LMFDB - Embedded newform 380.3.h.a.39.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,3,Mod(39,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("380.39");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	380.h (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:	$10.3542500457$
Analytic rank:	$0$
Dimension:	$108$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			39.1
Character	$\chi$	$=$	380.39
Dual form			380.3.h.a.39.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.99911 - 0.0595768i) q^{2} -2.57497 q^{3} +(3.99290 + 0.238201i) q^{4} +(2.22773 - 4.47629i) q^{5} +(5.14765 + 0.153408i) q^{6} -1.63196 q^{7} +(-7.96807 - 0.714075i) q^{8} -2.36954 q^{9} +O(q^{10})$	\(q+(-1.99911 - 0.0595768i) q^{2} -2.57497 q^{3} +(3.99290 + 0.238201i) q^{4} +(2.22773 - 4.47629i) q^{5} +(5.14765 + 0.153408i) q^{6} -1.63196 q^{7} +(-7.96807 - 0.714075i) q^{8} -2.36954 q^{9} +(-4.72017 + 8.81589i) q^{10} -10.0708i q^{11} +(-10.2816 - 0.613361i) q^{12} +2.27729i q^{13} +(3.26246 + 0.0972267i) q^{14} +(-5.73634 + 11.5263i) q^{15} +(15.8865 + 1.90223i) q^{16} -5.69199i q^{17} +(4.73697 + 0.141169i) q^{18} +4.35890i q^{19} +(9.96138 - 17.3428i) q^{20} +4.20224 q^{21} +(-0.599987 + 20.1327i) q^{22} +7.62452 q^{23} +(20.5175 + 1.83872i) q^{24} +(-15.0744 - 19.9440i) q^{25} +(0.135674 - 4.55256i) q^{26} +29.2762 q^{27} +(-6.51624 - 0.388734i) q^{28} -11.2210 q^{29} +(12.1543 - 22.7006i) q^{30} +4.16767i q^{31} +(-31.6456 - 4.74924i) q^{32} +25.9321i q^{33} +(-0.339111 + 11.3789i) q^{34} +(-3.63556 + 7.30512i) q^{35} +(-9.46133 - 0.564427i) q^{36} +53.1159i q^{37} +(0.259689 - 8.71393i) q^{38} -5.86395i q^{39} +(-20.9471 + 34.0766i) q^{40} -29.2518 q^{41} +(-8.40074 - 0.250356i) q^{42} -52.6182 q^{43} +(2.39888 - 40.2118i) q^{44} +(-5.27869 + 10.6067i) q^{45} +(-15.2423 - 0.454244i) q^{46} -44.4213 q^{47} +(-40.9073 - 4.89818i) q^{48} -46.3367 q^{49} +(28.9473 + 40.7683i) q^{50} +14.6567i q^{51} +(-0.542453 + 9.09299i) q^{52} +47.8562i q^{53} +(-58.5264 - 1.74418i) q^{54} +(-45.0800 - 22.4351i) q^{55} +(13.0035 + 1.16534i) q^{56} -11.2240i q^{57} +(22.4321 + 0.668512i) q^{58} +32.2036i q^{59} +(-25.6502 + 44.6570i) q^{60} -81.8613 q^{61} +(0.248296 - 8.33165i) q^{62} +3.86698 q^{63} +(62.9802 + 11.3796i) q^{64} +(10.1938 + 5.07319i) q^{65} +(1.54495 - 51.8411i) q^{66} -27.8201 q^{67} +(1.35584 - 22.7276i) q^{68} -19.6329 q^{69} +(7.70311 - 14.3872i) q^{70} -66.6953i q^{71} +(18.8806 + 1.69203i) q^{72} +79.9780i q^{73} +(3.16448 - 106.185i) q^{74} +(38.8161 + 51.3551i) q^{75} +(-1.03830 + 17.4047i) q^{76} +16.4352i q^{77} +(-0.349355 + 11.7227i) q^{78} +87.0019i q^{79} +(43.9059 - 66.8751i) q^{80} -54.0595 q^{81} +(58.4776 + 1.74273i) q^{82} +55.1557 q^{83} +(16.7791 + 1.00098i) q^{84} +(-25.4790 - 12.6802i) q^{85} +(105.190 + 3.13482i) q^{86} +28.8938 q^{87} +(-7.19133 + 80.2451i) q^{88} +23.7889 q^{89} +(11.1846 - 20.8896i) q^{90} -3.71644i q^{91} +(30.4440 + 1.81617i) q^{92} -10.7316i q^{93} +(88.8032 + 2.64648i) q^{94} +(19.5117 + 9.71046i) q^{95} +(81.4865 + 12.2291i) q^{96} -173.823i q^{97} +(92.6323 + 2.76059i) q^{98} +23.8632i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q + 4 q^{5} + 324 q^{9}+O(q^{10}) $ 108 * q + 4 * q^5 + 324 * q^9	$ 108 q + 4 q^{5} + 324 q^{9} - 8 q^{10} + 8 q^{14} - 104 q^{16} - 16 q^{21} - 8 q^{24} - 76 q^{25} + 80 q^{26} - 88 q^{29} - 140 q^{30} - 88 q^{34} - 256 q^{36} + 44 q^{40} - 200 q^{41} - 8 q^{44} + 108 q^{45} + 272 q^{46} + 916 q^{49} - 276 q^{50} - 320 q^{54} - 328 q^{56} + 172 q^{60} + 200 q^{61} - 216 q^{64} - 192 q^{65} + 152 q^{66} - 592 q^{69} + 200 q^{70} - 232 q^{74} + 340 q^{80} + 1052 q^{81} + 208 q^{84} + 248 q^{85} - 1048 q^{86} + 760 q^{89} + 268 q^{90} - 320 q^{94} + 720 q^{96}+O(q^{100}) $ 108 * q + 4 * q^5 + 324 * q^9 - 8 * q^10 + 8 * q^14 - 104 * q^16 - 16 * q^21 - 8 * q^24 - 76 * q^25 + 80 * q^26 - 88 * q^29 - 140 * q^30 - 88 * q^34 - 256 * q^36 + 44 * q^40 - 200 * q^41 - 8 * q^44 + 108 * q^45 + 272 * q^46 + 916 * q^49 - 276 * q^50 - 320 * q^54 - 328 * q^56 + 172 * q^60 + 200 * q^61 - 216 * q^64 - 192 * q^65 + 152 * q^66 - 592 * q^69 + 200 * q^70 - 232 * q^74 + 340 * q^80 + 1052 * q^81 + 208 * q^84 + 248 * q^85 - 1048 * q^86 + 760 * q^89 + 268 * q^90 - 320 * q^94 + 720 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−1.99911	−	0.0595768i	−0.999556	−	0.0297884i
$2$	−1.99911	−	0.0595768i	−0.999556	−	0.0297884i
$3$	−2.57497			−0.858323			−0.429161	−	0.903228i	$-0.641191\pi$
$3$	−2.57497			−0.858323			−0.429161	+	0.903228i	$0.641191\pi$
$4$	3.99290	+	0.238201i	0.998225	+	0.0595503i
$5$	2.22773	−	4.47629i	0.445547	−	0.895259i
$5$	2.22773	−	4.47629i	0.445547	−	0.895259i
$6$	5.14765	+	0.153408i	0.857942	+	0.0255680i
$7$	−1.63196			−0.233137			−0.116568	−	0.993183i	$-0.537189\pi$
$7$	−1.63196			−0.233137			−0.116568	+	0.993183i	$0.537189\pi$
$8$	−7.96807	−	0.714075i	−0.996008	−	0.0892594i
$9$	−2.36954			−0.263282
$10$	−4.72017	+	8.81589i	−0.472017	+	0.881589i
$11$		−	10.0708i		−	0.915530i	−0.889073	−	0.457765i	$-0.848650\pi$
$11$		−	10.0708i		−	0.915530i	0.889073	−	0.457765i	$-0.151350\pi$
$12$	−10.2816	−	0.613361i	−0.856800	−	0.0511134i
$13$			2.27729i			0.175176i	0.996157	+	0.0875881i	$0.0279159\pi$
$13$			2.27729i			0.175176i	−0.996157	+	0.0875881i	$0.972084\pi$
$14$	3.26246	+	0.0972267i	0.233033	+	0.00694476i
$15$	−5.73634	+	11.5263i	−0.382423	+	0.768421i
$16$	15.8865	+	1.90223i	0.992908	+	0.118889i
$17$		−	5.69199i		−	0.334823i	−0.985887	−	0.167412i	$-0.946459\pi$
$17$		−	5.69199i		−	0.334823i	0.985887	−	0.167412i	$-0.0535409\pi$
$18$	4.73697	+	0.141169i	0.263165	+	0.00784274i
$19$			4.35890i			0.229416i
$19$			4.35890i			0.229416i
$20$	9.96138	−	17.3428i	0.498069	−	0.867138i
$21$	4.20224			0.200106
$22$	−0.599987	+	20.1327i	−0.0272722	+	0.915124i
$23$	7.62452			0.331501			0.165751	−	0.986168i	$-0.446995\pi$
$23$	7.62452			0.331501			0.165751	+	0.986168i	$0.446995\pi$
$24$	20.5175	+	1.83872i	0.854897	+	0.0766134i
$25$	−15.0744	−	19.9440i	−0.602977	−	0.797759i
$26$	0.135674	−	4.55256i	0.00521821	−	0.175098i
$27$	29.2762			1.08430
$28$	−6.51624	−	0.388734i	−0.232723	−	0.0138834i
$29$	−11.2210			−0.386932			−0.193466	−	0.981107i	$-0.561973\pi$
$29$	−11.2210			−0.386932			−0.193466	+	0.981107i	$0.561973\pi$
$30$	12.1543	−	22.7006i	0.405143	−	0.756688i
$31$			4.16767i			0.134441i	0.997738	+	0.0672205i	$0.0214131\pi$
$31$			4.16767i			0.134441i	−0.997738	+	0.0672205i	$0.978587\pi$
$32$	−31.6456	−	4.74924i	−0.988925	−	0.148414i
$33$			25.9321i			0.785820i
$34$	−0.339111	+	11.3789i	−0.00997384	+	0.334675i
$35$	−3.63556	+	7.30512i	−0.103873	+	0.208718i
$36$	−9.46133	−	0.564427i	−0.262815	−	0.0156785i
$37$			53.1159i			1.43557i	0.696267	+	0.717783i	$0.254843\pi$
$37$			53.1159i			1.43557i	−0.696267	+	0.717783i	$0.745157\pi$
$38$	0.259689	−	8.71393i	0.00683392	−	0.229314i
$39$		−	5.86395i		−	0.150358i
$40$	−20.9471	+	34.0766i	−0.523678	+	0.851916i
$41$	−29.2518			−0.713458			−0.356729	−	0.934208i	$-0.616108\pi$
$41$	−29.2518			−0.713458			−0.356729	+	0.934208i	$0.616108\pi$
$42$	−8.40074	−	0.250356i	−0.200018	−	0.00596085i
$43$	−52.6182			−1.22368			−0.611840	−	0.790982i	$-0.709570\pi$
$43$	−52.6182			−1.22368			−0.611840	+	0.790982i	$0.709570\pi$
$44$	2.39888	−	40.2118i	0.0545201	−	0.913905i
$45$	−5.27869	+	10.6067i	−0.117304	+	0.235705i
$46$	−15.2423	−	0.454244i	−0.331354	−	0.00987488i
$47$	−44.4213			−0.945134			−0.472567	−	0.881295i	$-0.656673\pi$
$47$	−44.4213			−0.945134			−0.472567	+	0.881295i	$0.656673\pi$
$48$	−40.9073	−	4.89818i	−0.852235	−	0.102045i
$49$	−46.3367			−0.945647
$50$	28.9473	+	40.7683i	0.578945	+	0.815367i
$51$			14.6567i			0.287386i
$52$	−0.542453	+	9.09299i	−0.0104318	+	0.174865i
$53$			47.8562i			0.902947i	0.892285	+	0.451473i	$0.149101\pi$
$53$			47.8562i			0.902947i	−0.892285	+	0.451473i	$0.850899\pi$
$54$	−58.5264	−	1.74418i	−1.08382	−	0.0322996i
$55$	−45.0800	−	22.4351i	−0.819636	−	0.407911i
$56$	13.0035	+	1.16534i	0.232206	+	0.0208096i
$57$		−	11.2240i		−	0.196913i
$58$	22.4321	+	0.668512i	0.386760	+	0.0115261i
$59$			32.2036i			0.545824i	0.962039	+	0.272912i	$0.0879867\pi$
$59$			32.2036i			0.545824i	−0.962039	+	0.272912i	$0.912013\pi$
$60$	−25.6502	+	44.6570i	−0.427504	+	0.744284i
$61$	−81.8613			−1.34199			−0.670994	−	0.741463i	$-0.734132\pi$
