LMFDB - Embedded newform 76.6.d.a.75.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,6,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, 6, names="a")

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

chi := DirichletCharacter("76.75");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
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:	$12.1891703058$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			75.7
Character	$\chi$	$=$	76.75
Dual form			76.6.d.a.75.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.06482 - 2.51944i) q^{2} -9.05324 q^{3} +(19.3048 + 25.5211i) q^{4} -89.6042 q^{5} +(45.8530 + 22.8091i) q^{6} +100.840i q^{7} +(-33.4765 - 177.897i) q^{8} -161.039 q^{9} +O(q^{10})$	\(q+(-5.06482 - 2.51944i) q^{2} -9.05324 q^{3} +(19.3048 + 25.5211i) q^{4} -89.6042 q^{5} +(45.8530 + 22.8091i) q^{6} +100.840i q^{7} +(-33.4765 - 177.897i) q^{8} -161.039 q^{9} +(453.829 + 225.753i) q^{10} +417.410i q^{11} +(-174.771 - 231.048i) q^{12} -221.235i q^{13} +(254.061 - 510.738i) q^{14} +811.208 q^{15} +(-278.649 + 985.358i) q^{16} +902.754 q^{17} +(815.633 + 405.728i) q^{18} +(-1559.55 - 209.566i) q^{19} +(-1729.79 - 2286.79i) q^{20} -912.931i q^{21} +(1051.64 - 2114.11i) q^{22} -3960.57i q^{23} +(303.071 + 1610.54i) q^{24} +4903.91 q^{25} +(-557.389 + 1120.52i) q^{26} +3657.86 q^{27} +(-2573.55 + 1946.70i) q^{28} -8184.48i q^{29} +(-4108.62 - 2043.79i) q^{30} +1615.19 q^{31} +(3893.86 - 4288.62i) q^{32} -3778.91i q^{33} +(-4572.29 - 2274.44i) q^{34} -9035.71i q^{35} +(-3108.82 - 4109.88i) q^{36} +15524.2i q^{37} +(7370.82 + 4990.60i) q^{38} +2002.90i q^{39} +(2999.64 + 15940.3i) q^{40} -3213.43i q^{41} +(-2300.08 + 4623.83i) q^{42} +5057.78i q^{43} +(-10652.7 + 8058.02i) q^{44} +14429.8 q^{45} +(-9978.44 + 20059.6i) q^{46} +16814.6i q^{47} +(2522.67 - 8920.69i) q^{48} +6638.25 q^{49} +(-24837.4 - 12355.1i) q^{50} -8172.85 q^{51} +(5646.15 - 4270.90i) q^{52} -3741.22i q^{53} +(-18526.4 - 9215.77i) q^{54} -37401.7i q^{55} +(17939.2 - 3375.78i) q^{56} +(14118.9 + 1897.26i) q^{57} +(-20620.3 + 41452.9i) q^{58} -20359.6 q^{59} +(15660.2 + 20702.9i) q^{60} +47252.9 q^{61} +(-8180.65 - 4069.38i) q^{62} -16239.2i q^{63} +(-30526.6 + 11910.8i) q^{64} +19823.6i q^{65} +(-9520.75 + 19139.5i) q^{66} -38393.4 q^{67} +(17427.5 + 23039.2i) q^{68} +35856.0i q^{69} +(-22765.0 + 45764.2i) q^{70} +40905.3 q^{71} +(5391.02 + 28648.3i) q^{72} +6030.26 q^{73} +(39112.5 - 78627.5i) q^{74} -44396.3 q^{75} +(-24758.4 - 43846.9i) q^{76} -42091.7 q^{77} +(5046.18 - 10144.3i) q^{78} +25243.5 q^{79} +(24968.1 - 88292.2i) q^{80} +6016.94 q^{81} +(-8096.05 + 16275.4i) q^{82} +2710.50i q^{83} +(23299.0 - 17624.0i) q^{84} -80890.6 q^{85} +(12742.8 - 25616.8i) q^{86} +74096.0i q^{87} +(74255.9 - 13973.4i) q^{88} -106968. i q^{89} +(-73084.1 - 36355.0i) q^{90} +22309.4 q^{91} +(101078. - 76458.1i) q^{92} -14622.7 q^{93} +(42363.4 - 85162.9i) q^{94} +(139742. + 18778.0i) q^{95} +(-35252.0 + 38825.9i) q^{96} -116325. i q^{97} +(-33621.5 - 16724.7i) q^{98} -67219.2i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 22 q^{4} - 4 q^{5} - 246 q^{6} + 3516 q^{9}+O(q^{10}) $ 48 * q - 22 * q^4 - 4 * q^5 - 246 * q^6 + 3516 * q^9	$ 48 q - 22 q^{4} - 4 q^{5} - 246 q^{6} + 3516 q^{9} - 1222 q^{16} + 1000 q^{17} - 300 q^{20} + 17158 q^{24} + 24996 q^{25} + 12102 q^{26} + 6382 q^{28} - 16528 q^{30} + 27524 q^{36} + 3598 q^{38} + 35966 q^{42} - 65408 q^{44} - 13476 q^{45} - 143096 q^{49} - 148446 q^{54} - 53980 q^{57} - 117018 q^{58} + 133740 q^{61} + 28068 q^{62} - 78130 q^{64} + 128204 q^{66} - 48338 q^{68} - 104080 q^{73} + 48932 q^{74} - 251688 q^{76} + 184844 q^{77} + 80080 q^{80} + 375128 q^{81} + 175628 q^{82} - 384748 q^{85} + 139810 q^{92} + 183272 q^{93} + 601258 q^{96}+O(q^{100}) $ 48 * q - 22 * q^4 - 4 * q^5 - 246 * q^6 + 3516 * q^9 - 1222 * q^16 + 1000 * q^17 - 300 * q^20 + 17158 * q^24 + 24996 * q^25 + 12102 * q^26 + 6382 * q^28 - 16528 * q^30 + 27524 * q^36 + 3598 * q^38 + 35966 * q^42 - 65408 * q^44 - 13476 * q^45 - 143096 * q^49 - 148446 * q^54 - 53980 * q^57 - 117018 * q^58 + 133740 * q^61 + 28068 * q^62 - 78130 * q^64 + 128204 * q^66 - 48338 * q^68 - 104080 * q^73 + 48932 * q^74 - 251688 * q^76 + 184844 * q^77 + 80080 * q^80 + 375128 * q^81 + 175628 * q^82 - 384748 * q^85 + 139810 * q^92 + 183272 * q^93 + 601258 * 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 $

$2$	−5.06482	−	2.51944i	−0.895342	−	0.445379i
$2$	−5.06482	−	2.51944i	−0.895342	−	0.445379i
$3$	−9.05324			−0.580766			−0.290383	−	0.956911i	$-0.593783\pi$
$3$	−9.05324			−0.580766			−0.290383	+	0.956911i	$0.593783\pi$
$4$	19.3048	+	25.5211i	0.603275	+	0.797533i
$5$	−89.6042			−1.60289			−0.801444	−	0.598069i	$-0.795935\pi$
$5$	−89.6042			−1.60289			−0.801444	+	0.598069i	$0.795935\pi$
$6$	45.8530	+	22.8091i	0.519984	+	0.258661i
$7$			100.840i			0.777837i	0.921272	+	0.388919i	$0.127151\pi$
$7$			100.840i			0.777837i	−0.921272	+	0.388919i	$0.872849\pi$
$8$	−33.4765	−	177.897i	−0.184934	−	0.982751i
$9$	−161.039			−0.662711
$10$	453.829	+	225.753i	1.43513	+	0.713893i
$11$			417.410i			1.04011i	0.854132	+	0.520057i	$0.174089\pi$
$11$			417.410i			1.04011i	−0.854132	+	0.520057i	$0.825911\pi$
$12$	−174.771	−	231.048i	−0.350362	−	0.463180i
$13$		−	221.235i		−	0.363074i	−0.983384	−	0.181537i	$-0.941893\pi$
$13$		−	221.235i		−	0.363074i	0.983384	−	0.181537i	$-0.0581073\pi$
$14$	254.061	−	510.738i	0.346432	−	0.696430i
$15$	811.208			0.930903
$16$	−278.649	+	985.358i	−0.272118	+	0.962264i
$17$	902.754			0.757613			0.378806	−	0.925476i	$-0.376335\pi$
$17$	902.754			0.757613			0.378806	+	0.925476i	$0.376335\pi$
$18$	815.633	+	405.728i	0.593353	+	0.295158i
$19$	−1559.55	−	209.566i	−0.991092	−	0.133180i
$19$	−1559.55	−	209.566i	−0.991092	−	0.133180i
$20$	−1729.79	−	2286.79i	−0.966983	−	1.27836i
$21$		−	912.931i		−	0.451741i
$22$	1051.64	−	2114.11i	0.463245	−	0.931258i
$23$		−	3960.57i		−	1.56113i	−0.625076	−	0.780564i	$-0.714932\pi$
$23$		−	3960.57i		−	1.56113i	0.625076	−	0.780564i	$-0.285068\pi$
$24$	303.071	+	1610.54i	0.107403	+	0.570748i
$25$	4903.91			1.56925
$26$	−557.389	+	1120.52i	−0.161706	+	0.325076i
$27$	3657.86			0.965646
$28$	−2573.55	+	1946.70i	−0.620351	+	0.469250i
$29$		−	8184.48i		−	1.80716i	−0.428422	−	0.903579i	$-0.640930\pi$
$29$		−	8184.48i		−	1.80716i	0.428422	−	0.903579i	$-0.359070\pi$
$30$	−4108.62	−	2043.79i	−0.833476	−	0.414604i
$31$	1615.19			0.301870			0.150935	−	0.988544i	$-0.451772\pi$
$31$	1615.19			0.301870			0.150935	+	0.988544i	$0.451772\pi$
$32$	3893.86	−	4288.62i	0.672211	−	0.740360i
$33$		−	3778.91i		−	0.604063i
$34$	−4572.29	−	2274.44i	−0.678323	−	0.337425i
$35$		−	9035.71i		−	1.24679i
$36$	−3108.82	−	4109.88i	−0.399797	−	0.528534i
$37$			15524.2i			1.86426i	0.362126	+	0.932129i	$0.382051\pi$
$37$			15524.2i			1.86426i	−0.362126	+	0.932129i	$0.617949\pi$
$38$	7370.82	+	4990.60i	0.828051	+	0.560653i
$39$			2002.90i			0.210861i
$40$	2999.64	+	15940.3i	0.296428	+	1.57524i
$41$		−	3213.43i		−	0.298544i	−0.988796	−	0.149272i	$-0.952307\pi$
$41$		−	3213.43i		−	0.298544i	0.988796	−	0.149272i	$-0.0476931\pi$
$42$	−2300.08	+	4623.83i	−0.201196	+	0.404463i
$43$			5057.78i			0.417147i	0.978007	+	0.208573i	$0.0668820\pi$
$43$			5057.78i			0.417147i	−0.978007	+	0.208573i	$0.933118\pi$
$44$	−10652.7	+	8058.02i	−0.829525	+	0.627475i
$45$	14429.8			1.06225
$46$	−9978.44	+	20059.6i	−0.695293	+	1.39774i
$47$			16814.6i			1.11030i	0.831749	+	0.555152i	$0.187340\pi$
$47$			16814.6i			1.11030i	−0.831749	+	0.555152i	$0.812660\pi$
$48$	2522.67	−	8920.69i	0.158037	−	0.558850i
$49$	6638.25			0.394969
$50$	−24837.4	−	12355.1i	−1.40502	−	0.698912i
$51$	−8172.85			−0.439995
$52$	5646.15	−	4270.90i	0.289564	−	0.219034i
$53$		−	3741.22i		−	0.182946i	−0.995808	−	0.0914732i	$-0.970842\pi$
$53$		−	3741.22i		−	0.182946i	0.995808	−	0.0914732i	$-0.0291576\pi$
$54$	−18526.4	−	9215.77i	−0.864583	−	0.430078i
$55$		−	37401.7i		−	1.66719i
$56$	17939.2	−	3375.78i	0.764420	−	0.143848i
$57$	14118.9	+	1897.26i	0.575592	+	0.0773462i
$58$	−20620.3	+	41452.9i	−0.804870	+	1.61802i
$59$	−20359.6			−0.761446			−0.380723	−	0.924689i	$-0.624325\pi$
$59$	−20359.6			−0.761446			−0.380723	+	0.924689i	$0.624325\pi$
$60$	15660.2	+	20702.9i	0.561591	+	0.742426i
$61$	47252.9			1.62594			0.812969	−	0.582307i	$-0.197850\pi$
