LMFDB - Embedded newform 105.4.b.b.41.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,4,Mod(41,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("105.41");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	105.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.19520055060$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 96 x^{14} + 3618 x^{12} + 68560 x^{10} + 697017 x^{8} + 3791184 x^{6} + 10461796 x^{4} + \cdots + 5760000 $ x^16 + 96x^14 + 3618x^12 + 68560x^10 + 697017x^8 + 3791184x^6 + 10461796x^4 + 13209792*x^2 + 5760000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			41.1
Root			$-5.54840i$ of defining polynomial
Character	$\chi$	$=$	105.41
Dual form			105.4.b.b.41.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.54840i q^{2} +(-3.35452 + 3.96828i) q^{3} -22.7847 q^{4} +5.00000 q^{5} +(22.0176 + 18.6122i) q^{6} +(9.21642 + 16.0642i) q^{7} +82.0315i q^{8} +(-4.49445 - 26.6233i) q^{9} +O(q^{10})$	\(q-5.54840i q^{2} +(-3.35452 + 3.96828i) q^{3} -22.7847 q^{4} +5.00000 q^{5} +(22.0176 + 18.6122i) q^{6} +(9.21642 + 16.0642i) q^{7} +82.0315i q^{8} +(-4.49445 - 26.6233i) q^{9} -27.7420i q^{10} +18.7401i q^{11} +(76.4317 - 90.4161i) q^{12} -6.49109i q^{13} +(89.1304 - 51.1364i) q^{14} +(-16.7726 + 19.8414i) q^{15} +272.866 q^{16} +11.6481 q^{17} +(-147.717 + 24.9370i) q^{18} +123.341i q^{19} -113.924 q^{20} +(-94.6637 - 17.3142i) q^{21} +103.978 q^{22} -5.61256i q^{23} +(-325.524 - 275.176i) q^{24} +25.0000 q^{25} -36.0152 q^{26} +(120.725 + 71.4730i) q^{27} +(-209.994 - 366.018i) q^{28} +174.503i q^{29} +(110.088 + 93.0609i) q^{30} +213.228i q^{31} -857.716i q^{32} +(-74.3661 - 62.8641i) q^{33} -64.6285i q^{34} +(46.0821 + 80.3209i) q^{35} +(102.405 + 606.604i) q^{36} -176.923 q^{37} +684.344 q^{38} +(25.7585 + 21.7745i) q^{39} +410.158i q^{40} +187.182 q^{41} +(-96.0661 + 525.232i) q^{42} +164.205 q^{43} -426.989i q^{44} +(-22.4723 - 133.116i) q^{45} -31.1407 q^{46} -440.829 q^{47} +(-915.333 + 1082.81i) q^{48} +(-173.115 + 296.108i) q^{49} -138.710i q^{50} +(-39.0739 + 46.2231i) q^{51} +147.898i q^{52} -144.867i q^{53} +(396.561 - 669.832i) q^{54} +93.7007i q^{55} +(-1317.77 + 756.037i) q^{56} +(-489.451 - 413.749i) q^{57} +968.213 q^{58} -49.8587 q^{59} +(382.159 - 452.081i) q^{60} +308.973i q^{61} +1183.07 q^{62} +(386.258 - 317.571i) q^{63} -2576.02 q^{64} -32.4555i q^{65} +(-348.795 + 412.613i) q^{66} +97.4253 q^{67} -265.400 q^{68} +(22.2722 + 18.8274i) q^{69} +(445.652 - 255.682i) q^{70} -491.851i q^{71} +(2183.95 - 368.687i) q^{72} -787.914i q^{73} +981.641i q^{74} +(-83.8629 + 99.2069i) q^{75} -2810.29i q^{76} +(-301.045 + 172.717i) q^{77} +(120.813 - 142.918i) q^{78} +824.749 q^{79} +1364.33 q^{80} +(-688.600 + 239.314i) q^{81} -1038.56i q^{82} -410.302 q^{83} +(2156.89 + 394.500i) q^{84} +58.2407 q^{85} -911.077i q^{86} +(-692.477 - 585.373i) q^{87} -1537.28 q^{88} -1612.66 q^{89} +(-738.583 + 124.685i) q^{90} +(104.274 - 59.8246i) q^{91} +127.881i q^{92} +(-846.148 - 715.277i) q^{93} +2445.90i q^{94} +616.704i q^{95} +(3403.66 + 2877.22i) q^{96} +747.334i q^{97} +(1642.93 + 960.513i) q^{98} +(498.924 - 84.2267i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{3} - 64 q^{4} + 80 q^{5} + 28 q^{6} - 4 q^{7} - 22 q^{9}+O(q^{10}) $ 16 * q + 2 * q^3 - 64 * q^4 + 80 * q^5 + 28 * q^6 - 4 * q^7 - 22 * q^9	$ 16 q + 2 q^{3} - 64 q^{4} + 80 q^{5} + 28 q^{6} - 4 q^{7} - 22 q^{9} + 66 q^{12} + 90 q^{14} + 10 q^{15} + 376 q^{16} + 72 q^{17} - 182 q^{18} - 320 q^{20} - 70 q^{21} - 276 q^{22} - 526 q^{24} + 400 q^{25} - 696 q^{26} + 128 q^{27} + 10 q^{28} + 140 q^{30} + 502 q^{33} - 20 q^{35} + 996 q^{36} - 812 q^{37} + 1200 q^{38} - 594 q^{39} + 936 q^{41} - 974 q^{42} - 548 q^{43} - 110 q^{45} + 1224 q^{46} - 912 q^{47} - 1850 q^{48} + 328 q^{49} + 750 q^{51} + 2950 q^{54} - 1254 q^{56} + 432 q^{57} + 576 q^{58} + 552 q^{59} + 330 q^{60} + 1860 q^{62} + 362 q^{63} - 4000 q^{64} - 1378 q^{66} + 1004 q^{67} - 3828 q^{68} - 1988 q^{69} + 450 q^{70} + 1988 q^{72} + 50 q^{75} - 1152 q^{77} + 1446 q^{78} + 1292 q^{79} + 1880 q^{80} - 2950 q^{81} + 1752 q^{83} - 420 q^{84} + 360 q^{85} - 1910 q^{87} - 912 q^{88} - 6096 q^{89} - 910 q^{90} - 552 q^{91} - 1080 q^{93} + 9546 q^{96} + 4824 q^{98} + 2530 q^{99}+O(q^{100}) $ 16 * q + 2 * q^3 - 64 * q^4 + 80 * q^5 + 28 * q^6 - 4 * q^7 - 22 * q^9 + 66 * q^12 + 90 * q^14 + 10 * q^15 + 376 * q^16 + 72 * q^17 - 182 * q^18 - 320 * q^20 - 70 * q^21 - 276 * q^22 - 526 * q^24 + 400 * q^25 - 696 * q^26 + 128 * q^27 + 10 * q^28 + 140 * q^30 + 502 * q^33 - 20 * q^35 + 996 * q^36 - 812 * q^37 + 1200 * q^38 - 594 * q^39 + 936 * q^41 - 974 * q^42 - 548 * q^43 - 110 * q^45 + 1224 * q^46 - 912 * q^47 - 1850 * q^48 + 328 * q^49 + 750 * q^51 + 2950 * q^54 - 1254 * q^56 + 432 * q^57 + 576 * q^58 + 552 * q^59 + 330 * q^60 + 1860 * q^62 + 362 * q^63 - 4000 * q^64 - 1378 * q^66 + 1004 * q^67 - 3828 * q^68 - 1988 * q^69 + 450 * q^70 + 1988 * q^72 + 50 * q^75 - 1152 * q^77 + 1446 * q^78 + 1292 * q^79 + 1880 * q^80 - 2950 * q^81 + 1752 * q^83 - 420 * q^84 + 360 * q^85 - 1910 * q^87 - 912 * q^88 - 6096 * q^89 - 910 * q^90 - 552 * q^91 - 1080 * q^93 + 9546 * q^96 + 4824 * q^98 + 2530 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$		−	5.54840i		−	1.96166i	−0.194878	−	0.980828i	$-0.562431\pi$
$2$		−	5.54840i		−	1.96166i	0.194878	−	0.980828i	$-0.437569\pi$
$3$	−3.35452	+	3.96828i	−0.645577	+	0.763695i
$3$	−3.35452	+	3.96828i	−0.645577	+	0.763695i
$4$	−22.7847			−2.84809
$5$	5.00000			0.447214
$5$	5.00000			0.447214
$6$	22.0176	+	18.6122i	1.49811	+	1.26640i
$7$	9.21642	+	16.0642i	0.497640	+	0.867384i
$7$	9.21642	+	16.0642i	0.497640	+	0.867384i
$8$			82.0315i			3.62532i
$9$	−4.49445	−	26.6233i	−0.166461	−	0.986048i
$10$		−	27.7420i		−	0.877279i
$11$			18.7401i			0.513670i	0.966455	+	0.256835i	$0.0826796\pi$
$11$			18.7401i			0.513670i	−0.966455	+	0.256835i	$0.917320\pi$
$12$	76.4317	−	90.4161i	1.83866	−	2.17507i
$13$		−	6.49109i		−	0.138485i	−0.997600	−	0.0692425i	$-0.977942\pi$
$13$		−	6.49109i		−	0.138485i	0.997600	−	0.0692425i	$-0.0220582\pi$
$14$	89.1304	−	51.1364i	1.70151	−	0.976198i
$15$	−16.7726	+	19.8414i	−0.288711	+	0.341535i
$16$	272.866			4.26353
$17$	11.6481			0.166182			0.0830909	−	0.996542i	$-0.473521\pi$
$17$	11.6481			0.166182			0.0830909	+	0.996542i	$0.473521\pi$
$18$	−147.717	+	24.9370i	−1.93429	+	0.326540i
$19$			123.341i			1.48928i	0.667466	+	0.744640i	$0.267379\pi$
$19$			123.341i			1.48928i	−0.667466	+	0.744640i	$0.732621\pi$
$20$	−113.924			−1.27370
$21$	−94.6637	−	17.3142i	−0.983682	−	0.179918i
$22$	103.978			1.00764
$23$		−	5.61256i		−	0.0508826i	−0.999676	−	0.0254413i	$-0.991901\pi$
$23$		−	5.61256i		−	0.0508826i	0.999676	−	0.0254413i	$-0.00809909\pi$
$24$	−325.524	−	275.176i	−2.76864	−	2.34042i
$25$	25.0000			0.200000
$26$	−36.0152			−0.271660
$27$	120.725	+	71.4730i	0.860504	+	0.509444i
$28$	−209.994	−	366.018i	−1.41732	−	2.47039i
$29$			174.503i			1.11739i	0.829372	+	0.558697i	$0.188698\pi$
$29$			174.503i			1.11739i	−0.829372	+	0.558697i	$0.811302\pi$
$30$	110.088	+	93.0609i	0.669974	+	0.566351i
$31$			213.228i			1.23538i	0.786420	+	0.617692i	$0.211932\pi$
$31$			213.228i			1.23538i	−0.786420	+	0.617692i	$0.788068\pi$
$32$		−	857.716i		−	4.73826i
$33$	−74.3661	−	62.8641i	−0.392287	−	0.331613i
$34$		−	64.6285i		−	0.325991i
$35$	46.0821	+	80.3209i	0.222551	+	0.387906i
$36$	102.405	+	606.604i	0.474097	+	2.80835i
$37$	−176.923			−0.786108			−0.393054	−	0.919515i	$-0.628581\pi$
$37$	−176.923			−0.786108			−0.393054	+	0.919515i	$0.628581\pi$
$38$	684.344			2.92146
$39$	25.7585	+	21.7745i	0.105760	+	0.0894027i
$40$			410.158i			1.62129i
$41$	187.182			0.712998			0.356499	−	0.934296i	$-0.383970\pi$
$41$	187.182			0.712998			0.356499	+	0.934296i	$0.383970\pi$
$42$	−96.0661	+	525.232i	−0.352936	+	1.92964i
$43$	164.205			0.582351			0.291175	−	0.956670i	$-0.405954\pi$
$43$	164.205			0.582351			0.291175	+	0.956670i	$0.405954\pi$
