LMFDB - Embedded newform 115.3.f.a.47.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,3,Mod(47,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(4))

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("115.47");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	115.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.13352304014$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.16
Character	$\chi$	$=$	115.47
Dual form			115.3.f.a.93.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.03401 + 1.03401i) q^{2} +(2.52164 - 2.52164i) q^{3} -1.86167i q^{4} +(-4.44006 - 2.29910i) q^{5} +5.21478 q^{6} +(1.69314 + 1.69314i) q^{7} +(6.06099 - 6.06099i) q^{8} -3.71736i q^{9} +(-2.21377 - 6.96833i) q^{10} +4.62790 q^{11} +(-4.69446 - 4.69446i) q^{12} +(0.745436 - 0.745436i) q^{13} +3.50143i q^{14} +(-16.9937 + 5.39875i) q^{15} +5.08753 q^{16} +(4.70270 + 4.70270i) q^{17} +(3.84377 - 3.84377i) q^{18} +23.9332i q^{19} +(-4.28015 + 8.26592i) q^{20} +8.53898 q^{21} +(4.78528 + 4.78528i) q^{22} +(-3.39116 + 3.39116i) q^{23} -30.5673i q^{24} +(14.4283 + 20.4163i) q^{25} +1.54157 q^{26} +(13.3209 + 13.3209i) q^{27} +(3.15206 - 3.15206i) q^{28} -4.06450i q^{29} +(-23.1540 - 11.9893i) q^{30} -7.63335 q^{31} +(-18.9834 - 18.9834i) q^{32} +(11.6699 - 11.6699i) q^{33} +9.72524i q^{34} +(-3.62495 - 11.4103i) q^{35} -6.92048 q^{36} +(3.46053 + 3.46053i) q^{37} +(-24.7471 + 24.7471i) q^{38} -3.75945i q^{39} +(-40.8460 + 12.9764i) q^{40} +7.52000 q^{41} +(8.82935 + 8.82935i) q^{42} +(-58.6288 + 58.6288i) q^{43} -8.61561i q^{44} +(-8.54656 + 16.5053i) q^{45} -7.01296 q^{46} +(-28.4763 - 28.4763i) q^{47} +(12.8289 - 12.8289i) q^{48} -43.2666i q^{49} +(-6.19158 + 36.0295i) q^{50} +23.7171 q^{51} +(-1.38775 - 1.38775i) q^{52} +(15.8331 - 15.8331i) q^{53} +27.5478i q^{54} +(-20.5482 - 10.6400i) q^{55} +20.5242 q^{56} +(60.3510 + 60.3510i) q^{57} +(4.20271 - 4.20271i) q^{58} -102.951i q^{59} +(10.0507 + 31.6367i) q^{60} -17.4817 q^{61} +(-7.89292 - 7.89292i) q^{62} +(6.29400 - 6.29400i) q^{63} -59.6081i q^{64} +(-5.02361 + 1.59595i) q^{65} +24.1335 q^{66} +(56.9571 + 56.9571i) q^{67} +(8.75487 - 8.75487i) q^{68} +17.1026i q^{69} +(8.05012 - 15.5466i) q^{70} +100.575 q^{71} +(-22.5309 - 22.5309i) q^{72} +(-78.3607 + 78.3607i) q^{73} +7.15642i q^{74} +(87.8655 + 15.0995i) q^{75} +44.5557 q^{76} +(7.83568 + 7.83568i) q^{77} +(3.88729 - 3.88729i) q^{78} -105.667i q^{79} +(-22.5890 - 11.6967i) q^{80} +100.637 q^{81} +(7.77572 + 7.77572i) q^{82} +(-74.3146 + 74.3146i) q^{83} -15.8967i q^{84} +(-10.0683 - 31.6923i) q^{85} -121.245 q^{86} +(-10.2492 - 10.2492i) q^{87} +(28.0497 - 28.0497i) q^{88} -21.1104i q^{89} +(-25.9038 + 8.22937i) q^{90} +2.52425 q^{91} +(6.31322 + 6.31322i) q^{92} +(-19.2486 + 19.2486i) q^{93} -58.8892i q^{94} +(55.0248 - 106.265i) q^{95} -95.7389 q^{96} +(60.1608 + 60.1608i) q^{97} +(44.7378 - 44.7378i) q^{98} -17.2036i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 4 q^{2} - 8 q^{5} - 16 q^{7} + 12 q^{8} - 4 q^{10} - 24 q^{11} + 48 q^{12} + 4 q^{13} + 60 q^{15} - 224 q^{16} + 24 q^{17} - 88 q^{18} - 56 q^{20} + 8 q^{21} - 48 q^{22} + 84 q^{25} + 56 q^{26} - 132 q^{27}+ \cdots + 780 q^{98}+O(q^{100}) $ 44 * q - 4 * q^2 - 8 * q^5 - 16 * q^7 + 12 * q^8 - 4 * q^10 - 24 * q^11 + 48 * q^12 + 4 * q^13 + 60 * q^15 - 224 * q^16 + 24 * q^17 - 88 * q^18 - 56 * q^20 + 8 * q^21 - 48 * q^22 + 84 * q^25 + 56 * q^26 - 132 * q^27 + 204 * q^28 - 200 * q^30 + 100 * q^31 + 184 * q^32 - 68 * q^33 - 48 * q^35 + 552 * q^36 - 48 * q^37 - 52 * q^38 + 200 * q^40 - 132 * q^41 - 248 * q^42 + 128 * q^43 + 204 * q^45 + 152 * q^47 - 500 * q^48 - 228 * q^50 - 264 * q^51 + 280 * q^52 + 324 * q^53 - 156 * q^55 - 312 * q^56 + 320 * q^57 + 364 * q^58 + 500 * q^60 + 32 * q^61 - 44 * q^62 - 220 * q^63 - 196 * q^65 - 552 * q^66 - 352 * q^67 - 616 * q^68 + 188 * q^70 + 108 * q^71 - 192 * q^72 + 168 * q^73 - 468 * q^75 + 464 * q^76 - 292 * q^77 + 596 * q^78 - 316 * q^80 - 332 * q^81 - 820 * q^82 - 144 * q^83 - 524 * q^85 + 536 * q^86 + 536 * q^87 - 132 * q^88 + 260 * q^90 + 312 * q^91 - 416 * q^93 + 304 * q^95 + 448 * q^96 + 620 * q^97 + 780 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	1.03401	+	1.03401i	0.517003	+	0.517003i	0.916663	−	0.399661i	$-0.130872\pi$
$2$	1.03401	+	1.03401i	0.517003	+	0.517003i	−0.399661	+	0.916663i	$0.630872\pi$
$3$	2.52164	−	2.52164i	0.840547	−	0.840547i	−0.148383	−	0.988930i	$-0.547407\pi$
$3$	2.52164	−	2.52164i	0.840547	−	0.840547i	0.988930	+	0.148383i	$0.0474067\pi$
$4$		−	1.86167i		−	0.465417i
$5$	−4.44006	−	2.29910i	−0.888012	−	0.459819i
$5$	−4.44006	−	2.29910i	−0.888012	−	0.459819i
$6$	5.21478			0.869130
$7$	1.69314	+	1.69314i	0.241877	+	0.241877i	0.817626	−	0.575749i	$-0.195290\pi$
$7$	1.69314	+	1.69314i	0.241877	+	0.241877i	−0.575749	+	0.817626i	$0.695290\pi$
$8$	6.06099	−	6.06099i	0.757624	−	0.757624i
$9$		−	3.71736i		−	0.413040i
$10$	−2.21377	−	6.96833i	−0.221377	−	0.696833i
$11$	4.62790			0.420719			0.210359	−	0.977624i	$-0.432537\pi$
$11$	4.62790			0.420719			0.210359	+	0.977624i	$0.432537\pi$
$12$	−4.69446	−	4.69446i	−0.391205	−	0.391205i
$13$	0.745436	−	0.745436i	0.0573413	−	0.0573413i	−0.677855	−	0.735196i	$-0.737090\pi$
$13$	0.745436	−	0.745436i	0.0573413	−	0.0573413i	0.735196	+	0.677855i	$0.237090\pi$
$14$			3.50143i			0.250102i
$15$	−16.9937	+	5.39875i	−1.13292	+	0.359917i
$16$	5.08753			0.317971
$17$	4.70270	+	4.70270i	0.276630	+	0.276630i	0.831762	−	0.555132i	$-0.187332\pi$
$17$	4.70270	+	4.70270i	0.276630	+	0.276630i	−0.555132	+	0.831762i	$0.687332\pi$
$18$	3.84377	−	3.84377i	0.213543	−	0.213543i
$19$			23.9332i			1.25964i	0.776740	+	0.629822i	$0.216872\pi$
$19$			23.9332i			1.25964i	−0.776740	+	0.629822i	$0.783128\pi$
$20$	−4.28015	+	8.26592i	−0.214008	+	0.413296i
$21$	8.53898			0.406618
$22$	4.78528	+	4.78528i	0.217513	+	0.217513i
$23$	−3.39116	+	3.39116i	−0.147442	+	0.147442i
$23$	−3.39116	+	3.39116i	−0.147442	+	0.147442i
$24$		−	30.5673i		−	1.27364i
$25$	14.4283	+	20.4163i	0.577132	+	0.816651i
$26$	1.54157			0.0592912
$27$	13.3209	+	13.3209i	0.493368	+	0.493368i
$28$	3.15206	−	3.15206i	0.112574	−	0.112574i
$29$		−	4.06450i		−	0.140155i	−0.997542	−	0.0700775i	$-0.977675\pi$
$29$		−	4.06450i		−	0.140155i	0.997542	−	0.0700775i	$-0.0223247\pi$
$30$	−23.1540	−	11.9893i	−0.771799	−	0.399643i
$31$	−7.63335			−0.246237			−0.123119	−	0.992392i	$-0.539290\pi$
$31$	−7.63335			−0.246237			−0.123119	+	0.992392i	$0.539290\pi$
$32$	−18.9834	−	18.9834i	−0.593232	−	0.593232i
$33$	11.6699	−	11.6699i	0.353634	−	0.353634i
$34$			9.72524i			0.286036i
$35$	−3.62495	−	11.4103i	−0.103570	−	0.326010i
$36$	−6.92048			−0.192235
$37$	3.46053	+	3.46053i	0.0935280	+	0.0935280i	0.752323	−	0.658795i	$-0.228933\pi$
$37$	3.46053	+	3.46053i	0.0935280	+	0.0935280i	−0.658795	+	0.752323i	$0.728933\pi$
$38$	−24.7471	+	24.7471i	−0.651239	+	0.651239i
$39$		−	3.75945i		−	0.0963961i
$40$	−40.8460	+	12.9764i	−1.02115	+	0.324410i
$41$	7.52000			0.183415			0.0917073	−	0.995786i	$-0.470768\pi$
$41$	7.52000			0.183415			0.0917073	+	0.995786i	$0.470768\pi$
$42$	8.82935	+	8.82935i	0.210223	+	0.210223i
$43$	−58.6288	+	58.6288i	−1.36346	+	1.36346i	−0.493995	+	0.869465i	$0.664464\pi$
$43$	−58.6288	+	58.6288i	−1.36346	+	1.36346i	−0.869465	+	0.493995i	$0.835536\pi$
$44$		−	8.61561i		−	0.195809i
$45$	−8.54656	+	16.5053i	−0.189924	+	0.366784i
$46$	−7.01296			−0.152456
$47$	−28.4763	−	28.4763i	−0.605878	−	0.605878i	0.335988	−	0.941866i	$-0.390930\pi$
$47$	−28.4763	−	28.4763i	−0.605878	−	0.605878i	−0.941866	+	0.335988i	$0.890930\pi$
$48$	12.8289	−	12.8289i	0.267269	−	0.267269i
$49$		−	43.2666i		−	0.882991i
$50$	−6.19158	+	36.0295i	−0.123832	+	0.720589i
$51$	23.7171			0.465041
$52$	−1.38775	−	1.38775i	−0.0266876	−	0.0266876i
$53$	15.8331	−	15.8331i	0.298738	−	0.298738i	−0.541781	−	0.840520i	$-0.682250\pi$
$53$	15.8331	−	15.8331i	0.298738	−	0.298738i	0.840520	+	0.541781i	$0.182250\pi$
$54$			27.5478i			0.510145i
$55$	−20.5482	−	10.6400i	−0.373603	−	0.193455i
$56$	20.5242			0.366504
$57$	60.3510	+	60.3510i	1.05879	+	1.05879i
$58$	4.20271	−	4.20271i	0.0724606	−	0.0724606i
$59$		−	102.951i		−	1.74494i	−0.488669	−	0.872469i	$-0.662518\pi$
$59$		−	102.951i		−	1.74494i	0.488669	−	0.872469i	$-0.337482\pi$
$60$	10.0507	+	31.6367i	0.167511	+	0.527278i
$61$	−17.4817			−0.286586			−0.143293	−	0.989680i	$-0.545769\pi$
$61$	−17.4817			−0.286586			−0.143293	+	0.989680i	$0.545769\pi$
