LMFDB - Embedded newform 76.4.d.a.75.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,4,Mod(75,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, 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("76.75");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	76.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:	$4.48414516044$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			75.18
Character	$\chi$	$=$	76.75
Dual form			76.4.d.a.75.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.929967 + 2.67117i) q^{2} -0.246541 q^{3} +(-6.27032 + 4.96820i) q^{4} -6.75093 q^{5} +(-0.229275 - 0.658553i) q^{6} +18.0267i q^{7} +(-19.1021 - 12.1288i) q^{8} -26.9392 q^{9} +O(q^{10})$	\(q+(0.929967 + 2.67117i) q^{2} -0.246541 q^{3} +(-6.27032 + 4.96820i) q^{4} -6.75093 q^{5} +(-0.229275 - 0.658553i) q^{6} +18.0267i q^{7} +(-19.1021 - 12.1288i) q^{8} -26.9392 q^{9} +(-6.27814 - 18.0329i) q^{10} +27.9384i q^{11} +(1.54589 - 1.22487i) q^{12} -12.9947i q^{13} +(-48.1525 + 16.7643i) q^{14} +1.66438 q^{15} +(14.6339 - 62.3045i) q^{16} +37.2438 q^{17} +(-25.0526 - 71.9593i) q^{18} +(61.2436 + 55.7514i) q^{19} +(42.3305 - 33.5400i) q^{20} -4.44433i q^{21} +(-74.6282 + 25.9818i) q^{22} +57.6544i q^{23} +(4.70945 + 2.99026i) q^{24} -79.4249 q^{25} +(34.7110 - 12.0846i) q^{26} +13.2982 q^{27} +(-89.5606 - 113.034i) q^{28} +132.033i q^{29} +(1.54782 + 4.44585i) q^{30} +246.064 q^{31} +(180.035 - 18.8515i) q^{32} -6.88795i q^{33} +(34.6355 + 99.4845i) q^{34} -121.697i q^{35} +(168.918 - 133.840i) q^{36} +240.930i q^{37} +(-91.9671 + 215.439i) q^{38} +3.20372i q^{39} +(128.957 + 81.8810i) q^{40} -83.9105i q^{41} +(11.8716 - 4.13308i) q^{42} +267.352i q^{43} +(-138.803 - 175.183i) q^{44} +181.865 q^{45} +(-154.005 + 53.6166i) q^{46} -221.335i q^{47} +(-3.60785 + 15.3606i) q^{48} +18.0364 q^{49} +(-73.8625 - 212.158i) q^{50} -9.18211 q^{51} +(64.5602 + 81.4808i) q^{52} -617.838i q^{53} +(12.3669 + 35.5218i) q^{54} -188.610i q^{55} +(218.644 - 344.349i) q^{56} +(-15.0991 - 13.7450i) q^{57} +(-352.684 + 122.787i) q^{58} -827.579 q^{59} +(-10.4362 + 8.26899i) q^{60} -13.9150 q^{61} +(228.831 + 657.278i) q^{62} -485.626i q^{63} +(217.782 + 463.373i) q^{64} +87.7262i q^{65} +(18.3989 - 6.40557i) q^{66} -524.989 q^{67} +(-233.530 + 185.035i) q^{68} -14.2142i q^{69} +(325.075 - 113.175i) q^{70} -460.480 q^{71} +(514.596 + 326.742i) q^{72} -56.8229 q^{73} +(-643.566 + 224.057i) q^{74} +19.5815 q^{75} +(-661.002 - 45.3086i) q^{76} -503.638 q^{77} +(-8.55768 + 2.97935i) q^{78} +760.715 q^{79} +(-98.7925 + 420.613i) q^{80} +724.080 q^{81} +(224.139 - 78.0340i) q^{82} +574.450i q^{83} +(22.0803 + 27.8674i) q^{84} -251.430 q^{85} +(-714.142 + 248.628i) q^{86} -32.5516i q^{87} +(338.860 - 533.682i) q^{88} -811.570i q^{89} +(169.128 + 485.792i) q^{90} +234.252 q^{91} +(-286.439 - 361.511i) q^{92} -60.6647 q^{93} +(591.225 - 205.835i) q^{94} +(-413.452 - 376.374i) q^{95} +(-44.3860 + 4.64765i) q^{96} +1512.68i q^{97} +(16.7733 + 48.1784i) q^{98} -752.638i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 10 q^{4} - 4 q^{5} - 6 q^{6} + 192 q^{9}+O(q^{10}) $ 28 * q + 10 * q^4 - 4 * q^5 - 6 * q^6 + 192 * q^9	$ 28 q + 10 q^{4} - 4 q^{5} - 6 q^{6} + 192 q^{9} - 134 q^{16} - 80 q^{17} - 300 q^{20} - 26 q^{24} + 496 q^{25} - 90 q^{26} + 254 q^{28} - 16 q^{30} - 556 q^{36} - 626 q^{38} - 850 q^{42} + 976 q^{44} - 612 q^{45} + 188 q^{49} + 354 q^{54} - 580 q^{57} + 2534 q^{58} - 948 q^{61} - 1068 q^{62} - 1634 q^{64} + 1244 q^{66} + 1630 q^{68} - 184 q^{73} + 2276 q^{74} + 1688 q^{76} + 308 q^{77} + 3376 q^{80} - 2284 q^{81} - 740 q^{82} + 684 q^{85} + 1810 q^{92} + 824 q^{93} - 5222 q^{96}+O(q^{100}) $ 28 * q + 10 * q^4 - 4 * q^5 - 6 * q^6 + 192 * q^9 - 134 * q^16 - 80 * q^17 - 300 * q^20 - 26 * q^24 + 496 * q^25 - 90 * q^26 + 254 * q^28 - 16 * q^30 - 556 * q^36 - 626 * q^38 - 850 * q^42 + 976 * q^44 - 612 * q^45 + 188 * q^49 + 354 * q^54 - 580 * q^57 + 2534 * q^58 - 948 * q^61 - 1068 * q^62 - 1634 * q^64 + 1244 * q^66 + 1630 * q^68 - 184 * q^73 + 2276 * q^74 + 1688 * q^76 + 308 * q^77 + 3376 * q^80 - 2284 * q^81 - 740 * q^82 + 684 * q^85 + 1810 * q^92 + 824 * q^93 - 5222 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$-1$	$-1$

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 $

$2$	0.929967	+	2.67117i	0.328793	+	0.944402i
$2$	0.929967	+	2.67117i	0.328793	+	0.944402i
$3$	−0.246541			−0.0474468			−0.0237234	−	0.999719i	$-0.507552\pi$
$3$	−0.246541			−0.0474468			−0.0237234	+	0.999719i	$0.507552\pi$
$4$	−6.27032	+	4.96820i	−0.783790	+	0.621025i
$5$	−6.75093			−0.603822			−0.301911	−	0.953336i	$-0.597625\pi$
$5$	−6.75093			−0.603822			−0.301911	+	0.953336i	$0.597625\pi$
$6$	−0.229275	−	0.658553i	−0.0156002	−	0.0448089i
$7$			18.0267i			0.973353i	0.873582	+	0.486676i	$0.161791\pi$
$7$			18.0267i			0.973353i	−0.873582	+	0.486676i	$0.838209\pi$
$8$	−19.1021	−	12.1288i	−0.844203	−	0.536024i
$9$	−26.9392			−0.997749
$10$	−6.27814	−	18.0329i	−0.198532	−	0.570251i
$11$			27.9384i			0.765794i	0.923791	+	0.382897i	$0.125074\pi$
$11$			27.9384i			0.765794i	−0.923791	+	0.382897i	$0.874926\pi$
$12$	1.54589	−	1.22487i	0.0371884	−	0.0294657i
$13$		−	12.9947i		−	0.277236i	−0.990346	−	0.138618i	$-0.955734\pi$
$13$		−	12.9947i		−	0.277236i	0.990346	−	0.138618i	$-0.0442661\pi$
$14$	−48.1525	+	16.7643i	−0.919236	+	0.320032i
$15$	1.66438			0.0286494
$16$	14.6339	−	62.3045i	0.228655	−	0.973508i
$17$	37.2438			0.531349			0.265675	−	0.964063i	$-0.414405\pi$
$17$	37.2438			0.531349			0.265675	+	0.964063i	$0.414405\pi$
$18$	−25.0526	−	71.9593i	−0.328053	−	0.942276i
$19$	61.2436	+	55.7514i	0.739487	+	0.673171i
$19$	61.2436	+	55.7514i	0.739487	+	0.673171i
$20$	42.3305	−	33.5400i	0.473270	−	0.374989i
$21$		−	4.44433i		−	0.0461825i
$22$	−74.6282	+	25.9818i	−0.723217	+	0.251788i
$23$			57.6544i			0.522685i	0.965246	+	0.261343i	$0.0841653\pi$
$23$			57.6544i			0.522685i	−0.965246	+	0.261343i	$0.915835\pi$
$24$	4.70945	+	2.99026i	0.0400547	+	0.0254327i
$25$	−79.4249			−0.635399
$26$	34.7110	−	12.0846i	0.261823	−	0.0911534i
$27$	13.2982			0.0947868
$28$	−89.5606	−	113.034i	−0.604477	−	0.762905i
$29$			132.033i			0.845447i	0.906259	+	0.422723i	$0.138926\pi$
$29$			132.033i			0.845447i	−0.906259	+	0.422723i	$0.861074\pi$
$30$	1.54782	+	4.44585i	0.00941973	+	0.0270566i
$31$	246.064			1.42562			0.712812	−	0.701356i	$-0.247421\pi$
$31$	246.064			1.42562			0.712812	+	0.701356i	$0.247421\pi$
$32$	180.035	−	18.8515i	0.994563	−	0.104141i
$33$		−	6.88795i		−	0.0363345i
$34$	34.6355	+	99.4845i	0.174704	+	0.501807i
$35$		−	121.697i		−	0.587732i
$36$	168.918	−	133.840i	0.782026	−	0.619627i
$37$			240.930i			1.07050i	0.844692	+	0.535252i	$0.179784\pi$
$37$			240.930i			1.07050i	−0.844692	+	0.535252i	$0.820216\pi$
$38$	−91.9671	+	215.439i	−0.392606	+	0.919707i
$39$			3.20372i			0.0131540i
$40$	128.957	+	81.8810i	0.509748	+	0.323663i
$41$		−	83.9105i		−	0.319625i	−0.987147	−	0.159812i	$-0.948911\pi$
$41$		−	83.9105i		−	0.319625i	0.987147	−	0.159812i	$-0.0510889\pi$
$42$	11.8716	−	4.13308i	0.0436148	−	0.0151845i
$43$			267.352i			0.948157i	0.880483	+	0.474078i	$0.157219\pi$
$43$			267.352i			0.948157i	−0.880483	+	0.474078i	$0.842781\pi$
$44$	−138.803	−	175.183i	−0.475578	−	0.600222i
$45$	181.865			0.602462
$46$	−154.005	+	53.6166i	−0.493625	+	0.171855i
$47$		−	221.335i		−	0.686916i	−0.939168	−	0.343458i	$-0.888402\pi$
$47$		−	221.335i		−	0.686916i	0.939168	−	0.343458i	$-0.111598\pi$
$48$	−3.60785	+	15.3606i	−0.0108489	+	0.0461898i
$49$	18.0364			0.0525844
$50$	−73.8625	−	212.158i	−0.208915	−	0.600072i
$51$	−9.18211			−0.0252108
$52$	64.5602	+	81.4808i	0.172171	+	0.217295i
$53$		−	617.838i		−	1.60126i	−0.599162	−	0.800628i	$-0.704499\pi$
$53$		−	617.838i		−	1.60126i	0.599162	−	0.800628i	$-0.295501\pi$
$54$	12.3669	+	35.5218i	0.0311652	+	0.0895169i
$55$		−	188.610i		−	0.462403i
$56$	218.644	−	344.349i	0.521741	−	0.821707i
$57$	−15.0991	−	13.7450i	−0.0350863	−	0.0319398i
$58$	−352.684	+	122.787i	−0.798442	+	0.277977i
$59$	−827.579			−1.82613			−0.913064	−	0.407816i	$-0.866290\pi$
