LMFDB - Embedded newform 38.4.e.b.35.3

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			35.3
Root			$-3.71222 + 6.42975i$ of defining polynomial
Character	$\chi$	$=$	38.35
Dual form			38.4.e.b.25.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.53209 - 1.28558i) q^{2} +(9.35607 - 3.40533i) q^{3} +(0.694593 + 3.93923i) q^{4} +(-0.989599 + 5.61230i) q^{5} +(-18.7121 - 6.81067i) q^{6} +(-3.91986 - 6.78940i) q^{7} +(4.00000 - 6.92820i) q^{8} +(55.2566 - 46.3658i) q^{9} +O(q^{10})$	\(q+(-1.53209 - 1.28558i) q^{2} +(9.35607 - 3.40533i) q^{3} +(0.694593 + 3.93923i) q^{4} +(-0.989599 + 5.61230i) q^{5} +(-18.7121 - 6.81067i) q^{6} +(-3.91986 - 6.78940i) q^{7} +(4.00000 - 6.92820i) q^{8} +(55.2566 - 46.3658i) q^{9} +(8.73118 - 7.32633i) q^{10} +(-17.7720 + 30.7821i) q^{11} +(19.9131 + 34.4904i) q^{12} +(-58.7189 - 21.3719i) q^{13} +(-2.72271 + 15.4413i) q^{14} +(9.85297 + 55.8790i) q^{15} +(-15.0351 + 5.47232i) q^{16} +(47.7967 + 40.1062i) q^{17} -144.265 q^{18} +(-51.9332 + 64.5131i) q^{19} -22.7955 q^{20} +(-59.7947 - 50.1737i) q^{21} +(66.8010 - 24.3136i) q^{22} +(19.2019 + 108.900i) q^{23} +(13.8315 - 78.4421i) q^{24} +(86.9430 + 31.6447i) q^{25} +(62.4873 + 108.231i) q^{26} +(224.681 - 389.159i) q^{27} +(24.0223 - 20.1571i) q^{28} +(-84.0517 + 70.5278i) q^{29} +(56.7410 - 98.2783i) q^{30} +(-166.666 - 288.675i) q^{31} +(30.0702 + 10.9446i) q^{32} +(-61.4533 + 348.519i) q^{33} +(-21.6693 - 122.893i) q^{34} +(41.9832 - 15.2806i) q^{35} +(221.027 + 185.463i) q^{36} +36.0219 q^{37} +(162.503 - 32.0758i) q^{38} -622.157 q^{39} +(34.9247 + 29.3053i) q^{40} +(-11.1312 + 4.05141i) q^{41} +(27.1087 + 153.741i) q^{42} +(13.6551 - 77.4420i) q^{43} +(-133.602 - 48.6271i) q^{44} +(205.537 + 356.000i) q^{45} +(110.579 - 191.529i) q^{46} +(179.894 - 150.949i) q^{47} +(-122.034 + 102.399i) q^{48} +(140.769 - 243.820i) q^{49} +(-92.5228 - 160.254i) q^{50} +(583.765 + 212.473i) q^{51} +(43.4033 - 246.152i) q^{52} +(13.5517 + 76.8557i) q^{53} +(-844.524 + 307.382i) q^{54} +(-155.171 - 130.204i) q^{55} -62.7178 q^{56} +(-266.202 + 780.439i) q^{57} +219.443 q^{58} +(-374.801 - 314.496i) q^{59} +(-213.276 + 77.6263i) q^{60} +(-24.0876 - 136.607i) q^{61} +(-115.765 + 656.538i) q^{62} +(-531.395 - 193.412i) q^{63} +(-32.0000 - 55.4256i) q^{64} +(178.054 - 308.398i) q^{65} +(542.199 - 454.959i) q^{66} +(378.424 - 317.535i) q^{67} +(-124.788 + 216.140i) q^{68} +(550.494 + 953.483i) q^{69} +(-83.9665 - 30.5613i) q^{70} +(-17.6696 + 100.210i) q^{71} +(-100.205 - 568.292i) q^{72} +(-533.078 + 194.025i) q^{73} +(-55.1888 - 46.3089i) q^{74} +921.206 q^{75} +(-290.204 - 159.767i) q^{76} +278.656 q^{77} +(953.200 + 799.830i) q^{78} +(351.428 - 127.909i) q^{79} +(-15.8336 - 89.7967i) q^{80} +(438.724 - 2488.13i) q^{81} +(22.2623 + 8.10283i) q^{82} +(-57.8821 - 100.255i) q^{83} +(156.113 - 270.396i) q^{84} +(-272.388 + 228.560i) q^{85} +(-120.478 + 101.093i) q^{86} +(-546.224 + 946.087i) q^{87} +(142.176 + 246.256i) q^{88} +(653.538 + 237.868i) q^{89} +(142.764 - 809.657i) q^{90} +(85.0674 + 482.441i) q^{91} +(-415.643 + 151.282i) q^{92} +(-2542.38 - 2133.31i) q^{93} -469.671 q^{94} +(-310.674 - 355.307i) q^{95} +318.609 q^{96} +(740.669 + 621.495i) q^{97} +(-529.120 + 192.584i) q^{98} +(445.213 + 2524.93i) 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 $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{2}{9}\right)$

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
$3$	9.35607	−	3.40533i	1.80058	−	0.655357i	0.802285	−	0.596941i	$-0.203617\pi$
$3$	9.35607	−	3.40533i	1.80058	−	0.655357i	0.998292	−	0.0584153i	$-0.0186048\pi$
$4$	0.694593	+	3.93923i	0.0868241	+	0.492404i
$5$	−0.989599	+	5.61230i	−0.0885124	+	0.501979i	0.908031	+	0.418903i	$0.137585\pi$
$5$	−0.989599	+	5.61230i	−0.0885124	+	0.501979i	−0.996543	+	0.0830756i	$0.973526\pi$
$6$	−18.7121	−	6.81067i	−1.27320	−	0.463407i
$7$	−3.91986	−	6.78940i	−0.211653	−	0.366593i	0.740579	−	0.671969i	$-0.234551\pi$
$7$	−3.91986	−	6.78940i	−0.211653	−	0.366593i	−0.952232	+	0.305376i	$0.901218\pi$
$8$	4.00000	−	6.92820i	0.176777	−	0.306186i
$9$	55.2566	−	46.3658i	2.04654	−	1.71725i
$10$	8.73118	−	7.32633i	0.276104	−	0.231679i
$11$	−17.7720	+	30.7821i	−0.487133	+	0.843740i	−0.999891	−	0.0147938i	$-0.995291\pi$
$11$	−17.7720	+	30.7821i	−0.487133	+	0.843740i	0.512757	+	0.858534i	$0.328624\pi$
$12$	19.9131	+	34.4904i	0.479034	+	0.829711i
$13$	−58.7189	−	21.3719i	−1.25275	−	0.455962i	−0.371417	−	0.928466i	$-0.621128\pi$
$13$	−58.7189	−	21.3719i	−1.25275	−	0.455962i	−0.881329	+	0.472504i	$0.843350\pi$
$14$	−2.72271	+	15.4413i	−0.0519768	+	0.294775i
$15$	9.85297	+	55.8790i	0.169602	+	0.961859i
$16$	−15.0351	+	5.47232i	−0.234923	+	0.0855050i
$17$	47.7967	+	40.1062i	0.681907	+	0.572188i	0.916563	−	0.399891i	$-0.130952\pi$
$17$	47.7967	+	40.1062i	0.681907	+	0.572188i	−0.234656	+	0.972078i	$0.575396\pi$
$18$	−144.265			−1.88909
$19$	−51.9332	+	64.5131i	−0.627068	+	0.778964i
$19$	−51.9332	+	64.5131i	−0.627068	+	0.778964i
$20$	−22.7955			−0.254861
$21$	−59.7947	−	50.1737i	−0.621347	−	0.521372i
$22$	66.8010	−	24.3136i	0.647364	−	0.235621i
$23$	19.2019	+	108.900i	0.174082	+	0.987266i	0.939199	+	0.343375i	$0.111570\pi$
$23$	19.2019	+	108.900i	0.174082	+	0.987266i	−0.765117	+	0.643891i	$0.777319\pi$
$24$	13.8315	−	78.4421i	0.117639	−	0.667164i
$25$	86.9430	+	31.6447i	0.695544	+	0.253157i
$26$	62.4873	+	108.231i	0.471338	+	0.816381i
$27$	224.681	−	389.159i	1.60148	−	2.77384i
$28$	24.0223	−	20.1571i	0.162135	−	0.136048i
$29$	−84.0517	+	70.5278i	−0.538207	+	0.451610i	−0.870924	−	0.491417i	$-0.836479\pi$
$29$	−84.0517	+	70.5278i	−0.538207	+	0.451610i	0.332717	+	0.943027i	$0.392035\pi$
$30$	56.7410	−	98.2783i	0.345315	−	0.598103i
$31$	−166.666	−	288.675i	−0.965619	−	1.67250i	−0.707943	−	0.706269i	$-0.750377\pi$
$31$	−166.666	−	288.675i	−0.965619	−	1.67250i	−0.257675	−	0.966232i	$-0.582957\pi$
$32$	30.0702	+	10.9446i	0.166116	+	0.0604612i
$33$	−61.4533	+	348.519i	−0.324171	+	1.83847i
$34$	−21.6693	−	122.893i	−0.109302	−	0.619880i
$35$	41.9832	−	15.2806i	0.202756	−	0.0737972i
$36$	221.027	+	185.463i	1.02327	+	0.858626i
$37$	36.0219			0.160053			0.0800266	−	0.996793i	$-0.474499\pi$
$37$	36.0219			0.160053			0.0800266	+	0.996793i	$0.474499\pi$
$38$	162.503	−	32.0758i	0.693722	−	0.136931i
$39$	−622.157			−2.55448
$40$	34.9247	+	29.3053i	0.138052	+	0.115839i
$41$	−11.1312	+	4.05141i	−0.0423999	+	0.0154323i	−0.363133	−	0.931737i	$-0.618293\pi$
$41$	−11.1312	+	4.05141i	−0.0423999	+	0.0154323i	0.320733	+	0.947170i	$0.396071\pi$
$42$	27.1087	+	153.741i	0.0995945	+	0.564828i
$43$	13.6551	−	77.4420i	0.0484275	−	0.274646i	−0.950973	−	0.309275i	$-0.899914\pi$
$43$	13.6551	−	77.4420i	0.0484275	−	0.274646i	0.999400	+	0.0346286i	$0.0110248\pi$
$44$	−133.602	−	48.6271i	−0.457756	−	0.166609i
$45$	205.537	+	356.000i	0.680880	+	1.17932i
$46$	110.579	−	191.529i	0.354436	−	0.613901i
$47$	179.894	−	150.949i	0.558304	−	0.468473i	−0.319437	−	0.947607i	$-0.603494\pi$
$47$	179.894	−	150.949i	0.558304	−	0.468473i	0.877741	+	0.479135i	$0.159049\pi$
$48$	−122.034	+	102.399i	−0.366961	+	0.307917i
$49$	140.769	−	243.820i	0.410406	−	0.710844i
$50$	−92.5228	−	160.254i	−0.261694	−	0.453267i
$51$	583.765	+	212.473i	1.60281	+	0.583376i
$52$	43.4033	−	246.152i	0.115749	−	0.656445i
$53$	13.5517	+	76.8557i	0.0351222	+	0.199188i	0.997320	−	0.0731641i	$-0.0233097\pi$
$53$	13.5517	+	76.8557i	0.0351222	+	0.199188i	−0.962198	+	0.272352i	$0.912199\pi$
$54$	−844.524	+	307.382i	−2.12824	+	0.774618i
$55$	−155.171	−	130.204i	−0.380422	−	0.319212i
$56$	−62.7178			−0.149661
$57$	−266.202	+	780.439i	−0.618585	+	1.81354i
$58$	219.443			0.496799
$59$	−374.801	−	314.496i	−0.827034	−	0.693964i	0.127574	−	0.991829i	$-0.459281\pi$
$59$	−374.801	−	314.496i	−0.827034	−	0.693964i	−0.954608	+	0.297865i	$0.903725\pi$
$60$	−213.276	+	77.6263i	−0.458898	+	0.167025i
$61$	−24.0876	−	136.607i	−0.0505590	−	0.286734i	0.949037	−	0.315165i	$-0.102060\pi$
$61$	−24.0876	−	136.607i	−0.0505590	−	0.286734i	−0.999596	+	0.0284312i	$0.990949\pi$
$62$	−115.765	+	656.538i	−0.237132	+	1.34484i
$63$	−531.395	−	193.412i	−1.06269	−	0.386787i
$64$	−32.0000	−	55.4256i	−0.0625000	−	0.108253i
$65$	178.054	−	308.398i	0.339767	−	0.588494i
$66$	542.199	−	454.959i	1.01121	−	0.848509i
$67$	378.424	−	317.535i	0.690028	−	0.579002i	−0.228890	−	0.973452i	$-0.573509\pi$
$67$	378.424	−	317.535i	0.690028	−	0.579002i	0.918917	+	0.394450i	$0.129065\pi$
$68$	−124.788	+	216.140i	−0.222541	+	0.385453i
$69$	550.494	+	953.483i	0.960459	+	1.66356i
$70$	−83.9665	−	30.5613i	−0.143370	−	0.0521825i
$71$	−17.6696	+	100.210i	−0.0295352	+	0.167503i	−0.996008	−	0.0892678i	$-0.971547\pi$
$71$	−17.6696	+	100.210i	−0.0295352	+	0.167503i	0.966472	+	0.256770i	$0.0826584\pi$
$72$	−100.205	−	568.292i	−0.164018	−	0.930193i
$73$	−533.078	+	194.025i	−0.854686	+	0.311080i	−0.731949	−	0.681359i	$-0.761389\pi$
$73$	−533.078	+	194.025i	−0.854686	+	0.311080i	−0.122737	+	0.992439i	$0.539167\pi$
$74$	−55.1888	−	46.3089i	−0.0866969	−	0.0727473i
$75$	921.206			1.41829
