LMFDB - Embedded newform 76.3.b.b.39.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,3,Mod(39,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("76.39");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	76.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.07085000914$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} + x^{12} + 14 x^{11} - 42 x^{10} + 28 x^{9} + 132 x^{8} - 440 x^{7} + 528 x^{6} + \cdots + 16384 $ x^14 - 2x^13 + x^12 + 14x^11 - 42x^10 + 28x^9 + 132x^8 - 440x^7 + 528x^6 + 448x^5 - 2688x^4 + 3584x^3 + 1024x^2 - 8192x + 16384
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			39.6
Root			$-0.0607713 - 1.99908i$ of defining polynomial
Character	$\chi$	$=$	76.39
Dual form			76.3.b.b.39.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0607713 + 1.99908i) q^{2} -5.37609i q^{3} +(-3.99261 - 0.242973i) q^{4} -5.82257 q^{5} +(10.7472 + 0.326712i) q^{6} -5.45132i q^{7} +(0.728358 - 7.96677i) q^{8} -19.9023 q^{9} +O(q^{10})$	\(q+(-0.0607713 + 1.99908i) q^{2} -5.37609i q^{3} +(-3.99261 - 0.242973i) q^{4} -5.82257 q^{5} +(10.7472 + 0.326712i) q^{6} -5.45132i q^{7} +(0.728358 - 7.96677i) q^{8} -19.9023 q^{9} +(0.353845 - 11.6398i) q^{10} -1.60915i q^{11} +(-1.30624 + 21.4646i) q^{12} +23.5274 q^{13} +(10.8976 + 0.331284i) q^{14} +31.3027i q^{15} +(15.8819 + 1.94019i) q^{16} -5.92676 q^{17} +(1.20949 - 39.7863i) q^{18} +4.35890i q^{19} +(23.2473 + 1.41473i) q^{20} -29.3068 q^{21} +(3.21681 + 0.0977900i) q^{22} -26.6121i q^{23} +(-42.8301 - 3.91572i) q^{24} +8.90234 q^{25} +(-1.42979 + 47.0331i) q^{26} +58.6120i q^{27} +(-1.32452 + 21.7650i) q^{28} -1.49241 q^{29} +(-62.5764 - 1.90230i) q^{30} -31.3933i q^{31} +(-4.84376 + 31.6313i) q^{32} -8.65093 q^{33} +(0.360177 - 11.8480i) q^{34} +31.7407i q^{35} +(79.4624 + 4.83573i) q^{36} +26.8255 q^{37} +(-8.71377 - 0.264896i) q^{38} -126.486i q^{39} +(-4.24092 + 46.3871i) q^{40} -44.0382 q^{41} +(1.78101 - 58.5865i) q^{42} -27.8586i q^{43} +(-0.390980 + 6.42471i) q^{44} +115.883 q^{45} +(53.1996 + 1.61725i) q^{46} +32.5166i q^{47} +(10.4307 - 85.3827i) q^{48} +19.2831 q^{49} +(-0.541007 + 17.7965i) q^{50} +31.8628i q^{51} +(-93.9360 - 5.71653i) q^{52} +76.7637 q^{53} +(-117.170 - 3.56193i) q^{54} +9.36938i q^{55} +(-43.4294 - 3.97051i) q^{56} +23.4338 q^{57} +(0.0906959 - 2.98345i) q^{58} +33.8895i q^{59} +(7.60570 - 124.979i) q^{60} +53.0162 q^{61} +(62.7575 + 1.90781i) q^{62} +108.494i q^{63} +(-62.9390 - 11.6053i) q^{64} -136.990 q^{65} +(0.525728 - 17.2939i) q^{66} -76.1917i q^{67} +(23.6632 + 1.44004i) q^{68} -143.069 q^{69} +(-63.4521 - 1.92892i) q^{70} -59.9326i q^{71} +(-14.4960 + 158.557i) q^{72} -49.8188 q^{73} +(-1.63022 + 53.6263i) q^{74} -47.8598i q^{75} +(1.05909 - 17.4034i) q^{76} -8.77198 q^{77} +(252.854 + 7.68670i) q^{78} +23.3990i q^{79} +(-92.4737 - 11.2969i) q^{80} +135.982 q^{81} +(2.67626 - 88.0358i) q^{82} +137.116i q^{83} +(117.011 + 7.12076i) q^{84} +34.5090 q^{85} +(55.6915 + 1.69300i) q^{86} +8.02335i q^{87} +(-12.8197 - 1.17204i) q^{88} +116.608 q^{89} +(-7.04235 + 231.659i) q^{90} -128.256i q^{91} +(-6.46602 + 106.252i) q^{92} -168.773 q^{93} +(-65.0032 - 1.97608i) q^{94} -25.3800i q^{95} +(170.053 + 26.0405i) q^{96} -65.7341 q^{97} +(-1.17186 + 38.5484i) q^{98} +32.0258i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 2 q^{2} + 2 q^{4} - 40 q^{8} - 68 q^{9}+O(q^{10}) $ 14 * q + 2 * q^2 + 2 * q^4 - 40 * q^8 - 68 * q^9	$ 14 q + 2 q^{2} + 2 q^{4} - 40 q^{8} - 68 q^{9} - 12 q^{10} + 4 q^{12} + 54 q^{13} + 30 q^{14} + 58 q^{16} + 34 q^{17} + 36 q^{18} + 32 q^{20} - 38 q^{21} + 36 q^{22} - 98 q^{24} - 86 q^{25} - 16 q^{26} + 18 q^{28} + 54 q^{29} - 204 q^{30} + 72 q^{32} + 20 q^{33} - 82 q^{34} + 96 q^{36} + 100 q^{37} - 148 q^{40} + 224 q^{41} + 224 q^{42} - 96 q^{44} - 168 q^{45} + 46 q^{46} + 296 q^{48} - 220 q^{49} - 58 q^{50} - 288 q^{52} + 14 q^{53} - 128 q^{54} + 12 q^{56} + 38 q^{57} - 72 q^{58} + 188 q^{60} + 28 q^{61} + 396 q^{62} - 118 q^{64} - 472 q^{65} - 32 q^{66} + 30 q^{68} + 122 q^{69} + 156 q^{70} + 80 q^{72} + 70 q^{73} - 224 q^{74} + 228 q^{77} + 274 q^{78} - 348 q^{80} + 334 q^{81} - 400 q^{82} - 216 q^{84} + 48 q^{85} - 124 q^{86} + 472 q^{88} + 416 q^{90} + 126 q^{92} - 176 q^{93} - 88 q^{94} - 106 q^{96} + 308 q^{97} + 68 q^{98}+O(q^{100}) $ 14 * q + 2 * q^2 + 2 * q^4 - 40 * q^8 - 68 * q^9 - 12 * q^10 + 4 * q^12 + 54 * q^13 + 30 * q^14 + 58 * q^16 + 34 * q^17 + 36 * q^18 + 32 * q^20 - 38 * q^21 + 36 * q^22 - 98 * q^24 - 86 * q^25 - 16 * q^26 + 18 * q^28 + 54 * q^29 - 204 * q^30 + 72 * q^32 + 20 * q^33 - 82 * q^34 + 96 * q^36 + 100 * q^37 - 148 * q^40 + 224 * q^41 + 224 * q^42 - 96 * q^44 - 168 * q^45 + 46 * q^46 + 296 * q^48 - 220 * q^49 - 58 * q^50 - 288 * q^52 + 14 * q^53 - 128 * q^54 + 12 * q^56 + 38 * q^57 - 72 * q^58 + 188 * q^60 + 28 * q^61 + 396 * q^62 - 118 * q^64 - 472 * q^65 - 32 * q^66 + 30 * q^68 + 122 * q^69 + 156 * q^70 + 80 * q^72 + 70 * q^73 - 224 * q^74 + 228 * q^77 + 274 * q^78 - 348 * q^80 + 334 * q^81 - 400 * q^82 - 216 * q^84 + 48 * q^85 - 124 * q^86 + 472 * q^88 + 416 * q^90 + 126 * q^92 - 176 * q^93 - 88 * q^94 - 106 * q^96 + 308 * q^97 + 68 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.0607713	+	1.99908i	−0.0303857	+	0.999538i
$2$	−0.0607713	+	1.99908i	−0.0303857	+	0.999538i
$3$		−	5.37609i		−	1.79203i	−0.444024	−	0.896015i	$-0.646449\pi$
$3$		−	5.37609i		−	1.79203i	0.444024	−	0.896015i	$-0.353551\pi$
$4$	−3.99261	−	0.242973i	−0.998153	−	0.0607433i
$5$	−5.82257			−1.16451			−0.582257	−	0.813005i	$-0.697830\pi$
$5$	−5.82257			−1.16451			−0.582257	+	0.813005i	$0.697830\pi$
$6$	10.7472	+	0.326712i	1.79120	+	0.0544520i
$7$		−	5.45132i		−	0.778760i	−0.921077	−	0.389380i	$-0.872689\pi$
$7$		−	5.45132i		−	0.778760i	0.921077	−	0.389380i	$-0.127311\pi$
$8$	0.728358	−	7.96677i	0.0910448	−	0.995847i
$9$	−19.9023			−2.21137
$10$	0.353845	−	11.6398i	0.0353845	−	1.16398i
$11$		−	1.60915i		−	0.146286i	−0.997321	−	0.0731431i	$-0.976697\pi$
$11$		−	1.60915i		−	0.146286i	0.997321	−	0.0731431i	$-0.0233030\pi$
$12$	−1.30624	+	21.4646i	−0.108854	+	1.78872i
$13$	23.5274			1.80980			0.904901	−	0.425622i	$-0.139945\pi$
$13$	23.5274			1.80980			0.904901	+	0.425622i	$0.139945\pi$
$14$	10.8976	+	0.331284i	0.778401	+	0.0236631i
$15$			31.3027i			2.08684i
$16$	15.8819	+	1.94019i	0.992621	+	0.121262i
$17$	−5.92676			−0.348633			−0.174316	−	0.984690i	$-0.555772\pi$
$17$	−5.92676			−0.348633			−0.174316	+	0.984690i	$0.555772\pi$
$18$	1.20949	−	39.7863i	0.0671940	−	2.21035i
$19$			4.35890i			0.229416i
$19$			4.35890i			0.229416i
$20$	23.2473	+	1.41473i	1.16236	+	0.0707364i
$21$	−29.3068			−1.39556
$22$	3.21681	+	0.0977900i	0.146219	+	0.00444500i
$23$		−	26.6121i		−	1.15705i	−0.815665	−	0.578524i	$-0.803629\pi$
$23$		−	26.6121i		−	1.15705i	0.815665	−	0.578524i	$-0.196371\pi$
$24$	−42.8301	−	3.91572i	−1.78459	−	0.163155i
$25$	8.90234			0.356094
$26$	−1.42979	+	47.0331i	−0.0549920	+	1.80897i
$27$			58.6120i			2.17081i
$28$	−1.32452	+	21.7650i	−0.0473044	+	0.777322i
$29$	−1.49241			−0.0514625			−0.0257313	−	0.999669i	$-0.508191\pi$
$29$	−1.49241			−0.0514625			−0.0257313	+	0.999669i	$0.508191\pi$
$30$	−62.5764	−	1.90230i	−2.08588	−	0.0634101i
$31$		−	31.3933i		−	1.01269i	−0.862332	−	0.506343i	$-0.830997\pi$
$31$		−	31.3933i		−	1.01269i	0.862332	−	0.506343i	$-0.169003\pi$
$32$	−4.84376	+	31.6313i	−0.151368	+	0.988478i
$33$	−8.65093			−0.262149
$34$	0.360177	−	11.8480i	0.0105934	−	0.348472i
$35$			31.7407i			0.906877i
$36$	79.4624	+	4.83573i	2.20729	+	0.134326i
$37$	26.8255			0.725015			0.362507	−	0.931981i	$-0.381921\pi$
$37$	26.8255			0.725015			0.362507	+	0.931981i	$0.381921\pi$
$38$	−8.71377	−	0.264896i	−0.229310	−	0.00697095i
$39$		−	126.486i		−	3.24322i
$40$	−4.24092	+	46.3871i	−0.106023	+	1.15968i
$41$	−44.0382			−1.07410			−0.537051	−	0.843550i	$-0.680462\pi$
$41$	−44.0382			−1.07410			−0.537051	+	0.843550i	$0.680462\pi$
$42$	1.78101	−	58.5865i	0.0424051	−	1.39492i
$43$		−	27.8586i		−	0.647875i	−0.946079	−	0.323937i	$-0.894993\pi$
$43$		−	27.8586i		−	0.647875i	0.946079	−	0.323937i	$-0.105007\pi$
$44$	−0.390980	+	6.42471i	−0.00888590	+	0.146016i
$45$	115.883			2.57517
$46$	53.1996	+	1.61725i	1.15651	+	0.0351577i