$44$		−	426.989i		−	1.46298i
$45$	−22.4723	−	133.116i	−0.0744438	−	0.440974i
$46$	−31.1407			−0.0998141
$47$	−440.829			−1.36812			−0.684059	−	0.729427i	$-0.739787\pi$
$47$	−440.829			−1.36812			−0.684059	+	0.729427i	$0.739787\pi$
$48$	−915.333	+	1082.81i	−2.75244	+	3.25604i
$49$	−173.115	+	296.108i	−0.504709	+	0.863289i
$50$		−	138.710i		−	0.392331i
$51$	−39.0739	+	46.2231i	−0.107283	+	0.126912i
$52$			147.898i			0.394418i
$53$		−	144.867i		−	0.375452i	−0.982221	−	0.187726i	$-0.939888\pi$
$53$		−	144.867i		−	0.375452i	0.982221	−	0.187726i	$-0.0601117\pi$
$54$	396.561	−	669.832i	0.999353	−	1.68801i
$55$			93.7007i			0.229720i
$56$	−1317.77	+	756.037i	−3.14454	+	1.80410i
$57$	−489.451	−	413.749i	−1.13736	−	0.961445i
$58$	968.213			2.19194
$59$	−49.8587			−0.110018			−0.0550089	−	0.998486i	$-0.517519\pi$
$59$	−49.8587			−0.110018			−0.0550089	+	0.998486i	$0.517519\pi$
$60$	382.159	−	452.081i	0.822274	−	0.972723i
$61$			308.973i			0.648523i	0.945968	+	0.324261i	$0.105116\pi$
$61$			308.973i			0.648523i	−0.945968	+	0.324261i	$0.894884\pi$
$62$	1183.07			2.42340
$63$	386.258	−	317.571i	0.772444	−	0.635083i
$64$	−2576.02			−5.03130
$65$		−	32.4555i		−	0.0619324i
$66$	−348.795	+	412.613i	−0.650511	+	0.769532i
$67$	97.4253			0.177648			0.0888239	−	0.996047i	$-0.471689\pi$
$67$	97.4253			0.177648			0.0888239	+	0.996047i	$0.471689\pi$
$68$	−265.400			−0.473301
$69$	22.2722	+	18.8274i	0.0388588	+	0.0328486i
$70$	445.652	−	255.682i	0.760937	−	0.436569i
$71$		−	491.851i		−	0.822140i	−0.911604	−	0.411070i	$-0.865155\pi$
$71$		−	491.851i		−	0.822140i	0.911604	−	0.411070i	$-0.134845\pi$
$72$	2183.95	−	368.687i	3.57474	−	0.603475i
$73$		−	787.914i		−	1.26327i	−0.775268	−	0.631633i	$-0.782385\pi$
$73$		−	787.914i		−	1.26327i	0.775268	−	0.631633i	$-0.217615\pi$
$74$			981.641i			1.54207i
$75$	−83.8629	+	99.2069i	−0.129115	+	0.152739i
$76$		−	2810.29i		−	4.24161i
$77$	−301.045	+	172.717i	−0.445549	+	0.255622i
$78$	120.813	−	142.918i	0.175377	−	0.207465i
$79$	824.749			1.17458			0.587288	−	0.809378i	$-0.300196\pi$
$79$	824.749			1.17458			0.587288	+	0.809378i	$0.300196\pi$
$80$	1364.33			1.90671
$81$	−688.600	+	239.314i	−0.944581	+	0.328278i
$82$		−	1038.56i		−	1.39866i
$83$	−410.302			−0.542608			−0.271304	−	0.962494i	$-0.587455\pi$
$83$	−410.302			−0.542608			−0.271304	+	0.962494i	$0.587455\pi$
$84$	2156.89	+	394.500i	2.80161	+	0.512422i
$85$	58.2407			0.0743187
$86$		−	911.077i		−	1.14237i
$87$	−692.477	−	585.373i	−0.853348	−	0.721363i
$88$	−1537.28			−1.86221
$89$	−1612.66			−1.92069			−0.960347	−	0.278806i	$-0.910061\pi$
$89$	−1612.66			−1.92069			−0.960347	+	0.278806i	$0.910061\pi$
$90$	−738.583	+	124.685i	−0.865039	+	0.146033i
$91$	104.274	−	59.8246i	0.120120	−	0.0689156i
$92$			127.881i			0.144918i
$93$	−846.148	−	715.277i	−0.943457	−	0.797535i
$94$			2445.90i			2.68377i
$95$			616.704i			0.666027i
$96$	3403.66	+	2877.22i	3.61859	+	3.05891i
$97$			747.334i			0.782271i	0.920333	+	0.391135i	$0.127918\pi$
$97$			747.334i			0.782271i	−0.920333	+	0.391135i	$0.872082\pi$
$98$	1642.93	+	960.513i	1.69348	+	0.990066i
$99$	498.924	−	84.2267i	0.506503	−	0.0855061i
$100$	−569.618			−0.569618
$101$	−173.565			−0.170993			−0.0854966	−	0.996338i	$-0.527248\pi$
$101$	−173.565			−0.170993			−0.0854966	+	0.996338i	$0.527248\pi$
$102$	256.464	+	216.797i	0.248958	+	0.210452i
$103$		−	318.905i		−	0.305074i	−0.988298	−	0.152537i	$-0.951256\pi$
$103$		−	318.905i		−	0.305074i	0.988298	−	0.152537i	$-0.0487443\pi$
$104$	532.474			0.502052
$105$	−473.319	−	86.5710i	−0.439916	−	0.0804616i
$106$	−803.777			−0.736507
$107$		−	380.520i		−	0.343797i	−0.985115	−	0.171898i	$-0.945010\pi$
$107$		−	380.520i		−	0.343797i	0.985115	−	0.171898i	$-0.0549900\pi$
$108$	−2750.69	−	1628.49i	−2.45079	−	1.45094i
$109$	1267.59			1.11388			0.556941	−	0.830552i	$-0.311975\pi$
$109$	1267.59			1.11388			0.556941	+	0.830552i	$0.311975\pi$
$110$	519.889			0.450631
$111$	593.492	−	702.081i	0.507493	−	0.600347i
$112$	2514.85	+	4383.37i	2.12170	+	3.69812i
$113$		−	813.858i		−	0.677534i	−0.940870	−	0.338767i	$-0.889990\pi$
$113$		−	813.858i		−	0.677534i	0.940870	−	0.338767i	$-0.110010\pi$
$114$	−2295.64	+	2715.67i	−1.88602	+	2.23110i
$115$		−	28.0628i		−	0.0227554i
$116$		−	3976.01i		−	3.18244i
$117$	−172.814	+	29.1739i	−0.136553	+	0.0230524i
$118$			276.636i			0.215817i
$119$	107.354	+	187.118i	0.0826986	+	0.144143i
$120$	−1627.62	−	1375.88i	−1.23817	−	1.04667i
$121$	979.807			0.736144
$122$	1714.30			1.27218
$123$	−627.905	+	742.790i	−0.460295	+	0.544513i
$124$		−	4858.34i		−	3.51848i
$125$	125.000			0.0894427
$126$	−1762.01	−	2143.12i	−1.24581	−	1.51527i
$127$	2494.12			1.74266			0.871328	−	0.490701i	$-0.163259\pi$
$127$	2494.12			1.74266			0.871328	+	0.490701i	$0.163259\pi$
$128$			7431.08i			5.13141i
$129$	−550.829	+	651.612i	−0.375952	+	0.444739i
$130$	−180.076			−0.121490
$131$	1728.89			1.15308			0.576542	−	0.817068i	$-0.304402\pi$
$131$	1728.89			1.15308			0.576542	+	0.817068i	$0.304402\pi$
$132$	1694.41	+	1432.34i	1.11727	+	0.944464i
$133$	−1981.37	+	1136.76i	−1.29178	+	0.741125i
$134$		−	540.554i		−	0.348484i
$135$	603.627	+	357.365i	0.384829	+	0.227830i
$136$			955.515i			0.602461i
$137$			1497.76i			0.934034i	0.884248	+	0.467017i	$0.154671\pi$
$137$			1497.76i			0.934034i	−0.884248	+	0.467017i	$0.845329\pi$
$138$	104.462	−	123.575i	0.0644377	−	0.0762276i
$139$			18.4288i			0.0112454i	0.999984	+	0.00562269i	$0.00178977\pi$
$139$			18.4288i			0.0112454i	−0.999984	+	0.00562269i	$0.998210\pi$
$140$	−1049.97	−	1830.09i	−0.633846	−	1.10479i
$141$	1478.77	−	1749.33i	0.883225	−	1.04483i
$142$	−2728.98			−1.61276
$143$	121.644			0.0711355
$144$	−1226.38	−	7264.59i	−0.709713	−	4.20404i
$145$			872.516i			0.499714i
$146$	−4371.66			−2.47809
$147$	−594.322	−	1680.27i	−0.333461	−	0.942764i
$148$	4031.15			2.23891
$149$			228.833i			0.125817i	0.998019	+	0.0629084i	$0.0200376\pi$
$149$			228.833i			0.125817i	−0.998019	+	0.0629084i	$0.979962\pi$
$150$	550.440	+	465.305i	0.299621	+	0.253280i
$151$	−1284.11			−0.692047			−0.346023	−	0.938226i	$-0.612468\pi$
$151$	−1284.11			−0.692047			−0.346023	+	0.938226i	$0.612468\pi$
$152$	−10117.8			−5.39911
$153$	−52.3520	−	310.112i	−0.0276628	−	0.163863i
$154$	958.303	+	1670.32i	0.501443	+	0.874013i
$155$			1066.14i			0.552480i
$156$	−586.899	−	496.125i	−0.301215	−	0.254627i
$157$		−	1828.95i		−	0.929719i	−0.885384	−	0.464860i	$-0.846105\pi$
$157$		−	1828.95i		−	0.929719i	0.885384	−	0.464860i	$-0.153895\pi$
$158$		−	4576.04i		−	2.30411i
$159$	574.871	+	485.957i	0.286731	+	0.242383i
$160$		−	4288.58i		−	2.11901i
$161$	90.1611	−	51.7277i	0.0441347	−	0.0253212i
$162$	1327.81	+	3820.63i	0.643968	+	1.85294i
$163$	−737.516			−0.354397			−0.177199	−	0.984175i	$-0.556703\pi$
$163$	−737.516			−0.354397			−0.177199	+	0.984175i	$0.556703\pi$
$164$	−4264.89			−2.03068
$165$	−371.830	−	314.320i	−0.175436	−	0.148302i
$166$			2276.52i			1.06441i
$167$	1641.58			0.760654			0.380327	−	0.924852i	$-0.375811\pi$
$167$	1641.58			0.760654			0.380327	+	0.924852i	$0.375811\pi$
$168$	1420.31	−	7765.41i	0.652258	−	3.56616i
$169$	2154.87			0.980822
$170$		−	323.143i		−	0.145788i
$171$	3283.74	−	554.350i	1.46850	−	0.247908i
$172$	−3741.37			−1.65859
$173$	2664.43			1.17094			0.585471	−	0.810693i	$-0.300910\pi$
$173$	2664.43			1.17094			0.585471	+	0.810693i	$0.300910\pi$
$174$	−3247.88	+	3842.14i	−1.41507	+	1.67398i
$175$	230.410	+	401.604i	0.0995280	+	0.173477i
$176$			5113.55i			2.19005i
$177$	167.252	−	197.853i	0.0710249	−	0.0840201i
$178$			8947.69i			3.76774i
$179$			4652.44i			1.94268i	0.237698	+	0.971339i	$0.423607\pi$
$179$			4652.44i			1.94268i	−0.237698	+	0.971339i	$0.576393\pi$
$180$	512.025	+	3033.02i	0.212023	+	1.25593i
$181$		−	863.374i		−	0.354553i	−0.984161	−	0.177276i	$-0.943271\pi$
$181$		−	863.374i		−	0.354553i	0.984161	−	0.177276i	$-0.0567287\pi$
$182$	−331.931	−	578.554i	−0.135189	−	0.235633i
$183$	−1226.09	−	1036.45i	−0.495274	−	0.418671i