$59$	−827.579			−1.82613			−0.913064	+	0.407816i	$0.866290\pi$
$60$	−10.4362	+	8.26899i	−0.0224551	+	0.0177920i
$61$	−13.9150			−0.0292070			−0.0146035	−	0.999893i	$-0.504649\pi$
$61$	−13.9150			−0.0292070			−0.0146035	+	0.999893i	$0.504649\pi$
$62$	228.831	+	657.278i	0.468735	+	1.34636i
$63$		−	485.626i		−	0.971162i
$64$	217.782	+	463.373i	0.425356	+	0.905026i
$65$			87.7262i			0.167401i
$66$	18.3989	−	6.40557i	0.0343144	−	0.0119465i
$67$	−524.989			−0.957278			−0.478639	−	0.878012i	$-0.658870\pi$
$67$	−524.989			−0.957278			−0.478639	+	0.878012i	$0.658870\pi$
$68$	−233.530	+	185.035i	−0.416466	+	0.329981i
$69$		−	14.2142i		−	0.0247998i
$70$	325.075	−	113.175i	0.555055	−	0.193242i
$71$	−460.480			−0.769703			−0.384851	−	0.922979i	$-0.625747\pi$
$71$	−460.480			−0.769703			−0.384851	+	0.922979i	$0.625747\pi$
$72$	514.596	+	326.742i	0.842302	+	0.534818i
$73$	−56.8229			−0.0911044			−0.0455522	−	0.998962i	$-0.514505\pi$
$73$	−56.8229			−0.0911044			−0.0455522	+	0.998962i	$0.514505\pi$
$74$	−643.566	+	224.057i	−1.01099	+	0.351975i
$75$	19.5815			0.0301477
$76$	−661.002	−	45.3086i	−0.997659	−	0.0683849i
$77$	−503.638			−0.745388
$78$	−8.55768	+	2.97935i	−0.0124227	+	0.00432494i
$79$	760.715			1.08338			0.541691	−	0.840578i	$-0.317784\pi$
$79$	760.715			1.08338			0.541691	+	0.840578i	$0.317784\pi$
$80$	−98.7925	+	420.613i	−0.138067	+	0.587825i
$81$	724.080			0.993251
$82$	224.139	−	78.0340i	0.301854	−	0.105090i
$83$			574.450i			0.759688i	0.925051	+	0.379844i	$0.124022\pi$
$83$			574.450i			0.759688i	−0.925051	+	0.379844i	$0.875978\pi$
$84$	22.0803	+	27.8674i	0.0286805	+	0.0361974i
$85$	−251.430			−0.320840
$86$	−714.142	+	248.628i	−0.895441	+	0.311747i
$87$		−	32.5516i		−	0.0401138i
$88$	338.860	−	533.682i	0.410484	−	0.646485i
$89$		−	811.570i		−	0.966587i	−0.875458	−	0.483293i	$-0.839440\pi$
$89$		−	811.570i		−	0.966587i	0.875458	−	0.483293i	$-0.160560\pi$
$90$	169.128	+	485.792i	0.198085	+	0.568967i
$91$	234.252			0.269849
$92$	−286.439	−	361.511i	−0.324601	−	0.409676i
$93$	−60.6647			−0.0676413
$94$	591.225	−	205.835i	0.648725	−	0.225853i
$95$	−413.452	−	376.374i	−0.446518	−	0.406475i
$96$	−44.3860	+	4.64765i	−0.0471888	+	0.00494114i
$97$			1512.68i			1.58339i	0.610915	+	0.791696i	$0.290802\pi$
$97$			1512.68i			1.58339i	−0.610915	+	0.791696i	$0.709198\pi$
$98$	16.7733	+	48.1784i	0.0172894	+	0.0496608i
$99$		−	752.638i		−	0.764070i
$100$	498.020	−	394.599i	0.498020	−	0.394599i
$101$	410.499			0.404417			0.202209	−	0.979342i	$-0.435188\pi$
$101$	410.499			0.404417			0.202209	+	0.979342i	$0.435188\pi$
$102$	−8.53906	−	24.5270i	−0.00828915	−	0.0238092i
$103$	215.919			0.206555			0.103277	−	0.994653i	$-0.467067\pi$
$103$	215.919			0.206555			0.103277	+	0.994653i	$0.467067\pi$
$104$	−157.610	+	248.226i	−0.148605	+	0.234044i
$105$			30.0034i			0.0278860i
$106$	1650.35	−	574.569i	1.51223	−	0.526482i
$107$	721.444			0.651819			0.325909	−	0.945401i	$-0.394330\pi$
$107$	721.444			0.651819			0.325909	+	0.945401i	$0.394330\pi$
$108$	−83.3842	+	66.0683i	−0.0742930	+	0.0588650i
$109$		−	445.834i		−	0.391772i	−0.980627	−	0.195886i	$-0.937242\pi$
$109$		−	445.834i		−	0.391772i	0.980627	−	0.195886i	$-0.0627582\pi$
$110$	503.810	−	175.401i	0.436694	−	0.152035i
$111$		−	59.3992i		−	0.0507921i
$112$	1123.15	+	263.802i	0.947566	+	0.222562i
$113$		−	19.2095i		−	0.0159918i	−0.999968	−	0.00799592i	$-0.997455\pi$
$113$		−	19.2095i		−	0.0159918i	0.999968	−	0.00799592i	$-0.00254521\pi$
$114$	22.6736	−	53.1146i	0.0186279	−	0.0436372i
$115$		−	389.221i		−	0.315609i
$116$	−655.968	−	827.891i	−0.525044	−	0.662653i
$117$			350.066i			0.276612i
$118$	−769.621	−	2210.60i	−0.600418	−	1.72460i
$119$			671.384i			0.517190i
$120$	−31.7932	−	20.1870i	−0.0241859	−	0.0153568i
$121$	550.448			0.413560
$122$	−12.9404	−	37.1692i	−0.00960306	−	0.0275831i
$123$			20.6874i			0.0151652i
$124$	−1542.90	+	1222.49i	−1.11739	+	0.885348i
$125$	1380.06			0.987490
$126$	1297.19	−	451.617i	0.917167	−	0.319311i
$127$	2429.88			1.69777			0.848885	−	0.528578i	$-0.177275\pi$
$127$	2429.88			1.69777			0.848885	+	0.528578i	$0.177275\pi$
$128$	−1035.22	+	1012.66i	−0.714855	+	0.699273i
$129$		−	65.9131i		−	0.0449870i
$130$	−234.332	+	81.5824i	−0.158094	+	0.0550404i
$131$			1610.26i			1.07396i	0.843593	+	0.536982i	$0.180436\pi$
$131$			1610.26i			1.07396i	−0.843593	+	0.536982i	$0.819564\pi$
$132$	34.2207	+	43.1897i	0.0225646	+	0.0284786i
$133$	−1005.02	+	1104.02i	−0.655233	+	0.719782i
$134$	−488.223	−	1402.34i	−0.314746	−	0.904056i
$135$	−89.7754			−0.0572344
$136$	−711.435	−	451.724i	−0.448566	−	0.284816i
$137$	−2303.04			−1.43622			−0.718109	−	0.695930i	$-0.754992\pi$
$137$	−2303.04			−1.43622			−0.718109	+	0.695930i	$0.754992\pi$
$138$	37.9685	−	13.2187i	0.0234209	−	0.00815399i
$139$			2187.99i			1.33513i	0.744551	+	0.667565i	$0.232663\pi$
$139$			2187.99i			1.33513i	−0.744551	+	0.667565i	$0.767337\pi$
$140$	604.617	+	763.082i	0.364996	+	0.460658i
$141$			54.5682i			0.0325920i
$142$	−428.231	−	1230.02i	−0.253073	−	0.726909i
$143$	363.050			0.212306
$144$	−394.226	+	1678.43i	−0.228140	+	0.971316i
$145$		−	891.348i		−	0.510499i
$146$	−52.8434	−	151.784i	−0.0299545	−	0.0860392i
$147$	−4.44672			−0.00249496
$148$	−1196.99	−	1510.71i	−0.664811	−	0.839051i
$149$	−1158.18			−0.636793			−0.318396	−	0.947958i	$-0.603144\pi$
$149$	−1158.18			−0.636793			−0.318396	+	0.947958i	$0.603144\pi$
$150$	18.2101	+	52.3055i	0.00991234	+	0.0284715i
$151$	213.320			0.114965			0.0574826	−	0.998347i	$-0.481693\pi$
$151$	213.320			0.114965			0.0574826	+	0.998347i	$0.481693\pi$
$152$	−493.683	−	1807.78i	−0.263440	−	0.964676i
$153$	−1003.32			−0.530153
$154$	−468.366	−	1345.30i	−0.245078	−	0.703946i
$155$	−1661.16			−0.860822
$156$	−15.9167	−	20.0883i	−0.00816896	−	0.0103100i
$157$	753.700			0.383133			0.191566	−	0.981480i	$-0.438643\pi$
$157$	753.700			0.383133			0.191566	+	0.981480i	$0.438643\pi$
$158$	707.440	+	2032.00i	0.356208	+	1.02315i
$159$			152.322i			0.0759745i
$160$	−1215.40	+	127.265i	−0.600539	+	0.0628823i
$161$	−1039.32			−0.508757
$162$	673.371	+	1934.14i	0.326574	+	0.938029i
$163$			3063.09i			1.47190i	0.677035	+	0.735951i	$0.263265\pi$
$163$			3063.09i			1.47190i	−0.677035	+	0.735951i	$0.736735\pi$
$164$	416.884	+	526.146i	0.198495	+	0.250519i
$165$			46.5001i			0.0219396i
$166$	−1534.45	+	534.219i	−0.717451	+	0.249780i
$167$	2186.60			1.01320			0.506601	−	0.862181i	$-0.330902\pi$
$167$	2186.60			1.01320			0.506601	+	0.862181i	$0.330902\pi$
$168$	−53.9046	+	84.8961i	−0.0247549	+	0.0389874i
$169$	2028.14			0.923140
$170$	−233.822	−	671.613i	−0.105490	−	0.303002i
$171$	−1649.86	−	1501.90i	−0.737822	−	0.671656i
$172$	−1328.26	−	1676.38i	−0.588829	−	0.743156i
$173$			2613.14i			1.14840i	0.818714	+	0.574201i	$0.194687\pi$
$173$			2613.14i			1.14840i	−0.818714	+	0.574201i	$0.805313\pi$
$174$	86.9509	−	30.2719i	0.0378835	−	0.0131891i
$175$		−	1431.77i		−	0.618468i
$176$	1740.69	+	408.847i	0.745506	+	0.175102i
$177$	204.032			0.0866440
$178$	2167.84	−	754.733i	0.912846	−	0.317807i
$179$	−2820.94			−1.17792			−0.588959	−	0.808163i	$-0.700462\pi$
$179$	−2820.94			−1.17792			−0.588959	+	0.808163i	$0.700462\pi$
$180$	−1140.35	+	903.542i	−0.472204	+	0.374145i
$181$		−	3475.99i		−	1.42745i	−0.700427	−	0.713724i	$-0.747007\pi$
$181$		−	3475.99i		−	1.42745i	0.700427	−	0.713724i	$-0.252993\pi$
$182$	217.846	+	625.726i	0.0887244	+	0.254846i
$183$	3.43060			0.00138578
$184$	699.281	−	1101.32i	0.280172	−	0.441252i
$185$		−	1626.50i		−	0.646394i
$186$	−56.4162	−	162.046i	−0.0222400	−	0.0638806i
$187$			1040.53i			0.406904i
$188$	1099.64	+	1387.84i	0.426593	+	0.538399i
$189$			239.724i			0.0922610i
$190$	620.864	−	1454.42i	0.237064	−	0.555339i
$191$		−	4511.47i		−	1.70910i	−0.519368	−	0.854551i	$-0.673833\pi$
$191$		−	4511.47i		−	1.70910i	0.519368	−	0.854551i	$-0.326167\pi$
$192$	−53.6922	−	114.241i	−0.0201818	−	0.0429406i
$193$		−	2908.28i		−	1.08467i	−0.840161	−	0.542337i	$-0.817539\pi$
$193$		−	2908.28i		−	1.08467i	0.840161	−	0.542337i	$-0.182461\pi$
$194$	−4040.62	+	1406.74i	−1.49536	+	0.520608i
