LMFDB - Embedded newform 64.5.j.a.3.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [64,5,Mod(3,64)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(64, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 3]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("64.3");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	64.j (of order $16$, degree $8$, 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:	$6.61567763737$
Analytic rank:	$0$
Dimension:	$248$
Relative dimension:	$31$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			3.3
Character	$\chi$	$=$	64.3
Dual form			64.5.j.a.43.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.78468 + 1.29468i) q^{2} +(4.98643 + 0.991863i) q^{3} +(12.6476 - 9.79988i) q^{4} +(-24.9007 - 16.6381i) q^{5} +(-20.1562 + 2.70193i) q^{6} +(16.4913 + 39.8136i) q^{7} +(-35.1796 + 53.4640i) q^{8} +(-50.9535 - 21.1056i) q^{9} +O(q^{10})$	\(q+(-3.78468 + 1.29468i) q^{2} +(4.98643 + 0.991863i) q^{3} +(12.6476 - 9.79988i) q^{4} +(-24.9007 - 16.6381i) q^{5} +(-20.1562 + 2.70193i) q^{6} +(16.4913 + 39.8136i) q^{7} +(-35.1796 + 53.4640i) q^{8} +(-50.9535 - 21.1056i) q^{9} +(115.782 + 30.7316i) q^{10} +(-1.15335 - 5.79830i) q^{11} +(72.7867 - 36.3217i) q^{12} +(-142.622 + 95.2968i) q^{13} +(-113.960 - 129.331i) q^{14} +(-107.663 - 107.663i) q^{15} +(63.9249 - 247.890i) q^{16} +(-357.469 - 357.469i) q^{17} +(220.168 + 13.9098i) q^{18} +(-336.361 + 224.749i) q^{19} +(-477.986 + 33.5911i) q^{20} +(42.7432 + 214.885i) q^{21} +(11.8720 + 20.4515i) q^{22} +(-480.396 - 198.987i) q^{23} +(-228.449 + 231.701i) q^{24} +(104.040 + 251.175i) q^{25} +(416.399 - 545.317i) q^{26} +(-575.553 - 384.572i) q^{27} +(598.744 + 341.934i) q^{28} +(892.973 + 177.623i) q^{29} +(546.858 + 268.081i) q^{30} +1476.43 q^{31} +(79.0026 + 1020.95i) q^{32} -30.0568i q^{33} +(1815.71 + 890.100i) q^{34} +(251.777 - 1265.77i) q^{35} +(-851.274 + 232.402i) q^{36} +(-735.800 + 1101.20i) q^{37} +(982.040 - 1286.08i) q^{38} +(-805.695 + 333.730i) q^{39} +(1765.53 - 745.969i) q^{40} +(-616.031 + 1487.23i) q^{41} +(-439.976 - 757.932i) q^{42} +(-2111.94 + 420.090i) q^{43} +(-71.4098 - 62.0320i) q^{44} +(917.620 + 1373.31i) q^{45} +(2075.77 + 131.143i) q^{46} +(375.581 - 375.581i) q^{47} +(564.630 - 1172.68i) q^{48} +(384.607 - 384.607i) q^{49} +(-718.950 - 815.921i) q^{50} +(-1427.94 - 2137.06i) q^{51} +(-869.929 + 2602.95i) q^{52} +(847.405 - 168.559i) q^{53} +(2676.18 + 710.329i) q^{54} +(-67.7534 + 163.571i) q^{55} +(-2708.75 - 518.932i) q^{56} +(-1900.16 + 787.072i) q^{57} +(-3609.58 + 483.863i) q^{58} +(2342.76 - 3506.19i) q^{59} +(-2416.76 - 306.597i) q^{60} +(-212.809 + 1069.87i) q^{61} +(-5587.82 + 1911.50i) q^{62} -2376.70i q^{63} +(-1620.80 - 3761.68i) q^{64} +5136.93 q^{65} +(38.9139 + 113.755i) q^{66} +(1769.18 + 351.913i) q^{67} +(-8024.29 - 1017.98i) q^{68} +(-2198.10 - 1468.72i) q^{69} +(685.865 + 5116.50i) q^{70} +(-519.523 - 1254.24i) q^{71} +(2920.91 - 1981.69i) q^{72} +(5251.26 + 2175.14i) q^{73} +(1359.07 - 5120.32i) q^{74} +(269.658 + 1355.66i) q^{75} +(-2051.65 + 6138.83i) q^{76} +(211.831 - 141.541i) q^{77} +(2617.23 - 2306.17i) q^{78} +(-946.307 - 946.307i) q^{79} +(-5716.20 + 5109.05i) q^{80} +(670.335 + 670.335i) q^{81} +(405.999 - 6426.26i) q^{82} +(-2760.52 + 1844.52i) q^{83} +(2646.45 + 2298.90i) q^{84} +(2953.62 + 14848.8i) q^{85} +(7449.13 - 4324.18i) q^{86} +(4276.57 + 1771.41i) q^{87} +(350.575 + 142.319i) q^{88} +(-3435.74 - 8294.61i) q^{89} +(-5250.90 - 4009.54i) q^{90} +(-6146.12 - 4106.71i) q^{91} +(-8025.92 + 2191.12i) q^{92} +(7362.12 + 1464.42i) q^{93} +(-935.199 + 1907.71i) q^{94} +12115.0 q^{95} +(-618.700 + 5169.25i) q^{96} -14299.6i q^{97} +(-957.673 + 1953.56i) q^{98} +(-63.6094 + 319.786i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 248 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) $ 248 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9	\( 248 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20} - 8 q^{21} - 2672 q^{22} - 8 q^{23} - 288 q^{24} - 8 q^{25} + 5392 q^{26} - 8 q^{27} + 5632 q^{28} - 8 q^{29} + 4712 q^{30} - 16 q^{31} - 2528 q^{32} - 7088 q^{34} - 8 q^{35} - 18808 q^{36} - 8 q^{37} - 7568 q^{38} - 8 q^{39} + 352 q^{40} - 8 q^{41} + 16272 q^{42} - 8 q^{43} + 8416 q^{44} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 8 q^{48} - 8 q^{49} + 21520 q^{50} - 16136 q^{51} + 8968 q^{52} - 8 q^{53} - 15560 q^{54} + 23544 q^{55} - 24704 q^{56} - 8 q^{57} - 32768 q^{58} + 26104 q^{59} - 31976 q^{60} - 8 q^{61} - 6040 q^{62} + 12184 q^{64} - 16 q^{65} + 35544 q^{66} - 37768 q^{67} + 26632 q^{68} - 8 q^{69} + 61144 q^{70} - 39944 q^{71} + 40816 q^{72} - 8 q^{73} + 16624 q^{74} - 4616 q^{75} - 14152 q^{76} - 8 q^{77} - 103952 q^{78} + 50168 q^{79} - 115040 q^{80} - 8 q^{81} - 5208 q^{82} - 8 q^{83} + 57896 q^{84} - 8 q^{85} + 85168 q^{86} - 8 q^{87} + 71112 q^{88} - 8 q^{89} + 111592 q^{90} - 8 q^{91} + 79792 q^{92} - 656 q^{93} + 17944 q^{94} - 16 q^{95} - 25984 q^{96} - 76304 q^{98} + 640 q^{99}+O(q^{100}) \) 248 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 8 * q^20 - 8 * q^21 - 2672 * q^22 - 8 * q^23 - 288 * q^24 - 8 * q^25 + 5392 * q^26 - 8 * q^27 + 5632 * q^28 - 8 * q^29 + 4712 * q^30 - 16 * q^31 - 2528 * q^32 - 7088 * q^34 - 8 * q^35 - 18808 * q^36 - 8 * q^37 - 7568 * q^38 - 8 * q^39 + 352 * q^40 - 8 * q^41 + 16272 * q^42 - 8 * q^43 + 8416 * q^44 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 8 * q^48 - 8 * q^49 + 21520 * q^50 - 16136 * q^51 + 8968 * q^52 - 8 * q^53 - 15560 * q^54 + 23544 * q^55 - 24704 * q^56 - 8 * q^57 - 32768 * q^58 + 26104 * q^59 - 31976 * q^60 - 8 * q^61 - 6040 * q^62 + 12184 * q^64 - 16 * q^65 + 35544 * q^66 - 37768 * q^67 + 26632 * q^68 - 8 * q^69 + 61144 * q^70 - 39944 * q^71 + 40816 * q^72 - 8 * q^73 + 16624 * q^74 - 4616 * q^75 - 14152 * q^76 - 8 * q^77 - 103952 * q^78 + 50168 * q^79 - 115040 * q^80 - 8 * q^81 - 5208 * q^82 - 8 * q^83 + 57896 * q^84 - 8 * q^85 + 85168 * q^86 - 8 * q^87 + 71112 * q^88 - 8 * q^89 + 111592 * q^90 - 8 * q^91 + 79792 * q^92 - 656 * q^93 + 17944 * q^94 - 16 * q^95 - 25984 * q^96 - 76304 * q^98 + 640 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/64\mathbb{Z}\right)^\times$.

$n$	$5$	$63$
$\chi(n)$	$e\left(\frac{3}{16}\right)$	$-1$

Coefficient data

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

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

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

$2$	−3.78468	+	1.29468i	−0.946170	+	0.323669i
$2$	−3.78468	+	1.29468i	−0.946170	+	0.323669i
$3$	4.98643	+	0.991863i	0.554048	+	0.110207i	0.464171	−	0.885746i	$-0.346352\pi$
$3$	4.98643	+	0.991863i	0.554048	+	0.110207i	0.0898775	+	0.995953i	$0.471352\pi$
$4$	12.6476	−	9.79988i	0.790477	−	0.612492i
$5$	−24.9007	−	16.6381i	−0.996027	−	0.665524i	−0.0531230	−	0.998588i	$-0.516918\pi$
$5$	−24.9007	−	16.6381i	−0.996027	−	0.665524i	−0.942904	+	0.333064i	$0.891918\pi$
$6$	−20.1562	+	2.70193i	−0.559894	+	0.0750537i
$7$	16.4913	+	39.8136i	0.336558	+	0.812522i	0.998041	+	0.0625621i	$0.0199272\pi$
$7$	16.4913	+	39.8136i	0.336558	+	0.812522i	−0.661484	+	0.749960i	$0.730073\pi$
$8$	−35.1796	+	53.4640i	−0.549681	+	0.835375i
$9$	−50.9535	−	21.1056i	−0.629056	−	0.260563i
$10$	115.782	+	30.7316i	1.15782	+	0.307316i
$11$	−1.15335	−	5.79830i	−0.00953185	−	0.0479199i	0.975727	−	0.218992i	$-0.0702769\pi$
$11$	−1.15335	−	5.79830i	−0.00953185	−	0.0479199i	−0.985258	+	0.171072i	$0.945277\pi$
$12$	72.7867	−	36.3217i	0.505463	−	0.252234i
$13$	−142.622	+	95.2968i	−0.843915	+	0.563886i	−0.900671	−	0.434502i	$-0.856924\pi$
$13$	−142.622	+	95.2968i	−0.843915	+	0.563886i	0.0567557	+	0.998388i	$0.481924\pi$
$14$	−113.960	−	129.331i	−0.581429	−	0.659851i
$15$	−107.663	−	107.663i	−0.478502	−	0.478502i
$16$	63.9249	−	247.890i	0.249706	−	0.968322i
$17$	−357.469	−	357.469i	−1.23692	−	1.23692i	−0.961254	−	0.275663i	$-0.911103\pi$
$17$	−357.469	−	357.469i	−1.23692	−	1.23692i	−0.275663	−	0.961254i	$-0.588897\pi$
$18$	220.168	+	13.9098i	0.679530	+	0.0429315i
$19$	−336.361	+	224.749i	−0.931747	+	0.622573i	−0.926046	−	0.377411i	$-0.876815\pi$
$19$	−336.361	+	224.749i	−0.931747	+	0.622573i	−0.00570056	+	0.999984i	$0.501815\pi$
$20$	−477.986	+	33.5911i	−1.19496	+	0.0839777i
$21$	42.7432	+	214.885i	0.0969235	+	0.487267i
$22$	11.8720	+	20.4515i	0.0245289	+	0.0422552i
$23$	−480.396	−	198.987i	−0.908122	−	0.376156i	−0.120784	−	0.992679i	$-0.538541\pi$
$23$	−480.396	−	198.987i	−0.908122	−	0.376156i	−0.787337	+	0.616523i	$0.788541\pi$
$24$	−228.449	+	231.701i	−0.396614	+	0.402259i
$25$	104.040	+	251.175i	0.166464	+	0.401881i
$26$	416.399	−	545.317i	0.615975	−	0.806682i
$27$	−575.553	−	384.572i	−0.789511	−	0.527534i
$28$	598.744	+	341.934i	0.763704	+	0.436141i
$29$	892.973	+	177.623i	1.06180	+	0.211205i	0.694937	−	0.719071i	$-0.255432\pi$
$29$	892.973	+	177.623i	1.06180	+	0.211205i	0.366862	+	0.930275i	$0.380432\pi$
$30$	546.858	+	268.081i	0.607620	+	0.297868i
$31$	1476.43			1.53635			0.768174	−	0.640242i	$-0.221166\pi$
$31$	1476.43			1.53635			0.768174	+	0.640242i	$0.221166\pi$
$32$	79.0026	+	1020.95i	0.0771509	+	0.997019i
$33$		−	30.0568i		−	0.0276004i
$34$	1815.71	+	890.100i	1.57069	+	0.769982i
$35$	251.777	−	1265.77i	0.205532	−	1.03328i
$36$	−851.274	+	232.402i	−0.656847	+	0.179323i
$37$	−735.800	+	1101.20i	−0.537472	+	0.804384i	−0.996461	−	0.0840581i	$-0.973212\pi$
$37$	−735.800	+	1101.20i	−0.537472	+	0.804384i	0.458989	+	0.888442i	$0.348212\pi$
$38$	982.040	−	1286.08i	0.680083	−	0.890638i
$39$	−805.695	+	333.730i	−0.529714	+	0.219415i
$40$	1765.53	−	745.969i	1.10346	−	0.466230i
$41$	−616.031	+	1487.23i	−0.366467	+	0.884730i	0.627856	+	0.778329i	$0.283933\pi$
$41$	−616.031	+	1487.23i	−0.366467	+	0.884730i	−0.994323	+	0.106401i	$0.966067\pi$
$42$	−439.976	−	757.932i	−0.249419	−	0.429667i
$43$	−2111.94	+	420.090i	−1.14221	+	0.227199i	−0.729707	−	0.683760i	$-0.760344\pi$