$47$			32.5166i			0.691843i	0.938264	+	0.345921i	$0.112434\pi$
$47$			32.5166i			0.691843i	−0.938264	+	0.345921i	$0.887566\pi$
$48$	10.4307	−	85.3827i	0.217305	−	1.77881i
$49$	19.2831			0.393533
$50$	−0.541007	+	17.7965i	−0.0108201	+	0.355929i
$51$			31.8628i			0.624760i
$52$	−93.9360	−	5.71653i	−1.80646	−	0.109933i
$53$	76.7637			1.44837			0.724186	−	0.689605i	$-0.242216\pi$
$53$	76.7637			1.44837			0.724186	+	0.689605i	$0.242216\pi$
$54$	−117.170	−	3.56193i	−2.16981	−	0.0659616i
$55$			9.36938i			0.170352i
$56$	−43.4294	−	3.97051i	−0.775526	−	0.0709020i
$57$	23.4338			0.411120
$58$	0.0906959	−	2.98345i	0.00156372	−	0.0514388i
$59$			33.8895i			0.574398i	0.957871	+	0.287199i	$0.0927241\pi$
$59$			33.8895i			0.574398i	−0.957871	+	0.287199i	$0.907276\pi$
$60$	7.60570	−	124.979i	0.126762	−	2.08299i
$61$	53.0162			0.869118			0.434559	−	0.900643i	$-0.356904\pi$
$61$	53.0162			0.869118			0.434559	+	0.900643i	$0.356904\pi$
$62$	62.7575	+	1.90781i	1.01222	+	0.0307711i
$63$			108.494i			1.72213i
$64$	−62.9390	−	11.6053i	−0.983422	−	0.181333i
$65$	−136.990			−2.10754
$66$	0.525728	−	17.2939i	0.00796558	−	0.262028i
$67$		−	76.1917i		−	1.13719i	−0.822618	−	0.568594i	$-0.807487\pi$
$67$		−	76.1917i		−	1.13719i	0.822618	−	0.568594i	$-0.192513\pi$
$68$	23.6632	+	1.44004i	0.347989	+	0.0211771i
$69$	−143.069			−2.07346
$70$	−63.4521	−	1.92892i	−0.906459	−	0.0275561i
$71$		−	59.9326i		−	0.844121i	−0.906568	−	0.422060i	$-0.861307\pi$
$71$		−	59.9326i		−	0.844121i	0.906568	−	0.422060i	$-0.138693\pi$
$72$	−14.4960	+	158.557i	−0.201334	+	2.20219i
$73$	−49.8188			−0.682450			−0.341225	−	0.939982i	$-0.610842\pi$
$73$	−49.8188			−0.682450			−0.341225	+	0.939982i	$0.610842\pi$
$74$	−1.63022	+	53.6263i	−0.0220301	+	0.724680i
$75$		−	47.8598i		−	0.638131i
$76$	1.05909	−	17.4034i	0.0139355	−	0.228992i
$77$	−8.77198			−0.113922
$78$	252.854	+	7.68670i	3.24172	+	0.0985474i
$79$			23.3990i			0.296190i	0.988973	+	0.148095i	$0.0473141\pi$
$79$			23.3990i			0.296190i	−0.988973	+	0.148095i	$0.952686\pi$
$80$	−92.4737	−	11.2969i	−1.15592	−	0.141212i
$81$	135.982			1.67879
$82$	2.67626	−	88.0358i	0.0326373	−	1.07361i
$83$			137.116i			1.65200i	0.563667	+	0.826002i	$0.309390\pi$
$83$			137.116i			1.65200i	−0.563667	+	0.826002i	$0.690610\pi$
$84$	117.011	+	7.12076i	1.39298	+	0.0847709i
$85$	34.5090			0.405988
$86$	55.6915	+	1.69300i	0.647576	+	0.0196861i
$87$			8.02335i			0.0922224i
$88$	−12.8197	−	1.17204i	−0.145679	−	0.0133186i
$89$	116.608			1.31020			0.655101	−	0.755541i	$-0.272626\pi$
$89$	116.608			1.31020			0.655101	+	0.755541i	$0.272626\pi$
$90$	−7.04235	+	231.659i	−0.0782483	+	2.57398i
$91$		−	128.256i		−	1.40940i
$92$	−6.46602	+	106.252i	−0.0702828	+	1.15491i
$93$	−168.773			−1.81476
$94$	−65.0032	−	1.97608i	−0.691523	−	0.0210221i
$95$		−	25.3800i		−	0.267158i
$96$	170.053	+	26.0405i	1.77138	+	0.271255i
$97$	−65.7341			−0.677671			−0.338836	−	0.940846i	$-0.610033\pi$
$97$	−65.7341			−0.677671			−0.338836	+	0.940846i	$0.610033\pi$
$98$	−1.17186	+	38.5484i	−0.0119577	+	0.393351i
$99$			32.0258i			0.323493i
$100$	−35.5436	−	2.16303i	−0.355436	−	0.0216303i
$101$	1.81406			0.0179609			0.00898047	−	0.999960i	$-0.497141\pi$
$101$	1.81406			0.0179609			0.00898047	+	0.999960i	$0.497141\pi$
$102$	−63.6961	−	1.93634i	−0.624472	−	0.0189837i
$103$			0.494673i			0.00480265i	0.999997	+	0.00240133i	$0.000764367\pi$
$103$			0.494673i			0.00480265i	−0.999997	+	0.00240133i	$0.999236\pi$
$104$	17.1364	−	187.438i	0.164773	−	1.80229i
$105$	170.641			1.62515
$106$	−4.66503	+	153.457i	−0.0440097	+	1.44770i
$107$			11.7361i			0.109684i	0.998495	+	0.0548418i	$0.0174654\pi$
$107$			11.7361i			0.109684i	−0.998495	+	0.0548418i	$0.982535\pi$
$108$	14.2411	−	234.015i	0.131862	−	2.16681i
$109$	−28.9819			−0.265889			−0.132945	−	0.991123i	$-0.542443\pi$
$109$	−28.9819			−0.265889			−0.132945	+	0.991123i	$0.542443\pi$
$110$	−18.7301	−	0.569390i	−0.170274	−	0.00517627i
$111$		−	144.217i		−	1.29925i
$112$	10.5766	−	86.5775i	0.0944341	−	0.773013i
$113$	−140.725			−1.24536			−0.622678	−	0.782478i	$-0.713955\pi$
$113$	−140.725			−1.24536			−0.622678	+	0.782478i	$0.713955\pi$
$114$	−1.42410	+	46.8460i	−0.0124921	+	0.410930i
$115$			154.951i			1.34740i
$116$	5.95863	+	0.362616i	0.0513675	+	0.00312600i
$117$	−468.251			−4.00215
$118$	−67.7477	−	2.05951i	−0.574133	−	0.0174535i
$119$			32.3086i			0.271501i
$120$	249.381	+	22.7996i	2.07818	+	0.189996i
$121$	118.411			0.978600
$122$	−3.22186	+	105.983i	−0.0264087	+	0.868716i
$123$			236.753i			1.92482i
$124$	−7.62772	+	125.341i	−0.0615138	+	1.01082i
$125$	93.7298			0.749838
$126$	−216.888	−	6.59333i	−1.72133	−	0.0523280i
$127$			50.4262i			0.397056i	0.980095	+	0.198528i	$0.0636161\pi$
$127$			50.4262i			0.397056i	−0.980095	+	0.198528i	$0.936384\pi$
$128$	27.0248	−	125.115i	0.211131	−	0.977458i
$129$	−149.770			−1.16101
$130$	8.32507	−	273.854i	0.0640390	−	2.10657i
$131$		−	124.954i		−	0.953847i	−0.878945	−	0.476924i	$-0.841752\pi$
$131$		−	124.954i		−	0.953847i	0.878945	−	0.476924i	$-0.158248\pi$
$132$	34.5398	+	2.10194i	0.261665	+	0.0159238i
$133$	23.7618			0.178660
$134$	152.313	+	4.63027i	1.13666	+	0.0345542i
$135$		−	341.272i		−	2.52794i
$136$	−4.31680	+	47.2171i	−0.0317412	+	0.347185i
$137$	137.151			1.00110			0.500551	−	0.865707i	$-0.333131\pi$
$137$	137.151			1.00110			0.500551	+	0.865707i	$0.333131\pi$
$138$	8.69449	−	286.006i	0.0630036	−	2.07251i
$139$			89.6885i			0.645241i	0.946528	+	0.322621i	$0.104564\pi$
$139$			89.6885i			0.645241i	−0.946528	+	0.322621i	$0.895436\pi$
$140$	7.71214	−	126.728i	0.0550867	−	0.905203i
$141$	174.812			1.23980
$142$	119.810	+	3.64218i	0.843731	+	0.0256492i
$143$		−	37.8591i		−	0.264749i
$144$	−316.088	−	38.6144i	−2.19505	−	0.268156i
$145$	8.68969			0.0599289
$146$	3.02756	−	99.5917i	0.0207367	−	0.682135i
$147$		−	103.668i		−	0.705222i
$148$	−107.104	−	6.51788i	−0.723676	−	0.0440398i
$149$	18.9194			0.126976			0.0634878	−	0.997983i	$-0.479778\pi$
$149$	18.9194			0.126976			0.0634878	+	0.997983i	$0.479778\pi$
$150$	95.6754	+	2.90850i	0.637836	+	0.0193900i
$151$			269.061i			1.78186i	0.454141	+	0.890930i	$0.349946\pi$
$151$			269.061i			1.78186i	−0.454141	+	0.890930i	$0.650054\pi$
$152$	34.7264	+	3.17484i	0.228463	+	0.0208871i
$153$	117.956			0.770956
$154$	0.533085	−	17.5359i	0.00346159	−	0.113869i
$155$			182.790i			1.17929i
$156$	−30.7326	+	505.008i	−0.197004	+	3.23723i
$157$	11.4972			0.0732305			0.0366153	−	0.999329i	$-0.488342\pi$
$157$	11.4972			0.0732305			0.0366153	+	0.999329i	$0.488342\pi$
$158$	−46.7764	−	1.42199i	−0.296053	−	0.00899993i
$159$		−	412.689i		−	2.59553i
$160$	28.2032	−	184.175i	0.176270	−	1.15110i
$161$	−145.071			−0.901063
$162$	−8.26381	+	271.839i	−0.0510112	+	1.67802i
$163$			126.564i			0.776465i	0.921562	+	0.388232i	$0.126914\pi$
$163$			126.564i			0.776465i	−0.921562	+	0.388232i	$0.873086\pi$
$164$	175.828	+	10.7001i	1.07212	+	0.0652445i
$165$	50.3706			0.305277
$166$	−274.106	−	8.33274i	−1.65124	−	0.0501972i
$167$			14.2424i			0.0852836i	0.999090	+	0.0426418i	$0.0135774\pi$
$167$			14.2424i			0.0852836i	−0.999090	+	0.0426418i	$0.986423\pi$
$168$	−21.3458	+	233.481i	−0.127059	+	1.38977i
$169$	384.540			2.27539
$170$	−2.09715	+	68.9860i	−0.0123362	+	0.405800i
$171$		−	86.7523i		−	0.507323i
$172$	−6.76889	+	111.229i	−0.0393540	+	0.646678i
$173$	−217.817			−1.25906			−0.629528	−	0.776978i	$-0.716752\pi$
$173$	−217.817			−1.25906			−0.629528	+	0.776978i	$0.716752\pi$
$174$	−16.0393	−	0.487590i	−0.0921798	−	0.00280224i
$175$		−	48.5295i		−	0.277312i
$176$	3.12206	−	25.5564i	0.0177390	−	0.145207i
$177$	182.193			1.02934
$178$	−7.08642	+	233.108i	−0.0398114	+	1.30960i
$179$		−	180.223i		−	1.00684i	−0.864043	−	0.503418i	$-0.832076\pi$
$179$		−	180.223i		−	1.00684i	0.864043	−	0.503418i	$-0.167924\pi$
$180$	−462.675	−	28.1564i	−2.57042	−	0.156424i
$181$	−95.0637			−0.525214			−0.262607	−	0.964903i	$-0.584582\pi$
$181$	−95.0637			−0.525214			−0.262607	+	0.964903i	$0.584582\pi$
$182$	256.393	+	7.79426i	1.40875	+	0.0428256i
$183$		−	285.020i		−	1.55748i
$184$	−212.013	−	19.3831i	−1.15224	−	0.105343i
$185$	−156.194			−0.844290
$186$	10.2566	−	337.390i	0.0551428	−	1.81393i
$187$			9.53703i			0.0510001i