$184$	460.407			0.184465
$185$	−884.616			−0.351558
$186$	−3968.64	+	4694.77i	−1.56449	+	1.85074i
$187$			218.288i			0.0853625i
$188$	10044.2			3.89652
$189$	−35.4996	+	2598.08i	−0.0136625	+	0.999907i
$190$	3421.72			1.30651
$191$			1100.30i			0.416832i	0.978040	+	0.208416i	$0.0668308\pi$
$191$			1100.30i			0.416832i	−0.978040	+	0.208416i	$0.933169\pi$
$192$	8641.32	−	10222.4i	3.24809	−	3.84238i
$193$	−3617.48			−1.34918			−0.674591	−	0.738192i	$-0.735680\pi$
$193$	−3617.48			−1.34918			−0.674591	+	0.738192i	$0.735680\pi$
$194$	4146.51			1.53455
$195$	128.792	+	108.872i	0.0472975	+	0.0399821i
$196$	3944.38	−	6746.75i	1.43746	−	2.45873i
$197$		−	2582.20i		−	0.933880i	−0.884289	−	0.466940i	$-0.845356\pi$
$197$		−	2582.20i		−	0.933880i	0.884289	−	0.466940i	$-0.154644\pi$
$198$	−467.323	−	2768.23i	−0.167733	−	0.993584i
$199$		−	999.161i		−	0.355923i	−0.984037	−	0.177962i	$-0.943050\pi$
$199$		−	999.161i		−	0.355923i	0.984037	−	0.177962i	$-0.0569503\pi$
$200$			2050.79i			0.725063i
$201$	−326.815	+	386.611i	−0.114685	+	0.135669i
$202$			963.005i			0.335430i
$203$	−2803.25	+	1608.29i	−0.969209	+	0.556060i
$204$	890.287	−	1053.18i	0.305552	−	0.361457i
$205$	935.910			0.318862
$206$	−1769.41			−0.598449
$207$	−149.425	+	25.2254i	−0.0501727	+	0.00846998i
$208$		−	1771.20i		−	0.590435i
$209$	−2311.43			−0.764998
$210$	−480.331	+	2626.16i	−0.157838	+	0.862963i
$211$	−677.895			−0.221177			−0.110588	−	0.993866i	$-0.535273\pi$
$211$	−677.895			−0.221177			−0.110588	+	0.993866i	$0.535273\pi$
$212$			3300.74i			1.06932i
$213$	1951.80	+	1649.92i	0.627865	+	0.530755i
$214$	−2111.27			−0.674410
$215$	821.027			0.260435
$216$	−5863.04	+	9903.29i	−1.84690	+	3.11960i
$217$	−3425.33	+	1965.20i	−1.07155	+	0.614776i
$218$		−	7033.09i		−	2.18505i
$219$	3126.66	+	2643.07i	0.964750	+	0.815535i
$220$		−	2134.94i		−	0.654263i
$221$		−	75.6092i		−	0.0230137i
$222$	−3895.42	−	3292.93i	−1.17767	−	0.995527i
$223$		−	3700.37i		−	1.11119i	−0.831453	−	0.555594i	$-0.812491\pi$
$223$		−	3700.37i		−	1.11119i	0.831453	−	0.555594i	$-0.187509\pi$
$224$	13778.5	−	7905.07i	4.10989	−	2.35795i
$225$	−112.361	−	665.582i	−0.0332923	−	0.197210i
$226$	−4515.61			−1.32909
$227$	4478.79			1.30955			0.654775	−	0.755823i	$-0.272763\pi$
$227$	4478.79			1.30955			0.654775	+	0.755823i	$0.272763\pi$
$228$	11152.0	+	9427.15i	3.23930	+	2.73828i
$229$			2746.50i			0.792549i	0.918132	+	0.396275i	$0.129697\pi$
$229$			2746.50i			0.792549i	−0.918132	+	0.396275i	$0.870303\pi$
$230$	−155.704			−0.0446382
$231$	324.471	−	1774.01i	0.0924182	−	0.505287i
$232$	−14314.8			−4.05091
$233$			1911.58i			0.537475i	0.963214	+	0.268737i	$0.0866064\pi$
$233$			1911.58i			0.537475i	−0.963214	+	0.268737i	$0.913394\pi$
$234$	161.869	+	958.842i	0.0452208	+	0.267870i
$235$	−2204.15			−0.611841
$236$	1136.02			0.313341
$237$	−2766.63	+	3272.83i	−0.758279	+	0.897019i
$238$	1038.20	−	595.644i	0.282760	−	0.162226i
$239$		−	847.733i		−	0.229436i	−0.993398	−	0.114718i	$-0.963404\pi$
$239$		−	847.733i		−	0.229436i	0.993398	−	0.114718i	$-0.0365965\pi$
$240$	−4576.66	+	5414.04i	−1.23093	+	1.45614i
$241$			303.879i			0.0812224i	0.999175	+	0.0406112i	$0.0129305\pi$
$241$			303.879i			0.0812224i	−0.999175	+	0.0406112i	$0.987069\pi$
$242$		−	5436.36i		−	1.44406i
$243$	1360.25	−	3535.34i	0.359096	−	0.933301i
$244$		−	7039.86i		−	1.84705i
$245$	−865.576	+	1480.54i	−0.225713	+	0.386075i
$246$	4121.30	+	3483.87i	1.06815	+	0.902940i
$247$	800.617			0.206243
$248$	−17491.4			−4.47866
$249$	1376.36	−	1628.19i	0.350295	−	0.414388i
$250$		−	693.550i		−	0.175456i
$251$	−2168.00			−0.545191			−0.272596	−	0.962129i	$-0.587882\pi$
$251$	−2168.00			−0.545191			−0.272596	+	0.962129i	$0.587882\pi$
$252$	−8800.79	+	7235.77i	−2.19999	+	1.80877i
$253$	105.180			0.0261368
$254$		−	13838.4i		−	3.41849i
$255$	−195.369	+	231.115i	−0.0479784	+	0.0567569i
$256$	20622.4			5.03477
$257$	3255.93			0.790269			0.395135	−	0.918623i	$-0.370698\pi$
$257$	3255.93			0.790269			0.395135	+	0.918623i	$0.370698\pi$
$258$	3615.40	+	3056.22i	0.872424	+	0.737488i
$259$	−1630.60	−	2842.13i	−0.391199	−	0.681858i
$260$			739.489i			0.176389i
$261$	4645.85	−	784.296i	1.10180	−	0.186003i
$262$		−	9592.58i		−	2.26195i
$263$		−	674.121i		−	0.158054i	−0.996872	−	0.0790268i	$-0.974819\pi$
$263$		−	674.121i		−	0.158054i	0.996872	−	0.0790268i	$-0.0251813\pi$
$264$	5156.84	−	6100.37i	1.20220	−	1.42216i
$265$		−	724.333i		−	0.167907i
$266$	6307.20	+	10993.4i	1.45383	+	2.53402i
$267$	5409.70	−	6399.49i	1.23996	−	1.46683i
$268$	−2219.81			−0.505957
$269$	−4438.66			−1.00606			−0.503030	−	0.864269i	$-0.667781\pi$
$269$	−4438.66			−1.00606			−0.503030	+	0.864269i	$0.667781\pi$
$270$	1982.80	−	3349.16i	0.446924	−	0.754902i
$271$			3333.97i			0.747323i	0.927565	+	0.373661i	$0.121898\pi$
$271$			3333.97i			0.747323i	−0.927565	+	0.373661i	$0.878102\pi$
$272$	3178.38			0.708521
$273$	−112.388	+	614.471i	−0.0249159	+	0.136225i
$274$	8310.19			1.83225
$275$			468.504i			0.102734i
$276$	−507.466	−	428.977i	−0.110673	−	0.0935558i
$277$	6771.34			1.46877			0.734387	−	0.678732i	$-0.237470\pi$
$277$	6771.34			1.46877			0.734387	+	0.678732i	$0.237470\pi$
$278$	102.250			0.0220596
$279$	5676.83	−	958.344i	1.21815	−	0.205644i
$280$	−6588.84	+	3780.18i	−1.40628	+	0.806819i
$281$		−	6822.02i		−	1.44828i	−0.689651	−	0.724142i	$-0.742236\pi$
$281$		−	6822.02i		−	1.44828i	0.689651	−	0.724142i	$-0.257764\pi$
$282$	−9705.99	−	8204.79i	−2.04959	−	1.73258i
$283$		−	6289.83i		−	1.32117i	−0.750751	−	0.660585i	$-0.770308\pi$
$283$		−	6289.83i		−	1.32117i	0.750751	−	0.660585i	$-0.229692\pi$
$284$			11206.7i			2.34153i
$285$	−2447.25	−	2068.74i	−0.508641	−	0.429971i
$286$		−	674.929i		−	0.139543i
$287$	1725.15	+	3006.92i	0.354816	+	0.618443i
$288$	−22835.2	+	3854.97i	−4.67215	+	0.788737i
$289$	−4777.32			−0.972384
$290$	4841.06			0.980266
$291$	−2965.63	−	2506.94i	−0.597417	−	0.505016i
$292$			17952.4i			3.59790i
$293$	−6461.28			−1.28830			−0.644150	−	0.764899i	$-0.722789\pi$
$293$	−6461.28			−1.28830			−0.644150	+	0.764899i	$0.722789\pi$
$294$	−9322.80	+	3297.53i	−1.84938	+	0.654136i
$295$	−249.294			−0.0492015
$296$		−	14513.3i		−	2.84989i
$297$	−1339.41	+	2262.41i	−0.261686	+	0.442015i
$298$	1269.66			0.246809
$299$	−36.4316			−0.00704647
$300$	1910.79	−	2260.40i	0.367732	−	0.435015i
$301$	1513.38	+	2637.82i	0.289801	+	0.505122i
$302$			7124.73i			1.35756i
$303$	582.225	−	688.752i	0.110389	−	0.130587i
$304$			33655.5i			6.34959i
$305$			1544.86i			0.290028i
$306$	−1720.62	+	290.470i	−0.321443	+	0.0542649i
$307$		−	8496.24i		−	1.57950i	−0.613429	−	0.789750i	$-0.710210\pi$
$307$		−	8496.24i		−	1.57950i	0.613429	−	0.789750i	$-0.289790\pi$
$308$	6859.22	−	3935.31i	1.26896	−	0.728036i
$309$	1265.50	+	1069.77i	0.232983	+	0.196949i
$310$	5915.37			1.08378
$311$	−3144.48			−0.573334			−0.286667	−	0.958030i	$-0.592547\pi$
$311$	−3144.48			−0.573334			−0.286667	+	0.958030i	$0.592547\pi$
$312$	−1786.19	+	2113.01i	−0.324113	+	0.383415i
$313$		−	5229.06i		−	0.944294i	−0.881520	−	0.472147i	$-0.843479\pi$
$313$		−	5229.06i		−	0.944294i	0.881520	−	0.472147i	$-0.156521\pi$
$314$	−10147.7			−1.82379
$315$	1931.29	−	1587.86i	0.345448	−	0.284018i
$316$	−18791.7			−3.34530
$317$			3838.85i			0.680162i	0.940396	+	0.340081i	$0.110455\pi$
$317$			3838.85i			0.680162i	−0.940396	+	0.340081i	$0.889545\pi$
$318$	2696.28	−	3189.61i	0.475472	−	0.562467i
$319$	−3270.21			−0.573971
$320$	−12880.1			−2.25007
$321$	1510.01	+	1276.46i	0.262556	+	0.221947i
$322$	−287.006	−	500.250i	−0.0496715	−	0.0865771i
$323$			1436.69i			0.247491i
$324$	15689.6	−	5452.71i	2.69025	−	0.934964i
$325$		−	162.277i		−	0.0276970i
$326$			4092.03i			0.695205i
$327$	−4252.15	+	5030.15i	−0.719096	+	0.850666i
$328$			15354.8i			2.58484i
$329$	−4062.86	−	7081.55i	−0.680830	−	1.18668i
$330$	−1743.98	+	2063.06i	−0.290917	+	0.344145i
$331$	10161.2			1.68734			0.843668	−	0.536866i	$-0.180392\pi$
