LMFDB - Embedded newform 76.6.e.a.45.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,6,Mod(45,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("76.45");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	76.e (of order $3$, degree $2$, 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:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 2 x^{17} + 1540 x^{16} - 768 x^{15} + 1608492 x^{14} - 1027368 x^{13} + 897054160 x^{12} + \cdots + 80\!\cdots\!36 $ x^18 - 2x^17 + 1540x^16 - 768x^15 + 1608492x^14 - 1027368x^13 + 897054160x^12 - 1275481376x^11 + 361098181456x^10 - 863969476320x^9 + 79755165392064x^8 - 375077568148992x^7 + 12736924096193536x^6 - 57314532742553600x^5 + 977121800205220864x^4 - 4977732006498379776x^3 + 53672321824823513088x^2 - 185653809995679793152*x + 804303742853852430336
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{3}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			45.6
Root			$-4.70426 + 8.14802i$ of defining polynomial
Character	$\chi$	$=$	76.45
Dual form			76.6.e.a.49.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.20426 + 7.28199i) q^{3} +(-18.6530 - 32.3080i) q^{5} +15.8772 q^{7} +(86.1484 - 149.213i) q^{9} +O(q^{10})$	\(q+(4.20426 + 7.28199i) q^{3} +(-18.6530 - 32.3080i) q^{5} +15.8772 q^{7} +(86.1484 - 149.213i) q^{9} -325.518 q^{11} +(519.710 - 900.165i) q^{13} +(156.844 - 271.662i) q^{15} +(778.938 + 1349.16i) q^{17} +(418.139 - 1516.99i) q^{19} +(66.7519 + 115.618i) q^{21} +(784.020 - 1357.96i) q^{23} +(866.629 - 1501.04i) q^{25} +3492.03 q^{27} +(4023.95 - 6969.69i) q^{29} -9529.39 q^{31} +(-1368.56 - 2370.42i) q^{33} +(-296.158 - 512.961i) q^{35} -451.140 q^{37} +8739.99 q^{39} +(2231.10 + 3864.38i) q^{41} +(5775.62 + 10003.7i) q^{43} -6427.72 q^{45} +(-3080.89 + 5336.26i) q^{47} -16554.9 q^{49} +(-6549.72 + 11344.4i) q^{51} +(-11186.9 + 19376.2i) q^{53} +(6071.91 + 10516.9i) q^{55} +(12804.7 - 3332.94i) q^{57} +(-3512.04 - 6083.03i) q^{59} +(4074.18 - 7056.68i) q^{61} +(1367.80 - 2369.09i) q^{63} -38776.7 q^{65} +(-27310.0 + 47302.3i) q^{67} +13184.9 q^{69} +(24835.7 + 43016.6i) q^{71} +(-29169.7 - 50523.3i) q^{73} +14574.1 q^{75} -5168.32 q^{77} +(-18324.7 - 31739.4i) q^{79} +(-6252.66 - 10829.9i) q^{81} +65668.7 q^{83} +(29059.1 - 50331.9i) q^{85} +67670.9 q^{87} +(-20103.8 + 34820.8i) q^{89} +(8251.55 - 14292.1i) q^{91} +(-40064.0 - 69393.0i) q^{93} +(-56810.5 + 14787.2i) q^{95} +(-5677.26 - 9833.30i) q^{97} +(-28042.9 + 48571.7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 11 q^{3} + 11 q^{5} + 336 q^{7} - 902 q^{9}+O(q^{10}) $ 18 * q - 11 * q^3 + 11 * q^5 + 336 * q^7 - 902 * q^9	$ 18 q - 11 q^{3} + 11 q^{5} + 336 q^{7} - 902 q^{9} - 320 q^{11} + 227 q^{13} - 101 q^{15} + 179 q^{17} - 868 q^{19} - 5700 q^{21} - 3425 q^{23} - 7054 q^{25} + 14722 q^{27} - 7349 q^{29} - 9960 q^{31} - 2998 q^{33} + 15888 q^{35} + 26444 q^{37} - 30246 q^{39} - 7311 q^{41} - 8283 q^{43} - 62164 q^{45} + 37603 q^{47} + 124738 q^{49} + 47227 q^{51} - 20337 q^{53} + 716 q^{55} - 57555 q^{57} - 74455 q^{59} - 7569 q^{61} - 52544 q^{63} + 188998 q^{65} - 26177 q^{67} + 116282 q^{69} - 53463 q^{71} - 14103 q^{73} + 120912 q^{75} - 31960 q^{77} + 31825 q^{79} - 21137 q^{81} + 82600 q^{83} - 50787 q^{85} - 339766 q^{87} - 155197 q^{89} - 2800 q^{91} - 46460 q^{93} + 49315 q^{95} + 111241 q^{97} - 193544 q^{99}+O(q^{100}) $ 18 * q - 11 * q^3 + 11 * q^5 + 336 * q^7 - 902 * q^9 - 320 * q^11 + 227 * q^13 - 101 * q^15 + 179 * q^17 - 868 * q^19 - 5700 * q^21 - 3425 * q^23 - 7054 * q^25 + 14722 * q^27 - 7349 * q^29 - 9960 * q^31 - 2998 * q^33 + 15888 * q^35 + 26444 * q^37 - 30246 * q^39 - 7311 * q^41 - 8283 * q^43 - 62164 * q^45 + 37603 * q^47 + 124738 * q^49 + 47227 * q^51 - 20337 * q^53 + 716 * q^55 - 57555 * q^57 - 74455 * q^59 - 7569 * q^61 - 52544 * q^63 + 188998 * q^65 - 26177 * q^67 + 116282 * q^69 - 53463 * q^71 - 14103 * q^73 + 120912 * q^75 - 31960 * q^77 + 31825 * q^79 - 21137 * q^81 + 82600 * q^83 - 50787 * q^85 - 339766 * q^87 - 155197 * q^89 - 2800 * q^91 - 46460 * q^93 + 49315 * q^95 + 111241 * q^97 - 193544 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	4.20426	+	7.28199i	0.269703	+	0.467140i	0.968785	−	0.247902i	$-0.0797410\pi$
$3$	4.20426	+	7.28199i	0.269703	+	0.467140i	−0.699082	+	0.715042i	$0.746408\pi$
$4$		0			0
$5$	−18.6530	−	32.3080i	−0.333676	−	0.577943i	0.649554	−	0.760316i	$-0.274956\pi$
$5$	−18.6530	−	32.3080i	−0.333676	−	0.577943i	−0.983230	+	0.182372i	$0.941622\pi$
$6$		0			0
$7$	15.8772			0.122470			0.0612349	−	0.998123i	$-0.480496\pi$
$7$	15.8772			0.122470			0.0612349	+	0.998123i	$0.480496\pi$
$8$		0			0
$9$	86.1484	−	149.213i	0.354520	−	0.614047i
$10$		0			0
$11$	−325.518			−0.811136			−0.405568	−	0.914065i	$-0.632926\pi$
$11$	−325.518			−0.811136			−0.405568	+	0.914065i	$0.632926\pi$
$12$		0			0
$13$	519.710	−	900.165i	0.852909	−	1.47728i	−0.0256616	−	0.999671i	$-0.508169\pi$
$13$	519.710	−	900.165i	0.852909	−	1.47728i	0.878571	−	0.477612i	$-0.158497\pi$
$14$		0			0
$15$	156.844	−	271.662i	0.179987	−	0.311746i
$16$		0			0
$17$	778.938	+	1349.16i	0.653703	+	1.13225i	0.982217	+	0.187748i	$0.0601190\pi$
$17$	778.938	+	1349.16i	0.653703	+	1.13225i	−0.328514	+	0.944499i	$0.606548\pi$