$43$	−2111.94	+	420.090i	−1.14221	+	0.227199i	−0.412498	+	0.910959i	$0.635344\pi$
$44$	−71.4098	−	62.0320i	−0.0368852	−	0.0320413i
$45$	917.620	+	1373.31i	0.453145	+	0.678180i
$46$	2075.77	+	131.143i	0.980988	+	0.0619770i
$47$	375.581	−	375.581i	0.170023	−	0.170023i	−0.616966	−	0.786990i	$-0.711639\pi$
$47$	375.581	−	375.581i	0.170023	−	0.170023i	0.786990	+	0.616966i	$0.211639\pi$
$48$	564.630	−	1172.68i	0.245065	−	0.508977i
$49$	384.607	−	384.607i	0.160186	−	0.160186i
$50$	−718.950	−	815.921i	−0.287580	−	0.326368i
$51$	−1427.94	−	2137.06i	−0.548995	−	0.821629i
$52$	−869.929	+	2602.95i	−0.321719	+	0.962630i
$53$	847.405	−	168.559i	0.301675	−	0.0600069i	−0.0419319	−	0.999120i	$-0.513351\pi$
$53$	847.405	−	168.559i	0.301675	−	0.0600069i	0.343607	+	0.939114i	$0.388351\pi$
$54$	2676.18	+	710.329i	0.917758	+	0.243597i
$55$	−67.7534	+	163.571i	−0.0223978	+	0.0540732i
$56$	−2708.75	−	518.932i	−0.863759	−	0.165476i
$57$	−1900.16	+	787.072i	−0.584844	+	0.242250i
$58$	−3609.58	+	483.863i	−1.07300	+	0.143836i
$59$	2342.76	−	3506.19i	0.673013	−	1.00724i	−0.325091	−	0.945683i	$-0.605395\pi$
$59$	2342.76	−	3506.19i	0.673013	−	1.00724i	0.998104	−	0.0615526i	$-0.0196052\pi$
$60$	−2416.76	−	306.597i	−0.671323	−	0.0851658i
$61$	−212.809	+	1069.87i	−0.0571915	+	0.287521i	−0.998788	−	0.0492227i	$-0.984326\pi$
$61$	−212.809	+	1069.87i	−0.0571915	+	0.287521i	0.941596	+	0.336744i	$0.109326\pi$
$62$	−5587.82	+	1911.50i	−1.45365	+	0.497268i
$63$		−	2376.70i		−	0.598816i
$64$	−1620.80	−	3761.68i	−0.395702	−	0.918379i
$65$	5136.93			1.21584
$66$	38.9139	+	113.755i	0.00893339	+	0.0261147i
$67$	1769.18	+	351.913i	0.394115	+	0.0783944i	0.388170	−	0.921588i	$-0.373107\pi$
$67$	1769.18	+	351.913i	0.394115	+	0.0783944i	0.00594566	+	0.999982i	$0.498107\pi$
$68$	−8024.29	−	1017.98i	−1.73536	−	0.220152i
$69$	−2198.10	−	1468.72i	−0.461688	−	0.308490i
$70$	685.865	+	5116.50i	0.139973	+	1.04418i
$71$	−519.523	−	1254.24i	−0.103060	−	0.248808i	0.863936	−	0.503602i	$-0.167992\pi$
$71$	−519.523	−	1254.24i	−0.103060	−	0.248808i	−0.966995	+	0.254794i	$0.917992\pi$
$72$	2920.91	−	1981.69i	0.563448	−	0.382271i
$73$	5251.26	+	2175.14i	0.985412	+	0.408171i	0.816428	−	0.577448i	$-0.195951\pi$
$73$	5251.26	+	2175.14i	0.985412	+	0.408171i	0.168984	+	0.985619i	$0.445951\pi$
$74$	1359.07	−	5120.32i	0.248186	−	0.935048i
$75$	269.658	+	1355.66i	0.0479392	+	0.241007i
$76$	−2051.65	+	6138.83i	−0.355203	+	1.06282i
$77$	211.831	−	141.541i	0.0357279	−	0.0238726i
$78$	2617.23	−	2306.17i	0.430182	−	0.379056i
$79$	−946.307	−	946.307i	−0.151627	−	0.151627i	0.627217	−	0.778844i	$-0.284194\pi$
$79$	−946.307	−	946.307i	−0.151627	−	0.151627i	−0.778844	+	0.627217i	$0.784194\pi$
$80$	−5716.20	+	5109.05i	−0.893156	+	0.798289i
$81$	670.335	+	670.335i	0.102170	+	0.102170i
$82$	405.999	−	6426.26i	0.0603806	−	0.955719i
$83$	−2760.52	+	1844.52i	−0.400714	+	0.267748i	−0.739556	−	0.673095i	$-0.764965\pi$
$83$	−2760.52	+	1844.52i	−0.400714	+	0.267748i	0.338842	+	0.940843i	$0.389965\pi$
$84$	2646.45	+	2298.90i	0.375063	+	0.325808i
$85$	2953.62	+	14848.8i	0.408805	+	2.05520i
$86$	7449.13	−	4324.18i	1.00718	−	0.584665i
$87$	4276.57	+	1771.41i	0.565011	+	0.234035i
$88$	350.575	+	142.319i	0.0452705	+	0.0183779i
$89$	−3435.74	−	8294.61i	−0.433751	−	1.04717i	−0.978068	−	0.208287i	$-0.933211\pi$
$89$	−3435.74	−	8294.61i	−0.433751	−	1.04717i	0.544317	−	0.838880i	$-0.316789\pi$
$90$	−5250.90	−	4009.54i	−0.648259	−	0.495005i
$91$	−6146.12	−	4106.71i	−0.742196	−	0.495919i
$92$	−8025.92	+	2191.12i	−0.948242	+	0.258875i
$93$	7362.12	+	1464.42i	0.851210	+	0.169316i
$94$	−935.199	+	1907.71i	−0.105840	+	0.215902i
$95$	12115.0			1.34238
$96$	−618.700	+	5169.25i	−0.0671332	+	0.560899i
$97$		−	14299.6i		−	1.51978i	−0.650054	−	0.759888i	$-0.725254\pi$
$97$		−	14299.6i		−	1.51978i	0.650054	−	0.759888i	$-0.274746\pi$
$98$	−957.673	+	1953.56i	−0.0997160	+	0.203411i
$99$	−63.6094	+	319.786i	−0.00649010	+	0.0326279i
$100$	3777.35	+	2157.19i	0.377735	+	0.215719i
$101$	−9906.71	+	14826.4i	−0.971151	+	1.45343i	−0.0815624	+	0.996668i	$0.525991\pi$
$101$	−9906.71	+	14826.4i	−0.971151	+	1.45343i	−0.889589	+	0.456762i	$0.849009\pi$
$102$	8171.08	+	6239.36i	0.785378	+	0.599708i
$103$	13337.5	−	5524.57i	1.25719	−	0.520744i	0.348142	−	0.937442i	$-0.386813\pi$
$103$	13337.5	−	5524.57i	1.25719	−	0.520744i	0.909045	+	0.416698i	$0.136813\pi$
$104$	−77.5769	−	10977.6i	−0.00717242	−	1.01494i
$105$	2510.94	−	6061.94i	0.227750	−	0.549836i
$106$	−2988.93	+	1735.06i	−0.266013	+	0.154420i
$107$	−21387.4	+	4254.22i	−1.86806	+	0.371580i	−0.993547	−	0.113422i	$-0.963819\pi$
$107$	−21387.4	+	4254.22i	−1.86806	+	0.371580i	−0.874513	+	0.485002i	$0.838819\pi$
$108$	−11048.1	+	776.423i	−0.947200	+	0.0665658i
$109$	−7803.77	−	11679.2i	−0.656827	−	0.983012i	−0.999058	−	0.0433956i	$-0.986182\pi$
$109$	−7803.77	−	11679.2i	−0.656827	−	0.983012i	0.342231	−	0.939616i	$-0.388818\pi$
$110$	44.6533	−	706.784i	0.00369036	−	0.0584119i
$111$	−4761.26	+	4761.26i	−0.386434	+	0.386434i
$112$	10923.6	−	1542.96i	0.870823	−	0.123004i
$113$	−2178.55	+	2178.55i	−0.170613	+	0.170613i	−0.787248	−	0.616636i	$-0.788495\pi$
$113$	−2178.55	+	2178.55i	−0.170613	+	0.170613i	0.616636	+	0.787248i	$0.288495\pi$
$114$	6172.49	−	5438.91i	0.474953	−	0.418506i
$115$	8651.43	+	12947.8i	0.654173	+	0.979039i
$116$	13034.7	−	6504.51i	0.968689	−	0.483391i
$117$	9278.38	−	1845.58i	0.677798	−	0.134822i
$118$	−4327.22	+	16302.9i	−0.310774	+	1.17085i
$119$	8336.98	−	20127.3i	0.588728	−	1.42132i
$120$	9543.62	−	1968.55i	0.662751	−	0.136705i
$121$	13494.2	−	5589.49i	0.921674	−	0.381770i
$122$	−579.714	−	4324.62i	−0.0389488	−	0.290555i
$123$	−4546.93	+	6804.96i	−0.300544	+	0.449796i
$124$	18673.3	−	14468.8i	1.21445	−	0.941001i
$125$	−2063.17	+	10372.2i	−0.132043	+	0.663824i
$126$	3077.06	+	8995.06i	0.193818	+	0.566582i
$127$			26499.5i			1.64297i	0.570230	+	0.821485i	$0.306854\pi$
$127$			26499.5i			1.64297i	−0.570230	+	0.821485i	$0.693146\pi$
$128$	11004.4	+	12138.4i	0.671653	+	0.740866i
$129$	−10947.7			−0.657876
$130$	−19441.7	+	6650.67i	−1.15039	+	0.393531i
$131$	−3906.78	−	777.108i	−0.227655	−	0.0452834i	0.0799446	−	0.996799i	$-0.474526\pi$
$131$	−3906.78	−	777.108i	−0.227655	−	0.0452834i	−0.307599	+	0.951516i	$0.599526\pi$
$132$	−294.553	−	380.147i	−0.0169050	−	0.0218175i
$133$	−14495.1	−	9685.31i	−0.819441	−	0.547533i
$134$	−7151.41	+	958.644i	−0.398274	+	0.0533885i
$135$	7933.11	+	19152.2i	0.435287	+	1.05088i
$136$	31687.3	−	6536.12i	1.71320	−	0.353380i
$137$	−19023.5	−	7879.78i	−1.01356	−	0.419829i	−0.186806	−	0.982397i	$-0.559814\pi$
$137$	−19023.5	−	7879.78i	−1.01356	−	0.419829i	−0.826751	+	0.562567i	$0.809814\pi$
$138$	10220.6	+	2712.82i	0.536684	+	0.142450i
$139$	−545.985	−	2744.85i	−0.0282586	−	0.142066i	0.964080	−	0.265611i	$-0.0855736\pi$
$139$	−545.985	−	2744.85i	−0.0282586	−	0.142066i	−0.992339	+	0.123545i	$0.960574\pi$
$140$	−9220.00	−	18476.4i	−0.470408	−	0.942671i
$141$	2245.34	−	1500.29i	0.112939	−	0.0754633i
$142$	3590.06	+	4074.28i	0.178043	+	0.202057i
$143$	717.053	+	717.053i	0.0350654	+	0.0350654i
$144$	−8489.08	+	11281.7i	−0.409389	+	0.544064i
$145$	−19280.3	−	19280.3i	−0.917019	−	0.917019i
$146$	−22690.4	−	1433.54i	−1.06448	−	0.0672518i
$147$	2299.29	−	1536.34i	0.106404	−	0.0710972i
$148$	1485.52	+	21138.3i	0.0678198	+	0.965044i
$149$	−165.462	−	831.834i	−0.00745291	−	0.0374683i	0.976880	−	0.213789i	$-0.0685805\pi$
$149$	−165.462	−	831.834i	−0.00745291	−	0.0374683i	−0.984333	+	0.176321i	$0.943580\pi$
$150$	−2775.72	−	4781.63i	−0.123365	−	0.212517i
$151$	−19969.3	−	8271.56i	−0.875809	−	0.362772i	−0.100939	−	0.994893i	$-0.532185\pi$
$151$	−19969.3	−	8271.56i	−0.875809	−	0.362772i	−0.774870	+	0.632121i	$0.782185\pi$
$152$	−182.958	−	25889.7i	−0.00791890	−	1.12057i
$153$	10669.7	+	25758.9i	0.455795	+	1.10039i
$154$	−618.462	+	809.939i	−0.0260779	+	0.0341516i
$155$	−36764.1	−	24565.0i	−1.53024	−	1.02248i
$156$	−6919.62	+	12116.6i	−0.284337	+	0.497888i
$157$	−11231.1	−	2234.01i	−0.455642	−	0.0906328i	−0.0380667	−	0.999275i	$-0.512120\pi$
$157$	−11231.1	−	2234.01i	−0.455642	−	0.0906328i	−0.417575	+	0.908642i	$0.637120\pi$
$158$	4806.63	+	2356.31i	0.192542	+	0.0943883i
$159$	4392.72			0.173756
$160$	15019.4	−	26736.8i	0.586696	−	1.04440i
$161$		−	22407.8i		−	0.864467i
$162$	−3404.87	−	1669.14i	−0.129739	−	0.0636007i
$163$	−3033.57	+	15250.8i	−0.114177	+	0.574007i	0.880765	+	0.473554i	$0.157029\pi$
$163$	−3033.57	+	15250.8i	−0.114177	+	0.574007i	−0.994942	+	0.100453i	$0.967971\pi$
$164$	6783.35	+	24847.0i	0.252207	+	0.923816i
$165$	−500.088	+	748.435i	−0.0183687	+	0.0274907i
$166$	8059.62	−	10554.9i	0.292482	−	0.383034i
$167$	5936.69	−	2459.06i	0.212868	−	0.0881730i	−0.273701	−	0.961815i	$-0.588248\pi$
$167$	5936.69	−	2459.06i	0.212868	−	0.0881730i	0.486570	+	0.873642i	$0.338248\pi$
$168$	−12992.3	−	5274.33i	−0.460328	−	0.186874i
$169$	329.648	−	795.841i	0.0115419	−	0.0278646i
$170$	−30402.9	−	52374.1i	−1.05200	−	1.81225i
$171$	21882.2	−	4352.64i	0.748340	−	0.148854i
$172$	−22594.2	+	26009.9i	−0.763729	+	0.879187i
$173$	10789.6	+	16147.7i	0.360506	+	0.539535i	0.966743	−	0.255749i	$-0.0823220\pi$
$173$	10789.6	+	16147.7i	0.360506	+	0.539535i	−0.606238	+	0.795284i	$0.707322\pi$
$174$	−18478.9	−	1167.46i	−0.610347	−	0.0385606i
$175$	−8284.43	+	8284.43i	−0.270512	+	0.270512i
$176$	−1511.07	−	84.7503i	−0.0487820	−	0.00273600i
$177$	15159.7	−	15159.7i	0.483886	−	0.483886i
$178$	23742.0	+	26944.3i	0.749338	+	0.850406i
$179$	1883.21	+	2818.43i	0.0587752	+	0.0879632i	0.859693	−	0.510811i	$-0.170655\pi$
$179$	1883.21	+	2818.43i	0.0587752	+	0.0879632i	−0.800918	+	0.598774i	$0.795655\pi$
$180$	25064.0	+	8376.61i	0.773581	+	0.258537i
$181$	−33598.8	+	6683.22i	−1.02557	+	0.203999i	−0.679088	−	0.734057i	$-0.737625\pi$
$181$	−33598.8	+	6683.22i	−1.02557	+	0.203999i	−0.346485	+	0.938056i	$0.612625\pi$
