LMFDB - Embedded newform 235.4.g.b.6.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [235,4,Mod(6,235)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(235, base_ring=CyclotomicField(46))

chi = DirichletCharacter(H, H._module([0, 38]))

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

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

chi := DirichletCharacter("235.6");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 235 = 5 \cdot 47 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	235.g (of order $23$, degree $22$, 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:	$13.8654488513$
Analytic rank:	$0$
Dimension:	$550$
Relative dimension:	$25$ over $\Q(\zeta_{23})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{23}]$

Embedding invariants

Embedding label			6.5
Character	$\chi$	$=$	235.6
Dual form			235.4.g.b.196.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.67791 + 1.59754i) q^{2} +(-0.200738 + 2.93469i) q^{3} +(5.51447 - 5.90455i) q^{4} +(-4.27210 + 2.59792i) q^{5} +(-3.94999 - 11.1142i) q^{6} +(1.65591 + 7.96866i) q^{7} +(-0.106316 + 0.299145i) q^{8} +(18.1764 + 2.49829i) q^{9} +O(q^{10})$	\(q+(-3.67791 + 1.59754i) q^{2} +(-0.200738 + 2.93469i) q^{3} +(5.51447 - 5.90455i) q^{4} +(-4.27210 + 2.59792i) q^{5} +(-3.94999 - 11.1142i) q^{6} +(1.65591 + 7.96866i) q^{7} +(-0.106316 + 0.299145i) q^{8} +(18.1764 + 2.49829i) q^{9} +(11.5621 - 16.3798i) q^{10} +(-48.9088 + 39.7902i) q^{11} +(16.2210 + 17.3685i) q^{12} +(-8.36953 - 2.34503i) q^{13} +(-18.8206 - 26.6627i) q^{14} +(-6.76651 - 13.0588i) q^{15} +(4.32386 + 63.2126i) q^{16} +(-28.6293 - 23.2917i) q^{17} +(-70.8424 + 19.8491i) q^{18} +(-87.2724 - 53.0715i) q^{19} +(-8.21878 + 39.5510i) q^{20} +(-23.7179 + 3.25996i) q^{21} +(116.316 - 224.479i) q^{22} +(64.2484 + 27.9070i) q^{23} +(-0.856555 - 0.372054i) q^{24} +(11.5016 - 22.1971i) q^{25} +(34.5287 - 4.74586i) q^{26} +(-27.1392 + 130.601i) q^{27} +(56.1828 + 34.1655i) q^{28} +(-219.732 + 61.5659i) q^{29} +(45.7486 + 37.2192i) q^{30} +(8.03042 + 117.401i) q^{31} +(-118.056 - 227.838i) q^{32} +(-106.954 - 151.519i) q^{33} +(142.506 + 39.9282i) q^{34} +(-27.7761 - 29.7410i) q^{35} +(114.985 - 93.5469i) q^{36} +(167.436 - 237.203i) q^{37} +(405.764 + 55.7710i) q^{38} +(8.56202 - 24.0912i) q^{39} +(-0.322962 - 1.55418i) q^{40} +(-47.0624 - 132.421i) q^{41} +(82.0246 - 49.8802i) q^{42} +(316.020 - 338.374i) q^{43} +(-34.7622 + 508.206i) q^{44} +(-84.1418 + 36.5480i) q^{45} -280.883 q^{46} +(160.602 - 279.338i) q^{47} -186.377 q^{48} +(253.846 - 110.261i) q^{49} +(-6.84110 + 100.013i) q^{50} +(74.1008 - 79.3426i) q^{51} +(-59.9998 + 36.4867i) q^{52} +(-68.9451 - 193.993i) q^{53} +(-108.825 - 523.696i) q^{54} +(105.571 - 297.049i) q^{55} +(-2.55984 - 0.351841i) q^{56} +(173.267 - 245.464i) q^{57} +(709.799 - 577.464i) q^{58} +(346.984 + 371.529i) q^{59} +(-114.420 - 32.0589i) q^{60} +(-284.879 - 403.581i) q^{61} +(-217.088 - 418.960i) q^{62} +(10.1904 + 148.979i) q^{63} +(404.986 + 329.481i) q^{64} +(41.8476 - 11.7252i) q^{65} +(635.426 + 386.411i) q^{66} +(92.8600 - 446.867i) q^{67} +(-295.402 + 40.6021i) q^{68} +(-94.7955 + 182.947i) q^{69} +(149.671 + 65.0112i) q^{70} +(-707.712 - 307.403i) q^{71} +(-2.67980 + 5.17178i) q^{72} +(-653.557 + 89.8294i) q^{73} +(-236.874 + 1139.90i) q^{74} +(62.8328 + 38.2095i) q^{75} +(-794.624 + 222.643i) q^{76} +(-398.063 - 323.849i) q^{77} +(6.99638 + 102.284i) q^{78} +(261.886 + 505.416i) q^{79} +(-182.693 - 258.817i) q^{80} +(99.1820 + 27.7895i) q^{81} +(384.640 + 411.849i) q^{82} +(-1019.09 + 829.093i) q^{83} +(-111.543 + 158.021i) q^{84} +(182.817 + 25.1276i) q^{85} +(-621.725 + 1749.37i) q^{86} +(-136.568 - 657.202i) q^{87} +(-6.70326 - 18.8612i) q^{88} +(293.519 - 178.493i) q^{89} +(251.079 - 268.840i) q^{90} +(4.82761 - 70.5771i) q^{91} +(519.074 - 225.466i) q^{92} -346.146 q^{93} +(-144.427 + 1283.95i) q^{94} +510.712 q^{95} +(692.332 - 300.722i) q^{96} +(-59.0138 + 862.751i) q^{97} +(-757.476 + 811.059i) q^{98} +(-988.394 + 601.056i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 550 q + 4 q^{2} - 2 q^{3} - 102 q^{4} + 125 q^{5} + 44 q^{6} - 2 q^{7} - 6 q^{8} - 175 q^{9}+O(q^{10}) $ 550 * q + 4 * q^2 - 2 * q^3 - 102 * q^4 + 125 * q^5 + 44 * q^6 - 2 * q^7 - 6 * q^8 - 175 * q^9	\( 550 q + 4 q^{2} - 2 q^{3} - 102 q^{4} + 125 q^{5} + 44 q^{6} - 2 q^{7} - 6 q^{8} - 175 q^{9} - 20 q^{10} + 74 q^{11} - 677 q^{12} + 132 q^{13} - 83 q^{14} + 10 q^{15} - 602 q^{16} - 62 q^{17} - 95 q^{18} + 590 q^{19} + 510 q^{20} - 148 q^{21} + 178 q^{22} - 2244 q^{23} + 625 q^{24} - 625 q^{25} - 2530 q^{26} + 472 q^{27} + 68 q^{28} - 40 q^{29} + 1505 q^{30} - 16 q^{31} + 301 q^{32} + 200 q^{33} + 104 q^{34} + 10 q^{35} - 778 q^{36} + 3435 q^{37} + 1724 q^{38} + 578 q^{39} + 30 q^{40} - 442 q^{41} - 3709 q^{42} - 484 q^{43} - 12170 q^{44} + 875 q^{45} + 614 q^{46} - 1743 q^{47} - 962 q^{48} - 2509 q^{49} + 100 q^{50} + 390 q^{51} - 7609 q^{52} + 758 q^{53} + 1373 q^{54} - 140 q^{55} + 106 q^{56} + 6740 q^{57} + 4800 q^{58} + 8566 q^{59} - 295 q^{60} + 1364 q^{61} - 7252 q^{62} - 3122 q^{63} - 4010 q^{64} - 660 q^{65} + 24646 q^{66} - 68 q^{67} - 905 q^{68} - 2624 q^{69} + 185 q^{70} - 318 q^{71} - 3352 q^{72} + 428 q^{73} + 506 q^{74} - 50 q^{75} + 2495 q^{76} + 18134 q^{77} + 16762 q^{78} + 4620 q^{79} - 785 q^{80} - 14403 q^{81} + 11899 q^{82} + 90 q^{83} + 15755 q^{84} + 310 q^{85} - 4050 q^{86} - 5440 q^{87} - 439 q^{88} - 2148 q^{89} + 475 q^{90} - 9933 q^{91} - 36335 q^{92} - 4472 q^{93} - 3725 q^{94} + 270 q^{95} - 1421 q^{96} - 7342 q^{97} - 39381 q^{98} - 11821 q^{99}+O(q^{100}) \) 550 * q + 4 * q^2 - 2 * q^3 - 102 * q^4 + 125 * q^5 + 44 * q^6 - 2 * q^7 - 6 * q^8 - 175 * q^9 - 20 * q^10 + 74 * q^11 - 677 * q^12 + 132 * q^13 - 83 * q^14 + 10 * q^15 - 602 * q^16 - 62 * q^17 - 95 * q^18 + 590 * q^19 + 510 * q^20 - 148 * q^21 + 178 * q^22 - 2244 * q^23 + 625 * q^24 - 625 * q^25 - 2530 * q^26 + 472 * q^27 + 68 * q^28 - 40 * q^29 + 1505 * q^30 - 16 * q^31 + 301 * q^32 + 200 * q^33 + 104 * q^34 + 10 * q^35 - 778 * q^36 + 3435 * q^37 + 1724 * q^38 + 578 * q^39 + 30 * q^40 - 442 * q^41 - 3709 * q^42 - 484 * q^43 - 12170 * q^44 + 875 * q^45 + 614 * q^46 - 1743 * q^47 - 962 * q^48 - 2509 * q^49 + 100 * q^50 + 390 * q^51 - 7609 * q^52 + 758 * q^53 + 1373 * q^54 - 140 * q^55 + 106 * q^56 + 6740 * q^57 + 4800 * q^58 + 8566 * q^59 - 295 * q^60 + 1364 * q^61 - 7252 * q^62 - 3122 * q^63 - 4010 * q^64 - 660 * q^65 + 24646 * q^66 - 68 * q^67 - 905 * q^68 - 2624 * q^69 + 185 * q^70 - 318 * q^71 - 3352 * q^72 + 428 * q^73 + 506 * q^74 - 50 * q^75 + 2495 * q^76 + 18134 * q^77 + 16762 * q^78 + 4620 * q^79 - 785 * q^80 - 14403 * q^81 + 11899 * q^82 + 90 * q^83 + 15755 * q^84 + 310 * q^85 - 4050 * q^86 - 5440 * q^87 - 439 * q^88 - 2148 * q^89 + 475 * q^90 - 9933 * q^91 - 36335 * q^92 - 4472 * q^93 - 3725 * q^94 + 270 * q^95 - 1421 * q^96 - 7342 * q^97 - 39381 * q^98 - 11821 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/235\mathbb{Z}\right)^\times$.

$n$	$142$	$146$
$\chi(n)$	$1$	$e\left(\frac{19}{23}\right)$

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 $

$2$	−3.67791	+	1.59754i	−1.30034	+	0.564817i	−0.931183	−	0.364551i	$-0.881222\pi$
$2$	−3.67791	+	1.59754i	−1.30034	+	0.564817i	−0.369155	+	0.929368i	$0.620353\pi$
$3$	−0.200738	+	2.93469i	−0.0386321	+	0.564781i	0.937553	+	0.347842i	$0.113085\pi$
$3$	−0.200738	+	2.93469i	−0.0386321	+	0.564781i	−0.976185	+	0.216939i	$0.930393\pi$
$4$	5.51447	−	5.90455i	0.689308	−	0.738069i
$5$	−4.27210	+	2.59792i	−0.382108	+	0.232365i
$5$	−4.27210	+	2.59792i	−0.382108	+	0.232365i
$6$	−3.94999	−	11.1142i	−0.268763	−	0.756226i
$7$	1.65591	+	7.96866i	0.0894106	+	0.430267i	0.999861	+	0.0166500i	$0.00530010\pi$
$7$	1.65591	+	7.96866i	0.0894106	+	0.430267i	−0.910451	+	0.413617i	$0.864265\pi$
$8$	−0.106316	+	0.299145i	−0.00469856	+	0.0132205i
$9$	18.1764	+	2.49829i	0.673201	+	0.0925294i
$10$	11.5621	−	16.3798i	0.365626	−	0.517974i
$11$	−48.9088	+	39.7902i	−1.34060	+	1.09066i	−0.352666	+	0.935749i	$0.614725\pi$
$11$	−48.9088	+	39.7902i	−1.34060	+	1.09066i	−0.987929	+	0.154906i	$0.950493\pi$
$12$	16.2210	+	17.3685i	0.390218	+	0.417821i
$13$	−8.36953	−	2.34503i	−0.178561	−	0.0500304i	0.179354	−	0.983785i	$-0.442599\pi$
$13$	−8.36953	−	2.34503i	−0.178561	−	0.0500304i	−0.357915	+	0.933754i	$0.616512\pi$
$14$	−18.8206	−	26.6627i	−0.359286	−	0.508992i
$15$	−6.76651	−	13.0588i	−0.116474	−	0.224784i
$16$	4.32386	+	63.2126i	0.0675604	+	0.987697i
$17$	−28.6293	−	23.2917i	−0.408449	−	0.332298i	0.404600	−	0.914494i	$-0.367411\pi$
$17$	−28.6293	−	23.2917i	−0.408449	−	0.332298i	−0.813048	+	0.582196i	$0.802194\pi$
$18$	−70.8424	+	19.8491i	−0.927651	+	0.259916i
$19$	−87.2724	−	53.0715i	−1.05377	−	0.640813i	−0.117854	−	0.993031i	$-0.537601\pi$
$19$	−87.2724	−	53.0715i	−1.05377	−	0.640813i	−0.935918	+	0.352218i	$0.885428\pi$
$20$	−8.21878	+	39.5510i	−0.0918888	+	0.442193i
$21$	−23.7179	+	3.25996i	−0.246461	+	0.0338753i
$22$	116.316	−	224.479i	1.12721	−	2.17541i
$23$	64.2484	+	27.9070i	0.582466	+	0.253001i	0.669018	−	0.743247i	$-0.266715\pi$
$23$	64.2484	+	27.9070i	0.582466	+	0.253001i	−0.0865512	+	0.996247i	$0.527585\pi$
$24$	−0.856555	−	0.372054i	−0.00728515	−	0.00316439i
$25$	11.5016	−	22.1971i	0.0920130	−	0.177577i
$26$	34.5287	−	4.74586i	0.260447	−	0.0357977i
$27$	−27.1392	+	130.601i	−0.193442	+	0.930896i
$28$	56.1828	+	34.1655i	0.379198	+	0.230596i
$29$	−219.732	+	61.5659i	−1.40700	+	0.394224i	−0.887723	−	0.460379i	$-0.847714\pi$
$29$	−219.732	+	61.5659i	−1.40700	+	0.394224i	−0.519282	+	0.854603i	$0.673801\pi$
$30$	45.7486	+	37.2192i	0.278417	+	0.226509i
$31$	8.03042	+	117.401i	0.0465260	+	0.680186i	0.961175	+	0.275938i	$0.0889885\pi$
$31$	8.03042	+	117.401i	0.0465260	+	0.680186i	−0.914649	+	0.404248i	$0.867533\pi$
$32$	−118.056	−	227.838i	−0.652174	−	1.25864i
$33$	−106.954	−	151.519i	−0.564191	−	0.799277i
$34$	142.506	+	39.9282i	0.718809	+	0.201401i
$35$	−27.7761	−	29.7410i	−0.134144	−	0.143633i
$36$	114.985	−	93.5469i	0.532336	−	0.433087i
$37$	167.436	−	237.203i	0.743956	−	1.05395i	−0.252313	−	0.967646i	$-0.581191\pi$