$62$	−7.89292	−	7.89292i	−0.127305	−	0.127305i
$63$	6.29400	−	6.29400i	0.0999048	−	0.0999048i
$64$		−	59.6081i		−	0.931376i
$65$	−5.02361	+	1.59595i	−0.0772864	+	0.0245531i
$66$	24.1335			0.365659
$67$	56.9571	+	56.9571i	0.850106	+	0.850106i	0.990146	−	0.140039i	$-0.0447229\pi$
$67$	56.9571	+	56.9571i	0.850106	+	0.850106i	−0.140039	+	0.990146i	$0.544723\pi$
$68$	8.75487	−	8.75487i	0.128748	−	0.128748i
$69$			17.1026i			0.247864i
$70$	8.05012	−	15.5466i	0.115002	−	0.222094i
$71$	100.575			1.41656			0.708278	−	0.705934i	$-0.249472\pi$
$71$	100.575			1.41656			0.708278	+	0.705934i	$0.249472\pi$
$72$	−22.5309	−	22.5309i	−0.312929	−	0.312929i
$73$	−78.3607	+	78.3607i	−1.07343	+	1.07343i	−0.0763528	+	0.997081i	$0.524328\pi$
$73$	−78.3607	+	78.3607i	−1.07343	+	1.07343i	−0.997081	+	0.0763528i	$0.975672\pi$
$74$			7.15642i			0.0967084i
$75$	87.8655	+	15.0995i	1.17154	+	0.201326i
$76$	44.5557			0.586259
$77$	7.83568	+	7.83568i	0.101762	+	0.101762i
$78$	3.88729	−	3.88729i	0.0498370	−	0.0498370i
$79$		−	105.667i		−	1.33755i	−0.743463	−	0.668777i	$-0.766818\pi$
$79$		−	105.667i		−	1.33755i	0.743463	−	0.668777i	$-0.233182\pi$
$80$	−22.5890	−	11.6967i	−0.282362	−	0.146209i
$81$	100.637			1.24244
$82$	7.77572	+	7.77572i	0.0948258	+	0.0948258i
$83$	−74.3146	+	74.3146i	−0.895357	+	0.895357i	−0.995021	−	0.0996640i	$-0.968223\pi$
$83$	−74.3146	+	74.3146i	−0.895357	+	0.895357i	0.0996640	+	0.995021i	$0.468223\pi$
$84$		−	15.8967i		−	0.189247i
$85$	−10.0683	−	31.6923i	−0.118451	−	0.372850i
$86$	−121.245			−1.40982
$87$	−10.2492	−	10.2492i	−0.117807	−	0.117807i
$88$	28.0497	−	28.0497i	0.318747	−	0.318747i
$89$		−	21.1104i		−	0.237196i	−0.992942	−	0.118598i	$-0.962160\pi$
$89$		−	21.1104i		−	0.237196i	0.992942	−	0.118598i	$-0.0378399\pi$
$90$	−25.9038	+	8.22937i	−0.287819	+	0.0914375i
$91$	2.52425			0.0277391
$92$	6.31322	+	6.31322i	0.0686219	+	0.0686219i
$93$	−19.2486	+	19.2486i	−0.206974	+	0.206974i
$94$		−	58.8892i		−	0.626481i
$95$	55.0248	−	106.265i	0.579208	−	1.11858i
$96$	−95.7389			−0.997280
$97$	60.1608	+	60.1608i	0.620214	+	0.620214i	0.945586	−	0.325372i	$-0.105489\pi$
$97$	60.1608	+	60.1608i	0.620214	+	0.620214i	−0.325372	+	0.945586i	$0.605489\pi$
$98$	44.7378	−	44.7378i	0.456509	−	0.456509i
$99$		−	17.2036i		−	0.173773i
$100$	38.0083	−	26.8607i	0.380083	−	0.268607i
$101$	−55.6355			−0.550846			−0.275423	−	0.961323i	$-0.588818\pi$
$101$	−55.6355			−0.550846			−0.275423	+	0.961323i	$0.588818\pi$
$102$	24.5236	+	24.5236i	0.240427	+	0.240427i
$103$	28.9656	−	28.9656i	0.281219	−	0.281219i	−0.552376	−	0.833595i	$-0.686279\pi$
$103$	28.9656	−	28.9656i	0.281219	−	0.281219i	0.833595	+	0.552376i	$0.186279\pi$
$104$		−	9.03617i		−	0.0868862i
$105$	−37.9136	−	19.6319i	−0.361082	−	0.186971i
$106$	32.7431			0.308897
$107$	−100.699	−	100.699i	−0.941109	−	0.941109i	0.0572512	−	0.998360i	$-0.481766\pi$
$107$	−100.699	−	100.699i	−0.941109	−	0.941109i	−0.998360	+	0.0572512i	$0.981766\pi$
$108$	24.7991	−	24.7991i	0.229622	−	0.229622i
$109$			87.1751i			0.799772i	0.916565	+	0.399886i	$0.130950\pi$
$109$			87.1751i			0.799772i	−0.916565	+	0.399886i	$0.869050\pi$
$110$	−10.2451	−	32.2487i	−0.0931374	−	0.293170i
$111$	17.4525			0.157229
$112$	8.61390	+	8.61390i	0.0769098	+	0.0769098i
$113$	−53.7810	+	53.7810i	−0.475938	+	0.475938i	−0.903830	−	0.427892i	$-0.859256\pi$
$113$	−53.7810	+	53.7810i	−0.475938	+	0.475938i	0.427892	+	0.903830i	$0.359256\pi$
$114$			124.807i			1.09479i
$115$	22.8536	−	7.26037i	0.198727	−	0.0631336i
$116$	−7.56674			−0.0652305
$117$	−2.77105	−	2.77105i	−0.0236842	−	0.0236842i
$118$	106.452	−	106.452i	0.902138	−	0.902138i
$119$			15.9247i			0.133821i
$120$	−70.2772	+	135.721i	−0.585643	+	1.13101i
$121$	−99.5825			−0.822996
$122$	−18.0762	−	18.0762i	−0.148166	−	0.148166i
$123$	18.9627	−	18.9627i	0.154169	−	0.154169i
$124$			14.2107i			0.114603i
$125$	−17.1236	−	123.822i	−0.136989	−	0.990573i
$126$	13.0161			0.103302
$127$	94.1613	+	94.1613i	0.741428	+	0.741428i	0.972853	−	0.231425i	$-0.0743388\pi$
$127$	94.1613	+	94.1613i	0.741428	+	0.741428i	−0.231425	+	0.972853i	$0.574339\pi$
$128$	−14.2987	+	14.2987i	−0.111709	+	0.111709i
$129$			295.682i			2.29210i
$130$	−6.84467	−	3.54422i	−0.0526513	−	0.0272632i
$131$	−66.9879			−0.511358			−0.255679	−	0.966762i	$-0.582299\pi$
$131$	−66.9879			−0.511358			−0.255679	+	0.966762i	$0.582299\pi$
$132$	−21.7255	−	21.7255i	−0.164587	−	0.164587i
$133$	−40.5223	+	40.5223i	−0.304679	+	0.304679i
$134$			117.788i			0.879015i
$135$	−28.5197	−	89.7719i	−0.211257	−	0.664977i
$136$	57.0061			0.419163
$137$	−51.8514	−	51.8514i	−0.378477	−	0.378477i	0.492075	−	0.870553i	$-0.336238\pi$
$137$	−51.8514	−	51.8514i	−0.378477	−	0.378477i	−0.870553	+	0.492075i	$0.836238\pi$
$138$	−17.6842	+	17.6842i	−0.128146	+	0.128146i
$139$			196.107i			1.41084i	0.708787	+	0.705422i	$0.249243\pi$
$139$			196.107i			1.41084i	−0.708787	+	0.705422i	$0.750757\pi$
$140$	−21.2422	+	6.74845i	−0.151730	+	0.0482032i
$141$	−143.614			−1.01854
$142$	103.996	+	103.996i	0.732363	+	0.732363i
$143$	3.44981	−	3.44981i	0.0241245	−	0.0241245i
$144$		−	18.9122i		−	0.131335i
$145$	−9.34467	+	18.0466i	−0.0644460	+	0.124459i
$146$	−162.051			−1.10994
$147$	−109.103	−	109.103i	−0.742196	−	0.742196i
$148$	6.44236	−	6.44236i	0.0435295	−	0.0435295i
$149$		−	153.289i		−	1.02878i	−0.857555	−	0.514392i	$-0.828018\pi$
$149$		−	153.289i		−	1.02878i	0.857555	−	0.514392i	$-0.171982\pi$
$150$	75.2405	+	106.466i	0.501603	+	0.709776i
$151$	60.5080			0.400715			0.200358	−	0.979723i	$-0.435790\pi$
$151$	60.5080			0.400715			0.200358	+	0.979723i	$0.435790\pi$
$152$	145.059	+	145.059i	0.954336	+	0.954336i
$153$	17.4816	−	17.4816i	0.114259	−	0.114259i
$154$			16.2043i			0.105223i
$155$	33.8925	+	17.5498i	0.218662	+	0.113225i
$156$	−6.99884			−0.0448643
$157$	−136.999	−	136.999i	−0.872607	−	0.872607i	0.120149	−	0.992756i	$-0.461663\pi$
$157$	−136.999	−	136.999i	−0.872607	−	0.872607i	−0.992756	+	0.120149i	$0.961663\pi$
$158$	109.260	−	109.260i	0.691519	−	0.691519i
$159$		−	79.8510i		−	0.502208i
$160$	40.6429	+	127.932i	0.254018	+	0.799578i
$161$	−11.4834			−0.0713256
$162$	104.060	+	104.060i	0.642344	+	0.642344i
$163$	121.580	−	121.580i	0.745889	−	0.745889i	−0.227815	−	0.973704i	$-0.573158\pi$
$163$	121.580	−	121.580i	0.745889	−	0.745889i	0.973704	+	0.227815i	$0.0731582\pi$
$164$		−	13.9997i		−	0.0853642i
$165$	−78.6454	+	24.9849i	−0.476639	+	0.151424i
$166$	−153.683			−0.925804
$167$	−139.121	−	139.121i	−0.833058	−	0.833058i	0.154876	−	0.987934i	$-0.450502\pi$
$167$	−139.121	−	139.121i	−0.833058	−	0.833058i	−0.987934	+	0.154876i	$0.950502\pi$
$168$	51.7547	−	51.7547i	0.308064	−	0.308064i
$169$			167.889i			0.993424i
$170$	22.3593	−	43.1807i	0.131525	−	0.254004i
$171$	88.9683			0.520283
$172$	109.147	+	109.147i	0.634577	+	0.634577i
$173$	−213.651	+	213.651i	−1.23498	+	1.23498i	−0.272951	+	0.962028i	$0.588000\pi$
$173$	−213.651	+	213.651i	−1.23498	+	1.23498i	−0.962028	+	0.272951i	$0.912000\pi$
$174$		−	21.1955i		−	0.121813i
$175$	−10.1384	+	58.9967i	−0.0579340	+	0.337124i
$176$	23.5446			0.133776
$177$	−259.606	−	259.606i	−1.46670	−	1.46670i
$178$	21.8283	−	21.8283i	0.122631	−	0.122631i
$179$		−	151.633i		−	0.847111i	−0.905870	−	0.423555i	$-0.860782\pi$
$179$		−	151.633i		−	0.847111i	0.905870	−	0.423555i	$-0.139218\pi$
$180$	30.7274	+	15.9108i	0.170708	+	0.0883936i
$181$	−188.498			−1.04143			−0.520713	−	0.853731i	$-0.674334\pi$
$181$	−188.498			−1.04143			−0.520713	+	0.853731i	$0.674334\pi$
$182$	2.61009	+	2.61009i	0.0143412	+	0.0143412i
$183$	−44.0827	+	44.0827i	−0.240889	+	0.240889i
$184$			41.1077i			0.223411i
$185$	−7.40889	−	23.3211i	−0.0400480	−	0.126060i
$186$	−39.8062			−0.214012
$187$	21.7637	+	21.7637i	0.116383	+	0.116383i
$188$	−53.0133	+	53.0133i	−0.281986	+	0.281986i
$189$			45.1084i			0.238669i
$190$	166.775	−	52.9827i	0.877761	−	0.278856i
$191$	380.375			1.99149			0.995747	−	0.0921270i	$-0.0293666\pi$
$191$	380.375			1.99149			0.995747	+	0.0921270i	$0.0293666\pi$
$192$	−150.310	−	150.310i	−0.782866	−	0.782866i
$193$	201.433	−	201.433i	1.04369	−	1.04369i	0.0446920	−	0.999001i	$-0.485769\pi$
$193$	201.433	−	201.433i	1.04369	−	1.04369i	0.999001	−	0.0446920i	$-0.0142306\pi$
$194$			124.413i			0.641305i
$195$	−8.64333	+	16.6922i	−0.0443248	+	0.0856009i
$196$	−80.5479			−0.410959
$197$	−104.279	−	104.279i	−0.529333	−	0.529333i	0.391040	−	0.920374i	$-0.372115\pi$