$195$		−	21.6281i		−	0.00794266i
$196$	−113.094	+	89.6087i	−0.0412151	+	0.0326562i
$197$	3842.55			1.38970			0.694848	−	0.719156i	$-0.255471\pi$
$197$	3842.55			1.38970			0.694848	+	0.719156i	$0.255471\pi$
$198$	2010.42	−	699.928i	0.721589	−	0.251221i
$199$		−	1428.56i		−	0.508886i	−0.967088	−	0.254443i	$-0.918108\pi$
$199$		−	1428.56i		−	0.508886i	0.967088	−	0.254443i	$-0.0818921\pi$
$200$	1517.18	+	963.332i	0.536406	+	0.340589i
$201$	129.431			0.0454198
$202$	381.750	+	1096.51i	0.132970	+	0.381933i
$203$	−2380.13			−0.822918
$204$	57.5748	−	45.6186i	0.0197600	−	0.0156566i
$205$			566.474i			0.192996i
$206$	200.798	+	576.758i	0.0679138	+	0.195071i
$207$		−	1553.16i		−	0.521509i
$208$	−809.626	−	190.163i	−0.269892	−	0.0633914i
$209$	−1557.60	+	1711.05i	−0.515510	+	0.566294i
$210$	−80.1442	+	27.9022i	−0.0263356	+	0.00916872i
$211$	−516.792			−0.168613			−0.0843067	−	0.996440i	$-0.526868\pi$
$211$	−516.792			−0.168613			−0.0843067	+	0.996440i	$0.526868\pi$
$212$	3069.54	+	3874.04i	0.994421	+	1.25505i
$213$	113.527			0.0365200
$214$	670.919	+	1927.10i	0.214313	+	0.615579i
$215$		−	1804.87i		−	0.572518i
$216$	−254.024	−	161.292i	−0.0800193	−	0.0508081i
$217$			4435.72i			1.38763i
$218$	1190.90	−	414.611i	0.369990	−	0.128812i
$219$	14.0092			0.00432261
$220$	937.053	+	1182.65i	0.287164	+	0.362427i
$221$		−	483.970i		−	0.147309i
$222$	158.665	−	55.2393i	0.0479681	−	0.0167001i
$223$	4415.35			1.32589			0.662945	−	0.748668i	$-0.269306\pi$
$223$	4415.35			1.32589			0.662945	+	0.748668i	$0.269306\pi$
$224$	339.830	+	3245.45i	0.101365	+	0.968060i
$225$	2139.64			0.633969
$226$	51.3119	−	17.8642i	0.0151027	−	0.00525800i
$227$	−717.608			−0.209821			−0.104910	−	0.994482i	$-0.533456\pi$
$227$	−717.608			−0.209821			−0.104910	+	0.994482i	$0.533456\pi$
$228$	162.964	+	11.1704i	0.0473358	+	0.00324464i
$229$	−4981.48			−1.43749			−0.718746	−	0.695273i	$-0.755284\pi$
$229$	−4981.48			−1.43749			−0.718746	+	0.695273i	$0.755284\pi$
$230$	1039.68	−	361.962i	0.298062	−	0.103770i
$231$	124.167			0.0353663
$232$	1601.41	−	2522.12i	0.453180	−	0.713728i
$233$	4850.87			1.36391			0.681956	−	0.731394i	$-0.261130\pi$
$233$	4850.87			1.36391			0.681956	+	0.731394i	$0.261130\pi$
$234$	−935.087	+	325.550i	−0.261233	+	0.0909482i
$235$			1494.22i			0.414775i
$236$	5189.18	−	4111.58i	1.43130	−	1.13407i
$237$	−187.547			−0.0514030
$238$	−1793.38	+	624.365i	−0.488436	+	0.170049i
$239$		−	2275.85i		−	0.615951i	−0.951394	−	0.307975i	$-0.900349\pi$
$239$		−	2275.85i		−	0.615951i	0.951394	−	0.307975i	$-0.0996515\pi$
$240$	24.3564	−	103.698i	0.00655082	−	0.0278904i
$241$			3540.83i			0.946410i	0.880952	+	0.473205i	$0.156903\pi$
$241$			3540.83i			0.946410i	−0.880952	+	0.473205i	$0.843097\pi$
$242$	511.898	+	1470.34i	0.135976	+	0.390567i
$243$	−537.567			−0.141913
$244$	87.2512	−	69.1323i	0.0228922	−	0.0181383i
$245$	−121.763			−0.0317516
$246$	−55.2595	+	19.2386i	−0.0143220	+	0.00498620i
$247$	724.471	−	795.841i	0.186628	−	0.205013i
$248$	−4700.34	−	2984.47i	−1.20351	−	0.764169i
$249$		−	141.625i		−	0.0360448i
$250$	1283.41	+	3686.37i	0.324680	+	0.932587i
$251$		−	1176.90i		−	0.295957i	−0.988991	−	0.147979i	$-0.952723\pi$
$251$		−	1176.90i		−	0.295957i	0.988991	−	0.147979i	$-0.0472766\pi$
$252$	2412.69	+	3045.03i	0.603116	+	0.761187i
$253$	−1610.77			−0.400269
$254$	2259.71	+	6490.62i	0.558215	+	1.60338i
$255$	61.9878			0.0152229
$256$	−3667.70	−	1823.52i	−0.895434	−	0.445194i
$257$		−	3859.07i		−	0.936663i	−0.883553	−	0.468331i	$-0.844855\pi$
$257$		−	3859.07i		−	0.936663i	0.883553	−	0.468331i	$-0.155145\pi$
$258$	176.065	−	61.2970i	0.0424858	−	0.0147914i
$259$	−4343.19			−1.04198
$260$	−435.841	−	550.071i	−0.103961	−	0.131208i
$261$		−	3556.87i		−	0.843544i
$262$	−4301.29	+	1497.49i	−1.01425	+	0.353112i
$263$		−	2998.38i		−	0.702996i	−0.936189	−	0.351498i	$-0.885672\pi$
$263$		−	2998.38i		−	0.702996i	0.936189	−	0.351498i	$-0.114328\pi$
$264$	−83.5429	+	131.574i	−0.0194762	+	0.0306737i
$265$			4170.98i			0.966873i
$266$	−3883.67	−	1657.87i	−0.895199	−	0.382144i
$267$			200.085i			0.0458615i
$268$	3291.85	−	2608.25i	0.750305	−	0.594494i
$269$		−	6994.80i		−	1.58543i	−0.609593	−	0.792714i	$-0.708667\pi$
$269$		−	6994.80i		−	1.58543i	0.609593	−	0.792714i	$-0.291333\pi$
$270$	−83.4882	−	239.806i	−0.0188183	−	0.0540522i
$271$			7456.46i			1.67139i	0.549191	+	0.835697i	$0.314936\pi$
$271$			7456.46i			1.67139i	−0.549191	+	0.835697i	$0.685064\pi$
$272$	545.021	−	2320.45i	0.121495	−	0.517273i
$273$	−57.7526			−0.0128035
$274$	−2141.75	−	6151.82i	−0.472219	−	1.35637i
$275$		−	2219.00i		−	0.486585i
$276$	70.6188	+	89.1274i	0.0154013	+	0.0194378i
$277$	4717.41			1.02326			0.511628	−	0.859207i	$-0.329043\pi$
$277$	4717.41			1.02326			0.511628	+	0.859207i	$0.329043\pi$
$278$	−5844.51	+	2034.76i	−1.26090	+	0.438982i
$279$	−6628.76			−1.42241
$280$	−1476.05	+	2324.68i	−0.315038	+	0.496165i
$281$		−	4619.68i		−	0.980736i	−0.871515	−	0.490368i	$-0.836862\pi$
$281$		−	4619.68i		−	0.980736i	0.871515	−	0.490368i	$-0.163138\pi$
$282$	−145.761	+	50.7466i	−0.0307800	+	0.0107160i
$283$			5346.10i			1.12294i	0.827496	+	0.561471i	$0.189765\pi$
$283$			5346.10i			1.12294i	−0.827496	+	0.561471i	$0.810235\pi$
$284$	2887.36	−	2287.76i	0.603286	−	0.478005i
$285$	101.933	+	92.7916i	0.0211859	+	0.0192860i
$286$	337.624	+	969.769i	0.0698047	+	0.200502i
$287$	1512.63			0.311108
$288$	−4850.00	+	507.843i	−0.992324	+	0.103906i
$289$	−3525.90			−0.717668
$290$	2380.94	−	828.924i	0.482116	−	0.167849i
$291$		−	372.937i		−	0.0751269i
$292$	356.298	−	282.308i	0.0714067	−	0.0565782i
$293$			7646.93i			1.52470i	0.647162	+	0.762352i	$0.275956\pi$
$293$			7646.93i			1.52470i	−0.647162	+	0.762352i	$0.724044\pi$
$294$	−4.13530	−	11.8780i	−0.000820326	−	0.00235625i
$295$	5586.93			1.10266
$296$	2922.21	−	4602.28i	0.573817	−	0.903723i
$297$			371.531i			0.0725872i
$298$	−1077.07	−	3093.71i	−0.209373	−	0.601388i
$299$	749.199			0.144907
$300$	−122.782	+	97.2848i	−0.0236295	+	0.0187225i
$301$	−4819.48			−0.922891
$302$	198.381	+	569.815i	0.0377997	+	0.108573i
$303$	−101.205			−0.0191883
$304$	4369.80	−	2999.89i	0.824424	−	0.565972i
$305$	93.9389			0.0176358
$306$	−933.052	−	2680.03i	−0.174311	−	0.500678i
$307$	6754.61			1.25572			0.627860	−	0.778326i	$-0.283931\pi$
$307$	6754.61			1.25572			0.627860	+	0.778326i	$0.283931\pi$
$308$	3157.97	−	2502.17i	0.584228	−	0.462905i
$309$	−53.2330			−0.00980038
$310$	−1544.82	−	4437.24i	−0.283032	−	0.812962i
$311$			8679.56i			1.58255i	0.611461	+	0.791274i	$0.290582\pi$
$311$			8679.56i			1.58255i	−0.611461	+	0.791274i	$0.709418\pi$
$312$	38.8574	−	61.1978i	0.00705086	−	0.0111046i
$313$	−7697.07			−1.38998			−0.694991	−	0.719019i	$-0.744592\pi$
$313$	−7697.07			−1.38998			−0.694991	+	0.719019i	$0.744592\pi$
$314$	700.916	+	2013.26i	0.125971	+	0.361831i
$315$			3278.43i			0.586409i
$316$	−4769.93	+	3779.39i	−0.849144	+	0.672807i
$317$			7703.18i			1.36484i	0.730961	+	0.682419i	$0.239072\pi$
$317$			7703.18i			1.36484i	−0.730961	+	0.682419i	$0.760928\pi$
$318$	−406.879	+	141.655i	−0.0717505	+	0.0249799i
$319$	−3688.79			−0.647438
$320$	−1470.23	−	3128.20i	−0.256839	−	0.546475i
$321$	−177.865			−0.0309267
$322$	−966.534	−	2776.20i	−0.167276	−	0.480471i
$323$	2280.94	+	2076.39i	0.392926	+	0.357689i
$324$	−4540.22	+	3597.38i	−0.778501	+	0.616834i
$325$			1032.10i			0.176156i
$326$	−8182.05	+	2848.58i	−1.39007	+	0.483951i
$327$			109.916i			0.0185883i
$328$	−1017.74	+	1602.87i	−0.171327	+	0.269828i
$329$	3989.96			0.668612
$330$	−124.210	+	43.2435i	−0.0207198	+	0.00721357i
$331$	2320.05			0.385261			0.192631	−	0.981271i	$-0.438298\pi$
$331$	2320.05			0.385261			0.192631	+	0.981271i	$0.438298\pi$
$332$	−2853.98	−	3601.99i	−0.471785	−	0.595436i
$333$		−	6490.47i		−	1.06810i
$334$	2033.47	+	5840.80i	0.333133	+	0.956869i
$335$	3544.17			0.578025
$336$	−276.902	−	65.0379i	−0.0449590	−	0.0105598i
$337$		−	8850.65i		−	1.43064i	−0.698797	−	0.715320i	$-0.746281\pi$
$337$		−	8850.65i		−	1.43064i	0.698797	−	0.715320i	$-0.253719\pi$
$338$	1886.10	+	5417.51i	0.303522	+	0.871815i
