LMFDB - Embedded newform 114.4.h.b.65.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,4,Mod(65,114)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(114, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("114.65");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	114.h (of order $6$, degree $2$, 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:	$6.72621774065$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 5 x^{19} + 10 x^{18} - 183 x^{17} + 864 x^{16} - 495 x^{15} - 1530 x^{14} + \cdots + 205891132094649 $ x^20 - 5x^19 + 10x^18 - 183x^17 + 864x^16 - 495x^15 - 1530x^14 + 118935x^13 - 524961x^12 + 4026996x^11 - 36285408x^10 + 108728892x^9 - 382696569x^8 + 2340997605x^7 - 813104730x^6 - 7102708965x^5 + 334731302496x^4 - 1914244636149x^3 + 2824295364810x^2 - 38127987424935*x + 205891132094649
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.8
Root			$5.00721 - 1.38847i$ of defining polynomial
Character	$\chi$	$=$	114.65
Dual form			114.4.h.b.107.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{2} +(3.70606 - 3.64214i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(13.6046 + 7.85461i) q^{5} +(-2.60231 - 10.0612i) q^{6} +16.2728 q^{7} -8.00000 q^{8} +(0.469703 - 26.9959i) q^{9} +O(q^{10})$	\(q+(1.00000 - 1.73205i) q^{2} +(3.70606 - 3.64214i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(13.6046 + 7.85461i) q^{5} +(-2.60231 - 10.0612i) q^{6} +16.2728 q^{7} -8.00000 q^{8} +(0.469703 - 26.9959i) q^{9} +(27.2092 - 15.7092i) q^{10} +39.4106i q^{11} +(-20.0288 - 5.55388i) q^{12} +(6.61751 - 3.82062i) q^{13} +(16.2728 - 28.1853i) q^{14} +(79.0269 - 20.4401i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-85.5673 - 49.4023i) q^{17} +(-46.2886 - 27.8095i) q^{18} +(-72.7908 - 39.5032i) q^{19} -62.8368i q^{20} +(60.3078 - 59.2676i) q^{21} +(68.2611 + 39.4106i) q^{22} +(-80.1041 + 46.2481i) q^{23} +(-29.6484 + 29.1371i) q^{24} +(60.8896 + 105.464i) q^{25} -15.2825i q^{26} +(-96.5820 - 101.759i) q^{27} +(-32.5455 - 56.3705i) q^{28} +(145.486 + 251.989i) q^{29} +(43.6236 - 157.319i) q^{30} -273.495i q^{31} +(16.0000 + 27.7128i) q^{32} +(143.539 + 146.058i) q^{33} +(-171.135 + 98.8046i) q^{34} +(221.384 + 127.816i) q^{35} +(-94.4560 + 52.3647i) q^{36} +19.0864i q^{37} +(-141.212 + 86.5741i) q^{38} +(10.6096 - 38.2613i) q^{39} +(-108.837 - 62.8368i) q^{40} +(-50.8201 + 88.0230i) q^{41} +(-42.3467 - 163.724i) q^{42} +(-151.079 + 261.676i) q^{43} +(136.522 - 78.8212i) q^{44} +(218.432 - 363.579i) q^{45} +184.993i q^{46} +(339.551 - 196.040i) q^{47} +(20.8185 + 80.4897i) q^{48} -78.1970 q^{49} +243.559 q^{50} +(-497.047 + 128.560i) q^{51} +(-26.4700 - 15.2825i) q^{52} +(265.245 + 459.418i) q^{53} +(-272.834 + 65.5259i) q^{54} +(-309.555 + 536.164i) q^{55} -130.182 q^{56} +(-413.643 + 118.713i) q^{57} +581.944 q^{58} +(-338.830 + 586.871i) q^{59} +(-228.860 - 232.877i) q^{60} +(87.8160 + 152.102i) q^{61} +(-473.707 - 273.495i) q^{62} +(7.64336 - 439.298i) q^{63} +64.0000 q^{64} +120.038 q^{65} +(396.518 - 102.558i) q^{66} +(212.132 - 122.474i) q^{67} +395.218i q^{68} +(-128.428 + 463.148i) q^{69} +(442.768 - 255.632i) q^{70} +(251.080 - 434.884i) q^{71} +(-3.75762 + 215.967i) q^{72} +(135.861 - 235.317i) q^{73} +(33.0586 + 19.0864i) q^{74} +(609.774 + 169.087i) q^{75} +(8.73846 + 331.161i) q^{76} +641.319i q^{77} +(-55.6609 - 56.6377i) q^{78} +(-456.187 - 263.379i) q^{79} +(-217.673 + 125.674i) q^{80} +(-728.559 - 25.3601i) q^{81} +(101.640 + 176.046i) q^{82} -983.108i q^{83} +(-325.925 - 90.3771i) q^{84} +(-776.071 - 1344.19i) q^{85} +(302.157 + 523.352i) q^{86} +(1456.96 + 404.006i) q^{87} -315.285i q^{88} +(-292.932 - 507.374i) q^{89} +(-411.304 - 741.915i) q^{90} +(107.685 - 62.1721i) q^{91} +(320.416 + 184.993i) q^{92} +(-996.105 - 1013.59i) q^{93} -784.160i q^{94} +(-680.006 - 1109.17i) q^{95} +(160.231 + 44.4311i) q^{96} +(355.280 + 205.121i) q^{97} +(-78.1970 + 135.441i) q^{98} +(1063.92 + 18.5113i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{2} + q^{3} - 40 q^{4} - 8 q^{6} - 10 q^{7} - 160 q^{8} - 37 q^{9}+O(q^{10}) $ 20 * q + 20 * q^2 + q^3 - 40 * q^4 - 8 * q^6 - 10 * q^7 - 160 * q^8 - 37 * q^9	\( 20 q + 20 q^{2} + q^{3} - 40 q^{4} - 8 q^{6} - 10 q^{7} - 160 q^{8} - 37 q^{9} - 20 q^{12} - 111 q^{13} - 10 q^{14} - 133 q^{15} - 160 q^{16} - 90 q^{17} - 10 q^{18} - 143 q^{19} + 191 q^{21} - 54 q^{22} - 8 q^{24} + 184 q^{25} - 524 q^{27} + 20 q^{28} - 96 q^{29} - 292 q^{30} + 320 q^{32} - 55 q^{33} - 180 q^{34} + 774 q^{35} + 128 q^{36} - 314 q^{38} + 1002 q^{39} + 537 q^{41} - 382 q^{42} + 571 q^{43} - 108 q^{44} + 1516 q^{45} - 126 q^{47} + 64 q^{48} + 558 q^{49} + 736 q^{50} - 757 q^{51} + 444 q^{52} + 126 q^{53} - 1388 q^{54} + 366 q^{55} + 80 q^{56} - 281 q^{57} - 384 q^{58} - 1383 q^{59} - 52 q^{60} + 149 q^{61} - 222 q^{62} + 1153 q^{63} + 1280 q^{64} + 3636 q^{65} + 32 q^{66} - 1626 q^{67} + 236 q^{69} + 1548 q^{70} - 1368 q^{71} + 296 q^{72} + 946 q^{73} + 474 q^{74} - 669 q^{75} - 56 q^{76} + 132 q^{78} - 2109 q^{79} + 311 q^{81} - 1074 q^{82} - 1528 q^{84} + 786 q^{85} - 1142 q^{86} - 816 q^{87} - 1938 q^{89} + 1234 q^{90} - 3459 q^{91} - 705 q^{93} + 2502 q^{95} + 160 q^{96} + 1791 q^{97} + 558 q^{98} - 2285 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 + q^3 - 40 * q^4 - 8 * q^6 - 10 * q^7 - 160 * q^8 - 37 * q^9 - 20 * q^12 - 111 * q^13 - 10 * q^14 - 133 * q^15 - 160 * q^16 - 90 * q^17 - 10 * q^18 - 143 * q^19 + 191 * q^21 - 54 * q^22 - 8 * q^24 + 184 * q^25 - 524 * q^27 + 20 * q^28 - 96 * q^29 - 292 * q^30 + 320 * q^32 - 55 * q^33 - 180 * q^34 + 774 * q^35 + 128 * q^36 - 314 * q^38 + 1002 * q^39 + 537 * q^41 - 382 * q^42 + 571 * q^43 - 108 * q^44 + 1516 * q^45 - 126 * q^47 + 64 * q^48 + 558 * q^49 + 736 * q^50 - 757 * q^51 + 444 * q^52 + 126 * q^53 - 1388 * q^54 + 366 * q^55 + 80 * q^56 - 281 * q^57 - 384 * q^58 - 1383 * q^59 - 52 * q^60 + 149 * q^61 - 222 * q^62 + 1153 * q^63 + 1280 * q^64 + 3636 * q^65 + 32 * q^66 - 1626 * q^67 + 236 * q^69 + 1548 * q^70 - 1368 * q^71 + 296 * q^72 + 946 * q^73 + 474 * q^74 - 669 * q^75 - 56 * q^76 + 132 * q^78 - 2109 * q^79 + 311 * q^81 - 1074 * q^82 - 1528 * q^84 + 786 * q^85 - 1142 * q^86 - 816 * q^87 - 1938 * q^89 + 1234 * q^90 - 3459 * q^91 - 705 * q^93 + 2502 * q^95 + 160 * q^96 + 1791 * q^97 + 558 * q^98 - 2285 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$3$	3.70606	−	3.64214i	0.713231	−	0.700929i
$3$	3.70606	−	3.64214i	0.713231	−	0.700929i
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	13.6046	+	7.85461i	1.21683	+	0.702537i	0.964239	−	0.265036i	$-0.0853838\pi$
$5$	13.6046	+	7.85461i	1.21683	+	0.702537i	0.252592	+	0.967573i	$0.418717\pi$
$6$	−2.60231	−	10.0612i	−0.177065	−	0.684579i
$7$	16.2728			0.878647			0.439323	−	0.898329i	$-0.355218\pi$
$7$	16.2728			0.878647			0.439323	+	0.898329i	$0.355218\pi$
$8$	−8.00000			−0.353553
$9$	0.469703	−	26.9959i	0.0173964	−	0.999849i
$10$	27.2092	−	15.7092i	0.860429	−	0.496769i
$11$			39.4106i			1.08025i	0.841585	+	0.540125i	$0.181623\pi$
$11$			39.4106i			1.08025i	−0.841585	+	0.540125i	$0.818377\pi$
$12$	−20.0288	−	5.55388i	−0.481819	−	0.133606i
$13$	6.61751	−	3.82062i	0.141182	−	0.0815115i	−0.427745	−	0.903899i	$-0.640692\pi$
$13$	6.61751	−	3.82062i	0.141182	−	0.0815115i	0.568927	+	0.822388i	$0.307359\pi$
$14$	16.2728	−	28.1853i	0.310649	−	0.538059i
$15$	79.0269	−	20.4401i	1.36031	−	0.351841i
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−85.5673	−	49.4023i	−1.22077	−	0.704813i	−0.255689	−	0.966759i	$-0.582302\pi$
$17$	−85.5673	−	49.4023i	−1.22077	−	0.704813i	−0.965082	+	0.261947i	$0.915636\pi$
$18$	−46.2886	−	27.8095i	−0.606129	−	0.364153i
$19$	−72.7908	−	39.5032i	−0.878913	−	0.476982i
$19$	−72.7908	−	39.5032i	−0.878913	−	0.476982i
$20$		−	62.8368i		−	0.702537i
$21$	60.3078	−	59.2676i	0.626678	−	0.615869i
$22$	68.2611	+	39.4106i	0.661515	+	0.381926i
$23$	−80.1041	+	46.2481i	−0.726211	+	0.419278i	−0.817035	−	0.576589i	$-0.804384\pi$
$23$	−80.1041	+	46.2481i	−0.726211	+	0.419278i	0.0908232	+	0.995867i	$0.471050\pi$
$24$	−29.6484	+	29.1371i	−0.252165	+	0.247816i
$25$	60.8896	+	105.464i	0.487117	+	0.843712i
$26$		−	15.2825i		−	0.115275i
$27$	−96.5820	−	101.759i	−0.688416	−	0.725317i
$28$	−32.5455	−	56.3705i	−0.219662	−	0.380465i
$29$	145.486	+	251.989i	0.931588	+	1.61356i	0.780607	+	0.625022i	$0.214910\pi$
$29$	145.486	+	251.989i	0.931588	+	1.61356i	0.150981	+	0.988537i	$0.451757\pi$
$30$	43.6236	−	157.319i	0.265485	−	0.957411i
$31$		−	273.495i		−	1.58455i	−0.610163	−	0.792276i	$-0.708896\pi$
$31$		−	273.495i		−	1.58455i	0.610163	−	0.792276i	$-0.291104\pi$
$32$	16.0000	+	27.7128i	0.0883883	+	0.153093i
$33$	143.539	+	146.058i	0.757178	+	0.770467i
$34$	−171.135	+	98.8046i	−0.863216	+	0.498378i
$35$	221.384	+	127.816i	1.06916	+	0.617282i
$36$	−94.4560	+	52.3647i	−0.437296	+	0.242429i
$37$			19.0864i			0.0848050i	0.999101	+	0.0424025i	$0.0135012\pi$
$37$			19.0864i			0.0848050i	−0.999101	+	0.0424025i	$0.986499\pi$
$38$	−141.212	+	86.5741i	−0.602833	+	0.369584i
$39$	10.6096	−	38.2613i	0.0435616	−	0.157095i
$40$	−108.837	−	62.8368i	−0.430214	−	0.248384i
$41$	−50.8201	+	88.0230i	−0.193580	+	0.335290i	−0.946434	−	0.322897i	$-0.895343\pi$
$41$	−50.8201	+	88.0230i	−0.193580	+	0.335290i	0.752854	+	0.658187i	$0.228676\pi$
$42$	−42.3467	−	163.724i	−0.155577	−	0.601503i