$76$	−290.204	−	159.767i	−0.438010	−	0.241138i
$77$	278.656			0.412413
$78$	953.200	+	799.830i	1.38370	+	1.16106i
$79$	351.428	−	127.909i	0.500491	−	0.182164i	−0.0794240	−	0.996841i	$-0.525308\pi$
$79$	351.428	−	127.909i	0.500491	−	0.182164i	0.579915	+	0.814677i	$0.303086\pi$
$80$	−15.8336	−	89.7967i	−0.0221281	−	0.125495i
$81$	438.724	−	2488.13i	0.601816	−	3.41307i
$82$	22.2623	+	8.10283i	0.0299813	+	0.0109123i
$83$	−57.8821	−	100.255i	−0.0765468	−	0.132583i	0.825211	−	0.564824i	$-0.191056\pi$
$83$	−57.8821	−	100.255i	−0.0765468	−	0.132583i	−0.901758	+	0.432242i	$0.857723\pi$
$84$	156.113	−	270.396i	0.202778	−	0.351221i
$85$	−272.388	+	228.560i	−0.347583	+	0.291657i
$86$	−120.478	+	101.093i	−0.151064	+	0.126758i
$87$	−546.224	+	946.087i	−0.673119	+	1.16588i
$88$	142.176	+	246.256i	0.172228	+	0.298307i
$89$	653.538	+	237.868i	0.778370	+	0.283303i	0.700493	−	0.713660i	$-0.252964\pi$
$89$	653.538	+	237.868i	0.778370	+	0.283303i	0.0778770	+	0.996963i	$0.475186\pi$
$90$	142.764	−	809.657i	0.167208	−	0.948281i
$91$	85.0674	+	482.441i	0.0979944	+	0.555754i
$92$	−415.643	+	151.282i	−0.471019	+	0.171437i
$93$	−2542.38	−	2133.31i	−2.83476	−	2.37864i
$94$	−469.671			−0.515349
$95$	−310.674	−	355.307i	−0.335520	−	0.383723i
$96$	318.609			0.338728
$97$	740.669	+	621.495i	0.775295	+	0.650549i	0.942059	−	0.335447i	$-0.108887\pi$
$97$	740.669	+	621.495i	0.775295	+	0.650549i	−0.166764	+	0.985997i	$0.553332\pi$
$98$	−529.120	+	192.584i	−0.545400	+	0.198509i
$99$	445.213	+	2524.93i	0.451976	+	2.56328i
$100$	−64.2657	+	364.469i	−0.0642657	+	0.364469i
$101$	1341.49	+	488.263i	1.32162	+	0.481030i	0.903976	−	0.427582i	$-0.140635\pi$
$101$	1341.49	+	488.263i	1.32162	+	0.481030i	0.417642	+	0.908612i	$0.362857\pi$
$102$	−621.230	−	1076.00i	−0.603048	−	1.04451i
$103$	−694.153	+	1202.31i	−0.664048	+	1.15016i	0.315495	+	0.948927i	$0.397829\pi$
$103$	−694.153	+	1202.31i	−0.664048	+	1.15016i	−0.979543	+	0.201237i	$0.935504\pi$
$104$	−382.945	+	321.329i	−0.361066	+	0.302970i
$105$	340.763	−	285.934i	0.316715	−	0.265755i
$106$	78.0414	−	135.172i	0.0715099	−	0.123859i
$107$	−704.658	−	1220.50i	−0.636652	−	1.10271i	−0.986162	−	0.165782i	$-0.946985\pi$
$107$	−704.658	−	1220.50i	−0.636652	−	1.10271i	0.349510	−	0.936933i	$-0.386348\pi$
$108$	1689.05	+	614.764i	1.50490	+	0.547737i
$109$	101.907	−	577.946i	0.0895502	−	0.507864i	−0.906732	−	0.421708i	$-0.861431\pi$
$109$	101.907	−	577.946i	0.0895502	−	0.507864i	0.996282	−	0.0861558i	$-0.0274583\pi$
$110$	70.3487	+	398.968i	0.0609772	+	0.345819i
$111$	337.024	−	122.667i	0.288188	−	0.104892i
$112$	96.0893	+	80.6285i	0.0810677	+	0.0680239i
$113$	476.597			0.396765			0.198383	−	0.980125i	$-0.436431\pi$
$113$	476.597			0.396765			0.198383	+	0.980125i	$0.436431\pi$
$114$	1411.16	−	853.479i	1.15936	−	0.701190i
$115$	−630.179			−0.510995
$116$	−336.207	−	282.111i	−0.269104	−	0.225805i
$117$	−4235.54	+	1541.61i	−3.34680	+	1.21814i
$118$	169.921	+	963.671i	0.132564	+	0.751806i
$119$	84.9406	−	481.722i	0.0654327	−	0.371088i
$120$	426.553	+	155.253i	0.324490	+	0.118105i
$121$	33.8100	+	58.5606i	0.0254019	+	0.0439975i
$122$	−138.715	+	240.261i	−0.102940	+	0.178297i
$123$	−90.3476	+	75.8106i	−0.0662306	+	0.0555741i
$124$	1021.39	−	857.049i	0.739707	−	0.620688i
$125$	−619.818	+	1073.56i	−0.443505	+	0.768174i
$126$	565.499	+	979.472i	0.399830	+	0.692526i
$127$	482.598	+	175.651i	0.337194	+	0.122729i	0.505067	−	0.863080i	$-0.331468\pi$
$127$	482.598	+	175.651i	0.337194	+	0.122729i	−0.167873	+	0.985809i	$0.553690\pi$
$128$	−22.2270	+	126.055i	−0.0153485	+	0.0870455i
$129$	−135.957	−	771.053i	−0.0927937	−	0.526259i
$130$	−669.263	+	243.592i	−0.451525	+	0.164342i
$131$	−592.343	−	497.035i	−0.395063	−	0.331497i	0.423519	−	0.905887i	$-0.360795\pi$
$131$	−592.343	−	497.035i	−0.395063	−	0.331497i	−0.818582	+	0.574390i	$0.805239\pi$
$132$	−1415.58			−0.933413
$133$	641.577	+	99.7129i	0.418284	+	0.0650091i
$134$	−987.995			−0.636939
$135$	1961.73	+	1646.09i	1.25066	+	1.04943i
$136$	469.051	−	170.721i	0.295741	−	0.107641i
$137$	−77.8584	−	441.557i	−0.0485540	−	0.275363i	0.950859	−	0.309624i	$-0.100203\pi$
$137$	−77.8584	−	441.557i	−0.0485540	−	0.275363i	−0.999413	+	0.0342612i	$0.989092\pi$
$138$	382.369	−	2168.52i	0.235865	−	1.33766i
$139$	−1582.62	−	576.025i	−0.965725	−	0.351495i	−0.189451	−	0.981890i	$-0.560671\pi$
$139$	−1582.62	−	576.025i	−0.965725	−	0.351495i	−0.776275	+	0.630395i	$0.782893\pi$
$140$	89.3553	+	154.768i	0.0539421	+	0.0934305i
$141$	1169.07	−	2024.89i	0.698253	−	1.20941i
$142$	155.898	−	130.814i	0.0921317	−	0.0773077i
$143$	1701.43	−	1427.67i	0.994968	−	0.834877i
$144$	−577.059	+	999.496i	−0.333946	+	0.578412i
$145$	−312.645	−	541.517i	−0.179060	−	0.310142i
$146$	1066.16	+	388.049i	0.604354	+	0.219967i
$147$	486.761	−	2760.56i	0.273112	−	1.54889i
$148$	25.0206	+	141.899i	0.0138965	+	0.0788108i
$149$	691.353	−	251.632i	0.380120	−	0.138352i	−0.144892	−	0.989448i	$-0.546283\pi$
$149$	691.353	−	251.632i	0.380120	−	0.138352i	0.525011	+	0.851095i	$0.324061\pi$
$150$	−1411.37	−	1184.28i	−0.768252	−	0.644640i
$151$	1111.52			0.599037			0.299518	−	0.954091i	$-0.403174\pi$
$151$	1111.52			0.599037			0.299518	+	0.954091i	$0.403174\pi$
$152$	239.227	+	617.856i	0.127657	+	0.329702i
$153$	4500.65			2.37814
$154$	−426.925	−	358.233i	−0.223394	−	0.187450i
$155$	1785.06	−	649.709i	0.925030	−	0.336683i
$156$	−432.146	−	2450.82i	−0.221791	−	1.25784i
$157$	−492.695	+	2794.21i	−0.250454	+	1.42040i	0.557022	+	0.830498i	$0.311944\pi$
$157$	−492.695	+	2794.21i	−0.250454	+	1.42040i	−0.807477	+	0.589900i	$0.799167\pi$
$158$	−702.856	−	255.819i	−0.353900	−	0.128809i
$159$	388.510	+	672.920i	0.193779	+	0.335635i
$160$	−91.1820	+	157.932i	−0.0450536	+	0.0780351i
$161$	664.094	−	557.241i	0.325080	−	0.272775i
$162$	−3870.84	+	3248.02i	−1.87729	+	1.57524i
$163$	−1147.76	+	1987.97i	−0.551529	+	0.955277i	0.446635	+	0.894716i	$0.352622\pi$
$163$	−1147.76	+	1987.97i	−0.551529	+	0.955277i	−0.998165	+	0.0605606i	$0.980711\pi$
$164$	−23.6911	−	41.0342i	−0.0112803	−	0.0195380i
$165$	−1895.18	−	689.788i	−0.894178	−	0.325454i
$166$	−40.2045	+	228.011i	−0.0187980	+	0.106609i
$167$	−154.002	−	873.388i	−0.0713594	−	0.404700i	−0.999475	−	0.0324067i	$-0.989683\pi$
$167$	−154.002	−	873.388i	−0.0713594	−	0.404700i	0.928115	−	0.372293i	$-0.121428\pi$
$168$	−586.793	+	213.575i	−0.269476	+	0.0980814i
$169$	1308.15	+	1097.67i	0.595426	+	0.499621i
$170$	711.154			0.320841
$171$	121.549	+	5972.70i	0.0543573	+	2.67102i
$172$	314.546			0.139442
$173$	−452.712	−	379.871i	−0.198954	−	0.166942i	0.537868	−	0.843029i	$-0.319230\pi$
$173$	−452.712	−	379.871i	−0.198954	−	0.166942i	−0.736822	+	0.676087i	$0.763674\pi$
$174$	2053.13	−	747.278i	0.894525	−	0.325580i
$175$	−125.956	−	714.334i	−0.0544080	−	0.308563i
$176$	98.7546	−	560.065i	0.0422949	−	0.239866i
$177$	−4577.63	−	1666.12i	−1.94393	−	0.707533i
$178$	−695.481	−	1204.61i	−0.292857	−	0.507243i
$179$	−506.912	+	877.997i	−0.211667	+	0.366618i	−0.952236	−	0.305362i	$-0.901223\pi$
$179$	−506.912	+	877.997i	−0.211667	+	0.366618i	0.740569	+	0.671980i	$0.234556\pi$
$180$	−1259.60	+	1056.93i	−0.521585	+	0.437661i
$181$	833.247	−	699.177i	0.342181	−	0.287124i	−0.455460	−	0.890256i	$-0.650525\pi$
$181$	833.247	−	699.177i	0.342181	−	0.287124i	0.797641	+	0.603132i	$0.206081\pi$
$182$	489.884	−	848.504i	0.199520	−	0.345578i
$183$	−690.559	−	1196.08i	−0.278948	−	0.483153i
$184$	831.286	+	302.563i	0.333061	+	0.121224i
$185$	−35.6473	+	202.166i	−0.0141667	+	0.0803434i
$186$	1152.62	+	6536.84i	0.454378	+	2.57690i
$187$	−2084.00	+	758.513i	−0.814957	+	0.296620i
$188$	719.577	+	603.797i	0.279152	+	0.234236i
$189$	−3522.88			−1.35583
$190$	19.2062	+	943.756i	0.00733348	+	0.360354i
$191$	−4113.64			−1.55839			−0.779195	−	0.626782i	$-0.784372\pi$
$191$	−4113.64			−1.55839			−0.779195	+	0.626782i	$0.784372\pi$
$192$	−488.137	−	409.596i	−0.183481	−	0.153958i
$193$	−1547.49	+	563.239i	−0.577153	+	0.210067i	−0.614070	−	0.789252i	$-0.710469\pi$
$193$	−1547.49	+	563.239i	−0.577153	+	0.210067i	0.0369165	+	0.999318i	$0.488246\pi$
$194$	−335.792	−	1904.37i	−0.124271	−	0.704773i
$195$	615.686	−	3491.73i	0.226104	−	1.28230i
$196$	1058.24	+	385.168i	0.385656	+	0.140367i
$197$	2580.13	+	4468.91i	0.933130	+	1.61623i	0.777935	+	0.628344i	$0.216267\pi$
$197$	2580.13	+	4468.91i	0.933130	+	1.61623i	0.155194	+	0.987884i	$0.450400\pi$
$198$	2563.88	−	4440.77i	0.920237	−	1.59390i
$199$	3300.71	−	2769.62i	1.17578	−	0.986600i	0.175786	−	0.984428i	$-0.443753\pi$
$199$	3300.71	−	2769.62i	1.17578	−	0.986600i	0.999998	−	0.00217131i	$-0.000691151\pi$
$200$	567.013	−	475.780i	0.200469	−	0.168214i
$201$	2459.25	−	4259.54i	0.862995	−	1.49475i
$202$	−1427.59	−	2472.65i	−0.497250	−	0.861263i
$203$	808.313	+	294.202i	0.279470	+	0.101719i
$204$	−431.502	+	2447.17i	−0.148094	+	0.839882i
$205$	−11.7223	−	66.4807i	−0.00399377	−	0.0226498i
$206$	2609.16	−	949.657i	0.882470	−	0.321193i
$207$	6110.25	+	5127.11i	2.05165	+	1.72154i
$208$	999.798			0.333286
$209$	−1062.89	−	2745.14i	−0.351777	−	0.908542i