$339$			4.73593i			0.000758762i
$340$	1576.55	−	1249.16i	0.251472	−	0.199250i
$341$			6874.61i			1.09173i
$342$	2477.52	−	5803.76i	0.391722	−	0.917636i
$343$			6508.31i			1.02454i
$344$	3242.67	−	5106.98i	0.508235	−	0.800436i
$345$			95.9588i			0.0149746i
$346$	−6980.15	+	2430.14i	−1.08455	+	0.377587i
$347$		−	3196.66i		−	0.494541i	−0.968946	−	0.247271i	$-0.920466\pi$
$347$		−	3196.66i		−	0.494541i	0.968946	−	0.247271i	$-0.0795337\pi$
$348$	161.723	+	204.109i	0.0249117	+	0.0314408i
$349$	2658.67			0.407780			0.203890	−	0.978994i	$-0.434642\pi$
$349$	2658.67			0.407780			0.203890	+	0.978994i	$0.434642\pi$
$350$	3824.51	−	1331.50i	0.584082	−	0.203348i
$351$		−	172.806i		−	0.0262784i
$352$	526.679	+	5029.88i	0.0797502	+	0.761630i
$353$	−2643.21			−0.398537			−0.199269	−	0.979945i	$-0.563857\pi$
$353$	−2643.21			−0.398537			−0.199269	+	0.979945i	$0.563857\pi$
$354$	189.743	+	545.005i	0.0284879	+	0.0818267i
$355$	3108.67			0.464763
$356$	4032.04	+	5088.80i	0.600275	+	0.757601i
$357$		−	165.524i		−	0.0245390i
$358$	−2623.38	−	7535.23i	−0.387291	−	1.11243i
$359$		−	6635.96i		−	0.975578i	−0.872961	−	0.487789i	$-0.837803\pi$
$359$		−	6635.96i		−	0.975578i	0.872961	−	0.487789i	$-0.162197\pi$
$360$	−3474.00	−	2205.81i	−0.508600	−	0.322935i
$361$	642.561	+	6828.84i	0.0936814	+	0.995602i
$362$	9284.96	−	3232.55i	1.34808	−	0.469335i
$363$	−135.708			−0.0196221
$364$	−1468.83	+	1163.81i	−0.211505	+	0.167583i
$365$	383.608			0.0550108
$366$	3.19035	+	9.16374i	0.000455634	+	0.00130873i
$367$		−	5628.20i		−	0.800517i	−0.916402	−	0.400259i	$-0.868920\pi$
$367$		−	5628.20i		−	0.800517i	0.916402	−	0.400259i	$-0.131080\pi$
$368$	3592.13	+	843.708i	0.508838	+	0.119514i
$369$			2260.48i			0.318905i
$370$	4344.67	−	1512.59i	0.610456	−	0.212530i
$371$	11137.6			1.55859
$372$	380.387	−	301.395i	0.0530166	−	0.0420070i
$373$			2806.30i			0.389558i	0.980847	+	0.194779i	$0.0623989\pi$
$373$			2806.30i			0.389558i	−0.980847	+	0.194779i	$0.937601\pi$
$374$	−2779.43	+	967.658i	−0.384281	+	0.133787i
$375$	−340.241			−0.0468532
$376$	−2684.54	+	4227.97i	−0.368204	+	0.579897i
$377$	1715.73			0.234389
$378$	−640.343	+	222.935i	−0.0871315	+	0.0303348i
$379$	−11151.1			−1.51133			−0.755666	−	0.654957i	$-0.772687\pi$
$379$	−11151.1			−1.51133			−0.755666	+	0.654957i	$0.772687\pi$
$380$	4462.38	+	305.875i	0.602408	+	0.0412923i
$381$	−599.064			−0.0805538
$382$	12050.9	−	4195.52i	1.61408	−	0.561940i
$383$	2665.61			0.355630			0.177815	−	0.984064i	$-0.443097\pi$
$383$	2665.61			0.355630			0.177815	+	0.984064i	$0.443097\pi$
$384$	255.224	−	249.661i	0.0339176	−	0.0331783i
$385$	3400.02			0.450081
$386$	7768.51	−	2704.60i	1.02437	−	0.356634i
$387$		−	7202.24i		−	0.946022i
$388$	−7515.28	−	9484.97i	−0.983327	−	1.24105i
$389$	9326.53			1.21561			0.607807	−	0.794085i	$-0.292049\pi$
$389$	9326.53			1.21561			0.607807	+	0.794085i	$0.292049\pi$
$390$	57.7723	−	20.1134i	0.00750107	−	0.00261149i
$391$			2147.27i			0.277729i
$392$	−344.534	−	218.761i	−0.0443919	−	0.0281865i
$393$		−	396.996i		−	0.0509562i
$394$	3573.44	+	10264.1i	0.456923	+	1.31243i
$395$	−5135.54			−0.654169
$396$	3739.26	+	4719.28i	0.474507	+	0.598871i
$397$	3278.46			0.414462			0.207231	−	0.978292i	$-0.433555\pi$
$397$	3278.46			0.414462			0.207231	+	0.978292i	$0.433555\pi$
$398$	3815.94	−	1328.52i	0.480593	−	0.167318i
$399$	247.778	−	272.187i	0.0310887	−	0.0341513i
$400$	−1162.30	+	4948.53i	−0.145287	+	0.618566i
$401$			13475.6i			1.67816i	0.544011	+	0.839078i	$0.316905\pi$
$401$			13475.6i			1.67816i	−0.544011	+	0.839078i	$0.683095\pi$
$402$	120.367	+	345.733i	0.0149337	+	0.0428946i
$403$		−	3197.51i		−	0.395235i
$404$	−2573.96	+	2039.44i	−0.316978	+	0.251153i
$405$	−4888.22			−0.599747
$406$	−2213.44	−	6357.74i	−0.270570	−	0.777165i
$407$	−6731.20			−0.819786
$408$	175.398	+	111.368i	0.0212831	+	0.0135136i
$409$		−	16339.3i		−	1.97537i	−0.156446	−	0.987686i	$-0.550004\pi$
$409$		−	16339.3i		−	1.97537i	0.156446	−	0.987686i	$-0.449996\pi$
$410$	−1513.15	+	526.802i	−0.182266	+	0.0634559i
$411$	567.794			0.0681440
$412$	−1353.88	+	1072.73i	−0.161896	+	0.128276i
$413$		−	14918.5i		−	1.77747i
$414$	4148.77	−	1444.39i	0.492514	−	0.171468i
$415$		−	3878.07i		−	0.458716i
$416$	−244.968	−	2339.50i	−0.0288715	−	0.275729i
$417$		−	539.430i		−	0.0633477i
$418$	−6019.02	−	2569.41i	−0.704306	−	0.300655i
$419$		−	9779.77i		−	1.14027i	−0.821551	−	0.570135i	$-0.806891\pi$
$419$		−	9779.77i		−	1.14027i	0.821551	−	0.570135i	$-0.193109\pi$
$420$	−149.063	−	188.131i	−0.0173179	−	0.0218568i
$421$		−	3549.76i		−	0.410938i	−0.978664	−	0.205469i	$-0.934128\pi$
$421$		−	3549.76i		−	0.410938i	0.978664	−	0.205469i	$-0.0658720\pi$
$422$	−480.600	−	1380.44i	−0.0554389	−	0.159239i
$423$			5962.60i			0.685370i
$424$	−7493.66	+	11802.0i	−0.858312	+	1.35178i
$425$	−2958.08			−0.337619
$426$	105.576	+	303.251i	0.0120075	+	0.0344895i
$427$		−	250.841i		−	0.0284287i
$428$	−4523.69	+	3584.28i	−0.510889	+	0.404796i
$429$	−89.5066			−0.0100732
$430$	4821.13	−	1678.47i	0.540687	−	0.188240i
$431$	−4190.52			−0.468330			−0.234165	−	0.972197i	$-0.575236\pi$
$431$	−4190.52			−0.468330			−0.234165	+	0.972197i	$0.575236\pi$
$432$	194.605	−	828.539i	0.0216735	−	0.0922757i
$433$		−	947.222i		−	0.105128i	−0.998618	−	0.0525642i	$-0.983261\pi$
$433$		−	947.222i		−	0.105128i	0.998618	−	0.0525642i	$-0.0167394\pi$
$434$	−11848.6	+	4125.08i	−1.31048	+	0.456244i
$435$			219.754i			0.0242216i
$436$	2214.99	+	2795.52i	0.243300	+	0.307067i
$437$	−3214.31	+	3530.96i	−0.351857	+	0.386519i
$438$	13.0281	+	37.4209i	0.00142125	+	0.00408229i
$439$	−12602.5			−1.37013			−0.685064	−	0.728483i	$-0.740226\pi$
$439$	−12602.5			−1.37013			−0.685064	+	0.728483i	$0.740226\pi$
$440$	−2287.62	+	3602.85i	−0.247859	+	0.390362i
$441$	−485.888			−0.0524660
$442$	1292.77	−	450.076i	0.139119	−	0.0484343i
$443$			12836.0i			1.37665i	0.725403	+	0.688324i	$0.241653\pi$
$443$			12836.0i			1.37665i	−0.725403	+	0.688324i	$0.758347\pi$
$444$	295.107	+	372.452i	0.0315432	+	0.0398103i
$445$			5478.85i			0.583646i
$446$	4106.13	+	11794.2i	0.435943	+	1.25217i
$447$	285.540			0.0302138
$448$	−8353.12	+	3925.90i	−0.880910	+	0.414021i
$449$			1709.97i			0.179730i	0.995954	+	0.0898648i	$0.0286435\pi$
$449$			1709.97i			0.179730i	−0.995954	+	0.0898648i	$0.971356\pi$
$450$	1989.80	+	5715.36i	0.208444	+	0.598721i
$451$	2344.32			0.244767
$452$	95.4367	+	120.450i	0.00993133	+	0.0125342i
$453$	−52.5921			−0.00545473
$454$	−667.352	−	1916.86i	−0.0689876	−	0.198155i
$455$	−1581.42			−0.162941
$456$	121.713	+	445.693i	0.0124994	+	0.0457708i
$457$	10689.7			1.09418			0.547091	−	0.837073i	$-0.315735\pi$
$457$	10689.7			1.09418			0.547091	+	0.837073i	$0.315735\pi$
$458$	−4632.62	−	13306.4i	−0.472637	−	1.35757i
$459$	495.276			0.0503649
$460$	1933.73	+	2440.54i	0.196001	+	0.247371i
$461$	−11078.7			−1.11927			−0.559637	−	0.828738i	$-0.689060\pi$
$461$	−11078.7			−1.11927			−0.559637	+	0.828738i	$0.689060\pi$
$462$	115.471	+	331.672i	0.0116282	+	0.0334000i
$463$		−	7553.41i		−	0.758179i	−0.925360	−	0.379089i	$-0.876237\pi$
$463$		−	7553.41i		−	0.758179i	0.925360	−	0.379089i	$-0.123763\pi$
$464$	8226.26	+	1932.16i	0.823049	+	0.193315i
$465$	409.544			0.0408433
$466$	4511.15	+	12957.5i	0.448444	+	1.28808i
$467$		−	8523.35i		−	0.844568i	−0.906463	−	0.422284i	$-0.861228\pi$
$467$		−	8523.35i		−	0.844568i	0.906463	−	0.422284i	$-0.138772\pi$
$468$	−1739.20	−	2195.03i	−0.171783	−	0.216806i
$469$		−	9463.85i		−	0.931769i
$470$	−3991.32	+	1389.58i	−0.391714	+	0.136375i
$471$	−185.818			−0.0181784
$472$	15808.5	+	10037.6i	1.54162	+	0.978849i
$473$	−7469.36			−0.726092
$474$	−174.413	−	500.971i	−0.0169009	−	0.0485451i
$475$	−4864.27	−	4428.05i	−0.469869	−	0.427732i
$476$	−3335.57	−	4209.79i	−0.321188	−	0.405369i
$477$			16644.1i			1.59765i
$478$	6079.18	−	2116.46i	0.581705	−	0.202520i
$479$			7333.27i			0.699511i	0.936841	+	0.349755i	$0.113735\pi$
$479$			7333.27i			0.699511i	−0.936841	+	0.349755i	$0.886265\pi$
$480$	299.647	−	31.3760i	0.0284936	−	0.00298357i
$481$	3130.81			0.296783
$482$	−9458.16	+	3292.85i	−0.893791	+	0.311173i
