667	−	0.185140i
$915$	1958.29	−	11106.0i	0.0707531	−	0.401261i
$916$	−2696.56	+	2262.68i	−0.0972673	+	0.0816170i
$917$	2977.24	+	2498.20i	0.107216	+	0.0899649i
$918$	683.514	+	3876.40i	0.0245744	+	0.139369i
$919$	11737.9	+	20330.7i	0.421326	+	0.729757i	0.996069	−	0.0885760i	$-0.0282316\pi$
$919$	11737.9	+	20330.7i	0.421326	+	0.729757i	−0.574744	+	0.818333i	$0.694898\pi$
$920$	1609.04	−	2786.93i	0.0576612	−	0.0998722i
$921$	44425.1	+	16169.4i	1.58942	+	0.578502i
$922$	10976.7	+	3995.21i	0.392082	+	0.142706i
$923$	38539.5	−	66752.3i	1.37437	−	2.38048i
$924$	5065.06	+	8772.94i	0.180334	+	0.312347i
$925$	6225.43	+	35306.2i	0.221288	+	1.25498i
$926$	−17716.6	−	14866.0i	−0.628731	−	0.527568i
$927$	4095.29	−	3436.36i	0.145099	−	0.121753i
$928$	968.080	−	5490.25i	0.0342444	−	0.194209i
$929$	−10709.6	+	3897.97i	−0.378224	+	0.137662i	−0.524134	−	0.851636i	$-0.675611\pi$
$929$	−10709.6	+	3897.97i	−0.378224	+	0.137662i	0.145911	+	0.989298i	$0.453389\pi$
$930$	−3694.40			−0.130263
$931$	22425.7	+	2196.33i	0.789445	+	0.0773168i
$932$	−1530.09			−0.0537767
$933$	−71394.4	+	25985.5i	−2.50520	+	0.911817i
$934$	−2508.78	+	14228.0i	−0.0878905	+	0.498452i
$935$	−12244.4	+	10274.3i	−0.428274	+	0.359364i
$936$	13230.5	+	11101.7i	0.462023	+	0.387683i
$937$	6822.68	+	38693.3i	0.237873	+	1.34905i	0.836478	+	0.548001i	$0.184611\pi$
$937$	6822.68	+	38693.3i	0.237873	+	1.34905i	−0.598605	+	0.801045i	$0.704278\pi$
$938$	−7873.56	−	13637.4i	−0.274073	−	0.474709i
$939$	−17042.6	+	29518.7i	−0.592295	+	1.02588i
$940$	1649.15	+	600.243i	0.0572228	+	0.0208274i
$941$	−8163.60	−	2971.31i	−0.282812	−	0.102935i	0.196720	−	0.980460i	$-0.436971\pi$
$941$	−8163.60	−	2971.31i	−0.282812	−	0.102935i	−0.479531	+	0.877525i	$0.659193\pi$
$942$	−14906.5	+	25818.8i	−0.515584	+	0.893017i
$943$	14235.0	+	24655.7i	0.491574	+	0.851432i
$944$	845.393	+	4794.46i	0.0291475	+	0.165303i
$945$	643.906	+	540.302i	0.0221654	+	0.0185990i
$946$	−12375.4	+	10384.2i	−0.425328	+	0.356893i
$947$	−4514.49	+	25602.9i	−0.154911	+	0.878546i	0.803955	+	0.594690i	$0.202725\pi$
$947$	−4514.49	+	25602.9i	−0.154911	+	0.878546i	−0.958867	+	0.283857i	$0.908386\pi$
$948$	2992.66	−	1089.24i	0.102528	−	0.0373173i
$949$	−74720.7			−2.55589
$950$	10090.0	−	14096.9i	0.344593	−	0.481436i
$951$	−78642.6			−2.68156
$952$	−5630.15	+	2049.21i	−0.191675	+	0.0697639i
$953$	4574.98	−	25946.0i	0.155507	−	0.881923i	−0.802814	−	0.596230i	$-0.796665\pi$
$953$	4574.98	−	25946.0i	0.155507	−	0.881923i	0.958321	−	0.285694i	$-0.0922241\pi$
$954$	19407.4	−	16284.7i	0.658635	−	0.552660i
$955$	7161.42	+	6009.14i	0.242658	+	0.203614i
$956$	2122.07	+	12034.9i	0.0717916	+	0.407150i
$957$	26194.9	+	45370.8i	0.884806	+	1.53253i
$958$	4432.03	−	7676.51i	0.149470	−	0.258890i
$959$	−1229.13	−	447.365i	−0.0413875	−	0.0150638i
$960$	2046.51	+	744.870i	0.0688031	+	0.0250423i
$961$	13422.2	−	23247.9i	0.450544	−	0.780366i
$962$	24705.7	+	42791.5i	0.828008	+	1.43415i
$963$	313.883	+	1780.12i	0.0105034	+	0.0595676i