$37$	167.436	−	237.203i	0.743956	−	1.05395i	0.996269	−	0.0862998i	$-0.0275043\pi$
$38$	405.764	+	55.7710i	1.73220	+	0.238086i
$39$	8.56202	−	24.0912i	0.0351544	−	0.0989149i
$40$	−0.322962	−	1.55418i	−0.00127662	−	0.00614343i
$41$	−47.0624	−	132.421i	−0.179266	−	0.504407i	0.818248	−	0.574865i	$-0.194945\pi$
$41$	−47.0624	−	132.421i	−0.179266	−	0.504407i	−0.997515	+	0.0704577i	$0.977554\pi$
$42$	82.0246	−	49.8802i	0.301349	−	0.183254i
$43$	316.020	−	338.374i	1.12076	−	1.20004i	0.143127	−	0.989704i	$-0.454284\pi$
$43$	316.020	−	338.374i	1.12076	−	1.20004i	0.977630	−	0.210333i	$-0.0674548\pi$
$44$	−34.7622	+	508.206i	−0.119105	+	1.74125i
$45$	−84.1418	+	36.5480i	−0.278736	+	0.121072i
$46$	−280.883			−0.900302
$47$	160.602	−	279.338i	0.498431	−	0.866929i
$47$	160.602	−	279.338i	0.498431	−	0.866929i
$48$	−186.377			−0.560443
$49$	253.846	−	110.261i	0.740076	−	0.321460i
$50$	−6.84110	+	100.013i	−0.0193496	+	0.282881i
$51$	74.1008	−	79.3426i	0.203455	−	0.217847i
$52$	−59.9998	+	36.4867i	−0.160009	+	0.0973037i
$53$	−68.9451	−	193.993i	−0.178686	−	0.502773i	0.818765	−	0.574128i	$-0.194659\pi$
$53$	−68.9451	−	193.993i	−0.178686	−	0.502773i	−0.997451	+	0.0713552i	$0.977268\pi$
$54$	−108.825	−	523.696i	−0.274245	−	1.31974i
$55$	105.571	−	297.049i	0.258822	−	0.728255i
$56$	−2.55984	−	0.351841i	−0.00610844	−	0.000839585i
$57$	173.267	−	245.464i	0.402628	−	0.570394i
$58$	709.799	−	577.464i	1.60692	−	1.30732i
$59$	346.984	+	371.529i	0.765652	+	0.819813i	0.987886	−	0.155180i	$-0.0495959\pi$
$59$	346.984	+	371.529i	0.765652	+	0.819813i	−0.222234	+	0.974993i	$0.571335\pi$
$60$	−114.420	−	32.0589i	−0.246192	−	0.0689798i
$61$	−284.879	−	403.581i	−0.597951	−	0.847103i	0.399626	−	0.916678i	$-0.369140\pi$
$61$	−284.879	−	403.581i	−0.597951	−	0.847103i	−0.997577	+	0.0695751i	$0.977836\pi$
$62$	−217.088	−	418.960i	−0.444680	−	0.858193i
$63$	10.1904	+	148.979i	0.0203789	+	0.297930i
$64$	404.986	+	329.481i	0.790988	+	0.643517i
$65$	41.8476	−	11.7252i	0.0798548	−	0.0223743i
$66$	635.426	+	386.411i	1.18508	+	0.720665i
$67$	92.8600	−	446.867i	0.169323	−	0.814828i	−0.805630	−	0.592419i	$-0.798173\pi$
$67$	92.8600	−	446.867i	0.169323	−	0.814828i	0.974953	−	0.222409i	$-0.0713921\pi$
$68$	−295.402	+	40.6021i	−0.526806	+	0.0724078i
$69$	−94.7955	+	182.947i	−0.165392	+	0.319192i
$70$	149.671	+	65.0112i	0.255558	+	0.111005i
$71$	−707.712	−	307.403i	−1.18296	−	0.513831i	−0.286982	−	0.957936i	$-0.592652\pi$
$71$	−707.712	−	307.403i	−1.18296	−	0.513831i	−0.895975	+	0.444105i	$0.853522\pi$
$72$	−2.67980	+	5.17178i	−0.00438635	+	0.00846528i
$73$	−653.557	+	89.8294i	−1.04785	+	0.144024i	−0.639492	−	0.768798i	$-0.720855\pi$
$73$	−653.557	+	89.8294i	−1.04785	+	0.144024i	−0.408359	+	0.912822i	$0.633899\pi$
$74$	−236.874	+	1139.90i	−0.372108	+	1.79068i
$75$	62.8328	+	38.2095i	0.0967374	+	0.0588273i
$76$	−794.624	+	222.643i	−1.19934	+	0.336039i
$77$	−398.063	−	323.849i	−0.589137	−	0.479298i
$78$	6.99638	+	102.284i	0.0101562	+	0.148479i
$79$	261.886	+	505.416i	0.372968	+	0.719795i	0.998157	−	0.0606779i	$-0.0193262\pi$
$79$	261.886	+	505.416i	0.372968	+	0.719795i	−0.625190	+	0.780473i	$0.714978\pi$
$80$	−182.693	−	258.817i	−0.255322	−	0.361708i
$81$	99.1820	+	27.7895i	0.136052	+	0.0381200i
$82$	384.640	+	411.849i	0.518004	+	0.554647i
$83$	−1019.09	+	829.093i	−1.34771	+	1.09644i	−0.361245	+	0.932471i	$0.617648\pi$
$83$	−1019.09	+	829.093i	−1.34771	+	1.09644i	−0.986465	+	0.163972i	$0.947569\pi$
$84$	−111.543	+	158.021i	−0.144885	+	0.205256i
$85$	182.817	+	25.1276i	0.233286	+	0.0320644i
$86$	−621.725	+	1749.37i	−0.779562	+	2.19348i
$87$	−136.568	−	657.202i	−0.168295	−	0.809879i
$88$	−6.70326	−	18.8612i	−0.00812011	−	0.0228478i
$89$	293.519	−	178.493i	0.349584	−	0.212587i	−0.333803	−	0.942643i	$-0.608332\pi$
$89$	293.519	−	178.493i	0.349584	−	0.212587i	0.683387	+	0.730056i	$0.260506\pi$
$90$	251.079	−	268.840i	0.294068	−	0.314869i
$91$	4.82761	−	70.5771i	0.00556122	−	0.0813021i
$92$	519.074	−	225.466i	0.588231	−	0.255505i
$93$	−346.146			−0.385953
$94$	−144.427	+	1283.95i	−0.158473	+	1.40882i
$95$	510.712			0.551557
$96$	692.332	−	300.722i	0.736050	−	0.319712i
$97$	−59.0138	+	862.751i	−0.0617726	+	0.903084i	0.858750	+	0.512395i	$0.171241\pi$
$97$	−59.0138	+	862.751i	−0.0617726	+	0.903084i	−0.920523	+	0.390689i	$0.872237\pi$
$98$	−757.476	+	811.059i	−0.780782	+	0.836014i
$99$	−988.394	+	601.056i	−1.00341	+	0.610186i
$100$	−67.6388	−	190.317i	−0.0676388	−	0.190317i
$101$	−303.428	−	1460.18i	−0.298933	−	1.43854i	−0.813736	−	0.581235i	$-0.802570\pi$
$101$	−303.428	−	1460.18i	−0.298933	−	1.43854i	0.514803	−	0.857309i	$-0.327865\pi$
$102$	−145.783	+	410.194i	−0.141516	+	0.398189i
$103$	1290.99	+	177.442i	1.23500	+	0.169747i	0.723978	−	0.689823i	$-0.242311\pi$
$103$	1290.99	+	177.442i	1.23500	+	0.169747i	0.511019	+	0.859569i	$0.329268\pi$
$104$	1.59132	−	2.25439i	0.00150040	−	0.00212559i
$105$	92.8562	−	75.5441i	0.0863032	−	0.0702129i
$106$	563.486	+	603.346i	0.516326	+	0.552850i
$107$	−1831.45	−	513.148i	−1.65470	−	0.463625i	−0.689316	−	0.724461i	$-0.742089\pi$
$107$	−1831.45	−	513.148i	−1.65470	−	0.463625i	−0.965383	+	0.260836i	$0.916002\pi$
$108$	621.483	+	880.440i	0.553724	+	0.784448i
$109$	−8.95604	−	17.2844i	−0.00787003	−	0.0151885i	0.883918	−	0.467642i	$-0.154897\pi$
$109$	−8.95604	−	17.2844i	−0.00787003	−	0.0151885i	−0.891788	+	0.452454i	$0.850549\pi$
$110$	86.2666	+	1261.17i	0.0747745	+	1.09317i
$111$	662.507	+	538.989i	0.566508	+	0.460888i
$112$	−496.560	+	139.130i	−0.418933	+	0.117380i
$113$	−4.95949	−	3.01593i	−0.00412875	−	0.00251075i	0.517518	−	0.855672i	$-0.326856\pi$
$113$	−4.95949	−	3.01593i	−0.00412875	−	0.00251075i	−0.521647	+	0.853162i	$0.674682\pi$
$114$	−245.123	+	1179.60i	−0.201385	+	0.969116i
$115$	−346.976	+	47.6907i	−0.281354	+	0.0386712i
$116$	−848.183	+	1636.92i	−0.678895	+	1.31021i
$117$	−146.270	−	63.5338i	−0.115578	−	0.0502026i
$118$	−1869.71	−	812.129i	−1.45865	−	0.633581i
$119$	138.196	−	266.706i	0.106457	−	0.205453i
$120$	4.62586	−	0.635809i	0.00351901	−	0.000483676i
$121$	538.005	−	2589.02i	0.404211	−	1.94517i
$122$	1692.50	+	1029.23i	1.25600	+	0.763788i
$123$	398.062	−	111.532i	0.291805	−	0.0817599i
$124$	737.481	+	599.986i	0.534095	+	0.434518i
$125$	8.53030	+	124.709i	0.00610379	+	0.0892342i
$126$	−275.479	−	531.651i	−0.194775	−	0.375899i
$127$	−1279.57	−	1812.73i	−0.894041	−	1.26657i	−0.963152	−	0.268959i	$-0.913320\pi$
$127$	−1279.57	−	1812.73i	−0.894041	−	1.26657i	0.0691101	−	0.997609i	$-0.477984\pi$
$128$	−39.1281	−	10.9632i	−0.0270193	−	0.00757044i
$129$	929.586	+	995.343i	0.634461	+	0.679342i
$130$	−135.180	+	109.977i	−0.0912009	+	0.0741974i
$131$	−604.139	+	855.871i	−0.402931	+	0.570823i	−0.966959	−	0.254933i	$-0.917947\pi$
$131$	−604.139	+	855.871i	−0.402931	+	0.570823i	0.564028	+	0.825756i	$0.309251\pi$
$132$	−1484.45	−	204.033i	−0.978823	−	0.134536i
$133$	278.394	−	783.326i	0.181503	−	0.510699i
$134$	372.358	+	1791.88i	0.240051	+	1.15519i
$135$	−223.350	−	628.446i	−0.142392	−	0.400652i
$136$	10.0113	−	6.08804i	0.00631225	−	0.00383856i
$137$	189.924	−	203.359i	0.118440	−	0.126818i	−0.668860	−	0.743388i	$-0.733217\pi$
$137$	189.924	−	203.359i	0.118440	−	0.126818i	0.787300	+	0.616570i	$0.211478\pi$
$138$	56.3839	−	824.303i	0.0347805	−	0.508473i
$139$	−827.507	+	359.437i	−0.504952	+	0.219331i	−0.635486	−	0.772112i	$-0.719200\pi$
$139$	−827.507	+	359.437i	−0.504952	+	0.219331i	0.130535	+	0.991444i	$0.458331\pi$
$140$	−328.778			−0.198477
$141$	787.531	+	527.392i	0.470369	+	0.314996i
$142$	3093.99			1.82846
$143$	502.653	−	218.333i	0.293943	−	0.127678i
$144$	−79.3313	+	1159.78i	−0.0459093	+	0.671170i
$145$	778.771	−	833.860i	0.446024	−	0.477575i
$146$	2260.22	−	1374.47i	1.28121	−	0.779123i
$147$	272.625	+	767.092i	0.152964	+	0.430399i
$148$	−477.257	−	2296.69i	−0.265069	−	1.27558i
$149$	−1111.03	+	3126.14i	−0.610867	+	1.71881i	0.0809281	+	0.996720i	$0.474212\pi$
$149$	−1111.03	+	3126.14i	−0.610867	+	1.71881i	−0.691795	+	0.722094i	$0.743180\pi$
$150$	−292.135	−	40.1530i	−0.159018	−	0.0218565i
$151$	463.094	−	656.055i	0.249577	−	0.353570i	−0.672825	−	0.739802i	$-0.734919\pi$
$151$	463.094	−	656.055i	0.249577	−	0.353570i	0.922402	+	0.386232i	$0.126224\pi$
$152$	25.1546	−	20.4647i	0.0134231	−	0.0109205i
$153$	−462.189	−	494.884i	−0.244221	−	0.261497i
$154$	1981.40	+	555.163i	1.03679	+	0.290496i
$155$	−339.304	−	480.684i	−0.175829	−	0.249094i
$156$	−95.0328	−	183.405i	−0.0487738	−	0.0941292i
$157$	−46.6863	−	682.530i	−0.0237323	−	0.346954i	−0.994337	−	0.106274i	$-0.966108\pi$
$157$	−46.6863	−	682.530i	−0.0237323	−	0.346954i	0.970605	−	0.240680i	$-0.0773704\pi$
$158$	−1770.62	−	1440.50i	−0.891536	−	0.725318i
$159$	583.148	−	163.391i	0.290860	−	0.0814950i
$160$	1096.25	+	666.646i	0.541665	+	0.329394i
$161$	−115.992	+	558.186i	−0.0567794	+	0.273237i
$162$	−409.177	+	56.2401i	−0.198445	+	0.0272756i
$163$	229.962	−	443.806i	0.110503	−	0.213261i	−0.826208	−	0.563366i	$-0.809506\pi$
$163$	229.962	−	443.806i	0.110503	−	0.213261i	0.936711	+	0.350105i	$0.113854\pi$
$164$	−1041.41	−	452.349i	−0.495857	−	0.215381i
$165$	850.553	+	369.447i	0.401306	+	0.174312i
$166$	2423.62	−	4677.37i	1.13319	−	2.18696i
$167$	1786.39	−	245.534i	0.827755	−	0.113772i	0.290163	−	0.956977i	$-0.406290\pi$
$167$	1786.39	−	245.534i	0.827755	−	0.113772i	0.537592	+	0.843205i	$0.319334\pi$
$168$	1.54640	−	7.44169i	0.000710163	−	0.00341749i
$169$	−1812.61	−	1102.27i	−0.825039	−	0.501717i
$170$	−712.528	+	199.641i	−0.321461	+	0.0900692i
$171$	−1453.71	−	1182.68i	−0.650106	−	0.528901i
$172$	−255.269	−	3731.91i	−0.113163	−	1.65439i
$173$	805.675	+	1554.88i	0.354071	+	0.683327i	0.996552	−	0.0829756i	$-0.0264424\pi$
$173$	805.675	+	1554.88i	0.354071	+	0.683327i	−0.642480	+	0.766302i	$0.722095\pi$
$174$	1552.19	+	2198.96i	0.676273	+	0.958060i
$175$	195.927	+	54.8962i	0.0846325	+	0.0237129i
$176$	−2726.72	−	2919.60i	−1.16781	−	1.25042i
$177$	−1159.97	+	943.709i	−0.492593	+	0.400754i
$178$	−794.388	+	1125.39i	−0.334505	+	0.473885i
$179$	−3789.58	−	520.866i	−1.58238	−	0.217494i	−0.709243	−	0.704964i	$-0.750963\pi$