$197$	−104.279	−	104.279i	−0.529333	−	0.529333i	−0.920374	+	0.391040i	$0.872115\pi$
$198$	17.7886	−	17.7886i	0.0898413	−	0.0898413i
$199$		−	387.138i		−	1.94542i	−0.232026	−	0.972709i	$-0.574536\pi$
$199$		−	387.138i		−	1.94542i	0.232026	−	0.972709i	$-0.425464\pi$
$200$	211.193	+	36.2930i	1.05596	+	0.181465i
$201$	287.251			1.42911
$202$	−57.5274	−	57.5274i	−0.284789	−	0.284789i
$203$	6.88176	−	6.88176i	0.0339003	−	0.0339003i
$204$		−	44.1533i		−	0.216438i
$205$	−33.3893	−	17.2892i	−0.162874	−	0.0843376i
$206$	59.9011			0.290782
$207$	12.6062	+	12.6062i	0.0608994	+	0.0608994i
$208$	3.79243	−	3.79243i	0.0182328	−	0.0182328i
$209$			110.761i			0.529955i
$210$	−18.9033	−	59.5024i	−0.0900159	−	0.283345i
$211$	169.957			0.805484			0.402742	−	0.915314i	$-0.368057\pi$
$211$	169.957			0.805484			0.402742	+	0.915314i	$0.368057\pi$
$212$	−29.4760	−	29.4760i	−0.139038	−	0.139038i
$213$	253.615	−	253.615i	1.19068	−	1.19068i
$214$		−	208.246i		−	0.973111i
$215$	395.109	−	125.522i	1.83771	−	0.583824i
$216$	161.476			0.747575
$217$	−12.9243	−	12.9243i	−0.0595591	−	0.0595591i
$218$	−90.1395	+	90.1395i	−0.413484	+	0.413484i
$219$			395.195i			1.80454i
$220$	−19.8081	+	38.2539i	−0.0900369	+	0.173881i
$221$	7.01113			0.0317246
$222$	18.0459	+	18.0459i	0.0812880	+	0.0812880i
$223$	−28.1137	+	28.1137i	−0.126071	+	0.126071i	−0.767327	−	0.641256i	$-0.778414\pi$
$223$	−28.1137	+	28.1137i	−0.126071	+	0.126071i	0.641256	+	0.767327i	$0.278414\pi$
$224$		−	64.2832i		−	0.286979i
$225$	75.8945	−	53.6352i	0.337309	−	0.238379i
$226$	−111.220			−0.492122
$227$	74.0799	+	74.0799i	0.326343	+	0.326343i	0.851194	−	0.524851i	$-0.175879\pi$
$227$	74.0799	+	74.0799i	0.326343	+	0.326343i	−0.524851	+	0.851194i	$0.675879\pi$
$228$	112.353	−	112.353i	0.492778	−	0.492778i
$229$			269.439i			1.17659i	0.808647	+	0.588294i	$0.200200\pi$
$229$			269.439i			1.17659i	−0.808647	+	0.588294i	$0.799800\pi$
$230$	31.1380	+	16.1235i	0.135383	+	0.0701021i
$231$	39.5176			0.171072
$232$	−24.6349	−	24.6349i	−0.106185	−	0.106185i
$233$	−59.1211	+	59.1211i	−0.253739	+	0.253739i	−0.822502	−	0.568763i	$-0.807422\pi$
$233$	−59.1211	+	59.1211i	−0.253739	+	0.253739i	0.568763	+	0.822502i	$0.307422\pi$
$234$		−	5.73057i		−	0.0244896i
$235$	60.9667	+	191.906i	0.259433	+	0.816622i
$236$	−191.661			−0.812123
$237$	−266.454	−	266.454i	−1.12428	−	1.12428i
$238$	−16.4662	+	16.4662i	−0.0691856	+	0.0691856i
$239$		−	224.425i		−	0.939016i	−0.882928	−	0.469508i	$-0.844431\pi$
$239$		−	224.425i		−	0.939016i	0.882928	−	0.469508i	$-0.155569\pi$
$240$	−86.4562	+	27.4663i	−0.360234	+	0.114443i
$241$	−224.036			−0.929610			−0.464805	−	0.885413i	$-0.653876\pi$
$241$	−224.036			−0.929610			−0.464805	+	0.885413i	$0.653876\pi$
$242$	−102.969	−	102.969i	−0.425491	−	0.425491i
$243$	133.883	−	133.883i	0.550960	−	0.550960i
$244$			32.5452i			0.133382i
$245$	−99.4740	+	192.106i	−0.406016	+	0.784107i
$246$	39.2152			0.159411
$247$	17.8407	+	17.8407i	0.0722295	+	0.0722295i
$248$	−46.2657	+	46.2657i	−0.186555	+	0.186555i
$249$			374.790i			1.50518i
$250$	110.326	−	145.738i	0.441305	−	0.582952i
$251$	−121.909			−0.485695			−0.242847	−	0.970065i	$-0.578081\pi$
$251$	−121.909			−0.485695			−0.242847	+	0.970065i	$0.578081\pi$
$252$	−11.7173	−	11.7173i	−0.0464973	−	0.0464973i
$253$	−15.6940	+	15.6940i	−0.0620316	+	0.0620316i
$254$			194.727i			0.766640i
$255$	−105.305	−	54.5278i	−0.412962	−	0.213835i
$256$	−268.002			−1.04688
$257$	306.849	+	306.849i	1.19397	+	1.19397i	0.975944	+	0.218023i	$0.0699607\pi$
$257$	306.849	+	306.849i	1.19397	+	1.19397i	0.218023	+	0.975944i	$0.430039\pi$
$258$	−305.736	+	305.736i	−1.18502	+	1.18502i
$259$			11.7183i			0.0452445i
$260$	2.97113	+	9.35229i	0.0114274	+	0.0359704i
$261$	−15.1092			−0.0578896
$262$	−69.2659	−	69.2659i	−0.264374	−	0.264374i
$263$	−277.398	+	277.398i	−1.05474	+	1.05474i	−0.0563322	+	0.998412i	$0.517941\pi$
$263$	−277.398	+	277.398i	−1.05474	+	1.05474i	−0.998412	+	0.0563322i	$0.982059\pi$
$264$		−	141.463i		−	0.535843i
$265$	−106.702	+	33.8982i	−0.402649	+	0.127918i
$266$	−83.8005			−0.315039
$267$	−53.2329	−	53.2329i	−0.199374	−	0.199374i
$268$	106.035	−	106.035i	0.395654	−	0.395654i
$269$			465.099i			1.72899i	0.502638	+	0.864497i	$0.332363\pi$
$269$			465.099i			1.72899i	−0.502638	+	0.864497i	$0.667637\pi$
$270$	63.3351	−	122.314i	0.234575	−	0.453015i
$271$	−106.366			−0.392493			−0.196247	−	0.980555i	$-0.562875\pi$
$271$	−106.366			−0.392493			−0.196247	+	0.980555i	$0.562875\pi$
$272$	23.9252	+	23.9252i	0.0879601	+	0.0879601i
$273$	6.36527	−	6.36527i	0.0233160	−	0.0233160i
$274$		−	107.229i		−	0.391347i
$275$	66.7728	+	94.4845i	0.242810	+	0.343580i
$276$	31.8394			0.115360
$277$	2.81668	+	2.81668i	0.0101685	+	0.0101685i	0.712173	−	0.702004i	$-0.247711\pi$
$277$	2.81668	+	2.81668i	0.0101685	+	0.0101685i	−0.702004	+	0.712173i	$0.747711\pi$
$278$	−202.776	+	202.776i	−0.729411	+	0.729411i
$279$			28.3759i			0.101706i
$280$	−91.1288	−	47.1871i	−0.325460	−	0.168526i
$281$	335.850			1.19520			0.597598	−	0.801796i	$-0.296122\pi$
$281$	335.850			1.19520			0.597598	+	0.801796i	$0.296122\pi$
$282$	−148.498	−	148.498i	−0.526587	−	0.526587i
$283$	−48.7921	+	48.7921i	−0.172410	+	0.172410i	−0.788037	−	0.615627i	$-0.788903\pi$
$283$	−48.7921	+	48.7921i	−0.172410	+	0.172410i	0.615627	+	0.788037i	$0.288903\pi$
$284$		−	187.238i		−	0.659289i
$285$	−129.209	−	406.715i	−0.453367	−	1.42707i
$286$	7.13424			0.0249449
$287$	12.7324	+	12.7324i	0.0443638	+	0.0443638i
$288$	−70.5682	+	70.5682i	−0.245029	+	0.245029i
$289$		−	244.769i		−	0.846952i
$290$	−28.3227	+	8.99786i	−0.0976646	+	0.0310271i
$291$	303.408			1.04264
$292$	145.881	+	145.881i	0.499594	+	0.499594i
$293$	229.346	−	229.346i	0.782752	−	0.782752i	−0.197542	−	0.980294i	$-0.563296\pi$
$293$	229.346	−	229.346i	0.782752	−	0.782752i	0.980294	+	0.197542i	$0.0632960\pi$
$294$		−	225.626i		−	0.767434i
$295$	−236.695	+	457.110i	−0.802356	+	1.54953i
$296$	41.9486			0.141718
$297$	61.6480	+	61.6480i	0.207569	+	0.207569i
$298$	158.502	−	158.502i	0.531884	−	0.531884i
$299$			5.05579i			0.0169090i
$300$	28.1102	−	163.576i	0.0937007	−	0.545254i
$301$	−198.533			−0.659579
$302$	62.5656	+	62.5656i	0.207171	+	0.207171i
$303$	−140.293	+	140.293i	−0.463012	+	0.463012i
$304$			121.761i			0.400530i
$305$	77.6200	+	40.1922i	0.254492	+	0.131778i
$306$	36.1522			0.118144
$307$	−75.7009	−	75.7009i	−0.246583	−	0.246583i	0.572984	−	0.819567i	$-0.305786\pi$
$307$	−75.7009	−	75.7009i	−0.246583	−	0.246583i	−0.819567	+	0.572984i	$0.805786\pi$
$308$	14.5874	−	14.5874i	0.0473618	−	0.0473618i
$309$		−	146.082i		−	0.472756i
$310$	16.8985	+	53.1917i	0.0545112	+	0.171586i
$311$	58.7187			0.188806			0.0944030	−	0.995534i	$-0.469906\pi$
$311$	58.7187			0.188806			0.0944030	+	0.995534i	$0.469906\pi$
$312$	−22.7860	−	22.7860i	−0.0730320	−	0.0730320i
$313$	−134.806	+	134.806i	−0.430691	+	0.430691i	−0.888863	−	0.458173i	$-0.848504\pi$
$313$	−134.806	+	134.806i	−0.430691	+	0.430691i	0.458173	+	0.888863i	$0.348504\pi$
$314$		−	283.316i		−	0.902280i
$315$	−42.4163	+	13.4752i	−0.134655	+	0.0427785i
$316$	−196.716			−0.622520
$317$	255.375	+	255.375i	0.805598	+	0.805598i	0.983964	−	0.178366i	$-0.0570810\pi$
$317$	255.375	+	255.375i	0.805598	+	0.805598i	−0.178366	+	0.983964i	$0.557081\pi$
$318$	82.5664	−	82.5664i	0.259643	−	0.259643i
$319$		−	18.8101i		−	0.0589658i
$320$	−137.045	+	264.664i	−0.428265	+	0.827074i
$321$	−507.852			−1.58209
$322$	−11.8739	−	11.8739i	−0.0368755	−	0.0368755i
$323$	−112.551	+	112.551i	−0.348455	+	0.348455i
$324$		−	187.353i		−	0.578251i
$325$	25.9744	+	4.46364i	0.0799213	+	0.0137343i
$326$	251.429			0.771253
$327$	219.824	+	219.824i	0.672246	+	0.672246i
$328$	45.5787	−	45.5787i	0.138959	−	0.138959i
$329$		−	96.4286i		−	0.293096i
$330$	−107.154	−	55.4853i	−0.324710	−	0.168137i
$331$	486.015			1.46832			0.734162	−	0.678974i	$-0.237575\pi$
$331$	486.015			1.46832			0.734162	+	0.678974i	$0.237575\pi$
$332$	138.349	+	138.349i	0.416714	+	0.416714i
$333$	12.8640	−	12.8640i	0.0386308	−	0.0386308i
$334$		−	287.703i		−	0.861386i
$335$	−121.943	−	383.843i	−0.364010	−	1.14580i
$336$	43.4423			0.129293
$337$	332.154	+	332.154i	0.985620	+	0.985620i	0.999898	−	0.0142784i	$-0.00454510\pi$
$337$	332.154	+	332.154i	0.985620	+	0.985620i	−0.0142784	+	0.999898i	$0.504545\pi$
$338$	−173.598	+	173.598i	−0.513603	+	0.513603i
$339$			271.233i			0.800096i
$340$	−59.0004	+	18.7439i	−0.173531	+	0.0551290i