$43$	−151.079	+	261.676i	−0.535797	+	0.928027i	0.463327	+	0.886187i	$0.346655\pi$
$43$	−151.079	+	261.676i	−0.535797	+	0.928027i	−0.999124	+	0.0418403i	$0.986678\pi$
$44$	136.522	−	78.8212i	0.467762	−	0.270062i
$45$	218.432	−	363.579i	0.723599	−	1.20442i
$46$			184.993i			0.592949i
$47$	339.551	−	196.040i	1.05380	−	0.608412i	0.130090	−	0.991502i	$-0.458473\pi$
$47$	339.551	−	196.040i	1.05380	−	0.608412i	0.923711	+	0.383090i	$0.125140\pi$
$48$	20.8185	+	80.4897i	0.0626018	+	0.242035i
$49$	−78.1970			−0.227980
$50$	243.559			0.688888
$51$	−497.047	+	128.560i	−1.36472	+	0.352980i
$52$	−26.4700	−	15.2825i	−0.0705910	−	0.0407558i
$53$	265.245	+	459.418i	0.687438	+	1.19068i	0.972664	+	0.232218i	$0.0745981\pi$
$53$	265.245	+	459.418i	0.687438	+	1.19068i	−0.285226	+	0.958460i	$0.592069\pi$
$54$	−272.834	+	65.5259i	−0.687555	+	0.165129i
$55$	−309.555	+	536.164i	−0.758915	+	1.31448i
$56$	−130.182			−0.310649
$57$	−413.643	+	118.713i	−0.961198	+	0.275858i
$58$	581.944			1.31746
$59$	−338.830	+	586.871i	−0.747659	+	1.29498i	0.201283	+	0.979533i	$0.435489\pi$
$59$	−338.830	+	586.871i	−0.747659	+	1.29498i	−0.948942	+	0.315450i	$0.897844\pi$
$60$	−228.860	−	232.877i	−0.492429	−	0.501071i
$61$	87.8160	+	152.102i	0.184323	+	0.319256i	0.943348	−	0.331805i	$-0.107658\pi$
$61$	87.8160	+	152.102i	0.184323	+	0.319256i	−0.759025	+	0.651061i	$0.774324\pi$
$62$	−473.707	−	273.495i	−0.970336	−	0.560224i
$63$	7.64336	−	439.298i	0.0152853	−	0.878514i
$64$	64.0000			0.125000
$65$	120.038			0.229059
$66$	396.518	−	102.558i	0.739516	−	0.191274i
$67$	212.132	−	122.474i	0.386806	−	0.223323i	−0.293969	−	0.955815i	$-0.594976\pi$
$67$	212.132	−	122.474i	0.386806	−	0.223323i	0.680775	+	0.732492i	$0.261643\pi$
$68$			395.218i			0.704813i
$69$	−128.428	+	463.148i	−0.224072	+	0.808065i
$70$	442.768	−	255.632i	0.756013	−	0.436484i
$71$	251.080	−	434.884i	0.419686	−	0.726918i	−0.576221	−	0.817294i	$-0.695473\pi$
$71$	251.080	−	434.884i	0.419686	−	0.726918i	0.995908	+	0.0903754i	$0.0288067\pi$
$72$	−3.75762	+	215.967i	−0.00615055	+	0.353500i
$73$	135.861	−	235.317i	0.217826	−	0.377285i	−0.736317	−	0.676636i	$-0.763437\pi$
$73$	135.861	−	235.317i	0.217826	−	0.377285i	0.954143	+	0.299351i	$0.0967703\pi$
$74$	33.0586	+	19.0864i	0.0519323	+	0.0299831i
$75$	609.774	+	169.087i	0.938809	+	0.260326i
$76$	8.73846	+	331.161i	0.0131891	+	0.499826i
$77$			641.319i			0.949157i
$78$	−55.6609	−	56.6377i	−0.0807994	−	0.0822175i
$79$	−456.187	−	263.379i	−0.649684	−	0.375095i	0.138651	−	0.990341i	$-0.455723\pi$
$79$	−456.187	−	263.379i	−0.649684	−	0.375095i	−0.788335	+	0.615246i	$0.789057\pi$
$80$	−217.673	+	125.674i	−0.304208	+	0.175634i
$81$	−728.559	−	25.3601i	−0.999395	−	0.0347875i
$82$	101.640	+	176.046i	0.136882	+	0.237086i
$83$		−	983.108i		−	1.30012i	−0.759882	−	0.650061i	$-0.774743\pi$
$83$		−	983.108i		−	1.30012i	0.759882	−	0.650061i	$-0.225257\pi$
$84$	−325.925	−	90.3771i	−0.423349	−	0.117392i
$85$	−776.071	−	1344.19i	−0.990314	−	1.71527i
$86$	302.157	+	523.352i	0.378866	+	0.656214i
$87$	1456.96	+	404.006i	1.79543	+	0.497862i
$88$		−	315.285i		−	0.381926i
$89$	−292.932	−	507.374i	−0.348885	−	0.604287i	0.637167	−	0.770726i	$-0.280106\pi$
$89$	−292.932	−	507.374i	−0.348885	−	0.604287i	−0.986052	+	0.166440i	$0.946773\pi$
$90$	−411.304	−	741.915i	−0.481725	−	0.868941i
$91$	107.685	−	62.1721i	0.124049	−	0.0716198i
$92$	320.416	+	184.993i	0.363106	+	0.209639i
$93$	−996.105	−	1013.59i	−1.11066	−	1.13015i
$94$		−	784.160i		−	0.860425i
$95$	−680.006	−	1109.17i	−0.734391	−	1.19788i
$96$	160.231	+	44.4311i	0.170349	+	0.0472367i
$97$	355.280	+	205.121i	0.371889	+	0.214710i	0.674283	−	0.738473i	$-0.264453\pi$
$97$	355.280	+	205.121i	0.371889	+	0.214710i	−0.302395	+	0.953183i	$0.597786\pi$
$98$	−78.1970	+	135.441i	−0.0806030	+	0.139608i
$99$	1063.92	+	18.5113i	1.08009	+	0.0187924i
$100$	243.559	−	421.856i	0.243559	−	0.421856i
$101$	−1024.28	+	591.366i	−1.00910	+	0.582605i	−0.910929	−	0.412564i	$-0.864633\pi$
$101$	−1024.28	+	591.366i	−1.00910	+	0.582605i	−0.0981732	+	0.995169i	$0.531300\pi$
$102$	−274.375	+	989.470i	−0.266344	+	0.960511i
$103$		−	346.050i		−	0.331042i	−0.986206	−	0.165521i	$-0.947069\pi$
$103$		−	346.050i		−	0.331042i	0.986206	−	0.165521i	$-0.0529306\pi$
$104$	−52.9401	+	30.5650i	−0.0499154	+	0.0288187i
$105$	1285.99	−	332.617i	1.19523	−	0.309144i
$106$	1060.98			0.972185
$107$	221.196			0.199848			0.0999242	−	0.994995i	$-0.468140\pi$
$107$	221.196			0.199848			0.0999242	+	0.994995i	$0.468140\pi$
$108$	−159.340	+	538.088i	−0.141967	+	0.479422i
$109$	623.897	+	360.207i	0.548243	+	0.316528i	0.748413	−	0.663233i	$-0.230816\pi$
$109$	623.897	+	360.207i	0.548243	+	0.316528i	−0.200170	+	0.979761i	$0.564149\pi$
$110$	619.109	+	1072.33i	0.536634	+	0.929477i
$111$	69.5153	+	70.7353i	0.0594423	+	0.0604855i
$112$	−130.182	+	225.482i	−0.109831	+	0.190233i
$113$	859.810			0.715789			0.357895	−	0.933762i	$-0.383495\pi$
$113$	859.810			0.715789			0.357895	+	0.933762i	$0.383495\pi$
$114$	−208.026	+	835.163i	−0.170907	+	0.686142i
$115$	−1453.04			−1.17823
$116$	581.944	−	1007.96i	0.465794	−	0.806779i
$117$	−100.033	−	180.440i	−0.0790431	−	0.142579i
$118$	677.660	+	1173.74i	0.528675	+	0.915692i
$119$	−1392.42	−	803.912i	−1.07263	−	0.619281i
$120$	−632.215	+	163.521i	−0.480942	+	0.124394i
$121$	−222.194			−0.166938
$122$	351.264			0.260672
$123$	132.250	+	511.312i	0.0969475	+	0.374825i
$124$	−947.413	+	546.989i	−0.686131	+	0.396138i
$125$		−	50.5949i		−	0.0362027i
$126$	−753.244	−	452.537i	−0.532574	−	0.319962i
$127$	2024.54	−	1168.87i	1.41456	−	0.816695i	0.418744	−	0.908104i	$-0.362470\pi$
$127$	2024.54	−	1168.87i	1.41456	−	0.816695i	0.995813	+	0.0914090i	$0.0291371\pi$
$128$	64.0000	−	110.851i	0.0441942	−	0.0765466i
$129$	393.153	+	1520.03i	0.268335	+	1.03745i
$130$	120.038	−	207.912i	0.0809848	−	0.140270i
$131$	527.735	+	304.688i	0.351973	+	0.203211i	0.665554	−	0.746350i	$-0.268195\pi$
$131$	527.735	+	304.688i	0.351973	+	0.203211i	−0.313581	+	0.949561i	$0.601529\pi$
$132$	218.882	−	789.348i	0.144327	−	0.520484i
$133$	−1184.51	−	642.826i	−0.772254	−	0.419099i
$134$		−	489.897i		−	0.315826i
$135$	−514.680	−	2143.00i	−0.328123	−	1.36622i
$136$	684.538	+	395.218i	0.431608	+	0.249189i
$137$	109.144	−	63.0144i	0.0680643	−	0.0392970i	−0.465582	−	0.885005i	$-0.654155\pi$
$137$	109.144	−	63.0144i	0.0680643	−	0.0392970i	0.533646	+	0.845708i	$0.320821\pi$
$138$	673.768	+	685.593i	0.415615	+	0.422910i
$139$	−994.276	−	1722.14i	−0.606715	−	1.05086i	−0.991778	−	0.127971i	$-0.959154\pi$
$139$	−994.276	−	1722.14i	−0.606715	−	1.05086i	0.385063	−	0.922890i	$-0.374180\pi$
$140$		−	1022.53i		−	0.617282i
$141$	544.392	−	1963.23i	0.325149	−	1.17258i
$142$	−502.160	−	869.767i	−0.296763	−	0.514009i
$143$	150.573	+	260.800i	0.0880527	+	0.152512i
$144$	370.309	+	222.476i	0.214299	+	0.128748i
$145$			4570.94i			2.61790i
$146$	−271.721	−	470.635i	−0.154026	−	0.266781i
$147$	−289.803	+	284.804i	−0.162602	+	0.159798i
$148$	66.1172	−	38.1728i	0.0367216	−	0.0212013i
$149$	−1389.83	−	802.418i	−0.764156	−	0.441186i	0.0666300	−	0.997778i	$-0.478775\pi$
$149$	−1389.83	−	802.418i	−0.764156	−	0.441186i	−0.830786	+	0.556592i	$0.812109\pi$
$150$	902.642	−	887.073i	0.491336	−	0.482862i
$151$			2168.82i			1.16885i	0.811449	+	0.584424i	$0.198679\pi$
$151$			2168.82i			1.16885i	−0.811449	+	0.584424i	$0.801321\pi$
$152$	582.326	+	316.026i	0.310743	+	0.168639i
$153$	−1373.85	+	2286.76i	−0.725943	+	1.20833i
$154$	1110.80	+	641.319i	0.581238	+	0.335578i
$155$	2148.19	−	3720.78i	1.11321	−	1.92813i
$156$	−153.760	+	39.7697i	−0.0789146	+	0.0204111i
$157$	−908.763	+	1574.02i	−0.461957	+	0.800133i	−0.999058	−	0.0433849i	$-0.986186\pi$
$157$	−908.763	+	1574.02i	−0.461957	+	0.800133i	0.537102	+	0.843518i	$0.319519\pi$
$158$	−912.373	+	526.759i	−0.459396	+	0.265232i
$159$	2656.28	+	736.571i	1.32488	+	0.367383i
$160$			502.695i			0.248384i
$161$	−1303.52	+	752.585i	−0.638083	+	0.368398i
$162$	−772.484	+	1236.54i	−0.374642	+	0.599703i
$163$	−2876.22			−1.38210			−0.691051	−	0.722806i	$-0.742852\pi$
$163$	−2876.22			−1.38210			−0.691051	+	0.722806i	$0.742852\pi$
$164$	406.561			0.193580
$165$	805.556	+	3114.49i	0.380076	+	1.46947i
$166$	−1702.79	−	983.108i	−0.796159	−	0.459662i
$167$	168.891	+	292.527i	0.0782584	+	0.135548i	0.902499	−	0.430693i	$-0.141731\pi$
$167$	168.891	+	292.527i	0.0782584	+	0.135548i	−0.824240	+	0.566240i	$0.808397\pi$
$168$	−482.462	+	474.141i	−0.221564	+	0.217743i
$169$	−1069.31	+	1852.09i	−0.486712	+	0.843009i
$170$	−3104.28			−1.40052
$171$	−1100.61	+	1946.50i	−0.492200	+	0.870482i
$172$	1208.63			0.535797
$173$	−1615.21	+	2797.63i	−0.709841	+	1.22948i	0.255075	+	0.966921i	$0.417900\pi$
$173$	−1615.21	+	2797.63i	−0.709841	+	1.22948i	−0.964916	+	0.262559i	$0.915433\pi$
$174$	2156.72	−	2119.52i	0.939657	−	0.923450i
$175$	990.843	+	1716.19i	0.428004	+	0.741325i
$176$	−546.089	−	315.285i	−0.233881	−	0.135031i
$177$	881.739	+	3409.04i	0.374438	+	1.44768i
$178$	−1171.73			−0.493398
$179$	1488.05			0.621352			0.310676	−	0.950516i	$-0.399445\pi$
$179$	1488.05			0.621352			0.310676	+	0.950516i	$0.399445\pi$
$180$	−1696.34	−	29.5146i	−0.702431	−	0.0122216i
$181$	1300.45	−	750.813i	0.534041	−	0.308329i	−0.208619	−	0.977997i	$-0.566897\pi$
$181$	1300.45	−	750.813i	0.534041	−	0.308329i	0.742661	+	0.669668i	$0.233564\pi$
$182$		−	248.688i		−	0.101286i
