LMFDB - Embedded newform 111.3.f.a.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [111,3,Mod(31,111)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(111, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("111.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 111 = 3 \cdot 37 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	111.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:	$3.02453093440$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.1
Character	$\chi$	$=$	111.31
Dual form			111.3.f.a.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.15816 - 2.15816i) q^{2} +1.73205i q^{3} +5.31533i q^{4} +(2.28543 - 2.28543i) q^{5} +(3.73805 - 3.73805i) q^{6} -10.9759 q^{7} +(2.83869 - 2.83869i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(-2.15816 - 2.15816i) q^{2} +1.73205i q^{3} +5.31533i q^{4} +(2.28543 - 2.28543i) q^{5} +(3.73805 - 3.73805i) q^{6} -10.9759 q^{7} +(2.83869 - 2.83869i) q^{8} -3.00000 q^{9} -9.86464 q^{10} +0.969781i q^{11} -9.20642 q^{12} +(-17.8824 + 17.8824i) q^{13} +(23.6878 + 23.6878i) q^{14} +(3.95848 + 3.95848i) q^{15} +9.00860 q^{16} +(8.49513 - 8.49513i) q^{17} +(6.47449 + 6.47449i) q^{18} +(-4.87907 + 4.87907i) q^{19} +(12.1478 + 12.1478i) q^{20} -19.0108i q^{21} +(2.09295 - 2.09295i) q^{22} +(-24.5599 + 24.5599i) q^{23} +(4.91676 + 4.91676i) q^{24} +14.5536i q^{25} +77.1861 q^{26} -5.19615i q^{27} -58.3405i q^{28} +(-21.3881 - 21.3881i) q^{29} -17.0861i q^{30} +(-9.51755 - 9.51755i) q^{31} +(-30.7968 - 30.7968i) q^{32} -1.67971 q^{33} -36.6677 q^{34} +(-25.0846 + 25.0846i) q^{35} -15.9460i q^{36} +(19.0337 - 31.7288i) q^{37} +21.0597 q^{38} +(-30.9732 - 30.9732i) q^{39} -12.9752i q^{40} -43.0947i q^{41} +(-41.0284 + 41.0284i) q^{42} +(-11.9595 + 11.9595i) q^{43} -5.15471 q^{44} +(-6.85628 + 6.85628i) q^{45} +106.009 q^{46} -16.0649 q^{47} +15.6033i q^{48} +71.4705 q^{49} +(31.4091 - 31.4091i) q^{50} +(14.7140 + 14.7140i) q^{51} +(-95.0507 - 95.0507i) q^{52} +67.0400 q^{53} +(-11.2141 + 11.2141i) q^{54} +(2.21636 + 2.21636i) q^{55} +(-31.1572 + 31.1572i) q^{56} +(-8.45080 - 8.45080i) q^{57} +92.3181i q^{58} +(30.6258 - 30.6258i) q^{59} +(-21.0406 + 21.0406i) q^{60} +(0.693850 + 0.693850i) q^{61} +41.0808i q^{62} +32.9277 q^{63} +96.8945i q^{64} +81.7377i q^{65} +(3.62509 + 3.62509i) q^{66} +66.4552i q^{67} +(45.1544 + 45.1544i) q^{68} +(-42.5390 - 42.5390i) q^{69} +108.273 q^{70} -111.337 q^{71} +(-8.51608 + 8.51608i) q^{72} -63.1614i q^{73} +(-109.554 + 27.3980i) q^{74} -25.2077 q^{75} +(-25.9339 - 25.9339i) q^{76} -10.6442i q^{77} +133.690i q^{78} +(-8.89024 + 8.89024i) q^{79} +(20.5885 - 20.5885i) q^{80} +9.00000 q^{81} +(-93.0054 + 93.0054i) q^{82} -72.1552 q^{83} +101.049 q^{84} -38.8300i q^{85} +51.6212 q^{86} +(37.0453 - 37.0453i) q^{87} +(2.75291 + 2.75291i) q^{88} +(44.2425 + 44.2425i) q^{89} +29.5939 q^{90} +(196.275 - 196.275i) q^{91} +(-130.544 - 130.544i) q^{92} +(16.4849 - 16.4849i) q^{93} +(34.6707 + 34.6707i) q^{94} +22.3015i q^{95} +(53.3416 - 53.3416i) q^{96} +(-115.352 + 115.352i) q^{97} +(-154.245 - 154.245i) q^{98} -2.90934i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{2} + 20 q^{5} - 60 q^{8} - 72 q^{9}+O(q^{10}) $ 24 * q + 8 * q^2 + 20 * q^5 - 60 * q^8 - 72 * q^9	$ 24 q + 8 q^{2} + 20 q^{5} - 60 q^{8} - 72 q^{9} + 24 q^{10} - 32 q^{13} + 60 q^{14} - 40 q^{16} - 8 q^{17} - 24 q^{18} - 48 q^{19} + 104 q^{20} + 32 q^{22} - 44 q^{23} + 88 q^{26} - 88 q^{29} - 192 q^{32} - 24 q^{33} - 56 q^{34} + 60 q^{35} + 56 q^{37} + 160 q^{38} + 72 q^{39} - 12 q^{42} - 8 q^{43} + 536 q^{44} - 60 q^{45} + 480 q^{46} + 88 q^{47} - 32 q^{49} + 172 q^{50} + 60 q^{51} - 488 q^{52} + 104 q^{53} - 208 q^{55} - 80 q^{56} - 456 q^{59} - 252 q^{60} - 96 q^{61} + 24 q^{66} - 44 q^{68} - 168 q^{69} - 1080 q^{70} - 528 q^{71} + 180 q^{72} + 136 q^{74} + 144 q^{75} - 24 q^{76} + 160 q^{79} + 48 q^{80} + 216 q^{81} - 392 q^{82} + 280 q^{83} + 720 q^{84} - 288 q^{86} + 12 q^{87} + 1424 q^{88} - 92 q^{89} - 72 q^{90} + 320 q^{91} + 48 q^{92} - 168 q^{93} - 56 q^{94} - 120 q^{96} + 352 q^{97} - 664 q^{98}+O(q^{100}) $ 24 * q + 8 * q^2 + 20 * q^5 - 60 * q^8 - 72 * q^9 + 24 * q^10 - 32 * q^13 + 60 * q^14 - 40 * q^16 - 8 * q^17 - 24 * q^18 - 48 * q^19 + 104 * q^20 + 32 * q^22 - 44 * q^23 + 88 * q^26 - 88 * q^29 - 192 * q^32 - 24 * q^33 - 56 * q^34 + 60 * q^35 + 56 * q^37 + 160 * q^38 + 72 * q^39 - 12 * q^42 - 8 * q^43 + 536 * q^44 - 60 * q^45 + 480 * q^46 + 88 * q^47 - 32 * q^49 + 172 * q^50 + 60 * q^51 - 488 * q^52 + 104 * q^53 - 208 * q^55 - 80 * q^56 - 456 * q^59 - 252 * q^60 - 96 * q^61 + 24 * q^66 - 44 * q^68 - 168 * q^69 - 1080 * q^70 - 528 * q^71 + 180 * q^72 + 136 * q^74 + 144 * q^75 - 24 * q^76 + 160 * q^79 + 48 * q^80 + 216 * q^81 - 392 * q^82 + 280 * q^83 + 720 * q^84 - 288 * q^86 + 12 * q^87 + 1424 * q^88 - 92 * q^89 - 72 * q^90 + 320 * q^91 + 48 * q^92 - 168 * q^93 - 56 * q^94 - 120 * q^96 + 352 * q^97 - 664 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/111\mathbb{Z}\right)^\times$.

$n$	$38$	$76$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−2.15816	−	2.15816i	−1.07908	−	1.07908i	−0.996592	−	0.0824892i	$-0.973713\pi$
$2$	−2.15816	−	2.15816i	−1.07908	−	1.07908i	−0.0824892	−	0.996592i	$-0.526287\pi$
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$			5.31533i			1.32883i
$5$	2.28543	−	2.28543i	0.457085	−	0.457085i	−0.440612	−	0.897698i	$-0.645239\pi$
$5$	2.28543	−	2.28543i	0.457085	−	0.457085i	0.897698	+	0.440612i	$0.145239\pi$
$6$	3.73805	−	3.73805i	0.623008	−	0.623008i
$7$	−10.9759			−1.56799			−0.783993	−	0.620769i	$-0.786820\pi$
$7$	−10.9759			−1.56799			−0.783993	+	0.620769i	$0.786820\pi$
$8$	2.83869	−	2.83869i	0.354837	−	0.354837i
$9$	−3.00000			−0.333333
$10$	−9.86464			−0.986464
$11$			0.969781i			0.0881619i	0.999028	+	0.0440810i	$0.0140360\pi$
$11$			0.969781i			0.0881619i	−0.999028	+	0.0440810i	$0.985964\pi$
$12$	−9.20642			−0.767202
$13$	−17.8824	+	17.8824i	−1.37557	+	1.37557i	−0.523608	+	0.851959i	$0.675414\pi$
$13$	−17.8824	+	17.8824i	−1.37557	+	1.37557i	−0.851959	+	0.523608i	$0.824586\pi$
$14$	23.6878	+	23.6878i	1.69198	+	1.69198i
$15$	3.95848	+	3.95848i	0.263898	+	0.263898i
$16$	9.00860			0.563037
$17$	8.49513	−	8.49513i	0.499713	−	0.499713i	−0.411635	−	0.911349i	$-0.635042\pi$
$17$	8.49513	−	8.49513i	0.499713	−	0.499713i	0.911349	+	0.411635i	$0.135042\pi$
$18$	6.47449	+	6.47449i	0.359694	+	0.359694i
$19$	−4.87907	+	4.87907i	−0.256793	+	0.256793i	−0.823749	−	0.566955i	$-0.808121\pi$
$19$	−4.87907	+	4.87907i	−0.256793	+	0.256793i	0.566955	+	0.823749i	$0.308121\pi$
$20$	12.1478	+	12.1478i	0.607390	+	0.607390i
$21$		−	19.0108i		−	0.905277i
$22$	2.09295	−	2.09295i	0.0951339	−	0.0951339i
$23$	−24.5599	+	24.5599i	−1.06782	+	1.06782i	−0.0702960	+	0.997526i	$0.522394\pi$
$23$	−24.5599	+	24.5599i	−1.06782	+	1.06782i	−0.997526	+	0.0702960i	$0.977606\pi$
$24$	4.91676	+	4.91676i	0.204865	+	0.204865i
$25$			14.5536i			0.582146i
$26$	77.1861			2.96870
$27$		−	5.19615i		−	0.192450i
$28$		−	58.3405i		−	2.08359i
$29$	−21.3881	−	21.3881i	−0.737521	−	0.737521i	0.234576	−	0.972098i	$-0.424630\pi$
$29$	−21.3881	−	21.3881i	−0.737521	−	0.737521i	−0.972098	+	0.234576i	$0.924630\pi$
$30$		−	17.0861i		−	0.569535i
$31$	−9.51755	−	9.51755i	−0.307018	−	0.307018i	0.536734	−	0.843752i	$-0.319658\pi$
$31$	−9.51755	−	9.51755i	−0.307018	−	0.307018i	−0.843752	+	0.536734i	$0.819658\pi$
$32$	−30.7968	−	30.7968i	−0.962399	−	0.962399i
$33$	−1.67971			−0.0509003
$34$	−36.6677			−1.07846
$35$	−25.0846	+	25.0846i	−0.716704	+	0.716704i
$36$		−	15.9460i		−	0.442944i
$37$	19.0337	−	31.7288i	0.514426	−	0.857535i
$37$	19.0337	−	31.7288i	0.514426	−	0.857535i
$38$	21.0597			0.554201
$39$	−30.9732	−	30.9732i	−0.794184	−	0.794184i
$40$		−	12.9752i		−	0.324381i
$41$		−	43.0947i		−	1.05109i	−0.850766	−	0.525545i	$-0.823861\pi$
$41$		−	43.0947i		−	1.05109i	0.850766	−	0.525545i	$-0.176139\pi$
$42$	−41.0284	+	41.0284i	−0.976868	+	0.976868i
$43$	−11.9595	+	11.9595i	−0.278128	+	0.278128i	−0.832361	−	0.554233i	$-0.813012\pi$
$43$	−11.9595	+	11.9595i	−0.278128	+	0.278128i	0.554233	+	0.832361i	$0.313012\pi$
$44$	−5.15471			−0.117152
$45$	−6.85628	+	6.85628i	−0.152362	+	0.152362i
$46$	106.009			2.30453
$47$	−16.0649			−0.341806			−0.170903	−	0.985288i	$-0.554669\pi$
$47$	−16.0649			−0.341806			−0.170903	+	0.985288i	$0.554669\pi$
$48$			15.6033i			0.325070i