$179$	−3789.58	−	520.866i	−1.58238	−	0.217494i	−0.873140	+	0.487470i	$0.837920\pi$
$180$	−248.198	+	698.362i	−0.102775	+	0.289182i
$181$	−96.9704	−	466.647i	−0.0398218	−	0.191633i	0.954473	−	0.298296i	$-0.0964183\pi$
$181$	−96.9704	−	466.647i	−0.0398218	−	0.191633i	−0.994295	+	0.106663i	$0.965983\pi$
$182$	94.9944	+	267.289i	0.0386893	+	0.108861i
$183$	1241.57	−	755.016i	0.501528	−	0.304986i
$184$	−15.1789	+	16.2526i	−0.00608154	+	0.00651174i
$185$	−99.0693	+	1448.34i	−0.0393715	+	0.575590i
$186$	1273.09	−	552.983i	0.501870	−	0.217993i
$187$	2327.01			0.909987
$188$	−763.730	−	2488.69i	−0.296281	−	0.965458i
$189$	−1085.66			−0.417830
$190$	−1878.35	+	815.884i	−0.717211	+	0.311529i
$191$	−141.957	+	2075.34i	−0.0537784	+	0.786212i	0.890068	+	0.455828i	$0.150657\pi$
$191$	−141.957	+	2075.34i	−0.0537784	+	0.786212i	−0.943846	+	0.330385i	$0.892822\pi$
$192$	−1048.22	+	1122.37i	−0.394003	+	0.421875i
$193$	−1321.10	+	803.377i	−0.492718	+	0.299629i	−0.743876	−	0.668317i	$-0.767015\pi$
$193$	−1321.10	+	803.377i	−0.492718	+	0.299629i	0.251158	+	0.967946i	$0.419189\pi$
$194$	−1161.23	−	3267.40i	−0.429751	−	1.20920i
$195$	26.0093	+	125.163i	0.00955160	+	0.0459648i
$196$	748.784	−	2106.88i	0.272880	−	0.767812i
$197$	−1953.34	−	268.480i	−0.706445	−	0.0970987i	−0.226005	−	0.974126i	$-0.572567\pi$
$197$	−1953.34	−	268.480i	−0.706445	−	0.0970987i	−0.480440	+	0.877027i	$0.659523\pi$
$198$	2675.01	−	3789.63i	0.960126	−	1.36019i
$199$	996.172	−	810.446i	0.354858	−	0.288698i	−0.436929	−	0.899496i	$-0.643934\pi$
$199$	996.172	−	810.446i	0.354858	−	0.288698i	0.791787	+	0.610798i	$0.209151\pi$
$200$	5.41735	+	5.80057i	0.00191532	+	0.00205081i
$201$	1292.77	+	362.218i	0.453658	+	0.127109i
$202$	3448.67	+	4885.66i	1.20123	+	1.70175i
$203$	−854.453	−	1649.02i	−0.295423	−	0.570140i
$204$	−59.8560	−	875.064i	−0.0205429	−	0.300327i
$205$	545.075	+	443.451i	0.185706	+	0.151083i
$206$	−5031.61	+	1409.79i	−1.70179	+	0.476819i
$207$	1098.09	+	667.762i	0.368707	+	0.224216i
$208$	112.047	−	539.199i	0.0373512	−	0.179744i
$209$	6380.11	−	876.926i	2.11159	−	0.290231i
$210$	−220.832	+	426.186i	−0.0725660	+	0.140046i
$211$	4154.40	+	1804.51i	1.35545	+	0.588757i	0.946176	−	0.323653i	$-0.104911\pi$
$211$	4154.40	+	1804.51i	1.35545	+	0.588757i	0.409278	+	0.912410i	$0.365781\pi$
$212$	−1525.64	−	662.677i	−0.494251	−	0.214683i
$213$	1044.20	−	2015.21i	0.335902	−	0.648261i
$214$	7555.68	−	1038.50i	2.41353	−	0.331732i
$215$	−470.997	+	2266.56i	−0.149403	+	0.718968i
$216$	−36.1833	−	22.0036i	−0.0113980	−	0.00693127i
$217$	−922.228	+	258.396i	−0.288502	+	0.0808345i
$218$	60.5520	+	49.2627i	0.0188124	+	0.0153050i
$219$	−132.427	−	1936.02i	−0.0408612	−	0.597370i
$220$	−1171.77	−	2261.42i	−0.359094	−	0.693021i
$221$	184.994	+	262.077i	0.0563079	+	0.0797702i
$222$	−3297.70	−	923.972i	−0.996969	−	0.279337i
$223$	−299.774	−	320.980i	−0.0900195	−	0.0963874i	0.684235	−	0.729261i	$-0.260136\pi$
$223$	−299.774	−	320.980i	−0.0900195	−	0.0963874i	−0.774255	+	0.632874i	$0.781875\pi$
$224$	1620.07	−	1318.03i	0.483240	−	0.393145i
$225$	264.513	−	374.730i	0.0783743	−	0.111031i
$226$	23.0586	+	3.16934i	0.00678689	+	0.000932836i
$227$	1368.24	−	3849.86i	0.400059	−	1.12566i	−0.555669	−	0.831404i	$-0.687538\pi$
$227$	1368.24	−	3849.86i	0.400059	−	1.12566i	0.955727	−	0.294253i	$-0.0950710\pi$
$228$	−493.877	−	2376.67i	−0.143455	−	0.690345i
$229$	−1511.00	−	4251.56i	−0.436026	−	1.22686i	−0.933247	−	0.359236i	$-0.883037\pi$
$229$	−1511.00	−	4251.56i	−0.436026	−	1.22686i	0.497220	−	0.867624i	$-0.334354\pi$
$230$	1199.96	−	729.711i	0.344013	−	0.209199i
$231$	1030.30	−	1103.18i	0.293458	−	0.314217i
$232$	4.94389	−	72.2771i	0.00139906	−	0.0204535i
$233$	668.210	−	290.245i	0.187879	−	0.0816076i	−0.302366	−	0.953192i	$-0.597777\pi$
$233$	668.210	−	290.245i	0.187879	−	0.0816076i	0.490246	+	0.871584i	$0.336907\pi$
$234$	639.464			0.178646
$235$	39.5891	+	1610.59i	0.0109894	+	0.447079i
$236$	4107.14			1.13285
$237$	−1535.81	+	667.096i	−0.420935	+	0.182838i
$238$	−82.1983	+	1201.70i	−0.0223871	+	0.327287i
$239$	−4718.80	+	5052.60i	−1.27713	+	1.36747i	−0.380442	+	0.924805i	$0.624228\pi$
$239$	−4718.80	+	5052.60i	−1.27713	+	1.36747i	−0.896687	+	0.442666i	$0.854033\pi$
$240$	796.222	−	484.193i	0.214150	−	0.130227i
$241$	−572.026	−	1609.53i	−0.152894	−	0.430203i	0.840934	−	0.541138i	$-0.182007\pi$
$241$	−572.026	−	1609.53i	−0.152894	−	0.430203i	−0.993828	+	0.110936i	$0.964615\pi$
$242$	2157.34	+	10381.7i	0.573053	+	2.75768i
$243$	−1307.55	+	3679.10i	−0.345183	+	0.971253i
$244$	−3953.92	−	543.454i	−1.03739	−	0.142586i
$245$	−798.006	+	1130.52i	−0.208093	+	0.294800i
$246$	−1285.86	+	1046.12i	−0.333266	+	0.271132i
$247$	605.974	+	648.840i	0.156102	+	0.167145i
$248$	−35.9736	−	10.0793i	−0.00921098	−	0.00258080i
$249$	−2228.56	−	3157.15i	−0.567185	−	0.803518i
$250$	−230.601	−	445.040i	−0.0583379	−	0.112587i
$251$	−80.9420	−	1183.33i	−0.0203546	−	0.297574i	−0.996689	−	0.0813079i	$-0.974090\pi$
$251$	−80.9420	−	1183.33i	−0.0203546	−	0.297574i	0.976334	−	0.216266i	$-0.0693880\pi$
$252$	935.848	+	761.368i	0.233940	+	0.190324i
$253$	−4252.74	+	1191.56i	−1.05679	+	0.296098i
$254$	7602.06	+	4622.91i	1.87793	+	1.14200i
$255$	−110.440	+	531.467i	−0.0271217	+	0.130517i
$256$	−3976.34	+	546.536i	−0.970787	+	0.133432i
$257$	375.854	−	725.366i	0.0912262	−	0.176059i	−0.837898	−	0.545828i	$-0.816215\pi$
$257$	375.854	−	725.366i	0.0912262	−	0.176059i	0.929124	+	0.369769i	$0.120563\pi$
$258$	−5009.04	−	2175.73i	−1.20872	−	0.525020i
$259$	2167.45	+	941.457i	0.519996	+	0.225866i
$260$	161.536	−	311.749i	0.0385308	−	0.0743611i
$261$	−4147.74	+	570.094i	−0.983674	+	0.135203i
$262$	854.682	−	4112.95i	0.201536	−	0.969844i
$263$	5496.73	+	3342.64i	1.28876	+	0.783710i	0.985578	−	0.169223i	$-0.0541259\pi$
$263$	5496.73	+	3342.64i	1.28876	+	0.783710i	0.303179	+	0.952934i	$0.401952\pi$
$264$	56.6972	−	15.8858i	0.0132177	−	0.00370342i
$265$	798.518	+	649.643i	0.185104	+	0.150593i
$266$	227.488	+	3325.75i	0.0524367	+	0.766597i
$267$	464.901	+	897.217i	0.106560	+	0.205651i
$268$	−2126.47	−	3012.53i	−0.484683	−	0.686640i
$269$	4105.21	+	1150.23i	0.930479	+	0.260708i	0.701456	−	0.712713i	$-0.252534\pi$
$269$	4105.21	+	1150.23i	0.930479	+	0.260708i	0.229023	+	0.973421i	$0.426447\pi$
$270$	1825.43	+	1954.56i	0.411452	+	0.440558i
$271$	−5870.04	+	4775.63i	−1.31579	+	1.07048i	−0.323541	+	0.946214i	$0.604873\pi$
$271$	−5870.04	+	4775.63i	−1.31579	+	1.07048i	−0.992250	+	0.124261i	$0.960344\pi$
$272$	1348.54	−	1910.44i	0.300615	−	0.425874i
$273$	206.153	+	28.3350i	0.0457030	+	0.00628174i
$274$	−373.649	+	1051.35i	−0.0823830	+	0.231804i
$275$	320.699	+	1543.29i	0.0703231	+	0.338413i
$276$	557.474	+	1568.58i	0.121580	+	0.342092i
$277$	−3126.90	+	1901.51i	−0.678257	+	0.412457i	−0.816032	−	0.578006i	$-0.803831\pi$
$277$	−3126.90	+	1901.51i	−0.678257	+	0.412457i	0.137775	+	0.990463i	$0.456005\pi$
$278$	2469.28	−	2643.96i	0.532726	−	0.570410i
$279$	−147.337	+	2153.99i	−0.0316158	+	0.462207i
$280$	11.8499	−	5.14715i	0.00252917	−	0.00109857i
$281$	−4740.87			−1.00647			−0.503233	−	0.864151i	$-0.667856\pi$
$281$	−4740.87			−1.00647			−0.503233	+	0.864151i	$0.667856\pi$
$282$	−3739.00	−	681.585i	−0.789554	−	0.143928i
$283$	−556.632			−0.116920			−0.0584600	−	0.998290i	$-0.518619\pi$
$283$	−556.632			−0.116920			−0.0584600	+	0.998290i	$0.518619\pi$
$284$	−5717.73	+	2483.56i	−1.19466	+	0.518916i
$285$	−102.519	+	1498.78i	−0.0213078	+	0.311509i
$286$	−1499.92	+	1606.02i	−0.310111	+	0.332048i
$287$	977.288	−	594.302i	0.201002	−	0.122232i
$288$	−1576.63	−	4436.22i	−0.322583	−	0.907662i
$289$	−722.444	−	3476.59i	−0.147047	−	0.707631i
$290$	−1532.12	+	4310.99i	−0.310239	+	0.872930i
$291$	−2520.06	−	346.374i	−0.507658	−	0.0697760i
$292$	−3073.62	+	4354.32i	−0.615993	+	0.872663i
$293$	−246.091	+	200.210i	−0.0490676	+	0.0399195i	−0.655306	−	0.755363i	$-0.727460\pi$
$293$	−246.091	+	200.210i	−0.0490676	+	0.0399195i	0.606238	+	0.795283i	$0.292678\pi$
$294$	−2228.15	−	2385.77i	−0.442001	−	0.473268i
$295$	−2447.55	−	685.772i	−0.483057	−	0.135346i
$296$	53.1570	+	75.3063i	0.0104381	+	0.0147875i
$297$	−3869.30	−	7467.42i	−0.755959	−	1.45893i
$298$	−907.869	−	13272.6i	−0.176481	−	2.58007i
$299$	−472.286	−	384.233i	−0.0913479	−	0.0743170i
$300$	572.099	−	160.295i	0.110101	−	0.0308487i
$301$	3219.69	+	1957.94i	0.616544	+	0.374929i
$302$	−655.144	+	3152.73i	−0.124832	+	0.600725i
$303$	4346.07	−	597.353i	0.824010	−	0.113258i
$304$	2977.44	−	5746.19i	0.561736	−	1.08410i
$305$	2265.50	+	984.046i	0.425319	+	0.184742i
$306$	2490.49	+	1081.77i	0.465267	+	0.202094i
$307$	−3300.06	+	6368.83i	−0.613500	+	1.18400i	0.354972	+	0.934877i	$0.384490\pi$
$307$	−3300.06	+	6368.83i	−0.613500	+	1.18400i	−0.968472	+	0.249124i	$0.919857\pi$
$308$	−4107.29	+	564.534i	−0.759852	+	0.104439i
$309$	−779.888	+	3753.03i	−0.143580	+	0.690945i
$310$	2015.84	+	1225.86i	0.369330	+	0.224594i
$311$	6370.17	−	1784.84i	1.16148	−	0.325431i	0.365532	−	0.930799i	$-0.380887\pi$
$311$	6370.17	−	1784.84i	1.16148	−	0.325431i	0.795945	+	0.605368i	$0.206974\pi$
$312$	6.29648	+	5.12257i	0.00114253	+	0.000929514i
$313$	692.069	+	10117.7i	0.124978	+	1.82711i	0.463438	+	0.886129i	$0.346616\pi$
$313$	692.069	+	10117.7i	0.124978	+	1.82711i	−0.338460	+	0.940981i	$0.609906\pi$
$314$	1262.08	+	2435.70i	0.226826	+	0.437753i
$315$	−430.569	−	609.978i	−0.0770154	−	0.109106i
$316$	4428.42	+	1240.78i	0.788348	+	0.220885i
$317$	−4550.68	−	4872.59i	−0.806282	−	0.863318i	0.186598	−	0.982436i	$-0.440254\pi$
$317$	−4550.68	−	4872.59i	−0.806282	−	0.863318i	−0.992880	+	0.119119i	$0.961993\pi$
$318$	−1883.74	+	1532.54i	−0.332186	+	0.270253i
$319$	8297.08	−	11754.3i	1.45626	−	2.06305i
$320$	−2586.10	−	355.452i	−0.451774	−	0.0620949i
$321$	1873.57	−	5271.72i	0.325771	−	0.916631i
$322$	−465.116	−	2238.26i	−0.0804966	−	0.387371i
$323$	1262.42	+	3552.12i	0.217471	+	0.611905i
$324$	711.020	−	432.381i	0.121917	−	0.0741394i
$325$	−148.316	+	158.808i	−0.0253142	+	0.0271048i
$326$	−136.780	+	1999.65i	−0.0232379	+	0.339726i
$327$	52.5220	−	22.8135i	0.00888219	−	0.00385808i
$328$	44.6166			0.00751079
$329$	2491.90	+	817.229i	0.417576	+	0.136946i