$61$	47252.9			1.62594			0.812969	+	0.582307i	$0.197850\pi$
$62$	−8180.65	−	4069.38i	−0.270277	−	0.134446i
$63$		−	16239.2i		−	0.515481i
$64$	−30526.6	+	11910.8i	−0.931599	+	0.363487i
$65$			19823.6i			0.581968i
$66$	−9520.75	+	19139.5i	−0.269037	+	0.540843i
$67$	−38393.4			−1.04489			−0.522444	−	0.852674i	$-0.674980\pi$
$67$	−38393.4			−1.04489			−0.522444	+	0.852674i	$0.674980\pi$
$68$	17427.5	+	23039.2i	0.457049	+	0.604221i
$69$			35856.0i			0.906649i
$70$	−22765.0	+	45764.2i	−0.555292	+	1.11630i
$71$	40905.3			0.963017			0.481508	−	0.876442i	$-0.340089\pi$
$71$	40905.3			0.963017			0.481508	+	0.876442i	$0.340089\pi$
$72$	5391.02	+	28648.3i	0.122558	+	0.651280i
$73$	6030.26			0.132443			0.0662215	−	0.997805i	$-0.478906\pi$
$73$	6030.26			0.132443			0.0662215	+	0.997805i	$0.478906\pi$
$74$	39112.5	−	78627.5i	0.830301	−	1.66915i
$75$	−44396.3			−0.911368
$76$	−24758.4	−	43846.9i	−0.491686	−	0.870772i
$77$	−42091.7			−0.809039
$78$	5046.18	−	10144.3i	0.0939131	−	0.188793i
$79$	25243.5			0.455073			0.227536	−	0.973770i	$-0.426933\pi$
$79$	25243.5			0.455073			0.227536	+	0.973770i	$0.426933\pi$
$80$	24968.1	−	88292.2i	0.436174	−	1.54240i
$81$	6016.94			0.101897
$82$	−8096.05	+	16275.4i	−0.132965	+	0.267299i
$83$			2710.50i			0.0431871i	0.999767	+	0.0215935i	$0.00687397\pi$
$83$			2710.50i			0.0431871i	−0.999767	+	0.0215935i	$0.993126\pi$
$84$	23299.0	−	17624.0i	0.360278	−	0.272524i
$85$	−80890.6			−1.21437
$86$	12742.8	−	25616.8i	0.185788	−	0.373489i
$87$			74096.0i			1.04953i
$88$	74255.9	−	13973.4i	1.02217	−	0.192352i
$89$		−	106968.i		−	1.43146i	−0.698376	−	0.715731i	$-0.746094\pi$
$89$		−	106968.i		−	1.43146i	0.698376	−	0.715731i	$-0.253906\pi$
$90$	−73084.1	−	36355.0i	−0.951079	−	0.473105i
$91$	22309.4			0.282413
$92$	101078.	−	76458.1i	1.24505	−	0.941790i
$93$	−14622.7			−0.175316
$94$	42363.4	−	85162.9i	0.494506	−	0.994102i
$95$	139742.	+	18778.0i	1.58861	+	0.213472i
$96$	−35252.0	+	38825.9i	−0.390397	+	0.429976i
$97$		−	116325.i		−	1.25529i	−0.778501	−	0.627643i	$-0.784020\pi$
$97$		−	116325.i		−	1.25529i	0.778501	−	0.627643i	$-0.215980\pi$
$98$	−33621.5	−	16724.7i	−0.353633	−	0.175911i
$99$		−	67219.2i		−	0.689295i
$100$	94669.1	+	125153.i	0.946691	+	1.25153i
$101$	−99014.8			−0.965821			−0.482911	−	0.875670i	$-0.660420\pi$
$101$	−99014.8			−0.965821			−0.482911	+	0.875670i	$0.660420\pi$
$102$	41394.0	+	20591.0i	0.393947	+	0.195965i
$103$	61394.2			0.570209			0.285105	−	0.958496i	$-0.407972\pi$
$103$	61394.2			0.570209			0.285105	+	0.958496i	$0.407972\pi$
$104$	−39357.1	+	7406.19i	−0.356812	+	0.0671446i
$105$			81802.4i			0.724091i
$106$	−9425.79	+	18948.6i	−0.0814804	+	0.163800i
$107$	−89989.5			−0.759858			−0.379929	−	0.925016i	$-0.624052\pi$
$107$	−89989.5			−0.759858			−0.379929	+	0.925016i	$0.624052\pi$
$108$	70614.3	+	93352.5i	0.582550	+	0.770134i
$109$		−	29551.0i		−	0.238235i	−0.992880	−	0.119118i	$-0.961993\pi$
$109$		−	29551.0i		−	0.238235i	0.992880	−	0.119118i	$-0.0380065\pi$
$110$	−94231.4	+	189433.i	−0.742530	+	1.49270i
$111$		−	140545.i		−	1.08270i
$112$	−99363.8	−	28099.0i	−0.748485	−	0.211663i
$113$			99594.9i			0.733738i	0.930273	+	0.366869i	$0.119570\pi$
$113$			99594.9i			0.733738i	−0.930273	+	0.366869i	$0.880430\pi$
$114$	−66729.9	−	45181.1i	−0.480904	−	0.325608i
$115$			354884.i			2.50231i
$116$	208876.	−	158000.i	1.44127	−	1.09021i
$117$			35627.4i			0.240614i
$118$	103118.	+	51294.8i	0.681754	+	0.339132i
$119$			91034.0i			0.589299i
$120$	−27156.5	−	144311.i	−0.172155	−	0.914846i
$121$	−13180.0			−0.0818372
$122$	−239328.	−	119051.i	−1.45577	−	0.724159i
$123$			29091.9i			0.173384i
$124$	31180.9	+	41221.4i	0.182111	+	0.240751i
$125$	−159398.			−0.912447
$126$	−40913.7	+	82248.6i	−0.229585	+	0.461532i
$127$	185630.			1.02126			0.510632	−	0.859799i	$-0.329411\pi$
$127$	185630.			1.02126			0.510632	+	0.859799i	$0.329411\pi$
$128$	184620.	+	16584.3i	0.995990	+	0.0894691i
$129$		−	45789.3i		−	0.242265i
$130$	49944.4	−	100403.i	0.259196	−	0.521060i
$131$		−	145085.i		−	0.738659i	−0.929299	−	0.369329i	$-0.879587\pi$
$131$		−	145085.i		−	0.738659i	0.929299	−	0.369329i	$-0.120413\pi$
$132$	96441.8	−	72951.2i	0.481760	−	0.364416i
$133$	21132.7	−	157265.i	0.103592	−	0.770908i
$134$	194456.	+	96730.0i	0.935532	+	0.465371i
$135$	−327760.			−1.54782
$136$	−30221.1	−	160597.i	−0.140108	−	0.744545i
$137$	−164349.			−0.748109			−0.374055	−	0.927407i	$-0.622033\pi$
$137$	−164349.			−0.748109			−0.374055	+	0.927407i	$0.622033\pi$
$138$	90337.2	−	181604.i	0.403802	−	0.811761i
$139$		−	49774.4i		−	0.218509i	−0.994014	−	0.109255i	$-0.965154\pi$
$139$		−	49774.4i		−	0.218509i	0.994014	−	0.109255i	$-0.0348463\pi$
$140$	230601.	−	174433.i	0.994353	−	0.752155i
$141$		−	152227.i		−	0.644827i
$142$	−207178.	−	103059.i	−0.862229	−	0.428907i
$143$	92345.7			0.377639
$144$	44873.2	−	158681.i	0.180335	−	0.637703i
$145$			733363.i			2.89667i
$146$	−30542.2	−	15192.9i	−0.118582	−	0.0589873i
$147$	−60097.7			−0.229385
$148$	−396195.	+	299693.i	−1.48681	+	1.12466i
$149$	−121876.			−0.449731			−0.224866	−	0.974390i	$-0.572194\pi$
$149$	−121876.			−0.449731			−0.224866	+	0.974390i	$0.572194\pi$
$150$	224859.	+	111854.i	0.815986	+	0.405904i
$151$	−459554.			−1.64019			−0.820094	−	0.572228i	$-0.806079\pi$
$151$	−459554.			−1.64019			−0.820094	+	0.572228i	$0.806079\pi$
$152$	14927.0	+	284454.i	0.0524037	+	0.998626i
$153$	−145379.			−0.502078
$154$	213187.	+	106048.i	0.724367	+	0.360329i
$155$	−144728.			−0.483863
$156$	−51116.0	+	38665.5i	−0.168169	+	0.127207i
$157$	93739.7			0.303511			0.151756	−	0.988418i	$-0.451507\pi$
$157$	93739.7			0.303511			0.151756	+	0.988418i	$0.451507\pi$
$158$	−127854.	−	63599.4i	−0.407446	−	0.202680i
$159$			33870.2i			0.106249i
$160$	−348906.	+	384279.i	−1.07748	+	1.18671i
$161$	399385.			1.21430
$162$	−30474.7	−	15159.3i	−0.0912331	−	0.0453830i
$163$		−	377188.i		−	1.11196i	−0.831196	−	0.555979i	$-0.812343\pi$
$163$		−	377188.i		−	1.11196i	0.831196	−	0.555979i	$-0.187657\pi$
$164$	82010.1	−	62034.6i	0.238099	−	0.180104i
$165$			338606.i			0.968245i
$166$	6828.94	−	13728.2i	0.0192346	−	0.0386672i
$167$	259950.			0.721271			0.360636	−	0.932707i	$-0.382560\pi$
$167$	259950.			0.721271			0.360636	+	0.932707i	$0.382560\pi$
$168$	−162408.	+	30561.8i	−0.443949	+	0.0835421i
$169$	322348.			0.868177
$170$	409696.	+	203799.i	1.08728	+	0.540854i
$171$	251147.	+	33748.3i	0.656808	+	0.0882596i
$172$	−129080.	+	97639.6i	−0.332688	+	0.251654i
$173$			199253.i			0.506163i	0.967445	+	0.253081i	$0.0814441\pi$
$173$			199253.i			0.506163i	−0.967445	+	0.253081i	$0.918556\pi$
$174$	186681.	−	375283.i	0.467441	−	0.939693i
$175$			494512.i			1.22062i
$176$	−411298.	−	116311.i	−1.00086	−	0.283033i
$177$	184320.			0.442221
$178$	−269500.	+	541775.i	−0.637543	+	1.28165i
$179$	508055.			1.18516			0.592582	−	0.805510i	$-0.298109\pi$
$179$	508055.			1.18516			0.592582	+	0.805510i	$0.298109\pi$
$180$	278564.	+	368263.i	0.640831	+	0.847181i
$181$		−	670394.i		−	1.52101i	−0.649329	−	0.760507i	$-0.724950\pi$
$181$		−	670394.i		−	1.52101i	0.649329	−	0.760507i	$-0.275050\pi$
$182$	−112993.	−	56207.3i	−0.252856	−	0.125781i
$183$	−427792.			−0.944289
$184$	−704574.	+	132586.i	−1.53420	+	0.288705i
$185$		−	1.39104e6i		−	2.98820i
$186$	74061.4	+	36841.1i	0.156967	+	0.0780818i
$187$			376819.i			0.788004i
$188$	−429126.	+	324603.i	−0.885504	+	0.669819i
$189$			368860.i			0.751115i
$190$	−660457.	−	447179.i	−1.32727	−	0.898664i
$191$		−	647949.i		−	1.28516i	−0.766218	−	0.642581i	$-0.777864\pi$
$191$		−	647949.i		−	1.28516i	0.766218	−	0.642581i	$-0.222136\pi$
$192$	276365.	−	107831.i	0.541041	−	0.211101i
$193$			405270.i			0.783161i	0.920144	+	0.391580i	$0.128072\pi$
$193$			405270.i			0.783161i	−0.920144	+	0.391580i	$0.871928\pi$
$194$	−293073.	+	589164.i	−0.559078	+	1.12391i
$195$		−	179468.i		−	0.337987i
$196$	128150.	+	169415.i	0.238275	+	0.315001i
$197$	887754.			1.62977			0.814887	−	0.579620i	$-0.196799\pi$
$197$	887754.			1.62977			0.814887	+	0.579620i	$0.196799\pi$
$198$	−169355.	+	340453.i	−0.306998	+	0.617155i
$199$		−	690085.i		−	1.23529i	−0.786456	−	0.617647i	$-0.788086\pi$
$199$		−	690085.i		−	1.23529i	0.786456	−	0.617647i	$-0.211914\pi$
$200$	−164166.	−	872391.i	−0.290207	−	1.54218i
$201$	347585.			0.606835