$483$	256.235			0.0241389
$484$	−3451.49	+	2734.74i	−0.324144	+	0.256831i
$485$		−	10212.0i		−	0.956086i
$486$	−499.920	−	1435.94i	−0.0466601	−	0.134023i
$487$	−13062.6			−1.21545			−0.607726	−	0.794147i	$-0.707918\pi$
$487$	−13062.6			−1.21545			−0.607726	+	0.794147i	$0.707918\pi$
$488$	265.805	+	168.772i	0.0246566	+	0.0156557i
$489$		−	755.178i		−	0.0698371i
$490$	−113.235	−	325.249i	−0.0104397	−	0.0299863i
$491$			4975.70i			0.457333i	0.973505	+	0.228666i	$0.0734365\pi$
$491$			4975.70i			0.457333i	−0.973505	+	0.228666i	$0.926563\pi$
$492$	−102.779	−	129.716i	−0.00941796	−	0.0118863i
$493$			4917.41i			0.449228i
$494$	2799.56	+	1195.08i	0.254976	+	0.108845i
$495$			5081.01i			0.461362i
$496$	3600.87	−	15330.9i	0.325975	−	1.38785i
$497$		−	8300.95i		−	0.749192i
$498$	378.306	−	131.707i	0.0340407	−	0.0118513i
$499$		−	21943.7i		−	1.96861i	−0.176482	−	0.984304i	$-0.556472\pi$
$499$		−	21943.7i		−	1.96861i	0.176482	−	0.984304i	$-0.443528\pi$
$500$	−8653.41	+	6856.41i	−0.773985	+	0.613256i
$501$	−539.088			−0.0480732
$502$	3143.70	−	1094.48i	0.279502	−	0.0973086i
$503$			13089.0i			1.16026i	0.814526	+	0.580128i	$0.196997\pi$
$503$			13089.0i			1.16026i	−0.814526	+	0.580128i	$0.803003\pi$
$504$	−5890.09	+	9276.50i	−0.520566	+	0.819857i
$505$	−2771.25			−0.244196
$506$	−1497.96	−	4302.64i	−0.131606	−	0.378015i
$507$	−500.019			−0.0438001
$508$	−15236.1	+	12072.1i	−1.33070	+	1.05436i
$509$		−	10972.3i		−	0.955481i	−0.878501	−	0.477740i	$-0.841456\pi$
$509$		−	10972.3i		−	0.955481i	0.878501	−	0.477740i	$-0.158544\pi$
$510$	57.6466	+	165.580i	0.00500517	+	0.0143765i
$511$		−	1024.33i		−	0.0886767i
$512$	1460.08	−	11492.9i	0.126030	−	0.992026i
$513$	814.431	+	741.395i	0.0700936	+	0.0638078i
$514$	10308.2	−	3588.81i	0.884586	−	0.307968i
$515$	−1457.66			−0.124722
$516$	327.470	+	413.296i	0.0279381	+	0.0352604i
$517$	6183.75			0.526036
$518$	−4039.02	−	11601.4i	−0.342595	−	0.984047i
$519$		−	644.247i		−	0.0544880i
$520$	1064.02	−	1675.76i	0.0897312	−	0.141321i
$521$			4576.17i			0.384809i	0.981316	+	0.192405i	$0.0616286\pi$
$521$			4576.17i			0.384809i	−0.981316	+	0.192405i	$0.938371\pi$
$522$	9501.02	−	3307.77i	0.796644	−	0.277351i
$523$	−3916.28			−0.327432			−0.163716	−	0.986507i	$-0.552348\pi$
$523$	−3916.28			−0.327432			−0.163716	+	0.986507i	$0.552348\pi$
$524$	−8000.12	−	10096.9i	−0.666959	−	0.841763i
$525$			352.991i			0.0293443i
$526$	8009.18	−	2788.39i	0.663911	−	0.231140i
$527$	9164.33			0.757504
$528$	−429.150	−	100.798i	−0.0353719	−	0.00830805i
$529$	8842.98			0.726800
$530$	−11141.4	+	3878.87i	−0.913117	+	0.317901i
$531$	22294.3			1.82202
$532$	816.766	−	11915.7i	0.0665626	−	0.971074i
$533$	−1090.39			−0.0886116
$534$	−534.462	+	186.073i	−0.0433117	+	0.0150789i
$535$	−4870.42			−0.393582
$536$	10028.4	+	6367.51i	0.808137	+	0.513124i
$537$	695.478			0.0558884
$538$	18684.3	−	6504.93i	1.49728	−	0.521278i
$539$			503.909i			0.0402688i
$540$	562.921	−	446.023i	0.0448597	−	0.0355440i
$541$	8269.02			0.657140			0.328570	−	0.944480i	$-0.393433\pi$
$541$	8269.02			0.657140			0.328570	+	0.944480i	$0.393433\pi$
$542$	−19917.5	+	6934.26i	−1.57847	+	0.549543i
$543$			856.973i			0.0677279i
$544$	6705.18	−	702.099i	0.528460	−	0.0553350i
$545$			3009.79i			0.236560i
$546$	−53.7080	−	154.267i	−0.00420969	−	0.0120916i
$547$	23472.3			1.83474			0.917371	−	0.398034i	$-0.130307\pi$
$547$	23472.3			1.83474			0.917371	+	0.398034i	$0.130307\pi$
$548$	14440.8	−	11442.0i	1.12569	−	0.891928i
$549$	374.858			0.0291412
$550$	5927.34	−	2063.60i	0.459532	−	0.159986i
$551$	−7361.04	+	8086.19i	−0.569130	+	0.625197i
$552$	−172.401	+	271.521i	−0.0132933	+	0.0209360i
$553$			13713.2i			1.05451i
$554$	4387.04	+	12601.0i	0.336439	+	0.966365i
$555$			401.000i			0.0306694i
$556$	−10870.4	−	13719.4i	−0.829150	−	1.04646i
$557$	−1240.44			−0.0943609			−0.0471804	−	0.998886i	$-0.515024\pi$
$557$	−1240.44			−0.0943609			−0.0471804	+	0.998886i	$0.515024\pi$
$558$	−6164.53	−	17706.6i	−0.467680	−	1.34333i
$559$	3474.15			0.262864
$560$	−7582.29	−	1780.91i	−0.572161	−	0.134388i
$561$		−	256.533i		−	0.0193063i
$562$	12340.0	−	4296.15i	0.926209	−	0.322459i
$563$	15015.3			1.12402			0.562008	−	0.827132i	$-0.310029\pi$
$563$	15015.3			1.12402			0.562008	+	0.827132i	$0.310029\pi$
$564$	−271.106	−	342.160i	−0.0202405	−	0.0255453i
$565$			129.682i			0.00965622i
$566$	−14280.4	+	4971.70i	−1.06051	+	0.369216i
$567$			13052.8i			0.966784i
$568$	8796.14	+	5585.09i	0.649785	+	0.412580i
$569$			15488.5i			1.14114i	0.821248	+	0.570572i	$0.193278\pi$
$569$			15488.5i			1.14114i	−0.821248	+	0.570572i	$0.806722\pi$
$570$	−153.068	+	358.573i	−0.0112479	+	0.0263491i
$571$		−	775.283i		−	0.0568207i	−0.999596	−	0.0284103i	$-0.990955\pi$
$571$		−	775.283i		−	0.0568207i	0.999596	−	0.0284103i	$-0.00904451\pi$
$572$	−2276.44	+	1803.71i	−0.166403	+	0.131847i
$573$			1112.26i			0.0810914i
$574$	1406.70	+	4040.50i	0.102290	+	0.293811i
$575$		−	4579.19i		−	0.332114i
$576$	−5866.88	−	12482.9i	−0.424398	−	0.902989i
$577$	−24620.6			−1.77638			−0.888189	−	0.459477i	$-0.848037\pi$
$577$	−24620.6			−1.77638			−0.888189	+	0.459477i	$0.848037\pi$
$578$	−3278.97	−	9418.29i	−0.235964	−	0.677767i
$579$			717.009i			0.0514644i
$580$	4428.40	+	5589.04i	0.317033	+	0.400124i
$581$	−10355.5			−0.739444
$582$	996.178	−	346.819i	0.0709500	−	0.0247012i
$583$	17261.4			1.22623
$584$	1085.44	+	689.197i	0.0769106	+	0.0488342i
$585$		−	2363.27i		−	0.167025i
$586$	−20426.3	+	7111.39i	−1.43993	+	0.501312i
$587$			11764.0i			0.827177i	0.910464	+	0.413589i	$0.135725\pi$
$587$			11764.0i			0.827177i	−0.910464	+	0.413589i	$0.864275\pi$
$588$	27.8824	−	22.0922i	0.00195553	−	0.00154943i
$589$	15069.8	+	13718.4i	1.05423	+	0.959688i
$590$	5195.66	+	14923.6i	0.362546	+	1.04135i
$591$	−947.345			−0.0659367
$592$	15011.0	+	3525.75i	1.04214	+	0.244776i
$593$	16530.7			1.14475			0.572374	−	0.819992i	$-0.306022\pi$
$593$	16530.7			1.14475			0.572374	+	0.819992i	$0.306022\pi$
$594$	−992.422	+	345.511i	−0.0685515	+	0.0238662i
$595$		−	4532.47i		−	0.312291i
$596$	7262.18	−	5754.09i	0.499112	−	0.395464i
$597$			352.200i			0.0241450i
$598$	696.731	+	2001.24i	0.0476445	+	0.136851i
$599$	−13931.4			−0.950287			−0.475144	−	0.879908i	$-0.657604\pi$
$599$	−13931.4			−0.950287			−0.475144	+	0.879908i	$0.657604\pi$
$600$	−374.048	−	237.501i	−0.0254507	−	0.0161599i
$601$		−	9827.90i		−	0.667035i	−0.942744	−	0.333518i	$-0.891764\pi$
$601$		−	9827.90i		−	0.667035i	0.942744	−	0.333518i	$-0.108236\pi$
$602$	−4481.96	−	12873.7i	−0.303440	−	0.871580i
$603$	14142.8			0.955123
$604$	−1337.59	+	1059.82i	−0.0901086	+	0.0713963i
$605$	−3716.04			−0.249716
$606$	−94.1171	−	270.335i	−0.00630898	−	0.0181215i
$607$	−17738.3			−1.18612			−0.593062	−	0.805157i	$-0.702081\pi$
$607$	−17738.3			−1.18612			−0.593062	+	0.805157i	$0.702081\pi$
$608$	12077.0	+	8882.68i	0.805570	+	0.592500i
$609$	586.799			0.0390448
$610$	87.3601	+	250.927i	0.00579853	+	0.0166553i
$611$	−2876.18			−0.190438
$612$	6291.13	−	4984.69i	0.415529	−	0.329239i
$613$	−20232.0			−1.33305			−0.666527	−	0.745481i	$-0.732220\pi$
$613$	−20232.0			−1.33305			−0.666527	+	0.745481i	$0.732220\pi$
$614$	6281.57	+	18042.7i	0.412872	+	1.18590i
$615$		−	139.659i		−	0.00915707i
$616$	9620.55	+	6108.54i	0.629258	+	0.399546i
$617$	−14241.5			−0.929237			−0.464619	−	0.885511i	$-0.653809\pi$
$617$	−14241.5			−0.929237			−0.464619	+	0.885511i	$0.653809\pi$
$618$	−49.5049	−	142.194i	−0.00322230	−	0.00925550i
$619$		−	5159.71i		−	0.335034i	−0.985869	−	0.167517i	$-0.946425\pi$
$619$		−	5159.71i		−	0.335034i	0.985869	−	0.167517i	$-0.0535750\pi$
$620$	10416.0	−	8252.97i	0.674704	−	0.534593i
$621$			766.701i			0.0495437i
$622$	−23184.6	+	8071.70i	−1.49456	+	0.520331i
$623$	14630.0			0.940830
$624$	199.606	+	46.8829i	0.0128055	+	0.00300772i
$625$	611.428			0.0391314
$626$	−7158.02	−	20560.2i	−0.457016	−	1.31270i
$627$	384.013	−	421.843i	0.0244593	−	0.0268689i
$628$	−4725.94	+	3744.54i	−0.300296	+	0.237935i
$629$			8973.15i			0.568812i
$630$	−8757.26	+	3048.83i	−0.553805	+	0.192807i