$210$	−889.668			−0.292347
$211$	−1381.41	−	1159.14i	−0.450713	−	0.378193i	0.388987	−	0.921243i	$-0.372825\pi$
$211$	−1381.41	−	1159.14i	−0.450713	−	0.378193i	−0.839701	+	0.543050i	$0.817269\pi$
$212$	−293.340	+	106.767i	−0.0950313	+	0.0345886i
$213$	175.928	+	997.739i	0.0565935	+	0.320958i
$214$	−489.450	+	2775.81i	−0.156346	+	0.886684i
$215$	421.114	+	153.273i	0.133580	+	0.0486192i
$216$	−1797.45	−	3113.27i	−0.566208	−	0.980701i
$217$	−1306.62	+	2263.13i	−0.408752	+	0.707979i
$218$	−899.125	+	754.455i	−0.279341	+	0.234395i
$219$	−4326.80	+	3630.62i	−1.33506	+	1.12025i
$220$	405.122	−	701.692i	0.124152	−	0.215037i
$221$	−1949.42	−	3376.50i	−0.593360	−	1.02773i
$222$	−674.048	−	245.333i	−0.203780	−	0.0741698i
$223$	−521.289	+	2956.38i	−0.156539	+	0.887774i	0.800827	+	0.598896i	$0.204394\pi$
$223$	−521.289	+	2956.38i	−0.156539	+	0.887774i	−0.957366	+	0.288879i	$0.906718\pi$
$224$	−43.5633	−	247.060i	−0.0129942	−	0.0736937i
$225$	6271.41	−	2282.61i	1.85820	−	0.676328i
$226$	−730.189	−	612.701i	−0.214918	−	0.180337i
$227$	−6582.24			−1.92457			−0.962287	−	0.272036i	$-0.912303\pi$
$227$	−6582.24			−1.92457			−0.962287	+	0.272036i	$0.912303\pi$
$228$	−3259.23	−	506.545i	−0.946702	−	0.147135i
$229$	−1811.29			−0.522677			−0.261339	−	0.965247i	$-0.584164\pi$
$229$	−1811.29			−0.522677			−0.261339	+	0.965247i	$0.584164\pi$
$230$	965.490	+	810.142i	0.276793	+	0.232257i
$231$	2607.12	−	948.916i	0.742581	−	0.270277i
$232$	152.424	+	864.438i	0.0431341	+	0.244626i
$233$	−762.435	+	4323.99i	−0.214373	+	1.21577i	0.667619	+	0.744503i	$0.267313\pi$
$233$	−762.435	+	4323.99i	−0.214373	+	1.21577i	−0.881992	+	0.471264i	$0.843798\pi$
$234$	8471.07	+	3083.22i	2.36654	+	0.861352i
$235$	669.149	+	1159.00i	0.185747	+	0.321723i
$236$	978.537	−	1694.88i	0.269904	−	0.467487i
$237$	2852.41	−	2393.46i	0.781790	−	0.656000i
$238$	−749.427	+	628.844i	−0.204110	+	0.171268i
$239$	219.920	−	380.913i	0.0595208	−	0.103093i	−0.834730	−	0.550660i	$-0.814376\pi$
$239$	219.920	−	380.913i	0.0595208	−	0.103093i	0.894250	+	0.447567i	$0.147709\pi$
$240$	−453.928	−	786.226i	−0.122087	−	0.211461i
$241$	2149.25	+	782.263i	0.574462	+	0.209087i	0.612882	−	0.790175i	$-0.290010\pi$
$241$	2149.25	+	782.263i	0.574462	+	0.209087i	−0.0384197	+	0.999262i	$0.512232\pi$
$242$	23.4842	−	133.185i	0.00623810	−	0.0353780i
$243$	−2261.33	−	12824.6i	−0.596973	−	3.38560i
$244$	521.397	−	189.773i	0.136799	−	0.0497909i
$245$	1229.08	+	1031.32i	0.320503	+	0.268934i
$246$	235.881			0.0611350
$247$	4428.23	−	2678.23i	1.14074	−	0.689925i
$248$	−2666.66			−0.682796
$249$	−882.950	−	740.883i	−0.224718	−	0.188560i
$250$	2329.75	−	847.961i	0.589386	−	0.214519i
$251$	584.034	+	3312.22i	0.146868	+	0.832931i	0.965848	+	0.259109i	$0.0834288\pi$
$251$	584.034	+	3312.22i	0.146868	+	0.832931i	−0.818980	+	0.573822i	$0.805460\pi$
$252$	392.791	−	2227.63i	0.0981886	−	0.556855i
$253$	−3693.41	−	1344.29i	−0.917797	−	0.334051i
$254$	−513.570	−	889.529i	−0.126867	−	0.219740i
$255$	−1770.15	+	3066.00i	−0.434711	+	0.752942i
$256$	196.107	−	164.554i	0.0478778	−	0.0401742i
$257$	4037.83	−	3388.14i	0.980051	−	0.822360i	−0.00404609	−	0.999992i	$-0.501288\pi$
$257$	4037.83	−	3388.14i	0.980051	−	0.822360i	0.984097	+	0.177631i	$0.0568435\pi$
$258$	−782.948	+	1356.10i	−0.188931	+	0.327238i
$259$	−141.201	−	244.567i	−0.0338757	−	0.0586745i
$260$	1338.53	+	487.184i	0.319277	+	0.116207i
$261$	−1374.34	+	7794.25i	−0.325936	+	1.84848i
$262$	268.547	+	1523.00i	0.0633239	+	0.359128i
$263$	−1760.74	+	640.857i	−0.412821	+	0.150255i	−0.540078	−	0.841615i	$-0.681605\pi$
$263$	−1760.74	+	640.857i	−0.412821	+	0.150255i	0.127256	+	0.991870i	$0.459383\pi$
$264$	2168.80	+	1819.84i	0.505607	+	0.424254i
$265$	−444.748			−0.103097
$266$	−854.764	−	977.564i	−0.197026	−	0.225332i
$267$	6924.57			1.58718
$268$	1513.70	+	1270.14i	0.345014	+	0.289501i
$269$	−4036.20	+	1469.06i	−0.914837	+	0.332974i	−0.756183	−	0.654361i	$-0.772938\pi$
$269$	−4036.20	+	1469.06i	−0.914837	+	0.332974i	−0.158655	+	0.987334i	$0.550716\pi$
$270$	−889.377	−	5043.91i	−0.200466	−	1.13690i
$271$	549.278	−	3115.11i	0.123123	−	0.698263i	−0.859283	−	0.511501i	$-0.829090\pi$
$271$	549.278	−	3115.11i	0.123123	−	0.698263i	0.982405	−	0.186762i	$-0.0597993\pi$
$272$	−938.102	−	341.441i	−0.209121	−	0.0761137i
$273$	2438.77	+	4224.07i	0.540663	+	0.936457i
$274$	−448.369	+	776.597i	−0.0988575	+	0.171226i
$275$	−2519.24	+	2113.89i	−0.552422	+	0.463537i
$276$	−3373.62	+	2830.80i	−0.735754	+	0.617371i
$277$	1170.64	−	2027.61i	0.253924	−	0.439809i	−0.710679	−	0.703517i	$-0.751612\pi$
$277$	1170.64	−	2027.61i	0.253924	−	0.439809i	0.964603	+	0.263707i	$0.0849453\pi$
$278$	1684.19	+	2917.10i	0.363348	+	0.629337i
$279$	−22594.1	−	8223.57i	−4.84829	−	1.76463i
$280$	62.0655	−	351.991i	0.0132469	−	0.0751267i
$281$	1441.05	+	8172.62i	0.305929	+	1.73501i	0.619100	+	0.785312i	$0.287497\pi$
$281$	1441.05	+	8172.62i	0.305929	+	1.73501i	−0.313171	+	0.949697i	$0.601391\pi$
$282$	−4394.27	+	1599.39i	−0.927926	+	0.337738i
$283$	222.338	+	186.563i	0.0467018	+	0.0391874i	0.665840	−	0.746095i	$-0.268073\pi$
$283$	222.338	+	186.563i	0.0467018	+	0.0391874i	−0.619138	+	0.785282i	$0.712518\pi$
$284$	−407.022			−0.0850433
$285$	−4116.62	−	2266.33i	−0.855606	−	0.471038i
$286$	−4442.11			−0.918417
$287$	71.1393	+	59.6930i	0.0146314	+	0.0122772i
$288$	2169.03	−	789.464i	0.443790	−	0.161526i
$289$	−177.115	−	1004.47i	−0.0360502	−	0.204451i
$290$	−217.161	+	1231.58i	−0.0439729	+	0.249383i
$291$	9046.16	+	3292.53i	1.82232	+	0.663270i
$292$	−1134.58	−	1965.15i	−0.227385	−	0.393842i
$293$	−1201.60	+	2081.24i	−0.239585	+	0.414973i	−0.960595	−	0.277951i	$-0.910345\pi$
$293$	−1201.60	+	2081.24i	−0.239585	+	0.414973i	0.721010	+	0.692924i	$0.243678\pi$
$294$	−4294.67	+	3603.66i	−0.851940	+	0.714862i
$295$	2135.95	−	1792.27i	0.421558	−	0.353729i
$296$	144.088	−	249.567i	0.0282937	−	0.0490061i
$297$	7986.08	+	13832.3i	1.56027	+	2.70246i
$298$	−1382.71	−	503.264i	−0.268785	−	0.0978298i
$299$	1199.88	−	6804.84i	0.232076	−	1.31617i
$300$	639.863	+	3628.84i	0.123142	+	0.698371i
$301$	−579.311	+	210.852i	−0.110933	+	0.0403764i
$302$	−1702.95	−	1428.95i	−0.324483	−	0.272274i
$303$	14213.8			2.69492
$304$	427.784	−	1254.16i	0.0807075	−	0.236614i
$305$	790.518			0.148410
$306$	−6895.39	−	5785.92i	−1.28818	−	1.08091i
$307$	9407.63	−	3424.10i	1.74893	−	0.636558i	0.749261	−	0.662275i	$-0.230409\pi$
$307$	9407.63	−	3424.10i	1.74893	−	0.636558i	0.999669	+	0.0257166i	$0.00818674\pi$
$308$	193.552	+	1097.69i	0.0358073	+	0.203074i
$309$	−2400.29	+	13612.7i	−0.441901	+	2.50615i
$310$	−3570.12	−	1299.42i	−0.654095	−	0.238071i
$311$	−2928.62	−	5072.51i	−0.533976	−	0.924874i	−0.999212	−	0.0396874i	$-0.987364\pi$
$311$	−2928.62	−	5072.51i	−0.533976	−	0.924874i	0.465236	−	0.885187i	$-0.345970\pi$
$312$	−2488.63	+	4310.43i	−0.451573	+	0.782148i
$313$	4694.41	−	3939.08i	0.847744	−	0.711342i	−0.111547	−	0.993759i	$-0.535581\pi$
$313$	4694.41	−	3939.08i	0.847744	−	0.711342i	0.959292	+	0.282417i	$0.0911362\pi$
$314$	4347.02	−	3647.58i	0.781263	−	0.655558i
$315$	1611.35	−	2790.94i	0.288220	−	0.499212i
$316$	747.964	+	1295.51i	0.133153	+	0.230627i
$317$	7262.63	+	2643.38i	1.28678	+	0.468350i	0.892670	−	0.450712i	$-0.148830\pi$
$317$	7262.63	+	2643.38i	1.28678	+	0.468350i	0.394113	+	0.919062i	$0.371052\pi$
$318$	269.857	−	1530.43i	0.0475874	−	0.269882i
$319$	−677.220	−	3840.71i	−0.118862	−	0.674101i
$320$	342.732	−	124.744i	0.0598728	−	0.0217919i
$321$	−10749.0	−	9019.52i	−1.86901	−	1.56829i
$322$	−1733.83			−0.300069
$323$	−5069.62	+	1000.67i	−0.873316	+	0.172380i
$324$	10106.0			1.73286
$325$	−4428.89	−	3716.28i	−0.755910	−	0.634284i
$326$	4314.16	−	1570.22i	0.732942	−	0.266769i
$327$	−1014.64	−	5754.34i	−0.171590	−	0.973136i
$328$	−16.4557	+	93.3246i	−0.00277016	+	0.0157103i
$329$	−1730.02	−	629.675i	−0.289906	−	0.105517i
$330$	2016.81	+	3493.21i	0.336429	+	0.582712i
$331$	−1951.74	+	3380.51i	−0.324101	+	0.561359i	−0.981330	−	0.192332i	$-0.938395\pi$
$331$	−1951.74	+	3380.51i	−0.324101	+	0.561359i	0.657229	+	0.753691i	$0.271728\pi$
$332$	354.722	−	297.647i	0.0586383	−	0.0492033i
$333$	1990.45	−	1670.19i	0.327556	−	0.274852i
$334$	−886.862	+	1536.09i	−0.145290	+	0.251650i
$335$	1407.61	+	2438.06i	0.229571	+	0.397628i
$336$	1173.59	+	427.150i	0.190549	+	0.0693540i
$337$	1700.05	−	9641.49i	0.274801	−	1.55847i	−0.464793	−	0.885419i	$-0.653871\pi$
$337$	1700.05	−	9641.49i	0.274801	−	1.55847i	0.739594	−	0.673054i	$-0.235018\pi$
$338$	−593.067	−	3363.45i	−0.0954396	−	0.541265i
$339$	4459.07	−	1622.97i	0.714406	−	0.260023i
$340$	−1089.55	−	914.241i	−0.173792	−	0.145829i
$341$	11848.0			1.88154
$342$	7492.14	−	9306.97i	1.18459	−	1.47153i
$343$	−4896.21			−0.770760
$344$	−481.913	−	404.373i	−0.0755320	−	0.0633789i
$345$	−5896.00	+	2145.97i	−0.920086	+	0.334884i
$346$	205.243	+	1163.99i	0.0318900	+	0.180857i
$347$	−481.811	+	2732.48i	−0.0745388	+	0.422730i	0.924589	+	0.380967i	$0.124409\pi$
$347$	−481.811	+	2732.48i	−0.0745388	+	0.422730i	−0.999128	+	0.0417636i	$0.986702\pi$