$202$	501492.	+	249462.i	0.864740	+	0.430156i
$203$	825324.			1.40567
$204$	−157775.	−	208580.i	−0.265438	−	0.350911i
$205$			287937.i			0.478533i
$206$	−310951.	−	154679.i	−0.510532	−	0.253959i
$207$			637806.i			1.03458i
$208$	217996.	+	61646.9i	0.349374	+	0.0987990i
$209$	87475.1	−	650969.i	0.138522	−	1.03085i
$210$	206097.	−	414315.i	0.322495	−	0.648309i
$211$	−810754.			−1.25367			−0.626835	−	0.779152i	$-0.715650\pi$
$211$	−810754.			−1.25367			−0.626835	+	0.779152i	$0.715650\pi$
$212$	95479.9	−	72223.6i	0.145906	−	0.110367i
$213$	−370326.			−0.559287
$214$	455781.	+	226724.i	0.680333	+	0.338425i
$215$		−	453199.i		−	0.668640i
$216$	−122453.	−	650722.i	−0.178580	−	0.948989i
$217$			162876.i			0.234805i
$218$	−74452.0	+	149670.i	−0.106105	+	0.213302i
$219$	−54593.4			−0.0769183
$220$	954530.	−	722032.i	1.32964	−	1.00577i
$221$		−	199721.i		−	0.275070i
$222$	−354094.	+	711834.i	−0.482211	+	0.969385i
$223$	1.18302e6			1.59305			0.796527	−	0.604603i	$-0.206668\pi$
$223$	1.18302e6			1.59305			0.796527	+	0.604603i	$0.206668\pi$
$224$	432466.	+	392658.i	0.575880	+	0.522870i
$225$	−789720.			−1.03996
$226$	250924.	−	504430.i	0.326791	−	0.656947i
$227$	−642350.			−0.827383			−0.413692	−	0.910417i	$-0.635761\pi$
$227$	−642350.			−0.827383			−0.413692	+	0.910417i	$0.635761\pi$
$228$	224143.	+	396956.i	0.285554	+	0.505715i
$229$	397616.			0.501043			0.250522	−	0.968111i	$-0.419398\pi$
$229$	397616.			0.501043			0.250522	+	0.968111i	$0.419398\pi$
$230$	894110.	−	1.79742e6i	1.11448	−	2.24043i
$231$	381066.			0.469862
$232$	−1.45599e6	+	273988.i	−1.77599	+	0.334204i
$233$	179419.			0.216510			0.108255	−	0.994123i	$-0.465474\pi$
$233$	179419.			0.216510			0.108255	+	0.994123i	$0.465474\pi$
$234$	89761.3	−	180447.i	0.107164	−	0.215431i
$235$		−	1.50666e6i		−	1.77969i
$236$	−393038.	−	519598.i	−0.459361	−	0.607278i
$237$	−228535.			−0.264291
$238$	229355.	−	461071.i	0.262461	−	0.527625i
$239$		−	134831.i		−	0.152685i	−0.997082	−	0.0763424i	$-0.975676\pi$
$239$		−	134831.i		−	0.152685i	0.997082	−	0.0763424i	$-0.0243242\pi$
$240$	−226042.	+	799331.i	−0.253315	+	0.895774i
$241$		−	210219.i		−	0.233146i	−0.993182	−	0.116573i	$-0.962809\pi$
$241$		−	210219.i		−	0.233146i	0.993182	−	0.116573i	$-0.0371910\pi$
$242$	66754.1	+	33206.2i	0.0732723	+	0.0364486i
$243$	−943333.			−1.02482
$244$	912209.	+	1.20594e6i	0.980889	+	1.29674i
$245$	−594815.			−0.633092
$246$	73295.5	−	147345.i	0.0772217	−	0.155238i
$247$	−46363.5	+	345026.i	−0.0483541	+	0.359840i
$248$	−54071.0	−	287337.i	−0.0558258	−	0.296663i
$249$		−	24538.8i		−	0.0250816i
$250$	807322.	+	401594.i	0.816953	+	0.406385i
$251$			709519.i			0.710853i	0.934704	+	0.355426i	$0.115664\pi$
$251$			709519.i			0.710853i	−0.934704	+	0.355426i	$0.884336\pi$
$252$	414441.	−	313495.i	0.411113	−	0.310977i
$253$	1.65318e6			1.62375
$254$	−940182.	−	467684.i	−0.914382	−	0.454850i
$255$	732322.			0.705264
$256$	−893286.	−	549137.i	−0.851904	−	0.523698i
$257$		−	338258.i		−	0.319460i	−0.987161	−	0.159730i	$-0.948938\pi$
$257$		−	338258.i		−	0.319460i	0.987161	−	0.159730i	$-0.0510623\pi$
$258$	−115364.	+	231915.i	−0.107900	+	0.216910i
$259$	−1.56547e6			−1.45009
$260$	−505919.	+	382691.i	−0.464139	+	0.351087i
$261$			1.31802e6i			1.19762i
$262$	−365533.	+	734829.i	−0.328983	+	0.661352i
$263$			1.92995e6i			1.72050i	0.509868	+	0.860252i	$0.329694\pi$
$263$			1.92995e6i			1.72050i	−0.509868	+	0.860252i	$0.670306\pi$
$264$	−672257.	+	126505.i	−0.593643	+	0.111711i
$265$			335229.i			0.293243i
$266$	−503253.	+	743276.i	−0.436097	+	0.644089i
$267$			968409.i			0.831344i
$268$	−741177.	−	979840.i	−0.630355	−	0.833332i
$269$			143394.i			0.120823i	0.998174	+	0.0604117i	$0.0192414\pi$
$269$			143394.i			0.120823i	−0.998174	+	0.0604117i	$0.980759\pi$
$270$	1.66004e6	+	825772.i	1.38583	+	0.689367i
$271$		−	1.85314e6i		−	1.53280i	−0.642366	−	0.766398i	$-0.722047\pi$
$271$		−	1.85314e6i		−	1.53280i	0.642366	−	0.766398i	$-0.277953\pi$
$272$	−251551.	+	889536.i	−0.206160	+	0.729023i
$273$	−201972.			−0.164016
$274$	832397.	+	414067.i	0.669814	+	0.333192i
$275$			2.04694e6i			1.63220i
$276$	−915083.	+	692194.i	−0.723083	+	0.546959i
$277$	−351068.			−0.274911			−0.137455	−	0.990508i	$-0.543892\pi$
$277$	−351068.			−0.274911			−0.137455	+	0.990508i	$0.543892\pi$
$278$	−125404.	+	252099.i	−0.0973193	+	0.195640i
$279$	−260108.			−0.200052
$280$	−1.60742e6	+	302484.i	−1.22528	+	0.230573i
$281$			1.53636e6i			1.16072i	0.814360	+	0.580360i	$0.197088\pi$
$281$			1.53636e6i			1.16072i	−0.814360	+	0.580360i	$0.802912\pi$
$282$	−383526.	+	771001.i	−0.287192	+	0.577340i
$283$		−	1.34720e6i		−	0.999923i	−0.866048	−	0.499961i	$-0.833348\pi$
$283$		−	1.34720e6i		−	0.999923i	0.866048	−	0.499961i	$-0.166652\pi$
$284$	789669.	+	1.04395e6i	0.580964	+	0.768037i
$285$	−1.26512e6	−	170002.i	−0.922610	−	0.123977i
$286$	−467714.	−	232660.i	−0.338116	−	0.168192i
$287$	324043.			0.232219
$288$	−627063.	+	690635.i	−0.445481	+	0.490645i
$289$	−604892.			−0.426023
$290$	1.84767e6	−	3.71435e6i	1.29012	−	2.59351i
$291$			1.05312e6i			0.729027i
$292$	116413.	+	153899.i	0.0798996	+	0.105628i
$293$		−	1.96763e6i		−	1.33898i	−0.742821	−	0.669491i	$-0.766512\pi$
$293$		−	1.96763e6i		−	1.33898i	0.742821	−	0.669491i	$-0.233488\pi$
$294$	304384.	+	151413.i	0.205378	+	0.102163i
$295$	1.82430e6			1.22051
$296$	2.76172e6	−	519698.i	1.83210	−	0.344764i
$297$			1.52683e6i			1.00438i
$298$	617281.	+	307060.i	0.402663	+	0.200301i
$299$	−876218.			−0.566806
$300$	−857062.	−	1.13304e6i	−0.549806	−	0.726846i
$301$	−510028.			−0.324472
$302$	2.32756e6	+	1.15782e6i	1.46853	+	0.730505i
$303$	896405.			0.560916
$304$	641063.	−	1.47832e6i	0.397848	−	0.917452i
$305$	−4.23406e6			−2.60620
$306$	736316.	+	366273.i	0.449532	+	0.223615i
$307$	−2.42351e6			−1.46757			−0.733785	−	0.679382i	$-0.762248\pi$
$307$	−2.42351e6			−1.46757			−0.733785	+	0.679382i	$0.762248\pi$
$308$	−812572.	−	1.07422e6i	−0.488074	−	0.645236i
$309$	−555816.			−0.331158
$310$	733021.	+	364634.i	0.433223	+	0.215503i
$311$		−	1.18323e6i		−	0.693694i	−0.937922	−	0.346847i	$-0.887252\pi$
$311$		−	1.18323e6i		−	0.693694i	0.937922	−	0.346847i	$-0.112748\pi$
$312$	356309.	−	67050.0i	0.207224	−	0.0389953i
$313$	741863.			0.428019			0.214009	−	0.976832i	$-0.431348\pi$
$313$	741863.			0.428019			0.214009	+	0.976832i	$0.431348\pi$
$314$	−474775.	−	236172.i	−0.271746	−	0.135177i
$315$			1.45510e6i			0.826259i
$316$	487320.	+	644240.i	0.274534	+	0.362936i
$317$			2.44055e6i			1.36408i	0.731314	+	0.682040i	$0.238907\pi$
$317$			2.44055e6i			1.36408i	−0.731314	+	0.682040i	$0.761093\pi$
$318$	85334.0	−	171546.i	0.0473210	−	0.0951292i
$319$	3.41628e6			1.87965
$320$	2.73532e6	−	1.06725e6i	1.49325	−	0.582630i
$321$	814697.			0.441300
$322$	−2.02281e6	−	1.00623e6i	−1.08722	−	0.540825i
$323$	−1.40789e6	−	189187.i	−0.750864	−	0.100899i
$324$	116156.	+	153559.i	0.0614722	+	0.0812666i
$325$		−	1.08492e6i		−	0.569755i
$326$	−950303.	+	1.91039e6i	−0.495243	+	0.995583i
$327$			267532.i			0.138359i
$328$	−571659.	+	107574.i	−0.293395	+	0.0552109i
$329$	−1.69559e6			−0.863636
$330$	853099.	−	1.71498e6i	0.431236	−	0.866911i
$331$	−2.23910e6			−1.12332			−0.561659	−	0.827369i	$-0.689837\pi$
$331$	−2.23910e6			−1.12332			−0.561659	+	0.827369i	$0.689837\pi$
$332$	−69174.7	+	52325.6i	−0.0344431	+	0.0260537i
$333$		−	2.50001e6i		−	1.23547i
$334$	−1.31660e6	−	654929.i	−0.645785	−	0.321239i
$335$	3.44021e6			1.67484
$336$	899564.	+	254387.i	0.434694	+	0.122927i
$337$			788139.i			0.378032i	0.981974	+	0.189016i	$0.0605297\pi$
$337$			788139.i			0.378032i	−0.981974	+	0.189016i	$0.939470\pi$
$338$	−1.63263e6	−	812138.i	−0.777315	−	0.386668i
$339$		−	901657.i		−	0.426130i
$340$	−1.56158e6	−	2.06441e6i	−0.732599	−	0.968499i
$341$			674196.i			0.313979i
$342$	−1.18699e6	−	803681.i	−0.548759	−	0.371551i
$343$			2.36422e6i			1.08506i
$344$	899764.	−	169317.i	0.409952	−	0.0771445i
$345$		−	3.21285e6i		−	1.45326i
$346$	502007.	−	1.00918e6i	0.225434	−	0.453189i
$347$		−	1.68282e6i		−	0.750265i	−0.926971	−	0.375132i	$-0.877597\pi$
$347$		−	1.68282e6i		−	0.750265i	0.926971	−	0.375132i	$-0.122403\pi$
$348$	−1.89101e6	+	1.43041e6i	−0.837039	+	0.633158i
$349$	3.53744e6			1.55463			0.777313	−	0.629114i	$-0.216582\pi$
$349$	3.53744e6			1.55463			0.777313	+	0.629114i	$0.216582\pi$