$61$	−81.8613			−1.34199			−0.670994	+	0.741463i	$0.734132\pi$
$62$	0.248296	−	8.33165i	0.00400478	−	0.134381i
$63$	3.86698			0.0613806
$64$	62.9802	+	11.3796i	0.984066	+	0.177806i
$65$	10.1938	+	5.07319i	0.156828	+	0.0780491i
$66$	1.54495	−	51.8411i	0.0234083	−	0.785472i
$67$	−27.8201			−0.415226			−0.207613	−	0.978211i	$-0.566569\pi$
$67$	−27.8201			−0.415226			−0.207613	+	0.978211i	$0.566569\pi$
$68$	1.35584	−	22.7276i	0.0199388	−	0.334229i
$69$	−19.6329			−0.284535
$70$	7.70311	−	14.3872i	0.110044	−	0.205531i
$71$		−	66.6953i		−	0.939370i	−0.882834	−	0.469685i	$-0.844367\pi$
$71$		−	66.6953i		−	0.939370i	0.882834	−	0.469685i	$-0.155633\pi$
$72$	18.8806	+	1.69203i	0.262231	+	0.0235004i
$73$			79.9780i			1.09559i	0.836613	+	0.547794i	$0.184532\pi$
$73$			79.9780i			1.09559i	−0.836613	+	0.547794i	$0.815468\pi$
$74$	3.16448	−	106.185i	0.0427632	−	1.43493i
$75$	38.8161	+	51.3551i	0.517549	+	0.684735i
$76$	−1.03830	+	17.4047i	−0.0136618	+	0.229009i
$77$			16.4352i			0.213444i
$78$	−0.349355	+	11.7227i	−0.00447891	+	0.150291i
$79$			87.0019i			1.10129i	0.834740	+	0.550645i	$0.185618\pi$
$79$			87.0019i			1.10129i	−0.834740	+	0.550645i	$0.814382\pi$
$80$	43.9059	−	66.8751i	0.548823	−	0.835938i
$81$	−54.0595			−0.667401
$82$	58.4776	+	1.74273i	0.713142	+	0.0212528i
$83$	55.1557			0.664527			0.332264	−	0.943187i	$-0.392188\pi$
$83$	55.1557			0.664527			0.332264	+	0.943187i	$0.392188\pi$
$84$	16.7791	+	1.00098i	0.199751	+	0.0119164i
$85$	−25.4790	−	12.6802i	−0.299753	−	0.149179i
$86$	105.190	+	3.13482i	1.22314	+	0.0364514i
$87$	28.8938			0.332112
$88$	−7.19133	+	80.2451i	−0.0817197	+	0.911876i
$89$	23.7889			0.267291			0.133645	−	0.991029i	$-0.457332\pi$
$89$	23.7889			0.267291			0.133645	+	0.991029i	$0.457332\pi$
$90$	11.1846	−	20.8896i	0.124274	−	0.232107i
$91$		−	3.71644i		−	0.0408400i
$92$	30.4440	+	1.81617i	0.330913	+	0.0197410i
$93$		−	10.7316i		−	0.115394i
$94$	88.8032	+	2.64648i	0.944715	+	0.0281540i
$95$	19.5117	+	9.71046i	0.205386	+	0.102215i
$96$	81.4865	+	12.2291i	0.848817	+	0.127387i
$97$		−	173.823i		−	1.79199i	−0.444061	−	0.895996i	$-0.646463\pi$
$97$		−	173.823i		−	1.79199i	0.444061	−	0.895996i	$-0.353537\pi$
$98$	92.6323	+	2.76059i	0.945228	+	0.0281693i
$99$			23.8632i			0.241042i
$100$	−55.4400	−	83.2251i	−0.554400	−	0.832251i
$101$	34.0738			0.337364			0.168682	−	0.985670i	$-0.446049\pi$
$101$	34.0738			0.337364			0.168682	+	0.985670i	$0.446049\pi$
$102$	0.873199	−	29.3004i	0.00856078	−	0.287259i
$103$	16.6233			0.161391			0.0806956	−	0.996739i	$-0.474286\pi$
$103$	16.6233			0.161391			0.0806956	+	0.996739i	$0.474286\pi$
$104$	1.62616	−	18.1456i	0.0156361	−	0.174477i
$105$	9.36146	−	18.8104i	0.0891568	−	0.179147i
$106$	2.85112	−	95.6699i	0.0268973	−	0.902546i
$107$	−7.86375			−0.0734930			−0.0367465	−	0.999325i	$-0.511699\pi$
$107$	−7.86375			−0.0734930			−0.0367465	+	0.999325i	$0.511699\pi$
$108$	116.897	+	6.97363i	1.08238	+	0.0645706i
$109$	−155.911			−1.43037			−0.715186	−	0.698934i	$-0.753658\pi$
$109$	−155.911			−1.43037			−0.715186	+	0.698934i	$0.753658\pi$
$110$	88.7834	+	47.5360i	0.807122	+	0.432146i
$111$		−	136.772i		−	1.23218i
$112$	−25.9261	−	3.10435i	−0.231483	−	0.0277174i
$113$			106.003i			0.938081i	0.883177	+	0.469041i	$0.155400\pi$
$113$			106.003i			0.938081i	−0.883177	+	0.469041i	$0.844600\pi$
$114$	−0.668691	+	22.4381i	−0.00586571	+	0.196825i
$115$	16.9854	−	34.1296i	0.147699	−	0.296779i
$116$	−44.8044	−	2.67286i	−0.386245	−	0.0230419i
$117$		−	5.39612i		−	0.0461207i
$118$	1.91859	−	64.3786i	0.0162592	−	0.545581i
$119$			9.28909i			0.0780595i
$120$	53.9382	−	87.7463i	0.449485	−	0.731219i
$121$	19.5784			0.161805
$122$	163.650	+	4.87703i	1.34139	+	0.0399757i
$123$	75.3224			0.612377
$124$	−0.992745	+	16.6411i	−0.00800601	+	0.134202i
$125$	−122.857	+	23.0477i	−0.982855	+	0.184381i
$126$	−7.73053	−	0.230382i	−0.0613534	−	0.00182843i
$127$	−97.1586			−0.765028			−0.382514	−	0.923950i	$-0.624942\pi$
$127$	−97.1586			−0.765028			−0.382514	+	0.923950i	$0.624942\pi$
$128$	−125.227	−	26.5013i	−0.978332	−	0.207041i
$129$	135.490			1.05031
$130$	−20.0763	−	10.7492i	−0.154433	−	0.0826861i
$131$		−	167.444i		−	1.27820i	−0.769125	−	0.639098i	$-0.779308\pi$
$131$		−	167.444i		−	1.27820i	0.769125	−	0.639098i	$-0.220692\pi$
$132$	−6.17705	+	103.544i	−0.0467959	+	0.784426i
$133$		−	7.11353i		−	0.0534852i
$134$	55.6156	+	1.65743i	0.415041	+	0.0123689i
$135$	65.2195	−	131.049i	0.483108	−	0.970732i
$136$	−4.06451	+	45.3542i	−0.0298861	+	0.333487i
$137$		−	42.9574i		−	0.313558i	−0.987634	−	0.156779i	$-0.949889\pi$
$137$		−	42.9574i		−	0.313558i	0.987634	−	0.156779i	$-0.0501110\pi$
$138$	39.2484	+	1.16967i	0.284409	+	0.00847583i
$139$			185.722i			1.33613i	0.744102	+	0.668066i	$0.232878\pi$
$139$			185.722i			1.33613i	−0.744102	+	0.668066i	$0.767122\pi$
$140$	−16.2565	+	28.3026i	−0.116118	+	0.202162i
$141$	114.383			0.811230
$142$	−3.97349	+	133.331i	−0.0279823	+	0.938953i
$143$	22.9342			0.160379
$144$	−37.6437	−	4.50740i	−0.261415	−	0.0313014i
$145$	−24.9974	+	50.2286i	−0.172396	+	0.346404i
$146$	4.76483	−	159.885i	0.0326358	−	1.09510i
$147$	119.316			0.811671
$148$	−12.6523	+	212.087i	−0.0854884	+	1.43302i
$149$	6.06541			0.0407075			0.0203537	−	0.999793i	$-0.493521\pi$
$149$	6.06541			0.0407075			0.0203537	+	0.999793i	$0.493521\pi$
$150$	−74.5383	−	104.977i	−0.496922	−	0.699848i
$151$		−	28.2256i		−	0.186925i	−0.995623	−	0.0934624i	$-0.970207\pi$
$151$		−	28.2256i		−	0.186925i	0.995623	−	0.0934624i	$-0.0297935\pi$
$152$	3.11258	−	34.7320i	0.0204775	−	0.228500i
$153$			13.4874i			0.0881529i
$154$	0.979153	−	32.8557i	0.00635814	−	0.213349i
$155$	18.6557	+	9.28446i	0.120360	+	0.0598998i
$156$	1.39680	−	23.4142i	0.00895385	−	0.150091i
$157$		−	114.754i		−	0.730919i	−0.930827	−	0.365460i	$-0.880912\pi$
$157$		−	114.754i		−	0.730919i	0.930827	−	0.365460i	$-0.119088\pi$
$158$	5.18329	−	173.927i	0.0328056	−	1.10080i
$159$		−	123.228i		−	0.775020i
$160$	−91.7569	+	131.075i	−0.573481	+	0.819219i
$161$	−12.4429			−0.0772850
$162$	108.071	+	3.22069i	0.667105	+	0.0198808i
$163$	−117.709			−0.722140			−0.361070	−	0.932539i	$-0.617588\pi$
$163$	−117.709			−0.722140			−0.361070	+	0.932539i	$0.617588\pi$
$164$	−116.799	−	6.96781i	−0.712192	−	0.0424867i
$165$	116.080	+	57.7697i	0.703513	+	0.350120i
$166$	−110.263	−	3.28600i	−0.664232	−	0.0197952i
$167$	216.089			1.29395			0.646975	−	0.762512i	$-0.276034\pi$
$167$	216.089			1.29395			0.646975	+	0.762512i	$0.276034\pi$
$168$	−33.4837	−	3.00071i	−0.199308	−	0.0178614i
$169$	163.814			0.969313
$170$	50.1800	+	26.8672i	0.295177	+	0.158042i
$171$		−	10.3286i		−	0.0604010i
$172$	−210.099	−	12.5337i	−1.22151	−	0.0728705i
$173$		−	87.8383i		−	0.507736i	−0.967239	−	0.253868i	$-0.918297\pi$
$173$		−	87.8383i		−	0.507736i	0.967239	−	0.253868i	$-0.0817029\pi$
$174$	−57.7619	−	1.72140i	−0.331965	−	0.00989308i
$175$	24.6008	+	32.5477i	0.140576	+	0.185987i
$176$	19.1570	−	159.990i	0.108847	−	0.909037i
$177$		−	82.9233i		−	0.468493i
$178$	−47.5566	−	1.41726i	−0.267172	−	0.00796216i
$179$			332.825i			1.85936i	0.368369	+	0.929680i	$0.379916\pi$
$179$			332.825i			1.85936i	−0.368369	+	0.929680i	$0.620084\pi$
$180$	−23.6038	+	41.0943i	−0.131132	+	0.228302i
$181$	−80.0042			−0.442012			−0.221006	−	0.975272i	$-0.570934\pi$
$181$	−80.0042			−0.442012			−0.221006	+	0.975272i	$0.570934\pi$
$182$	−0.221413	+	7.42958i	−0.00121656	+	0.0408219i
$183$	210.790			1.15186
$184$	−60.7527	−	5.44448i	−0.330178	−	0.0295896i
$185$	237.763	+	118.328i	1.28520	+	0.639611i
$186$	−0.639356	+	21.4537i	−0.00343740	+	0.115343i
$187$	−57.3231			−0.306541
$188$	−177.370	−	10.5812i	−0.943457	−	0.0562831i
$189$	−47.7775			−0.252791
$190$	−38.4276	−	20.5747i	−0.202250	−	0.108288i
$191$		−	263.163i		−	1.37782i	−0.724849	−	0.688908i	$-0.758091\pi$
$191$		−	263.163i		−	1.37782i	0.724849	−	0.688908i	$-0.241909\pi$
$192$	−162.172	−	29.3021i	−0.844646	−	0.152615i
$193$			125.114i			0.648257i	0.946013	+	0.324129i	$0.105071\pi$
$193$			125.114i			0.648257i	−0.946013	+	0.324129i	$0.894929\pi$
$194$	−10.3558	+	347.492i	−0.0533806	+	1.79120i
$195$	−26.2488	−	13.0633i	−0.134609	−	0.0669913i
$196$	−185.018	−	11.0375i	−0.943969	−	0.0563136i
$197$		−	164.517i		−	0.835111i	−0.908651	−	0.417556i	$-0.862887\pi$