$182$	28578.0	+	7585.34i	0.862757	+	0.228998i
$183$	−2122.32	+	5123.73i	−0.0633737	+	0.152998i
$184$	27538.8	−	18683.6i	0.813408	−	0.551856i
$185$	36643.8	−	15178.4i	1.07067	−	0.443488i
$186$	−29759.2	+	3989.21i	−0.860192	+	0.115308i
$187$	−1660.43	+	2485.00i	−0.0474828	+	0.0710630i
$188$	1069.56	−	8430.86i	0.0302615	−	0.238537i
$189$	5819.57	−	29256.9i	0.162917	−	0.819040i
$190$	−45851.4	+	15685.0i	−1.27012	+	0.434488i
$191$			46100.3i			1.26368i	0.775099	+	0.631839i	$0.217700\pi$
$191$			46100.3i			1.26368i	−0.775099	+	0.631839i	$0.782300\pi$
$192$	−4350.92	−	20365.0i	−0.118026	−	0.552435i
$193$	−55246.1			−1.48316			−0.741578	−	0.670867i	$-0.765922\pi$
$193$	−55246.1			−1.48316			−0.741578	+	0.670867i	$0.765922\pi$
$194$	18513.3	+	54119.3i	0.491905	+	1.43797i
$195$	25615.0	+	5095.14i	0.673635	+	0.133994i
$196$	1095.26	−	8633.46i	0.0285106	−	0.224736i
$197$	614.298	+	410.461i	0.0158288	+	0.0105764i	0.563459	−	0.826144i	$-0.309470\pi$
$197$	614.298	+	410.461i	0.0158288	+	0.0105764i	−0.547631	+	0.836720i	$0.684470\pi$
$198$	−173.278	−	1292.64i	−0.00441991	−	0.0329722i
$199$	−15793.0	−	38127.6i	−0.398802	−	0.962793i	−0.987951	−	0.154768i	$-0.950537\pi$
$199$	−15793.0	−	38127.6i	−0.398802	−	0.962793i	0.589149	−	0.808025i	$-0.299463\pi$
$200$	−17088.9	−	3273.83i	−0.427223	−	0.0818458i
$201$	8472.87	+	3509.58i	0.209719	+	0.0868686i
$202$	18298.3	−	68939.4i	0.448444	−	1.68952i
$203$	7654.48	+	38481.7i	0.185748	+	0.933817i
$204$	−39002.9	−	13035.1i	−0.937209	−	0.313223i
$205$	40084.3	−	26783.5i	0.953820	−	0.637322i
$206$	−43325.6	+	38176.5i	−1.02096	+	0.899625i
$207$	20278.1	+	20278.1i	0.473247	+	0.473247i
$208$	14506.1	+	41446.4i	0.335292	+	0.957987i
$209$	1691.10	+	1691.10i	0.0387149	+	0.0387149i
$210$	−1654.85	+	26193.4i	−0.0375249	+	0.593954i
$211$	29581.5	−	19765.7i	0.664440	−	0.443965i	−0.177076	−	0.984197i	$-0.556664\pi$
$211$	29581.5	−	19765.7i	0.664440	−	0.443965i	0.841516	+	0.540233i	$0.181664\pi$
$212$	9065.80	−	10436.3i	0.201713	−	0.232208i
$213$	−1346.53	−	6769.48i	−0.0296796	−	0.149209i
$214$	75436.7	−	43790.7i	1.64723	−	0.956212i
$215$	59578.2	+	24678.1i	1.28887	+	0.533869i
$216$	40808.5	−	17242.3i	0.874667	−	0.369562i
$217$	24348.3	+	58781.9i	0.517069	+	1.24832i
$218$	44655.5	+	34098.5i	0.939641	+	0.717502i
$219$	24027.6	+	16054.7i	0.500982	+	0.334746i
$220$	746.058	+	2732.76i	0.0154144	+	0.0564621i
$221$	85048.5	+	16917.2i	1.74133	+	0.346373i
$222$	11855.6	−	24184.1i	0.240556	−	0.490709i
$223$	−26818.3			−0.539288			−0.269644	−	0.962960i	$-0.586906\pi$
$223$	−26818.3			−0.539288			−0.269644	+	0.962960i	$0.586906\pi$
$224$	−39344.7	+	19982.2i	−0.784134	+	0.398241i
$225$		−	14994.1i		−	0.296180i
$226$	5424.61	−	11065.6i	0.106207	−	0.216651i
$227$	18414.7	−	92577.0i	0.357366	−	1.79660i	−0.215014	−	0.976611i	$-0.568980\pi$
$227$	18414.7	−	92577.0i	0.357366	−	1.79660i	0.572380	−	0.819988i	$-0.306020\pi$
$228$	−16319.3	+	28575.9i	−0.313929	+	0.549706i
$229$	−4757.88	+	7120.67i	−0.0907282	+	0.135784i	−0.874057	−	0.485823i	$-0.838520\pi$
$229$	−4757.88	+	7120.67i	−0.0907282	+	0.135784i	0.783329	+	0.621607i	$0.213520\pi$
$230$	−49506.1	−	37802.4i	−0.935843	−	0.714602i
$231$	1196.67	−	495.677i	0.0224259	−	0.00928912i
$232$	−40910.8	+	41493.2i	−0.760086	+	0.770905i
$233$	−22057.9	+	53252.4i	−0.406305	+	0.980907i	0.579796	+	0.814761i	$0.303132\pi$
$233$	−22057.9	+	53252.4i	−0.406305	+	0.980907i	−0.986101	+	0.166145i	$0.946868\pi$
$234$	−32726.3	+	18997.4i	−0.597674	+	0.346947i
$235$	−15601.2	+	3103.27i	−0.282502	+	0.0561932i
$236$	−4729.86	−	67303.7i	−0.0849227	−	1.20841i
$237$	−3780.09	−	5657.30i	−0.0672985	−	0.100719i
$238$	−5494.54	+	86968.9i	−0.0970012	+	1.53536i
$239$	40054.4	−	40054.4i	0.701221	−	0.701221i	−0.263452	−	0.964673i	$-0.584861\pi$
$239$	40054.4	−	40054.4i	0.701221	−	0.701221i	0.964673	+	0.263452i	$0.0848610\pi$
$240$	−33570.9	+	19806.2i	−0.582828	+	0.343858i
$241$	30221.0	−	30221.0i	0.520325	−	0.520325i	−0.397345	−	0.917669i	$-0.630068\pi$
$241$	30221.0	−	30221.0i	0.520325	−	0.520325i	0.917669	+	0.397345i	$0.130068\pi$
$242$	−43834.8	+	38625.1i	−0.748494	+	0.659537i
$243$	33828.1	+	50627.3i	0.572881	+	0.857377i
$244$	7793.01	+	15616.8i	0.130896	+	0.262308i
$245$	−15976.1	+	3177.84i	−0.266157	+	0.0529420i
$246$	8398.45	−	31641.4i	0.138781	−	0.522860i
$247$	26554.5	−	64108.1i	0.435255	−	1.05080i
$248$	−51940.1	+	78935.8i	−0.844500	+	1.28343i
$249$	−15594.6	+	6459.51i	−0.251523	+	0.104184i
$250$	−5620.27	−	41926.8i	−0.0899243	−	0.670829i
$251$	−29213.7	+	43721.4i	−0.463702	+	0.693979i	−0.987457	−	0.157890i	$-0.949531\pi$
$251$	−29213.7	+	43721.4i	−0.463702	+	0.693979i	0.523755	+	0.851869i	$0.324531\pi$
$252$	−23291.4	−	30059.6i	−0.366770	−	0.473350i
$253$	−599.718	+	3014.98i	−0.00936927	+	0.0471025i
$254$	−34308.2	−	100292.i	−0.531779	−	1.55453i
$255$			76972.3i			1.18373i
$256$	−57363.2	−	31692.7i	−0.875293	−	0.483592i
$257$	13038.2			0.197402			0.0987008	−	0.995117i	$-0.468531\pi$
$257$	13038.2			0.197402			0.0987008	+	0.995117i	$0.468531\pi$
$258$	41433.6	−	14173.7i	0.622462	−	0.212934i
$259$	−55977.1	−	11134.5i	−0.834470	−	0.165986i
$260$	64970.0	−	50341.3i	0.961095	−	0.744694i
$261$	−41751.3	−	27897.3i	−0.612899	−	0.409526i
$262$	15792.0	−	2116.92i	0.230057	−	0.0308391i
$263$	−42891.0	−	103548.i	−0.620089	−	1.49703i	−0.851598	−	0.524195i	$-0.824366\pi$
$263$	−42891.0	−	103548.i	−0.620089	−	1.49703i	0.231509	−	0.972833i	$-0.425634\pi$
$264$	1606.96	+	1057.39i	0.0230567	+	0.0151714i
$265$	−23905.5	−	9901.97i	−0.340412	−	0.141003i
$266$	67398.6	+	17889.4i	0.952550	+	0.252832i
$267$	−8904.97	−	44768.3i	−0.124914	−	0.627983i
$268$	25824.7	−	12886.9i	0.359555	−	0.179424i
$269$	−3251.35	+	2172.48i	−0.0449324	+	0.0300228i	−0.577834	−	0.816155i	$-0.696102\pi$
$269$	−3251.35	+	2172.48i	−0.0449324	+	0.0300228i	0.532901	+	0.846177i	$0.321102\pi$
$270$	−54820.2	−	62214.3i	−0.751992	−	0.853419i
$271$	−81171.0	−	81171.0i	−1.10525	−	1.10525i	−0.993766	−	0.111489i	$-0.964438\pi$
$271$	−81171.0	−	81171.0i	−1.10525	−	1.10525i	−0.111489	−	0.993766i	$-0.535562\pi$
$272$	−111464.	+	65762.0i	−1.50660	+	0.888867i
$273$	−26573.9	−	26573.9i	−0.356558	−	0.356558i
$274$	82199.5	+	5193.21i	1.09488	+	0.0691727i
$275$	1336.40	−	892.951i	0.0176714	−	0.0118076i
$276$	−42194.0	+	2965.24i	−0.553901	+	0.0389262i
$277$	2606.31	+	13102.8i	0.0339677	+	0.170767i	0.994045	−	0.108966i	$-0.0347540\pi$
$277$	2606.31	+	13102.8i	0.0339677	+	0.170767i	−0.960078	+	0.279733i	$0.909754\pi$
$278$	5620.08	+	9681.52i	0.0727198	+	0.125272i
$279$	−75229.3	−	31161.0i	−0.966448	−	0.400316i
$280$	58815.7	+	57990.2i	0.750200	+	0.739671i
$281$	57210.4	+	138118.i	0.724541	+	1.74920i	0.659982	+	0.751282i	$0.270564\pi$
$281$	57210.4	+	138118.i	0.724541	+	1.74920i	0.0645587	+	0.997914i	$0.479436\pi$
$282$	−6555.49	+	8585.08i	−0.0824342	+	0.107956i
$283$	−112150.	−	74936.1i	−1.40031	−	0.935660i	−0.999813	−	0.0193635i	$-0.993836\pi$
$283$	−112150.	−	74936.1i	−1.40031	−	0.935660i	−0.400501	−	0.916296i	$-0.631164\pi$
$284$	−18862.1	−	10771.9i	−0.233859	−	0.133553i
$285$	60410.6	+	12016.4i	0.743744	+	0.147940i
$286$	−3642.17	−	1785.46i	−0.0445274	−	0.0218283i
$287$	−69371.1			−0.842200
$288$	17522.3	−	53688.3i	0.211255	−	0.647284i
$289$			172047.i			2.05993i
$290$	97931.6	+	48008.1i	1.16447	+	0.570845i
$291$	14183.2	−	71303.9i	0.167490	−	0.842029i
$292$	87732.1	−	23951.3i	1.02895	−	0.280908i
$293$	−90951.5	+	136119.i	−1.05944	+	1.58556i	−0.279032	+	0.960282i	$0.590013\pi$
$293$	−90951.5	+	136119.i	−1.05944	+	1.58556i	−0.780404	+	0.625276i	$0.784987\pi$
$294$	−6713.03	+	8791.39i	−0.0776648	+	0.101710i
$295$	−116673.	+	48327.4i	−1.34068	+	0.555327i
$296$	−32989.5	−	78078.6i	−0.376524	−	0.891145i
$297$	−1566.05	+	3780.78i	−0.0177539	+	0.0428616i
$298$	1703.18	+	2934.01i	0.0191791	+	0.0330391i
$299$	87477.7	−	17400.4i	0.978487	−	0.194633i
$300$	16695.9	+	14503.3i	0.185510	+	0.161148i
$301$	−51553.9	−	77155.9i	−0.569022	−	0.851601i
$302$	86286.5	+	5451.42i	0.946082	+	0.0597717i
$303$	−64105.0	+	64105.0i	−0.698243	+	0.698243i
$304$	34211.3	+	97747.6i	0.370188	+	1.05769i
$305$	23099.6	−	23099.6i	0.248316	−	0.248316i
$306$	−73730.9	−	83675.5i	−0.787420	−	0.893625i
$307$	82813.2	+	123939.i	0.878664	+	1.31501i	0.948279	+	0.317439i	$0.102823\pi$
$307$	82813.2	+	123939.i	0.878664	+	1.31501i	−0.0696149	+	0.997574i	$0.522177\pi$
$308$	1292.07	−	3866.07i	0.0136203	−	0.0407538i
$309$	71986.1	−	14318.9i	0.753932	−	0.149966i
$310$	170944.	+	45373.0i	1.77882	+	0.472144i
$311$	35988.1	−	86883.0i	0.372082	−	0.898285i	−0.621315	−	0.783560i	$-0.713401\pi$
$311$	35988.1	−	86883.0i	0.372082	−	0.898285i	0.993397	−	0.114725i	$-0.0365985\pi$
$312$	10501.5	−	54816.1i	0.107880	−	0.563118i
$313$	69485.9	−	28782.0i	0.709264	−	0.293787i	0.00126415	−	0.999999i	$-0.499598\pi$
$313$	69485.9	−	28782.0i	0.709264	−	0.293787i	0.708000	+	0.706212i	$0.249598\pi$
$314$	45398.5	−	6085.65i	0.460450	−	0.0617231i
$315$	−39543.8	+	59181.5i	−0.398527	+	0.596437i
$316$	−21242.2	−	2694.84i	−0.212729	−	0.0269873i
$317$	11378.4	−	57202.9i	0.113230	−	0.569245i	−0.881964	−	0.471317i	$-0.843779\pi$
$317$	11378.4	−	57202.9i	0.113230	−	0.569245i	0.995194	−	0.0979276i	$-0.0312214\pi$
$318$	−16625.0	+	5687.15i	−0.164402	+	0.0562393i
$319$		−	5382.59i		−	0.0528944i
$320$	−22228.3	+	120635.i	−0.217073	+	1.17808i
$321$	−110867.			−1.07595
$322$	29010.9	+	84806.5i	0.279801	+	0.817933i
$323$	200579.	+	39897.7i	1.92256	+	0.382422i
$324$	15047.3	+	1908.95i	0.143341	+	0.0181846i
$325$	−38774.6	−	25908.4i	−0.367097	−	0.245286i
$326$	−8263.75	−	61646.9i	−0.0777574	−	0.580064i
$327$	−27328.8	−	65977.6i	−0.255579	−	0.617023i
$328$	−57841.6	−	85255.6i	−0.537641	−	0.792456i
$329$	21147.1	+	8759.40i	0.195370	+	0.0809249i
$330$	923.694	−	3480.04i	0.00848204	−	0.0319563i
$331$	−14083.1	−	70800.6i	−0.128541	−	0.646220i	−0.990305	−	0.138911i	$-0.955640\pi$