$18$		0			0
$19$	418.139	−	1516.99i	0.265728	−	0.964048i
$19$	418.139	−	1516.99i	0.265728	−	0.964048i
$20$		0			0
$21$	66.7519	+	115.618i	0.0330305	+	0.0572105i
$22$		0			0
$23$	784.020	−	1357.96i	0.309035	−	0.535264i	−0.669116	−	0.743158i	$-0.733327\pi$
$23$	784.020	−	1357.96i	0.309035	−	0.535264i	0.978152	+	0.207893i	$0.0666606\pi$
$24$		0			0
$25$	866.629	−	1501.04i	0.277321	−	0.480334i
$26$		0			0
$27$	3492.03			0.921868
$28$		0			0
$29$	4023.95	−	6969.69i	0.888501	−	1.53893i	0.0468525	−	0.998902i	$-0.485081\pi$
$29$	4023.95	−	6969.69i	0.888501	−	1.53893i	0.841648	−	0.540026i	$-0.181586\pi$
$30$		0			0
$31$	−9529.39			−1.78099			−0.890494	−	0.454995i	$-0.849641\pi$
$31$	−9529.39			−1.78099			−0.890494	+	0.454995i	$0.849641\pi$
$32$		0			0
$33$	−1368.56	−	2370.42i	−0.218766	−	0.378914i
$34$		0			0
$35$	−296.158	−	512.961i	−0.0408652	−	0.0707806i
$36$		0			0
$37$	−451.140			−0.0541760			−0.0270880	−	0.999633i	$-0.508623\pi$
$37$	−451.140			−0.0541760			−0.0270880	+	0.999633i	$0.508623\pi$
$38$		0			0
$39$	8739.99			0.920130
$40$		0			0
$41$	2231.10	+	3864.38i	0.207281	+	0.359021i	0.950857	−	0.309630i	$-0.100205\pi$
$41$	2231.10	+	3864.38i	0.207281	+	0.359021i	−0.743576	+	0.668651i	$0.766872\pi$
$42$		0			0
$43$	5775.62	+	10003.7i	0.476352	+	0.825066i	0.999633	−	0.0270946i	$-0.00862554\pi$
$43$	5775.62	+	10003.7i	0.476352	+	0.825066i	−0.523281	+	0.852160i	$0.675292\pi$
$44$		0			0
$45$	−6427.72			−0.473179
$46$		0			0
$47$	−3080.89	+	5336.26i	−0.203438	+	0.352365i	−0.949634	−	0.313362i	$-0.898545\pi$
$47$	−3080.89	+	5336.26i	−0.203438	+	0.352365i	0.746196	+	0.665726i	$0.231878\pi$
$48$		0			0
$49$	−16554.9			−0.985001
$50$		0			0
$51$	−6549.72	+	11344.4i	−0.352612	+	0.610742i
$52$		0			0
$53$	−11186.9	+	19376.2i	−0.547039	+	0.947500i	0.451436	+	0.892303i	$0.350912\pi$
$53$	−11186.9	+	19376.2i	−0.547039	+	0.947500i	−0.998476	+	0.0551965i	$0.982421\pi$
$54$		0			0
$55$	6071.91	+	10516.9i	0.270656	+	0.468791i
$56$		0			0
$57$	12804.7	−	3332.94i	0.522013	−	0.135875i
$58$		0			0
$59$	−3512.04	−	6083.03i	−0.131350	−	0.227504i	0.792847	−	0.609420i	$-0.208598\pi$
$59$	−3512.04	−	6083.03i	−0.131350	−	0.227504i	−0.924197	+	0.381916i	$0.875264\pi$
$60$		0			0
$61$	4074.18	−	7056.68i	0.140189	−	0.242815i	−0.787378	−	0.616470i	$-0.788562\pi$
$61$	4074.18	−	7056.68i	0.140189	−	0.242815i	0.927568	+	0.373655i	$0.121896\pi$
$62$		0			0
$63$	1367.80	−	2369.09i	0.0434180	−	0.0752022i
$64$		0			0
$65$	−38776.7			−1.13838
$66$		0			0
$67$	−27310.0	+	47302.3i	−0.743250	+	1.28735i	0.207758	+	0.978180i	$0.433383\pi$
$67$	−27310.0	+	47302.3i	−0.743250	+	1.28735i	−0.951008	+	0.309167i	$0.899950\pi$
$68$		0			0
$69$	13184.9			0.333391
$70$		0			0
$71$	24835.7	+	43016.6i	0.584696	+	1.01272i	0.994913	+	0.100735i	$0.0321194\pi$
$71$	24835.7	+	43016.6i	0.584696	+	1.01272i	−0.410218	+	0.911988i	$0.634547\pi$
$72$		0			0
$73$	−29169.7	−	50523.3i	−0.640655	−	1.10965i	−0.985287	−	0.170909i	$-0.945330\pi$
$73$	−29169.7	−	50523.3i	−0.640655	−	1.10965i	0.344632	−	0.938738i	$-0.388004\pi$
$74$		0			0
$75$	14574.1			0.299178
$76$		0			0
$77$	−5168.32			−0.0993397
$78$		0			0
$79$	−18324.7	−	31739.4i	−0.330347	−	0.572177i	0.652233	−	0.758018i	$-0.273832\pi$
$79$	−18324.7	−	31739.4i	−0.330347	−	0.572177i	−0.982580	+	0.185841i	$0.940499\pi$
$80$		0			0
$81$	−6252.66	−	10829.9i	−0.105889	−	0.183406i
$82$		0			0
$83$	65668.7			1.04632			0.523158	−	0.852236i	$-0.324754\pi$
$83$	65668.7			1.04632			0.523158	+	0.852236i	$0.324754\pi$
$84$		0			0
$85$	29059.1	−	50331.9i	0.436250	−	0.755607i
$86$		0			0
$87$	67670.9			0.958526
$88$		0			0
$89$	−20103.8	+	34820.8i	−0.269032	+	0.465976i	−0.968612	−	0.248577i	$-0.920037\pi$
$89$	−20103.8	+	34820.8i	−0.269032	+	0.465976i	0.699580	+	0.714554i	$0.253370\pi$
$90$		0			0
$91$	8251.55	−	14292.1i	0.104456	−	0.180923i
$92$		0			0
$93$	−40064.0	−	69393.0i	−0.480338	−	0.831971i
$94$		0			0
$95$	−56810.5	+	14787.2i	−0.645832	+	0.168104i
$96$		0			0
$97$	−5677.26	−	9833.30i	−0.0612645	−	0.106113i	0.833766	−	0.552117i	$-0.186180\pi$
$97$	−5677.26	−	9833.30i	−0.0612645	−	0.106113i	−0.895031	+	0.446004i	$0.852847\pi$
$98$		0			0
$99$	−28042.9	+	48571.7i	−0.287564	+	0.498076i
$100$		0			0
$101$	96363.2	−	166906.i	0.939957	−	1.62805i	0.174409	−	0.984673i	$-0.444199\pi$
$101$	96363.2	−	166906.i	0.939957	−	1.62805i	0.765548	−	0.643379i	$-0.222468\pi$
$102$		0			0
$103$	174119.			1.61716			0.808579	−	0.588387i	$-0.200237\pi$
$103$	174119.			1.61716			0.808579	+	0.588387i	$0.200237\pi$
$104$		0			0
$105$	2490.25	−	4313.24i	0.0220430	−	0.0381795i
$106$		0			0
$107$	−24682.3			−0.208413			−0.104207	−	0.994556i	$-0.533230\pi$
$107$	−24682.3			−0.208413			−0.104207	+	0.994556i	$0.533230\pi$
$108$		0			0
$109$	16094.5	+	27876.5i	0.129751	+	0.224735i	0.923580	−	0.383406i	$-0.125249\pi$
$109$	16094.5	+	27876.5i	0.129751	+	0.224735i	−0.793829	+	0.608141i	$0.791916\pi$
$110$		0			0
$111$	−1896.71	−	3285.20i	−0.0146115	−	0.0253078i
$112$		0			0
$113$	115981.			0.854455			0.427228	−	0.904144i	$-0.359490\pi$
$113$	115981.			0.854455			0.427228	+	0.904144i	$0.359490\pi$
$114$		0			0
$115$	−58497.4			−0.412470
$116$		0			0
$117$	−89544.4	−	155095.i	−0.604747	−	1.04745i