$341$	−35.3264			−0.103596
$342$	91.9937	+	91.9937i	0.268988	+	0.268988i
$343$	156.220	−	156.220i	0.455452	−	0.455452i
$344$			710.697i			2.06598i
$345$	39.3205	−	75.9366i	0.113973	−	0.220106i
$346$	−441.833			−1.27697
$347$	136.762	+	136.762i	0.394128	+	0.394128i	0.876156	−	0.482028i	$-0.160100\pi$
$347$	136.762	+	136.762i	0.394128	+	0.394128i	−0.482028	+	0.876156i	$0.660100\pi$
$348$	−19.0806	+	19.0806i	−0.0548293	+	0.0548293i
$349$		−	13.6533i		−	0.0391211i	−0.999809	−	0.0195606i	$-0.993773\pi$
$349$		−	13.6533i		−	0.0391211i	0.999809	−	0.0195606i	$-0.00622672\pi$
$350$	−71.4861	+	50.5197i	−0.204246	+	0.144342i
$351$	19.8598			0.0565807
$352$	−87.8535	−	87.8535i	−0.249584	−	0.249584i
$353$	297.538	−	297.538i	0.842885	−	0.842885i	−0.146348	−	0.989233i	$-0.546752\pi$
$353$	297.538	−	297.538i	0.842885	−	0.842885i	0.989233	+	0.146348i	$0.0467521\pi$
$354$		−	536.869i		−	1.51658i
$355$	−446.561	−	231.233i	−1.25792	−	0.651360i
$356$	−39.3005			−0.110395
$357$	40.1563	+	40.1563i	0.112483	+	0.112483i
$358$	156.789	−	156.789i	0.437959	−	0.437959i
$359$		−	396.762i		−	1.10519i	−0.833451	−	0.552593i	$-0.813638\pi$
$359$		−	396.762i		−	1.10519i	0.833451	−	0.552593i	$-0.186362\pi$
$360$	48.2378	+	151.839i	0.133994	+	0.421775i
$361$	−211.799			−0.586702
$362$	−194.908	−	194.908i	−0.538420	−	0.538420i
$363$	−251.111	+	251.111i	−0.691767	+	0.691767i
$364$		−	4.69932i		−	0.0129102i
$365$	528.085	−	167.767i	1.44681	−	0.459637i
$366$	−91.1634			−0.249080
$367$	−15.5067	−	15.5067i	−0.0422526	−	0.0422526i	0.685665	−	0.727917i	$-0.259512\pi$
$367$	−15.5067	−	15.5067i	−0.0422526	−	0.0422526i	−0.727917	+	0.685665i	$0.759512\pi$
$368$	−17.2527	+	17.2527i	−0.0468822	+	0.0468822i
$369$		−	27.9545i		−	0.0757575i
$370$	16.4533	−	31.7750i	0.0444684	−	0.0858783i
$371$	53.6154			0.144516
$372$	35.8344	+	35.8344i	0.0963291	+	0.0963291i
$373$	−122.795	+	122.795i	−0.329210	+	0.329210i	−0.852286	−	0.523076i	$-0.824784\pi$
$373$	−122.795	+	122.795i	−0.329210	+	0.329210i	0.523076	+	0.852286i	$0.324784\pi$
$374$			45.0075i			0.120341i
$375$	−355.413	−	269.054i	−0.947769	−	0.717477i
$376$	−345.189			−0.918056
$377$	−3.02982	−	3.02982i	−0.00803667	−	0.00803667i
$378$	−46.6423	+	46.6423i	−0.123392	+	0.123392i
$379$		−	385.500i		−	1.01715i	−0.861017	−	0.508576i	$-0.830172\pi$
$379$		−	385.500i		−	1.01715i	0.861017	−	0.508576i	$-0.169828\pi$
$380$	−197.830	−	102.438i	−0.520605	−	0.269573i
$381$	474.882			1.24641
$382$	393.310	+	393.310i	1.02961	+	1.02961i
$383$	170.561	−	170.561i	0.445330	−	0.445330i	−0.448469	−	0.893798i	$-0.648030\pi$
$383$	170.561	−	170.561i	0.445330	−	0.445330i	0.893798	+	0.448469i	$0.148030\pi$
$384$			72.1124i			0.187793i
$385$	−16.7759	−	52.8059i	−0.0435738	−	0.137158i
$386$	416.565			1.07918
$387$	217.944	+	217.944i	0.563163	+	0.563163i
$388$	111.999	−	111.999i	0.288658	−	0.288658i
$389$			5.08436i			0.0130703i	0.999979	+	0.00653517i	$0.00208022\pi$
$389$			5.08436i			0.0130703i	−0.999979	+	0.00653517i	$0.997920\pi$
$390$	−26.1970	+	8.32255i	−0.0671719	+	0.0213399i
$391$	−31.8953			−0.0815736
$392$	−262.238	−	262.238i	−0.668975	−	0.668975i
$393$	−168.920	+	168.920i	−0.429821	+	0.429821i
$394$		−	215.649i		−	0.547333i
$395$	−242.938	+	469.167i	−0.615033	+	1.18776i
$396$	−32.0273			−0.0808770
$397$	−181.841	−	181.841i	−0.458039	−	0.458039i	0.439973	−	0.898011i	$-0.354988\pi$
$397$	−181.841	−	181.841i	−0.458039	−	0.458039i	−0.898011	+	0.439973i	$0.854988\pi$
$398$	400.303	−	400.303i	1.00579	−	1.00579i
$399$			204.365i			0.512194i
$400$	73.4045	+	103.868i	0.183511	+	0.259671i
$401$	540.641			1.34823			0.674115	−	0.738626i	$-0.264525\pi$
$401$	540.641			1.34823			0.674115	+	0.738626i	$0.264525\pi$
$402$	297.019	+	297.019i	0.738853	+	0.738853i
$403$	−5.69017	+	5.69017i	−0.0141195	+	0.0141195i
$404$			103.575i			0.256373i
$405$	−446.837	−	231.375i	−1.10330	−	0.571297i
$406$	14.2316			0.0350531
$407$	16.0150	+	16.0150i	0.0393489	+	0.0393489i
$408$	143.749	−	143.749i	0.352326	−	0.352326i
$409$			217.985i			0.532971i	0.963839	+	0.266485i	$0.0858624\pi$
$409$			217.985i			0.532971i	−0.963839	+	0.266485i	$0.914138\pi$
$410$	−16.6475	−	52.4018i	−0.0406038	−	0.127809i
$411$	−261.501			−0.636256
$412$	−53.9242	−	53.9242i	−0.130884	−	0.130884i
$413$	174.311	−	174.311i	0.422060	−	0.422060i
$414$			26.0697i			0.0629703i
$415$	500.818	−	159.105i	1.20679	−	0.383386i
$416$	−28.3019			−0.0680334
$417$	494.513	+	494.513i	1.18588	+	1.18588i
$418$	−114.527	+	114.527i	−0.273988	+	0.273988i
$419$		−	338.783i		−	0.808552i	−0.914637	−	0.404276i	$-0.867524\pi$
$419$		−	338.783i		−	0.808552i	0.914637	−	0.404276i	$-0.132476\pi$
$420$	−36.5481	+	70.5825i	−0.0870194	+	0.168054i
$421$	−289.362			−0.687320			−0.343660	−	0.939094i	$-0.611667\pi$
$421$	−289.362			−0.687320			−0.343660	+	0.939094i	$0.611667\pi$
$422$	175.736	+	175.736i	0.416437	+	0.416437i
$423$	−105.856	+	105.856i	−0.250252	+	0.250252i
$424$		−	191.929i		−	0.452663i
$425$	−28.1596	+	163.864i	−0.0662578	+	0.385562i
$426$	524.479			1.23117
$427$	−29.5990	−	29.5990i	−0.0693185	−	0.0693185i
$428$	−187.467	+	187.467i	−0.438008	+	0.438008i
$429$		−	17.3984i		−	0.0405556i
$430$	538.335	+	278.754i	1.25194	+	0.648265i
$431$	138.445			0.321218			0.160609	−	0.987018i	$-0.448654\pi$
$431$	138.445			0.321218			0.160609	+	0.987018i	$0.448654\pi$
$432$	67.7707	+	67.7707i	0.156877	+	0.156877i
$433$	317.290	−	317.290i	0.732771	−	0.732771i	−0.238397	−	0.971168i	$-0.576622\pi$
$433$	317.290	−	317.290i	0.732771	−	0.732771i	0.971168	+	0.238397i	$0.0766219\pi$
$434$		−	26.7276i		−	0.0615844i
$435$	21.9432	+	69.0710i	0.0504441	+	0.158784i
$436$	162.291			0.372227
$437$	−81.1615	−	81.1615i	−0.185724	−	0.185724i
$438$	−408.634	+	408.634i	−0.932954	+	0.932954i
$439$		−	848.423i		−	1.93263i	−0.257369	−	0.966313i	$-0.582856\pi$
$439$		−	848.423i		−	1.93263i	0.257369	−	0.966313i	$-0.417144\pi$
$440$	−189.031	+	60.0534i	−0.429617	+	0.136485i
$441$	−160.837			−0.364710
$442$	7.24955	+	7.24955i	0.0164017	+	0.0164017i
$443$	−108.547	+	108.547i	−0.245028	+	0.245028i	−0.818926	−	0.573898i	$-0.805430\pi$
$443$	−108.547	+	108.547i	−0.245028	+	0.245028i	0.573898	+	0.818926i	$0.305430\pi$
$444$		−	32.4907i		−	0.0731772i
$445$	−48.5349	+	93.7315i	−0.109067	+	0.210633i
$446$	−58.1395			−0.130358
$447$	−386.540	−	386.540i	−0.864742	−	0.864742i
$448$	100.925	−	100.925i	0.225278	−	0.225278i
$449$			416.488i			0.927590i	0.885943	+	0.463795i	$0.153513\pi$
$449$			416.488i			0.927590i	−0.885943	+	0.463795i	$0.846487\pi$
$450$	133.934	+	23.0163i	0.297632	+	0.0511473i
$451$	34.8018			0.0771659
$452$	100.122	+	100.122i	0.221509	+	0.221509i
$453$	152.580	−	152.580i	0.336820	−	0.336820i
$454$			153.198i			0.337441i
$455$	−11.2078	−	5.80350i	−0.0246326	−	0.0127550i
$456$	731.574			1.60433
$457$	−341.097	−	341.097i	−0.746382	−	0.746382i	0.227416	−	0.973798i	$-0.426972\pi$
$457$	−341.097	−	341.097i	−0.746382	−	0.746382i	−0.973798	+	0.227416i	$0.926972\pi$
$458$	−278.601	+	278.601i	−0.608299	+	0.608299i
$459$			125.289i			0.272960i
$460$	−13.5164	−	42.5458i	−0.0293834	−	0.0924908i
$461$	437.249			0.948479			0.474239	−	0.880396i	$-0.342723\pi$
$461$	437.249			0.948479			0.474239	+	0.880396i	$0.342723\pi$
$462$	40.8614	+	40.8614i	0.0884446	+	0.0884446i
$463$	−171.391	+	171.391i	−0.370175	+	0.370175i	−0.867541	−	0.497366i	$-0.834301\pi$
$463$	−171.391	+	171.391i	−0.370175	+	0.370175i	0.497366	+	0.867541i	$0.334301\pi$
$464$		−	20.6783i		−	0.0445652i
$465$	129.719	−	41.2105i	0.278966	−	0.0886248i
$466$	−122.263			−0.262367
$467$	−484.898	−	484.898i	−1.03833	−	1.03833i	−0.999236	−	0.0390904i	$-0.987554\pi$
$467$	−484.898	−	484.898i	−1.03833	−	1.03833i	−0.0390904	−	0.999236i	$-0.512446\pi$
$468$	−5.15878	+	5.15878i	−0.0110230	+	0.0110230i
$469$			192.873i			0.411242i
$470$	−135.392	+	261.472i	−0.288068	+	0.556323i
$471$	−690.926			−1.46693
$472$	−623.987	−	623.987i	−1.32201	−	1.32201i
$473$	−271.328	+	271.328i	−0.573633	+	0.573633i
$474$		−	551.029i		−	1.16251i
$475$	−488.627	+	345.316i	−1.02869	+	0.726981i
$476$	29.6464			0.0622824
$477$	−58.8574	−	58.8574i	−0.123391	−	0.123391i
$478$	232.056	−	232.056i	0.485474	−	0.485474i
$479$		−	210.909i		−	0.440312i	−0.975465	−	0.220156i	$-0.929343\pi$
$479$		−	210.909i		−	0.440312i	0.975465	−	0.220156i	$-0.0706566\pi$
$480$	425.087	+	220.113i	0.885597	+	0.458569i
$481$	5.15922			0.0107260
$482$	−231.654	−	231.654i	−0.480611	−	0.480611i