$330$	−3718.47			−0.620287
$331$	−2496.25	+	1084.28i	−0.414521	+	0.180052i	−0.595357	−	0.803461i	$-0.702989\pi$
$331$	−2496.25	+	1084.28i	−0.414521	+	0.180052i	0.180836	+	0.983513i	$0.442120\pi$
$332$	−724.327	+	10589.3i	−0.119737	+	1.75049i
$333$	3636.00	−	3893.20i	0.598353	−	0.640679i
$334$	−6177.94	+	3756.89i	−1.01210	+	0.615472i
$335$	764.217	+	2150.30i	0.124638	+	0.350697i
$336$	−308.623	−	1485.18i	−0.0501095	−	0.241140i
$337$	−2664.00	+	7495.78i	−0.430615	+	1.21164i	0.506385	+	0.862307i	$0.330981\pi$
$337$	−2664.00	+	7495.78i	−0.430615	+	1.21164i	−0.937001	+	0.349328i	$0.886410\pi$
$338$	8427.54	+	1158.34i	1.35621	+	0.186406i
$339$	9.84637	−	13.9491i	0.00157753	−	0.00223485i
$340$	1156.51	−	940.887i	0.184472	−	0.150079i
$341$	−5064.15	−	5422.39i	−0.804221	−	0.861110i
$342$	7236.01	+	2027.44i	1.14409	+	0.320559i
$343$	2908.86	+	4120.92i	0.457912	+	0.648713i
$344$	67.6250	+	130.510i	0.0105991	+	0.0204554i
$345$	−70.3061	−	1027.84i	−0.0109715	−	0.160397i
$346$	−5447.19	−	4431.62i	−0.846367	−	0.688570i
$347$	9523.13	−	2668.26i	1.47328	−	0.412794i	0.562886	−	0.826534i	$-0.309691\pi$
$347$	9523.13	−	2668.26i	1.47328	−	0.412794i	0.910395	+	0.413740i	$0.135778\pi$
$348$	−4633.58	−	2817.74i	−0.713753	−	0.434043i
$349$	−2002.52	+	9636.65i	−0.307141	+	1.47805i	0.488653	+	0.872478i	$0.337489\pi$
$349$	−2002.52	+	9636.65i	−0.307141	+	1.47805i	−0.795794	+	0.605567i	$0.792946\pi$
$350$	−808.301	+	111.098i	−0.123444	+	0.0169670i
$351$	533.406	−	1029.43i	0.0811143	−	0.156544i
$352$	14839.7	+	6445.79i	2.24704	+	0.976028i
$353$	−11059.6	−	4803.87i	−1.66755	−	0.724318i	−0.667749	−	0.744386i	$-0.732742\pi$
$353$	−11059.6	−	4803.87i	−1.66755	−	0.724318i	−0.999799	+	0.0200680i	$0.993612\pi$
$354$	2758.67	−	5323.99i	0.414185	−	0.799341i
$355$	3822.02	−	525.325i	0.571414	−	0.0785390i
$356$	564.681	−	2717.39i	0.0840675	−	0.404555i
$357$	754.958	+	459.100i	0.111923	+	0.0680621i
$358$	14769.8	−	4138.32i	2.18048	−	0.610941i
$359$	−1287.59	−	1047.53i	−0.189293	−	0.154001i	0.531726	−	0.846916i	$-0.321544\pi$
$359$	−1287.59	−	1047.53i	−0.189293	−	0.154001i	−0.721019	+	0.692915i	$0.756326\pi$
$360$	−1.98750	−	29.0562i	−0.000290974	−	0.00425389i
$361$	1644.30	+	3173.36i	0.239729	+	0.462656i
$362$	1102.14	+	1561.37i	0.160019	+	0.226696i
$363$	7489.97	+	2098.59i	1.08298	+	0.303436i
$364$	−390.104	−	417.700i	−0.0561731	−	0.0601468i
$365$	2558.69	−	2081.65i	0.366926	−	0.298516i
$366$	−3360.22	+	4760.34i	−0.479894	+	0.679856i
$367$	−3968.94	−	545.518i	−0.564514	−	0.0775907i	−0.151734	−	0.988421i	$-0.548486\pi$
$367$	−3968.94	−	545.518i	−0.564514	−	0.0775907i	−0.412780	+	0.910831i	$0.635442\pi$
$368$	−1486.28	+	4181.98i	−0.210537	+	0.592393i
$369$	−524.601	−	2524.52i	−0.0740098	−	0.356155i
$370$	−1949.42	−	5485.14i	−0.273907	−	0.770700i
$371$	1431.70	−	870.635i	0.200350	−	0.121836i
$372$	−1908.81	+	2043.84i	−0.266041	+	0.284860i
$373$	331.514	−	4846.56i	0.0460191	−	0.672776i	−0.916238	−	0.400634i	$-0.868790\pi$
$373$	331.514	−	4846.56i	0.0460191	−	0.672776i	0.962257	−	0.272142i	$-0.0877319\pi$
$374$	−8558.52	+	3717.49i	−1.18329	+	0.513975i
$375$	−367.693			−0.0506336
$376$	66.4880	+	77.7416i	0.00911930	+	0.0106628i
$377$	1983.42			0.270959
$378$	3992.95	−	1734.38i	0.543320	−	0.235997i
$379$	−137.205	+	2005.86i	−0.0185956	+	0.271858i	0.979068	+	0.203535i	$0.0652430\pi$
$379$	−137.205	+	2005.86i	−0.0185956	+	0.271858i	−0.997663	+	0.0683228i	$0.978235\pi$
$380$	2816.30	−	3015.52i	0.380193	−	0.407087i
$381$	5576.67	−	3391.25i	0.749872	−	0.456007i
$382$	−2793.34	−	7859.71i	−0.374136	−	1.05272i
$383$	2352.46	+	11320.6i	0.313851	+	1.51033i	0.780086	+	0.625672i	$0.215175\pi$
$383$	2352.46	+	11320.6i	0.313851	+	1.51033i	−0.466235	+	0.884661i	$0.654390\pi$
$384$	40.0280	−	112.628i	0.00531945	−	0.0149675i
$385$	2541.90	+	349.376i	0.336486	+	0.0462489i
$386$	3575.45	−	5065.26i	0.471465	−	0.667914i
$387$	6589.47	−	5360.93i	0.865533	−	0.704163i
$388$	4768.73	+	5106.06i	0.623957	+	0.668095i
$389$	−10936.5	−	3064.27i	−1.42546	−	0.399395i	−0.531316	−	0.847173i	$-0.678302\pi$
$389$	−10936.5	−	3064.27i	−1.42546	−	0.399395i	−0.894145	+	0.447778i	$0.852215\pi$
$390$	−295.614	−	418.789i	−0.0383820	−	0.0543749i
$391$	−1189.39	−	2295.41i	−0.153836	−	0.296890i
$392$	5.99606	+	87.6593i	0.000772568	+	0.0112945i
$393$	−2390.44	−	1944.77i	−0.306824	−	0.249620i
$394$	7613.12	−	2133.10i	0.973461	−	0.272751i
$395$	−2431.83	−	1478.83i	−0.309769	−	0.188375i
$396$	−1901.50	+	9150.52i	−0.241298	+	1.16119i
$397$	−2281.99	+	313.653i	−0.288488	+	0.0396518i	−0.278960	−	0.960303i	$-0.589990\pi$
$397$	−2281.99	+	313.653i	−0.288488	+	0.0396518i	−0.00952866	+	0.999955i	$0.503033\pi$
$398$	−2369.11	+	4572.18i	−0.298374	+	0.575835i
$399$	2242.93	+	974.243i	0.281421	+	0.122238i
$400$	1452.87	+	631.071i	0.181609	+	0.0788838i
$401$	603.093	−	1163.92i	0.0751048	−	0.144946i	−0.847370	−	0.531003i	$-0.821815\pi$
$401$	603.093	−	1163.92i	0.0751048	−	0.144946i	0.922475	+	0.386057i	$0.126163\pi$
$402$	−5333.37	+	733.054i	−0.661702	+	0.0909488i
$403$	208.097	−	1001.42i	0.0257222	−	0.123782i
$404$	−10294.9	−	6260.48i	−1.26780	−	0.770967i
$405$	−495.910	+	138.947i	−0.0608443	+	0.0170478i
$406$	5776.98	+	4699.92i	0.706174	+	0.574515i
$407$	1249.27	+	18263.7i	0.152147	+	2.22431i
$408$	15.8568	+	30.6023i	0.00192409	+	0.00371333i
$409$	−3740.81	−	5299.52i	−0.452252	−	0.640695i	0.525417	−	0.850845i	$-0.323909\pi$
$409$	−3740.81	−	5299.52i	−0.452252	−	0.640695i	−0.977669	+	0.210149i	$0.932605\pi$
$410$	−2713.17	−	760.194i	−0.326814	−	0.0915690i
$411$	558.669	+	598.189i	0.0670490	+	0.0717919i
$412$	8166.82	−	6644.20i	0.976579	−	0.794506i
$413$	−2386.02	+	3380.22i	−0.284281	+	0.402735i
$414$	−5105.45	−	701.727i	−0.606084	−	0.0833044i
$415$	2199.74	−	6189.49i	0.260196	−	0.732120i
$416$	453.787	+	2183.74i	0.0534825	+	0.257372i
$417$	−888.723	−	2500.63i	−0.104367	−	0.293660i
$418$	−22064.6	+	13417.8i	−2.58185	+	1.57006i
$419$	−5555.24	+	5948.21i	−0.647712	+	0.693530i	−0.967187	−	0.254065i	$-0.918232\pi$
$419$	−5555.24	+	5948.21i	−0.647712	+	0.693530i	0.319476	+	0.947594i	$0.396493\pi$
$420$	65.9982	−	964.860i	0.00766758	−	0.112096i
$421$	−10808.1	+	4694.61i	−1.25119	+	0.543471i	−0.916945	−	0.399014i	$-0.869353\pi$
$421$	−10808.1	+	4694.61i	−1.25119	+	0.543471i	−0.334250	+	0.942485i	$0.608483\pi$
$422$	−18162.3			−2.09509
$423$	3617.05	−	4676.14i	0.415761	−	0.537498i
$424$	65.3620			0.00748646
$425$	−846.292	+	367.597i	−0.0965910	+	0.0419554i
$426$	−621.082	+	9079.89i	−0.0706373	+	1.03268i
$427$	2744.27	−	2938.40i	0.311018	−	0.333019i
$428$	−13129.4	+	7984.14i	−1.48278	+	0.901701i
$429$	539.837	+	1518.96i	0.0607543	+	0.170946i
$430$	−1888.64	−	9088.65i	−0.211810	−	1.01929i
$431$	2546.78	−	7165.94i	0.284626	−	0.800861i	−0.710629	−	0.703567i	$-0.751590\pi$
$431$	2546.78	−	7165.94i	0.284626	−	0.800861i	0.995256	−	0.0972948i	$-0.0310190\pi$
$432$	−8372.99	−	1150.84i	−0.932513	−	0.128171i
$433$	918.716	−	1301.52i	0.101965	−	0.144451i	−0.762789	−	0.646648i	$-0.776170\pi$
$433$	918.716	−	1301.52i	0.101965	−	0.144451i	0.864753	+	0.502197i	$0.167475\pi$
$434$	2979.07	−	2423.66i	0.329493	−	0.268063i
$435$	2290.79	+	2452.84i	0.252494	+	0.270355i
$436$	−151.444	−	42.4327i	−0.0166350	−	0.00466091i
$437$	−4126.05	−	5845.28i	−0.451660	−	0.639857i
$438$	3579.93	+	6908.95i	0.390538	+	0.753704i
$439$	343.798	+	5026.15i	0.0373772	+	0.546435i	0.978217	+	0.207584i	$0.0665600\pi$
$439$	343.798	+	5026.15i	0.0373772	+	0.546435i	−0.940840	+	0.338851i	$0.889962\pi$
$440$	77.6367	+	63.1622i	0.00841179	+	0.00684350i
$441$	4889.48	−	1369.97i	0.527964	−	0.147929i
$442$	−1099.07	−	668.360i	−0.118275	−	0.0719245i
$443$	3214.55	−	15469.3i	0.344758	−	1.65907i	−0.347696	−	0.937607i	$-0.613036\pi$
$443$	3214.55	−	15469.3i	0.344758	−	1.65907i	0.692455	−	0.721461i	$-0.256529\pi$
$444$	6835.86	−	939.567i	0.730665	−	0.100428i
$445$	−790.232	+	1525.08i	−0.0841811	+	0.162462i
$446$	1615.32	+	701.633i	0.171497	+	0.0744917i
$447$	−8951.21	−	3888.06i	−0.947154	−	0.411407i
$448$	−1954.90	+	3772.79i	−0.206162	+	0.397874i
$449$	7226.33	−	993.236i	0.759536	−	0.104396i	0.254003	−	0.967203i	$-0.418253\pi$
$449$	7226.33	−	993.236i	0.759536	−	0.104396i	0.505533	+	0.862808i	$0.331296\pi$
$450$	−374.210	+	1800.80i	−0.0392009	+	0.188645i
$451$	7570.83	+	4603.92i	0.790458	+	0.480688i
$452$	−45.1566	+	12.6523i	−0.00469909	+	0.00131662i
$453$	1832.36	+	1490.73i	0.190048	+	0.154615i
$454$	1118.05	+	16345.3i	0.115578	+	1.68969i
$455$	162.730	+	314.054i	0.0167668	+	0.0323584i
$456$	55.0082	+	77.9288i	0.00564911	+	0.00800296i
$457$	318.987	+	89.3759i	0.0326511	+	0.00914842i	0.286084	−	0.958205i	$-0.407647\pi$
$457$	318.987	+	89.3759i	0.0326511	+	0.00914842i	−0.253432	+	0.967353i	$0.581560\pi$
$458$	12349.4	+	13223.0i	1.25993	+	1.34906i
$459$	3818.90	−	3106.90i	0.388346	−	0.315943i
$460$	−1631.79	+	2311.73i	−0.165397	+	0.234315i
$461$	−4836.16	−	664.715i	−0.488595	−	0.0671559i	−0.112336	−	0.993670i	$-0.535833\pi$
$461$	−4836.16	−	664.715i	−0.488595	−	0.0671559i	−0.376259	+	0.926514i	$0.622790\pi$
$462$	−2026.97	+	5703.36i	−0.204120	+	0.574338i
$463$	1947.22	+	9370.52i	0.195453	+	0.940573i	0.956468	+	0.291838i	$0.0942667\pi$
$463$	1947.22	+	9370.52i	0.195453	+	0.940573i	−0.761015	+	0.648735i	$0.775298\pi$
$464$	−4841.83	−	13623.6i	−0.484432	−	1.36306i
$465$	1478.77	−	899.260i	0.147476	−	0.0896821i
$466$	−1993.94	+	2134.99i	−0.198214	+	0.212235i
$467$	635.315	−	9287.97i	0.0629526	−	0.920334i	−0.853729	−	0.520717i	$-0.825665\pi$
$467$	635.315	−	9287.97i	0.0629526	−	0.920334i	0.916682	−	0.399617i	$-0.130857\pi$
$468$	−1181.74	+	513.301i	−0.116722	+	0.0506994i
$469$	3714.70			0.365733
$470$	−2718.59	−	5860.37i	−0.266807	−	0.575146i
$471$	2012.38			0.196870
$472$	−148.031	+	64.2990i	−0.0144358	+	0.00627034i
$473$	−1992.13	+	29124.0i	−0.193654	+	2.83112i
$474$	4582.86	−	4907.04i	0.444088	−	0.475502i
$475$	−2181.81	+	1326.79i	−0.210754	+	0.128163i
$476$	−812.703	−	2286.73i	−0.0782567	−	0.220193i
$477$	−768.525	−	3698.34i	−0.0737701	−	0.355001i
$478$	9283.58	−	26121.5i	0.888329	−	2.49952i
$479$	−885.618	−	121.725i	−0.0844779	−	0.0116112i	0.0938039	−	0.995591i	$-0.470097\pi$