$631$			10372.3i			0.654379i	0.944959	+	0.327189i	$0.106102\pi$
$631$			10372.3i			0.654379i	−0.944959	+	0.327189i	$0.893898\pi$
$632$	−14531.3	−	9226.59i	−0.914593	−	0.580719i
$633$	127.410			0.00800017
$634$	−20576.5	+	7163.70i	−1.28896	+	0.448749i
$635$	−16403.9			−1.02515
$636$	−756.768	−	955.110i	−0.0471821	−	0.0595481i
$637$		−	234.378i		−	0.0145783i
$638$	−3430.45	−	9853.40i	−0.212873	−	0.611442i
$639$	12405.0			0.767970
$640$	6988.70	−	6836.37i	0.431645	−	0.422236i
$641$		−	11020.9i		−	0.679095i	−0.940589	−	0.339548i	$-0.889726\pi$
$641$		−	11020.9i		−	0.679095i	0.940589	−	0.339548i	$-0.110274\pi$
$642$	−165.409	−	475.109i	−0.0101685	−	0.0292073i
$643$			7290.19i			0.447118i	0.974690	+	0.223559i	$0.0717676\pi$
$643$			7290.19i			0.447118i	−0.974690	+	0.223559i	$0.928232\pi$
$644$	6516.87	−	5163.56i	0.398759	−	0.315951i
$645$			444.975i			0.0271641i
$646$	−3425.20	+	8023.77i	−0.208611	+	0.488686i
$647$			28226.3i			1.71513i	0.514374	+	0.857566i	$0.328024\pi$
$647$			28226.3i			1.71513i	−0.514374	+	0.857566i	$0.671976\pi$
$648$	−13831.5	−	8782.26i	−0.838505	−	0.532407i
$649$		−	23121.2i		−	1.39844i
$650$	−2756.92	+	959.819i	−0.166362	+	0.0579188i
$651$		−	1093.59i		−	0.0658388i
$652$	−15218.1	−	19206.6i	−0.914089	−	1.15366i
$653$	10817.7			0.648282			0.324141	−	0.946009i	$-0.394925\pi$
$653$	10817.7			0.648282			0.324141	+	0.946009i	$0.394925\pi$
$654$	−293.605	+	102.218i	−0.0175549	+	0.00611171i
$655$		−	10870.8i		−	0.648483i
$656$	−5228.00	−	1227.94i	−0.311157	−	0.0730837i
$657$	1530.77			0.0908993
$658$	3710.53	+	10657.9i	0.219835	+	0.631439i
$659$	1116.92			0.0660228			0.0330114	−	0.999455i	$-0.489490\pi$
$659$	1116.92			0.0660228			0.0330114	+	0.999455i	$0.489490\pi$
$660$	−231.022	−	291.571i	−0.0136250	−	0.0171960i
$661$		−	4627.22i		−	0.272282i	−0.990689	−	0.136141i	$-0.956530\pi$
$661$		−	4627.22i		−	0.272282i	0.990689	−	0.136141i	$-0.0434700\pi$
$662$	2157.57	+	6197.25i	0.126671	+	0.363842i
$663$			119.319i			0.00698936i
$664$	6967.42	−	10973.2i	0.407211	−	0.641330i
$665$	6784.80	−	7453.19i	0.395644	−	0.434620i
$666$	17337.2	−	6035.92i	1.00871	−	0.351182i
$667$	−7612.29			−0.441903
$668$	−13710.7	+	10863.5i	−0.794137	+	0.629224i
$669$	−1088.56			−0.0629093
$670$	3295.96	+	9467.08i	0.190051	+	0.545888i
$671$		−	388.761i		−	0.0223665i
$672$	−83.7821	−	800.135i	−0.00480947	−	0.0459314i
$673$			14665.8i			0.840005i	0.907523	+	0.420003i	$0.137971\pi$
$673$			14665.8i			0.840005i	−0.907523	+	0.420003i	$0.862029\pi$
$674$	23641.6	−	8230.81i	1.35110	−	0.470384i
$675$	−1056.21			−0.0602275
$676$	−12717.1	+	10076.2i	−0.723548	+	0.573293i
$677$		−	14128.4i		−	0.802068i	−0.916063	−	0.401034i	$-0.868651\pi$
$677$		−	14128.4i		−	0.802068i	0.916063	−	0.401034i	$-0.131349\pi$
$678$	−12.6505	+	4.40425i	−0.000716576	+	0.000249475i
$679$	−27268.6			−1.54120
$680$	4802.85	+	3049.56i	0.270854	+	0.171978i
$681$	176.920			0.00995533
$682$	−18363.3	+	6393.16i	−1.03104	+	0.358954i
$683$	−733.205			−0.0410766			−0.0205383	−	0.999789i	$-0.506538\pi$
$683$	−733.205			−0.0410766			−0.0205383	+	0.999789i	$0.506538\pi$
$684$	17806.9	+	1220.58i	0.995413	+	0.0682309i
$685$	15547.7			0.867220
$686$	−17384.8	+	6052.52i	−0.967574	+	0.336860i
$687$	1228.14			0.0682044
$688$	16657.2	+	3912.40i	0.923038	+	0.216800i
$689$	−8028.60			−0.443926
$690$	−256.323	+	89.2385i	−0.0141421	+	0.00492356i
$691$		−	23761.7i		−	1.30816i	−0.756425	−	0.654081i	$-0.773056\pi$
$691$		−	23761.7i		−	1.30816i	0.756425	−	0.654081i	$-0.226944\pi$
$692$	−12982.6	−	16385.2i	−0.713187	−	0.900107i
$693$	13567.6			0.743710
$694$	8538.83	−	2972.79i	0.467046	−	0.162602i
$695$		−	14771.0i		−	0.806181i
$696$	−394.813	+	621.805i	−0.0215020	+	0.0338641i
$697$		−	3125.14i		−	0.169832i
$698$	2472.47	+	7101.76i	0.134075	+	0.385108i
$699$	−1195.94			−0.0647132
$700$	7113.34	+	8977.68i	0.384084	+	0.484749i
$701$	−11502.4			−0.619744			−0.309872	−	0.950778i	$-0.600286\pi$
$701$	−11502.4			−0.619744			−0.309872	+	0.950778i	$0.600286\pi$
$702$	461.595	−	160.704i	0.0248173	−	0.00864014i
$703$	−13432.2	+	14755.4i	−0.720633	+	0.791624i
$704$	−12945.9	+	6084.48i	−0.693064	+	0.325735i
$705$		−	368.386i		−	0.0196798i
$706$	−2458.09	−	7060.46i	−0.131036	−	0.376379i
$707$			7399.96i			0.393641i
$708$	−1279.35	+	1013.67i	−0.0679107	+	0.0538081i
$709$	−1059.93			−0.0561446			−0.0280723	−	0.999606i	$-0.508937\pi$
$709$	−1059.93			−0.0561446			−0.0280723	+	0.999606i	$0.508937\pi$
$710$	2890.96	+	8303.79i	0.152811	+	0.438924i
$711$	−20493.1			−1.08094
$712$	−9843.40	+	15502.7i	−0.518114	+	0.815995i
$713$			14186.6i			0.745152i
$714$	442.142	−	153.931i	0.0231747	−	0.00806826i
$715$	−2450.92			−0.128195
$716$	17688.2	−	14015.0i	0.923240	−	0.731517i
$717$			561.089i			0.0292249i
$718$	17725.8	−	6171.22i	0.921338	−	0.320763i
$719$		−	29499.6i		−	1.53011i	−0.643964	−	0.765056i	$-0.722711\pi$
$719$		−	29499.6i		−	1.53011i	0.643964	−	0.765056i	$-0.277289\pi$
$720$	2661.39	−	11331.0i	0.137756	−	0.586502i
$721$			3892.32i			0.201051i
$722$	−17643.4	+	8066.98i	−0.909447	+	0.415820i
$723$		−	872.959i		−	0.0449041i
$724$	17269.4	+	21795.6i	0.886482	+	1.11882i
$725$		−	10486.7i		−	0.537196i
$726$	−126.204	−	362.499i	−0.00645161	−	0.0185311i
$727$			1252.42i			0.0638921i	0.999490	+	0.0319460i	$0.0101705\pi$
$727$			1252.42i			0.0638921i	−0.999490	+	0.0319460i	$0.989830\pi$
$728$	−4474.70	−	2841.20i	−0.227807	−	0.144646i
$729$	−19417.6			−0.986518
$730$	356.743	+	1024.68i	0.0180872	+	0.0519523i
$731$			9957.18i			0.503802i
$732$	−21.5110	+	17.0439i	−0.00108616	+	0.000860604i
$733$	−16775.4			−0.845311			−0.422656	−	0.906290i	$-0.638902\pi$
$733$	−16775.4			−0.845311			−0.422656	+	0.906290i	$0.638902\pi$
$734$	15033.9	−	5234.04i	0.756010	−	0.263205i
$735$	30.0195			0.00150651
$736$	1086.87	+	10379.8i	0.0544327	+	0.519843i
$737$		−	14667.3i		−	0.733078i
$738$	−6038.14	+	2102.17i	−0.301175	+	0.104854i
$739$		−	34345.2i		−	1.70962i	−0.518943	−	0.854809i	$-0.673674\pi$
$739$		−	34345.2i		−	1.70962i	0.518943	−	0.854809i	$-0.326326\pi$
$740$	8080.80	+	10198.7i	0.401427	+	0.506638i
$741$	−178.612	+	196.207i	−0.00885488	+	0.00972720i
$742$	10357.6	+	29750.5i	0.512452	+	1.47193i
$743$	792.738			0.0391423			0.0195712	−	0.999808i	$-0.493770\pi$
$743$	792.738			0.0391423			0.0195712	+	0.999808i	$0.493770\pi$
$744$	1158.83	+	735.793i	0.0571029	+	0.0362574i
$745$	7818.82			0.384509
$746$	−7496.12	+	2609.77i	−0.367899	+	0.128084i
$747$		−	15475.2i		−	0.757977i
$748$	−5169.56	−	6524.46i	−0.252698	−	0.318927i
$749$			13005.3i			0.634450i
$750$	−316.413	−	908.842i	−0.0154050	−	0.0442483i
$751$	13768.5			0.668999			0.334499	−	0.942396i	$-0.391433\pi$
$751$	13768.5			0.668999			0.334499	+	0.942396i	$0.391433\pi$
$752$	−13790.2	−	3239.00i	−0.668718	−	0.157067i
$753$			290.154i			0.0140422i
$754$	1595.57	+	4583.01i	0.0770653	+	0.221357i
$755$	−1440.11			−0.0694185
$756$	−1191.00	−	1503.15i	−0.0572965	−	0.0723133i
$757$	8227.22			0.395011			0.197505	−	0.980302i	$-0.436716\pi$
$757$	8227.22			0.395011			0.197505	+	0.980302i	$0.436716\pi$
$758$	−10370.2	−	29786.6i	−0.496915	−	1.42730i
$759$	397.120			0.0189915
$760$	3332.82	+	12204.2i	0.159071	+	0.582492i
$761$	22146.6			1.05495			0.527473	−	0.849572i	$-0.323140\pi$
$761$	22146.6			1.05495			0.527473	+	0.849572i	$0.323140\pi$
$762$	−557.110	−	1600.20i	−0.0264855	−	0.0760751i
$763$	8036.93			0.381332
$764$	22413.9	+	28288.4i	1.06140	+	1.33958i
$765$	6773.33			0.320118
$766$	2478.93	+	7120.30i	0.116929	+	0.335858i
$767$			10754.1i			0.506269i
$768$	904.238	+	449.571i	0.0424855	+	0.0211230i
$769$	24420.5			1.14516			0.572578	−	0.819850i	$-0.305943\pi$
$769$	24420.5			1.14516			0.572578	+	0.819850i	$0.305943\pi$
$770$	3161.91	+	9082.05i	0.147984	+	0.425058i
$771$			951.419i			0.0444417i
$772$	14448.9	+	18235.8i	0.673611	+	0.850158i
$773$			19056.5i			0.886693i	0.896350	+	0.443347i	$0.146209\pi$
$773$			19056.5i			0.886693i	−0.896350	+	0.443347i	$0.853791\pi$
$774$	19238.4	−	6697.85i	0.893425	−	0.311045i
$775$	−19543.6			−0.905840
$776$	18347.0	−	28895.3i	0.848737	−	1.33670i
$777$	1070.77			0.0494386