$348$	−4106.26	−	1494.56i	−0.632525	−	0.230220i
$349$	−2579.98	−	4468.65i	−0.395711	−	0.685391i	0.597481	−	0.801883i	$-0.296168\pi$
$349$	−2579.98	−	4468.65i	−0.395711	−	0.685391i	−0.993192	+	0.116492i	$0.962835\pi$
$350$	−725.354	+	1256.35i	−0.110777	+	0.191871i
$351$	−21510.1	+	18049.1i	−3.27101	+	2.74470i
$352$	−871.306	+	731.113i	−0.131934	+	0.110706i
$353$	−1667.72	+	2888.57i	−0.251455	+	0.435532i	−0.963927	−	0.266168i	$-0.914242\pi$
$353$	−1667.72	+	2888.57i	−0.251455	+	0.435532i	0.712472	+	0.701701i	$0.247576\pi$
$354$	4871.41	+	8437.54i	0.731392	+	1.26681i
$355$	−544.920	−	198.335i	−0.0814686	−	0.0296521i
$356$	−483.076	+	2739.66i	−0.0719185	+	0.407870i
$357$	−845.714	−	4796.28i	−0.125378	−	0.711054i
$358$	1905.37	−	693.496i	0.281290	−	0.102381i
$359$	5631.07	+	4725.03i	0.827846	+	0.694645i	0.954795	−	0.297264i	$-0.0960742\pi$
$359$	5631.07	+	4725.03i	0.827846	+	0.694645i	−0.126950	+	0.991909i	$0.540519\pi$
$360$	3288.59			0.481455
$361$	−1464.88	−	6700.75i	−0.213571	−	0.976928i
$362$	−2175.45			−0.315854
$363$	515.747	+	432.763i	0.0745722	+	0.0625735i
$364$	−1841.36	+	670.201i	−0.265147	+	0.0965056i
$365$	−561.390	−	3183.80i	−0.0805054	−	0.456569i
$366$	−479.657	+	2720.27i	−0.0685029	+	0.388499i
$367$	−1006.84	−	366.461i	−0.143207	−	0.0521230i	0.269422	−	0.963022i	$-0.413167\pi$
$367$	−1006.84	−	366.461i	−0.143207	−	0.0521230i	−0.412629	+	0.910899i	$0.635389\pi$
$368$	−884.636	−	1532.23i	−0.125312	−	0.217047i
$369$	−427.224	+	739.973i	−0.0602720	+	0.104394i
$370$	314.514	−	263.909i	0.0441914	−	0.0370810i
$371$	468.684	−	393.272i	0.0655872	−	0.0550342i
$372$	6637.68	−	11496.8i	0.925128	−	1.60237i
$373$	−3995.92	−	6921.13i	−0.554694	−	0.960758i	−0.997927	−	0.0643516i	$-0.979502\pi$
$373$	−3995.92	−	6921.13i	−0.554694	−	0.960758i	0.443234	−	0.896406i	$-0.353831\pi$
$374$	4167.99	+	1517.03i	0.576262	+	0.209742i
$375$	−2143.25	+	12155.0i	−0.295138	+	1.67381i
$376$	−326.230	−	1850.14i	−0.0447447	−	0.253760i
$377$	6442.74	−	2344.97i	0.880154	−	0.320350i
$378$	5397.36	+	4528.92i	0.734419	+	0.616250i
$379$	11748.4			1.59228			0.796141	−	0.605111i	$-0.206871\pi$
$379$	11748.4			1.59228			0.796141	+	0.605111i	$0.206871\pi$
$380$	1183.84	−	1470.61i	0.159815	−	0.198528i
$381$	5113.37			0.687575
$382$	6302.46	+	5288.39i	0.844141	+	0.708318i
$383$	−7172.44	+	2610.55i	−0.956904	+	0.348285i	−0.772820	−	0.634626i	$-0.781154\pi$
$383$	−7172.44	+	2610.55i	−0.956904	+	0.348285i	−0.184085	+	0.982910i	$0.558932\pi$
$384$	221.303	+	1255.07i	0.0294097	+	0.166791i
$385$	−275.758	+	1563.90i	−0.0365036	+	0.207022i
$386$	3094.98	+	1126.48i	0.408109	+	0.148540i
$387$	−2836.12	−	4912.31i	−0.372528	−	0.645237i
$388$	−1933.75	+	3349.35i	−0.253019	+	0.438241i
$389$	−5317.45	+	4461.87i	−0.693074	+	0.581558i	−0.919794	−	0.392402i	$-0.871644\pi$
$389$	−5317.45	+	4461.87i	−0.693074	+	0.581558i	0.226720	+	0.973960i	$0.427200\pi$
$390$	−5432.17	+	4558.13i	−0.705304	+	0.591820i
$391$	−3449.76	+	5975.16i	−0.446194	+	0.772831i
$392$	−1126.15	−	1950.56i	−0.145101	−	0.251321i
$393$	−7234.57	−	2633.17i	−0.928590	−	0.337979i
$394$	1792.14	−	10163.7i	0.229154	−	1.29960i
$395$	370.092	+	2098.90i	0.0471427	+	0.267360i
$396$	−9637.03	+	3507.59i	−1.22293	+	0.445109i
$397$	3592.36	+	3014.35i	0.454144	+	0.381072i	0.840971	−	0.541080i	$-0.181984\pi$
$397$	3592.36	+	3014.35i	0.454144	+	0.381072i	−0.386827	+	0.922152i	$0.626429\pi$
$398$	−8617.54			−1.08532
$399$	6342.19	−	1251.86i	0.795757	−	0.157071i
$400$	−1480.37			−0.185046
$401$	−11378.2	−	9547.43i	−1.41696	−	1.18897i	−0.952947	−	0.303138i	$-0.901966\pi$
$401$	−11378.2	−	9547.43i	−1.41696	−	1.18897i	−0.464010	−	0.885830i	$-0.653590\pi$
$402$	−9243.75	+	3364.45i	−1.14686	+	0.417422i
$403$	3616.93	+	20512.7i	0.447078	+	2.53550i
$404$	−991.591	+	5623.59i	−0.122113	+	0.692535i
$405$	13529.9	+	4924.50i	1.66002	+	0.604198i
$406$	−860.189	−	1489.89i	−0.105149	−	0.182123i
$407$	−640.183	+	1108.83i	−0.0779673	+	0.135043i
$408$	3807.12	−	3194.55i	0.461962	−	0.387632i
$409$	−5410.93	+	4540.31i	−0.654164	+	0.548909i	−0.908331	−	0.418251i	$-0.862643\pi$
$409$	−5410.93	+	4540.31i	−0.654164	+	0.548909i	0.254167	+	0.967160i	$0.418199\pi$
$410$	−67.5062	+	116.924i	−0.00813145	+	0.0140841i
$411$	−2232.10	−	3866.11i	−0.267886	−	0.463993i
$412$	−5218.32	−	1899.31i	−0.624001	−	0.227118i
$413$	−666.068	+	3777.46i	−0.0793585	+	0.450064i
$414$	−2770.16	−	15710.4i	−0.328855	−	1.86503i
$415$	619.939	−	225.639i	0.0733292	−	0.0266897i
$416$	−1531.78	−	1285.31i	−0.180533	−	0.151485i
$417$	−16768.6			−1.96922
$418$	−1900.65	+	5572.22i	−0.222401	+	0.652024i
$419$	2685.43			0.313107			0.156553	−	0.987669i	$-0.449962\pi$
$419$	2685.43			0.313107			0.156553	+	0.987669i	$0.449962\pi$
$420$	1363.05	+	1143.74i	0.158357	+	0.132878i
$421$	4258.19	−	1549.85i	0.492949	−	0.179419i	−0.0835710	−	0.996502i	$-0.526633\pi$
$421$	4258.19	−	1549.85i	0.492949	−	0.179419i	0.576520	+	0.817083i	$0.304410\pi$
$422$	626.283	+	3551.83i	0.0722440	+	0.409716i
$423$	2941.47	−	16681.9i	0.338107	−	1.91750i
$424$	586.679	+	213.534i	0.0671973	+	0.0244578i
$425$	2886.44	+	4999.47i	0.329443	+	0.570611i
$426$	1013.13	−	1754.79i	0.115226	−	0.199578i
$427$	−833.063	+	699.023i	−0.0944139	+	0.0792227i
$428$	4318.39	−	3623.56i	0.487704	−	0.409232i
$429$	11057.0	−	19151.3i	1.24437	−	2.15532i
$430$	−448.140	−	776.202i	−0.0502587	−	0.0870506i
$431$	7494.17	+	2727.66i	0.837544	+	0.304841i	0.724951	−	0.688800i	$-0.241862\pi$
$431$	7494.17	+	2727.66i	0.837544	+	0.304841i	0.112593	+	0.993641i	$0.464084\pi$
$432$	−1248.49	+	7080.56i	−0.139047	+	0.788574i
$433$	2234.63	+	12673.2i	0.248013	+	1.40655i	0.813390	+	0.581719i	$0.197620\pi$
$433$	2234.63	+	12673.2i	0.248013	+	1.40655i	−0.565377	+	0.824833i	$0.691269\pi$
$434$	4911.28	−	1787.56i	0.543201	−	0.197709i
$435$	−4769.18	−	4001.82i	−0.525666	−	0.441086i
$436$	2347.45			0.257849
$437$	−8022.66	−	4416.73i	−0.878206	−	0.483480i
$438$	11296.5			1.23234
$439$	5434.26	+	4559.88i	0.590804	+	0.495743i	0.888475	−	0.458925i	$-0.151765\pi$
$439$	5434.26	+	4559.88i	0.590804	+	0.495743i	−0.297671	+	0.954669i	$0.596210\pi$
$440$	−1522.76	+	554.240i	−0.164988	+	0.0600508i
$441$	−3526.46	−	19999.5i	−0.380786	−	2.15954i
$442$	−1354.06	+	7679.23i	−0.145715	+	0.826389i
$443$	−9485.10	−	3452.29i	−1.01727	−	0.370256i	−0.221050	−	0.975263i	$-0.570948\pi$
$443$	−9485.10	−	3452.29i	−1.01727	−	0.370256i	−0.796221	+	0.605006i	$0.793171\pi$
$444$	717.307	+	1242.41i	0.0766709	+	0.132798i
$445$	−1981.73	+	3432.46i	−0.211108	+	0.365649i
$446$	4599.31	−	3859.28i	0.488304	−	0.409736i
$447$	5611.46	−	4708.57i	0.593765	−	0.498228i
$448$	−250.871	+	434.522i	−0.0264566	+	0.0458242i
$449$	3147.97	+	5452.44i	0.330873	+	0.573088i	0.982683	−	0.185293i	$-0.0593236\pi$
$449$	3147.97	+	5452.44i	0.330873	+	0.573088i	−0.651810	+	0.758382i	$0.725990\pi$
$450$	−12542.8	−	4565.21i	−1.31394	−	0.478236i
$451$	73.1126	−	414.642i	0.00763356	−	0.0432921i
$452$	331.041	+	1877.42i	0.0344488	+	0.195369i
$453$	10399.5	−	3785.11i	1.07861	−	0.392583i
$454$	10084.6	+	8461.96i	1.04249	+	0.874756i
$455$	−2791.79			−0.287650
$456$	4342.23	+	4966.06i	0.445929	+	0.509994i
$457$	−6438.99			−0.659088			−0.329544	−	0.944140i	$-0.606895\pi$
$457$	−6438.99			−0.659088			−0.329544	+	0.944140i	$0.606895\pi$
$458$	2775.05	+	2328.54i	0.283121	+	0.237567i
$459$	26346.7	−	9589.42i	2.67921	−	0.975154i
$460$	−437.717	−	2482.42i	−0.0443667	−	0.251616i
$461$	2006.65	−	11380.3i	0.202731	−	1.14975i	−0.698239	−	0.715865i	$-0.746033\pi$
$461$	2006.65	−	11380.3i	0.202731	−	1.14975i	0.900970	−	0.433881i	$-0.142856\pi$
$462$	−5214.25	−	1897.83i	−0.525084	−	0.191115i
$463$	3993.64	+	6917.19i	0.400865	+	0.694318i	0.993830	−	0.110910i	$-0.0353765\pi$
$463$	3993.64	+	6917.19i	0.400865	+	0.694318i	−0.592966	+	0.805228i	$0.702043\pi$
$464$	877.774	−	1520.35i	0.0878225	−	0.152113i
$465$	14488.7	−	12157.5i	1.44494	−	1.21245i
$466$	6726.93	−	5644.56i	0.668710	−	0.561114i
$467$	−7703.66	+	13343.1i	−0.763347	+	1.32216i	0.177769	+	0.984072i	$0.443112\pi$
$467$	−7703.66	+	13343.1i	−0.763347	+	1.32216i	−0.941116	+	0.338084i	$0.890221\pi$
$468$	−9014.73	−	15614.0i	−0.890397	−	1.54221i
$469$	−3639.25	−	1324.58i	−0.358305	−	0.130412i
$470$	464.786	−	2635.93i	0.0456148	−	0.258695i
$471$	4905.53	+	27820.6i	0.479904	+	2.72167i
$472$	−3678.10	+	1338.72i	−0.358682	+	0.130550i
$473$	2141.14	+	1796.63i	0.208139	+	0.174650i
$474$	−7447.12			−0.721641
$475$	−6556.73	+	3965.56i	−0.633354	+	0.383057i
$476$	1956.61			0.188406
$477$	4312.30	+	3618.45i	0.413935	+	0.347332i
$478$	−826.630	+	300.869i	−0.0790987	+	0.0287896i
$479$	−3177.73	−	18021.8i	−0.303120	−	1.71908i	−0.632227	−	0.774784i	$-0.717859\pi$
$479$	−3177.73	−	18021.8i	−0.303120	−	1.71908i	0.329107	−	0.944293i	$-0.393252\pi$
$480$	−315.295	+	1788.13i	−0.0299816	+	0.170034i
$481$	−2115.17	−	769.858i	−0.200506	−	0.0729782i
$482$	−2287.18	−	3961.52i	−0.216138	−	0.374362i
$483$	4315.72	−	7475.05i	0.406568	−	0.704196i
$484$	−207.200	+	173.861i	−0.0194590	+	0.0163281i