$183$	879.426	+	243.860i	0.355241	+	0.0985062i
$184$	640.833	−	369.985i	0.256755	−	0.148237i
$185$	−149.916	+	259.662i	−0.0595787	+	0.103193i
$186$	−2751.69	+	711.717i	−1.08475	+	0.280568i
$187$	1946.97	−	3372.26i	0.761373	−	1.31874i
$188$	−1358.21	−	784.160i	−0.526901	−	0.304206i
$189$	−1571.66	−	1655.90i	−0.604874	−	0.637297i
$190$	−2601.14	+	68.6372i	−0.993192	+	0.0262077i
$191$		−	4367.97i		−	1.65474i	−0.561658	−	0.827369i	$-0.689836\pi$
$191$		−	4367.97i		−	1.65474i	0.561658	−	0.827369i	$-0.310164\pi$
$192$	237.188	−	233.097i	0.0891539	−	0.0876162i
$193$	1305.90	+	753.961i	0.487050	+	0.281198i	0.723350	−	0.690482i	$-0.242601\pi$
$193$	1305.90	+	753.961i	0.487050	+	0.281198i	−0.236300	+	0.971680i	$0.575935\pi$
$194$	710.560	−	410.242i	0.262965	−	0.151823i
$195$	444.867	−	437.194i	0.163372	−	0.160554i
$196$	156.394	+	270.882i	0.0569949	+	0.0987181i
$197$			1385.73i			0.501163i	0.968096	+	0.250581i	$0.0806217\pi$
$197$			1385.73i			0.501163i	−0.968096	+	0.250581i	$0.919378\pi$
$198$	1095.99	−	1824.26i	0.393376	−	0.654770i
$199$	−1607.26	−	2783.85i	−0.572540	−	0.991669i	−0.996304	−	0.0858962i	$-0.972625\pi$
$199$	−1607.26	−	2783.85i	−0.572540	−	0.991669i	0.423764	−	0.905773i	$-0.360709\pi$
$200$	−487.117	−	843.712i	−0.172222	−	0.298297i
$201$	340.104	−	1226.51i	0.119349	−	0.430404i
$202$			2365.46i			0.823928i
$203$	2367.46	+	4100.56i	0.818537	+	1.41775i
$204$	1439.44	+	1464.70i	0.494024	+	0.502694i
$205$	−1382.77	+	798.344i	−0.471107	+	0.271994i
$206$	−599.376	−	346.050i	−0.202721	−	0.117041i
$207$	1210.89	+	2184.21i	0.406581	+	0.733395i
$208$			122.260i			0.0407558i
$209$	1556.84	−	2868.73i	0.515259	−	0.949445i
$210$	709.876	−	2560.01i	0.233267	−	0.841226i
$211$	−2433.91	−	1405.22i	−0.794110	−	0.458480i	0.0472975	−	0.998881i	$-0.484939\pi$
$211$	−2433.91	−	1405.22i	−0.794110	−	0.458480i	−0.841407	+	0.540401i	$0.818272\pi$
$212$	1060.98	−	1837.67i	0.343719	−	0.595339i
$213$	−653.388	−	2526.17i	−0.210185	−	0.812631i
$214$	221.196	−	383.122i	0.0706571	−	0.122382i
$215$	−4110.72	+	2373.33i	−1.30395	+	0.752835i
$216$	772.656	+	814.073i	0.243392	+	0.256438i
$217$		−	4450.52i		−	1.39226i
$218$	1247.79	−	720.414i	0.387666	−	0.223819i
$219$	−353.551	−	1366.92i	−0.109090	−	0.421772i
$220$	2476.44			0.758915
$221$	−754.990			−0.229801
$222$	192.032	−	49.6687i	0.0580557	−	0.0150160i
$223$	−1400.23	−	808.424i	−0.420477	−	0.242763i	0.274804	−	0.961500i	$-0.411387\pi$
$223$	−1400.23	−	808.424i	−0.420477	−	0.242763i	−0.695281	+	0.718738i	$0.744720\pi$
$224$	260.364	+	450.964i	0.0776621	+	0.134515i
$225$	2875.70	−	1594.23i	0.852058	−	0.472366i
$226$	859.810	−	1489.24i	0.253070	−	0.438329i
$227$	3419.80			0.999913			0.499957	−	0.866050i	$-0.333349\pi$
$227$	3419.80			0.999913			0.499957	+	0.866050i	$0.333349\pi$
$228$	1238.52	+	1195.47i	0.359750	+	0.347247i
$229$	4902.49			1.41470			0.707349	−	0.706864i	$-0.249891\pi$
$229$	4902.49			1.41470			0.707349	+	0.706864i	$0.249891\pi$
$230$	−1453.04	+	2516.74i	−0.416569	+	0.721518i
$231$	2335.77	+	2376.77i	0.665292	+	0.676968i
$232$	−1163.89	−	2015.91i	−0.329366	−	0.570479i
$233$	3097.54	+	1788.37i	0.870929	+	0.502831i	0.867657	−	0.497163i	$-0.165625\pi$
$233$	3097.54	+	1788.37i	0.870929	+	0.502831i	0.00327242	+	0.999995i	$0.498958\pi$
$234$	−412.565	−	7.17822i	−0.115257	−	0.00200536i
$235$	6159.27			1.70973
$236$	2710.64			0.747659
$237$	−2649.92	+	685.394i	−0.726289	+	0.187853i
$238$	−2784.83	+	1607.82i	−0.758462	+	0.437898i
$239$			2682.93i			0.726127i	0.931764	+	0.363064i	$0.118269\pi$
$239$			2682.93i			0.726127i	−0.931764	+	0.363064i	$0.881731\pi$
$240$	−348.989	+	1258.55i	−0.0938630	+	0.338496i
$241$	5342.40	−	3084.43i	1.42794	−	0.824423i	0.430984	−	0.902360i	$-0.358167\pi$
$241$	5342.40	−	3084.43i	1.42794	−	0.824423i	0.996958	+	0.0779366i	$0.0248332\pi$
$242$	−222.194	+	384.852i	−0.0590215	+	0.102228i
$243$	−2792.44	+	2559.52i	−0.737183	+	0.675693i
$244$	351.264	−	608.407i	0.0921613	−	0.159628i
$245$	−1063.84	−	614.207i	−0.277413	−	0.160164i
$246$	1017.87	+	282.249i	0.263809	+	0.0731526i
$247$	−632.620	+	16.6932i	−0.162966	+	0.00430025i
$248$			2187.96i			0.560224i
$249$	−3580.61	−	3643.45i	−0.911293	−	0.927287i
$250$	−87.6329	−	50.5949i	−0.0221696	−	0.0127996i
$251$	3066.71	−	1770.56i	0.771190	−	0.445247i	−0.0621087	−	0.998069i	$-0.519783\pi$
$251$	3066.71	−	1770.56i	0.771190	−	0.445247i	0.833299	+	0.552822i	$0.186449\pi$
$252$	−1537.06	+	852.119i	−0.384229	+	0.213010i
$253$	−1822.67	−	3156.95i	−0.452925	−	0.784489i
$254$		−	4675.47i		−	1.15498i
$255$	−7771.90	−	2155.10i	−1.90861	−	0.529246i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−3412.16	−	5910.04i	−0.828190	−	1.43447i	−0.899456	−	0.437011i	$-0.856037\pi$
$257$	−3412.16	−	5910.04i	−0.828190	−	1.43447i	0.0712659	−	0.997457i	$-0.477296\pi$
$258$	3025.93	+	839.073i	0.730179	+	0.202474i
$259$			310.589i			0.0745137i
$260$	−240.076	−	415.823i	−0.0572649	−	0.0991857i
$261$	6871.01	−	3809.17i	1.62952	−	0.903377i
$262$	1055.47	−	609.376i	0.248882	−	0.143692i
$263$	1567.83	+	905.186i	0.367591	+	0.212229i	0.672406	−	0.740183i	$-0.265261\pi$
$263$	1567.83	+	905.186i	0.367591	+	0.212229i	−0.304814	+	0.952412i	$0.598594\pi$
$264$	−1148.31	−	1168.46i	−0.267703	−	0.272401i
$265$			8333.58i			1.93180i
$266$	−2297.92	+	1408.80i	−0.529678	+	0.324733i
$267$	−2933.55	−	813.456i	−0.672398	−	0.186452i
$268$	−848.527	−	489.897i	−0.193403	−	0.111661i
$269$	−1683.30	+	2915.56i	−0.381534	+	0.660836i	−0.991282	−	0.131759i	$-0.957937\pi$
$269$	−1683.30	+	2915.56i	−0.381534	+	0.660836i	0.609748	+	0.792596i	$0.291271\pi$
$270$	−4226.47	−	1251.55i	−0.952647	−	0.282100i
$271$	3193.70	−	5531.66i	0.715881	−	1.23994i	−0.246738	−	0.969082i	$-0.579359\pi$
$271$	3193.70	−	5531.66i	0.715881	−	1.23994i	0.962619	−	0.270859i	$-0.0873078\pi$
$272$	1369.08	−	790.437i	0.305193	−	0.176203i
$273$	172.648	−	622.617i	0.0382753	−	0.138031i
$274$		−	252.058i		−	0.0555743i
$275$	−4156.40	+	2399.70i	−0.911419	+	0.526208i
$276$	1861.25	−	481.407i	0.405920	−	0.104990i
$277$	7929.30			1.71995			0.859974	−	0.510338i	$-0.170480\pi$
$277$	7929.30			1.71995			0.859974	+	0.510338i	$0.170480\pi$
$278$	−3977.10			−0.858024
$279$	−7383.24	−	128.461i	−1.58431	−	0.0275655i
$280$	−1771.07	−	1022.53i	−0.378007	−	0.218242i
$281$	940.968	+	1629.80i	0.199763	+	0.346000i	0.948452	−	0.316922i	$-0.102649\pi$
$281$	940.968	+	1629.80i	0.199763	+	0.346000i	−0.748688	+	0.662922i	$0.769316\pi$
$282$	−2856.02	−	2906.14i	−0.603097	−	0.613682i
$283$	−740.601	+	1282.76i	−0.155562	+	0.269442i	−0.933264	−	0.359192i	$-0.883052\pi$
$283$	−740.601	+	1282.76i	−0.155562	+	0.269442i	0.777701	+	0.628634i	$0.216386\pi$
$284$	−2008.64			−0.419686
$285$	−6559.88	−	1633.96i	−1.36342	−	0.339606i
$286$	602.292			0.124525
$287$	−826.984	+	1432.38i	−0.170088	+	0.294601i
$288$	755.648	−	418.918i	0.154608	−	0.0857117i
$289$	2424.67	+	4199.65i	0.493522	+	0.854804i
$290$	7917.10	+	4570.94i	1.60313	+	0.925568i
$291$	2063.77	−	533.788i	0.415739	−	0.107530i
$292$	−1086.88			−0.217826
$293$	−4765.90			−0.950263			−0.475132	−	0.879915i	$-0.657600\pi$
$293$	−4765.90			−0.950263			−0.475132	+	0.879915i	$0.657600\pi$
$294$	203.493	+	786.757i	0.0403671	+	0.156070i
$295$	−9219.27	+	5322.75i	−1.81955	+	1.05052i
$296$		−	152.691i		−	0.0299831i
$297$	4010.39	−	3806.35i	0.783522	−	0.743660i
$298$	−2779.66	+	1604.84i	−0.540340	+	0.311965i
$299$	−353.393	+	612.095i	−0.0683520	+	0.118389i
$300$	−633.814	−	2450.49i	−0.121978	−	0.471598i
$301$	−2458.47	+	4258.19i	−0.470776	+	0.815408i
$302$	3756.50	+	2168.82i	0.715770	+	0.413250i
$303$	−1642.19	+	5922.19i	−0.311357	+	1.12284i
$304$	1129.70	−	692.593i	0.213134	−	0.130668i
$305$			2759.04i			0.517974i
$306$	2586.94	+	4666.34i	0.483285	+	0.871755i
$307$	8779.18	+	5068.66i	1.63210	+	0.942292i	0.983445	+	0.181209i	$0.0580009\pi$
$307$	8779.18	+	5068.66i	1.63210	+	0.942292i	0.648654	+	0.761084i	$0.275332\pi$
$308$	2221.60	−	1282.64i	0.410997	−	0.237289i
$309$	−1260.36	−	1282.48i	−0.232037	−	0.236109i
$310$	−4296.39	−	7441.56i	−0.787156	−	1.36339i
$311$			4295.33i			0.783170i	0.920142	+	0.391585i	$0.128073\pi$
$311$			4295.33i			0.783170i	−0.920142	+	0.391585i	$0.871927\pi$
$312$	−84.8771	+	306.090i	−0.0154014	+	0.0555415i
$313$	−5098.00	−	8829.99i	−0.920626	−	1.59457i	−0.798449	−	0.602062i	$-0.794346\pi$
$313$	−5098.00	−	8829.99i	−0.920626	−	1.59457i	−0.122177	−	0.992508i	$-0.538988\pi$
$314$	1817.53	+	3148.05i	0.326653	+	0.565779i
$315$	3554.50	−	5916.43i	0.635788	−	1.05826i
$316$			2107.04i			0.375095i
$317$	−1995.47	−	3456.25i	−0.353554	−	0.612374i	0.633315	−	0.773894i	$-0.281694\pi$
$317$	−1995.47	−	3456.25i	−0.353554	−	0.612374i	−0.986869	+	0.161520i	$0.948360\pi$
$318$	3932.05	−	3864.24i	0.693392	−	0.681433i
$319$	−9931.04	+	5733.69i	−1.74304	+	1.00635i
$320$	870.693	+	502.695i	0.152104	+	0.0878172i
$321$	819.763	−	805.624i	0.142538	−	0.140080i
$322$			3010.34i			0.520993i
$323$	4276.96	+	6976.21i	0.736769	+	1.20175i
$324$	1369.27	+	2574.52i	0.234785	+	0.441447i
$325$	805.876	+	465.272i	0.137544	+	0.0794113i
$326$	−2876.22	+	4981.75i	−0.488647	+	0.846361i
$327$	3624.12	−	937.370i	0.612888	−	0.158522i
$328$	406.561	−	704.184i	0.0684408	−	0.118543i
$329$	5525.44	−	3190.11i	0.925919	−	0.534580i
$330$	6200.02	+	1719.23i	1.03424	+	0.286789i
$331$		−	7812.31i		−	1.29729i	−0.761091	−	0.648645i	$-0.775336\pi$