$188$	7.90066	−	129.826i	0.0420248	−	0.690565i
$189$	319.513			1.69054
$190$	50.7366	+	1.54238i	0.267035	+	0.00811777i
$191$			25.4789i			0.133397i	0.997773	+	0.0666987i	$0.0212466\pi$
$191$			25.4789i			0.133397i	−0.997773	+	0.0666987i	$0.978753\pi$
$192$	−62.3913	+	338.366i	−0.324955	+	1.76232i
$193$	339.566			1.75941			0.879705	−	0.475520i	$-0.157740\pi$
$193$	339.566			1.75941			0.879705	+	0.475520i	$0.157740\pi$
$194$	3.99475	−	131.407i	0.0205915	−	0.677358i
$195$			736.471i			3.77678i
$196$	−76.9900	−	4.68527i	−0.392806	−	0.0239045i
$197$	136.859			0.694717			0.347358	−	0.937732i	$-0.387079\pi$
$197$	136.859			0.694717			0.347358	+	0.937732i	$0.387079\pi$
$198$	−64.0221	−	1.94625i	−0.323344	−	0.00982955i
$199$		−	199.411i		−	1.00207i	−0.865428	−	0.501034i	$-0.832953\pi$
$199$		−	199.411i		−	1.00207i	0.865428	−	0.501034i	$-0.167047\pi$
$200$	6.48409	−	70.9230i	0.0324205	−	0.354615i
$201$	−409.613			−2.03788
$202$	−0.110243	+	3.62644i	−0.000545755	+	0.0179527i
$203$			8.13563i			0.0400770i
$204$	7.74179	−	127.216i	0.0379500	−	0.623606i
$205$	256.416			1.25081
$206$	−0.988890	−	0.0300619i	−0.00480044	−	0.000145932i
$207$			529.643i			2.55866i
$208$	373.661	+	45.6478i	1.79645	+	0.219461i
$209$	7.01411			0.0335604
$210$	−10.3701	+	341.124i	−0.0493813	+	1.62440i
$211$		−	363.655i		−	1.72348i	−0.507347	−	0.861742i	$-0.669374\pi$
$211$		−	363.655i		−	1.72348i	0.507347	−	0.861742i	$-0.330626\pi$
$212$	−306.488	−	18.6515i	−1.44570	−	0.0879788i
$213$	−322.203			−1.51269
$214$	−23.4614	−	0.713221i	−0.109633	−	0.00333281i
$215$			162.209i			0.754460i
$216$	466.948	+	42.6905i	2.16180	+	0.197641i
$217$	−171.135			−0.788640
$218$	1.76127	−	57.9371i	0.00807922	−	0.265766i
$219$			267.831i			1.22297i
$220$	2.27651	−	37.4083i	0.0103478	−	0.170038i
$221$	−139.441			−0.630956
$222$	288.300	+	8.76423i	1.29865	+	0.0394785i
$223$			268.968i			1.20614i	0.797690	+	0.603068i	$0.206055\pi$
$223$			268.968i			1.20614i	−0.797690	+	0.603068i	$0.793945\pi$
$224$	172.432	+	26.4049i	0.769787	+	0.117879i
$225$	−177.177			−0.787455
$226$	8.55206	−	281.320i	0.0378410	−	1.24478i
$227$		−	79.9913i		−	0.352384i	−0.984356	−	0.176192i	$-0.943622\pi$
$227$		−	79.9913i		−	0.352384i	0.984356	−	0.176192i	$-0.0563780\pi$
$228$	−93.5622	−	5.69379i	−0.410361	−	0.0249728i
$229$	297.342			1.29843			0.649217	−	0.760603i	$-0.275097\pi$
$229$	297.342			1.29843			0.649217	+	0.760603i	$0.275097\pi$
$230$	−309.759	−	9.41657i	−1.34678	−	0.0409416i
$231$			47.1590i			0.204151i
$232$	−1.08701	+	11.8897i	−0.00468539	+	0.0512488i
$233$	−255.975			−1.09860			−0.549302	−	0.835624i	$-0.685106\pi$
$233$	−255.975			−1.09860			−0.549302	+	0.835624i	$0.685106\pi$
$234$	28.4562	−	936.070i	0.121608	−	4.00030i
$235$		−	189.330i		−	0.805661i
$236$	8.23423	−	135.308i	0.0348908	−	0.573337i
$237$	125.795			0.530781
$238$	−64.5875	−	1.96344i	−0.271376	−	0.00824974i
$239$		−	148.674i		−	0.622067i	−0.950399	−	0.311034i	$-0.899325\pi$
$239$		−	148.674i		−	0.622067i	0.950399	−	0.311034i	$-0.100675\pi$
$240$	−60.7333	+	497.147i	−0.253055	+	2.07144i
$241$	−330.295			−1.37052			−0.685259	−	0.728299i	$-0.740311\pi$
$241$	−330.295			−1.37052			−0.685259	+	0.728299i	$0.740311\pi$
$242$	−7.19597	+	236.712i	−0.0297354	+	0.978148i
$243$		−	203.544i		−	0.837632i
$244$	−211.673	−	12.8815i	−0.867513	−	0.0527930i
$245$	−112.277			−0.458274
$246$	−473.288	−	14.3878i	−1.92394	−	0.0584871i
$247$			102.554i			0.415197i
$248$	−250.103	−	22.8655i	−1.00848	−	0.0921997i
$249$	737.150			2.96044
$250$	−5.69608	+	187.373i	−0.0227843	+	0.749492i
$251$		−	253.493i		−	1.00993i	−0.863139	−	0.504966i	$-0.831505\pi$
$251$		−	253.493i		−	1.00993i	0.863139	−	0.504966i	$-0.168495\pi$
$252$	26.3611	−	433.175i	0.104608	−	1.71895i
$253$	−42.8228			−0.169260
$254$	−100.806	−	3.06446i	−0.396873	−	0.0120648i
$255$		−	185.523i		−	0.727542i
$256$	248.471	+	61.6281i	0.970591	+	0.240735i
$257$	254.160			0.988950			0.494475	−	0.869192i	$-0.335360\pi$
$257$	254.160			0.988950			0.494475	+	0.869192i	$0.335360\pi$
$258$	9.10175	−	299.403i	0.0352781	−	1.16048i
$259$		−	146.235i		−	0.564613i
$260$	546.949	+	33.2849i	2.10365	+	0.128019i
$261$	29.7025			0.113803
$262$	249.793	+	7.59362i	0.953407	+	0.0289833i
$263$		−	190.047i		−	0.722613i	−0.932447	−	0.361306i	$-0.882331\pi$
$263$		−	190.047i		−	0.722613i	0.932447	−	0.361306i	$-0.117669\pi$
$264$	−6.30097	+	68.9200i	−0.0238673	+	0.261060i
$265$	−446.962			−1.68665
$266$	−1.44403	+	47.5016i	−0.00542870	+	0.178577i
$267$		−	626.895i		−	2.34792i
$268$	−18.5125	+	304.204i	−0.0690766	+	1.13509i
$269$	233.427			0.867758			0.433879	−	0.900971i	$-0.357145\pi$
$269$	233.427			0.867758			0.433879	+	0.900971i	$0.357145\pi$
$270$	682.230	+	20.7396i	2.52678	+	0.0768132i
$271$			2.73196i			0.0100810i	0.999987	+	0.00504051i	$0.00160445\pi$
$271$			2.73196i			0.0100810i	−0.999987	+	0.00504051i	$0.998396\pi$
$272$	−94.1283	−	11.4991i	−0.346060	−	0.0422760i
$273$	−689.514			−2.52569
$274$	−8.33485	+	274.175i	−0.0304192	+	1.00064i
$275$		−	14.3252i		−	0.0520916i
$276$	571.219	+	34.7619i	2.06964	+	0.125949i
$277$	−20.4896			−0.0739697			−0.0369848	−	0.999316i	$-0.511775\pi$
$277$	−20.4896			−0.0739697			−0.0369848	+	0.999316i	$0.511775\pi$
$278$	−179.294	−	5.45049i	−0.644943	−	0.0196061i
$279$			624.800i			2.23942i
$280$	252.871	+	23.1186i	0.903111	+	0.0825664i
$281$	−285.339			−1.01544			−0.507721	−	0.861522i	$-0.669512\pi$
$281$	−285.339			−1.01544			−0.507721	+	0.861522i	$0.669512\pi$
$282$	−10.6236	+	349.463i	−0.0376722	+	1.23923i
$283$			4.45505i			0.0157422i	0.999969	+	0.00787112i	$0.00250548\pi$
$283$			4.45505i			0.0157422i	−0.999969	+	0.00787112i	$0.997495\pi$
$284$	−14.5620	+	239.288i	−0.0512746	+	0.842562i
$285$	−136.445			−0.478755
$286$	75.6833	+	2.30075i	0.264627	+	0.00804458i
$287$			240.066i			0.836468i
$288$	96.4022	−	629.537i	0.334730	−	2.18589i
$289$	−253.874			−0.878455
$290$	−0.528084	+	17.3713i	−0.00182098	+	0.0599012i
$291$			353.392i			1.21441i
$292$	198.907	+	12.1046i	0.681190	+	0.0414542i
$293$	326.981			1.11598			0.557988	−	0.829849i	$-0.311574\pi$
$293$	326.981			1.11598			0.557988	+	0.829849i	$0.311574\pi$
$294$	207.240	+	6.30002i	0.704897	+	0.0214286i
$295$		−	197.324i		−	0.668895i
$296$	19.5386	−	213.713i	0.0660088	−	0.722004i
$297$	94.3153			0.317560
$298$	−1.14975	+	37.8213i	−0.00385824	+	0.126917i
$299$		−	626.114i		−	2.09403i
$300$	−11.6286	+	191.086i	−0.0387621	+	0.636952i
$301$	−151.866			−0.504539
$302$	−537.873	−	16.3512i	−1.78104	−	0.0541430i
$303$		−	9.75253i		−	0.0321866i
$304$	−8.45711	+	69.2277i	−0.0278195	+	0.227723i
$305$	−308.690			−1.01210
$306$	−7.16836	+	235.804i	−0.0234260	+	0.770600i
$307$			352.091i			1.14688i	0.819249	+	0.573438i	$0.194391\pi$
$307$			352.091i			1.14688i	−0.819249	+	0.573438i	$0.805609\pi$
$308$	35.0231	+	2.13136i	0.113711	+	0.00691998i
$309$	2.65941			0.00860650
$310$	−365.410	−	11.1084i	−1.17874	−	0.0358334i
$311$			75.4387i			0.242568i	0.992618	+	0.121284i	$0.0387012\pi$
$311$			75.4387i			0.242568i	−0.992618	+	0.121284i	$0.961299\pi$
$312$	−1007.68	−	92.1268i	−3.22975	−	0.295278i
$313$	−13.1951			−0.0421569			−0.0210784	−	0.999778i	$-0.506710\pi$
$313$	−13.1951			−0.0421569			−0.0210784	+	0.999778i	$0.506710\pi$
$314$	−0.698699	+	22.9838i	−0.00222516	+	0.0731967i
$315$		−	631.714i		−	2.00544i
$316$	5.68533	−	93.4232i	0.0179915	−	0.295643i
$317$	276.427			0.872011			0.436005	−	0.899944i	$-0.356393\pi$
$317$	276.427			0.872011			0.436005	+	0.899944i	$0.356393\pi$
$318$	824.996	+	25.0796i	2.59433	+	0.0788668i
$319$			2.40151i			0.00752826i
$320$	366.467	+	67.5729i	1.14521	+	0.211165i
$321$	63.0946			0.196556
$322$	8.81616	−	290.008i	0.0273794	−	0.900647i
$323$		−	25.8341i		−	0.0799818i
$324$	−542.924	−	33.0400i	−1.67569	−	0.101975i
$325$	209.449			0.644459
$326$	−253.011	−	7.69145i	−0.776106	−	0.0235934i
$327$			155.809i			0.476481i
$328$	−32.0756	+	350.843i	−0.0977914	+	1.06964i
$329$	177.258			0.538779
$330$	−3.06109	+	100.695i	−0.00927603	+	0.305136i
$331$			550.110i			1.66196i	0.556301	+	0.830981i	$0.312220\pi$
$331$			550.110i			1.66196i	−0.556301	+	0.830981i	$0.687780\pi$
$332$	33.3156	−	547.453i	0.100348	−	1.64895i
$333$	−533.891			−1.60328