$331$	10161.2			1.68734			0.843668	+	0.536866i	$0.180392\pi$
$332$	9348.62			1.54540
$333$	795.174	+	4710.28i	0.130857	+	0.775140i
$334$		−	9108.14i		−	1.49214i
$335$	487.127			0.0794465
$336$	−25830.5	−	4724.46i	−4.19396	−	0.767084i
$337$	−5788.64			−0.935689			−0.467844	−	0.883811i	$-0.654969\pi$
$337$	−5788.64			−0.935689			−0.467844	+	0.883811i	$0.654969\pi$
$338$		−	11956.1i		−	1.92403i
$339$	3229.61	+	2730.10i	0.517429	+	0.437400i
$340$	−1327.00			−0.211666
$341$	−3995.92			−0.634579
$342$	−3075.75	−	18219.5i	−0.486309	−	2.88070i
$343$	−6352.24	−	51.8969i	−0.999967	−	0.00816959i
$344$			13470.0i			2.11121i
$345$	111.361	+	94.1371i	0.0173782	+	0.0146903i
$346$		−	14783.3i		−	2.29698i
$347$			6776.50i			1.04836i	0.851607	+	0.524181i	$0.175628\pi$
$347$			6776.50i			1.04836i	−0.851607	+	0.524181i	$0.824372\pi$
$348$	15777.9	+	13337.6i	2.43041	+	2.05451i
$349$			9032.04i			1.38531i	0.721268	+	0.692656i	$0.243560\pi$
$349$			9032.04i			1.38531i	−0.721268	+	0.692656i	$0.756440\pi$
$350$	2228.26	−	1278.41i	0.340302	−	0.195240i
$351$	463.938	−	783.639i	0.0705503	−	0.119167i
$352$	16073.7			2.43390
$353$	−1699.72			−0.256280			−0.128140	−	0.991756i	$-0.540901\pi$
$353$	−1699.72			−0.256280			−0.128140	+	0.991756i	$0.540901\pi$
$354$	−1097.77	−	927.980i	−0.164818	−	0.139326i
$355$		−	2459.25i		−	0.367672i
$356$	36744.1			5.47031
$357$	−1102.66	−	201.678i	−0.163470	−	0.0298990i
$358$	25813.6			3.81086
$359$			3740.14i			0.549852i	0.961465	+	0.274926i	$0.0886534\pi$
$359$			3740.14i			0.549852i	−0.961465	+	0.274926i	$0.911347\pi$
$360$	10919.8	−	1843.44i	1.59867	−	0.269882i
$361$	−8353.97			−1.21796
$362$	−4790.34			−0.695510
$363$	−3286.78	+	3888.15i	−0.475237	+	0.562189i
$364$	−2375.85	+	1363.09i	−0.342112	+	0.196278i
$365$		−	3939.57i		−	0.564950i
$366$	−5750.66	+	6802.83i	−0.821289	+	0.971556i
$367$			5266.61i			0.749086i	0.927209	+	0.374543i	$0.122200\pi$
$367$			5266.61i			0.749086i	−0.927209	+	0.374543i	$0.877800\pi$
$368$		−	1531.48i		−	0.216939i
$369$	−841.281	−	4983.40i	−0.118687	−	0.703050i
$370$			4908.20i			0.689636i
$371$	2327.16	−	1335.15i	0.325661	−	0.186840i
$372$	19279.3	+	16297.4i	2.68705	+	2.27145i
$373$	7562.34			1.04977			0.524883	−	0.851174i	$-0.324109\pi$
$373$	7562.34			1.04977			0.524883	+	0.851174i	$0.324109\pi$
$374$	1211.15			0.167452
$375$	−419.314	+	496.035i	−0.0577421	+	0.0683070i
$376$		−	36161.9i		−	4.95986i
$377$	1132.72			0.154742
$378$	14415.2	+	196.966i	1.96147	+	0.0268011i
$379$	−541.939			−0.0734500			−0.0367250	−	0.999325i	$-0.511693\pi$
$379$	−541.939			−0.0734500			−0.0367250	+	0.999325i	$0.511693\pi$
$380$		−	14051.4i		−	1.89690i
$381$	−8366.56	+	9897.36i	−1.12502	+	1.33086i
$382$	6104.90			0.817680
$383$	−3823.22			−0.510072			−0.255036	−	0.966932i	$-0.582087\pi$
$383$	−3823.22			−0.510072			−0.255036	+	0.966932i	$0.582087\pi$
$384$	−29488.6	−	24927.7i	−3.91884	−	3.31272i
$385$	−1505.22	+	863.585i	−0.199255	+	0.114318i
$386$			20071.2i			2.64663i
$387$	−738.013	−	4371.69i	−0.0969388	−	0.574226i
$388$		−	17027.8i		−	2.22798i
$389$		−	10947.0i		−	1.42682i	−0.700748	−	0.713409i	$-0.747150\pi$
$389$		−	10947.0i		−	1.42682i	0.700748	−	0.713409i	$-0.252850\pi$
$390$	604.067	−	714.591i	0.0784311	−	0.0927813i
$391$		−	65.3759i		−	0.00845576i
$392$	−24290.2	−	14200.9i	−3.12970	−	1.82973i
$393$	−5799.59	+	6860.72i	−0.744404	+	0.880605i
$394$	−14327.1			−1.83195
$395$	4123.75			0.525286
$396$	−11367.9	+	1919.08i	−1.44257	+	0.243529i
$397$			2895.36i			0.366030i	0.983110	+	0.183015i	$0.0585857\pi$
$397$			2895.36i			0.366030i	−0.983110	+	0.183015i	$0.941414\pi$
$398$	−5543.75			−0.698198
$399$	2135.55	−	11675.9i	0.267948	−	1.46498i
$400$	6821.65			0.852706
$401$		−	203.105i		−	0.0252932i	−0.999920	−	0.0126466i	$-0.995974\pi$
$401$		−	203.105i		−	0.0252932i	0.999920	−	0.0126466i	$-0.00402565\pi$
$402$	2145.07	+	1813.30i	0.266135	+	0.224973i
$403$	1384.08			0.171082
$404$	3954.62			0.487004
$405$	−3443.00	+	1196.57i	−0.422430	+	0.146810i
$406$	8923.45	+	15553.5i	1.09080	+	1.90125i
$407$		−	3315.57i		−	0.403800i
$408$	−3791.75	−	3205.29i	−0.460097	−	0.388935i
$409$		−	9842.26i		−	1.18990i	−0.803763	−	0.594949i	$-0.797172\pi$
$409$		−	9842.26i		−	1.18990i	0.803763	−	0.594949i	$-0.202828\pi$
$410$		−	5192.80i		−	0.625498i
$411$	−5943.55	−	5024.27i	−0.713317	−	0.602991i
$412$			7266.15i			0.868878i
$413$	−459.519	−	800.939i	−0.0547492	−	0.0954277i
$414$	139.961	+	829.068i	0.0166152	+	0.0984215i
$415$	−2051.51			−0.242662
$416$	−5567.52			−0.656178
$417$	−73.1305	−	61.8196i	−0.00858805	−	0.00725976i
$418$			12824.7i			1.50066i
$419$	11114.8			1.29592			0.647961	−	0.761674i	$-0.275622\pi$
$419$	11114.8			1.29592			0.647961	+	0.761674i	$0.275622\pi$
$420$	10784.4	+	1972.50i	1.25292	+	0.229162i
$421$	−463.160			−0.0536176			−0.0268088	−	0.999641i	$-0.508535\pi$
$421$	−463.160			−0.0536176			−0.0268088	+	0.999641i	$0.508535\pi$
$422$			3761.23i			0.433872i
$423$	1981.29	+	11736.3i	0.227739	+	1.34903i
$424$	11883.6			1.36113
$425$	291.204			0.0332363
$426$	9154.42	−	10829.4i	1.04116	−	1.23165i
$427$	−4963.39	+	2847.62i	−0.562518	+	0.322731i
$428$			8670.04i			0.979164i
$429$	−408.057	+	482.717i	−0.0459234	+	0.0543259i
$430$		−	4555.38i		−	0.510884i
$431$		−	7154.24i		−	0.799554i	−0.916612	−	0.399777i	$-0.869088\pi$
$431$		−	7154.24i		−	0.799554i	0.916612	−	0.399777i	$-0.130912\pi$
$432$	32941.8	+	19502.5i	3.66878	+	2.17203i
$433$			12534.7i			1.39118i	0.718439	+	0.695590i	$0.244857\pi$
$433$			12534.7i			1.39118i	−0.718439	+	0.695590i	$0.755143\pi$
$434$	10903.7	+	19005.1i	1.20598	+	2.10202i
$435$	−3462.38	−	2926.87i	−0.381629	−	0.322604i
$436$	−28881.7			−3.17244
$437$	692.258			0.0757785
$438$	14664.8	−	17348.0i	1.59980	−	1.89251i
$439$			11313.5i			1.22999i	0.788533	+	0.614993i	$0.210841\pi$
$439$			11313.5i			1.22999i	−0.788533	+	0.614993i	$0.789159\pi$
$440$	−7686.41			−0.832808
$441$	8661.44	+	3278.05i	0.935259	+	0.353963i
$442$	−419.510			−0.0451449
$443$			12875.0i			1.38083i	0.723411	+	0.690417i	$0.242573\pi$
$443$			12875.0i			1.38083i	−0.723411	+	0.690417i	$0.757427\pi$
$444$	−13522.5	+	15996.7i	−1.44539	+	1.70984i
$445$	−8063.31			−0.858961
$446$	−20531.1			−2.17977
$447$	−908.072	−	767.623i	−0.0960858	−	0.0812245i
$448$	−23741.7	−	41381.7i	−2.50377	−	4.36407i
$449$		−	14421.7i		−	1.51582i	−0.652360	−	0.757909i	$-0.726221\pi$
$449$		−	14421.7i		−	1.51582i	0.652360	−	0.757909i	$-0.273779\pi$
$450$	−3692.92	+	623.426i	−0.386857	+	0.0653079i
$451$			3507.82i			0.366245i
$452$			18543.5i			1.92968i
$453$	4307.55	−	5095.69i	0.446769	−	0.528513i
$454$		−	24850.1i		−	2.56889i
$455$	521.370	−	299.123i	0.0537191	−	0.0308200i
$456$	33940.5	−	40150.4i	3.48554	−	4.12328i
$457$	−4556.30			−0.466378			−0.233189	−	0.972431i	$-0.574916\pi$
$457$	−4556.30			−0.466378			−0.233189	+	0.972431i	$0.574916\pi$
$458$	15238.7			1.55471
$459$	1406.23	+	832.528i	0.143000	+	0.0846603i
$460$			639.403i			0.0648094i
$461$	14975.4			1.51295			0.756477	−	0.654020i	$-0.226919\pi$
$461$	14975.4			1.51295			0.756477	+	0.654020i	$0.226919\pi$
$462$	−9842.92	−	1800.29i	−0.991200	−	0.181293i
$463$	−592.960			−0.0595188			−0.0297594	−	0.999557i	$-0.509474\pi$
$463$	−592.960			−0.0595188			−0.0297594	+	0.999557i	$0.509474\pi$
$464$			47616.0i			4.76404i
$465$	−4230.74	−	3576.38i	−0.421927	−	0.356668i
$466$	10606.2			1.05434
$467$	7962.35			0.788980			0.394490	−	0.918900i	$-0.370921\pi$
$467$	7962.35			0.788980			0.394490	+	0.918900i	$0.370921\pi$
$468$	3937.53	−	664.720i	0.388915	−	0.0656553i
$469$	897.912	+	1565.06i	0.0884046	+	0.154089i
$470$			12229.5i			1.20022i
$471$	7257.77	+	6135.23i	0.710022	+	0.600205i
$472$		−	4089.99i		−	0.398849i
$473$			3077.23i			0.299136i
$474$	18159.0	+	15350.4i	1.75964	+	1.48748i
$475$			3083.52i			0.297856i
$476$	−2446.03	−	4263.43i	−0.235533	−	0.410533i
$477$	−3856.82	+	651.096i	−0.370214	+	0.0624982i
$478$	−4703.56			−0.450075
$479$	−9675.27			−0.922911			−0.461455	−	0.887163i	$-0.652673\pi$