$483$	−28.9571	+	28.9571i	−0.0599526	+	0.0599526i
$484$			185.389i			0.383036i
$485$	−128.802	−	405.433i	−0.265572	−	0.835945i
$486$	276.872			0.569695
$487$	−5.58269	−	5.58269i	−0.0114634	−	0.0114634i	0.701352	−	0.712815i	$-0.252580\pi$
$487$	−5.58269	−	5.58269i	−0.0114634	−	0.0114634i	−0.712815	+	0.701352i	$0.752580\pi$
$488$	−105.957	+	105.957i	−0.217124	+	0.217124i
$489$		−	613.162i		−	1.25391i
$490$	−301.495	+	95.7822i	−0.615297	+	0.195474i
$491$	564.434			1.14956			0.574780	−	0.818308i	$-0.305088\pi$
$491$	564.434			1.14956			0.574780	+	0.818308i	$0.305088\pi$
$492$	−35.3023	−	35.3023i	−0.0717527	−	0.0717527i
$493$	19.1141	−	19.1141i	0.0387711	−	0.0387711i
$494$			36.8947i			0.0746857i
$495$	−39.5527	+	76.3849i	−0.0799044	+	0.154313i
$496$	−38.8349			−0.0782962
$497$	170.288	+	170.288i	0.342632	+	0.342632i
$498$	−387.535	+	387.535i	−0.778182	+	0.778182i
$499$			36.5966i			0.0733398i	0.999327	+	0.0366699i	$0.0116750\pi$
$499$			36.5966i			0.0733398i	−0.999327	+	0.0366699i	$0.988325\pi$
$500$	−230.514	+	31.8785i	−0.461029	+	0.0637570i
$501$	−701.625			−1.40045
$502$	−126.055	−	126.055i	−0.251105	−	0.251105i
$503$	−426.241	+	426.241i	−0.847398	+	0.847398i	−0.989808	−	0.142410i	$-0.954515\pi$
$503$	−426.241	+	426.241i	−0.847398	+	0.847398i	0.142410	+	0.989808i	$0.454515\pi$
$504$		−	76.2958i		−	0.151381i
$505$	247.025	+	127.911i	0.489158	+	0.253290i
$506$	−32.4553			−0.0641410
$507$	423.355	+	423.355i	0.835020	+	0.835020i
$508$	175.297	−	175.297i	0.345073	−	0.345073i
$509$		−	263.396i		−	0.517478i	−0.965947	−	0.258739i	$-0.916693\pi$
$509$		−	263.396i		−	0.517478i	0.965947	−	0.258739i	$-0.0833070\pi$
$510$	−52.5041	−	165.268i	−0.102949	−	0.324055i
$511$	−265.351			−0.519278
$512$	−219.921	−	219.921i	−0.429533	−	0.429533i
$513$	−318.813	+	318.813i	−0.621468	+	0.621468i
$514$			634.568i			1.23457i
$515$	−195.203	+	62.0143i	−0.379036	+	0.120416i
$516$	550.460			1.06678
$517$	−131.785	−	131.785i	−0.254904	−	0.254904i
$518$	−12.1168	+	12.1168i	−0.0233915	+	0.0233915i
$519$			1077.50i			2.07612i
$520$	−20.7750	+	40.1212i	−0.0399520	+	0.0771561i
$521$	89.9544			0.172657			0.0863286	−	0.996267i	$-0.472486\pi$
$521$	89.9544			0.172657			0.0863286	+	0.996267i	$0.472486\pi$
$522$	−15.6230	−	15.6230i	−0.0299291	−	0.0299291i
$523$	−347.413	+	347.413i	−0.664269	+	0.664269i	−0.956384	−	0.292114i	$-0.905641\pi$
$523$	−347.413	+	347.413i	−0.664269	+	0.664269i	0.292114	+	0.956384i	$0.405641\pi$
$524$			124.709i			0.237995i
$525$	123.203	+	174.334i	0.234672	+	0.332065i
$526$	−573.661			−1.09061
$527$	−35.8974	−	35.8974i	−0.0681165	−	0.0681165i
$528$	59.3711	−	59.3711i	0.112445	−	0.112445i
$529$		−	23.0000i		−	0.0434783i
$530$	−145.381	−	75.2795i	−0.274305	−	0.142037i
$531$	−382.707			−0.720729
$532$	75.4390	+	75.4390i	0.141803	+	0.141803i
$533$	5.60568	−	5.60568i	0.0105172	−	0.0105172i
$534$		−	110.086i		−	0.206154i
$535$	215.592	+	678.624i	0.402976	+	1.26846i
$536$	690.434			1.28812
$537$	−382.364	−	382.364i	−0.712037	−	0.712037i
$538$	−480.915	+	480.915i	−0.893894	+	0.893894i
$539$		−	200.233i		−	0.371491i
$540$	−167.125	+	53.0941i	−0.309491	+	0.0983224i
$541$	683.618			1.26362			0.631810	−	0.775124i	$-0.282312\pi$
$541$	683.618			1.26362			0.631810	+	0.775124i	$0.282312\pi$
$542$	−109.983	−	109.983i	−0.202920	−	0.202920i
$543$	−475.325	+	475.325i	−0.875369	+	0.875369i
$544$		−	178.547i		−	0.328211i
$545$	200.424	−	387.063i	0.367750	−	0.710207i
$546$	13.1634			0.0241089
$547$	204.068	+	204.068i	0.373067	+	0.373067i	0.868593	−	0.495526i	$-0.165025\pi$
$547$	204.068	+	204.068i	0.373067	+	0.373067i	−0.495526	+	0.868593i	$0.665025\pi$
$548$	−96.5300	+	96.5300i	−0.176150	+	0.176150i
$549$			64.9858i			0.118371i
$550$	−28.6540	+	166.741i	−0.0520982	+	0.303165i
$551$	97.2766			0.176545
$552$	103.659	+	103.659i	0.187788	+	0.187788i
$553$	178.909	−	178.909i	0.323524	−	0.323524i
$554$			5.82493i			0.0105143i
$555$	−77.4900	−	40.1249i	−0.139622	−	0.0722971i
$556$	365.087			0.656631
$557$	439.695	+	439.695i	0.789399	+	0.789399i	0.981396	−	0.191997i	$-0.0614963\pi$
$557$	439.695	+	439.695i	0.789399	+	0.789399i	−0.191997	+	0.981396i	$0.561496\pi$
$558$	−29.3408	+	29.3408i	−0.0525821	+	0.0525821i
$559$			87.4080i			0.156365i
$560$	−18.4421	−	58.0504i	−0.0329323	−	0.103661i
$561$	109.760			0.195651
$562$	347.271	+	347.271i	0.617920	+	0.617920i
$563$	587.221	−	587.221i	1.04302	−	1.04302i	0.0439893	−	0.999032i	$-0.485993\pi$
$563$	587.221	−	587.221i	1.04302	−	1.04302i	0.999032	−	0.0439893i	$-0.0140067\pi$
$564$			267.361i			0.474045i
$565$	362.438	−	115.143i	0.641484	−	0.203793i
$566$	−100.903			−0.178273
$567$	170.393	+	170.393i	0.300517	+	0.300517i
$568$	609.587	−	609.587i	1.07322	−	1.07322i
$569$			693.156i			1.21820i	0.793093	+	0.609100i	$0.208469\pi$
$569$			693.156i			1.21820i	−0.793093	+	0.609100i	$0.791531\pi$
$570$	286.942	−	554.149i	0.503408	−	0.972191i
$571$	−978.135			−1.71302			−0.856510	−	0.516130i	$-0.827372\pi$
$571$	−978.135			−1.71302			−0.856510	+	0.516130i	$0.827372\pi$
$572$	−6.42239	−	6.42239i	−0.0112280	−	0.0112280i
$573$	959.171	−	959.171i	1.67395	−	1.67395i
$574$			26.3307i			0.0458724i
$575$	−118.164	−	20.3061i	−0.205502	−	0.0353150i
$576$	−221.584			−0.384695
$577$	491.120	+	491.120i	0.851161	+	0.851161i	0.990276	−	0.139115i	$-0.0444258\pi$
$577$	491.120	+	491.120i	0.851161	+	0.851161i	−0.139115	+	0.990276i	$0.544426\pi$
$578$	253.093	−	253.093i	0.437876	−	0.437876i
$579$		−	1015.88i		−	1.75455i
$580$	33.5968	+	17.3967i	0.0579255	+	0.0299942i
$581$	−251.650			−0.433133
$582$	313.725	+	313.725i	0.539047	+	0.539047i
$583$	73.2742	−	73.2742i	0.125685	−	0.125685i
$584$			949.887i			1.62652i
$585$	5.93273	+	18.6746i	0.0101414	+	0.0319223i
$586$	474.291			0.809370
$587$	−377.790	−	377.790i	−0.643595	−	0.643595i	0.307842	−	0.951437i	$-0.400393\pi$
$587$	−377.790	−	377.790i	−0.643595	−	0.643595i	−0.951437	+	0.307842i	$0.900393\pi$
$588$	−203.113	+	203.113i	−0.345430	+	0.345430i
$589$		−	182.691i		−	0.310171i
$590$	−717.398	+	227.911i	−1.21593	+	0.386289i
$591$	−525.907			−0.889859
$592$	17.6056	+	17.6056i	0.0297392	+	0.0297392i
$593$	380.065	−	380.065i	0.640919	−	0.640919i	−0.309862	−	0.950782i	$-0.600283\pi$
$593$	380.065	−	380.065i	0.640919	−	0.640919i	0.950782	+	0.309862i	$0.100283\pi$
$594$			127.489i			0.214627i
$595$	36.6123	−	70.7065i	0.0615333	−	0.118834i
$596$	−285.373			−0.478813
$597$	−976.224	−	976.224i	−1.63522	−	1.63522i
$598$	−5.22772	+	5.22772i	−0.00874200	+	0.00874200i
$599$			453.590i			0.757246i	0.925551	+	0.378623i	$0.123602\pi$
$599$			453.590i			0.757246i	−0.925551	+	0.378623i	$0.876398\pi$
$600$	624.070	−	441.035i	1.04012	−	0.735058i
$601$	151.861			0.252680			0.126340	−	0.991987i	$-0.459677\pi$
$601$	151.861			0.252680			0.126340	+	0.991987i	$0.459677\pi$
$602$	−205.284	−	205.284i	−0.341004	−	0.341004i
$603$	211.730	−	211.730i	0.351128	−	0.351128i
$604$		−	112.646i		−	0.186500i
$605$	442.153	+	228.950i	0.730831	+	0.378429i
$606$	−290.127			−0.478757
$607$	461.935	+	461.935i	0.761013	+	0.761013i	0.976505	−	0.215493i	$-0.0691357\pi$
$607$	461.935	+	461.935i	0.761013	+	0.761013i	−0.215493	+	0.976505i	$0.569136\pi$
$608$	454.335	−	454.335i	0.747261	−	0.747261i
$609$		−	34.7067i		−	0.0569896i
$610$	38.7005	+	121.818i	0.0634435	+	0.199702i
$611$	−42.4545			−0.0694836
$612$	−32.5450	−	32.5450i	−0.0531780	−	0.0531780i
$613$	−42.7083	+	42.7083i	−0.0696710	+	0.0696710i	−0.741084	−	0.671413i	$-0.765688\pi$
$613$	−42.7083	+	42.7083i	−0.0696710	+	0.0696710i	0.671413	+	0.741084i	$0.265688\pi$
$614$		−	156.550i		−	0.254968i
$615$	−127.793	+	40.5986i	−0.207793	+	0.0660140i
$616$	94.9841			0.154195
$617$	−348.039	−	348.039i	−0.564083	−	0.564083i	0.366382	−	0.930465i	$-0.380596\pi$
$617$	−348.039	−	348.039i	−0.564083	−	0.564083i	−0.930465	+	0.366382i	$0.880596\pi$
$618$	151.049	−	151.049i	0.244416	−	0.244416i
$619$			121.712i			0.196628i	0.995155	+	0.0983138i	$0.0313449\pi$
$619$			121.712i			0.196628i	−0.995155	+	0.0983138i	$0.968655\pi$
$620$	32.6719	−	63.0966i	0.0526966	−	0.101769i
$621$	−90.3470			−0.145486
$622$	60.7154	+	60.7154i	0.0976132	+	0.0976132i
$623$	35.7429	−	35.7429i	0.0573722	−	0.0573722i
$624$		−	19.1263i		−	0.0306511i
$625$	−208.648	+	589.144i	−0.333836	+	0.942631i
$626$	−278.781			−0.445336
$627$	279.299	+	279.299i	0.445453	+	0.445453i
$628$	−255.047	+	255.047i	−0.406126	+	0.406126i
$629$			32.5477i			0.0517452i