$350$	1.24589e6	−	2.50461e6i	0.543639	−	1.09287i
$351$		−	809247.i		−	0.350601i
$352$	1.79011e6	+	1.62534e6i	0.770059	+	0.699176i
$353$	−259762.			−0.110953			−0.0554765	−	0.998460i	$-0.517668\pi$
$353$	−259762.			−0.110953			−0.0554765	+	0.998460i	$0.517668\pi$
$354$	−933549.	−	464384.i	−0.395940	−	0.196956i
$355$	−3.66529e6			−1.54361
$356$	2.72994e6	−	2.06500e6i	1.14164	−	0.863566i
$357$		−	824152.i		−	0.342245i
$358$	−2.57321e6	−	1.28002e6i	−1.06113	−	0.527847i
$359$			429777.i			0.175998i	0.996121	+	0.0879989i	$0.0280472\pi$
$359$			429777.i			0.175998i	−0.996121	+	0.0879989i	$0.971953\pi$
$360$	−483058.	−	2.56701e6i	−0.196446	−	1.04393i
$361$	2.38826e6	+	653657.i	0.964526	+	0.263986i
$362$	−1.68902e6	+	3.39542e6i	−0.677428	+	1.36183i
$363$	119321.			0.0475282
$364$	430679.	+	569359.i	0.170373	+	0.225234i
$365$	−540336.			−0.212291
$366$	2.16669e6	+	1.07780e6i	0.845462	+	0.420566i
$367$			39567.2i			0.0153345i	0.999971	+	0.00766727i	$0.00244059\pi$
$367$			39567.2i			0.0153345i	−0.999971	+	0.00766727i	$0.997559\pi$
$368$	3.90258e6	+	1.10361e6i	1.50222	+	0.424811i
$369$			517487.i			0.197849i
$370$	−3.50464e6	+	7.04535e6i	−1.33088	+	2.67546i
$371$	377266.			0.142302
$372$	−282289.	−	373187.i	−0.105764	−	0.139820i
$373$		−	1.21157e6i		−	0.450897i	−0.974255	−	0.225449i	$-0.927615\pi$
$373$		−	1.21157e6i		−	0.450897i	0.974255	−	0.225449i	$-0.0723848\pi$
$374$	949373.	−	1.90852e6i	0.350960	−	0.705533i
$375$	1.44307e6			0.529918
$376$	2.99127e6	−	562895.i	1.09115	−	0.205332i
$377$	−1.81069e6			−0.656133
$378$	929321.	−	1.86821e6i	0.334531	−	0.672505i
$379$	913764.			0.326765			0.163383	−	0.986563i	$-0.447759\pi$
$379$	913764.			0.326765			0.163383	+	0.986563i	$0.447759\pi$
$380$	2.21845e6	+	3.92886e6i	0.788118	+	1.39575i
$381$	−1.68055e6			−0.593116
$382$	−1.63247e6	+	3.28175e6i	−0.572384	+	1.15066i
$383$	5.24344e6			1.82650			0.913249	−	0.407401i	$-0.133565\pi$
$383$	5.24344e6			1.82650			0.913249	+	0.407401i	$0.133565\pi$
$384$	−1.67141e6	−	150142.i	−0.578437	−	0.0519606i
$385$	3.77159e6			1.29680
$386$	1.02105e6	−	2.05262e6i	0.348803	−	0.701197i
$387$		−	814500.i		−	0.276448i
$388$	2.96873e6	−	2.24563e6i	1.00113	−	0.757283i
$389$	−2.47368e6			−0.828838			−0.414419	−	0.910086i	$-0.636015\pi$
$389$	−2.47368e6			−0.828838			−0.414419	+	0.910086i	$0.636015\pi$
$390$	−452159.	+	908972.i	−0.150532	+	0.302614i
$391$		−	3.57542e6i		−	1.18273i
$392$	−222226.	−	1.18092e6i	−0.0730431	−	0.388156i
$393$			1.31349e6i			0.428988i
$394$	−4.49632e6	−	2.23665e6i	−1.45920	−	0.725867i
$395$	−2.26192e6			−0.729431
$396$	1.71550e6	−	1.29765e6i	0.549736	−	0.415835i
$397$	5.56429e6			1.77188			0.885939	−	0.463803i	$-0.153515\pi$
$397$	5.56429e6			1.77188			0.885939	+	0.463803i	$0.153515\pi$
$398$	−1.73863e6	+	3.49516e6i	−0.550174	+	1.10601i
$399$	−191320.	+	1.42376e6i	−0.0601627	+	0.447717i
$400$	−1.36647e6	+	4.83211e6i	−0.427021	+	1.51003i
$401$			1.64009e6i			0.509339i	0.967028	+	0.254669i	$0.0819667\pi$
$401$			1.64009e6i			0.509339i	−0.967028	+	0.254669i	$0.918033\pi$
$402$	−1.76045e6	−	875720.i	−0.543325	−	0.270271i
$403$		−	357337.i		−	0.109601i
$404$	−1.91146e6	−	2.52696e6i	−0.582656	−	0.770274i
$405$	−539143.			−0.163330
$406$	−4.18012e6	−	2.07936e6i	−1.25856	−	0.626058i
$407$	−6.47997e6			−1.93904
$408$	273599.	+	1.45393e6i	0.0813699	+	0.432406i
$409$		−	1.86331e6i		−	0.550778i	−0.961333	−	0.275389i	$-0.911193\pi$
$409$		−	1.86331e6i		−	0.550778i	0.961333	−	0.275389i	$-0.0888066\pi$
$410$	725440.	−	1.45835e6i	0.213129	−	0.428451i
$411$	1.48789e6			0.434476
$412$	1.18520e6	+	1.56684e6i	0.343993	+	0.454761i
$413$		−	2.05307e6i		−	0.592281i
$414$	1.60692e6	−	3.23037e6i	0.460779	−	0.926300i
$415$		−	242872.i		−	0.0692240i
$416$	−948794.	−	861459.i	−0.268806	−	0.244062i
$417$			450620.i			0.126903i
$418$	−2.08313e6	+	3.07665e6i	−0.583143	+	0.861267i
$419$			6.62511e6i			1.84356i	0.387711	+	0.921781i	$0.373266\pi$
$419$			6.62511e6i			1.84356i	−0.387711	+	0.921781i	$0.626734\pi$
$420$	−2.08768e6	+	1.57918e6i	−0.577486	+	0.436826i
$421$		−	2.03383e6i		−	0.559254i	−0.960109	−	0.279627i	$-0.909789\pi$
$421$		−	2.03383e6i		−	0.559254i	0.960109	−	0.279627i	$-0.0902108\pi$
$422$	4.10632e6	+	2.04265e6i	1.12246	+	0.558358i
$423$		−	2.70780e6i		−	0.735811i
$424$	−665552.	+	125243.i	−0.179791	+	0.0338329i
$425$	4.42703e6			1.18889
$426$	1.87563e6	+	933014.i	0.500753	+	0.249095i
$427$			4.76500e6i			1.26472i
$428$	−1.73723e6	−	2.29663e6i	−0.458404	−	0.606012i
$429$	−836028.			−0.219320
$430$	−1.14181e6	+	2.29537e6i	−0.297798	+	0.598662i
$431$	−2.94684e6			−0.764124			−0.382062	−	0.924137i	$-0.624786\pi$
$431$	−2.94684e6			−0.764124			−0.382062	+	0.924137i	$0.624786\pi$
$432$	−1.01926e6	+	3.60430e6i	−0.262769	+	0.929206i
$433$		−	1.76848e6i		−	0.453295i	−0.973977	−	0.226647i	$-0.927223\pi$
$433$		−	1.76848e6i		−	0.453295i	0.973977	−	0.226647i	$-0.0727765\pi$
$434$	410357.	−	824939.i	0.104577	−	0.210231i
$435$		−	6.63932e6i		−	1.68229i
$436$	754172.	−	570476.i	0.190000	−	0.143721i
$437$	−830003.	+	6.17669e6i	−0.207910	+	1.54722i
$438$	276506.	+	137545.i	0.0688682	+	0.0342578i
$439$	4.02981e6			0.997984			0.498992	−	0.866607i	$-0.333704\pi$
$439$	4.02981e6			0.997984			0.498992	+	0.866607i	$0.333704\pi$
$440$	−6.65364e6	+	1.25208e6i	−1.63843	+	0.308319i
$441$	−1.06902e6			−0.261751
$442$	−503186.	+	1.01155e6i	−0.122510	+	0.246282i
$443$		−	2.63966e6i		−	0.639057i	−0.947577	−	0.319528i	$-0.896476\pi$
$443$		−	2.63966e6i		−	0.639057i	0.947577	−	0.319528i	$-0.103524\pi$
$444$	3.58685e6	−	2.71319e6i	0.863487	−	0.653165i
$445$			9.58480e6i			2.29447i
$446$	−5.99179e6	−	2.98056e6i	−1.42633	−	0.709513i
$447$	1.10337e6			0.261189
$448$	−1.20108e6	−	3.07831e6i	−0.282734	−	0.724632i
$449$		−	7.05534e6i		−	1.65159i	−0.563970	−	0.825795i	$-0.690727\pi$
$449$		−	7.05534e6i		−	1.65159i	0.563970	−	0.825795i	$-0.309273\pi$
$450$	3.99979e6	+	1.98966e6i	0.931121	+	0.463177i
$451$	1.34132e6			0.310520
$452$	−2.54177e6	+	1.92266e6i	−0.585180	+	0.442646i
$453$	4.16045e6			0.952565
$454$	3.25339e6	+	1.61836e6i	0.740791	+	0.368499i
$455$	−1.99902e6			−0.452676
$456$	−135137.	−	2.57523e6i	−0.0304343	−	0.579968i
$457$	368371.			0.0825079			0.0412539	−	0.999149i	$-0.486865\pi$
$457$	368371.			0.0825079			0.0412539	+	0.999149i	$0.486865\pi$
$458$	−2.01385e6	−	1.00177e6i	−0.448605	−	0.223154i
$459$	3.30215e6			0.731585
$460$	−9.05701e6	+	6.85097e6i	−1.99568	+	1.50958i
$461$	4.25279e6			0.932013			0.466006	−	0.884781i	$-0.345692\pi$
$461$	4.25279e6			0.932013			0.466006	+	0.884781i	$0.345692\pi$
$462$	−1.93003e6	−	960075.i	−0.420688	−	0.209267i
$463$		−	7.51673e6i		−	1.62958i	−0.579754	−	0.814792i	$-0.696851\pi$
$463$		−	7.51673e6i		−	1.62958i	0.579754	−	0.814792i	$-0.303149\pi$
$464$	8.06464e6	+	2.28059e6i	1.73896	+	0.491760i
$465$	1.31026e6			0.281011
$466$	−908723.	−	452035.i	−0.193850	−	0.0964289i
$467$		−	6.23071e6i		−	1.32204i	−0.750367	−	0.661021i	$-0.770123\pi$
$467$		−	6.23071e6i		−	1.32204i	0.750367	−	0.661021i	$-0.229877\pi$
$468$	−909250.	+	687781.i	−0.191897	+	0.145156i
$469$		−	3.87160e6i		−	0.812752i
$470$	−3.79594e6	+	7.63096e6i	−0.792638	+	1.59344i
$471$	−848648.			−0.176269
$472$	681569.	+	3.62191e6i	0.140817	+	0.748311i
$473$	−2.11117e6			−0.433880
$474$	1.15749e6	+	575781.i	0.236631	+	0.117710i
$475$	−7.64787e6	−	1.02770e6i	−1.55527	−	0.208992i
$476$	−2.32328e6	+	1.75739e6i	−0.469986	+	0.355510i
$477$			602482.i			0.121241i
$478$	−339700.	+	682896.i	−0.0680026	+	0.136705i
$479$			5.70290e6i			1.13568i	0.823138	+	0.567841i	$0.192221\pi$
$479$			5.70290e6i			1.13568i	−0.823138	+	0.567841i	$0.807779\pi$
$480$	3.15873e6	−	3.47897e6i	0.625763	−	0.689203i
$481$	3.43451e6			0.676865
$482$	−529634.	+	1.06472e6i	−0.103838	+	0.208746i
$483$	−3.61573e6			−0.705226
$484$	−254437.	−	336367.i	−0.0493704	−	0.0652679i
$485$			1.04232e7i			2.01208i
$486$	4.77781e6	+	2.37667e6i	0.917568	+	0.456435i
$487$	3.05364e6			0.583440			0.291720	−	0.956504i	$-0.405772\pi$
$487$	3.05364e6			0.583440			0.291720	+	0.956504i	$0.405772\pi$
$488$	−1.58186e6	−	8.40615e6i	−0.300691	−	1.59789i
$489$			3.41477e6i			0.645787i
$490$	3.01263e6	+	1.49860e6i	0.566834	+	0.281966i
$491$		−	1.65778e6i		−	0.310330i	−0.987889	−	0.155165i	$-0.950409\pi$
$491$		−	1.65778e6i		−	0.310330i	0.987889	−	0.155165i	$-0.0495910\pi$