$118$		0			0
$119$	12367.4	+	21420.9i	0.0800589	+	0.138666i
$120$		0			0
$121$	−55088.7			−0.342058
$122$		0			0
$123$	−18760.3	+	32493.7i	−0.111809	+	0.193659i
$124$		0			0
$125$	−181242.			−1.03749
$126$		0			0
$127$	94476.0	−	163637.i	0.519771	−	0.900270i	−0.479964	−	0.877288i	$-0.659350\pi$
$127$	94476.0	−	163637.i	0.519771	−	0.900270i	0.999736	−	0.0229825i	$-0.00731621\pi$
$128$		0			0
$129$	−48564.4	+	84116.1i	−0.256947	+	0.445046i
$130$		0			0
$131$	156242.	+	270619.i	0.795462	+	1.37778i	0.922545	+	0.385889i	$0.126105\pi$
$131$	156242.	+	270619.i	0.795462	+	1.37778i	−0.127083	+	0.991892i	$0.540562\pi$
$132$		0			0
$133$	6638.88	−	24085.6i	0.0325436	−	0.118067i
$134$		0			0
$135$	−65137.0	−	112821.i	−0.307605	−	0.532787i
$136$		0			0
$137$	8354.62	−	14470.6i	0.0380299	−	0.0658697i	−0.846384	−	0.532573i	$-0.821225\pi$
$137$	8354.62	−	14470.6i	0.0380299	−	0.0658697i	0.884414	+	0.466703i	$0.154558\pi$
$138$		0			0
$139$	−37890.7	+	65628.7i	−0.166340	+	0.288109i	−0.937130	−	0.348980i	$-0.886528\pi$
$139$	−37890.7	+	65628.7i	−0.166340	+	0.288109i	0.770790	+	0.637089i	$0.219862\pi$
$140$		0			0
$141$	−51811.4			−0.219471
$142$		0			0
$143$	−169175.	+	293020.i	−0.691826	+	1.19828i
$144$		0			0
$145$	−300236.			−1.18588
$146$		0			0
$147$	−69601.2	−	120553.i	−0.265658	−	0.460133i
$148$		0			0
$149$	213642.	+	370039.i	0.788353	+	1.36547i	0.926975	+	0.375123i	$0.122399\pi$
$149$	213642.	+	370039.i	0.788353	+	1.36547i	−0.138622	+	0.990345i	$0.544267\pi$
$150$		0			0
$151$	−123090.			−0.439319			−0.219659	−	0.975577i	$-0.570495\pi$
$151$	−123090.			−0.439319			−0.219659	+	0.975577i	$0.570495\pi$
$152$		0			0
$153$	268417.			0.927004
$154$		0			0
$155$	177752.	+	307876.i	0.594272	+	1.02931i
$156$		0			0
$157$	262647.	+	454918.i	0.850401	+	1.47294i	0.880847	+	0.473401i	$0.156974\pi$
$157$	262647.	+	454918.i	0.850401	+	1.47294i	−0.0304458	+	0.999536i	$0.509693\pi$
$158$		0			0
$159$	−188130.			−0.590153
$160$		0			0
$161$	12448.1	−	21560.7i	0.0378475	−	0.0655537i
$162$		0			0
$163$	−201402.			−0.593737			−0.296868	−	0.954918i	$-0.595942\pi$
$163$	−201402.			−0.593737			−0.296868	+	0.954918i	$0.595942\pi$
$164$		0			0
$165$	−51055.7	+	88431.1i	−0.145994	+	0.252869i
$166$		0			0
$167$	−84718.2	+	146736.i	−0.235064	+	0.407142i	−0.959291	−	0.282419i	$-0.908863\pi$
$167$	−84718.2	+	146736.i	−0.235064	+	0.407142i	0.724227	+	0.689561i	$0.242197\pi$
$168$		0			0
$169$	−354551.	−	614100.i	−0.954909	−	1.65395i
$170$		0			0
$171$	−190333.	−	193078.i	−0.497765	−	0.504944i
$172$		0			0
$173$	31933.9	+	55311.1i	0.0811216	+	0.140507i	0.903732	−	0.428099i	$-0.140816\pi$
$173$	31933.9	+	55311.1i	0.0811216	+	0.140507i	−0.822610	+	0.568605i	$0.807483\pi$
$174$		0			0
$175$	13759.6	−	23832.4i	0.0339635	−	0.0588265i
$176$		0			0
$177$	29531.0	−	51149.3i	0.0708509	−	0.122717i
$178$		0			0
$179$	116034.			0.270677			0.135339	−	0.990799i	$-0.456788\pi$
$179$	116034.			0.270677			0.135339	+	0.990799i	$0.456788\pi$
$180$		0			0
$181$	26722.9	−	46285.5i	0.0606301	−	0.105014i	−0.834117	−	0.551587i	$-0.814022\pi$
$181$	26722.9	−	46285.5i	0.0606301	−	0.105014i	0.894747	+	0.446573i	$0.147356\pi$
$182$		0			0
$183$	68515.6			0.151238
$184$		0			0
$185$	8415.13	+	14575.4i	0.0180772	+	0.0313107i
$186$		0			0
$187$	−253559.	−	439177.i	−0.530243	−	0.918407i
$188$		0			0
$189$	55443.7			0.112901
$190$		0			0
$191$	564257.			1.11916			0.559582	−	0.828775i	$-0.310962\pi$
$191$	564257.			1.11916			0.559582	+	0.828775i	$0.310962\pi$
$192$		0			0
$193$	146535.	+	253806.i	0.283170	+	0.490466i	0.972164	−	0.234302i	$-0.0752804\pi$
$193$	146535.	+	253806.i	0.283170	+	0.490466i	−0.688993	+	0.724768i	$0.741947\pi$
$194$		0			0
$195$	−163027.	−	282372.i	−0.307025	−	0.531783i
$196$		0			0
$197$	377908.			0.693778			0.346889	−	0.937906i	$-0.387238\pi$
$197$	377908.			0.693778			0.346889	+	0.937906i	$0.387238\pi$
$198$		0			0
$199$	443715.	−	768537.i	0.794276	−	1.37573i	−0.129021	−	0.991642i	$-0.541184\pi$
$199$	443715.	−	768537.i	0.794276	−	1.37573i	0.923298	−	0.384085i	$-0.125483\pi$
$200$		0			0
$201$	−459274.			−0.801828
$202$		0			0
$203$	63889.1	−	110659.i	0.108815	−	0.188472i
$204$		0			0
$205$	83233.6	−	144165.i	0.138329	−	0.239593i
$206$		0			0
$207$	−135084.	−	233973.i	−0.219118	−	0.379524i
$208$		0			0
$209$	−136112.	+	493808.i	−0.215541	+	0.781975i
$210$		0			0
$211$	62683.9	+	108572.i	0.0969282	+	0.167885i	0.910412	−	0.413703i	$-0.135765\pi$
$211$	62683.9	+	108572.i	0.0969282	+	0.167885i	−0.813484	+	0.581588i	$0.802432\pi$
$212$		0			0
$213$	−208831.	+	361706.i	−0.315389	+	0.546269i
$214$		0			0
$215$	215466.	−	373198.i	0.317894	−	0.550608i
$216$		0			0
$217$	−151300.			−0.218117
$218$		0			0
$219$	245274.	−	424826.i	0.345574	−	0.598551i
$220$		0			0
$221$	1.61929e6			2.23020
$222$		0			0
$223$	214409.	+	371367.i	0.288723	+	0.500082i	0.973505	−	0.228665i	$-0.0734361\pi$
$223$	214409.	+	371367.i	0.288723	+	0.500082i	−0.684782	+	0.728748i	$0.740103\pi$
$224$		0			0
$225$	−149317.	−	258625.i	−0.196632	−	0.340576i
$226$		0			0
$227$	169489.			0.218312			0.109156	−	0.994025i	$-0.465185\pi$
$227$	169489.			0.218312			0.109156	+	0.994025i	$0.465185\pi$
$228$		0			0
$229$	−380975.			−0.480073			−0.240037	−	0.970764i	$-0.577159\pi$