$49$	71.4705			1.45858
$50$	31.4091	−	31.4091i	0.628183	−	0.628183i
$51$	14.7140	+	14.7140i	0.288510	+	0.288510i
$52$	−95.0507	−	95.0507i	−1.82790	−	1.82790i
$53$	67.0400			1.26490			0.632452	−	0.774599i	$-0.282048\pi$
$53$	67.0400			1.26490			0.632452	+	0.774599i	$0.282048\pi$
$54$	−11.2141	+	11.2141i	−0.207669	+	0.207669i
$55$	2.21636	+	2.21636i	0.0402975	+	0.0402975i
$56$	−31.1572	+	31.1572i	−0.556379	+	0.556379i
$57$	−8.45080	−	8.45080i	−0.148260	−	0.148260i
$58$			92.3181i			1.59169i
$59$	30.6258	−	30.6258i	0.519081	−	0.519081i	−0.398212	−	0.917293i	$-0.630369\pi$
$59$	30.6258	−	30.6258i	0.519081	−	0.519081i	0.917293	+	0.398212i	$0.130369\pi$
$60$	−21.0406	+	21.0406i	−0.350677	+	0.350677i
$61$	0.693850	+	0.693850i	0.0113746	+	0.0113746i	0.712771	−	0.701397i	$-0.247440\pi$
$61$	0.693850	+	0.693850i	0.0113746	+	0.0113746i	−0.701397	+	0.712771i	$0.747440\pi$
$62$			41.0808i			0.662594i
$63$	32.9277			0.522662
$64$			96.8945i			1.51398i
$65$			81.7377i			1.25750i
$66$	3.62509	+	3.62509i	0.0549256	+	0.0549256i
$67$			66.4552i			0.991869i	0.868360	+	0.495934i	$0.165174\pi$
$67$			66.4552i			0.991869i	−0.868360	+	0.495934i	$0.834826\pi$
$68$	45.1544	+	45.1544i	0.664035	+	0.664035i
$69$	−42.5390	−	42.5390i	−0.616507	−	0.616507i
$70$	108.273			1.54676
$71$	−111.337			−1.56813			−0.784065	−	0.620679i	$-0.786857\pi$
$71$	−111.337			−1.56813			−0.784065	+	0.620679i	$0.786857\pi$
$72$	−8.51608	+	8.51608i	−0.118279	+	0.118279i
$73$		−	63.1614i		−	0.865224i	−0.901580	−	0.432612i	$-0.857592\pi$
$73$		−	63.1614i		−	0.865224i	0.901580	−	0.432612i	$-0.142408\pi$
$74$	−109.554	+	27.3980i	−1.48046	+	0.370243i
$75$	−25.2077			−0.336102
$76$	−25.9339	−	25.9339i	−0.341235	−	0.341235i
$77$		−	10.6442i		−	0.138237i
$78$			133.690i			1.71398i
$79$	−8.89024	+	8.89024i	−0.112535	+	0.112535i	−0.761132	−	0.648597i	$-0.775356\pi$
$79$	−8.89024	+	8.89024i	−0.112535	+	0.112535i	0.648597	+	0.761132i	$0.275356\pi$
$80$	20.5885	−	20.5885i	0.257356	−	0.257356i
$81$	9.00000			0.111111
$82$	−93.0054	+	93.0054i	−1.13421	+	1.13421i
$83$	−72.1552			−0.869339			−0.434670	−	0.900590i	$-0.643135\pi$
$83$	−72.1552			−0.869339			−0.434670	+	0.900590i	$0.643135\pi$
$84$	101.049			1.20296
$85$		−	38.8300i		−	0.456823i
$86$	51.6212			0.600246
$87$	37.0453	−	37.0453i	0.425808	−	0.425808i
$88$	2.75291	+	2.75291i	0.0312831	+	0.0312831i
$89$	44.2425	+	44.2425i	0.497107	+	0.497107i	0.910536	−	0.413429i	$-0.135669\pi$
$89$	44.2425	+	44.2425i	0.497107	+	0.497107i	−0.413429	+	0.910536i	$0.635669\pi$
$90$	29.5939			0.328821
$91$	196.275	−	196.275i	2.15687	−	2.15687i
$92$	−130.544	−	130.544i	−1.41896	−	1.41896i
$93$	16.4849	−	16.4849i	0.177257	−	0.177257i
$94$	34.6707	+	34.6707i	0.368837	+	0.368837i
$95$			22.3015i			0.234753i
$96$	53.3416	−	53.3416i	0.555642	−	0.555642i
$97$	−115.352	+	115.352i	−1.18920	+	1.18920i	−0.211909	+	0.977289i	$0.567968\pi$
$97$	−115.352	+	115.352i	−1.18920	+	1.18920i	−0.977289	+	0.211909i	$0.932032\pi$
$98$	−154.245	−	154.245i	−1.57393	−	1.57393i
$99$		−	2.90934i		−	0.0293873i
$100$	−77.3574			−0.773574
$101$			89.0150i			0.881337i	0.897670	+	0.440669i	$0.145259\pi$
$101$			89.0150i			0.881337i	−0.897670	+	0.440669i	$0.854741\pi$
$102$		−	63.5104i		−	0.622651i
$103$	61.3575	+	61.3575i	0.595703	+	0.595703i	0.939166	−	0.343463i	$-0.111600\pi$
$103$	61.3575	+	61.3575i	0.595703	+	0.595703i	−0.343463	+	0.939166i	$0.611600\pi$
$104$			101.525i			0.976203i
$105$	−43.4478	−	43.4478i	−0.413789	−	0.413789i
$106$	−144.683	−	144.683i	−1.36494	−	1.36494i
$107$	161.831			1.51244			0.756220	−	0.654318i	$-0.227044\pi$
$107$	161.831			1.51244			0.756220	+	0.654318i	$0.227044\pi$
$108$	27.6193			0.255734
$109$	−29.7254	+	29.7254i	−0.272710	+	0.272710i	−0.830190	−	0.557480i	$-0.811768\pi$
$109$	−29.7254	+	29.7254i	−0.272710	+	0.272710i	0.557480	+	0.830190i	$0.311768\pi$
$110$		−	9.56655i		−	0.0869686i
$111$	54.9559	+	32.9674i	0.495098	+	0.297004i
$112$	−98.8775			−0.882835
$113$	−117.398	−	117.398i	−1.03892	−	1.03892i	−0.999211	−	0.0397067i	$-0.987358\pi$
$113$	−117.398	−	117.398i	−1.03892	−	1.03892i	−0.0397067	−	0.999211i	$-0.512642\pi$
$114$			36.4764i			0.319968i
$115$			112.260i			0.976172i
$116$	113.685	−	113.685i	0.980042	−	0.980042i
$117$	53.6471	−	53.6471i	0.458522	−	0.458522i
$118$	−132.191			−1.12026
$119$	−93.2417	+	93.2417i	−0.783544	+	0.783544i
$120$	22.4738			0.187282
$121$	120.060			0.992227
$122$		−	2.99488i		−	0.0245482i
$123$	74.6422			0.606847
$124$	50.5889	−	50.5889i	0.407975	−	0.407975i
$125$	90.3970	+	90.3970i	0.723176	+	0.723176i
$126$	−71.0634	−	71.0634i	−0.563995	−	0.563995i
$127$	−94.5780			−0.744708			−0.372354	−	0.928091i	$-0.621449\pi$
$127$	−94.5780			−0.744708			−0.372354	+	0.928091i	$0.621449\pi$
$128$	85.9270	−	85.9270i	0.671304	−	0.671304i
$129$	−20.7145	−	20.7145i	−0.160577	−	0.160577i
$130$	176.403	−	176.403i	1.35695	−	1.35695i
$131$	−71.2131	−	71.2131i	−0.543611	−	0.543611i	0.380974	−	0.924586i	$-0.375589\pi$
$131$	−71.2131	−	71.2131i	−0.543611	−	0.543611i	−0.924586	+	0.380974i	$0.875589\pi$
$132$		−	8.92821i		−	0.0676380i
$133$	53.5522	−	53.5522i	0.402648	−	0.402648i
$134$	143.421	−	143.421i	1.07031	−	1.07031i
$135$	−11.8754	−	11.8754i	−0.0879661	−	0.0879661i
$136$		−	48.2301i		−	0.354633i
$137$	95.9248			0.700181			0.350091	−	0.936716i	$-0.386151\pi$
$137$	95.9248			0.700181			0.350091	+	0.936716i	$0.386151\pi$
$138$			183.612i			1.33052i
$139$			208.274i			1.49838i	0.662357	+	0.749188i	$0.269556\pi$
$139$			208.274i			1.49838i	−0.662357	+	0.749188i	$0.730444\pi$
$140$	−133.333	−	133.333i	−0.952379	−	0.952379i
$141$		−	27.8252i		−	0.197342i
$142$	240.284	+	240.284i	1.69214	+	1.69214i
$143$	−17.3420	−	17.3420i	−0.121273	−	0.121273i
$144$	−27.0258			−0.187679
$145$	−97.7620			−0.674221
$146$	−136.312	+	136.312i	−0.933647	+	0.933647i
$147$			123.791i			0.842112i
$148$	168.649	+	101.171i	1.13952	+	0.683585i
$149$	−27.0747			−0.181709			−0.0908547	−	0.995864i	$-0.528960\pi$
$149$	−27.0747			−0.181709			−0.0908547	+	0.995864i	$0.528960\pi$
$150$	54.4022	+	54.4022i	0.362681	+	0.362681i
$151$			195.358i			1.29376i	0.762592	+	0.646880i	$0.223926\pi$
$151$			195.358i			1.29376i	−0.762592	+	0.646880i	$0.776074\pi$
$152$			27.7004i			0.182239i
$153$	−25.4854	+	25.4854i	−0.166571	+	0.166571i
$154$	−22.9720	+	22.9720i	−0.149169	+	0.149169i
$155$	−43.5033			−0.280667
$156$	164.633	−	164.633i	1.05534	−	1.05534i
$157$	−173.936			−1.10787			−0.553936	−	0.832559i	$-0.686875\pi$
$157$	−173.936			−1.10787			−0.553936	+	0.832559i	$0.686875\pi$
$158$	38.3732			0.242868
$159$			116.117i			0.730293i
$160$	−140.768			−0.879797
$161$	269.567	−	269.567i	1.67433	−	1.67433i
$162$	−19.4235	−	19.4235i	−0.119898	−	0.119898i
$163$	−204.208	−	204.208i	−1.25281	−	1.25281i	−0.954454	−	0.298358i	$-0.903561\pi$
$163$	−204.208	−	204.208i	−1.25281	−	1.25281i	−0.298358	−	0.954454i	$-0.596439\pi$
$164$	229.063			1.39672
$165$	−3.83886	+	3.83886i	−0.0232658	+	0.0232658i
$166$	155.723	+	155.723i	0.938088	+	0.938088i
$167$	−140.351	+	140.351i	−0.840427	+	0.840427i	−0.988914	−	0.148488i	$-0.952559\pi$
$167$	−140.351	+	140.351i	−0.840427	+	0.840427i	0.148488	+	0.988914i	$0.452559\pi$
$168$	−53.9659	−	53.9659i	−0.321226	−	0.321226i
$169$		−	470.559i		−	2.78437i
$170$	−83.8014	+	83.8014i	−0.492949	+	0.492949i
$171$	14.6372	−	14.6372i	0.0855977	−	0.0855977i
$172$	−63.5688	−	63.5688i	−0.369586	−	0.369586i
$173$			124.395i			0.719047i	0.933136	+	0.359523i	$0.117061\pi$
$173$			124.395i			0.719047i	−0.933136	+	0.359523i	$0.882939\pi$
$174$	−159.900			−0.918963
$175$		−	159.739i		−	0.912797i
$176$			8.73637i			0.0496385i
$177$	53.0455	+	53.0455i	0.299692	+	0.299692i
$178$		−	190.965i		−	1.07284i
$179$	156.892	+	156.892i	0.876490	+	0.876490i	0.993170	−	0.116680i	$-0.0372252\pi$
$179$	156.892	+	156.892i	0.876490	+	0.876490i	−0.116680	+	0.993170i	$0.537225\pi$
$180$	−36.4434	−	36.4434i	−0.202463	−	0.202463i
$181$	266.634			1.47312			0.736558	−	0.676374i	$-0.236450\pi$
$181$	266.634			1.47312			0.736558	+	0.676374i	$0.236450\pi$
$182$	−847.188			−4.65488
$183$	−1.20178	+	1.20178i	−0.00656712	+	0.00656712i
$184$			139.436i			0.757805i
$185$	−29.0136	−	116.014i	−0.156830	−	0.627103i
$186$	−71.1541			−0.382549
$187$	8.23842	+	8.23842i	0.0440557	+	0.0440557i
$188$		−	85.3902i		−	0.454203i
$189$			57.0325i			0.301759i
$190$	48.1303	−	48.1303i	0.253317	−	0.253317i
