LMFDB - Embedded newform 124.4.d.c.123.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,4,Mod(123,124)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("124.123");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	124.d (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:	$7.31623684071$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			123.19
Character	$\chi$	$=$	124.123
Dual form			124.4.d.c.123.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.546214 + 2.77518i) q^{2} -7.92016 q^{3} +(-7.40330 - 3.03169i) q^{4} +15.6847 q^{5} +(4.32610 - 21.9799i) q^{6} -9.09573i q^{7} +(12.4573 - 18.8896i) q^{8} +35.7289 q^{9} +O(q^{10})$	\(q+(-0.546214 + 2.77518i) q^{2} -7.92016 q^{3} +(-7.40330 - 3.03169i) q^{4} +15.6847 q^{5} +(4.32610 - 21.9799i) q^{6} -9.09573i q^{7} +(12.4573 - 18.8896i) q^{8} +35.7289 q^{9} +(-8.56720 + 43.5279i) q^{10} -3.40609 q^{11} +(58.6353 + 24.0115i) q^{12} +11.0814i q^{13} +(25.2423 + 4.96821i) q^{14} -124.225 q^{15} +(45.6177 + 44.8890i) q^{16} +59.9340i q^{17} +(-19.5156 + 99.1544i) q^{18} +97.2624i q^{19} +(-116.119 - 47.5511i) q^{20} +72.0396i q^{21} +(1.86045 - 9.45253i) q^{22} +185.382 q^{23} +(-98.6637 + 149.608i) q^{24} +121.010 q^{25} +(-30.7530 - 6.05282i) q^{26} -69.1347 q^{27} +(-27.5754 + 67.3384i) q^{28} -216.556i q^{29} +(67.8536 - 344.748i) q^{30} +(45.2797 + 166.556i) q^{31} +(-149.492 + 102.079i) q^{32} +26.9768 q^{33} +(-166.328 - 32.7368i) q^{34} -142.664i q^{35} +(-264.512 - 108.319i) q^{36} +44.9299i q^{37} +(-269.921 - 53.1261i) q^{38} -87.7666i q^{39} +(195.389 - 296.277i) q^{40} +130.209 q^{41} +(-199.923 - 39.3491i) q^{42} +396.299 q^{43} +(25.2163 + 10.3262i) q^{44} +560.398 q^{45} +(-101.258 + 514.468i) q^{46} -111.175i q^{47} +(-361.300 - 355.528i) q^{48} +260.268 q^{49} +(-66.0971 + 335.824i) q^{50} -474.687i q^{51} +(33.5954 - 82.0391i) q^{52} +730.700i q^{53} +(37.7623 - 191.861i) q^{54} -53.4235 q^{55} +(-171.815 - 113.308i) q^{56} -770.334i q^{57} +(600.984 + 118.286i) q^{58} +371.889i q^{59} +(919.677 + 376.612i) q^{60} +718.011i q^{61} +(-486.955 + 34.6846i) q^{62} -324.981i q^{63} +(-201.632 - 470.626i) q^{64} +173.809i q^{65} +(-14.7351 + 74.8655i) q^{66} -672.930i q^{67} +(181.701 - 443.709i) q^{68} -1468.25 q^{69} +(395.918 + 77.9249i) q^{70} -168.035i q^{71} +(445.086 - 674.905i) q^{72} -1040.35i q^{73} +(-124.689 - 24.5413i) q^{74} -958.415 q^{75} +(294.869 - 720.063i) q^{76} +30.9809i q^{77} +(243.569 + 47.9393i) q^{78} -661.896 q^{79} +(715.500 + 704.070i) q^{80} -417.124 q^{81} +(-71.1222 + 361.355i) q^{82} +144.965 q^{83} +(218.402 - 533.331i) q^{84} +940.046i q^{85} +(-216.464 + 1099.80i) q^{86} +1715.16i q^{87} +(-42.4306 + 64.3396i) q^{88} -734.388i q^{89} +(-306.097 + 1555.21i) q^{90} +100.794 q^{91} +(-1372.44 - 562.019i) q^{92} +(-358.622 - 1319.15i) q^{93} +(308.530 + 60.7251i) q^{94} +1525.53i q^{95} +(1184.00 - 808.479i) q^{96} +343.759 q^{97} +(-142.162 + 722.291i) q^{98} -121.696 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{2} + 10 q^{4} - 4 q^{5} + 94 q^{8} + 536 q^{9}+O(q^{10}) $ 40 * q - 2 * q^2 + 10 * q^4 - 4 * q^5 + 94 * q^8 + 536 * q^9	$ 40 q - 2 q^{2} + 10 q^{4} - 4 q^{5} + 94 q^{8} + 536 q^{9} + 228 q^{10} - 104 q^{14} - 78 q^{16} + 114 q^{18} - 44 q^{20} + 28 q^{25} + 48 q^{28} - 602 q^{32} - 136 q^{33} - 482 q^{36} + 420 q^{38} - 516 q^{40} - 4 q^{41} - 1596 q^{45} + 1876 q^{49} - 662 q^{50} + 1576 q^{56} - 838 q^{62} - 302 q^{64} - 3900 q^{66} - 872 q^{69} - 912 q^{70} - 2166 q^{72} + 3220 q^{76} - 476 q^{78} + 572 q^{80} - 2056 q^{81} + 3096 q^{82} - 6220 q^{90} - 2904 q^{93} + 6408 q^{94} - 1836 q^{97} - 1358 q^{98}+O(q^{100}) $ 40 * q - 2 * q^2 + 10 * q^4 - 4 * q^5 + 94 * q^8 + 536 * q^9 + 228 * q^10 - 104 * q^14 - 78 * q^16 + 114 * q^18 - 44 * q^20 + 28 * q^25 + 48 * q^28 - 602 * q^32 - 136 * q^33 - 482 * q^36 + 420 * q^38 - 516 * q^40 - 4 * q^41 - 1596 * q^45 + 1876 * q^49 - 662 * q^50 + 1576 * q^56 - 838 * q^62 - 302 * q^64 - 3900 * q^66 - 872 * q^69 - 912 * q^70 - 2166 * q^72 + 3220 * q^76 - 476 * q^78 + 572 * q^80 - 2056 * q^81 + 3096 * q^82 - 6220 * q^90 - 2904 * q^93 + 6408 * q^94 - 1836 * q^97 - 1358 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−0.546214	+	2.77518i	−0.193116	+	0.981176i
$2$	−0.546214	+	2.77518i	−0.193116	+	0.981176i
$3$	−7.92016			−1.52424			−0.762118	−	0.647438i	$-0.775840\pi$
$3$	−7.92016			−1.52424			−0.762118	+	0.647438i	$0.775840\pi$
$4$	−7.40330	−	3.03169i	−0.925413	−	0.378961i
$5$	15.6847			1.40288			0.701441	−	0.712728i	$-0.252540\pi$
$5$	15.6847			1.40288			0.701441	+	0.712728i	$0.252540\pi$
$6$	4.32610	−	21.9799i	0.294354	−	1.49554i
$7$		−	9.09573i		−	0.491123i	−0.969381	−	0.245562i	$-0.921028\pi$
$7$		−	9.09573i		−	0.491123i	0.969381	−	0.245562i	$-0.0789724\pi$
$8$	12.4573	−	18.8896i	0.550539	−	0.834809i
$9$	35.7289			1.32329
$10$	−8.56720	+	43.5279i	−0.270919	+	1.37647i
$11$	−3.40609			−0.0933613			−0.0466807	−	0.998910i	$-0.514864\pi$
$11$	−3.40609			−0.0933613			−0.0466807	+	0.998910i	$0.514864\pi$
$12$	58.6353	+	24.0115i	1.41055	+	0.577626i
$13$			11.0814i			0.236418i	0.992989	+	0.118209i	$0.0377153\pi$
$13$			11.0814i			0.236418i	−0.992989	+	0.118209i	$0.962285\pi$
$14$	25.2423	+	4.96821i	0.481878	+	0.0948436i
$15$	−124.225			−2.13832
$16$	45.6177	+	44.8890i	0.712777	+	0.701391i
$17$			59.9340i			0.855066i	0.904000	+	0.427533i	$0.140617\pi$
$17$			59.9340i			0.855066i	−0.904000	+	0.427533i	$0.859383\pi$
$18$	−19.5156	+	99.1544i	−0.255549	+	1.29838i
$19$			97.2624i			1.17440i	0.809443	+	0.587198i	$0.199769\pi$
$19$			97.2624i			1.17440i	−0.809443	+	0.587198i	$0.800231\pi$
$20$	−116.119	−	47.5511i	−1.29824	−	0.531638i
$21$			72.0396i			0.748588i
$22$	1.86045	−	9.45253i	0.0180295	−	0.0916039i
$23$	185.382			1.68064			0.840321	−	0.542090i	$-0.182367\pi$
$23$	185.382			1.68064			0.840321	+	0.542090i	$0.182367\pi$
$24$	−98.6637	+	149.608i	−0.839152	+	1.27245i
$25$	121.010			0.968077
$26$	−30.7530	−	6.05282i	−0.231968	−	0.0456560i
$27$	−69.1347			−0.492777
$28$	−27.5754	+	67.3384i	−0.186117	+	0.454492i
$29$		−	216.556i		−	1.38667i	−0.720614	−	0.693337i	$-0.756140\pi$
$29$		−	216.556i		−	1.38667i	0.720614	−	0.693337i	$-0.243860\pi$
$30$	67.8536	−	344.748i	0.412944	−	2.09807i
$31$	45.2797	+	166.556i	0.262338	+	0.964976i
$31$	45.2797	+	166.556i	0.262338	+	0.964976i
$32$	−149.492	+	102.079i	−0.825836	+	0.563910i
$33$	26.9768			0.142305
$34$	−166.328	−	32.7368i	−0.838970	−	0.165127i
$35$		−	142.664i		−	0.688988i
$36$	−264.512	−	108.319i	−1.22459	−	0.501477i
$37$			44.9299i			0.199633i	0.995006	+	0.0998166i	$0.0318256\pi$
$37$			44.9299i			0.199633i	−0.995006	+	0.0998166i	$0.968174\pi$
$38$	−269.921	−	53.1261i	−1.15229	−	0.226794i
$39$		−	87.7666i		−	0.360357i
$40$	195.389	−	296.277i	0.772341	−	1.17114i
$41$	130.209			0.495983			0.247991	−	0.968762i	$-0.420230\pi$
$41$	130.209			0.495983			0.247991	+	0.968762i	$0.420230\pi$
$42$	−199.923	−	39.3491i	−0.734496	−	0.144564i
$43$	396.299			1.40547			0.702733	−	0.711453i	$-0.251963\pi$
$43$	396.299			1.40547			0.702733	+	0.711453i	$0.251963\pi$
$44$	25.2163	+	10.3262i	0.0863977	+	0.0353803i
$45$	560.398			1.85643
$46$	−101.258	+	514.468i	−0.324558	+	1.64900i
$47$		−	111.175i		−	0.345032i	−0.985007	−	0.172516i	$-0.944810\pi$
$47$		−	111.175i		−	0.345032i	0.985007	−	0.172516i	$-0.0551896\pi$
$48$	−361.300	−	355.528i	−1.08644	−	1.06908i
$49$	260.268			0.758798
$50$	−66.0971	+	335.824i	−0.186951	+	0.949854i
$51$		−	474.687i		−	1.30332i
$52$	33.5954	−	82.0391i	0.0895932	−	0.218784i
$53$			730.700i			1.89376i	0.321585	+	0.946881i	$0.395784\pi$
$53$			730.700i			1.89376i	−0.321585	+	0.946881i	$0.604216\pi$
$54$	37.7623	−	191.861i	0.0951629	−	0.483501i
$55$	−53.4235			−0.130975
$56$	−171.815	−	113.308i	−0.409994	−	0.270383i
$57$		−	770.334i		−	1.79006i
$58$	600.984	+	118.286i	1.36057	+	0.267788i
$59$			371.889i			0.820608i	0.911949	+	0.410304i	$0.134577\pi$
$59$			371.889i			0.820608i	−0.911949	+	0.410304i	$0.865423\pi$