$479$	−9675.27			−0.922911			−0.461455	+	0.887163i	$0.652673\pi$
$480$	17018.3	+	14386.1i	1.61828	+	1.36799i
$481$			1148.43i			0.108864i
$482$	1686.04			0.159330
$483$	−97.1770	+	531.306i	−0.00915467	+	0.0500523i
$484$	−22324.6			−2.09660
$485$			3736.67i			0.349842i
$486$	−19615.5	−	7547.22i	−1.83081	−	0.704422i
$487$	10987.9			1.02241			0.511203	−	0.859460i	$-0.329200\pi$
$487$	10987.9			1.02241			0.511203	+	0.859460i	$0.329200\pi$
$488$	−25345.5			−2.35110
$489$	2474.01	−	2926.67i	0.228791	−	0.270651i
$490$	8214.63	+	4802.56i	0.757345	+	0.442771i
$491$			9557.43i			0.878454i	0.898376	+	0.439227i	$0.144748\pi$
$491$			9557.43i			0.878454i	−0.898376	+	0.439227i	$0.855252\pi$
$492$	14306.6	−	16924.3i	1.31096	−	1.55082i
$493$			2032.64i			0.185690i
$494$		−	4442.14i		−	0.404578i
$495$	2494.62	−	421.134i	0.226515	−	0.0382395i
$496$			58182.7i			5.26710i
$497$	7901.18	−	4533.10i	0.713111	−	0.409130i
$498$	−9033.86	−	7636.62i	−0.812886	−	0.687159i
$499$	−1519.24			−0.136293			−0.0681467	−	0.997675i	$-0.521709\pi$
$499$	−1519.24			−0.136293			−0.0681467	+	0.997675i	$0.521709\pi$
$500$	−2848.09			−0.254741
$501$	−5506.70	+	6514.24i	−0.491061	+	0.580908i
$502$			12028.9i			1.06948i
$503$	−14261.9			−1.26423			−0.632114	−	0.774876i	$-0.717812\pi$
$503$	−14261.9			−1.26423			−0.632114	+	0.774876i	$0.717812\pi$
$504$	26050.8	+	31685.4i	2.30238	+	2.80036i
$505$	−867.823			−0.0764705
$506$		−	583.581i		−	0.0512715i
$507$	−7228.53	+	8551.11i	−0.633196	+	0.749049i
$508$	−56827.8			−4.96324
$509$	2659.40			0.231583			0.115792	−	0.993274i	$-0.463060\pi$
$509$	2659.40			0.231583			0.115792	+	0.993274i	$0.463060\pi$
$510$	1282.32	+	1083.99i	0.111337	+	0.0941172i
$511$	12657.2	−	7261.75i	1.09574	−	0.628651i
$512$		−	54972.7i		−	4.74506i
$513$	−8815.54	+	14890.4i	−0.758705	+	1.28153i
$514$		−	18065.2i		−	1.55024i
$515$		−	1594.52i		−	0.136433i
$516$	12550.5	−	14846.8i	1.07075	−	1.26666i
$517$		−	8261.20i		−	0.702760i
$518$	−15769.2	+	9047.21i	−1.33757	+	0.767397i
$519$	−8937.87	+	10573.2i	−0.755933	+	0.894243i
$520$	2662.37			0.224524
$521$	13959.0			1.17381			0.586903	−	0.809657i	$-0.300347\pi$
$521$	13959.0			1.17381			0.586903	+	0.809657i	$0.300347\pi$
$522$	−4351.59	−	25777.0i	−0.364873	−	2.16136i
$523$			2.96902i			0.000248234i	1.00000		0.000124117i	$3.95076e-5\pi$
$523$			2.96902i			0.000248234i	−1.00000		0.000124117i	$0.999960\pi$
$524$	−39392.3			−3.28409
$525$	−2366.59	−	432.855i	−0.196736	−	0.0359835i
$526$	−3740.29			−0.310047
$527$			2483.71i			0.205298i
$528$	−20292.0	−	17153.5i	−1.67253	−	1.41384i
$529$	12135.5			0.997411
$530$	−4018.89			−0.329376
$531$	224.088	+	1327.40i	0.0183137	+	0.108483i
$532$	45145.0	−	25900.8i	3.67910	−	2.11079i
$533$		−	1215.02i		−	0.0987395i
$534$	−35506.9	−	30015.2i	−2.87741	−	2.43237i
$535$		−	1902.60i		−	0.153750i
$536$			7991.95i			0.644029i
$537$	−18462.2	−	15606.7i	−1.48361	−	1.25415i
$538$			24627.5i			1.97354i
$539$	−5549.11	−	3244.21i	−0.443445	−	0.259254i
$540$	−13753.5	−	8142.46i	−1.09603	−	0.648881i
$541$	14095.7			1.12019			0.560096	−	0.828428i	$-0.310764\pi$
$541$	14095.7			1.12019			0.560096	+	0.828428i	$0.310764\pi$
$542$	18498.2			1.46599
$543$	3426.11	+	2896.20i	0.270770	+	0.228891i
$544$		−	9990.80i		−	0.787412i
$545$	6337.95			0.498143
$546$	3409.33	+	623.574i	0.267227	+	0.0488764i
$547$	13091.9			1.02334			0.511671	−	0.859181i	$-0.329027\pi$
$547$	13091.9			1.02334			0.511671	+	0.859181i	$0.329027\pi$
$548$		−	34126.2i		−	2.66021i
$549$	8225.87	−	1388.66i	0.639475	−	0.107954i
$550$	2599.44			0.201529
$551$	−21523.4			−1.66411
$552$	−1544.44	+	1827.02i	−0.119087	+	0.140875i
$553$	7601.23	+	13248.9i	0.584516	+	1.01881i
$554$		−	37570.1i		−	2.88123i
$555$	2967.46	−	3510.40i	0.226958	−	0.268483i
$556$		−	419.895i		−	0.0320279i
$557$			8963.95i			0.681894i	0.940083	+	0.340947i	$0.110748\pi$
$557$			8963.95i			0.681894i	−0.940083	+	0.340947i	$0.889252\pi$
$558$	−5317.27	−	31497.3i	−0.403402	−	2.38959i
$559$		−	1065.87i		−	0.0806468i
$560$	12574.2	+	21916.8i	0.948854	+	1.65385i
$561$	−866.227	−	732.250i	−0.0651909	−	0.0551080i
$562$	−37851.3			−2.84103
$563$	−7101.36			−0.531592			−0.265796	−	0.964029i	$-0.585635\pi$
$563$	−7101.36			−0.531592			−0.265796	+	0.964029i	$0.585635\pi$
$564$	−33693.3	+	39858.1i	−2.51550	+	2.97576i
$565$		−	4069.29i		−	0.303002i
$566$	−34898.5			−2.59168
$567$	−10190.8	−	8856.16i	−0.754804	−	0.655950i
$568$	40347.3			2.98052
$569$		−	14232.2i		−	1.04858i	−0.851539	−	0.524292i	$-0.824330\pi$
$569$		−	14232.2i		−	1.04858i	0.851539	−	0.524292i	$-0.175670\pi$
$570$	−11478.2	+	13578.3i	−0.843455	+	0.997779i
$571$	17815.6			1.30571			0.652856	−	0.757482i	$-0.273571\pi$
$571$	17815.6			1.30571			0.652856	+	0.757482i	$0.273571\pi$
$572$	−2771.62			−0.202600
$573$	−4366.29	−	3690.97i	−0.318333	−	0.269097i
$574$	16683.6	−	9571.80i	1.21317	−	0.696027i
$575$		−	140.314i		−	0.0101765i
$576$	11577.8	+	68582.3i	0.837516	+	4.96110i
$577$		−	18446.7i		−	1.33093i	−0.746431	−	0.665463i	$-0.768234\pi$
$577$		−	18446.7i		−	1.33093i	0.746431	−	0.665463i	$-0.231766\pi$
$578$			26506.5i			1.90748i
$579$	12134.9	−	14355.2i	0.871001	−	1.03036i
$580$		−	19880.0i		−	1.42323i
$581$	−3781.52	−	6591.16i	−0.270024	−	0.470650i
$582$	−13909.5	+	16454.5i	−0.990667	+	1.17193i
$583$	2714.82			0.192858
$584$	64633.8			4.57974
$585$	−864.071	+	145.870i	−0.0610683	+	0.0103093i
$586$			35849.8i			2.52720i
$587$	18600.1			1.30785			0.653927	−	0.756558i	$-0.273120\pi$
$587$	18600.1			1.30785			0.653927	+	0.756558i	$0.273120\pi$
$588$	13541.5	+	38284.5i	0.949729	+	2.68508i
$589$	−26299.7			−1.83983
$590$			1383.18i			0.0965163i
$591$	10246.9	+	8662.04i	0.713200	+	0.602891i
$592$	−48276.3			−3.35160
$593$	23387.1			1.61955			0.809774	−	0.586742i	$-0.199590\pi$
$593$	23387.1			1.61955			0.809774	+	0.586742i	$0.199590\pi$
$594$	12552.8	+	7431.60i	0.867080	+	0.513337i
$595$	536.771	+	935.589i	0.0369840	+	0.0644629i
$596$		−	5213.89i		−	0.358338i
$597$	3964.95	+	3351.70i	0.271817	+	0.229776i
$598$			202.137i			0.0138228i
$599$		−	17459.8i		−	1.19096i	−0.803369	−	0.595481i	$-0.796961\pi$
$599$		−	17459.8i		−	1.19096i	0.803369	−	0.595481i	$-0.203039\pi$
$600$	−8138.10	−	6879.40i	−0.553727	−	0.468084i
$601$		−	10590.8i		−	0.718812i	−0.933181	−	0.359406i	$-0.882979\pi$
$601$		−	10590.8i		−	0.718812i	0.933181	−	0.359406i	$-0.117021\pi$
$602$	14635.7	−	8396.86i	0.990874	−	0.568489i
$603$	−437.874	−	2593.78i	−0.0295715	−	0.175169i
$604$	29258.0			1.97101
$605$	4899.04			0.329213
$606$	−3821.47	−	3230.42i	−0.256166	−	0.216546i
$607$			19339.1i			1.29316i	0.762846	+	0.646580i	$0.223801\pi$
$607$			19339.1i			1.29316i	−0.762846	+	0.646580i	$0.776199\pi$
$608$	105791.			7.05660
$609$	3021.38	−	16519.1i	0.201039	−	1.09916i
$610$	8571.52			0.568935
$611$			2861.46i			0.189464i
$612$	1192.83	+	7065.81i	0.0787862	+	0.466697i
$613$	21825.2			1.43803			0.719013	−	0.694997i	$-0.244594\pi$
$613$	21825.2			1.43803			0.719013	+	0.694997i	$0.244594\pi$
$614$	−47140.5			−3.09843
$615$	−3139.52	+	3713.95i	−0.205850	+	0.243514i
$616$	−14168.2	−	24695.2i	−0.926712	−	1.61525i
$617$		−	1526.94i		−	0.0996309i	−0.998758	−	0.0498154i	$-0.984137\pi$
$617$		−	1526.94i		−	0.0996309i	0.998758	−	0.0498154i	$-0.0158633\pi$
$618$	5935.51	−	7021.51i	0.386345	−	0.457033i
$619$		−	304.669i		−	0.0197830i	−0.999951	−	0.00989151i	$-0.996851\pi$
$619$		−	304.669i		−	0.0197830i	0.999951	−	0.00989151i	$-0.00314862\pi$
$620$		−	24291.7i		−	1.57351i
$621$	401.146	−	677.578i	0.0259218	−	0.0437847i
$622$			17446.8i			1.12468i
$623$	−14863.0	−	25906.1i	−0.955814	−	1.66598i
$624$	7028.60	+	5941.51i	0.450912	+	0.381171i
$625$	625.000			0.0400000
$626$	−29012.9			−1.85238
$627$	7753.71	−	9172.38i	0.493865	−	0.584226i
$628$			41672.1i			2.64792i
$629$	−2060.83			−0.130637
$630$	−8810.06	−	10715.6i	−0.557144	−	0.677649i
$631$	−20101.3			−1.26818			−0.634090	−	0.773259i	$-0.718625\pi$
$631$	−20101.3			−1.26818			−0.634090	+	0.773259i	$0.718625\pi$