$197$		−	164.517i		−	0.835111i	0.908651	−	0.417556i	$-0.137113\pi$
$198$	1.42169	−	47.7052i	0.00718026	−	0.240936i
$199$			311.623i			1.56594i	0.622057	+	0.782972i	$0.286297\pi$
$199$			311.623i			1.56594i	−0.622057	+	0.782972i	$0.713703\pi$
$200$	105.872	+	169.679i	0.529362	+	0.848396i
$201$	71.6359			0.356398
$202$	−68.1174	−	2.03001i	−0.337215	−	0.0100495i
$203$	18.3122			0.0902079
$204$	−3.49125	+	58.5228i	−0.0171140	+	0.286876i
$205$	−65.1652	+	130.940i	−0.317879	+	0.638730i
$206$	−33.2319	−	0.990363i	−0.161320	−	0.00480759i
$207$	−18.0666			−0.0872782
$208$	−4.33193	+	36.1782i	−0.0208266	+	0.173934i
$209$	43.8977			0.210037
$210$	−19.8353	+	37.0465i	−0.0944537	+	0.176412i
$211$		−	301.957i		−	1.43108i	−0.698574	−	0.715538i	$-0.746182\pi$
$211$		−	301.957i		−	1.43108i	0.698574	−	0.715538i	$-0.253818\pi$
$212$	−11.3994	+	191.085i	−0.0537708	+	0.901344i
$213$			171.738i			0.806283i
$214$	15.7205	+	0.468497i	0.0734604	+	0.00218924i
$215$	−117.219	+	235.535i	−0.545206	+	1.09551i
$216$	−233.275	−	20.9054i	−1.07998	−	0.0967843i
$217$		−	6.80146i		−	0.0313431i
$218$	311.683	+	9.28864i	1.42974	+	0.0426085i
$219$		−	205.941i		−	0.940369i
$220$	−174.656	−	100.319i	−0.793890	−	0.455997i
$221$	12.9623			0.0586530
$222$	−8.14842	+	273.422i	−0.0367046	+	1.23163i
$223$	−126.756			−0.568413			−0.284206	−	0.958763i	$-0.591730\pi$
$223$	−126.756			−0.568413			−0.284206	+	0.958763i	$0.591730\pi$
$224$	51.6443	+	7.75055i	0.230555	+	0.0346006i
$225$	35.7194	+	47.2580i	0.158753	+	0.210035i
$226$	6.31533	−	211.912i	0.0279439	−	0.937665i
$227$	−138.222			−0.608906			−0.304453	−	0.952527i	$-0.598474\pi$
$227$	−138.222			−0.608906			−0.304453	+	0.952527i	$0.598474\pi$
$228$	2.67358	−	44.8164i	0.0117262	−	0.196563i
$229$	209.739			0.915891			0.457946	−	0.888980i	$-0.348585\pi$
$229$	209.739			0.915891			0.457946	+	0.888980i	$0.348585\pi$
$230$	−35.9891	+	67.2170i	−0.156474	+	0.292248i
$231$		−	42.3200i		−	0.183203i
$232$	89.4098	+	8.01265i	0.385387	+	0.0345373i
$233$		−	331.914i		−	1.42452i	−0.701914	−	0.712261i	$-0.747671\pi$
$233$		−	331.914i		−	1.42452i	0.701914	−	0.712261i	$-0.252329\pi$
$234$	−0.321483	+	10.7875i	−0.00137386	+	0.0461002i
$235$	−98.9588	+	198.843i	−0.421101	+	0.846140i
$236$	−7.67094	+	128.586i	−0.0325040	+	0.544855i
$237$		−	224.027i		−	0.945262i
$238$	0.553414	−	18.5699i	0.00232527	−	0.0780249i
$239$		−	149.214i		−	0.624327i	−0.950028	−	0.312163i	$-0.898946\pi$
$239$		−	149.214i		−	0.624327i	0.950028	−	0.312163i	$-0.101054\pi$
$240$	−113.056	+	172.201i	−0.471067	+	0.717505i
$241$	81.7193			0.339084			0.169542	−	0.985523i	$-0.445771\pi$
$241$	81.7193			0.339084			0.169542	+	0.985523i	$0.445771\pi$
$242$	−39.1394	−	1.16642i	−0.161733	−	0.00481990i
$243$	−124.284			−0.511458
$244$	−326.864	−	19.4995i	−1.33961	−	0.0799158i
$245$	−103.226	+	207.417i	−0.421330	+	0.846599i
$246$	−150.578	−	4.48747i	−0.612106	−	0.0182417i
$247$	−9.92648			−0.0401882
$248$	2.97603	−	33.2083i	0.0120001	−	0.133904i
$249$	−142.024			−0.570379
$250$	246.978	−	38.7555i	0.987911	−	0.155022i
$251$			69.2677i			0.275967i	0.990435	+	0.137983i	$0.0440621\pi$
$251$			69.2677i			0.275967i	−0.990435	+	0.137983i	$0.955938\pi$
$252$	15.4405	+	0.921120i	0.0612717	+	0.00365524i
$253$		−	76.7853i		−	0.303499i
$254$	194.231	+	5.78839i	0.764689	+	0.0227890i
$255$	65.6077	+	32.6512i	0.257285	+	0.128044i
$256$	248.763	+	60.4396i	0.971731	+	0.236092i
$257$		−	477.874i		−	1.85943i	−0.368276	−	0.929716i	$-0.620052\pi$
$257$		−	477.874i		−	1.85943i	0.368276	−	0.929716i	$-0.379948\pi$
$258$	−270.860	−	8.07207i	−1.04985	−	0.0312871i
$259$		−	86.6829i		−	0.334683i
$260$	39.4945	+	22.6849i	0.151902	+	0.0872498i
$261$	26.5886			0.101872
$262$	−9.97575	+	334.739i	−0.0380754	+	1.27763i
$263$	−64.8298			−0.246501			−0.123251	−	0.992376i	$-0.539332\pi$
$263$	−64.8298			−0.246501			−0.123251	+	0.992376i	$0.539332\pi$
$264$	18.5175	−	206.628i	0.0701419	−	0.782684i
$265$	214.218	+	106.611i	0.808371	+	0.402305i
$266$	−0.423801	+	14.2208i	−0.00159324	+	0.0534615i
$267$	−61.2556			−0.229422
$268$	−111.083	−	6.62679i	−0.414489	−	0.0247268i
$269$	−63.8655			−0.237418			−0.118709	−	0.992929i	$-0.537876\pi$
$269$	−63.8655			−0.237418			−0.118709	+	0.992929i	$0.537876\pi$
$270$	−138.189	+	258.096i	−0.511810	+	0.955911i
$271$		−	68.0899i		−	0.251254i	−0.992078	−	0.125627i	$-0.959906\pi$
$271$		−	68.0899i		−	0.251254i	0.992078	−	0.125627i	$-0.0400943\pi$
$272$	10.8275	−	90.4260i	0.0398069	−	0.332448i
$273$			9.56971i			0.0350539i
$274$	−2.55926	+	85.8767i	−0.00934038	+	0.313419i
$275$	−200.852	+	151.812i	−0.730372	+	0.552043i
$276$	−78.3923	−	4.67658i	−0.284030	−	0.0169441i
$277$		−	350.082i		−	1.26383i	−0.775036	−	0.631917i	$-0.782268\pi$
$277$		−	350.082i		−	1.26383i	0.775036	−	0.631917i	$-0.217732\pi$
$278$	11.0647	−	371.280i	0.0398012	−	1.33554i
$279$		−	9.87546i		−	0.0353959i
$280$	34.1848	−	55.6116i	0.122089	−	0.198613i
$281$	157.084			0.559018			0.279509	−	0.960143i	$-0.409828\pi$
$281$	157.084			0.559018			0.279509	+	0.960143i	$0.409828\pi$
$282$	−228.665	−	6.81460i	−0.810870	−	0.0241652i
$283$	−372.418			−1.31596			−0.657982	−	0.753033i	$-0.728590\pi$
$283$	−372.418			−1.31596			−0.657982	+	0.753033i	$0.728590\pi$
$284$	15.8869	−	266.308i	0.0559398	−	0.937703i
$285$	−50.2420	−	25.0041i	−0.176288	−	0.0877338i
$286$	−45.8480	−	1.36635i	−0.160308	−	0.00477743i
$287$	47.7376			0.166333
$288$	74.9854	+	11.2535i	0.260366	+	0.0390746i
$289$	256.601			0.887893
$290$	52.9651	−	98.9233i	0.182638	−	0.341115i
$291$			447.590i			1.53811i
$292$	−19.0509	+	319.344i	−0.0652427	+	1.09364i
$293$			431.082i			1.47127i	0.677378	+	0.735635i	$0.263116\pi$
$293$			431.082i			1.47127i	−0.677378	+	0.735635i	$0.736884\pi$
$294$	−238.525	−	7.10844i	−0.811311	−	0.0241784i
$295$	144.153	+	71.7410i	0.488653	+	0.243190i
$296$	37.9288	−	423.231i	0.128138	−	1.42984i
$297$		−	294.836i		−	0.992713i
$298$	−12.1254	−	0.361358i	−0.0406894	−	0.00121261i
$299$			17.3633i			0.0580711i
$300$	142.756	+	214.302i	0.475854	+	0.714340i
$301$	85.8707			0.285285
$302$	−1.68159	+	56.4262i	−0.00556818	+	0.186842i
$303$	−87.7390			−0.289568
$304$	−8.29162	+	69.2477i	−0.0272751	+	0.227789i
$305$	−182.365	+	366.435i	−0.597918	+	1.20143i
$306$	0.803535	−	26.9628i	0.00262593	−	0.0881138i
$307$	−430.695			−1.40291			−0.701457	−	0.712712i	$-0.747467\pi$
$307$	−430.695			−1.40291			−0.701457	+	0.712712i	$0.747467\pi$
$308$	−3.91488	+	65.6240i	−0.0127106	+	0.213065i
$309$	−42.8045			−0.138526
$310$	−36.7418	−	19.6721i	−0.118522	−	0.0634585i
$311$			16.5073i			0.0530783i	0.999648	+	0.0265391i	$0.00844866\pi$
$311$			16.5073i			0.0530783i	−0.999648	+	0.0265391i	$0.991551\pi$
$312$	−4.18730	+	46.7243i	−0.0134208	+	0.149758i
$313$		−	221.515i		−	0.707714i	−0.935299	−	0.353857i	$-0.884870\pi$
$313$		−	221.515i		−	0.707714i	0.935299	−	0.353857i	$-0.115130\pi$
$314$	−6.83669	+	229.407i	−0.0217729	+	0.730595i
$315$	8.61460	−	17.3097i	0.0273479	−	0.0549516i
$316$	−20.7240	+	347.390i	−0.0655822	+	1.09934i
$317$			264.859i			0.835517i	0.908558	+	0.417758i	$0.137184\pi$
$317$			264.859i			0.835517i	−0.908558	+	0.417758i	$0.862816\pi$
$318$	−7.34153	+	246.347i	−0.0230866	+	0.774676i
$319$			113.005i			0.354247i
$320$	191.241	−	256.567i	0.597630	−	0.801772i
$321$	20.2489			0.0630807
$322$	24.8747	+	0.741307i	0.0772507	+	0.00230220i
$323$	24.8108			0.0768137
$324$	−215.854	−	12.8770i	−0.666216	−	0.0397439i
$325$	45.4182	−	34.3288i	0.139748	−	0.105627i
$326$	235.313	+	7.01271i	0.721820	+	0.0215114i
$327$	401.465			1.22772
$328$	233.080	+	20.8880i	0.710610	+	0.0636829i
$329$	72.4936			0.220345
$330$	−228.614	−	122.404i	−0.692771	−	0.370921i
$331$			508.479i			1.53619i	0.640336	+	0.768095i	$0.278795\pi$
$331$			508.479i			1.53619i	−0.640336	+	0.768095i	$0.721205\pi$
$332$	220.231	+	13.1382i	0.663348	+	0.0395728i
$333$		−	125.860i		−	0.377958i
$334$	−431.987	−	12.8739i	−1.29337	−	0.0385446i
$335$	−61.9758	+	124.531i	−0.185002	+	0.371734i
$336$	66.7589	+	7.99361i	0.198687	+	0.0237905i
$337$			20.4607i			0.0607141i	0.999539	+	0.0303571i	$0.00966443\pi$
$337$			20.4607i			0.0607141i	−0.999539	+	0.0303571i	$0.990336\pi$
$338$	−327.483	−	9.75950i	−0.968883	−	0.0288743i
$339$		−	272.955i		−	0.805177i
$340$	−98.7148	−	56.7001i	−0.290338	−	0.166765i
$341$	41.9719			0.123085