$492$	−742457.	+	561614.i	−0.138280	+	0.104598i
$493$		−	7.38857e6i		−	1.36913i
$494$	1.10410e6	−	1.63069e6i	0.203559	−	0.300644i
$495$			6.02312e6i			1.10486i
$496$	−450070.	+	1.59154e6i	−0.0821441	+	0.290478i
$497$			4.12490e6i			0.749070i
$498$	−61824.1	+	124284.i	−0.0111708	+	0.0224566i
$499$			8.19460e6i			1.47325i	0.676302	+	0.736625i	$0.263582\pi$
$499$			8.19460e6i			1.47325i	−0.676302	+	0.736625i	$0.736418\pi$
$500$	−3.07715e6	−	4.06801e6i	−0.550457	−	0.727707i
$501$	−2.35339e6			−0.418890
$502$	1.78759e6	−	3.59359e6i	0.316599	−	0.636456i
$503$		−	2.68920e6i		−	0.473918i	−0.971520	−	0.236959i	$-0.923849\pi$
$503$		−	2.68920e6i		−	0.473918i	0.971520	−	0.236959i	$-0.0761507\pi$
$504$	−2.88890e6	+	543632.i	−0.506590	+	0.0953298i
$505$	8.87214e6			1.54810
$506$	−8.37307e6	−	4.16510e6i	−1.45381	−	0.723184i
$507$	−2.91829e6			−0.504207
$508$	3.58355e6	+	4.73747e6i	0.616104	+	0.814493i
$509$		−	6.49123e6i		−	1.11054i	−0.831672	−	0.555268i	$-0.812616\pi$
$509$		−	6.49123e6i		−	1.11054i	0.831672	−	0.555268i	$-0.187384\pi$
$510$	−3.70908e6	−	1.84504e6i	−0.631452	−	0.314110i
$511$			608093.i			0.103019i
$512$	3.14081e6	+	5.03187e6i	0.529501	+	0.848309i
$513$	−5.70460e6	−	766565.i	−0.957044	−	0.128604i
$514$	−852223.	+	1.71322e6i	−0.142281	+	0.286026i
$515$	−5.50118e6			−0.913982
$516$	1.16859e6	−	883954.i	0.193214	−	0.146152i
$517$	−7.01858e6			−1.15484
$518$	7.92882e6	+	3.94411e6i	1.29833	+	0.645839i
$519$		−	1.80389e6i		−	0.293962i
$520$	3.52656e6	−	663626.i	0.571930	−	0.107625i
$521$		−	1.52202e6i		−	0.245655i	−0.992428	−	0.122828i	$-0.960804\pi$
$521$		−	1.52202e6i		−	0.245655i	0.992428	−	0.122828i	$-0.0391963\pi$
$522$	3.32067e6	−	6.67553e6i	0.533396	−	1.07228i
$523$	7.49821e6			1.19868			0.599340	−	0.800494i	$-0.295430\pi$
$523$	7.49821e6			1.19868			0.599340	+	0.800494i	$0.295430\pi$
$524$	3.70272e6	−	2.80084e6i	0.589105	−	0.445615i
$525$		−	4.47693e6i		−	0.708896i
$526$	4.86239e6	−	9.77483e6i	0.766276	−	1.54044i
$527$	1.45812e6			0.228700
$528$	3.72358e6	+	1.05299e6i	0.581268	+	0.164376i
$529$	−9.24979e6			−1.43712
$530$	844591.	−	1.69788e6i	0.130604	−	0.262552i
$531$	3.27868e6			0.504619
$532$	4.42153e6	−	2.49664e6i	0.677319	−	0.382452i
$533$	−710923.			−0.108394
$534$	2.43985e6	−	4.90482e6i	0.370263	−	0.744337i
$535$	8.06344e6			1.21797
$536$	1.28528e6	+	6.83007e6i	0.193235	+	1.02686i
$537$	−4.59955e6			−0.688302
$538$	361274.	−	726266.i	0.0538122	−	0.108178i
$539$			2.77087e6i			0.410813i
$540$	−6.32734e6	−	8.36477e6i	−0.933763	−	1.23444i
$541$	−7.58813e6			−1.11466			−0.557329	−	0.830292i	$-0.688174\pi$
$541$	−7.58813e6			−1.11466			−0.557329	+	0.830292i	$0.688174\pi$
$542$	−4.66888e6	+	9.38581e6i	−0.682675	+	1.37238i
$543$			6.06923e6i			0.883353i
$544$	3.51520e6	−	3.87157e6i	0.509275	−	0.560906i
$545$			2.64789e6i			0.381864i
$546$	1.02295e6	+	508858.i	0.146850	+	0.0730491i
$547$	−1.34294e6			−0.191906			−0.0959528	−	0.995386i	$-0.530590\pi$
$547$	−1.34294e6			−0.191906			−0.0959528	+	0.995386i	$0.530590\pi$
$548$	−3.17272e6	−	4.19435e6i	−0.451316	−	0.596642i
$549$	−7.60956e6			−1.07753
$550$	5.15715e6	−	1.03674e7i	0.726948	−	1.46138i
$551$	−1.71519e6	+	1.27641e7i	−0.240677	+	1.79106i
$552$	6.37868e6	−	1.20034e6i	0.891011	−	0.167670i
$553$			2.54556e6i			0.353973i
$554$	1.77810e6	+	884496.i	0.246139	+	0.122439i
$555$			1.25934e7i			1.73544i
$556$	1.27030e6	−	960886.i	0.174268	−	0.131821i
$557$	−3.11770e6			−0.425791			−0.212895	−	0.977075i	$-0.568289\pi$
$557$	−3.11770e6			−0.425791			−0.212895	+	0.977075i	$0.568289\pi$
$558$	1.31740e6	+	655328.i	0.179115	+	0.0890991i
$559$	1.11896e6			0.151455
$560$	8.90341e6	+	2.51779e6i	1.19974	+	0.339273i
$561$		−	3.41143e6i		−	0.457645i
$562$	3.87078e6	−	7.78140e6i	0.516961	−	1.03924i
$563$	3.61915e6			0.481211			0.240606	−	0.970623i	$-0.422654\pi$
$563$	3.61915e6			0.481211			0.240606	+	0.970623i	$0.422654\pi$
$564$	3.88498e6	−	2.93871e6i	0.514270	−	0.389008i
$565$		−	8.92412e6i		−	1.17610i
$566$	−3.39420e6	+	6.82333e6i	−0.445344	+	0.895273i
$567$			606750.i			0.0792596i
$568$	−1.36937e6	−	7.27693e6i	−0.178094	−	0.946405i
$569$			993114.i			0.128593i	0.997931	+	0.0642966i	$0.0204804\pi$
$569$			993114.i			0.128593i	−0.997931	+	0.0642966i	$0.979520\pi$
$570$	5.97927e6	+	4.04842e6i	0.770835	+	0.521913i
$571$		−	8.22860e6i		−	1.05617i	−0.849190	−	0.528087i	$-0.822910\pi$
$571$		−	8.22860e6i		−	1.05617i	0.849190	−	0.528087i	$-0.177090\pi$
$572$	1.78272e6	+	2.35676e6i	0.227820	+	0.301179i
$573$			5.86604e6i			0.746378i
$574$	−1.64122e6	−	816407.i	−0.207915	−	0.103425i
$575$		−	1.94223e7i		−	2.44980i
$576$	4.91597e6	−	1.91809e6i	0.617381	−	0.240887i
$577$	5.19606e6			0.649732			0.324866	−	0.945760i	$-0.394681\pi$
$577$	5.19606e6			0.649732			0.324866	+	0.945760i	$0.394681\pi$
$578$	3.06367e6	+	1.52399e6i	0.381436	+	0.189742i
$579$		−	3.66900e6i		−	0.454833i
$580$	−1.87162e7	+	1.41574e7i	−2.31019	+	1.74749i
$581$	−273327.			−0.0335925
$582$	2.65326e6	−	5.33384e6i	0.324693	−	0.652728i
$583$	1.56162e6			0.190285
$584$	−201872.	−	1.07276e6i	−0.0244931	−	0.130158i
$585$		−	3.19237e6i		−	0.385677i
$586$	−4.95733e6	+	9.96569e6i	−0.596354	+	1.19885i
$587$			7.31334e6i			0.876034i	0.898967	+	0.438017i	$0.144319\pi$
$587$			7.31334e6i			0.876034i	−0.898967	+	0.438017i	$0.855681\pi$
$588$	−1.16017e6	−	1.53376e6i	−0.138382	−	0.182942i
$589$	−2.51896e6	−	338490.i	−0.299181	−	0.0402029i
$590$	−9.23977e6	−	4.59623e6i	−1.09278	−	0.543590i
$591$	−8.03705e6			−0.946516
$592$	−1.52969e7	−	4.32581e6i	−1.79391	−	0.507298i
$593$	3.49646e6			0.408312			0.204156	−	0.978938i	$-0.434555\pi$
$593$	3.49646e6			0.408312			0.204156	+	0.978938i	$0.434555\pi$
$594$	3.84675e6	−	7.73310e6i	0.447330	−	0.899265i
$595$		−	8.15702e6i		−	0.944581i
$596$	−2.35280e6	−	3.11041e6i	−0.271312	−	0.358676i
$597$			6.24751e6i			0.717416i
$598$	4.43789e6	+	2.20758e6i	0.507485	+	0.252443i
$599$	2.29383e6			0.261213			0.130606	−	0.991434i	$-0.458308\pi$
$599$	2.29383e6			0.261213			0.130606	+	0.991434i	$0.458308\pi$
$600$	1.48623e6	+	7.89797e6i	0.168542	+	0.895647i
$601$			1.09895e6i			0.124105i	0.998073	+	0.0620526i	$0.0197647\pi$
$601$			1.09895e6i			0.124105i	−0.998073	+	0.0620526i	$0.980235\pi$
$602$	2.58320e6	+	1.28499e6i	0.290514	+	0.144513i
$603$	6.18283e6			0.692459
$604$	−8.87160e6	−	1.17283e7i	−0.989486	−	1.30810i
$605$	1.18098e6			0.131176
$606$	−4.54013e6	−	2.25844e6i	−0.502212	−	0.249820i
$607$	−3.90028e6			−0.429660			−0.214830	−	0.976652i	$-0.568920\pi$
$607$	−3.90028e6			−0.429660			−0.214830	+	0.976652i	$0.568920\pi$
$608$	−6.97140e6	+	5.87228e6i	−0.764823	+	0.644240i
$609$	−7.47186e6			−0.816367
$610$	2.14448e7	+	1.06675e7i	2.33344	+	1.16075i
$611$	3.71998e6			0.403123
$612$	−2.80650e6	−	3.71021e6i	−0.302892	−	0.400424i
$613$	1.18865e7			1.27762			0.638809	−	0.769365i	$-0.279427\pi$
$613$	1.18865e7			1.27762			0.638809	+	0.769365i	$0.279427\pi$
$614$	1.22746e7	+	6.10589e6i	1.31398	+	0.653624i
$615$		−	2.60676e6i		−	0.277916i
$616$	1.40908e6	+	7.48798e6i	0.149619	+	0.795084i
$617$	1.42631e6			0.150835			0.0754175	−	0.997152i	$-0.475971\pi$
$617$	1.42631e6			0.150835			0.0754175	+	0.997152i	$0.475971\pi$
$618$	2.81511e6	+	1.40035e6i	0.296500	+	0.147491i
$619$		−	1.33296e7i		−	1.39827i	−0.714990	−	0.699134i	$-0.753569\pi$
$619$		−	1.33296e7i		−	1.39827i	0.714990	−	0.699134i	$-0.246431\pi$
$620$	−2.79394e6	−	3.69361e6i	−0.291903	−	0.385897i
$621$		−	1.44872e7i		−	1.50750i
$622$	−2.98108e6	+	5.99284e6i	−0.308956	+	0.621093i
$623$	1.07867e7			1.11344
$624$	−1.97357e6	−	558104.i	−0.202904	−	0.0573791i
$625$	−1.04200e6			−0.106700
$626$	−3.75740e6	−	1.86908e6i	−0.383223	−	0.190630i
$627$	−791933.	+	5.89338e6i	−0.0804488	+	0.598681i
$628$	1.80963e6	+	2.39234e6i	0.183101	+	0.242060i
$629$			1.40146e7i			1.41239i
$630$	3.66604e6	−	7.36982e6i	0.367998	−	0.739785i
$631$		−	984449.i		−	0.0984283i	−0.998788	−	0.0492141i	$-0.984328\pi$
$631$		−	984449.i		−	0.0984283i	0.998788	−	0.0492141i	$-0.0156717\pi$
$632$	−845064.	−	4.49073e6i	−0.0841582	−	0.447223i
$633$	7.33995e6			0.728088
$634$	6.14884e6	−	1.23610e7i	0.607533	−	1.22132i
$635$	−1.66332e7			−1.63697
$636$	−864403.	+	653857.i	−0.0847370	+	0.0640974i
$637$		−	1.46861e6i		−	0.143403i
$638$	−1.73028e7	−	8.60713e6i	−1.68293	−	0.837156i
$639$	−6.58734e6			−0.638202
