LMFDB - Embedded newform 76.6.d.a.75.8

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

$q$-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	$-0.872849\pi$
$7$		−	100.840i		−	0.777837i	0.921272	−	0.388919i	$-0.127151\pi$
$8$	−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	$-0.825911\pi$
$11$		−	417.410i		−	1.04011i	0.854132	−	0.520057i	$-0.174089\pi$
$12$	−174.771	+	231.048i	−0.350362	+	0.463180i
$13$			221.235i			0.363074i	0.983384	+	0.181537i	$0.0581073\pi$
$13$			221.235i			0.363074i	−0.983384	+	0.181537i	$0.941893\pi$
$14$	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	$0.285068\pi$
$23$			3960.57i			1.56113i	−0.625076	+	0.780564i	$0.714932\pi$
$24$	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	$0.359070\pi$
$29$			8184.48i			1.80716i	−0.428422	+	0.903579i	$0.640930\pi$
$30$	−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	$-0.617949\pi$
$37$		−	15524.2i		−	1.86426i	0.362126	−	0.932129i	$-0.382051\pi$
$38$	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	$0.0476931\pi$
$41$			3213.43i			0.298544i	−0.988796	+	0.149272i	$0.952307\pi$
$42$	−2300.08	−	4623.83i	−0.201196	−	0.404463i
$43$		−	5057.78i		−	0.417147i	−0.978007	−	0.208573i	$-0.933118\pi$
$43$		−	5057.78i		−	0.417147i	0.978007	−	0.208573i	$-0.0668820\pi$
$44$	−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	$-0.812660\pi$
$47$		−	16814.6i		−	1.11030i	0.831749	−	0.555152i	$-0.187340\pi$
$48$	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	$0.0291576\pi$
$53$			3741.22i			0.182946i	−0.995808	+	0.0914732i	$0.970842\pi$
$54$	−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	$-0.993126\pi$
$83$		−	2710.50i		−	0.0431871i	0.999767	−	0.0215935i	$-0.00687397\pi$
$84$	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	$0.253906\pi$
$89$			106968.i			1.43146i	−0.698376	+	0.715731i	$0.746094\pi$
$90$	−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	$0.215980\pi$
$97$			116325.i			1.25529i	−0.778501	+	0.627643i	$0.784020\pi$
$98$	−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	$0.0380065\pi$
$109$			29551.0i			0.238235i	−0.992880	+	0.119118i	$0.961993\pi$
$110$	−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	$-0.880430\pi$
$113$		−	99594.9i		−	0.733738i	0.930273	−	0.366869i	$-0.119570\pi$
$114$	−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	$0.120413\pi$
$131$			145085.i			0.738659i	−0.929299	+	0.369329i	$0.879587\pi$
$132$	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	$0.0348463\pi$
$139$			49774.4i			0.218509i	−0.994014	+	0.109255i	$0.965154\pi$
$140$	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	$0.187657\pi$
$163$			377188.i			1.11196i	−0.831196	+	0.555979i	$0.812343\pi$
$164$	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	$-0.918556\pi$
$173$		−	199253.i		−	0.506163i	0.967445	−	0.253081i	$-0.0814441\pi$
$174$	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	$0.275050\pi$
$181$			670394.i			1.52101i	−0.649329	+	0.760507i	$0.724950\pi$
$182$	−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	$0.222136\pi$
$191$			647949.i			1.28516i	−0.766218	+	0.642581i	$0.777864\pi$
$192$	276365.	+	107831.i	0.541041	+	0.211101i
$193$		−	405270.i		−	0.783161i	−0.920144	−	0.391580i	$-0.871928\pi$
$193$		−	405270.i		−	0.783161i	0.920144	−	0.391580i	$-0.128072\pi$
$194$	−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	$0.211914\pi$
$199$			690085.i			1.23529i	−0.786456	+	0.617647i	$0.788086\pi$
$200$	−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	$0.0243242\pi$
$239$			134831.i			0.152685i	−0.997082	+	0.0763424i	$0.975676\pi$
$240$	−226042.	−	799331.i	−0.253315	−	0.895774i
$241$			210219.i			0.233146i	0.993182	+	0.116573i	$0.0371910\pi$
$241$			210219.i			0.233146i	−0.993182	+	0.116573i	$0.962809\pi$
$242$	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	$-0.884336\pi$
$251$		−	709519.i		−	0.710853i	0.934704	−	0.355426i	$-0.115664\pi$
$252$	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	$0.0510623\pi$
$257$			338258.i			0.319460i	−0.987161	+	0.159730i	$0.948938\pi$
$258$	−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	$-0.670306\pi$
$263$		−	1.92995e6i		−	1.72050i	0.509868	−	0.860252i	$-0.329694\pi$
$264$	−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	$-0.980759\pi$