$342$	−0.615343	+	20.6480i	−0.00179925	+	0.0603742i
$343$	155.585			0.453602
$344$	419.266	+	37.5734i	1.21880	+	0.109225i
$345$	−43.7369	+	87.8827i	−0.126774	+	0.254732i
$346$	−5.23312	+	175.599i	−0.0151246	+	0.507511i
$347$	−587.245			−1.69235			−0.846174	−	0.532907i	$-0.821100\pi$
$347$	−587.245			−1.69235			−0.846174	+	0.532907i	$0.821100\pi$
$348$	115.370	+	6.88253i	0.331523	+	0.0197774i
$349$	221.052			0.633388			0.316694	−	0.948528i	$-0.397427\pi$
$349$	221.052			0.633388			0.316694	+	0.948528i	$0.397427\pi$
$350$	−47.2407	−	66.5321i	−0.134973	−	0.190092i
$351$			66.6704i			0.189944i
$352$	−47.8287	+	318.698i	−0.135877	+	0.905391i
$353$		−	258.393i		−	0.731992i	−0.930616	−	0.365996i	$-0.880728\pi$
$353$		−	258.393i		−	0.731992i	0.930616	−	0.365996i	$-0.119272\pi$
$354$	−4.94030	+	165.773i	−0.0139556	+	0.468285i
$355$	−298.548	−	148.579i	−0.840980	−	0.418533i
$356$	94.9866	+	5.66654i	0.266816	+	0.0159172i
$357$		−	23.9191i		−	0.0670003i
$358$	19.8287	−	665.355i	0.0553873	−	1.85853i
$359$		−	396.822i		−	1.10536i	−0.833395	−	0.552678i	$-0.813606\pi$
$359$		−	396.822i		−	1.10536i	0.833395	−	0.552678i	$-0.186394\pi$
$360$	49.6350	−	80.7459i	0.137875	−	0.224294i
$361$	−19.0000			−0.0526316
$362$	159.937	+	4.76639i	0.441816	+	0.0131668i
$363$	−50.4137			−0.138881
$364$	0.885260	−	14.8394i	0.00243203	−	0.0407675i
$365$	358.005	+	178.170i	0.980835	+	0.488136i
$366$	−421.393	−	12.5582i	−1.15135	−	0.0343120i
$367$	84.8954			0.231323			0.115661	−	0.993289i	$-0.463101\pi$
$367$	84.8954			0.231323			0.115661	+	0.993289i	$0.463101\pi$
$368$	121.127	+	14.5036i	0.329150	+	0.0394119i
$369$	69.3132			0.187841
$370$	−468.264	−	250.716i	−1.26558	−	0.677612i
$371$		−	78.0992i		−	0.210510i
$372$	2.55629	−	42.8503i	0.00687174	−	0.115189i
$373$		−	453.419i		−	1.21560i	−0.794089	−	0.607801i	$-0.792052\pi$
$373$		−	453.419i		−	1.21560i	0.794089	−	0.607801i	$-0.207948\pi$
$374$	114.595	+	3.41513i	0.306405	+	0.00913135i
$375$	316.353	−	59.3470i	0.843607	−	0.158259i
$376$	353.952	+	31.7202i	0.941362	+	0.0843621i
$377$		−	25.5535i		−	0.0677812i
$378$	95.5126	+	2.84643i	0.252679	+	0.00753023i
$379$		−	486.945i		−	1.28481i	−0.766364	−	0.642407i	$-0.777936\pi$
$379$		−	486.945i		−	1.28481i	0.766364	−	0.642407i	$-0.222064\pi$
$380$	75.5953	+	43.4206i	0.198935	+	0.114265i
$381$	250.180			0.656641
$382$	−15.6784	+	526.092i	−0.0410429	+	1.37720i
$383$	336.678			0.879055			0.439527	−	0.898229i	$-0.355146\pi$
$383$	336.678			0.879055			0.439527	+	0.898229i	$0.355146\pi$
$384$	322.454	+	68.2399i	0.839725	+	0.177708i
$385$	73.5686	+	36.6131i	0.191087	+	0.0950990i
$386$	7.45386	−	250.116i	0.0193105	−	0.647969i
$387$	124.681			0.322173
$388$	41.4049	−	694.059i	0.106714	−	1.78881i
$389$	−229.061			−0.588847			−0.294423	−	0.955675i	$-0.595128\pi$
$389$	−229.061			−0.588847			−0.294423	+	0.955675i	$0.595128\pi$
$390$	51.6960	+	27.6788i	0.132554	+	0.0709714i
$391$		−	43.3987i		−	0.110994i
$392$	369.214	+	33.0879i	0.941873	+	0.0844079i
$393$			431.162i			1.09710i
$394$	−9.80138	+	328.888i	−0.0248766	+	0.834740i
$395$	389.446	+	193.817i	0.985940	+	0.490676i
$396$	−5.68425	+	95.2834i	−0.0143542	+	0.240615i
$397$			415.528i			1.04667i	0.852127	+	0.523335i	$0.175312\pi$
$397$			415.528i			1.04667i	−0.852127	+	0.523335i	$0.824688\pi$
$398$	18.5655	−	622.969i	0.0466469	−	1.56525i
$399$			18.3171i			0.0459076i
$400$	−201.542	−	345.515i	−0.503855	−	0.863788i
$401$	−603.429			−1.50481			−0.752405	−	0.658701i	$-0.771106\pi$
$401$	−603.429			−1.50481			−0.752405	+	0.658701i	$0.771106\pi$
$402$	−143.208	−	4.26784i	−0.356240	−	0.0106165i
$403$	−9.49100			−0.0235509
$404$	136.053	+	8.11642i	0.336766	+	0.0200902i
$405$	−120.430	+	241.986i	−0.297358	+	0.597496i
$406$	−36.6082	−	1.09098i	−0.0901679	−	0.00268715i
$407$	534.922			1.31430
$408$	10.4660	−	116.786i	0.0256519	−	0.286239i
$409$	−88.5966			−0.216618			−0.108309	−	0.994117i	$-0.534544\pi$
$409$	−88.5966			−0.216618			−0.108309	+	0.994117i	$0.534544\pi$
$410$	138.073	−	257.881i	0.336764	−	0.628977i
$411$			110.614i			0.269134i
$412$	66.3752	+	3.95969i	0.161105	+	0.00961090i
$413$		−	52.5549i		−	0.127251i
$414$	36.1171	+	1.07635i	0.0872395	+	0.00259988i
$415$	122.872	−	246.893i	0.296078	−	0.594924i
$416$	10.8154	−	72.0662i	0.0259985	−	0.173236i
$417$		−	478.229i		−	1.14683i
$418$	−87.7565	−	2.61528i	−0.209944	−	0.00625666i
$419$		−	386.404i		−	0.922206i	−0.887347	−	0.461103i	$-0.847454\pi$
$419$		−	386.404i		−	0.922206i	0.887347	−	0.461103i	$-0.152546\pi$
$420$	41.8601	−	72.8783i	0.0996668	−	0.173520i
$421$	716.966			1.70301			0.851503	−	0.524349i	$-0.175691\pi$
$421$	716.966			1.70301			0.851503	+	0.524349i	$0.175691\pi$
$422$	−17.9896	+	603.646i	−0.0426294	+	1.43044i
$423$	105.258			0.248837
$424$	34.1729	−	381.321i	0.0805965	−	0.899342i
$425$	−113.521	+	85.8035i	−0.267108	+	0.201891i
$426$	10.2316	−	343.324i	0.0240179	−	0.805925i
$427$	133.594			0.312867
$428$	−31.3992	−	1.87316i	−0.0733626	−	0.00437653i
$429$	−59.0548			−0.137657
$430$	248.367	−	463.877i	0.577598	−	1.07878i
$431$		−	150.522i		−	0.349238i	−0.984636	−	0.174619i	$-0.944131\pi$
$431$		−	150.522i		−	0.349238i	0.984636	−	0.174619i	$-0.0558694\pi$
$432$	465.097	+	55.6900i	1.07661	+	0.128912i
$433$			90.9055i			0.209944i	0.994475	+	0.104972i	$0.0334752\pi$
$433$			90.9055i			0.209944i	−0.994475	+	0.104972i	$0.966525\pi$
$434$	−0.405209	+	13.5969i	−0.000933661	+	0.0313292i
$435$	64.3676	−	129.337i	0.147971	−	0.297326i
$436$	−622.535	−	37.1381i	−1.42783	−	0.0851791i
$437$			33.2345i			0.0760516i
$438$	−12.2693	+	411.699i	−0.0280121	+	0.939952i
$439$		−	249.359i		−	0.568015i	−0.958822	−	0.284008i	$-0.908336\pi$
$439$		−	249.359i		−	0.568015i	0.958822	−	0.284008i	$-0.0916641\pi$
$440$	343.180	+	210.955i	0.779955	+	0.479443i
$441$	109.797			0.248972
$442$	−25.9131	−	0.772253i	−0.0586270	−	0.00174718i
$443$	443.965			1.00218			0.501089	−	0.865396i	$-0.332933\pi$
$443$	443.965			1.00218			0.501089	+	0.865396i	$0.332933\pi$
$444$	32.5792	−	546.117i	0.0733766	−	1.22999i
$445$	52.9953	−	106.486i	0.119090	−	0.239294i
$446$	253.399	+	7.55171i	0.568160	+	0.0169321i
$447$	−15.6182			−0.0349401
$448$	−102.781	−	18.5710i	−0.229422	−	0.0414531i
$449$	−547.333			−1.21900			−0.609502	−	0.792785i	$-0.708630\pi$
$449$	−547.333			−1.21900			−0.609502	+	0.792785i	$0.708630\pi$
$450$	−68.5916	−	96.6021i	−0.152426	−	0.214671i
$451$			294.590i			0.653192i
$452$	−25.2501	+	423.260i	−0.0558630	+	0.936417i
$453$			72.6801i			0.160442i
$454$	276.320	+	8.23479i	0.608635	+	0.0181383i
$455$	−16.6359	−	8.27923i	−0.0365623	−	0.0181961i
$456$	−8.01480	+	89.4338i	−0.0175763	+	0.196127i
$457$			315.086i			0.689465i	0.938701	+	0.344733i	$0.112030\pi$
$457$			315.086i			0.689465i	−0.938701	+	0.344733i	$0.887970\pi$
$458$	−419.292	−	12.4956i	−0.915485	−	0.0272829i
$459$		−	166.640i		−	0.363050i
$460$	75.9507	−	132.230i	0.165110	−	0.287457i
$461$	−891.929			−1.93477			−0.967385	−	0.253309i	$-0.918481\pi$
$461$	−891.929			−1.93477			−0.967385	+	0.253309i	$0.918481\pi$
$462$	−2.52129	+	84.6025i	−0.00545734	+	0.183122i
$463$	428.696			0.925909			0.462954	−	0.886382i	$-0.346789\pi$
$463$	428.696			0.925909			0.462954	+	0.886382i	$0.346789\pi$
$464$	−178.263	−	21.3449i	−0.384187	−	0.0460020i
$465$	−48.0379	−	23.9072i	−0.103307	−	0.0514133i
$466$	−19.7743	+	663.533i	−0.0424342	+	1.42389i
$467$	6.80247			0.0145663			0.00728316	−	0.999973i	$-0.497682\pi$
$467$	6.80247			0.0145663			0.00728316	+	0.999973i	$0.497682\pi$
$468$	1.28536	−	21.5462i	0.00274650	−	0.0460389i
$469$	45.4012			0.0968043
$470$	209.676	−	391.614i	0.446120	−	0.833220i
$471$			295.489i			0.627365i
$472$	22.9958	−	256.600i	0.0487199	−	0.543645i
$473$			529.909i			1.12032i
$474$	−13.3468	+	447.856i	−0.0281578	+	0.944843i
$475$	86.9338	−	65.7078i	0.183018	−	0.138332i
$476$	−2.21267	+	37.0904i	−0.00464847	+	0.0779210i
$477$		−	113.397i		−	0.237729i
$478$	−8.88969	+	298.296i	−0.0185977	+	0.624050i
$479$			117.351i			0.244991i	0.992469	+	0.122495i	$0.0390896\pi$
$479$			117.351i			0.244991i	−0.992469	+	0.122495i	$0.960910\pi$
$480$	236.271	−	337.514i	0.492232	−	0.703154i
$481$	−120.960			−0.251477
$482$	−163.366	−	4.86857i	−0.338934	−	0.0101008i
$483$	32.0400			0.0663355
$484$	78.1745	+	4.66359i	0.161518	+	0.00963552i
$485$	−778.084	−	387.232i	−1.60430	−	0.798416i
