LMFDB - Embedded newform 123.4.e.a.73.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [123,4,Mod(73,123)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(123, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("123.73");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 123 = 3 \cdot 41 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	123.e (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:	$7.25723493071$
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			73.9
Character	$\chi$	$=$	123.73
Dual form			123.4.e.a.91.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.23251i q^{2} +(-2.12132 + 2.12132i) q^{3} +6.48091 q^{4} +10.4273i q^{5} +(2.61456 + 2.61456i) q^{6} +(-9.33905 + 9.33905i) q^{7} -17.8479i q^{8} -9.00000i q^{9} +O(q^{10})$	\(q-1.23251i q^{2} +(-2.12132 + 2.12132i) q^{3} +6.48091 q^{4} +10.4273i q^{5} +(2.61456 + 2.61456i) q^{6} +(-9.33905 + 9.33905i) q^{7} -17.8479i q^{8} -9.00000i q^{9} +12.8517 q^{10} +(-24.1540 + 24.1540i) q^{11} +(-13.7481 + 13.7481i) q^{12} +(-46.0019 + 46.0019i) q^{13} +(11.5105 + 11.5105i) q^{14} +(-22.1195 - 22.1195i) q^{15} +29.8494 q^{16} +(-30.6693 - 30.6693i) q^{17} -11.0926 q^{18} +(114.902 + 114.902i) q^{19} +67.5781i q^{20} -39.6222i q^{21} +(29.7702 + 29.7702i) q^{22} +30.8783 q^{23} +(37.8612 + 37.8612i) q^{24} +16.2724 q^{25} +(56.6980 + 56.6980i) q^{26} +(19.0919 + 19.0919i) q^{27} +(-60.5255 + 60.5255i) q^{28} +(-184.029 + 184.029i) q^{29} +(-27.2627 + 27.2627i) q^{30} -63.6191 q^{31} -179.573i q^{32} -102.477i q^{33} +(-37.8003 + 37.8003i) q^{34} +(-97.3807 - 97.3807i) q^{35} -58.3282i q^{36} +419.786 q^{37} +(141.619 - 141.619i) q^{38} -195.169i q^{39} +186.105 q^{40} +(-114.898 + 236.050i) q^{41} -48.8350 q^{42} -507.251i q^{43} +(-156.540 + 156.540i) q^{44} +93.8453 q^{45} -38.0580i q^{46} +(-318.524 - 318.524i) q^{47} +(-63.3202 + 63.3202i) q^{48} +168.564i q^{49} -20.0560i q^{50} +130.119 q^{51} +(-298.134 + 298.134i) q^{52} +(424.503 - 424.503i) q^{53} +(23.5310 - 23.5310i) q^{54} +(-251.860 - 251.860i) q^{55} +(166.683 + 166.683i) q^{56} -487.489 q^{57} +(226.818 + 226.818i) q^{58} +29.0249 q^{59} +(-143.355 - 143.355i) q^{60} -396.963i q^{61} +78.4115i q^{62} +(84.0515 + 84.0515i) q^{63} +17.4686 q^{64} +(-479.673 - 479.673i) q^{65} -126.304 q^{66} +(252.159 + 252.159i) q^{67} +(-198.765 - 198.765i) q^{68} +(-65.5028 + 65.5028i) q^{69} +(-120.023 + 120.023i) q^{70} +(527.232 - 527.232i) q^{71} -160.631 q^{72} +959.749i q^{73} -517.393i q^{74} +(-34.5189 + 34.5189i) q^{75} +(744.672 + 744.672i) q^{76} -451.151i q^{77} -240.549 q^{78} +(-103.283 + 103.283i) q^{79} +311.247i q^{80} -81.0000 q^{81} +(290.935 + 141.613i) q^{82} +394.030 q^{83} -256.788i q^{84} +(319.796 - 319.796i) q^{85} -625.194 q^{86} -780.768i q^{87} +(431.099 + 431.099i) q^{88} +(158.298 - 158.298i) q^{89} -115.666i q^{90} -859.227i q^{91} +200.119 q^{92} +(134.957 - 134.957i) q^{93} +(-392.585 + 392.585i) q^{94} +(-1198.12 + 1198.12i) q^{95} +(380.933 + 380.933i) q^{96} +(263.736 + 263.736i) q^{97} +207.758 q^{98} +(217.386 + 217.386i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 192 q^{4}+O(q^{10}) $ 44 * q - 192 * q^4	$ 44 q - 192 q^{4} + 224 q^{10} + 96 q^{11} - 24 q^{12} - 196 q^{13} + 148 q^{14} + 24 q^{15} + 896 q^{16} - 308 q^{17} + 112 q^{19} - 612 q^{22} - 208 q^{23} - 180 q^{24} - 1452 q^{25} + 1172 q^{26} - 220 q^{28} + 300 q^{29} + 456 q^{30} + 128 q^{31} - 552 q^{34} + 504 q^{35} - 88 q^{37} + 1204 q^{38} - 2112 q^{40} + 1316 q^{41} + 1560 q^{42} - 1412 q^{44} - 504 q^{45} + 520 q^{47} + 192 q^{48} + 936 q^{51} + 2652 q^{52} + 1116 q^{53} - 560 q^{55} - 4088 q^{56} - 936 q^{57} - 2860 q^{58} - 992 q^{59} - 804 q^{60} - 8472 q^{64} - 1480 q^{65} + 1968 q^{66} + 2592 q^{67} + 3836 q^{68} + 1368 q^{69} + 2468 q^{70} + 1888 q^{71} + 1512 q^{72} - 48 q^{75} + 996 q^{76} + 1392 q^{78} - 3000 q^{79} - 3564 q^{81} - 236 q^{82} - 2080 q^{83} - 1160 q^{85} - 5520 q^{86} + 7940 q^{88} - 2748 q^{89} + 14712 q^{92} + 1680 q^{93} - 6400 q^{94} - 7456 q^{95} + 4320 q^{96} + 5516 q^{97} + 11008 q^{98} - 864 q^{99}+O(q^{100}) $ 44 * q - 192 * q^4 + 224 * q^10 + 96 * q^11 - 24 * q^12 - 196 * q^13 + 148 * q^14 + 24 * q^15 + 896 * q^16 - 308 * q^17 + 112 * q^19 - 612 * q^22 - 208 * q^23 - 180 * q^24 - 1452 * q^25 + 1172 * q^26 - 220 * q^28 + 300 * q^29 + 456 * q^30 + 128 * q^31 - 552 * q^34 + 504 * q^35 - 88 * q^37 + 1204 * q^38 - 2112 * q^40 + 1316 * q^41 + 1560 * q^42 - 1412 * q^44 - 504 * q^45 + 520 * q^47 + 192 * q^48 + 936 * q^51 + 2652 * q^52 + 1116 * q^53 - 560 * q^55 - 4088 * q^56 - 936 * q^57 - 2860 * q^58 - 992 * q^59 - 804 * q^60 - 8472 * q^64 - 1480 * q^65 + 1968 * q^66 + 2592 * q^67 + 3836 * q^68 + 1368 * q^69 + 2468 * q^70 + 1888 * q^71 + 1512 * q^72 - 48 * q^75 + 996 * q^76 + 1392 * q^78 - 3000 * q^79 - 3564 * q^81 - 236 * q^82 - 2080 * q^83 - 1160 * q^85 - 5520 * q^86 + 7940 * q^88 - 2748 * q^89 + 14712 * q^92 + 1680 * q^93 - 6400 * q^94 - 7456 * q^95 + 4320 * q^96 + 5516 * q^97 + 11008 * q^98 - 864 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/123\mathbb{Z}\right)^\times$.

$n$	$83$	$88$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		−	1.23251i		−	0.435760i	−0.975976	−	0.217880i	$-0.930086\pi$
$2$		−	1.23251i		−	0.435760i	0.975976	−	0.217880i	$-0.0699141\pi$
$3$	−2.12132	+	2.12132i	−0.408248	+	0.408248i
$3$	−2.12132	+	2.12132i	−0.408248	+	0.408248i
$4$	6.48091			0.810113
$5$			10.4273i			0.932642i	0.884616	+	0.466321i	$0.154421\pi$
$5$			10.4273i			0.932642i	−0.884616	+	0.466321i	$0.845579\pi$
$6$	2.61456	+	2.61456i	0.177898	+	0.177898i
$7$	−9.33905	+	9.33905i	−0.504261	+	0.504261i	−0.912759	−	0.408498i	$-0.866053\pi$
$7$	−9.33905	+	9.33905i	−0.504261	+	0.504261i	0.408498	+	0.912759i	$0.366053\pi$
$8$		−	17.8479i		−	0.788775i
$9$		−	9.00000i		−	0.333333i
$10$	12.8517			0.406408
$11$	−24.1540	+	24.1540i	−0.662064	+	0.662064i	−0.955866	−	0.293802i	$-0.905079\pi$
$11$	−24.1540	+	24.1540i	−0.662064	+	0.662064i	0.293802	+	0.955866i	$0.405079\pi$
$12$	−13.7481	+	13.7481i	−0.330727	+	0.330727i
$13$	−46.0019	+	46.0019i	−0.981432	+	0.981432i	−0.999831	−	0.0183986i	$-0.994143\pi$
$13$	−46.0019	+	46.0019i	−0.981432	+	0.981432i	0.0183986	+	0.999831i	$0.494143\pi$
$14$	11.5105	+	11.5105i	0.219737	+	0.219737i
$15$	−22.1195	−	22.1195i	−0.380749	−	0.380749i
$16$	29.8494			0.466397
$17$	−30.6693	−	30.6693i	−0.437552	−	0.437552i	0.453635	−	0.891188i	$-0.350127\pi$
$17$	−30.6693	−	30.6693i	−0.437552	−	0.437552i	−0.891188	+	0.453635i	$0.850127\pi$
$18$	−11.0926			−0.145253
$19$	114.902	+	114.902i	1.38739	+	1.38739i	0.830762	+	0.556628i	$0.187905\pi$
$19$	114.902	+	114.902i	1.38739	+	1.38739i	0.556628	+	0.830762i	$0.312095\pi$
$20$			67.5781i			0.755546i
$21$		−	39.6222i		−	0.411728i
$22$	29.7702	+	29.7702i	0.288501	+	0.288501i
$23$	30.8783			0.279938			0.139969	−	0.990156i	$-0.455300\pi$
$23$	30.8783			0.279938			0.139969	+	0.990156i	$0.455300\pi$
$24$	37.8612	+	37.8612i	0.322016	+	0.322016i
$25$	16.2724			0.130179
$26$	56.6980	+	56.6980i	0.427669	+	0.427669i
$27$	19.0919	+	19.0919i	0.136083	+	0.136083i
$28$	−60.5255	+	60.5255i	−0.408509	+	0.408509i
$29$	−184.029	+	184.029i	−1.17839	+	1.17839i	−0.198235	+	0.980155i	$0.563521\pi$
$29$	−184.029	+	184.029i	−1.17839	+	1.17839i	−0.980155	+	0.198235i	$0.936479\pi$
$30$	−27.2627	+	27.2627i	−0.165915	+	0.165915i
$31$	−63.6191			−0.368591			−0.184296	−	0.982871i	$-0.559000\pi$
$31$	−63.6191			−0.368591			−0.184296	+	0.982871i	$0.559000\pi$
$32$		−	179.573i		−	0.992012i
$33$		−	102.477i		−	0.540573i
$34$	−37.8003	+	37.8003i	−0.190668	+	0.190668i
$35$	−97.3807	−	97.3807i	−0.470295	−	0.470295i
$36$		−	58.3282i		−	0.270038i
$37$	419.786			1.86520			0.932601	−	0.360909i	$-0.117534\pi$
$37$	419.786			1.86520			0.932601	+	0.360909i	$0.117534\pi$
$38$	141.619	−	141.619i	0.604569	−	0.604569i
$39$		−	195.169i		−	0.801336i
$40$	186.105			0.735644
$41$	−114.898	+	236.050i	−0.437660	+	0.899141i
$41$	−114.898	+	236.050i	−0.437660	+	0.899141i
$42$	−48.8350			−0.179414
$43$		−	507.251i		−	1.79895i	−0.436968	−	0.899477i	$-0.643948\pi$
$43$		−	507.251i		−	1.79895i	0.436968	−	0.899477i	$-0.356052\pi$
$44$	−156.540	+	156.540i	−0.536347	+	0.536347i
$45$	93.8453			0.310881
$46$		−	38.0580i		−	0.121986i
$47$	−318.524	−	318.524i	−0.988541	−	0.988541i	0.0113940	−	0.999935i	$-0.496373\pi$
$47$	−318.524	−	318.524i	−0.988541	−	0.988541i	−0.999935	+	0.0113940i	$0.996373\pi$