$632$			67655.4i			4.25821i
$633$	2274.01	−	2690.08i	0.142786	−	0.168912i
$634$	21299.5			1.33424
$635$	12470.6			0.779340
$636$	−13098.3	−	11072.4i	−0.816635	−	0.690329i
$637$	1922.07	+	1123.71i	0.119553	+	0.0698947i
$638$			18144.4i			1.12593i
$639$	−13094.7	+	2210.60i	−0.810670	+	0.136854i
$640$			37155.4i			2.29484i
$641$			10581.1i			0.651994i	0.945371	+	0.325997i	$0.105700\pi$
$641$			10581.1i			0.651994i	−0.945371	+	0.325997i	$0.894300\pi$
$642$	7082.30	−	8378.12i	0.435384	−	0.515044i
$643$		−	24367.8i		−	1.49452i	−0.664534	−	0.747258i	$-0.731370\pi$
$643$		−	24367.8i		−	1.49452i	0.664534	−	0.747258i	$-0.268630\pi$
$644$	−2054.30	+	1178.60i	−0.125700	+	0.0721171i
$645$	−2754.15	+	3258.06i	−0.168131	+	0.198893i
$646$	7971.34			0.485492
$647$	−13640.0			−0.828817			−0.414409	−	0.910091i	$-0.636012\pi$
$647$	−13640.0			−0.828817			−0.414409	+	0.910091i	$0.636012\pi$
$648$	−19631.3	−	56486.9i	−1.19011	−	3.42441i
$649$		−	934.359i		−	0.0565128i
$650$	−900.379			−0.0543320
$651$	3691.88	−	20185.0i	0.222267	−	1.21522i
$652$	16804.1			1.00936
$653$		−	4838.29i		−	0.289950i	−0.989435	−	0.144975i	$-0.953690\pi$
$653$		−	4838.29i		−	0.289950i	0.989435	−	0.144975i	$-0.0463101\pi$
$654$	27909.3	+	23592.6i	1.66871	+	1.41062i
$655$	8644.46			0.515675
$656$	51075.6			3.03989
$657$	−20976.9	+	3541.25i	−1.24564	+	0.210285i
$658$	−39291.3	+	22542.4i	−2.32786	+	1.33555i
$659$			24510.9i			1.44887i	0.689341	+	0.724437i	$0.257900\pi$
$659$			24510.9i			1.44887i	−0.689341	+	0.724437i	$0.742100\pi$
$660$	8472.05	+	7161.71i	0.499658	+	0.422377i
$661$		−	17541.7i		−	1.03222i	−0.856524	−	0.516108i	$-0.827380\pi$
$661$		−	17541.7i		−	1.03222i	0.856524	−	0.516108i	$-0.172620\pi$
$662$		−	56378.2i		−	3.30997i
$663$	300.038	+	253.632i	0.0175754	+	0.0148571i
$664$		−	33657.7i		−	1.96713i
$665$	−9906.85	+	5683.80i	−0.577701	+	0.331441i
$666$	26134.5	−	4411.94i	1.52056	−	0.256695i
$667$	979.409			0.0568559
$668$	−37402.9			−2.16641
$669$	14684.1	+	12412.9i	0.848610	+	0.717358i
$670$		−	2702.77i		−	0.155847i
$671$	−5790.19			−0.333126
$672$	−14850.7	+	81194.6i	−0.852496	+	4.66094i
$673$	2132.83			0.122161			0.0610807	−	0.998133i	$-0.480545\pi$
$673$	2132.83			0.122161			0.0610807	+	0.998133i	$0.480545\pi$
$674$			32117.7i			1.83550i
$675$	3018.13	+	1786.83i	0.172101	+	0.101889i
$676$	−49098.0			−2.79347
$677$	7517.97			0.426793			0.213397	−	0.976966i	$-0.431547\pi$
$677$	7517.97			0.426793			0.213397	+	0.976966i	$0.431547\pi$
$678$	15147.7	−	17919.2i	0.858028	−	1.01502i
$679$	−12005.3	+	6887.74i	−0.678529	+	0.389289i
$680$			4777.58i			0.269429i
$681$	−15024.2	+	17773.1i	−0.845416	+	1.00010i
$682$			22171.0i			1.24483i
$683$		−	8048.07i		−	0.450880i	−0.974257	−	0.225440i	$-0.927618\pi$
$683$		−	8048.07i		−	0.450880i	0.974257	−	0.225440i	$-0.0723819\pi$
$684$	−74819.1	+	12630.7i	−4.18243	+	0.706063i
$685$			7488.82i			0.417713i
$686$	−287.945	+	35244.7i	−0.0160259	+	1.96159i
$687$	−10898.9	−	9213.17i	−0.605266	−	0.511651i
$688$	44806.0			2.48287
$689$	−940.342			−0.0519944
$690$	522.310	−	617.875i	0.0288174	−	0.0340900i
$691$			29318.1i			1.61406i	0.590513	+	0.807028i	$0.298926\pi$
$691$			29318.1i			1.61406i	−0.590513	+	0.807028i	$0.701074\pi$
$692$	−60708.3			−3.33495
$693$	5951.33	+	7238.54i	0.326223	+	0.396781i
$694$	37598.7			2.05652
$695$			92.1439i			0.00502909i
$696$	48019.1	−	56804.9i	2.61517	−	3.09366i
$697$	2180.32			0.118487
$698$	50113.4			2.71751
$699$	−7585.67	−	6412.42i	−0.410467	−	0.346981i
$700$	−5249.84	−	9150.44i	−0.283465	−	0.494078i
$701$			14078.5i			0.758542i	0.925286	+	0.379271i	$0.123825\pi$
$701$			14078.5i			0.758542i	−0.925286	+	0.379271i	$0.876175\pi$
$702$	−4347.94	−	2574.11i	−0.233764	−	0.138395i
$703$		−	21821.9i		−	1.17074i
$704$		−	48275.1i		−	2.58443i
$705$	7393.84	−	8746.66i	0.394990	−	0.467260i
$706$			9430.72i			0.502733i
$707$	−1599.64	−	2788.17i	−0.0850930	−	0.148317i
$708$	−3810.79	+	4508.03i	−0.202285	+	0.239297i
$709$	20441.0			1.08276			0.541380	−	0.840778i	$-0.317902\pi$
$709$	20441.0			1.08276			0.541380	+	0.840778i	$0.317902\pi$
$710$	−13644.9			−0.721246
$711$	−3706.80	−	21957.5i	−0.195521	−	1.15819i
$712$		−	132289.i		−	6.96313i
$713$	1196.76			0.0628595
$714$	−1118.99	+	6117.98i	−0.0586516	+	0.320672i
$715$	608.220			0.0318128
$716$		−	106004.i		−	5.53292i
$717$	3364.04	+	2843.73i	0.175219	+	0.148119i
$718$	20751.8			1.07862
$719$	−1258.67			−0.0652856			−0.0326428	−	0.999467i	$-0.510392\pi$
$719$	−1258.67			−0.0652856			−0.0326428	+	0.999467i	$0.510392\pi$
$720$	−6131.92	−	36322.9i	−0.317393	−	1.88011i
$721$	5122.94	−	2939.16i	0.264616	−	0.151817i
$722$			46351.2i			2.38921i
$723$	−1205.88	−	1019.37i	−0.0620292	−	0.0524353i
$724$			19671.7i			1.00980i
$725$			4362.58i			0.223479i
$726$	21573.0	+	18236.4i	1.10282	+	0.932251i
$727$			17851.5i			0.910695i	0.890314	+	0.455348i	$0.150485\pi$
$727$			17851.5i			0.910695i	−0.890314	+	0.455348i	$0.849515\pi$
$728$	4907.51	+	8553.76i	0.249841	+	0.435472i
$729$	9466.22	+	17257.2i	0.480934	+	0.876757i
$730$	−21858.3			−1.10824
$731$	1912.69			0.0967760
$732$	27936.1	+	23615.3i	1.41058	+	1.19241i
$733$		−	32092.7i		−	1.61715i	−0.588394	−	0.808575i	$-0.700239\pi$
$733$		−	32092.7i		−	1.61715i	0.588394	−	0.808575i	$-0.299761\pi$
$734$	29221.2			1.46945
$735$	−2971.61	−	8401.35i	−0.149129	−	0.421617i
$736$	−4813.98			−0.241095
$737$			1825.76i			0.0912522i
$738$	−27649.9	+	4667.76i	−1.37914	+	0.232822i
$739$	−21633.8			−1.07688			−0.538439	−	0.842664i	$-0.680986\pi$
$739$	−21633.8			−1.07688			−0.538439	+	0.842664i	$0.680986\pi$
$740$	20155.7			1.00127
$741$	−2685.68	+	3177.07i	−0.133146	+	0.157507i
$742$	−7407.95	−	12912.0i	−0.366515	−	0.638834i
$743$			29593.1i			1.46119i	0.682811	+	0.730595i	$0.260757\pi$
$743$			29593.1i			1.46119i	−0.682811	+	0.730595i	$0.739243\pi$
$744$	58675.3	−	69410.8i	2.89132	−	3.42033i
$745$			1144.16i			0.0562670i
$746$		−	41958.9i		−	2.05928i
$747$	1844.08	+	10923.6i	0.0903233	+	0.535038i
$748$		−	4973.63i		−	0.243120i
$749$	6112.73	−	3507.03i	0.298204	−	0.171087i
$750$	2752.20	+	2326.52i	0.133995	+	0.113270i
$751$	−34339.9			−1.66855			−0.834275	−	0.551349i	$-0.814113\pi$
$751$	−34339.9			−1.66855			−0.834275	+	0.551349i	$0.814113\pi$
$752$	−120287.			−5.83301
$753$	7272.59	−	8603.23i	0.351963	−	0.416360i
$754$		−	6284.76i		−	0.303551i
$755$	−6420.53			−0.309493
$756$	808.848	−	59196.5i	0.0389120	−	2.84782i
$757$	−26304.2			−1.26294			−0.631469	−	0.775401i	$-0.717548\pi$
$757$	−26304.2			−1.26294			−0.631469	+	0.775401i	$0.717548\pi$
$758$			3006.90i			0.144084i
$759$	−352.828	+	417.384i	−0.0168733	+	0.0199606i
$760$	−50589.2			−2.41456
$761$	−723.191			−0.0344489			−0.0172245	−	0.999852i	$-0.505483\pi$
$761$	−723.191			−0.0344489			−0.0172245	+	0.999852i	$0.505483\pi$
$762$	54914.5	+	46421.0i	2.61069	+	2.20690i
$763$	11682.6	+	20362.8i	0.554312	+	0.966163i
$764$		−	25070.0i		−	1.18718i
$765$	−261.760	−	1550.56i	−0.0123712	−	0.0732818i
$766$			21212.8i			1.00058i
$767$			323.637i			0.0152358i
$768$	−69178.2	+	81835.4i	−3.25033	+	3.84503i
$769$			19076.4i			0.894553i	0.894396	+	0.447276i	$0.147606\pi$
$769$			19076.4i			0.894553i	−0.894396	+	0.447276i	$0.852394\pi$
$770$	4791.51	+	8351.58i	0.224252	+	0.390870i
$771$	−10922.1	+	12920.4i	−0.510179	+	0.603525i
$772$	82423.4			3.84259
$773$	24103.5			1.12153			0.560764	−	0.827975i	$-0.310507\pi$
$773$	24103.5			1.12153			0.560764	+	0.827975i	$0.310507\pi$
$774$	−24255.9	+	4094.79i	−1.12643	+	0.190161i
$775$			5330.70i			0.247077i
$776$	−61305.0			−2.83598
$777$	16748.2	+	3063.29i	0.773280	+	0.141435i
$778$	−60738.0			−2.79893
$779$			23087.2i			1.06185i
$780$	−2934.50	−	2480.63i	−0.134707	−	0.113873i
$781$	9217.35			0.422308
$782$	−362.731			−0.0165873
$783$	−12472.3	+	21067.0i	−0.569249	+	0.961522i
$784$	−47237.3	+	80797.8i	−2.15184	+	3.68066i
$785$		−	9144.74i		−	0.415783i
$786$	38066.0	+	32178.4i	1.72744	+	1.46026i