$60$	919.677	+	376.612i	1.97883	+	0.810341i
$61$			718.011i			1.50708i	0.657402	+	0.753540i	$0.271655\pi$
$61$			718.011i			1.50708i	−0.657402	+	0.753540i	$0.728345\pi$
$62$	−486.955	+	34.6846i	−0.997473	+	0.0710475i
$63$		−	324.981i		−	0.649901i
$64$	−201.632	−	470.626i	−0.393813	−	0.919191i
$65$			173.809i			0.331666i
$66$	−14.7351	+	74.8655i	−0.0274813	+	0.139626i
$67$		−	672.930i		−	1.22704i	−0.789680	−	0.613519i	$-0.789753\pi$
$67$		−	672.930i		−	1.22704i	0.789680	−	0.613519i	$-0.210247\pi$
$68$	181.701	−	443.709i	0.324037	−	0.791289i
$69$	−1468.25			−2.56169
$70$	395.918	+	77.9249i	0.676018	+	0.133054i
$71$		−	168.035i		−	0.280875i	−0.990090	−	0.140437i	$-0.955149\pi$
$71$		−	168.035i		−	0.280875i	0.990090	−	0.140437i	$-0.0448509\pi$
$72$	445.086	−	674.905i	0.728525	−	1.10470i
$73$		−	1040.35i		−	1.66800i	−0.551763	−	0.834001i	$-0.686045\pi$
$73$		−	1040.35i		−	1.66800i	0.551763	−	0.834001i	$-0.313955\pi$
$74$	−124.689	−	24.5413i	−0.195875	−	0.0385523i
$75$	−958.415			−1.47558
$76$	294.869	−	720.063i	0.445050	−	1.08680i
$77$			30.9809i			0.0458519i
$78$	243.569	+	47.9393i	0.353573	+	0.0695905i
$79$	−661.896			−0.942647			−0.471323	−	0.881960i	$-0.656224\pi$
$79$	−661.896			−0.942647			−0.471323	+	0.881960i	$0.656224\pi$
$80$	715.500	+	704.070i	0.999942	+	0.983968i
$81$	−417.124			−0.572187
$82$	−71.1222	+	361.355i	−0.0957821	+	0.486647i
$83$	144.965			0.191710			0.0958552	−	0.995395i	$-0.469441\pi$
$83$	144.965			0.191710			0.0958552	+	0.995395i	$0.469441\pi$
$84$	218.402	−	533.331i	0.283686	−	0.692752i
$85$			940.046i			1.19956i
$86$	−216.464	+	1099.80i	−0.271418	+	1.37901i
$87$			1715.16i			2.11362i
$88$	−42.4306	+	64.3396i	−0.0513991	+	0.0779389i
$89$		−	734.388i		−	0.874663i	−0.899300	−	0.437332i	$-0.855924\pi$
$89$		−	734.388i		−	0.874663i	0.899300	−	0.437332i	$-0.144076\pi$
$90$	−306.097	+	1555.21i	−0.358505	+	1.82148i
$91$	100.794			0.116110
$92$	−1372.44	−	562.019i	−1.55529	−	0.636898i
$93$	−358.622	−	1319.15i	−0.399865	−	1.47085i
$94$	308.530	+	60.7251i	0.338537	+	0.0666310i
$95$			1525.53i			1.64754i
$96$	1184.00	−	808.479i	1.25877	−	0.859532i
$97$	343.759			0.359830			0.179915	−	0.983682i	$-0.442418\pi$
$97$	343.759			0.359830			0.179915	+	0.983682i	$0.442418\pi$
$98$	−142.162	+	722.291i	−0.146536	+	0.744514i
$99$	−121.696			−0.123544
$100$	−895.870	−	366.863i	−0.895870	−	0.366863i
$101$	492.768			0.485468			0.242734	−	0.970093i	$-0.421956\pi$
$101$	492.768			0.485468			0.242734	+	0.970093i	$0.421956\pi$
$102$	1317.34	+	259.280i	1.27879	+	0.251692i
$103$		−	1484.14i		−	1.41977i	−0.704318	−	0.709884i	$-0.748747\pi$
$103$		−	1484.14i		−	1.41977i	0.704318	−	0.709884i	$-0.251253\pi$
$104$	209.323	+	138.044i	0.197364	+	0.130157i
$105$			1129.92i			1.05018i
$106$	−2027.83	−	399.118i	−1.85811	−	0.365715i
$107$			995.557i			0.899478i	0.893160	+	0.449739i	$0.148483\pi$
$107$			995.557i			0.899478i	−0.893160	+	0.449739i	$0.851517\pi$
$108$	511.825	+	209.595i	0.456022	+	0.186743i
$109$	−652.327			−0.573226			−0.286613	−	0.958047i	$-0.592529\pi$
$109$	−652.327			−0.573226			−0.286613	+	0.958047i	$0.592529\pi$
$110$	29.1806	−	148.260i	0.0252933	−	0.128509i
$111$		−	355.852i		−	0.304288i
$112$	408.298	−	414.927i	0.344469	−	0.350061i
$113$	1268.26			1.05582			0.527909	−	0.849301i	$-0.322976\pi$
$113$	1268.26			1.05582			0.527909	+	0.849301i	$0.322976\pi$
$114$	2137.82	+	420.767i	1.75636	+	0.345688i
$115$	2907.65			2.35774
$116$	−656.532	+	1603.23i	−0.525495	+	1.28324i
$117$			395.927i			0.312850i
$118$	−1032.06	−	203.131i	−0.805161	−	0.158472i
$119$	545.143			0.419943
$120$	−1547.51	+	2346.56i	−1.17723	+	1.78509i
$121$	−1319.40			−0.991284
$122$	−1992.61	−	392.188i	−1.47871	−	0.291041i
$123$	−1031.28			−0.755995
$124$	169.725	−	1370.33i	0.122918	−	0.992417i
$125$	−62.5883			−0.0447846
$126$	901.882	+	177.509i	0.637667	+	0.125506i
$127$	1864.84			1.30298			0.651489	−	0.758658i	$-0.274145\pi$
$127$	1864.84			1.30298			0.651489	+	0.758658i	$0.274145\pi$
$128$	1416.21	−	302.505i	0.977939	−	0.208890i
$129$	−3138.75			−2.14226
$130$	−482.351	−	94.9367i	−0.325423	−	0.0640500i
$131$			1710.86i			1.14106i	0.821276	+	0.570530i	$0.193262\pi$
$131$			1710.86i			1.14106i	−0.821276	+	0.570530i	$0.806738\pi$
$132$	−199.717	−	81.7852i	−0.131691	−	0.0539279i
$133$	884.673			0.576773
$134$	1867.51	+	367.564i	1.20394	+	0.236960i
$135$	−1084.36			−0.691307
$136$	1132.13	+	746.614i	0.713817	+	0.470748i
$137$		−	446.214i		−	0.278267i	−0.990274	−	0.139134i	$-0.955568\pi$
$137$		−	446.214i		−	0.278267i	0.990274	−	0.139134i	$-0.0444318\pi$
$138$	801.980	−	4074.67i	0.494703	−	2.51347i
$139$	−748.720			−0.456875			−0.228437	−	0.973559i	$-0.573362\pi$
$139$	−748.720			−0.456875			−0.228437	+	0.973559i	$0.573362\pi$
$140$	−432.512	+	1056.18i	−0.261100	+	0.637598i
$141$			880.521i			0.525909i
$142$	466.329	+	91.7832i	0.275588	+	0.0542414i
$143$		−	37.7443i		−	0.0220723i
$144$	1629.87	+	1603.84i	0.943214	+	0.928146i
$145$		−	3396.62i		−	1.94534i
$146$	2887.17	+	568.255i	1.63660	+	0.322117i
$147$	−2061.36			−1.15659
$148$	136.213	−	332.630i	0.0756532	−	0.184743i
$149$	−1855.59			−1.02024			−0.510121	−	0.860103i	$-0.670399\pi$
$149$	−1855.59			−1.02024			−0.510121	+	0.860103i	$0.670399\pi$
$150$	523.500	−	2659.78i	0.284957	−	1.44780i
$151$	−550.586			−0.296729			−0.148364	−	0.988933i	$-0.547401\pi$
$151$	−550.586			−0.296729			−0.148364	+	0.988933i	$0.547401\pi$
$152$	1837.25	+	1211.63i	0.980397	+	0.646551i
$153$			2141.38i			1.13150i
$154$	−85.9776	−	16.9222i	−0.0449888	−	0.00885473i
$155$	710.198	+	2612.37i	0.368029	+	1.35375i
$156$	−266.081	+	649.763i	−0.136561	+	0.333479i
$157$	2840.75			1.44405			0.722027	−	0.691865i	$-0.243211\pi$
$157$	2840.75			1.44405			0.722027	+	0.691865i	$0.243211\pi$
$158$	361.537	−	1836.88i	0.182040	−	0.924903i
$159$		−	5787.26i		−	2.88654i
$160$	−2344.74	+	1601.07i	−1.15855	+	0.791099i
$161$		−	1686.18i		−	0.825402i
$162$	227.839	−	1157.60i	0.110498	−	0.561416i
$163$		−	1046.77i		−	0.503001i	−0.967857	−	0.251500i	$-0.919076\pi$
$163$		−	1046.77i		−	0.503001i	0.967857	−	0.251500i	$-0.0809240\pi$
$164$	−963.980	−	394.754i	−0.458989	−	0.187958i
$165$	423.122			0.199637
$166$	−79.1818	+	402.304i	−0.0370223	+	0.188102i
$167$	593.507			0.275011			0.137506	−	0.990501i	$-0.456091\pi$
$167$	593.507			0.275011			0.137506	+	0.990501i	$0.456091\pi$
$168$	1360.80	+	897.418i	0.624928	+	0.412127i
$169$	2074.20			0.944107
$170$	−2608.80	−	513.466i	−1.17698	−	0.231653i
$171$			3475.08i			1.55407i
$172$	−2933.92	−	1201.46i	−1.30064	−	0.532617i
$173$	−3527.47			−1.55022			−0.775111	−	0.631825i	$-0.782306\pi$
$173$	−3527.47			−1.55022			−0.775111	+	0.631825i	$0.782306\pi$
$174$	−4759.89	−	936.845i	−2.07383	−	0.408173i
$175$		−	1100.67i		−	0.475445i
$176$	−155.378	−	152.896i	−0.0665458	−	0.0654828i
$177$		−	2945.42i		−	1.25080i
$178$	2038.06	+	401.133i	0.858198	+	0.168911i
$179$	−3512.91			−1.46685			−0.733427	−	0.679768i	$-0.762080\pi$
$179$	−3512.91			−1.46685			−0.733427	+	0.679768i	$0.762080\pi$
$180$	−4148.79	−	1698.95i	−1.71796	−	0.703513i
$181$			4220.06i			1.73301i	0.499171	+	0.866504i	$0.333638\pi$
$181$			4220.06i			1.73301i	−0.499171	+	0.866504i	$0.666362\pi$
$182$	−55.0549	+	279.721i	−0.0224227	+	0.113925i
$183$		−	5686.76i		−	2.29715i
$184$	2309.35	−	3501.78i	0.925259	−	1.40301i
$185$			704.712i			0.280062i
$186$	3856.76	−	274.707i	1.52038	−	0.108293i
$187$		−	204.140i		−	0.0798301i
$188$	−337.047	+	823.059i	−0.130754	+	0.319297i
$189$			628.830i			0.242014i
$190$	−4233.63	−	833.266i	−1.61653	−	0.318166i
$191$		−	1983.97i		−	0.751596i	−0.926702	−	0.375798i	$-0.877369\pi$
$191$		−	1983.97i		−	0.751596i	0.926702	−	0.375798i	$-0.122631\pi$
$192$	1596.96	+	3727.43i	0.600264	+	1.40106i
$193$	1921.71			0.716725			0.358362	−	0.933583i	$-0.383335\pi$
$193$	1921.71			0.716725			0.358362	+	0.933583i	$0.383335\pi$
$194$	−187.766	+	953.996i	−0.0694888	+	0.353056i
$195$		−	1376.59i		−	0.505538i
$196$	−1926.84	−	789.051i	−0.702201	−	0.287555i