$485$	−4220.98	+	3541.82i	−0.395185	+	0.331600i
$486$	−13022.5	+	22555.6i	−1.21546	+	2.10523i
$487$	−3906.70	−	6766.60i	−0.363510	−	0.629618i	0.625026	−	0.780604i	$-0.285088\pi$
$487$	−3906.70	−	6766.60i	−0.363510	−	0.629618i	−0.988536	+	0.150986i	$0.951755\pi$
$488$	−1042.79	−	379.546i	−0.0967317	−	0.0352075i
$489$	−3968.79	+	22508.1i	−0.367024	+	2.08150i
$490$	−557.221	−	3160.16i	−0.0513728	−	0.291350i
$491$	−4634.67	+	1686.88i	−0.425987	+	0.155047i	−0.546112	−	0.837712i	$-0.683893\pi$
$491$	−4634.67	+	1686.88i	−0.425987	+	0.155047i	0.120125	+	0.992759i	$0.461670\pi$
$492$	−361.390	−	303.243i	−0.0331153	−	0.0277871i
$493$	−6846.00			−0.625412
$494$	−10227.5	−	1589.54i	−0.931492	−	0.144771i
$495$	−14611.2			−1.32672
$496$	4085.57	+	3428.20i	0.369853	+	0.310344i
$497$	749.626	−	272.841i	0.0676566	−	0.0246250i
$498$	400.297	+	2270.20i	0.0360196	+	0.204277i
$499$	352.749	−	2000.54i	0.0316457	−	0.179472i	−0.964888	−	0.262662i	$-0.915400\pi$
$499$	352.749	−	2000.54i	0.0316457	−	0.179472i	0.996534	+	0.0831899i	$0.0265108\pi$
$500$	−4659.50	−	1695.92i	−0.416759	−	0.151688i
$501$	−4415.03	−	7647.06i	−0.393711	−	0.681927i
$502$	3363.32	−	5825.44i	0.299028	−	0.517933i
$503$	16909.2	−	14188.5i	1.49889	−	1.25772i	0.616359	−	0.787466i	$-0.288607\pi$
$503$	16909.2	−	14188.5i	1.49889	−	1.25772i	0.882532	−	0.470253i	$-0.155837\pi$
$504$	−3465.58	+	2907.96i	−0.306288	+	0.257006i
$505$	−4067.82	+	7045.66i	−0.358446	+	0.620847i
$506$	3930.44	+	6807.73i	0.345315	+	0.598104i
$507$	15977.1	+	5815.18i	1.39954	+	0.509391i
$508$	−356.722	+	2023.07i	−0.0311555	+	0.176691i
$509$	−446.161	−	2530.31i	−0.0388522	−	0.220342i	0.959200	−	0.282729i	$-0.0912397\pi$
$509$	−446.161	−	2530.31i	−0.0388522	−	0.220342i	−0.998052	+	0.0623873i	$0.980129\pi$
$510$	6653.61	−	2421.71i	0.577699	−	0.210265i
$511$	3406.91	+	2858.73i	0.294937	+	0.247481i
$512$	−512.000			−0.0441942
$513$	13437.4	+	34705.1i	1.15649	+	2.98688i
$514$	−10542.0			−0.904648
$515$	−6060.78	−	5085.59i	−0.518582	−	0.435142i
$516$	2942.92	−	1071.14i	0.251075	−	0.0913839i
$517$	1449.44	+	8220.19i	0.123301	+	0.699272i
$518$	−98.0773	+	556.224i	−0.00831905	+	0.0471797i
$519$	−5529.19	−	2012.46i	−0.467639	−	0.170207i
$520$	−1424.43	−	2467.19i	−0.120126	−	0.208064i
$521$	6814.97	−	11803.9i	0.573069	−	0.992585i	−0.423179	−	0.906046i	$-0.639086\pi$
$521$	6814.97	−	11803.9i	0.573069	−	0.992585i	0.996248	−	0.0865391i	$-0.0275807\pi$
$522$	12125.7	−	10174.7i	1.01672	−	0.853129i
$523$	−7237.71	+	6073.16i	−0.605130	+	0.507765i	−0.893090	−	0.449878i	$-0.851467\pi$
$523$	−7237.71	+	6073.16i	−0.605130	+	0.507765i	0.287960	+	0.957642i	$0.407023\pi$
$524$	1546.50	−	2678.61i	0.128930	−	0.223312i
$525$	−3611.00	−	6254.44i	−0.300185	−	0.519935i
$526$	3521.48	+	1281.71i	0.291909	+	0.106246i
$527$	3611.54	−	20482.1i	0.298522	−	1.69300i
$528$	−983.252	−	5576.30i	−0.0810428	−	0.459616i
$529$	−57.1523	+	20.8017i	−0.00469732	+	0.00170968i
$530$	681.393	+	571.757i	0.0558450	+	0.0468595i
$531$	−35292.1			−2.88427
$532$	52.8424	+	2596.58i	0.00430641	+	0.211609i
$533$	740.196			0.0601528
$534$	−10609.1	−	8902.06i	−0.859736	−	0.721404i
$535$	7547.15	−	2746.94i	0.609891	−	0.221982i
$536$	−686.254	−	3891.94i	−0.0553016	−	0.313631i
$537$	−1752.83	+	9940.81i	−0.140857	+	0.798841i
$538$	8072.39	+	2938.11i	0.646888	+	0.235448i
$539$	5003.51	+	8666.34i	0.399845	+	0.692552i
$540$	−5121.72	+	8871.07i	−0.408155	+	0.706945i
$541$	−3523.85	+	2956.86i	−0.280041	+	0.234982i	−0.771979	−	0.635648i	$-0.780733\pi$
$541$	−3523.85	+	2956.86i	−0.280041	+	0.234982i	0.491938	+	0.870630i	$0.336289\pi$
$542$	−4846.25	+	4066.48i	−0.384067	+	0.322270i
$543$	5414.99	−	9379.04i	0.427955	−	0.741239i
$544$	998.307	+	1729.12i	0.0786803	+	0.136278i
$545$	3142.76	+	1143.87i	0.247011	+	0.0899046i
$546$	1693.95	−	9606.88i	0.132774	−	0.752997i
$547$	615.786	+	3492.29i	0.0481336	+	0.272979i	0.999370	−	0.0354826i	$-0.0112968\pi$
$547$	615.786	+	3492.29i	0.0481336	+	0.272979i	−0.951237	+	0.308462i	$0.900186\pi$
$548$	1685.31	−	613.404i	0.131374	−	0.0478163i
$549$	−7664.91	−	6431.62i	−0.595866	−	0.499991i
$550$	6577.27			0.509920
$551$	−184.890	−	9085.17i	−0.0142951	−	0.702434i
$552$	8807.90			0.679147
$553$	−2245.98	−	1884.60i	−0.172710	−	0.144921i
$554$	−4400.17	+	1601.53i	−0.337446	+	0.122820i
$555$	354.923	+	2012.87i	0.0271453	+	0.153949i
$556$	1169.82	−	6634.40i	0.0892294	−	0.506045i
$557$	17443.3	+	6348.83i	1.32692	+	0.482960i	0.905670	−	0.423984i	$-0.139369\pi$
$557$	17443.3	+	6348.83i	1.32692	+	0.482960i	0.421251	+	0.906944i	$0.361591\pi$
$558$	24044.1	+	41645.6i	1.82414	+	3.15950i
$559$	−2456.90	+	4255.47i	−0.185896	+	0.321981i
$560$	−547.601	+	459.492i	−0.0413221	+	0.0346733i
$561$	−16915.0	+	14193.4i	−1.27300	+	1.06817i
$562$	8298.69	−	14373.8i	0.622881	−	1.07886i
$563$	−7676.62	−	13296.3i	−0.574655	−	0.995332i	−0.996079	−	0.0884685i	$-0.971803\pi$
$563$	−7676.62	−	13296.3i	−0.574655	−	0.995332i	0.421424	−	0.906864i	$-0.361531\pi$
$564$	8788.55	+	3198.77i	0.656143	+	0.238817i
$565$	−471.640	+	2674.80i	−0.0351186	+	0.199168i
$566$	−100.800	−	571.663i	−0.00748574	−	0.0424537i
$567$	−18612.6	+	6774.45i	−1.37858	+	0.501764i
$568$	623.594	+	523.257i	0.0460659	+	0.0386538i
$569$	277.505			0.0204457			0.0102229	−	0.999948i	$-0.496746\pi$
$569$	277.505			0.0204457			0.0102229	+	0.999948i	$0.496746\pi$
$570$	3393.50	+	8764.45i	0.249365	+	0.644039i
$571$	−10298.2			−0.754757			−0.377379	−	0.926059i	$-0.623174\pi$
$571$	−10298.2			−0.754757			−0.377379	+	0.926059i	$0.623174\pi$
$572$	6805.70	+	5710.66i	0.497484	+	0.417439i
$573$	−38487.5	+	14008.3i	−2.80600	+	1.02130i
$574$	−32.2520	−	182.910i	−0.00234525	−	0.0133005i
$575$	−1776.62	+	10075.7i	−0.128852	+	0.730757i
$576$	−4338.07	−	1578.93i	−0.313807	−	0.114216i
$577$	−10290.4	−	17823.5i	−0.742454	−	1.28597i	−0.951375	−	0.308036i	$-0.900328\pi$
$577$	−10290.4	−	17823.5i	−0.742454	−	1.28597i	0.208921	−	0.977933i	$-0.433005\pi$
$578$	−1019.96	+	1766.63i	−0.0733994	+	0.127131i
$579$	−12560.4	+	10539.4i	−0.901541	+	0.756482i
$580$	1916.00	−	1607.72i	0.137168	−	0.115098i
$581$	−453.780	+	785.970i	−0.0324027	+	0.0561231i
$582$	−9626.72	−	16674.0i	−0.685636	−	1.18756i
$583$	−2606.62	−	948.732i	−0.185172	−	0.0673970i
$584$	−788.071	+	4469.37i	−0.0558401	+	0.316685i
$585$	−4460.48	−	25296.7i	−0.315245	−	1.78784i
$586$	4516.55	−	1643.89i	0.318391	−	0.115885i
$587$	9705.45	+	8143.84i	0.682431	+	0.572627i	0.916715	−	0.399541i	$-0.130830\pi$
$587$	9705.45	+	8143.84i	0.682431	+	0.572627i	−0.234285	+	0.972168i	$0.575275\pi$
$588$	11212.6			0.786393
$589$	27278.8	+	4239.64i	1.90833	+	0.296589i
$590$	−5576.56			−0.389124
$591$	39358.0	+	33025.3i	2.73938	+	2.29861i
$592$	−541.593	+	197.124i	−0.0376002	+	0.0136854i
$593$	−574.939	−	3260.64i	−0.0398144	−	0.225798i	0.958408	−	0.285403i	$-0.0921273\pi$
$593$	−574.939	−	3260.64i	−0.0398144	−	0.225798i	−0.998222	+	0.0596041i	$0.981016\pi$
$594$	5547.07	−	31459.0i	0.383163	−	2.17303i
$595$	2619.51	+	953.424i	0.180487	+	0.0656917i
$596$	1471.44	+	2548.62i	0.101129	+	0.175160i
$597$	21450.2	−	37152.8i	1.47051	−	2.54701i
$598$	−10586.5	+	8883.09i	−0.723934	+	0.607453i
$599$	−633.399	+	531.485i	−0.0432053	+	0.0362535i	−0.664135	−	0.747613i	$-0.731200\pi$
$599$	−633.399	+	531.485i	−0.0432053	+	0.0362535i	0.620929	+	0.783867i	$0.286755\pi$
$600$	3684.82	−	6382.30i	0.250721	−	0.434261i
$601$	−1953.51	−	3383.58i	−0.132588	−	0.229649i	0.792085	−	0.610410i	$-0.208995\pi$
$601$	−1953.51	−	3383.58i	−0.132588	−	0.229649i	−0.924674	+	0.380761i	$0.875662\pi$
$602$	1158.62	+	421.704i	0.0784417	+	0.0285504i
$603$	6187.65	−	35091.9i	0.417878	−	2.36990i
$604$	772.057	+	4378.55i	0.0520108	+	0.294968i
$605$	−362.118	+	131.800i	−0.0243342	+	0.00885692i
$606$	−21776.8	−	18272.9i	−1.45977	−	1.22489i
$607$	25332.2			1.69391			0.846955	−	0.531664i	$-0.178433\pi$
$607$	25332.2			1.69391			0.846955	+	0.531664i	$0.178433\pi$
$608$	−2267.71	+	1371.53i	−0.151263	+	0.0914850i
$609$	8564.49			0.569870
$610$	−1211.14	−	1016.27i	−0.0803898	−	0.0674551i
$611$	−13789.3	+	5018.89i	−0.913019	+	0.332312i
$612$	3126.12	+	17729.1i	0.206480	+	1.17101i
$613$	3894.75	−	22088.2i	0.256619	−	1.45536i	−0.535263	−	0.844686i	$-0.679787\pi$
$613$	3894.75	−	22088.2i	0.256619	−	1.45536i	0.791882	−	0.610674i	$-0.209102\pi$
$614$	−18815.3	−	6848.19i	−1.23668	−	0.450115i
$615$	−336.064	−	582.080i	−0.0220348	−	0.0381654i
$616$	1114.62	−	1930.58i	0.0729049	−	0.126275i
$617$	2099.59	−	1761.77i	0.136996	−	0.114953i	−0.571715	−	0.820452i	$-0.693722\pi$
$617$	2099.59	−	1761.77i	0.136996	−	0.114953i	0.708711	+	0.705499i	$0.249277\pi$
$618$	21177.6	−	17770.1i	1.37846	−	1.15667i
$619$	−2637.31	+	4567.96i	−0.171248	+	0.296610i	−0.938856	−	0.344309i	$-0.888113\pi$
$619$	−2637.31	+	4567.96i	−0.171248	+	0.296610i	0.767608	+	0.640919i	$0.221447\pi$
$620$	3799.25	+	6580.49i	0.246099	+	0.426256i
$621$	46693.5	+	16995.1i	3.01731	+	1.09821i
$622$	−2034.20	+	11536.5i	−0.131132	+	0.743684i
$623$	−946.796	−	5369.55i	−0.0608870	−	0.345307i
$624$	9354.18	−	3404.64i	0.600107	−	0.218421i