$191$	−193.281	+	193.281i	−1.01194	+	1.01194i	−0.0120127	+	0.999928i	$0.503824\pi$
$191$	−193.281	+	193.281i	−1.01194	+	1.01194i	−0.999928	+	0.0120127i	$0.996176\pi$
$192$	−167.826			−0.874095
$193$	96.7021	−	96.7021i	0.501047	−	0.501047i	−0.410716	−	0.911763i	$-0.634721\pi$
$193$	96.7021	−	96.7021i	0.501047	−	0.501047i	0.911763	+	0.410716i	$0.134721\pi$
$194$	497.898			2.56648
$195$	−141.574			−0.726020
$196$			379.889i			1.93821i
$197$	−209.474			−1.06332			−0.531659	−	0.846958i	$-0.678431\pi$
$197$	−209.474			−1.06332			−0.531659	+	0.846958i	$0.678431\pi$
$198$	−6.27884	+	6.27884i	−0.0317113	+	0.0317113i
$199$	3.59083	+	3.59083i	0.0180444	+	0.0180444i	0.716071	−	0.698027i	$-0.245938\pi$
$199$	3.59083	+	3.59083i	0.0180444	+	0.0180444i	−0.698027	+	0.716071i	$0.745938\pi$
$200$	41.3133	+	41.3133i	0.206567	+	0.206567i
$201$	−115.104			−0.572656
$202$	192.109	−	192.109i	0.951034	−	0.951034i
$203$	234.754	+	234.754i	1.15642	+	1.15642i
$204$	−78.2097	+	78.2097i	−0.383381	+	0.383381i
$205$	−98.4898	−	98.4898i	−0.480438	−	0.480438i
$206$		−	264.839i		−	1.28562i
$207$	73.6797	−	73.6797i	0.355941	−	0.355941i
$208$	−161.095	+	161.095i	−0.774496	+	0.774496i
$209$	−4.73163	−	4.73163i	−0.0226394	−	0.0226394i
$210$			187.535i			0.893024i
$211$	−83.5358			−0.395904			−0.197952	−	0.980212i	$-0.563429\pi$
$211$	−83.5358			−0.395904			−0.197952	+	0.980212i	$0.563429\pi$
$212$			356.339i			1.68085i
$213$		−	192.842i		−	0.905360i
$214$	−349.258	−	349.258i	−1.63205	−	1.63205i
$215$			54.6652i			0.254257i
$216$	−14.7503	−	14.7503i	−0.0682883	−	0.0682883i
$217$	104.464	+	104.464i	0.481400	+	0.481400i
$218$	128.305			0.588553
$219$	109.399			0.499537
$220$	−11.7807	+	11.7807i	−0.0535487	+	0.0535487i
$221$			303.826i			1.37478i
$222$	−47.4547	−	189.753i	−0.213760	−	0.854742i
$223$	376.026			1.68621			0.843107	−	0.537746i	$-0.180724\pi$
$223$	376.026			1.68621			0.843107	+	0.537746i	$0.180724\pi$
$224$	338.023	+	338.023i	1.50903	+	1.50903i
$225$		−	43.6609i		−	0.194049i
$226$			506.727i			2.24215i
$227$	102.479	−	102.479i	0.451451	−	0.451451i	−0.444385	−	0.895836i	$-0.646578\pi$
$227$	102.479	−	102.479i	0.451451	−	0.451451i	0.895836	+	0.444385i	$0.146578\pi$
$228$	44.9188	−	44.9188i	0.197012	−	0.197012i
$229$	−31.1728			−0.136126			−0.0680628	−	0.997681i	$-0.521682\pi$
$229$	−31.1728			−0.136126			−0.0680628	+	0.997681i	$0.521682\pi$
$230$	242.275	−	242.275i	1.05337	−	1.05337i
$231$	18.4363			0.0798110
$232$	−121.429			−0.523399
$233$			150.691i			0.646742i	0.946272	+	0.323371i	$0.104816\pi$
$233$			150.691i			0.646742i	−0.946272	+	0.323371i	$0.895184\pi$
$234$	−231.558			−0.989566
$235$	−36.7151	+	36.7151i	−0.156235	+	0.156235i
$236$	162.786	+	162.786i	0.689772	+	0.689772i
$237$	−15.3984	−	15.3984i	−0.0649720	−	0.0649720i
$238$	402.461			1.69101
$239$	23.0375	−	23.0375i	0.0963914	−	0.0963914i	−0.657267	−	0.753658i	$-0.728287\pi$
$239$	23.0375	−	23.0375i	0.0963914	−	0.0963914i	0.753658	+	0.657267i	$0.228287\pi$
$240$	35.6603	+	35.6603i	0.148585	+	0.148585i
$241$	−142.303	+	142.303i	−0.590469	+	0.590469i	−0.937758	−	0.347289i	$-0.887102\pi$
$241$	−142.303	+	142.303i	−0.590469	+	0.590469i	0.347289	+	0.937758i	$0.387102\pi$
$242$	−259.108	−	259.108i	−1.07069	−	1.07069i
$243$			15.5885i			0.0641500i
$244$	−3.68804	+	3.68804i	−0.0151149	+	0.0151149i
$245$	163.341	−	163.341i	0.666696	−	0.666696i
$246$	−161.090	−	161.090i	−0.654838	−	0.654838i
$247$		−	174.499i		−	0.706473i
$248$	−54.0348			−0.217882
$249$		−	124.976i		−	0.501913i
$250$		−	390.183i		−	1.56073i
$251$	−30.2139	−	30.2139i	−0.120374	−	0.120374i	0.644354	−	0.764728i	$-0.277127\pi$
$251$	−30.2139	−	30.2139i	−0.120374	−	0.120374i	−0.764728	+	0.644354i	$0.777127\pi$
$252$			175.022i			0.694530i
$253$	−23.8177	−	23.8177i	−0.0941413	−	0.0941413i
$254$	204.115	+	204.115i	0.803601	+	0.803601i
$255$	67.2555			0.263747
$256$	16.6894			0.0651930
$257$	41.6958	−	41.6958i	0.162240	−	0.162240i	−0.621318	−	0.783559i	$-0.713402\pi$
$257$	41.6958	−	41.6958i	0.162240	−	0.162240i	0.783559	+	0.621318i	$0.213402\pi$
$258$			89.4105i			0.346552i
$259$	−208.913	+	348.252i	−0.806612	+	1.34460i
$260$	−434.463			−1.67101
$261$	64.1644	+	64.1644i	0.245840	+	0.245840i
$262$			307.379i			1.17320i
$263$		−	88.7373i		−	0.337404i	−0.985667	−	0.168702i	$-0.946042\pi$
$263$		−	88.7373i		−	0.337404i	0.985667	−	0.168702i	$-0.0539576\pi$
$264$	−4.76818	+	4.76818i	−0.0180613	+	0.0180613i
$265$	153.215	−	153.215i	0.578170	−	0.578170i
$266$	−231.149			−0.868980
$267$	−76.6303	+	76.6303i	−0.287005	+	0.287005i
$268$	−353.231			−1.31803
$269$	−366.344			−1.36187			−0.680937	−	0.732342i	$-0.738427\pi$
$269$	−366.344			−1.36187			−0.680937	+	0.732342i	$0.738427\pi$
$270$			51.2582i			0.189845i
$271$	79.8680			0.294716			0.147358	−	0.989083i	$-0.452923\pi$
$271$	79.8680			0.294716			0.147358	+	0.989083i	$0.452923\pi$
$272$	76.5292	−	76.5292i	0.281357	−	0.281357i
$273$	339.959	+	339.959i	1.24527	+	1.24527i
$274$	−207.021	−	207.021i	−0.755552	−	0.755552i
$275$	−14.1139			−0.0513231
$276$	226.109	−	226.109i	0.819235	−	0.819235i
$277$	−359.703	−	359.703i	−1.29857	−	1.29857i	−0.929340	−	0.369225i	$-0.879623\pi$
$277$	−359.703	−	359.703i	−1.29857	−	1.29857i	−0.369225	−	0.929340i	$-0.620377\pi$
$278$	449.490	−	449.490i	1.61687	−	1.61687i
$279$	28.5526	+	28.5526i	0.102339	+	0.102339i
$280$			142.415i			0.508625i
$281$	175.894	−	175.894i	0.625959	−	0.625959i	−0.321090	−	0.947049i	$-0.604049\pi$
$281$	175.894	−	175.894i	0.625959	−	0.625959i	0.947049	+	0.321090i	$0.104049\pi$
$282$	−60.0513	+	60.0513i	−0.212948	+	0.212948i
$283$	−206.883	−	206.883i	−0.731035	−	0.731035i	0.239790	−	0.970825i	$-0.422921\pi$
$283$	−206.883	−	206.883i	−0.731035	−	0.731035i	−0.970825	+	0.239790i	$0.922921\pi$
$284$		−	591.794i		−	2.08378i
$285$	−38.6274			−0.135535
$286$			74.8537i			0.261726i
$287$			473.003i			1.64810i
$288$	92.3903	+	92.3903i	0.320800	+	0.320800i
$289$			144.666i			0.500573i
$290$	210.986	+	210.986i	0.727539	+	0.727539i
$291$	−199.796	−	199.796i	−0.686584	−	0.686584i
$292$	335.723			1.14974
$293$	111.353			0.380044			0.190022	−	0.981780i	$-0.439144\pi$
$293$	111.353			0.380044			0.190022	+	0.981780i	$0.439144\pi$
$294$	267.160	−	267.160i	0.908708	−	0.908708i
$295$		−	139.986i		−	0.474529i
$296$	−36.0373	−	144.099i	−0.121748	−	0.486822i
$297$	5.03913			0.0169668
$298$	58.4316	+	58.4316i	0.196079	+	0.196079i
$299$		−	878.379i		−	2.93772i
$300$		−	133.987i		−	0.446623i
$301$	131.267	−	131.267i	0.436102	−	0.436102i
$302$	421.614	−	421.614i	1.39607	−	1.39607i
$303$	−154.179			−0.508840
$304$	−43.9536	+	43.9536i	−0.144584	+	0.144584i
$305$	3.17148			0.0103983
$306$	110.003			0.359488
$307$		−	14.5596i		−	0.0474255i	−0.999719	−	0.0237127i	$-0.992451\pi$
$307$		−	14.5596i		−	0.0474255i	0.999719	−	0.0237127i	$-0.00754871\pi$
$308$	56.5776			0.183693
$309$	−106.274	+	106.274i	−0.343930	+	0.343930i
$310$	93.8872	+	93.8872i	0.302862	+	0.302862i
$311$	−33.0820	−	33.0820i	−0.106373	−	0.106373i	0.651917	−	0.758290i	$-0.273965\pi$
$311$	−33.0820	−	33.0820i	−0.106373	−	0.106373i	−0.758290	+	0.651917i	$0.773965\pi$
$312$	−175.847			−0.563611
$313$	−177.910	+	177.910i	−0.568403	+	0.568403i	−0.931681	−	0.363278i	$-0.881658\pi$
$313$	−177.910	+	177.910i	−0.568403	+	0.568403i	0.363278	+	0.931681i	$0.381658\pi$
$314$	375.382	+	375.382i	1.19548	+	1.19548i
$315$	75.2539	−	75.2539i	0.238901	−	0.238901i
$316$	−47.2546	−	47.2546i	−0.149540	−	0.149540i
$317$		−	488.662i		−	1.54152i	−0.637125	−	0.770761i	$-0.719876\pi$
$317$		−	488.662i		−	1.54152i	0.637125	−	0.770761i	$-0.280124\pi$
$318$	250.599	−	250.599i	0.788046	−	0.788046i
$319$	20.7418	−	20.7418i	0.0650213	−	0.0650213i
$320$	221.445	+	221.445i	0.692017	+	0.692017i
$321$			280.300i			0.873207i
$322$	−1163.54			−3.61348
$323$			82.8967i			0.256646i
$324$			47.8380i			0.147648i
$325$	−260.254	−	260.254i	−0.800781	−	0.800781i
$326$			881.430i			2.70377i
$327$	−51.4859	−	51.4859i	−0.157449	−	0.157449i
$328$	−122.333	−	122.333i	−0.372965	−	0.372965i
$329$	176.327			0.535948
$330$	16.5697			0.0502114
$331$	11.6462	−	11.6462i	0.0351850	−	0.0351850i	−0.689295	−	0.724480i	$-0.742080\pi$
$331$	11.6462	−	11.6462i	0.0351850	−	0.0351850i	0.724480	+	0.689295i	$0.242080\pi$
$332$		−	383.528i		−	1.15521i
$333$	−57.1012	+	95.1864i	−0.171475	+	0.285845i
$334$	605.802			1.81378
$335$	151.879	+	151.879i	0.453369	+	0.453369i