$640$	−1.65428e7	−	1.48603e6i	−1.59646	−	0.143409i
$641$		−	6.56567e6i		−	0.631152i	−0.948900	−	0.315576i	$-0.897802\pi$
$641$		−	6.56567e6i		−	0.631152i	0.948900	−	0.315576i	$-0.102198\pi$
$642$	−4.12629e6	−	2.05258e6i	−0.395114	−	0.196545i
$643$			1.66218e7i			1.58545i	0.609582	+	0.792723i	$0.291337\pi$
$643$			1.66218e7i			1.58545i	−0.609582	+	0.792723i	$0.708663\pi$
$644$	7.71005e6	+	1.01927e7i	0.732559	+	0.968447i
$645$			4.10292e6i			0.388323i
$646$	6.65404e6	+	4.50529e6i	0.627342	+	0.424758i
$647$		−	5.66661e6i		−	0.532185i	−0.963948	−	0.266092i	$-0.914267\pi$
$647$		−	5.66661e6i		−	0.532185i	0.963948	−	0.266092i	$-0.0857326\pi$
$648$	−201426.	−	1.07040e6i	−0.0188443	−	0.100140i
$649$		−	8.49829e6i		−	0.791990i
$650$	−2.73339e6	+	5.49491e6i	−0.253757	+	0.510126i
$651$		−	1.47456e6i		−	0.136367i
$652$	9.62623e6	−	7.28154e6i	0.886824	−	0.670817i
$653$	−1.10136e7			−1.01076			−0.505378	−	0.862898i	$-0.668647\pi$
$653$	−1.10136e7			−1.01076			−0.505378	+	0.862898i	$0.668647\pi$
$654$	674032.	−	1.35500e6i	0.0616221	−	0.123878i
$655$			1.30002e7i			1.18399i
$656$	3.16638e6	+	895417.i	0.287278	+	0.0812392i
$657$	−971106.			−0.0877714
$658$	8.58785e6	+	4.27194e6i	0.773250	+	0.384645i
$659$	1.41306e7			1.26750			0.633748	−	0.773539i	$-0.281515\pi$
$659$	1.41306e7			1.26750			0.633748	+	0.773539i	$0.281515\pi$
$660$	−8.64159e6	+	6.53673e6i	−0.772207	+	0.584118i
$661$			4.21517e6i			0.375242i	0.982242	+	0.187621i	$0.0600776\pi$
$661$			4.21517e6i			0.375242i	−0.982242	+	0.187621i	$0.939922\pi$
$662$	1.13406e7	+	5.64128e6i	1.00575	+	0.500302i
$663$			1.80812e6i			0.159751i
$664$	482189.	−	90738.1i	0.0424421	−	0.00798674i
$665$	−1.89358e6	+	1.40916e7i	−0.166047	+	1.23568i
$666$	−6.29862e6	+	1.26621e7i	−0.550250	+	1.10616i
$667$	−3.24152e7			−2.82120
$668$	5.01829e6	+	6.63420e6i	0.435125	+	0.575238i
$669$	−1.07102e7			−0.925191
$670$	−1.74240e7	−	8.66741e6i	−1.49955	−	0.745938i
$671$			1.97238e7i			1.69116i
$672$	−3.91522e6	−	3.55482e6i	−0.334451	−	0.303665i
$673$			1.14948e7i			0.978283i	0.872204	+	0.489142i	$0.162690\pi$
$673$			1.14948e7i			0.978283i	−0.872204	+	0.489142i	$0.837310\pi$
$674$	1.98567e6	−	3.99178e6i	0.168367	−	0.338468i
$675$	1.79378e7			1.51534
$676$	6.22287e6	+	8.22666e6i	0.523750	+	0.692400i
$677$			1.66009e7i			1.39207i	0.718008	+	0.696035i	$0.245054\pi$
$677$			1.66009e7i			1.39207i	−0.718008	+	0.696035i	$0.754946\pi$
$678$	−2.27167e6	+	4.56673e6i	−0.189789	+	0.381532i
$679$	1.17302e7			0.976408
$680$	2.70794e6	+	1.43902e7i	0.224578	+	1.19342i
$681$	5.81535e6			0.480516
$682$	1.69860e6	−	3.41468e6i	0.139840	−	0.281119i
$683$	−1.76378e7			−1.44675			−0.723373	−	0.690457i	$-0.757409\pi$
$683$	−1.76378e7			−1.44675			−0.723373	+	0.690457i	$0.757409\pi$
$684$	3.98706e6	+	7.06105e6i	0.325846	+	0.577071i
$685$	1.47263e7			1.19914
$686$	5.95653e6	−	1.19744e7i	0.483262	−	0.971499i
$687$	−3.59971e6			−0.290989
$688$	−4.98373e6	−	1.40934e6i	−0.401406	−	0.113513i
$689$	−827690.			−0.0664231
$690$	−8.09459e6	+	1.62725e7i	−0.647250	+	1.30116i
$691$			3.05145e6i			0.243114i	0.992584	+	0.121557i	$0.0387888\pi$
$691$			3.05145e6i			0.243114i	−0.992584	+	0.121557i	$0.961211\pi$
$692$	−5.08516e6	+	3.84655e6i	−0.403682	+	0.305356i
$693$	6.77840e6			0.536159
$694$	−4.23978e6	+	8.52319e6i	−0.334152	+	0.671744i
$695$			4.46000e6i			0.350246i
$696$	1.31815e7	−	2.48048e6i	1.03143	−	0.194094i
$697$		−	2.90094e6i		−	0.226181i
$698$	−1.79165e7	−	8.91239e6i	−1.39192	−	0.692397i
$699$	−1.62432e6			−0.125741
$700$	−1.26205e7	+	9.54645e6i	−0.973487	+	0.736371i
$701$	1.35230e7			1.03939			0.519696	−	0.854351i	$-0.326045\pi$
$701$	1.35230e7			1.03939			0.519696	+	0.854351i	$0.326045\pi$
$702$	−2.03885e6	+	4.09869e6i	−0.156150	+	0.313908i
$703$	3.25336e6	−	2.42108e7i	0.248281	−	1.84765i
$704$	−4.97166e6	−	1.27421e7i	−0.378068	−	0.968969i
$705$			1.36401e7i			1.03359i
$706$	1.31565e6	+	654455.i	0.0993408	+	0.0494161i
$707$		−	9.98468e6i		−	0.751252i
$708$	3.55827e6	+	4.70405e6i	0.266781	+	0.352686i
$709$	−1.10885e7			−0.828436			−0.414218	−	0.910178i	$-0.635945\pi$
$709$	−1.10885e7			−0.828436			−0.414218	+	0.910178i	$0.635945\pi$
$710$	1.85640e7	+	9.23448e6i	1.38206	+	0.687490i
$711$	−4.06518e6			−0.301582
$712$	−1.90293e7	+	3.58093e6i	−1.40677	+	0.264725i
$713$		−	6.39708e6i		−	0.471257i
$714$	−2.07640e6	+	4.17418e6i	−0.152429	+	0.306426i
$715$	−8.27456e6			−0.605313
$716$	9.80791e6	+	1.29661e7i	0.714980	+	0.945207i
$717$			1.22066e6i			0.0886741i
$718$	1.08280e6	−	2.17674e6i	0.0783857	−	0.157578i
$719$		−	1.67102e7i		−	1.20548i	−0.797939	−	0.602738i	$-0.794076\pi$
$719$		−	1.67102e7i		−	1.20548i	0.797939	−	0.602738i	$-0.205924\pi$
$720$	−4.02083e6	+	1.42185e7i	−0.289058	+	1.02217i
$721$			6.19100e6i			0.443530i
$722$	−1.04493e7	−	9.32775e6i	−0.746007	−	0.665938i
$723$			1.90316e6i			0.135403i
$724$	1.71092e7	−	1.29418e7i	1.21306	−	0.917591i
$725$		−	4.01360e7i		−	2.83588i
$726$	−604341.	−	300623.i	−0.0425540	−	0.0211681i
$727$		−	7.24993e6i		−	0.508742i	−0.967107	−	0.254371i	$-0.918132\pi$
$727$		−	7.24993e6i		−	0.508742i	0.967107	−	0.254371i	$-0.0818685\pi$
$728$	−746842.	−	3.96877e6i	−0.0522276	−	0.277542i
$729$	7.07810e6			0.493285
$730$	2.73671e6	+	1.36135e6i	0.190073	+	0.0945500i
$731$			4.56594e6i			0.316036i
$732$	−8.25845e6	−	1.09177e7i	−0.569666	−	0.753102i
$733$	2.55597e7			1.75710			0.878548	−	0.477655i	$-0.158513\pi$
$733$	2.55597e7			1.75710			0.878548	+	0.477655i	$0.158513\pi$
$734$	99687.4	−	200401.i	0.00682968	−	0.0137297i
$735$	5.38500e6			0.367678
$736$	−1.69854e7	−	1.54219e7i	−1.15580	−	1.04941i
$737$		−	1.60258e7i		−	1.08680i
$738$	1.30378e6	−	2.62098e6i	0.0881176	−	0.177142i
$739$		−	2.63197e7i		−	1.77284i	−0.462878	−	0.886422i	$-0.653183\pi$
$739$		−	2.63197e7i		−	1.77284i	0.462878	−	0.886422i	$-0.346817\pi$
$740$	3.55007e7	−	2.68537e7i	2.38319	−	1.80271i
$741$	419740.	−	3.12361e6i	0.0280824	−	0.208983i
$742$	−1.91078e6	−	950499.i	−0.127409	−	0.0633785i
$743$	−2.00959e7			−1.33547			−0.667737	−	0.744397i	$-0.732737\pi$
$743$	−2.00959e7			−1.33547			−0.667737	+	0.744397i	$0.732737\pi$
$744$	489518.	+	2.60133e6i	0.0324217	+	0.172292i
$745$	1.09206e7			0.720869
$746$	−3.05249e6	+	6.13640e6i	−0.200820	+	0.403707i
$747$		−	436495.i		−	0.0286205i
$748$	−9.61681e6	+	7.27441e6i	−0.628459	+	0.475383i
$749$		−	9.07456e6i		−	0.591046i
$750$	−7.30888e6	−	3.63573e6i	−0.474458	−	0.236014i
$751$	1.38487e7			0.896001			0.448001	−	0.894033i	$-0.352136\pi$
$751$	1.38487e7			0.896001			0.448001	+	0.894033i	$0.352136\pi$
$752$	−1.65684e7	−	4.68537e6i	−1.06841	−	0.302133i
$753$		−	6.42344e6i		−	0.412839i
$754$	9.17084e6	+	4.56194e6i	0.587463	+	0.292228i
$755$	4.11779e7			2.62904
$756$	−9.41368e6	+	7.12076e6i	−0.599039	+	0.453129i
$757$	2.34771e7			1.48903			0.744517	−	0.667603i	$-0.232680\pi$
$757$	2.34771e7			1.48903			0.744517	+	0.667603i	$0.232680\pi$
$758$	−4.62805e6	−	2.30218e6i	−0.292567	−	0.145534i
$759$	−1.49667e7			−0.943019
$760$	−1.33752e6	−	2.54883e7i	−0.0839973	−	1.60069i
$761$	−5.35310e6			−0.335076			−0.167538	−	0.985866i	$-0.553582\pi$
$761$	−5.35310e6			−0.335076			−0.167538	+	0.985866i	$0.553582\pi$
$762$	8.51169e6	+	4.23405e6i	0.531041	+	0.264161i
$763$	2.97993e6			0.185308
$764$	1.65364e7	−	1.25085e7i	1.02496	−	0.775306i
$765$	1.30265e7			0.804776
$766$	−2.65571e7	−	1.32106e7i	−1.63534	−	0.813484i
$767$			4.50426e6i			0.276461i
$768$	8.08713e6	+	4.97147e6i	0.494757	+	0.304146i
$769$	−1.05042e7			−0.640544			−0.320272	−	0.947326i	$-0.603774\pi$
$769$	−1.05042e7			−0.640544			−0.320272	+	0.947326i	$0.603774\pi$
$770$	−1.91024e7	−	9.50231e6i	−1.16108	−	0.577567i
$771$			3.06234e6i			0.185531i
$772$	−1.03429e7	+	7.82366e6i	−0.624597	+	0.472462i
$773$		−	7.56121e6i		−	0.455137i	−0.973762	−	0.227569i	$-0.926922\pi$
$773$		−	7.56121e6i		−	0.455137i	0.973762	−	0.227569i	$-0.0730776\pi$
$774$	−2.05209e6	+	4.12529e6i	−0.123124	+	0.247516i
$775$	7.92075e6			0.473710
$776$	−2.06938e7	+	3.89415e6i	−1.23363	+	0.232144i
$777$	1.41726e7			0.842162
$778$	1.25287e7	+	6.23230e6i	0.742094	+	0.369147i
$779$	−673427.	+	5.01149e6i	−0.0397600	+	0.295885i
$780$	4.58021e6	−	3.46459e6i	0.269556	−	0.203899i
$781$			1.70743e7i			1.00165i
$782$	−9.00808e6	+	1.81089e7i	−0.526763	+	1.05895i
$783$		−	2.99377e7i		−	1.74507i
$784$	−1.84974e6	+	6.54105e6i	−0.107478	+	0.380065i