$331$		−	7812.31i		−	1.29729i	0.761091	−	0.648645i	$-0.224664\pi$
$332$	−3405.58	+	1966.22i	−0.562969	+	0.325030i
$333$	515.255	+	8.96493i	0.0847922	+	0.00147530i
$334$	675.563			0.110674
$335$	3847.95			0.627570
$336$	338.774	+	1309.79i	0.0550049	+	0.212663i
$337$	−416.749	−	240.610i	−0.0673643	−	0.0388928i	0.465940	−	0.884817i	$-0.345716\pi$
$337$	−416.749	−	240.610i	−0.0673643	−	0.0388928i	−0.533304	+	0.845924i	$0.679050\pi$
$338$	2138.61	+	3704.18i	0.344157	+	0.596098i
$339$	3186.51	−	3131.55i	0.510523	−	0.501717i
$340$	−3104.28	+	5376.78i	−0.495157	+	0.857637i
$341$	10778.6			1.71171
$342$	2270.82	+	3852.82i	0.359041	+	0.609171i
$343$	−6854.04			−1.07896
$344$	1208.63	−	2093.41i	0.189433	−	0.328107i
$345$	−5385.06	+	5292.18i	−0.840353	+	0.825859i
$346$	3230.43	+	5595.27i	0.501933	+	0.869374i
$347$	−6501.64	−	3753.73i	−1.00584	−	0.580722i	−0.0958692	−	0.995394i	$-0.530563\pi$
$347$	−6501.64	−	3753.73i	−1.00584	−	0.580722i	−0.909971	+	0.414672i	$0.863896\pi$
$348$	−1514.40	−	5855.06i	−0.233276	−	0.901909i
$349$	−8657.63			−1.32789			−0.663943	−	0.747783i	$-0.731118\pi$
$349$	−8657.63			−1.32789			−0.663943	+	0.747783i	$0.731118\pi$
$350$	3963.37			0.605289
$351$	−1027.92	−	304.388i	−0.156314	−	0.0462879i
$352$	−1092.18	+	630.569i	−0.165379	+	0.0954814i
$353$		−	11800.0i		−	1.77918i	−0.456759	−	0.889591i	$-0.650990\pi$
$353$		−	11800.0i		−	1.77918i	0.456759	−	0.889591i	$-0.349010\pi$
$354$	6786.37	+	1881.82i	1.01890	+	0.282536i
$355$	6831.68	−	3944.27i	1.02137	−	0.589691i
$356$	−1171.73	+	2029.49i	−0.174442	+	0.302143i
$357$	−8088.33	+	2092.03i	−1.19910	+	0.310145i
$358$	1488.05	−	2577.38i	0.219681	−	0.380499i
$359$	−10322.3	−	5959.57i	−1.51752	−	0.876140i	−0.999788	−	0.0205957i	$-0.993444\pi$
$359$	−10322.3	−	5959.57i	−1.51752	−	0.876140i	−0.517730	−	0.855544i	$-0.673223\pi$
$360$	−1747.46	+	2908.63i	−0.255831	+	0.425828i
$361$	3737.99	+	5750.94i	0.544977	+	0.838451i
$362$		−	3003.25i		−	0.436043i
$363$	−823.465	+	809.262i	−0.119065	+	0.117012i
$364$	−430.741	−	248.688i	−0.0620246	−	0.0358099i
$365$	3696.65	−	2134.26i	0.530114	−	0.306061i
$366$	1301.80	−	1279.35i	0.185919	−	0.182712i
$367$	2683.39	+	4647.76i	0.381667	+	0.661066i	0.991301	−	0.131617i	$-0.0420169\pi$
$367$	2683.39	+	4647.76i	0.381667	+	0.661066i	−0.609634	+	0.792683i	$0.708684\pi$
$368$		−	1479.94i		−	0.209639i
$369$	2352.39	+	1413.28i	0.331872	+	0.199383i
$370$	299.832	+	519.325i	0.0421285	+	0.0729687i
$371$	4316.27	+	7476.00i	0.604015	+	1.04619i
$372$	−1518.96	+	5477.78i	−0.211705	+	0.763467i
$373$			4537.75i			0.629908i	0.949107	+	0.314954i	$0.101989\pi$
$373$			4537.75i			0.629908i	−0.949107	+	0.314954i	$0.898011\pi$
$374$	−3893.95	−	6744.51i	−0.538372	−	0.932488i
$375$	−184.273	−	187.507i	−0.0253756	−	0.0258209i
$376$	−2716.41	+	1568.32i	−0.372575	+	0.215106i
$377$	1925.51	+	1111.69i	0.263047	+	0.151870i
$378$	−4439.76	+	1066.29i	−0.604118	+	0.145090i
$379$		−	7810.00i		−	1.05850i	−0.848465	−	0.529252i	$-0.822473\pi$
$379$		−	7810.00i		−	1.05850i	0.848465	−	0.529252i	$-0.177527\pi$
$380$	−2482.26	+	4573.94i	−0.335098	+	0.617469i
$381$	3245.88	−	11705.5i	0.436461	−	1.57400i
$382$	−7565.54	−	4367.97i	−1.01332	−	0.585039i
$383$	−4675.87	+	8098.85i	−0.623827	+	1.08050i	0.364939	+	0.931031i	$0.381090\pi$
$383$	−4675.87	+	8098.85i	−0.623827	+	1.08050i	−0.988766	+	0.149469i	$0.952244\pi$
$384$	−166.548	−	643.918i	−0.0221331	−	0.0855724i
$385$	−5037.31	+	8724.88i	−0.666818	+	1.15496i
$386$	2611.80	−	1507.92i	0.344396	−	0.198837i
$387$	6993.21	+	4201.41i	0.918566	+	0.551860i
$388$		−	1640.97i		−	0.214710i
$389$	5057.47	−	2919.93i	0.659187	−	0.380582i	−0.132780	−	0.991146i	$-0.542390\pi$
$389$	5057.47	−	2919.93i	0.659187	−	0.380582i	0.791967	+	0.610564i	$0.209057\pi$
$390$	−312.375	−	1207.73i	−0.0405583	−	0.156809i
$391$	9139.05			1.18205
$392$	625.576			0.0806030
$393$	3065.53	−	792.891i	0.393475	−	0.101771i
$394$	2400.15	+	1385.73i	0.306898	+	0.177188i
$395$	−4137.48	−	7166.33i	−0.527036	−	0.912854i
$396$	−2063.72	−	3722.57i	−0.261884	−	0.472389i
$397$	−2201.41	+	3812.96i	−0.278302	+	0.482033i	−0.970963	−	0.239230i	$-0.923105\pi$
$397$	−2201.41	+	3812.96i	−0.278302	+	0.482033i	0.692661	+	0.721263i	$0.256438\pi$
$398$	−6429.03			−0.809694
$399$	−6731.11	+	1931.79i	−0.844554	+	0.242382i
$400$	−1948.47			−0.243559
$401$	−5962.52	+	10327.4i	−0.742528	+	1.28610i	0.208813	+	0.977956i	$0.433040\pi$
$401$	−5962.52	+	10327.4i	−0.742528	+	1.28610i	−0.951341	+	0.308141i	$0.900293\pi$
$402$	−1784.27	−	1815.59i	−0.221372	−	0.225257i
$403$	−1044.92	−	1809.85i	−0.129159	−	0.223710i
$404$	4097.10	+	2365.46i	0.504551	+	0.291303i
$405$	−9712.54	−	6067.55i	−1.19165	−	0.744443i
$406$	9469.84			1.15759
$407$	−752.206			−0.0916105
$408$	3976.38	−	1028.48i	0.482500	−	0.124797i
$409$	8625.52	−	4979.94i	1.04280	−	0.602060i	0.122173	−	0.992509i	$-0.461014\pi$
$409$	8625.52	−	4979.94i	1.04280	−	0.602060i	0.920625	+	0.390449i	$0.127680\pi$
$410$			3193.38i			0.384658i
$411$	174.987	−	631.053i	0.0210012	−	0.0757361i
$412$	−1198.75	+	692.100i	−0.143345	+	0.0827605i
$413$	−5513.70	+	9550.01i	−0.656928	+	1.13783i
$414$	4994.04	+	86.8915i	0.592859	+	0.0103152i
$415$	7721.92	−	13374.8i	0.913384	−	1.58203i
$416$	211.760	+	122.260i	0.0249577	+	0.0144093i
$417$	−9957.09	−	2761.05i	−1.16931	−	0.324242i
$418$	−3411.94	−	5565.26i	−0.399242	−	0.651210i
$419$			2544.28i			0.296649i	0.988939	+	0.148325i	$0.0473880\pi$
$419$			2544.28i			0.296649i	−0.988939	+	0.148325i	$0.952612\pi$
$420$	−3724.19	−	3789.55i	−0.432671	−	0.440265i
$421$	9140.93	+	5277.52i	1.05820	+	0.610951i	0.924934	−	0.380129i	$-0.124120\pi$
$421$	9140.93	+	5277.52i	1.05820	+	0.610951i	0.133266	+	0.991080i	$0.457454\pi$
$422$	−4867.82	+	2810.44i	−0.561521	+	0.324194i
$423$	−5132.79	−	9258.58i	−0.589988	−	1.06423i
$424$	−2121.96	−	3675.35i	−0.243046	−	0.420968i
$425$		−	12032.3i		−	1.37331i
$426$	−5028.85	−	1394.47i	−0.571944	−	0.158597i
$427$	1429.01	+	2475.12i	0.161955	+	0.280513i
$428$	−442.391	−	766.244i	−0.0499621	−	0.0865369i
$429$	1507.90	+	418.132i	0.169702	+	0.0470574i
$430$			9493.30i			1.06467i
$431$	−7092.60	−	12284.7i	−0.792665	−	1.37294i	−0.924312	−	0.381639i	$-0.875360\pi$
$431$	−7092.60	−	12284.7i	−0.792665	−	1.37294i	0.131647	−	0.991297i	$-0.457974\pi$
$432$	2182.67	−	524.207i	0.243088	−	0.0583818i
$433$	−8775.35	+	5066.45i	−0.973941	+	0.562305i	−0.900435	−	0.434990i	$-0.856752\pi$
$433$	−8775.35	+	5066.45i	−0.973941	+	0.562305i	−0.0735052	+	0.997295i	$0.523419\pi$
$434$	−7708.52	−	4450.52i	−0.852582	−	0.492239i
$435$	16648.0	+	16940.2i	1.83496	+	1.86717i
$436$		−	2881.66i		−	0.316528i
$437$	7657.79	−	202.069i	0.838265	−	0.0221196i
$438$	−2721.13	−	754.554i	−0.296851	−	0.0823150i
$439$	2442.69	+	1410.29i	0.265566	+	0.153325i	0.626871	−	0.779123i	$-0.284335\pi$
$439$	2442.69	+	1410.29i	0.265566	+	0.153325i	−0.361305	+	0.932448i	$0.617669\pi$
$440$	2476.44	−	4289.31i	0.268317	−	0.464739i
$441$	−36.7293	+	2111.00i	−0.00396602	+	0.227945i
$442$	−754.990	+	1307.68i	−0.0812470	+	0.140724i
$443$	4947.68	−	2856.54i	0.530635	−	0.306362i	−0.210640	−	0.977564i	$-0.567555\pi$
$443$	4947.68	−	2856.54i	0.530635	−	0.306362i	0.741275	+	0.671201i	$0.234221\pi$
$444$	106.004	−	382.279i	0.0113304	−	0.0408607i
$445$		−	9203.47i		−	0.980419i
$446$	−2800.46	+	1616.85i	−0.297322	+	0.171659i
$447$	−8073.30	+	2088.14i	−0.854259	+	0.220952i
$448$	1041.46			0.109831
$449$	5474.99			0.575459			0.287729	−	0.957712i	$-0.407100\pi$
$449$	5474.99			0.575459			0.287729	+	0.957712i	$0.407100\pi$
$450$	114.400	−	6575.09i	0.0119842	−	0.688783i
$451$	−3469.04	−	2002.85i	−0.362197	−	0.209114i
$452$	−1719.62	−	2978.47i	−0.178947	−	0.309946i
$453$	7899.13	+	8037.76i	0.819279	+	0.833658i
$454$	3419.80	−	5923.27i	0.353523	−	0.612319i
$455$	1953.35			0.201262
$456$	3309.14	−	949.702i	0.339835	−	0.0975304i
$457$	492.731			0.0504354			0.0252177	−	0.999682i	$-0.491972\pi$
$457$	492.731			0.0504354			0.0252177	+	0.999682i	$0.491972\pi$
$458$	4902.49	−	8491.37i	0.500171	−	0.866322i
$459$	3237.13	+	13478.6i	0.329186	+	1.37065i
$460$	2906.09	+	5033.49i	0.294559	+	0.510191i
$461$	11854.0	+	6843.90i	1.19760	+	0.691437i	0.960020	−	0.279931i	$-0.0903115\pi$
$461$	11854.0	+	6843.90i	1.19760	+	0.691437i	0.237583	+	0.971367i	$0.423645\pi$
$462$	6452.45	−	1668.91i	0.649773	−	0.168062i
$463$	1393.46			0.139870			0.0699348	−	0.997552i	$-0.477721\pi$
$463$	1393.46			0.139870			0.0699348	+	0.997552i	$0.477721\pi$
$464$	−4655.55			−0.465794
$465$	−5590.26	−	21613.4i	−0.557510	−	2.15548i
$466$	6195.08	−	3576.73i	0.615840	−	0.355555i
$467$		−	4290.83i		−	0.425173i	−0.977142	−	0.212587i	$-0.931811\pi$
$467$		−	4290.83i		−	0.425173i	0.977142	−	0.212587i	$-0.0681888\pi$
$468$	−424.998	+	707.405i	−0.0419776	+	0.0698713i
$469$	3451.97	−	1993.00i	0.339866	−	0.196222i
$470$	6159.27	−	10668.2i	0.604481	−	1.04699i
$471$	2364.88	+	9143.26i	0.231355	+	0.894478i
$472$	2710.64	−	4694.96i	0.264337	−	0.457846i
$473$	−10312.8	−	5954.10i	−1.00250	−	0.578794i
$474$	−1462.78	+	5275.18i	−0.141746	+	0.511176i
$475$	−266.041	−	10082.1i	−0.0256985	−	0.973895i
$476$			6431.30i			0.619281i
$477$	12527.0	−	6944.75i	1.20246	−	0.666621i
$478$	4646.97	+	2682.93i	0.444660	+	0.256725i
$479$	−3868.54	+	2233.50i	−0.369015	+	0.213051i	−0.673028	−	0.739617i	$-0.735007\pi$
$479$	−3868.54	+	2233.50i	−0.369015	+	0.213051i	0.304013	+	0.952668i	$0.401673\pi$