$336$		−	171.261i		−	0.509705i
$337$			577.717i			1.71429i	0.515072	+	0.857147i	$0.327765\pi$
$337$			577.717i			1.71429i	−0.515072	+	0.857147i	$0.672235\pi$
$338$	−1015.54	+	1015.54i	−3.00456	+	3.00456i
$339$	203.339	−	203.339i	0.599820	−	0.599820i
$340$	206.394			0.607042
$341$	9.22994	−	9.22994i	0.0270673	−	0.0270673i
$342$	−63.1790			−0.184734
$343$	−246.634			−0.719049
$344$			67.8988i			0.197380i
$345$	−194.440			−0.563593
$346$	268.465	−	268.465i	0.775910	−	0.775910i
$347$	−482.333	−	482.333i	−1.39001	−	1.39001i	−0.825267	−	0.564742i	$-0.808976\pi$
$347$	−482.333	−	482.333i	−1.39001	−	1.39001i	−0.564742	−	0.825267i	$-0.691024\pi$
$348$	196.908	+	196.908i	0.565828	+	0.565828i
$349$	21.2577			0.0609103			0.0304552	−	0.999536i	$-0.490304\pi$
$349$	21.2577			0.0609103			0.0304552	+	0.999536i	$0.490304\pi$
$350$	−344.744	+	344.744i	−0.984982	+	0.984982i
$351$	92.9195	+	92.9195i	0.264728	+	0.264728i
$352$	29.8661	−	29.8661i	0.0848470	−	0.0848470i
$353$	133.387	+	133.387i	0.377866	+	0.377866i	0.870332	−	0.492466i	$-0.163904\pi$
$353$	133.387	+	133.387i	0.377866	+	0.377866i	−0.492466	+	0.870332i	$0.663904\pi$
$354$		−	228.961i		−	0.646784i
$355$	−254.453	+	254.453i	−0.716769	+	0.716769i
$356$	−235.164	+	235.164i	−0.660572	+	0.660572i
$357$	−161.499	−	161.499i	−0.452379	−	0.452379i
$358$		−	677.195i		−	1.89161i
$359$	109.355			0.304611			0.152305	−	0.988333i	$-0.451330\pi$
$359$	109.355			0.304611			0.152305	+	0.988333i	$0.451330\pi$
$360$			38.9257i			0.108127i
$361$			313.389i			0.868115i
$362$	−575.440	−	575.440i	−1.58961	−	1.58961i
$363$			207.949i			0.572863i
$364$	1043.27	+	1043.27i	2.86612	+	2.86612i
$365$	−144.351	−	144.351i	−0.395481	−	0.395481i
$366$	5.18728			0.0141729
$367$	496.199			1.35204			0.676021	−	0.736882i	$-0.263703\pi$
$367$	496.199			1.35204			0.676021	+	0.736882i	$0.263703\pi$
$368$	−221.250	+	221.250i	−0.601224	+	0.601224i
$369$			129.284i			0.350364i
$370$	−187.761	+	312.993i	−0.507462	+	0.845928i
$371$	−735.824			−1.98335
$372$	87.6225	+	87.6225i	0.235544	+	0.235544i
$373$			5.84280i			0.0156643i	0.999969	+	0.00783217i	$0.00249308\pi$
$373$			5.84280i			0.0156643i	−0.999969	+	0.00783217i	$0.997507\pi$
$374$		−	35.5597i		−	0.0950794i
$375$	−156.572	+	156.572i	−0.417526	+	0.417526i
$376$	−45.6033	+	45.6033i	−0.121285	+	0.121285i
$377$	764.941			2.02902
$378$	123.085	−	123.085i	0.325623	−	0.325623i
$379$	314.643			0.830194			0.415097	−	0.909777i	$-0.363748\pi$
$379$	314.643			0.830194			0.415097	+	0.909777i	$0.363748\pi$
$380$	−118.540			−0.311947
$381$		−	163.814i		−	0.429958i
$382$	834.262			2.18393
$383$	14.3062	−	14.3062i	0.0373530	−	0.0373530i	−0.688184	−	0.725537i	$-0.741592\pi$
$383$	14.3062	−	14.3062i	0.0373530	−	0.0373530i	0.725537	+	0.688184i	$0.241592\pi$
$384$	148.830	+	148.830i	0.387578	+	0.387578i
$385$	−24.3266	−	24.3266i	−0.0631860	−	0.0631860i
$386$	−417.398			−1.08134
$387$	35.8786	−	35.8786i	0.0927095	−	0.0927095i
$388$	−613.135	−	613.135i	−1.58025	−	1.58025i
$389$	−342.427	+	342.427i	−0.880274	+	0.880274i	−0.993562	−	0.113288i	$-0.963862\pi$
$389$	−342.427	+	342.427i	−0.880274	+	0.880274i	0.113288	+	0.993562i	$0.463862\pi$
$390$	305.539	+	305.539i	0.783434	+	0.783434i
$391$			417.279i			1.06721i
$392$	202.883	−	202.883i	0.517558	−	0.517558i
$393$	123.345	−	123.345i	0.313854	−	0.313854i
$394$	452.078	+	452.078i	1.14741	+	1.14741i
$395$			40.6360i			0.102876i
$396$	15.4641			0.0390508
$397$			235.413i			0.592980i	0.955036	+	0.296490i	$0.0958162\pi$
$397$			235.413i			0.592980i	−0.955036	+	0.296490i	$0.904184\pi$
$398$		−	15.4992i		−	0.0389427i
$399$	92.7552	+	92.7552i	0.232469	+	0.232469i
$400$			131.108i			0.327770i
$401$	121.562	+	121.562i	0.303148	+	0.303148i	0.842244	−	0.539096i	$-0.181234\pi$
$401$	121.562	+	121.562i	0.303148	+	0.303148i	−0.539096	+	0.842244i	$0.681234\pi$
$402$	248.413	+	248.413i	0.617942	+	0.617942i
$403$	340.393			0.844647
$404$	−473.144			−1.17115
$405$	20.5688	−	20.5688i	0.0507873	−	0.0507873i
$406$		−	1013.27i		−	2.49575i
$407$	30.7700	+	18.4586i	0.0756020	+	0.0453528i
$408$	83.5370			0.204748
$409$	−145.274	−	145.274i	−0.355192	−	0.355192i	0.506845	−	0.862037i	$-0.330812\pi$
$409$	−145.274	−	145.274i	−0.355192	−	0.355192i	−0.862037	+	0.506845i	$0.830812\pi$
$410$			425.114i			1.03686i
$411$			166.147i			0.404250i
$412$	−326.135	+	326.135i	−0.791590	+	0.791590i
$413$	−336.146	+	336.146i	−0.813913	+	0.813913i
$414$	−318.026			−0.768178
$415$	−164.905	+	164.905i	−0.397362	+	0.397362i
$416$	1101.44			2.64769
$417$	−360.742			−0.865088
$418$			20.4233i			0.0488595i
$419$	−279.980			−0.668211			−0.334105	−	0.942536i	$-0.608434\pi$
$419$	−279.980			−0.668211			−0.334105	+	0.942536i	$0.608434\pi$
$420$	230.940	−	230.940i	0.549856	−	0.549856i
$421$	−123.480	−	123.480i	−0.293302	−	0.293302i	0.545081	−	0.838383i	$-0.316499\pi$
$421$	−123.480	−	123.480i	−0.293302	−	0.293302i	−0.838383	+	0.545081i	$0.816499\pi$
$422$	180.284	+	180.284i	0.427213	+	0.427213i
$423$	48.1947			0.113935
$424$	190.306	−	190.306i	0.448835	−	0.448835i
$425$	123.635	+	123.635i	0.290906	+	0.290906i
$426$	−416.184	+	416.184i	−0.976957	+	0.976957i
$427$	−7.61563	−	7.61563i	−0.0178352	−	0.0178352i
$428$			860.185i			2.00978i
$429$	30.0372	−	30.0372i	0.0700168	−	0.0700168i
$430$	117.976	−	117.976i	0.274364	−	0.274364i
$431$	−564.850	−	564.850i	−1.31056	−	1.31056i	−0.921004	−	0.389554i	$-0.872629\pi$
$431$	−564.850	−	564.850i	−1.31056	−	1.31056i	−0.389554	−	0.921004i	$-0.627371\pi$
$432$		−	46.8100i		−	0.108357i
$433$	254.461			0.587670			0.293835	−	0.955856i	$-0.405068\pi$
$433$	254.461			0.587670			0.293835	+	0.955856i	$0.405068\pi$
$434$		−	450.899i		−	1.03894i
$435$		−	169.329i		−	0.389261i
$436$	−158.000	−	158.000i	−0.362386	−	0.362386i
$437$		−	239.659i		−	0.548419i
$438$	−236.100	−	236.100i	−0.539041	−	0.539041i
$439$	361.947	+	361.947i	0.824481	+	0.824481i	0.986747	−	0.162266i	$-0.0518802\pi$
$439$	361.947	+	361.947i	0.824481	+	0.824481i	−0.162266	+	0.986747i	$0.551880\pi$
$440$	12.5832			0.0285981
$441$	−214.411			−0.486194
$442$	655.706	−	655.706i	1.48350	−	1.48350i
$443$		−	43.8396i		−	0.0989607i	−0.998775	−	0.0494803i	$-0.984243\pi$
$443$		−	43.8396i		−	0.0989607i	0.998775	−	0.0494803i	$-0.0157565\pi$
$444$	−175.233	+	292.109i	−0.394668	+	0.657902i
$445$	202.226			0.454441
$446$	−811.525	−	811.525i	−1.81956	−	1.81956i
$447$		−	46.8947i		−	0.104910i
$448$		−	1063.51i		−	2.37390i
$449$	138.939	−	138.939i	0.309441	−	0.309441i	−0.535252	−	0.844693i	$-0.679783\pi$
$449$	138.939	−	138.939i	0.309441	−	0.309441i	0.844693	+	0.535252i	$0.179783\pi$
$450$	−94.2274	+	94.2274i	−0.209394	+	0.209394i
$451$	41.7925			0.0926662
$452$	624.008	−	624.008i	1.38055	−	1.38055i
$453$	−338.369			−0.746952
$454$	−442.334			−0.974304
$455$		−	897.145i		−	1.97175i
$456$	−47.9784			−0.105216
$457$	−352.275	+	352.275i	−0.770842	+	0.770842i	−0.978254	−	0.207412i	$-0.933496\pi$
$457$	−352.275	+	352.275i	−0.770842	+	0.770842i	0.207412	+	0.978254i	$0.433496\pi$
$458$	67.2759	+	67.2759i	0.146891	+	0.146891i
$459$	−44.1420	−	44.1420i	−0.0961699	−	0.0961699i
$460$	−596.697			−1.29717
$461$	−234.964	+	234.964i	−0.509683	+	0.509683i	−0.914429	−	0.404746i	$-0.867360\pi$
$461$	−234.964	+	234.964i	−0.509683	+	0.509683i	0.404746	+	0.914429i	$0.367360\pi$
$462$	−39.7886	−	39.7886i	−0.0861226	−	0.0861226i
$463$	296.272	−	296.272i	0.639897	−	0.639897i	−0.310633	−	0.950530i	$-0.600541\pi$
$463$	296.272	−	296.272i	0.639897	−	0.639897i	0.950530	+	0.310633i	$0.100541\pi$
$464$	−192.677	−	192.677i	−0.415252	−	0.415252i
$465$		−	75.3500i		−	0.162043i
$466$	325.216	−	325.216i	0.697887	−	0.697887i
$467$	−10.8838	+	10.8838i	−0.0233058	+	0.0233058i	−0.718664	−	0.695358i	$-0.755246\pi$
$467$	−10.8838	+	10.8838i	−0.0233058	+	0.0233058i	0.695358	+	0.718664i	$0.255246\pi$
$468$	285.152	+	285.152i	0.609299	+	0.609299i
$469$		−	729.406i		−	1.55524i
$470$	158.474			0.337180
$471$		−	301.266i		−	0.639630i
$472$		−	173.874i		−	0.368378i
$473$	−11.5981	−	11.5981i	−0.0245203	−	0.0245203i
$474$			66.4643i			0.140220i
$475$	−71.0083	−	71.0083i	−0.149491	−	0.149491i
$476$	−495.610	−	495.610i	−1.04120	−	1.04120i
$477$	−201.120			−0.421635
$478$	−99.4375			−0.208028
$479$	441.786	−	441.786i	0.922308	−	0.922308i	−0.0748842	−	0.997192i	$-0.523859\pi$
$479$	441.786	−	441.786i	0.922308	−	0.922308i	0.997192	+	0.0748842i	$0.0238587\pi$