$269$		−	143394.i		−	0.120823i	0.998174	−	0.0604117i	$-0.0192414\pi$
$270$	1.66004e6	−	825772.i	1.38583	−	0.689367i
$271$			1.85314e6i			1.53280i	0.642366	+	0.766398i	$0.277953\pi$
$271$			1.85314e6i			1.53280i	−0.642366	+	0.766398i	$0.722047\pi$
$272$	−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	$-0.802912\pi$
$281$		−	1.53636e6i		−	1.16072i	0.814360	−	0.580360i	$-0.197088\pi$
$282$	−383526.	−	771001.i	−0.287192	−	0.577340i
$283$			1.34720e6i			0.999923i	0.866048	+	0.499961i	$0.166652\pi$
$283$			1.34720e6i			0.999923i	−0.866048	+	0.499961i	$0.833348\pi$
$284$	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	$0.233488\pi$
$293$			1.96763e6i			1.33898i	−0.742821	+	0.669491i	$0.766512\pi$
$294$	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	$0.112748\pi$
$311$			1.18323e6i			0.693694i	−0.937922	+	0.346847i	$0.887252\pi$
$312$	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	$-0.761093\pi$
$317$		−	2.44055e6i		−	1.36408i	0.731314	−	0.682040i	$-0.238907\pi$
$318$	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	$-0.939470\pi$
$337$		−	788139.i		−	0.378032i	0.981974	−	0.189016i	$-0.0605297\pi$
$338$	−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	$0.122403\pi$
$347$			1.68282e6i			0.750265i	−0.926971	+	0.375132i	$0.877597\pi$
$348$	−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	$-0.971953\pi$
$359$		−	429777.i		−	0.175998i	0.996121	−	0.0879989i	$-0.0280472\pi$
$360$	−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	$-0.997559\pi$
$367$		−	39567.2i		−	0.0153345i	0.999971	−	0.00766727i	$-0.00244059\pi$
$368$	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	$0.0723848\pi$
$373$			1.21157e6i			0.450897i	−0.974255	+	0.225449i	$0.927615\pi$
$374$	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	$-0.918033\pi$
$401$		−	1.64009e6i		−	0.509339i	0.967028	−	0.254669i	$-0.0819667\pi$
$402$	−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	$0.0888066\pi$
$409$			1.86331e6i			0.550778i	−0.961333	+	0.275389i	$0.911193\pi$
$410$	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	$-0.626734\pi$
$419$		−	6.62511e6i		−	1.84356i	0.387711	−	0.921781i	$-0.373266\pi$
$420$	−2.08768e6	−	1.57918e6i	−0.577486	−	0.436826i
$421$			2.03383e6i			0.559254i	0.960109	+	0.279627i	$0.0902108\pi$
$421$			2.03383e6i			0.559254i	−0.960109	+	0.279627i	$0.909789\pi$
$422$	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	$0.0727765\pi$
$433$			1.76848e6i			0.453295i	−0.973977	+	0.226647i	$0.927223\pi$
$434$	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	$0.103524\pi$
$443$			2.63966e6i			0.639057i	−0.947577	+	0.319528i	$0.896476\pi$
$444$	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	$0.309273\pi$
$449$			7.05534e6i			1.65159i	−0.563970	+	0.825795i	$0.690727\pi$
$450$	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	$0.303149\pi$
$463$			7.51673e6i			1.62958i	−0.579754	+	0.814792i	$0.696851\pi$
$464$	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	$0.229877\pi$
$467$			6.23071e6i			1.32204i	−0.750367	+	0.661021i	$0.770123\pi$
$468$	−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	$-0.807779\pi$
$479$		−	5.70290e6i		−	1.13568i	0.823138	−	0.567841i	$-0.192221\pi$
$480$	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	$0.0495910\pi$
$491$			1.65778e6i			0.310330i	−0.987889	+	0.155165i	$0.950409\pi$
$492$	−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	$-0.736418\pi$
$499$		−	8.19460e6i		−	1.47325i	0.676302	−	0.736625i	$-0.263582\pi$
$500$	−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	$0.0761507\pi$
$503$			2.68920e6i			0.473918i	−0.971520	+	0.236959i	$0.923849\pi$
$504$	−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	$0.187384\pi$
$509$			6.49123e6i			1.11054i	−0.831672	+	0.555268i	$0.812616\pi$
$510$	−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	$0.0391963\pi$
$521$			1.52202e6i			0.245655i	−0.992428	+	0.122828i	$0.960804\pi$
$522$	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	$-0.979520\pi$
$569$		−	993114.i		−	0.128593i	0.997931	−	0.0642966i	$-0.0204804\pi$
$570$	5.97927e6	−	4.04842e6i	0.770835	−	0.521913i
$571$			8.22860e6i			1.05617i	0.849190	+	0.528087i	$0.177090\pi$
$571$			8.22860e6i			1.05617i	−0.849190	+	0.528087i	$0.822910\pi$
$572$	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	$-0.855681\pi$