$48$	−63.3202	+	63.3202i	−0.190406	+	0.190406i
$49$			168.564i			0.491441i
$50$		−	20.0560i		−	0.0567268i
$51$	130.119			0.357260
$52$	−298.134	+	298.134i	−0.795071	+	0.795071i
$53$	424.503	−	424.503i	1.10019	−	1.10019i	0.105799	−	0.994387i	$-0.466260\pi$
$53$	424.503	−	424.503i	1.10019	−	1.10019i	0.994387	−	0.105799i	$-0.0337401\pi$
$54$	23.5310	−	23.5310i	0.0592994	−	0.0592994i
$55$	−251.860	−	251.860i	−0.617469	−	0.617469i
$56$	166.683	+	166.683i	0.397749	+	0.397749i
$57$	−487.489			−1.13280
$58$	226.818	+	226.818i	0.513495	+	0.513495i
$59$	29.0249			0.0640461			0.0320230	−	0.999487i	$-0.489805\pi$
$59$	29.0249			0.0640461			0.0320230	+	0.999487i	$0.489805\pi$
$60$	−143.355	−	143.355i	−0.308450	−	0.308450i
$61$		−	396.963i		−	0.833212i	−0.909087	−	0.416606i	$-0.863220\pi$
$61$		−	396.963i		−	0.833212i	0.909087	−	0.416606i	$-0.136780\pi$
$62$			78.4115i			0.160617i
$63$	84.0515	+	84.0515i	0.168087	+	0.168087i
$64$	17.4686			0.0341184
$65$	−479.673	−	479.673i	−0.915325	−	0.915325i
$66$	−126.304			−0.235560
$67$	252.159	+	252.159i	0.459792	+	0.459792i	0.898587	−	0.438795i	$-0.144595\pi$
$67$	252.159	+	252.159i	0.459792	+	0.459792i	−0.438795	+	0.898587i	$0.644595\pi$
$68$	−198.765	−	198.765i	−0.354467	−	0.354467i
$69$	−65.5028	+	65.5028i	−0.114284	+	0.114284i
$70$	−120.023	+	120.023i	−0.204936	+	0.204936i
$71$	527.232	−	527.232i	0.881280	−	0.881280i	−0.112385	−	0.993665i	$-0.535849\pi$
$71$	527.232	−	527.232i	0.881280	−	0.881280i	0.993665	+	0.112385i	$0.0358488\pi$
$72$	−160.631			−0.262925
$73$			959.749i			1.53877i	0.638786	+	0.769385i	$0.279437\pi$
$73$			959.749i			1.53877i	−0.638786	+	0.769385i	$0.720563\pi$
$74$		−	517.393i		−	0.812780i
$75$	−34.5189	+	34.5189i	−0.0531454	+	0.0531454i
$76$	744.672	+	744.672i	1.12394	+	1.12394i
$77$		−	451.151i		−	0.667707i
$78$	−240.549			−0.349190
$79$	−103.283	+	103.283i	−0.147092	+	0.147092i	−0.776818	−	0.629726i	$-0.783167\pi$
$79$	−103.283	+	103.283i	−0.147092	+	0.147092i	0.629726	+	0.776818i	$0.283167\pi$
$80$			311.247i			0.434982i
$81$	−81.0000			−0.111111
$82$	290.935	+	141.613i	0.391809	+	0.190714i
$83$	394.030			0.521089			0.260545	−	0.965462i	$-0.416098\pi$
$83$	394.030			0.521089			0.260545	+	0.965462i	$0.416098\pi$
$84$		−	256.788i		−	0.333546i
$85$	319.796	−	319.796i	0.408080	−	0.408080i
$86$	−625.194			−0.783912
$87$		−	780.768i		−	0.962151i
$88$	431.099	+	431.099i	0.522219	+	0.522219i
$89$	158.298	−	158.298i	0.188534	−	0.188534i	−0.606528	−	0.795062i	$-0.707438\pi$
$89$	158.298	−	158.298i	0.188534	−	0.188534i	0.795062	+	0.606528i	$0.207438\pi$
$90$		−	115.666i		−	0.135469i
$91$		−	859.227i		−	0.989797i
$92$	200.119			0.226781
$93$	134.957	−	134.957i	0.150477	−	0.150477i
$94$	−392.585	+	392.585i	−0.430766	+	0.430766i
$95$	−1198.12	+	1198.12i	−1.29394	+	1.29394i
$96$	380.933	+	380.933i	0.404987	+	0.404987i
$97$	263.736	+	263.736i	0.276065	+	0.276065i	0.831536	−	0.555471i	$-0.187462\pi$
$97$	263.736	+	263.736i	0.276065	+	0.276065i	−0.555471	+	0.831536i	$0.687462\pi$
$98$	207.758			0.214150
$99$	217.386	+	217.386i	0.220688	+	0.220688i
$100$	105.460			0.105460
$101$	815.968	+	815.968i	0.803880	+	0.803880i	0.983700	−	0.179820i	$-0.0575515\pi$
$101$	815.968	+	815.968i	0.803880	+	0.803880i	−0.179820	+	0.983700i	$0.557551\pi$
$102$		−	160.373i		−	0.155680i
$103$		−	520.370i		−	0.497802i	−0.968529	−	0.248901i	$-0.919931\pi$
$103$		−	520.370i		−	0.497802i	0.968529	−	0.248901i	$-0.0800693\pi$
$104$	821.038	+	821.038i	0.774129	+	0.774129i
$105$	413.151			0.383994
$106$	−523.206	−	523.206i	−0.479417	−	0.479417i
$107$	943.150			0.852128			0.426064	−	0.904693i	$-0.359900\pi$
$107$	943.150			0.852128			0.426064	+	0.904693i	$0.359900\pi$
$108$	123.733	+	123.733i	0.110242	+	0.110242i
$109$	−291.953	−	291.953i	−0.256551	−	0.256551i	0.567099	−	0.823650i	$-0.308066\pi$
$109$	−291.953	−	291.953i	−0.256551	−	0.256551i	−0.823650	+	0.567099i	$0.808066\pi$
$110$	−310.421	+	310.421i	−0.269068	+	0.269068i
$111$	−890.502	+	890.502i	−0.761465	+	0.761465i
$112$	−278.765	+	278.765i	−0.235186	+	0.235186i
$113$	−1472.44			−1.22580			−0.612899	−	0.790161i	$-0.709997\pi$
$113$	−1472.44			−1.22580			−0.612899	+	0.790161i	$0.709997\pi$
$114$			600.838i			0.493628i
$115$			321.976i			0.261082i
$116$	−1192.67	+	1192.67i	−0.954629	+	0.954629i
$117$	414.017	+	414.017i	0.327144	+	0.327144i
$118$		−	35.7736i		−	0.0279087i
$119$	572.844			0.441282
$120$	−394.788	+	394.788i	−0.300326	+	0.300326i
$121$			164.169i			0.123342i
$122$	−489.263			−0.363080
$123$	−257.002	−	744.472i	−0.188399	−	0.545746i
$124$	−412.310			−0.298601
$125$			1473.08i			1.05405i
$126$	103.595	−	103.595i	0.0732456	−	0.0732456i
$127$	149.210			0.104254			0.0521268	−	0.998640i	$-0.483400\pi$
$127$	149.210			0.104254			0.0521268	+	0.998640i	$0.483400\pi$
$128$		−	1458.12i		−	1.00688i
$129$	1076.04	+	1076.04i	0.734420	+	0.734420i
$130$	−591.204	+	591.204i	−0.398862	+	0.398862i
$131$			714.490i			0.476529i	0.971200	+	0.238264i	$0.0765785\pi$
$131$			714.490i			0.476529i	−0.971200	+	0.238264i	$0.923422\pi$
$132$		−	664.142i		−	0.437925i
$133$	−2146.16			−1.39921
$134$	310.789	−	310.789i	0.200359	−	0.200359i
$135$	−199.076	+	199.076i	−0.126916	+	0.126916i
$136$	−547.383	+	547.383i	−0.345130	+	0.345130i
$137$	695.293	+	695.293i	0.433598	+	0.433598i	0.889850	−	0.456253i	$-0.150809\pi$
$137$	695.293	+	695.293i	0.433598	+	0.433598i	−0.456253	+	0.889850i	$0.650809\pi$
$138$	80.7331	+	80.7331i	0.0498004	+	0.0498004i
$139$	−186.282			−0.113671			−0.0568354	−	0.998384i	$-0.518101\pi$
$139$	−186.282			−0.113671			−0.0568354	+	0.998384i	$0.518101\pi$
$140$	−631.115	−	631.115i	−0.380993	−	0.380993i
$141$	1351.38			0.807140
$142$	−649.821	−	649.821i	−0.384026	−	0.384026i
$143$		−	2222.26i		−	1.29954i
$144$		−	268.645i		−	0.155466i
$145$	−1918.92	−	1918.92i	−1.09902	−	1.09902i
$146$	1182.91			0.670534
$147$	−357.579	−	357.579i	−0.200630	−	0.200630i
$148$	2720.60			1.51103
$149$	882.376	+	882.376i	0.485148	+	0.485148i	0.906771	−	0.421623i	$-0.138539\pi$
$149$	882.376	+	882.376i	0.485148	+	0.485148i	−0.421623	+	0.906771i	$0.638539\pi$
$150$	42.5451	+	42.5451i	0.0231586	+	0.0231586i
$151$	1163.38	−	1163.38i	0.626986	−	0.626986i	−0.320323	−	0.947309i	$-0.603791\pi$
$151$	1163.38	−	1163.38i	0.626986	−	0.626986i	0.947309	+	0.320323i	$0.103791\pi$
$152$	2050.77	−	2050.77i	1.09434	−	1.09434i
$153$	−276.023	+	276.023i	−0.145851	+	0.145851i
$154$	−556.050			−0.290960
$155$		−	663.373i		−	0.343764i
$156$		−	1264.87i		−	0.649173i
$157$	887.564	−	887.564i	0.451180	−	0.451180i	−0.444566	−	0.895746i	$-0.646642\pi$
$157$	887.564	−	887.564i	0.451180	−	0.451180i	0.895746	+	0.444566i	$0.146642\pi$
$158$	127.298	+	127.298i	0.0640968	+	0.0640968i
$159$			1801.01i			0.898299i
$160$	1872.46			0.925192
$161$	−288.374	+	288.374i	−0.141162	+	0.141162i
$162$			99.8337i			0.0484178i
$163$	−3830.06			−1.84045			−0.920224	−	0.391391i	$-0.871994\pi$
$163$	−3830.06			−1.84045			−0.920224	+	0.391391i	$0.871994\pi$
$164$	−744.643	+	1529.82i	−0.354554	+	0.728406i
$165$	1068.55			0.504161
$166$		−	485.648i		−	0.227070i
$167$	2112.29	−	2112.29i	0.978766	−	0.978766i	−0.0210128	−	0.999779i	$-0.506689\pi$
$167$	2112.29	−	2112.29i	0.978766	−	0.978766i	0.999779	+	0.0210128i	$0.00668906\pi$
$168$	−707.175			−0.324760
$169$		−	2035.34i		−	0.926418i
$170$	−394.154	−	394.154i	−0.177825	−	0.177825i
$171$	1034.12	−	1034.12i	0.462463	−	0.462463i
$172$		−	3287.45i		−	1.45736i
$173$			2633.18i			1.15721i	0.815609	+	0.578604i	$0.196402\pi$
$173$			2633.18i			1.15721i	−0.815609	+	0.578604i	$0.803598\pi$
$174$	−962.308			−0.419267
$175$	−151.969	+	151.969i	−0.0656443	+	0.0656443i
$176$	−720.983	+	720.983i	−0.308785	+	0.308785i
$177$	−61.5711	+	61.5711i	−0.0261467	+	0.0261467i
$178$	−195.105	−	195.105i	−0.0821556	−	0.0821556i
$179$	−1073.96	−	1073.96i	−0.448445	−	0.448445i	0.446393	−	0.894837i	$-0.352709\pi$
$179$	−1073.96	−	1073.96i	−0.448445	−	0.448445i	−0.894837	+	0.446393i	$0.852709\pi$
$180$	608.203			0.251849
$181$	−1480.89	−	1480.89i	−0.608141	−	0.608141i	0.334319	−	0.942460i	$-0.391494\pi$
$181$	−1480.89	−	1480.89i	−0.608141	−	0.608141i	−0.942460	+	0.334319i	$0.891494\pi$
$182$	−1059.01			−0.431314
$183$	842.086	+	842.086i	0.340157	+	0.340157i
$184$		−	551.114i		−	0.220808i
$185$			4377.22i			1.73957i
$186$	−166.336	−	166.336i	−0.0655717	−	0.0655717i
$187$	1481.57			0.579375