$480$		−	243.817i		−	0.507951i
$481$	227.018	+	907.755i	0.471970	+	1.88722i
$482$	614.226			1.27433
$483$	466.904	+	466.904i	0.966675	+	0.966675i
$484$			638.156i			1.31850i
$485$			527.258i			1.08713i
$486$	33.6424	−	33.6424i	0.0692231	−	0.0692231i
$487$	42.7661	−	42.7661i	0.0878154	−	0.0878154i	−0.661835	−	0.749650i	$-0.730222\pi$
$487$	42.7661	−	42.7661i	0.0878154	−	0.0878154i	0.749650	+	0.661835i	$0.230222\pi$
$488$	3.93925			0.00807223
$489$	353.699	−	353.699i	0.723311	−	0.723311i
$490$	−705.031			−1.43884
$491$	−540.708			−1.10124			−0.550619	−	0.834756i	$-0.685608\pi$
$491$	−540.708			−1.10124			−0.550619	+	0.834756i	$0.685608\pi$
$492$			396.748i			0.806398i
$493$	−363.390			−0.737099
$494$	−376.597	+	376.597i	−0.762341	+	0.762341i
$495$	−6.64909	−	6.64909i	−0.0134325	−	0.0134325i
$496$	−85.7397	−	85.7397i	−0.172862	−	0.172862i
$497$	1222.03			2.45881
$498$	−269.719	+	269.719i	−0.541605	+	0.541605i
$499$	−4.62257	−	4.62257i	−0.00926366	−	0.00926366i	0.702460	−	0.711723i	$-0.252085\pi$
$499$	−4.62257	−	4.62257i	−0.00926366	−	0.00926366i	−0.711723	+	0.702460i	$0.752085\pi$
$500$	−480.490	+	480.490i	−0.960979	+	0.960979i
$501$	−243.095	−	243.095i	−0.485221	−	0.485221i
$502$			130.413i			0.259787i
$503$	−127.766	+	127.766i	−0.254007	+	0.254007i	−0.822611	−	0.568604i	$-0.807484\pi$
$503$	−127.766	+	127.766i	−0.254007	+	0.254007i	0.568604	+	0.822611i	$0.307484\pi$
$504$	93.4717	−	93.4717i	0.185460	−	0.185460i
$505$	203.437	+	203.437i	0.402846	+	0.402846i
$506$			102.805i			0.203172i
$507$	815.031			1.60756
$508$		−	502.713i		−	0.989592i
$509$		−	984.713i		−	1.93460i	−0.253629	−	0.967302i	$-0.581624\pi$
$509$		−	984.713i		−	1.93460i	0.253629	−	0.967302i	$-0.418376\pi$
$510$	−145.148	−	145.148i	−0.284604	−	0.284604i
$511$			693.253i			1.35666i
$512$	−379.726	−	379.726i	−0.741653	−	0.741653i
$513$	25.3524	+	25.3524i	0.0494199	+	0.0494199i
$514$	−179.973			−0.350141
$515$	280.456			0.544575
$516$	110.104	−	110.104i	0.213381	−	0.213381i
$517$		−	15.5794i		−	0.0301343i
$518$	1202.45	−	300.718i	2.32134	−	0.580536i
$519$	−215.459			−0.415142
$520$	232.028	+	232.028i	0.446208	+	0.446208i
$521$			822.494i			1.57868i	0.613955	+	0.789341i	$0.289578\pi$
$521$			822.494i			1.57868i	−0.613955	+	0.789341i	$0.710422\pi$
$522$		−	276.954i		−	0.530564i
$523$	233.557	−	233.557i	0.446572	−	0.446572i	−0.447641	−	0.894213i	$-0.647736\pi$
$523$	233.557	−	233.557i	0.446572	−	0.446572i	0.894213	+	0.447641i	$0.147736\pi$
$524$	378.521	−	378.521i	0.722368	−	0.722368i
$525$	276.677			0.527004
$526$	−191.509	+	191.509i	−0.364086	+	0.364086i
$527$	−161.706			−0.306842
$528$	−15.1318			−0.0286588
$529$		−	677.378i		−	1.28049i
$530$	−661.325			−1.24778
$531$	−91.8774	+	91.8774i	−0.173027	+	0.173027i
$532$	284.648	+	284.648i	0.535052	+	0.535052i
$533$	770.636	+	770.636i	1.44585	+	1.44585i
$534$	330.761			0.619403
$535$	369.853	−	369.853i	0.691314	−	0.691314i
$536$	188.646	+	188.646i	0.351951	+	0.351951i
$537$	−271.744	+	271.744i	−0.506041	+	0.506041i
$538$	790.630	+	790.630i	1.46957	+	1.46957i
$539$			69.3108i			0.128591i
$540$	63.1218	−	63.1218i	0.116892	−	0.116892i
$541$	−688.022	+	688.022i	−1.27176	+	1.27176i	−0.326596	+	0.945164i	$0.605902\pi$
$541$	−688.022	+	688.022i	−1.27176	+	1.27176i	−0.945164	+	0.326596i	$0.894098\pi$
$542$	−172.368	−	172.368i	−0.318023	−	0.318023i
$543$			461.824i			0.850504i
$544$	−523.245			−0.961848
$545$			135.871i			0.249304i
$546$		−	1467.37i		−	2.68749i
$547$	682.125	+	682.125i	1.24703	+	1.24703i	0.957026	+	0.290004i	$0.0936565\pi$
$547$	682.125	+	682.125i	1.24703	+	1.24703i	0.290004	+	0.957026i	$0.406344\pi$
$548$			509.872i			0.930423i
$549$	−2.08155	−	2.08155i	−0.00379153	−	0.00379153i
$550$	30.4600	+	30.4600i	0.0553818	+	0.0553818i
$551$	208.708			0.378781
$552$	−241.510			−0.437519
$553$	97.5785	−	97.5785i	0.176453	−	0.176453i
$554$			1552.59i			2.80251i
$555$	200.942	−	50.2531i	0.362058	−	0.0905460i
$556$	−1107.05			−1.99109
$557$	643.961	+	643.961i	1.15612	+	1.15612i	0.985302	+	0.170822i	$0.0546422\pi$
$557$	643.961	+	643.961i	1.15612	+	1.15612i	0.170822	+	0.985302i	$0.445358\pi$
$558$		−	123.242i		−	0.220865i
$559$		−	427.729i		−	0.765169i
$560$	−225.977	+	225.977i	−0.403531	+	0.403531i
$561$	−14.2694	+	14.2694i	−0.0254356	+	0.0254356i
$562$	−759.217			−1.35092
$563$	619.633	−	619.633i	1.10059	−	1.10059i	0.106252	−	0.994339i	$-0.466115\pi$
$563$	619.633	−	619.633i	1.10059	−	1.10059i	0.994339	−	0.106252i	$-0.0338851\pi$
$564$	147.900			0.262234
$565$	−536.608			−0.949748
$566$			892.973i			1.57769i
$567$	−98.7831			−0.174221
$568$	−316.052	+	316.052i	−0.556430	+	0.556430i
$569$	−432.358	−	432.358i	−0.759856	−	0.759856i	0.216440	−	0.976296i	$-0.430555\pi$
$569$	−432.358	−	432.358i	−0.759856	−	0.759856i	−0.976296	+	0.216440i	$0.930555\pi$
$570$	83.3641	+	83.3641i	0.146253	+	0.146253i
$571$	−519.920			−0.910543			−0.455271	−	0.890353i	$-0.650458\pi$
$571$	−519.920			−0.910543			−0.455271	+	0.890353i	$0.650458\pi$
$572$	92.1784	−	92.1784i	0.161151	−	0.161151i
$573$	−334.772	−	334.772i	−0.584244	−	0.584244i
$574$	1020.82	−	1020.82i	1.77843	−	1.77843i
$575$	−357.436	−	357.436i	−0.621628	−	0.621628i
$576$		−	290.684i		−	0.504659i
$577$	359.015	−	359.015i	0.622210	−	0.622210i	−0.323886	−	0.946096i	$-0.604989\pi$
$577$	359.015	−	359.015i	0.622210	−	0.622210i	0.946096	+	0.323886i	$0.104989\pi$
$578$	312.212	−	312.212i	0.540159	−	0.540159i
$579$	167.493	+	167.493i	0.289280	+	0.289280i
$580$		−	519.637i		−	0.895926i
$581$	791.968			1.36311
$582$			862.384i			1.48176i
$583$			65.0141i			0.111516i
$584$	−179.296	−	179.296i	−0.307013	−	0.307013i
$585$		−	245.213i		−	0.419168i
$586$	−240.318	−	240.318i	−0.410099	−	0.410099i
$587$	10.1104	+	10.1104i	0.0172239	+	0.0172239i	0.715666	−	0.698442i	$-0.246123\pi$
$587$	10.1104	+	10.1104i	0.0172239	+	0.0172239i	−0.698442	+	0.715666i	$0.746123\pi$
$588$	−657.987			−1.11903
$589$	92.8736			0.157680
$590$	−302.113	+	302.113i	−0.512055	+	0.512055i
$591$		−	362.819i		−	0.613907i
$592$	171.467	−	285.832i	0.289641	−	0.482824i
$593$	619.896			1.04536			0.522678	−	0.852530i	$-0.324933\pi$
$593$	619.896			1.04536			0.522678	+	0.852530i	$0.324933\pi$
$594$	−10.8753	−	10.8753i	−0.0183085	−	0.0183085i
$595$			426.194i			0.716293i
$596$		−	143.911i		−	0.241461i
$597$	−6.21950	+	6.21950i	−0.0104179	+	0.0104179i
$598$	−1895.68	+	1895.68i	−3.17004	+	3.17004i
$599$	−489.263			−0.816800			−0.408400	−	0.912803i	$-0.633913\pi$
$599$	−489.263			−0.816800			−0.408400	+	0.912803i	$0.633913\pi$
$600$	−71.5568	+	71.5568i	−0.119261	+	0.119261i
$601$	483.840			0.805058			0.402529	−	0.915407i	$-0.368131\pi$
$601$	483.840			0.805058			0.402529	+	0.915407i	$0.368131\pi$
$602$	−566.589			−0.941178
$603$		−	199.366i		−	0.330623i
$604$	−1038.39			−1.71919
$605$	274.387	−	274.387i	0.453533	−	0.453533i
$606$	332.742	+	332.742i	0.549080	+	0.549080i
$607$	−11.5502	−	11.5502i	−0.0190283	−	0.0190283i	0.697529	−	0.716557i	$-0.254283\pi$
$607$	−11.5502	−	11.5502i	−0.0190283	−	0.0190283i	−0.716557	+	0.697529i	$0.754283\pi$
$608$	300.519			0.494275
$609$	−406.606	+	406.606i	−0.667662	+	0.667662i
$610$	−6.84458	−	6.84458i	−0.0112206	−	0.0112206i
$611$	287.278	−	287.278i	0.470178	−	0.470178i
$612$	−135.463	−	135.463i	−0.221345	−	0.221345i
$613$			354.333i			0.578031i	0.957324	+	0.289015i	$0.0933279\pi$
$613$			354.333i			0.578031i	−0.957324	+	0.289015i	$0.906672\pi$
$614$	−31.4220	+	31.4220i	−0.0511759	+	0.0511759i
$615$	170.589	−	170.589i	0.277381	−	0.277381i
$616$	−30.2157	−	30.2157i	−0.0490514	−	0.0490514i
$617$		−	81.5664i		−	0.132198i	−0.997813	−	0.0660992i	$-0.978945\pi$
$617$		−	81.5664i		−	0.132198i	0.997813	−	0.0660992i	$-0.0210554\pi$
$618$	458.714			0.742256
$619$		−	271.428i		−	0.438494i	−0.975669	−	0.219247i	$-0.929640\pi$
$619$		−	271.428i		−	0.438494i	0.975669	−	0.219247i	$-0.0703600\pi$
$620$		−	231.234i		−	0.372959i
$621$	127.617	+	127.617i	0.205502	+	0.205502i
$622$			142.792i			0.229570i
$623$	−485.602	−	485.602i	−0.779457	−	0.779457i
$624$	−279.025	−	279.025i	−0.447155	−	0.447155i
$625$	49.3501			0.0789602
$626$	767.918			1.22671
$627$	8.19543	−	8.19543i	0.0130709	−	0.0130709i
$628$		−	924.526i		−	1.47218i
$629$	−107.846	−	431.234i	−0.171456	−	0.685587i
$630$	−324.820			−0.515588
$631$	−477.186	−	477.186i	−0.756237	−	0.756237i	0.219398	−	0.975635i	$-0.429591\pi$