$197$		−	1170.71i		−	0.423398i	−0.977335	−	0.211699i	$-0.932100\pi$
$197$		−	1170.71i		−	0.423398i	0.977335	−	0.211699i	$-0.0678997\pi$
$198$	66.4720	−	337.729i	0.0238584	−	0.121219i
$199$	−2687.83			−0.957463			−0.478732	−	0.877961i	$-0.658903\pi$
$199$	−2687.83			−0.957463			−0.478732	+	0.877961i	$0.658903\pi$
$200$	1507.45	−	2285.82i	0.532964	−	0.808159i
$201$			5329.72i			1.87029i
$202$	−269.157	+	1367.52i	−0.0937515	+	0.476329i
$203$	−1969.74			−0.681027
$204$	−1439.10	+	3514.25i	−0.493908	+	1.20611i
$205$	2042.30			0.695805
$206$	4118.75	+	810.655i	1.39304	+	0.274180i
$207$	6623.49			2.22398
$208$	−497.434	+	505.509i	−0.165821	+	0.168513i
$209$		−	331.284i		−	0.109643i
$210$	−3135.74	−	617.178i	−1.03041	−	0.202806i
$211$			2813.05i			0.917813i	0.888485	+	0.458906i	$0.151759\pi$
$211$			2813.05i			0.917813i	−0.888485	+	0.458906i	$0.848241\pi$
$212$	2215.25	−	5409.59i	0.717662	−	1.75251i
$213$			1330.87i			0.428119i
$214$	−2762.86	−	543.787i	−0.882546	−	0.173703i
$215$	6215.83			1.97170
$216$	−861.230	+	1305.92i	−0.271293	+	0.411375i
$217$	1514.94	−	411.852i	0.473922	−	0.128840i
$218$	356.310	−	1810.33i	0.110699	−	0.562435i
$219$			8239.77i			2.54243i
$220$	395.510	+	161.963i	0.121206	+	0.0496344i
$221$	−664.154			−0.202153
$222$	987.555	+	194.371i	0.298560	+	0.0587628i
$223$	−894.008			−0.268463			−0.134231	−	0.990950i	$-0.542857\pi$
$223$	−894.008			−0.268463			−0.134231	+	0.990950i	$0.542857\pi$
$224$	928.480	+	1359.74i	0.276949	+	0.405587i
$225$	4323.55			1.28105
$226$	−692.739	+	3519.64i	−0.203895	+	1.03594i
$227$			561.947i			0.164307i	0.996620	+	0.0821536i	$0.0261798\pi$
$227$			561.947i			0.164307i	−0.996620	+	0.0821536i	$0.973820\pi$
$228$	−2335.41	+	5703.01i	−0.678362	+	1.65654i
$229$		−	5898.83i		−	1.70221i	−0.524996	−	0.851105i	$-0.675933\pi$
$229$		−	5898.83i		−	1.70221i	0.524996	−	0.851105i	$-0.324067\pi$
$230$	−1588.20	+	8069.28i	−0.455317	+	2.31336i
$231$		−	245.373i		−	0.0698891i
$232$	−4090.66	−	2697.70i	−1.15761	−	0.763418i
$233$	2443.93			0.687156			0.343578	−	0.939124i	$-0.388361\pi$
$233$	2443.93			0.687156			0.343578	+	0.939124i	$0.388361\pi$
$234$	−1098.77	−	216.261i	−0.306961	−	0.0604163i
$235$		−	1743.74i		−	0.484038i
$236$	1127.45	−	2753.21i	0.310978	−	0.759401i
$237$	5242.32			1.43682
$238$	−297.765	+	1512.87i	−0.0810976	+	0.412038i
$239$	−4430.05			−1.19898			−0.599489	−	0.800383i	$-0.704630\pi$
$239$	−4430.05			−1.19898			−0.599489	+	0.800383i	$0.704630\pi$
$240$	−5666.88	−	5576.35i	−1.52415	−	1.49980i
$241$			1688.20i			0.451232i	0.974216	+	0.225616i	$0.0724394\pi$
$241$			1688.20i			0.451232i	−0.974216	+	0.225616i	$0.927561\pi$
$242$	720.674	−	3661.57i	0.191432	−	0.972624i
$243$	5170.32			1.36492
$244$	2176.79	−	5315.65i	0.571125	−	1.39467i
$245$	4082.22			1.06450
$246$	563.299	−	2861.99i	0.145995	−	0.741764i
$247$	−1077.81			−0.277648
$248$	3710.23	+	1219.51i	0.949998	+	0.312255i
$249$	−1148.14			−0.292212
$250$	34.1866	−	173.694i	0.00864860	−	0.0439415i
$251$	2952.92			0.742577			0.371288	−	0.928518i	$-0.378916\pi$
$251$	2952.92			0.742577			0.371288	+	0.928518i	$0.378916\pi$
$252$	−985.241	+	2405.93i	−0.246287	+	0.601426i
$253$	−631.426			−0.156907
$254$	−1018.60	+	5175.29i	−0.251626	+	1.27845i
$255$		−	7445.32i		−	1.82841i
$256$	65.9543	+	4095.47i	0.0161021	+	0.999870i
$257$	−5740.41			−1.39330			−0.696648	−	0.717413i	$-0.745326\pi$
$257$	−5740.41			−1.39330			−0.696648	+	0.717413i	$0.745326\pi$
$258$	1714.43	−	8710.62i	0.413705	−	2.10194i
$259$	408.670			0.0980445
$260$	526.934	−	1286.76i	0.125689	−	0.306928i
$261$		−	7737.33i		−	1.83498i
$262$	−4747.97	−	934.498i	−1.11958	−	0.220357i
$263$	−6103.66			−1.43106			−0.715528	−	0.698584i	$-0.753814\pi$
$263$	−6103.66			−1.43106			−0.715528	+	0.698584i	$0.753814\pi$
$264$	336.057	−	509.580i	0.0783443	−	0.118797i
$265$			11460.8i			2.65672i
$266$	−483.220	+	2455.13i	−0.111384	+	0.565916i
$267$			5816.47i			1.33319i
$268$	−2040.12	+	4981.91i	−0.465000	+	1.13552i
$269$		−	529.518i		−	0.120020i	−0.998198	−	0.0600098i	$-0.980887\pi$
$269$		−	529.518i		−	0.120020i	0.998198	−	0.0600098i	$-0.0191132\pi$
$270$	592.290	−	3009.29i	0.133502	−	0.678294i
$271$	3044.79			0.682502			0.341251	−	0.939972i	$-0.389149\pi$
$271$	3044.79			0.682502			0.341251	+	0.939972i	$0.389149\pi$
$272$	−2690.38	+	2734.05i	−0.599736	+	0.609472i
$273$	−798.301			−0.176979
$274$	1238.33	+	243.728i	0.273029	+	0.0537378i
$275$	−412.169			−0.0903809
$276$	10869.9	+	4451.28i	2.37062	+	0.970782i
$277$			961.729i			0.208609i	0.994545	+	0.104304i	$0.0332616\pi$
$277$			961.729i			0.208609i	−0.994545	+	0.104304i	$0.966738\pi$
$278$	408.961	−	2077.84i	0.0882297	−	0.448275i
$279$	1617.80	+	5950.85i	0.347150	+	1.27695i
$280$	−2694.86	−	1777.20i	−0.575173	−	0.379315i
$281$	−235.260			−0.0499445			−0.0249723	−	0.999688i	$-0.507950\pi$
$281$	−235.260			−0.0499445			−0.0249723	+	0.999688i	$0.507950\pi$
$282$	−2443.61	−	480.953i	−0.516010	−	0.101561i
$283$		−	1645.92i		−	0.345724i	−0.984946	−	0.172862i	$-0.944699\pi$
$283$		−	1645.92i		−	0.345724i	0.984946	−	0.172862i	$-0.0553015\pi$
$284$	−509.430	+	1244.02i	−0.106441	+	0.259925i
$285$		−	12082.4i		−	2.51124i
$286$	104.747	+	20.6165i	0.0216568	+	0.00426251i
$287$		−	1184.35i		−	0.243589i
$288$	−5341.20	+	3647.16i	−1.09282	+	0.746219i
$289$	1320.92			0.268862
$290$	9426.25	+	1855.28i	1.90872	+	0.375675i
$291$	−2722.63			−0.548465
$292$	−3154.03	+	7702.05i	−0.632108	+	1.54359i
$293$	−3310.11			−0.659996			−0.329998	−	0.943982i	$-0.607048\pi$
$293$	−3310.11			−0.659996			−0.329998	+	0.943982i	$0.607048\pi$
$294$	1125.94	−	5720.66i	0.223355	−	1.13482i
$295$			5832.97i			1.15122i
$296$	848.707	+	559.704i	0.166656	+	0.109906i
$297$	235.479			0.0460063
$298$	1013.55	−	5149.61i	0.197025	−	1.00104i
$299$			2054.29i			0.397334i
$300$	7095.44	+	2905.62i	1.36552	+	0.559186i
$301$		−	3604.63i		−	0.690257i
$302$	300.737	−	1527.98i	0.0573030	−	0.291143i
$303$	−3902.80			−0.739967
$304$	−4366.01	+	4436.89i	−0.823710	+	0.837082i
$305$			11261.8i			2.11425i
$306$	−5942.72	−	1169.65i	−1.11020	−	0.218511i
$307$		−	466.223i		−	0.0866735i	−0.999061	−	0.0433368i	$-0.986201\pi$
$307$		−	466.223i		−	0.0866735i	0.999061	−	0.0433368i	$-0.0137988\pi$
$308$	93.9243	−	229.361i	0.0173761	−	0.0424319i
$309$			11754.6i			2.16406i
$310$	−7637.74	+	544.017i	−1.39934	+	0.0996712i
$311$			3415.40i			0.622732i	0.950290	+	0.311366i	$0.100786\pi$
$311$			3415.40i			0.622732i	−0.950290	+	0.311366i	$0.899214\pi$
$312$	−1657.87	−	1093.33i	−0.300829	−	0.198390i
$313$			5068.77i			0.915348i	0.889120	+	0.457674i	$0.151317\pi$
$313$			5068.77i			0.915348i	−0.889120	+	0.457674i	$0.848683\pi$
$314$	−1551.66	+	7883.60i	−0.278869	+	1.41687i
$315$		−	5097.23i		−	0.911734i
$316$	4900.21	+	2006.66i	0.872337	+	0.357227i
$317$	−4064.80			−0.720196			−0.360098	−	0.932915i	$-0.617257\pi$
$317$	−4064.80			−0.720196			−0.360098	+	0.932915i	$0.617257\pi$
$318$	16060.7	+	3161.08i	2.83220	+	0.557436i
$319$			737.611i			0.129462i
$320$	−3162.54	−	7381.62i	−0.552473	−	1.28952i
$321$		−	7884.97i		−	1.37102i
$322$	4679.47	+	921.016i	0.809865	+	0.159398i
$323$	−5829.32			−1.00419
$324$	3088.09	+	1264.59i	0.529509	+	0.216836i
$325$			1340.96i			0.228871i
$326$	2904.97	+	571.759i	0.493532	+	0.0971374i
$327$	5166.53			0.873731
$328$	1622.06	−	2459.60i	0.273058	−	0.414051i
$329$	−1011.21			−0.169453
$330$	−231.115	+	1174.24i	−0.0385530	+	0.195879i
$331$	−11087.6			−1.84117			−0.920587	−	0.390538i	$-0.872289\pi$
$331$	−11087.6			−1.84117			−0.920587	+	0.390538i	$0.872289\pi$
$332$	−1073.22	−	439.488i	−0.177411	−	0.0726508i
$333$			1605.30i			0.264173i
$334$	−324.181	+	1647.09i	−0.0531090	+	0.269835i
$335$		−	10554.7i		−	1.72139i
$336$	−3233.79	+	3286.29i	−0.525052	+	0.533576i
$337$		−	8108.58i		−	1.31069i	−0.755330	−	0.655345i	$-0.772523\pi$
$337$		−	8108.58i		−	1.31069i	0.755330	−	0.655345i	$-0.227477\pi$
$338$	−1132.96	+	5756.29i	−0.182322	+	0.926335i
$339$	−10044.8			−1.60932