$486$	248.458	+	7.40446i	0.511231	+	0.0152355i
$487$	358.790			0.736734			0.368367	−	0.929680i	$-0.379917\pi$
$487$	358.790			0.736734			0.368367	+	0.929680i	$0.379917\pi$
$488$	652.276	+	58.4551i	1.33663	+	0.119785i
$489$	303.097			0.619829
$490$	218.717	−	408.500i	0.446362	−	0.833673i
$491$		−	55.7494i		−	0.113543i	−0.998387	−	0.0567713i	$-0.981919\pi$
$491$		−	55.7494i		−	0.113543i	0.998387	−	0.0567713i	$-0.0180806\pi$
$492$	300.755	+	17.9419i	0.611291	+	0.0364673i
$493$			63.8699i			0.129554i
$494$	19.8441	+	0.591387i	0.0401703	+	0.00119714i
$495$	106.819	+	53.1608i	0.215795	+	0.107396i
$496$	−7.92787	+	66.2098i	−0.0159836	+	0.133488i
$497$			108.844i			0.219002i
$498$	283.923	+	8.46135i	0.570126	+	0.0169907i
$499$			137.646i			0.275845i	0.990443	+	0.137922i	$0.0440424\pi$
$499$			137.646i			0.275845i	−0.990443	+	0.137922i	$0.955958\pi$
$500$	−496.045	+	62.7624i	−0.992090	+	0.125525i
$501$	−556.424			−1.11063
$502$	4.12674	−	138.474i	0.00822060	−	0.275844i
$503$	221.758			0.440871			0.220436	−	0.975402i	$-0.429252\pi$
$503$	221.758			0.440871			0.220436	+	0.975402i	$0.429252\pi$
$504$	−30.8124	−	2.76132i	−0.0611356	−	0.00547880i
$505$	75.9073	−	152.524i	0.150312	−	0.302028i
$506$	−4.57462	+	153.502i	−0.00904075	+	0.303364i
$507$	−421.816			−0.831984
$508$	−387.945	−	23.1433i	−0.763671	−	0.0455577i
$509$	−653.600			−1.28409			−0.642043	−	0.766668i	$-0.721913\pi$
$509$	−653.600			−1.28409			−0.642043	+	0.766668i	$0.721913\pi$
$510$	−129.212	−	69.1822i	−0.253357	−	0.135651i
$511$		−	130.521i		−	0.255422i
$512$	−493.705	−	135.646i	−0.964267	−	0.264934i
$513$			127.612i			0.248756i
$514$	−28.4702	+	955.324i	−0.0553895	+	1.85861i
$515$	37.0323	−	74.4108i	0.0719073	−	0.144487i
$516$	540.999	+	32.2740i	1.04845	+	0.0625464i
$517$			447.360i			0.865299i
$518$	−5.16429	+	173.289i	−0.00996966	+	0.334534i
$519$			226.181i			0.435801i
$520$	−77.6024	−	47.7027i	−0.149235	−	0.0917360i
$521$	−596.323			−1.14457			−0.572287	−	0.820054i	$-0.693944\pi$
$521$	−596.323			−1.14457			−0.572287	+	0.820054i	$0.693944\pi$
$522$	−53.1536	−	1.58406i	−0.101827	−	0.00303460i
$523$	−981.644			−1.87695			−0.938474	−	0.345350i	$-0.887760\pi$
$523$	−981.644			−1.87695			−0.938474	+	0.345350i	$0.887760\pi$
$524$	39.8853	−	668.586i	0.0761170	−	1.27593i
$525$	−63.3463	−	83.8093i	−0.120660	−	0.159637i
$526$	129.602	+	3.86235i	0.246392	+	0.00734287i
$527$	23.7224			0.0450140
$528$	−49.3287	+	411.970i	−0.0934256	+	0.780247i
$529$	−470.867			−0.890107
$530$	−421.895	−	225.889i	−0.796028	−	0.426206i
$531$		−	76.3076i		−	0.143705i
$532$	1.69445	−	28.4036i	0.00318506	−	0.0533903i
$533$		−	66.6148i		−	0.124981i
$534$	122.457	+	3.64941i	0.229320	+	0.00683410i
$535$	−17.5183	+	35.2005i	−0.0327445	+	0.0657952i
$536$	221.673	+	19.8657i	0.413568	+	0.0370628i
$537$		−	857.015i		−	1.59593i
$538$	127.674	+	3.80490i	0.237313	+	0.00707231i
$539$			466.649i			0.865769i
$540$	291.631	−	507.730i	0.540058	−	0.940240i
$541$	−209.619			−0.387465			−0.193733	−	0.981054i	$-0.562059\pi$
$541$	−209.619			−0.387465			−0.193733	+	0.981054i	$0.562059\pi$
$542$	−4.05657	+	136.119i	−0.00748445	+	0.251143i
$543$	206.008			0.379389
$544$	−27.0326	+	180.127i	−0.0496923	+	0.331115i
$545$	−347.327	+	697.901i	−0.637297	+	1.28055i
$546$	0.570132	−	19.1309i	0.00104420	−	0.0350383i
$547$	99.7485			0.182356			0.0911778	−	0.995835i	$-0.470937\pi$
$547$	99.7485			0.182356			0.0911778	+	0.995835i	$0.470937\pi$
$548$	10.2325	−	171.525i	0.0186725	−	0.313001i
$549$	193.973			0.353321
$550$	410.571	−	291.523i	0.746493	−	0.530042i
$551$		−	48.9113i		−	0.0887682i
$552$	156.436	+	14.0194i	0.283399	+	0.0253974i
$553$		−	141.983i		−	0.256751i
$554$	−20.8567	+	699.853i	−0.0376476	+	1.26327i
$555$	−612.231	−	304.691i	−1.10312	−	0.548993i
$556$	−44.2393	+	741.571i	−0.0795671	+	1.33376i
$557$			33.2605i			0.0597137i	0.999554	+	0.0298568i	$0.00950514\pi$
$557$			33.2605i			0.0597137i	−0.999554	+	0.0298568i	$0.990495\pi$
$558$	−0.588348	+	19.7421i	−0.00105439	+	0.0353802i
$559$		−	119.827i		−	0.214360i
$560$	−71.6524	+	109.137i	−0.127951	+	0.194888i
$561$	147.605			0.263111
$562$	−314.029	−	9.35855i	−0.558770	−	0.0166522i
$563$	−384.497			−0.682944			−0.341472	−	0.939892i	$-0.610925\pi$
$563$	−384.497			−0.682944			−0.341472	+	0.939892i	$0.610925\pi$
$564$	456.722	+	27.2463i	0.809791	+	0.0483090i
$565$	474.501	+	236.147i	0.839826	+	0.417959i
$566$	744.505	+	22.1875i	1.31538	+	0.0392005i
$567$	88.2227			0.155596
$568$	−47.6255	+	531.433i	−0.0838476	+	0.935621i
$569$	−654.076			−1.14952			−0.574759	−	0.818323i	$-0.694904\pi$
$569$	−654.076			−1.14952			−0.574759	+	0.818323i	$0.694904\pi$
$570$	98.9498	+	52.9793i	0.173596	+	0.0929462i
$571$			714.364i			1.25108i	0.780194	+	0.625538i	$0.215120\pi$
$571$			714.364i			1.25108i	−0.780194	+	0.625538i	$0.784880\pi$
$572$	91.5740	+	5.46296i	0.160094	+	0.00955062i
$573$			677.636i			1.18261i
$574$	−95.4329	−	2.84405i	−0.166259	−	0.00495480i
$575$	−114.935	−	152.063i	−0.199887	−	0.264458i
$576$	−149.234	−	26.9644i	−0.259087	−	0.0468132i
$577$			492.771i			0.854023i	0.904246	+	0.427011i	$0.140434\pi$
$577$			492.771i			0.854023i	−0.904246	+	0.427011i	$0.859566\pi$
$578$	−512.975	−	15.2875i	−0.887499	−	0.0264489i
$579$		−	322.164i		−	0.556414i
$580$	−111.777	+	194.603i	−0.192718	+	0.335523i
$581$	−90.0118			−0.154926
$582$	26.6659	−	894.782i	0.0458178	−	1.53743i
$583$	481.951			0.826675
$584$	57.1103	−	637.270i	0.0977916	−	1.09122i
$585$	−24.1546	−	12.0211i	−0.0412900	−	0.0205489i
$586$	25.6825	−	861.782i	0.0438267	−	1.47062i
$587$	294.419			0.501565			0.250782	−	0.968043i	$-0.419312\pi$
$587$	294.419			0.501565			0.250782	+	0.968043i	$0.419312\pi$
$588$	476.415	+	28.4211i	0.810230	+	0.0483352i
$589$	−18.1665			−0.0308429
$590$	−283.904	−	152.006i	−0.481192	−	0.257638i
$591$			423.626i			0.716795i
$592$	−101.039	+	843.827i	−0.170673	+	1.42538i
$593$			1136.46i			1.91646i	0.286000	+	0.958230i	$0.407674\pi$
$593$			1136.46i			1.91646i	−0.286000	+	0.958230i	$0.592326\pi$
$594$	−17.5654	+	589.410i	−0.0295713	+	0.992272i
$595$	41.5807	+	20.6936i	0.0698835	+	0.0347792i
$596$	24.2186	+	1.44479i	0.0406352	+	0.00242414i
$597$		−	802.419i		−	1.34409i
$598$	1.03445	−	34.7111i	0.00172984	−	0.0580453i
$599$		−	828.525i		−	1.38318i	−0.722290	−	0.691590i	$-0.756911\pi$
$599$		−	828.525i		−	1.38318i	0.722290	−	0.691590i	$-0.243089\pi$
$600$	−272.618	−	436.919i	−0.454364	−	0.728198i
$601$	752.041			1.25132			0.625658	−	0.780097i	$-0.284830\pi$
$601$	752.041			1.25132			0.625658	+	0.780097i	$0.284830\pi$
$602$	−171.665	−	5.11590i	−0.285158	−	0.00849817i
$603$	65.9208			0.109321
$604$	6.72338	−	112.702i	0.0111314	−	0.186593i
$605$	43.6154	−	87.6386i	0.0720915	−	0.144857i
$606$	175.400	+	5.22720i	0.289439	+	0.00862575i
$607$	−471.096			−0.776106			−0.388053	−	0.921637i	$-0.626852\pi$
$607$	−471.096			−0.776106			−0.388053	+	0.921637i	$0.626852\pi$
$608$	20.7014	−	137.940i	0.0340484	−	0.226875i
$609$	−47.1533			−0.0774275
$610$	386.399	−	721.680i	0.633441	−	1.18308i
$611$		−	101.160i		−	0.165565i
$612$	−3.21271	+	53.8538i	−0.00524953	+	0.0879964i
$613$		−	989.741i		−	1.61459i	−0.590151	−	0.807293i	$-0.700932\pi$
$613$		−	989.741i		−	1.61459i	0.590151	−	0.807293i	$-0.299068\pi$
$614$	861.007	+	25.6594i	1.40229	+	0.0417905i
$615$	167.798	−	337.165i	0.272843	−	0.548236i
$616$	11.7359	−	130.956i	0.0190518	−	0.212592i
$617$		−	1040.38i		−	1.68619i	−0.537762	−	0.843097i	$-0.680730\pi$
$617$		−	1040.38i		−	1.68619i	0.537762	−	0.843097i	$-0.319270\pi$
$618$	85.5710	+	2.55015i	0.138464	+	0.00412646i
$619$			948.995i			1.53311i	0.642179	+	0.766555i	$0.278031\pi$
$619$			948.995i			1.53311i	−0.642179	+	0.766555i	$0.721969\pi$
$620$	72.2789	+	41.5158i	0.116579	+	0.0669609i
$621$	223.217			0.359448
$622$	0.983454	−	33.0000i	0.00158112	−	0.0530547i
$623$	−38.8224			−0.0623153
$624$	11.1546	−	93.1578i	0.0178759	−	0.149291i
$625$	−170.524	+	601.287i	−0.272838	+	0.962060i
$626$	−13.1971	+	442.833i	−0.0210817	+	0.707400i
$627$	−113.035			−0.180280
$628$	27.3346	−	458.203i	0.0435265	−	0.729622i
$629$	302.336			0.480661
$630$	−18.2528	+	34.0909i	−0.0289727	+	0.0541125i
$631$		−	411.976i		−	0.652894i	−0.945215	−	0.326447i	$-0.894148\pi$
$631$		−	411.976i		−	0.652894i	0.945215	−	0.326447i	$-0.105852\pi$
$632$	62.1259	−	693.237i	0.0983005	−	1.09689i