$631$	−477.186	−	477.186i	−0.756237	−	0.756237i	−0.975635	+	0.219398i	$0.929591\pi$
$632$			50.4733i			0.0798629i
$633$		−	144.688i		−	0.228576i
$634$	−1054.61	+	1054.61i	−1.66343	+	1.66343i
$635$	−216.151	+	216.151i	−0.340395	+	0.340395i
$636$	−617.198			−0.970437
$637$	−1278.06	+	1278.06i	−2.00638	+	2.00638i
$638$	−89.5284			−0.140327
$639$	334.012			0.522710
$640$		−	392.760i		−	0.613687i
$641$	−440.149			−0.686660			−0.343330	−	0.939215i	$-0.611555\pi$
$641$	−440.149			−0.686660			−0.343330	+	0.939215i	$0.611555\pi$
$642$	604.932	−	604.932i	0.942262	−	0.942262i
$643$	−337.948	−	337.948i	−0.525580	−	0.525580i	0.393672	−	0.919251i	$-0.371205\pi$
$643$	−337.948	−	337.948i	−0.525580	−	0.525580i	−0.919251	+	0.393672i	$0.871205\pi$
$644$	1432.84	+	1432.84i	2.22490	+	2.22490i
$645$	−94.6829			−0.146795
$646$	178.904	−	178.904i	0.276942	−	0.276942i
$647$	280.399	+	280.399i	0.433384	+	0.433384i	0.889778	−	0.456394i	$-0.150859\pi$
$647$	280.399	+	280.399i	0.433384	+	0.433384i	−0.456394	+	0.889778i	$0.650859\pi$
$648$	25.5482	−	25.5482i	0.0394263	−	0.0394263i
$649$	29.7003	+	29.7003i	0.0457632	+	0.0457632i
$650$			1123.34i			1.72822i
$651$	−180.936	+	180.936i	−0.277936	+	0.277936i
$652$	1085.43	−	1085.43i	1.66478	−	1.66478i
$653$	−177.171	−	177.171i	−0.271318	−	0.271318i	0.558312	−	0.829631i	$-0.311449\pi$
$653$	−177.171	−	177.171i	−0.271318	−	0.271318i	−0.829631	+	0.558312i	$0.811449\pi$
$654$			222.230i			0.339801i
$655$	−325.505			−0.496954
$656$		−	388.223i		−	0.591803i
$657$			189.484i			0.288408i
$658$	−380.542	−	380.542i	−0.578331	−	0.578331i
$659$		−	192.732i		−	0.292461i	−0.989251	−	0.146231i	$-0.953286\pi$
$659$		−	192.732i		−	0.292461i	0.989251	−	0.146231i	$-0.0467141\pi$
$660$	−20.4048	−	20.4048i	−0.0309163	−	0.0309163i
$661$	327.577	+	327.577i	0.495578	+	0.495578i	0.910058	−	0.414481i	$-0.136037\pi$
$661$	327.577	+	327.577i	0.495578	+	0.495578i	−0.414481	+	0.910058i	$0.636037\pi$
$662$	−50.2689			−0.0759349
$663$	−526.242			−0.793729
$664$	−204.826	+	204.826i	−0.308473	+	0.308473i
$665$		−	244.779i		−	0.368089i
$666$	328.661	−	82.1939i	0.493486	−	0.123414i
$667$	1050.58			1.57508
$668$	−746.013	−	746.013i	−1.11679	−	1.11679i
$669$			651.296i			0.973536i
$670$		−	655.557i		−	0.978443i
$671$	−0.672882	+	0.672882i	−0.00100281	+	0.00100281i
$672$	−585.472	+	585.472i	−0.871238	+	0.871238i
$673$	605.035			0.899012			0.449506	−	0.893277i	$-0.351600\pi$
$673$	605.035			0.899012			0.449506	+	0.893277i	$0.351600\pi$
$674$	1246.81	−	1246.81i	1.84986	−	1.84986i
$675$	75.6230			0.112034
$676$	2501.17			3.69996
$677$		−	54.0242i		−	0.0797995i	−0.999204	−	0.0398997i	$-0.987296\pi$
$677$		−	54.0242i		−	0.0797995i	0.999204	−	0.0398997i	$-0.0127038\pi$
$678$	−877.676			−1.29451
$679$	1266.10	−	1266.10i	1.86465	−	1.86465i
$680$	−110.226	−	110.226i	−0.162098	−	0.162098i
$681$	177.499	+	177.499i	0.260645	+	0.260645i
$682$	−39.8394			−0.0584156
$683$	−299.954	+	299.954i	−0.439172	+	0.439172i	−0.891733	−	0.452561i	$-0.850510\pi$
$683$	−299.954	+	299.954i	−0.439172	+	0.439172i	0.452561	+	0.891733i	$0.350510\pi$
$684$	77.8016	+	77.8016i	0.113745	+	0.113745i
$685$	219.229	−	219.229i	0.320043	−	0.320043i
$686$	532.276	+	532.276i	0.775913	+	0.775913i
$687$		−	53.9928i		−	0.0785922i
$688$	−107.738	+	107.738i	−0.156597	+	0.156597i
$689$	−1198.83	+	1198.83i	−1.73996	+	1.73996i
$690$	419.632	+	419.632i	0.608163	+	0.608163i
$691$			511.600i			0.740377i	0.928957	+	0.370188i	$0.120707\pi$
$691$			511.600i			0.740377i	−0.928957	+	0.370188i	$0.879293\pi$
$692$	−661.201			−0.955492
$693$			31.9327i			0.0460789i
$694$			2081.91i			2.99987i
$695$	475.996	+	475.996i	0.684886	+	0.684886i
$696$		−	210.321i		−	0.302185i
$697$	−366.095	−	366.095i	−0.525244	−	0.525244i
$698$	−45.8776	−	45.8776i	−0.0657272	−	0.0657272i
$699$	−261.004			−0.373397
$700$	849.068			1.21295
$701$	−129.848	+	129.848i	−0.185233	+	0.185233i	−0.793631	−	0.608399i	$-0.791812\pi$
$701$	−129.848	+	129.848i	−0.185233	+	0.185233i	0.608399	+	0.793631i	$0.291812\pi$
$702$		−	401.071i		−	0.571326i
$703$	61.9401	+	247.674i	0.0881082	+	0.352310i
$704$	−93.9665			−0.133475
$705$	−63.5925	−	63.5925i	−0.0902021	−	0.0902021i
$706$		−	575.740i		−	0.815496i
$707$		−	977.021i		−	1.38192i
$708$	−281.954	+	281.954i	−0.398240	+	0.398240i
$709$	−600.195	+	600.195i	−0.846538	+	0.846538i	−0.989699	−	0.143162i	$-0.954273\pi$
$709$	−600.195	+	600.195i	−0.846538	+	0.846538i	0.143162	+	0.989699i	$0.454273\pi$
$710$	1098.30			1.54690
$711$	26.6707	−	26.6707i	0.0375116	−	0.0375116i
$712$	251.182			0.352784
$713$	467.500			0.655681
$714$			697.084i			0.976308i
$715$	−79.2677			−0.110864
$716$	−833.931	+	833.931i	−1.16471	+	1.16471i
$717$	39.9022	+	39.9022i	0.0556516	+	0.0556516i
$718$	−236.006	−	236.006i	−0.328700	−	0.328700i
$719$	−732.323			−1.01853			−0.509265	−	0.860610i	$-0.670083\pi$
$719$	−732.323			−1.01853			−0.509265	+	0.860610i	$0.670083\pi$
$720$	−61.7655	+	61.7655i	−0.0857854	+	0.0857854i
$721$	−673.454	−	673.454i	−0.934055	−	0.934055i
$722$	676.345	−	676.345i	0.936766	−	0.936766i
$723$	−246.476	−	246.476i	−0.340907	−	0.340907i
$724$			1417.25i			1.95753i
$725$	311.275	−	311.275i	0.429345	−	0.429345i
$726$	448.788	−	448.788i	0.618165	−	0.618165i
$727$	−672.967	−	672.967i	−0.925676	−	0.925676i	0.0717466	−	0.997423i	$-0.477143\pi$
$727$	−672.967	−	672.967i	−0.925676	−	0.925676i	−0.997423	+	0.0717466i	$0.977143\pi$
$728$		−	1114.33i		−	1.53067i
$729$	−27.0000			−0.0370370
$730$			623.064i			0.853513i
$731$			203.195i			0.277969i
$732$	−6.38787	−	6.38787i	−0.00872660	−	0.00872660i
$733$		−	965.483i		−	1.31717i	−0.752508	−	0.658583i	$-0.771156\pi$
$733$		−	965.483i		−	1.31717i	0.752508	−	0.658583i	$-0.228844\pi$
$734$	−1070.88	−	1070.88i	−1.45896	−	1.45896i
$735$	282.914	+	282.914i	0.384917	+	0.384917i
$736$	1512.73			2.05534
$737$	−64.4470			−0.0874451
$738$	279.016	−	279.016i	0.378071	−	0.378071i
$739$		−	1320.04i		−	1.78625i	−0.449804	−	0.893127i	$-0.648506\pi$
$739$		−	1320.04i		−	1.78625i	0.449804	−	0.893127i	$-0.351494\pi$
$740$	616.653	−	154.217i	0.833315	−	0.208401i
$741$	302.241			0.407882
$742$	1588.03	+	1588.03i	2.14020	+	2.14020i
$743$			369.729i			0.497617i	0.968553	+	0.248808i	$0.0800389\pi$
$743$			369.729i			0.497617i	−0.968553	+	0.248808i	$0.919961\pi$
$744$		−	93.5910i		−	0.125794i
$745$	−61.8772	+	61.8772i	−0.0830567	+	0.0830567i
$746$	12.6097	−	12.6097i	0.0169031	−	0.0169031i
$747$	216.466			0.289780
$748$	−43.7899	+	43.7899i	−0.0585426	+	0.0585426i
$749$	−1776.24			−2.37148
$750$	675.816			0.901088
$751$		−	812.762i		−	1.08224i	−0.840946	−	0.541120i	$-0.818001\pi$
$751$		−	812.762i		−	1.08224i	0.840946	−	0.541120i	$-0.181999\pi$
$752$	−144.722			−0.192450
$753$	52.3320	−	52.3320i	0.0694980	−	0.0694980i
$754$	−1650.87	−	1650.87i	−2.18948	−	2.18948i
$755$	446.476	+	446.476i	0.591358	+	0.591358i
$756$	−303.146			−0.400987
$757$	−376.656	+	376.656i	−0.497564	+	0.497564i	−0.910679	−	0.413115i	$-0.864441\pi$
$757$	−376.656	+	376.656i	−0.497564	+	0.497564i	0.413115	+	0.910679i	$0.364441\pi$
$758$	−679.052	−	679.052i	−0.895846	−	0.895846i
$759$	41.2535	−	41.2535i	0.0543525	−	0.0543525i
$760$	63.3072	+	63.3072i	0.0832989	+	0.0832989i
$761$			1068.79i			1.40445i	0.711954	+	0.702226i	$0.247810\pi$
$761$			1068.79i			1.40445i	−0.711954	+	0.702226i	$0.752190\pi$
$762$	−353.537	+	353.537i	−0.463959	+	0.463959i
$763$	326.263	−	326.263i	0.427606	−	0.427606i
$764$	−1027.35	−	1027.35i	−1.34470	−	1.34470i
$765$			116.490i			0.152274i
$766$	−61.7502			−0.0806138
$767$			1095.32i			1.42806i
$768$			28.9069i			0.0376392i
$769$	681.999	+	681.999i	0.886864	+	0.886864i	0.994221	−	0.107356i	$-0.0342385\pi$
$769$	681.999	+	681.999i	0.886864	+	0.886864i	−0.107356	+	0.994221i	$0.534239\pi$
$770$			105.002i			0.136366i
$771$	72.2193	+	72.2193i	0.0936696	+	0.0936696i
$772$	514.003	+	514.003i	0.665808	+	0.665808i
$773$	−959.024			−1.24065			−0.620326	−	0.784344i	$-0.713000\pi$
$773$	−959.024			−1.24065			−0.620326	+	0.784344i	$0.713000\pi$
$774$	−154.864			−0.200082
$775$	138.515	−	138.515i	0.178729	−	0.178729i
$776$			654.899i			0.843942i
$777$	−603.191	−	361.847i	−0.776307	−	0.465698i
$778$	1478.02			1.89977
$779$	210.262	+	210.262i	0.269913	+	0.269913i
$780$		−	752.512i		−	0.964759i
$781$		−	107.973i		−	0.138249i
$782$	900.556	−	900.556i	1.15161	−	1.15161i
$783$	−111.136	+	111.136i	−0.141936	+	0.141936i
$784$	643.849			0.821236