$480$	1830.88	+	1863.01i	0.174100	+	0.177155i
$481$	72.9219	+	126.304i	0.00691258	+	0.0119729i
$482$		−	12337.7i		−	1.16591i
$483$	−2089.89	+	7536.70i	−0.196880	+	0.710004i
$484$	444.389	+	769.704i	0.0417345	+	0.0722863i
$485$	3222.29	+	5581.17i	0.301684	+	0.522531i
$486$	1640.78	+	7396.18i	0.153143	+	0.690324i
$487$			6638.69i			0.617716i	0.951108	+	0.308858i	$0.0999468\pi$
$487$			6638.69i			0.617716i	−0.951108	+	0.308858i	$0.900053\pi$
$488$	−702.528	−	1216.81i	−0.0651679	−	0.112874i
$489$	−10659.4	+	10475.6i	−0.985758	+	0.968756i
$490$	−2127.67	+	1228.41i	−0.196160	+	0.113253i
$491$	3356.61	+	1937.94i	0.308517	+	0.178122i	0.646263	−	0.763115i	$-0.276331\pi$
$491$	3356.61	+	1937.94i	0.308517	+	0.178122i	−0.337746	+	0.941237i	$0.609664\pi$
$492$	1506.74	−	1480.75i	0.138067	−	0.135686i
$493$		−	28749.4i		−	2.62638i
$494$	−603.707	+	1112.42i	−0.0549839	+	0.101316i
$495$	14328.8	+	8608.55i	1.30108	+	0.781668i
$496$	3789.65	+	2187.96i	0.343065	+	0.198069i
$497$	4085.77	−	7076.76i	0.368756	−	0.638704i
$498$	−9891.26	+	2558.35i	−0.890036	+	0.230205i
$499$	−1222.21	+	2116.94i	−0.109647	+	0.189914i	−0.915627	−	0.402028i	$-0.868305\pi$
$499$	−1222.21	+	2116.94i	−0.109647	+	0.189914i	0.805980	+	0.591942i	$0.201639\pi$
$500$	−175.266	+	101.190i	−0.0156762	+	0.00905068i
$501$	1691.34	+	469.000i	0.150826	+	0.0418231i
$502$		−	7082.25i		−	0.629674i
$503$	−9076.47	+	5240.30i	−0.804573	+	0.464520i	−0.845068	−	0.534660i	$-0.820440\pi$
$503$	−9076.47	+	5240.30i	−0.804573	+	0.464520i	0.0404950	+	0.999180i	$0.487107\pi$
$504$	−61.1469	+	3514.39i	−0.00540416	+	0.310602i
$505$	−18579.8			−1.63721
$506$	−7290.66			−0.640533
$507$	2782.66	+	10758.5i	0.243752	+	0.942411i
$508$	−8098.16	−	4675.47i	−0.707279	−	0.408348i
$509$	−3739.71	−	6477.37i	−0.325658	−	0.564055i	0.655988	−	0.754772i	$-0.272252\pi$
$509$	−3739.71	−	6477.37i	−0.325658	−	0.564055i	−0.981645	+	0.190716i	$0.938919\pi$
$510$	−11504.6	+	11306.2i	−0.998891	+	0.981662i
$511$	2210.83	−	3829.26i	0.191392	−	0.331500i
$512$	−512.000			−0.0441942
$513$	3010.47	+	11222.4i	0.259095	+	0.965852i
$514$	−13648.7			−1.17124
$515$	2718.09	−	4707.86i	0.232569	−	0.402822i
$516$	4479.25	−	4401.99i	0.382147	−	0.375556i
$517$	7726.05	+	13381.9i	0.657237	+	1.13837i
$518$	537.955	+	310.589i	0.0456301	+	0.0263446i
$519$	4203.28	+	16251.0i	0.355498	+	1.37445i
$520$	−960.303			−0.0809848
$521$	−12800.7			−1.07641			−0.538204	−	0.842815i	$-0.680897\pi$
$521$	−12800.7			−1.07641			−0.538204	+	0.842815i	$0.680897\pi$
$522$	273.341	−	15710.1i	0.0229191	−	1.31727i
$523$	−13431.3	+	7754.58i	−1.12297	+	0.648345i	−0.942156	−	0.335173i	$-0.891205\pi$
$523$	−13431.3	+	7754.58i	−1.12297	+	0.648345i	−0.180810	+	0.983518i	$0.557872\pi$
$524$		−	2437.50i		−	0.203211i
$525$	9922.72	+	2751.51i	0.824882	+	0.228735i
$526$	3135.66	−	1810.37i	0.259926	−	0.150068i
$527$	−13511.3	+	23402.2i	−1.11681	+	1.93437i
$528$	−3172.15	+	820.468i	−0.261458	+	0.0676255i
$529$	−1805.72	+	3127.60i	−0.148411	+	0.257056i
$530$	14434.2	+	8333.58i	1.18298	+	0.682996i
$531$	15684.0	+	9422.68i	1.28178	+	0.770074i
$532$	142.199	+	5388.91i	0.0115885	+	0.439171i
$533$			776.658i			0.0631159i
$534$	−4342.49	+	4267.60i	−0.351907	+	0.345837i
$535$	3009.27	+	1737.40i	0.243182	+	0.140401i
$536$	−1697.05	+	979.794i	−0.136757	+	0.0789564i
$537$	5514.79	−	5419.67i	0.443167	−	0.435524i
$538$	3366.60	+	5831.13i	0.269785	+	0.467282i
$539$		−	3081.79i		−	0.246275i
$540$	−6394.22	+	6068.91i	−0.509562	+	0.483638i
$541$	3354.57	+	5810.28i	0.266588	+	0.461744i	0.967978	−	0.251033i	$-0.0807703\pi$
$541$	3354.57	+	5810.28i	0.266588	+	0.461744i	−0.701390	+	0.712777i	$0.747437\pi$
$542$	−6387.41	−	11063.3i	−0.506204	−	0.876771i
$543$	2084.97	−	7518.96i	0.164778	−	0.594235i
$544$		−	3161.75i		−	0.249189i
$545$	5658.57	+	9800.93i	0.444746	+	0.770322i
$546$	−905.756	−	921.653i	−0.0709941	−	0.0722401i
$547$	−1081.65	+	624.491i	−0.0845485	+	0.0488141i	−0.541678	−	0.840586i	$-0.682211\pi$
$547$	−1081.65	+	624.491i	−0.0845485	+	0.0488141i	0.457130	+	0.889400i	$0.348878\pi$
$548$	−436.577	−	252.058i	−0.0340322	−	0.0196485i
$549$	4147.37	−	2299.23i	0.322414	−	0.178741i
$550$			9598.79i			0.744170i
$551$	−635.662	−	24089.6i	−0.0491472	−	1.86253i
$552$	1027.43	−	3705.19i	0.0792214	−	0.285694i
$553$	−7423.42	−	4285.91i	−0.570842	−	0.329576i
$554$	7929.30	−	13733.9i	0.608093	−	1.05325i
$555$	390.128	+	1508.34i	0.0298379	+	0.115361i
$556$	−3977.10	+	6888.54i	−0.303357	+	0.525430i
$557$	−6018.25	+	3474.64i	−0.457812	+	0.264318i	−0.711124	−	0.703067i	$-0.751813\pi$
$557$	−6018.25	+	3474.64i	−0.457812	+	0.264318i	0.253312	+	0.967385i	$0.418480\pi$
$558$	−7605.74	+	12659.7i	−0.577019	+	0.960443i
$559$			2308.86i			0.174694i
$560$	−3542.15	+	2045.06i	−0.267291	+	0.154321i
$561$	−5066.62	−	19588.9i	−0.381306	−	1.47423i
$562$	3763.87			0.282508
$563$	−4075.15			−0.305057			−0.152529	−	0.988299i	$-0.548742\pi$
$563$	−4075.15			−0.305057			−0.152529	+	0.988299i	$0.548742\pi$
$564$	−7889.60	+	2040.63i	−0.589029	+	0.152351i
$565$	11697.4	+	6753.47i	0.870994	+	0.502868i
$566$	1481.20	+	2565.52i	0.109999	+	0.190524i
$567$	−11855.7	−	412.679i	−0.878115	−	0.0305659i
$568$	−2008.64	+	3479.07i	−0.148382	+	0.257004i
$569$	22300.6			1.64304			0.821521	−	0.570178i	$-0.193126\pi$
$569$	22300.6			1.64304			0.821521	+	0.570178i	$0.193126\pi$
$570$	−9389.98	+	9728.07i	−0.690005	+	0.714849i
$571$	−13113.2			−0.961068			−0.480534	−	0.876976i	$-0.659557\pi$
$571$	−13113.2			−0.961068			−0.480534	+	0.876976i	$0.659557\pi$
$572$	602.292	−	1043.20i	0.0440264	−	0.0762559i
$573$	−15908.7	−	16187.9i	−1.15985	−	1.18021i
$574$	1653.97	+	2864.76i	0.120271	+	0.208315i
$575$	−9755.02	−	5632.06i	−0.707500	−	0.408475i
$576$	30.0610	−	1727.74i	0.00217455	−	0.124981i
$577$	20235.3			1.45998			0.729988	−	0.683460i	$-0.239525\pi$
$577$	20235.3			1.45998			0.729988	+	0.683460i	$0.239525\pi$
$578$	9698.69			0.697945
$579$	7585.76	−	1962.04i	0.544479	−	0.140828i
$580$	15834.2	−	9141.88i	1.13358	−	0.654475i
$581$		−	15997.9i		−	1.14235i
$582$	1139.22	−	4108.33i	0.0811376	−	0.292605i
$583$	−18105.9	+	10453.5i	−1.28623	+	0.742605i
$584$	−1086.88	+	1882.54i	−0.0770130	+	0.133390i
$585$	56.3821	−	3240.53i	0.00398481	−	0.229025i
$586$	−4765.90	+	8254.79i	−0.335969	+	0.581915i
$587$	7093.90	+	4095.66i	0.498802	+	0.287983i	0.728219	−	0.685345i	$-0.240349\pi$
$587$	7093.90	+	4095.66i	0.498802	+	0.287983i	−0.229417	+	0.973328i	$0.573682\pi$
$588$	1566.20	+	434.297i	0.109845	+	0.0304594i
$589$	−10803.9	+	19907.9i	−0.755802	+	1.39268i
$590$			21291.0i			1.48566i
$591$	5047.01	+	5135.59i	0.351280	+	0.357445i
$592$	−264.469	−	152.691i	−0.0183608	−	0.0106006i
$593$	−10686.2	+	6169.66i	−0.740014	+	0.427247i	−0.822074	−	0.569380i	$-0.807183\pi$
$593$	−10686.2	+	6169.66i	−0.740014	+	0.427247i	0.0820606	+	0.996627i	$0.473850\pi$
$594$	−2582.41	−	10752.5i	−0.178380	−	0.742731i
$595$	−12628.8	−	21873.8i	−0.870136	−	1.50712i
$596$			6419.35i			0.441186i
$597$	−16095.8	−	4463.26i	−1.10344	−	0.305979i
$598$	706.786	+	1224.19i	0.0483322	+	0.0837138i
$599$	9430.74	+	16334.5i	0.643288	+	1.11421i	0.984694	+	0.174292i	$0.0557636\pi$
$599$	9430.74	+	16334.5i	0.643288	+	1.11421i	−0.341406	+	0.939916i	$0.610903\pi$
$600$	−4878.20	−	1352.70i	−0.331919	−	0.0920393i
$601$			13156.5i			0.892953i	0.894795	+	0.446476i	$0.147321\pi$
$601$			13156.5i			0.892953i	−0.894795	+	0.446476i	$0.852679\pi$
$602$	4916.93	+	8516.38i	0.332889	+	0.576581i
$603$	−3206.67	−	5784.21i	−0.216560	−	0.390632i
$604$	7513.01	−	4337.64i	0.506126	−	0.292212i
$605$	−3022.86	−	1745.25i	−0.203135	−	0.117280i
$606$	8615.34	+	8766.54i	0.577515	+	0.587651i
$607$		−	12725.3i		−	0.850910i	−0.904980	−	0.425455i	$-0.860114\pi$
$607$		−	12725.3i		−	0.850910i	0.904980	−	0.425455i	$-0.139886\pi$
$608$	−69.9077	−	2649.29i	−0.00466304	−	0.176715i
$609$	23708.7	+	6574.30i	1.57755	+	0.437445i
$610$	4778.80	+	2759.04i	0.317193	+	0.183132i
$611$	1497.99	−	2594.59i	0.0991852	−	0.171794i
$612$	10669.3	+	185.635i	0.704706	+	0.0122612i
$613$	−10915.1	+	18905.4i	−0.719176	+	1.24565i	0.242150	+	0.970239i	$0.422147\pi$
$613$	−10915.1	+	18905.4i	−0.719176	+	1.24565i	−0.961326	+	0.275411i	$0.911186\pi$
$614$	17558.4	−	10137.3i	1.15407	−	0.666301i
$615$	−2216.95	+	7994.95i	−0.145360	+	0.524207i
$616$		−	5130.55i		−	0.335578i
$617$	−13888.3	+	8018.39i	−0.906192	+	0.523190i	−0.879204	−	0.476446i	$-0.841925\pi$
$617$	−13888.3	+	8018.39i	−0.906192	+	0.523190i	−0.0269879	+	0.999636i	$0.508592\pi$
$618$	−3481.68	+	900.528i	−0.226624	+	0.0586158i
$619$	16566.6			1.07572			0.537859	−	0.843035i	$-0.319233\pi$
$619$	16566.6			1.07572			0.537859	+	0.843035i	$0.319233\pi$
$620$	−17185.5			−1.11321
$621$	12442.8	+	3684.58i	0.804045	+	0.238095i
$622$	7439.73	+	4295.33i	0.479592	+	0.276892i
$623$	−4766.82	−	8256.37i	−0.306547	−	0.530954i
$624$	445.287	+	453.102i	0.0285669	+	0.0290683i
$625$	8008.61	−	13871.3i	0.512551	−	0.887764i
$626$	−20392.0			−1.30196
$627$	−4678.54	−	16301.9i	−0.297995	−	1.03833i
$628$	7270.11			0.461957
$629$	942.912	−	1633.17i	0.0597716	−	0.103528i
$630$	−6693.06	−	12073.0i	−0.423266	−	0.763492i
$631$	−6546.44	−	11338.8i	−0.413011	−	0.715355i	0.582207	−	0.813041i	$-0.302189\pi$
$631$	−6546.44	−	11338.8i	−0.413011	−	0.715355i	−0.995217	+	0.0976853i	$0.968856\pi$
$632$	3649.49	+	2107.04i	0.229698	+	0.132616i