$479$	−885.618	−	121.725i	−0.0844779	−	0.0116112i	−0.178282	+	0.983979i	$0.557054\pi$
$480$	−2176.46	+	3083.34i	−0.206961	+	0.293197i
$481$	−1957.61	+	1592.64i	−0.185571	+	0.150973i
$482$	4675.15	+	5005.87i	0.441799	+	0.473052i
$483$	−1614.82	−	452.450i	−0.152126	−	0.0426236i
$484$	−12320.2	−	17453.7i	−1.15704	−	1.63916i
$485$	−1989.25	−	3839.07i	−0.186241	−	0.359429i
$486$	−1068.46	−	15620.3i	−0.0997246	−	1.45792i
$487$	−13499.9	−	10983.0i	−1.25614	−	1.02194i	−0.998447	−	0.0557162i	$-0.982256\pi$
$487$	−13499.9	−	10983.0i	−1.25614	−	1.02194i	−0.257691	−	0.966227i	$-0.582962\pi$
$488$	151.017	−	42.3129i	0.0140086	−	0.00392503i
$489$	1256.27	+	763.955i	0.116177	+	0.0706487i
$490$	1128.95	−	5432.79i	0.104083	−	0.500874i
$491$	9007.44	−	1238.04i	0.827902	−	0.113793i	0.290241	−	0.956954i	$-0.406265\pi$
$491$	9007.44	−	1238.04i	0.827902	−	0.113793i	0.537661	+	0.843161i	$0.319308\pi$
$492$	1536.55	−	2965.41i	0.140799	−	0.271730i
$493$	7724.74	+	3355.33i	0.705689	+	0.306524i
$494$	−3265.27	−	1418.31i	−0.297392	−	0.129175i
$495$	2661.02	−	5135.54i	0.241624	−	0.466314i
$496$	−7386.48	+	1015.25i	−0.668675	+	0.0919072i
$497$	1277.68	−	6148.55i	0.115316	−	0.554930i
$498$	13240.1	+	8051.49i	1.19137	+	0.724490i
$499$	6287.27	−	1761.61i	0.564041	−	0.158037i	0.0240548	−	0.999711i	$-0.492342\pi$
$499$	6287.27	−	1761.61i	0.564041	−	0.158037i	0.539987	+	0.841674i	$0.318429\pi$
$500$	783.388	+	637.334i	0.0700684	+	0.0570049i
$501$	361.968	+	5291.79i	0.0322785	+	0.471896i
$502$	2188.12	+	4222.88i	0.194543	+	0.375451i
$503$	−3457.02	−	4897.48i	−0.306443	−	0.434131i	0.634384	−	0.773018i	$-0.281254\pi$
$503$	−3457.02	−	4897.48i	−0.306443	−	0.434131i	−0.940827	+	0.338887i	$0.889950\pi$
$504$	−45.6497	−	12.7904i	−0.00403452	−	0.00113042i
$505$	5089.69	+	5449.73i	0.448492	+	0.480217i
$506$	13737.6	−	11176.4i	1.20694	−	0.981919i
$507$	3598.68	−	5098.17i	0.315233	−	0.446584i
$508$	−17759.5	−	2440.99i	−1.55108	−	0.213192i
$509$	−3198.68	+	9000.21i	−0.278544	+	0.783747i	0.717636	+	0.696419i	$0.245224\pi$
$509$	−3198.68	+	9000.21i	−0.278544	+	0.783747i	−0.996180	+	0.0873287i	$0.972167\pi$
$510$	−442.852	−	2131.12i	−0.0384506	−	0.185035i
$511$	−1798.05	−	5059.23i	−0.155658	−	0.437979i
$512$	14029.3	−	8531.39i	1.21096	−	0.736402i
$513$	9299.71	−	9957.56i	0.800375	−	0.856992i
$514$	−223.556	+	3268.27i	−0.0191841	+	0.280462i
$515$	−5976.20	+	2595.83i	−0.511346	+	0.222109i
$516$	11003.2			0.938740
$517$	3260.07	+	20052.5i	0.277326	+	1.70582i
$518$	−9475.72			−0.803743
$519$	−4724.82	+	2052.28i	−0.399608	+	0.173574i
$520$	−0.941558	+	13.7651i	−7.94039e−5	+	0.00116084i
$521$	1537.47	−	1646.23i	0.129286	−	0.138431i	−0.662908	−	0.748701i	$-0.730678\pi$
$521$	1537.47	−	1646.23i	0.129286	−	0.138431i	0.792194	+	0.610270i	$0.208939\pi$
$522$	14344.3	−	8722.95i	1.20274	−	0.731405i
$523$	1495.34	+	4207.49i	0.125023	+	0.351780i	0.988210	−	0.153104i	$-0.0489268\pi$
$523$	1495.34	+	4207.49i	0.125023	+	0.351780i	−0.863188	+	0.504883i	$0.831535\pi$
$524$	1722.03	+	8286.84i	0.143563	+	0.690863i
$525$	−200.433	+	563.965i	−0.0166621	+	0.0468828i
$526$	−25556.5	−	3512.66i	−2.11847	−	0.291177i
$527$	2504.55	−	3548.14i	0.207021	−	0.293282i
$528$	9115.48	−	7415.99i	0.751327	−	0.611249i
$529$	−4955.56	−	5306.11i	−0.407295	−	0.436107i
$530$	−3974.71	−	1113.66i	−0.325755	−	0.0912724i
$531$	5378.74	+	7619.94i	0.439581	+	0.622744i
$532$	−3089.99	−	5963.42i	−0.251820	−	0.485990i
$533$	83.3589	+	1218.66i	0.00677425	+	0.0990360i
$534$	−3143.21	−	2557.19i	−0.254719	−	0.207229i
$535$	9157.24	−	2565.74i	0.740004	−	0.207339i
$536$	123.805	+	75.2878i	0.00997683	+	0.00606705i
$537$	2289.29	−	11016.7i	0.183967	−	0.885297i
$538$	−16936.1	+	2327.82i	−1.35719	+	0.186541i
$539$	−8027.98	+	15493.3i	−0.641539	+	1.23812i
$540$	−4942.35	−	2146.76i	−0.393861	−	0.171078i
$541$	−1978.64	−	859.443i	−0.157243	−	0.0683001i	0.318313	−	0.947986i	$-0.396884\pi$
$541$	−1978.64	−	859.443i	−0.157243	−	0.0683001i	−0.475556	+	0.879685i	$0.657753\pi$
$542$	13960.2	−	26942.0i	1.10635	−	2.13516i
$543$	1388.93	−	190.904i	0.109769	−	0.0150874i
$544$	−1926.86	+	9272.57i	−0.151863	+	0.730805i
$545$	83.1645	+	50.5734i	0.00653647	+	0.00397491i
$546$	−803.477	+	225.124i	−0.0629774	+	0.0176454i
$547$	−8957.45	−	7287.42i	−0.700170	−	0.569630i	0.213078	−	0.977035i	$-0.431651\pi$
$547$	−8957.45	−	7287.42i	−0.700170	−	0.569630i	−0.913248	+	0.407405i	$0.866434\pi$
$548$	−153.414	−	2242.83i	−0.0119590	−	0.174834i
$549$	−4169.81	−	8047.38i	−0.324159	−	0.625599i
$550$	−3644.97	−	5163.74i	−0.282585	−	0.400332i
$551$	22443.9	+	6288.49i	1.73529	+	0.486204i
$552$	−44.6494	−	47.8078i	−0.00344276	−	0.00368630i
$553$	−3593.84	+	2923.80i	−0.276357	+	0.224833i
$554$	8462.71	−	11988.9i	0.649001	−	0.919424i
$555$	−4230.54	−	581.475i	−0.323561	−	0.0444725i
$556$	−2440.95	+	6868.16i	−0.186186	+	0.523876i
$557$	−1521.74	−	7323.02i	−0.115760	−	0.557067i	−0.996509	−	0.0834843i	$-0.973395\pi$
$557$	−1521.74	−	7323.02i	−0.115760	−	0.557067i	0.880749	−	0.473583i	$-0.157040\pi$
$558$	−2899.19	−	8157.55i	−0.219951	−	0.618883i
$559$	−3438.43	+	2090.96i	−0.260161	+	0.158208i
$560$	1759.91	−	1884.40i	0.132803	−	0.142197i
$561$	−467.119	+	6829.03i	−0.0351547	+	0.513943i
$562$	17436.5	−	7573.74i	1.30874	−	0.568468i
$563$	−12115.3			−0.906927			−0.453464	−	0.891275i	$-0.649812\pi$
$563$	−12115.3			−0.906927			−0.453464	+	0.891275i	$0.649812\pi$
$564$	7456.83	−	1741.73i	0.556718	−	0.130036i
$565$	29.0225			0.00216104
$566$	2047.24	−	889.243i	0.152035	−	0.0660383i
$567$	−57.2089	+	836.365i	−0.00423730	+	0.0619471i
$568$	167.199	−	179.027i	0.0123513	−	0.0132250i
$569$	2701.35	−	1642.73i	0.199027	−	0.121031i	−0.416534	−	0.909120i	$-0.636755\pi$
$569$	2701.35	−	1642.73i	0.199027	−	0.121031i	0.615561	+	0.788089i	$0.288929\pi$
$570$	−2017.31	−	5676.16i	−0.148238	−	0.417102i
$571$	2394.33	+	11522.2i	0.175481	+	0.844462i	0.971102	+	0.238667i	$0.0767103\pi$
$571$	2394.33	+	11522.2i	0.175481	+	0.844462i	−0.795620	+	0.605796i	$0.792855\pi$
$572$	1482.70	−	4171.93i	0.108383	−	0.304960i
$573$	−6061.99	−	833.201i	−0.441960	−	0.0607460i
$574$	−2644.95	+	3747.05i	−0.192332	+	0.272472i
$575$	1358.42	−	1105.15i	0.0985216	−	0.0801533i
$576$	6538.06	+	7000.55i	0.472950	+	0.506406i
$577$	10893.3	+	3052.16i	0.785952	+	0.220213i	0.639282	−	0.768972i	$-0.279232\pi$
$577$	10893.3	+	3052.16i	0.785952	+	0.220213i	0.146669	+	0.989186i	$0.453145\pi$
$578$	8211.09	+	11632.5i	0.590893	+	0.837105i
$579$	−2092.47	−	4038.27i	−0.150190	−	0.289853i
$580$	−629.064	−	9196.59i	−0.0450353	−	0.658392i
$581$	−8294.29	−	6747.90i	−0.592263	−	0.481842i
$582$	9821.90	−	2751.97i	0.699537	−	0.196001i
$583$	11091.0	+	6744.61i	0.787897	+	0.479131i
$584$	42.6117	−	205.059i	0.00301932	−	0.0145298i
$585$	789.933	−	108.574i	0.0558286	−	0.00767346i
$586$	585.258	−	1129.50i	0.0412573	−	0.0796230i
$587$	−8426.77	−	3660.26i	−0.592521	−	0.257368i	0.0807857	−	0.996731i	$-0.474257\pi$
$587$	−8426.77	−	3660.26i	−0.592521	−	0.257368i	−0.673307	+	0.739363i	$0.735127\pi$
$588$	6032.71	+	2620.38i	0.423103	+	0.183780i
$589$	5529.80	−	10672.0i	0.386844	−	0.746575i
$590$	10097.4	−	1387.86i	0.704584	−	0.0968428i
$591$	1180.02	−	5678.55i	0.0821309	−	0.395236i
$592$	15718.2	+	9558.46i	1.09124	+	0.663598i
$593$	10183.7	−	2853.33i	0.705216	−	0.197592i	0.101551	−	0.994830i	$-0.467620\pi$
$593$	10183.7	−	2853.33i	0.705216	−	0.197592i	0.603665	+	0.797238i	$0.293707\pi$
$594$	26160.5	+	21283.1i	1.80703	+	1.47013i
$595$	102.495	+	1498.42i	0.00706196	+	0.103242i
$596$	12331.7	+	23799.1i	0.847528	+	1.63565i
$597$	2178.44	+	3086.14i	0.149342	+	0.211570i
$598$	2350.86	+	658.679i	0.160759	+	0.0450425i
$599$	−5066.01	−	5424.37i	−0.345562	−	0.370006i	0.534252	−	0.845326i	$-0.320593\pi$
$599$	−5066.01	−	5424.37i	−0.345562	−	0.370006i	−0.879813	+	0.475319i	$0.842333\pi$
$600$	−18.1103	+	14.7338i	−0.00123225	+	0.00100251i
$601$	1500.81	−	2126.16i	0.101862	−	0.144306i	−0.762846	−	0.646580i	$-0.776199\pi$
$601$	1500.81	−	2126.16i	0.101862	−	0.144306i	0.864709	+	0.502274i	$0.167503\pi$
$602$	−14969.6	−	2057.53i	−1.01348	−	0.139300i
$603$	2804.27	−	7890.45i	0.189384	−	0.532876i
$604$	−1319.99	−	6352.16i	−0.0889235	−	0.427923i
$605$	4427.66	+	12458.2i	0.297537	+	0.837189i
$606$	−15030.2	+	9140.04i	−1.00752	+	0.612688i
$607$	1395.26	−	1493.96i	0.0932980	−	0.0998978i	−0.682478	−	0.730906i	$-0.739098\pi$
$607$	1395.26	−	1493.96i	0.0932980	−	0.0998978i	0.775776	+	0.631008i	$0.217359\pi$
$608$	−1788.67	+	26149.4i	−0.119309	+	1.74424i
$609$	5010.88	−	2176.53i	0.333417	−	0.144823i
$610$	−9904.37			−0.657404
$611$	−1999.22	+	1961.31i	−0.132373	+	0.129863i
$612$	−5470.79			−0.361346
$613$	−11509.4	+	4999.26i	−0.758339	+	0.329393i	−0.741935	−	0.670472i	$-0.766092\pi$
$613$	−11509.4	+	4999.26i	−0.758339	+	0.329393i	−0.0164046	+	0.999865i	$0.505222\pi$
$614$	1962.86	−	28696.0i	0.129014	−	1.88612i
$615$	−1410.81	+	1510.61i	−0.0925028	+	0.0990463i
$616$	139.198	−	84.6483i	0.00910464	−	0.00553665i
$617$	−5620.94	−	15815.8i	−0.366759	−	1.03196i	−0.971808	−	0.235773i	$-0.924238\pi$
$617$	−5620.94	−	15815.8i	−0.366759	−	1.03196i	0.605049	−	0.796188i	$-0.293154\pi$
$618$	−3127.26	−	15049.2i	−0.203555	−	0.979559i
$619$	6924.23	−	19482.9i	0.449609	−	1.26508i	−0.473586	−	0.880748i	$-0.657041\pi$
$619$	6924.23	−	19482.9i	0.449609	−	1.26508i	0.923195	−	0.384332i	$-0.125568\pi$
$620$	−4709.31	−	647.279i	−0.305049	−	0.0419280i
$621$	−5388.34	+	7633.55i	−0.348191	+	0.493275i
$622$	−20577.6	+	16741.1i	−1.32650	+	1.07919i
$623$	1908.39	+	2043.39i	0.122726	+	0.131407i
$624$	1559.89	+	437.061i	0.100073	+	0.0280391i
$625$	−360.425	−	510.606i	−0.0230672	−	0.0326788i
$626$	−18708.8	−	36106.3i	−1.19450	−	2.30527i
$627$	1292.77	+	18899.7i	0.0823419	+	1.20380i
$628$	−4287.48	−	3488.13i	−0.272435	−	0.221642i
$629$	−10318.5	+	2891.09i	−0.654092	+	0.183268i
$630$	2558.06	+	1555.59i	0.161771	+	0.0983750i
$631$	−4633.31	+	22296.7i	−0.292313	+	1.40669i	0.534956	+	0.844880i	$0.320328\pi$
$631$	−4633.31	+	22296.7i	−0.292313	+	1.40669i	−0.827269	+	0.561806i	$0.810107\pi$
$632$	−179.036	+	24.6079i	−0.0112684	+	0.00154881i