$340$	2849.93	−	6959.44i	0.454585	−	1.11008i
$341$	−154.227	−	567.303i	−0.0244922	−	0.0900914i
$342$	−9644.00	−	1898.14i	−1.52482	−	0.300116i
$343$		−	5487.16i		−	0.863787i
$344$	4936.81	−	7485.92i	0.773764	−	1.17330i
$345$	−23029.1			−3.59375
$346$	1926.75	−	9789.38i	0.299372	−	1.52104i
$347$	6608.18			1.02232			0.511161	−	0.859485i	$-0.329216\pi$
$347$	6608.18			1.02232			0.511161	+	0.859485i	$0.329216\pi$
$348$	5199.84	−	12697.9i	0.800978	−	1.95597i
$349$	10460.9			1.60447			0.802237	−	0.597005i	$-0.203643\pi$
$349$	10460.9			1.60447			0.802237	+	0.597005i	$0.203643\pi$
$350$	3054.56	+	601.202i	0.466495	+	0.0918159i
$351$		−	766.110i		−	0.116501i
$352$	509.184	−	347.689i	0.0771012	−	0.0526474i
$353$		−	5197.14i		−	0.783614i	−0.920047	−	0.391807i	$-0.871850\pi$
$353$		−	5197.14i		−	0.783614i	0.920047	−	0.391807i	$-0.128150\pi$
$354$	8174.09	+	1608.83i	1.22725	+	0.241549i
$355$		−	2635.58i		−	0.394034i
$356$	−2226.44	+	5436.90i	−0.331463	+	0.809424i
$357$	−4317.62			−0.640092
$358$	1918.80	−	9748.96i	0.283273	−	1.43924i
$359$			3893.82i			0.572446i	0.958163	+	0.286223i	$0.0923998\pi$
$359$			3893.82i			0.572446i	−0.958163	+	0.286223i	$0.907600\pi$
$360$	6981.03	−	10585.7i	1.02203	−	1.54976i
$361$	−2600.97			−0.379206
$362$	−11711.4	−	2305.05i	−1.70038	−	0.334671i
$363$	10449.8			1.51095
$364$	−746.205	−	305.575i	−0.107450	−	0.0440013i
$365$		−	16317.6i		−	2.34001i
$366$	15781.8	+	3106.19i	2.25390	+	0.443615i
$367$	4339.68			0.617246			0.308623	−	0.951184i	$-0.400132\pi$
$367$	4339.68			0.617246			0.308623	+	0.951184i	$0.400132\pi$
$368$	8456.69	+	8321.60i	1.19792	+	1.17879i
$369$	4652.25			0.656331
$370$	−1955.70	−	384.923i	−0.274790	−	0.0540843i
$371$	6646.25			0.930070
$372$	−1344.25	+	10853.3i	−0.187355	+	1.51268i
$373$	−11464.0			−1.59137			−0.795686	−	0.605709i	$-0.792890\pi$
$373$	−11464.0			−1.59137			−0.795686	+	0.605709i	$0.792890\pi$
$374$	566.528	+	111.504i	0.0783274	+	0.0154165i
$375$	495.710			0.0682622
$376$	−2100.04	−	1384.93i	−0.288036	−	0.189953i
$377$	2399.75			0.327834
$378$	−1745.12	−	343.476i	−0.237458	−	0.0467367i
$379$		−	12965.6i		−	1.75724i	−0.477517	−	0.878622i	$-0.658463\pi$
$379$		−	12965.6i		−	1.75724i	0.477517	−	0.878622i	$-0.341537\pi$
$380$	4624.93	−	11294.0i	0.624353	−	1.52465i
$381$	−14769.9			−1.98605
$382$	5505.87	+	1083.67i	0.737448	+	0.145145i
$383$	2262.11			0.301797			0.150899	−	0.988549i	$-0.451783\pi$
$383$	2262.11			0.301797			0.150899	+	0.988549i	$0.451783\pi$
$384$	−11216.6	+	2395.89i	−1.49061	+	0.318397i
$385$			485.925i			0.0643248i
$386$	−1049.67	+	5333.11i	−0.138411	+	0.703233i
$387$	14159.4			1.85985
$388$	−2544.95	−	1042.17i	−0.332991	−	0.136361i
$389$			8250.98i			1.07543i	0.843127	+	0.537714i	$0.180712\pi$
$389$			8250.98i			1.07543i	−0.843127	+	0.537714i	$0.819288\pi$
$390$	3820.30	+	751.914i	0.496021	+	0.0976273i
$391$			11110.7i			1.43706i
$392$	3242.23	−	4916.35i	0.417748	−	0.633452i
$393$		−	13550.3i		−	1.73925i
$394$	3248.93	+	639.457i	0.415428	+	0.0817649i
$395$	−10381.6			−1.32242
$396$	900.952	+	368.944i	0.114330	+	0.0468186i
$397$	7980.19			1.00885			0.504426	−	0.863455i	$-0.331704\pi$
$397$	7980.19			1.00885			0.504426	+	0.863455i	$0.331704\pi$
$398$	1468.13	−	7459.23i	0.184901	−	0.939440i
$399$	−7006.75			−0.879138
$400$	5520.18	+	5432.00i	0.690023	+	0.679000i
$401$			7656.85i			0.953529i	0.879031	+	0.476764i	$0.158190\pi$
$401$			7656.85i			0.953529i	−0.879031	+	0.476764i	$0.841810\pi$
$402$	−14790.9	−	2911.16i	−1.83509	−	0.361183i
$403$	−1845.67	+	501.763i	−0.228138	+	0.0620214i
$404$	−3648.11	−	1493.92i	−0.449258	−	0.183973i
$405$	−6542.46			−0.802710
$406$	1075.90	−	5466.39i	0.131517	−	0.668208i
$407$		−	153.035i		−	0.0186380i
$408$	−8966.63	−	5913.31i	−1.08803	−	0.717530i
$409$			5613.64i			0.678672i	0.940665	+	0.339336i	$0.110202\pi$
$409$			5613.64i			0.678672i	−0.940665	+	0.339336i	$0.889798\pi$
$410$	−1115.53	+	5667.75i	−0.134371	+	0.682707i
$411$			3534.08i			0.424145i
$412$	−4499.44	+	10987.5i	−0.538037	+	1.31387i
$413$	3382.61			0.403020
$414$	−3617.84	+	18381.4i	−0.429486	+	2.18212i
$415$	2273.73			0.268947
$416$	−1131.18	−	1656.59i	−0.133318	−	0.195242i
$417$	5929.98			0.696385
$418$	919.375	+	180.952i	0.107579	+	0.0211738i
$419$			10283.5i			1.19900i	0.800374	+	0.599500i	$0.204634\pi$
$419$			10283.5i			1.19900i	−0.800374	+	0.599500i	$0.795366\pi$
$420$	3425.56	−	8365.14i	0.397977	−	0.971850i
$421$	15237.5			1.76397			0.881984	−	0.471280i	$-0.156208\pi$
$421$	15237.5			1.76397			0.881984	+	0.471280i	$0.156208\pi$
$422$	−7806.74	−	1536.53i	−0.900536	−	0.177244i
$423$		−	3972.15i		−	0.456578i
$424$	13802.6	+	9102.54i	1.58093	+	1.04259i
$425$			7252.59i			0.827770i
$426$	−3693.40	−	726.937i	−0.420060	−	0.0826766i
$427$	6530.83			0.740162
$428$	3018.22	−	7370.41i	0.340867	−	0.832388i
$429$			298.941i			0.0336434i
$430$	−3395.17	+	17250.1i	−0.380767	+	1.93459i
$431$		−	8770.35i		−	0.980169i	−0.871675	−	0.490085i	$-0.836966\pi$
$431$		−	8770.35i		−	0.980169i	0.871675	−	0.490085i	$-0.163034\pi$
$432$	−3153.77	−	3103.39i	−0.351240	−	0.345629i
$433$			10178.1i			1.12963i	0.825218	+	0.564814i	$0.191052\pi$
$433$			10178.1i			1.12963i	−0.825218	+	0.564814i	$0.808948\pi$
$434$	315.482	+	4429.21i	0.0348931	+	0.489882i
$435$			26901.8i			2.96515i
$436$	4829.37	+	1977.65i	0.530470	+	0.217230i
$437$			18030.7i			1.97374i
$438$	−22866.9	−	4500.67i	−2.49457	−	0.490983i
$439$		−	7362.52i		−	0.800442i	−0.916419	−	0.400221i	$-0.868933\pi$
$439$		−	7362.52i		−	0.800442i	0.916419	−	0.400221i	$-0.131067\pi$
$440$	−665.511	+	1009.15i	−0.0721068	+	0.109339i
$441$	9299.09			1.00411
$442$	362.770	−	1843.15i	0.0390389	−	0.198348i
$443$		−	7483.34i		−	0.802583i	−0.915950	−	0.401291i	$-0.868561\pi$
$443$		−	7483.34i		−	0.802583i	0.915950	−	0.401291i	$-0.131439\pi$
$444$	−1078.83	+	2634.48i	−0.115313	+	0.281592i
$445$		−	11518.7i		−	1.22705i
$446$	488.319	−	2481.04i	0.0518444	−	0.263409i
$447$	14696.6			1.55509
$448$	−4280.68	+	1833.99i	−0.451436	+	0.193411i
$449$		−	9018.44i		−	0.947898i	−0.880552	−	0.473949i	$-0.842828\pi$
$449$		−	9018.44i		−	0.947898i	0.880552	−	0.473949i	$-0.157172\pi$
$450$	−2361.58	+	11998.6i	−0.247391	+	1.25694i
$451$	−443.505			−0.0463056
$452$	−9389.28	−	3844.96i	−0.977068	−	0.400114i
$453$	4360.73			0.452284
$454$	−1559.51	−	306.943i	−0.161214	−	0.0317303i
$455$	1580.92			0.162889
$456$	−14551.3	−	9596.27i	−1.49436	−	0.985496i
$457$			4148.67i			0.424654i	0.977199	+	0.212327i	$0.0681041\pi$
$457$			4148.67i			0.424654i	−0.977199	+	0.212327i	$0.931896\pi$
$458$	16370.4	+	3222.02i	1.67017	+	0.328723i
$459$		−	4143.52i		−	0.421357i
$460$	−21526.2	−	8815.10i	−2.18188	−	0.893492i
$461$		−	14426.8i		−	1.45753i	−0.684764	−	0.728765i	$-0.740095\pi$
$461$		−	14426.8i		−	1.45753i	0.684764	−	0.728765i	$-0.259905\pi$
$462$	680.957	+	134.026i	0.0685735	+	0.0134967i
$463$	4812.32			0.483040			0.241520	−	0.970396i	$-0.422354\pi$
$463$	4812.32			0.483040			0.241520	+	0.970396i	$0.422354\pi$
$464$	9721.00	−	9878.81i	0.972600	−	0.988389i
$465$	−5624.88	−	20690.4i	−0.560963	−	2.06343i
$466$	−1334.91	+	6782.36i	−0.132701	+	0.674221i
$467$			10323.9i			1.02298i	0.859288	+	0.511492i	$0.170907\pi$
$467$			10323.9i			1.02298i	−0.859288	+	0.511492i	$0.829093\pi$
$468$	1200.33	−	2931.17i	0.118558	−	0.289516i
$469$	−6120.79			−0.602627
$470$	4839.20	+	952.455i	0.474927	+	0.0934755i
$471$	−22499.2			−2.20108
$472$	7024.83	+	4632.73i	0.685051	+	0.451777i
$473$	−1349.83			−0.131216
$474$	−2863.43	+	14548.4i	−0.277472	+	1.40977i
$475$			11769.7i			1.13691i
$476$	−4035.86	−	1652.70i	−0.388620	−	0.159142i
$477$			26107.1i			2.50600i
$478$	2419.75	−	12294.2i	0.231542	−	1.17641i
$479$		−	15679.8i		−	1.49568i	−0.663880	−	0.747839i	$-0.731091\pi$
$479$		−	15679.8i		−	1.49568i	0.663880	−	0.747839i	$-0.268909\pi$
$480$	18570.7	−	12680.7i	1.76590	−	1.20582i
$481$	−497.887			−0.0471969
$482$	−4685.08	−	922.121i	−0.442738	−	0.0871399i
$483$			13354.8i			1.25811i