$778$	8673.37	+	24912.8i	0.399685	+	1.14803i
$779$	4678.13	−	5138.98i	0.215162	−	0.236358i
$780$	107.453	+	135.615i	0.00493260	+	0.00622538i
$781$		−	12865.1i		−	0.589434i
$782$	−5735.71	+	1996.89i	−0.262287	+	0.0913152i
$783$			1755.81i			0.0801372i
$784$	263.943	−	1123.75i	0.0120237	−	0.0511913i
$785$	−5088.18			−0.231344
$786$	1060.44	−	369.193i	0.0481232	−	0.0167540i
$787$	20928.6			0.947932			0.473966	−	0.880543i	$-0.342822\pi$
$787$	20928.6			0.947932			0.473966	+	0.880543i	$0.342822\pi$
$788$	−24094.0	+	19090.6i	−1.08923	+	0.863037i
$789$			739.223i			0.0333549i
$790$	−4775.88	−	13717.9i	−0.215086	−	0.617799i
$791$	346.285			0.0155657
$792$	−9128.63	+	14377.0i	−0.409560	+	0.645030i
$793$			180.820i			0.00809724i
$794$	3048.86	+	8757.34i	0.136272	+	0.391419i
$795$		−	1028.32i		−	0.0458751i
$796$	7097.40	+	8957.56i	0.316031	+	0.398860i
$797$		−	10768.1i		−	0.478578i	−0.970948	−	0.239289i	$-0.923086\pi$
$797$		−	10768.1i		−	0.478578i	0.970948	−	0.239289i	$-0.0769143\pi$
$798$	957.483	+	408.732i	0.0424744	+	0.0181315i
$799$		−	8243.36i		−	0.364993i
$800$	−14299.3	+	1497.27i	−0.631944	+	0.0661708i
$801$			21863.1i			0.964411i
$802$	−35995.7	+	12531.9i	−1.58485	+	0.551766i
$803$		−	1587.54i		−	0.0697672i
$804$	−811.576	+	643.041i	−0.0355996	+	0.0282069i
$805$	7016.38			0.307199
$806$	8541.11	−	2973.58i	0.373260	−	0.129950i
$807$			1724.50i			0.0752236i
$808$	−7841.40	−	4978.88i	−0.341410	−	0.216778i
$809$	−3047.27			−0.132431			−0.0662153	−	0.997805i	$-0.521092\pi$
$809$	−3047.27			−0.132431			−0.0662153	+	0.997805i	$0.521092\pi$
$810$	−4545.88	−	13057.3i	−0.197193	−	0.566402i
$811$	7771.01			0.336470			0.168235	−	0.985747i	$-0.446193\pi$
$811$	7771.01			0.336470			0.168235	+	0.985747i	$0.446193\pi$
$812$	14924.2	−	11825.0i	0.644995	−	0.511053i
$813$		−	1838.32i		−	0.0793023i
$814$	−6259.79	−	17980.2i	−0.269540	−	0.774208i
$815$		−	20678.7i		−	0.888766i
$816$	−134.370	+	572.087i	−0.00576458	+	0.0245429i
$817$	−14905.2	+	16373.6i	−0.638272	+	0.701149i
$818$	43645.1	−	15195.0i	1.86555	−	0.649489i
$819$	−6310.56			−0.269241
$820$	−2814.36	−	3551.98i	−0.119856	−	0.151269i
$821$	5007.21			0.212854			0.106427	−	0.994321i	$-0.466059\pi$
$821$	5007.21			0.212854			0.106427	+	0.994321i	$0.466059\pi$
$822$	528.029	+	1516.67i	0.0224053	+	0.0643553i
$823$		−	9911.92i		−	0.419815i	−0.977721	−	0.209908i	$-0.932684\pi$
$823$		−	9911.92i		−	0.419815i	0.977721	−	0.209908i	$-0.0673163\pi$
$824$	−4124.52	−	2618.85i	−0.174374	−	0.110719i
$825$			547.075i			0.0230869i
$826$	39850.0	−	13873.8i	1.67864	−	0.584419i
$827$	−9110.45			−0.383073			−0.191536	−	0.981485i	$-0.561347\pi$
$827$	−9110.45			−0.383073			−0.191536	+	0.981485i	$0.561347\pi$
$828$	7716.43	+	9738.84i	0.323870	+	0.408754i
$829$		−	2360.30i		−	0.0988863i	−0.998777	−	0.0494432i	$-0.984255\pi$
$829$		−	2360.30i		−	0.0988863i	0.998777	−	0.0494432i	$-0.0157447\pi$
$830$	10359.0	−	3606.48i	0.433212	−	0.150823i
$831$	−1163.04			−0.0485503
$832$	6021.39	−	2830.01i	0.250906	−	0.117924i
$833$	671.745			0.0279407
$834$	1440.91	−	501.652i	0.0598257	−	0.0208283i
$835$	−14761.6			−0.611793
$836$	1265.85	−	18467.3i	0.0523687	−	0.764001i
$837$	3272.21			0.135130
$838$	26123.4	−	9094.86i	1.07687	−	0.374913i
$839$	21524.2			0.885696			0.442848	−	0.896597i	$-0.353968\pi$
$839$	21524.2			0.885696			0.442848	+	0.896597i	$0.353968\pi$
$840$	363.906	−	573.128i	0.0149476	−	0.0235414i
$841$	6956.22			0.285220
$842$	9482.03	−	3301.16i	0.388091	−	0.135114i
$843$			1138.94i			0.0465328i
$844$	3240.45	−	2567.53i	0.132158	−	0.104713i
$845$	−13691.8			−0.557412
$846$	−15927.1	+	5545.02i	−0.647265	+	0.225345i
$847$			9922.79i			0.402540i
$848$	−38494.1	−	9041.37i	−1.55883	−	0.366135i
$849$		−	1318.03i		−	0.0532801i
$850$	−2750.92	−	7901.55i	−0.111007	−	0.318848i
$851$	−13890.7			−0.559537
$852$	−711.852	+	564.026i	−0.0286240	+	0.0226798i
$853$	−10117.8			−0.406126			−0.203063	−	0.979166i	$-0.565090\pi$
$853$	−10117.8			−0.406126			−0.203063	+	0.979166i	$0.565090\pi$
$854$	670.040	−	233.274i	0.0268481	−	0.00934716i
$855$	11138.1	+	10139.2i	0.445513	+	0.405560i
$856$	−13781.1	−	8750.28i	−0.550267	−	0.349391i
$857$		−	24285.1i		−	0.967984i	−0.875072	−	0.483992i	$-0.839186\pi$
$857$		−	24285.1i		−	0.967984i	0.875072	−	0.483992i	$-0.160814\pi$
$858$	−83.2382	−	239.088i	−0.00331201	−	0.00951319i
$859$			3504.97i			0.139218i	0.997574	+	0.0696089i	$0.0221751\pi$
$859$			3504.97i			0.139218i	−0.997574	+	0.0696089i	$0.977825\pi$
$860$	8966.98	+	11317.1i	0.355548	+	0.448734i
$861$	−372.926			−0.0147611
$862$	−3897.04	−	11193.6i	−0.153984	−	0.442292i
$863$	24288.9			0.958057			0.479029	−	0.877799i	$-0.340989\pi$
$863$	24288.9			0.958057			0.479029	+	0.877799i	$0.340989\pi$
$864$	2394.15	−	250.691i	0.0942714	−	0.00987115i
$865$		−	17641.2i		−	0.693430i
$866$	2530.19	−	880.886i	0.0992835	−	0.0345655i
$867$	869.279			0.0340511
$868$	−22037.6	−	27813.4i	−0.861756	−	1.08761i
$869$			21253.1i			0.829647i
$870$	−587.000	+	204.364i	−0.0228749	+	0.00796388i
$871$			6822.06i			0.265392i
$872$	−5407.45	+	8516.37i	−0.209999	+	0.330735i
$873$		−	40750.3i		−	1.57983i
$874$	−12421.0	−	5302.30i	−0.480717	−	0.205209i
$875$			24878.0i			0.961176i
$876$	−87.8421	+	69.6004i	−0.00338802	+	0.00268445i
$877$			11128.3i			0.428477i	0.976781	+	0.214239i	$0.0687270\pi$
$877$			11128.3i			0.428477i	−0.976781	+	0.214239i	$0.931273\pi$
$878$	−11719.9	−	33663.5i	−0.450488	−	1.29395i
$879$		−	1885.28i		−	0.0723424i
$880$	−11751.2	−	2760.10i	−0.450153	−	0.105731i
$881$	−3121.00			−0.119352			−0.0596761	−	0.998218i	$-0.519007\pi$
$881$	−3121.00			−0.119352			−0.0596761	+	0.998218i	$0.519007\pi$
$882$	−451.859	−	1297.89i	−0.0172504	−	0.0495490i
$883$			23347.6i			0.889820i	0.895575	+	0.444910i	$0.146764\pi$
$883$			23347.6i			0.889820i	−0.895575	+	0.444910i	$0.853236\pi$
$884$	2404.46	+	3034.65i	0.0914829	+	0.115460i
$885$	−1377.41			−0.0523175
$886$	−34287.1	+	11937.0i	−1.30011	+	0.452632i
$887$	−30824.0			−1.16682			−0.583410	−	0.812178i	$-0.698282\pi$
$887$	−30824.0			−1.16682			−0.583410	+	0.812178i	$0.698282\pi$
$888$	−720.443	+	1134.65i	−0.0272258	+	0.0428788i
$889$			43802.8i			1.65253i
$890$	−14635.0	+	5095.15i	−0.551197	+	0.191899i
$891$			20229.6i			0.760626i
$892$	−27685.7	+	21936.3i	−1.03922	+	0.823412i
$893$	12339.8	−	13555.4i	0.462412	−	0.507966i
$894$	265.542	+	762.726i	0.00993408	+	0.0285340i
$895$	19044.0			0.711252
$896$	−18254.9	−	18661.6i	−0.680639	−	0.695806i
$897$	−184.708			−0.00687540
$898$	−4567.63	+	1590.22i	−0.169737	+	0.0590939i
$899$			32488.6i			1.20529i
$900$	−13416.3	+	10630.2i	−0.496899	+	0.393711i
$901$		−	23010.6i		−	0.850826i
$902$	2180.14	+	6262.09i	0.0804776	+	0.231158i
$903$	1188.20			0.0437882
$904$	−232.989	+	366.942i	−0.00857201	+	0.0135003i
$905$			23466.2i			0.861924i
$906$	−48.9089	−	140.483i	−0.00179348	−	0.00515146i
$907$	−25818.0			−0.945175			−0.472588	−	0.881284i	$-0.656680\pi$
$907$	−25818.0			−0.945175			−0.472588	+	0.881284i	$0.656680\pi$
$908$	4499.64	−	3565.22i	0.164456	−	0.130304i
$909$	−11058.5			−0.403507
$910$	−1470.67	−	4224.24i	−0.0535737	−	0.153881i
$911$	48823.6			1.77563			0.887814	−	0.460203i	$-0.152223\pi$
$911$	48823.6			1.77563			0.887814	+	0.460203i	$0.152223\pi$
$912$	−1077.33	+	739.596i	−0.0391163	+	0.0268536i
$913$	−16049.2			−0.581764
$914$	9941.03	+	28553.9i	0.359759	+	1.03335i
$915$	−23.1598			−0.000836764
$916$	31235.5	−	24749.0i	1.12669	−	0.892719i
$917$	−29027.8			−1.04535
$918$	460.590	+	1322.97i	0.0165596	+	0.0475647i
$919$		−	6701.62i		−	0.240550i	−0.992741	−	0.120275i	$-0.961622\pi$
$919$		−	6701.62i		−	0.240550i	0.992741	−	0.120275i	$-0.0383777\pi$
$920$	−4720.80	+	7434.94i	−0.169174	+	0.266438i
$921$	−1665.29			−0.0595799
$922$	−10302.8	−	29593.1i	−0.368010	−	1.05705i
$923$			5983.78i			0.213390i
$924$	−778.569	+	616.889i	−0.0277197	+	0.0219634i
$925$		−	19135.9i		−	0.680198i
$926$	20176.5	−	7024.42i	0.716026	−	0.249284i
$927$	−5816.70			−0.206090
$928$	2489.02	+	23770.6i	0.0880453	+	0.840850i
$929$	13923.4			0.491726			0.245863	−	0.969305i	$-0.420929\pi$