$633$	−6129.62	+	11829.6i	−0.384883	+	0.742790i
$634$	24521.1	+	10651.0i	1.53606	+	0.667203i
$635$	10175.8	+	4419.96i	0.635927	+	0.276222i
$636$	2251.00	−	4344.24i	0.140343	−	0.270850i
$637$	−2383.14	+	327.554i	−0.148231	+	0.0203739i
$638$	−11738.0	+	56486.1i	−0.728386	+	3.50518i
$639$	−12095.7	−	7355.55i	−0.748823	−	0.455370i
$640$	195.640	−	54.8158i	0.0120834	−	0.00338560i
$641$	−342.372	−	278.540i	−0.0210965	−	0.0171633i	0.620481	−	0.784221i	$-0.286937\pi$
$641$	−342.372	−	278.540i	−0.0210965	−	0.0171633i	−0.641578	+	0.767058i	$0.721720\pi$
$642$	1530.97	+	22382.0i	0.0941163	+	1.37593i
$643$	−263.877	−	509.260i	−0.0161840	−	0.0312337i	0.879656	−	0.475611i	$-0.157773\pi$
$643$	−263.877	−	509.260i	−0.0161840	−	0.0312337i	−0.895840	+	0.444377i	$0.853425\pi$
$644$	2656.20	+	3762.98i	0.162529	+	0.230252i
$645$	−6557.10	−	1837.21i	−0.400288	−	0.112155i
$646$	−10317.8	−	11047.6i	−0.628400	−	0.672852i
$647$	−4461.78	+	3629.92i	−0.271114	+	0.220567i	−0.756934	−	0.653491i	$-0.773304\pi$
$647$	−4461.78	+	3629.92i	−0.271114	+	0.220567i	0.485820	+	0.874059i	$0.338521\pi$
$648$	−18.8577	+	26.7153i	−0.00114321	+	0.00161956i
$649$	−31753.8	−	4364.46i	−1.92056	−	0.263975i
$650$	291.791	−	821.022i	0.0176077	−	0.0495433i
$651$	−573.186	−	2758.32i	−0.0345083	−	0.166063i
$652$	−1352.36	−	3805.18i	−0.0812308	−	0.228562i
$653$	−6114.60	+	3718.37i	−0.366436	+	0.222835i	−0.690715	−	0.723127i	$-0.742704\pi$
$653$	−6114.60	+	3718.37i	−0.366436	+	0.222835i	0.324279	+	0.945961i	$0.394878\pi$
$654$	−156.726	+	167.812i	−0.00937074	+	0.0100336i
$655$	357.459	−	5225.87i	0.0213238	−	0.311743i
$656$	8167.19	−	3547.51i	0.486090	−	0.211139i
$657$	−12103.8			−0.718741
$658$	−10470.5	+	975.214i	−0.620340	+	0.0577778i
$659$	31455.1			1.85936			0.929678	−	0.368372i	$-0.120085\pi$
$659$	31455.1			1.85936			0.929678	+	0.368372i	$0.120085\pi$
$660$	6871.76	−	2984.83i	0.405277	−	0.176037i
$661$	−1088.84	+	15918.3i	−0.0640713	+	0.936689i	0.848871	+	0.528600i	$0.177283\pi$
$661$	−1088.84	+	15918.3i	−0.0640713	+	0.936689i	−0.912942	+	0.408089i	$0.866195\pi$
$662$	7448.82	−	7975.74i	0.437321	−	0.468256i
$663$	−806.249	+	490.291i	−0.0472279	+	0.0287199i
$664$	−139.673	−	393.002i	−0.00816320	−	0.0229691i
$665$	845.691	+	4069.69i	0.0493150	+	0.237317i
$666$	−7153.32	+	20127.5i	−0.416195	+	1.17106i
$667$	−15835.5	−	2176.54i	−0.919272	−	0.126351i
$668$	8401.23	−	11901.8i	0.486607	−	0.689365i
$669$	1002.15	−	815.310i	0.0579154	−	0.0471177i
$670$	−6245.92	−	6687.75i	−0.360151	−	0.385627i
$671$	29991.7	+	8403.27i	1.72551	+	0.483464i
$672$	3542.79	+	5018.99i	0.203372	+	0.288113i
$673$	5266.30	+	10163.5i	0.301636	+	0.582131i	0.989639	−	0.143576i	$-0.0458603\pi$
$673$	5266.30	+	10163.5i	0.301636	+	0.582131i	−0.688003	+	0.725708i	$0.741512\pi$
$674$	−2176.87	−	31824.7i	−0.124406	−	1.81875i
$675$	2586.83	+	2104.54i	0.147507	+	0.120006i
$676$	−16504.0	+	4624.20i	−0.939007	+	0.263098i
$677$	−5742.82	−	3492.29i	−0.326019	−	0.198256i	0.347031	−	0.937854i	$-0.387190\pi$
$677$	−5742.82	−	3492.29i	−0.326019	−	0.198256i	−0.673050	+	0.739597i	$0.735016\pi$
$678$	−13.9298	+	67.0336i	−0.000789040	+	0.00379707i
$679$	−6972.69	+	958.375i	−0.394091	+	0.0541665i
$680$	−26.9532	+	52.0174i	−0.00152001	+	0.00293349i
$681$	11023.5	+	4788.17i	0.620294	+	0.269432i
$682$	27288.0	+	11852.9i	1.53213	+	0.665497i
$683$	3036.68	−	5860.52i	0.170125	−	0.328326i	−0.787515	−	0.616296i	$-0.788632\pi$
$683$	3036.68	−	5860.52i	0.170125	−	0.328326i	0.957639	+	0.287970i	$0.0929803\pi$
$684$	−14999.7	+	2061.66i	−0.838489	+	0.115248i
$685$	−283.063	+	1362.17i	−0.0157887	+	0.0759796i
$686$	−17281.9	−	10509.3i	−0.961844	−	0.584910i
$687$	12780.3	−	3580.88i	0.709752	−	0.198863i
$688$	22756.0	+	18513.3i	1.26099	+	1.02589i
$689$	122.118	+	1785.31i	0.00675231	+	0.0987152i
$690$	1900.60	+	3667.98i	0.104862	+	0.202374i
$691$	−5237.96	−	7420.50i	−0.288367	−	0.408523i	0.646839	−	0.762626i	$-0.276090\pi$
$691$	−5237.96	−	7420.50i	−0.288367	−	0.408523i	−0.935206	+	0.354103i	$0.884786\pi$
$692$	13623.7	+	3817.19i	0.748406	+	0.209694i
$693$	−6426.30	−	6880.89i	−0.352258	−	0.377177i
$694$	−30762.6	+	25027.2i	−1.68261	+	1.36891i
$695$	2601.40	−	3685.35i	0.141981	−	0.201141i
$696$	211.118	+	29.0175i	0.0114977	+	0.00158032i
$697$	−1736.94	+	4887.29i	−0.0943922	+	0.265594i
$698$	−8029.87	−	38641.8i	−0.435437	−	2.09544i
$699$	717.642	+	2019.25i	0.0388322	+	0.109263i
$700$	1404.57	−	854.138i	0.0758397	−	0.0461191i
$701$	−2977.14	+	3187.74i	−0.160407	+	0.171754i	−0.805976	−	0.591948i	$-0.798359\pi$
$701$	−2977.14	+	3187.74i	−0.160407	+	0.171754i	0.645570	+	0.763702i	$0.276620\pi$
$702$	−317.267	+	4638.28i	−0.0170577	+	0.249374i
$703$	−27201.3	+	11815.2i	−1.45934	+	0.633881i
$704$	−32917.5			−1.76225
$705$	−4734.53	−	207.126i	−0.252926	−	0.0110650i
$706$	48350.7			2.57748
$707$	11133.2	−	4835.83i	0.592231	−	0.257242i
$708$	−824.460	+	12053.2i	−0.0437643	+	0.639811i
$709$	−1023.26	+	1095.65i	−0.0542022	+	0.0580364i	−0.757361	−	0.652997i	$-0.773512\pi$
$709$	−1023.26	+	1095.65i	−0.0542022	+	0.0580364i	0.703159	+	0.711033i	$0.251772\pi$
$710$	−13217.8	+	8037.94i	−0.698671	+	0.424871i
$711$	3497.47	+	9840.93i	0.184480	+	0.519077i
$712$	22.1895	+	106.782i	0.00116796	+	0.00562051i
$713$	−2760.36	+	7766.91i	−0.144988	+	0.407957i
$714$	−3510.10	−	482.452i	−0.183981	−	0.0252876i
$715$	−1580.17	+	2238.59i	−0.0826503	+	0.117089i
$716$	−23973.0	+	19503.5i	−1.25127	+	1.01799i
$717$	−13880.6	−	14862.4i	−0.722983	−	0.774126i
$718$	6409.10	+	1795.75i	0.333128	+	0.0933380i
$719$	16680.1	+	23630.3i	0.865177	+	1.22568i	0.972838	+	0.231489i	$0.0743596\pi$
$719$	16680.1	+	23630.3i	0.865177	+	1.22568i	−0.107661	+	0.994188i	$0.534336\pi$
$720$	−2674.11	−	5160.80i	−0.138414	−	0.267127i
$721$	723.779	+	10581.3i	0.0373855	+	0.546556i
$722$	−11117.2	−	9044.48i	−0.573044	−	0.466206i
$723$	4838.29	−	1355.63i	0.248877	−	0.0697320i
$724$	−3290.08	−	2000.74i	−0.168888	−	0.102703i
$725$	−1160.68	+	5585.52i	−0.0594575	+	0.286125i
$726$	−30900.0	+	4247.11i	−1.57962	+	0.217114i
$727$	−4866.39	+	9391.70i	−0.248259	+	0.479118i	−0.979087	−	0.203444i	$-0.934787\pi$
$727$	−4866.39	+	9391.70i	−0.248259	+	0.479118i	0.730828	+	0.682562i	$0.239134\pi$
$728$	20.5995	+	8.94764i	0.00104872	+	0.000455524i
$729$	−7983.73	−	3467.82i	−0.405615	−	0.176184i
$730$	−6085.12	+	11743.7i	−0.308521	+	0.595418i
$731$	−16928.7	+	2326.80i	−0.856541	+	0.117729i
$732$	2388.57	−	11494.4i	0.120607	−	0.580391i
$733$	7895.44	+	4801.32i	0.397851	+	0.241938i	0.704231	−	0.709971i	$-0.251292\pi$
$733$	7895.44	+	4801.32i	0.397851	+	0.241938i	−0.306380	+	0.951909i	$0.599118\pi$
$734$	15468.9	−	4334.18i	0.777884	−	0.217953i
$735$	−3157.52	−	2568.83i	−0.158458	−	0.128915i
$736$	−1226.64	−	17932.8i	−0.0614328	−	0.898116i
$737$	13239.3	+	25550.6i	0.661702	+	1.27703i
$738$	5962.46	+	8446.88i	0.297400	+	0.421320i
$739$	23670.8	+	6632.24i	1.17827	+	0.330137i	0.802544	−	0.596593i	$-0.203479\pi$
$739$	23670.8	+	6632.24i	1.17827	+	0.330137i	0.375729	+	0.926729i	$0.377392\pi$
$740$	8005.49	+	8571.79i	0.397686	+	0.425818i
$741$	−2025.78	+	1648.10i	−0.100431	+	0.0817063i
$742$	−3874.78	+	5489.31i	−0.191708	+	0.271589i
$743$	−14371.9	−	1975.38i	−0.709630	−	0.0975364i	−0.227681	−	0.973736i	$-0.573114\pi$
$743$	−14371.9	−	1975.38i	−0.709630	−	0.0975364i	−0.481949	+	0.876199i	$0.660071\pi$
$744$	36.8009	−	103.548i	0.00181342	−	0.00510249i
$745$	−3375.03	−	16241.5i	−0.165975	−	0.798717i
$746$	6523.31	+	18354.8i	0.320154	+	0.900828i
$747$	−20594.8	+	12524.0i	−1.00873	+	0.613424i
$748$	12832.2	−	13739.9i	0.627261	−	0.671633i
$749$	1056.39	−	15443.9i	0.0515351	−	0.753416i
$750$	1352.34	−	587.405i	0.0658408	−	0.0285987i
$751$	15769.5			0.766230			0.383115	−	0.923701i	$-0.374851\pi$
$751$	15769.5			0.766230			0.383115	+	0.923701i	$0.374851\pi$
$752$	18352.1	+	8944.28i	0.889938	+	0.433729i
$753$	3488.95			0.168851
$754$	−7294.86	+	3168.60i	−0.352338	+	0.153042i
$755$	−274.005	+	4005.81i	−0.0132080	+	0.193095i
$756$	−5986.82	+	6410.31i	−0.288014	+	0.308387i
$757$	−15940.1	+	9693.41i	−0.765329	+	0.465407i	−0.847225	−	0.531234i	$-0.821729\pi$
$757$	−15940.1	+	9693.41i	−0.765329	+	0.465407i	0.0818960	+	0.996641i	$0.473902\pi$
$758$	−2699.82	−	7596.56i	−0.129369	−	0.364010i
$759$	−2643.17	−	12719.7i	−0.126405	−	0.608293i
$760$	−54.2969	+	152.777i	−0.00259152	+	0.00729184i
$761$	−24642.2	−	3386.99i	−1.17382	−	0.161338i	−0.477211	−	0.878789i	$-0.658352\pi$
$761$	−24642.2	−	3386.99i	−1.17382	−	0.161338i	−0.696609	+	0.717451i	$0.745309\pi$
$762$	−15092.8	+	21381.7i	−0.717527	+	1.01650i
$763$	122.903	−	99.9890i	0.00583144	−	0.00474422i
$764$	11471.1	+	12282.6i	0.543209	+	0.581635i
$765$	3260.19	+	913.461i	0.154081	+	0.0431716i
$766$	−26737.3	−	37878.2i	−1.26117	−	1.78668i
$767$	−2032.84	−	3923.21i	−0.0956998	−	0.184692i
$768$	−805.708	−	11779.0i	−0.0378561	−	0.553436i
$769$	−8463.61	−	6885.66i	−0.396886	−	0.322891i	0.411645	−	0.911344i	$-0.364954\pi$
$769$	−8463.61	−	6885.66i	−0.396886	−	0.322891i	−0.808531	+	0.588453i	$0.799737\pi$
$770$	−9907.02	+	2775.82i	−0.463668	+	0.129914i
$771$	2053.27	+	1248.62i	0.0959103	+	0.0583243i
$772$	−2541.56	+	12230.7i	−0.118488	+	0.570197i
$773$	35235.8	−	4843.06i	1.63952	−	0.225346i	0.743298	−	0.668961i	$-0.233261\pi$
$773$	35235.8	−	4843.06i	1.63952	−	0.225346i	0.896218	+	0.443615i	$0.146304\pi$
$774$	−15671.2	+	30244.0i	−0.727763	+	1.40452i
$775$	2698.32	+	1172.05i	0.125066	+	0.0543240i
$776$	−251.814	−	109.378i	−0.0116489	−	0.00505985i
$777$	−3197.97	+	6171.81i	−0.147653	+	0.284958i
$778$	45118.9	−	6201.45i	2.07917	−	0.285775i
$779$	−2920.53	+	14054.4i	−0.134325	+	0.646406i
$780$	882.461	+	536.636i	0.0405092	+	0.0246342i
$781$	46844.9	−	13125.3i	2.14628	−	0.601359i
$782$	8041.48	+	6542.23i	0.367727	+	0.299168i
$783$	−2077.23	−	30368.0i	−0.0948074	−	1.38604i
$784$	8067.47	+	15569.5i	0.367505	+	0.709253i
$785$	1972.61	+	2794.55i	0.0896883	+	0.127059i
$786$	11898.7	+	3333.85i	0.539964	+	0.151291i
$787$	16684.6	+	17864.8i	0.755707	+	0.809165i	0.986487	−	0.163841i	$-0.0523885\pi$
$787$	16684.6	+	17864.8i	0.755707	+	0.809165i	−0.230780	+	0.973006i	$0.574128\pi$