$633$	−14138.2	+	3656.81i	−0.887745	+	0.229613i
$634$	−7981.87			−0.500001
$635$	36724.0			2.29504
$636$	−2761.00	−	10674.8i	−0.172139	−	0.665537i
$637$	−517.470	+	298.761i	−0.0321866	+	0.0185830i
$638$			22934.7i			1.42319i
$639$	−11622.1	−	6982.41i	−0.719507	−	0.432269i
$640$	1741.39	−	1005.39i	0.107554	−	0.0620961i
$641$	5758.50	−	9974.02i	0.354832	−	0.614587i	−0.632257	−	0.774758i	$-0.717872\pi$
$641$	5758.50	−	9974.02i	0.354832	−	0.614587i	0.987089	+	0.160172i	$0.0512048\pi$
$642$	−575.619	−	2225.50i	−0.0353861	−	0.136812i
$643$	−4035.48	+	6989.66i	−0.247502	+	0.428686i	−0.962832	−	0.270101i	$-0.912943\pi$
$643$	−4035.48	+	6989.66i	−0.247502	+	0.428686i	0.715330	+	0.698787i	$0.246276\pi$
$644$	5214.06	+	3010.34i	0.319042	+	0.184199i
$645$	−6590.59	+	23767.5i	−0.402332	+	1.45092i
$646$	16360.1	−	431.700i	0.996409	−	0.0262926i
$647$			4605.82i			0.279867i	0.990161	+	0.139933i	$0.0446888\pi$
$647$			4605.82i			0.279867i	−0.990161	+	0.139933i	$0.955311\pi$
$648$	5828.47	+	202.881i	0.353339	+	0.0122992i
$649$	−23128.9	−	13353.5i	−1.39890	−	0.807658i
$650$	1611.75	−	930.545i	0.0972586	−	0.0561523i
$651$	−16209.4	−	16493.9i	−0.975877	−	0.993004i
$652$	5752.43	+	9963.50i	0.345526	+	0.598468i
$653$		−	7068.36i		−	0.423593i	−0.977314	−	0.211797i	$-0.932069\pi$
$653$		−	7068.36i		−	0.423593i	0.977314	−	0.211797i	$-0.0679314\pi$
$654$	2000.55	−	7214.53i	0.119614	−	0.431362i
$655$	4786.41	+	8290.30i	0.285527	+	0.494548i
$656$	−813.122	−	1408.37i	−0.0483949	−	0.0838225i
$657$	−6288.79	−	3778.21i	−0.373439	−	0.224356i
$658$		−	12760.5i		−	0.756010i
$659$	6950.97	+	12039.4i	0.410882	+	0.711669i	0.994986	−	0.100010i	$-0.0318875\pi$
$659$	6950.97	+	12039.4i	0.410882	+	0.711669i	−0.584104	+	0.811679i	$0.698554\pi$
$660$	9177.81	−	9019.52i	0.541282	−	0.531946i
$661$	15158.7	−	8751.85i	0.891987	−	0.514989i	0.0173950	−	0.999849i	$-0.494463\pi$
$661$	15158.7	−	8751.85i	0.891987	−	0.514989i	0.874592	+	0.484860i	$0.161129\pi$
$662$	−13531.3	−	7812.31i	−0.794425	−	0.458662i
$663$	−2798.03	+	2749.77i	−0.163901	+	0.161074i
$664$			7864.86i			0.459662i
$665$	−11065.6	−	18049.2i	−0.645270	−	1.05251i
$666$	530.783	−	883.483i	0.0308820	−	0.0514028i
$667$	−23308.0	−	13456.9i	−1.35306	−	0.781190i
$668$	675.563	−	1170.11i	0.0391292	−	0.0677738i
$669$	−8133.72	+	2103.77i	−0.470057	+	0.121579i
$670$	3847.95	−	6664.84i	0.221879	−	0.384306i
$671$	−5994.42	+	3460.88i	−0.344876	+	0.199114i
$672$	2607.40	+	723.017i	0.149676	+	0.0415044i
$673$			21811.3i			1.24928i	0.780913	+	0.624640i	$0.214754\pi$
$673$			21811.3i			1.24928i	−0.780913	+	0.624640i	$0.785246\pi$
$674$	−833.498	+	481.220i	−0.0476338	+	0.0275014i
$675$	4851.07	−	16382.0i	0.276619	−	0.934138i
$676$	8554.45			0.486712
$677$	−9888.39			−0.561361			−0.280681	−	0.959801i	$-0.590560\pi$
$677$	−9888.39			−0.561361			−0.280681	+	0.959801i	$0.590560\pi$
$678$	−2237.49	−	8650.74i	−0.126741	−	0.490014i
$679$	5781.39	+	3337.89i	0.326759	+	0.188654i
$680$	6208.57	+	10753.6i	0.350129	+	0.606441i
$681$	12674.0	−	12455.4i	0.713169	−	0.700868i
$682$	10778.6	−	18669.1i	0.605181	−	1.04820i
$683$	15903.3			0.890957			0.445478	−	0.895293i	$-0.353034\pi$
$683$	15903.3			0.890957			0.445478	+	0.895293i	$0.353034\pi$
$684$	8944.10	−	80.3555i	0.499980	−	0.00449192i
$685$	1979.81			0.110430
$686$	−6854.04	+	11871.5i	−0.381470	+	0.660726i
$687$	18168.9	−	17855.5i	1.00901	−	0.991604i
$688$	−2417.26	−	4186.81i	−0.133949	−	0.232007i
$689$	3510.53	+	2026.80i	0.194108	+	0.112068i
$690$	3781.26	+	14619.4i	0.208624	+	0.806594i
$691$	−16830.5			−0.926571			−0.463286	−	0.886209i	$-0.653330\pi$
$691$	−16830.5			−0.926571			−0.463286	+	0.886209i	$0.653330\pi$
$692$	12921.7			0.709841
$693$	17313.0	+	301.229i	0.949014	+	0.0165119i
$694$	−13003.3	+	7507.45i	−0.711236	+	0.410633i
$695$		−	31238.6i		−	1.70496i
$696$	−11655.7	−	3232.05i	−0.634780	−	0.176021i
$697$	8697.08	−	5021.26i	0.472633	−	0.272875i
$698$	−8657.63	+	14995.4i	−0.469478	+	0.813161i
$699$	17993.1	−	4653.88i	0.973623	−	0.251825i
$700$	3963.37	−	6864.76i	0.214002	−	0.370662i
$701$	6422.95	+	3708.29i	0.346065	+	0.199801i	0.662951	−	0.748663i	$-0.269304\pi$
$701$	6422.95	+	3708.29i	0.346065	+	0.199801i	−0.316886	+	0.948464i	$0.602637\pi$
$702$	−1555.13	+	1476.01i	−0.0836106	+	0.0793569i
$703$	753.974	−	1389.31i	0.0404505	−	0.0745362i
$704$			2522.28i			0.135031i
$705$	22826.6	−	22432.9i	1.21943	−	1.19840i
$706$	−20438.2	−	11800.0i	−1.08952	−	0.629036i
$707$	−16667.8	+	9623.16i	−0.886644	+	0.511904i
$708$	10045.8	−	9872.51i	0.533254	−	0.524056i
$709$	3498.80	+	6060.09i	0.185332	+	0.321004i	0.943688	−	0.330836i	$-0.107331\pi$
$709$	3498.80	+	6060.09i	0.185332	+	0.321004i	−0.758357	+	0.651840i	$0.773997\pi$
$710$		−	15777.1i		−	0.833949i
$711$	−7324.44	+	12191.5i	−0.386340	+	0.643060i
$712$	2343.46	+	4058.99i	0.123349	+	0.213648i
$713$	12648.6	+	21908.0i	0.664368	+	1.15072i
$714$	−4464.83	+	16101.4i	−0.234023	+	0.843950i
$715$			4730.76i			0.247441i
$716$	−2976.10	−	5154.75i	−0.155338	−	0.269053i
$717$	9771.60	+	9943.10i	0.508964	+	0.517896i
$718$	−20644.6	+	11919.1i	−1.07305	+	0.619524i
$719$	−10281.4	−	5935.95i	−0.533283	−	0.307891i	0.209069	−	0.977901i	$-0.432957\pi$
$719$	−10281.4	−	5935.95i	−0.533283	−	0.307891i	−0.742352	+	0.670010i	$0.766290\pi$
$720$	3290.43	+	5935.32i	0.170316	+	0.307217i
$721$		−	5631.19i		−	0.290869i
$722$	13698.9	−	723.460i	0.706123	−	0.0372914i
$723$	8565.30	−	30888.8i	0.440590	−	1.58889i
$724$	−5201.79	−	3003.25i	−0.267021	−	0.154164i
$725$	−17717.2	+	30687.0i	−0.907585	+	1.57198i
$726$	578.218	+	2235.55i	0.0295588	+	0.114282i
$727$	14337.2	−	24832.8i	0.731415	−	1.26685i	−0.224863	−	0.974390i	$-0.572194\pi$
$727$	14337.2	−	24832.8i	0.731415	−	1.26685i	0.956278	−	0.292458i	$-0.0944731\pi$
$728$	−861.482	+	497.377i	−0.0438580	+	0.0253214i
$729$	−1026.83	+	19656.2i	−0.0521681	+	0.998638i
$730$		−	8537.05i		−	0.432836i
$731$	25854.8	−	14927.3i	1.30817	−	0.755273i
$732$	−914.097	−	3534.14i	−0.0461557	−	0.178450i
$733$	1543.10			0.0777566			0.0388783	−	0.999244i	$-0.487622\pi$
$733$	1543.10			0.0777566			0.0388783	+	0.999244i	$0.487622\pi$
$734$	10733.5			0.539758
$735$	−6179.66	+	1598.35i	−0.310123	+	0.0802125i
$736$	−2563.33	−	1479.94i	−0.128377	−	0.0741186i
$737$	4826.78	+	8360.23i	0.241244	+	0.417847i
$738$	4800.27	−	2661.18i	0.239431	−	0.132736i
$739$	−3356.97	+	5814.44i	−0.167102	+	0.289428i	−0.937400	−	0.348256i	$-0.886774\pi$
$739$	−3356.97	+	5814.44i	−0.167102	+	0.289428i	0.770298	+	0.637684i	$0.220107\pi$
$740$	1199.33			0.0595787
$741$	−2283.73	+	2365.95i	−0.113218	+	0.117295i
$742$	17265.1			0.854207
$743$	−458.404	+	793.978i	−0.0226342	+	0.0392035i	−0.877121	−	0.480270i	$-0.840539\pi$
$743$	−458.404	+	793.978i	−0.0226342	+	0.0392035i	0.854486	+	0.519474i	$0.173872\pi$
$744$	7968.84	+	8108.69i	0.392677	+	0.399569i
$745$	−12605.4	−	21833.1i	−0.619899	−	1.07370i
$746$	7859.61	+	4537.75i	0.385739	+	0.222706i
$747$	−26539.9	−	461.768i	−1.29992	−	0.0226174i
$748$	−15575.8			−0.761373
$749$	3599.46			0.175596
$750$	−509.046	+	131.663i	−0.0247836	+	0.00641022i
$751$	14808.1	−	8549.47i	0.719515	−	0.415412i	−0.0950591	−	0.995472i	$-0.530304\pi$
$751$	14808.1	−	8549.47i	0.719515	−	0.415412i	0.814574	+	0.580059i	$0.196971\pi$
$752$			6273.28i			0.304206i
$753$	4916.75	−	17731.2i	0.237950	−	0.858114i
$754$	3851.02	−	2223.39i	0.186002	−	0.107389i
$755$	−17035.2	+	29505.9i	−0.821159	+	1.42229i
$756$	−2592.90	+	8756.18i	−0.124739	+	0.421242i
$757$	−586.119	+	1015.19i	−0.0281411	+	0.0487419i	−0.879753	−	0.475431i	$-0.842292\pi$
$757$	−586.119	+	1015.19i	−0.0281411	+	0.0487419i	0.851612	+	0.524173i	$0.175625\pi$
$758$	−13527.3	−	7810.00i	−0.648198	−	0.374237i
$759$	−18252.9	−	5061.44i	−0.872911	−	0.242053i
$760$	5440.04	+	8873.34i	0.259646	+	0.423513i
$761$		−	8457.38i		−	0.402865i	−0.979502	−	0.201432i	$-0.935440\pi$
$761$		−	8457.38i		−	0.402865i	0.979502	−	0.201432i	$-0.0645596\pi$
$762$	−17028.7	−	17327.6i	−0.809560	−	0.823768i
$763$	10152.5	+	5861.57i	0.481712	+	0.278117i
$764$	−15131.1	+	8735.94i	−0.716523	+	0.413685i
$765$	−36652.3	+	20319.4i	−1.73224	+	0.960325i
$766$	9351.74	+	16197.7i	0.441112	+	0.764029i
$767$			5178.16i			0.243771i
$768$	−1281.85	−	355.449i	−0.0602274	−	0.0167007i
$769$	4720.87	+	8176.78i	0.221377	+	0.383436i	0.955226	−	0.295876i	$-0.0956116\pi$
$769$	4720.87	+	8176.78i	0.221377	+	0.383436i	−0.733849	+	0.679312i	$0.762278\pi$
$770$	10074.6	+	17449.8i	0.471512	+	0.816682i
$771$	−34170.8	−	9475.38i	−1.59615	−	0.442604i
$772$		−	6031.69i		−	0.281198i
$773$	−6383.37	−	11056.3i	−0.297016	−	0.514448i	0.678435	−	0.734660i	$-0.262658\pi$
$773$	−6383.37	−	11056.3i	−0.297016	−	0.514448i	−0.975452	+	0.220212i	$0.929325\pi$
$774$	14270.3	−	7911.19i	0.662706	−	0.367393i
$775$	28843.8	−	16653.0i	1.33690	−	0.771862i
$776$	−2842.24	−	1640.97i	−0.131483	−	0.0759115i
$777$	1131.21	+	1151.06i	0.0522288	+	0.0531454i
$778$		−	11679.7i		−	0.538224i
$779$	7176.43	−	4399.71i	0.330067	−	0.202357i
$780$	−2404.22	−	666.676i	−0.110365	−	0.0306036i
$781$	17139.0	+	9895.22i	0.785253	+	0.453366i
$782$	9139.05	−	15829.3i	0.417918	−	0.723855i
$783$	11590.8	−	39142.1i	0.529021	−	1.78650i
$784$	625.576	−	1083.53i	0.0284975	−	0.0493590i
$785$	−24726.7	+	14276.0i	−1.12425	+	0.649084i
$786$	1692.20	−	6102.54i	0.0767924	−	0.276935i
$787$			27982.7i			1.26744i	0.773563	+	0.633720i	$0.218473\pi$