$964$	−165.536	−	138.901i	−0.00553065	−	0.00464076i
$965$	15998.4	−	13424.2i	0.533686	−	0.447815i
$966$	−1968.43	+	11163.5i	−0.0655624	+	0.371823i
$967$	25876.7	−	9418.34i	0.860535	−	0.313209i	0.126207	−	0.992004i	$-0.459720\pi$
$967$	25876.7	−	9418.34i	0.860535	−	0.313209i	0.734328	+	0.678795i	$0.237497\pi$
$968$	−2058.79			−0.0683597
$969$	45849.9	−	31401.6i	1.52003	−	1.04104i
$970$	8893.24			0.294376
$971$	−22590.8	+	8222.39i	−0.746627	+	0.271750i	−0.687186	−	0.726482i	$-0.741154\pi$
$971$	−22590.8	+	8222.39i	−0.746627	+	0.271750i	−0.0594410	+	0.998232i	$0.518932\pi$
$972$	3775.59	−	21412.4i	0.124591	−	0.706588i
$973$	−119.089	+	99.9274i	−0.00392375	+	0.00329242i
$974$	942.000	+	790.432i	0.0309893	+	0.0260032i
$975$	−9890.51	−	56091.9i	−0.324872	−	1.84244i
$976$	2651.23	+	4592.07i	0.0869507	+	0.150603i
$977$	2945.22	−	5101.26i	0.0964440	−	0.167046i	−0.813766	−	0.581192i	$-0.802586\pi$
$977$	2945.22	−	5101.26i	0.0964440	−	0.167046i	0.910210	+	0.414146i	$0.135920\pi$
$978$	−15439.8	−	5619.62i	−0.504815	−	0.183738i
$979$	5960.83	+	2169.56i	0.194595	+	0.0708270i
$980$	2454.06	−	4250.56i	0.0799920	−	0.138550i
$981$	−4883.47	−	8458.42i	−0.158937	−	0.275287i
$982$	3040.77	+	17245.1i	0.0988134	+	0.560399i
$983$	−2112.34	−	1772.47i	−0.0685384	−	0.0575105i	0.607875	−	0.794033i	$-0.292022\pi$
$983$	−2112.34	−	1772.47i	−0.0685384	−	0.0575105i	−0.676413	+	0.736522i	$0.736467\pi$
$984$	−14759.6	+	12384.8i	−0.478169	+	0.401231i
$985$	2009.33	−	11395.5i	0.0649974	−	0.368619i
$986$	−29117.3	+	10597.8i	−0.940451	+	0.342296i
$987$	−6182.02			−0.199368
$988$	6422.76	−	23013.7i	0.206817	−	0.741055i
$989$	−18077.7			−0.581230
$990$	−10111.3	+	3680.21i	−0.324604	+	0.118146i
$991$	1177.25	−	6676.50i	0.0377361	−	0.214012i	−0.960109	−	0.279626i	$-0.909789\pi$
$991$	1177.25	−	6676.50i	0.0377361	−	0.214012i	0.997845	+	0.0656140i	$0.0209006\pi$
$992$	1330.67	−	1116.56i	0.0425894	−	0.0357368i
$993$	47486.1	+	39845.6i	1.51755	+	1.27338i
$994$	3125.74	+	17727.0i	0.0997410	+	0.565659i
$995$	−2297.09	−	3978.68i	−0.0731886	−	0.126766i
$996$	−13179.5	+	22827.5i	−0.419285	+	0.726223i
$997$	−26221.4	−	9543.82i	−0.832940	−	0.303165i	−0.109875	−	0.993945i	$-0.535045\pi$
$997$	−26221.4	−	9543.82i	−0.832940	−	0.303165i	−0.723065	+	0.690780i	$0.757267\pi$
$998$	22330.5	+	8127.65i	0.708277	+	0.257792i
$999$	−3790.42	+	6565.21i	−0.120044	+	0.207922i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.4.e.b.5.1	✓	18
19.2	odd	18		722.4.a.u.1.8		9
19.4	even	9	inner	38.4.e.b.23.1	yes	18
19.17	even	9		722.4.a.t.1.2		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.4.e.b.5.1	✓	18	1.1	even	1	trivial
38.4.e.b.23.1	yes	18	19.4	even	9	inner
722.4.a.t.1.2		9	19.17	even	9
722.4.a.u.1.8		9	19.2	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)