$484$	9767.90	+	4000.01i	0.917346	+	0.375658i
$485$	5391.76			0.504798
$486$	−2824.10	+	14348.6i	−0.263588	+	1.33923i
$487$	−16232.3			−1.51038			−0.755189	−	0.655507i	$-0.772455\pi$
$487$	−16232.3			−1.51038			−0.755189	+	0.655507i	$0.772455\pi$
$488$	13562.9	+	8944.46i	1.25812	+	0.829707i
$489$			8290.56i			0.766692i
$490$	−2229.76	+	11328.9i	−0.205572	+	1.04447i
$491$	−14068.5			−1.29308			−0.646542	−	0.762879i	$-0.723785\pi$
$491$	−14068.5			−1.29308			−0.646542	+	0.762879i	$0.723785\pi$
$492$	7634.87	+	3126.52i	0.699607	+	0.286493i
$493$	12979.1			1.18570
$494$	588.712	−	2991.11i	0.0536182	−	0.272422i
$495$	−1908.76			−0.173318
$496$	−5410.96	+	9630.45i	−0.489837	+	0.871814i
$497$	−1528.40			−0.137944
$498$	627.133	−	3186.31i	0.0564307	−	0.286711i
$499$	−10442.8			−0.936842			−0.468421	−	0.883505i	$-0.655177\pi$
$499$	−10442.8			−0.936842			−0.468421	+	0.883505i	$0.655177\pi$
$500$	463.360	+	189.748i	0.0414442	+	0.0169716i
$501$	−4700.67			−0.419182
$502$	−1612.93	+	8194.90i	−0.143403	+	0.728598i
$503$		−	772.411i		−	0.0684694i	−0.999414	−	0.0342347i	$-0.989101\pi$
$503$		−	772.411i		−	0.0684694i	0.999414	−	0.0342347i	$-0.0108994\pi$
$504$	−6138.75	−	4048.38i	−0.542543	−	0.357796i
$505$	7728.91			0.681054
$506$	344.894	−	1752.32i	0.0303012	−	0.153953i
$507$	−16428.0			−1.43904
$508$	−13806.0	−	5653.63i	−1.20579	−	0.493778i
$509$		−	16424.2i		−	1.43024i	−0.699004	−	0.715118i	$-0.746373\pi$
$509$		−	16424.2i		−	1.43024i	0.699004	−	0.715118i	$-0.253627\pi$
$510$	20662.1	+	4066.73i	1.79399	+	0.353094i
$511$	−9462.77			−0.819195
$512$	−11401.7	−	2053.97i	−0.984158	−	0.177292i
$513$		−	6724.20i		−	0.578715i
$514$	3135.49	−	15930.7i	0.269067	−	1.36707i
$515$		−	23278.2i		−	1.99177i
$516$	23237.1	+	9515.72i	1.98248	+	0.811834i
$517$			378.671i			0.0322126i
$518$	−223.221	+	1134.14i	−0.0189339	+	0.0961989i
$519$	27938.1			2.36290
$520$	3283.17	+	2165.18i	0.276878	+	0.182595i
$521$	−17230.3			−1.44889			−0.724447	−	0.689331i	$-0.757905\pi$
$521$	−17230.3			−1.44889			−0.724447	+	0.689331i	$0.757905\pi$
$522$	21472.5	+	4226.24i	1.80044	+	0.354363i
$523$	13444.1			1.12403			0.562015	−	0.827127i	$-0.310026\pi$
$523$	13444.1			1.12403			0.562015	+	0.827127i	$0.310026\pi$
$524$	5186.81	−	12666.0i	0.432418	−	1.05595i
$525$			8717.49i			0.724690i
$526$	3333.90	−	16938.8i	0.276360	−	1.40412i
$527$	−9982.34	+	2713.79i	−0.825118	+	0.224316i
$528$	1230.62	+	1210.96i	0.101431	+	0.0998112i
$529$	22199.4			1.82455
$530$	−31805.9	−	6260.05i	−2.60671	−	0.513055i
$531$			13287.2i			1.08591i
$532$	−6549.50	−	2682.05i	−0.533753	−	0.218575i
$533$			1442.91i			0.117259i
$534$	−16141.8	−	3177.04i	−1.30810	−	0.257461i
$535$			15615.0i			1.26186i
$536$	−12711.4	−	8382.88i	−1.02434	−	0.675532i
$537$	27822.8			2.23583
$538$	1469.51	+	289.230i	0.117760	+	0.0231777i
$539$	−886.495			−0.0708424
$540$	8027.81	+	3287.43i	0.639745	+	0.261979i
$541$	3787.71			0.301010			0.150505	−	0.988609i	$-0.451910\pi$
$541$	3787.71			0.301010			0.150505	+	0.988609i	$0.451910\pi$
$542$	−1663.11	+	8449.86i	−0.131802	+	0.669654i
$543$		−	33423.5i		−	2.64151i
$544$	−6117.98	−	8959.67i	−0.482180	−	0.706145i
$545$	−10231.5			−0.804168
$546$	436.043	−	2215.43i	0.0341775	−	0.173648i
$547$		−	16909.4i		−	1.32175i	−0.750498	−	0.660873i	$-0.770186\pi$
$547$		−	16909.4i		−	1.32175i	0.750498	−	0.660873i	$-0.229814\pi$
$548$	−1352.78	+	3303.45i	−0.105452	+	0.257512i
$549$			25653.8i			1.99431i
$550$	225.133	−	1143.85i	0.0174540	−	0.0886796i
$551$	21062.8			1.62850
$552$	−18290.4	+	27734.7i	−1.41031	+	2.13853i
$553$			6020.43i			0.462956i
$554$	−2668.97	−	525.309i	−0.204682	−	0.0402857i
$555$		−	5581.43i		−	0.426880i
$556$	5543.00	+	2269.89i	0.422798	+	0.173138i
$557$		−	4461.53i		−	0.339392i	−0.985496	−	0.169696i	$-0.945721\pi$
$557$		−	4461.53i		−	0.339392i	0.985496	−	0.169696i	$-0.0542785\pi$
$558$	−17398.4	+	1239.24i	−1.31995	+	0.0940168i
$559$			4391.56i			0.332277i
$560$	6404.03	−	6508.00i	0.483250	−	0.491095i
$561$			1616.83i			0.121680i
$562$	128.502	−	652.889i	0.00964508	−	0.0490044i
$563$			17092.9i			1.27954i	0.768567	+	0.639769i	$0.220970\pi$
$563$			17092.9i			1.27954i	−0.768567	+	0.639769i	$0.779030\pi$
$564$	2669.47	−	6518.76i	0.199299	−	0.486683i
$565$	19892.2			1.48119
$566$	4567.74	+	899.025i	0.339216	+	0.0667648i
$567$			3794.05i			0.281014i
$568$	−3174.11	−	2093.26i	−0.234477	−	0.154633i
$569$		−	16090.4i		−	1.18549i	−0.805389	−	0.592746i	$-0.798044\pi$
$569$		−	16090.4i		−	1.18549i	0.805389	−	0.592746i	$-0.201956\pi$
$570$	33531.0	+	6599.60i	2.46397	+	0.484959i
$571$	6253.47			0.458318			0.229159	−	0.973389i	$-0.426402\pi$
$571$	6253.47			0.458318			0.229159	+	0.973389i	$0.426402\pi$
$572$	−114.429	+	279.432i	−0.00836454	+	0.0204260i
$573$			15713.3i			1.14561i
$574$	3286.79	+	646.908i	0.239003	+	0.0470408i
$575$	22433.0			1.62699
$576$	−7204.11	−	16815.0i	−0.521131	−	1.21636i
$577$	12660.8			0.913475			0.456737	−	0.889602i	$-0.349018\pi$
$577$	12660.8			0.913475			0.456737	+	0.889602i	$0.349018\pi$
$578$	−721.504	+	3665.79i	−0.0519214	+	0.263801i
$579$	−15220.3			−1.09246
$580$	−10297.5	+	25146.2i	−0.737207	+	1.80024i
$581$		−	1318.56i		−	0.0941534i
$582$	1487.14	−	7555.80i	0.105917	−	0.538141i
$583$		−	2488.83i		−	0.176804i
$584$	−19651.8	−	12960.0i	−1.39246	−	0.918301i
$585$			6210.00i			0.438892i
$586$	1808.03	−	9186.17i	0.127456	−	0.647572i
$587$	6740.11			0.473925			0.236963	−	0.971519i	$-0.423848\pi$
$587$	6740.11			0.473925			0.236963	+	0.971519i	$0.423848\pi$
$588$	15260.9	+	6249.41i	1.07032	+	0.438301i
$589$	−16199.6	+	4404.01i	−1.13326	+	0.308089i
$590$	−16187.6	−	3186.05i	−1.12955	−	0.222318i
$591$			9272.19i			0.645359i
$592$	−2016.86	+	2049.60i	−0.140021	+	0.142294i
$593$	−4514.18			−0.312605			−0.156303	−	0.987709i	$-0.549958\pi$
$593$	−4514.18			−0.312605			−0.156303	+	0.987709i	$0.549958\pi$
$594$	−128.622	+	653.497i	−0.00888454	+	0.0451403i
$595$	8550.41			0.589130
$596$	13737.5	+	5625.58i	0.944145	+	0.386632i
$597$	21288.0			1.45940
$598$	−5701.04	−	1122.08i	−0.389854	−	0.0767314i
$599$		−	19569.2i		−	1.33485i	−0.744678	−	0.667424i	$-0.767397\pi$
$599$		−	19569.2i		−	1.33485i	0.744678	−	0.667424i	$-0.232603\pi$
$600$	−11939.3	+	18104.1i	−0.812363	+	1.23183i
$601$		−	11489.6i		−	0.779815i	−0.920854	−	0.389908i	$-0.872507\pi$
$601$		−	11489.6i		−	0.779815i	0.920854	−	0.389908i	$-0.127493\pi$
$602$	10003.5	+	1968.90i	0.677264	+	0.133300i
$603$		−	24043.1i		−	1.62373i
$604$	4076.15	+	1669.20i	0.274596	+	0.112449i
$605$	−20694.4			−1.39065
$606$	2131.76	−	10831.0i	0.142899	−	0.726038i
$607$			7295.75i			0.487851i	0.969794	+	0.243926i	$0.0784352\pi$
$607$			7295.75i			0.487851i	−0.969794	+	0.243926i	$0.921565\pi$
$608$	−9928.41	−	14540.0i	−0.662254	−	0.969859i
$609$	15600.7			1.03805
$610$	−31253.5	−	6151.34i	−2.07446	−	0.408296i
$611$	1231.97			0.0815716
$612$	6491.99	−	15853.3i	0.428796	−	1.04711i
$613$		−	5217.80i		−	0.343793i	−0.985115	−	0.171896i	$-0.945011\pi$
$613$		−	5217.80i		−	0.343793i	0.985115	−	0.171896i	$-0.0549894\pi$
$614$	1293.86	+	254.658i	0.0850420	+	0.0167380i
$615$	−16175.3			−1.06057
$616$	585.216	+	385.937i	0.0382776	+	0.0252433i
$617$	−7283.67			−0.475251			−0.237625	−	0.971357i	$-0.576369\pi$
$617$	−7283.67			−0.475251			−0.237625	+	0.971357i	$0.576369\pi$
$618$	−32621.2	−	6420.52i	−2.12333	−	0.417914i
$619$	20209.6			1.31227			0.656133	−	0.754645i	$-0.272191\pi$
$619$	20209.6			1.31227			0.656133	+	0.754645i	$0.272191\pi$
$620$	2662.09	−	21493.3i	0.172439	−	1.39224i
$621$	−12816.3			−0.828181
$622$	−9478.37	−	1865.54i	−0.611009	−	0.120259i
$623$	−6679.80			−0.429567
$624$	3939.76	−	4003.71i	0.252751	−	0.256854i
$625$	−16107.9			−1.03090
$626$	−14066.8	−	2768.63i	−0.898118	−	0.176768i
$627$			2623.83i			0.167122i
$628$	−21030.9	−	8612.26i	−1.33634	−	0.547240i
$629$	−2692.83			−0.170700
$630$	14145.7	+	2784.17i	0.894571	+	0.176070i
$631$	13241.4			0.835394			0.417697	−	0.908586i	$-0.362837\pi$
$631$	13241.4			0.835394			0.417697	+	0.908586i	$0.362837\pi$