$334$	−28.4716	−	0.865527i	−0.0852442	−	0.00259140i
$335$			443.631i			1.32427i
$336$	−465.448	−	56.8609i	−1.38526	−	0.169229i
$337$	−179.034			−0.531259			−0.265630	−	0.964075i	$-0.585580\pi$
$337$	−179.034			−0.531259			−0.265630	+	0.964075i	$0.585580\pi$
$338$	−23.3690	+	768.725i	−0.0691391	+	2.27433i
$339$			756.551i			2.23171i
$340$	−137.781	−	8.38475i	−0.405238	−	0.0246610i
$341$	−50.5164			−0.148142
$342$	173.424	+	5.27205i	0.507089	+	0.0154154i
$343$		−	372.233i		−	1.08523i
$344$	−221.943	−	20.2910i	−0.645184	−	0.0589856i
$345$	833.030			2.41458
$346$	13.2370	−	435.432i	0.0382573	−	1.25848i
$347$			161.757i			0.466157i	0.972458	+	0.233079i	$0.0748800\pi$
$347$			161.757i			0.466157i	−0.972458	+	0.233079i	$0.925120\pi$
$348$	1.94946	−	32.0341i	0.00560189	−	0.0920521i
$349$	−472.810			−1.35476			−0.677378	−	0.735635i	$-0.736884\pi$
$349$	−472.810			−1.35476			−0.677378	+	0.735635i	$0.736884\pi$
$350$	97.0142	+	2.94920i	0.277184	+	0.00842629i
$351$			1378.99i			3.92874i
$352$	50.8994	+	7.79433i	0.144601	+	0.0221430i
$353$	319.200			0.904249			0.452125	−	0.891955i	$-0.350666\pi$
$353$	319.200			0.904249			0.452125	+	0.891955i	$0.350666\pi$
$354$	−11.0721	+	364.217i	−0.0312771	+	1.02886i
$355$			348.962i			0.982991i
$356$	−465.571	−	28.3326i	−1.30778	−	0.0795860i
$357$	173.694			0.486538
$358$	360.281	+	10.9524i	1.00637	+	0.0305933i
$359$		−	545.770i		−	1.52025i	−0.649776	−	0.760126i	$-0.725137\pi$
$359$		−	545.770i		−	1.52025i	0.649776	−	0.760126i	$-0.274863\pi$
$360$	84.4042	−	923.212i	0.234456	−	2.56448i
$361$	−19.0000			−0.0526316
$362$	5.77715	−	190.040i	0.0159590	−	0.524971i
$363$		−	636.586i		−	1.75368i
$364$	−31.1626	+	512.075i	−0.0856117	+	1.40680i
$365$	290.074			0.794723
$366$	569.776	+	17.3210i	1.55677	+	0.0473252i
$367$		−	90.4491i		−	0.246455i	−0.992378	−	0.123228i	$-0.960675\pi$
$367$		−	90.4491i		−	0.246455i	0.992378	−	0.123228i	$-0.0393246\pi$
$368$	51.6327	−	422.651i	0.140306	−	1.14851i
$369$	876.464			2.37524
$370$	9.49210	−	312.243i	0.0256543	−	0.843900i
$371$		−	418.464i		−	1.12793i
$372$	673.845	+	41.0073i	1.81141	+	0.110235i
$373$	468.975			1.25731			0.628653	−	0.777686i	$-0.283606\pi$
$373$	468.975			1.25731			0.628653	+	0.777686i	$0.283606\pi$
$374$	−19.0652	−	0.579578i	−0.0509766	−	0.00154967i
$375$		−	503.900i		−	1.34373i
$376$	259.052	+	23.6837i	0.688969	+	0.0629886i
$377$	−35.1127			−0.0931370
$378$	−19.4172	+	638.730i	−0.0513683	+	1.68976i
$379$		−	196.529i		−	0.518545i	−0.965804	−	0.259273i	$-0.916517\pi$
$379$		−	196.529i		−	0.518545i	0.965804	−	0.259273i	$-0.0834828\pi$
$380$	−6.16666	+	101.333i	−0.0162280	+	0.266665i
$381$	271.096			0.711537
$382$	−50.9342	−	1.54839i	−0.133336	−	0.00405337i
$383$		−	24.8045i		−	0.0647637i	−0.999476	−	0.0323819i	$-0.989691\pi$
$383$		−	24.8045i		−	0.0647637i	0.999476	−	0.0323819i	$-0.0103093\pi$
$384$	−672.627	−	145.288i	−1.75163	−	0.378354i
$385$	51.0755			0.132664
$386$	−20.6359	+	678.819i	−0.0534608	+	1.75860i
$387$			554.452i			1.43269i
$388$	262.451	+	15.9716i	0.676420	+	0.0411639i
$389$	−126.462			−0.325095			−0.162547	−	0.986701i	$-0.551971\pi$
$389$	−126.462			−0.325095			−0.162547	+	0.986701i	$0.551971\pi$
$390$	−1472.26	−	44.7563i	−3.77503	−	0.114760i
$391$			157.723i			0.403385i
$392$	14.0450	−	153.624i	0.0358291	−	0.391898i
$393$	−671.764			−1.70932
$394$	−8.31712	+	273.592i	−0.0211094	+	0.694396i
$395$		−	136.242i		−	0.344917i
$396$	7.78141	−	127.867i	0.0196500	−	0.322896i
$397$	403.878			1.01732			0.508662	−	0.860966i	$-0.330140\pi$
$397$	403.878			1.01732			0.508662	+	0.860966i	$0.330140\pi$
$398$	398.639	+	12.1185i	1.00160	+	0.0304485i
$399$		−	127.745i		−	0.320164i
$400$	141.386	+	17.2723i	0.353466	+	0.0431807i
$401$	345.608			0.861865			0.430933	−	0.902384i	$-0.358185\pi$
$401$	345.608			0.861865			0.430933	+	0.902384i	$0.358185\pi$
$402$	24.8927	−	818.848i	0.0619222	−	2.03694i
$403$		−	738.603i		−	1.83276i
$404$	−7.24282	−	0.440767i	−0.0179278	−	0.00109101i
$405$	−791.766			−1.95498
$406$	−16.2637	−	0.494413i	−0.0400585	−	0.00121777i
$407$		−	43.1663i		−	0.106060i
$408$	253.843	+	23.2075i	0.622165	+	0.0568811i
$409$	−429.506			−1.05014			−0.525069	−	0.851060i	$-0.675960\pi$
$409$	−429.506			−1.05014			−0.525069	+	0.851060i	$0.675960\pi$
$410$	−15.5827	+	512.595i	−0.0380066	+	1.25023i
$411$		−	737.336i		−	1.79401i
$412$	0.120192	−	1.97504i	0.000291729	−	0.00479378i
$413$	184.742			0.447318
$414$	−1058.80	−	32.1871i	−2.55748	−	0.0777466i
$415$		−	798.370i		−	1.92378i
$416$	−113.961	+	744.203i	−0.273945	+	1.78895i
$417$	482.174			1.15629
$418$	−0.426257	+	14.0218i	−0.00101975	+	0.0335449i
$419$			345.206i			0.823881i	0.911211	+	0.411940i	$0.135149\pi$
$419$			345.206i			0.823881i	−0.911211	+	0.411940i	$0.864851\pi$
$420$	−681.303	−	41.4611i	−1.62215	−	0.0987170i
$421$	−195.468			−0.464295			−0.232148	−	0.972681i	$-0.574575\pi$
$421$	−195.468			−0.464295			−0.232148	+	0.972681i	$0.574575\pi$
$422$	726.974	+	22.0998i	1.72269	+	0.0523692i
$423$		−	647.156i		−	1.52992i
$424$	55.9115	−	611.559i	0.131867	−	1.44236i
$425$	−52.7620			−0.124146
$426$	19.5807	−	644.108i	0.0459641	−	1.51199i
$427$		−	289.008i		−	0.676834i
$428$	2.85157	−	46.8579i	0.00666254	−	0.109481i
$429$	−203.534			−0.474438
$430$	−324.268	−	9.85764i	−0.754111	−	0.0229247i
$431$			643.698i			1.49350i	0.665106	+	0.746749i	$0.268386\pi$
$431$			643.698i			1.49350i	−0.665106	+	0.746749i	$0.731614\pi$
$432$	−113.719	+	930.871i	−0.263238	+	2.15479i
$433$	−755.385			−1.74454			−0.872269	−	0.489026i	$-0.837352\pi$
$433$	−755.385			−1.74454			−0.872269	+	0.489026i	$0.837352\pi$
$434$	10.4001	−	342.112i	0.0239633	−	0.788275i
$435$		−	46.7165i		−	0.107394i
$436$	115.714	+	7.04183i	0.265398	+	0.0161510i
$437$	115.999			0.265445
$438$	−535.414	−	16.2764i	−1.22241	−	0.0371608i
$439$			522.862i			1.19103i	0.803345	+	0.595514i	$0.203052\pi$
$439$			522.862i			1.19103i	−0.803345	+	0.595514i	$0.796948\pi$
$440$	74.6437	+	6.82426i	0.169645	+	0.0155097i
$441$	−383.779			−0.870247
$442$	8.47403	−	278.754i	0.0191720	−	0.630665i
$443$			5.86286i			0.0132345i	0.999978	+	0.00661723i	$0.00210634\pi$
$443$			5.86286i			0.0132345i	−0.999978	+	0.00661723i	$0.997894\pi$
$444$	−35.0407	+	575.801i	−0.0789206	+	1.29685i
$445$	−678.959			−1.52575
$446$	−537.688	−	16.3455i	−1.20558	−	0.0366492i
$447$		−	101.712i		−	0.227544i
$448$	−63.2644	+	343.101i	−0.141215	+	0.765850i
$449$	626.982			1.39640			0.698199	−	0.715904i	$-0.253985\pi$
$449$	626.982			1.39640			0.698199	+	0.715904i	$0.253985\pi$
$450$	10.7673	−	354.191i	0.0239273	−	0.787092i
$451$			70.8640i			0.157126i
$452$	561.861	+	34.1924i	1.24306	+	0.0756470i
$453$	1446.50			3.19315
$454$	159.909	+	4.86117i	0.352222	+	0.0107074i
$455$			746.777i			1.64127i
$456$	17.0682	−	186.692i	0.0374303	−	0.409412i
$457$	−451.537			−0.988046			−0.494023	−	0.869449i	$-0.664474\pi$
$457$	−451.537			−0.988046			−0.494023	+	0.869449i	$0.664474\pi$
$458$	−18.0698	+	594.408i	−0.0394538	+	1.29784i
$459$		−	347.379i		−	0.756817i
$460$	37.6489	−	618.659i	0.0818454	−	1.34491i
$461$	50.7723			0.110135			0.0550675	−	0.998483i	$-0.482463\pi$
$461$	50.7723			0.110135			0.0550675	+	0.998483i	$0.482463\pi$
$462$	−94.2744	−	2.86591i	−0.204057	−	0.00620327i
$463$			69.7862i			0.150726i	0.997156	+	0.0753631i	$0.0240116\pi$
$463$			69.7862i			0.150726i	−0.997156	+	0.0753631i	$0.975988\pi$
$464$	−23.7024	−	2.89557i	−0.0510828	−	0.00624046i
$465$	982.693			2.11332
$466$	15.5559	−	511.713i	0.0333818	−	1.09810i
$467$			461.829i			0.988927i	0.869198	+	0.494464i	$0.164635\pi$
$467$			461.829i			0.988927i	−0.869198	+	0.494464i	$0.835365\pi$
$468$	1869.55	+	113.772i	3.99476	+	0.243103i
$469$	−415.345			−0.885597
$470$	378.486	+	11.5058i	0.805289	+	0.0244805i
$471$		−	61.8099i		−	0.131231i
$472$	269.990	+	24.6837i	0.572012	+	0.0522959i
$473$	−44.8286			−0.0947751
$474$	−7.64474	+	251.474i	−0.0161281	+	0.530536i
$475$			38.8044i			0.0816935i
$476$	7.85013	−	128.996i	0.0164919	−	0.271000i
$477$	−1527.78			−3.20289
$478$	297.211	+	9.03512i	0.621780	+	0.0189019i
$479$			814.201i			1.69979i	0.526949	+	0.849897i	$0.323336\pi$
$479$			814.201i			1.69979i	−0.526949	+	0.849897i	$0.676664\pi$
$480$	−990.144	−	151.623i	−2.06280	−	0.315881i