$785$	−8.39947e6			−0.486494
$786$	3.30926e6	−	6.65258e6i	0.191062	−	0.384091i
$787$	2.33749e7			1.34528			0.672640	−	0.739969i	$-0.265160\pi$
$787$	2.33749e7			1.34528			0.672640	+	0.739969i	$0.265160\pi$
$788$	1.71379e7	+	2.26564e7i	0.983202	+	1.29980i
$789$		−	1.74723e7i		−	0.999210i
$790$	1.14562e7	+	5.69878e6i	0.653091	+	0.324873i
$791$	−1.00432e7			−0.570729
$792$	−1.19581e7	+	2.25027e6i	−0.677406	+	0.127474i
$793$		−	1.04540e7i		−	0.590337i
$794$	−2.81821e7	−	1.40189e7i	−1.58644	−	0.789157i
$795$		−	3.03491e6i		−	0.170305i
$796$	1.76117e7	−	1.33220e7i	0.985187	−	0.745222i
$797$			2.82123e7i			1.57323i	0.617443	+	0.786615i	$0.288169\pi$
$797$			2.82123e7i			1.57323i	−0.617443	+	0.786615i	$0.711831\pi$
$798$	4.55607e6	−	6.72905e6i	0.253270	−	0.374065i
$799$			1.51795e7i			0.841181i
$800$	1.90951e7	−	2.10310e7i	1.05487	−	1.16181i
$801$			1.72260e7i			0.948646i
$802$	4.13211e6	−	8.30676e6i	0.226849	−	0.456033i
$803$			2.51709e6i			0.137756i
$804$	6.71006e6	+	8.87073e6i	0.366088	+	0.483971i
$805$	−3.57866e7			−1.94639
$806$	−900290.	+	1.80985e6i	−0.0488140	+	0.0981306i
$807$		−	1.29818e6i		−	0.0701701i
$808$	3.31467e6	+	1.76144e7i	0.178613	+	0.949162i
$809$	−1.79004e7			−0.961591			−0.480796	−	0.876833i	$-0.659652\pi$
$809$	−1.79004e7			−0.961591			−0.480796	+	0.876833i	$0.659652\pi$
$810$	2.73066e6	+	1.35834e6i	0.146236	+	0.0727438i
$811$	−5.15764e6			−0.275359			−0.137679	−	0.990477i	$-0.543964\pi$
$811$	−5.15764e6			−0.275359			−0.137679	+	0.990477i	$0.543964\pi$
$812$	1.59327e7	+	2.10632e7i	0.848008	+	1.12107i
$813$			1.67769e7i			0.890195i
$814$	3.28199e7	+	1.63259e7i	1.73611	+	0.863608i
$815$			3.37976e7i			1.78235i
$816$	2.27735e6	−	8.05319e6i	0.119731	−	0.423392i
$817$	1.05994e6	−	7.88784e6i	0.0555555	−	0.413431i
$818$	−4.69450e6	+	9.43732e6i	−0.245305	+	0.493135i
$819$	−3.59268e6			−0.187158
$820$	−7.34845e6	+	5.55856e6i	−0.381646	+	0.288687i
$821$	1.12543e7			0.582722			0.291361	−	0.956613i	$-0.405892\pi$
$821$	1.12543e7			0.582722			0.291361	+	0.956613i	$0.405892\pi$
$822$	−7.53589e6	−	3.74865e6i	−0.389005	−	0.193507i
$823$			1.63921e7i			0.843600i	0.906689	+	0.421800i	$0.138601\pi$
$823$			1.63921e7i			0.843600i	−0.906689	+	0.421800i	$0.861399\pi$
$824$	−2.05527e6	−	1.09218e7i	−0.105451	−	0.560374i
$825$		−	1.85315e7i		−	0.947926i
$826$	−5.17258e6	+	1.03984e7i	−0.263789	+	0.530294i
$827$	8.95732e6			0.455422			0.227711	−	0.973729i	$-0.426876\pi$
$827$	8.95732e6			0.455422			0.227711	+	0.973729i	$0.426876\pi$
$828$	−1.62775e7	+	1.23127e7i	−0.825109	+	0.624135i
$829$		−	2.68358e7i		−	1.35621i	−0.734964	−	0.678106i	$-0.762801\pi$
$829$		−	2.68358e7i		−	1.35621i	0.734964	−	0.678106i	$-0.237199\pi$
$830$	−611902.	+	1.23010e6i	−0.0308309	+	0.0619792i
$831$	3.17830e6			0.159659
$832$	2.63508e6	+	6.75357e6i	0.131973	+	0.338240i
$833$	5.99271e6			0.299234
$834$	1.13531e6	−	2.28231e6i	0.0565197	−	0.113621i
$835$	−2.32926e7			−1.15612
$836$	1.83021e7	−	1.03344e7i	0.905703	−	0.511410i
$837$	5.90814e6			0.291499
$838$	1.66916e7	−	3.35550e7i	0.821083	−	1.65062i
$839$	2.60421e6			0.127723			0.0638617	−	0.997959i	$-0.479658\pi$
$839$	2.60421e6			0.127723			0.0638617	+	0.997959i	$0.479658\pi$
$840$	1.45524e7	−	2.73846e6i	0.711601	−	0.133909i
$841$	−4.64745e7			−2.26582
$842$	−5.12412e6	+	1.03010e7i	−0.249080	+	0.500724i
$843$		−	1.39091e7i		−	0.674107i
$844$	−1.56515e7	−	2.06913e7i	−0.756308	−	0.999843i
$845$	−2.88837e7			−1.39159
$846$	−6.82216e6	+	1.37145e7i	−0.327715	+	0.658803i
$847$		−	1.32907e6i		−	0.0636560i
$848$	3.68644e6	+	1.04249e6i	0.176043	+	0.0497829i
$849$			1.21965e7i			0.580721i
$850$	−2.24221e7	−	1.11536e7i	−1.06446	−	0.529504i
$851$	6.14849e7			2.91035
$852$	−7.14906e6	−	9.45110e6i	−0.337404	−	0.446050i
$853$	−1.31085e7			−0.616853			−0.308426	−	0.951248i	$-0.599802\pi$
$853$	−1.31085e7			−0.616853			−0.308426	+	0.951248i	$0.599802\pi$
$854$	1.20051e7	−	2.41338e7i	0.563277	−	1.13235i
$855$	−2.25039e7	−	3.02399e6i	−1.05279	−	0.141470i
$856$	3.01254e6	+	1.60089e7i	0.140523	+	0.746751i
$857$		−	1.97780e7i		−	0.919880i	−0.887950	−	0.459940i	$-0.847871\pi$
$857$		−	1.97780e7i		−	0.919880i	0.887950	−	0.459940i	$-0.152129\pi$
$858$	4.23433e6	+	2.10633e6i	0.196366	+	0.0976804i
$859$			3.30886e7i			1.53001i	0.644022	+	0.765007i	$0.277265\pi$
$859$			3.30886e7i			1.53001i	−0.644022	+	0.765007i	$0.722735\pi$
$860$	1.15661e7	−	8.74891e6i	0.533263	−	0.403374i
$861$	−2.93364e6			−0.134865
$862$	1.49252e7	+	7.42441e6i	0.684153	+	0.340325i
$863$	−2.21963e7			−1.01450			−0.507252	−	0.861798i	$-0.669339\pi$
$863$	−2.21963e7			−1.01450			−0.507252	+	0.861798i	$0.669339\pi$
$864$	1.42432e7	−	1.56872e7i	0.649117	−	0.714925i
$865$		−	1.78539e7i		−	0.811323i
$866$	−4.45559e6	+	8.95704e6i	−0.201888	+	0.405854i
$867$	5.47623e6			0.247419
$868$	−4.15677e6	+	3.14429e6i	−0.187265	+	0.141652i
$869$			1.05369e7i			0.473328i
$870$	−1.67274e7	+	3.36269e7i	−0.749255	+	1.50622i
$871$			8.49397e6i			0.379372i
$872$	−5.25703e6	+	989265.i	−0.234126	+	0.0440577i
$873$			1.87328e7i			0.831892i
$874$	1.97656e7	−	2.91927e7i	0.875250	−	1.29269i
$875$		−	1.60737e7i		−	0.709736i
$876$	−1.05391e6	−	1.39328e6i	−0.0464029	−	0.0613449i
$877$			3.85576e7i			1.69282i	0.532533	+	0.846409i	$0.321240\pi$
$877$			3.85576e7i			1.69282i	−0.532533	+	0.846409i	$0.678760\pi$
$878$	−2.04103e7	−	1.01529e7i	−0.893537	−	0.444481i
$879$			1.78134e7i			0.777634i
$880$	3.68540e7	+	1.04219e7i	1.60427	+	0.453671i
$881$	3.26844e7			1.41874			0.709368	−	0.704839i	$-0.248981\pi$
$881$	3.26844e7			1.41874			0.709368	+	0.704839i	$0.248981\pi$
$882$	5.41437e6	+	2.69332e6i	0.234356	+	0.116578i
$883$			1.01695e7i			0.438934i	0.975620	+	0.219467i	$0.0704318\pi$
$883$			1.01695e7i			0.438934i	−0.975620	+	0.219467i	$0.929568\pi$
$884$	5.09709e6	−	3.85558e6i	0.219377	−	0.165943i
$885$	−1.65159e7			−0.708832
$886$	−6.65049e6	+	1.33694e7i	−0.284622	+	0.572175i
$887$	−3.69088e7			−1.57514			−0.787572	−	0.616222i	$-0.788662\pi$
$887$	−3.69088e7			−1.57514			−0.787572	+	0.616222i	$0.788662\pi$
$888$	−2.50025e7	+	4.70495e6i	−1.06402	+	0.200227i
$889$			1.87190e7i			0.794378i
$890$	2.41484e7	−	4.85453e7i	1.02191	−	2.05434i
$891$			2.51153e6i			0.105985i
$892$	2.28380e7	+	3.01920e7i	0.961050	+	1.27051i
$893$	3.52378e6	−	2.62231e7i	0.147870	−	1.10041i
$894$	−5.58839e6	−	2.77989e6i	−0.233853	−	0.116328i
$895$	−4.55239e7			−1.89968
$896$	−1.67237e6	+	1.86172e7i	−0.0695924	+	0.774718i
$897$	7.93261e6			0.329181
$898$	−1.77755e7	+	3.57340e7i	−0.735583	+	1.47874i
$899$		−	1.32195e7i		−	0.545526i
$900$	−1.52454e7	−	2.01545e7i	−0.627383	−	0.829403i
$901$		−	3.37740e6i		−	0.138602i
$902$	−6.79353e6	−	3.37937e6i	−0.278022	−	0.138299i
$903$	4.61741e6			0.188442
$904$	1.77176e7	−	3.33409e6i	0.721082	−	0.135693i
$905$			6.00701e7i			2.43802i
$906$	−2.10719e7	−	1.04820e7i	−0.852872	−	0.424252i
$907$	1.80170e7			0.727218			0.363609	−	0.931552i	$-0.381544\pi$
$907$	1.80170e7			0.727218			0.363609	+	0.931552i	$0.381544\pi$
$908$	−1.24004e7	−	1.63934e7i	−0.499140	−	0.659866i
$909$	1.59452e7			0.640061
$910$	1.01247e7	+	5.03641e6i	0.405300	+	0.201612i
$911$	−3.74475e7			−1.49495			−0.747475	−	0.664290i	$-0.768734\pi$
$911$	−3.74475e7			−1.49495			−0.747475	+	0.664290i	$0.768734\pi$
$912$	−5.80370e6	+	1.33835e7i	−0.231056	+	0.532824i
$913$	−1.13139e6			−0.0449195
$914$	−1.86574e6	−	928091.i	−0.0738728	−	0.0367473i
$915$	3.83320e7			1.51359
$916$	7.67590e6	+	1.01476e7i	0.302267	+	0.399598i
$917$	1.46304e7			0.574556
$918$	−1.67248e7	−	8.31958e6i	−0.655019	−	0.325833i
$919$			1.85058e7i			0.722803i	0.932410	+	0.361401i	$0.117702\pi$
$919$			1.85058e7i			0.722803i	−0.932410	+	0.361401i	$0.882298\pi$
$920$	6.31328e7	−	1.18803e7i	2.45915	−	0.462762i
$921$	2.19406e7			0.852314
$922$	−2.15396e7	−	1.07147e7i	−0.834470	−	0.415099i
$923$		−	9.04969e6i		−	0.349647i
$924$	7.35641e6	+	9.72521e6i	0.283456	+	0.374731i
$925$			7.61295e7i			2.92549i
$926$	−1.89380e7	+	3.80709e7i	−0.725782	+	1.45903i
$927$	−9.88685e6			−0.377884
$928$	−3.51001e7	−	3.18692e7i	−1.33795	−	1.21479i
$929$	−3.95063e7			−1.50185			−0.750926	−	0.660386i	$-0.770393\pi$
$929$	−3.95063e7			−1.50185			−0.750926	+	0.660386i	$0.770393\pi$
$930$	−6.63621e6	−	3.30112e6i	−0.251601	−	0.125156i
$931$	−1.03526e7	−	1.39115e6i	−0.391451	−	0.0526019i