$229$	−380975.			−0.480073			−0.240037	+	0.970764i	$0.577159\pi$
$230$		0			0
$231$	−21729.0	−	37635.7i	−0.0267923	−	0.0464056i
$232$		0			0
$233$	−137211.	−	237656.i	−0.165576	−	0.286787i	0.771283	−	0.636492i	$-0.219615\pi$
$233$	−137211.	−	237656.i	−0.165576	−	0.286787i	−0.936860	+	0.349705i	$0.886282\pi$
$234$		0			0
$235$	229872.			0.271529
$236$		0			0
$237$	154084.	−	266881.i	0.178191	−	0.308636i
$238$		0			0
$239$	−1.30763e6			−1.48078			−0.740390	−	0.672178i	$-0.765359\pi$
$239$	−1.30763e6			−1.48078			−0.740390	+	0.672178i	$0.765359\pi$
$240$		0			0
$241$	284474.	−	492723.i	0.315500	−	0.546463i	−0.664043	−	0.747694i	$-0.731161\pi$
$241$	284474.	−	492723.i	0.315500	−	0.546463i	0.979544	+	0.201231i	$0.0644943\pi$
$242$		0			0
$243$	476857.	−	825941.i	0.518051	−	0.897291i
$244$		0			0
$245$	308799.	+	534856.i	0.328671	+	0.569275i
$246$		0			0
$247$	−1.14823e6	−	1.16479e6i	−1.19753	−	1.21480i
$248$		0			0
$249$	276088.	+	478199.i	0.282195	+	0.488776i
$250$		0			0
$251$	−687152.	+	1.19018e6i	−0.688443	+	1.19242i	0.283898	+	0.958855i	$0.408372\pi$
$251$	−687152.	+	1.19018e6i	−0.688443	+	1.19242i	−0.972341	+	0.233565i	$0.924961\pi$
$252$		0			0
$253$	−255213.	+	442042.i	−0.250670	+	0.434172i
$254$		0			0
$255$	488688.			0.470632
$256$		0			0
$257$	−628934.	+	1.08935e6i	−0.593981	+	1.02880i	0.399709	+	0.916642i	$0.369111\pi$
$257$	−628934.	+	1.08935e6i	−0.593981	+	1.02880i	−0.993690	+	0.112162i	$0.964222\pi$
$258$		0			0
$259$	−7162.85			−0.00663493
$260$		0			0
$261$	−693314.	−	1.20086e6i	−0.629983	−	1.09116i
$262$		0			0
$263$	130295.	+	225678.i	0.116155	+	0.201187i	0.918241	−	0.396022i	$-0.129610\pi$
$263$	130295.	+	225678.i	0.116155	+	0.201187i	−0.802086	+	0.597209i	$0.796276\pi$
$264$		0			0
$265$	834675.			0.730135
$266$		0			0
$267$	−338086.			−0.290235
$268$		0			0
$269$	649714.	+	1.12534e6i	0.547447	+	0.948205i	0.998449	+	0.0556823i	$0.0177334\pi$
$269$	649714.	+	1.12534e6i	0.547447	+	0.948205i	−0.451002	+	0.892523i	$0.648933\pi$
$270$		0			0
$271$	249281.	+	431768.i	0.206189	+	0.357130i	0.950511	−	0.310691i	$-0.100560\pi$
$271$	249281.	+	431768.i	0.206189	+	0.357130i	−0.744322	+	0.667821i	$0.767227\pi$
$272$		0			0
$273$	138767.			0.112688
$274$		0			0
$275$	−282104.	+	488618.i	−0.224945	+	0.389617i
$276$		0			0
$277$	420798.			0.329514			0.164757	−	0.986334i	$-0.447316\pi$
$277$	420798.			0.329514			0.164757	+	0.986334i	$0.447316\pi$
$278$		0			0
$279$	−820942.	+	1.42191e6i	−0.631396	+	1.09361i
$280$		0			0
$281$	−1.22359e6	+	2.11933e6i	−0.924425	+	1.60115i	−0.131942	+	0.991257i	$0.542121\pi$
$281$	−1.22359e6	+	2.11933e6i	−0.924425	+	1.60115i	−0.792483	+	0.609894i	$0.791212\pi$
$282$		0			0
$283$	−995765.	−	1.72472e6i	−0.739079	−	1.28012i	−0.952910	−	0.303252i	$-0.901928\pi$
$283$	−995765.	−	1.72472e6i	−0.739079	−	1.28012i	0.213831	−	0.976871i	$-0.431406\pi$
$284$		0			0
$285$	−346526.	−	351524.i	−0.252711	−	0.256356i
$286$		0			0
$287$	35423.7	+	61355.6i	0.0253857	+	0.0439693i
$288$		0			0
$289$	−503561.	+	872194.i	−0.354656	+	0.614283i
$290$		0			0
$291$	47737.3	−	82683.5i	0.0330465	−	0.0572382i
$292$		0			0
$293$	1.82155e6			1.23957			0.619786	−	0.784771i	$-0.287220\pi$
$293$	1.82155e6			1.23957			0.619786	+	0.784771i	$0.287220\pi$
$294$		0			0
$295$	−131020.	+	226934.i	−0.0876564	+	0.151825i
$296$		0			0
$297$	−1.13672e6			−0.747761
$298$		0			0
$299$	−814927.	−	1.41149e6i	−0.527158	−	0.913064i
$300$		0			0
$301$	91700.8	+	158830.i	0.0583387	+	0.101046i
$302$		0			0
$303$	1.62054e6			1.01404
$304$		0			0
$305$	−303983.			−0.187111
$306$		0			0
$307$	1.04066e6	+	1.80247e6i	0.630177	+	1.09150i	0.987515	+	0.157523i	$0.0503508\pi$
$307$	1.04066e6	+	1.80247e6i	0.630177	+	1.09150i	−0.357339	+	0.933975i	$0.616316\pi$
$308$		0			0
$309$	732041.	+	1.26793e6i	0.436153	+	0.755439i
$310$		0			0
$311$	−2.82534e6			−1.65642			−0.828208	−	0.560421i	$-0.810639\pi$
$311$	−2.82534e6			−1.65642			−0.828208	+	0.560421i	$0.810639\pi$
$312$		0			0
$313$	−231895.	+	401655.i	−0.133792	+	0.231735i	−0.925135	−	0.379637i	$-0.876049\pi$
$313$	−231895.	+	401655.i	−0.133792	+	0.231735i	0.791343	+	0.611372i	$0.209382\pi$
$314$		0			0
$315$	−102054.			−0.0579501
$316$		0			0
$317$	1.37200e6	−	2.37637e6i	0.766840	−	1.32821i	−0.172428	−	0.985022i	$-0.555161\pi$
$317$	1.37200e6	−	2.37637e6i	0.766840	−	1.32821i	0.939268	−	0.343184i	$-0.111505\pi$
$318$		0			0
$319$	−1.30987e6	+	2.26876e6i	−0.720695	+	1.24828i
$320$		0			0
$321$	−103771.	−	179736.i	−0.0562098	−	0.0973582i
$322$		0			0
$323$	2.37237e6	−	617505.i	1.26525	−	0.329332i
$324$		0			0
$325$	−900792.	−	1.56022e6i	−0.473060	−	0.819363i
$326$		0			0
$327$	−135331.	+	234400.i	−0.0699886	+	0.121224i
$328$		0			0
$329$	−48915.9	+	84724.9i	−0.0249150	+	0.0431540i
$330$		0			0
$331$	−402928.			−0.202142			−0.101071	−	0.994879i	$-0.532227\pi$
$331$	−402928.			−0.202142			−0.101071	+	0.994879i	$0.532227\pi$
$332$		0			0
$333$	−38865.0	+	67316.2i	−0.0192065	+	0.0332666i
$334$		0			0
$335$	2.03766e6			0.992018
$336$		0			0
$337$	−1.94189e6	−	3.36345e6i	−0.931429	−	1.61328i	−0.780880	−	0.624681i	$-0.785229\pi$
$337$	−1.94189e6	−	3.36345e6i	−0.931429	−	1.61328i	−0.150549	−	0.988603i	$-0.548104\pi$