$188$	−2064.32	−	2064.32i	−0.800830	−	0.800830i
$189$	−356.600			−0.137243
$190$	1476.70	+	1476.70i	0.563846	+	0.563846i
$191$	751.114	+	751.114i	0.284548	+	0.284548i	0.834920	−	0.550372i	$-0.185514\pi$
$191$	751.114	+	751.114i	0.284548	+	0.284548i	−0.550372	+	0.834920i	$0.685514\pi$
$192$	−37.0565	+	37.0565i	−0.0139288	+	0.0139288i
$193$	−1053.09	+	1053.09i	−0.392764	+	0.392764i	−0.875671	−	0.482908i	$-0.839581\pi$
$193$	−1053.09	+	1053.09i	−0.392764	+	0.392764i	0.482908	+	0.875671i	$0.339581\pi$
$194$	325.058	−	325.058i	0.120298	−	0.120298i
$195$	2035.08			0.747360
$196$			1092.45i			0.398123i
$197$			1388.84i			0.502288i	0.967950	+	0.251144i	$0.0808068\pi$
$197$			1388.84i			0.502288i	−0.967950	+	0.251144i	$0.919193\pi$
$198$	267.931	−	267.931i	0.0961670	−	0.0961670i
$199$	599.070	+	599.070i	0.213402	+	0.213402i	0.805711	−	0.592309i	$-0.201784\pi$
$199$	599.070	+	599.070i	0.213402	+	0.213402i	−0.592309	+	0.805711i	$0.701784\pi$
$200$		−	290.428i		−	0.102682i
$201$	−1069.82			−0.375419
$202$	1005.69	−	1005.69i	0.350298	−	0.350298i
$203$		−	3437.31i		−	1.18843i
$204$	843.287			0.289421
$205$	−2461.35	−	1198.07i	−0.838576	−	0.408180i
$206$	−641.364			−0.216922
$207$		−	277.905i		−	0.0933126i
$208$	−1373.13	+	1373.13i	−0.457737	+	0.457737i
$209$	−5550.70			−1.83708
$210$		−	509.215i		−	0.167329i
$211$	1201.22	+	1201.22i	0.391921	+	0.391921i	0.875372	−	0.483451i	$-0.160617\pi$
$211$	1201.22	+	1201.22i	0.391921	+	0.391921i	−0.483451	+	0.875372i	$0.660617\pi$
$212$	2751.16	−	2751.16i	0.891276	−	0.891276i
$213$			2236.85i			0.719562i
$214$		−	1162.45i		−	0.371323i
$215$	5289.23			1.67778
$216$	340.751	−	340.751i	0.107339	−	0.107339i
$217$	594.142	−	594.142i	0.185866	−	0.185866i
$218$	−359.836	+	359.836i	−0.111794	+	0.111794i
$219$	−2035.94	−	2035.94i	−0.628200	−	0.628200i
$220$	−1632.28	−	1632.28i	−0.500220	−	0.500220i
$221$	2821.69			0.858856
$222$	1097.56	+	1097.56i	0.331816	+	0.331816i
$223$	560.618			0.168349			0.0841744	−	0.996451i	$-0.473175\pi$
$223$	560.618			0.168349			0.0841744	+	0.996451i	$0.473175\pi$
$224$	1677.04	+	1677.04i	0.500233	+	0.500233i
$225$		−	146.451i		−	0.0433930i
$226$			1814.80i			0.534154i
$227$	−1484.89	−	1484.89i	−0.434167	−	0.434167i	0.455876	−	0.890043i	$-0.349326\pi$
$227$	−1484.89	−	1484.89i	−0.434167	−	0.434167i	−0.890043	+	0.455876i	$0.849326\pi$
$228$	−3159.37			−0.917696
$229$	−507.141	−	507.141i	−0.146344	−	0.146344i	0.630139	−	0.776483i	$-0.282998\pi$
$229$	−507.141	−	507.141i	−0.146344	−	0.146344i	−0.776483	+	0.630139i	$0.782998\pi$
$230$	396.840			0.113769
$231$	957.036	+	957.036i	0.272590	+	0.272590i
$232$	3284.53	+	3284.53i	0.929484	+	0.929484i
$233$	−3371.39	+	3371.39i	−0.947927	+	0.947927i	−0.998710	−	0.0507828i	$-0.983828\pi$
$233$	−3371.39	+	3371.39i	−0.947927	+	0.947927i	0.0507828	+	0.998710i	$0.483828\pi$
$234$	510.282	−	510.282i	0.142556	−	0.142556i
$235$	3321.33	−	3321.33i	0.921955	−	0.921955i
$236$	188.108			0.0518846
$237$		−	438.194i		−	0.120100i
$238$		−	706.038i		−	0.192293i
$239$	−1475.49	+	1475.49i	−0.399336	+	0.399336i	−0.877999	−	0.478663i	$-0.841122\pi$
$239$	−1475.49	+	1475.49i	−0.399336	+	0.399336i	0.478663	+	0.877999i	$0.341122\pi$
$240$	−660.256	−	660.256i	−0.177580	−	0.177580i
$241$			4528.35i			1.21036i	0.796089	+	0.605180i	$0.206899\pi$
$241$			4528.35i			1.21036i	−0.796089	+	0.605180i	$0.793101\pi$
$242$	202.340			0.0537476
$243$	171.827	−	171.827i	0.0453609	−	0.0453609i
$244$		−	2572.68i		−	0.674996i
$245$	−1757.66			−0.458338
$246$	−917.573	+	316.758i	−0.237814	+	0.0820967i
$247$	−10571.4			−2.72326
$248$			1135.47i			0.290736i
$249$	−835.863	+	835.863i	−0.212734	+	0.212734i
$250$	1815.60			0.459314
$251$			3302.16i			0.830401i	0.909730	+	0.415201i	$0.136289\pi$
$251$			3302.16i			0.830401i	−0.909730	+	0.415201i	$0.863711\pi$
$252$	544.730	+	544.730i	0.136170	+	0.136170i
$253$	−745.834	+	745.834i	−0.185337	+	0.185337i
$254$		−	183.903i		−	0.0454295i
$255$			1356.78i			0.333196i
$256$	−1657.40			−0.404639
$257$	2010.54	−	2010.54i	0.487992	−	0.487992i	−0.419680	−	0.907672i	$-0.637858\pi$
$257$	2010.54	−	2010.54i	0.487992	−	0.487992i	0.907672	+	0.419680i	$0.137858\pi$
$258$	1326.24	−	1326.24i	0.320031	−	0.320031i
$259$	−3920.41	+	3920.41i	−0.940549	+	0.940549i
$260$	−3108.72	−	3108.72i	−0.741517	−	0.741517i
$261$	1656.26	+	1656.26i	0.392797	+	0.392797i
$262$	880.620			0.207652
$263$	2546.53	+	2546.53i	0.597057	+	0.597057i	0.939528	−	0.342471i	$-0.111264\pi$
$263$	2546.53	+	2546.53i	0.597057	+	0.597057i	−0.342471	+	0.939528i	$0.611264\pi$
$264$	−1829.00			−0.426390
$265$	4426.40	+	4426.40i	1.02608	+	1.02608i
$266$			2645.17i			0.609721i
$267$			671.601i			0.153938i
$268$	1634.22	+	1634.22i	0.372484	+	0.372484i
$269$	4241.10			0.961281			0.480641	−	0.876918i	$-0.340404\pi$
$269$	4241.10			0.961281			0.480641	+	0.876918i	$0.340404\pi$
$270$	245.364	+	245.364i	0.0553051	+	0.0553051i
$271$	3796.72			0.851048			0.425524	−	0.904947i	$-0.360090\pi$
$271$	3796.72			0.851048			0.425524	+	0.904947i	$0.360090\pi$
$272$	−915.460	−	915.460i	−0.204073	−	0.204073i
$273$	1822.70	+	1822.70i	0.404083	+	0.404083i
$274$	856.959	−	856.959i	0.188944	−	0.188944i
$275$	−393.043	+	393.043i	−0.0861869	+	0.0861869i
$276$	−424.517	+	424.517i	−0.0925831	+	0.0925831i
$277$	1228.11			0.266391			0.133195	−	0.991090i	$-0.457476\pi$
$277$	1228.11			0.266391			0.133195	+	0.991090i	$0.457476\pi$
$278$			229.596i			0.0495332i
$279$			572.572i			0.122864i
$280$	−1738.04	+	1738.04i	−0.370957	+	0.370957i
$281$	290.585	+	290.585i	0.0616898	+	0.0616898i	0.737279	−	0.675589i	$-0.236111\pi$
$281$	290.585	+	290.585i	0.0616898	+	0.0616898i	−0.675589	+	0.737279i	$0.736111\pi$
$282$		−	1665.60i		−	0.351719i
$283$	−350.522			−0.0736268			−0.0368134	−	0.999322i	$-0.511721\pi$
$283$	−350.522			−0.0736268			−0.0368134	+	0.999322i	$0.511721\pi$
$284$	3416.94	−	3416.94i	0.713937	−	0.713937i
$285$		−	5083.18i		−	1.05650i
$286$	−2738.96			−0.566288
$287$	−1131.44	−	3277.52i	−0.232707	−	0.674097i
$288$	−1616.16			−0.330671
$289$		−	3031.79i		−	0.617096i
$290$	−2365.09	+	2365.09i	−0.478907	+	0.478907i
$291$	−1118.94			−0.225406
$292$			6220.05i			1.24658i
$293$	5466.40	+	5466.40i	1.08993	+	1.08993i	0.995534	+	0.0943984i	$0.0300928\pi$
$293$	5466.40	+	5466.40i	1.08993	+	1.08993i	0.0943984	+	0.995534i	$0.469907\pi$
$294$	−440.721	+	440.721i	−0.0874264	+	0.0874264i
$295$			302.650i			0.0597321i
$296$		−	7492.32i		−	1.47122i
$297$	−922.291			−0.180191
$298$	1087.54	−	1087.54i	0.211408	−	0.211408i
$299$	−1420.46	+	1420.46i	−0.274740	+	0.274740i
$300$	−223.714	+	223.714i	−0.0430538	+	0.0430538i
$301$	4737.24	+	4737.24i	0.907143	+	0.907143i
$302$	−1433.89	−	1433.89i	−0.273215	−	0.273215i
$303$	−3461.86			−0.656365
$304$	3429.77	+	3429.77i	0.647075	+	0.647075i
$305$	4139.24			0.777088
$306$	340.203	+	340.203i	0.0635559	+	0.0635559i
$307$			3823.11i			0.710738i	0.934726	+	0.355369i	$0.115645\pi$
$307$			3823.11i			0.710738i	−0.934726	+	0.355369i	$0.884355\pi$
$308$		−	2923.87i		−	0.540918i
$309$	1103.87	+	1103.87i	0.203227	+	0.203227i
$310$	−817.617			−0.149798
$311$	−6441.63	−	6441.63i	−1.17451	−	1.17451i	−0.981123	−	0.193383i	$-0.938054\pi$
$311$	−6441.63	−	6441.63i	−1.17451	−	1.17451i	−0.193383	−	0.981123i	$-0.561946\pi$
$312$	−3483.37			−0.632073
$313$	2313.97	+	2313.97i	0.417869	+	0.417869i	0.884469	−	0.466599i	$-0.154521\pi$
$313$	2313.97	+	2313.97i	0.417869	+	0.417869i	−0.466599	+	0.884469i	$0.654521\pi$
$314$	−1093.94	−	1093.94i	−0.196606	−	0.196606i
$315$	−876.426	+	876.426i	−0.156765	+	0.156765i
$316$	−669.369	+	669.369i	−0.119161	+	0.119161i
$317$	−5122.90	+	5122.90i	−0.907667	+	0.907667i	−0.996084	−	0.0884165i	$-0.971819\pi$
$317$	−5122.90	+	5122.90i	−0.907667	+	0.907667i	0.0884165	+	0.996084i	$0.471819\pi$
$318$	2219.77			0.391442
$319$		−	8890.06i		−	1.56034i
$320$			182.150i			0.0318203i
$321$	−2000.72	+	2000.72i	−0.347880	+	0.347880i
$322$	355.425	+	355.425i	0.0615126	+	0.0615126i
$323$		−	7047.94i		−	1.21411i
$324$	−524.954			−0.0900126
$325$	−748.560	+	748.560i	−0.127762	+	0.127762i
$326$			4720.60i			0.801993i
$327$	1238.65			0.209473
$328$	4213.00	+	2050.69i	0.709219	+	0.345215i
$329$	5949.41			0.996966
$330$		−	1317.00i		−	0.219693i
$331$	3054.32	−	3054.32i	0.507192	−	0.507192i	−0.406472	−	0.913663i	$-0.633241\pi$
$331$	3054.32	−	3054.32i	0.507192	−	0.507192i	0.913663	+	0.406472i	$0.133241\pi$
$332$	2553.67			0.422141