$625$	3447.83	+	2893.08i	0.220661	+	0.185157i
$626$	−12256.2			−0.782521
$627$	−19292.6	−	22064.2i	−1.22882	−	1.40536i
$628$	−11349.3			−0.721155
$629$	1721.73	+	1444.70i	0.109141	+	0.0915805i
$630$	−6056.70	+	2204.46i	−0.383024	+	0.139409i
$631$	231.284	+	1311.68i	0.0145916	+	0.0827530i	0.991234	−	0.132118i	$-0.0421779\pi$
$631$	231.284	+	1311.68i	0.0145916	+	0.0827530i	−0.976642	+	0.214871i	$0.931067\pi$
$632$	519.530	−	2946.40i	0.0326991	−	0.185446i
$633$	−16871.9	−	6140.87i	−1.05940	−	0.385589i
$634$	−7728.73	−	13386.6i	−0.484144	−	0.838561i
$635$	−1463.39	+	2534.66i	−0.0914530	+	0.158401i
$636$	−2380.93	+	1997.84i	−0.148443	+	0.124559i
$637$	−13476.7	+	11308.3i	−0.838253	+	0.703378i
$638$	−3899.96	+	6754.92i	−0.242007	+	0.419169i
$639$	3669.93	+	6356.51i	0.227199	+	0.393521i
$640$	−685.464	−	249.489i	−0.0423365	−	0.0154092i
$641$	−380.118	+	2155.76i	−0.0234224	+	0.132835i	−0.994277	−	0.106835i	$-0.965928\pi$
$641$	−380.118	+	2155.76i	−0.0234224	+	0.132835i	0.970854	+	0.239670i	$0.0770394\pi$
$642$	4873.22	+	27637.4i	0.299581	+	1.69901i
$643$	−4235.35	+	1541.54i	−0.259760	+	0.0945450i	−0.468618	−	0.883401i	$-0.655248\pi$
$643$	−4235.35	+	1541.54i	−0.259760	+	0.0945450i	0.208857	+	0.977946i	$0.433026\pi$
$644$	2656.38	+	2228.96i	0.162540	+	0.136387i
$645$	4461.92			0.272384
$646$	9053.54	+	4984.25i	0.551404	+	0.303565i
$647$	18162.4			1.10361			0.551807	−	0.833972i	$-0.313939\pi$
$647$	18162.4			1.10361			0.551807	+	0.833972i	$0.313939\pi$
$648$	−15483.4	−	12992.1i	−0.938647	−	0.787619i
$649$	16341.8	−	5947.93i	0.988401	−	0.359748i
$650$	2007.90	+	11387.3i	0.121163	+	0.687151i
$651$	−4518.12	+	25623.5i	−0.272011	+	1.54265i
$652$	−8628.31	−	3140.45i	−0.518268	−	0.188634i
$653$	3260.93	+	5648.09i	0.195421	+	0.338479i	0.947038	−	0.321120i	$-0.104059\pi$
$653$	3260.93	+	5648.09i	0.195421	+	0.338479i	−0.751618	+	0.659599i	$0.770726\pi$
$654$	−5843.11	+	10120.6i	−0.349363	+	0.605115i
$655$	3375.69	−	2832.54i	0.201373	−	0.168972i
$656$	145.187	−	121.827i	0.00864118	−	0.00725081i
$657$	−20460.0	+	35437.8i	−1.21495	+	2.10435i
$658$	1841.05	+	3188.78i	0.109075	+	0.188924i
$659$	1027.89	+	374.121i	0.0607600	+	0.0221148i	0.372221	−	0.928144i	$-0.378596\pi$
$659$	1027.89	+	374.121i	0.0607600	+	0.0221148i	−0.311461	+	0.950259i	$0.600818\pi$
$660$	1400.86	−	7944.66i	0.0826187	−	0.468554i
$661$	−4365.29	−	24756.8i	−0.256869	−	1.45677i	−0.791230	−	0.611518i	$-0.790559\pi$
$661$	−4365.29	−	24756.8i	−0.256869	−	1.45677i	0.534362	−	0.845256i	$-0.320552\pi$
$662$	7336.15	−	2670.14i	0.430706	−	0.156764i
$663$	−29737.1	−	24952.4i	−1.74192	−	1.46164i
$664$	−926.114			−0.0541268
$665$	−1194.52	+	3502.04i	−0.0696565	+	0.204216i
$666$	−5196.70			−0.302354
$667$	−9294.39	−	7798.92i	−0.539551	−	0.452737i
$668$	3333.51	−	1213.30i	0.193080	−	0.0702753i
$669$	5190.23	+	29435.3i	0.299949	+	1.70110i
$670$	977.719	−	5544.92i	0.0563770	−	0.319730i
$671$	4633.14	+	1686.33i	0.266558	+	0.0970192i
$672$	−1248.90	−	2163.16i	−0.0716927	−	0.124175i
$673$	−13756.3	+	23826.5i	−0.787912	+	1.36470i	0.139333	+	0.990246i	$0.455504\pi$
$673$	−13756.3	+	23826.5i	−0.787912	+	1.36470i	−0.927244	+	0.374457i	$0.877829\pi$
$674$	−14999.5	+	12586.1i	−0.857209	+	0.719284i
$675$	31849.3	−	26724.7i	1.81612	−	1.52390i
$676$	−3415.34	+	5915.54i	−0.194318	+	0.336569i
$677$	16953.0	+	29363.4i	0.962415	+	1.66695i	0.716406	+	0.697684i	$0.245786\pi$
$677$	16953.0	+	29363.4i	0.962415	+	1.66695i	0.246009	+	0.969268i	$0.420881\pi$
$678$	−8918.15	−	3245.94i	−0.505161	−	0.183864i
$679$	1316.26	−	7464.88i	0.0743938	−	0.421908i
$680$	493.962	+	2801.40i	0.0278567	+	0.157983i
$681$	−61583.9	+	22414.7i	−3.46534	+	1.26128i
$682$	−18152.2	−	15231.5i	−1.01918	−	0.855197i
$683$	−3969.45			−0.222382			−0.111191	−	0.993799i	$-0.535467\pi$
$683$	−3969.45			−0.222382			−0.111191	+	0.993799i	$0.535467\pi$
$684$	−23443.4	+	4627.41i	−1.31050	+	0.258674i
$685$	2555.20			0.142524
$686$	7501.43	+	6294.45i	0.417502	+	0.350325i
$687$	−16946.5	+	6168.03i	−0.941121	+	0.342540i
$688$	218.482	+	1239.07i	0.0121069	+	0.0686616i
$689$	846.812	−	4802.51i	0.0468229	−	0.265546i
$690$	11792.0	+	4291.94i	0.650599	+	0.236799i
$691$	−10451.7	−	18102.9i	−0.575402	−	0.996626i	−0.995998	−	0.0893776i	$-0.971512\pi$
$691$	−10451.7	−	18102.9i	−0.575402	−	0.996626i	0.420596	−	0.907248i	$-0.361821\pi$
$692$	1181.95	−	2047.19i	0.0649290	−	0.112460i
$693$	15397.6	−	12920.1i	0.844020	−	0.708217i
$694$	4250.99	−	3567.00i	0.232515	−	0.195103i
$695$	4798.98	−	8312.08i	0.261922	−	0.453662i
$696$	4369.79	+	7568.70i	0.237983	+	0.412199i
$697$	−694.520	−	252.785i	−0.0377429	−	0.0137373i
$698$	−1792.03	+	10163.1i	−0.0971769	+	0.551117i
$699$	7591.21	+	43051.9i	0.410767	+	2.32957i
$700$	2726.44	−	992.342i	0.147214	−	0.0535815i
$701$	3888.15	+	3262.55i	0.209491	+	0.175784i	0.741496	−	0.670957i	$-0.234117\pi$
$701$	3888.15	+	3262.55i	0.209491	+	0.175784i	−0.532005	+	0.846742i	$0.678561\pi$
$702$	56158.9			3.01935
$703$	−1870.73	+	2323.89i	−0.100364	+	0.124676i
$704$	2274.82			0.121783
$705$	10207.4	+	8565.01i	0.545294	+	0.457556i
$706$	6268.56	−	2281.57i	0.334165	−	0.121626i
$707$	−1943.45	−	11021.9i	−0.103382	−	0.586308i
$708$	3383.65	−	19189.6i	0.179612	−	1.01863i
$709$	2751.79	+	1001.57i	0.145763	+	0.0530532i	0.413871	−	0.910335i	$-0.364176\pi$
$709$	2751.79	+	1001.57i	0.145763	+	0.0530532i	−0.268109	+	0.963389i	$0.586399\pi$
$710$	579.892	+	1004.40i	0.0306520	+	0.0530909i
$711$	13488.1	−	23362.1i	0.711454	−	1.23227i
$712$	4262.15	−	3576.37i	0.224341	−	0.188245i
$713$	28236.2	−	23693.0i	1.48311	−	1.24447i
$714$	−4870.27	+	8435.56i	−0.255274	+	0.442147i
$715$	6328.75	+	10961.7i	0.331024	+	0.573350i
$716$	−3810.73	−	1386.99i	−0.198902	−	0.0723943i
$717$	760.455	−	4312.75i	0.0396091	−	0.224634i
$718$	−2552.92	−	14478.3i	−0.132694	−	0.752544i
$719$	−30481.1	+	11094.2i	−1.58102	+	0.575445i	−0.975426	−	0.220328i	$-0.929287\pi$
$719$	−30481.1	+	11094.2i	−1.58102	+	0.575445i	−0.605595	+	0.795773i	$0.707065\pi$
$720$	−5038.41	−	4227.73i	−0.260792	−	0.218831i
$721$	10883.9			0.562190
$722$	−6369.98	+	12149.4i	−0.328346	+	0.626250i
$723$	22772.4			1.17139
$724$	3332.99	+	2796.71i	0.171090	+	0.143562i
$725$	−9539.54	+	3472.11i	−0.488675	+	0.177863i
$726$	−233.821	−	1326.06i	−0.0119530	−	0.0677890i
$727$	5539.15	−	31414.1i	0.282580	−	1.60259i	−0.431223	−	0.902245i	$-0.641918\pi$
$727$	5539.15	−	31414.1i	0.282580	−	1.60259i	0.713804	−	0.700346i	$-0.246971\pi$
$728$	3682.72	+	1340.40i	0.187487	+	0.0682398i
$729$	−30721.5	−	53211.2i	−1.56081	−	2.70341i
$730$	−3232.92	+	5599.57i	−0.163912	+	0.283903i
$731$	3758.57	−	3153.82i	0.190172	−	0.159573i
$732$	4231.99	−	3551.06i	0.213687	−	0.179305i
$733$	−10125.3	+	17537.6i	−0.510215	+	0.883718i	0.489715	+	0.871882i	$0.337101\pi$
$733$	−10125.3	+	17537.6i	−0.510215	+	0.883718i	−0.999930	+	0.0118353i	$0.996233\pi$
$734$	1071.46	+	1855.83i	0.0538806	+	0.0933239i
$735$	15011.4	+	5463.70i	0.753338	+	0.274193i
$736$	−614.462	+	3484.78i	−0.0307736	+	0.174526i
$737$	3049.03	+	17291.9i	0.152391	+	0.864255i
$738$	1605.84	−	584.476i	0.0800971	−	0.0291529i
$739$	−10551.5	−	8853.77i	−0.525228	−	0.440719i	0.341222	−	0.939983i	$-0.389159\pi$
$739$	−10551.5	−	8853.77i	−0.525228	−	0.440719i	−0.866450	+	0.499264i	$0.833604\pi$
$740$	−821.138			−0.0407914
$741$	32310.6	−	40137.3i	1.60184	−	1.98985i
$742$	−1223.65			−0.0605411
$743$	−4752.77	−	3988.04i	−0.234673	−	0.196914i	0.517866	−	0.855462i	$-0.326727\pi$
$743$	−4752.77	−	3988.04i	−0.234673	−	0.196914i	−0.752539	+	0.658548i	$0.771171\pi$
$744$	−24949.5	+	9080.88i	−1.22943	+	0.447475i
$745$	728.070	+	4129.09i	0.0358046	+	0.203058i
$746$	−2775.54	+	15740.8i	−0.136219	+	0.772538i
$747$	−7846.76	−	2855.99i	−0.384335	−	0.139886i
$748$	−4435.49	−	7682.49i	−0.216815	−	0.375534i
$749$	−5524.32	+	9568.41i	−0.269499	+	0.466785i
$750$	18909.7	−	15867.2i	0.920649	−	0.772516i
$751$	−11978.7	+	10051.3i	−0.582037	+	0.488387i	−0.885615	−	0.464420i	$-0.846263\pi$
$751$	−11978.7	+	10051.3i	−0.582037	+	0.488387i	0.303578	+	0.952806i	$0.401819\pi$
$752$	−1878.68	+	3253.97i	−0.0911018	+	0.157793i
$753$	16743.5	+	29000.6i	0.810314	+	1.40351i
$754$	−12885.5	−	4689.93i	−0.622363	−	0.226521i
$755$	−1099.96	+	6238.20i	−0.0530222	+	0.300704i
$756$	−2446.96	−	13877.4i	−0.117719	−	0.667615i
$757$	5394.53	−	1963.45i	0.259006	−	0.0942705i	−0.209254	−	0.977861i	$-0.567103\pi$
$757$	5394.53	−	1963.45i	0.259006	−	0.0942705i	0.468260	+	0.883591i	$0.344881\pi$
$758$	−17999.6	−	15103.5i	−0.862500	−	0.723723i
$759$	−39133.6			−1.87149
$760$	−3704.33	+	731.183i	−0.176803	+	0.0348984i
$761$	19056.0			0.907725			0.453862	−	0.891072i	$-0.350046\pi$
$761$	19056.0			0.907725			0.453862	+	0.891072i	$0.350046\pi$
$762$	−7834.14	−	6573.62i	−0.372442	−	0.312516i
$763$	−4323.37	+	1573.58i	−0.205133	+	0.0746624i
$764$	−2857.30	−	16204.6i	−0.135306	−	0.767357i
$765$	−4453.83	+	25259.0i	−0.210495	+	1.19378i
$766$	14344.9	+	5221.11i	0.676633	+	0.246274i
$767$	15286.5	+	26477.1i	0.719642	+	1.24646i
$768$	1274.44	−	2207.39i	0.0598792	−	0.103714i