$331$	−14083.1	−	70800.6i	−0.128541	−	0.646220i	0.861764	−	0.507310i	$-0.169360\pi$
$332$	−16837.9	+	50381.5i	−0.152761	+	0.457083i
$333$	60733.1	−	40580.6i	0.547693	−	0.365957i
$334$	−19284.8	+	16992.8i	−0.172871	+	0.152326i
$335$	−38198.7	−	38198.7i	−0.340376	−	0.340376i
$336$	56000.2	+	3140.84i	0.496034	+	0.0278207i
$337$	−51925.1	−	51925.1i	−0.457212	−	0.457212i	0.440527	−	0.897739i	$-0.354792\pi$
$337$	−51925.1	−	51925.1i	−0.457212	−	0.457212i	−0.897739	+	0.440527i	$0.854792\pi$
$338$	−217.256	+	3438.79i	−0.00190169	+	0.0301004i
$339$	−13024.0	+	8702.38i	−0.113330	+	0.0757249i
$340$	182873.	+	158857.i	1.58195	+	1.37420i
$341$	−1702.85	−	8560.78i	−0.0146442	−	0.0736215i
$342$	−77182.0	+	44803.8i	−0.659878	+	0.383056i
$343$	117248.	+	48565.6i	0.996588	+	0.412800i
$344$	51837.3	−	127691.i	0.438052	−	1.07906i
$345$	30297.4	+	73144.3i	0.254546	+	0.614529i
$346$	−61741.2	−	47145.0i	−0.515730	−	0.393807i
$347$	2070.74	+	1383.62i	0.0171975	+	0.0114910i	0.564139	−	0.825680i	$-0.309208\pi$
$347$	2070.74	+	1383.62i	0.0171975	+	0.0114910i	−0.546942	+	0.837171i	$0.684208\pi$
$348$	71448.1	−	19505.7i	0.589973	−	0.161066i
$349$	−194909.	−	38769.9i	−1.60023	−	0.318305i	−0.687283	−	0.726390i	$-0.741197\pi$
$349$	−194909.	−	38769.9i	−1.60023	−	0.318305i	−0.912944	+	0.408085i	$0.866197\pi$
$350$	20628.3	−	42079.6i	0.168394	−	0.343507i
$351$	118735.			0.963749
$352$	5828.65	−	1635.60i	0.0470416	−	0.0132005i
$353$			125239.i			1.00506i	0.864560	+	0.502530i	$0.167597\pi$
$353$			125239.i			1.00506i	−0.864560	+	0.502530i	$0.832403\pi$
$354$	−37747.6	+	77001.4i	−0.301220	+	0.614458i
$355$	−7931.69	+	39875.3i	−0.0629374	+	0.316408i
$356$	−124740.	−	71237.3i	−0.984251	−	0.562092i
$357$	61535.3	−	92094.1i	0.482823	−	0.722595i
$358$	−10776.3	−	8228.71i	−0.0840823	−	0.0642045i
$359$	−112329.	+	46528.0i	−0.871568	+	0.361015i	−0.773221	−	0.634137i	$-0.781356\pi$
$359$	−112329.	+	46528.0i	−0.871568	+	0.361015i	−0.0983475	+	0.995152i	$0.531356\pi$
$360$	−105704.	+	746.994i	−0.815620	+	0.00576384i
$361$	12754.6	−	30792.4i	0.0978709	−	0.236281i
$362$	118508.	−	68793.4i	0.904339	−	0.524964i
$363$	72832.1	−	14487.2i	0.552725	−	0.109944i
$364$	−117979.	+	8291.14i	−0.890435	+	0.0625765i
$365$	−94569.7	−	141534.i	−0.709849	−	1.06236i
$366$	1398.73	−	22139.4i	0.0104417	−	0.165274i
$367$	−113248.	+	113248.i	−0.840811	+	0.840811i	−0.988964	−	0.148153i	$-0.952667\pi$
$367$	−113248.	+	113248.i	−0.840811	+	0.840811i	0.148153	+	0.988964i	$0.452667\pi$
$368$	−80036.1	+	106365.i	−0.591004	+	0.785425i
$369$	62777.9	−	62777.9i	0.461057	−	0.461057i
$370$	−119034.	+	104887.i	−0.869497	+	0.766159i
$371$	20685.8	+	30958.4i	0.150288	+	0.224922i
$372$	107464.	−	53626.4i	0.776567	−	0.387519i
$373$	120946.	−	24057.7i	0.869309	−	0.172916i	0.259768	−	0.965671i	$-0.416354\pi$
$373$	120946.	−	24057.7i	0.869309	−	0.172916i	0.609541	+	0.792755i	$0.291354\pi$
$374$	3066.91	−	11554.7i	0.0219259	−	0.0826064i
$375$	−20575.7	+	49674.1i	−0.146316	+	0.353238i
$376$	6867.29	+	33292.8i	0.0485746	+	0.235492i
$377$	−144284.	+	59764.5i	−1.01516	+	0.420495i
$378$	15853.1	+	118263.i	0.110951	+	0.827683i
$379$	101297.	−	151601.i	0.705207	−	1.05542i	−0.289943	−	0.957044i	$-0.593636\pi$
$379$	101297.	−	151601.i	0.705207	−	1.05542i	0.995150	−	0.0983724i	$-0.0313636\pi$
$380$	153226.	−	118726.i	1.06112	−	0.822199i
$381$	−26283.8	+	132138.i	−0.181067	+	0.910284i
$382$	−59684.9	−	174475.i	−0.409014	−	1.19566i
$383$			23940.3i			0.163204i	0.996665	+	0.0816022i	$0.0260037\pi$
$383$			23940.3i			0.163204i	−0.996665	+	0.0816022i	$0.973996\pi$
$384$	42832.9	+	71441.9i	0.290479	+	0.484496i
$385$	−7629.70			−0.0514738
$386$	209089.	−	71525.8i	1.40332	−	0.480052i
$387$	116477.	+	23168.7i	0.777711	+	0.154696i
$388$	−140134.	−	180856.i	−0.930851	−	1.20135i
$389$	−47140.6	−	31498.3i	−0.311527	−	0.208156i	0.389971	−	0.920827i	$-0.372485\pi$
$389$	−47140.6	−	31498.3i	−0.311527	−	0.208156i	−0.701498	+	0.712671i	$0.747485\pi$
$390$	−103541.	+	13879.6i	−0.680743	+	0.0912534i
$391$	100595.	+	242858.i	0.657997	+	1.58855i
$392$	7032.32	+	34092.9i	0.0457642	+	0.221867i
$393$	−18710.1	−	7749.99i	−0.121141	−	0.0501783i
$394$	−2856.34	−	758.147i	−0.0184000	−	0.00488383i
$395$	7818.93	+	39308.4i	0.0501133	+	0.251937i
$396$	2329.36	+	4667.90i	0.0148541	+	0.0297667i
$397$	148456.	−	99195.1i	0.941926	−	0.629375i	0.0131092	−	0.999914i	$-0.495827\pi$
$397$	148456.	−	99195.1i	0.941926	−	0.629375i	0.928817	+	0.370539i	$0.120827\pi$
$398$	109134.	+	123854.i	0.688961	+	0.781886i
$399$	−62672.3	−	62672.3i	−0.393668	−	0.393668i
$400$	68914.7	−	9734.22i	0.430717	−	0.0608389i
$401$	112554.	+	112554.i	0.699957	+	0.699957i	0.964401	−	0.264444i	$-0.0851885\pi$
$401$	112554.	+	112554.i	0.699957	+	0.699957i	−0.264444	+	0.964401i	$0.585189\pi$
$402$	−36610.9	−	2313.01i	−0.226547	−	0.0143128i
$403$	−210571.	+	140699.i	−1.29655	+	0.866325i
$404$	20000.9	+	284604.i	0.122543	+	1.74373i
$405$	−5538.69	−	27844.9i	−0.0337674	−	0.169760i
$406$	−78791.1	−	135731.i	−0.477997	−	0.823429i
$407$	7233.74	+	2996.31i	0.0436691	+	0.0180883i
$408$	164490.	−	1162.42i	0.988140	−	0.00698301i
$409$	−65462.8	−	158041.i	−0.391335	−	0.944765i	−0.989650	−	0.143504i	$-0.954163\pi$
$409$	−65462.8	−	158041.i	−0.391335	−	0.944765i	0.598315	−	0.801261i	$-0.295837\pi$
$410$	−117030.	+	153263.i	−0.696195	+	0.911738i
$411$	−87043.6	−	58160.7i	−0.515292	−	0.344307i
$412$	114548.	−	200579.i	0.674825	−	1.18165i
$413$	178229.	+	35452.0i	1.04491	+	0.207845i
$414$	−103000.	−	50492.7i	−0.600947	−	0.294597i
$415$	99428.1			0.577315
$416$	−108560.	−	138081.i	−0.627314	−	0.797896i
$417$		−	14228.6i		−	0.0818256i
$418$	−8589.73	−	4210.86i	−0.0491617	−	0.0241001i
$419$	16420.1	−	82549.4i	0.0935293	−	0.470203i	−0.905426	−	0.424504i	$-0.860448\pi$
$419$	16420.1	−	82549.4i	0.0935293	−	0.470203i	0.998955	−	0.0456992i	$-0.0145516\pi$
$420$	−27648.9	−	101276.i	−0.156740	−	0.574128i
$421$	−9168.81	+	13722.1i	−0.0517308	+	0.0774205i	−0.856433	−	0.516258i	$-0.827325\pi$
$421$	−9168.81	+	13722.1i	−0.0517308	+	0.0774205i	0.804703	+	0.593678i	$0.202325\pi$
$422$	−86366.4	+	113106.i	−0.484976	+	0.635125i
$423$	−27064.1	+	11210.3i	−0.151256	+	0.0626522i
$424$	−20799.5	+	51235.5i	−0.115697	+	0.284996i
$425$	52596.3	−	126979.i	0.291190	−	0.702996i
$426$	13860.5	+	23877.0i	0.0763764	+	0.131571i
$427$	−46104.7	+	9170.79i	−0.252865	+	0.0502980i
$428$	−228809.	+	263400.i	−1.24907	+	1.43790i
$429$	2864.32	+	4286.75i	0.0155635	+	0.0232924i
$430$	−257435.	−	16264.2i	−1.39229	−	0.0879623i
$431$	149950.	−	149950.i	0.807222	−	0.807222i	−0.176991	−	0.984213i	$-0.556636\pi$
$431$	149950.	−	149950.i	0.807222	−	0.807222i	0.984213	+	0.176991i	$0.0566362\pi$
$432$	−132124.	+	118090.i	−0.707969	+	0.632771i
$433$	113927.	−	113927.i	0.607646	−	0.607646i	−0.334684	−	0.942330i	$-0.608630\pi$
$433$	113927.	−	113927.i	0.607646	−	0.607646i	0.942330	+	0.334684i	$0.108630\pi$
$434$	−168254.	−	190948.i	−0.893277	−	1.01376i
$435$	−77016.6	−	115263.i	−0.407011	−	0.609134i
$436$	−213153.	−	71237.7i	−1.12129	−	0.374746i
$437$	206308.	−	41037.3i	1.08032	−	0.214890i
$438$	−111723.	−	29654.1i	−0.582361	−	0.154574i
$439$	106131.	−	256222.i	0.550695	−	1.32950i	−0.366263	−	0.930511i	$-0.619363\pi$
$439$	106131.	−	256222.i	0.550695	−	1.32950i	0.916958	−	0.398984i	$-0.130637\pi$
$440$	−6361.64	−	9376.74i	−0.0328597	−	0.0484336i
$441$	−27714.4	+	11479.7i	−0.142505	+	0.0590273i
$442$	−343784.	+	46084.1i	−1.75971	+	0.235888i
$443$	−122755.	+	183715.i	−0.625504	+	0.936133i	0.374456	+	0.927245i	$0.377829\pi$
$443$	−122755.	+	183715.i	−0.625504	+	0.936133i	−0.999960	+	0.00888867i	$0.997171\pi$
$444$	−13558.9	+	106878.i	−0.0687792	+	0.542155i
$445$	−52454.3	+	263706.i	−0.264887	+	1.33168i
$446$	101499.	−	34721.0i	0.510258	−	0.174551i
$447$		−	4312.00i		−	0.0215806i
$448$	123037.	−	126565.i	0.613026	−	0.630604i
$449$	−66328.7			−0.329010			−0.164505	−	0.986376i	$-0.552603\pi$
$449$	−66328.7			−0.329010			−0.164505	+	0.986376i	$0.552603\pi$
$450$	19412.5	+	56747.9i	0.0958643	+	0.280237i
$451$	9333.92	+	1856.63i	0.0458892	+	0.00912794i
$452$	−6203.97	+	48903.0i	−0.0303664	+	0.239364i
$453$	−91371.4	−	61052.4i	−0.445260	−	0.297513i
$454$	50163.4	+	374215.i	0.243375	+	1.81556i
$455$	84714.8	+	204520.i	0.409201	+	0.987898i
$456$	24766.8	−	129279.i	0.119108	−	0.621725i
$457$	−309643.	−	128258.i	−1.48261	−	0.614119i	−0.512919	−	0.858437i	$-0.671436\pi$
$457$	−309643.	−	128258.i	−1.48261	−	0.614119i	−0.969695	+	0.244318i	$0.921436\pi$
$458$	8788.09	−	33109.4i	0.0418951	−	0.157841i
$459$	68269.7	+	343215.i	0.324043	+	1.62908i
$460$	236307.	+	78975.8i	1.11676	+	0.373231i
$461$	116395.	−	77772.8i	0.547688	−	0.365953i	−0.250730	−	0.968057i	$-0.580671\pi$
$461$	116395.	−	77772.8i	0.547688	−	0.365953i	0.798418	+	0.602104i	$0.205671\pi$
$462$	−3887.27	+	3425.28i	−0.0182121	+	0.0160477i
$463$	191588.	+	191588.i	0.893728	+	0.893728i	0.994872	−	0.101144i	$-0.0322503\pi$
$463$	191588.	+	191588.i	0.893728	+	0.893728i	−0.101144	+	0.994872i	$0.532250\pi$
$464$	101114.	−	210005.i	0.469652	−	0.975424i
$465$	−158957.	−	158957.i	−0.735144	−	0.735144i
$466$	14537.4	−	230101.i	0.0669444	−	1.05961i
$467$	3556.04	−	2376.07i	0.0163055	−	0.0108950i	−0.547391	−	0.836877i	$-0.684379\pi$
$467$	3556.04	−	2376.07i	0.0163055	−	0.0108950i	0.563696	+	0.825982i	$0.309379\pi$
$468$	99262.9	−	114269.i	0.453206	−	0.521720i
$469$	15165.3	+	76241.0i	0.0689453	+	0.346612i
$470$	55027.8	−	31943.4i	0.249107	−	0.144606i
$471$	−53787.4	−	22279.5i	−0.242459	−	0.100430i
$472$	105037.	+	248599.i	0.471477	+	1.11588i
$473$	4871.62	+	11761.1i	0.0217747	+	0.0525687i
$474$	21630.8	+	16517.1i	0.0962755	+	0.0735152i
$475$	−91446.5	−	61102.6i	−0.405303	−	0.270815i
$476$	−91801.6	−	336263.i	−0.405169	−	1.48411i
$477$	−46735.8	−	9296.33i	−0.205406	−	0.0408578i
$478$	−99735.7	+	203451.i	−0.436511	+	0.890438i