$338$		0			0
$339$	487613.	+	844570.i	0.230449	+	0.399150i
$340$		0			0
$341$	3.10199e6			1.44462
$342$		0			0
$343$	−529694.			−0.243103
$344$		0			0
$345$	−245938.	−	425978.i	−0.111244	−	0.192681i
$346$		0			0
$347$	−308844.	−	534934.i	−0.137694	−	0.238493i	0.788929	−	0.614484i	$-0.210636\pi$
$347$	−308844.	−	534934.i	−0.137694	−	0.238493i	−0.926623	+	0.375991i	$0.877302\pi$
$348$		0			0
$349$	3.25327e6			1.42974			0.714869	−	0.699258i	$-0.246486\pi$
$349$	3.25327e6			1.42974			0.714869	+	0.699258i	$0.246486\pi$
$350$		0			0
$351$	1.81484e6	−	3.14340e6i	0.786270	−	1.36186i
$352$		0			0
$353$	−3.59695e6			−1.53637			−0.768187	−	0.640225i	$-0.778841\pi$
$353$	−3.59695e6			−1.53637			−0.768187	+	0.640225i	$0.778841\pi$
$354$		0			0
$355$	926521.	−	1.60478e6i	0.390197	−	0.675842i
$356$		0			0
$357$	−103991.	+	180118.i	−0.0431843	+	0.0747975i
$358$		0			0
$359$	637110.	+	1.10351e6i	0.260903	+	0.451897i	0.966482	−	0.256734i	$-0.0826465\pi$
$359$	637110.	+	1.10351e6i	0.260903	+	0.451897i	−0.705579	+	0.708631i	$0.749313\pi$
$360$		0			0
$361$	−2.12642e6	−	1.26863e6i	−0.858778	−	0.512348i
$362$		0			0
$363$	−231607.	−	401156.i	−0.0922541	−	0.159789i
$364$		0			0
$365$	−1.08821e6	+	1.88483e6i	−0.427542	+	0.740524i
$366$		0			0
$367$	466637.	−	808238.i	0.180848	−	0.313238i	−0.761322	−	0.648374i	$-0.775449\pi$
$367$	466637.	−	808238.i	0.180848	−	0.313238i	0.942170	+	0.335137i	$0.108782\pi$
$368$		0			0
$369$	768823.			0.293941
$370$		0			0
$371$	−177616.	+	307640.i	−0.0669958	+	0.116040i
$372$		0			0
$373$	−218803.			−0.0814295			−0.0407147	−	0.999171i	$-0.512963\pi$
$373$	−218803.			−0.0814295			−0.0407147	+	0.999171i	$0.512963\pi$
$374$		0			0
$375$	−761990.	−	1.31981e6i	−0.279815	−	0.484654i
$376$		0			0
$377$	−4.18258e6	−	7.24444e6i	−1.51562	−	2.62513i
$378$		0			0
$379$	5.19678e6			1.85839			0.929193	−	0.369594i	$-0.120503\pi$
$379$	5.19678e6			1.85839			0.929193	+	0.369594i	$0.120503\pi$
$380$		0			0
$381$	1.58881e6			0.560736
$382$		0			0
$383$	1.96378e6	+	3.40136e6i	0.684062	+	1.18483i	0.973731	+	0.227703i	$0.0731214\pi$
$383$	1.96378e6	+	3.40136e6i	0.684062	+	1.18483i	−0.289669	+	0.957127i	$0.593545\pi$
$384$		0			0
$385$	96404.9	+	166978.i	0.0331472	+	0.0574127i
$386$		0			0
$387$	1.99024e6			0.675505
$388$		0			0
$389$	1.80860e6	−	3.13258e6i	0.605993	−	1.04961i	−0.385901	−	0.922540i	$-0.626109\pi$
$389$	1.80860e6	−	3.13258e6i	0.605993	−	1.04961i	0.991894	−	0.127070i	$-0.0405574\pi$
$390$		0			0
$391$	2.44281e6			0.808069
$392$		0			0
$393$	−1.31376e6	+	2.27551e6i	−0.429078	+	0.743184i
$394$		0			0
$395$	−683624.	+	1.18407e6i	−0.220457	+	0.381843i
$396$		0			0
$397$	−456990.	−	791530.i	−0.145523	−	0.252053i	0.784045	−	0.620704i	$-0.213153\pi$
$397$	−456990.	−	791530.i	−0.145523	−	0.252053i	−0.929568	+	0.368651i	$0.879820\pi$
$398$		0			0
$399$	203302.	−	52917.7i	0.0639308	−	0.0166406i
$400$		0			0
$401$	255520.	+	442574.i	0.0793533	+	0.137444i	0.902971	−	0.429701i	$-0.141381\pi$
$401$	255520.	+	442574.i	0.0793533	+	0.137444i	−0.823618	+	0.567145i	$0.808048\pi$
$402$		0			0
$403$	−4.95252e6	+	8.57802e6i	−1.51902	+	2.63102i
$404$		0			0
$405$	−233262.	+	404022.i	−0.0706654	+	0.122396i
$406$		0			0
$407$	146854.			0.0439442
$408$		0			0
$409$	423156.	−	732928.i	0.125081	−	0.216647i	−0.796683	−	0.604397i	$-0.793414\pi$
$409$	423156.	−	732928.i	0.125081	−	0.216647i	0.921765	+	0.387750i	$0.126747\pi$
$410$		0			0
$411$	140500.			0.0410272
$412$		0			0
$413$	−55761.4	−	96581.5i	−0.0160864	−	0.0278624i
$414$		0			0
$415$	−1.22492e6	−	2.12162e6i	−0.349130	−	0.604711i
$416$		0			0
$417$	−637210.			−0.179450
$418$		0			0
$419$	−2.38214e6			−0.662877			−0.331438	−	0.943477i	$-0.607534\pi$
$419$	−2.38214e6			−0.662877			−0.331438	+	0.943477i	$0.607534\pi$
$420$		0			0
$421$	1.20667e6	+	2.09001e6i	0.331805	+	0.574704i	0.982866	−	0.184322i	$-0.0590090\pi$
$421$	1.20667e6	+	2.09001e6i	0.331805	+	0.574704i	−0.651061	+	0.759026i	$0.725676\pi$
$422$		0			0
$423$	530828.	+	919420.i	0.144246	+	0.249841i
$424$		0			0
$425$	2.70020e6			0.725143
$426$		0			0
$427$	64686.6	−	112040.i	0.0171690	−	0.0297375i
$428$		0			0
$429$	−2.84503e6			−0.746351
$430$		0			0
$431$	−811120.	+	1.40490e6i	−0.210326	+	0.364295i	−0.951816	−	0.306668i	$-0.900786\pi$
$431$	−811120.	+	1.40490e6i	−0.210326	+	0.364295i	0.741491	+	0.670963i	$0.234119\pi$
$432$		0			0
$433$	−1.54921e6	+	2.68330e6i	−0.397090	+	0.687781i	−0.993366	−	0.114999i	$-0.963313\pi$
$433$	−1.54921e6	+	2.68330e6i	−0.397090	+	0.687781i	0.596275	+	0.802780i	$0.296647\pi$
$434$		0			0
$435$	−1.26227e6	−	2.18631e6i	−0.319837	−	0.553974i
$436$		0			0
$437$	−1.73219e6	−	1.75717e6i	−0.433902	−	0.440159i
$438$		0			0
$439$	1.27415e6	+	2.20689e6i	0.315544	+	0.546538i	0.979553	−	0.201187i	$-0.0644798\pi$
$439$	1.27415e6	+	2.20689e6i	0.315544	+	0.546538i	−0.664009	+	0.747724i	$0.731146\pi$
$440$		0			0
$441$	−1.42618e6	+	2.47022e6i	−0.349203	+	0.604837i
$442$		0			0
$443$	2.21590e6	−	3.83805e6i	0.536463	−	0.929182i	−0.462627	−	0.886553i	$-0.653093\pi$
$443$	2.21590e6	−	3.83805e6i	0.536463	−	0.929182i	0.999091	−	0.0426292i	$-0.0135734\pi$
$444$		0			0
$445$	1.49999e6			0.359077
$446$		0			0
$447$	−1.79641e6	+	3.11148e6i	−0.425243	+	0.736543i