$587$		−	7.31334e6i		−	0.876034i	0.898967	−	0.438017i	$-0.144319\pi$
$588$	−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	$-0.980235\pi$
$601$		−	1.09895e6i		−	0.124105i	0.998073	−	0.0620526i	$-0.0197647\pi$
$602$	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	$0.246431\pi$
$619$			1.33296e7i			1.39827i	−0.714990	+	0.699134i	$0.753569\pi$
$620$	−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	$0.0156717\pi$
$631$			984449.i			0.0984283i	−0.998788	+	0.0492141i	$0.984328\pi$
$632$	−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	$0.102198\pi$
$641$			6.56567e6i			0.631152i	−0.948900	+	0.315576i	$0.897802\pi$
$642$	−4.12629e6	+	2.05258e6i	−0.395114	+	0.196545i
$643$		−	1.66218e7i		−	1.58545i	−0.609582	−	0.792723i	$-0.708663\pi$
$643$		−	1.66218e7i		−	1.58545i	0.609582	−	0.792723i	$-0.291337\pi$
$644$	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	$0.0857326\pi$
$647$			5.66661e6i			0.532185i	−0.963948	+	0.266092i	$0.914267\pi$
$648$	−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	$-0.939922\pi$
$661$		−	4.21517e6i		−	0.375242i	0.982242	−	0.187621i	$-0.0600776\pi$
$662$	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	$-0.837310\pi$
$673$		−	1.14948e7i		−	0.978283i	0.872204	−	0.489142i	$-0.162690\pi$
$674$	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	$-0.754946\pi$
$677$		−	1.66009e7i		−	1.39207i	0.718008	−	0.696035i	$-0.245054\pi$
$678$	−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	$-0.961211\pi$
$691$		−	3.05145e6i		−	0.243114i	0.992584	−	0.121557i	$-0.0387888\pi$
$692$	−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	$0.205924\pi$
$719$			1.67102e7i			1.20548i	−0.797939	+	0.602738i	$0.794076\pi$
$720$	−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	$0.0818685\pi$
$727$			7.24993e6i			0.508742i	−0.967107	+	0.254371i	$0.918132\pi$
$728$	−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	$0.346817\pi$
$739$			2.63197e7i			1.77284i	−0.462878	+	0.886422i	$0.653183\pi$
$740$	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	$0.0730776\pi$
$773$			7.56121e6i			0.455137i	−0.973762	+	0.227569i	$0.926922\pi$
$774$	−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	$-0.711831\pi$
$797$		−	2.82123e7i		−	1.57323i	0.617443	−	0.786615i	$-0.288169\pi$
$798$	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	$-0.861399\pi$
$823$		−	1.63921e7i		−	0.843600i	0.906689	−	0.421800i	$-0.138601\pi$
$824$	−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	$0.237199\pi$
$829$			2.68358e7i			1.35621i	−0.734964	+	0.678106i	$0.762801\pi$
$830$	−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	$0.152129\pi$
$857$			1.97780e7i			0.919880i	−0.887950	+	0.459940i	$0.847871\pi$
$858$	4.23433e6	−	2.10633e6i	0.196366	−	0.0976804i
$859$		−	3.30886e7i		−	1.53001i	−0.644022	−	0.765007i	$-0.722735\pi$
$859$		−	3.30886e7i		−	1.53001i	0.644022	−	0.765007i	$-0.277265\pi$
$860$	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	$-0.678760\pi$
$877$		−	3.85576e7i		−	1.69282i	0.532533	−	0.846409i	$-0.321240\pi$
$878$	−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	$-0.929568\pi$
$883$		−	1.01695e7i		−	0.438934i	0.975620	−	0.219467i	$-0.0704318\pi$
$884$	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	$-0.882298\pi$
$919$		−	1.85058e7i		−	0.722803i	0.932410	−	0.361401i	$-0.117702\pi$
$920$	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	$0.260594\pi$
$941$			3.96709e7i			1.46049i	−0.683186	+	0.730245i	$0.739406\pi$
$942$	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	$0.315807\pi$
$947$			4.62096e7i			1.67439i	−0.546902	+	0.837197i	$0.684193\pi$
$948$	−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	$0.346805\pi$
$953$			4.97044e7i			1.77281i	−0.462911	+	0.886405i	$0.653195\pi$
$954$	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	$0.00141722\pi$
$967$			258929.i			0.00890460i	−0.999990	+	0.00445230i	$0.998583\pi$
$968$	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	$-0.757391\pi$
$977$		−	4.12031e7i		−	1.38100i	0.723332	−	0.690500i	$-0.242609\pi$
$978$	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.75.8	yes	48
4.3	odd	2	inner	76.6.d.a.75.42	yes	48
19.18	odd	2	inner	76.6.d.a.75.41	yes	48
76.75	even	2	inner	76.6.d.a.75.7	✓	48

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