$479$	295309.			1.28708			0.643541	−	0.765412i	$-0.277465\pi$
$479$	295309.			1.28708			0.643541	+	0.765412i	$0.277465\pi$
$480$	101413.	−	118424.i	0.440158	−	0.513992i
$481$		−	227175.i		−	0.981905i
$482$	−75250.4	+	153503.i	−0.323903	+	0.660729i
$483$	22225.5	−	111735.i	0.0952703	−	0.478956i
$484$	115894.	−	202936.i	0.494731	−	0.866298i
$485$	−237918.	+	356069.i	−1.01145	+	1.51374i
$486$	−193574.	−	147812.i	−0.819550	−	0.625801i
$487$	−217434.	+	90063.9i	−0.916787	+	0.379746i	−0.790651	−	0.612267i	$-0.790258\pi$
$487$	−217434.	+	90063.9i	−0.916787	+	0.379746i	−0.126136	+	0.992013i	$0.540258\pi$
$488$	−49712.7	−	49015.0i	−0.208751	−	0.205821i
$489$	−30253.4	+	73038.2i	−0.126519	+	0.305445i
$490$	56350.2	−	32711.0i	0.234695	−	0.136239i
$491$	387246.	−	77028.0i	1.60629	−	0.319511i	0.691169	−	0.722693i	$-0.257096\pi$
$491$	387246.	−	77028.0i	1.60629	−	0.319511i	0.915120	+	0.403182i	$0.132096\pi$
$492$	9179.91	+	130626.i	0.0379235	+	0.539634i
$493$	−255715.	−	382705.i	−1.05211	−	1.57460i
$494$	−17500.9	+	277008.i	−0.0717143	+	1.13511i
$495$	6904.55	−	6904.55i	0.0281790	−	0.0281790i
$496$	94380.6	−	365993.i	0.383636	−	1.48768i
$497$	41368.1	−	41368.1i	0.167476	−	0.167476i
$498$	50657.8	−	44637.2i	0.204262	−	0.179986i
$499$	20382.1	+	30504.0i	0.0818555	+	0.122505i	0.870138	−	0.492808i	$-0.164029\pi$
$499$	20382.1	+	30504.0i	0.0818555	+	0.122505i	−0.788283	+	0.615313i	$0.789029\pi$
$500$	75552.6	+	151403.i	0.302210	+	0.605612i
$501$	32041.9	−	6373.54i	0.127657	−	0.0253925i
$502$	53959.5	−	203294.i	0.214121	−	0.806708i
$503$	34810.7	−	84040.5i	0.137587	−	0.332164i	−0.840036	−	0.542531i	$-0.817466\pi$
$503$	34810.7	−	84040.5i	0.137587	−	0.332164i	0.977622	+	0.210367i	$0.0674660\pi$
$504$	127068.	+	83611.3i	0.500236	+	0.329158i
$505$	493368.	−	204360.i	1.93459	−	0.801332i
$506$	−1633.69	−	12187.2i	−0.00638070	−	0.0475995i
$507$	2433.13	−	3641.44i	0.00946564	−	0.0141663i
$508$	259691.	+	335155.i	1.00631	+	1.29873i
$509$	−99976.6	+	502616.i	−0.385889	+	1.94000i	−0.0478827	+	0.998853i	$0.515247\pi$
$509$	−99976.6	+	502616.i	−0.385889	+	1.94000i	−0.338007	+	0.941144i	$0.609753\pi$
$510$	−99654.2	−	291316.i	−0.383138	−	1.12001i
$511$			244942.i			0.938042i
$512$	258133.	+	45680.0i	0.984701	+	0.174255i
$513$	280026.			1.06405
$514$	−49345.3	+	16880.2i	−0.186776	+	0.0638928i
$515$	−424031.	−	84345.0i	−1.59876	−	0.318013i
$516$	−138462.	+	107286.i	−0.520035	+	0.402944i
$517$	−2610.91	−	1744.55i	−0.00976812	−	0.00652685i
$518$	226271.	−	30331.6i	0.843275	−	0.113041i
$519$	37785.1	+	91221.4i	0.140277	+	0.338658i
$520$	−180715.	+	274641.i	−0.668325	+	1.01568i
$521$	−45443.1	−	18823.1i	−0.167414	−	0.0693453i	0.297402	−	0.954752i	$-0.403880\pi$
$521$	−45443.1	−	18823.1i	−0.167414	−	0.0693453i	−0.464817	+	0.885407i	$0.653880\pi$
$522$	194133.	+	51528.0i	0.712457	+	0.189105i
$523$	41669.8	+	209488.i	0.152342	+	0.765873i	0.979110	+	0.203331i	$0.0651766\pi$
$523$	41669.8	+	209488.i	0.152342	+	0.765873i	−0.826769	+	0.562542i	$0.809823\pi$
$524$	−57027.1	+	28457.4i	−0.207691	+	0.103641i
$525$	−49526.8	+	33092.7i	−0.179689	+	0.120064i
$526$	296390.	+	336366.i	1.07125	+	1.21574i
$527$	−527778.	−	527778.i	−1.90033	−	1.90033i
$528$	−7450.79	−	1921.38i	−0.0267260	−	0.00689199i
$529$	−6692.57	−	6692.57i	−0.0239156	−	0.0239156i
$530$	103294.	+	6525.95i	0.367727	+	0.0232323i
$531$	−193372.	+	129207.i	−0.685812	+	0.458245i
$532$	−278243.	+	19553.9i	−0.983108	+	0.0690892i
$533$	−53868.9	−	270817.i	−0.189620	−	0.953283i
$534$	91662.9	+	157905.i	0.321448	+	0.553748i
$535$	603343.	+	249913.i	2.10793	+	0.873135i
$536$	−81053.8	+	82207.5i	−0.282126	+	0.286142i
$537$	6595.03	+	15921.8i	0.0228701	+	0.0552133i
$538$	9492.66	−	12431.6i	0.0327962	−	0.0429499i
$539$	−2673.65	−	1786.48i	−0.00920296	−	0.00614922i
$540$	288024.	+	164487.i	0.987738	+	0.564083i
$541$	217856.	+	43334.3i	0.744346	+	0.148060i	0.552672	−	0.833399i	$-0.313608\pi$
$541$	217856.	+	43334.3i	0.744346	+	0.148060i	0.191674	+	0.981459i	$0.438608\pi$
$542$	412297.	+	202116.i	1.40350	+	0.688022i
$543$	−174167.			−0.590699
$544$	336716.	−	393198.i	1.13780	−	1.32866i
$545$			420659.i			1.41624i
$546$	134979.	+	66169.2i	0.452772	+	0.221958i
$547$	53340.6	−	268162.i	0.178272	−	0.896235i	−0.783292	−	0.621654i	$-0.786461\pi$
$547$	53340.6	−	268162.i	0.178272	−	0.896235i	0.961564	−	0.274581i	$-0.0885390\pi$
$548$	−317823.	+	86767.1i	−1.05834	+	0.288931i
$549$	33423.6	−	50021.9i	0.110894	−	0.165965i
$550$	−3901.75	+	5109.74i	−0.0128983	+	0.0168917i
$551$	−340281.	+	140949.i	−1.12082	+	0.464258i
$552$	155852.	−	65850.0i	0.511486	−	0.216112i
$553$	22070.0	−	53281.7i	0.0721692	−	0.174232i
$554$	−26827.9	−	46215.5i	−0.0874112	−	0.150580i
$555$	197777.	−	39340.3i	0.642080	−	0.127718i
$556$	−33804.6	−	29365.3i	−0.109352	−	0.0949915i
$557$	90952.0	+	136119.i	0.293158	+	0.438742i	0.948588	−	0.316514i	$-0.102512\pi$
$557$	90952.0	+	136119.i	0.293158	+	0.438742i	−0.655430	+	0.755256i	$0.727512\pi$
$558$	325062.	+	20536.8i	1.04399	+	0.0659576i
$559$	261175.	−	261175.i	0.835810	−	0.835810i
$560$	−297677.	−	143327.i	−0.949226	−	0.457038i
$561$	−10744.4	+	10744.4i	−0.0341394	+	0.0341394i
$562$	−395342.	−	448664.i	−1.25170	−	1.42053i
$563$	−213604.	−	319681.i	−0.673895	−	1.00856i	−0.998042	−	0.0625485i	$-0.980077\pi$
$563$	−213604.	−	319681.i	−0.673895	−	1.00856i	0.324147	−	0.946007i	$-0.394923\pi$
$564$	13695.6	−	40979.0i	0.0430548	−	0.128826i
$565$	90494.4	−	18000.5i	0.283482	−	0.0563880i
$566$	521469.	+	138411.i	1.62778	+	0.432055i
$567$	−15633.7	+	37743.1i	−0.0486291	+	0.117401i
$568$	85333.2	+	16347.8i	0.264497	+	0.0506714i
$569$	−302388.	+	125253.i	−0.933987	+	0.386870i	−0.797189	−	0.603729i	$-0.793681\pi$
$569$	−302388.	+	125253.i	−0.933987	+	0.386870i	−0.136797	+	0.990599i	$0.543681\pi$
$570$	−244192.	+	32733.9i	−0.751593	+	0.100751i
$571$	−235052.	+	351781.i	−0.720929	+	1.07895i	0.272237	+	0.962230i	$0.412237\pi$
$571$	−235052.	+	351781.i	−0.720929	+	1.07895i	−0.993165	+	0.116716i	$0.962763\pi$
$572$	16096.0	+	2041.99i	0.0491957	+	0.00624109i
$573$	−45725.2	+	229876.i	−0.139266	+	0.700139i
$574$	262548.	−	89813.2i	0.796864	−	0.272594i
$575$		−	141366.i		−	0.427573i
$576$	3192.65	+	225879.i	0.00962291	+	0.680817i
$577$	−207607.			−0.623578			−0.311789	−	0.950151i	$-0.600928\pi$
$577$	−207607.			−0.623578			−0.311789	+	0.950151i	$0.600928\pi$
$578$	−222746.	−	651144.i	−0.666735	−	1.94904i
$579$	−275481.	−	54796.5i	−0.821739	−	0.163454i
$580$	−432795.	−	54905.5i	−1.28655	−	0.163215i
$581$	−118961.	−	79487.5i	−0.352415	−	0.235476i
$582$	38636.5	+	288225.i	0.114065	+	0.850914i
$583$	−1954.72	−	4719.10i	−0.00575104	−	0.0138842i
$584$	−301029.	+	204233.i	−0.882638	+	0.598825i
$585$	−261745.	−	108418.i	−0.764833	−	0.316804i
$586$	167993.	−	632918.i	0.489211	−	1.84311i
$587$	−90313.2	−	454035.i	−0.262105	−	1.31769i	−0.857594	−	0.514327i	$-0.828042\pi$
$587$	−90313.2	−	454035.i	−0.262105	−	1.31769i	0.595490	−	0.803363i	$-0.296958\pi$
$588$	14024.7	−	41963.8i	0.0405637	−	0.121373i
$589$	−496613.	+	331826.i	−1.43149	+	0.956489i
$590$	379000.	−	333957.i	1.08877	−	0.959371i
$591$	2656.04	+	2656.04i	0.00760430	+	0.00760430i
$592$	225941.	+	252792.i	0.644692	+	0.721306i
$593$	320720.	+	320720.i	0.912046	+	0.912046i	0.996433	−	0.0843872i	$-0.0268933\pi$
$593$	320720.	+	320720.i	0.912046	+	0.912046i	−0.0843872	+	0.996433i	$0.526893\pi$
$594$	1032.11	−	16336.6i	0.00292520	−	0.0463008i
$595$	−542476.	+	362471.i	−1.53231	+	1.02386i
$596$	−10244.6	−	8899.21i	−0.0288404	−	0.0250530i
$597$	−40933.2	−	205785.i	−0.114849	−	0.577384i
$598$	−308547.	+	179110.i	−0.862818	+	0.500862i
$599$	−371402.	−	153840.i	−1.03512	−	0.428761i	−0.200563	−	0.979681i	$-0.564277\pi$
$599$	−371402.	−	153840.i	−1.03512	−	0.428761i	−0.834558	+	0.550920i	$0.814277\pi$
$600$	−81965.6	−	33274.6i	−0.227682	−	0.0924295i
$601$	−109229.	−	263702.i	−0.302405	−	0.730070i	−0.999909	−	0.0134895i	$-0.995706\pi$
$601$	−109229.	−	263702.i	−0.302405	−	0.730070i	0.697504	−	0.716581i	$-0.254294\pi$
$602$	295007.	+	225265.i	0.814028	+	0.621585i
$603$	−82718.8	−	55270.9i	−0.227494	−	0.152007i
$604$	−333625.	+	91081.2i	−0.914501	+	0.249663i
$605$	−429014.	−	85336.2i	−1.17209	−	0.233143i
$606$	159622.	−	325612.i	0.434657	−	0.886656i
$607$	221098.			0.600076			0.300038	−	0.953927i	$-0.403001\pi$
$607$	221098.			0.600076			0.300038	+	0.953927i	$0.403001\pi$
$608$	−256030.	−	325651.i	−0.692603	−	0.880937i
$609$			199479.i			0.537850i
$610$	−57518.2	+	117331.i	−0.154577	+	0.315322i
$611$	−17774.3	+	89357.7i	−0.0476114	+	0.239359i
$612$	387381.	+	221228.i	1.03427	+	0.590658i
$613$	−9114.11	+	13640.2i	−0.0242545	+	0.0362995i	−0.843399	−	0.537288i	$-0.819449\pi$
$613$	−9114.11	+	13640.2i	−0.0242545	+	0.0362995i	0.819144	+	0.573588i	$0.194449\pi$
$614$	−473882.	−	361852.i	−1.25699	−	0.959830i
$615$	226443.	−	93795.8i	0.598700	−	0.247990i
$616$	115.222	+	16304.7i	0.000303651	+	0.0429685i
$617$	134936.	−	325764.i	0.354451	−	0.855721i	−0.641608	−	0.767033i	$-0.721732\pi$
$617$	134936.	−	325764.i	0.354451	−	0.855721i	0.996059	−	0.0886885i	$-0.0282676\pi$
$618$	−253906.	+	147391.i	−0.664808	+	0.385918i
$619$	99035.5	−	19699.4i	0.258470	−	0.0514128i	−0.0641545	−	0.997940i	$-0.520435\pi$
$619$	99035.5	−	19699.4i	0.258470	−	0.0514128i	0.322624	+	0.946527i	$0.395435\pi$
$620$	−705712.	+	49594.9i	−1.83588	+	0.129019i
$621$	199969.	+	299275.i	0.518536	+	0.776044i
$622$	−23718.2	+	375418.i	−0.0613057	+	0.970362i
$623$	273578.	−	273578.i	0.704864	−	0.704864i
$624$	31224.4	+	221058.i	0.0801910	+	0.567723i
$625$	344100.	−	344100.i	0.880895	−	0.880895i
$626$	−225719.	+	198892.i	−0.575995	+	0.507539i
$627$	6755.24	+	10109.9i	0.0171833	+	0.0257166i
$628$	−163940.	+	81808.6i	−0.415686	+	0.207434i
$629$	656671.	−	130620.i	1.65977	−	0.330148i
$630$	73039.8	−	275179.i	0.184026	−	0.693322i
$631$	−87425.7	+	211064.i	−0.219574	+	0.530098i	−0.994831	−	0.101548i	$-0.967620\pi$