$787$			27982.7i			1.26744i	−0.773563	+	0.633720i	$0.781527\pi$
$788$	4800.30	−	2771.46i	0.217010	−	0.125291i
$789$	9107.27	−	2355.57i	0.410935	−	0.106287i
$790$	−16549.9			−0.745342
$791$	13991.5			0.628926
$792$	−8511.40	−	148.090i	−0.381868	−	0.00664413i
$793$	1162.25	+	671.023i	0.0520461	+	0.0300488i
$794$	4402.83	+	7625.92i	0.196789	+	0.340849i
$795$	30352.0	+	30884.7i	1.35406	+	1.37782i
$796$	−6429.03	+	11135.4i	−0.286270	+	0.495834i
$797$	21930.2			0.974664			0.487332	−	0.873217i	$-0.337970\pi$
$797$	21930.2			0.974664			0.487332	+	0.873217i	$0.337970\pi$
$798$	−3385.16	+	13590.4i	−0.150167	+	0.602876i
$799$	−38739.3			−1.71527
$800$	−1948.47	+	3374.85i	−0.0861110	+	0.149149i
$801$	−13834.6	+	7669.66i	−0.610264	+	0.338320i
$802$	11925.0	+	20654.8i	0.525047	+	0.909408i
$803$	9273.99	+	5354.34i	0.407562	+	0.235306i
$804$	−4928.96	+	1274.86i	−0.216208	+	0.0559216i
$805$	−23645.0			−1.03525
$806$	−4179.68			−0.182659
$807$	4380.47	+	16936.0i	0.191078	+	0.738757i
$808$	8194.21	−	4730.93i	0.356771	−	0.205982i
$809$			22217.0i			0.965522i	0.875752	+	0.482761i	$0.160366\pi$
$809$			22217.0i			0.965522i	−0.875752	+	0.482761i	$0.839634\pi$
$810$	−20221.9	+	10755.1i	−0.877189	+	0.466536i
$811$	−1100.74	+	635.515i	−0.0476601	+	0.0275166i	−0.523641	−	0.851939i	$-0.675427\pi$
$811$	−1100.74	+	635.515i	−0.0476601	+	0.0275166i	0.475981	+	0.879456i	$0.342093\pi$
$812$	9469.84	−	16402.2i	0.409269	−	0.708874i
$813$	−8311.00	−	32132.5i	−0.358523	−	1.38615i
$814$	−752.206	+	1302.86i	−0.0323892	+	0.0560998i
$815$	−39129.7	−	22591.5i	−1.68178	−	0.970978i
$816$	2195.00	−	7915.76i	0.0941670	−	0.339592i
$817$	21334.2	−	13079.5i	0.913571	−	0.560090i
$818$		−	19919.8i		−	0.851441i
$819$	−1627.81	−	2936.26i	−0.0694510	−	0.125276i
$820$	5531.09	+	3193.38i	0.235554	+	0.135997i
$821$	11146.7	−	6435.56i	0.473841	−	0.273572i	−0.244006	−	0.969774i	$-0.578462\pi$
$821$	11146.7	−	6435.56i	0.473841	−	0.273572i	0.717846	+	0.696202i	$0.245128\pi$
$822$	−918.028	−	934.140i	−0.0389537	−	0.0396373i
$823$	6732.47	+	11661.0i	0.285151	+	0.493896i	0.972646	−	0.232293i	$-0.0746230\pi$
$823$	6732.47	+	11661.0i	0.285151	+	0.493896i	−0.687495	+	0.726189i	$0.741290\pi$
$824$			2768.40i			0.117041i
$825$	−6663.82	+	24031.6i	−0.281217	+	1.01415i
$826$	11027.4	+	19100.0i	0.464518	+	0.804570i
$827$	2509.46	+	4346.51i	0.105517	+	0.182761i	0.913949	−	0.405828i	$-0.133017\pi$
$827$	2509.46	+	4346.51i	0.105517	+	0.182761i	−0.808432	+	0.588589i	$0.799684\pi$
$828$	5144.54	−	8563.04i	0.215924	−	0.359404i
$829$		−	40083.2i		−	1.67931i	−0.543122	−	0.839654i	$-0.682758\pi$
$829$		−	40083.2i		−	1.67931i	0.543122	−	0.839654i	$-0.317242\pi$
$830$	−15443.8	−	26749.5i	−0.645860	−	1.11866i
$831$	29386.4	−	28879.6i	1.22672	−	1.20556i
$832$	423.521	−	244.520i	0.0176478	−	0.0101889i
$833$	6691.11	+	3863.11i	0.278311	+	0.160683i
$834$	−14739.4	+	14485.1i	−0.611969	+	0.601414i
$835$			5306.28i			0.219918i
$836$	−13051.3	+	344.388i	−0.539937	+	0.0142475i
$837$	−27830.6	+	26414.7i	−1.14930	+	1.09083i
$838$	4406.82	+	2544.28i	0.181660	+	0.104881i
$839$	−3774.49	+	6537.60i	−0.155316	+	0.269015i	−0.933174	−	0.359425i	$-0.882973\pi$
$839$	−3774.49	+	6537.60i	−0.155316	+	0.269015i	0.777858	+	0.628440i	$0.216306\pi$
$840$	−10287.9	+	2660.94i	−0.422578	+	0.109299i
$841$	−30137.8	+	52200.2i	−1.23571	+	2.14032i
$842$	18281.9	−	10555.0i	0.748260	−	0.432008i
$843$	9423.24	+	2613.01i	0.384999	+	0.106758i
$844$			11241.7i			0.458480i
$845$	−29094.9	+	16797.9i	−1.18449	+	0.683866i
$846$	−21169.1	−	368.322i	−0.860295	−	0.0149683i
$847$	−3615.72			−0.146680
$848$	−8487.85			−0.343719
$849$	1927.27	+	7451.35i	0.0779079	+	0.301213i
$850$	−20840.6	−	12032.3i	−0.840974	−	0.485537i
$851$	−882.711	−	1528.90i	−0.0355569	−	0.0615864i
$852$	−7444.14	+	7315.74i	−0.299333	+	0.294171i
$853$	11369.8	−	19693.1i	0.456383	−	0.790478i	−0.542384	−	0.840131i	$-0.682478\pi$
$853$	11369.8	−	19693.1i	0.456383	−	0.790478i	0.998767	+	0.0496530i	$0.0158115\pi$
$854$	5716.04			0.229038
$855$	−30262.4	+	17836.4i	−1.21047	+	0.713441i
$856$	−1769.56			−0.0706571
$857$	−19813.9	+	34318.7i	−0.789766	+	1.36791i	0.136344	+	0.990662i	$0.456465\pi$
$857$	−19813.9	+	34318.7i	−0.789766	+	1.36791i	−0.926110	+	0.377253i	$0.876869\pi$
$858$	2232.13	−	2193.63i	0.0888153	−	0.0872835i
$859$	13688.3	+	23708.9i	0.543702	+	0.941720i	0.998687	+	0.0512207i	$0.0163112\pi$
$859$	13688.3	+	23708.9i	0.543702	+	0.941720i	−0.454985	+	0.890499i	$0.650355\pi$
$860$	16442.9	+	9493.30i	0.651974	+	0.376417i
$861$	2152.07	+	8320.46i	0.0851826	+	0.329339i
$862$	−28370.4			−1.12100
$863$	26213.1			1.03396			0.516978	−	0.855999i	$-0.327057\pi$
$863$	26213.1			1.03396			0.516978	+	0.855999i	$0.327057\pi$
$864$	1274.72	−	4304.71i	0.0501931	−	0.169501i
$865$	−43948.6	+	25373.7i	−1.72751	+	0.997379i
$866$			20265.8i			0.795219i
$867$	24281.7	+	6733.17i	0.951152	+	0.263749i
$868$	−15417.0	+	8901.03i	−0.602867	+	0.348065i
$869$	10379.9	−	17978.6i	0.405196	−	0.701820i
$870$	45989.2	−	11895.0i	1.79216	−	0.463538i
$871$	935.855	−	1620.95i	0.0364067	−	0.0630583i
$872$	−4991.18	−	2881.66i	−0.193833	−	0.111910i
$873$	5704.30	−	9494.76i	0.221147	−	0.368097i
$874$	7307.80	−	13465.7i	0.282826	−	0.521151i
$875$		−	823.319i		−	0.0318094i
$876$	−4028.05	+	3958.58i	−0.155360	+	0.152680i
$877$	5394.08	+	3114.27i	0.207691	+	0.119911i	0.600238	−	0.799822i	$-0.295073\pi$
$877$	5394.08	+	3114.27i	0.207691	+	0.119911i	−0.392547	+	0.919732i	$0.628406\pi$
$878$	4885.39	−	2820.58i	0.187783	−	0.108417i
$879$	−17662.7	+	17358.1i	−0.677757	+	0.666067i
$880$	−4952.87	−	8578.63i	−0.189729	−	0.328620i
$881$		−	9329.36i		−	0.356770i	−0.983961	−	0.178385i	$-0.942913\pi$
$881$		−	9329.36i		−	0.356770i	0.983961	−	0.178385i	$-0.0570872\pi$
$882$	3619.63	+	2174.62i	0.138185	+	0.0830195i
$883$	20832.9	+	36083.6i	0.793978	+	1.37521i	0.923486	+	0.383632i	$0.125327\pi$
$883$	20832.9	+	36083.6i	0.793978	+	1.37521i	−0.129508	+	0.991578i	$0.541340\pi$
$884$	1509.98	+	2615.36i	0.0574503	+	0.0995069i
$885$	−14781.0	+	53304.2i	−0.561420	+	2.02464i
$886$		−	11426.2i		−	0.433262i
$887$	19033.7	+	32967.4i	0.720507	+	1.24795i	0.960797	+	0.277254i	$0.0894242\pi$
$887$	19033.7	+	32967.4i	0.720507	+	1.24795i	−0.240290	+	0.970701i	$0.577242\pi$
$888$	−556.122	−	565.882i	−0.0210160	−	0.0213849i
$889$	32944.9	−	19020.7i	1.24290	−	0.717587i
$890$	−15940.9	−	9203.47i	−0.600381	−	0.346630i
$891$	999.457	−	28712.9i	0.0375792	−	1.07960i
$892$			6467.39i			0.242763i
$893$	−32460.4	+	856.544i	−1.21640	+	0.0320976i
$894$	−4456.54	+	16071.5i	−0.166721	+	0.601243i
$895$	20244.3	+	11688.0i	0.756080	+	0.436523i
$896$	1041.46	−	1803.86i	0.0388311	−	0.0672574i
$897$	919.638	+	3555.56i	0.0342317	+	0.132349i
$898$	5474.99	−	9482.97i	0.203455	−	0.352395i
$899$	68917.7	−	39789.6i	2.55677	−	1.47615i
$900$	−11274.0	−	6773.23i	−0.417555	−	0.250860i
$901$		−	52414.9i		−	1.93806i
$902$	−6938.08	+	4005.70i	−0.256112	+	0.147866i
$903$	6397.69	+	24735.2i	0.235771	+	0.911555i
$904$	−6878.48			−0.253070
$905$	23589.4			0.866450
$906$	21820.9	−	5643.93i	0.800168	−	0.206961i
$907$	−11948.5	−	6898.45i	−0.437423	−	0.252546i	0.265081	−	0.964226i	$-0.414601\pi$
$907$	−11948.5	−	6898.45i	−0.437423	−	0.252546i	−0.702504	+	0.711680i	$0.747935\pi$
$908$	−6839.61	−	11846.5i	−0.249978	−	0.432975i
$909$	15483.4	+	27929.0i	0.564962	+	1.01908i
$910$	1953.35	−	3383.30i	0.0711570	−	0.123248i
$911$	−28186.7			−1.02510			−0.512550	−	0.858657i	$-0.671299\pi$
$911$	−28186.7			−1.02510			−0.512550	+	0.858657i	$0.671299\pi$
$912$	1664.21	−	6681.30i	0.0604249	−	0.242588i
$913$	38744.9			1.40446
$914$	492.731	−	853.435i	0.0178316	−	0.0308852i
$915$	10048.8	+	10225.2i	0.363063	+	0.369435i
$916$	−9804.99	−	16982.7i	−0.353675	−	0.612582i
$917$	8587.71	+	4958.11i	0.309260	+	0.178551i
$918$	26582.8	+	7871.75i	0.955733	+	0.283014i
$919$	−14498.9			−0.520429			−0.260215	−	0.965551i	$-0.583793\pi$
$919$	−14498.9			−0.520429			−0.260215	+	0.965551i	$0.583793\pi$
$920$	11624.3			0.416569
$921$	50996.9	−	13190.2i	1.82454	−	0.471913i
$922$	23708.0	−	13687.8i	0.846833	−	0.488920i
$923$		−	3837.13i		−	0.136837i
$924$	3561.81	−	12844.9i	0.126813	−	0.457322i
$925$	−2012.93	+	1162.16i	−0.0715510	+	0.0413100i
$926$	1393.46	−	2413.54i	0.0494513	−	0.0856522i
$927$	−9341.94	−	162.541i	−0.330992	−	0.00575894i
$928$	−4655.55	+	8063.65i	−0.164683	+	0.285240i
$929$	−30920.2	−	17851.8i	−1.09199	−	0.630462i	−0.157886	−	0.987457i	$-0.550468\pi$
$929$	−30920.2	−	17851.8i	−1.09199	−	0.630462i	−0.934106	+	0.356996i	$0.883801\pi$
$930$	−43025.8	−	11930.8i	−1.51707	−	0.420674i
$931$	5692.02	+	3089.03i	0.200374	+	0.108742i
$932$		−	14306.9i		−	0.502831i
$933$	15644.2	+	15918.7i	0.548947	+	0.558581i
$934$	−7431.93	−	4290.83i	−0.260364	−	0.150321i
$935$	52975.5	−	30585.4i	1.85292	−	1.06979i
$936$	800.263	+	1443.52i	0.0279460	+	0.0504092i
$937$	3625.91	+	6280.26i	0.126418	+	0.218962i	0.922286	−	0.386508i	$-0.126319\pi$
$937$	3625.91	+	6280.26i	0.126418	+	0.218962i	−0.795869	+	0.605469i	$0.792985\pi$
$938$		−	7971.98i		−	0.277499i
$939$	−51053.5	−	14156.8i	−1.77430	−	0.492003i
$940$	−12318.5	−	21336.3i	−0.427432	−	0.740335i
$941$	−18391.6	−	31855.2i	−0.637141	−	1.10356i	−0.986057	−	0.166406i	$-0.946784\pi$
$941$	−18391.6	−	31855.2i	−0.637141	−	1.10356i	0.348917	−	0.937154i	$-0.386550\pi$
$942$	18201.5	+	5047.17i	0.629550	+	0.174571i