$785$	−397.518	+	397.518i	−0.506392	+	0.506392i
$786$	−532.396			−0.677348
$787$	−203.997			−0.259209			−0.129604	−	0.991566i	$-0.541371\pi$
$787$	−203.997			−0.259209			−0.129604	+	0.991566i	$0.541371\pi$
$788$		−	1113.42i		−	1.41297i
$789$	153.697			0.194800
$790$	87.6991	−	87.6991i	0.111012	−	0.111012i
$791$	1288.55	+	1288.55i	1.62901	+	1.62901i
$792$	−8.25873	−	8.25873i	−0.0104277	−	0.0104277i
$793$	−24.8154			−0.0312930
$794$	508.060	−	508.060i	0.639874	−	0.639874i
$795$	265.376	+	265.376i	0.333806	+	0.333806i
$796$	−19.0865	+	19.0865i	−0.0239780	+	0.0239780i
$797$	−384.783	−	384.783i	−0.482789	−	0.482789i	0.423232	−	0.906021i	$-0.360895\pi$
$797$	−384.783	−	384.783i	−0.482789	−	0.482789i	−0.906021	+	0.423232i	$0.860895\pi$
$798$		−	400.361i		−	0.501706i
$799$	−136.473	+	136.473i	−0.170805	+	0.170805i
$800$	448.206	−	448.206i	0.560257	−	0.560257i
$801$	−132.728	−	132.728i	−0.165702	−	0.165702i
$802$		−	524.703i		−	0.654243i
$803$	61.2527			0.0762798
$804$		−	611.815i		−	0.760963i
$805$		−	1232.15i		−	1.53062i
$806$	−734.623	−	734.623i	−0.911443	−	0.911443i
$807$		−	634.526i		−	0.786278i
$808$	252.686	+	252.686i	0.312731	+	0.312731i
$809$	219.412	+	219.412i	0.271214	+	0.271214i	0.829589	−	0.558375i	$-0.188575\pi$
$809$	219.412	+	219.412i	0.271214	+	0.271214i	−0.558375	+	0.829589i	$0.688575\pi$
$810$	−88.7818			−0.109607
$811$	−219.613			−0.270792			−0.135396	−	0.990792i	$-0.543231\pi$
$811$	−219.613			−0.270792			−0.135396	+	0.990792i	$0.543231\pi$
$812$	−1247.79	+	1247.79i	−1.53669	+	1.53669i
$813$			138.336i			0.170154i
$814$	−26.5701	−	106.243i	−0.0326413	−	0.130520i
$815$	−933.407			−1.14528
$816$	132.552	+	132.552i	0.162442	+	0.162442i
$817$		−	116.703i		−	0.142843i
$818$			627.048i			0.766562i
$819$	−588.826	+	588.826i	−0.718957	+	0.718957i
$820$	523.506	−	523.506i	0.638422	−	0.638422i
$821$	−228.001			−0.277712			−0.138856	−	0.990313i	$-0.544342\pi$
$821$	−228.001			−0.277712			−0.138856	+	0.990313i	$0.544342\pi$
$822$	358.572	−	358.572i	0.436218	−	0.436218i
$823$	−1140.60			−1.38591			−0.692955	−	0.720981i	$-0.743692\pi$
$823$	−1140.60			−1.38591			−0.692955	+	0.720981i	$0.743692\pi$
$824$	348.350			0.422755
$825$		−	24.4459i		−	0.0296314i
$826$	1450.92			1.75656
$827$	−651.423	+	651.423i	−0.787694	+	0.787694i	−0.981116	−	0.193422i	$-0.938041\pi$
$827$	−651.423	+	651.423i	−0.787694	+	0.787694i	0.193422	+	0.981116i	$0.438041\pi$
$828$	391.632	+	391.632i	0.472985	+	0.472985i
$829$	−35.7910	−	35.7910i	−0.0431737	−	0.0431737i	0.685190	−	0.728364i	$-0.259719\pi$
$829$	−35.7910	−	35.7910i	−0.0431737	−	0.0431737i	−0.728364	+	0.685190i	$0.759719\pi$
$830$	711.785			0.857572
$831$	623.023	−	623.023i	0.749727	−	0.749727i
$832$	−1732.70	−	1732.70i	−2.08258	−	2.08258i
$833$	607.151	−	607.151i	0.728873	−	0.728873i
$834$	778.539	+	778.539i	0.933500	+	0.933500i
$835$			641.525i			0.768293i
$836$	25.1502	−	25.1502i	0.0300839	−	0.0300839i
$837$	−49.4546	+	49.4546i	−0.0590856	+	0.0590856i
$838$	604.243	+	604.243i	0.721054	+	0.721054i
$839$		−	600.009i		−	0.715147i	−0.933885	−	0.357574i	$-0.883604\pi$
$839$		−	600.009i		−	0.715147i	0.933885	−	0.357574i	$-0.116396\pi$
$840$	−246.670			−0.293655
$841$			73.9036i			0.0878759i
$842$			532.981i			0.632994i
$843$	304.658	+	304.658i	0.361397	+	0.361397i
$844$		−	444.020i		−	0.526091i
$845$	−1075.43	−	1075.43i	−1.27270	−	1.27270i
$846$	−104.012	−	104.012i	−0.122946	−	0.122946i
$847$	−1317.76			−1.55580
$848$	603.936			0.712189
$849$	358.332	−	358.332i	0.422063	−	0.422063i
$850$		−	533.649i		−	0.627823i
$851$	311.789	+	1246.72i	0.366380	+	1.46501i
$852$	1025.02			1.20307
$853$	−164.570	−	164.570i	−0.192930	−	0.192930i	0.604031	−	0.796961i	$-0.293560\pi$
$853$	−164.570	−	164.570i	−0.192930	−	0.192930i	−0.796961	+	0.604031i	$0.793560\pi$
$854$			32.8715i			0.0384912i
$855$		−	66.9046i		−	0.0782509i
$856$	459.389	−	459.389i	0.536669	−	0.536669i
$857$	254.114	−	254.114i	0.296516	−	0.296516i	−0.543131	−	0.839648i	$-0.682761\pi$
$857$	254.114	−	254.114i	0.296516	−	0.296516i	0.839648	+	0.543131i	$0.182761\pi$
$858$	−129.650			−0.151108
$859$	−780.640	+	780.640i	−0.908778	+	0.908778i	−0.996174	−	0.0873955i	$-0.972146\pi$
$859$	−780.640	+	780.640i	−0.908778	+	0.908778i	0.0873955	+	0.996174i	$0.472146\pi$
$860$	−290.564			−0.337865
$861$	−819.266			−0.951528
$862$			2438.08i			2.82840i
$863$	654.307			0.758178			0.379089	−	0.925360i	$-0.376237\pi$
$863$	654.307			0.758178			0.379089	+	0.925360i	$0.376237\pi$
$864$	−160.025	+	160.025i	−0.185214	+	0.185214i
$865$	284.296	+	284.296i	0.328666	+	0.328666i
$866$	−549.168	−	549.168i	−0.634143	−	0.634143i
$867$	−250.568			−0.289006
$868$	−555.259	+	555.259i	−0.639699	+	0.639699i
$869$	−8.62159	−	8.62159i	−0.00992128	−	0.00992128i
$870$	−365.439	+	365.439i	−0.420045	+	0.420045i
$871$	−1188.38	−	1188.38i	−1.36438	−	1.36438i
$872$			168.763i			0.193535i
$873$	346.057	−	346.057i	0.396400	−	0.396400i
$874$	−517.223	+	517.223i	−0.591789	+	0.591789i
$875$	−992.189	−	992.189i	−1.13393	−	1.13393i
$876$			581.490i			0.663801i
$877$	−1326.93			−1.51303			−0.756516	−	0.653975i	$-0.773100\pi$
$877$	−1326.93			−1.51303			−0.756516	+	0.653975i	$0.773100\pi$
$878$		−	1562.28i		−	1.77936i
$879$			192.869i			0.219419i
$880$	19.9663	+	19.9663i	0.0226890	+	0.0226890i
$881$			125.246i			0.142163i	0.997470	+	0.0710817i	$0.0226451\pi$
$881$			125.246i			0.142163i	−0.997470	+	0.0710817i	$0.977355\pi$
$882$	462.735	+	462.735i	0.524643	+	0.524643i
$883$	426.323	+	426.323i	0.482812	+	0.482812i	0.906029	−	0.423216i	$-0.139099\pi$
$883$	426.323	+	426.323i	0.482812	+	0.482812i	−0.423216	+	0.906029i	$0.639099\pi$
$884$	−1614.94			−1.82685
$885$	242.463			0.273970
$886$	−94.6129	+	94.6129i	−0.106787	+	0.106787i
$887$			440.144i			0.496216i	0.968732	+	0.248108i	$0.0798088\pi$
$887$			440.144i			0.496216i	−0.968732	+	0.248108i	$0.920191\pi$
$888$	249.587	−	62.4185i	0.281067	−	0.0702911i
$889$	1038.08			1.16769
$890$	−436.437	−	436.437i	−0.490379	−	0.490379i
$891$			8.72803i			0.00979577i
$892$			1998.70i			2.24070i
$893$	78.3818	−	78.3818i	0.0877735	−	0.0877735i
$894$	−101.206	+	101.206i	−0.113206	+	0.113206i
$895$	717.129			0.801261
$896$	−943.126	+	943.126i	−1.05260	+	1.05260i
$897$	1521.40			1.69609
$898$	−599.706			−0.667824
$899$			407.125i			0.452864i
$900$	232.072			0.257858
$901$	569.513	−	569.513i	0.632090	−	0.632090i
$902$	−90.1949	−	90.1949i	−0.0999943	−	0.0999943i
$903$	227.360	+	227.360i	0.251783	+	0.251783i
$904$	−666.512			−0.737292
$905$	609.373	−	609.373i	0.673340	−	0.673340i
$906$	730.256	+	730.256i	0.806022	+	0.806022i
$907$	−84.7839	+	84.7839i	−0.0934773	+	0.0934773i	−0.752299	−	0.658822i	$-0.771055\pi$
$907$	−84.7839	+	84.7839i	−0.0934773	+	0.0934773i	0.658822	+	0.752299i	$0.271055\pi$
$908$	544.711	+	544.711i	0.599902	+	0.599902i
$909$		−	267.045i		−	0.293779i
$910$	−1936.19	+	1936.19i	−2.12768	+	2.12768i
$911$	−627.518	+	627.518i	−0.688823	+	0.688823i	−0.961972	−	0.273149i	$-0.911935\pi$
$911$	−627.518	+	627.518i	−0.688823	+	0.688823i	0.273149	+	0.961972i	$0.411935\pi$
$912$	−76.1298	−	76.1298i	−0.0834757	−	0.0834757i
$913$		−	69.9747i		−	0.0766427i
$914$	1520.53			1.66360
$915$			5.49317i			0.00600347i
$916$		−	165.694i		−	0.180888i
$917$	781.628	+	781.628i	0.852375	+	0.852375i
$918$			190.531i			0.207550i
$919$	622.830	+	622.830i	0.677726	+	0.677726i	0.959485	−	0.281759i	$-0.0909179\pi$
$919$	622.830	+	622.830i	0.677726	+	0.677726i	−0.281759	+	0.959485i	$0.590918\pi$
$920$	318.671	+	318.671i	0.346381	+	0.346381i
$921$	25.2180			0.0273811
$922$	1014.18			1.09998
$923$	1990.97	−	1990.97i	2.15707	−	2.15707i
$924$			97.9952i			0.106055i
$925$	461.770	+	277.010i	0.499211	+	0.299471i
$926$	−1278.81			−1.38100
$927$	−184.072	−	184.072i	−0.198568	−	0.198568i
$928$			1317.37i			1.41958i
$929$			1258.89i			1.35510i	0.735477	+	0.677549i	$0.236958\pi$
$929$			1258.89i			1.35510i	−0.735477	+	0.677549i	$0.763042\pi$
$930$	−162.617	+	162.617i	−0.174857	+	0.174857i
$931$	−348.710	+	348.710i	−0.374554	+	0.374554i
$932$	−800.972			−0.859412
$933$	57.2996	−	57.2996i	0.0614144	−	0.0614144i
$934$	46.9780			0.0502976
$935$	37.6566			0.0402744
$936$		−	304.575i		−	0.325401i
$937$	248.811			0.265540			0.132770	−	0.991147i	$-0.457613\pi$
$937$	248.811			0.265540			0.132770	+	0.991147i	$0.457613\pi$
$938$	−1574.18	+	1574.18i	−1.67823	+	1.67823i