$631$	−87425.7	+	211064.i	−0.219574	+	0.530098i	0.775257	+	0.631646i	$0.217620\pi$
$632$	83884.0	−	17302.7i	0.210012	−	0.0433191i
$633$	167111.	−	69219.7i	0.417060	−	0.172752i
$634$	30995.8	+	231226.i	0.0771123	+	0.575252i
$635$	440901.	−	659855.i	1.09344	−	1.63644i
$636$	55557.4	−	43048.1i	0.137350	−	0.106424i
$637$	−18201.5	+	91505.0i	−0.0448568	+	0.225510i
$638$	6968.71	+	20371.4i	0.0171203	+	0.0500471i
$639$			74872.8i			0.183367i
$640$	−72056.9	−	485345.i	−0.175920	−	1.18492i
$641$	−161135.			−0.392169			−0.196085	−	0.980587i	$-0.562823\pi$
$641$	−161135.			−0.392169			−0.196085	+	0.980587i	$0.562823\pi$
$642$	419594.	−	143536.i	1.01803	−	0.348250i
$643$	92943.3	+	18487.6i	0.224800	+	0.0447155i	0.306205	−	0.951966i	$-0.400941\pi$
$643$	92943.3	+	18487.6i	0.224800	+	0.0447155i	−0.0814050	+	0.996681i	$0.525941\pi$
$644$	−219594.	−	283406.i	−0.529479	−	0.683341i
$645$	272605.	+	182149.i	0.655262	+	0.437832i
$646$	−810783.	+	108685.i	−1.94285	+	0.260439i
$647$	−112547.	−	271713.i	−0.268860	−	0.649085i	0.730570	−	0.682837i	$-0.239254\pi$
$647$	−112547.	−	271713.i	−0.268860	−	0.649085i	−0.999430	+	0.0337524i	$0.989254\pi$
$648$	−59420.9	+	12256.7i	−0.141511	+	0.0291893i
$649$	−23032.0	−	9540.15i	−0.0546816	−	0.0226499i
$650$	180292.	+	47854.3i	0.426728	+	0.113265i
$651$	63107.4	+	317262.i	0.148908	+	0.748612i
$652$	111088.	+	222615.i	0.261321	+	0.523672i
$653$	−464752.	+	310537.i	−1.08992	+	0.728262i	−0.964564	−	0.263850i	$-0.915008\pi$
$653$	−464752.	+	310537.i	−1.08992	+	0.728262i	−0.125357	+	0.992112i	$0.540008\pi$
$654$	188851.	+	214322.i	0.441533	+	0.501085i
$655$	84352.0	+	84352.0i	0.196613	+	0.196613i
$656$	329290.	+	247779.i	0.765194	+	0.575781i
$657$	−221662.	−	221662.i	−0.513525	−	0.513525i
$658$	−91375.4	−	5772.93i	−0.211046	−	0.0133335i
$659$	151639.	−	101322.i	0.349172	−	0.233309i	−0.368599	−	0.929589i	$-0.620162\pi$
$659$	151639.	−	101322.i	0.349172	−	0.233309i	0.717771	+	0.696279i	$0.245162\pi$
$660$	1009.64	+	14366.7i	0.00231782	+	0.0329815i
$661$	167507.	+	842114.i	0.383380	+	1.92738i	0.374006	+	0.927426i	$0.377984\pi$
$661$	167507.	+	842114.i	0.383380	+	1.92738i	0.00937420	+	0.999956i	$0.497016\pi$
$662$	144964.	+	249724.i	0.330784	+	0.569830i
$663$	407309.	+	168713.i	0.926610	+	0.383814i
$664$	−1501.54	−	212478.i	−0.00340566	−	0.481922i
$665$	199792.	+	482341.i	0.451789	+	1.09071i
$666$	−177317.	+	232214.i	−0.399762	+	0.523529i
$667$	−393636.	−	263019.i	−0.884796	−	0.591202i
$668$	50986.5	−	89280.0i	0.114262	−	0.200079i
$669$	−133727.	−	26600.0i	−0.298792	−	0.0594333i
$670$	194025.	+	95115.0i	0.432223	+	0.211885i
$671$	6448.85			0.0143231
$672$	−216009.	+	60615.1i	−0.478337	+	0.134228i
$673$			403901.i			0.891754i	0.895094	+	0.445877i	$0.147108\pi$
$673$			403901.i			0.891754i	−0.895094	+	0.445877i	$0.852892\pi$
$674$	263746.	+	129294.i	0.580586	+	0.284615i
$675$	36714.4	−	184576.i	0.0805803	−	0.405105i
$676$	−3629.87	−	13296.0i	−0.00794325	−	0.0290956i
$677$	389629.	−	583122.i	0.850109	−	1.27228i	−0.110361	−	0.993892i	$-0.535201\pi$
$677$	389629.	−	583122.i	0.850109	−	1.27228i	0.960469	−	0.278386i	$-0.0897994\pi$
$678$	38025.0	−	49797.6i	0.0827199	−	0.108330i
$679$	569317.	−	235819.i	1.23485	−	0.511492i
$680$	−897785.	−	364463.i	−1.94158	−	0.788199i
$681$	183647.	−	443364.i	0.395996	−	0.956018i
$682$	17528.2	+	30195.2i	0.0376850	+	0.0649186i
$683$	−113403.	+	22557.3i	−0.243100	+	0.0483555i	−0.315136	−	0.949046i	$-0.602050\pi$
$683$	−113403.	+	22557.3i	−0.243100	+	0.0483555i	0.0720365	+	0.997402i	$0.477050\pi$
$684$	234103.	−	269494.i	0.500374	−	0.576018i
$685$	342593.	+	512726.i	0.730125	+	1.09271i
$686$	−506622.	−	32007.4i	−1.07655	−	0.0680146i
$687$	−30787.6	+	30787.6i	−0.0652322	+	0.0652322i
$688$	−30868.9	+	550383.i	−0.0652146	+	1.16275i
$689$	−104795.	+	104795.i	−0.220751	+	0.220751i
$690$	−209364.	−	237603.i	−0.439748	−	0.499060i
$691$	278699.	+	417102.i	0.583686	+	0.873548i	0.999353	−	0.0359691i	$-0.0114518\pi$
$691$	278699.	+	417102.i	0.583686	+	0.873548i	−0.415667	+	0.909517i	$0.636452\pi$
$692$	294708.	+	98494.0i	0.615432	+	0.205683i
$693$	−13780.8	+	2741.18i	−0.0286952	+	0.00570783i
$694$	−9628.43	−	2555.64i	−0.0199911	−	0.00530616i
$695$	−32073.7	+	77432.8i	−0.0664018	+	0.160308i
$696$	−245155.	+	166325.i	−0.506083	+	0.343352i
$697$	751851.	−	311427.i	1.54763	−	0.641048i
$698$	787864.	−	105613.i	1.61711	−	0.216773i
$699$	−162809.	+	243661.i	−0.333215	+	0.498692i
$700$	−23592.0	+	185965.i	−0.0481469	+	0.379520i
$701$	21098.5	−	106069.i	0.0429355	−	0.215851i	−0.953361	−	0.301831i	$-0.902402\pi$
$701$	21098.5	−	106069.i	0.0429355	−	0.215851i	0.996297	+	0.0859800i	$0.0274021\pi$
$702$	−449374.	+	153723.i	−0.911871	+	0.311936i
$703$		−	535771.i		−	1.08410i
$704$	−19942.0	+	13736.4i	−0.0402368	+	0.0277158i
$705$	−80872.3			−0.162713
$706$	−162145.	−	473991.i	−0.325307	−	0.950957i
$707$	−753668.	−	149914.i	−1.50779	−	0.299919i
$708$	43170.9	−	340297.i	0.0861241	−	0.678877i
$709$	316462.	+	211453.i	0.629549	+	0.420651i	0.828994	−	0.559258i	$-0.188914\pi$
$709$	316462.	+	211453.i	0.629549	+	0.420651i	−0.199445	+	0.979909i	$0.563914\pi$
$710$	−21606.7	−	161184.i	−0.0428619	−	0.319747i
$711$	28245.3	+	68190.1i	0.0558735	+	0.134891i
$712$	564331.	+	108112.i	1.11320	+	0.213263i
$713$	−709271.	−	293790.i	−1.39519	−	0.577907i
$714$	−113659.	+	428215.i	−0.222951	+	0.839973i
$715$	−5924.70	−	29785.5i	−0.0115892	−	0.0582630i
$716$	51438.5	+	17191.2i	0.100337	+	0.0335336i
$717$	239457.	−	160000.i	0.465789	−	0.311231i
$718$	364889.	−	321523.i	0.707803	−	0.623682i
$719$	−205614.	−	205614.i	−0.397736	−	0.397736i	0.479698	−	0.877434i	$-0.340746\pi$
$719$	−205614.	−	205614.i	−0.397736	−	0.397736i	−0.877434	+	0.479698i	$0.840746\pi$
$720$	399090.	−	139680.i	0.769850	−	0.269445i
$721$	439906.	+	439906.i	0.846231	+	0.846231i
$722$	−8406.02	+	133053.i	−0.0161256	+	0.255240i
$723$	180670.	−	120720.i	0.345628	−	0.230942i
$724$	−359450.	+	413791.i	−0.685744	+	0.789412i
$725$	48290.5	+	242773.i	0.0918726	+	0.461875i
$726$	−256890.	+	149123.i	−0.487387	+	0.282926i
$727$	196342.	+	81327.5i	0.371488	+	0.153875i	0.560613	−	0.828078i	$-0.310565\pi$
$727$	196342.	+	81327.5i	0.371488	+	0.153875i	−0.189126	+	0.981953i	$0.560565\pi$
$728$	435779.	−	184124.i	0.822249	−	0.347414i
$729$	89080.6	+	215060.i	0.167621	+	0.404673i
$730$	541156.	+	413222.i	1.01549	+	0.775422i
$731$	905122.	+	604783.i	1.69384	+	1.13179i
$732$	23369.6	+	85601.5i	0.0436144	+	0.159757i
$733$	588639.	+	117088.i	1.09557	+	0.217923i	0.709612	−	0.704593i	$-0.248870\pi$
$733$	588639.	+	117088.i	1.09557	+	0.217923i	0.385960	+	0.922515i	$0.373870\pi$
$734$	281988.	−	575227.i	0.523406	−	1.06770i
$735$	−82815.7			−0.153299
$736$	165202.	−	506180.i	0.304973	−	0.934436i
$737$		−	10664.1i		−	0.0196332i
$738$	−156317.	+	318871.i	−0.287008	+	0.585468i
$739$	89708.3	−	450994.i	0.164265	−	0.825814i	−0.807501	−	0.589866i	$-0.799181\pi$
$739$	89708.3	−	450994.i	0.164265	−	0.825814i	0.971766	−	0.235948i	$-0.0758194\pi$
$740$	314711.	−	551075.i	0.574710	−	1.00635i
$741$	195999.	−	293332.i	0.356957	−	0.534224i
$742$	−118370.	−	90386.5i	−0.214998	−	0.164171i
$743$	−756015.	+	313152.i	−1.36947	+	0.567253i	−0.941645	−	0.336608i	$-0.890720\pi$
$743$	−756015.	+	313152.i	−1.36947	+	0.567253i	−0.427826	+	0.903861i	$0.640720\pi$
$744$	−337290.	+	342091.i	−0.609336	+	0.618010i
$745$	−9720.02	+	23466.2i	−0.0175128	+	0.0422795i
$746$	−426596.	+	247637.i	−0.766547	+	0.444977i
$747$	179588.	−	35722.2i	0.321837	−	0.0640173i
$748$	3352.28	+	47701.3i	0.00599151	+	0.0852565i
$749$	−522083.	−	781352.i	−0.930627	−	1.39278i
$750$	13560.5	−	214640.i	0.0241076	−	0.381582i
$751$	−293400.	+	293400.i	−0.520211	+	0.520211i	−0.917635	−	0.397424i	$-0.869904\pi$
$751$	−293400.	+	293400.i	−0.520211	+	0.520211i	0.397424	+	0.917635i	$0.369904\pi$
$752$	−69094.0	−	117112.i	−0.122181	−	0.207093i
$753$	−189038.	+	189038.i	−0.333394	+	0.333394i
$754$	468694.	−	412991.i	0.824417	−	0.726437i
$755$	359626.	+	538219.i	0.630896	+	0.944202i
$756$	−213111.	−	427062.i	−0.372873	−	0.747218i
$757$	−420571.	+	83656.8i	−0.733918	+	0.145985i	−0.547880	−	0.836557i	$-0.684565\pi$
$757$	−420571.	+	83656.8i	−0.733918	+	0.145985i	−0.186038	+	0.982542i	$0.559565\pi$
$758$	−187101.	+	704908.i	−0.325640	+	1.22686i
$759$	−5980.90	+	14439.2i	−0.0103821	+	0.0250645i
$760$	−426200.	+	647716.i	−0.737882	+	1.12139i
$761$	−818947.	+	339219.i	−1.41412	+	0.585748i	−0.953376	−	0.301785i	$-0.902417\pi$
$761$	−818947.	+	339219.i	−1.41412	+	0.585748i	−0.460744	+	0.887533i	$0.652417\pi$
$762$	−71599.7	−	534128.i	−0.123311	−	0.919890i
$763$	336295.	−	503301.i	0.577658	−	0.864527i
$764$	451777.	+	583059.i	0.773993	+	0.998909i
$765$	162897.	−	818938.i	0.278349	−	1.39936i
$766$	−30994.9	−	90606.4i	−0.0528243	−	0.154419i
$767$			723316.i			1.22952i
$768$	−254603.	−	214930.i	−0.431659	−	0.364397i
$769$	126884.			0.214563			0.107282	−	0.994229i	$-0.465785\pi$
$769$	126884.			0.214563			0.107282	+	0.994229i	$0.465785\pi$
$770$	28876.0	−	9877.99i	0.0487030	−	0.0166605i
$771$	65014.0	+	12932.1i	0.109370	+	0.0217550i
$772$	−698731.	+	541404.i	−1.17240	+	0.908421i
$773$	−412818.	−	275836.i	−0.690875	−	0.461628i	0.159917	−	0.987130i	$-0.448877\pi$
$773$	−412818.	−	275836.i	−0.690875	−	0.461628i	−0.850792	+	0.525503i	$0.823877\pi$
$774$	−470824.	+	63113.8i	−0.785917	+	0.105352i
$775$	153608.	+	370843.i	0.255747	+	0.617428i
$776$	764512.	+	503053.i	1.26958	+	0.835391i
$777$	−268082.	−	111043.i	−0.444044	−	0.183929i
$778$	219192.	+	58179.3i	0.362131	+	0.0961190i
$779$	−127045.	−	638698.i	−0.209355	−	1.05250i
$780$	373900.	−	186582.i	0.614563	−	0.306677i
$781$	−6673.27	+	4458.93i	−0.0109405	+	0.00731019i
$782$	−695144.	−	788903.i	−1.13674	−	1.29006i
$783$	−445644.	−	445644.i	−0.726884	−	0.726884i
$784$	−70754.4	−	119926.i	−0.115112	−	0.195111i
$785$	242493.	+	242493.i	0.393513	+	0.393513i