$633$			777.530i			1.22833i
$634$	15.7794	−	529.482i	0.0248887	−	0.835146i
$635$	−216.443	+	434.910i	−0.340856	+	0.684898i
$636$	29.3531	−	492.038i	0.0461527	−	0.773644i
$637$		−	105.522i		−	0.165655i
$638$	6.73247	−	225.910i	0.0105525	−	0.354090i
$639$			158.037i			0.247319i
$640$	−397.599	+	501.513i	−0.621248	+	0.783614i
$641$	−869.459			−1.35641			−0.678205	−	0.734873i	$-0.737242\pi$
$641$	−869.459			−1.35641			−0.678205	+	0.734873i	$0.737242\pi$
$642$	−40.4798	−	1.20636i	−0.0630527	−	0.00187907i
$643$	−874.880			−1.36062			−0.680311	−	0.732923i	$-0.738155\pi$
$643$	−874.880			−1.36062			−0.680311	+	0.732923i	$0.738155\pi$
$644$	−49.6832	−	2.96391i	−0.0771479	−	0.00460235i
$645$	301.836	−	606.494i	0.467963	−	0.940302i
$646$	−49.5996	−	1.47815i	−0.0767796	−	0.00228816i
$647$	−304.535			−0.470687			−0.235344	−	0.971912i	$-0.575622\pi$
$647$	−304.535			−0.470687			−0.235344	+	0.971912i	$0.575622\pi$
$648$	430.749	+	38.6025i	0.664737	+	0.0595718i
$649$	324.317			0.499718
$650$	−92.8413	+	65.9213i	−0.142833	+	0.101417i
$651$			17.5135i			0.0269025i
$652$	−470.000	−	28.0384i	−0.720859	−	0.0430037i
$653$			780.000i			1.19449i	0.802060	+	0.597244i	$0.203737\pi$
$653$			780.000i			1.19449i	−0.802060	+	0.597244i	$0.796263\pi$
$654$	−802.573	−	23.9180i	−1.22718	−	0.0365718i
$655$	−749.527	−	373.020i	−1.14432	−	0.569496i
$656$	−464.709	−	55.6436i	−0.708398	−	0.0848225i
$657$		−	189.511i		−	0.288449i
$658$	−144.923	−	4.31894i	−0.220248	−	0.00656373i
$659$		−	295.228i		−	0.447995i	−0.974590	−	0.223997i	$-0.928089\pi$
$659$		−	295.228i		−	0.447995i	0.974590	−	0.223997i	$-0.0719107\pi$
$660$	449.733	+	258.319i	0.681414	+	0.391393i
$661$	696.421			1.05359			0.526793	−	0.849993i	$-0.323394\pi$
$661$	696.421			1.05359			0.526793	+	0.849993i	$0.323394\pi$
$662$	30.2935	−	1016.51i	0.0457606	−	1.53551i
$663$	−33.3776			−0.0503432
$664$	−439.485	−	39.3854i	−0.661875	−	0.0593153i
$665$	−31.8423	−	15.8470i	−0.0478831	−	0.0238301i
$666$	−7.49834	+	251.609i	−0.0112588	+	0.377791i
$667$	−85.5549			−0.128268
$668$	862.824	+	51.4728i	1.29165	+	0.0770551i
$669$	326.393			0.487881
$670$	131.316	−	245.259i	0.195994	−	0.366059i
$671$			824.411i			1.22863i
$672$	−132.982	−	19.9574i	−0.197890	−	0.0296985i
$673$		−	109.205i		−	0.162266i	−0.996703	−	0.0811328i	$-0.974146\pi$
$673$		−	109.205i		−	0.162266i	0.996703	−	0.0811328i	$-0.0258538\pi$
$674$	1.21898	−	40.9031i	0.00180857	−	0.0606872i
$675$	−441.322	−	583.884i	−0.653810	−	0.865013i
$676$	654.093	+	39.0207i	0.967593	+	0.0577229i
$677$			33.0107i			0.0487602i	0.999703	+	0.0243801i	$0.00776120\pi$
$677$			33.0107i			0.0487602i	−0.999703	+	0.0243801i	$0.992239\pi$
$678$	−16.2618	+	545.668i	−0.0239849	+	0.804819i
$679$			283.672i			0.417779i
$680$	193.964	+	119.231i	0.285241	+	0.175340i
$681$	355.916			0.522638
$682$	−83.9066	−	2.50055i	−0.123030	−	0.00366650i
$683$	−171.789			−0.251521			−0.125760	−	0.992061i	$-0.540137\pi$
$683$	−171.789			−0.251521			−0.125760	+	0.992061i	$0.540137\pi$
$684$	2.46028	−	41.2410i	0.00359690	−	0.0602938i
$685$	−192.290	−	95.6977i	−0.280715	−	0.139705i
$686$	−311.033	−	9.26927i	−0.453400	−	0.0135121i
$687$	−540.072			−0.786131
$688$	−835.921	−	100.092i	−1.21500	−	0.145482i
$689$	−108.982			−0.158175
$690$	92.6707	−	173.082i	0.134305	−	0.250843i
$691$			955.979i			1.38347i	0.722150	+	0.691736i	$0.243154\pi$
$691$			955.979i			1.38347i	−0.722150	+	0.691736i	$0.756846\pi$
$692$	20.9232	−	350.730i	0.0302358	−	0.506835i
$693$		−	38.9437i		−	0.0561958i
$694$	1173.97	+	34.9861i	1.69160	+	0.0504123i
$695$	831.348	+	413.740i	1.19618	+	0.595309i
$696$	−230.227	−	20.6323i	−0.330786	−	0.0296441i
$697$			166.501i			0.238882i
$698$	−441.909	−	13.1696i	−0.633107	−	0.0188676i
$699$			854.667i			1.22270i
$700$	90.4756	+	135.820i	0.129251	+	0.194028i
$701$	956.268			1.36415			0.682074	−	0.731283i	$-0.261078\pi$
$701$	956.268			1.36415			0.682074	+	0.731283i	$0.261078\pi$
$702$	3.97201	−	133.282i	0.00565813	−	0.189860i
$703$	−231.527			−0.329341
$704$	114.602	−	634.263i	0.162787	−	0.900942i
$705$	254.816	−	512.014i	0.361441	−	0.726261i
$706$	−15.3942	+	516.557i	−0.0218049	+	0.731668i
$707$	−55.6070			−0.0786520
$708$	19.7524	−	331.104i	0.0278989	−	0.467662i
$709$	1098.41			1.54924			0.774622	−	0.632425i	$-0.217940\pi$
$709$	1098.41			1.54924			0.774622	+	0.632425i	$0.217940\pi$
$710$	587.979	+	314.813i	0.828139	+	0.443399i
$711$		−	206.154i		−	0.289950i
$712$	−189.551	−	16.9870i	−0.266224	−	0.0238582i
$713$			31.7765i			0.0445674i
$714$	−1.42502	+	47.8170i	−0.00199583	+	0.0669706i
$715$	51.0913	−	102.660i	0.0714563	−	0.143581i
$716$	−79.2794	+	1328.94i	−0.110725	+	1.85606i
$717$			384.222i			0.535874i
$718$	−23.6414	+	793.293i	−0.0329267	+	1.10486i
$719$			45.0056i			0.0625947i	0.999510	+	0.0312973i	$0.00996388\pi$
$719$			45.0056i			0.0625947i	−0.999510	+	0.0312973i	$0.990036\pi$
$720$	−104.037	+	158.463i	−0.144495	+	0.220087i
$721$	−27.1285			−0.0376262
$722$	37.9831	+	1.13196i	0.0526082	+	0.00156781i
$723$	−210.425			−0.291044
$724$	−319.449	−	19.0571i	−0.441228	−	0.0263220i
$725$	169.150	+	223.792i	0.233311	+	0.308678i
$726$	100.783	+	3.00348i	0.138819	+	0.00413703i
$727$	686.860			0.944787			0.472394	−	0.881388i	$-0.343390\pi$
$727$	686.860			0.944787			0.472394	+	0.881388i	$0.343390\pi$
$728$	−2.65382	+	29.6128i	−0.00364535	+	0.0406770i
$729$	806.564			1.10640
$730$	−705.077	−	377.510i	−0.965859	−	0.517137i
$731$			299.503i			0.409716i
$732$	841.665	+	50.2105i	1.14981	+	0.0685936i
$733$		−	687.150i		−	0.937449i	−0.883344	−	0.468725i	$-0.844714\pi$
$733$		−	687.150i		−	0.937449i	0.883344	−	0.468725i	$-0.155286\pi$
$734$	−169.715	−	5.05779i	−0.231220	−	0.00689072i
$735$	265.803	−	534.092i	0.361637	−	0.726655i
$736$	−241.283	−	36.2107i	−0.327830	−	0.0491993i
$737$			280.172i			0.380152i
$738$	−138.565	−	4.12946i	−0.187757	−	0.00559547i
$739$			264.410i			0.357795i	0.983868	+	0.178897i	$0.0572530\pi$
$739$			264.410i			0.357795i	−0.983868	+	0.178897i	$0.942747\pi$
$740$	921.176	+	529.108i	1.24483	+	0.715010i
$741$	25.5604			0.0344944
$742$	−4.65290	+	156.129i	−0.00627075	+	0.210416i
$743$	−915.667			−1.23239			−0.616196	−	0.787593i	$-0.711327\pi$
$743$	−915.667			−1.23239			−0.616196	+	0.787593i	$0.711327\pi$
$744$	−7.66319	+	85.5103i	−0.0103000	+	0.114933i
$745$	13.5121	−	27.1506i	0.0181371	−	0.0364437i
$746$	−27.0133	+	906.436i	−0.0362108	+	1.21506i
$747$	−130.694			−0.174958
$748$	−228.886	−	13.6544i	−0.305997	−	0.0182546i
$749$	12.8333			0.0171339
$750$	−635.960	+	99.7941i	−0.847947	+	0.133059i
$751$		−	1300.74i		−	1.73201i	−0.500031	−	0.866007i	$-0.666678\pi$
$751$		−	1300.74i		−	1.73201i	0.500031	−	0.866007i	$-0.333322\pi$
$752$	−705.700	−	84.4995i	−0.938431	−	0.112366i
$753$		−	178.362i		−	0.236869i
$754$	−1.52239	+	51.0843i	−0.00201909	+	0.0677511i
$755$	−126.346	−	62.8792i	−0.167346	−	0.0832837i
$756$	−190.771	−	11.3807i	−0.252342	−	0.0150538i
$757$		−	767.245i		−	1.01353i	−0.862083	−	0.506767i	$-0.830841\pi$
$757$		−	767.245i		−	1.01353i	0.862083	−	0.506767i	$-0.169159\pi$
$758$	−29.0106	+	973.457i	−0.0382725	+	1.28424i
$759$			197.720i			0.260500i
$760$	−148.537	−	91.3064i	−0.195443	−	0.120140i
$761$	176.262			0.231619			0.115809	−	0.993271i	$-0.463054\pi$
$761$	176.262			0.231619			0.115809	+	0.993271i	$0.463054\pi$
$762$	−500.139	−	14.9049i	−0.656350	−	0.0195603i
$763$	254.439			0.333472
$764$	62.6857	−	1050.78i	0.0820493	−	1.37537i
$765$	60.3735	+	30.0463i	0.0789196	+	0.0392762i
$766$	−673.057	−	20.0582i	−0.878665	−	0.0261856i
$767$	−73.3369			−0.0956153
$768$	−640.557	−	155.630i	−0.834059	−	0.202643i
$769$	−1027.61			−1.33630			−0.668150	−	0.744027i	$-0.732913\pi$
$769$	−1027.61			−1.33630			−0.668150	+	0.744027i	$0.732913\pi$
$770$	−144.891	−	77.5767i	−0.188170	−	0.100749i
$771$			1230.51i			1.59599i
$772$	−29.8022	+	499.566i	−0.0386039	+	0.647107i
$773$			333.507i			0.431445i	0.976455	+	0.215722i	$0.0692106\pi$
$773$			333.507i			0.431445i	−0.976455	+	0.215722i	$0.930789\pi$
$774$	−249.251	−	7.42808i	−0.322030	−	0.00959701i
$775$	83.1200	−	62.8252i	0.107252	−	0.0810648i
$776$	−124.123	+	1385.04i	−0.159952	+	1.78484i
$777$			223.206i			0.287266i
$778$	457.920	+	13.6467i	0.588586	+	0.0175408i
$779$		−	127.506i		−	0.163679i
$780$	−101.697	−	58.4130i	−0.130381	−	0.0748885i