$448$		0			0
$449$	3.77649e6			0.884041			0.442020	−	0.897005i	$-0.354262\pi$
$449$	3.77649e6			0.884041			0.442020	+	0.897005i	$0.354262\pi$
$450$		0			0
$451$	−726265.	−	1.25793e6i	−0.168133	−	0.291215i
$452$		0			0
$453$	−517501.	−	896339.i	−0.118486	−	0.205223i
$454$		0			0
$455$	−615666.			−0.139417
$456$		0			0
$457$	−2.33032e6			−0.521946			−0.260973	−	0.965346i	$-0.584043\pi$
$457$	−2.33032e6			−0.521946			−0.260973	+	0.965346i	$0.584043\pi$
$458$		0			0
$459$	2.72008e6	+	4.71131e6i	0.602628	+	1.04378i
$460$		0			0
$461$	−1.33563e6	−	2.31338e6i	−0.292707	−	0.506984i	0.681742	−	0.731593i	$-0.261223\pi$
$461$	−1.33563e6	−	2.31338e6i	−0.292707	−	0.506984i	−0.974449	+	0.224609i	$0.927889\pi$
$462$		0			0
$463$	−4.04208e6			−0.876299			−0.438150	−	0.898902i	$-0.644366\pi$
$463$	−4.04208e6			−0.876299			−0.438150	+	0.898902i	$0.644366\pi$
$464$		0			0
$465$	−1.49463e6	+	2.58878e6i	−0.320554	+	0.555217i
$466$		0			0
$467$	−8.27237e6			−1.75525			−0.877623	−	0.479352i	$-0.840872\pi$
$467$	−8.27237e6			−1.75525			−0.877623	+	0.479352i	$0.840872\pi$
$468$		0			0
$469$	−433607.	+	751029.i	−0.0910257	+	0.157661i
$470$		0			0
$471$	−2.20847e6	+	3.82519e6i	−0.458712	+	0.794513i
$472$		0			0
$473$	−1.88007e6	−	3.25638e6i	−0.386386	−	0.669241i
$474$		0			0
$475$	−1.91470e6	−	1.94231e6i	−0.389374	−	0.394989i
$476$		0			0
$477$	1.92746e6	+	3.33846e6i	0.387873	+	0.671816i
$478$		0			0
$479$	−316364.	+	547958.i	−0.0630011	+	0.109121i	−0.895806	−	0.444446i	$-0.853400\pi$
$479$	−316364.	+	547958.i	−0.0630011	+	0.109121i	0.832804	+	0.553567i	$0.186734\pi$
$480$		0			0
$481$	−234462.	+	406100.i	−0.0462073	+	0.0800333i
$482$		0			0
$483$	209339.			0.0408304
$484$		0			0
$485$	−211796.	+	366842.i	−0.0408850	+	0.0708148i
$486$		0			0
$487$	6.59560e6			1.26018			0.630089	−	0.776523i	$-0.283019\pi$
$487$	6.59560e6			1.26018			0.630089	+	0.776523i	$0.283019\pi$
$488$		0			0
$489$	−846745.	−	1.46660e6i	−0.160133	−	0.277358i
$490$		0			0
$491$	1.84714e6	+	3.19933e6i	0.345776	+	0.598902i	0.985494	−	0.169707i	$-0.0542823\pi$
$491$	1.84714e6	+	3.19933e6i	0.345776	+	0.598902i	−0.639718	+	0.768610i	$0.720949\pi$
$492$		0			0
$493$	1.25376e7			2.32326
$494$		0			0
$495$	2.09234e6			0.383813
$496$		0			0
$497$	394321.	+	682984.i	0.0716076	+	0.124028i
$498$		0			0
$499$	5.21061e6	+	9.02504e6i	0.936779	+	1.62255i	0.771431	+	0.636313i	$0.219541\pi$
$499$	5.21061e6	+	9.02504e6i	0.936779	+	1.62255i	0.165347	+	0.986235i	$0.447125\pi$
$500$		0			0
$501$	−1.42471e6			−0.253590
$502$		0			0
$503$	2.40212e6	−	4.16060e6i	0.423326	−	0.733222i	−0.572937	−	0.819600i	$-0.694196\pi$
$503$	2.40212e6	−	4.16060e6i	0.423326	−	0.733222i	0.996262	+	0.0863777i	$0.0275292\pi$
$504$		0			0
$505$	−7.18986e6			−1.25456
$506$		0			0
$507$	2.98125e6	−	5.16367e6i	0.515084	−	0.892152i
$508$		0			0
$509$	−3.40004e6	+	5.88905e6i	−0.581688	+	1.00751i	0.413592	+	0.910462i	$0.364274\pi$
$509$	−3.40004e6	+	5.88905e6i	−0.581688	+	1.00751i	−0.995279	+	0.0970502i	$0.969059\pi$
$510$		0			0
$511$	−463133.	−	802169.i	−0.0784609	−	0.135898i
$512$		0			0
$513$	1.46015e6	−	5.29738e6i	0.244966	−	0.888725i
$514$		0			0
$515$	−3.24784e6	−	5.62543e6i	−0.539606	−	0.934626i
$516$		0			0
$517$	1.00289e6	−	1.73705e6i	0.165016	−	0.285816i
$518$		0			0
$519$	−268517.	+	465084.i	−0.0437575	+	0.0757903i
$520$		0			0
$521$	1.12409e6			0.181429			0.0907145	−	0.995877i	$-0.471085\pi$
$521$	1.12409e6			0.181429			0.0907145	+	0.995877i	$0.471085\pi$
$522$		0			0
$523$	−3.80982e6	+	6.59880e6i	−0.609046	+	1.05490i	0.382352	+	0.924017i	$0.375114\pi$
$523$	−3.80982e6	+	6.59880e6i	−0.609046	+	1.05490i	−0.991398	+	0.130882i	$0.958219\pi$
$524$		0			0
$525$	231396.			0.0366403
$526$		0			0
$527$	−7.42281e6	−	1.28567e7i	−1.16424	−	2.01652i
$528$		0			0
$529$	1.98880e6	+	3.44470e6i	0.308995	+	0.535194i
$530$		0			0
$531$	−1.21023e6			−0.186265
$532$		0			0
$533$	4.63811e6			0.707168
$534$		0			0
$535$	460399.	+	797435.i	0.0695425	+	0.120451i
$536$		0			0
$537$	487836.	+	844956.i	0.0730025	+	0.126444i
$538$		0			0
$539$	5.38893e6			0.798970
$540$		0			0
$541$	1.96214e6	−	3.39853e6i	0.288228	−	0.499226i	−0.685159	−	0.728394i	$-0.740267\pi$
$541$	1.96214e6	−	3.39853e6i	0.288228	−	0.499226i	0.973387	+	0.229168i	$0.0736004\pi$
$542$		0			0
$543$	449401.			0.0654085
$544$		0			0
$545$	600422.	−	1.03996e6i	0.0865895	−	0.149977i
$546$		0			0
$547$	6.72115e6	−	1.16414e7i	0.960451	−	1.66355i	0.239080	−	0.971000i	$-0.423154\pi$
$547$	6.72115e6	−	1.16414e7i	0.960451	−	1.66355i	0.721370	−	0.692549i	$-0.243513\pi$
$548$		0			0
$549$	−701968.	−	1.21584e6i	−0.0994000	−	0.172166i
$550$		0			0
$551$	−8.89038e6	−	9.01859e6i	−1.24750	−	1.26549i
$552$		0			0
$553$	−290946.	−	503933.i	−0.0404575	−	0.0700745i
$554$		0			0
$555$	−70758.8	+	122558.i	−0.00975098	+	0.0168892i
$556$		0			0
$557$	969505.	−	1.67923e6i	0.132407	−	0.229336i	−0.792197	−	0.610266i	$-0.791063\pi$
$557$	969505.	−	1.67923e6i	0.132407	−	0.229336i	0.924604	+	0.380930i	$0.124396\pi$
$558$		0			0
$559$	1.20066e7			1.62514
$560$		0			0
$561$	2.13205e6	−	3.69283e6i	0.286016	−	0.495395i
$562$		0			0
$563$	−7.32095e6			−0.973412			−0.486706	−	0.873566i	$-0.661802\pi$
$563$	−7.32095e6			−0.973412			−0.486706	+	0.873566i	$0.661802\pi$