$630$	−57.7921	−	29.9252i	−0.0917335	−	0.0475003i
$631$	881.578			1.39711			0.698556	−	0.715555i	$-0.253826\pi$
$631$	881.578			1.39711			0.698556	+	0.715555i	$0.253826\pi$
$632$	−640.446	−	640.446i	−1.01336	−	1.01336i
$633$	428.571	−	428.571i	0.677047	−	0.677047i
$634$			528.118i			0.832993i
$635$	−201.596	−	634.568i	−0.317474	−	0.999320i
$636$	−148.656			−0.233736
$637$	−32.2525	−	32.2525i	−0.0506318	−	0.0506318i
$638$	19.4497	−	19.4497i	0.0304855	−	0.0304855i
$639$		−	373.875i		−	0.585094i
$640$	96.3612	−	30.6130i	0.150564	−	0.0478328i
$641$	−1173.20			−1.83026			−0.915130	−	0.403159i	$-0.867912\pi$
$641$	−1173.20			−1.83026			−0.915130	+	0.403159i	$0.867912\pi$
$642$	−525.121	−	525.121i	−0.817946	−	0.817946i
$643$	780.859	−	780.859i	1.21440	−	1.21440i	0.244836	−	0.969565i	$-0.421266\pi$
$643$	780.859	−	780.859i	1.21440	−	1.21440i	0.969565	−	0.244836i	$-0.0787341\pi$
$644$			21.3783i			0.0331961i
$645$	679.800	−	1312.84i	1.05395	−	2.03542i
$646$	−232.756			−0.360304
$647$	−118.588	−	118.588i	−0.183289	−	0.183289i	0.609499	−	0.792787i	$-0.291371\pi$
$647$	−118.588	−	118.588i	−0.183289	−	0.183289i	−0.792787	+	0.609499i	$0.791371\pi$
$648$	609.963	−	609.963i	0.941301	−	0.941301i
$649$		−	476.449i		−	0.734128i
$650$	22.2422	+	31.4731i	0.0342188	+	0.0484202i
$651$	−65.1810			−0.100124
$652$	−226.341	−	226.341i	−0.347149	−	0.347149i
$653$	−482.761	+	482.761i	−0.739297	+	0.739297i	−0.972442	−	0.233145i	$-0.925098\pi$
$653$	−482.761	+	482.761i	−0.739297	+	0.739297i	0.233145	+	0.972442i	$0.425098\pi$
$654$			454.599i			0.695106i
$655$	297.431	+	154.012i	0.454092	+	0.235132i
$656$	38.2582			0.0583205
$657$	291.295	+	291.295i	0.443371	+	0.443371i
$658$	99.7076	−	99.7076i	0.151531	−	0.151531i
$659$		−	322.308i		−	0.489087i	−0.969638	−	0.244543i	$-0.921362\pi$
$659$		−	322.308i		−	0.489087i	0.969638	−	0.244543i	$-0.0786380\pi$
$660$	46.5135	+	146.412i	0.0704751	+	0.221836i
$661$	−856.871			−1.29632			−0.648162	−	0.761502i	$-0.724462\pi$
$661$	−856.871			−1.29632			−0.648162	+	0.761502i	$0.724462\pi$
$662$	502.542	+	502.542i	0.759127	+	0.759127i
$663$	17.6796	−	17.6796i	0.0266660	−	0.0266660i
$664$			900.841i			1.35669i
$665$	273.086	−	86.7568i	0.410656	−	0.130461i
$666$	26.6030			0.0399444
$667$	13.7834	+	13.7834i	0.0206647	+	0.0206647i
$668$	−258.996	+	258.996i	−0.387719	+	0.387719i
$669$			141.786i			0.211937i
$670$	270.806	−	522.986i	0.404188	−	0.780576i
$671$	−80.9038			−0.120572
$672$	−162.099	−	162.099i	−0.241219	−	0.241219i
$673$	710.155	−	710.155i	1.05521	−	1.05521i	0.0568242	−	0.998384i	$-0.481903\pi$
$673$	710.155	−	710.155i	1.05521	−	1.05521i	0.998384	−	0.0568242i	$-0.0180975\pi$
$674$			686.898i			1.01914i
$675$	−79.7652	+	464.162i	−0.118171	+	0.687648i
$676$	312.553			0.462356
$677$	−341.603	−	341.603i	−0.504584	−	0.504584i	0.408275	−	0.912859i	$-0.366130\pi$
$677$	−341.603	−	341.603i	−0.504584	−	0.504584i	−0.912859	+	0.408275i	$0.866130\pi$
$678$	−280.456	+	280.456i	−0.413652	+	0.413652i
$679$			203.721i			0.300031i
$680$	−253.111	−	131.063i	−0.372222	−	0.192739i
$681$	373.606			0.548614
$682$	−36.5277	−	36.5277i	−0.0535597	−	0.0535597i
$683$	−181.805	+	181.805i	−0.266185	+	0.266185i	−0.827561	−	0.561376i	$-0.810272\pi$
$683$	−181.805	+	181.805i	−0.266185	+	0.266185i	0.561376	+	0.827561i	$0.310272\pi$
$684$		−	165.629i		−	0.242148i
$685$	111.012	+	349.435i	0.162061	+	0.510124i
$686$	323.065			0.470940
$687$	679.428	+	679.428i	0.988978	+	0.988978i
$688$	−298.276	+	298.276i	−0.433540	+	0.433540i
$689$		−	23.6052i		−	0.0342601i
$690$	119.177	−	37.8612i	0.172720	−	0.0548714i
$691$	85.3541			0.123523			0.0617613	−	0.998091i	$-0.480328\pi$
$691$	85.3541			0.123523			0.0617613	+	0.998091i	$0.480328\pi$
$692$	397.748	+	397.748i	0.574780	+	0.574780i
$693$	29.1280	−	29.1280i	0.0420318	−	0.0420318i
$694$			282.826i			0.407531i
$695$	450.870	−	870.729i	0.648734	−	1.25285i
$696$	−124.241			−0.178507
$697$	35.3643	+	35.3643i	0.0507379	+	0.0507379i
$698$	14.1176	−	14.1176i	0.0202257	−	0.0202257i
$699$			298.165i			0.426559i
$700$	109.832	+	18.8744i	0.156903	+	0.0269634i
$701$	−418.790			−0.597418			−0.298709	−	0.954344i	$-0.596556\pi$
$701$	−418.790			−0.597418			−0.298709	+	0.954344i	$0.596556\pi$
$702$	20.5352	+	20.5352i	0.0292524	+	0.0292524i
$703$	−82.8218	+	82.8218i	−0.117812	+	0.117812i
$704$		−	275.860i		−	0.391847i
$705$	637.655	+	330.182i	0.904475	+	0.468344i
$706$	615.312			0.871547
$707$	−94.1986	−	94.1986i	−0.133237	−	0.133237i
$708$	−483.301	+	483.301i	−0.682628	+	0.682628i
$709$		−	1100.84i		−	1.55266i	−0.630327	−	0.776330i	$-0.717079\pi$
$709$		−	1100.84i		−	1.55266i	0.630327	−	0.776330i	$-0.282921\pi$
$710$	−222.651	−	700.843i	−0.313593	−	0.987102i
$711$	−392.801			−0.552463
$712$	−127.950	−	127.950i	−0.179705	−	0.179705i
$713$	25.8859	−	25.8859i	0.0363057	−	0.0363057i
$714$			83.0436i			0.116308i
$715$	−23.2488	+	7.38592i	−0.0325158	+	0.0103300i
$716$	−282.290			−0.394259
$717$	−565.919	−	565.919i	−0.789288	−	0.789288i
$718$	410.254	−	410.254i	0.571384	−	0.571384i
$719$			961.181i			1.33683i	0.743788	+	0.668415i	$0.233027\pi$
$719$			961.181i			1.33683i	−0.743788	+	0.668415i	$0.766973\pi$
$720$	−43.4809	+	83.9712i	−0.0603902	+	0.116627i
$721$	98.0854			0.136041
$722$	−219.002	−	219.002i	−0.303326	−	0.303326i
$723$	−564.939	+	564.939i	−0.781381	+	0.781381i
$724$			350.921i			0.484697i
$725$	82.9819	−	58.6438i	0.114458	−	0.0808880i
$726$	−519.301			−0.715291
$727$	401.879	+	401.879i	0.552791	+	0.552791i	0.927245	−	0.374454i	$-0.122170\pi$
$727$	401.879	+	401.879i	0.552791	+	0.552791i	−0.374454	+	0.927245i	$0.622170\pi$
$728$	15.2995	−	15.2995i	0.0210158	−	0.0210158i
$729$			230.526i			0.316222i
$730$	719.515	+	372.570i	0.985637	+	0.510370i
$731$	−551.427			−0.754347
$732$	82.0672	+	82.0672i	0.112114	+	0.112114i
$733$	−282.482	+	282.482i	−0.385378	+	0.385378i	−0.873035	−	0.487657i	$-0.837852\pi$
$733$	−282.482	+	282.482i	−0.385378	+	0.385378i	0.487657	+	0.873035i	$0.337852\pi$
$734$		−	32.0680i		−	0.0436894i
$735$	233.585	+	735.261i	0.317803	+	1.00036i
$736$	128.752			0.174935
$737$	263.592	+	263.592i	0.357656	+	0.357656i
$738$	28.9051	−	28.9051i	0.0391668	−	0.0391668i
$739$		−	267.647i		−	0.362174i	−0.983467	−	0.181087i	$-0.942038\pi$
$739$		−	267.647i		−	0.362174i	0.983467	−	0.181087i	$-0.0579616\pi$
$740$	−43.4161	+	13.7929i	−0.0586704	+	0.0186390i
$741$	89.9757			0.121425
$742$	55.4386	+	55.4386i	0.0747151	+	0.0747151i
$743$	−156.612	+	156.612i	−0.210784	+	0.210784i	−0.804600	−	0.593817i	$-0.797620\pi$
$743$	−156.612	+	156.612i	−0.210784	+	0.210784i	0.593817	+	0.804600i	$0.297620\pi$
$744$			233.331i			0.313617i
$745$	−352.426	+	680.612i	−0.473055	+	0.913573i
$746$	−253.942			−0.340405
$747$	276.254	+	276.254i	0.369818	+	0.369818i
$748$	40.5167	−	40.5167i	0.0541667	−	0.0541667i
$749$		−	340.994i		−	0.455265i
$750$	−89.2960	−	645.702i	−0.119061	−	0.860937i
$751$	−764.900			−1.01851			−0.509254	−	0.860616i	$-0.670079\pi$
$751$	−764.900			−1.01851			−0.509254	+	0.860616i	$0.670079\pi$
$752$	−144.874	−	144.874i	−0.192651	−	0.192651i
$753$	−307.412	+	307.412i	−0.408249	+	0.408249i
$754$		−	6.26571i		−	0.00830996i
$755$	−268.659	−	139.114i	−0.355840	−	0.184257i
$756$	83.9768			0.111080
$757$	253.598	+	253.598i	0.335004	+	0.335004i	0.854483	−	0.519479i	$-0.173874\pi$
$757$	253.598	+	253.598i	0.335004	+	0.335004i	−0.519479	+	0.854483i	$0.673874\pi$
$758$	398.609	−	398.609i	0.525870	−	0.525870i
$759$			79.1492i			0.104281i
$760$	−310.567	−	977.577i	−0.408640	−	1.28629i
$761$	−1366.32			−1.79543			−0.897716	−	0.440574i	$-0.854775\pi$
$761$	−1366.32			−1.79543			−0.897716	+	0.440574i	$0.854775\pi$
$762$	491.031	+	491.031i	0.644397	+	0.644397i
$763$	−147.600	+	147.600i	−0.193446	+	0.193446i
$764$		−	708.132i		−	0.926875i
$765$	−117.811	+	37.4276i	−0.154002	+	0.0489249i
$766$	352.723			0.460473
$767$	−76.7437	−	76.7437i	−0.100057	−	0.100057i
$768$	−675.806	+	675.806i	−0.879955	+	0.879955i
$769$			774.842i			1.00760i	0.863821	+	0.503798i	$0.168064\pi$
$769$			774.842i			1.00760i	−0.863821	+	0.503798i	$0.831936\pi$
$770$	37.2552	−	71.9480i	0.0483834	−	0.0934390i
$771$	1547.53			2.00717
$772$	−375.001	−	375.001i	−0.485752	−	0.485752i
$773$	−119.304	+	119.304i	−0.154339	+	0.154339i	−0.780053	−	0.625714i	$-0.784808\pi$
$773$	−119.304	+	119.304i	−0.154339	+	0.154339i	0.625714	+	0.780053i	$0.284808\pi$
$774$			450.711i			0.582313i
$775$	−110.136	−	155.844i	−0.142111	−	0.201090i