$781$	−671.677			−0.860022
$782$	−2.58556	+	86.7590i	−0.00330634	+	0.110945i
$783$	−328.509			−0.419551
$784$	−736.129	−	88.1430i	−0.938940	−	0.112427i
$785$	−513.674	−	255.642i	−0.654362	−	0.325658i
$786$	25.6872	−	861.942i	0.0326810	−	1.09662i
$787$	−674.378			−0.856897			−0.428448	−	0.903566i	$-0.640940\pi$
$787$	−674.378			−0.856897			−0.428448	+	0.903566i	$0.640940\pi$
$788$	39.1881	−	656.900i	0.0497311	−	0.833629i
$789$	166.935			0.211577
$790$	−767.000	−	410.664i	−0.970886	−	0.519828i
$791$		−	172.993i		−	0.218701i
$792$	17.0401	−	190.144i	0.0215153	−	0.240080i
$793$		−	186.422i		−	0.235084i
$794$	24.7558	−	830.687i	0.0311786	−	1.04621i
$795$	−551.605	−	274.519i	−0.693843	−	0.345307i
$796$	−74.2290	+	1244.28i	−0.0932525	+	1.56317i
$797$			607.800i			0.762610i	0.924449	+	0.381305i	$0.124525\pi$
$797$			607.800i			0.762610i	−0.924449	+	0.381305i	$0.875475\pi$
$798$	1.09127	−	36.6180i	0.00136751	−	0.0458872i
$799$			252.846i			0.316453i
$800$	382.320	+	702.731i	0.477901	+	0.878414i
$801$	−56.3686			−0.0703728
$802$	1206.32	+	35.9503i	1.50414	+	0.0448258i
$803$	805.445			1.00304
$804$	286.035	+	17.0638i	0.355765	+	0.0212236i
$805$	−27.7194	+	55.6980i	−0.0344341	+	0.0691901i
$806$	18.9736	+	0.565443i	0.0235404	+	0.000701542i
$807$	164.452			0.203782
$808$	−271.502	−	24.3313i	−0.336018	−	0.0301130i
$809$	−1292.37			−1.59749			−0.798745	−	0.601669i	$-0.794502\pi$
$809$	−1292.37			−1.59749			−0.798745	+	0.601669i	$0.794502\pi$
$810$	255.170	−	476.582i	0.315025	−	0.588373i
$811$		−	726.343i		−	0.895614i	−0.894130	−	0.447807i	$-0.852205\pi$
$811$		−	726.343i		−	0.895614i	0.894130	−	0.447807i	$-0.147795\pi$
$812$	73.1188	+	4.36199i	0.0900478	+	0.00537191i
$813$			175.329i			0.215657i
$814$	−1069.37	−	31.8689i	−1.31372	−	0.0391510i
$815$	−262.224	+	526.899i	−0.321747	+	0.646502i
$816$	−27.8804	+	232.844i	−0.0341672	+	0.285348i
$817$		−	229.358i		−	0.280731i
$818$	177.115	+	5.27830i	0.216521	+	0.00645269i
$819$			8.80624i			0.0107524i
$820$	−291.388	+	507.306i	−0.355351	+	0.618666i
$821$	−733.005			−0.892820			−0.446410	−	0.894829i	$-0.647298\pi$
$821$	−733.005			−0.892820			−0.446410	+	0.894829i	$0.647298\pi$
$822$	6.59002	−	221.130i	0.00801706	−	0.269014i
$823$	1520.61			1.84764			0.923819	−	0.382828i	$-0.125050\pi$
$823$	1520.61			1.84764			0.923819	+	0.382828i	$0.125050\pi$
$824$	−132.456	−	11.8703i	−0.160747	−	0.0144057i
$825$	517.189	−	390.911i	0.626895	−	0.473831i
$826$	−3.13105	+	105.063i	−0.00379062	+	0.127195i
$827$	601.727			0.727602			0.363801	−	0.931477i	$-0.381479\pi$
$827$	601.727			0.727602			0.363801	+	0.931477i	$0.381479\pi$
$828$	−72.1381	−	4.30349i	−0.0871233	−	0.00519745i
$829$	−600.577			−0.724459			−0.362230	−	0.932089i	$-0.617984\pi$
$829$	−600.577			−0.724459			−0.362230	+	0.932089i	$0.617984\pi$
$830$	−260.345	+	486.247i	−0.313668	+	0.585840i
$831$			901.450i			1.08478i
$832$	−25.9146	+	143.424i	−0.0311474	+	0.172385i
$833$			263.748i			0.316625i
$834$	−28.4913	+	956.034i	−0.0341623	+	1.14632i
$835$	481.390	−	967.280i	0.576515	−	1.15842i
$836$	175.279	+	10.4565i	0.209664	+	0.0125078i
$837$			122.014i			0.145775i
$838$	−23.0207	+	772.465i	−0.0274710	+	0.921796i
$839$		−	1641.56i		−	1.95657i	−0.207272	−	0.978283i	$-0.566458\pi$
$839$		−	1641.56i		−	1.95657i	0.207272	−	0.978283i	$-0.433542\pi$
$840$	−88.0248	+	143.198i	−0.104791	+	0.170474i
$841$	−715.089			−0.850284
$842$	−1433.30	−	42.7145i	−1.70225	−	0.0507298i
$843$	−404.486			−0.479818
$844$	71.9266	−	1205.68i	0.0852210	−	1.42854i
$845$	364.934	−	733.279i	0.431874	−	0.867786i
$846$	−210.422	−	6.27093i	−0.248726	−	0.00741244i
$847$	−31.9511			−0.0377226
$848$	−91.0334	+	760.268i	−0.107351	+	0.896542i
$849$	958.965			1.12952
$850$	232.053	−	164.768i	0.273004	−	0.193844i
$851$			404.984i			0.475892i
$852$	−40.9083	+	685.734i	−0.0480144	+	0.804852i
$853$		−	676.949i		−	0.793609i	−0.917903	−	0.396805i	$-0.870119\pi$
$853$		−	676.949i		−	0.793609i	0.917903	−	0.396805i	$-0.129881\pi$
$854$	−267.070	−	7.95910i	−0.312728	−	0.00931979i
$855$	−46.2337	−	23.0093i	−0.0540745	−	0.0269115i
$856$	62.6589	+	5.61531i	0.0731996	+	0.00655994i
$857$		−	791.028i		−	0.923020i	−0.887135	−	0.461510i	$-0.847308\pi$
$857$		−	791.028i		−	0.923020i	0.887135	−	0.461510i	$-0.152692\pi$
$858$	118.057	+	3.51830i	0.137596	+	0.00410058i
$859$		−	930.879i		−	1.08368i	−0.840483	−	0.541839i	$-0.817728\pi$
$859$		−	930.879i		−	1.08368i	0.840483	−	0.541839i	$-0.182272\pi$
$860$	−524.150	+	912.545i	−0.609477	+	1.06110i
$861$	−122.923			−0.142768
$862$	−8.96759	+	300.910i	−0.0104032	+	0.349083i
$863$	625.920			0.725284			0.362642	−	0.931929i	$-0.381875\pi$
$863$	625.920			0.725284			0.362642	+	0.931929i	$0.381875\pi$
$864$	−926.463	−	139.040i	−1.07230	−	0.160925i
$865$	−393.190	−	195.680i	−0.454555	−	0.226220i
$866$	5.41586	−	181.730i	0.00625388	−	0.209850i
$867$	−660.740			−0.762099
$868$	1.62012	−	27.1576i	0.00186649	−	0.0312875i
$869$	876.182			1.00826
$870$	−136.383	+	254.724i	−0.156763	+	0.292787i
$871$		−	63.3545i		−	0.0727376i
$872$	1242.31	+	111.332i	1.42466	+	0.127674i
$873$			411.881i			0.471799i
$874$	1.98001	−	66.4396i	0.00226545	−	0.0760178i
$875$	200.497	−	37.6128i	0.229139	−	0.0429861i
$876$	49.0554	−	822.301i	0.0559993	−	0.938700i
$877$			990.974i			1.12996i	0.825105	+	0.564979i	$0.191116\pi$
$877$			990.974i			1.12996i	−0.825105	+	0.564979i	$0.808884\pi$
$878$	−14.8560	+	498.496i	−0.0169203	+	0.567763i
$879$		−	1110.02i		−	1.26282i
$880$	−673.488	−	442.168i	−0.765327	−	0.502464i
$881$	812.639			0.922405			0.461203	−	0.887295i	$-0.347418\pi$
$881$	812.639			0.922405			0.461203	+	0.887295i	$0.347418\pi$
$882$	−219.496	−	6.54132i	−0.248861	−	0.00741647i
$883$	1442.75			1.63392			0.816960	−	0.576695i	$-0.195658\pi$
$883$	1442.75			1.63392			0.816960	+	0.576695i	$0.195658\pi$
$884$	51.7573	+	3.08764i	0.0585489	+	0.00349281i
$885$	−371.189	−	184.731i	−0.419422	−	0.208735i
$886$	−887.536	−	26.4500i	−1.00173	−	0.0298533i
$887$	−341.303			−0.384784			−0.192392	−	0.981318i	$-0.561624\pi$
$887$	−341.303			−0.384784			−0.192392	+	0.981318i	$0.561624\pi$
$888$	−97.6654	+	1089.81i	−0.109984	+	1.22726i
$889$	158.559			0.178356
$890$	−112.288	+	209.720i	−0.126166	+	0.235641i
$891$			544.424i			0.611025i
$892$	−506.124	−	30.1934i	−0.567404	−	0.0338491i
$893$		−	193.628i		−	0.216829i
$894$	31.2226	+	0.930484i	0.0349246	+	0.00104081i
$895$	1489.82	+	741.446i	1.66461	+	0.828431i
$896$	204.364	+	43.2489i	0.228085	+	0.0482689i
$897$		−	44.7098i		−	0.0498437i
$898$	1094.18	+	32.6083i	1.21846	+	0.0363121i
$899$		−	46.7655i		−	0.0520195i
$900$	131.367	+	197.205i	0.145963	+	0.219117i
$901$	272.397			0.302327
$902$	17.5507	−	588.918i	0.0194575	−	0.652903i
$903$	−221.114			−0.244866
$904$	75.6943	−	844.641i	0.0837326	−	0.934337i
$905$	−178.228	+	358.122i	−0.196937	+	0.395715i
$906$	4.33005	−	145.296i	0.00477930	−	0.160371i
$907$	748.615			0.825375			0.412687	−	0.910873i	$-0.364590\pi$
$907$	748.615			0.825375			0.412687	+	0.910873i	$0.364590\pi$
$908$	−551.905	−	32.9246i	−0.607825	−	0.0362605i
$909$	−80.7392			−0.0888219
$910$	32.7637	+	17.5422i	0.0360041	+	0.0192772i
$911$		−	914.813i		−	1.00419i	−0.864814	−	0.502093i	$-0.832564\pi$
$911$		−	914.813i		−	1.00419i	0.864814	−	0.502093i	$-0.167436\pi$
$912$	21.3507	−	178.311i	0.0234108	−	0.195516i
$913$		−	555.464i		−	0.608395i
$914$	18.7718	−	629.892i	0.0205381	−	0.689159i
$915$	469.584	−	943.559i	0.513207	−	1.03121i
$916$	837.468	+	49.9601i	0.914266	+	0.0545416i
$917$			273.261i			0.297994i
$918$	−9.92787	+	333.132i	−0.0108147	+	0.362889i
$919$			1558.01i			1.69534i	0.530527	+	0.847668i	$0.321994\pi$
$919$			1558.01i			1.69534i	−0.530527	+	0.847668i	$0.678006\pi$
$920$	−159.712	+	259.818i	−0.173600	+	0.282411i
$921$	1109.02			1.20415
$922$	1783.07	+	53.1383i	1.93391	+	0.0576337i
$923$	151.885			0.164555
$924$	10.0807	−	168.980i	0.0109098	−	0.182878i
$925$	1059.34	−	800.692i	1.14524	−	0.865613i
$926$	−857.011	−	25.5403i	−0.925498	−	0.0275813i
$927$	−39.3895			−0.0424914
$928$	355.096	+	53.2912i	0.382646	+	0.0574259i
$929$	220.609			0.237470			0.118735	−	0.992926i	$-0.462116\pi$
$929$	220.609			0.237470			0.118735	+	0.992926i	$0.462116\pi$
$930$	94.6089	+	50.6551i	0.101730	+	0.0544679i
$931$		−	201.977i		−	0.216946i