$632$	−8245.42	+	12502.9i	−0.518964	+	0.786930i
$633$		−	22279.8i		−	1.39896i
$634$	2220.25	−	11280.6i	0.139081	−	0.706639i
$635$	29249.5			1.82792
$636$	−17545.2	+	42844.8i	−1.09389	+	2.67124i
$637$			2884.14i			0.179393i
$638$	−2047.01	−	402.893i	−0.127025	−	0.0250011i
$639$		−	6003.72i		−	0.371680i
$640$	22212.8	−	4744.69i	1.37193	−	0.293048i
$641$			3898.84i			0.240242i	0.992759	+	0.120121i	$0.0383282\pi$
$641$			3898.84i			0.240242i	−0.992759	+	0.120121i	$0.961672\pi$
$642$	21882.3	+	4306.88i	1.34521	+	0.264765i
$643$	−9634.65			−0.590908			−0.295454	−	0.955357i	$-0.595471\pi$
$643$	−9634.65			−0.590908			−0.295454	+	0.955357i	$0.595471\pi$
$644$	−5111.98	+	12483.3i	−0.312795	+	0.763837i
$645$	−49230.4			−3.00534
$646$	3184.06	−	16177.4i	0.193924	−	0.985284i
$647$	−11404.3			−0.692968			−0.346484	−	0.938056i	$-0.612625\pi$
$647$	−11404.3			−0.692968			−0.346484	+	0.938056i	$0.612625\pi$
$648$	−5196.23	+	7879.30i	−0.315011	+	0.477667i
$649$		−	1266.69i		−	0.0766130i
$650$	−3721.41	−	732.450i	−0.224562	−	0.0441985i
$651$	−11998.6	+	3261.93i	−0.722369	+	0.196383i
$652$	−3173.47	+	7749.53i	−0.190618	+	0.465483i
$653$	2264.94			0.135734			0.0678668	−	0.997694i	$-0.478381\pi$
$653$	2264.94			0.135734			0.0678668	+	0.997694i	$0.478381\pi$
$654$	−2822.03	+	14338.1i	−0.168731	+	0.857284i
$655$			26834.4i			1.60077i
$656$	5939.86	+	5844.97i	0.353525	+	0.347878i
$657$		−	37170.7i		−	2.20726i
$658$	552.339	−	2806.31i	0.0327241	−	0.166263i
$659$			22065.6i			1.30433i	0.758076	+	0.652166i	$0.226139\pi$
$659$			22065.6i			1.30433i	−0.758076	+	0.652166i	$0.773861\pi$
$660$	−3132.50	−	1282.78i	−0.184746	−	0.0756545i
$661$	−14896.3			−0.876547			−0.438274	−	0.898842i	$-0.644410\pi$
$661$	−14896.3			−0.876547			−0.438274	+	0.898842i	$0.644410\pi$
$662$	6056.19	−	30770.1i	0.355560	−	1.80652i
$663$	5260.20			0.308129
$664$	1805.87	−	2738.32i	0.105544	−	0.160042i
$665$	13875.8			0.809145
$666$	−4455.00	−	876.836i	−0.259201	−	0.0510161i
$667$		−	40145.6i		−	2.33050i
$668$	−4393.91	−	1799.33i	−0.254499	−	0.104219i
$669$	7080.69			0.409200
$670$	29291.3	+	5765.13i	1.68899	+	0.332427i
$671$		−	2445.61i		−	0.140703i
$672$	−7353.71	−	10769.4i	−0.422136	−	0.618211i
$673$		−	16623.9i		−	0.952159i	−0.879402	−	0.476079i	$-0.842057\pi$
$673$		−	16623.9i		−	0.952159i	0.879402	−	0.476079i	$-0.157943\pi$
$674$	22502.8	+	4429.02i	1.28602	+	0.253115i
$675$	−8365.96			−0.477046
$676$	−15355.9	−	6288.34i	−0.873688	−	0.357780i
$677$			19148.5i			1.08705i	0.839392	+	0.543527i	$0.182911\pi$
$677$			19148.5i			1.08705i	−0.839392	+	0.543527i	$0.817089\pi$
$678$	5486.60	−	27876.1i	0.310784	−	1.57902i
$679$		−	3126.74i		−	0.176721i
$680$	17757.1	+	11710.4i	1.00140	+	0.660403i
$681$		−	4450.71i		−	0.250443i
$682$	1658.61	−	118.139i	0.0931254	−	0.00663309i
$683$		−	12166.0i		−	0.681579i	−0.940140	−	0.340789i	$-0.889306\pi$
$683$		−	12166.0i		−	0.681579i	0.940140	−	0.340789i	$-0.110694\pi$
$684$	10535.4	−	25727.1i	0.588933	−	1.43816i
$685$		−	6998.73i		−	0.390376i
$686$	15227.9	+	2997.16i	0.847527	+	0.166811i
$687$			46719.7i			2.59457i
$688$	18078.3	+	17789.5i	1.00178	+	0.985781i
$689$	−8097.19			−0.447719
$690$	12578.8	−	63910.0i	0.694010	−	3.52610i
$691$			2767.65i			0.152368i	0.997094	+	0.0761841i	$0.0242737\pi$
$691$			2767.65i			0.152368i	−0.997094	+	0.0761841i	$0.975726\pi$
$692$	26114.9	+	10694.2i	1.43460	+	0.587474i
$693$			1106.91i			0.0606756i
$694$	−3609.48	+	18338.9i	−0.197426	+	1.00308i
$695$	−11743.4			−0.640941
$696$	32398.7	+	21366.3i	1.76447	+	1.16363i
$697$			7803.97i			0.424098i
$698$	−5713.91	+	29031.1i	−0.309849	+	1.57427i
$699$	−19356.3			−1.04739
$700$	−3336.89	+	8148.60i	−0.180175	+	0.439983i
$701$	−18030.7			−0.971483			−0.485741	−	0.874103i	$-0.661450\pi$
$701$	−18030.7			−0.971483			−0.485741	+	0.874103i	$0.661450\pi$
$702$	2126.10	+	418.460i	0.114308	+	0.0224982i
$703$	−4369.99			−0.234448
$704$	686.778	+	1602.99i	0.0367669	+	0.0858168i
$705$			13810.7i			0.737789i
$706$	14423.0	+	2838.75i	0.768864	+	0.151328i
$707$		−	4482.08i		−	0.238425i
$708$	−8929.61	+	21805.9i	−0.474004	+	1.15751i
$709$			13388.0i			0.709165i	0.935025	+	0.354583i	$0.115377\pi$
$709$			13388.0i			0.709165i	−0.935025	+	0.354583i	$0.884623\pi$
$710$	7314.22	+	1439.59i	0.386617	+	0.0760942i
$711$	−23648.8			−1.24740
$712$	−13872.3	−	9148.48i	−0.730177	−	0.481536i
$713$	8394.02	+	30876.3i	0.440896	+	1.62178i
$714$	2358.35	−	11982.2i	0.123612	−	0.628043i
$715$		−	592.008i		−	0.0309648i
$716$	26007.1	+	10650.0i	1.35745	+	0.555881i
$717$	35086.7			1.82753
$718$	−10806.1	−	2126.86i	−0.561670	−	0.110548i
$719$	12176.6			0.631587			0.315793	−	0.948828i	$-0.397729\pi$
$719$	12176.6			0.631587			0.315793	+	0.948828i	$0.397729\pi$
$720$	25564.1	+	25155.7i	1.32322	+	1.30208i
$721$	−13499.3			−0.697281
$722$	1420.69	−	7218.18i	0.0732306	−	0.372068i
$723$		−	13370.9i		−	0.687783i
$724$	12793.9	−	31242.3i	0.656742	−	1.60375i
$725$		−	26205.4i		−	1.34241i
$726$	−5707.85	+	29000.3i	−0.291788	+	1.48251i
$727$		−	7445.60i		−	0.379838i	−0.981800	−	0.189919i	$-0.939178\pi$
$727$		−	7445.60i		−	0.379838i	0.981800	−	0.189919i	$-0.0608225\pi$
$728$	1255.61	−	1903.95i	0.0639233	−	0.0969300i
$729$	−29687.5			−1.50828
$730$	45284.4	+	8912.91i	2.29596	+	0.451893i
$731$			23751.8i			1.20177i
$732$	−17240.5	+	42100.8i	−0.870529	+	2.12581i
$733$	−15411.9			−0.776606			−0.388303	−	0.921532i	$-0.626939\pi$
$733$	−15411.9			−0.776606			−0.388303	+	0.921532i	$0.626939\pi$
$734$	−2370.39	+	12043.4i	−0.119200	+	0.605627i
$735$	−32331.8			−1.62255
$736$	−27713.1	+	18923.5i	−1.38793	+	0.947730i
$737$			2292.06i			0.114558i
$738$	−2541.12	+	12910.8i	−0.126748	+	0.643977i
$739$	5197.09			0.258698			0.129349	−	0.991599i	$-0.458711\pi$
$739$	5197.09			0.258698			0.129349	+	0.991599i	$0.458711\pi$
$740$	2136.47	−	5217.19i	0.106133	−	0.259173i
$741$	8536.39			0.423201
$742$	−3630.27	+	18444.6i	−0.179611	+	0.912563i
$743$	−9414.09			−0.464831			−0.232416	−	0.972617i	$-0.574663\pi$
$743$	−9414.09			−0.464831			−0.232416	+	0.972617i	$0.574663\pi$
$744$	−29385.6	−	9658.75i	−1.44802	−	0.475950i
$745$	−29104.4			−1.43128
$746$	6261.78	−	31814.6i	0.307319	−	1.56142i
$747$	5179.44			0.253689
$748$	−618.890	+	1511.31i	−0.0302525	+	0.0738758i
$749$	9055.32			0.441755
$750$	−270.763	+	1375.69i	−0.0131825	+	0.0669772i
$751$			31297.6i			1.52073i	0.649498	+	0.760364i	$0.274979\pi$
$751$			31297.6i			1.52073i	−0.649498	+	0.760364i	$0.725021\pi$
$752$	4990.52	−	5071.53i	0.242002	−	0.245931i
$753$	−23387.6			−1.13186
$754$	−1310.78	+	6659.76i	−0.0633100	+	0.321663i
$755$	−8635.77			−0.416275
$756$	1906.42	−	4655.42i	0.0917139	−	0.223963i
$757$			2399.59i			0.115211i	0.998339	+	0.0576054i	$0.0183465\pi$
$757$			2399.59i			0.115211i	−0.998339	+	0.0576054i	$0.981653\pi$
$758$	35981.8	+	7081.96i	1.72417	+	0.339352i
$759$	5001.00			0.239163
$760$	28816.6	+	19004.0i	1.37538	+	0.907035i
$761$			4533.32i			0.215943i	0.994154	+	0.107972i	$0.0344355\pi$
$761$			4533.32i			0.215943i	−0.994154	+	0.107972i	$0.965564\pi$
$762$	8067.51	−	40989.1i	0.383537	−	1.94866i
$763$			5933.39i			0.281524i
$764$	−6014.77	+	14687.9i	−0.284826	+	0.695536i
$765$			33586.9i			1.58737i
$766$	−1235.59	+	6277.76i	−0.0582818	+	0.296116i
$767$	−4121.06			−0.194006
$768$	−522.369	−	32436.8i	−0.0245434	−	1.52404i
$769$	18308.8			0.858557			0.429279	−	0.903172i	$-0.358768\pi$
$769$	18308.8			0.858557			0.429279	+	0.903172i	$0.358768\pi$
$770$	−1348.53	−	265.419i	−0.0631140	−	0.0124221i
$771$	45465.0			2.12371
$772$	−14227.0	−	5826.03i	−0.663266	−	0.271611i
$773$			6966.02i			0.324127i	0.986780	+	0.162064i	$0.0518149\pi$
$773$			6966.02i			0.324127i	−0.986780	+	0.162064i	$0.948185\pi$
$774$	−7734.03	+	39294.8i	−0.359165	+	1.82484i
$775$	5479.28	+	20154.8i	0.253963	+	0.934171i
$776$	4282.31	−	6493.47i	0.198100	−	0.300389i
$777$	−3236.73			−0.149443
$778$	−22898.0	−	4506.80i	−1.05518	−	0.207682i
$779$			12664.5i			0.582480i