$939$	−308.149	−	308.149i	−0.328168	−	0.328168i
$940$	−195.153	−	195.153i	−0.207610	−	0.207610i
$941$	1765.10			1.87577			0.937886	−	0.346943i	$-0.112780\pi$
$941$	1765.10			1.87577			0.937886	+	0.346943i	$0.112780\pi$
$942$	−650.180	+	650.180i	−0.690213	+	0.690213i
$943$	1058.40	+	1058.40i	1.12238	+	1.12238i
$944$	275.896	−	275.896i	0.292262	−	0.292262i
$945$	130.344	+	130.344i	0.137930	+	0.137930i
$946$			50.0612i			0.0529189i
$947$	−215.176	+	215.176i	−0.227219	+	0.227219i	−0.811530	−	0.584311i	$-0.801365\pi$
$947$	−215.176	+	215.176i	−0.227219	+	0.227219i	0.584311	+	0.811530i	$0.301365\pi$
$948$	81.8473	−	81.8473i	0.0863368	−	0.0863368i
$949$	1129.47	+	1129.47i	1.19017	+	1.19017i
$950$			306.495i			0.322626i
$951$	846.388			0.889998
$952$			529.369i			0.556060i
$953$			728.670i			0.764606i	0.924037	+	0.382303i	$0.124869\pi$
$953$			728.670i			0.764606i	−0.924037	+	0.382303i	$0.875131\pi$
$954$	434.049	+	434.049i	0.454978	+	0.454978i
$955$			883.458i			0.925086i
$956$	122.452	+	122.452i	0.128088	+	0.128088i
$957$	35.9259	+	35.9259i	0.0375401	+	0.0375401i
$958$	−1906.89			−1.99049
$959$	−1052.86			−1.09787
$960$	−383.555	+	383.555i	−0.399536	+	0.399536i
$961$		−	779.833i		−	0.811480i
$962$	1469.14	−	2449.02i	1.52717	−	2.54576i
$963$	−485.493			−0.504147
$964$	−756.387	−	756.387i	−0.784634	−	0.784634i
$965$		−	442.011i		−	0.458043i
$966$		−	2015.31i		−	2.08624i
$967$	216.709	−	216.709i	0.224104	−	0.224104i	−0.586120	−	0.810224i	$-0.699345\pi$
$967$	216.709	−	216.709i	0.224104	−	0.224104i	0.810224	+	0.586120i	$0.199345\pi$
$968$	340.812	−	340.812i	0.352079	−	0.352079i
$969$	−143.581			−0.148175
$970$	1137.91	−	1137.91i	1.17310	−	1.17310i
$971$	67.4729			0.0694880			0.0347440	−	0.999396i	$-0.488938\pi$
$971$	67.4729			0.0694880			0.0347440	+	0.999396i	$0.488938\pi$
$972$	−82.8578			−0.0852446
$973$		−	2286.00i		−	2.34943i
$974$	−184.592			−0.189520
$975$	450.773	−	450.773i	0.462331	−	0.462331i
$976$	6.25061	+	6.25061i	0.00640431	+	0.00640431i
$977$	−539.723	−	539.723i	−0.552429	−	0.552429i	0.374712	−	0.927141i	$-0.377741\pi$
$977$	−539.723	−	539.723i	−0.552429	−	0.552429i	−0.927141	+	0.374712i	$0.877741\pi$
$978$	−1526.68			−1.56102
$979$	−42.9056	+	42.9056i	−0.0438259	+	0.0438259i
$980$	868.209	+	868.209i	0.885927	+	0.885927i
$981$	89.1763	−	89.1763i	0.0909034	−	0.0909034i
$982$	1166.94	+	1166.94i	1.18833	+	1.18833i
$983$		−	1470.30i		−	1.49573i	−0.663852	−	0.747864i	$-0.731079\pi$
$983$		−	1470.30i		−	1.49573i	0.663852	−	0.747864i	$-0.268921\pi$
$984$	211.886	−	211.886i	0.215332	−	0.215332i
$985$	−478.737	+	478.737i	−0.486027	+	0.486027i
$986$	784.254	+	784.254i	0.795389	+	0.795389i
$987$			305.407i			0.309429i
$988$	927.518			0.938784
$989$		−	587.449i		−	0.593983i
$990$			28.6996i			0.0289895i
$991$	−284.439	−	284.439i	−0.287022	−	0.287022i	0.548879	−	0.835902i	$-0.315055\pi$
$991$	−284.439	−	284.439i	−0.287022	−	0.287022i	−0.835902	+	0.548879i	$0.815055\pi$
$992$			586.220i			0.590947i
$993$	20.1719	+	20.1719i	0.0203141	+	0.0203141i
$994$	−2637.33	−	2637.33i	−2.65325	−	2.65325i
$995$	16.4132			0.0164956
$996$	664.291			0.666959
$997$	−836.580	+	836.580i	−0.839097	+	0.839097i	−0.988740	−	0.149643i	$-0.952188\pi$
$997$	−836.580	+	836.580i	−0.839097	+	0.839097i	0.149643	+	0.988740i	$0.452188\pi$
$998$			19.9525i			0.0199925i
$999$	−164.868	−	98.9022i	−0.165033	−	0.0990012i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	111.3.f.a.31.1	✓	24
3.2	odd	2		333.3.i.b.253.12		24
37.6	odd	4	inner	111.3.f.a.43.1	yes	24
111.80	even	4		333.3.i.b.154.12		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
111.3.f.a.31.1	✓	24	1.1	even	1	trivial
111.3.f.a.43.1	yes	24	37.6	odd	4	inner
333.3.i.b.154.12		24	111.80	even	4
333.3.i.b.253.12		24	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 111 = 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	111.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.15816 - 2.15816i) q^{2} +1.73205i q^{3} +5.31533i q^{4} +(2.28543 - 2.28543i) q^{5} +(3.73805 - 3.73805i) q^{6} -10.9759 q^{7} +(2.83869 - 2.83869i) q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(-2.15816 - 2.15816i) q^{2} +1.73205i q^{3} +5.31533i q^{4} +(2.28543 - 2.28543i) q^{5} +(3.73805 - 3.73805i) q^{6} -10.9759 q^{7} +(2.83869 - 2.83869i) q^{8} -3.00000 q^{9} -9.86464 q^{10} +0.969781i q^{11} -9.20642 q^{12} +(-17.8824 + 17.8824i) q^{13} +(23.6878 + 23.6878i) q^{14} +(3.95848 + 3.95848i) q^{15} +9.00860 q^{16} +(8.49513 - 8.49513i) q^{17} +(6.47449 + 6.47449i) q^{18} +(-4.87907 + 4.87907i) q^{19} +(12.1478 + 12.1478i) q^{20} -19.0108i q^{21} +(2.09295 - 2.09295i) q^{22} +(-24.5599 + 24.5599i) q^{23} +(4.91676 + 4.91676i) q^{24} +14.5536i q^{25} +77.1861 q^{26} -5.19615i q^{27} -58.3405i q^{28} +(-21.3881 - 21.3881i) q^{29} -17.0861i q^{30} +(-9.51755 - 9.51755i) q^{31} +(-30.7968 - 30.7968i) q^{32} -1.67971 q^{33} -36.6677 q^{34} +(-25.0846 + 25.0846i) q^{35} -15.9460i q^{36} +(19.0337 - 31.7288i) q^{37} +21.0597 q^{38} +(-30.9732 - 30.9732i) q^{39} -12.9752i q^{40} -43.0947i q^{41} +(-41.0284 + 41.0284i) q^{42} +(-11.9595 + 11.9595i) q^{43} -5.15471 q^{44} +(-6.85628 + 6.85628i) q^{45} +106.009 q^{46} -16.0649 q^{47} +15.6033i q^{48} +71.4705 q^{49} +(31.4091 - 31.4091i) q^{50} +(14.7140 + 14.7140i) q^{51} +(-95.0507 - 95.0507i) q^{52} +67.0400 q^{53} +(-11.2141 + 11.2141i) q^{54} +(2.21636 + 2.21636i) q^{55} +(-31.1572 + 31.1572i) q^{56} +(-8.45080 - 8.45080i) q^{57} +92.3181i q^{58} +(30.6258 - 30.6258i) q^{59} +(-21.0406 + 21.0406i) q^{60} +(0.693850 + 0.693850i) q^{61} +41.0808i q^{62} +32.9277 q^{63} +96.8945i q^{64} +81.7377i q^{65} +(3.62509 + 3.62509i) q^{66} +66.4552i q^{67} +(45.1544 + 45.1544i) q^{68} +(-42.5390 - 42.5390i) q^{69} +108.273 q^{70} -111.337 q^{71} +(-8.51608 + 8.51608i) q^{72} -63.1614i q^{73} +(-109.554 + 27.3980i) q^{74} -25.2077 q^{75} +(-25.9339 - 25.9339i) q^{76} -10.6442i q^{77} +133.690i q^{78} +(-8.89024 + 8.89024i) q^{79} +(20.5885 - 20.5885i) q^{80} +9.00000 q^{81} +(-93.0054 + 93.0054i) q^{82} -72.1552 q^{83} +101.049 q^{84} -38.8300i q^{85} +51.6212 q^{86} +(37.0453 - 37.0453i) q^{87} +(2.75291 + 2.75291i) q^{88} +(44.2425 + 44.2425i) q^{89} +29.5939 q^{90} +(196.275 - 196.275i) q^{91} +(-130.544 - 130.544i) q^{92} +(16.4849 - 16.4849i) q^{93} +(34.6707 + 34.6707i) q^{94} +22.3015i q^{95} +(53.3416 - 53.3416i) q^{96} +(-115.352 + 115.352i) q^{97} +(-154.245 - 154.245i) q^{98} -2.90934i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} + 20 q^{5} - 60 q^{8} - 72 q^{9}+O(q^{10}) \) 24 * q + 8 * q^2 + 20 * q^5 - 60 * q^8 - 72 * q^9	\( 24 q + 8 q^{2} + 20 q^{5} - 60 q^{8} - 72 q^{9} + 24 q^{10} - 32 q^{13} + 60 q^{14} - 40 q^{16} - 8 q^{17} - 24 q^{18} - 48 q^{19} + 104 q^{20} + 32 q^{22} - 44 q^{23} + 88 q^{26} - 88 q^{29} - 192 q^{32} - 24 q^{33} - 56 q^{34} + 60 q^{35} + 56 q^{37} + 160 q^{38} + 72 q^{39} - 12 q^{42} - 8 q^{43} + 536 q^{44} - 60 q^{45} + 480 q^{46} + 88 q^{47} - 32 q^{49} + 172 q^{50} + 60 q^{51} - 488 q^{52} + 104 q^{53} - 208 q^{55} - 80 q^{56} - 456 q^{59} - 252 q^{60} - 96 q^{61} + 24 q^{66} - 44 q^{68} - 168 q^{69} - 1080 q^{70} - 528 q^{71} + 180 q^{72} + 136 q^{74} + 144 q^{75} - 24 q^{76} + 160 q^{79} + 48 q^{80} + 216 q^{81} - 392 q^{82} + 280 q^{83} + 720 q^{84} - 288 q^{86} + 12 q^{87} + 1424 q^{88} - 92 q^{89} - 72 q^{90} + 320 q^{91} + 48 q^{92} - 168 q^{93} - 56 q^{94} - 120 q^{96} + 352 q^{97} - 664 q^{98}+O(q^{100}) \) 24 * q + 8 * q^2 + 20 * q^5 - 60 * q^8 - 72 * q^9 + 24 * q^10 - 32 * q^13 + 60 * q^14 - 40 * q^16 - 8 * q^17 - 24 * q^18 - 48 * q^19 + 104 * q^20 + 32 * q^22 - 44 * q^23 + 88 * q^26 - 88 * q^29 - 192 * q^32 - 24 * q^33 - 56 * q^34 + 60 * q^35 + 56 * q^37 + 160 * q^38 + 72 * q^39 - 12 * q^42 - 8 * q^43 + 536 * q^44 - 60 * q^45 + 480 * q^46 + 88 * q^47 - 32 * q^49 + 172 * q^50 + 60 * q^51 - 488 * q^52 + 104 * q^53 - 208 * q^55 - 80 * q^56 - 456 * q^59 - 252 * q^60 - 96 * q^61 + 24 * q^66 - 44 * q^68 - 168 * q^69 - 1080 * q^70 - 528 * q^71 + 180 * q^72 + 136 * q^74 + 144 * q^75 - 24 * q^76 + 160 * q^79 + 48 * q^80 + 216 * q^81 - 392 * q^82 + 280 * q^83 + 720 * q^84 - 288 * q^86 + 12 * q^87 + 1424 * q^88 - 92 * q^89 - 72 * q^90 + 320 * q^91 + 48 * q^92 - 168 * q^93 - 56 * q^94 - 120 * q^96 + 352 * q^97 - 664 * q^98

Introduction

L-functions

Modular forms

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