$481$	631.136			1.31213
$482$	20.0725	−	660.285i	0.0416441	−	1.36989i
$483$			779.915i			1.61473i
$484$	−472.768	−	28.7706i	−0.976793	−	0.0594434i
$485$	382.742			0.789158
$486$	406.901	+	12.3697i	0.837245	+	0.0254520i
$487$		−	149.015i		−	0.305986i	−0.988227	−	0.152993i	$-0.951109\pi$
$487$		−	149.015i		−	0.305986i	0.988227	−	0.152993i	$-0.0488912\pi$
$488$	38.6148	−	422.368i	0.0791286	−	0.865508i
$489$	680.418			1.39145
$490$	6.82323	−	224.451i	0.0139250	−	0.458063i
$491$			367.294i			0.748053i	0.927418	+	0.374027i	$0.122023\pi$
$491$			367.294i			0.748053i	−0.927418	+	0.374027i	$0.877977\pi$
$492$	57.5247	−	945.265i	0.116920	−	1.92127i
$493$	8.84517			0.0179415
$494$	−205.013	−	6.23232i	−0.415005	−	0.0126160i
$495$		−	186.473i		−	0.376712i
$496$	60.9091	−	498.586i	0.122801	−	1.00521i
$497$	−326.712			−0.657368
$498$	−44.7976	+	1473.62i	−0.0899549	+	2.95907i
$499$			138.107i			0.276767i	0.990379	+	0.138384i	$0.0441907\pi$
$499$			138.107i			0.276767i	−0.990379	+	0.138384i	$0.955809\pi$
$500$	−374.227	−	22.7738i	−0.748454	−	0.0455476i
$501$	76.5682			0.152831
$502$	506.752	+	15.4051i	1.00947	+	0.0306875i
$503$		−	31.6936i		−	0.0630092i	−0.999504	−	0.0315046i	$-0.989970\pi$
$503$		−	31.6936i		−	0.0630092i	0.999504	−	0.0315046i	$-0.0100299\pi$
$504$	864.348	+	79.0225i	1.71498	+	0.156791i
$505$	−10.5625			−0.0209158
$506$	2.60240	−	85.6061i	0.00514308	−	0.169182i
$507$		−	2067.32i		−	4.07756i
$508$	12.2522	−	201.332i	0.0241185	−	0.396323i
$509$	−564.839			−1.10970			−0.554852	−	0.831949i	$-0.687225\pi$
$509$	−564.839			−1.10970			−0.554852	+	0.831949i	$0.687225\pi$
$510$	370.875	+	11.2745i	0.727206	+	0.0221068i
$511$			271.578i			0.531465i
$512$	−138.299	+	492.968i	−0.270116	+	0.962828i
$513$	−255.484			−0.498019
$514$	−15.4457	+	508.086i	−0.0300499	+	0.988494i
$515$		−	2.88027i		−	0.00559276i
$516$	597.975	+	36.3902i	1.15887	+	0.0705236i
$517$	52.3240			0.101207
$518$	292.334	+	8.88687i	0.564352	+	0.0171561i
$519$			1171.00i			2.25627i
$520$	−99.7779	+	1091.37i	−0.191881	+	2.09879i
$521$	−304.845			−0.585114			−0.292557	−	0.956248i	$-0.594506\pi$
$521$	−304.845			−0.585114			−0.292557	+	0.956248i	$0.594506\pi$
$522$	−1.80506	+	59.3776i	−0.00345797	+	0.113750i
$523$			812.948i			1.55439i	0.629257	+	0.777197i	$0.283359\pi$
$523$			812.948i			1.55439i	−0.629257	+	0.777197i	$0.716641\pi$
$524$	−30.3604	+	498.893i	−0.0579398	+	0.952086i
$525$	−260.899			−0.496951
$526$	379.919	+	11.5494i	0.722279	+	0.0219571i
$527$			186.060i			0.353055i
$528$	−137.393	−	16.7845i	−0.260215	−	0.0317888i
$529$	−179.204			−0.338759
$530$	27.1625	−	893.512i	0.0512500	−	1.68587i
$531$		−	674.480i		−	1.27021i
$532$	−94.8715	−	5.77347i	−0.178330	−	0.0108524i
$533$	−1036.11			−1.94391
$534$	1253.21	+	38.0973i	2.34684	+	0.0713432i
$535$		−	68.3345i		−	0.127728i
$536$	−607.002	−	55.4948i	−1.13247	−	0.103535i
$537$	−968.898			−1.80428
$538$	−14.1857	+	466.638i	−0.0263674	+	0.867357i
$539$		−	31.0294i		−	0.0575684i
$540$	−82.9200	+	1362.57i	−0.153556	+	2.52328i
$541$	−396.300			−0.732532			−0.366266	−	0.930510i	$-0.619364\pi$
$541$	−396.300			−0.732532			−0.366266	+	0.930510i	$0.619364\pi$
$542$	−5.46139	−	0.166025i	−0.0100764	−	0.000306319i
$543$			511.071i			0.941199i
$544$	28.7078	−	187.471i	0.0527717	−	0.344616i
$545$	168.749			0.309632
$546$	41.9026	−	1378.39i	0.0767448	−	2.52452i
$547$			526.396i			0.962333i	0.876629	+	0.481167i	$0.159787\pi$
$547$			526.396i			0.962333i	−0.876629	+	0.481167i	$0.840213\pi$
$548$	−547.591	−	33.3240i	−0.999254	−	0.0608102i
$549$	−1055.15			−1.92194
$550$	28.6371	+	0.870560i	0.0520675	+	0.00158284i
$551$		−	6.50528i		−	0.0118063i
$552$	−104.205	+	1139.80i	−0.188778	+	2.06485i
$553$	127.555			0.230661
$554$	1.24518	−	40.9603i	0.00224762	−	0.0739355i
$555$			839.711i			1.51299i
$556$	21.7919	−	358.092i	0.0391940	−	0.644050i
$557$	68.8105			0.123538			0.0617688	−	0.998090i	$-0.480326\pi$
$557$	68.8105			0.123538			0.0617688	+	0.998090i	$0.480326\pi$
$558$	−1249.02	−	37.9699i	−2.23839	−	0.0680464i
$559$		−	655.442i		−	1.17253i
$560$	−61.5832	+	504.104i	−0.109970	+	0.900185i
$561$	51.2719			0.0913938
$562$	17.3404	−	570.415i	0.0308549	−	1.01497i
$563$		−	588.997i		−	1.04618i	−0.852279	−	0.523088i	$-0.824780\pi$
$563$		−	588.997i		−	1.04618i	0.852279	−	0.523088i	$-0.175220\pi$
$564$	−697.957	−	42.4746i	−1.23751	−	0.0753096i
$565$	819.383			1.45023
$566$	−8.90599	−	0.270739i	−0.0157350	−	0.000478338i
$567$		−	741.282i		−	1.30738i
$568$	−477.469	−	43.6524i	−0.840615	−	0.0768528i
$569$	−421.857			−0.741401			−0.370700	−	0.928752i	$-0.620882\pi$
$569$	−421.857			−0.741401			−0.370700	+	0.928752i	$0.620882\pi$
$570$	8.29195	−	272.764i	0.0145473	−	0.478534i
$571$		−	393.676i		−	0.689451i	−0.938704	−	0.344725i	$-0.887972\pi$
$571$		−	393.676i		−	0.689451i	0.938704	−	0.344725i	$-0.112028\pi$
$572$	−9.19875	+	151.157i	−0.0160817	+	0.264260i
$573$	136.977			0.239052
$574$	−479.911	−	14.5892i	−0.836082	−	0.0254166i
$575$		−	236.910i		−	0.412017i
$576$	1252.63	+	230.973i	2.17471	+	0.400995i
$577$	703.416			1.21909			0.609546	−	0.792751i	$-0.291352\pi$
$577$	703.416			1.21909			0.609546	+	0.792751i	$0.291352\pi$
$578$	15.4282	−	507.513i	0.0266924	−	0.878050i
$579$		−	1825.54i		−	3.15292i
$580$	−34.6946	−	2.11136i	−0.0598182	−	0.00364027i
$581$	747.465			1.28651
$582$	−706.458	−	21.4761i	−1.21385	−	0.0369006i
$583$		−	123.524i		−	0.211877i
$584$	−36.2860	+	396.895i	−0.0621335	+	0.679615i
$585$	2726.43			4.66056
$586$	−19.8711	+	653.660i	−0.0339097	+	1.11546i
$587$			56.2392i			0.0958078i	0.998852	+	0.0479039i	$0.0152541\pi$
$587$			56.2392i			0.0958078i	−0.998852	+	0.0479039i	$0.984746\pi$
$588$	−25.1884	+	413.905i	−0.0428375	+	0.703920i
$589$	136.840			0.232326
$590$	394.466	+	11.9916i	0.668586	+	0.0203248i
$591$		−	735.768i		−	1.24495i
$592$	426.041	+	52.0468i	0.719665	+	0.0879169i
$593$	553.916			0.934090			0.467045	−	0.884233i	$-0.345319\pi$
$593$	553.916			0.934090			0.467045	+	0.884233i	$0.345319\pi$
$594$	−5.73167	+	188.544i	−0.00964927	+	0.317413i
$595$		−	188.119i		−	0.316167i
$596$	−75.5377	−	4.59690i	−0.126741	−	0.00771291i
$597$	−1072.05			−1.79574
$598$	1251.65	+	38.0498i	2.09306	+	0.0636284i
$599$		−	724.179i		−	1.20898i	−0.796613	−	0.604490i	$-0.793377\pi$
$599$		−	724.179i		−	1.20898i	0.796613	−	0.604490i	$-0.206623\pi$
$600$	−381.288	−	34.8591i	−0.635480	−	0.0580984i
$601$	−393.734			−0.655132			−0.327566	−	0.944828i	$-0.606228\pi$
$601$	−393.734			−0.655132			−0.327566	+	0.944828i	$0.606228\pi$
$602$	9.22911	−	303.592i	0.0153308	−	0.504306i
$603$			1516.39i			2.51475i
$604$	65.3745	−	1074.26i	0.108236	−	1.77857i
$605$	−689.454			−1.13959
$606$	19.4960	+	0.592674i	0.0321717	+	0.000978010i
$607$			860.362i			1.41740i	0.705510	+	0.708700i	$0.250718\pi$
$607$			860.362i			1.41740i	−0.705510	+	0.708700i	$0.749282\pi$
$608$	−137.878	−	21.1135i	−0.226772	−	0.0347261i
$609$	43.7379			0.0718191
$610$	18.7595	−	617.096i	0.0307533	−	1.01163i
$611$			765.032i			1.25210i
$612$	−470.954	−	28.6602i	−0.769533	−	0.0468304i
$613$	563.747			0.919652			0.459826	−	0.888009i	$-0.347912\pi$
$613$	563.747			0.919652			0.459826	+	0.888009i	$0.347912\pi$
$614$	−703.856	−	21.3970i	−1.14635	−	0.0348486i
$615$		−	1378.51i		−	2.24149i
$616$	−6.38914	+	69.8844i	−0.0103720	+	0.113449i
$617$	−677.849			−1.09862			−0.549310	−	0.835619i	$-0.685109\pi$
$617$	−677.849			−1.09862			−0.549310	+	0.835619i	$0.685109\pi$
$618$	−0.161616	+	5.31636i	−0.000261514	+	0.00860252i
$619$			997.063i			1.61076i	0.592756	+	0.805382i	$0.298040\pi$
$619$			997.063i			1.61076i	−0.592756	+	0.805382i	$0.701960\pi$
$620$	44.4129	−	729.808i	0.0716338	−	1.17711i
$621$	1559.79			2.51174
$622$	−150.808	−	4.58451i	−0.242456	−	0.00737060i
$623$		−	635.668i		−	1.02033i
$624$	245.407	−	2008.84i	0.393280	−	3.21929i
$625$	−768.307			−1.22929
$626$	0.801884	−	26.3780i	0.00128096	−	0.0421374i
$627$		−	37.7085i		−	0.0601412i
$628$	−45.9038	−	2.79351i	−0.0730953	−	0.00444826i
$629$	−158.988			−0.252764
$630$	1262.85	+	38.3901i	2.00452	+	0.0609367i
$631$		−	1071.78i		−	1.69854i	−0.527959	−	0.849270i	$-0.677042\pi$
$631$		−	1071.78i		−	1.69854i	0.527959	−	0.849270i	$-0.322958\pi$
$632$	186.415	+	17.0429i	0.294960	+	0.0269665i