$564$		0			0
$565$	−2.16339e6	−	3.74710e6i	−0.285111	−	0.493826i
$566$		0			0
$567$	−99274.8	−	171949.i	−0.0129682	−	0.0224617i
$568$		0			0
$569$	6.26910e6			0.811754			0.405877	−	0.913928i	$-0.366966\pi$
$569$	6.26910e6			0.811754			0.405877	+	0.913928i	$0.366966\pi$
$570$		0			0
$571$	7.57087e6			0.971753			0.485876	−	0.874028i	$-0.338501\pi$
$571$	7.57087e6			0.971753			0.485876	+	0.874028i	$0.338501\pi$
$572$		0			0
$573$	2.37228e6	+	4.10892e6i	0.301842	+	0.522806i
$574$		0			0
$575$	−1.35891e6	−	2.35370e6i	−0.171404	−	0.296880i
$576$		0			0
$577$	−8.39531e6			−1.04978			−0.524889	−	0.851171i	$-0.675893\pi$
$577$	−8.39531e6			−1.04978			−0.524889	+	0.851171i	$0.675893\pi$
$578$		0			0
$579$	−1.23214e6	+	2.13413e6i	−0.152744	+	0.264560i
$580$		0			0
$581$	1.04264e6			0.128142
$582$		0			0
$583$	3.64153e6	−	6.30731e6i	0.443723	−	0.768552i
$584$		0			0
$585$	−3.34055e6	+	5.78600e6i	−0.403579	+	0.699019i
$586$		0			0
$587$	−5.58455e6	−	9.67272e6i	−0.668949	−	1.15865i	−0.978199	−	0.207672i	$-0.933411\pi$
$587$	−5.58455e6	−	9.67272e6i	−0.668949	−	1.15865i	0.309250	−	0.950981i	$-0.399922\pi$
$588$		0			0
$589$	−3.98461e6	+	1.44560e7i	−0.473258	+	1.71696i
$590$		0			0
$591$	1.58882e6	+	2.75192e6i	0.187114	+	0.324091i
$592$		0			0
$593$	−3.63578e6	+	6.29735e6i	−0.424581	+	0.735396i	−0.996381	−	0.0849969i	$-0.972912\pi$
$593$	−3.63578e6	+	6.29735e6i	−0.424581	+	0.735396i	0.571800	+	0.820393i	$0.306245\pi$
$594$		0			0
$595$	461378.	−	799130.i	0.0534274	−	0.0925390i
$596$		0			0
$597$	7.46198e6			0.856876
$598$		0			0
$599$	1.55634e6	−	2.69567e6i	0.177231	−	0.306972i	−0.763700	−	0.645571i	$-0.776620\pi$
$599$	1.55634e6	−	2.69567e6i	0.177231	−	0.306972i	0.940931	+	0.338599i	$0.109953\pi$
$600$		0			0
$601$	1.24917e6			0.141070			0.0705350	−	0.997509i	$-0.477529\pi$
$601$	1.24917e6			0.141070			0.0705350	+	0.997509i	$0.477529\pi$
$602$		0			0
$603$	4.70543e6	+	8.15004e6i	0.526994	+	0.912781i
$604$		0			0
$605$	1.02757e6	+	1.77981e6i	0.114136	+	0.197690i
$606$		0			0
$607$	−7.52150e6			−0.828577			−0.414288	−	0.910146i	$-0.635969\pi$
$607$	−7.52150e6			−0.828577			−0.414288	+	0.910146i	$0.635969\pi$
$608$		0			0
$609$	1.07443e6			0.117391
$610$		0			0
$611$	3.20234e6	+	5.54662e6i	0.347028	+	0.601070i
$612$		0			0
$613$	−1.18369e6	−	2.05021e6i	−0.127229	−	0.220367i	0.795373	−	0.606120i	$-0.207275\pi$
$613$	−1.18369e6	−	2.05021e6i	−0.127229	−	0.220367i	−0.922602	+	0.385753i	$0.873942\pi$
$614$		0			0
$615$	1.39974e6			0.149231
$616$		0			0
$617$	8.23863e6	−	1.42697e7i	0.871249	−	1.50905i	0.0105434	−	0.999944i	$-0.496644\pi$
$617$	8.23863e6	−	1.42697e7i	0.871249	−	1.50905i	0.860706	−	0.509103i	$-0.170023\pi$
$618$		0			0
$619$	−1.22489e7			−1.28491			−0.642453	−	0.766325i	$-0.722083\pi$
$619$	−1.22489e7			−1.28491			−0.642453	+	0.766325i	$0.722083\pi$
$620$		0			0
$621$	2.73782e6	−	4.74205e6i	0.284889	−	0.493443i
$622$		0			0
$623$	−319192.	+	552857.i	−0.0329483	+	0.0570680i
$624$		0			0
$625$	672507.	+	1.16482e6i	0.0688647	+	0.119277i
$626$		0			0
$627$	−4.16816e6	+	1.08493e6i	−0.423424	+	0.110213i
$628$		0			0
$629$	−351410.	−	608661.i	−0.0354151	−	0.0613407i
$630$		0			0
$631$	−8.33519e6	+	1.44370e7i	−0.833378	+	1.44345i	0.0619660	+	0.998078i	$0.480263\pi$
$631$	−8.33519e6	+	1.44370e7i	−0.833378	+	1.44345i	−0.895344	+	0.445375i	$0.853070\pi$
$632$		0			0
$633$	−527079.	+	912928.i	−0.0522837	+	0.0905580i
$634$		0			0
$635$	−7.04906e6			−0.693740
$636$		0			0
$637$	−8.60376e6	+	1.49021e7i	−0.840117	+	1.45512i
$638$		0			0
$639$	8.55821e6			0.829146
$640$		0			0
$641$	7.23074e6	+	1.25240e7i	0.695084	+	1.20392i	0.970152	+	0.242496i	$0.0779663\pi$
$641$	7.23074e6	+	1.25240e7i	0.695084	+	1.20392i	−0.275068	+	0.961425i	$0.588700\pi$
$642$		0			0
$643$	−2.79841e6	−	4.84699e6i	−0.266922	−	0.462322i	0.701144	−	0.713020i	$-0.252673\pi$
$643$	−2.79841e6	−	4.84699e6i	−0.266922	−	0.462322i	−0.968065	+	0.250698i	$0.919340\pi$
$644$		0			0
$645$	3.62350e6			0.342948
$646$		0			0
$647$	−8.75822e6			−0.822536			−0.411268	−	0.911514i	$-0.634914\pi$
$647$	−8.75822e6			−0.822536			−0.411268	+	0.911514i	$0.634914\pi$
$648$		0			0
$649$	1.14323e6	+	1.98014e6i	0.106543	+	0.184537i
$650$		0			0
$651$	−636105.	−	1.10177e6i	−0.0588270	−	0.101891i
$652$		0			0
$653$	4.42311e6			0.405924			0.202962	−	0.979187i	$-0.434943\pi$
$653$	4.42311e6			0.405924			0.202962	+	0.979187i	$0.434943\pi$
$654$		0			0
$655$	5.82877e6	−	1.00957e7i	0.530853	−	0.919464i
$656$		0			0
$657$	−1.00517e7			−0.908500
$658$		0			0
$659$	−3.31380e6	+	5.73967e6i	−0.297244	+	0.514842i	−0.975504	−	0.219980i	$-0.929401\pi$
$659$	−3.31380e6	+	5.73967e6i	−0.297244	+	0.514842i	0.678260	+	0.734822i	$0.262734\pi$
$660$		0			0
$661$	−4.70847e6	+	8.15532e6i	−0.419157	+	0.726001i	−0.995855	−	0.0909565i	$-0.971008\pi$
$661$	−4.70847e6	+	8.15532e6i	−0.419157	+	0.726001i	0.576698	+	0.816957i	$0.304341\pi$
$662$		0			0
$663$	6.80791e6	+	1.17916e7i	0.601492	+	1.04182i
$664$		0			0
$665$	−901992.	+	234780.i	−0.0790949	+	0.0205877i
$666$		0			0
$667$	−6.30972e6	−	1.09288e7i	−0.549156	−	0.951166i
$668$		0			0
$669$	−1.80286e6	+	3.12265e6i	−0.155739	+	0.269748i
$670$		0			0
$671$	−1.32622e6	+	2.29708e6i	−0.113713	+	0.196956i