$333$		−	3778.08i		−	0.621734i
$334$	−2603.43	−	2603.43i	−0.426507	−	0.426507i
$335$	−2629.32	+	2629.32i	−0.428822	+	0.428822i
$336$		−	1182.70i		−	0.192029i
$337$		−	9853.16i		−	1.59269i	−0.604844	−	0.796344i	$-0.706765\pi$
$337$		−	9853.16i		−	1.59269i	0.604844	−	0.796344i	$-0.293235\pi$
$338$	−2508.59			−0.403696
$339$	3123.51	−	3123.51i	0.500430	−	0.500430i
$340$	2072.57	−	2072.57i	0.330591	−	0.330591i
$341$	1536.66	−	1536.66i	0.244031	−	0.244031i
$342$	−1274.57	−	1274.57i	−0.201523	−	0.201523i
$343$	−4777.52	−	4777.52i	−0.752076	−	0.752076i
$344$	−9053.38			−1.41897
$345$	−683.014	−	683.014i	−0.106586	−	0.106586i
$346$	3245.43			0.504265
$347$	−6394.42	−	6394.42i	−0.989253	−	0.989253i	0.0106903	−	0.999943i	$-0.496597\pi$
$347$	−6394.42	−	6394.42i	−0.989253	−	0.989253i	−0.999943	+	0.0106903i	$0.996597\pi$
$348$		−	5060.09i		−	0.779451i
$349$		−	8285.86i		−	1.27087i	−0.772156	−	0.635433i	$-0.780822\pi$
$349$		−	8285.86i		−	1.27087i	0.772156	−	0.635433i	$-0.219178\pi$
$350$	187.304	+	187.304i	0.0286051	+	0.0286051i
$351$	−1756.52			−0.267112
$352$	4337.41	+	4337.41i	0.656775	+	0.656775i
$353$	2147.42			0.323784			0.161892	−	0.986808i	$-0.448240\pi$
$353$	2147.42			0.323784			0.161892	+	0.986808i	$0.448240\pi$
$354$	75.8873	+	75.8873i	0.0113937	+	0.0113937i
$355$	5497.58	+	5497.58i	0.821919	+	0.821919i
$356$	1025.91	−	1025.91i	0.152734	−	0.152734i
$357$	−1215.19	+	1215.19i	−0.180152	+	0.180152i
$358$	−1323.67	+	1323.67i	−0.195414	+	0.195414i
$359$	10693.1			1.57203			0.786014	−	0.618208i	$-0.212141\pi$
$359$	10693.1			1.57203			0.786014	+	0.618208i	$0.212141\pi$
$360$		−	1674.94i		−	0.245215i
$361$			19546.1i			2.84970i
$362$	−1825.22	+	1825.22i	−0.265003	+	0.265003i
$363$	−348.254	−	348.254i	−0.0503543	−	0.0503543i
$364$		−	5568.57i		−	0.801848i
$365$	−10007.6			−1.43512
$366$	1037.88	−	1037.88i	0.148227	−	0.148227i
$367$		−	2672.21i		−	0.380077i	−0.981777	−	0.190038i	$-0.939139\pi$
$367$		−	2672.21i		−	0.380077i	0.981777	−	0.190038i	$-0.0608612\pi$
$368$	921.699			0.130562
$369$	2124.45	+	1034.08i	0.299714	+	0.145887i
$370$	5394.99			0.758033
$371$			7928.90i			1.10956i
$372$	874.641	−	874.641i	0.121903	−	0.121903i
$373$	−8106.71			−1.12533			−0.562667	−	0.826684i	$-0.690225\pi$
$373$	−8106.71			−1.12533			−0.562667	+	0.826684i	$0.690225\pi$
$374$		−	1826.06i		−	0.252468i
$375$	−3124.88	−	3124.88i	−0.430315	−	0.430315i
$376$	−5684.99	+	5684.99i	−0.779736	+	0.779736i
$377$		−	16931.3i		−	2.31302i
$378$			439.515i			0.0598048i
$379$	6118.88			0.829302			0.414651	−	0.909980i	$-0.363904\pi$
$379$	6118.88			0.829302			0.414651	+	0.909980i	$0.363904\pi$
$380$	−7764.88	+	7764.88i	−1.04824	+	1.04824i
$381$	−316.521	+	316.521i	−0.0425613	+	0.0425613i
$382$	925.760	−	925.760i	0.123995	−	0.123995i
$383$	−4768.56	−	4768.56i	−0.636194	−	0.636194i	0.313421	−	0.949614i	$-0.398525\pi$
$383$	−4768.56	−	4768.56i	−0.636194	−	0.636194i	−0.949614	+	0.313421i	$0.898525\pi$
$384$	3093.13	+	3093.13i	0.411057	+	0.411057i
$385$	4704.26			0.622731
$386$	1297.95	+	1297.95i	0.171151	+	0.171151i
$387$	−4565.26			−0.599651
$388$	1709.25	+	1709.25i	0.223644	+	0.223644i
$389$		−	6152.95i		−	0.801971i	−0.916084	−	0.400986i	$-0.868668\pi$
$389$		−	6152.95i		−	0.801971i	0.916084	−	0.400986i	$-0.131332\pi$
$390$		−	2508.27i		−	0.325669i
$391$	−947.015	−	947.015i	−0.122487	−	0.122487i
$392$	3008.52			0.387636
$393$	−1515.66	−	1515.66i	−0.194542	−	0.194542i
$394$	1711.77			0.218877
$395$	−1076.96	−	1076.96i	−0.137184	−	0.137184i
$396$	1408.86	+	1408.86i	0.178782	+	0.178782i
$397$	7625.86	−	7625.86i	0.964058	−	0.964058i	−0.0353179	−	0.999376i	$-0.511244\pi$
$397$	7625.86	−	7625.86i	0.964058	−	0.964058i	0.999376	+	0.0353179i	$0.0112444\pi$
$398$	738.363	−	738.363i	0.0929919	−	0.0929919i
$399$	4552.69	−	4552.69i	0.571227	−	0.571227i
$400$	485.721			0.0607152
$401$			1009.55i			0.125722i	0.998022	+	0.0628608i	$0.0200224\pi$
$401$			1009.55i			0.125722i	−0.998022	+	0.0628608i	$0.979978\pi$
$402$			1318.57i			0.163592i
$403$	2926.60	−	2926.60i	0.361747	−	0.361747i
$404$	5288.21	+	5288.21i	0.651234	+	0.651234i
$405$		−	844.608i		−	0.103627i
$406$	−4236.53			−0.517871
$407$	−10139.5	+	10139.5i	−1.23488	+	1.23488i
$408$		−	2322.35i		−	0.281798i
$409$	−4738.25			−0.572840			−0.286420	−	0.958104i	$-0.592465\pi$
$409$	−4738.25			−0.572840			−0.286420	+	0.958104i	$0.592465\pi$
$410$	−1476.64	+	3033.65i	−0.177868	+	0.365418i
$411$	−2949.88			−0.354031
$412$		−	3372.47i		−	0.403276i
$413$	−271.065	+	271.065i	−0.0322960	+	0.0322960i
$414$	−342.522			−0.0406619
$415$			4108.65i			0.485989i
$416$	8260.70	+	8260.70i	0.973592	+	0.973592i
$417$	395.164	−	395.164i	0.0464059	−	0.0464059i
$418$			6841.32i			0.800526i
$419$		−	16376.0i		−	1.90935i	−0.297649	−	0.954675i	$-0.596202\pi$
$419$		−	16376.0i		−	1.90935i	0.297649	−	0.954675i	$-0.403798\pi$
$420$	2677.59			0.311079
$421$	−8582.83	+	8582.83i	−0.993591	+	0.993591i	−0.999980	−	0.00638899i	$-0.997966\pi$
$421$	−8582.83	+	8582.83i	−0.993591	+	0.993591i	0.00638899	+	0.999980i	$0.497966\pi$
$422$	1480.52	−	1480.52i	0.170783	−	0.170783i
$423$	−2866.71	+	2866.71i	−0.329514	+	0.329514i
$424$	−7576.49	−	7576.49i	−0.867799	−	0.867799i
$425$	−499.062	−	499.062i	−0.0569602	−	0.0569602i
$426$	2756.96			0.313556
$427$	3707.26	+	3707.26i	0.420157	+	0.420157i
$428$	6112.47			0.690321
$429$	4714.12	+	4714.12i	0.530536	+	0.530536i
$430$		−	6519.06i		−	0.731109i
$431$			8307.51i			0.928442i	0.885719	+	0.464221i	$0.153666\pi$
$431$			8307.51i			0.928442i	−0.885719	+	0.464221i	$0.846334\pi$
$432$	569.882	+	569.882i	0.0634686	+	0.0634686i
$433$	−5549.28			−0.615892			−0.307946	−	0.951404i	$-0.599642\pi$
$433$	−5549.28			−0.615892			−0.307946	+	0.951404i	$0.599642\pi$
$434$	−732.289	−	732.289i	−0.0809931	−	0.0809931i
$435$	8141.27			0.897342
$436$	−1892.12	−	1892.12i	−0.207835	−	0.207835i
$437$	3547.99	+	3547.99i	0.388383	+	0.388383i
$438$	−2509.32	+	2509.32i	−0.273744	+	0.273744i
$439$	−2729.74	+	2729.74i	−0.296773	+	0.296773i	−0.839749	−	0.542975i	$-0.817298\pi$
$439$	−2729.74	+	2729.74i	−0.296773	+	0.296773i	0.542975	+	0.839749i	$0.317298\pi$
$440$	−4495.18	+	4495.18i	−0.487044	+	0.487044i
$441$	1517.08			0.163814
$442$		−	3477.77i		−	0.374255i
$443$			2092.13i			0.224379i	0.993687	+	0.112190i	$0.0357864\pi$
$443$			2092.13i			0.224379i	−0.993687	+	0.112190i	$0.964214\pi$
$444$	−5771.26	+	5771.26i	−0.616873	+	0.616873i
$445$	1650.61	+	1650.61i	0.175835	+	0.175835i
$446$		−	690.970i		−	0.0733596i
$447$	−3743.60			−0.396122
$448$	−163.140	+	163.140i	−0.0172046	+	0.0172046i
$449$		−	3420.76i		−	0.359544i	−0.983708	−	0.179772i	$-0.942464\pi$
$449$		−	3420.76i		−	0.359544i	0.983708	−	0.179772i	$-0.0575361\pi$
$450$	−180.504			−0.0189089
$451$	−2926.30	−	8476.79i	−0.305530	−	0.885047i
$452$	−9542.73			−0.993036
$453$			4935.82i			0.511932i
$454$	−1830.15	+	1830.15i	−0.189192	+	0.189192i
$455$	8959.38			0.923126
$456$			8700.68i			0.893523i
$457$	−7804.09	−	7804.09i	−0.798819	−	0.798819i	0.184091	−	0.982909i	$-0.441066\pi$
$457$	−7804.09	−	7804.09i	−0.798819	−	0.798819i	−0.982909	+	0.184091i	$0.941066\pi$
$458$	−625.059	+	625.059i	−0.0637709	+	0.0637709i
$459$		−	1171.07i		−	0.119087i
$460$			2086.70i			0.211506i
$461$	16936.2			1.71106			0.855528	−	0.517757i	$-0.173233\pi$
$461$	16936.2			1.71106			0.855528	+	0.517757i	$0.173233\pi$
$462$	1179.56	−	1179.56i	0.118784	−	0.118784i
$463$	9927.18	−	9927.18i	0.996447	−	0.996447i	−0.00354661	−	0.999994i	$-0.501129\pi$
$463$	9927.18	−	9927.18i	0.996447	−	0.996447i	0.999994	+	0.00354661i	$0.00112892\pi$
$464$	−5493.15	+	5493.15i	−0.549598	+	0.549598i
$465$	1407.23	+	1407.23i	0.140341	+	0.140341i
$466$	4155.29	+	4155.29i	0.413068	+	0.413068i
$467$	4147.15			0.410936			0.205468	−	0.978664i	$-0.434128\pi$
$467$	4147.15			0.410936			0.205468	+	0.978664i	$0.434128\pi$
$468$	2683.20	+	2683.20i	0.265024	+	0.265024i
$469$	−4709.84			−0.463711
$470$	−4093.58	−	4093.58i	−0.401751	−	0.401751i
$471$			3765.62i			0.368387i
$472$		−	518.034i		−	0.0505179i
$473$	12252.1	+	12252.1i	1.19102	+	1.19102i
$474$	−540.080			−0.0523348
$475$	1869.74	+	1869.74i	0.180609	+	0.180609i
$476$	3712.55			0.357488
$477$	−3820.52	−	3820.52i	−0.366729	−	0.366729i
$478$	1818.56	+	1818.56i	0.174015	+	0.174015i
$479$	−2954.40	+	2954.40i	−0.281816	+	0.281816i	−0.833833	−	0.552017i	$-0.813858\pi$
$479$	−2954.40	+	2954.40i	−0.281816	+	0.281816i	0.552017	+	0.833833i	$0.313858\pi$