$633$	−1955.04			−3.08853
$634$	−16.7989	+	552.599i	−0.0264966	+	0.871608i
$635$		−	293.610i		−	0.462378i
$636$	−100.272	+	1647.71i	−0.157661	+	2.59073i
$637$	453.682			0.712216
$638$	−4.80081	−	0.145943i	−0.00752478	−	0.000228751i
$639$			1192.80i			1.86666i
$640$	−157.354	+	728.489i	−0.245866	+	1.13826i
$641$	−627.241			−0.978536			−0.489268	−	0.872134i	$-0.662736\pi$
$641$	−627.241			−0.978536			−0.489268	+	0.872134i	$0.662736\pi$
$642$	−3.83434	+	126.131i	−0.00597249	+	0.196466i
$643$		−	620.131i		−	0.964433i	−0.876052	−	0.482217i	$-0.839832\pi$
$643$		−	620.131i		−	0.964433i	0.876052	−	0.482217i	$-0.160168\pi$
$644$	579.213	+	35.2484i	0.899399	+	0.0547335i
$645$	872.049			1.35201
$646$	51.6444	+	1.56997i	0.0799449	+	0.00243030i
$647$			1270.23i			1.96327i	0.190778	+	0.981633i	$0.438899\pi$
$647$			1270.23i			1.96327i	−0.190778	+	0.981633i	$0.561101\pi$
$648$	99.0437	−	1083.34i	0.152845	−	1.67182i
$649$	54.5332			0.0840265
$650$	−12.7285	+	418.705i	−0.0195823	+	0.644162i
$651$			920.036i			1.41327i
$652$	30.7516	−	505.320i	0.0471650	−	0.775031i
$653$	775.383			1.18742			0.593708	−	0.804681i	$-0.297663\pi$
$653$	775.383			1.18742			0.593708	+	0.804681i	$0.297663\pi$
$654$	−311.475	−	9.46874i	−0.476261	−	0.0144782i
$655$			727.554i			1.11077i
$656$	−699.412	−	85.4427i	−1.06618	−	0.130248i
$657$	991.512			1.50915
$658$	−10.7722	+	354.353i	−0.0163712	+	0.538531i
$659$		−	516.735i		−	0.784119i	−0.919940	−	0.392060i	$-0.871763\pi$
$659$		−	516.735i		−	0.784119i	0.919940	−	0.392060i	$-0.128237\pi$
$660$	−201.110	−	12.2387i	−0.304713	−	0.0185435i
$661$	−987.675			−1.49421			−0.747107	−	0.664704i	$-0.768558\pi$
$661$	−987.675			−1.49421			−0.747107	+	0.664704i	$0.768558\pi$
$662$	−1099.71	−	33.4309i	−1.66119	−	0.0504998i
$663$			749.649i			1.13069i
$664$	1092.37	+	99.8698i	1.64514	+	0.150406i
$665$	−138.355			−0.208052
$666$	32.4453	−	1067.29i	0.0487166	−	1.60254i
$667$			39.7163i			0.0595446i
$668$	3.46051	−	56.8643i	0.00518041	−	0.0851261i
$669$	1446.00			2.16143
$670$	−886.853	−	26.9601i	−1.32366	−	0.0402389i
$671$		−	85.3109i		−	0.127140i
$672$	141.955	−	927.011i	0.211243	−	1.37948i
$673$	−237.022			−0.352187			−0.176094	−	0.984373i	$-0.556346\pi$
$673$	−237.022			−0.352187			−0.176094	+	0.984373i	$0.556346\pi$
$674$	10.8802	−	357.904i	0.0161427	−	0.531014i
$675$			521.784i			0.773013i
$676$	−1535.32	−	93.4329i	−2.27118	−	0.138214i
$677$	894.692			1.32155			0.660777	−	0.750582i	$-0.270227\pi$
$677$	894.692			1.32155			0.660777	+	0.750582i	$0.270227\pi$
$678$	−1512.40	−	45.9766i	−2.23068	−	0.0678121i
$679$			358.338i			0.527743i
$680$	25.1349	−	274.925i	0.0369631	−	0.404302i
$681$	−430.040			−0.631483
$682$	3.06995	−	100.986i	0.00450139	−	0.148074i
$683$		−	1327.94i		−	1.94427i	−0.234421	−	0.972135i	$-0.575320\pi$
$683$		−	1327.94i		−	1.94427i	0.234421	−	0.972135i	$-0.424680\pi$
$684$	−21.0785	+	346.368i	−0.0308165	+	0.506387i
$685$	−798.572			−1.16580
$686$	744.122	+	22.6211i	1.08473	+	0.0329754i
$687$		−	1598.53i		−	2.32683i
$688$	54.0511	−	442.449i	0.0785627	−	0.643094i
$689$	1806.05			2.62127
$690$	−50.6243	+	1665.29i	−0.0733686	+	2.41346i
$691$			552.974i			0.800252i	0.916460	+	0.400126i	$0.131034\pi$
$691$			552.974i			0.800252i	−0.916460	+	0.400126i	$0.868966\pi$
$692$	869.658	+	52.9236i	1.25673	+	0.0764792i
$693$	174.583			0.251924
$694$	−323.364	−	9.83016i	−0.465942	−	0.0141645i
$695$		−	522.218i		−	0.751393i
$696$	63.9202	+	5.84387i	0.0918394	+	0.00839637i
$697$	261.004			0.374467
$698$	28.7333	−	945.183i	0.0411652	−	1.35413i
$699$			1376.14i			1.96873i
$700$	−11.7914	+	193.760i	−0.0168448	+	0.276799i
$701$	815.608			1.16349			0.581746	−	0.813370i	$-0.302370\pi$
$701$	815.608			1.16349			0.581746	+	0.813370i	$0.302370\pi$
$702$	−2756.70	−	83.8030i	−3.92693	−	0.119377i
$703$			116.930i			0.166330i
$704$	−18.6747	+	101.278i	−0.0265266	+	0.143861i
$705$	−1017.86			−1.44377
$706$	−19.3982	+	638.105i	−0.0274762	+	0.903832i
$707$		−	9.88900i		−	0.0139873i
$708$	−727.426	−	44.2680i	−1.02744	−	0.0625254i
$709$	764.747			1.07863			0.539314	−	0.842105i	$-0.318684\pi$
$709$	764.747			1.07863			0.539314	+	0.842105i	$0.318684\pi$
$710$	−697.601	−	21.2069i	−0.982537	−	0.0298688i
$711$		−	465.695i		−	0.654986i
$712$	84.9324	−	928.990i	0.119287	−	1.30476i
$713$	−835.441			−1.17173
$714$	−10.5556	+	347.228i	−0.0147838	+	0.486314i
$715$			220.437i			0.308304i
$716$	−43.7894	+	719.563i	−0.0611584	+	1.00498i
$717$	−799.285			−1.11476
$718$	1091.04	+	33.1672i	1.51955	+	0.0461938i
$719$			713.170i			0.991892i	0.868353	+	0.495946i	$0.165179\pi$
$719$			713.170i			0.991892i	−0.868353	+	0.495946i	$0.834821\pi$
$720$	1840.44	+	224.835i	2.55617	+	0.312271i
$721$	2.69662			0.00374011
$722$	1.15465	−	37.9825i	0.00159925	−	0.0526073i
$723$			1775.70i			2.45601i
$724$	379.553	+	23.0979i	0.524244	+	0.0319032i
$725$	−13.2860			−0.0183255
$726$	1272.58	+	38.6862i	1.75287	+	0.0532868i
$727$		−	890.749i		−	1.22524i	−0.790378	−	0.612619i	$-0.790116\pi$
$727$		−	890.749i		−	1.22524i	0.790378	−	0.612619i	$-0.209884\pi$
$728$	−1021.78	−	93.4160i	−1.40355	−	0.128319i
$729$	129.566			0.177731
$730$	−17.6282	+	579.880i	−0.0241482	+	0.794356i
$731$			165.111i			0.225870i
$732$	−69.2521	+	1137.97i	−0.0946067	+	1.55461i
$733$	−221.785			−0.302572			−0.151286	−	0.988490i	$-0.548341\pi$
$733$	−221.785			−0.302572			−0.151286	+	0.988490i	$0.548341\pi$
$734$	180.815	+	5.49671i	0.246342	+	0.00748871i
$735$			603.612i			0.821241i
$736$	841.775	+	128.903i	1.14372	+	0.175140i
$737$	−122.604			−0.166355
$738$	−53.2638	+	1752.12i	−0.0721732	+	2.37414i
$739$		−	635.372i		−	0.859772i	−0.902883	−	0.429886i	$-0.858554\pi$
$739$		−	635.372i		−	0.859772i	0.902883	−	0.429886i	$-0.141446\pi$
$740$	623.621	+	37.9508i	0.842731	+	0.0512849i
$741$	551.338			0.744046
$742$	836.541	+	25.4306i	1.12741	+	0.0342730i
$743$			795.274i			1.07036i	0.844740	+	0.535178i	$0.179755\pi$
$743$			795.274i			1.07036i	−0.844740	+	0.535178i	$0.820245\pi$
$744$	−122.927	+	1344.58i	−0.165225	+	1.80723i
$745$	−110.159			−0.147865
$746$	−28.5002	+	937.518i	−0.0382041	+	1.25673i
$747$		−	2728.94i		−	3.65319i
$748$	2.31724	−	38.0777i	0.00309791	−	0.0509060i
$749$	63.9775			0.0854172
$750$	1007.33	+	30.6226i	1.34311	+	0.0408302i
$751$		−	84.7437i		−	0.112841i	−0.998407	−	0.0564206i	$-0.982031\pi$
$751$		−	84.7437i		−	0.112841i	0.998407	−	0.0564206i	$-0.0179688\pi$
$752$	−63.0885	+	516.426i	−0.0838943	+	0.686737i
$753$	−1362.80			−1.80983
$754$	2.13384	−	70.1929i	0.00283003	−	0.0930940i
$755$		−	1566.63i		−	2.07500i
$756$	−1275.69	−	77.6330i	−1.68742	−	0.102689i
$757$	1207.44			1.59503			0.797514	−	0.603301i	$-0.206148\pi$
$757$	1207.44			1.59503			0.797514	+	0.603301i	$0.206148\pi$
$758$	392.876	+	11.9433i	0.518306	+	0.0157563i
$759$			230.219i			0.303319i
$760$	−202.197	−	18.4857i	−0.266048	−	0.0243233i
$761$	524.706			0.689495			0.344748	−	0.938695i	$-0.387965\pi$
$761$	524.706			0.689495			0.344748	+	0.938695i	$0.387965\pi$
$762$	−16.4748	+	541.941i	−0.0216205	+	0.711208i
$763$			157.990i			0.207064i
$764$	6.19068	−	101.727i	0.00810299	−	0.133151i
$765$	−686.809			−0.897790
$766$	49.5861	+	1.50740i	0.0647338	+	0.00196789i
$767$			797.332i			1.03955i
$768$	331.318	−	1335.80i	0.431404	−	1.73933i
$769$	531.656			0.691360			0.345680	−	0.938352i	$-0.387648\pi$
$769$	531.656			0.691360			0.345680	+	0.938352i	$0.387648\pi$
$770$	−3.10393	+	102.104i	−0.00403107	+	0.132602i
$771$		−	1366.39i		−	1.77223i
$772$	−1355.76	−	82.5054i	−1.75616	−	0.106872i
$773$	−249.261			−0.322459			−0.161229	−	0.986917i	$-0.551546\pi$
$773$	−249.261			−0.322459			−0.161229	+	0.986917i	$0.551546\pi$
$774$	−1108.39	−	33.6948i	−1.43203	−	0.0435333i
$775$		−	279.474i		−	0.360611i
$776$	−47.8780	+	523.689i	−0.0616984	+	0.674857i
$777$	−786.171			−1.01180
$778$	7.68525	−	252.807i	0.00987821	−	0.324944i
$779$		−	191.958i		−	0.246416i
$780$	178.943	−	2940.45i	0.229414	−	3.76980i
$781$	−96.4404			−0.123483
$782$	−315.301	−	9.58506i	−0.403198	−	0.0122571i
$783$		−	87.4733i		−	0.111716i
$784$	306.253	+	37.4130i	0.390629	+	0.0477206i
$785$	−66.9432			−0.0852780
$786$	40.8240	−	1342.91i	0.0519389	−	1.70853i
$787$		−	226.270i		−	0.287509i	−0.989613	−	0.143755i	$-0.954082\pi$