$776$	729.269			0.939779
$777$	29.5494	+	29.5494i	0.0380302	+	0.0380302i
$778$	−5.25725	+	5.25725i	−0.00675740	+	0.00675740i
$779$			179.978i			0.231037i
$780$	31.0753	+	16.0910i	0.0398401	+	0.0206295i
$781$	465.454			0.595971
$782$	−32.9799	−	32.9799i	−0.0421738	−	0.0421738i
$783$	54.1429	−	54.1429i	0.0691480	−	0.0691480i
$784$		−	220.120i		−	0.280765i
$785$	293.311	+	923.260i	0.373644	+	1.17613i
$786$	−349.327			−0.444437
$787$	−74.0164	−	74.0164i	−0.0940488	−	0.0940488i	0.658517	−	0.752566i	$-0.271184\pi$
$787$	−74.0164	−	74.0164i	−0.0940488	−	0.0940488i	−0.752566	+	0.658517i	$0.771184\pi$
$788$	−194.132	+	194.132i	−0.246360	+	0.246360i
$789$			1399.00i			1.77313i
$790$	−736.321	+	233.922i	−0.932051	+	0.296104i
$791$	−182.117			−0.230237
$792$	−104.271	−	104.271i	−0.131655	−	0.131655i
$793$	−13.0315	+	13.0315i	−0.0164332	+	0.0164332i
$794$		−	376.050i		−	0.473614i
$795$	−183.585	+	354.544i	−0.230925	+	0.445967i
$796$	−720.723			−0.905430
$797$	−600.344	−	600.344i	−0.753255	−	0.753255i	0.221831	−	0.975085i	$-0.428797\pi$
$797$	−600.344	−	600.344i	−0.753255	−	0.753255i	−0.975085	+	0.221831i	$0.928797\pi$
$798$	−211.315	+	211.315i	−0.264806	+	0.264806i
$799$		−	267.831i		−	0.335208i
$800$	113.672	−	661.470i	0.142090	−	0.826837i
$801$	−78.4749			−0.0979712
$802$	559.025	+	559.025i	0.697039	+	0.697039i
$803$	−362.646	+	362.646i	−0.451613	+	0.451613i
$804$		−	534.766i		−	0.665131i
$805$	50.9871	+	26.4015i	0.0633381	+	0.0327969i
$806$	−11.7673			−0.0145997
$807$	1172.81	+	1172.81i	1.45330	+	1.45330i
$808$	−337.206	+	337.206i	−0.417335	+	0.417335i
$809$			14.5439i			0.0179777i	0.999960	+	0.00898883i	$0.00286127\pi$
$809$			14.5439i			0.0179777i	−0.999960	+	0.00898883i	$0.997139\pi$
$810$	−222.788	−	701.275i	−0.275047	−	0.865771i
$811$	23.7253			0.0292544			0.0146272	−	0.999893i	$-0.495344\pi$
$811$	23.7253			0.0292544			0.0146272	+	0.999893i	$0.495344\pi$
$812$	−12.8115	−	12.8115i	−0.0157778	−	0.0157778i
$813$	−268.216	+	268.216i	−0.329909	+	0.329909i
$814$			33.1192i			0.0406870i
$815$	−819.347	+	260.299i	−1.00533	+	0.319385i
$816$	120.661			0.147869
$817$	−1403.18	−	1403.18i	−1.71747	−	1.71747i
$818$	−225.398	+	225.398i	−0.275547	+	0.275547i
$819$		−	9.38355i		−	0.0114573i
$820$	−32.1867	+	62.1597i	−0.0392521	+	0.0758045i
$821$	−1005.57			−1.22481			−0.612407	−	0.790543i	$-0.709798\pi$
$821$	−1005.57			−1.22481			−0.612407	+	0.790543i	$0.709798\pi$
$822$	−270.394	−	270.394i	−0.328946	−	0.328946i
$823$	−1134.97	+	1134.97i	−1.37907	+	1.37907i	−0.532876	+	0.846193i	$0.678889\pi$
$823$	−1134.97	+	1134.97i	−1.37907	+	1.37907i	−0.846193	+	0.532876i	$0.821111\pi$
$824$		−	351.120i		−	0.426117i
$825$	406.633	+	69.8789i	0.492889	+	0.0847018i
$826$	360.477			0.436413
$827$	−197.108	−	197.108i	−0.238341	−	0.238341i	0.577822	−	0.816163i	$-0.303903\pi$
$827$	−197.108	−	197.108i	−0.238341	−	0.238341i	−0.816163	+	0.577822i	$0.803903\pi$
$828$	23.4685	−	23.4685i	0.0283436	−	0.0283436i
$829$		−	1078.11i		−	1.30050i	−0.759722	−	0.650248i	$-0.774665\pi$
$829$		−	1078.11i		−	1.30050i	0.759722	−	0.650248i	$-0.225335\pi$
$830$	682.364	+	353.333i	0.822125	+	0.425703i
$831$	14.2053			0.0170943
$832$	−44.4340	−	44.4340i	−0.0534063	−	0.0534063i
$833$	203.470	−	203.470i	0.244261	−	0.244261i
$834$			1022.66i			1.22621i
$835$	297.853	+	937.557i	0.356710	+	1.12282i
$836$	206.199			0.246650
$837$	−101.683	−	101.683i	−0.121485	−	0.121485i
$838$	350.304	−	350.304i	0.418023	−	0.418023i
$839$		−	538.218i		−	0.641499i	−0.947164	−	0.320750i	$-0.896065\pi$
$839$		−	538.218i		−	0.641499i	0.947164	−	0.320750i	$-0.103935\pi$
$840$	−348.783	+	110.805i	−0.415218	+	0.131911i
$841$	824.480			0.980357
$842$	−299.202	−	299.202i	−0.355346	−	0.355346i
$843$	846.894	−	846.894i	1.00462	−	1.00462i
$844$		−	316.403i		−	0.374885i
$845$	385.992	−	745.436i	0.456796	−	0.882173i
$846$	−218.912			−0.258761
$847$	−168.607	−	168.607i	−0.199064	−	0.199064i
$848$	80.5516	−	80.5516i	0.0949901	−	0.0949901i
$849$			246.072i			0.289838i
$850$	−198.553	+	140.319i	−0.233592	+	0.165081i
$851$	−23.4705			−0.0275799
$852$	−472.147	−	472.147i	−0.554163	−	0.554163i
$853$	−964.718	+	964.718i	−1.13097	+	1.13097i	−0.140955	+	0.990016i	$0.545017\pi$
$853$	−964.718	+	964.718i	−1.13097	+	1.13097i	−0.990016	+	0.140955i	$0.954983\pi$
$854$		−	61.2110i		−	0.0716757i
$855$	−395.025	−	204.547i	−0.462018	−	0.239236i
$856$	−1220.67			−1.42601
$857$	1063.23	+	1063.23i	1.24065	+	1.24065i	0.959733	+	0.280915i	$0.0906377\pi$
$857$	1063.23	+	1063.23i	1.24065	+	1.24065i	0.280915	+	0.959733i	$0.409362\pi$
$858$	17.9900	−	17.9900i	0.0209674	−	0.0209674i
$859$		−	155.199i		−	0.180674i	−0.995911	−	0.0903368i	$-0.971206\pi$
$859$		−	155.199i		−	0.180674i	0.995911	−	0.0903368i	$-0.0287944\pi$
$860$	−233.680	−	735.560i	−0.271721	−	0.855303i
$861$	64.2131			0.0745797
$862$	143.153	+	143.153i	0.166070	+	0.166070i
$863$	727.461	−	727.461i	0.842944	−	0.842944i	−0.146296	−	0.989241i	$-0.546735\pi$
$863$	727.461	−	727.461i	0.842944	−	0.842944i	0.989241	+	0.146296i	$0.0467354\pi$
$864$		−	505.754i		−	0.585364i
$865$	1439.83	−	457.420i	1.66454	−	0.528810i
$866$	656.159			0.757689
$867$	−617.220	−	617.220i	−0.711903	−	0.711903i
$868$	−24.0608	+	24.0608i	−0.0277198	+	0.0277198i
$869$		−	489.016i		−	0.562734i
$870$	−48.7304	+	94.1092i	−0.0560120	+	0.108172i
$871$	84.9158			0.0974923
$872$	528.368	+	528.368i	0.605926	+	0.605926i
$873$	223.639	−	223.639i	0.256173	−	0.256173i
$874$		−	167.843i		−	0.192040i
$875$	180.654	−	238.640i	0.206462	−	0.272731i
$876$	735.721			0.839865
$877$	−561.300	−	561.300i	−0.640023	−	0.640023i	0.310538	−	0.950561i	$-0.399491\pi$
$877$	−561.300	−	561.300i	−0.640023	−	0.640023i	−0.950561	+	0.310538i	$0.899491\pi$
$878$	877.274	−	877.274i	0.999173	−	0.999173i
$879$		−	1156.66i		−	1.31588i
$880$	−104.540	−	54.1313i	−0.118795	−	0.0615129i
$881$	1090.88			1.23823			0.619113	−	0.785302i	$-0.287492\pi$
$881$	1090.88			1.23823			0.619113	+	0.785302i	$0.287492\pi$
$882$	−166.307	−	166.307i	−0.188556	−	0.188556i
$883$	1006.75	−	1006.75i	1.14015	−	1.14015i	0.151723	−	0.988423i	$-0.451518\pi$
$883$	1006.75	−	1006.75i	1.14015	−	1.14015i	0.988423	−	0.151723i	$-0.0484823\pi$
$884$		−	13.0524i		−	0.0147651i
$885$	555.808	+	1749.53i	0.628032	+	1.97687i
$886$	−224.477			−0.253360
$887$	422.708	+	422.708i	0.476559	+	0.476559i	0.904029	−	0.427471i	$-0.140595\pi$
$887$	422.708	+	422.708i	0.476559	+	0.476559i	−0.427471	+	0.904029i	$0.640595\pi$
$888$	105.779	−	105.779i	0.119121	−	0.119121i
$889$			318.856i			0.358669i
$890$	−147.104	+	46.7336i	−0.165286	+	0.0525096i
$891$	465.741			0.522717
$892$	52.3384	+	52.3384i	0.0586754	+	0.0586754i
$893$	681.529	−	681.529i	0.763190	−	0.763190i
$894$		−	799.368i		−	0.894148i
$895$	−348.619	+	673.259i	−0.389518	+	0.752245i
$896$	−48.4193			−0.0540395
$897$	12.7489	+	12.7489i	0.0142128	+	0.0142128i
$898$	−430.650	+	430.650i	−0.479566	+	0.479566i
$899$			31.0257i			0.0345114i
$900$	−99.8508	−	141.290i	−0.110945	−	0.156989i
$901$	148.917			0.165280
$902$	35.9853	+	35.9853i	0.0398950	+	0.0398950i
$903$	−500.630	+	500.630i	−0.554407	+	0.554407i
$904$			651.932i			0.721164i
$905$	836.944	+	433.376i	0.924800	+	0.478868i
$906$	315.536			0.348274
$907$	−377.666	−	377.666i	−0.416390	−	0.416390i	0.467567	−	0.883958i	$-0.345131\pi$
$907$	−377.666	−	377.666i	−0.416390	−	0.416390i	−0.883958	+	0.467567i	$0.845131\pi$
$908$	137.912	−	137.912i	0.151886	−	0.151886i
$909$			206.817i			0.227521i
$910$	−5.58812	−	17.5898i	−0.00614079	−	0.0193295i
$911$	589.108			0.646661			0.323331	−	0.946286i	$-0.395197\pi$
$911$	589.108			0.646661			0.323331	+	0.946286i	$0.395197\pi$
$912$	307.038	+	307.038i	0.336664	+	0.336664i
$913$	−343.921	+	343.921i	−0.376693	+	0.376693i
$914$		−	705.391i		−	0.771763i
$915$	297.080	−	94.3795i	0.324678	−	0.103147i
$916$	501.605			0.547603
$917$	−113.420	−	113.420i	−0.123686	−	0.123686i
$918$	−129.549	+	129.549i	−0.141121	+	0.141121i
$919$		−	360.212i		−	0.391960i	−0.980608	−	0.195980i	$-0.937211\pi$
$919$		−	360.212i		−	0.391960i	0.980608	−	0.195980i	$-0.0627888\pi$
$920$	94.5105	−	182.521i	0.102729	−	0.198392i
$921$	−381.781			−0.414529
$922$	452.117	+	452.117i	0.490366	+	0.490366i
$923$	74.9726	−	74.9726i	0.0812271	−	0.0812271i
$924$		−	73.5686i		−	0.0796196i
$925$	−20.7215	+	120.581i	−0.0224017	+	0.130358i
$926$	−354.439			−0.382763
$927$	−107.675	−	107.675i	−0.116155	−	0.116155i