$480$	−3972.08	+	3972.08i	−0.377708	+	0.377708i
$481$	−19311.0	+	19311.0i	−1.83057	+	1.83057i
$482$	5581.26			0.527426
$483$		−	1223.47i		−	0.115258i
$484$			1063.96i			0.0999213i
$485$	−2750.04	+	2750.04i	−0.257470	+	0.257470i
$486$	−211.779	−	211.779i	−0.0197665	−	0.0197665i
$487$		−	4269.34i		−	0.397253i	−0.980075	−	0.198627i	$-0.936352\pi$
$487$		−	4269.34i		−	0.397253i	0.980075	−	0.198627i	$-0.0636481\pi$
$488$	−7084.97			−0.657216
$489$	8124.78	−	8124.78i	0.751360	−	0.751360i
$490$			2166.34i			0.199725i
$491$	8431.29			0.774946			0.387473	−	0.921881i	$-0.373348\pi$
$491$	8431.29			0.774946			0.387473	+	0.921881i	$0.373348\pi$
$492$	−1665.60	−	4824.86i	−0.152624	−	0.442117i
$493$	11288.1			1.03121
$494$			13029.5i			1.18669i
$495$	−2266.74	+	2266.74i	−0.205823	+	0.205823i
$496$	−1898.99			−0.171910
$497$			9847.69i			0.888791i
$498$	1030.21	+	1030.21i	0.0927008	+	0.0927008i
$499$	9313.36	−	9313.36i	0.835518	−	0.835518i	−0.152747	−	0.988265i	$-0.548812\pi$
$499$	9313.36	−	9313.36i	0.835518	−	0.835518i	0.988265	+	0.152747i	$0.0488121\pi$
$500$			9546.91i			0.853902i
$501$			8961.69i			0.799159i
$502$	4069.96			0.361855
$503$	10890.1	−	10890.1i	0.965342	−	0.965342i	−0.0340776	−	0.999419i	$-0.510849\pi$
$503$	10890.1	−	10890.1i	0.965342	−	0.965342i	0.999419	+	0.0340776i	$0.0108493\pi$
$504$	1500.14	−	1500.14i	0.132583	−	0.132583i
$505$	−8508.31	+	8508.31i	−0.749732	+	0.749732i
$506$	919.252	+	919.252i	0.0807623	+	0.0807623i
$507$	4317.61	+	4317.61i	0.378209	+	0.378209i
$508$	967.013			0.0844572
$509$	−14057.9	−	14057.9i	−1.22417	−	1.22417i	−0.966135	−	0.258037i	$-0.916924\pi$
$509$	−14057.9	−	14057.9i	−1.22417	−	1.22417i	−0.258037	−	0.966135i	$-0.583076\pi$
$510$	1672.25			0.145193
$511$	−8963.15	−	8963.15i	−0.775942	−	0.775942i
$512$		−	9622.16i		−	0.830554i
$513$			4387.40i			0.377600i
$514$	−2478.02	−	2478.02i	−0.212647	−	0.212647i
$515$	5426.03			0.464271
$516$	6973.73	+	6973.73i	0.594964	+	0.594964i
$517$	15387.2			1.30896
$518$	4831.96	+	4831.96i	0.409854	+	0.409854i
$519$	−5585.82	−	5585.82i	−0.472428	−	0.472428i
$520$	−8561.17	+	8561.17i	−0.721985	+	0.721985i
$521$	−417.689	+	417.689i	−0.0351234	+	0.0351234i	−0.724450	−	0.689327i	$-0.757906\pi$
$521$	−417.689	+	417.689i	−0.0351234	+	0.0351234i	0.689327	+	0.724450i	$0.257906\pi$
$522$	2041.36	−	2041.36i	0.171165	−	0.171165i
$523$	−7410.94			−0.619613			−0.309807	−	0.950800i	$-0.600264\pi$
$523$	−7410.94			−0.619613			−0.309807	+	0.950800i	$0.600264\pi$
$524$			4630.54i			0.386042i
$525$		−	644.748i		−	0.0535983i
$526$	3138.64	−	3138.64i	0.260174	−	0.260174i
$527$	1951.15	+	1951.15i	0.161278	+	0.161278i
$528$		−	3058.87i		−	0.252122i
$529$	−11213.5			−0.921635
$530$	5455.60	−	5455.60i	0.447125	−	0.447125i
$531$		−	261.224i		−	0.0213487i
$532$	−13909.1			−1.13352
$533$	−5573.21	−	16144.2i	−0.452912	−	1.31198i
$534$	827.759			0.0670798
$535$			9834.46i			0.794731i
$536$	4500.51	−	4500.51i	0.362672	−	0.362672i
$537$	4556.43			0.366154
$538$		−	5227.22i		−	0.418888i
$539$	−4071.50	−	4071.50i	−0.325365	−	0.325365i
$540$	−1290.19	+	1290.19i	−0.102817	+	0.102817i
$541$		−	20520.2i		−	1.63075i	−0.578936	−	0.815373i	$-0.696532\pi$
$541$		−	20520.2i		−	1.63075i	0.578936	−	0.815373i	$-0.303468\pi$
$542$		−	4679.51i		−	0.370853i
$543$	6282.87			0.496545
$544$	−5507.38	+	5507.38i	−0.434057	+	0.434057i
$545$	3044.27	−	3044.27i	0.239270	−	0.239270i
$546$	2246.50	−	2246.50i	0.176083	−	0.176083i
$547$	−11221.8	−	11221.8i	−0.877166	−	0.877166i	0.116075	−	0.993240i	$-0.462969\pi$
$547$	−11221.8	−	11221.8i	−0.877166	−	0.877166i	−0.993240	+	0.116075i	$0.962969\pi$
$548$	4506.13	+	4506.13i	0.351263	+	0.351263i
$549$	−3572.67			−0.277737
$550$	484.432	+	484.432i	0.0375568	+	0.0375568i
$551$	−42290.7			−3.26977
$552$	1169.09	+	1169.09i	0.0901444	+	0.0901444i
$553$		−	1929.14i		−	0.148346i
$554$		−	1513.67i		−	0.116082i
$555$	−9285.49	−	9285.49i	−0.710175	−	0.710175i
$556$	−1207.28			−0.0920863
$557$	9482.50	+	9482.50i	0.721340	+	0.721340i	0.968878	−	0.247538i	$-0.0796215\pi$
$557$	9482.50	+	9482.50i	0.721340	+	0.721340i	−0.247538	+	0.968878i	$0.579622\pi$
$558$	705.704			0.0535391
$559$	23334.5	+	23334.5i	1.76555	+	1.76555i
$560$	−2906.76	−	2906.76i	−0.219344	−	0.219344i
$561$	−3142.89	+	3142.89i	−0.236529	+	0.236529i
$562$	358.150	−	358.150i	0.0268819	−	0.0268819i
$563$	−15980.0	+	15980.0i	−1.19623	+	1.19623i	−0.220941	+	0.975287i	$0.570913\pi$
$563$	−15980.0	+	15980.0i	−1.19623	+	1.19623i	−0.975287	+	0.220941i	$0.929087\pi$
$564$	8758.17			0.653875
$565$		−	15353.5i		−	1.14323i
$566$			432.024i			0.0320836i
$567$	756.463	−	756.463i	0.0560290	−	0.0560290i
$568$	−9410.00	−	9410.00i	−0.695131	−	0.695131i
$569$			15291.4i			1.12662i	0.826245	+	0.563312i	$0.190473\pi$
$569$			15291.4i			1.12662i	−0.826245	+	0.563312i	$0.809527\pi$
$570$	−6265.09			−0.460378
$571$	13420.4	−	13420.4i	0.983580	−	0.983580i	−0.0162869	−	0.999867i	$-0.505185\pi$
$571$	13420.4	−	13420.4i	0.983580	−	0.983580i	0.999867	+	0.0162869i	$0.00518452\pi$
$572$		−	14402.2i		−	1.05278i
$573$	−3186.71			−0.232333
$574$	−4039.59	+	1394.52i	−0.293744	+	0.101404i
$575$	502.464			0.0364421
$576$		−	157.218i		−	0.0113728i
$577$	1523.81	−	1523.81i	0.109943	−	0.109943i	−0.649995	−	0.759938i	$-0.725229\pi$
$577$	1523.81	−	1523.81i	0.109943	−	0.109943i	0.759938	+	0.649995i	$0.225229\pi$
$578$	−3736.73			−0.268906
$579$		−	4467.90i		−	0.320690i
$580$	−12436.3	−	12436.3i	−0.890327	−	0.890327i
$581$	−3679.86	+	3679.86i	−0.262765	+	0.262765i
$582$			1379.10i			0.0982229i
$583$			20506.9i			1.45679i
$584$	17129.5			1.21374
$585$	−4317.06	+	4317.06i	−0.305108	+	0.305108i
$586$	6737.42	−	6737.42i	0.474949	−	0.474949i
$587$	−3840.09	+	3840.09i	−0.270013	+	0.270013i	−0.829105	−	0.559093i	$-0.811150\pi$
$587$	−3840.09	+	3840.09i	−0.270013	+	0.270013i	0.559093	+	0.829105i	$0.311150\pi$
$588$	−2317.43	−	2317.43i	−0.162533	−	0.162533i
$589$	−7309.99	−	7309.99i	−0.511380	−	0.511380i
$590$	373.020			0.0260288
$591$	−2946.18	−	2946.18i	−0.205058	−	0.205058i
$592$	12530.4			0.869925
$593$	−13552.7	−	13552.7i	−0.938518	−	0.938518i	0.0596986	−	0.998216i	$-0.480986\pi$
$593$	−13552.7	−	13552.7i	−0.938518	−	0.938518i	−0.998216	+	0.0596986i	$0.980986\pi$
$594$			1136.74i			0.0785200i
$595$			5973.19i			0.411558i
$596$	5718.60	+	5718.60i	0.393025	+	0.393025i
$597$	−2541.64			−0.174242
$598$	1750.74	+	1750.74i	0.119721	+	0.119721i
$599$	5744.76			0.391861			0.195930	−	0.980618i	$-0.437227\pi$
$599$	5744.76			0.391861			0.195930	+	0.980618i	$0.437227\pi$
$600$	616.092	+	616.092i	0.0419197	+	0.0419197i
$601$	2487.52	+	2487.52i	0.168832	+	0.168832i	0.786466	−	0.617634i	$-0.211909\pi$
$601$	2487.52	+	2487.52i	0.168832	+	0.168832i	−0.617634	+	0.786466i	$0.711909\pi$
$602$	5838.72	−	5838.72i	0.395297	−	0.395297i
$603$	2269.43	−	2269.43i	0.153264	−	0.153264i
$604$	7539.79	−	7539.79i	0.507930	−	0.507930i
$605$	−1711.83			−0.115034
$606$			4266.79i			0.286017i
$607$			10819.5i			0.723476i	0.932280	+	0.361738i	$0.117816\pi$
$607$			10819.5i			0.723476i	−0.932280	+	0.361738i	$0.882184\pi$
$608$	20633.4	−	20633.4i	1.37631	−	1.37631i
$609$	7291.63	+	7291.63i	0.485176	+	0.485176i
$610$		−	5101.67i		−	0.338624i
$611$	29305.3			1.94037
$612$	−1788.88	+	1788.88i	−0.118156	+	0.118156i
$613$		−	17858.0i		−	1.17663i	−0.808630	−	0.588317i	$-0.799791\pi$
$613$		−	17858.0i		−	1.17663i	0.808630	−	0.588317i	$-0.200209\pi$
$614$	4712.04			0.309711
$615$	7762.80	−	2679.82i	0.508986	−	0.175709i
$616$	−8052.11			−0.526670
$617$			10437.8i			0.681054i	0.940235	+	0.340527i	$0.110606\pi$
$617$			10437.8i			0.681054i	−0.940235	+	0.340527i	$0.889394\pi$
$618$	1360.54	−	1360.54i	0.0885580	−	0.0885580i
$619$	15397.9			0.999828			0.499914	−	0.866075i	$-0.333365\pi$
$619$	15397.9			0.999828			0.499914	+	0.866075i	$0.333365\pi$
$620$		−	4299.26i		−	0.278488i
$621$	589.525	+	589.525i	0.0380947	+	0.0380947i
$622$	−7939.41	+	7939.41i	−0.511803	+	0.511803i
$623$			2956.71i			0.190141i
$624$		−	5825.69i		−	0.373741i
$625$	−13326.2			−0.852874
$626$	2852.00	−	2852.00i	0.182091	−	0.182091i
$627$	11774.8	−	11774.8i	0.749986	−	0.749986i
$628$	5752.22	−	5752.22i	0.365507	−	0.365507i
$629$	−12874.5	−	12874.5i	−0.816123	−	0.816123i
$630$	1080.21	+	1080.21i	0.0683119	+	0.0683119i
$631$	5285.76			0.333475			0.166737	−	0.986001i	$-0.446677\pi$
$631$	5285.76			0.333475			0.166737	+	0.986001i	$0.446677\pi$