$787$		−	226.270i		−	0.287509i	0.989613	−	0.143755i	$-0.0459176\pi$
$788$	−546.426	−	33.2531i	−0.693434	−	0.0421994i
$789$	−1021.71			−1.29494
$790$	272.359	+	8.27963i	0.344758	+	0.0104805i
$791$			767.138i			0.969833i
$792$	255.142	+	23.3263i	0.322150	+	0.0294523i
$793$	1247.33			1.57293
$794$	−24.5442	+	807.383i	−0.0309121	+	1.01685i
$795$			2402.91i			3.02253i
$796$	−48.4516	+	796.173i	−0.0608688	+	1.00022i
$797$	−874.323			−1.09702			−0.548509	−	0.836145i	$-0.684804\pi$
$797$	−874.323			−1.09702			−0.548509	+	0.836145i	$0.684804\pi$
$798$	255.373	+	7.76325i	0.320016	+	0.00972839i
$799$		−	192.718i		−	0.241199i
$800$	−43.1208	+	281.592i	−0.0539010	+	0.351991i
$801$	−2320.77			−2.89734
$802$	−21.0031	+	690.897i	−0.0261883	+	0.861467i
$803$			80.1659i			0.0998330i
$804$	1635.43	+	99.5250i	2.03411	+	0.123787i
$805$	844.687			1.04930
$806$	1476.52	+	44.8859i	1.83192	+	0.0556897i
$807$		−	1254.92i		−	1.55505i
$808$	1.32128	−	14.4522i	0.00163525	−	0.0178864i
$809$	−314.242			−0.388433			−0.194216	−	0.980959i	$-0.562216\pi$
$809$	−314.242			−0.388433			−0.194216	+	0.980959i	$0.562216\pi$
$810$	48.1166	−	1582.80i	0.0594033	−	1.95407i
$811$			1244.45i			1.53446i	0.641371	+	0.767231i	$0.278366\pi$
$811$			1244.45i			1.53446i	−0.641371	+	0.767231i	$0.721634\pi$
$812$	1.97674	−	32.4824i	0.00243441	−	0.0400030i
$813$	14.6873			0.0180655
$814$	86.2927	+	2.62327i	0.106011	+	0.00322269i
$815$		−	736.927i		−	0.904204i
$816$	−61.8200	+	506.042i	−0.0757598	+	0.620150i
$817$	121.433			0.148633
$818$	26.1017	−	858.616i	0.0319091	−	1.04965i
$819$			2552.59i			3.11671i
$820$	−1023.77	−	62.3021i	−1.24850	−	0.0759782i
$821$	406.689			0.495358			0.247679	−	0.968842i	$-0.420332\pi$
$821$	406.689			0.495358			0.247679	+	0.968842i	$0.420332\pi$
$822$	1473.99	+	44.8089i	1.79318	+	0.0545120i
$823$		−	1354.51i		−	1.64582i	−0.568171	−	0.822910i	$-0.692349\pi$
$823$		−	1354.51i		−	1.64582i	0.568171	−	0.822910i	$-0.307651\pi$
$824$	3.94095	+	0.360299i	0.00478271	+	0.000437256i
$825$	−77.0135			−0.0933497
$826$	−11.2270	+	369.314i	−0.0135921	+	0.447112i
$827$		−	465.660i		−	0.563072i	−0.959551	−	0.281536i	$-0.909156\pi$
$827$		−	465.660i		−	0.563072i	0.959551	−	0.281536i	$-0.0908439\pi$
$828$	128.689	−	2114.66i	0.155421	−	2.55394i
$829$	−1349.16			−1.62745			−0.813727	−	0.581248i	$-0.802565\pi$
$829$	−1349.16			−1.62745			−0.813727	+	0.581248i	$0.802565\pi$
$830$	1596.00	+	48.5180i	1.92289	+	0.0584554i
$831$			110.154i			0.132556i
$832$	−1480.79	−	273.044i	−1.77980	−	0.328177i
$833$	−114.286			−0.137198
$834$	−29.3023	+	963.902i	−0.0351347	+	1.15576i
$835$		−	82.9272i		−	0.0993140i
$836$	−28.0046	−	1.70424i	−0.0334984	−	0.00203857i
$837$	1840.02			2.19835
$838$	−690.093	−	20.9786i	−0.823500	−	0.0250342i
$839$		−	860.694i		−	1.02586i	−0.858431	−	0.512929i	$-0.828561\pi$
$839$		−	860.694i		−	1.02586i	0.858431	−	0.512929i	$-0.171439\pi$
$840$	124.288	−	1359.46i	0.147962	−	1.61840i
$841$	−838.773			−0.997352
$842$	11.8789	−	390.756i	0.0141079	−	0.464081i
$843$			1534.01i			1.81970i
$844$	−88.3584	+	1451.93i	−0.104690	+	1.72030i
$845$	−2239.01			−2.64972
$846$	1293.72	+	39.3286i	1.52921	+	0.0464876i
$847$		−	645.494i		−	0.762095i
$848$	1219.16	+	148.937i	1.43768	+	0.175633i
$849$	23.9508			0.0282106
$850$	3.20642	−	105.475i	0.00377225	−	0.124089i
$851$		−	713.884i		−	0.838877i
$852$	1286.43	+	78.2866i	1.50990	+	0.0918857i
$853$	−279.325			−0.327462			−0.163731	−	0.986505i	$-0.552353\pi$
$853$	−279.325			−0.327462			−0.163731	+	0.986505i	$0.552353\pi$
$854$	577.749	+	17.5634i	0.676522	+	0.0205660i
$855$			505.121i			0.590785i
$856$	93.4992	+	8.54811i	0.109228	+	0.00998611i
$857$	548.748			0.640313			0.320157	−	0.947365i	$-0.396264\pi$
$857$	548.748			0.640313			0.320157	+	0.947365i	$0.396264\pi$
$858$	12.3690	−	406.880i	0.0144161	−	0.474219i
$859$			241.447i			0.281079i	0.990075	+	0.140539i	$0.0448837\pi$
$859$			241.447i			0.281079i	−0.990075	+	0.140539i	$0.955116\pi$
$860$	39.4124	−	647.637i	0.0458283	−	0.753066i
$861$	1290.62			1.49898
$862$	−1286.80	−	39.1184i	−1.49281	−	0.0453809i
$863$		−	316.519i		−	0.366766i	−0.983042	−	0.183383i	$-0.941295\pi$
$863$		−	316.519i		−	0.366766i	0.983042	−	0.183383i	$-0.0587048\pi$
$864$	−1853.97	−	283.903i	−2.14580	−	0.328591i
$865$	1268.25			1.46619
$866$	45.9058	−	1510.07i	0.0530090	−	1.74373i
$867$			1364.85i			1.57422i
$868$	683.275	+	41.5811i	0.787183	+	0.0479045i
$869$	37.6525			0.0433285
$870$	93.3899	+	2.83903i	0.107345	+	0.00326325i
$871$		−	1792.59i		−	2.05809i
$872$	−21.1092	+	230.892i	−0.0242078	+	0.264785i
$873$	1308.26			1.49858
$874$	−7.04944	+	231.892i	−0.00806572	+	0.265322i
$875$		−	510.951i		−	0.583944i
$876$	65.0756	−	1069.34i	0.0742872	−	1.22071i
$877$	883.893			1.00786			0.503930	−	0.863744i	$-0.331887\pi$
$877$	883.893			1.00786			0.503930	+	0.863744i	$0.331887\pi$
$878$	−1045.24	−	31.7750i	−1.19048	−	0.0361902i
$879$		−	1757.88i		−	1.99986i
$880$	−18.1784	+	148.804i	−0.0206573	+	0.169095i
$881$	−823.058			−0.934231			−0.467116	−	0.884196i	$-0.654707\pi$
$881$	−823.058			−0.934231			−0.467116	+	0.884196i	$0.654707\pi$
$882$	23.3227	−	767.203i	0.0264430	−	0.869845i
$883$			1295.31i			1.46694i	0.679721	+	0.733470i	$0.262101\pi$
$883$			1295.31i			1.46694i	−0.679721	+	0.733470i	$0.737899\pi$
$884$	556.735	+	33.8805i	0.629791	+	0.0383263i
$885$	−1060.83			−1.19868
$886$	−11.7203	−	0.356294i	−0.0132283	−	0.000402138i
$887$		−	229.109i		−	0.258297i	−0.991625	−	0.129148i	$-0.958776\pi$
$887$		−	229.109i		−	0.258297i	0.991625	−	0.129148i	$-0.0412244\pi$
$888$	−1148.94	−	105.041i	−1.29385	−	0.118290i
$889$	274.889			0.309212
$890$	41.2612	−	1357.29i	0.0463609	−	1.52505i
$891$		−	218.815i		−	0.245584i
$892$	65.3520	−	1073.89i	0.0732646	−	1.20391i
$893$	−141.737			−0.158720
$894$	203.330	+	6.18118i	0.227439	+	0.00691408i
$895$			1049.36i			1.17247i
$896$	−682.040	−	147.321i	−0.761205	−	0.164421i
$897$	−3366.05			−3.75256
$898$	−38.1025	+	1253.39i	−0.0424304	+	1.39575i
$899$			46.8517i			0.0521154i
$900$	707.401	+	43.0493i	0.786001	+	0.0478326i
$901$	−454.960			−0.504950
$902$	−141.663	−	4.30650i	−0.157054	−	0.00477439i
$903$			816.447i			0.904149i
$904$	−102.498	+	1121.13i	−0.113383	+	1.24018i
$905$	553.515			0.611619
$906$	−87.9054	+	2891.66i	−0.0970259	+	3.19167i
$907$			1024.23i			1.12925i	0.825347	+	0.564626i	$0.190980\pi$
$907$			1024.23i			1.12925i	−0.825347	+	0.564626i	$0.809020\pi$
$908$	−19.4357	+	319.374i	−0.0214050	+	0.351734i
$909$	−36.1040			−0.0397183
$910$	−1492.87	−	45.3826i	−1.64051	−	0.0498710i
$911$		−	596.394i		−	0.654659i	−0.944910	−	0.327329i	$-0.893851\pi$
$911$		−	596.394i		−	0.654659i	0.944910	−	0.327329i	$-0.106149\pi$
$912$	372.174	+	45.4662i	0.408086	+	0.0498533i
$913$	220.640			0.241665
$914$	27.4405	−	902.657i	0.0300224	−	0.987590i
$915$			1659.55i			1.81371i
$916$	−1187.17	−	72.2460i	−1.29604	−	0.0788711i
$917$	−681.164			−0.742818
$918$	694.437	+	21.1107i	0.756467	+	0.0229964i
$919$		−	1761.71i		−	1.91699i	−0.285116	−	0.958493i	$-0.592032\pi$
$919$		−	1761.71i		−	1.91699i	0.285116	−	0.958493i	$-0.407968\pi$
$920$	1234.46	+	112.860i	1.34180	+	0.122674i
$921$	1892.87			2.05524
$922$	−3.08550	+	101.498i	−0.00334653	+	0.110084i
$923$		−	1410.06i		−	1.52769i
$924$	11.4584	−	188.288i	0.0124008	−	0.203774i
$925$	238.810			0.258173
$926$	−139.508	−	4.24100i	−0.150657	−	0.00457991i
$927$		−	9.84516i		−	0.0106204i
$928$	7.22890	−	47.2070i	0.00778976	−	0.0508696i
$929$	146.570			0.157771			0.0788857	−	0.996884i	$-0.474864\pi$
$929$	146.570			0.157771			0.0788857	+	0.996884i	$0.474864\pi$
$930$	−59.7195	+	1964.48i	−0.0642146	+	2.11234i
$931$			84.0531i			0.0902826i
$932$	1022.01	+	62.1950i	1.09658	+	0.0667328i
$933$	405.565			0.434690
$934$	−923.232	−	28.0660i	−0.988471	−	0.0300492i
$935$		−	55.5300i		−	0.0593904i
$936$	−341.054	+	3730.45i	−0.364374	+	3.98552i
$937$	813.237			0.867915			0.433958	−	0.900933i	$-0.357117\pi$
$937$	813.237			0.867915			0.433958	+	0.900933i	$0.357117\pi$
$938$	25.2411	−	830.307i	0.0269095	−	0.885188i
$939$			70.9381i			0.0755464i
$940$	−46.0021	+	755.922i	−0.0489384	+	0.804173i
$941$	573.885			0.609867			0.304934	−	0.952374i	$-0.401366\pi$