$929$	13923.4			0.491726			0.245863	+	0.969305i	$0.420929\pi$
$930$	380.862	+	1093.96i	0.0134290	+	0.0385725i
$931$	1104.62	+	1005.56i	0.0388854	+	0.0353983i
$932$	−30416.5	+	24100.1i	−1.06902	+	0.847024i
$933$		−	2139.87i		−	0.0750869i
$934$	22767.3	−	7926.43i	0.797612	−	0.277688i
$935$		−	7024.55i		−	0.245698i
$936$	4245.90	−	6687.01i	0.148271	−	0.233517i
$937$	−18429.2			−0.642536			−0.321268	−	0.946988i	$-0.604109\pi$
$937$	−18429.2			−0.642536			−0.321268	+	0.946988i	$0.604109\pi$
$938$	25279.6	−	8801.07i	0.879965	−	0.306359i
$939$	1897.64			0.0659502
$940$	−7423.59	−	9369.24i	−0.257586	−	0.325097i
$941$			6879.91i			0.238341i	0.992874	+	0.119170i	$0.0380235\pi$
$941$			6879.91i			0.238341i	−0.992874	+	0.119170i	$0.961977\pi$
$942$	−172.804	−	496.352i	−0.00597694	−	0.0171677i
$943$	4837.80			0.167063
$944$	−12110.7	+	51561.9i	−0.417553	+	1.77775i
$945$		−	1618.36i		−	0.0557092i
$946$	−6946.26	−	19952.0i	−0.238734	−	0.685723i
$947$			16211.0i			0.556269i	0.960542	+	0.278134i	$0.0897161\pi$
$947$			16211.0i			0.556269i	−0.960542	+	0.278134i	$0.910284\pi$
$948$	1175.98	−	931.774i	0.0402892	−	0.0319226i
$949$			738.395i			0.0252575i
$950$	7304.48	−	17111.2i	0.249462	−	0.584381i
$951$		−	1899.15i		−	0.0647572i
$952$	8143.11	−	12824.9i	0.277227	−	0.436613i
$953$			32845.9i			1.11646i	0.829687	+	0.558229i	$0.188519\pi$
$953$			32845.9i			1.11646i	−0.829687	+	0.558229i	$0.811481\pi$
$954$	−44459.2	+	15478.4i	−1.50882	+	0.525296i
$955$			30456.6i			1.03199i
$956$	11306.9	+	14270.3i	0.382521	+	0.482776i
$957$	909.438			0.0307189
$958$	−19588.4	+	6819.70i	−0.660619	+	0.229994i
$959$		−	41516.3i		−	1.39795i
$960$	362.473	+	771.230i	0.0121862	+	0.0259285i
$961$	30756.3			1.03240
$962$	2911.55	+	8362.93i	0.0975801	+	0.280282i
$963$	−19435.1			−0.650351
$964$	−17591.6	−	22202.1i	−0.587745	−	0.741787i
$965$			19633.6i			0.654950i
$966$	238.290	+	684.448i	0.00793671	+	0.0227968i
$967$			56506.8i			1.87915i	0.342344	+	0.939575i	$0.388779\pi$
$967$			56506.8i			1.87915i	−0.342344	+	0.939575i	$0.611221\pi$
$968$	−10514.7	−	6676.30i	−0.349128	−	0.221678i
$969$	−562.346	−	511.916i	−0.0186431	−	0.0169712i
$970$	27277.9	−	9496.80i	0.902930	−	0.314355i
$971$	−3515.59			−0.116190			−0.0580951	−	0.998311i	$-0.518503\pi$
$971$	−3515.59			−0.116190			−0.0580951	+	0.998311i	$0.518503\pi$
$972$	3370.72	−	2670.74i	0.111230	−	0.0881319i
$973$	−39442.4			−1.29955
$974$	−12147.8	−	34892.6i	−0.399632	−	1.14787i
$975$		−	254.455i		−	0.00835803i
$976$	−203.630	+	866.964i	−0.00667832	+	0.0284332i
$977$		−	13862.2i		−	0.453930i	−0.973903	−	0.226965i	$-0.927120\pi$
$977$		−	13862.2i		−	0.453930i	0.973903	−	0.226965i	$-0.0728803\pi$
$978$	2017.21	−	702.290i	0.0659543	−	0.0229619i
$979$	22673.9			0.740206
$980$	763.492	−	604.942i	0.0248866	−	0.0197185i
$981$			12010.4i			0.390890i
$982$	−13291.0	+	4627.24i	−0.431906	+	0.150368i
$983$	49556.9			1.60795			0.803977	−	0.594660i	$-0.202713\pi$
$983$	49556.9			1.60795			0.803977	+	0.594660i	$0.202713\pi$
$984$	250.914	−	395.173i	0.00812891	−	0.0128025i
$985$	−25940.8			−0.839129
$986$	−13135.3	+	4573.03i	−0.424251	+	0.147703i
$987$	−983.687			−0.0317235
$988$	−588.770	+	8589.50i	−0.0189588	+	0.276587i
$989$	−15414.0			−0.495588
$990$	−13572.2	+	4725.17i	−0.435711	+	0.151693i
$991$	−5834.20			−0.187013			−0.0935063	−	0.995619i	$-0.529808\pi$
$991$	−5834.20			−0.187013			−0.0935063	+	0.995619i	$0.529808\pi$
$992$	44300.1	−	4638.65i	1.41787	−	0.148465i
$993$	−571.987			−0.0182794
$994$	22173.3	−	7719.61i	0.707539	−	0.246329i
$995$			9644.15i			0.307276i
$996$	703.624	+	888.037i	0.0223847	+	0.0282515i
$997$	1423.78			0.0452271			0.0226136	−	0.999744i	$-0.492801\pi$
$997$	1423.78			0.0452271			0.0226136	+	0.999744i	$0.492801\pi$
$998$	58615.4	−	20406.9i	1.85916	−	0.647264i
$999$			3203.94i			0.101470i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.4.d.a.75.18	yes	28
4.3	odd	2	inner	76.4.d.a.75.12	yes	28
19.18	odd	2	inner	76.4.d.a.75.11	✓	28
76.75	even	2	inner	76.4.d.a.75.17	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.4.d.a.75.11	✓	28	19.18	odd	2	inner
76.4.d.a.75.12	yes	28	4.3	odd	2	inner
76.4.d.a.75.17	yes	28	76.75	even	2	inner
76.4.d.a.75.18	yes	28	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	76.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.929967 + 2.67117i) q^{2} -0.246541 q^{3} +(-6.27032 + 4.96820i) q^{4} -6.75093 q^{5} +(-0.229275 - 0.658553i) q^{6} +18.0267i q^{7} +(-19.1021 - 12.1288i) q^{8} -26.9392 q^{9} +O(q^{10})\)	\(q+(0.929967 + 2.67117i) q^{2} -0.246541 q^{3} +(-6.27032 + 4.96820i) q^{4} -6.75093 q^{5} +(-0.229275 - 0.658553i) q^{6} +18.0267i q^{7} +(-19.1021 - 12.1288i) q^{8} -26.9392 q^{9} +(-6.27814 - 18.0329i) q^{10} +27.9384i q^{11} +(1.54589 - 1.22487i) q^{12} -12.9947i q^{13} +(-48.1525 + 16.7643i) q^{14} +1.66438 q^{15} +(14.6339 - 62.3045i) q^{16} +37.2438 q^{17} +(-25.0526 - 71.9593i) q^{18} +(61.2436 + 55.7514i) q^{19} +(42.3305 - 33.5400i) q^{20} -4.44433i q^{21} +(-74.6282 + 25.9818i) q^{22} +57.6544i q^{23} +(4.70945 + 2.99026i) q^{24} -79.4249 q^{25} +(34.7110 - 12.0846i) q^{26} +13.2982 q^{27} +(-89.5606 - 113.034i) q^{28} +132.033i q^{29} +(1.54782 + 4.44585i) q^{30} +246.064 q^{31} +(180.035 - 18.8515i) q^{32} -6.88795i q^{33} +(34.6355 + 99.4845i) q^{34} -121.697i q^{35} +(168.918 - 133.840i) q^{36} +240.930i q^{37} +(-91.9671 + 215.439i) q^{38} +3.20372i q^{39} +(128.957 + 81.8810i) q^{40} -83.9105i q^{41} +(11.8716 - 4.13308i) q^{42} +267.352i q^{43} +(-138.803 - 175.183i) q^{44} +181.865 q^{45} +(-154.005 + 53.6166i) q^{46} -221.335i q^{47} +(-3.60785 + 15.3606i) q^{48} +18.0364 q^{49} +(-73.8625 - 212.158i) q^{50} -9.18211 q^{51} +(64.5602 + 81.4808i) q^{52} -617.838i q^{53} +(12.3669 + 35.5218i) q^{54} -188.610i q^{55} +(218.644 - 344.349i) q^{56} +(-15.0991 - 13.7450i) q^{57} +(-352.684 + 122.787i) q^{58} -827.579 q^{59} +(-10.4362 + 8.26899i) q^{60} -13.9150 q^{61} +(228.831 + 657.278i) q^{62} -485.626i q^{63} +(217.782 + 463.373i) q^{64} +87.7262i q^{65} +(18.3989 - 6.40557i) q^{66} -524.989 q^{67} +(-233.530 + 185.035i) q^{68} -14.2142i q^{69} +(325.075 - 113.175i) q^{70} -460.480 q^{71} +(514.596 + 326.742i) q^{72} -56.8229 q^{73} +(-643.566 + 224.057i) q^{74} +19.5815 q^{75} +(-661.002 - 45.3086i) q^{76} -503.638 q^{77} +(-8.55768 + 2.97935i) q^{78} +760.715 q^{79} +(-98.7925 + 420.613i) q^{80} +724.080 q^{81} +(224.139 - 78.0340i) q^{82} +574.450i q^{83} +(22.0803 + 27.8674i) q^{84} -251.430 q^{85} +(-714.142 + 248.628i) q^{86} -32.5516i q^{87} +(338.860 - 533.682i) q^{88} -811.570i q^{89} +(169.128 + 485.792i) q^{90} +234.252 q^{91} +(-286.439 - 361.511i) q^{92} -60.6647 q^{93} +(591.225 - 205.835i) q^{94} +(-413.452 - 376.374i) q^{95} +(-44.3860 + 4.64765i) q^{96} +1512.68i q^{97} +(16.7733 + 48.1784i) q^{98} -752.638i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 10 q^{4} - 4 q^{5} - 6 q^{6} + 192 q^{9}+O(q^{10}) \) 28 * q + 10 * q^4 - 4 * q^5 - 6 * q^6 + 192 * q^9	\( 28 q + 10 q^{4} - 4 q^{5} - 6 q^{6} + 192 q^{9} - 134 q^{16} - 80 q^{17} - 300 q^{20} - 26 q^{24} + 496 q^{25} - 90 q^{26} + 254 q^{28} - 16 q^{30} - 556 q^{36} - 626 q^{38} - 850 q^{42} + 976 q^{44} - 612 q^{45} + 188 q^{49} + 354 q^{54} - 580 q^{57} + 2534 q^{58} - 948 q^{61} - 1068 q^{62} - 1634 q^{64} + 1244 q^{66} + 1630 q^{68} - 184 q^{73} + 2276 q^{74} + 1688 q^{76} + 308 q^{77} + 3376 q^{80} - 2284 q^{81} - 740 q^{82} + 684 q^{85} + 1810 q^{92} + 824 q^{93} - 5222 q^{96}+O(q^{100}) \) 28 * q + 10 * q^4 - 4 * q^5 - 6 * q^6 + 192 * q^9 - 134 * q^16 - 80 * q^17 - 300 * q^20 - 26 * q^24 + 496 * q^25 - 90 * q^26 + 254 * q^28 - 16 * q^30 - 556 * q^36 - 626 * q^38 - 850 * q^42 + 976 * q^44 - 612 * q^45 + 188 * q^49 + 354 * q^54 - 580 * q^57 + 2534 * q^58 - 948 * q^61 - 1068 * q^62 - 1634 * q^64 + 1244 * q^66 + 1630 * q^68 - 184 * q^73 + 2276 * q^74 + 1688 * q^76 + 308 * q^77 + 3376 * q^80 - 2284 * q^81 - 740 * q^82 + 684 * q^85 + 1810 * q^92 + 824 * q^93 - 5222 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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