$632$	1843.39	+	1843.39i	0.116023	+	0.116023i
$633$	−5096.34			−0.320002
$634$	6314.04	+	6314.04i	0.395525	+	0.395525i
$635$			1555.85i			0.0972313i
$636$			11672.2i			0.727724i
$637$	−7754.27	−	7754.27i	−0.482316	−	0.482316i
$638$	−10957.1			−0.679933
$639$	−4745.09	−	4745.09i	−0.293760	−	0.293760i
$640$	15204.2			0.939058
$641$	14121.4	+	14121.4i	0.870143	+	0.870143i	0.992488	−	0.122345i	$-0.0390414\pi$
$641$	14121.4	+	14121.4i	0.870143	+	0.870143i	−0.122345	+	0.992488i	$0.539041\pi$
$642$	2465.92	+	2465.92i	0.151592	+	0.151592i
$643$	−8377.49	+	8377.49i	−0.513804	+	0.513804i	−0.915690	−	0.401886i	$-0.868355\pi$
$643$	−8377.49	+	8377.49i	−0.513804	+	0.513804i	0.401886	+	0.915690i	$0.368355\pi$
$644$	−1868.93	+	1868.93i	−0.114357	+	0.114357i
$645$	−11220.2	+	11220.2i	−0.684951	+	0.684951i
$646$	−8686.69			−0.529061
$647$		−	32831.4i		−	1.99495i	−0.0710009	−	0.997476i	$-0.522619\pi$
$647$		−	32831.4i		−	1.99495i	0.0710009	−	0.997476i	$-0.477381\pi$
$648$			1445.68i			0.0876416i
$649$	−701.067	+	701.067i	−0.0424026	+	0.0424026i
$650$	922.611	+	922.611i	0.0556735	+	0.0556735i
$651$			2520.73i			0.151759i
$652$	−24822.2			−1.49097
$653$	4960.78	−	4960.78i	0.297290	−	0.297290i	−0.542662	−	0.839951i	$-0.682583\pi$
$653$	4960.78	−	4960.78i	0.297290	−	0.297290i	0.839951	+	0.542662i	$0.182583\pi$
$654$		−	1526.66i		−	0.0912798i
$655$	−7450.17			−0.444431
$656$	−3429.64	+	7045.95i	−0.204123	+	0.419357i
$657$	8637.74			0.512923
$658$		−	7332.74i		−	0.434438i
$659$	−3764.40	+	3764.40i	−0.222519	+	0.222519i	−0.809559	−	0.587039i	$-0.800293\pi$
$659$	−3764.40	+	3764.40i	−0.222519	+	0.222519i	0.587039	+	0.809559i	$0.300293\pi$
$660$	6925.18			0.408428
$661$		−	18122.6i		−	1.06640i	−0.845990	−	0.533199i	$-0.820990\pi$
$661$		−	18122.6i		−	1.06640i	0.845990	−	0.533199i	$-0.179010\pi$
$662$	−3764.49	−	3764.49i	−0.221014	−	0.221014i
$663$	−5985.70	+	5985.70i	−0.350626	+	0.350626i
$664$		−	7032.62i		−	0.411022i
$665$		−	22378.5i		−	1.30497i
$666$	−4656.54			−0.270927
$667$	−5682.50	+	5682.50i	−0.329876	+	0.329876i
$668$	13689.6	−	13689.6i	0.792912	−	0.792912i
$669$	−1189.25	+	1189.25i	−0.0687281	+	0.0687281i
$670$	3240.68	+	3240.68i	0.186863	+	0.186863i
$671$	9588.25	+	9588.25i	0.551640	+	0.551640i
$672$	−7115.10			−0.408439
$673$	18415.7	+	18415.7i	1.05479	+	1.05479i	0.998409	+	0.0563807i	$0.0179561\pi$
$673$	18415.7	+	18415.7i	1.05479	+	1.05479i	0.0563807	+	0.998409i	$0.482044\pi$
$674$	−12144.2			−0.694029
$675$	310.671	+	310.671i	0.0177151	+	0.0177151i
$676$		−	13190.9i		−	0.750504i
$677$			5094.93i			0.289238i	0.989487	+	0.144619i	$0.0461956\pi$
$677$			5094.93i			0.289238i	−0.989487	+	0.144619i	$0.953804\pi$
$678$	−3849.77	−	3849.77i	−0.218067	−	0.218067i
$679$	−4926.08			−0.278418
$680$	−5707.70	−	5707.70i	−0.321883	−	0.321883i
$681$	6299.87			0.354496
$682$	−1893.95	−	1893.95i	−0.106339	−	0.106339i
$683$	−1861.37	−	1861.37i	−0.104280	−	0.104280i	0.653042	−	0.757322i	$-0.273493\pi$
$683$	−1861.37	−	1861.37i	−0.104280	−	0.104280i	−0.757322	+	0.653042i	$0.773493\pi$
$684$	6702.04	−	6702.04i	0.374648	−	0.374648i
$685$	−7250.00	+	7250.00i	−0.404391	+	0.404391i
$686$	−5888.37	+	5888.37i	−0.327724	+	0.327724i
$687$	2151.62			0.119490
$688$		−	15141.1i		−	0.839027i
$689$			39055.8i			2.15952i
$690$	−841.825	+	841.825i	−0.0464460	+	0.0464460i
$691$	2520.28	+	2520.28i	0.138750	+	0.138750i	0.773070	−	0.634320i	$-0.218720\pi$
$691$	2520.28	+	2520.28i	0.138750	+	0.138750i	−0.634320	+	0.773070i	$0.718720\pi$
$692$			17065.4i			0.937470i
$693$	−4060.36			−0.222569
$694$	−7881.22	+	7881.22i	−0.431076	+	0.431076i
$695$		−	1942.41i		−	0.106014i
$696$	−13935.1			−0.758920
$697$	10763.3	−	3715.64i	0.584920	−	0.201922i
$698$	−10212.4			−0.553792
$699$		−	14303.6i		−	0.773979i
$700$	−984.895	+	984.895i	−0.0531793	+	0.0531793i
$701$	−8532.27			−0.459714			−0.229857	−	0.973224i	$-0.573826\pi$
$701$	−8532.27			−0.459714			−0.229857	+	0.973224i	$0.573826\pi$
$702$			2164.94i			0.116397i
$703$	48234.5	+	48234.5i	2.58776	+	2.58776i
$704$	−421.937	+	421.937i	−0.0225886	+	0.0225886i
$705$			14091.2i			0.752773i
$706$		−	2646.73i		−	0.141092i
$707$	−15240.7			−0.810731
$708$	−399.037	+	399.037i	−0.0211818	+	0.0211818i
$709$	3200.36	−	3200.36i	0.169523	−	0.169523i	−0.617246	−	0.786770i	$-0.711752\pi$
$709$	3200.36	−	3200.36i	0.169523	−	0.169523i	0.786770	+	0.617246i	$0.211752\pi$
$710$	6775.85	−	6775.85i	0.358159	−	0.358159i
$711$	929.549	+	929.549i	0.0490307	+	0.0490307i
$712$	−2825.29	−	2825.29i	−0.148711	−	0.148711i
$713$	−1964.45			−0.103183
$714$	1497.73	+	1497.73i	0.0785032	+	0.0785032i
$715$	23172.0			1.21201
$716$	−6960.24	−	6960.24i	−0.363291	−	0.363291i
$717$		−	6259.97i		−	0.326057i
$718$		−	13179.4i		−	0.685027i
$719$	785.729	+	785.729i	0.0407549	+	0.0407549i	0.727191	−	0.686436i	$-0.240826\pi$
$719$	785.729	+	785.729i	0.0407549	+	0.0407549i	−0.686436	+	0.727191i	$0.740826\pi$
$720$	2801.23			0.144994
$721$	4859.76	+	4859.76i	0.251022	+	0.251022i
$722$	24090.9			1.24179
$723$	−9606.08	−	9606.08i	−0.494127	−	0.494127i
$724$	−9597.50	−	9597.50i	−0.492663	−	0.492663i
$725$	−2994.59	+	2994.59i	−0.153402	+	0.153402i
$726$	−429.229	+	429.229i	−0.0219424	+	0.0219424i
$727$	−20346.4	+	20346.4i	−1.03798	+	1.03798i	−0.0387252	+	0.999250i	$0.512330\pi$
$727$	−20346.4	+	20346.4i	−1.03798	+	1.03798i	−0.999250	+	0.0387252i	$0.987670\pi$
$728$	−15335.4			−0.780726
$729$			729.000i			0.0370370i
$730$			12334.5i			0.625368i
$731$	−15557.0	+	15557.0i	−0.787137	+	0.787137i
$732$	5457.48	+	5457.48i	0.275566	+	0.275566i
$733$			17934.3i			0.903706i	0.892092	+	0.451853i	$0.149237\pi$
$733$			17934.3i			0.903706i	−0.892092	+	0.451853i	$0.850763\pi$
$734$	−3293.54			−0.165622
$735$	3728.56	−	3728.56i	0.187116	−	0.187116i
$736$		−	5544.92i		−	0.277702i
$737$	−12181.3			−0.608824
$738$	1274.52	−	2618.41i	0.0635715	−	0.130603i
$739$	21687.6			1.07956			0.539778	−	0.841808i	$-0.318508\pi$
$739$	21687.6			1.07956			0.539778	+	0.841808i	$0.318508\pi$
$740$			28368.4i			1.40925i
$741$	22425.4	−	22425.4i	1.11177	−	1.11177i
$742$	9772.49			0.483503
$743$			6464.70i			0.319202i	0.987182	+	0.159601i	$0.0510207\pi$
$743$			6464.70i			0.319202i	−0.987182	+	0.159601i	$0.948979\pi$
$744$	−2408.70	−	2408.70i	−0.118692	−	0.118692i
$745$	−9200.76	+	9200.76i	−0.452469	+	0.452469i
$746$			9991.64i			0.490375i
$747$		−	3546.27i		−	0.173696i
$748$	9601.92			0.469360
$749$	−8808.12	+	8808.12i	−0.429695	+	0.429695i
$750$	−3851.46	+	3851.46i	−0.187514	+	0.187514i
$751$	−16009.4	+	16009.4i	−0.777886	+	0.777886i	−0.979471	−	0.201585i	$-0.935391\pi$
$751$	−16009.4	+	16009.4i	−0.777886	+	0.777886i	0.201585	+	0.979471i	$0.435391\pi$
$752$	−9507.74	−	9507.74i	−0.461053	−	0.461053i
$753$	−7004.95	−	7004.95i	−0.339010	−	0.339010i
$754$	−20868.1			−1.00792
$755$	12130.9	+	12130.9i	0.584753	+	0.584753i
$756$	−2311.09			−0.111182
$757$	−13852.5	−	13852.5i	−0.665096	−	0.665096i	0.291481	−	0.956577i	$-0.405852\pi$
$757$	−13852.5	−	13852.5i	−0.665096	−	0.665096i	−0.956577	+	0.291481i	$0.905852\pi$
$758$		−	7541.60i		−	0.361376i
$759$		−	3164.31i		−	0.151327i
$760$	21383.9	+	21383.9i	1.02063	+	1.02063i
$761$	−17268.6			−0.822586			−0.411293	−	0.911503i	$-0.634923\pi$
$761$	−17268.6			−0.822586			−0.411293	+	0.911503i	$0.634923\pi$
$762$	390.117	+	390.117i	0.0185465	+	0.0185465i
$763$	5453.13			0.258737
$764$	4867.90	+	4867.90i	0.230516	+	0.230516i
$765$	−2878.17	−	2878.17i	−0.136027	−	0.136027i
$766$	−5877.32	+	5877.32i	−0.277228	+	0.277228i
$767$	−1335.20	+	1335.20i	−0.0628569	+	0.0628569i
$768$	3515.88	−	3515.88i	0.165193	−	0.165193i
$769$	27683.8			1.29818			0.649092	−	0.760710i	$-0.275149\pi$
$769$	27683.8			1.29818			0.649092	+	0.760710i	$0.275149\pi$
$770$		−	5798.08i		−	0.271361i
$771$			8530.00i			0.398444i
$772$	−6825.01	+	6825.01i	−0.318183	+	0.318183i
$773$	16555.3	+	16555.3i	0.770312	+	0.770312i	0.978161	−	0.207849i	$-0.0666461\pi$
$773$	16555.3	+	16555.3i	0.770312	+	0.770312i	−0.207849	+	0.978161i	$0.566646\pi$
$774$			5626.75i			0.261304i
$775$	−1035.24			−0.0479829
$776$	4707.14	−	4707.14i	0.217753	−	0.217753i
$777$		−	16632.9i		−	0.767955i
$778$	−7583.60			−0.349467
$779$	−40324.7	+	13920.6i	−1.85466	+	0.640254i
$780$	13189.2			0.605446
$781$			25469.5i			1.16693i
$782$	−1167.21	+	1167.21i	−0.0533751	+	0.0533751i
$783$	−7026.91			−0.320717
$784$			5031.55i			0.229207i