$787$		−	13295.4i		−	0.602196i	−0.953593	−	0.301098i	$-0.902647\pi$
$787$		−	13295.4i		−	0.602196i	0.953593	−	0.301098i	$-0.0973532\pi$
$788$			58834.8i			2.65977i
$789$	2675.10	+	2261.35i	0.120705	+	0.102036i
$790$		−	22880.2i		−	1.03043i
$791$	13074.0	−	7500.86i	0.587682	−	0.337168i
$792$	6909.25	+	40927.5i	0.309987	+	1.83623i
$793$	2005.57			0.0898107
$794$	16064.6			0.718025
$795$	2874.35	+	2429.78i	0.128230	+	0.108397i
$796$			22765.6i			1.01370i
$797$	16548.1			0.735464			0.367732	−	0.929932i	$-0.380134\pi$
$797$	16548.1			0.735464			0.367732	+	0.929932i	$0.380134\pi$
$798$	−64782.6	−	11848.9i	−2.87378	−	0.525621i
$799$	−5134.84			−0.227356
$800$		−	21442.9i		−	0.947652i
$801$	7248.04	+	42934.4i	0.319721	+	1.89390i
$802$	−1126.91			−0.0496166
$803$	14765.6			0.648901
$804$	7446.38	−	8808.82i	0.326634	−	0.386397i
$805$	450.806	−	258.638i	0.0197377	−	0.0113240i
$806$		−	7679.44i		−	0.335604i
$807$	14889.6	−	17613.8i	0.649489	−	0.768323i
$808$		−	14237.8i		−	0.619905i
$809$		−	4138.35i		−	0.179847i	−0.995949	−	0.0899237i	$-0.971338\pi$
$809$		−	4138.35i		−	0.179847i	0.995949	−	0.0899237i	$-0.0286623\pi$
$810$	6639.06	+	19103.1i	0.287991	+	0.828661i
$811$		−	33412.9i		−	1.44672i	−0.690473	−	0.723358i	$-0.742598\pi$
$811$		−	33412.9i		−	1.44672i	0.690473	−	0.723358i	$-0.257402\pi$
$812$	63871.2	−	36644.5i	2.76040	−	1.58371i
$813$	−13230.1	−	11183.9i	−0.570727	−	0.482454i
$814$	−18396.1			−0.792116
$815$	−3687.58			−0.158491
$816$	−10661.9	+	12612.7i	−0.457405	+	0.541094i
$817$			20253.2i			0.867284i
$818$	−54608.8			−2.33417
$819$	−2061.38	−	2507.24i	−0.0879494	−	0.106972i
$820$	−21324.5			−0.908149
$821$		−	23640.6i		−	1.00495i	−0.864592	−	0.502475i	$-0.832423\pi$
$821$		−	23640.6i		−	1.00495i	0.864592	−	0.502475i	$-0.167577\pi$
$822$	−27876.7	+	32977.2i	−1.18286	+	1.39928i
$823$	−32543.6			−1.37837			−0.689184	−	0.724586i	$-0.742031\pi$
$823$	−32543.6			−1.37837			−0.689184	+	0.724586i	$0.742031\pi$
$824$	26160.2			1.10599
$825$	−1859.15	−	1571.60i	−0.0784574	−	0.0663226i
$826$	−4443.93	+	2549.59i	−0.187196	+	0.107399i
$827$		−	25872.7i		−	1.08789i	−0.839122	−	0.543943i	$-0.816931\pi$
$827$		−	25872.7i		−	1.08789i	0.839122	−	0.543943i	$-0.183069\pi$
$828$	3404.60	−	574.754i	0.142896	−	0.0241233i
$829$		−	12902.7i		−	0.540565i	−0.962781	−	0.270283i	$-0.912883\pi$
$829$		−	12902.7i		−	0.540565i	0.962781	−	0.270283i	$-0.0871172\pi$
$830$			11382.6i			0.476019i
$831$	−22714.5	+	26870.5i	−0.948206	+	1.12170i
$832$			16721.2i			0.696759i
$833$	−2016.47	+	3449.11i	−0.0838735	+	0.143463i
$834$	−343.000	+	405.757i	−0.0142411	+	0.0168468i
$835$	8207.90			0.340175
$836$	52665.2			2.17878
$837$	−15240.1	+	25742.0i	−0.629359	+	1.06305i
$838$		−	61669.1i		−	2.54215i
$839$	−23510.4			−0.967426			−0.483713	−	0.875227i	$-0.660712\pi$
$839$	−23510.4			−0.967426			−0.483713	+	0.875227i	$0.660712\pi$
$840$	7101.56	−	38827.1i	0.291699	−	1.59483i
$841$	−6062.34			−0.248569
$842$			2569.79i			0.105179i
$843$	27071.7	+	22884.6i	1.10605	+	0.934978i
$844$	15445.7			0.629931
$845$	10774.3			0.438637
$846$	65117.8	−	10993.0i	2.64633	−	0.446745i
$847$	9030.31	+	15739.8i	0.366334	+	0.638519i
$848$		−	39529.1i		−	1.60075i
$849$	24959.8	+	21099.3i	1.00897	+	0.852917i
$850$		−	1615.71i		−	0.0651982i
$851$			992.992i			0.0399992i
$852$	−44471.2	−	37593.0i	−1.78822	−	1.51164i
$853$			3950.89i			0.158588i	0.996851	+	0.0792942i	$0.0252667\pi$
$853$			3950.89i			0.158588i	−0.996851	+	0.0792942i	$0.974733\pi$
$854$	15799.7	+	27538.9i	0.633086	+	1.10347i
$855$	16418.7	−	2771.75i	0.656734	−	0.110868i
$856$	31214.6			1.24637
$857$	−13960.3			−0.556446			−0.278223	−	0.960517i	$-0.589745\pi$
$857$	−13960.3			−0.556446			−0.278223	+	0.960517i	$0.589745\pi$
$858$	2678.31	+	2264.06i	0.106569	+	0.0900860i
$859$			28049.3i			1.11412i	0.830472	+	0.557061i	$0.188071\pi$
$859$			28049.3i			1.11412i	−0.830472	+	0.557061i	$0.811929\pi$
$860$	−18706.9			−0.741743
$861$	−17719.3	−	3240.91i	−0.701363	−	0.128281i
$862$	−39694.6			−1.56845
$863$		−	9980.33i		−	0.393667i	−0.980437	−	0.196833i	$-0.936934\pi$
$863$		−	9980.33i		−	0.393667i	0.980437	−	0.196833i	$-0.0630658\pi$
$864$	61303.6	−	103548.i	2.41388	−	4.07729i
$865$	13322.2			0.523661
$866$	69547.7			2.72902
$867$	16025.6	−	18957.7i	0.627748	−	0.742605i
$868$	78045.3	−	44776.5i	3.05188	−	1.75094i
$869$			15455.9i			0.603344i
$870$	−16239.4	+	19210.7i	−0.632837	+	0.748625i
$871$		−	632.397i		−	0.0246015i
$872$			103982.i			4.03817i
$873$	19896.5	−	3358.86i	0.771357	−	0.130218i
$874$		−	3840.92i		−	0.148651i
$875$	1152.05	+	2008.02i	0.0445103	+	0.0775812i
$876$	−71240.2	−	60221.6i	−2.74770	−	2.32272i
$877$	−20922.9			−0.805607			−0.402804	−	0.915286i	$-0.631964\pi$
$877$	−20922.9			−0.805607			−0.402804	+	0.915286i	$0.631964\pi$
$878$	62771.8			2.41281
$879$	21674.5	−	25640.2i	0.831697	−	0.983869i
$880$			25567.7i			0.979418i
$881$	36072.2			1.37946			0.689730	−	0.724067i	$-0.257729\pi$
$881$	36072.2			1.37946			0.689730	+	0.724067i	$0.257729\pi$
$882$	18188.0	−	48057.1i	0.694354	−	1.83466i
$883$	−5680.10			−0.216479			−0.108239	−	0.994125i	$-0.534521\pi$
$883$	−5680.10			−0.216479			−0.108239	+	0.994125i	$0.534521\pi$
$884$			1722.73i			0.0655450i
$885$	836.259	−	989.266i	0.0317633	−	0.0375749i
$886$	71435.6			2.70872
$887$	−28585.7			−1.08209			−0.541044	−	0.840994i	$-0.681971\pi$
$887$	−28585.7			−1.08209			−0.541044	+	0.840994i	$0.681971\pi$
$888$	57592.8	+	48685.0i	2.17645	+	1.83982i
$889$	22986.9	+	40066.0i	0.867215	+	1.51155i
$890$			44738.5i			1.68498i
$891$	−4484.79	−	12904.5i	−0.168626	−	0.485203i
$892$			84311.9i			3.16477i
$893$		−	54372.2i		−	2.03751i
$894$	−4259.08	+	5038.35i	−0.159334	+	0.188487i
$895$			23262.2i			0.868792i
$896$	−119374.	+	68488.0i	−4.45091	+	2.55360i
$897$	122.210	−	144.571i	0.00454904	−	0.00538136i
$898$	−80017.4			−2.97351
$899$	−37209.0			−1.38041
$900$	2560.12	+	15165.1i	0.0948194	+	0.561671i
$901$		−	1687.43i		−	0.0623932i
$902$	19462.8			0.718447
$903$	−15544.3	−	2843.09i	−0.572848	−	0.104775i
$904$	66762.0			2.45627
$905$		−	4316.87i		−	0.158561i
$906$	−28272.9	−	23900.0i	−1.03676	−	0.876407i
$907$	−14916.9			−0.546093			−0.273046	−	0.962001i	$-0.588031\pi$
$907$	−14916.9			−0.546093			−0.273046	+	0.962001i	$0.588031\pi$
$908$	−102048.			−3.72972
$909$	780.078	+	4620.86i	0.0284638	+	0.168608i
$910$	−1659.65	−	2892.77i	−0.0604582	−	0.105378i
$911$			4273.11i			0.155406i	0.996977	+	0.0777028i	$0.0247585\pi$
$911$			4273.11i			0.155406i	−0.996977	+	0.0777028i	$0.975241\pi$
$912$	−133554.	−	112898.i	−4.84916	−	4.09915i
$913$		−	7689.12i		−	0.278721i
$914$			25280.2i			0.914873i
$915$	−6130.45	−	5182.27i	−0.221493	−	0.187235i
$916$		−	62578.2i		−	2.25725i
$917$	15934.2	+	27773.2i	0.573820	+	1.00017i
$918$	4619.20	−	7802.30i	0.166074	−	0.280517i
$919$	−22213.5			−0.797342			−0.398671	−	0.917094i	$-0.630528\pi$
$919$	−22213.5			−0.797342			−0.398671	+	0.917094i	$0.630528\pi$
$920$	2302.03			0.0824955
$921$	33715.5	+	28500.8i	1.20626	+	1.01969i
$922$		−	83089.3i		−	2.96789i
$923$	−3192.65			−0.113854
$924$	−7392.98	+	40420.4i	−0.263215	+	1.43910i
$925$	−4423.08			−0.157222
$926$			3289.98i			0.116755i
$927$	−8490.29	+	1433.30i	−0.300817	+	0.0507830i
$928$	149674.			5.29450
$929$	−15956.8			−0.563537			−0.281769	−	0.959482i	$-0.590921\pi$
$929$	−15956.8			−0.563537			−0.281769	+	0.959482i	$0.590921\pi$
$930$	−19843.2	+	23473.8i	−0.699661	+	0.827675i
$931$	−36522.2	−	21352.2i	−1.28568	−	0.751654i
$932$		−	43554.8i		−	1.53078i
$933$	10548.2	−	12478.2i	0.370131	−	0.437853i
$934$		−	44178.3i		−	1.54771i
$935$			1091.44i			0.0381753i
$936$	−2393.18	−	14176.2i	−0.0835722	−	0.495047i
$937$		−	15709.5i		−	0.547714i	−0.961770	−	0.273857i	$-0.911700\pi$
$937$		−	15709.5i		−	0.547714i	0.961770	−	0.273857i	$-0.0882996\pi$
$938$	8683.56	−	4981.98i	0.302269	−	0.173419i
$939$	20750.4	+	17541.0i	0.721153	+	0.609614i
$940$	50220.8			1.74258
$941$	−51405.4			−1.78084			−0.890419	−	0.455142i	$-0.849588\pi$