$928$	−77.1582	+	77.1582i	−0.0831446	+	0.0831446i
$929$			1244.48i			1.33959i	0.742544	+	0.669797i	$0.233619\pi$
$929$			1244.48i			1.33959i	−0.742544	+	0.669797i	$0.766381\pi$
$930$	176.742	+	91.5184i	0.190045	+	0.0984069i
$931$	1035.51			1.11225
$932$	110.064	+	110.064i	0.118094	+	0.118094i
$933$	148.068	−	148.068i	0.158700	−	0.158700i
$934$		−	1002.77i		−	1.07363i
$935$	−46.5953	−	146.669i	−0.0498345	−	0.156865i
$936$	−33.5907			−0.0358875
$937$	−13.9938	−	13.9938i	−0.0149347	−	0.0149347i	0.699600	−	0.714535i	$-0.253362\pi$
$937$	−13.9938	−	13.9938i	−0.0149347	−	0.0149347i	−0.714535	+	0.699600i	$0.753362\pi$
$938$	−199.431	+	199.431i	−0.212613	+	0.212613i
$939$			679.866i			0.724032i
$940$	357.265	−	113.500i	0.380069	−	0.120744i
$941$	1159.02			1.23169			0.615846	−	0.787867i	$-0.288814\pi$
$941$	1159.02			1.23169			0.615846	+	0.787867i	$0.288814\pi$
$942$	−714.421	−	714.421i	−0.758409	−	0.758409i
$943$	−25.5016	+	25.5016i	−0.0270430	+	0.0270430i
$944$		−	523.768i		−	0.554839i
$945$	103.709	−	200.284i	0.109744	−	0.211941i
$946$	−561.110			−0.593139
$947$	−692.669	−	692.669i	−0.731435	−	0.731435i	0.239469	−	0.970904i	$-0.423027\pi$
$947$	−692.669	−	692.669i	−0.731435	−	0.731435i	−0.970904	+	0.239469i	$0.923027\pi$
$948$	−496.048	+	496.048i	−0.523258	+	0.523258i
$949$			116.826i			0.123104i
$950$	−862.302	−	148.184i	−0.907686	−	0.155984i
$951$	1287.93			1.35429
$952$	96.5193	+	96.5193i	0.101386	+	0.101386i
$953$	−326.337	+	326.337i	−0.342431	+	0.342431i	−0.857281	−	0.514850i	$-0.827848\pi$
$953$	−326.337	+	326.337i	−0.342431	+	0.342431i	0.514850	+	0.857281i	$0.327848\pi$
$954$		−	121.718i		−	0.127587i
$955$	−1688.89	−	874.520i	−1.76847	−	0.915728i
$956$	−417.804			−0.437034
$957$	−47.4323	−	47.4323i	−0.0495636	−	0.0495636i
$958$	218.081	−	218.081i	0.227642	−	0.227642i
$959$		−	175.583i		−	0.183090i
$960$	321.809	+	1012.96i	0.335218	+	1.05517i
$961$	−902.732			−0.939367
$962$	5.33466	+	5.33466i	0.00554538	+	0.00554538i
$963$	−374.333	+	374.333i	−0.388715	+	0.388715i
$964$			417.080i			0.432656i
$965$	−1357.49	+	431.261i	−1.40672	+	0.446902i
$966$	−59.8836			−0.0619913
$967$	786.670	+	786.670i	0.813517	+	0.813517i	0.985159	−	0.171643i	$-0.0549075\pi$
$967$	786.670	+	786.670i	0.813517	+	0.813517i	−0.171643	+	0.985159i	$0.554907\pi$
$968$	−603.569	+	603.569i	−0.623522	+	0.623522i
$969$			567.626i			0.585785i
$970$	286.038	−	552.402i	0.294884	−	0.569487i
$971$	547.200			0.563543			0.281771	−	0.959482i	$-0.409078\pi$
$971$	547.200			0.563543			0.281771	+	0.959482i	$0.409078\pi$
$972$	−249.246	−	249.246i	−0.256426	−	0.256426i
$973$	−332.037	+	332.037i	−0.341251	+	0.341251i
$974$		−	11.5451i		−	0.0118533i
$975$	76.7539	−	54.2425i	0.0787219	−	0.0556333i
$976$	−88.9389			−0.0911259
$977$	1187.60	+	1187.60i	1.21556	+	1.21556i	0.969172	+	0.246386i	$0.0792430\pi$
$977$	1187.60	+	1187.60i	1.21556	+	1.21556i	0.246386	+	0.969172i	$0.420757\pi$
$978$	634.013	−	634.013i	0.648275	−	0.648275i
$979$		−	97.6969i		−	0.0997926i
$980$	357.638	+	185.187i	0.364936	+	0.188967i
$981$	324.061			0.330337
$982$	583.628	+	583.628i	0.594325	+	0.594325i
$983$	793.359	−	793.359i	0.807079	−	0.807079i	−0.177111	−	0.984191i	$-0.556675\pi$
$983$	793.359	−	793.359i	0.807079	−	0.807079i	0.984191	+	0.177111i	$0.0566753\pi$
$984$		−	229.866i		−	0.233604i
$985$	223.257	+	702.750i	0.226657	+	0.713452i
$986$	39.5282			0.0400895
$987$	−243.158	−	243.158i	−0.246361	−	0.246361i
$988$	33.2134	−	33.2134i	0.0336168	−	0.0336168i
$989$		−	397.640i		−	0.402062i
$990$	−119.880	+	38.0847i	−0.121091	+	0.0384694i
$991$	−961.596			−0.970329			−0.485164	−	0.874423i	$-0.661240\pi$
$991$	−961.596			−0.970329			−0.485164	+	0.874423i	$0.661240\pi$
$992$	144.907	+	144.907i	0.146076	+	0.146076i
$993$	1225.56	−	1225.56i	1.23420	−	1.23420i
$994$			352.158i			0.354284i
$995$	−890.069	+	1718.92i	−0.894541	+	1.72756i
$996$	697.734			0.700536
$997$	−808.883	−	808.883i	−0.811317	−	0.811317i	0.173514	−	0.984831i	$-0.444488\pi$
$997$	−808.883	−	808.883i	−0.811317	−	0.811317i	−0.984831	+	0.173514i	$0.944488\pi$
$998$	−37.8410	+	37.8410i	−0.0379169	+	0.0379169i
$999$			92.1951i			0.0922874i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.3.f.a.47.16	✓	44
5.3	odd	4	inner	115.3.f.a.93.16	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.3.f.a.47.16	✓	44	1.1	even	1	trivial
115.3.f.a.93.16	yes	44	5.3	odd	4	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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	115.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.03401 + 1.03401i) q^{2} +(2.52164 - 2.52164i) q^{3} -1.86167i q^{4} +(-4.44006 - 2.29910i) q^{5} +5.21478 q^{6} +(1.69314 + 1.69314i) q^{7} +(6.06099 - 6.06099i) q^{8} -3.71736i q^{9} +(-2.21377 - 6.96833i) q^{10} +4.62790 q^{11} +(-4.69446 - 4.69446i) q^{12} +(0.745436 - 0.745436i) q^{13} +3.50143i q^{14} +(-16.9937 + 5.39875i) q^{15} +5.08753 q^{16} +(4.70270 + 4.70270i) q^{17} +(3.84377 - 3.84377i) q^{18} +23.9332i q^{19} +(-4.28015 + 8.26592i) q^{20} +8.53898 q^{21} +(4.78528 + 4.78528i) q^{22} +(-3.39116 + 3.39116i) q^{23} -30.5673i q^{24} +(14.4283 + 20.4163i) q^{25} +1.54157 q^{26} +(13.3209 + 13.3209i) q^{27} +(3.15206 - 3.15206i) q^{28} -4.06450i q^{29} +(-23.1540 - 11.9893i) q^{30} -7.63335 q^{31} +(-18.9834 - 18.9834i) q^{32} +(11.6699 - 11.6699i) q^{33} +9.72524i q^{34} +(-3.62495 - 11.4103i) q^{35} -6.92048 q^{36} +(3.46053 + 3.46053i) q^{37} +(-24.7471 + 24.7471i) q^{38} -3.75945i q^{39} +(-40.8460 + 12.9764i) q^{40} +7.52000 q^{41} +(8.82935 + 8.82935i) q^{42} +(-58.6288 + 58.6288i) q^{43} -8.61561i q^{44} +(-8.54656 + 16.5053i) q^{45} -7.01296 q^{46} +(-28.4763 - 28.4763i) q^{47} +(12.8289 - 12.8289i) q^{48} -43.2666i q^{49} +(-6.19158 + 36.0295i) q^{50} +23.7171 q^{51} +(-1.38775 - 1.38775i) q^{52} +(15.8331 - 15.8331i) q^{53} +27.5478i q^{54} +(-20.5482 - 10.6400i) q^{55} +20.5242 q^{56} +(60.3510 + 60.3510i) q^{57} +(4.20271 - 4.20271i) q^{58} -102.951i q^{59} +(10.0507 + 31.6367i) q^{60} -17.4817 q^{61} +(-7.89292 - 7.89292i) q^{62} +(6.29400 - 6.29400i) q^{63} -59.6081i q^{64} +(-5.02361 + 1.59595i) q^{65} +24.1335 q^{66} +(56.9571 + 56.9571i) q^{67} +(8.75487 - 8.75487i) q^{68} +17.1026i q^{69} +(8.05012 - 15.5466i) q^{70} +100.575 q^{71} +(-22.5309 - 22.5309i) q^{72} +(-78.3607 + 78.3607i) q^{73} +7.15642i q^{74} +(87.8655 + 15.0995i) q^{75} +44.5557 q^{76} +(7.83568 + 7.83568i) q^{77} +(3.88729 - 3.88729i) q^{78} -105.667i q^{79} +(-22.5890 - 11.6967i) q^{80} +100.637 q^{81} +(7.77572 + 7.77572i) q^{82} +(-74.3146 + 74.3146i) q^{83} -15.8967i q^{84} +(-10.0683 - 31.6923i) q^{85} -121.245 q^{86} +(-10.2492 - 10.2492i) q^{87} +(28.0497 - 28.0497i) q^{88} -21.1104i q^{89} +(-25.9038 + 8.22937i) q^{90} +2.52425 q^{91} +(6.31322 + 6.31322i) q^{92} +(-19.2486 + 19.2486i) q^{93} -58.8892i q^{94} +(55.0248 - 106.265i) q^{95} -95.7389 q^{96} +(60.1608 + 60.1608i) q^{97} +(44.7378 - 44.7378i) q^{98} -17.2036i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 4 q^{2} - 8 q^{5} - 16 q^{7} + 12 q^{8} - 4 q^{10} - 24 q^{11} + 48 q^{12} + 4 q^{13} + 60 q^{15} - 224 q^{16} + 24 q^{17} - 88 q^{18} - 56 q^{20} + 8 q^{21} - 48 q^{22} + 84 q^{25} + 56 q^{26} - 132 q^{27}+ \cdots + 780 q^{98}+O(q^{100}) \) 44 * q - 4 * q^2 - 8 * q^5 - 16 * q^7 + 12 * q^8 - 4 * q^10 - 24 * q^11 + 48 * q^12 + 4 * q^13 + 60 * q^15 - 224 * q^16 + 24 * q^17 - 88 * q^18 - 56 * q^20 + 8 * q^21 - 48 * q^22 + 84 * q^25 + 56 * q^26 - 132 * q^27 + 204 * q^28 - 200 * q^30 + 100 * q^31 + 184 * q^32 - 68 * q^33 - 48 * q^35 + 552 * q^36 - 48 * q^37 - 52 * q^38 + 200 * q^40 - 132 * q^41 - 248 * q^42 + 128 * q^43 + 204 * q^45 + 152 * q^47 - 500 * q^48 - 228 * q^50 - 264 * q^51 + 280 * q^52 + 324 * q^53 - 156 * q^55 - 312 * q^56 + 320 * q^57 + 364 * q^58 + 500 * q^60 + 32 * q^61 - 44 * q^62 - 220 * q^63 - 196 * q^65 - 552 * q^66 - 352 * q^67 - 616 * q^68 + 188 * q^70 + 108 * q^71 - 192 * q^72 + 168 * q^73 - 468 * q^75 + 464 * q^76 - 292 * q^77 + 596 * q^78 - 316 * q^80 - 332 * q^81 - 820 * q^82 - 144 * q^83 - 524 * q^85 + 536 * q^86 + 536 * q^87 - 132 * q^88 + 260 * q^90 + 312 * q^91 - 416 * q^93 + 304 * q^95 + 448 * q^96 + 620 * q^97 + 780 * q^98

Introduction

L-functions

Modular forms

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Representations

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Database

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