$932$	3.46364e6	+	4.57895e6i	0.130615	+	0.172674i
$933$			1.07121e7i			0.402873i
$934$	−1.56979e7	+	3.15574e7i	−0.588810	+	1.18368i
$935$		−	3.37645e7i		−	1.26308i
$936$	6.33801e6	−	1.19268e6i	0.236463	−	0.0444975i
$937$	−8.35201e6			−0.310772			−0.155386	−	0.987854i	$-0.549662\pi$
$937$	−8.35201e6			−0.310772			−0.155386	+	0.987854i	$0.549662\pi$
$938$	−9.75427e6	+	1.96090e7i	−0.361983	+	0.727691i
$939$	−6.71626e6			−0.248579
$940$	3.84515e7	−	2.90858e7i	1.41936	−	1.07365i
$941$		−	3.96709e7i		−	1.46049i	−0.683186	−	0.730245i	$-0.739406\pi$
$941$		−	3.96709e7i		−	1.46049i	0.683186	−	0.730245i	$-0.260594\pi$
$942$	4.29825e6	+	2.13812e6i	0.157821	+	0.0785064i
$943$	−1.27270e7			−0.466066
$944$	5.67317e6	−	2.00615e7i	0.207203	−	0.732712i
$945$		−	3.30514e7i		−	1.20395i
$946$	1.06927e7	+	5.31897e6i	0.388471	+	0.193241i
$947$		−	4.62096e7i		−	1.67439i	−0.546902	−	0.837197i	$-0.684193\pi$
$947$		−	4.62096e7i		−	1.67439i	0.546902	−	0.837197i	$-0.315807\pi$
$948$	−4.41183e6	−	5.83246e6i	−0.159440	−	0.210781i
$949$		−	1.33411e6i		−	0.0480867i
$950$	3.61459e7	+	2.44735e7i	1.29942	+	0.879805i
$951$		−	2.20949e7i		−	0.792211i
$952$	1.61947e7	−	3.04750e6i	0.579135	−	0.108981i
$953$		−	4.97044e7i		−	1.77281i	−0.462911	−	0.886405i	$-0.653195\pi$
$953$		−	4.97044e7i		−	1.77281i	0.462911	−	0.886405i	$-0.346805\pi$
$954$	1.51792e6	−	3.05146e6i	0.0539980	−	0.108552i
$955$			5.80590e7i			2.05997i
$956$	3.44104e6	−	2.60289e6i	0.121771	−	0.0921110i
$957$	−3.09284e7			−1.09164
$958$	1.43681e7	−	2.88842e7i	0.505809	−	1.01682i
$959$		−	1.65730e7i		−	0.581907i
$960$	−2.47635e7	+	9.66210e6i	−0.867228	+	0.338371i
$961$	−2.60203e7			−0.908875
$962$	−1.73952e7	−	8.65305e6i	−0.606026	−	0.301461i
$963$	1.44918e7			0.503567
$964$	5.36500e6	−	4.05823e6i	0.185942	−	0.140652i
$965$		−	3.63139e7i		−	1.25532i
$966$	1.83130e7	+	9.10962e6i	0.631418	+	0.314093i
$967$		−	258929.i		−	0.00890460i	−0.999990	−	0.00445230i	$-0.998583\pi$
$967$		−	258929.i		−	0.00890460i	0.999990	−	0.00445230i	$-0.00141722\pi$
$968$	441220.	+	2.34467e6i	0.0151344	+	0.0804256i
$969$	1.27459e7	+	1.71276e6i	0.436076	+	0.0585984i
$970$	2.62606e7	−	5.27915e7i	0.896139	−	1.80150i
$971$	3.08275e7			1.04928			0.524639	−	0.851325i	$-0.324200\pi$
$971$	3.08275e7			1.04928			0.524639	+	0.851325i	$0.324200\pi$
$972$	−1.82109e7	−	2.40749e7i	−0.618251	−	0.817331i
$973$	5.01927e6			0.169964
$974$	−1.54662e7	−	7.69348e6i	−0.522378	−	0.259852i
$975$			9.82202e6i			0.330894i
$976$	−1.31670e7	+	4.65611e7i	−0.442447	+	1.56458i
$977$			4.12031e7i			1.38100i	0.723332	+	0.690500i	$0.242609\pi$
$977$			4.12031e7i			1.38100i	−0.723332	+	0.690500i	$0.757391\pi$
$978$	8.60332e6	−	1.72952e7i	0.287620	−	0.578201i
$979$	4.46496e7			1.48888
$980$	−1.14828e7	−	1.51803e7i	−0.381929	−	0.504912i
$981$			4.75886e6i			0.157881i
$982$	−4.17669e6	+	8.39638e6i	−0.138215	+	0.277852i
$983$	1.03462e6			0.0341505			0.0170752	−	0.999854i	$-0.494565\pi$
$983$	1.03462e6			0.0341505			0.0170752	+	0.999854i	$0.494565\pi$
$984$	5.17537e6	−	973897.i	0.170394	−	0.0320646i
$985$	−7.95465e7			−2.61235
$986$	−1.86151e7	+	3.74218e7i	−0.609779	+	1.22584i
$987$	1.53506e7			0.501570
$988$	−9.70047e6	+	5.47742e6i	−0.316155	+	0.178519i
$989$	2.00317e7			0.651220
$990$	1.51749e7	−	3.05060e7i	0.492083	−	0.989231i
$991$	2.05835e7			0.665786			0.332893	−	0.942965i	$-0.391975\pi$
$991$	2.05835e7			0.665786			0.332893	+	0.942965i	$0.391975\pi$
$992$	6.28932e6	−	6.92694e6i	0.202920	−	0.223492i
$993$	2.02711e7			0.652385
$994$	1.03925e7	−	2.08919e7i	0.333620	−	0.670674i
$995$			6.18346e7i			1.98004i
$996$	626255.	−	473716.i	0.0200034	−	0.0151311i
$997$	−1.45636e7			−0.464015			−0.232008	−	0.972714i	$-0.574529\pi$
$997$	−1.45636e7			−0.464015			−0.232008	+	0.972714i	$0.574529\pi$
$998$	2.06458e7	−	4.15042e7i	0.656154	−	1.31906i
$999$			5.67855e7i			1.80021i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.6.d.a.75.7	✓	48
4.3	odd	2	inner	76.6.d.a.75.41	yes	48
19.18	odd	2	inner	76.6.d.a.75.42	yes	48
76.75	even	2	inner	76.6.d.a.75.8	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.6.d.a.75.7	✓	48	1.1	even	1	trivial
76.6.d.a.75.8	yes	48	76.75	even	2	inner
76.6.d.a.75.41	yes	48	4.3	odd	2	inner
76.6.d.a.75.42	yes	48	19.18	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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	76.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.06482 - 2.51944i) q^{2} -9.05324 q^{3} +(19.3048 + 25.5211i) q^{4} -89.6042 q^{5} +(45.8530 + 22.8091i) q^{6} +100.840i q^{7} +(-33.4765 - 177.897i) q^{8} -161.039 q^{9} +O(q^{10})\)	\(q+(-5.06482 - 2.51944i) q^{2} -9.05324 q^{3} +(19.3048 + 25.5211i) q^{4} -89.6042 q^{5} +(45.8530 + 22.8091i) q^{6} +100.840i q^{7} +(-33.4765 - 177.897i) q^{8} -161.039 q^{9} +(453.829 + 225.753i) q^{10} +417.410i q^{11} +(-174.771 - 231.048i) q^{12} -221.235i q^{13} +(254.061 - 510.738i) q^{14} +811.208 q^{15} +(-278.649 + 985.358i) q^{16} +902.754 q^{17} +(815.633 + 405.728i) q^{18} +(-1559.55 - 209.566i) q^{19} +(-1729.79 - 2286.79i) q^{20} -912.931i q^{21} +(1051.64 - 2114.11i) q^{22} -3960.57i q^{23} +(303.071 + 1610.54i) q^{24} +4903.91 q^{25} +(-557.389 + 1120.52i) q^{26} +3657.86 q^{27} +(-2573.55 + 1946.70i) q^{28} -8184.48i q^{29} +(-4108.62 - 2043.79i) q^{30} +1615.19 q^{31} +(3893.86 - 4288.62i) q^{32} -3778.91i q^{33} +(-4572.29 - 2274.44i) q^{34} -9035.71i q^{35} +(-3108.82 - 4109.88i) q^{36} +15524.2i q^{37} +(7370.82 + 4990.60i) q^{38} +2002.90i q^{39} +(2999.64 + 15940.3i) q^{40} -3213.43i q^{41} +(-2300.08 + 4623.83i) q^{42} +5057.78i q^{43} +(-10652.7 + 8058.02i) q^{44} +14429.8 q^{45} +(-9978.44 + 20059.6i) q^{46} +16814.6i q^{47} +(2522.67 - 8920.69i) q^{48} +6638.25 q^{49} +(-24837.4 - 12355.1i) q^{50} -8172.85 q^{51} +(5646.15 - 4270.90i) q^{52} -3741.22i q^{53} +(-18526.4 - 9215.77i) q^{54} -37401.7i q^{55} +(17939.2 - 3375.78i) q^{56} +(14118.9 + 1897.26i) q^{57} +(-20620.3 + 41452.9i) q^{58} -20359.6 q^{59} +(15660.2 + 20702.9i) q^{60} +47252.9 q^{61} +(-8180.65 - 4069.38i) q^{62} -16239.2i q^{63} +(-30526.6 + 11910.8i) q^{64} +19823.6i q^{65} +(-9520.75 + 19139.5i) q^{66} -38393.4 q^{67} +(17427.5 + 23039.2i) q^{68} +35856.0i q^{69} +(-22765.0 + 45764.2i) q^{70} +40905.3 q^{71} +(5391.02 + 28648.3i) q^{72} +6030.26 q^{73} +(39112.5 - 78627.5i) q^{74} -44396.3 q^{75} +(-24758.4 - 43846.9i) q^{76} -42091.7 q^{77} +(5046.18 - 10144.3i) q^{78} +25243.5 q^{79} +(24968.1 - 88292.2i) q^{80} +6016.94 q^{81} +(-8096.05 + 16275.4i) q^{82} +2710.50i q^{83} +(23299.0 - 17624.0i) q^{84} -80890.6 q^{85} +(12742.8 - 25616.8i) q^{86} +74096.0i q^{87} +(74255.9 - 13973.4i) q^{88} -106968. i q^{89} +(-73084.1 - 36355.0i) q^{90} +22309.4 q^{91} +(101078. - 76458.1i) q^{92} -14622.7 q^{93} +(42363.4 - 85162.9i) q^{94} +(139742. + 18778.0i) q^{95} +(-35252.0 + 38825.9i) q^{96} -116325. i q^{97} +(-33621.5 - 16724.7i) q^{98} -67219.2i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 22 q^{4} - 4 q^{5} - 246 q^{6} + 3516 q^{9}+O(q^{10}) \) 48 * q - 22 * q^4 - 4 * q^5 - 246 * q^6 + 3516 * q^9	\( 48 q - 22 q^{4} - 4 q^{5} - 246 q^{6} + 3516 q^{9} - 1222 q^{16} + 1000 q^{17} - 300 q^{20} + 17158 q^{24} + 24996 q^{25} + 12102 q^{26} + 6382 q^{28} - 16528 q^{30} + 27524 q^{36} + 3598 q^{38} + 35966 q^{42} - 65408 q^{44} - 13476 q^{45} - 143096 q^{49} - 148446 q^{54} - 53980 q^{57} - 117018 q^{58} + 133740 q^{61} + 28068 q^{62} - 78130 q^{64} + 128204 q^{66} - 48338 q^{68} - 104080 q^{73} + 48932 q^{74} - 251688 q^{76} + 184844 q^{77} + 80080 q^{80} + 375128 q^{81} + 175628 q^{82} - 384748 q^{85} + 139810 q^{92} + 183272 q^{93} + 601258 q^{96}+O(q^{100}) \) 48 * q - 22 * q^4 - 4 * q^5 - 246 * q^6 + 3516 * q^9 - 1222 * q^16 + 1000 * q^17 - 300 * q^20 + 17158 * q^24 + 24996 * q^25 + 12102 * q^26 + 6382 * q^28 - 16528 * q^30 + 27524 * q^36 + 3598 * q^38 + 35966 * q^42 - 65408 * q^44 - 13476 * q^45 - 143096 * q^49 - 148446 * q^54 - 53980 * q^57 - 117018 * q^58 + 133740 * q^61 + 28068 * q^62 - 78130 * q^64 + 128204 * q^66 - 48338 * q^68 - 104080 * q^73 + 48932 * q^74 - 251688 * q^76 + 184844 * q^77 + 80080 * q^80 + 375128 * q^81 + 175628 * q^82 - 384748 * q^85 + 139810 * q^92 + 183272 * q^93 + 601258 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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