$769$	2397.40	−	2011.66i	0.112422	−	0.0943333i	−0.584844	−	0.811146i	$-0.698844\pi$
$769$	2397.40	−	2011.66i	0.112422	−	0.0943333i	0.697266	+	0.716813i	$0.254400\pi$
$770$	2432.99	−	2041.52i	0.113869	−	0.0955473i
$771$	26240.5	−	45449.9i	1.22572	−	2.12301i
$772$	−3293.60	−	5704.69i	−0.153548	−	0.265954i
$773$	−10320.6	−	3756.38i	−0.480213	−	0.174783i	0.0905601	−	0.995891i	$-0.471134\pi$
$773$	−10320.6	−	3756.38i	−0.480213	−	0.174783i	−0.570773	+	0.821108i	$0.693356\pi$
$774$	−1969.95	+	11172.1i	−0.0914838	+	0.518830i
$775$	−5355.47	−	30372.4i	−0.248225	−	1.40775i
$776$	7268.52	−	2645.53i	0.336243	−	0.122383i
$777$	−2153.92	−	1807.35i	−0.0994485	−	0.0834472i
$778$	13882.9			0.639750
$779$	316.708	−	928.509i	0.0145664	−	0.0427051i
$780$	14182.4			0.651039
$781$	−2770.63	−	2324.84i	−0.126941	−	0.106516i
$782$	12966.9	−	4719.55i	0.592959	−	0.215819i
$783$	8561.69	+	48555.7i	0.390766	+	2.21614i
$784$	−782.219	+	4436.18i	−0.0356331	+	0.202086i
$785$	−15194.4	−	5530.30i	−0.690841	−	0.251446i
$786$	7698.87	+	13334.8i	0.349376	+	0.605137i
$787$	4117.14	−	7131.09i	0.186481	−	0.322994i	−0.757594	−	0.652726i	$-0.773625\pi$
$787$	4117.14	−	7131.09i	0.186481	−	0.322994i	0.944074	+	0.329732i	$0.106959\pi$
$788$	−15811.9	+	13267.8i	−0.714819	+	0.599804i
$789$	−14291.3	+	11991.8i	−0.644846	+	0.541090i
$790$	2131.28	−	3691.48i	0.0959841	−	0.166249i
$791$	−1868.19	−	3235.81i	−0.0839764	−	0.145451i
$792$	19274.1	+	7015.19i	0.864740	+	0.314740i
$793$	−1505.17	+	8536.23i	−0.0674024	+	0.382258i
$794$	−1628.64	−	9236.49i	−0.0727939	−	0.412835i
$795$	−4161.10	+	1514.51i	−0.185634	+	0.0675652i
$796$	13202.8	+	11078.5i	0.587892	+	0.493300i
$797$	−27065.1			−1.20288			−0.601440	−	0.798918i	$-0.705406\pi$
$797$	−27065.1			−1.20288			−0.601440	+	0.798918i	$0.705406\pi$
$798$	−11326.2	−	6235.41i	−0.502434	−	0.276605i
$799$	14652.4			0.648765
$800$	2268.05	+	1903.12i	0.100235	+	0.0841069i
$801$	47141.3	−	17158.0i	2.07947	−	0.756865i
$802$	5158.45	+	29255.0i	0.227121	+	1.28807i
$803$	3501.41	−	19857.5i	0.153875	−	0.872671i
$804$	18487.5	+	6728.90i	0.810950	+	0.295162i
$805$	2470.21	+	4278.54i	0.108154	+	0.187327i
$806$	20829.1	−	36077.0i	0.910265	−	1.57662i
$807$	−32760.3	+	27489.2i	−1.42902	+	1.19909i
$808$	8748.75	−	7341.08i	0.380916	−	0.319626i
$809$	7678.39	−	13299.4i	0.333693	−	0.577973i	−0.649540	−	0.760328i	$-0.725038\pi$
$809$	7678.39	−	13299.4i	0.333693	−	0.577973i	0.983233	+	0.182354i	$0.0583718\pi$
$810$	−14398.3	−	24938.5i	−0.624572	−	1.08179i
$811$	4358.32	+	1586.30i	0.188707	+	0.0686837i	0.434645	−	0.900602i	$-0.356874\pi$
$811$	4358.32	+	1586.30i	0.188707	+	0.0686837i	−0.245938	+	0.969286i	$0.579096\pi$
$812$	−597.481	+	3388.48i	−0.0258220	+	0.146444i
$813$	−5468.90	−	31015.7i	−0.235920	−	1.33797i
$814$	2406.30	−	875.822i	0.103613	−	0.0377120i
$815$	−10021.3	−	8408.85i	−0.430712	−	0.361410i
$816$	−9939.67			−0.426419
$817$	4286.87	+	4902.74i	0.183572	+	0.209945i
$818$	14126.9			0.603835
$819$	27069.3	+	22713.9i	1.15492	+	0.969093i
$820$	253.740	−	92.3540i	0.0108061	−	0.00393310i
$821$	1944.57	+	11028.2i	0.0826625	+	0.468802i	0.997837	+	0.0657434i	$0.0209419\pi$
$821$	1944.57	+	11028.2i	0.0826625	+	0.468802i	−0.915174	+	0.403059i	$0.867947\pi$
$822$	−1550.40	+	8792.75i	−0.0657863	+	0.373093i
$823$	17650.7	+	6424.33i	0.747588	+	0.272100i	0.687590	−	0.726099i	$-0.258668\pi$
$823$	17650.7	+	6424.33i	0.747588	+	0.272100i	0.0599976	+	0.998199i	$0.480891\pi$
$824$	5553.22	+	9618.46i	0.234776	+	0.406645i
$825$	−16371.7	+	28356.6i	−0.690896	+	1.19667i
$826$	5876.68	−	4931.12i	0.247550	−	0.207719i
$827$	−19474.3	+	16340.8i	−0.818847	+	0.687094i	−0.952702	−	0.303907i	$-0.901709\pi$
$827$	−19474.3	+	16340.8i	−0.818847	+	0.687094i	0.133855	+	0.991001i	$0.457264\pi$
$828$	−15952.7	+	27630.9i	−0.669560	+	1.15971i
$829$	−21804.2	−	37765.9i	−0.913498	−	1.58222i	−0.809086	−	0.587691i	$-0.800037\pi$
$829$	−21804.2	−	37765.9i	−0.913498	−	1.58222i	−0.104412	−	0.994534i	$-0.533296\pi$
$830$	−1239.88	−	451.279i	−0.0518516	−	0.0188724i
$831$	4047.92	−	22956.9i	0.168978	−	0.958322i
$832$	694.452	+	3938.43i	0.0289373	+	0.164111i
$833$	16507.0	−	6008.06i	0.686595	−	0.249900i
$834$	25691.0	+	21557.3i	1.06668	+	0.895048i
$835$	5054.11			0.209467
$836$	10075.5	−	6093.71i	0.416827	−	0.252100i
$837$	−149787.			−6.18567
$838$	−4114.32	−	3452.32i	−0.169602	−	0.142313i
$839$	−16053.7	+	5843.08i	−0.660592	+	0.240436i	−0.650492	−	0.759513i	$-0.725437\pi$
$839$	−16053.7	+	5843.08i	−0.660592	+	0.240436i	−0.0101000	+	0.999949i	$0.503215\pi$
$840$	−617.957	−	3504.61i	−0.0253828	−	0.143953i
$841$	−2144.58	+	12162.5i	−0.0879323	+	0.498689i
$842$	−8516.38	−	3099.71i	−0.348568	−	0.126868i
$843$	41313.1	+	71556.3i	1.68790	+	2.92352i
$844$	3606.62	−	6246.85i	0.147091	−	0.254769i
$845$	−7454.98	+	6255.47i	−0.303502	+	0.254668i
$846$	−25952.4	+	21776.7i	−1.05468	+	0.884985i
$847$	265.061	−	459.099i	0.0107528	−	0.0186244i
$848$	−624.331	−	1081.37i	−0.0252826	−	0.0437907i
$849$	2715.52	+	988.368i	0.109772	+	0.0399537i
$850$	2004.90	−	11370.4i	0.0809031	−	0.458824i
$851$	691.691	+	3922.77i	0.0278623	+	0.158015i
$852$	−3808.13	+	1386.04i	−0.153127	+	0.0557337i
$853$	19653.1	+	16490.9i	0.788875	+	0.661945i	0.945467	−	0.325719i	$-0.105606\pi$
$853$	19653.1	+	16490.9i	0.788875	+	0.661945i	−0.156592	+	0.987663i	$0.550051\pi$
$854$	2174.97			0.0871499
$855$	−33640.9	−	5228.41i	−1.34561	−	0.209132i
$856$	−11274.5			−0.450181
$857$	−23459.8	−	19685.1i	−0.935091	−	0.784634i	0.0416334	−	0.999133i	$-0.486744\pi$
$857$	−23459.8	−	19685.1i	−0.935091	−	0.784634i	−0.976724	+	0.214498i	$0.931188\pi$
$858$	−41560.7	+	15126.9i	−1.65368	+	0.601891i
$859$	−6758.35	−	38328.5i	−0.268442	−	1.52241i	−0.759051	−	0.651031i	$-0.774337\pi$
$859$	−6758.35	−	38328.5i	−0.268442	−	1.52241i	0.490609	−	0.871380i	$-0.336774\pi$
$860$	−311.275	+	1765.33i	−0.0123423	+	0.0699967i
$861$	868.859	+	316.239i	0.0343910	+	0.0125173i
$862$	−7975.13	−	13813.3i	−0.315121	−	0.545805i
$863$	14164.8	−	24534.2i	0.558722	−	0.967735i	−0.438881	−	0.898545i	$-0.644625\pi$
$863$	14164.8	−	24534.2i	0.558722	−	0.967735i	0.997604	−	0.0691899i	$-0.0220415\pi$
$864$	11015.4	−	9243.02i	0.433740	−	0.363951i
$865$	2579.95	−	2164.83i	0.101411	−	0.0850943i
$866$	12868.7	−	22289.3i	0.504963	−	0.874621i
$867$	−5077.64	−	8794.73i	−0.198899	−	0.344504i
$868$	−9822.57	−	3575.12i	−0.384101	−	0.139801i
$869$	−2308.28	+	13090.9i	−0.0901070	+	0.511022i
$870$	2162.17	+	12262.3i	0.0842580	+	0.477851i
$871$	−29007.0	+	10557.7i	−1.12843	+	0.410716i
$872$	−3596.50	−	3017.82i	−0.139671	−	0.117198i
$873$	69743.0			2.70383
$874$	6613.40	+	17080.6i	0.255952	+	0.661051i
$875$	9718.40			0.375477
$876$	−17307.2	−	14522.5i	−0.667530	−	0.560124i
$877$	38356.7	−	13960.7i	1.47687	−	0.537537i	0.526913	−	0.849919i	$-0.323349\pi$
$877$	38356.7	−	13960.7i	1.47687	−	0.537537i	0.949956	+	0.312382i	$0.101127\pi$
$878$	−2463.69	−	13972.3i	−0.0946988	−	0.537064i
$879$	−4154.98	+	23564.1i	−0.159436	+	0.904205i
$880$	3045.52	+	1108.48i	0.116664	+	0.0424623i
$881$	−14688.4	−	25441.0i	−0.561708	−	0.972906i	−0.997348	−	0.0727851i	$-0.976811\pi$
$881$	−14688.4	−	25441.0i	−0.561708	−	0.972906i	0.435640	−	0.900121i	$-0.356522\pi$
$882$	−20308.1	+	35174.6i	−0.775293	+	1.34285i
$883$	−19313.7	+	16206.1i	−0.736078	+	0.617643i	−0.931781	−	0.363021i	$-0.881745\pi$
$883$	−19313.7	+	16206.1i	−0.736078	+	0.617643i	0.195703	+	0.980663i	$0.437301\pi$
$884$	11946.8	−	10024.5i	0.454540	−	0.381404i
$885$	13880.8	−	24042.2i	0.527229	−	0.913187i
$886$	10093.8	+	17483.0i	0.382742	+	0.662928i
$887$	−2758.81	−	1004.12i	−0.104433	−	0.0380104i	0.289275	−	0.957246i	$-0.406586\pi$
$887$	−2758.81	−	1004.12i	−0.104433	−	0.0380104i	−0.393708	+	0.919236i	$0.628808\pi$
$888$	498.236	−	2825.64i	0.0188285	−	0.106782i
$889$	−699.151	−	3965.08i	−0.0263766	−	0.149589i
$890$	7448.86	−	2711.16i	0.280547	−	0.102111i
$891$	68792.6	+	57723.9i	2.58658	+	2.17040i
$892$	−12007.9			−0.450735
$893$	395.717	+	19444.8i	0.0148289	+	0.728663i
$894$	−14650.5			−0.548082
$895$	−4425.94	−	3713.80i	−0.165299	−	0.138703i
$896$	942.968	−	343.212i	0.0351589	−	0.0127968i
$897$	−11946.6	−	67752.6i	−0.444689	−	2.52195i
$898$	2186.56	−	12400.6i	0.0812543	−	0.460816i
$899$	34368.2	+	12509.0i	1.27502	+	0.464069i
$900$	13347.8	+	23119.1i	0.494363	+	0.856261i
$901$	−2434.66	+	4216.96i	−0.0900227	+	0.155924i
$902$	−645.068	+	541.277i	−0.0238120	+	0.0199806i
$903$	−4702.05	+	3945.49i	−0.173283	+	0.145402i
$904$	1906.39	−	3301.96i	0.0701388	−	0.121484i
$905$	3099.41	+	5368.33i	0.113843	+	0.197182i
$906$	−20799.0	−	7570.22i	−0.762694	−	0.277598i
$907$	−6812.73	+	38636.9i	−0.249408	+	1.41446i	0.560621	+	0.828073i	$0.310563\pi$
$907$	−6812.73	+	38636.9i	−0.249408	+	1.41446i	−0.810029	+	0.586390i	$0.800549\pi$
$908$	−4571.97	−	25928.9i	−0.167099	−	0.947668i
$909$	96765.0	−	35219.6i	3.53080	−	1.28510i
$910$	4277.27	+	3589.05i	0.155813	+	0.130743i
$911$	−45768.5			−1.66452			−0.832260	−	0.554386i	$-0.812953\pi$
$911$	−45768.5			−1.66452			−0.832260	+	0.554386i	$0.812953\pi$