$785$	9254.86	+	9254.86i	0.420790	+	0.420790i
$786$	−1868.08	+	1868.08i	−0.0847736	+	0.0847736i
$787$			8485.19i			0.384326i	0.981363	+	0.192163i	$0.0615502\pi$
$787$			8485.19i			0.384326i	−0.981363	+	0.192163i	$0.938450\pi$
$788$			9000.95i			0.406910i
$789$	−10804.0			−0.487495
$790$	−1327.37	+	1327.37i	−0.0597794	+	0.0597794i
$791$	13751.2	−	13751.2i	0.618123	−	0.618123i
$792$	3879.89	−	3879.89i	0.174073	−	0.174073i
$793$	18261.0	+	18261.0i	0.817741	+	0.817741i
$794$	−9398.99	−	9398.99i	−0.420098	−	0.420098i
$795$	−18779.6			−0.837791
$796$	3882.52	+	3882.52i	0.172880	+	0.172880i
$797$	11846.8			0.526516			0.263258	−	0.964725i	$-0.415203\pi$
$797$	11846.8			0.526516			0.263258	+	0.964725i	$0.415203\pi$
$798$	−5611.26	−	5611.26i	−0.248918	−	0.248918i
$799$			19537.8i			0.865077i
$800$		−	2922.09i		−	0.129139i
$801$	−1424.68	−	1424.68i	−0.0628448	−	0.0628448i
$802$	1244.28			0.0547844
$803$	−23181.8	−	23181.8i	−1.01876	−	1.01876i
$804$	−6933.39			−0.304132
$805$	−3006.95	−	3006.95i	−0.131653	−	0.131653i
$806$	−3607.08	−	3607.08i	−0.157635	−	0.157635i
$807$	−8996.74	+	8996.74i	−0.392441	+	0.392441i
$808$	14563.3	−	14563.3i	0.634080	−	0.634080i
$809$	29527.1	−	29527.1i	1.28321	−	1.28321i	0.344379	−	0.938831i	$-0.388090\pi$
$809$	29527.1	−	29527.1i	1.28321	−	1.28321i	0.938831	−	0.344379i	$-0.111910\pi$
$810$	−1040.99			−0.0451564
$811$			21568.4i			0.933870i	0.884292	+	0.466935i	$0.154642\pi$
$811$			21568.4i			0.933870i	−0.884292	+	0.466935i	$0.845358\pi$
$812$		−	22276.9i		−	0.962765i
$813$	−8054.05	+	8054.05i	−0.347439	+	0.347439i
$814$	12497.1	+	12497.1i	0.538112	+	0.538112i
$815$		−	39937.0i		−	1.71648i
$816$	3883.97			0.166625
$817$	58284.3	−	58284.3i	2.49585	−	2.49585i
$818$			5839.96i			0.249620i
$819$	−7733.05			−0.329932
$820$	−15951.8	−	7764.58i	−0.679342	−	0.330672i
$821$	−4915.76			−0.208966			−0.104483	−	0.994527i	$-0.533319\pi$
$821$	−4915.76			−0.208966			−0.104483	+	0.994527i	$0.533319\pi$
$822$			3635.77i			0.154272i
$823$	−1274.55	+	1274.55i	−0.0539832	+	0.0539832i	−0.733583	−	0.679600i	$-0.762153\pi$
$823$	−1274.55	+	1274.55i	−0.0539832	+	0.0539832i	0.679600	+	0.733583i	$0.262153\pi$
$824$	−9287.53			−0.392653
$825$		−	1667.54i		−	0.0703713i
$826$	334.092	+	334.092i	0.0140733	+	0.0140733i
$827$	−11740.2	+	11740.2i	−0.493646	+	0.493646i	−0.909453	−	0.415807i	$-0.863499\pi$
$827$	−11740.2	+	11740.2i	−0.493646	+	0.493646i	0.415807	+	0.909453i	$0.363499\pi$
$828$		−	1801.07i		−	0.0755938i
$829$		−	14964.9i		−	0.626965i	−0.949594	−	0.313482i	$-0.898504\pi$
$829$		−	14964.9i		−	0.626965i	0.949594	−	0.313482i	$-0.101496\pi$
$830$	5063.97			0.211775
$831$	−2605.22	+	2605.22i	−0.108754	+	0.108754i
$832$	−803.589	+	803.589i	−0.0334849	+	0.0334849i
$833$	5169.74	−	5169.74i	0.215031	−	0.215031i
$834$	−487.046	−	487.046i	−0.0202218	−	0.0202218i
$835$	22025.4	+	22025.4i	0.912839	+	0.912839i
$836$	−35973.6			−1.48824
$837$	−1214.61	−	1214.61i	−0.0501589	−	0.0501589i
$838$	−20183.6			−0.832018
$839$	−4093.87	−	4093.87i	−0.168458	−	0.168458i	0.617843	−	0.786301i	$-0.288007\pi$
$839$	−4093.87	−	4093.87i	−0.168458	−	0.168458i	−0.786301	+	0.617843i	$0.788007\pi$
$840$		−	7373.89i		−	0.302885i
$841$		−	43344.2i		−	1.77720i
$842$	10578.5	+	10578.5i	0.432967	+	0.432967i
$843$	−1232.85			−0.0503695
$844$	7784.99	+	7784.99i	0.317500	+	0.317500i
$845$	21223.0			0.864016
$846$	3533.26	+	3533.26i	0.143589	+	0.143589i
$847$	−1533.18	−	1533.18i	−0.0621968	−	0.0621968i
$848$	12671.2	−	12671.2i	0.513124	−	0.513124i
$849$	743.570	−	743.570i	0.0300580	−	0.0300580i
$850$	−615.102	+	615.102i	−0.0248210	+	0.0248210i
$851$	12962.3			0.522140
$852$			14496.8i			0.582927i
$853$		−	4954.91i		−	0.198890i	−0.995043	−	0.0994448i	$-0.968293\pi$
$853$		−	4954.91i		−	0.198890i	0.995043	−	0.0994448i	$-0.0317067\pi$
$854$	4569.25	−	4569.25i	0.183087	−	0.183087i
$855$	10783.0	+	10783.0i	0.431313	+	0.431313i
$856$		−	16833.3i		−	0.672137i
$857$	12098.4			0.482231			0.241116	−	0.970496i	$-0.422487\pi$
$857$	12098.4			0.482231			0.241116	+	0.970496i	$0.422487\pi$
$858$	5810.22	−	5810.22i	0.231186	−	0.231186i
$859$			1607.60i			0.0638541i	0.999490	+	0.0319270i	$0.0101644\pi$
$859$			1607.60i			0.0638541i	−0.999490	+	0.0319270i	$0.989836\pi$
$860$	34279.0			1.35919
$861$	9352.82	+	4552.51i	0.370201	+	0.180197i
$862$	10239.1			0.404578
$863$		−	10825.1i		−	0.426988i	−0.976944	−	0.213494i	$-0.931516\pi$
$863$		−	10825.1i		−	0.426988i	0.976944	−	0.213494i	$-0.0684844\pi$
$864$	3428.39	−	3428.39i	0.134996	−	0.134996i
$865$	−27456.8			−1.07926
$866$			6839.56i			0.268381i
$867$	6431.40	+	6431.40i	0.251928	+	0.251928i
$868$	3850.58	−	3850.58i	0.150573	−	0.150573i
$869$		−	4989.41i		−	0.194769i
$870$		−	10034.2i		−	0.391026i
$871$	−23199.5			−0.902510
$872$	−5210.76	+	5210.76i	−0.202361	+	0.202361i
$873$	2373.62	−	2373.62i	0.0920216	−	0.0920216i
$874$	4372.95	−	4372.95i	0.169242	−	0.169242i
$875$	−13757.2	−	13757.2i	−0.531518	−	0.531518i
$876$	−13194.7	−	13194.7i	−0.508913	−	0.508913i
$877$	−28245.6			−1.08755			−0.543777	−	0.839229i	$-0.683006\pi$
$877$	−28245.6			−1.08755			−0.543777	+	0.839229i	$0.683006\pi$
$878$	3364.45	+	3364.45i	0.129322	+	0.129322i
$879$	−23192.0			−0.889927
$880$	−7517.87	−	7517.87i	−0.287986	−	0.287986i
$881$			30389.7i			1.16215i	0.813850	+	0.581076i	$0.197368\pi$
$881$			30389.7i			1.16215i	−0.813850	+	0.581076i	$0.802632\pi$
$882$		−	1869.82i		−	0.0713834i
$883$	19602.3	+	19602.3i	0.747077	+	0.747077i	0.973929	−	0.226852i	$-0.0728433\pi$
$883$	19602.3	+	19602.3i	0.747077	+	0.747077i	−0.226852	+	0.973929i	$0.572843\pi$
$884$	18287.1			0.695771
$885$	−642.017	−	642.017i	−0.0243855	−	0.0243855i
$886$	2578.58			0.0977754
$887$	−5771.11	−	5771.11i	−0.218461	−	0.218461i	0.589389	−	0.807850i	$-0.299369\pi$
$887$	−5771.11	−	5771.11i	−0.218461	−	0.218461i	−0.807850	+	0.589389i	$0.799369\pi$
$888$	15893.6	+	15893.6i	0.600625	+	0.600625i
$889$	−1393.48	+	1393.48i	−0.0525711	+	0.0525711i
$890$	2034.40	−	2034.40i	0.0766218	−	0.0766218i
$891$	1956.47	−	1956.47i	0.0735627	−	0.0735627i
$892$	3633.31			0.136382
$893$		−	73198.2i		−	2.74298i
$894$			4614.05i			0.172614i
$895$	11198.5	−	11198.5i	0.418238	−	0.418238i
$896$	13617.4	+	13617.4i	0.507730	+	0.507730i
$897$		−	6026.50i		−	0.224324i
$898$	−4216.13			−0.156675
$899$	11707.8	−	11707.8i	0.434344	−	0.434344i
$900$		−	949.139i		−	0.0351533i
$901$	−26038.4			−0.962779
$902$	−10447.8	+	3606.71i	−0.385668	+	0.133138i
$903$	−20098.4			−0.740679
$904$			26280.0i			0.966878i
$905$	15441.6	−	15441.6i	0.567178	−	0.567178i
$906$	6083.47			0.223079
$907$			9982.65i			0.365456i	0.983164	+	0.182728i	$0.0584927\pi$
$907$			9982.65i			0.365456i	−0.983164	+	0.182728i	$0.941507\pi$
$908$	−9623.46	−	9623.46i	−0.351724	−	0.351724i
$909$	7343.71	−	7343.71i	0.267960	−	0.267960i
$910$		−	11042.6i		−	0.402261i
$911$		−	2104.56i		−	0.0765390i	−0.999267	−	0.0382695i	$-0.987815\pi$
$911$		−	2104.56i		−	0.0765390i	0.999267	−	0.0382695i	$-0.0121845\pi$
$912$	−14551.3			−0.528334
$913$	−9517.40	+	9517.40i	−0.344994	+	0.344994i
$914$	−9618.66	+	9618.66i	−0.348093	+	0.348093i
$915$	−8780.64	+	8780.64i	−0.317245	+	0.317245i
$916$	−3286.73	−	3286.73i	−0.118555	−	0.118555i
$917$	−6672.66	−	6672.66i	−0.240295	−	0.240295i
$918$	−1443.36			−0.0518932
$919$	13732.3	+	13732.3i	0.492912	+	0.492912i	0.909222	−	0.416311i	$-0.136677\pi$
$919$	13732.3	+	13732.3i	0.492912	+	0.492912i	−0.416311	+	0.909222i	$0.636677\pi$
$920$	5746.60			0.205935
$921$	−8110.05	−	8110.05i	−0.290158	−	0.290158i
$922$		−	20874.1i		−	0.745609i
$923$			48507.3i			1.72983i
$924$	6202.46	+	6202.46i	0.220829	+	0.220829i
$925$	6830.93			0.242810
$926$	−12235.4	−	12235.4i	−0.434212	−	0.434212i
$927$	−4683.33			−0.165934
$928$	33046.7	+	33046.7i	1.16898	+	1.16898i
$929$	5257.88	+	5257.88i	0.185689	+	0.185689i	0.793830	−	0.608140i	$-0.208084\pi$
$929$	5257.88	+	5257.88i	0.185689	+	0.185689i	−0.608140	+	0.793830i	$0.708084\pi$
$930$	1734.43	−	1734.43i	0.0611550	−	0.0611550i
$931$	−19368.4	+	19368.4i	−0.681820	+	0.681820i
$932$	−21849.7	+	21849.7i	−0.767928	+	0.767928i
$933$	27329.5			0.958980
$934$		−	5111.43i		−	0.179070i
$935$			15448.7i			0.540350i
$936$	7389.34	−	7389.34i	0.258043	−	0.258043i
$937$	−17447.4	−	17447.4i	−0.608303	−	0.608303i	0.334199	−	0.942502i	$-0.391534\pi$
$937$	−17447.4	−	17447.4i	−0.608303	−	0.608303i	−0.942502	+	0.334199i	$0.891534\pi$
$938$			5804.95i			0.202067i