$788$	−12356.9	+	10053.1i	−0.558624	+	0.454474i
$789$	−10913.0	+	15460.2i	−0.492412	+	0.697589i
$790$	11306.6	+	1554.05i	0.509202	+	0.0699882i
$791$	15.8205	−	44.5146i	0.000711140	−	0.00200096i
$792$	−74.7206	−	359.575i	−0.00335237	−	0.0161325i
$793$	1437.89	+	4045.83i	0.0643896	+	0.181175i
$794$	7891.89	−	4799.17i	0.352737	−	0.214504i
$795$	−2066.79	+	2212.99i	−0.0922032	+	0.0987255i
$796$	708.036	−	10351.1i	0.0315272	−	0.460912i
$797$	−4210.33	+	1828.80i	−0.187124	+	0.0812792i	−0.489885	−	0.871787i	$-0.662961\pi$
$797$	−4210.33	+	1828.80i	−0.187124	+	0.0812792i	0.302761	+	0.953066i	$0.402092\pi$
$798$	−9805.70			−0.434985
$799$	−11104.2	+	4256.56i	−0.491662	+	0.188469i
$800$	−6415.19			−0.283514
$801$	5781.06	−	2511.07i	0.255011	−	0.110767i
$802$	−358.716	+	5244.25i	−0.0157939	+	0.230899i
$803$	28390.3	−	30398.6i	1.24766	−	1.33592i
$804$	9267.69	−	5635.81i	0.406525	−	0.247213i
$805$	−954.591	−	2685.96i	−0.0417949	−	0.117600i
$806$	834.446	+	4015.58i	0.0364666	+	0.175487i
$807$	−4199.62	+	11816.6i	−0.183189	+	0.515445i
$808$	469.064	+	64.4713i	0.0204228	+	0.00280705i
$809$	444.733	−	630.043i	0.0193275	−	0.0273809i	−0.807191	−	0.590290i	$-0.799013\pi$
$809$	444.733	−	630.043i	0.0193275	−	0.0273809i	0.826519	+	0.562909i	$0.190318\pi$
$810$	1601.94	−	1303.27i	0.0694893	−	0.0565338i
$811$	−5718.59	−	6123.11i	−0.247604	−	0.265119i	0.594912	−	0.803791i	$-0.297187\pi$
$811$	−5718.59	−	6123.11i	−0.247604	−	0.265119i	−0.842516	+	0.538672i	$0.818926\pi$
$812$	−14448.6	−	4048.30i	−0.624440	−	0.174960i
$813$	−12836.6	−	18185.4i	−0.553752	−	0.784488i
$814$	−33771.7	−	65176.3i	−1.45417	−	2.80642i
$815$	170.554	+	2493.41i	0.00733035	+	0.107166i
$816$	5335.85	+	4341.04i	0.228912	+	0.186234i
$817$	−45537.8	+	12759.1i	−1.95002	+	0.546370i
$818$	22224.6	+	13515.1i	0.949956	+	0.577681i
$819$	264.071	−	1270.78i	0.0112666	−	0.0542181i
$820$	5624.17	−	773.025i	0.239518	−	0.0329210i
$821$	7841.84	−	15134.1i	0.333352	−	0.643340i	−0.660892	−	0.750481i	$-0.729822\pi$
$821$	7841.84	−	15134.1i	0.333352	−	0.643340i	0.994244	+	0.107141i	$0.0341696\pi$
$822$	−3010.37	−	1307.59i	−0.127736	−	0.0554834i
$823$	−17955.1	−	7799.00i	−0.760481	−	0.330323i	−0.0176868	−	0.999844i	$-0.505630\pi$
$823$	−17955.1	−	7799.00i	−0.760481	−	0.330323i	−0.742794	+	0.669520i	$0.766500\pi$
$824$	−190.334	+	367.328i	−0.00804683	+	0.0155297i
$825$	−4593.44	+	631.354i	−0.193846	+	0.0266435i
$826$	3375.52	−	16243.9i	0.142191	−	0.684258i
$827$	1251.57	+	761.100i	0.0526258	+	0.0320024i	0.545650	−	0.838013i	$-0.316283\pi$
$827$	1251.57	+	761.100i	0.0526258	+	0.0320024i	−0.493025	+	0.870015i	$0.664109\pi$
$828$	9998.20	−	2801.36i	0.419639	−	0.117577i
$829$	−538.589	−	438.175i	−0.0225645	−	0.0183576i	0.619739	−	0.784808i	$-0.287238\pi$
$829$	−538.589	−	438.175i	−0.0225645	−	0.0183576i	−0.642303	+	0.766450i	$0.722021\pi$
$830$	1797.50	+	26278.6i	0.0751714	+	1.09897i
$831$	−4952.65	−	9558.17i	−0.206745	−	0.399000i
$832$	−2616.90	−	3707.30i	−0.109044	−	0.154480i
$833$	−9835.59	−	2755.80i	−0.409103	−	0.114625i
$834$	7263.50	+	7777.31i	0.301576	+	0.322909i
$835$	−6993.76	+	5689.85i	−0.289855	+	0.235815i
$836$	30005.1	−	42507.5i	1.24132	−	1.75856i
$837$	−15550.6	−	2137.38i	−0.642183	−	0.0882660i
$838$	10929.2	−	30751.7i	0.450527	−	1.26766i
$839$	−7671.81	−	36918.8i	−0.315686	−	1.51916i	−0.775614	−	0.631207i	$-0.782560\pi$
$839$	−7671.81	−	36918.8i	−0.315686	−	1.51916i	0.459929	−	0.887956i	$-0.347875\pi$
$840$	12.7265	+	35.8090i	0.000522747	+	0.00147087i
$841$	23653.2	−	14383.8i	0.969829	−	0.589766i
$842$	32251.3	−	34532.7i	1.32001	−	1.41339i
$843$	951.673	−	13913.0i	0.0388818	−	0.568432i
$844$	33564.1	−	14579.0i	1.36887	−	0.594584i
$845$	10607.3			0.431835
$846$	−5832.85	+	22976.8i	−0.237042	+	0.933758i
$847$	21521.9			0.873084
$848$	11964.7	−	5197.00i	0.484516	−	0.210455i
$849$	111.737	−	1633.54i	0.00451686	−	0.0660341i
$850$	2525.34	−	2703.97i	0.101904	−	0.109112i
$851$	17377.2	−	10567.3i	0.699978	−	0.425666i
$852$	−6140.70	−	17278.3i	−0.246921	−	0.694770i
$853$	−4887.38	−	23519.4i	−0.196179	−	0.944065i	−0.955872	−	0.293783i	$-0.905086\pi$
$853$	−4887.38	−	23519.4i	−0.196179	−	0.944065i	0.759693	−	0.650282i	$-0.225349\pi$
$854$	−5398.97	+	15191.3i	−0.216334	+	0.608705i
$855$	9282.92	+	1275.91i	0.371309	+	0.0510352i
$856$	348.218	−	493.313i	0.0139040	−	0.0196975i
$857$	−21966.6	+	17871.2i	−0.875573	+	0.712331i	−0.958764	−	0.284202i	$-0.908271\pi$
$857$	−21966.6	+	17871.2i	−0.875573	+	0.712331i	0.0831917	+	0.996534i	$0.473489\pi$
$858$	−4412.07	−	4724.17i	−0.175554	−	0.187973i
$859$	34389.4	+	9635.46i	1.36595	+	0.382721i	0.873163	−	0.487429i	$-0.162065\pi$
$859$	34389.4	+	9635.46i	1.36595	+	0.382721i	0.492787	+	0.870150i	$0.335978\pi$
$860$	10785.7	+	15279.9i	0.427663	+	0.605861i
$861$	1547.91	+	2987.33i	0.0612691	+	0.118244i
$862$	2081.08	+	30424.3i	0.0822295	+	1.20215i
$863$	−5077.86	−	4131.15i	−0.200293	−	0.162950i	0.525660	−	0.850695i	$-0.323818\pi$
$863$	−5077.86	−	4131.15i	−0.200293	−	0.162950i	−0.725953	+	0.687745i	$0.758601\pi$
$864$	32959.9	−	9234.92i	1.29782	−	0.363632i
$865$	−7481.38	−	4549.53i	−0.294075	−	0.178831i
$866$	−1299.72	+	6254.58i	−0.0510002	+	0.245426i
$867$	10347.7	−	1422.26i	0.405337	−	0.0557123i
$868$	−3559.88	+	6870.26i	−0.139205	+	0.268654i
$869$	−32919.1	−	14298.8i	−1.28505	−	0.558174i
$870$	−12343.8	−	5361.68i	−0.481029	−	0.208940i
$871$	−1825.11	+	3522.30i	−0.0710006	+	0.137025i
$872$	6.12270	−	0.841546i	0.000237776	−	3.26816e-5i
$873$	−3228.06	+	15534.3i	−0.125147	+	0.602241i
$874$	24513.3	+	14906.9i	0.948713	+	0.576925i
$875$	−979.635	+	274.481i	−0.0378488	+	0.0106047i
$876$	−12161.6	−	9894.18i	−0.469066	−	0.381614i
$877$	−961.672	−	14059.1i	−0.0370278	−	0.541327i	−0.978766	−	0.204980i	$-0.934287\pi$
$877$	−961.672	−	14059.1i	−0.0370278	−	0.541327i	0.941738	−	0.336346i	$-0.109191\pi$
$878$	−9293.94	−	17936.5i	−0.357238	−	0.689439i
$879$	−538.154	−	762.391i	−0.0206502	−	0.0292546i
$880$	19233.7	+	5389.03i	0.736782	+	0.206437i
$881$	−23684.4	−	25359.8i	−0.905731	−	0.969801i	0.0939369	−	0.995578i	$-0.470055\pi$
$881$	−23684.4	−	25359.8i	−0.905731	−	0.969801i	−0.999668	+	0.0257773i	$0.991794\pi$
$882$	−15794.5	+	12849.8i	−0.602979	+	0.490560i
$883$	20123.1	−	28508.0i	0.766928	−	1.08649i	−0.226720	−	0.973960i	$-0.572800\pi$
$883$	20123.1	−	28508.0i	0.766928	−	1.08649i	0.993648	−	0.112530i	$-0.0358953\pi$
$884$	2567.59	+	352.907i	0.0976894	+	0.0134271i
$885$	2503.84	−	7045.14i	0.0951025	−	0.267593i
$886$	12890.0	+	62030.0i	0.488767	+	2.35208i
$887$	−523.781	−	1473.78i	−0.0198273	−	0.0557887i	0.931934	−	0.362627i	$-0.118120\pi$
$887$	−523.781	−	1473.78i	−0.0198273	−	0.0557887i	−0.951762	+	0.306838i	$0.900729\pi$
$888$	−231.671	+	140.882i	−0.00875492	+	0.00532399i
$889$	12326.2	−	13198.2i	0.465026	−	0.497922i
$890$	470.026	−	6871.53i	0.0177026	−	0.258803i
$891$	−5956.62	+	2587.32i	−0.223967	+	0.0972824i
$892$	−3548.33			−0.133192
$893$	−28841.1	+	15855.1i	−1.08077	+	0.594144i
$894$	39133.1			1.46399
$895$	17542.6	−	7619.84i	0.655179	−	0.284584i
$896$	22.5694	−	329.952i	0.000841506	−	0.0123024i
$897$	1222.41	−	1308.88i	0.0455018	−	0.0487205i
$898$	−24991.1	+	15197.4i	−0.928689	+	0.564748i
$899$	−8992.41	−	25302.2i	−0.333608	−	0.938683i
$900$	−753.963	−	3628.27i	−0.0279246	−	0.134380i
$901$	−2544.57	+	7159.73i	−0.0940864	+	0.264734i
$902$	−35199.8	−	4838.10i	−1.29936	−	0.178593i
$903$	−6392.25	+	9055.75i	−0.235571	+	0.333728i
$904$	1.42947	−	1.16296i	5.25925e−5	−	4.27872e-5i
$905$	1626.58	+	1741.64i	0.0597451	+	0.0639714i
$906$	−9120.75	−	2555.51i	−0.334455	−	0.0937100i
$907$	10648.2	+	15085.0i	0.389820	+	0.552249i	0.963802	−	0.266619i	$-0.0859065\pi$
$907$	10648.2	+	15085.0i	0.389820	+	0.552249i	−0.573982	+	0.818868i	$0.694602\pi$
$908$	−15186.6	−	29308.8i	−0.555049	−	1.07120i
$909$	−1867.29	−	27298.8i	−0.0681344	−	0.996089i
$910$	−1100.22	−	895.095i	−0.0400790	−	0.0326067i
$911$	50387.3	−	14117.9i	1.83250	−	0.513442i	0.833275	−	0.552858i	$-0.186463\pi$
$911$	50387.3	−	14117.9i	1.83250	−	0.513442i	0.999223	+	0.0394163i	$0.0125499\pi$
$912$	16265.6	+	9891.33i	0.590579	+	0.359139i
$913$	16852.7	−	81099.8i	0.610892	−	2.93977i
$914$	−1315.99	+	180.878i	−0.0476247	+	0.00654586i
$915$	−3342.64	+	6451.00i	−0.120770	+	0.233075i
$916$	−33435.9	−	14523.3i	−1.20606	−	0.523867i
$917$	−7820.54	−	3396.94i	−0.281633	−	0.122330i
$918$	−9082.16	+	17527.8i	−0.326531	+	0.630177i
$919$	−14344.8	+	1971.65i	−0.514898	+	0.0707711i	−0.388937	−	0.921264i	$-0.627158\pi$
$919$	−14344.8	+	1971.65i	−0.514898	+	0.0707711i	−0.125960	+	0.992035i	$0.540201\pi$
$920$	22.6227	−	108.866i	0.000810705	−	0.00390132i
$921$	−18028.1	−	10963.1i	−0.645000	−	0.392233i
$922$	18848.9	−	5281.21i	0.673270	−	0.188641i
$923$	5202.35	+	4232.42i	0.185523	+	0.150934i
$924$	−832.240	−	12166.9i	−0.0296306	−	0.433184i
$925$	−3339.44	−	6444.83i	−0.118703	−	0.229086i
$926$	−22131.5	−	31353.2i	−0.785406	−	1.11267i
$927$	23022.2	+	6450.53i	0.815695	+	0.228547i
$928$	39967.7	+	42795.0i	1.41380	+	1.51381i
$929$	36943.4	−	30055.7i	1.30471	−	1.06146i	0.310889	−	0.950446i	$-0.399373\pi$
$929$	36943.4	−	30055.7i	1.30471	−	1.06146i	0.993819	−	0.111013i	$-0.0354095\pi$
$930$	−4002.18	+	5669.79i	−0.141115	+	0.199914i
$931$	−28005.5	−	3849.26i	−0.985867	−	0.135504i
$932$	1971.06	−	5546.03i	0.0692748	−	0.194921i
$933$	3959.21	+	19052.8i	0.138927	+	0.668552i
$934$	12501.3	+	35175.3i	0.437960	+	1.23230i
$935$	−9941.19	+	6045.37i	−0.347713	+	0.211449i
$936$	34.5566	−	37.0011i	0.00120675	−	0.00129212i
$937$	419.244	−	6129.13i	0.0146170	−	0.213693i	−0.984622	−	0.174696i	$-0.944106\pi$
$937$	419.244	−	6129.13i	0.0146170	−	0.213693i	0.999239	−	0.0389964i	$-0.0124161\pi$
$938$	−13662.3	+	5934.39i	−0.475577	+	0.206572i
$939$	−29831.2			−1.03674
$940$	9728.14	+	8647.80i	0.337550	+	0.300064i
$941$	42877.4			1.48540			0.742702	−	0.669622i	$-0.233544\pi$
$941$	42877.4			1.48540			0.742702	+	0.669622i	$0.233544\pi$
$942$	−7401.37	+	3214.87i	−0.255997	+	0.111195i
$943$	671.790	−	9821.22i	0.0231988	−	0.339155i
$944$	−21985.0	+	23540.2i	−0.757999	+	0.811619i
$945$	4638.03	−	2820.45i	0.159656	−	0.0970891i