$941$	573.885			0.609867			0.304934	+	0.952374i	$0.401366\pi$
$942$	123.563	+	3.75627i	0.131171	+	0.00398755i
$943$			1171.95i			1.24279i
$944$	−65.7522	+	538.230i	−0.0696527	+	0.570159i
$945$	−1860.39			−1.96866
$946$	2.72430	−	89.6159i	0.00287981	−	0.0947314i
$947$			1186.01i			1.25239i	0.779666	+	0.626195i	$0.215389\pi$
$947$			1186.01i			1.25239i	−0.779666	+	0.626195i	$0.784611\pi$
$948$	−502.251	−	30.5648i	−0.529801	−	0.0322414i
$949$	−1172.11			−1.23510
$950$	−77.5730	−	2.35819i	−0.0816558	−	0.00248231i
$951$		−	1486.10i		−	1.56267i
$952$	257.396	+	23.5323i	0.270374	+	0.0247188i
$953$	132.421			0.138951			0.0694757	−	0.997584i	$-0.477867\pi$
$953$	132.421			0.138951			0.0694757	+	0.997584i	$0.477867\pi$
$954$	92.8451	−	3054.14i	0.0973219	−	3.20141i
$955$		−	148.353i		−	0.155343i
$956$	−36.1238	+	593.598i	−0.0377864	+	0.620918i
$957$	12.9108			0.0134909
$958$	−1627.65	−	49.4801i	−1.69901	−	0.0516493i
$959$		−	747.654i		−	0.779619i
$960$	363.278	−	1970.16i	0.378414	−	2.05225i
$961$	−24.5372			−0.0255330
$962$	−38.3550	+	1261.69i	−0.0398700	+	1.31153i
$963$		−	233.577i		−	0.242551i
$964$	1318.74	+	80.2528i	1.36799	+	0.0832498i
$965$	−1977.15			−2.04886
$966$	−1559.11	−	47.3965i	−1.61399	−	0.0490647i
$967$			949.146i			0.981536i	0.871290	+	0.490768i	$0.163284\pi$
$967$			949.146i			0.981536i	−0.871290	+	0.490768i	$0.836716\pi$
$968$	86.2453	−	943.351i	0.0890964	−	0.974536i
$969$	−138.887			−0.143330
$970$	−23.2597	+	765.130i	−0.0239791	+	0.788793i
$971$		−	1700.58i		−	1.75137i	−0.482883	−	0.875685i	$-0.660410\pi$
$971$		−	1700.58i		−	1.75137i	0.482883	−	0.875685i	$-0.339590\pi$
$972$	−49.4558	+	812.674i	−0.0508805	+	0.836085i
$973$	488.921			0.502488
$974$	297.893	+	9.05585i	0.305845	+	0.00929759i
$975$		−	1126.02i		−	1.15489i
$976$	841.999	+	102.862i	0.862704	+	0.105391i
$977$	1288.94			1.31929			0.659643	−	0.751579i	$-0.270707\pi$
$977$	1288.94			1.31929			0.659643	+	0.751579i	$0.270707\pi$
$978$	−41.3499	+	1360.21i	−0.0422801	+	1.39081i
$979$		−	187.640i		−	0.191665i
$980$	448.280	+	27.2803i	0.457428	+	0.0278371i
$981$	576.808			0.587980
$982$	−734.249	−	22.3209i	−0.747708	−	0.0227301i
$983$			1526.52i			1.55292i	0.630168	+	0.776459i	$0.282986\pi$
$983$			1526.52i			1.55292i	−0.630168	+	0.776459i	$0.717014\pi$
$984$	1886.16	+	172.441i	1.91683	+	0.175245i
$985$	−796.873			−0.809008
$986$	−0.537533	+	17.6822i	−0.000545165	+	0.0179332i
$987$		−	952.957i		−	0.965509i
$988$	24.9178	−	409.457i	0.0252204	−	0.414430i
$989$	−741.376			−0.749622
$990$	372.773	+	11.3322i	0.376538	+	0.0114467i
$991$		−	613.326i		−	0.618896i	−0.950916	−	0.309448i	$-0.899856\pi$
$991$		−	613.326i		−	0.618896i	0.950916	−	0.309448i	$-0.100144\pi$
$992$	993.009	+	152.062i	1.00102	+	0.153288i
$993$	2957.44			2.97829
$994$	19.8547	−	653.122i	0.0199745	−	0.657064i
$995$			1161.09i			1.16692i
$996$	−2943.15	−	179.107i	−2.95497	−	0.179827i
$997$	−34.6625			−0.0347668			−0.0173834	−	0.999849i	$-0.505534\pi$
$997$	−34.6625			−0.0347668			−0.0173834	+	0.999849i	$0.505534\pi$
$998$	−276.086	−	8.39293i	−0.276639	−	0.00840975i
$999$			1572.30i			1.57387i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.3.b.b.39.6	yes	14
3.2	odd	2		684.3.g.b.343.9		14
4.3	odd	2	inner	76.3.b.b.39.5	✓	14
8.3	odd	2		1216.3.d.d.191.1		14
8.5	even	2		1216.3.d.d.191.14		14
12.11	even	2		684.3.g.b.343.10		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.3.b.b.39.5	✓	14	4.3	odd	2	inner
76.3.b.b.39.6	yes	14	1.1	even	1	trivial
684.3.g.b.343.9		14	3.2	odd	2
684.3.g.b.343.10		14	12.11	even	2
1216.3.d.d.191.1		14	8.3	odd	2
1216.3.d.d.191.14		14	8.5	even	2

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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	76.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0607713 + 1.99908i) q^{2} -5.37609i q^{3} +(-3.99261 - 0.242973i) q^{4} -5.82257 q^{5} +(10.7472 + 0.326712i) q^{6} -5.45132i q^{7} +(0.728358 - 7.96677i) q^{8} -19.9023 q^{9} +O(q^{10})\)	\(q+(-0.0607713 + 1.99908i) q^{2} -5.37609i q^{3} +(-3.99261 - 0.242973i) q^{4} -5.82257 q^{5} +(10.7472 + 0.326712i) q^{6} -5.45132i q^{7} +(0.728358 - 7.96677i) q^{8} -19.9023 q^{9} +(0.353845 - 11.6398i) q^{10} -1.60915i q^{11} +(-1.30624 + 21.4646i) q^{12} +23.5274 q^{13} +(10.8976 + 0.331284i) q^{14} +31.3027i q^{15} +(15.8819 + 1.94019i) q^{16} -5.92676 q^{17} +(1.20949 - 39.7863i) q^{18} +4.35890i q^{19} +(23.2473 + 1.41473i) q^{20} -29.3068 q^{21} +(3.21681 + 0.0977900i) q^{22} -26.6121i q^{23} +(-42.8301 - 3.91572i) q^{24} +8.90234 q^{25} +(-1.42979 + 47.0331i) q^{26} +58.6120i q^{27} +(-1.32452 + 21.7650i) q^{28} -1.49241 q^{29} +(-62.5764 - 1.90230i) q^{30} -31.3933i q^{31} +(-4.84376 + 31.6313i) q^{32} -8.65093 q^{33} +(0.360177 - 11.8480i) q^{34} +31.7407i q^{35} +(79.4624 + 4.83573i) q^{36} +26.8255 q^{37} +(-8.71377 - 0.264896i) q^{38} -126.486i q^{39} +(-4.24092 + 46.3871i) q^{40} -44.0382 q^{41} +(1.78101 - 58.5865i) q^{42} -27.8586i q^{43} +(-0.390980 + 6.42471i) q^{44} +115.883 q^{45} +(53.1996 + 1.61725i) q^{46} +32.5166i q^{47} +(10.4307 - 85.3827i) q^{48} +19.2831 q^{49} +(-0.541007 + 17.7965i) q^{50} +31.8628i q^{51} +(-93.9360 - 5.71653i) q^{52} +76.7637 q^{53} +(-117.170 - 3.56193i) q^{54} +9.36938i q^{55} +(-43.4294 - 3.97051i) q^{56} +23.4338 q^{57} +(0.0906959 - 2.98345i) q^{58} +33.8895i q^{59} +(7.60570 - 124.979i) q^{60} +53.0162 q^{61} +(62.7575 + 1.90781i) q^{62} +108.494i q^{63} +(-62.9390 - 11.6053i) q^{64} -136.990 q^{65} +(0.525728 - 17.2939i) q^{66} -76.1917i q^{67} +(23.6632 + 1.44004i) q^{68} -143.069 q^{69} +(-63.4521 - 1.92892i) q^{70} -59.9326i q^{71} +(-14.4960 + 158.557i) q^{72} -49.8188 q^{73} +(-1.63022 + 53.6263i) q^{74} -47.8598i q^{75} +(1.05909 - 17.4034i) q^{76} -8.77198 q^{77} +(252.854 + 7.68670i) q^{78} +23.3990i q^{79} +(-92.4737 - 11.2969i) q^{80} +135.982 q^{81} +(2.67626 - 88.0358i) q^{82} +137.116i q^{83} +(117.011 + 7.12076i) q^{84} +34.5090 q^{85} +(55.6915 + 1.69300i) q^{86} +8.02335i q^{87} +(-12.8197 - 1.17204i) q^{88} +116.608 q^{89} +(-7.04235 + 231.659i) q^{90} -128.256i q^{91} +(-6.46602 + 106.252i) q^{92} -168.773 q^{93} +(-65.0032 - 1.97608i) q^{94} -25.3800i q^{95} +(170.053 + 26.0405i) q^{96} -65.7341 q^{97} +(-1.17186 + 38.5484i) q^{98} +32.0258i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{2} + 2 q^{4} - 40 q^{8} - 68 q^{9}+O(q^{10}) \) 14 * q + 2 * q^2 + 2 * q^4 - 40 * q^8 - 68 * q^9	\( 14 q + 2 q^{2} + 2 q^{4} - 40 q^{8} - 68 q^{9} - 12 q^{10} + 4 q^{12} + 54 q^{13} + 30 q^{14} + 58 q^{16} + 34 q^{17} + 36 q^{18} + 32 q^{20} - 38 q^{21} + 36 q^{22} - 98 q^{24} - 86 q^{25} - 16 q^{26} + 18 q^{28} + 54 q^{29} - 204 q^{30} + 72 q^{32} + 20 q^{33} - 82 q^{34} + 96 q^{36} + 100 q^{37} - 148 q^{40} + 224 q^{41} + 224 q^{42} - 96 q^{44} - 168 q^{45} + 46 q^{46} + 296 q^{48} - 220 q^{49} - 58 q^{50} - 288 q^{52} + 14 q^{53} - 128 q^{54} + 12 q^{56} + 38 q^{57} - 72 q^{58} + 188 q^{60} + 28 q^{61} + 396 q^{62} - 118 q^{64} - 472 q^{65} - 32 q^{66} + 30 q^{68} + 122 q^{69} + 156 q^{70} + 80 q^{72} + 70 q^{73} - 224 q^{74} + 228 q^{77} + 274 q^{78} - 348 q^{80} + 334 q^{81} - 400 q^{82} - 216 q^{84} + 48 q^{85} - 124 q^{86} + 472 q^{88} + 416 q^{90} + 126 q^{92} - 176 q^{93} - 88 q^{94} - 106 q^{96} + 308 q^{97} + 68 q^{98}+O(q^{100}) \) 14 * q + 2 * q^2 + 2 * q^4 - 40 * q^8 - 68 * q^9 - 12 * q^10 + 4 * q^12 + 54 * q^13 + 30 * q^14 + 58 * q^16 + 34 * q^17 + 36 * q^18 + 32 * q^20 - 38 * q^21 + 36 * q^22 - 98 * q^24 - 86 * q^25 - 16 * q^26 + 18 * q^28 + 54 * q^29 - 204 * q^30 + 72 * q^32 + 20 * q^33 - 82 * q^34 + 96 * q^36 + 100 * q^37 - 148 * q^40 + 224 * q^41 + 224 * q^42 - 96 * q^44 - 168 * q^45 + 46 * q^46 + 296 * q^48 - 220 * q^49 - 58 * q^50 - 288 * q^52 + 14 * q^53 - 128 * q^54 + 12 * q^56 + 38 * q^57 - 72 * q^58 + 188 * q^60 + 28 * q^61 + 396 * q^62 - 118 * q^64 - 472 * q^65 - 32 * q^66 + 30 * q^68 + 122 * q^69 + 156 * q^70 + 80 * q^72 + 70 * q^73 - 224 * q^74 + 228 * q^77 + 274 * q^78 - 348 * q^80 + 334 * q^81 - 400 * q^82 - 216 * q^84 + 48 * q^85 - 124 * q^86 + 472 * q^88 + 416 * q^90 + 126 * q^92 - 176 * q^93 - 88 * q^94 - 106 * q^96 + 308 * q^97 + 68 * q^98

Introduction

L-functions

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