$912$	−268.441	−	13190.7i	−0.00974669	−	0.478934i
$913$	4114.73			0.149154
$914$	9865.10	+	8277.80i	0.357011	+	0.299568i
$915$	7396.15	−	2691.98i	0.267223	−	0.0972612i
$916$	−1258.11	−	7135.07i	−0.0453810	−	0.257368i
$917$	−1052.67	+	5969.97i	−0.0379085	+	0.214990i
$918$	−52693.4	−	19178.8i	−1.89449	−	0.689538i
$919$	3782.53	+	6551.53i	0.135772	+	0.235163i	0.925892	−	0.377789i	$-0.123315\pi$
$919$	3782.53	+	6551.53i	0.135772	+	0.235163i	−0.790120	+	0.612952i	$0.789982\pi$
$920$	−2520.71	+	4366.01i	−0.0903321	+	0.156460i
$921$	76358.3	−	64072.2i	2.73191	−	2.29235i
$922$	−17704.6	+	14855.9i	−0.632396	+	0.530643i
$923$	3179.21	−	5506.56i	0.113375	−	0.196371i
$924$	5548.89	+	9610.95i	0.197559	+	0.342183i
$925$	3131.86	+	1139.90i	0.111324	+	0.0405187i
$926$	2773.95	−	15731.9i	0.0984426	−	0.558296i
$927$	17389.4	+	98620.5i	0.616121	+	3.49420i
$928$	−3299.35	+	1200.87i	−0.116710	+	0.0424788i
$929$	−15951.0	−	13384.5i	−0.563332	−	0.472692i	0.316093	−	0.948728i	$-0.397629\pi$
$929$	−15951.0	−	13384.5i	−0.563332	−	0.472692i	−0.879426	+	0.476036i	$0.842073\pi$
$930$	−37827.3			−1.33377
$931$	8418.96	+	21743.8i	0.296370	+	0.765440i
$932$	−17562.8			−0.617261
$933$	−44674.0	−	37485.9i	−1.56759	−	1.31536i
$934$	28956.3	−	10539.2i	1.01443	−	0.369223i
$935$	−2194.68	−	12446.6i	−0.0767632	−	0.435346i
$936$	−6261.56	+	35511.1i	−0.218660	+	1.24008i
$937$	−1115.51	−	406.011i	−0.0388922	−	0.0141556i	0.322501	−	0.946569i	$-0.395476\pi$
$937$	−1115.51	−	406.011i	−0.0388922	−	0.0141556i	−0.361393	+	0.932414i	$0.617699\pi$
$938$	3872.81	+	6707.90i	0.134810	+	0.233497i
$939$	30507.4	−	52840.4i	1.06025	−	1.83640i
$940$	−4100.78	+	3440.96i	−0.142290	+	0.119396i
$941$	−27221.5	+	22841.6i	−0.943036	+	0.791301i	−0.978111	−	0.208084i	$-0.933277\pi$
$941$	−27221.5	+	22841.6i	−0.943036	+	0.791301i	0.0350751	+	0.999385i	$0.488833\pi$
$942$	28249.8	−	48930.1i	0.977101	−	1.69239i
$943$	−654.937	−	1134.38i	−0.0226168	−	0.0391735i
$944$	7356.19	+	2677.43i	0.253627	+	0.0923126i
$945$	3486.24	−	19771.4i	0.120008	−	0.680597i
$946$	−970.716	−	5505.20i	−0.0333623	−	0.189207i
$947$	20129.0	−	7326.37i	0.690714	−	0.251399i	0.0272731	−	0.999628i	$-0.491318\pi$
$947$	20129.0	−	7326.37i	0.690714	−	0.251399i	0.663441	+	0.748229i	$0.269095\pi$
$948$	11409.7	+	9573.84i	0.390895	+	0.328000i
$949$	35448.5			1.21255
$950$	15143.5	+	2353.58i	0.517179	+	0.0803792i
$951$	76951.3			2.62389
$952$	−2997.71	−	2515.38i	−0.102055	−	0.0856342i
$953$	−3608.04	+	1313.22i	−0.122640	+	0.0446373i	−0.402611	−	0.915371i	$-0.631897\pi$
$953$	−3608.04	+	1313.22i	−0.122640	+	0.0446373i	0.279971	+	0.960008i	$0.409675\pi$
$954$	−1955.04	−	11087.6i	−0.0663488	−	0.376283i
$955$	4070.85	−	23087.0i	0.137937	−	0.782279i
$956$	1653.26	+	601.738i	0.0559312	+	0.0203573i
$957$	−19415.0	−	33627.8i	−0.655797	−	1.13587i
$958$	−18299.8	+	31696.2i	−0.617161	+	1.06895i
$959$	−2692.71	+	2259.46i	−0.0906697	+	0.0760809i
$960$	2781.83	−	2334.23i	0.0935242	−	0.0784761i
$961$	−40659.9	+	70425.1i	−1.36484	+	2.36397i
$962$	2250.92	+	3898.70i	0.0754391	+	0.130664i
$963$	−95526.6	−	34768.8i	−3.19658	−	1.16346i
$964$	−1588.66	+	9009.75i	−0.0530782	+	0.301021i
$965$	−1629.67	−	9242.34i	−0.0543638	−	0.308312i
$966$	−16221.8	+	5904.25i	−0.540298	+	0.196652i
$967$	−7457.92	−	6257.94i	−0.248015	−	0.208109i	0.510302	−	0.859995i	$-0.329534\pi$
$967$	−7457.92	−	6257.94i	−0.248015	−	0.208109i	−0.758317	+	0.651886i	$0.773978\pi$
$968$	540.960			0.0179619
$969$	−44024.1	+	26626.1i	−1.45950	+	0.882717i
$970$	11020.2			0.364781
$971$	1438.05	+	1206.66i	0.0475274	+	0.0398802i	0.666242	−	0.745736i	$-0.267902\pi$
$971$	1438.05	+	1206.66i	0.0475274	+	0.0398802i	−0.618715	+	0.785616i	$0.712346\pi$
$972$	48948.5	−	17815.8i	1.61525	−	0.587904i
$973$	2292.77	+	13003.0i	0.0755426	+	0.428423i
$974$	−2713.56	+	15389.4i	−0.0892692	+	0.506271i
$975$	−54092.2	−	19688.0i	−1.77676	−	0.646686i
$976$	1109.72	+	1922.09i	0.0363947	+	0.0630374i
$977$	4164.93	−	7213.86i	0.136385	−	0.236225i	−0.789741	−	0.613441i	$-0.789785\pi$
$977$	4164.93	−	7213.86i	0.136385	−	0.236225i	0.926126	+	0.377215i	$0.123118\pi$
$978$	35016.4	−	29382.3i	1.14489	−	0.960676i
$979$	−18936.8	+	15889.8i	−0.618204	+	0.518735i
$980$	−3208.91	+	5557.99i	−0.104597	+	0.181167i
$981$	−21165.9	−	36660.4i	−0.688863	−	1.19315i
$982$	9269.33	+	3373.76i	0.301218	+	0.109634i
$983$	−4455.37	+	25267.7i	−0.144562	+	0.819851i	0.823156	+	0.567815i	$0.192211\pi$
$983$	−4455.37	+	25267.7i	−0.144562	+	0.819851i	−0.967718	+	0.252036i	$0.918900\pi$
$984$	163.841	+	929.189i	0.00530799	+	0.0301031i
$985$	−27634.2	+	10058.0i	−0.893906	+	0.325355i
$986$	10488.7	+	8801.05i	0.338770	+	0.284262i
$987$	−18330.4			−0.591149
$988$	13626.0	+	15583.5i	0.438765	+	0.501800i
$989$	8695.60			0.279579
$990$	22385.7	+	18783.8i	0.718651	+	0.603019i
$991$	51205.3	−	18637.2i	1.64136	−	0.597406i	0.654084	−	0.756422i	$-0.273054\pi$
$991$	51205.3	−	18637.2i	1.64136	−	0.597406i	0.987276	+	0.159015i	$0.0508319\pi$
$992$	−1852.25	−	10504.6i	−0.0592831	−	0.336211i
$993$	−6748.86	+	38274.7i	−0.215678	+	1.22317i
$994$	−1499.25	−	545.683i	−0.0478404	−	0.0174125i
$995$	12277.6	+	21265.4i	0.391181	+	0.677545i
$996$	2305.22	−	3992.76i	0.0733370	−	0.127023i
$997$	−22426.5	+	18818.1i	−0.712391	+	0.597767i	−0.925269	−	0.379312i	$-0.876161\pi$
$997$	−22426.5	+	18818.1i	−0.712391	+	0.597767i	0.212878	+	0.977079i	$0.431716\pi$
$998$	−3112.29	+	2611.52i	−0.0987152	+	0.0828318i
$999$	8093.45	−	14018.3i	0.256322	−	0.443962i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.4.e.b.35.3	yes	18
19.5	even	9		722.4.a.t.1.1		9
19.6	even	9	inner	38.4.e.b.25.3	✓	18
19.14	odd	18		722.4.a.u.1.9		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.4.e.b.25.3	✓	18	19.6	even	9	inner
38.4.e.b.35.3	yes	18	1.1	even	1	trivial
722.4.a.t.1.1		9	19.5	even	9
722.4.a.u.1.9		9	19.14	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)

\(f(q)\)	\(=\)	\(q+(-1.53209 - 1.28558i) q^{2} +(9.35607 - 3.40533i) q^{3} +(0.694593 + 3.93923i) q^{4} +(-0.989599 + 5.61230i) q^{5} +(-18.7121 - 6.81067i) q^{6} +(-3.91986 - 6.78940i) q^{7} +(4.00000 - 6.92820i) q^{8} +(55.2566 - 46.3658i) q^{9} +O(q^{10})\)	\(q+(-1.53209 - 1.28558i) q^{2} +(9.35607 - 3.40533i) q^{3} +(0.694593 + 3.93923i) q^{4} +(-0.989599 + 5.61230i) q^{5} +(-18.7121 - 6.81067i) q^{6} +(-3.91986 - 6.78940i) q^{7} +(4.00000 - 6.92820i) q^{8} +(55.2566 - 46.3658i) q^{9} +(8.73118 - 7.32633i) q^{10} +(-17.7720 + 30.7821i) q^{11} +(19.9131 + 34.4904i) q^{12} +(-58.7189 - 21.3719i) q^{13} +(-2.72271 + 15.4413i) q^{14} +(9.85297 + 55.8790i) q^{15} +(-15.0351 + 5.47232i) q^{16} +(47.7967 + 40.1062i) q^{17} -144.265 q^{18} +(-51.9332 + 64.5131i) q^{19} -22.7955 q^{20} +(-59.7947 - 50.1737i) q^{21} +(66.8010 - 24.3136i) q^{22} +(19.2019 + 108.900i) q^{23} +(13.8315 - 78.4421i) q^{24} +(86.9430 + 31.6447i) q^{25} +(62.4873 + 108.231i) q^{26} +(224.681 - 389.159i) q^{27} +(24.0223 - 20.1571i) q^{28} +(-84.0517 + 70.5278i) q^{29} +(56.7410 - 98.2783i) q^{30} +(-166.666 - 288.675i) q^{31} +(30.0702 + 10.9446i) q^{32} +(-61.4533 + 348.519i) q^{33} +(-21.6693 - 122.893i) q^{34} +(41.9832 - 15.2806i) q^{35} +(221.027 + 185.463i) q^{36} +36.0219 q^{37} +(162.503 - 32.0758i) q^{38} -622.157 q^{39} +(34.9247 + 29.3053i) q^{40} +(-11.1312 + 4.05141i) q^{41} +(27.1087 + 153.741i) q^{42} +(13.6551 - 77.4420i) q^{43} +(-133.602 - 48.6271i) q^{44} +(205.537 + 356.000i) q^{45} +(110.579 - 191.529i) q^{46} +(179.894 - 150.949i) q^{47} +(-122.034 + 102.399i) q^{48} +(140.769 - 243.820i) q^{49} +(-92.5228 - 160.254i) q^{50} +(583.765 + 212.473i) q^{51} +(43.4033 - 246.152i) q^{52} +(13.5517 + 76.8557i) q^{53} +(-844.524 + 307.382i) q^{54} +(-155.171 - 130.204i) q^{55} -62.7178 q^{56} +(-266.202 + 780.439i) q^{57} +219.443 q^{58} +(-374.801 - 314.496i) q^{59} +(-213.276 + 77.6263i) q^{60} +(-24.0876 - 136.607i) q^{61} +(-115.765 + 656.538i) q^{62} +(-531.395 - 193.412i) q^{63} +(-32.0000 - 55.4256i) q^{64} +(178.054 - 308.398i) q^{65} +(542.199 - 454.959i) q^{66} +(378.424 - 317.535i) q^{67} +(-124.788 + 216.140i) q^{68} +(550.494 + 953.483i) q^{69} +(-83.9665 - 30.5613i) q^{70} +(-17.6696 + 100.210i) q^{71} +(-100.205 - 568.292i) q^{72} +(-533.078 + 194.025i) q^{73} +(-55.1888 - 46.3089i) q^{74} +921.206 q^{75} +(-290.204 - 159.767i) q^{76} +278.656 q^{77} +(953.200 + 799.830i) q^{78} +(351.428 - 127.909i) q^{79} +(-15.8336 - 89.7967i) q^{80} +(438.724 - 2488.13i) q^{81} +(22.2623 + 8.10283i) q^{82} +(-57.8821 - 100.255i) q^{83} +(156.113 - 270.396i) q^{84} +(-272.388 + 228.560i) q^{85} +(-120.478 + 101.093i) q^{86} +(-546.224 + 946.087i) q^{87} +(142.176 + 246.256i) q^{88} +(653.538 + 237.868i) q^{89} +(142.764 - 809.657i) q^{90} +(85.0674 + 482.441i) q^{91} +(-415.643 + 151.282i) q^{92} +(-2542.38 - 2133.31i) q^{93} -469.671 q^{94} +(-310.674 - 355.307i) q^{95} +318.609 q^{96} +(740.669 + 621.495i) q^{97} +(-529.120 + 192.584i) q^{98} +(445.213 + 2524.93i) 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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