$932$	79.0623	−	1325.30i	0.0848308	−	1.42199i
$933$		−	42.5059i		−	0.0455583i
$934$	−13.5989	−	0.405269i	−0.0145599	−	0.000433907i
$935$	−127.701	+	256.595i	−0.136578	+	0.274433i
$936$	−3.85324	+	42.9967i	−0.00411671	+	0.0459366i
$937$		−	221.948i		−	0.236871i	−0.992962	−	0.118436i	$-0.962212\pi$
$937$		−	221.948i		−	0.236871i	0.992962	−	0.118436i	$-0.0377879\pi$
$938$	−90.7622	−	2.70486i	−0.0967614	−	0.00288364i
$939$			570.393i			0.607447i
$940$	−442.497	+	770.388i	−0.470742	+	0.819561i
$941$	574.430			0.610447			0.305223	−	0.952281i	$-0.401269\pi$
$941$	574.430			0.610447			0.305223	+	0.952281i	$0.401269\pi$
$942$	17.6043	−	590.715i	0.0186882	−	0.627086i
$943$	−223.031			−0.236512
$944$	−61.2586	+	511.603i	−0.0648926	+	0.541952i
$945$	−106.435	+	213.866i	−0.112630	+	0.226313i
$946$	31.5703	−	1059.35i	0.0333724	−	1.11982i
$947$	1124.47			1.18741			0.593703	−	0.804684i	$-0.297665\pi$
$947$	1124.47			1.18741			0.593703	+	0.804684i	$0.297665\pi$
$948$	53.3636	−	894.518i	0.0562907	−	0.943585i
$949$	−182.133			−0.191921
$950$	−177.705	+	126.178i	−0.187058	+	0.132819i
$951$		−	682.003i		−	0.717143i
$952$	6.63311	−	74.0161i	0.00696755	−	0.0777480i
$953$			143.423i			0.150497i	0.997165	+	0.0752483i	$0.0239750\pi$
$953$			143.423i			0.150497i	−0.997165	+	0.0752483i	$0.976025\pi$
$954$	−6.75582	+	226.693i	−0.00708158	+	0.237624i
$955$	−1177.99	−	586.256i	−1.23350	−	0.613881i
$956$	35.5430	−	595.797i	0.0371789	−	0.623219i
$957$		−	290.984i		−	0.304059i
$958$	6.99136	−	234.597i	0.00729787	−	0.244882i
$959$			70.1046i			0.0731018i
$960$	−492.441	+	660.652i	−0.512959	+	0.688180i
$961$	943.630			0.981926
$962$	241.813	+	7.20643i	0.251365	+	0.00749109i
$963$	18.6334			0.0193494
$964$	326.297	+	19.4656i	0.338483	+	0.0201926i
$965$	560.045	+	278.720i	0.580358	+	0.288829i
$966$	−64.0517	−	1.90884i	−0.0663061	−	0.00197603i
$967$	1582.65			1.63666			0.818328	−	0.574751i	$-0.194901\pi$
$967$	1582.65			1.63666			0.818328	+	0.574751i	$0.194901\pi$
$968$	−156.002	−	13.9804i	−0.161159	−	0.0144426i
$969$	−63.8871			−0.0659310
$970$	1532.41	+	820.476i	1.57980	+	0.845851i
$971$			1293.41i			1.33204i	0.745934	+	0.666020i	$0.232003\pi$
$971$			1293.41i			1.33204i	−0.745934	+	0.666020i	$0.767997\pi$
$972$	−496.255	−	29.6047i	−0.510551	−	0.0304575i
$973$		−	303.091i		−	0.311501i
$974$	−717.261	−	21.3755i	−0.736407	−	0.0219461i
$975$	−116.950	+	88.3956i	−0.119949	+	0.0906622i
$976$	−1300.49	−	155.719i	−1.33247	−	0.159548i
$977$			820.617i			0.839936i	0.907539	+	0.419968i	$0.137959\pi$
$977$			820.617i			0.839936i	−0.907539	+	0.419968i	$0.862041\pi$
$978$	−605.924	−	18.0575i	−0.619554	−	0.0184637i
$979$		−	239.574i		−	0.244713i
$980$	−461.577	+	803.606i	−0.470997	+	0.820006i
$981$	369.436			0.376591
$982$	−3.32137	+	111.449i	−0.00338225	+	0.113492i
$983$	−872.279			−0.887364			−0.443682	−	0.896184i	$-0.646328\pi$
$983$	−872.279			−0.887364			−0.443682	+	0.896184i	$0.646328\pi$
$984$	−600.174	−	53.7859i	−0.609933	−	0.0546605i
$985$	−736.426	−	366.500i	−0.747641	−	0.372081i
$986$	3.80516	−	127.683i	0.00385919	−	0.129496i
$987$	−186.669			−0.189128
$988$	−39.6354	−	2.36450i	−0.0401168	−	0.00239322i
$989$	−401.189			−0.405651
$990$	−210.375	−	112.638i	−0.212500	−	0.113776i
$991$		−	1585.91i		−	1.60031i	−0.599791	−	0.800157i	$-0.704750\pi$
$991$		−	1585.91i		−	1.60031i	0.599791	−	0.800157i	$-0.295250\pi$
$992$	19.7933	−	131.889i	0.0199529	−	0.132952i
$993$		−	1309.32i		−	1.31855i
$994$	6.48456	−	217.591i	0.00652370	−	0.218904i
$995$	1394.92	+	694.212i	1.40193	+	0.697701i
$996$	−567.089	−	33.8304i	−0.569367	−	0.0339662i
$997$			1569.26i			1.57398i	0.616966	+	0.786989i	$0.288361\pi$
$997$			1569.26i			1.57398i	−0.616966	+	0.786989i	$0.711639\pi$
$998$	8.20053	−	275.171i	0.00821696	−	0.275722i
$999$			1555.03i			1.55659i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.3.h.a.39.1	✓	108
4.3	odd	2	inner	380.3.h.a.39.107	yes	108
5.4	even	2	inner	380.3.h.a.39.108	yes	108
20.19	odd	2	inner	380.3.h.a.39.2	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.3.h.a.39.1	✓	108	1.1	even	1	trivial
380.3.h.a.39.2	yes	108	20.19	odd	2	inner
380.3.h.a.39.107	yes	108	4.3	odd	2	inner
380.3.h.a.39.108	yes	108	5.4	even	2	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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	380.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.99911 - 0.0595768i) q^{2} -2.57497 q^{3} +(3.99290 + 0.238201i) q^{4} +(2.22773 - 4.47629i) q^{5} +(5.14765 + 0.153408i) q^{6} -1.63196 q^{7} +(-7.96807 - 0.714075i) q^{8} -2.36954 q^{9} +O(q^{10})\)	\(q+(-1.99911 - 0.0595768i) q^{2} -2.57497 q^{3} +(3.99290 + 0.238201i) q^{4} +(2.22773 - 4.47629i) q^{5} +(5.14765 + 0.153408i) q^{6} -1.63196 q^{7} +(-7.96807 - 0.714075i) q^{8} -2.36954 q^{9} +(-4.72017 + 8.81589i) q^{10} -10.0708i q^{11} +(-10.2816 - 0.613361i) q^{12} +2.27729i q^{13} +(3.26246 + 0.0972267i) q^{14} +(-5.73634 + 11.5263i) q^{15} +(15.8865 + 1.90223i) q^{16} -5.69199i q^{17} +(4.73697 + 0.141169i) q^{18} +4.35890i q^{19} +(9.96138 - 17.3428i) q^{20} +4.20224 q^{21} +(-0.599987 + 20.1327i) q^{22} +7.62452 q^{23} +(20.5175 + 1.83872i) q^{24} +(-15.0744 - 19.9440i) q^{25} +(0.135674 - 4.55256i) q^{26} +29.2762 q^{27} +(-6.51624 - 0.388734i) q^{28} -11.2210 q^{29} +(12.1543 - 22.7006i) q^{30} +4.16767i q^{31} +(-31.6456 - 4.74924i) q^{32} +25.9321i q^{33} +(-0.339111 + 11.3789i) q^{34} +(-3.63556 + 7.30512i) q^{35} +(-9.46133 - 0.564427i) q^{36} +53.1159i q^{37} +(0.259689 - 8.71393i) q^{38} -5.86395i q^{39} +(-20.9471 + 34.0766i) q^{40} -29.2518 q^{41} +(-8.40074 - 0.250356i) q^{42} -52.6182 q^{43} +(2.39888 - 40.2118i) q^{44} +(-5.27869 + 10.6067i) q^{45} +(-15.2423 - 0.454244i) q^{46} -44.4213 q^{47} +(-40.9073 - 4.89818i) q^{48} -46.3367 q^{49} +(28.9473 + 40.7683i) q^{50} +14.6567i q^{51} +(-0.542453 + 9.09299i) q^{52} +47.8562i q^{53} +(-58.5264 - 1.74418i) q^{54} +(-45.0800 - 22.4351i) q^{55} +(13.0035 + 1.16534i) q^{56} -11.2240i q^{57} +(22.4321 + 0.668512i) q^{58} +32.2036i q^{59} +(-25.6502 + 44.6570i) q^{60} -81.8613 q^{61} +(0.248296 - 8.33165i) q^{62} +3.86698 q^{63} +(62.9802 + 11.3796i) q^{64} +(10.1938 + 5.07319i) q^{65} +(1.54495 - 51.8411i) q^{66} -27.8201 q^{67} +(1.35584 - 22.7276i) q^{68} -19.6329 q^{69} +(7.70311 - 14.3872i) q^{70} -66.6953i q^{71} +(18.8806 + 1.69203i) q^{72} +79.9780i q^{73} +(3.16448 - 106.185i) q^{74} +(38.8161 + 51.3551i) q^{75} +(-1.03830 + 17.4047i) q^{76} +16.4352i q^{77} +(-0.349355 + 11.7227i) q^{78} +87.0019i q^{79} +(43.9059 - 66.8751i) q^{80} -54.0595 q^{81} +(58.4776 + 1.74273i) q^{82} +55.1557 q^{83} +(16.7791 + 1.00098i) q^{84} +(-25.4790 - 12.6802i) q^{85} +(105.190 + 3.13482i) q^{86} +28.8938 q^{87} +(-7.19133 + 80.2451i) q^{88} +23.7889 q^{89} +(11.1846 - 20.8896i) q^{90} -3.71644i q^{91} +(30.4440 + 1.81617i) q^{92} -10.7316i q^{93} +(88.8032 + 2.64648i) q^{94} +(19.5117 + 9.71046i) q^{95} +(81.4865 + 12.2291i) q^{96} -173.823i q^{97} +(92.6323 + 2.76059i) q^{98} +23.8632i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q + 4 q^{5} + 324 q^{9}+O(q^{10}) \) 108 * q + 4 * q^5 + 324 * q^9	\( 108 q + 4 q^{5} + 324 q^{9} - 8 q^{10} + 8 q^{14} - 104 q^{16} - 16 q^{21} - 8 q^{24} - 76 q^{25} + 80 q^{26} - 88 q^{29} - 140 q^{30} - 88 q^{34} - 256 q^{36} + 44 q^{40} - 200 q^{41} - 8 q^{44} + 108 q^{45} + 272 q^{46} + 916 q^{49} - 276 q^{50} - 320 q^{54} - 328 q^{56} + 172 q^{60} + 200 q^{61} - 216 q^{64} - 192 q^{65} + 152 q^{66} - 592 q^{69} + 200 q^{70} - 232 q^{74} + 340 q^{80} + 1052 q^{81} + 208 q^{84} + 248 q^{85} - 1048 q^{86} + 760 q^{89} + 268 q^{90} - 320 q^{94} + 720 q^{96}+O(q^{100}) \) 108 * q + 4 * q^5 + 324 * q^9 - 8 * q^10 + 8 * q^14 - 104 * q^16 - 16 * q^21 - 8 * q^24 - 76 * q^25 + 80 * q^26 - 88 * q^29 - 140 * q^30 - 88 * q^34 - 256 * q^36 + 44 * q^40 - 200 * q^41 - 8 * q^44 + 108 * q^45 + 272 * q^46 + 916 * q^49 - 276 * q^50 - 320 * q^54 - 328 * q^56 + 172 * q^60 + 200 * q^61 - 216 * q^64 - 192 * q^65 + 152 * q^66 - 592 * q^69 + 200 * q^70 - 232 * q^74 + 340 * q^80 + 1052 * q^81 + 208 * q^84 + 248 * q^85 - 1048 * q^86 + 760 * q^89 + 268 * q^90 - 320 * q^94 + 720 * q^96

Introduction

L-functions

Modular forms

Varieties

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Database

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