$946$	−39199.9	−	110298.i	−1.34725	−	3.79080i
$947$	−8555.08	−	41169.3i	−0.293561	−	1.41270i	−0.824777	−	0.565458i	$-0.808699\pi$
$947$	−8555.08	−	41169.3i	−0.293561	−	1.41270i	0.531215	−	0.847237i	$-0.321736\pi$
$948$	−4530.27	+	12746.9i	−0.155207	+	0.436710i
$949$	5680.62	+	780.783i	0.194311	+	0.0267074i
$950$	5904.90	−	8365.34i	0.201664	−	0.285692i
$951$	15213.0	−	12376.7i	0.518734	−	0.422021i
$952$	65.0914	+	69.6958i	0.00221599	+	0.00237275i
$953$	−3595.59	−	1007.44i	−0.122217	−	0.0342436i	0.208145	−	0.978098i	$-0.433258\pi$
$953$	−3595.59	−	1007.44i	−0.122217	−	0.0342436i	−0.330361	+	0.943855i	$0.607171\pi$
$954$	8734.82	+	12374.4i	0.296436	+	0.419955i
$955$	−4785.12	−	9234.86i	−0.162139	−	0.312914i
$956$	3811.68	+	55724.8i	0.128952	+	1.88522i
$957$	32829.6	+	26708.9i	1.10891	+	0.902168i
$958$	3451.69	−	967.117i	0.116408	−	0.0326160i
$959$	1934.99	+	1176.70i	0.0651556	+	0.0396220i
$960$	1562.27	−	7518.05i	0.0525229	−	0.252754i
$961$	15795.1	−	2170.99i	0.530197	−	0.0728740i
$962$	4655.62	−	8984.94i	0.156033	−	0.301129i
$963$	−32007.2	−	13902.7i	−1.07105	−	0.465221i
$964$	−12658.0	−	5498.13i	−0.422910	−	0.183696i
$965$	3556.75	−	6864.21i	0.118648	−	0.228981i
$966$	6661.96	−	915.665i	0.221889	−	0.0304980i
$967$	−5570.84	+	26808.3i	−0.185260	+	0.891518i	0.779095	+	0.626906i	$0.215679\pi$
$967$	−5570.84	+	26808.3i	−0.185260	+	0.891518i	−0.964355	+	0.264613i	$0.914756\pi$
$968$	717.294	+	436.196i	0.0238168	+	0.0144833i
$969$	−10677.8	+	2991.77i	−0.353994	+	0.0991844i
$970$	13449.3	+	10941.9i	0.445188	+	0.362187i
$971$	−981.597	−	14350.4i	−0.0324417	−	0.474282i	−0.985296	−	0.170854i	$-0.945347\pi$
$971$	−981.597	−	14350.4i	−0.0324417	−	0.474282i	0.952855	−	0.303427i	$-0.0981310\pi$
$972$	14513.0	+	28008.8i	0.478914	+	0.924261i
$973$	−4234.51	−	5998.93i	−0.139519	−	0.197654i
$974$	67197.2	+	18827.8i	2.21061	+	0.619385i
$975$	−436.279	−	467.140i	−0.0143304	−	0.0153441i
$976$	24279.7	−	19753.0i	0.796284	−	0.647825i
$977$	21526.0	−	30495.4i	0.704890	−	0.998601i	−0.294192	−	0.955746i	$-0.595050\pi$
$977$	21526.0	−	30495.4i	0.704890	−	0.998601i	0.999081	−	0.0428545i	$-0.0136452\pi$
$978$	−5840.90	−	802.813i	−0.190973	−	0.0262486i
$979$	−7253.38	+	20409.1i	−0.236792	+	0.666268i
$980$	2274.62	+	10946.1i	0.0741428	+	0.356795i
$981$	−119.607	−	336.543i	−0.00389273	−	0.0109531i
$982$	−31150.7	+	18943.2i	−1.01228	+	0.615582i
$983$	−9144.68	+	9791.56i	−0.296714	+	0.317703i	−0.861720	−	0.507383i	$-0.830613\pi$
$983$	−9144.68	+	9791.56i	−0.296714	+	0.317703i	0.565006	+	0.825086i	$0.308874\pi$
$984$	−8.95625	+	130.936i	−0.000290157	+	0.00424195i
$985$	9042.35	−	3927.65i	0.292501	−	0.127051i
$986$	−33771.2			−1.09076
$987$	−2898.53	+	7148.88i	−0.0934764	+	0.230549i
$988$	7172.73			0.230967
$989$	29746.8	−	12920.9i	0.956414	−	0.415429i
$990$	−1582.76	+	23139.1i	−0.0508116	+	0.742839i
$991$	−12654.5	+	13549.6i	−0.405633	+	0.434327i	−0.900643	−	0.434560i	$-0.856904\pi$
$991$	−12654.5	+	13549.6i	−0.405633	+	0.434327i	0.495009	+	0.868888i	$0.335165\pi$
$992$	25800.3	−	15689.5i	0.825766	−	0.502159i
$993$	−2680.92	−	7543.37i	−0.0856760	−	0.241069i
$994$	5123.36	+	24655.0i	0.163484	+	0.786728i
$995$	−2150.27	+	6050.28i	−0.0685107	+	0.192771i
$996$	−30930.8	−	4251.35i	−0.984017	−	0.135250i
$997$	−4690.85	+	6645.42i	−0.149008	+	0.211096i	−0.884627	−	0.466299i	$-0.845587\pi$
$997$	−4690.85	+	6645.42i	−0.149008	+	0.211096i	0.735619	+	0.677395i	$0.236891\pi$
$998$	−20309.8	+	16523.2i	−0.644183	+	0.524081i
$999$	26434.9	+	28304.9i	0.837201	+	0.896424i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	235.4.g.b.6.5	✓	550
47.8	even	23	inner	235.4.g.b.196.5	yes	550

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
235.4.g.b.6.5	✓	550	1.1	even	1	trivial
235.4.g.b.196.5	yes	550	47.8	even	23	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:	\( N \)	\(=\)	\( 235 = 5 \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	235.g (of order \(23\), degree \(22\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.67791 + 1.59754i) q^{2} +(-0.200738 + 2.93469i) q^{3} +(5.51447 - 5.90455i) q^{4} +(-4.27210 + 2.59792i) q^{5} +(-3.94999 - 11.1142i) q^{6} +(1.65591 + 7.96866i) q^{7} +(-0.106316 + 0.299145i) q^{8} +(18.1764 + 2.49829i) q^{9} +O(q^{10})\)	\(q+(-3.67791 + 1.59754i) q^{2} +(-0.200738 + 2.93469i) q^{3} +(5.51447 - 5.90455i) q^{4} +(-4.27210 + 2.59792i) q^{5} +(-3.94999 - 11.1142i) q^{6} +(1.65591 + 7.96866i) q^{7} +(-0.106316 + 0.299145i) q^{8} +(18.1764 + 2.49829i) q^{9} +(11.5621 - 16.3798i) q^{10} +(-48.9088 + 39.7902i) q^{11} +(16.2210 + 17.3685i) q^{12} +(-8.36953 - 2.34503i) q^{13} +(-18.8206 - 26.6627i) q^{14} +(-6.76651 - 13.0588i) q^{15} +(4.32386 + 63.2126i) q^{16} +(-28.6293 - 23.2917i) q^{17} +(-70.8424 + 19.8491i) q^{18} +(-87.2724 - 53.0715i) q^{19} +(-8.21878 + 39.5510i) q^{20} +(-23.7179 + 3.25996i) q^{21} +(116.316 - 224.479i) q^{22} +(64.2484 + 27.9070i) q^{23} +(-0.856555 - 0.372054i) q^{24} +(11.5016 - 22.1971i) q^{25} +(34.5287 - 4.74586i) q^{26} +(-27.1392 + 130.601i) q^{27} +(56.1828 + 34.1655i) q^{28} +(-219.732 + 61.5659i) q^{29} +(45.7486 + 37.2192i) q^{30} +(8.03042 + 117.401i) q^{31} +(-118.056 - 227.838i) q^{32} +(-106.954 - 151.519i) q^{33} +(142.506 + 39.9282i) q^{34} +(-27.7761 - 29.7410i) q^{35} +(114.985 - 93.5469i) q^{36} +(167.436 - 237.203i) q^{37} +(405.764 + 55.7710i) q^{38} +(8.56202 - 24.0912i) q^{39} +(-0.322962 - 1.55418i) q^{40} +(-47.0624 - 132.421i) q^{41} +(82.0246 - 49.8802i) q^{42} +(316.020 - 338.374i) q^{43} +(-34.7622 + 508.206i) q^{44} +(-84.1418 + 36.5480i) q^{45} -280.883 q^{46} +(160.602 - 279.338i) q^{47} -186.377 q^{48} +(253.846 - 110.261i) q^{49} +(-6.84110 + 100.013i) q^{50} +(74.1008 - 79.3426i) q^{51} +(-59.9998 + 36.4867i) q^{52} +(-68.9451 - 193.993i) q^{53} +(-108.825 - 523.696i) q^{54} +(105.571 - 297.049i) q^{55} +(-2.55984 - 0.351841i) q^{56} +(173.267 - 245.464i) q^{57} +(709.799 - 577.464i) q^{58} +(346.984 + 371.529i) q^{59} +(-114.420 - 32.0589i) q^{60} +(-284.879 - 403.581i) q^{61} +(-217.088 - 418.960i) q^{62} +(10.1904 + 148.979i) q^{63} +(404.986 + 329.481i) q^{64} +(41.8476 - 11.7252i) q^{65} +(635.426 + 386.411i) q^{66} +(92.8600 - 446.867i) q^{67} +(-295.402 + 40.6021i) q^{68} +(-94.7955 + 182.947i) q^{69} +(149.671 + 65.0112i) q^{70} +(-707.712 - 307.403i) q^{71} +(-2.67980 + 5.17178i) q^{72} +(-653.557 + 89.8294i) q^{73} +(-236.874 + 1139.90i) q^{74} +(62.8328 + 38.2095i) q^{75} +(-794.624 + 222.643i) q^{76} +(-398.063 - 323.849i) q^{77} +(6.99638 + 102.284i) q^{78} +(261.886 + 505.416i) q^{79} +(-182.693 - 258.817i) q^{80} +(99.1820 + 27.7895i) q^{81} +(384.640 + 411.849i) q^{82} +(-1019.09 + 829.093i) q^{83} +(-111.543 + 158.021i) q^{84} +(182.817 + 25.1276i) q^{85} +(-621.725 + 1749.37i) q^{86} +(-136.568 - 657.202i) q^{87} +(-6.70326 - 18.8612i) q^{88} +(293.519 - 178.493i) q^{89} +(251.079 - 268.840i) q^{90} +(4.82761 - 70.5771i) q^{91} +(519.074 - 225.466i) q^{92} -346.146 q^{93} +(-144.427 + 1283.95i) q^{94} +510.712 q^{95} +(692.332 - 300.722i) q^{96} +(-59.0138 + 862.751i) q^{97} +(-757.476 + 811.059i) q^{98} +(-988.394 + 601.056i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 550 q + 4 q^{2} - 2 q^{3} - 102 q^{4} + 125 q^{5} + 44 q^{6} - 2 q^{7} - 6 q^{8} - 175 q^{9}+O(q^{10}) \) 550 * q + 4 * q^2 - 2 * q^3 - 102 * q^4 + 125 * q^5 + 44 * q^6 - 2 * q^7 - 6 * q^8 - 175 * q^9	\( 550 q + 4 q^{2} - 2 q^{3} - 102 q^{4} + 125 q^{5} + 44 q^{6} - 2 q^{7} - 6 q^{8} - 175 q^{9} - 20 q^{10} + 74 q^{11} - 677 q^{12} + 132 q^{13} - 83 q^{14} + 10 q^{15} - 602 q^{16} - 62 q^{17} - 95 q^{18} + 590 q^{19} + 510 q^{20} - 148 q^{21} + 178 q^{22} - 2244 q^{23} + 625 q^{24} - 625 q^{25} - 2530 q^{26} + 472 q^{27} + 68 q^{28} - 40 q^{29} + 1505 q^{30} - 16 q^{31} + 301 q^{32} + 200 q^{33} + 104 q^{34} + 10 q^{35} - 778 q^{36} + 3435 q^{37} + 1724 q^{38} + 578 q^{39} + 30 q^{40} - 442 q^{41} - 3709 q^{42} - 484 q^{43} - 12170 q^{44} + 875 q^{45} + 614 q^{46} - 1743 q^{47} - 962 q^{48} - 2509 q^{49} + 100 q^{50} + 390 q^{51} - 7609 q^{52} + 758 q^{53} + 1373 q^{54} - 140 q^{55} + 106 q^{56} + 6740 q^{57} + 4800 q^{58} + 8566 q^{59} - 295 q^{60} + 1364 q^{61} - 7252 q^{62} - 3122 q^{63} - 4010 q^{64} - 660 q^{65} + 24646 q^{66} - 68 q^{67} - 905 q^{68} - 2624 q^{69} + 185 q^{70} - 318 q^{71} - 3352 q^{72} + 428 q^{73} + 506 q^{74} - 50 q^{75} + 2495 q^{76} + 18134 q^{77} + 16762 q^{78} + 4620 q^{79} - 785 q^{80} - 14403 q^{81} + 11899 q^{82} + 90 q^{83} + 15755 q^{84} + 310 q^{85} - 4050 q^{86} - 5440 q^{87} - 439 q^{88} - 2148 q^{89} + 475 q^{90} - 9933 q^{91} - 36335 q^{92} - 4472 q^{93} - 3725 q^{94} + 270 q^{95} - 1421 q^{96} - 7342 q^{97} - 39381 q^{98} - 11821 q^{99}+O(q^{100}) \) 550 * q + 4 * q^2 - 2 * q^3 - 102 * q^4 + 125 * q^5 + 44 * q^6 - 2 * q^7 - 6 * q^8 - 175 * q^9 - 20 * q^10 + 74 * q^11 - 677 * q^12 + 132 * q^13 - 83 * q^14 + 10 * q^15 - 602 * q^16 - 62 * q^17 - 95 * q^18 + 590 * q^19 + 510 * q^20 - 148 * q^21 + 178 * q^22 - 2244 * q^23 + 625 * q^24 - 625 * q^25 - 2530 * q^26 + 472 * q^27 + 68 * q^28 - 40 * q^29 + 1505 * q^30 - 16 * q^31 + 301 * q^32 + 200 * q^33 + 104 * q^34 + 10 * q^35 - 778 * q^36 + 3435 * q^37 + 1724 * q^38 + 578 * q^39 + 30 * q^40 - 442 * q^41 - 3709 * q^42 - 484 * q^43 - 12170 * q^44 + 875 * q^45 + 614 * q^46 - 1743 * q^47 - 962 * q^48 - 2509 * q^49 + 100 * q^50 + 390 * q^51 - 7609 * q^52 + 758 * q^53 + 1373 * q^54 - 140 * q^55 + 106 * q^56 + 6740 * q^57 + 4800 * q^58 + 8566 * q^59 - 295 * q^60 + 1364 * q^61 - 7252 * q^62 - 3122 * q^63 - 4010 * q^64 - 660 * q^65 + 24646 * q^66 - 68 * q^67 - 905 * q^68 - 2624 * q^69 + 185 * q^70 - 318 * q^71 - 3352 * q^72 + 428 * q^73 + 506 * q^74 - 50 * q^75 + 2495 * q^76 + 18134 * q^77 + 16762 * q^78 + 4620 * q^79 - 785 * q^80 - 14403 * q^81 + 11899 * q^82 + 90 * q^83 + 15755 * q^84 + 310 * q^85 - 4050 * q^86 - 5440 * q^87 - 439 * q^88 - 2148 * q^89 + 475 * q^90 - 9933 * q^91 - 36335 * q^92 - 4472 * q^93 - 3725 * q^94 + 270 * q^95 - 1421 * q^96 - 7342 * q^97 - 39381 * q^98 - 11821 * q^99

Introduction

L-functions

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