$941$	−51405.4			−1.78084			−0.890419	+	0.455142i	$0.849588\pi$
$942$	34040.7	−	40269.0i	1.17740	−	1.39282i
$943$		−	1050.57i		−	0.0362792i
$944$	−13604.7			−0.469064
$945$	−177.498	+	12990.4i	−0.00611006	+	0.447172i
$946$	17073.7			0.586801
$947$			4989.31i			0.171205i	0.996329	+	0.0856024i	$0.0272815\pi$
$947$			4989.31i			0.171205i	−0.996329	+	0.0856024i	$0.972719\pi$
$948$	63037.0	−	74570.6i	2.15965	−	2.55479i
$949$	−5114.42			−0.174943
$950$	17108.6			0.584291
$951$	−15233.6	−	12877.5i	−0.519437	−	0.439097i
$952$	−15349.6	+	8806.43i	−0.522565	+	0.299809i
$953$		−	34625.9i		−	1.17696i	−0.808512	−	0.588479i	$-0.799727\pi$
$953$		−	34625.9i		−	1.17696i	0.808512	−	0.588479i	$-0.200273\pi$
$954$	3612.54	+	21399.2i	0.122600	+	0.726231i
$955$			5501.50i			0.186413i
$956$			19315.4i			0.653455i
$957$	10970.0	−	12977.1i	0.370542	−	0.438339i
$958$			53682.2i			1.81043i
$959$	−24060.3	+	13804.0i	−0.810166	+	0.464812i
$960$	43206.6	−	51111.9i	1.45259	−	1.71836i
$961$	−15675.2			−0.526173
$962$	6371.92			0.213554
$963$	−10130.7	+	1710.23i	−0.339000	+	0.0572288i
$964$		−	6923.81i		−	0.231329i
$965$	−18087.4			−0.603373
$966$	2947.90	+	539.177i	0.0981853	+	0.0179583i
$967$	9368.14			0.311540			0.155770	−	0.987793i	$-0.450214\pi$
$967$	9368.14			0.311540			0.155770	+	0.987793i	$0.450214\pi$
$968$			80375.1i			2.66875i
$969$	−5701.19	−	4819.41i	−0.189008	−	0.159775i
$970$	20732.5			0.686270
$971$	−50834.8			−1.68009			−0.840045	−	0.542517i	$-0.817471\pi$
$971$	−50834.8			−1.68009			−0.840045	+	0.542517i	$0.817471\pi$
$972$	−30993.0	+	80551.7i	−1.02274	+	2.65813i
$973$	−296.043	+	169.847i	−0.00975406	+	0.00559615i
$974$		−	60965.5i		−	2.00561i
$975$	643.961	+	544.362i	0.0211521	+	0.0178805i
$976$			84308.1i			2.76500i
$977$			25561.3i			0.837031i	0.908210	+	0.418516i	$0.137449\pi$
$977$			25561.3i			0.837031i	−0.908210	+	0.418516i	$0.862551\pi$
$978$	−16238.3	−	13726.8i	−0.530925	−	0.448808i
$979$		−	30221.5i		−	0.986603i
$980$	19721.9	−	33733.7i	0.642851	−	1.09958i
$981$	−5697.12	−	33747.4i	−0.185418	−	1.09834i
$982$	53028.4			1.72322
$983$	309.306			0.0100359			0.00501797	−	0.999987i	$-0.498403\pi$
$983$	309.306			0.0100359			0.00501797	+	0.999987i	$0.498403\pi$
$984$	−60932.2	−	51508.0i	−1.97403	−	1.66871i
$985$		−	12911.0i		−	0.417644i
$986$	11277.9			0.364261
$987$	41730.5	+	7632.61i	1.34579	+	0.246148i
$988$	−18241.8			−0.587399
$989$		−	921.612i		−	0.0296315i
$990$	−2336.62	−	13841.2i	−0.0750127	−	0.444344i
$991$	−35306.7			−1.13174			−0.565870	−	0.824495i	$-0.691459\pi$
$991$	−35306.7			−1.13174			−0.565870	+	0.824495i	$0.691459\pi$
$992$	182889.			5.85357
$993$	−34085.8	+	40322.3i	−1.08930	+	1.28861i
$994$	−25151.5	−	43838.9i	−0.802571	−	1.39888i
$995$		−	4995.81i		−	0.159174i
$996$	−31360.1	+	37097.9i	−0.997673	+	1.18021i
$997$		−	27795.5i		−	0.882940i	−0.897276	−	0.441470i	$-0.854457\pi$
$997$		−	27795.5i		−	0.882940i	0.897276	−	0.441470i	$-0.145543\pi$
$998$			8429.33i			0.267361i
$999$	−21359.1	−	12645.2i	−0.676449	−	0.400478i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.b.b.41.1	yes	16
3.2	odd	2		105.4.b.a.41.16	yes	16
7.6	odd	2		105.4.b.a.41.1	✓	16
21.20	even	2	inner	105.4.b.b.41.16	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.b.a.41.1	✓	16	7.6	odd	2
105.4.b.a.41.16	yes	16	3.2	odd	2
105.4.b.b.41.1	yes	16	1.1	even	1	trivial
105.4.b.b.41.16	yes	16	21.20	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-5.54840i q^{2} +(-3.35452 + 3.96828i) q^{3} -22.7847 q^{4} +5.00000 q^{5} +(22.0176 + 18.6122i) q^{6} +(9.21642 + 16.0642i) q^{7} +82.0315i q^{8} +(-4.49445 - 26.6233i) q^{9} +O(q^{10})\)	\(q-5.54840i q^{2} +(-3.35452 + 3.96828i) q^{3} -22.7847 q^{4} +5.00000 q^{5} +(22.0176 + 18.6122i) q^{6} +(9.21642 + 16.0642i) q^{7} +82.0315i q^{8} +(-4.49445 - 26.6233i) q^{9} -27.7420i q^{10} +18.7401i q^{11} +(76.4317 - 90.4161i) q^{12} -6.49109i q^{13} +(89.1304 - 51.1364i) q^{14} +(-16.7726 + 19.8414i) q^{15} +272.866 q^{16} +11.6481 q^{17} +(-147.717 + 24.9370i) q^{18} +123.341i q^{19} -113.924 q^{20} +(-94.6637 - 17.3142i) q^{21} +103.978 q^{22} -5.61256i q^{23} +(-325.524 - 275.176i) q^{24} +25.0000 q^{25} -36.0152 q^{26} +(120.725 + 71.4730i) q^{27} +(-209.994 - 366.018i) q^{28} +174.503i q^{29} +(110.088 + 93.0609i) q^{30} +213.228i q^{31} -857.716i q^{32} +(-74.3661 - 62.8641i) q^{33} -64.6285i q^{34} +(46.0821 + 80.3209i) q^{35} +(102.405 + 606.604i) q^{36} -176.923 q^{37} +684.344 q^{38} +(25.7585 + 21.7745i) q^{39} +410.158i q^{40} +187.182 q^{41} +(-96.0661 + 525.232i) q^{42} +164.205 q^{43} -426.989i q^{44} +(-22.4723 - 133.116i) q^{45} -31.1407 q^{46} -440.829 q^{47} +(-915.333 + 1082.81i) q^{48} +(-173.115 + 296.108i) q^{49} -138.710i q^{50} +(-39.0739 + 46.2231i) q^{51} +147.898i q^{52} -144.867i q^{53} +(396.561 - 669.832i) q^{54} +93.7007i q^{55} +(-1317.77 + 756.037i) q^{56} +(-489.451 - 413.749i) q^{57} +968.213 q^{58} -49.8587 q^{59} +(382.159 - 452.081i) q^{60} +308.973i q^{61} +1183.07 q^{62} +(386.258 - 317.571i) q^{63} -2576.02 q^{64} -32.4555i q^{65} +(-348.795 + 412.613i) q^{66} +97.4253 q^{67} -265.400 q^{68} +(22.2722 + 18.8274i) q^{69} +(445.652 - 255.682i) q^{70} -491.851i q^{71} +(2183.95 - 368.687i) q^{72} -787.914i q^{73} +981.641i q^{74} +(-83.8629 + 99.2069i) q^{75} -2810.29i q^{76} +(-301.045 + 172.717i) q^{77} +(120.813 - 142.918i) q^{78} +824.749 q^{79} +1364.33 q^{80} +(-688.600 + 239.314i) q^{81} -1038.56i q^{82} -410.302 q^{83} +(2156.89 + 394.500i) q^{84} +58.2407 q^{85} -911.077i q^{86} +(-692.477 - 585.373i) q^{87} -1537.28 q^{88} -1612.66 q^{89} +(-738.583 + 124.685i) q^{90} +(104.274 - 59.8246i) q^{91} +127.881i q^{92} +(-846.148 - 715.277i) q^{93} +2445.90i q^{94} +616.704i q^{95} +(3403.66 + 2877.22i) q^{96} +747.334i q^{97} +(1642.93 + 960.513i) q^{98} +(498.924 - 84.2267i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{3} - 64 q^{4} + 80 q^{5} + 28 q^{6} - 4 q^{7} - 22 q^{9}+O(q^{10}) \) 16 * q + 2 * q^3 - 64 * q^4 + 80 * q^5 + 28 * q^6 - 4 * q^7 - 22 * q^9	\( 16 q + 2 q^{3} - 64 q^{4} + 80 q^{5} + 28 q^{6} - 4 q^{7} - 22 q^{9} + 66 q^{12} + 90 q^{14} + 10 q^{15} + 376 q^{16} + 72 q^{17} - 182 q^{18} - 320 q^{20} - 70 q^{21} - 276 q^{22} - 526 q^{24} + 400 q^{25} - 696 q^{26} + 128 q^{27} + 10 q^{28} + 140 q^{30} + 502 q^{33} - 20 q^{35} + 996 q^{36} - 812 q^{37} + 1200 q^{38} - 594 q^{39} + 936 q^{41} - 974 q^{42} - 548 q^{43} - 110 q^{45} + 1224 q^{46} - 912 q^{47} - 1850 q^{48} + 328 q^{49} + 750 q^{51} + 2950 q^{54} - 1254 q^{56} + 432 q^{57} + 576 q^{58} + 552 q^{59} + 330 q^{60} + 1860 q^{62} + 362 q^{63} - 4000 q^{64} - 1378 q^{66} + 1004 q^{67} - 3828 q^{68} - 1988 q^{69} + 450 q^{70} + 1988 q^{72} + 50 q^{75} - 1152 q^{77} + 1446 q^{78} + 1292 q^{79} + 1880 q^{80} - 2950 q^{81} + 1752 q^{83} - 420 q^{84} + 360 q^{85} - 1910 q^{87} - 912 q^{88} - 6096 q^{89} - 910 q^{90} - 552 q^{91} - 1080 q^{93} + 9546 q^{96} + 4824 q^{98} + 2530 q^{99}+O(q^{100}) \) 16 * q + 2 * q^3 - 64 * q^4 + 80 * q^5 + 28 * q^6 - 4 * q^7 - 22 * q^9 + 66 * q^12 + 90 * q^14 + 10 * q^15 + 376 * q^16 + 72 * q^17 - 182 * q^18 - 320 * q^20 - 70 * q^21 - 276 * q^22 - 526 * q^24 + 400 * q^25 - 696 * q^26 + 128 * q^27 + 10 * q^28 + 140 * q^30 + 502 * q^33 - 20 * q^35 + 996 * q^36 - 812 * q^37 + 1200 * q^38 - 594 * q^39 + 936 * q^41 - 974 * q^42 - 548 * q^43 - 110 * q^45 + 1224 * q^46 - 912 * q^47 - 1850 * q^48 + 328 * q^49 + 750 * q^51 + 2950 * q^54 - 1254 * q^56 + 432 * q^57 + 576 * q^58 + 552 * q^59 + 330 * q^60 + 1860 * q^62 + 362 * q^63 - 4000 * q^64 - 1378 * q^66 + 1004 * q^67 - 3828 * q^68 - 1988 * q^69 + 450 * q^70 + 1988 * q^72 + 50 * q^75 - 1152 * q^77 + 1446 * q^78 + 1292 * q^79 + 1880 * q^80 - 2950 * q^81 + 1752 * q^83 - 420 * q^84 + 360 * q^85 - 1910 * q^87 - 912 * q^88 - 6096 * q^89 - 910 * q^90 - 552 * q^91 - 1080 * q^93 + 9546 * q^96 + 4824 * q^98 + 2530 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more