$939$	−9817.33			−0.341189
$940$	21525.2	−	21525.2i	0.746888	−	0.746888i
$941$		−	49727.8i		−	1.72272i	−0.507994	−	0.861361i	$-0.669613\pi$
$941$		−	49727.8i		−	1.72272i	0.507994	−	0.861361i	$-0.330387\pi$
$942$	4641.18			0.160528
$943$	−3547.85	+	7288.81i	−0.122517	+	0.251703i
$944$	866.376			0.0298709
$945$		−	3718.36i		−	0.127998i
$946$	15100.9	−	15100.9i	0.519000	−	0.519000i
$947$	4498.71			0.154370			0.0771851	−	0.997017i	$-0.475407\pi$
$947$	4498.71			0.154370			0.0771851	+	0.997017i	$0.475407\pi$
$948$		−	2839.89i		−	0.0972948i
$949$	−44150.3	−	44150.3i	−1.51020	−	1.51020i
$950$	2304.48	−	2304.48i	0.0787022	−	0.0787022i
$951$		−	21734.6i		−	0.741107i
$952$		−	10224.1i		−	0.348072i
$953$	−20592.7			−0.699959			−0.349980	−	0.936757i	$-0.613812\pi$
$953$	−20592.7			−0.699959			−0.349980	+	0.936757i	$0.613812\pi$
$954$	−4708.85	+	4708.85i	−0.159806	+	0.159806i
$955$	−7832.06	+	7832.06i	−0.265382	+	0.265382i
$956$	−9562.50	+	9562.50i	−0.323508	+	0.323508i
$957$	18858.7	+	18858.7i	0.637006	+	0.637006i
$958$	3641.34	+	3641.34i	0.122804	+	0.122804i
$959$	−12986.8			−0.437293
$960$	−386.398	−	386.398i	−0.0129906	−	0.0129906i
$961$	−25743.6			−0.864140
$962$	23801.0	+	23801.0i	0.797688	+	0.797688i
$963$		−	8488.35i		−	0.284043i
$964$			29347.8i			0.980529i
$965$	−10980.9	−	10980.9i	−0.366308	−	0.366308i
$966$	−1507.94			−0.0502249
$967$	−39411.8	−	39411.8i	−1.31065	−	1.31065i	−0.920935	−	0.389716i	$-0.872573\pi$
$967$	−39411.8	−	39411.8i	−1.31065	−	1.31065i	−0.389716	−	0.920935i	$-0.627427\pi$
$968$	2930.07			0.0972893
$969$	14950.9	+	14950.9i	0.495659	+	0.495659i
$970$	3389.46	+	3389.46i	0.112195	+	0.112195i
$971$	−19435.4	+	19435.4i	−0.642340	+	0.642340i	−0.951130	−	0.308790i	$-0.900076\pi$
$971$	−19435.4	+	19435.4i	−0.642340	+	0.642340i	0.308790	+	0.951130i	$0.400076\pi$
$972$	1113.59	−	1113.59i	0.0367475	−	0.0367475i
$973$	1739.70	−	1739.70i	0.0573198	−	0.0573198i
$974$	−5262.03			−0.173107
$975$		−	3175.87i		−	0.104317i
$976$		−	11849.1i		−	0.388608i
$977$	12866.1	−	12866.1i	0.421315	−	0.421315i	−0.464342	−	0.885656i	$-0.653709\pi$
$977$	12866.1	−	12866.1i	0.421315	−	0.421315i	0.885656	+	0.464342i	$0.153709\pi$
$978$	−10013.9	−	10013.9i	−0.327412	−	0.327412i
$979$			7647.06i			0.249644i
$980$	−11391.2			−0.371306
$981$	−2627.58	+	2627.58i	−0.0855169	+	0.0855169i
$982$		−	10391.7i		−	0.337690i
$983$	5602.08			0.181769			0.0908844	−	0.995861i	$-0.471031\pi$
$983$	5602.08			0.181769			0.0908844	+	0.995861i	$0.471031\pi$
$984$	−13287.3	+	4586.95i	−0.430471	+	0.148604i
$985$	−14481.8			−0.468455
$986$		−	13912.7i		−	0.449362i
$987$	−12620.6	+	12620.6i	−0.407010	+	0.407010i
$988$	−68512.5			−2.20615
$989$		−	15663.0i		−	0.503595i
$990$	2793.79	+	2793.79i	0.0896893	+	0.0896893i
$991$	22034.5	−	22034.5i	0.706305	−	0.706305i	−0.259451	−	0.965756i	$-0.583542\pi$
$991$	22034.5	−	22034.5i	0.706305	−	0.706305i	0.965756	+	0.259451i	$0.0835416\pi$
$992$			11424.3i			0.365647i
$993$			12958.4i			0.414120i
$994$	12137.4			0.387299
$995$	−6246.66	+	6246.66i	−0.199027	+	0.199027i
$996$	−5417.15	+	5417.15i	−0.172338	+	0.172338i
$997$	27823.0	−	27823.0i	0.883814	−	0.883814i	−0.110106	−	0.993920i	$-0.535119\pi$
$997$	27823.0	−	27823.0i	0.883814	−	0.883814i	0.993920	+	0.110106i	$0.0351189\pi$
$998$	−11478.9	−	11478.9i	−0.364085	−	0.364085i
$999$	8014.51	+	8014.51i	0.253822	+	0.253822i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	123.4.e.a.73.9	✓	44
41.9	even	4	inner	123.4.e.a.91.14	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
123.4.e.a.73.9	✓	44	1.1	even	1	trivial
123.4.e.a.91.14	yes	44	41.9	even	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:	\( N \)	\(=\)	\( 123 = 3 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	123.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.23251i q^{2} +(-2.12132 + 2.12132i) q^{3} +6.48091 q^{4} +10.4273i q^{5} +(2.61456 + 2.61456i) q^{6} +(-9.33905 + 9.33905i) q^{7} -17.8479i q^{8} -9.00000i q^{9} +O(q^{10})\)	\(q-1.23251i q^{2} +(-2.12132 + 2.12132i) q^{3} +6.48091 q^{4} +10.4273i q^{5} +(2.61456 + 2.61456i) q^{6} +(-9.33905 + 9.33905i) q^{7} -17.8479i q^{8} -9.00000i q^{9} +12.8517 q^{10} +(-24.1540 + 24.1540i) q^{11} +(-13.7481 + 13.7481i) q^{12} +(-46.0019 + 46.0019i) q^{13} +(11.5105 + 11.5105i) q^{14} +(-22.1195 - 22.1195i) q^{15} +29.8494 q^{16} +(-30.6693 - 30.6693i) q^{17} -11.0926 q^{18} +(114.902 + 114.902i) q^{19} +67.5781i q^{20} -39.6222i q^{21} +(29.7702 + 29.7702i) q^{22} +30.8783 q^{23} +(37.8612 + 37.8612i) q^{24} +16.2724 q^{25} +(56.6980 + 56.6980i) q^{26} +(19.0919 + 19.0919i) q^{27} +(-60.5255 + 60.5255i) q^{28} +(-184.029 + 184.029i) q^{29} +(-27.2627 + 27.2627i) q^{30} -63.6191 q^{31} -179.573i q^{32} -102.477i q^{33} +(-37.8003 + 37.8003i) q^{34} +(-97.3807 - 97.3807i) q^{35} -58.3282i q^{36} +419.786 q^{37} +(141.619 - 141.619i) q^{38} -195.169i q^{39} +186.105 q^{40} +(-114.898 + 236.050i) q^{41} -48.8350 q^{42} -507.251i q^{43} +(-156.540 + 156.540i) q^{44} +93.8453 q^{45} -38.0580i q^{46} +(-318.524 - 318.524i) q^{47} +(-63.3202 + 63.3202i) q^{48} +168.564i q^{49} -20.0560i q^{50} +130.119 q^{51} +(-298.134 + 298.134i) q^{52} +(424.503 - 424.503i) q^{53} +(23.5310 - 23.5310i) q^{54} +(-251.860 - 251.860i) q^{55} +(166.683 + 166.683i) q^{56} -487.489 q^{57} +(226.818 + 226.818i) q^{58} +29.0249 q^{59} +(-143.355 - 143.355i) q^{60} -396.963i q^{61} +78.4115i q^{62} +(84.0515 + 84.0515i) q^{63} +17.4686 q^{64} +(-479.673 - 479.673i) q^{65} -126.304 q^{66} +(252.159 + 252.159i) q^{67} +(-198.765 - 198.765i) q^{68} +(-65.5028 + 65.5028i) q^{69} +(-120.023 + 120.023i) q^{70} +(527.232 - 527.232i) q^{71} -160.631 q^{72} +959.749i q^{73} -517.393i q^{74} +(-34.5189 + 34.5189i) q^{75} +(744.672 + 744.672i) q^{76} -451.151i q^{77} -240.549 q^{78} +(-103.283 + 103.283i) q^{79} +311.247i q^{80} -81.0000 q^{81} +(290.935 + 141.613i) q^{82} +394.030 q^{83} -256.788i q^{84} +(319.796 - 319.796i) q^{85} -625.194 q^{86} -780.768i q^{87} +(431.099 + 431.099i) q^{88} +(158.298 - 158.298i) q^{89} -115.666i q^{90} -859.227i q^{91} +200.119 q^{92} +(134.957 - 134.957i) q^{93} +(-392.585 + 392.585i) q^{94} +(-1198.12 + 1198.12i) q^{95} +(380.933 + 380.933i) q^{96} +(263.736 + 263.736i) q^{97} +207.758 q^{98} +(217.386 + 217.386i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 192 q^{4}+O(q^{10}) \) 44 * q - 192 * q^4	\( 44 q - 192 q^{4} + 224 q^{10} + 96 q^{11} - 24 q^{12} - 196 q^{13} + 148 q^{14} + 24 q^{15} + 896 q^{16} - 308 q^{17} + 112 q^{19} - 612 q^{22} - 208 q^{23} - 180 q^{24} - 1452 q^{25} + 1172 q^{26} - 220 q^{28} + 300 q^{29} + 456 q^{30} + 128 q^{31} - 552 q^{34} + 504 q^{35} - 88 q^{37} + 1204 q^{38} - 2112 q^{40} + 1316 q^{41} + 1560 q^{42} - 1412 q^{44} - 504 q^{45} + 520 q^{47} + 192 q^{48} + 936 q^{51} + 2652 q^{52} + 1116 q^{53} - 560 q^{55} - 4088 q^{56} - 936 q^{57} - 2860 q^{58} - 992 q^{59} - 804 q^{60} - 8472 q^{64} - 1480 q^{65} + 1968 q^{66} + 2592 q^{67} + 3836 q^{68} + 1368 q^{69} + 2468 q^{70} + 1888 q^{71} + 1512 q^{72} - 48 q^{75} + 996 q^{76} + 1392 q^{78} - 3000 q^{79} - 3564 q^{81} - 236 q^{82} - 2080 q^{83} - 1160 q^{85} - 5520 q^{86} + 7940 q^{88} - 2748 q^{89} + 14712 q^{92} + 1680 q^{93} - 6400 q^{94} - 7456 q^{95} + 4320 q^{96} + 5516 q^{97} + 11008 q^{98} - 864 q^{99}+O(q^{100}) \) 44 * q - 192 * q^4 + 224 * q^10 + 96 * q^11 - 24 * q^12 - 196 * q^13 + 148 * q^14 + 24 * q^15 + 896 * q^16 - 308 * q^17 + 112 * q^19 - 612 * q^22 - 208 * q^23 - 180 * q^24 - 1452 * q^25 + 1172 * q^26 - 220 * q^28 + 300 * q^29 + 456 * q^30 + 128 * q^31 - 552 * q^34 + 504 * q^35 - 88 * q^37 + 1204 * q^38 - 2112 * q^40 + 1316 * q^41 + 1560 * q^42 - 1412 * q^44 - 504 * q^45 + 520 * q^47 + 192 * q^48 + 936 * q^51 + 2652 * q^52 + 1116 * q^53 - 560 * q^55 - 4088 * q^56 - 936 * q^57 - 2860 * q^58 - 992 * q^59 - 804 * q^60 - 8472 * q^64 - 1480 * q^65 + 1968 * q^66 + 2592 * q^67 + 3836 * q^68 + 1368 * q^69 + 2468 * q^70 + 1888 * q^71 + 1512 * q^72 - 48 * q^75 + 996 * q^76 + 1392 * q^78 - 3000 * q^79 - 3564 * q^81 - 236 * q^82 - 2080 * q^83 - 1160 * q^85 - 5520 * q^86 + 7940 * q^88 - 2748 * q^89 + 14712 * q^92 + 1680 * q^93 - 6400 * q^94 - 7456 * q^95 + 4320 * q^96 + 5516 * q^97 + 11008 * q^98 - 864 * q^99

Introduction

L-functions

Modular forms

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Database

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