$786$	80845.6	+	5107.68i	0.130861	+	0.00826758i
$787$	90461.2	−	60444.2i	0.146054	−	0.0975900i	−0.480396	−	0.877051i	$-0.659507\pi$
$787$	90461.2	−	60444.2i	0.146054	−	0.0975900i	0.626450	+	0.779461i	$0.284507\pi$
$788$	11791.9	−	828.690i	0.0189903	−	0.00133457i
$789$	−111168.	−	558877.i	−0.178576	−	0.897764i
$790$	−80483.9	−	138647.i	−0.128960	−	0.222155i
$791$	−122663.	−	50808.7i	−0.196047	−	0.0812055i
$792$	−14859.3	−	14650.8i	−0.0236891	−	0.0233566i
$793$	−71603.5	−	172866.i	−0.113864	−	0.274893i
$794$	−433433.	+	567625.i	−0.687513	+	0.900368i
$795$	−109382.	−	73086.4i	−0.173065	−	0.115639i
$796$	−573389.	−	327454.i	−0.904947	−	0.516802i
$797$	−157886.	−	31405.4i	−0.248557	−	0.0494411i	0.0692393	−	0.997600i	$-0.477943\pi$
$797$	−157886.	−	31405.4i	−0.248557	−	0.0494411i	−0.317796	+	0.948159i	$0.602943\pi$
$798$	318335.	+	156054.i	0.499895	+	0.245059i
$799$	−268517.			−0.420609
$800$	−248218.	+	126063.i	−0.387840	+	0.196974i
$801$			495153.i			0.771746i
$802$	−571701.	−	280259.i	−0.888833	−	0.435724i
$803$	6555.57	−	32957.1i	0.0101667	−	0.0511114i
$804$	141555.	−	38645.2i	0.218984	−	0.0597839i
$805$	−372824.	+	557971.i	−0.575323	+	0.861032i
$806$	614784.	−	805122.i	0.946351	−	1.23934i
$807$	−18367.4	+	7608.05i	−0.0282034	+	0.0116822i
$808$	−444167.	−	1.05124e6i	−0.680336	−	1.61020i
$809$	−220205.	+	531621.i	−0.336457	+	0.812279i	0.661593	+	0.749863i	$0.269881\pi$
$809$	−220205.	+	531621.i	−0.336457	+	0.812279i	−0.998050	+	0.0624161i	$0.980119\pi$
$810$	57012.3	+	98213.2i	0.0868958	+	0.149693i
$811$	406585.	−	80874.8i	0.618172	−	0.122962i	0.123937	−	0.992290i	$-0.460448\pi$
$811$	406585.	−	80874.8i	0.618172	−	0.122962i	0.494236	+	0.869328i	$0.335448\pi$
$812$	473927.	+	411689.i	0.718785	+	0.624392i
$813$	−324243.	−	485264.i	−0.490558	−	0.734171i
$814$	−31256.6	−	1974.74i	−0.0471730	−	0.00298030i
$815$	329282.	−	329282.i	0.495739	−	0.495739i
$816$	−621036.	+	217360.i	−0.932688	+	0.326437i
$817$	615957.	−	615957.i	0.922798	−	0.922798i
$818$	452368.	+	513383.i	0.676061	+	0.767246i
$819$	226492.	+	338969.i	0.337664	+	0.505350i
$820$	244496.	−	731568.i	0.363618	−	1.08800i
$821$	756097.	−	150397.i	1.12174	−	0.223128i	0.400826	−	0.916154i	$-0.368723\pi$
$821$	756097.	−	150397.i	1.12174	−	0.223128i	0.720912	+	0.693027i	$0.243723\pi$
$822$	404731.	+	107426.i	0.598995	+	0.158989i
$823$	−390397.	+	942502.i	−0.576377	+	1.39150i	0.319666	+	0.947530i	$0.396429\pi$
$823$	−390397.	+	942502.i	−0.576377	+	1.39150i	−0.896043	+	0.443968i	$0.853571\pi$
$824$	−173842.	+	907428.i	−0.256035	+	1.33647i
$825$	7549.53	−	3127.12i	0.0110921	−	0.00459448i
$826$	−720439.	+	96574.6i	−1.05593	+	0.141548i
$827$	−667871.	+	999540.i	−0.976521	+	1.46147i	−0.0915617	+	0.995799i	$0.529186\pi$
$827$	−667871.	+	999540.i	−0.976521	+	1.46147i	−0.884960	+	0.465668i	$0.845814\pi$
$828$	455194.	+	57747.1i	0.663950	+	0.0842305i
$829$	124110.	−	623945.i	0.180592	−	0.907899i	−0.779112	−	0.626885i	$-0.784329\pi$
$829$	124110.	−	623945.i	0.180592	−	0.907899i	0.959704	−	0.281013i	$-0.0906705\pi$
$830$	−376304.	+	128727.i	−0.546238	+	0.186859i
$831$			67921.3i			0.0983566i
$832$	589637.	+	382040.i	0.851800	+	0.551903i
$833$	−274970.			−0.396274
$834$	18421.4	+	53850.6i	0.0264844	+	0.0774209i
$835$	−188742.	−	37543.0i	−0.270704	−	0.0538464i
$836$	37961.1	+	4815.84i	0.0543158	+	0.00689064i
$837$	−849764.	−	567794.i	−1.21296	−	0.810475i
$838$	44729.9	+	333682.i	0.0636957	+	0.475165i
$839$	−75346.9	−	181904.i	−0.107039	−	0.258415i	0.861280	−	0.508130i	$-0.169663\pi$
$839$	−75346.9	−	181904.i	−0.107039	−	0.258415i	−0.968319	+	0.249715i	$0.919663\pi$
$840$	235762.	+	347501.i	0.334130	+	0.492491i
$841$	112408.	+	46561.0i	0.158930	+	0.0658309i
$842$	16935.4	−	63804.4i	0.0238875	−	0.0899967i
$843$	148282.	+	745462.i	0.208657	+	1.04899i
$844$	180434.	−	539885.i	0.253299	−	0.757908i
$845$	−21449.7	+	14332.3i	−0.0300406	+	0.0200725i
$846$	87915.1	−	77466.6i	0.122835	−	0.108237i
$847$	445075.	+	445075.i	0.620393	+	0.620393i
$848$	12386.0	−	220839.i	0.0172242	−	0.307102i
$849$	−484901.	−	484901.i	−0.672725	−	0.672725i
$850$	−34663.9	+	548669.i	−0.0479777	+	0.759403i
$851$	572600.	−	382599.i	0.790664	−	0.528305i
$852$	−83370.5	−	72422.0i	−0.114851	−	0.0997679i
$853$	−158748.	−	798078.i	−0.218177	−	1.09685i	−0.922212	−	0.386685i	$-0.873620\pi$
$853$	−158748.	−	798078.i	−0.218177	−	1.09685i	0.704035	−	0.710165i	$-0.251380\pi$
$854$	162618.	−	94399.1i	0.222974	−	0.129435i
$855$	−617302.	−	255695.i	−0.844433	−	0.349776i
$856$	524952.	−	1.29312e6i	0.716428	−	1.76478i
$857$	−251842.	−	608001.i	−0.342900	−	0.827833i	−0.997420	−	0.0717886i	$-0.977129\pi$
$857$	−251842.	−	608001.i	−0.342900	−	0.827833i	0.654520	−	0.756045i	$-0.272871\pi$
$858$	−16390.5	−	12515.6i	−0.0222647	−	0.0170011i
$859$	226252.	+	151177.i	0.306624	+	0.204879i	0.699356	−	0.714773i	$-0.253470\pi$
$859$	226252.	+	151177.i	0.306624	+	0.204879i	−0.392733	+	0.919653i	$0.628470\pi$
$860$	995365.	−	271740.i	1.34582	−	0.367414i
$861$	−345914.	−	68806.7i	−0.466619	−	0.0928163i
$862$	−373377.	+	761652.i	−0.502497	+	1.02504i
$863$	459285.			0.616681			0.308341	−	0.951276i	$-0.400226\pi$
$863$	459285.			0.616681			0.308341	+	0.951276i	$0.400226\pi$
$864$	347158.	−	617992.i	0.465050	−	0.827857i
$865$		−	581608.i		−	0.777316i
$866$	−283679.	+	578676.i	−0.378261	+	0.771613i
$867$	−170647.	+	857902.i	−0.227019	+	1.14130i
$868$	884003.	+	504842.i	1.17331	+	0.670063i
$869$	−4395.55	+	6578.40i	−0.00582067	+	0.00871125i
$870$	440712.	+	336524.i	0.582259	+	0.444608i
$871$	−285860.	+	118407.i	−0.376806	+	0.156078i
$872$	898948.	−	6352.70i	1.18223	−	0.00835460i
$873$	−301802.	+	728614.i	−0.395998	+	0.956024i
$874$	−727681.	+	422416.i	−0.952617	+	0.552990i
$875$	−446981.	+	88910.0i	−0.583811	+	0.116127i
$876$	461227.	−	32413.3i	0.601044	−	0.0422392i
$877$	62917.4	+	94162.6i	0.0818035	+	0.122428i	0.870115	−	0.492849i	$-0.164044\pi$
$877$	62917.4	+	94162.6i	0.0818035	+	0.122428i	−0.788311	+	0.615276i	$0.789044\pi$
$878$	−69945.9	+	1.10712e6i	−0.0907347	+	1.43617i
$879$	−588534.	+	588534.i	−0.761718	+	0.761718i
$880$	36216.6	+	27251.7i	0.0467673	+	0.0351907i
$881$	−701126.	+	701126.i	−0.903325	+	0.903325i	−0.995722	−	0.0923969i	$-0.970547\pi$
$881$	−701126.	+	701126.i	−0.903325	+	0.903325i	0.0923969	+	0.995722i	$0.470547\pi$
$882$	90027.8	−	79328.2i	0.115728	−	0.101974i
$883$	−499276.	−	747219.i	−0.640353	−	0.958355i	−0.999684	−	0.0251452i	$-0.991995\pi$
$883$	−499276.	−	747219.i	−0.640353	−	0.958355i	0.359331	−	0.933210i	$-0.383005\pi$
$884$	1.24145e6	−	619502.i	1.58863	−	0.792754i
$885$	−629714.	+	125258.i	−0.804002	+	0.159926i
$886$	226735.	−	854231.i	0.288836	−	1.08820i
$887$	−40968.1	+	98905.8i	−0.0520714	+	0.125711i	−0.947775	−	0.318941i	$-0.896673\pi$
$887$	−40968.1	+	98905.8i	−0.0520714	+	0.125711i	0.895703	+	0.444652i	$0.146673\pi$
$888$	−87056.9	−	422055.i	−0.110402	−	0.535233i
$889$	−1.05504e6	+	437011.i	−1.33495	+	0.552954i
$890$	−142891.	−	1.06595e6i	−0.180395	−	1.34573i
$891$	3113.67	−	4659.94i	0.00392209	−	0.00586982i
$892$	−339187.	+	262816.i	−0.426295	+	0.330310i
$893$	−41919.2	+	210742.i	−0.0525666	+	0.264270i
$894$	5582.64	+	16319.5i	0.00698498	+	0.0204189i
$895$		−	101514.i		−	0.126730i
$896$	−301795.	+	638300.i	−0.375920	+	0.795077i
$897$	453461.			0.563579
$898$	251033.	−	85874.3i	0.311300	−	0.106490i
$899$	1.31841e6	+	262248.i	1.63129	+	0.324484i
$900$	−146940.	−	189640.i	−0.181408	−	0.234123i
$901$	−363176.	−	242666.i	−0.447370	−	0.298923i
$902$	−37729.6	+	5057.64i	−0.0463735	+	0.00621635i
$903$	−180542.	−	435867.i	−0.221413	−	0.534538i
$904$	−39833.6	−	193115.i	−0.0487430	−	0.236308i
$905$	947829.	+	392604.i	1.15726	+	0.479355i
$906$	424855.	+	112768.i	0.517588	+	0.137381i
$907$	99105.3	+	498236.i	0.120471	+	0.605648i	0.993101	+	0.117266i	$0.0374129\pi$
$907$	99105.3	+	498236.i	0.120471	+	0.605648i	−0.872630	+	0.488382i	$0.837587\pi$
$908$	−674341.	−	1.35134e6i	−0.817914	−	1.63905i
$909$	817704.	−	546372.i	0.989619	−	0.661242i
$910$	−585405.	−	664363.i	−0.706926	−	0.802274i
$911$	164937.	+	164937.i	0.198738	+	0.198738i	0.799459	−	0.600721i	$-0.205120\pi$
$911$	164937.	+	164937.i	0.198738	+	0.198738i	−0.600721	+	0.799459i	$0.705120\pi$
$912$	73640.1	+	521345.i	0.0885369	+	0.626809i
$913$	13878.9	+	13878.9i	0.0166500	+	0.0166500i
$914$	1.33795e6	+	84529.3i	1.60158	+	0.101185i
$915$	138096.	−	92273.1i	0.164945	−	0.110213i
$916$	9605.80	+	136686.i	0.0114483	+	0.162905i
$917$	−33488.6	−	168359.i	−0.0398252	−	0.200215i
$918$	−702732.	−	1.21057e6i	−0.833881	−	1.43650i
$919$	−1.46543e6	−	606999.i	−1.73513	−	0.718715i	−0.999129	−	0.0417384i	$-0.986710\pi$
$919$	−1.46543e6	−	606999.i	−1.73513	−	0.718715i	−0.736004	−	0.676977i	$-0.763290\pi$
$920$	−996594.	+	7042.75i	−1.17745	+	0.00832083i
$921$	290012.	+	700151.i	0.341898	+	0.825415i
$922$	−339828.	+	445039.i	−0.399758	+	0.523524i
$923$	193620.	+	129373.i	0.227273	+	0.151859i
$924$	10277.5	−	17996.3i	0.0120376	−	0.0210785i
$925$	−353148.	−	70245.4i	−0.412737	−	0.0820984i
$926$	−973142.	−	477054.i	−1.13489	−	0.556347i
$927$	−796192.			−0.926527
$928$	−110797.	+	925711.i	−0.128657	+	1.07493i
$929$		−	1.61567e6i		−	1.87207i	−0.351912	−	0.936033i	$-0.614469\pi$
$929$		−	1.61567e6i		−	1.87207i	0.351912	−	0.936033i	$-0.385531\pi$
$930$	807398.	+	395803.i	0.933515	+	0.457628i
$931$	−42926.6	+	215806.i	−0.0495253	+	0.248980i
$932$	242887.	+	889681.i	0.279623	+	1.02424i
$933$	265628.	−	397541.i	0.305149	−	0.456687i
$934$	−10382.2	+	13596.6i	−0.0119014	+	0.0155861i
$935$	82691.4	−	34251.9i	0.0945883	−	0.0391797i
$936$	−227737.	+	560986.i	−0.259945	+	0.640325i
$937$	−91900.3	+	221867.i	−0.104674	+	0.252705i	−0.967535	−	0.252735i	$-0.918670\pi$
$937$	−91900.3	+	221867.i	−0.104674	+	0.252705i	0.862862	+	0.505440i	$0.168670\pi$
$938$	−156103.	−	268914.i	−0.177422	−	0.305638i
$939$	375035.	−	74599.0i	0.425344	−	0.0846062i