$943$		−	9401.34i		−	0.324655i
$944$	−5421.28	−	9389.93i	−0.186915	−	0.323746i
$945$	−8375.27	−	34872.6i	−0.288304	−	1.20043i
$946$	−20625.6	+	11908.2i	−0.708875	+	0.409269i
$947$	12575.1	+	7260.21i	0.431504	+	0.249129i	0.699987	−	0.714155i	$-0.253189\pi$
$947$	12575.1	+	7260.21i	0.431504	+	0.249129i	−0.268483	+	0.963284i	$0.586522\pi$
$948$	7674.11	+	7808.79i	0.262915	+	0.267529i
$949$		−	2076.29i		−	0.0710212i
$950$	−17728.8	−	9621.34i	−0.605472	−	0.328587i
$951$	−19983.5	−	5541.30i	−0.681397	−	0.188947i
$952$	11139.3	+	6431.30i	0.379231	+	0.218949i
$953$	−15434.4	+	26733.1i	−0.524625	+	0.908678i	0.474964	+	0.880005i	$0.342461\pi$
$953$	−15434.4	+	26733.1i	−0.524625	+	0.908678i	−0.999589	+	0.0286722i	$0.990872\pi$
$954$	498.345	−	28642.1i	0.0169125	−	0.972037i
$955$	34308.7	−	59424.4i	1.16252	−	2.01354i
$956$	9293.95	−	5365.86i	0.314422	−	0.181532i
$957$	−15922.1	+	57419.5i	−0.537815	+	1.93951i
$958$			8934.01i			0.301299i
$959$	1776.08	−	1025.42i	0.0598045	−	0.0345282i
$960$	5057.72	−	1308.17i	0.170039	−	0.0439801i
$961$	−45008.3			−1.51080
$962$	291.688			0.00977587
$963$	103.896	−	5971.38i	0.00347664	−	0.199818i
$964$	−21369.6	−	12337.7i	−0.713971	−	0.412211i
$965$	11844.1	+	20514.6i	0.395105	+	0.684341i
$966$	10964.1	+	11156.5i	0.365179	+	0.371588i
$967$	−19466.7	+	33717.4i	−0.647371	+	1.12128i	0.336377	+	0.941727i	$0.390798\pi$
$967$	−19466.7	+	33717.4i	−0.647371	+	1.12128i	−0.983748	+	0.179553i	$0.942535\pi$
$968$	1777.56			0.0590215
$969$	41259.0	+	10277.0i	1.36783	+	0.340706i
$970$	12889.2			0.426645
$971$	−12399.8	+	21477.2i	−0.409814	+	0.709819i	−0.994869	−	0.101175i	$-0.967740\pi$
$971$	−12399.8	+	21477.2i	−0.409814	+	0.709819i	0.585054	+	0.810994i	$0.301073\pi$
$972$	14451.3	+	4554.26i	0.476880	+	0.150286i
$973$	−16179.6	−	28023.9i	−0.533088	−	0.923336i
$974$	11498.6	+	6638.69i	0.378272	+	0.218396i
$975$	4681.21	−	1210.78i	0.153763	−	0.0397703i
$976$	−2810.11			−0.0921613
$977$	11629.3			0.380813			0.190406	−	0.981705i	$-0.439019\pi$
$977$	11629.3			0.380813			0.190406	+	0.981705i	$0.439019\pi$
$978$	7484.80	+	28938.2i	0.244721	+	0.946158i
$979$	19995.9	−	11544.6i	0.652780	−	0.376883i
$980$			4913.65i			0.160164i
$981$	10017.2	−	16673.5i	0.326018	−	0.542654i
$982$	6713.22	−	3875.88i	0.218154	−	0.125951i
$983$	−14472.9	+	25067.7i	−0.469595	+	0.813363i	−0.999396	−	0.0347592i	$-0.988934\pi$
$983$	−14472.9	+	25067.7i	−0.469595	+	0.813363i	0.529800	+	0.848122i	$0.322267\pi$
$984$	−1058.00	−	4090.50i	−0.0342761	−	0.132521i
$985$	−10884.3	+	18852.2i	−0.352085	+	0.609830i
$986$	−49795.3	−	28749.4i	−1.60832	−	0.928566i
$987$	8858.76	−	31947.1i	0.285692	−	1.03028i
$988$	1323.07	+	2158.08i	0.0426036	+	0.0694914i
$989$		−	27948.4i		−	0.898592i
$990$	29239.3	−	16209.7i	0.938672	−	0.520383i
$991$	−16405.5	−	9471.72i	−0.525871	−	0.303612i	0.213463	−	0.976951i	$-0.431526\pi$
$991$	−16405.5	−	9471.72i	−0.525871	−	0.303612i	−0.739333	+	0.673340i	$0.764859\pi$
$992$	7579.31	−	4375.92i	0.242584	−	0.140056i
$993$	−28453.5	−	28952.8i	−0.909309	−	0.925268i
$994$	−8171.54	−	14153.5i	−0.260750	−	0.451632i
$995$		−	50497.5i		−	1.60892i
$996$	−5460.07	+	19690.5i	−0.173704	+	0.626423i
$997$	−5349.66	−	9265.87i	−0.169935	−	0.294336i	0.768462	−	0.639896i	$-0.221022\pi$
$997$	−5349.66	−	9265.87i	−0.169935	−	0.294336i	−0.938397	+	0.345560i	$0.887689\pi$
$998$	2444.43	+	4233.87i	0.0775320	+	0.134289i
$999$	1942.22	−	1843.40i	0.0615105	−	0.0583811i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.4.h.b.65.8	yes	20
3.2	odd	2		114.4.h.a.65.5	✓	20
19.12	odd	6		114.4.h.a.107.5	yes	20
57.50	even	6	inner	114.4.h.b.107.8	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.4.h.a.65.5	✓	20	3.2	odd	2
114.4.h.a.107.5	yes	20	19.12	odd	6
114.4.h.b.65.8	yes	20	1.1	even	1	trivial
114.4.h.b.107.8	yes	20	57.50	even	6	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:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	114.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(3.70606 - 3.64214i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(13.6046 + 7.85461i) q^{5} +(-2.60231 - 10.0612i) q^{6} +16.2728 q^{7} -8.00000 q^{8} +(0.469703 - 26.9959i) q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{2} +(3.70606 - 3.64214i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(13.6046 + 7.85461i) q^{5} +(-2.60231 - 10.0612i) q^{6} +16.2728 q^{7} -8.00000 q^{8} +(0.469703 - 26.9959i) q^{9} +(27.2092 - 15.7092i) q^{10} +39.4106i q^{11} +(-20.0288 - 5.55388i) q^{12} +(6.61751 - 3.82062i) q^{13} +(16.2728 - 28.1853i) q^{14} +(79.0269 - 20.4401i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-85.5673 - 49.4023i) q^{17} +(-46.2886 - 27.8095i) q^{18} +(-72.7908 - 39.5032i) q^{19} -62.8368i q^{20} +(60.3078 - 59.2676i) q^{21} +(68.2611 + 39.4106i) q^{22} +(-80.1041 + 46.2481i) q^{23} +(-29.6484 + 29.1371i) q^{24} +(60.8896 + 105.464i) q^{25} -15.2825i q^{26} +(-96.5820 - 101.759i) q^{27} +(-32.5455 - 56.3705i) q^{28} +(145.486 + 251.989i) q^{29} +(43.6236 - 157.319i) q^{30} -273.495i q^{31} +(16.0000 + 27.7128i) q^{32} +(143.539 + 146.058i) q^{33} +(-171.135 + 98.8046i) q^{34} +(221.384 + 127.816i) q^{35} +(-94.4560 + 52.3647i) q^{36} +19.0864i q^{37} +(-141.212 + 86.5741i) q^{38} +(10.6096 - 38.2613i) q^{39} +(-108.837 - 62.8368i) q^{40} +(-50.8201 + 88.0230i) q^{41} +(-42.3467 - 163.724i) q^{42} +(-151.079 + 261.676i) q^{43} +(136.522 - 78.8212i) q^{44} +(218.432 - 363.579i) q^{45} +184.993i q^{46} +(339.551 - 196.040i) q^{47} +(20.8185 + 80.4897i) q^{48} -78.1970 q^{49} +243.559 q^{50} +(-497.047 + 128.560i) q^{51} +(-26.4700 - 15.2825i) q^{52} +(265.245 + 459.418i) q^{53} +(-272.834 + 65.5259i) q^{54} +(-309.555 + 536.164i) q^{55} -130.182 q^{56} +(-413.643 + 118.713i) q^{57} +581.944 q^{58} +(-338.830 + 586.871i) q^{59} +(-228.860 - 232.877i) q^{60} +(87.8160 + 152.102i) q^{61} +(-473.707 - 273.495i) q^{62} +(7.64336 - 439.298i) q^{63} +64.0000 q^{64} +120.038 q^{65} +(396.518 - 102.558i) q^{66} +(212.132 - 122.474i) q^{67} +395.218i q^{68} +(-128.428 + 463.148i) q^{69} +(442.768 - 255.632i) q^{70} +(251.080 - 434.884i) q^{71} +(-3.75762 + 215.967i) q^{72} +(135.861 - 235.317i) q^{73} +(33.0586 + 19.0864i) q^{74} +(609.774 + 169.087i) q^{75} +(8.73846 + 331.161i) q^{76} +641.319i q^{77} +(-55.6609 - 56.6377i) q^{78} +(-456.187 - 263.379i) q^{79} +(-217.673 + 125.674i) q^{80} +(-728.559 - 25.3601i) q^{81} +(101.640 + 176.046i) q^{82} -983.108i q^{83} +(-325.925 - 90.3771i) q^{84} +(-776.071 - 1344.19i) q^{85} +(302.157 + 523.352i) q^{86} +(1456.96 + 404.006i) q^{87} -315.285i q^{88} +(-292.932 - 507.374i) q^{89} +(-411.304 - 741.915i) q^{90} +(107.685 - 62.1721i) q^{91} +(320.416 + 184.993i) q^{92} +(-996.105 - 1013.59i) q^{93} -784.160i q^{94} +(-680.006 - 1109.17i) q^{95} +(160.231 + 44.4311i) q^{96} +(355.280 + 205.121i) q^{97} +(-78.1970 + 135.441i) q^{98} +(1063.92 + 18.5113i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{2} + q^{3} - 40 q^{4} - 8 q^{6} - 10 q^{7} - 160 q^{8} - 37 q^{9}+O(q^{10}) \) 20 * q + 20 * q^2 + q^3 - 40 * q^4 - 8 * q^6 - 10 * q^7 - 160 * q^8 - 37 * q^9	\( 20 q + 20 q^{2} + q^{3} - 40 q^{4} - 8 q^{6} - 10 q^{7} - 160 q^{8} - 37 q^{9} - 20 q^{12} - 111 q^{13} - 10 q^{14} - 133 q^{15} - 160 q^{16} - 90 q^{17} - 10 q^{18} - 143 q^{19} + 191 q^{21} - 54 q^{22} - 8 q^{24} + 184 q^{25} - 524 q^{27} + 20 q^{28} - 96 q^{29} - 292 q^{30} + 320 q^{32} - 55 q^{33} - 180 q^{34} + 774 q^{35} + 128 q^{36} - 314 q^{38} + 1002 q^{39} + 537 q^{41} - 382 q^{42} + 571 q^{43} - 108 q^{44} + 1516 q^{45} - 126 q^{47} + 64 q^{48} + 558 q^{49} + 736 q^{50} - 757 q^{51} + 444 q^{52} + 126 q^{53} - 1388 q^{54} + 366 q^{55} + 80 q^{56} - 281 q^{57} - 384 q^{58} - 1383 q^{59} - 52 q^{60} + 149 q^{61} - 222 q^{62} + 1153 q^{63} + 1280 q^{64} + 3636 q^{65} + 32 q^{66} - 1626 q^{67} + 236 q^{69} + 1548 q^{70} - 1368 q^{71} + 296 q^{72} + 946 q^{73} + 474 q^{74} - 669 q^{75} - 56 q^{76} + 132 q^{78} - 2109 q^{79} + 311 q^{81} - 1074 q^{82} - 1528 q^{84} + 786 q^{85} - 1142 q^{86} - 816 q^{87} - 1938 q^{89} + 1234 q^{90} - 3459 q^{91} - 705 q^{93} + 2502 q^{95} + 160 q^{96} + 1791 q^{97} + 558 q^{98} - 2285 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 + q^3 - 40 * q^4 - 8 * q^6 - 10 * q^7 - 160 * q^8 - 37 * q^9 - 20 * q^12 - 111 * q^13 - 10 * q^14 - 133 * q^15 - 160 * q^16 - 90 * q^17 - 10 * q^18 - 143 * q^19 + 191 * q^21 - 54 * q^22 - 8 * q^24 + 184 * q^25 - 524 * q^27 + 20 * q^28 - 96 * q^29 - 292 * q^30 + 320 * q^32 - 55 * q^33 - 180 * q^34 + 774 * q^35 + 128 * q^36 - 314 * q^38 + 1002 * q^39 + 537 * q^41 - 382 * q^42 + 571 * q^43 - 108 * q^44 + 1516 * q^45 - 126 * q^47 + 64 * q^48 + 558 * q^49 + 736 * q^50 - 757 * q^51 + 444 * q^52 + 126 * q^53 - 1388 * q^54 + 366 * q^55 + 80 * q^56 - 281 * q^57 - 384 * q^58 - 1383 * q^59 - 52 * q^60 + 149 * q^61 - 222 * q^62 + 1153 * q^63 + 1280 * q^64 + 3636 * q^65 + 32 * q^66 - 1626 * q^67 + 236 * q^69 + 1548 * q^70 - 1368 * q^71 + 296 * q^72 + 946 * q^73 + 474 * q^74 - 669 * q^75 - 56 * q^76 + 132 * q^78 - 2109 * q^79 + 311 * q^81 - 1074 * q^82 - 1528 * q^84 + 786 * q^85 - 1142 * q^86 - 816 * q^87 - 1938 * q^89 + 1234 * q^90 - 3459 * q^91 - 705 * q^93 + 2502 * q^95 + 160 * q^96 + 1791 * q^97 + 558 * q^98 - 2285 * q^99

Introduction

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