\(f(q)\)	\(=\)	\(q+(1.87939 - 0.684040i) q^{2} +(-1.31024 + 7.43077i) q^{3} +(3.06418 - 2.57115i) q^{4} +(3.45478 + 2.89891i) q^{5} +(2.62049 + 14.8615i) q^{6} +(4.21085 + 7.29340i) q^{7} +(4.00000 - 6.92820i) q^{8} +(-28.1279 - 10.2377i) q^{9} +O(q^{10})\)	\(q+(1.87939 - 0.684040i) q^{2} +(-1.31024 + 7.43077i) q^{3} +(3.06418 - 2.57115i) q^{4} +(3.45478 + 2.89891i) q^{5} +(2.62049 + 14.8615i) q^{6} +(4.21085 + 7.29340i) q^{7} +(4.00000 - 6.92820i) q^{8} +(-28.1279 - 10.2377i) q^{9} +(8.47584 + 3.08495i) q^{10} +(19.9270 - 34.5147i) q^{11} +(15.0908 + 26.1380i) q^{12} +(-12.5243 - 71.0287i) q^{13} +(12.9028 + 10.8267i) q^{14} +(-26.0677 + 21.8734i) q^{15} +(2.77837 - 15.7569i) q^{16} +(-83.5662 + 30.4156i) q^{17} -59.8661 q^{18} +(34.2213 + 75.4182i) q^{19} +18.0396 q^{20} +(-59.7128 + 21.7337i) q^{21} +(13.8412 - 78.4973i) q^{22} +(68.3271 - 57.3332i) q^{23} +(46.2409 + 38.8007i) q^{24} +(-18.1742 - 103.071i) q^{25} +(-72.1244 - 124.923i) q^{26} +(11.0655 - 19.1661i) q^{27} +(31.6552 + 11.5216i) q^{28} +(163.711 + 59.5858i) q^{29} +(-34.0290 + 58.9399i) q^{30} +(27.1416 + 47.0106i) q^{31} +(-5.55674 - 31.5138i) q^{32} +(230.361 + 193.296i) q^{33} +(-136.248 + 114.325i) q^{34} +(-6.59533 + 37.4040i) q^{35} +(-112.511 + 40.9508i) q^{36} -342.543 q^{37} +(115.904 + 118.331i) q^{38} +544.207 q^{39} +(33.9033 - 12.3398i) q^{40} +(-55.4266 + 314.340i) q^{41} +(-97.3567 + 81.6919i) q^{42} +(-155.259 - 130.278i) q^{43} +(-27.6824 - 156.995i) q^{44} +(-67.4975 - 116.909i) q^{45} +(89.1947 - 154.490i) q^{46} +(91.4185 + 33.2736i) q^{47} +(113.446 + 41.2909i) q^{48} +(136.038 - 235.624i) q^{49} +(-104.661 - 181.278i) q^{50} +(-116.519 - 660.813i) q^{51} +(-221.002 - 185.443i) q^{52} +(-324.180 + 272.019i) q^{53} +(7.68604 - 43.5897i) q^{54} +(168.898 - 61.4740i) q^{55} +67.3736 q^{56} +(-605.253 + 155.475i) q^{57} +348.434 q^{58} +(-285.926 + 104.069i) q^{59} +(-23.6363 + 134.048i) q^{60} +(-253.870 + 213.022i) q^{61} +(83.1667 + 69.7851i) q^{62} +(-43.7745 - 248.257i) q^{63} +(-32.0000 - 55.4256i) q^{64} +(162.637 - 281.695i) q^{65} +(565.160 + 205.701i) q^{66} +(-878.531 - 319.759i) q^{67} +(-177.859 + 308.060i) q^{68} +(336.505 + 582.843i) q^{69} +(13.1907 + 74.8079i) q^{70} +(818.667 + 686.944i) q^{71} +(-183.440 + 153.925i) q^{72} +(179.899 - 1020.26i) q^{73} +(-643.770 + 234.313i) q^{74} +789.708 q^{75} +(298.772 + 143.106i) q^{76} +335.639 q^{77} +(1022.78 - 372.260i) q^{78} +(18.3231 - 103.915i) q^{79} +(55.2765 - 46.3825i) q^{80} +(-491.191 - 412.158i) q^{81} +(110.853 + 628.679i) q^{82} +(436.673 + 756.340i) q^{83} +(-127.090 + 220.126i) q^{84} +(-376.875 - 137.171i) q^{85} +(-380.908 - 138.639i) q^{86} +(-657.269 + 1138.42i) q^{87} +(-159.416 - 276.117i) q^{88} +(27.6387 + 156.747i) q^{89} +(-206.824 - 173.546i) q^{90} +(465.303 - 390.435i) q^{91} +(61.9540 - 351.358i) q^{92} +(-384.887 + 140.087i) q^{93} +194.571 q^{94} +(-100.403 + 359.758i) q^{95} +241.453 q^{96} +(926.508 - 337.221i) q^{97} +(94.4907 - 535.883i) q^{98} +(-913.857 + 766.817i) 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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