$940$	−166906.	+	192139.i	−0.188893	+	0.217450i
$941$	394417.	+	590286.i	0.445426	+	0.666628i	0.984450	−	0.175663i	$-0.0562068\pi$
$941$	394417.	+	590286.i	0.445426	+	0.666628i	−0.539024	+	0.842290i	$0.681207\pi$
$942$	232413.	+	14683.4i	0.261914	+	0.0165472i
$943$	591878.	−	591878.i	0.665593	−	0.665593i
$944$	−719389.	−	804880.i	−0.807272	−	0.903206i
$945$	−631691.	+	631691.i	−0.707361	+	0.707361i
$946$	−33664.4	−	38205.0i	−0.0376174	−	0.0426911i
$947$	−127794.	−	191257.i	−0.142499	−	0.213264i	0.753354	−	0.657615i	$-0.228434\pi$
$947$	−127794.	−	191257.i	−0.142499	−	0.213264i	−0.895853	+	0.444351i	$0.853434\pi$
$948$	−103250.	−	34507.0i	−0.114888	−	0.0383964i
$949$	−956227.	+	190205.i	−1.06177	+	0.211198i
$950$	425204.	+	112860.i	0.471140	+	0.125053i
$951$	113475.	−	273952.i	0.125470	−	0.302910i
$952$	782792.	+	1.15380e6i	0.863719	+	1.27308i
$953$	901076.	−	373238.i	0.992146	−	0.410960i	0.173235	−	0.984881i	$-0.444578\pi$
$953$	901076.	−	373238.i	0.992146	−	0.410960i	0.818911	+	0.573920i	$0.194578\pi$
$954$	188916.	−	25324.1i	0.207573	−	0.0278251i
$955$	767021.	−	1.14793e6i	0.841009	−	1.25866i
$956$	114065.	−	899122.i	0.124806	−	0.983791i
$957$	5338.79	−	26839.9i	0.00582934	−	0.0293061i
$958$	−1.11765e6	+	382330.i	−1.21780	+	0.416589i
$959$		−	887340.i		−	0.964835i
$960$	−230494.	+	579493.i	−0.250102	+	0.628790i
$961$	1.25632e6			1.36036
$962$	294118.	+	859783.i	0.317812	+	0.929049i
$963$	1.17955e6	+	234628.i	1.27193	+	0.253003i
$964$	86061.8	−	678386.i	0.0926097	−	0.730000i
$965$	1.37566e6	+	919190.i	1.47726	+	0.987076i
$966$	60544.5	+	451657.i	0.0648814	+	0.484010i
$967$	85599.8	+	206656.i	0.0915419	+	0.221002i	0.963018	−	0.269436i	$-0.0868371\pi$
$967$	85599.8	+	206656.i	0.0915419	+	0.221002i	−0.871477	+	0.490437i	$0.836837\pi$
$968$	−175884.	+	918091.i	−0.187705	+	0.979795i
$969$	960602.	+	397894.i	1.02305	+	0.423760i
$970$	439449.	−	1.65563e6i	0.467051	−	1.75963i
$971$	60079.0	+	302037.i	0.0637212	+	0.320348i	0.999478	−	0.0322971i	$-0.0102823\pi$
$971$	60079.0	+	302037.i	0.0637212	+	0.320348i	−0.935757	+	0.352645i	$0.885282\pi$
$972$	923986.	+	308804.i	0.977986	+	0.326851i
$973$	100278.	−	67003.8i	0.105921	−	0.0707741i
$974$	706313.	−	622369.i	0.744525	−	0.656040i
$975$	−167649.	−	167649.i	−0.176357	−	0.176357i
$976$	251605.	+	121144.i	0.264132	+	0.127176i
$977$	379259.	+	379259.i	0.397326	+	0.397326i	0.877289	−	0.479963i	$-0.159350\pi$
$977$	379259.	+	379259.i	0.397326	+	0.397326i	−0.479963	+	0.877289i	$0.659350\pi$
$978$	19938.7	−	315595.i	0.0208458	−	0.329953i
$979$	−44132.0	+	29488.1i	−0.0460456	+	0.0307667i
$980$	−170917.	+	196756.i	−0.177965	+	0.204869i
$981$	151133.	+	759798.i	0.157044	+	0.789514i
$982$	−1.36588e6	+	792884.i	−1.41641	+	0.822218i
$983$	866041.	+	358726.i	0.896255	+	0.371241i	0.782779	−	0.622300i	$-0.213801\pi$
$983$	866041.	+	358726.i	0.896255	+	0.371241i	0.113476	+	0.993541i	$0.463801\pi$
$984$	−203861.	−	482492.i	−0.210545	−	0.498311i
$985$	−8467.16	−	20441.5i	−0.00872700	−	0.0210688i
$986$	1.46328e6	+	1.11735e6i	1.50513	+	1.14930i
$987$	96760.2	+	64653.1i	0.0993259	+	0.0663675i
$988$	−292401.	−	1.07105e6i	−0.299547	−	1.09722i
$989$	1.09816e6	+	218437.i	1.12272	+	0.223324i
$990$	−17192.4	+	35070.7i	−0.0175414	+	0.0357828i
$991$	129464.			0.131826			0.0659129	−	0.997825i	$-0.479004\pi$
$991$	129464.			0.131826			0.0659129	+	0.997825i	$0.479004\pi$
$992$	116642.	+	1.50736e6i	0.118531	+	1.53177i
$993$		−	367011.i		−	0.372203i
$994$	−103007.	+	210124.i	−0.104254	+	0.212668i
$995$	−241115.	+	1.21217e6i	−0.243544	+	1.22438i
$996$	−133933.	+	234523.i	−0.135011	+	0.236411i
$997$	154681.	−	231496.i	0.155613	−	0.232891i	−0.745469	−	0.666541i	$-0.767774\pi$
$997$	154681.	−	231496.i	0.155613	−	0.232891i	0.901082	+	0.433649i	$0.142774\pi$
$998$	−116632.	−	89059.5i	−0.117100	−	0.0894168i
$999$	846984.	−	350832.i	0.848680	−	0.351535i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.5.j.a.3.3	✓	248
64.43	odd	16	inner	64.5.j.a.43.3	yes	248

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.5.j.a.3.3	✓	248	1.1	even	1	trivial
64.5.j.a.43.3	yes	248	64.43	odd	16	inner

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:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	64.j (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.78468 + 1.29468i) q^{2} +(4.98643 + 0.991863i) q^{3} +(12.6476 - 9.79988i) q^{4} +(-24.9007 - 16.6381i) q^{5} +(-20.1562 + 2.70193i) q^{6} +(16.4913 + 39.8136i) q^{7} +(-35.1796 + 53.4640i) q^{8} +(-50.9535 - 21.1056i) q^{9} +O(q^{10})\)	\(q+(-3.78468 + 1.29468i) q^{2} +(4.98643 + 0.991863i) q^{3} +(12.6476 - 9.79988i) q^{4} +(-24.9007 - 16.6381i) q^{5} +(-20.1562 + 2.70193i) q^{6} +(16.4913 + 39.8136i) q^{7} +(-35.1796 + 53.4640i) q^{8} +(-50.9535 - 21.1056i) q^{9} +(115.782 + 30.7316i) q^{10} +(-1.15335 - 5.79830i) q^{11} +(72.7867 - 36.3217i) q^{12} +(-142.622 + 95.2968i) q^{13} +(-113.960 - 129.331i) q^{14} +(-107.663 - 107.663i) q^{15} +(63.9249 - 247.890i) q^{16} +(-357.469 - 357.469i) q^{17} +(220.168 + 13.9098i) q^{18} +(-336.361 + 224.749i) q^{19} +(-477.986 + 33.5911i) q^{20} +(42.7432 + 214.885i) q^{21} +(11.8720 + 20.4515i) q^{22} +(-480.396 - 198.987i) q^{23} +(-228.449 + 231.701i) q^{24} +(104.040 + 251.175i) q^{25} +(416.399 - 545.317i) q^{26} +(-575.553 - 384.572i) q^{27} +(598.744 + 341.934i) q^{28} +(892.973 + 177.623i) q^{29} +(546.858 + 268.081i) q^{30} +1476.43 q^{31} +(79.0026 + 1020.95i) q^{32} -30.0568i q^{33} +(1815.71 + 890.100i) q^{34} +(251.777 - 1265.77i) q^{35} +(-851.274 + 232.402i) q^{36} +(-735.800 + 1101.20i) q^{37} +(982.040 - 1286.08i) q^{38} +(-805.695 + 333.730i) q^{39} +(1765.53 - 745.969i) q^{40} +(-616.031 + 1487.23i) q^{41} +(-439.976 - 757.932i) q^{42} +(-2111.94 + 420.090i) q^{43} +(-71.4098 - 62.0320i) q^{44} +(917.620 + 1373.31i) q^{45} +(2075.77 + 131.143i) q^{46} +(375.581 - 375.581i) q^{47} +(564.630 - 1172.68i) q^{48} +(384.607 - 384.607i) q^{49} +(-718.950 - 815.921i) q^{50} +(-1427.94 - 2137.06i) q^{51} +(-869.929 + 2602.95i) q^{52} +(847.405 - 168.559i) q^{53} +(2676.18 + 710.329i) q^{54} +(-67.7534 + 163.571i) q^{55} +(-2708.75 - 518.932i) q^{56} +(-1900.16 + 787.072i) q^{57} +(-3609.58 + 483.863i) q^{58} +(2342.76 - 3506.19i) q^{59} +(-2416.76 - 306.597i) q^{60} +(-212.809 + 1069.87i) q^{61} +(-5587.82 + 1911.50i) q^{62} -2376.70i q^{63} +(-1620.80 - 3761.68i) q^{64} +5136.93 q^{65} +(38.9139 + 113.755i) q^{66} +(1769.18 + 351.913i) q^{67} +(-8024.29 - 1017.98i) q^{68} +(-2198.10 - 1468.72i) q^{69} +(685.865 + 5116.50i) q^{70} +(-519.523 - 1254.24i) q^{71} +(2920.91 - 1981.69i) q^{72} +(5251.26 + 2175.14i) q^{73} +(1359.07 - 5120.32i) q^{74} +(269.658 + 1355.66i) q^{75} +(-2051.65 + 6138.83i) q^{76} +(211.831 - 141.541i) q^{77} +(2617.23 - 2306.17i) q^{78} +(-946.307 - 946.307i) q^{79} +(-5716.20 + 5109.05i) q^{80} +(670.335 + 670.335i) q^{81} +(405.999 - 6426.26i) q^{82} +(-2760.52 + 1844.52i) q^{83} +(2646.45 + 2298.90i) q^{84} +(2953.62 + 14848.8i) q^{85} +(7449.13 - 4324.18i) q^{86} +(4276.57 + 1771.41i) q^{87} +(350.575 + 142.319i) q^{88} +(-3435.74 - 8294.61i) q^{89} +(-5250.90 - 4009.54i) q^{90} +(-6146.12 - 4106.71i) q^{91} +(-8025.92 + 2191.12i) q^{92} +(7362.12 + 1464.42i) q^{93} +(-935.199 + 1907.71i) q^{94} +12115.0 q^{95} +(-618.700 + 5169.25i) q^{96} -14299.6i q^{97} +(-957.673 + 1953.56i) q^{98} +(-63.6094 + 319.786i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 248 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) \) 248 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9	\( 248 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20} - 8 q^{21} - 2672 q^{22} - 8 q^{23} - 288 q^{24} - 8 q^{25} + 5392 q^{26} - 8 q^{27} + 5632 q^{28} - 8 q^{29} + 4712 q^{30} - 16 q^{31} - 2528 q^{32} - 7088 q^{34} - 8 q^{35} - 18808 q^{36} - 8 q^{37} - 7568 q^{38} - 8 q^{39} + 352 q^{40} - 8 q^{41} + 16272 q^{42} - 8 q^{43} + 8416 q^{44} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 8 q^{48} - 8 q^{49} + 21520 q^{50} - 16136 q^{51} + 8968 q^{52} - 8 q^{53} - 15560 q^{54} + 23544 q^{55} - 24704 q^{56} - 8 q^{57} - 32768 q^{58} + 26104 q^{59} - 31976 q^{60} - 8 q^{61} - 6040 q^{62} + 12184 q^{64} - 16 q^{65} + 35544 q^{66} - 37768 q^{67} + 26632 q^{68} - 8 q^{69} + 61144 q^{70} - 39944 q^{71} + 40816 q^{72} - 8 q^{73} + 16624 q^{74} - 4616 q^{75} - 14152 q^{76} - 8 q^{77} - 103952 q^{78} + 50168 q^{79} - 115040 q^{80} - 8 q^{81} - 5208 q^{82} - 8 q^{83} + 57896 q^{84} - 8 q^{85} + 85168 q^{86} - 8 q^{87} + 71112 q^{88} - 8 q^{89} + 111592 q^{90} - 8 q^{91} + 79792 q^{92} - 656 q^{93} + 17944 q^{94} - 16 q^{95} - 25984 q^{96} - 76304 q^{98} + 640 q^{99}+O(q^{100}) \) 248 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 8 * q^20 - 8 * q^21 - 2672 * q^22 - 8 * q^23 - 288 * q^24 - 8 * q^25 + 5392 * q^26 - 8 * q^27 + 5632 * q^28 - 8 * q^29 + 4712 * q^30 - 16 * q^31 - 2528 * q^32 - 7088 * q^34 - 8 * q^35 - 18808 * q^36 - 8 * q^37 - 7568 * q^38 - 8 * q^39 + 352 * q^40 - 8 * q^41 + 16272 * q^42 - 8 * q^43 + 8416 * q^44 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 8 * q^48 - 8 * q^49 + 21520 * q^50 - 16136 * q^51 + 8968 * q^52 - 8 * q^53 - 15560 * q^54 + 23544 * q^55 - 24704 * q^56 - 8 * q^57 - 32768 * q^58 + 26104 * q^59 - 31976 * q^60 - 8 * q^61 - 6040 * q^62 + 12184 * q^64 - 16 * q^65 + 35544 * q^66 - 37768 * q^67 + 26632 * q^68 - 8 * q^69 + 61144 * q^70 - 39944 * q^71 + 40816 * q^72 - 8 * q^73 + 16624 * q^74 - 4616 * q^75 - 14152 * q^76 - 8 * q^77 - 103952 * q^78 + 50168 * q^79 - 115040 * q^80 - 8 * q^81 - 5208 * q^82 - 8 * q^83 + 57896 * q^84 - 8 * q^85 + 85168 * q^86 - 8 * q^87 + 71112 * q^88 - 8 * q^89 + 111592 * q^90 - 8 * q^91 + 79792 * q^92 - 656 * q^93 + 17944 * q^94 - 16 * q^95 - 25984 * q^96 - 76304 * q^98 + 640 * q^99

Introduction

L-functions

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