$780$	−4173.40	+	10191.3i	−0.191579	+	0.467831i
$781$			572.343i			0.0262228i
$782$	−30834.1	−	6068.80i	−1.41001	−	0.277519i
$783$			14971.6i			0.683320i
$784$	11872.8	+	11683.2i	0.540854	+	0.532214i
$785$	44556.3			2.02584
$786$	37604.7	+	7401.38i	1.70651	+	0.335876i
$787$	−30860.5			−1.39779			−0.698893	−	0.715226i	$-0.746324\pi$
$787$	−30860.5			−1.39779			−0.698893	+	0.715226i	$0.746324\pi$
$788$	−3549.22	+	8667.10i	−0.160451	+	0.391818i
$789$	48342.0			2.18127
$790$	5670.59	−	28811.0i	0.255381	−	1.29753i
$791$		−	11535.7i		−	0.518537i
$792$	−1516.00	+	2298.79i	−0.0680161	+	0.103136i
$793$	−7956.58			−0.356301
$794$	−4358.89	+	22146.5i	−0.194825	+	0.989861i
$795$		−	90771.4i		−	4.04947i
$796$	19898.8	+	8148.66i	0.886049	+	0.362841i
$797$		−	27971.8i		−	1.24318i	−0.783343	−	0.621590i	$-0.786487\pi$
$797$		−	27971.8i		−	1.24318i	0.783343	−	0.621590i	$-0.213513\pi$
$798$	3827.18	−	19445.0i	0.169775	−	0.862589i
$799$	6663.14			0.295025
$800$	−18090.0	+	12352.5i	−0.799473	+	0.545908i
$801$		−	26238.9i		−	1.15744i
$802$	−21249.2	−	4182.28i	−0.935579	−	0.184141i
$803$			3543.54i			0.155727i
$804$	16158.0	−	39457.5i	0.708769	−	1.73079i
$805$		−	26447.2i		−	1.15794i
$806$	−384.354	−	5396.15i	−0.0167969	−	0.235820i
$807$			4193.87i			0.182938i
$808$	6138.55	−	9308.18i	0.267269	−	0.405273i
$809$		−	9283.77i		−	0.403461i	−0.979441	−	0.201730i	$-0.935344\pi$
$809$		−	9283.77i		−	0.403461i	0.979441	−	0.201730i	$-0.0646565\pi$
$810$	3573.58	−	18156.5i	0.155016	−	0.787600i
$811$		−	1439.69i		−	0.0623357i	−0.999514	−	0.0311678i	$-0.990077\pi$
$811$		−	1439.69i		−	0.0623357i	0.999514	−	0.0311678i	$-0.00992264\pi$
$812$	14582.6	+	5971.64i	0.630231	+	0.258083i
$813$	−24115.2			−1.04029
$814$	424.701	+	83.5899i	0.0182872	+	0.00359930i
$815$		−	16418.2i		−	0.705651i
$816$	21308.2	−	21654.1i	0.914138	−	0.928978i
$817$			38545.0i			1.65057i
$818$	−15578.9	−	3066.25i	−0.665897	−	0.131062i
$819$	3601.25			0.153648
$820$	−15119.7	−	6191.60i	−0.643907	−	0.263683i
$821$		−	24320.3i		−	1.03384i	−0.856033	−	0.516921i	$-0.827078\pi$
$821$		−	24320.3i		−	1.03384i	0.856033	−	0.516921i	$-0.172922\pi$
$822$	−9807.74	−	1930.37i	−0.416161	−	0.0819090i
$823$	9930.94			0.420621			0.210310	−	0.977635i	$-0.432553\pi$
$823$	9930.94			0.420621			0.210310	+	0.977635i	$0.432553\pi$
$824$	−28034.7	−	18488.3i	−1.18524	−	0.781638i
$825$	3264.45			0.137762
$826$	−1847.63	+	9387.35i	−0.0778294	+	0.395433i
$827$	−3723.92			−0.156582			−0.0782911	−	0.996931i	$-0.524946\pi$
$827$	−3723.92			−0.156582			−0.0782911	+	0.996931i	$0.524946\pi$
$828$	−49035.7	−	20080.4i	−2.05810	−	0.842803i
$829$		−	23115.5i		−	0.968436i	−0.874947	−	0.484218i	$-0.839104\pi$
$829$		−	23115.5i		−	0.968436i	0.874947	−	0.484218i	$-0.160896\pi$
$830$	−1241.94	+	6310.02i	−0.0519379	+	0.263884i
$831$		−	7617.05i		−	0.317969i
$832$	5215.20	−	2234.37i	0.217313	−	0.0931044i
$833$			15598.9i			0.648822i
$834$	−3239.04	+	16456.8i	−0.134483	+	0.683276i
$835$	9308.97			0.385809
$836$	−1004.35	+	2452.60i	−0.0415505	+	0.101465i
$837$	−3130.40	−	11514.8i	−0.129274	−	0.475518i
$838$	−28538.6	−	5616.98i	−1.17643	−	0.231546i
$839$			26982.8i			1.11031i	0.831747	+	0.555155i	$0.187341\pi$
$839$			26982.8i			1.11031i	−0.831747	+	0.555155i	$0.812659\pi$
$840$	21343.7	+	14075.7i	0.876700	+	0.578165i
$841$	−22507.7			−0.922863
$842$	−8322.93	+	42286.9i	−0.340650	+	1.73076i
$843$	1863.29			0.0761273
$844$	8528.30	−	20825.9i	0.347815	−	0.849355i
$845$	32533.2			1.32447
$846$	11023.5	+	2169.64i	0.447984	+	0.0881725i
$847$			12000.9i			0.486842i
$848$	−32800.4	+	33332.9i	−1.32827	+	1.34983i
$849$			13036.0i			0.526965i
$850$	−20127.3	−	3961.46i	−0.812188	−	0.159855i
$851$			8329.18i			0.335512i
$852$	4034.77	−	9852.80i	0.162241	−	0.396187i
$853$	−16714.3			−0.670910			−0.335455	−	0.942056i	$-0.608890\pi$
$853$	−16714.3			−0.670910			−0.335455	+	0.942056i	$0.608890\pi$
$854$	−3567.23	+	18124.3i	−0.142937	+	0.726229i
$855$			54505.6i			2.18018i
$856$	18805.7	+	12401.9i	0.750893	+	0.495198i
$857$	24112.6			0.961108			0.480554	−	0.876965i	$-0.340436\pi$
$857$	24112.6			0.961108			0.480554	+	0.876965i	$0.340436\pi$
$858$	−829.616	−	163.286i	−0.0330101	−	0.00649706i
$859$	33616.3			1.33524			0.667622	−	0.744500i	$-0.267312\pi$
$859$	33616.3			1.33524			0.667622	+	0.744500i	$0.267312\pi$
$860$	−46017.7	−	18844.5i	−1.82464	−	0.747199i
$861$			9380.24i			0.371287i
$862$	24339.3	+	4790.49i	0.961719	+	0.189286i
$863$	28581.0			1.12736			0.563678	−	0.825995i	$-0.309386\pi$
$863$	28581.0			1.12736			0.563678	+	0.825995i	$0.309386\pi$
$864$	10335.1	−	7057.17i	0.406953	−	0.277882i
$865$	−55327.3			−2.17478
$866$	−28246.1	−	5559.42i	−1.10836	−	0.218149i
$867$	−10461.9			−0.409809
$868$	−12464.2	−	1543.78i	−0.487399	−	0.0603677i
$869$	2254.48			0.0880068
$870$	−74657.4	−	14694.1i	−2.90934	−	0.572618i
$871$	7457.02			0.290094
$872$	−8126.22	+	12322.2i	−0.315583	+	0.478534i
$873$	12282.2			0.476160
$874$	−50038.4	−	9848.60i	−1.93658	−	0.381160i
$875$			569.286i			0.0219947i
$876$	24980.4	−	61001.5i	0.963481	−	2.35280i
$877$	−12048.2			−0.463900			−0.231950	−	0.972728i	$-0.574511\pi$
$877$	−12048.2			−0.463900			−0.231950	+	0.972728i	$0.574511\pi$
$878$	20432.4	+	4021.51i	0.785374	+	0.154578i
$879$	26216.6			1.00599
$880$	−2437.06	−	2398.13i	−0.0933559	−	0.0918646i
$881$			36908.6i			1.41144i	0.708489	+	0.705721i	$0.249377\pi$
$881$			36908.6i			1.41144i	−0.708489	+	0.705721i	$0.750623\pi$
$882$	−5079.29	+	25806.7i	−0.193910	+	0.985212i
$883$	−13330.7			−0.508056			−0.254028	−	0.967197i	$-0.581756\pi$
$883$	−13330.7			−0.508056			−0.254028	+	0.967197i	$0.581756\pi$
$884$	4916.93	+	2013.51i	0.187075	+	0.0766081i
$885$		−	46198.1i		−	1.75472i
$886$	20767.6	+	4087.50i	0.787475	+	0.154991i
$887$			14119.9i			0.534499i	0.963627	+	0.267249i	$0.0861148\pi$
$887$			14119.9i			0.534499i	−0.963627	+	0.267249i	$0.913885\pi$
$888$	−6721.89	−	4432.95i	−0.254022	−	0.167523i
$889$		−	16962.1i		−	0.639923i
$890$	31966.4	+	6291.65i	1.20395	+	0.236962i
$891$	1420.76			0.0534201
$892$	6618.61	+	2710.35i	0.248439	+	0.101737i
$893$	10813.1			0.405204
$894$	−8027.48	+	40785.8i	−0.300312	+	1.52582i
$895$	−55098.9			−2.05782
$896$	−2751.50	−	12881.4i	−0.102591	−	0.480289i
$897$		−	16270.3i		−	0.605630i
$898$	25027.8	+	4926.00i	0.930055	+	0.183054i
$899$	36068.7	−	9805.61i	1.33811	−	0.363777i
$900$	−32008.5	−	13107.6i	−1.18550	−	0.485468i
$901$	−43793.8			−1.61929
$902$	242.249	−	1230.81i	0.00894234	−	0.0454340i
$903$			28549.3i			1.05211i
$904$	15799.0	−	23956.8i	0.581269	−	0.881407i
$905$			66190.3i			2.43120i
$906$	−2381.89	+	12101.8i	−0.0873432	+	0.443770i
$907$		−	6471.26i		−	0.236907i	−0.992960	−	0.118453i	$-0.962206\pi$
$907$		−	6471.26i		−	0.236907i	0.992960	−	0.118453i	$-0.0377936\pi$
$908$	1703.65	−	4160.26i	0.0622660	−	0.152052i
$909$	17606.1			0.642417
$910$	−863.519	+	4387.34i	−0.0314564	+	0.159823i
$911$	−9777.00			−0.355572			−0.177786	−	0.984069i	$-0.556894\pi$
$911$	−9777.00			−0.355572			−0.177786	+	0.984069i	$0.556894\pi$
$912$	34579.5	−	35140.9i	1.25553	−	1.27591i
$913$	−493.763			−0.0178983
$914$	−11513.3	−	2266.06i	−0.416660	−	0.0820073i
$915$		−	89195.1i		−	3.22262i
$916$	−17883.4	+	43670.8i	−0.645071	+	1.57525i
$917$	15561.6			0.560402
$918$	11499.0	+	2263.25i	0.413425	+	0.0813706i
$919$		−	18815.1i		−	0.675358i	−0.941261	−	0.337679i	$-0.890358\pi$
$919$		−	18815.1i		−	0.675358i	0.941261	−	0.337679i	$-0.109642\pi$
$920$	36221.5	−	54924.4i	1.29803	−	1.96826i
$921$			3692.56i			0.132111i
$922$	40036.9	+	7880.10i	1.43009	+	0.281472i
$923$	1862.07			0.0664038
$924$	−743.896	+	1816.57i	−0.0264853	+	0.0646763i
$925$			5436.95i			0.193260i
$926$	−2628.56	+	13355.1i	−0.0932826	+	0.473947i
$927$		−	53026.6i		−	1.87877i
$928$	22105.8	+	32373.5i	0.781959	+	1.14516i
$929$			1971.64i			0.0696311i	0.999394	+	0.0348156i	$0.0110844\pi$
$929$			1971.64i			0.0696311i	−0.999394	+	0.0348156i	$0.988916\pi$
$930$	60492.1	−	4308.70i	2.13292	−	0.151922i
$931$			25314.3i			0.891129i
$932$	−18093.2	−	7409.24i	−0.635903	−	0.260405i
$933$		−	27050.5i		−	0.949190i
$934$	−28650.7	−	5639.06i	−1.00373	−	0.197554i
$935$		−	3201.88i		−	0.111992i
$936$	7478.90	+	4932.18i	0.261170	+	0.172236i
$937$	22661.7			0.790100			0.395050	−	0.918660i	$-0.370727\pi$
$937$	22661.7			0.790100			0.395050	+	0.918660i	$0.370727\pi$
$938$	3343.26	−	16986.3i	0.116377	−	0.591283i
$939$		−	40145.5i		−	1.39521i
$940$	−5286.48	+	12909.4i	−0.183432	+	0.447935i
$941$			44662.0i			1.54723i	0.633658	+	0.773613i	$0.281553\pi$
$941$			44662.0i			1.54723i	−0.633658	+	0.773613i	$0.718447\pi$
$942$	12289.4	−	62439.4i	0.425063	−	2.15964i
$943$	24138.4			0.833569
$944$	−16693.7	+	16964.7i	−0.575567	+	0.584910i
$945$			9863.01i			0.339517i
$946$	737.296	−	3746.03i	0.0253399	−	0.128746i
$947$	−19690.9			−0.675679			−0.337840	−	0.941204i	$-0.609696\pi$
$947$	−19690.9			−0.675679			−0.337840	+	0.941204i	$0.609696\pi$
$948$	−38810.5	−	15893.1i	−1.32965	−	0.544497i
$949$	11528.6			0.394346
$950$	−32663.0	−	6428.76i	−1.11550	−	0.219554i
$951$	32193.9			1.09775
$952$	6791.00	−	10297.5i	0.231195	−	0.350572i
$953$		−	16394.6i		−	0.557263i	−0.960398	−	0.278632i	$-0.910119\pi$
$953$		−	16394.6i		−	0.557263i	0.960398	−	0.278632i	$-0.0898808\pi$
$954$	−72452.1	−	14260.1i	−2.45883	−	0.483949i
$955$		−	31117.9i		−	1.05440i
$956$	32797.0	+	13430.5i	1.10955	+	0.454366i
$957$		−	5841.99i		−	0.197330i
$958$	43514.5	+	8564.54i	1.46752	+	0.288839i
$959$	−4058.64			−0.136664
$960$	25047.8	+	58463.6i	0.842099	+	1.96553i
$961$	−25690.5	+	15083.2i	−0.862358	+	0.506299i
$962$	271.953	−	1381.73i	0.00911446	−	0.0463084i
$963$			35570.2i			1.19027i
$964$	5118.11	−	12498.3i	0.170999	−	0.417575i
$965$	30141.5			1.00548
$966$	−37062.1	−	7294.59i	−1.23442	−	0.242960i
$967$	−8642.86			−0.287421			−0.143710	−	0.989620i	$-0.545903\pi$
$967$	−8642.86			−0.287421			−0.143710	+	0.989620i	$0.545903\pi$
$968$	−16436.1	+	24922.9i	−0.545741	+	0.827533i
$969$	46169.2			1.53062
$970$	−2945.05	+	14963.1i	−0.0974845	+	0.495296i
$971$		−	50112.1i		−	1.65620i	−0.560578	−	0.828101i	$-0.689421\pi$
$971$		−	50112.1i		−	1.65620i	0.560578	−	0.828101i	$-0.310579\pi$
$972$	−38277.5	−	15674.8i	−1.26312	−	0.517253i
$973$			6810.15i			0.224382i
$974$	8866.29	−	45047.5i	0.291678	−	1.48195i
$975$		−	10620.6i		−	0.348853i
$976$	−32230.8	+	32754.0i	−1.05705	+	1.07421i
$977$	3145.38			0.102999			0.0514994	−	0.998673i	$-0.483600\pi$
$977$	3145.38			0.102999			0.0514994	+	0.998673i	$0.483600\pi$
$978$	−23007.8	−	4528.42i	−0.752260	−	0.148060i
$979$			2501.39i			0.0816597i
$980$	−30221.9	−	12376.0i	−0.985105	−	0.403405i
$981$	−23307.0			−0.758546
$982$	7684.43	−	39042.8i	0.249715	−	1.26874i
$983$	18586.0			0.603053			0.301526	−	0.953458i	$-0.402504\pi$
$983$	18586.0			0.603053			0.301526	+	0.953458i	$0.402504\pi$
$984$	−12846.9	+	19480.4i	−0.416205	+	0.631111i
$985$		−	18362.2i		−	0.593978i
$986$	−7089.36	+	36019.4i	−0.228977	+	1.16338i
$987$	8008.98			0.258286
$988$	7979.32	+	3267.57i	0.256939	+	0.105218i
$989$	73466.6			2.36208
$990$	1042.59	−	5297.17i	0.0334705	−	0.170056i
$991$	−13231.2			−0.424120			−0.212060	−	0.977257i	$-0.568017\pi$
$991$	−13231.2			−0.424120			−0.212060	+	0.977257i	$0.568017\pi$
$992$	−23770.7	−	20276.7i	−0.760808	−	0.648977i
$993$	87815.4			2.80638
$994$	834.835	−	4241.60i	0.0266392	−	0.135348i
$995$	−42157.8			−1.34321
$996$	8500.06	+	3480.82i	0.270416	+	0.110737i
$997$	35452.7			1.12618			0.563089	−	0.826396i	$-0.309613\pi$
$997$	35452.7			1.12618			0.563089	+	0.826396i	$0.309613\pi$
$998$	5704.01	−	28980.7i	0.180919	−	0.919207i
$999$		−	3106.21i		−	0.0983746i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.4.d.c.123.19	yes	40
4.3	odd	2	inner	124.4.d.c.123.18	yes	40
31.30	odd	2	inner	124.4.d.c.123.20	yes	40
124.123	even	2	inner	124.4.d.c.123.17	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.4.d.c.123.17	✓	40	124.123	even	2	inner
124.4.d.c.123.18	yes	40	4.3	odd	2	inner
124.4.d.c.123.19	yes	40	1.1	even	1	trivial
124.4.d.c.123.20	yes	40	31.30	odd	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:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	124.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.546214 + 2.77518i) q^{2} -7.92016 q^{3} +(-7.40330 - 3.03169i) q^{4} +15.6847 q^{5} +(4.32610 - 21.9799i) q^{6} -9.09573i q^{7} +(12.4573 - 18.8896i) q^{8} +35.7289 q^{9} +O(q^{10})\)	\(q+(-0.546214 + 2.77518i) q^{2} -7.92016 q^{3} +(-7.40330 - 3.03169i) q^{4} +15.6847 q^{5} +(4.32610 - 21.9799i) q^{6} -9.09573i q^{7} +(12.4573 - 18.8896i) q^{8} +35.7289 q^{9} +(-8.56720 + 43.5279i) q^{10} -3.40609 q^{11} +(58.6353 + 24.0115i) q^{12} +11.0814i q^{13} +(25.2423 + 4.96821i) q^{14} -124.225 q^{15} +(45.6177 + 44.8890i) q^{16} +59.9340i q^{17} +(-19.5156 + 99.1544i) q^{18} +97.2624i q^{19} +(-116.119 - 47.5511i) q^{20} +72.0396i q^{21} +(1.86045 - 9.45253i) q^{22} +185.382 q^{23} +(-98.6637 + 149.608i) q^{24} +121.010 q^{25} +(-30.7530 - 6.05282i) q^{26} -69.1347 q^{27} +(-27.5754 + 67.3384i) q^{28} -216.556i q^{29} +(67.8536 - 344.748i) q^{30} +(45.2797 + 166.556i) q^{31} +(-149.492 + 102.079i) q^{32} +26.9768 q^{33} +(-166.328 - 32.7368i) q^{34} -142.664i q^{35} +(-264.512 - 108.319i) q^{36} +44.9299i q^{37} +(-269.921 - 53.1261i) q^{38} -87.7666i q^{39} +(195.389 - 296.277i) q^{40} +130.209 q^{41} +(-199.923 - 39.3491i) q^{42} +396.299 q^{43} +(25.2163 + 10.3262i) q^{44} +560.398 q^{45} +(-101.258 + 514.468i) q^{46} -111.175i q^{47} +(-361.300 - 355.528i) q^{48} +260.268 q^{49} +(-66.0971 + 335.824i) q^{50} -474.687i q^{51} +(33.5954 - 82.0391i) q^{52} +730.700i q^{53} +(37.7623 - 191.861i) q^{54} -53.4235 q^{55} +(-171.815 - 113.308i) q^{56} -770.334i q^{57} +(600.984 + 118.286i) q^{58} +371.889i q^{59} +(919.677 + 376.612i) q^{60} +718.011i q^{61} +(-486.955 + 34.6846i) q^{62} -324.981i q^{63} +(-201.632 - 470.626i) q^{64} +173.809i q^{65} +(-14.7351 + 74.8655i) q^{66} -672.930i q^{67} +(181.701 - 443.709i) q^{68} -1468.25 q^{69} +(395.918 + 77.9249i) q^{70} -168.035i q^{71} +(445.086 - 674.905i) q^{72} -1040.35i q^{73} +(-124.689 - 24.5413i) q^{74} -958.415 q^{75} +(294.869 - 720.063i) q^{76} +30.9809i q^{77} +(243.569 + 47.9393i) q^{78} -661.896 q^{79} +(715.500 + 704.070i) q^{80} -417.124 q^{81} +(-71.1222 + 361.355i) q^{82} +144.965 q^{83} +(218.402 - 533.331i) q^{84} +940.046i q^{85} +(-216.464 + 1099.80i) q^{86} +1715.16i q^{87} +(-42.4306 + 64.3396i) q^{88} -734.388i q^{89} +(-306.097 + 1555.21i) q^{90} +100.794 q^{91} +(-1372.44 - 562.019i) q^{92} +(-358.622 - 1319.15i) q^{93} +(308.530 + 60.7251i) q^{94} +1525.53i q^{95} +(1184.00 - 808.479i) q^{96} +343.759 q^{97} +(-142.162 + 722.291i) q^{98} -121.696 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{2} + 10 q^{4} - 4 q^{5} + 94 q^{8} + 536 q^{9}+O(q^{10}) \) 40 * q - 2 * q^2 + 10 * q^4 - 4 * q^5 + 94 * q^8 + 536 * q^9	\( 40 q - 2 q^{2} + 10 q^{4} - 4 q^{5} + 94 q^{8} + 536 q^{9} + 228 q^{10} - 104 q^{14} - 78 q^{16} + 114 q^{18} - 44 q^{20} + 28 q^{25} + 48 q^{28} - 602 q^{32} - 136 q^{33} - 482 q^{36} + 420 q^{38} - 516 q^{40} - 4 q^{41} - 1596 q^{45} + 1876 q^{49} - 662 q^{50} + 1576 q^{56} - 838 q^{62} - 302 q^{64} - 3900 q^{66} - 872 q^{69} - 912 q^{70} - 2166 q^{72} + 3220 q^{76} - 476 q^{78} + 572 q^{80} - 2056 q^{81} + 3096 q^{82} - 6220 q^{90} - 2904 q^{93} + 6408 q^{94} - 1836 q^{97} - 1358 q^{98}+O(q^{100}) \) 40 * q - 2 * q^2 + 10 * q^4 - 4 * q^5 + 94 * q^8 + 536 * q^9 + 228 * q^10 - 104 * q^14 - 78 * q^16 + 114 * q^18 - 44 * q^20 + 28 * q^25 + 48 * q^28 - 602 * q^32 - 136 * q^33 - 482 * q^36 + 420 * q^38 - 516 * q^40 - 4 * q^41 - 1596 * q^45 + 1876 * q^49 - 662 * q^50 + 1576 * q^56 - 838 * q^62 - 302 * q^64 - 3900 * q^66 - 872 * q^69 - 912 * q^70 - 2166 * q^72 + 3220 * q^76 - 476 * q^78 + 572 * q^80 - 2056 * q^81 + 3096 * q^82 - 6220 * q^90 - 2904 * q^93 + 6408 * q^94 - 1836 * q^97 - 1358 * q^98

Introduction

L-functions

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