$672$		0			0
$673$	−6.15773e6			−0.524062			−0.262031	−	0.965059i	$-0.584392\pi$
$673$	−6.15773e6			−0.524062			−0.262031	+	0.965059i	$0.584392\pi$
$674$		0			0
$675$	3.02629e6	−	5.24170e6i	0.255653	−	0.442805i
$676$		0			0
$677$	−4.98624e6			−0.418120			−0.209060	−	0.977903i	$-0.567040\pi$
$677$	−4.98624e6			−0.418120			−0.209060	+	0.977903i	$0.567040\pi$
$678$		0			0
$679$	−90139.0	−	156125.i	−0.00750306	−	0.0129957i
$680$		0			0
$681$	712577.	+	1.23422e6i	0.0588795	+	0.101982i
$682$		0			0
$683$	−4.31513e6			−0.353951			−0.176975	−	0.984215i	$-0.556631\pi$
$683$	−4.31513e6			−0.353951			−0.176975	+	0.984215i	$0.556631\pi$
$684$		0			0
$685$	−623356.			−0.0507586
$686$		0			0
$687$	−1.60172e6	−	2.77426e6i	−0.129477	−	0.224261i
$688$		0			0
$689$	1.16279e7	+	2.01400e7i	0.933150	+	1.61626i
$690$		0			0
$691$	4.03514e6			0.321487			0.160744	−	0.986996i	$-0.448611\pi$
$691$	4.03514e6			0.321487			0.160744	+	0.986996i	$0.448611\pi$
$692$		0			0
$693$	−445243.	+	771183.i	−0.0352179	+	0.0609993i
$694$		0			0
$695$	2.82711e6			0.222014
$696$		0			0
$697$	−3.47578e6	+	6.02023e6i	−0.271001	+	0.469387i
$698$		0			0
$699$	1.15374e6	−	1.99834e6i	0.0893130	−	0.154695i
$700$		0			0
$701$	−8.80091e6	−	1.52436e7i	−0.676445	−	1.17164i	−0.976044	−	0.217572i	$-0.930186\pi$
$701$	−8.80091e6	−	1.52436e7i	−0.676445	−	1.17164i	0.299599	−	0.954065i	$-0.403147\pi$
$702$		0			0
$703$	−188639.	+	684375.i	−0.0143961	+	0.0522283i
$704$		0			0
$705$	966441.	+	1.67392e6i	0.0732322	+	0.126842i
$706$		0			0
$707$	1.52998e6	−	2.65000e6i	0.115116	−	0.199387i
$708$		0			0
$709$	1.41587e6	−	2.45236e6i	0.105781	−	0.183218i	−0.808276	−	0.588804i	$-0.799599\pi$
$709$	1.41587e6	−	2.45236e6i	0.105781	−	0.183218i	0.914057	+	0.405586i	$0.132932\pi$
$710$		0			0
$711$	−6.31459e6			−0.468458
$712$		0			0
$713$	−7.47124e6	+	1.29406e7i	−0.550388	+	0.953300i
$714$		0			0
$715$	1.26225e7			0.923382
$716$		0			0
$717$	−5.49762e6	−	9.52215e6i	−0.399371	−	0.691731i
$718$		0			0
$719$	−2.92205e6	−	5.06114e6i	−0.210797	−	0.365112i	0.741167	−	0.671321i	$-0.234273\pi$
$719$	−2.92205e6	−	5.06114e6i	−0.210797	−	0.365112i	−0.951964	+	0.306209i	$0.900939\pi$
$720$		0			0
$721$	2.76452e6			0.198053
$722$		0			0
$723$	4.78401e6			0.340366
$724$		0			0
$725$	−6.97454e6	−	1.20803e7i	−0.492800	−	0.853555i
$726$		0			0
$727$	−3.41280e6	−	5.91114e6i	−0.239483	−	0.414797i	0.721083	−	0.692849i	$-0.243645\pi$
$727$	−3.41280e6	−	5.91114e6i	−0.239483	−	0.414797i	−0.960566	+	0.278052i	$0.910311\pi$
$728$		0			0
$729$	4.98054e6			0.347102
$730$		0			0
$731$	−8.99771e6	+	1.55845e7i	−0.622786	+	1.07870i
$732$		0			0
$733$	1.74557e7			1.19999			0.599994	−	0.800005i	$-0.295170\pi$
$733$	1.74557e7			1.19999			0.599994	+	0.800005i	$0.295170\pi$
$734$		0			0
$735$	−2.59655e6	+	4.49735e6i	−0.177287	+	0.307071i
$736$		0			0
$737$	8.88991e6	−	1.53978e7i	0.602877	−	1.04421i
$738$		0			0
$739$	887503.	+	1.53720e6i	0.0597804	+	0.103543i	0.894367	−	0.447334i	$-0.147627\pi$
$739$	887503.	+	1.53720e6i	0.0597804	+	0.103543i	−0.834586	+	0.550877i	$0.814293\pi$
$740$		0			0
$741$	3.65453e6	−	1.32585e7i	0.244504	−	0.887050i
$742$		0			0
$743$	1.00081e7	+	1.73345e7i	0.665089	+	1.15197i	0.979261	+	0.202602i	$0.0649398\pi$
$743$	1.00081e7	+	1.73345e7i	0.665089	+	1.15197i	−0.314172	+	0.949366i	$0.601727\pi$
$744$		0			0
$745$	7.97014e6	−	1.38047e7i	0.526109	−	0.911247i
$746$		0			0
$747$	5.65725e6	−	9.79865e6i	0.370940	−	0.642488i
$748$		0			0
$749$	−391886.			−0.0255244
$750$		0			0
$751$	4.81707e6	−	8.34342e6i	0.311662	−	0.539814i	−0.667061	−	0.745004i	$-0.732448\pi$
$751$	4.81707e6	−	8.34342e6i	0.311662	−	0.539814i	0.978722	+	0.205190i	$0.0657811\pi$
$752$		0			0
$753$	−1.15559e7			−0.742702
$754$		0			0
$755$	2.29600e6	+	3.97679e6i	0.146590	+	0.253901i
$756$		0			0
$757$	−1.23551e6	−	2.13997e6i	−0.0783623	−	0.135728i	0.824181	−	0.566326i	$-0.191636\pi$
$757$	−1.23551e6	−	2.13997e6i	−0.0783623	−	0.135728i	−0.902543	+	0.430599i	$0.858302\pi$
$758$		0			0
$759$	−4.29193e6			−0.270426
$760$		0			0
$761$	2.42819e7			1.51992			0.759960	−	0.649970i	$-0.225218\pi$
$761$	2.42819e7			1.51992			0.759960	+	0.649970i	$0.225218\pi$
$762$		0			0
$763$	255536.	+	442601.i	0.0158906	+	0.0275233i
$764$		0			0
$765$	−5.00679e6	−	8.67202e6i	−0.309319	−	0.535756i
$766$		0			0
$767$	−7.30097e6			−0.448118
$768$		0			0
$769$	−2.98240e6	+	5.16567e6i	−0.181866	+	0.315000i	−0.942516	−	0.334161i	$-0.891547\pi$
$769$	−2.98240e6	+	5.16567e6i	−0.181866	+	0.315000i	0.760650	+	0.649162i	$0.224880\pi$
$770$		0			0
$771$	−1.05768e7			−0.640794
$772$		0			0
$773$	−4.87274e6	+	8.43984e6i	−0.293308	+	0.508025i	−0.974590	−	0.223996i	$-0.928090\pi$
$773$	−4.87274e6	+	8.43984e6i	−0.293308	+	0.508025i	0.681282	+	0.732022i	$0.261423\pi$
$774$		0			0
$775$	−8.25845e6	+	1.43040e7i	−0.493906	+	0.855470i
$776$		0			0
$777$	−30114.5	−	52159.8i	−0.00178946	−	0.00309944i
$778$		0			0
$779$	6.79514e6	−	1.76871e6i	0.401194	−	0.104427i
$780$		0			0
$781$	−8.08447e6	−	1.40027e7i	−0.474268	−	0.821456i
$782$		0			0
$783$	1.40518e7	−	2.43384e7i	0.819080	−	1.41869i
$784$		0			0
$785$	9.79834e6	−	1.69712e7i	0.567516	−	0.982967i
$786$		0			0
$787$	1.96481e7			1.13080			0.565398	−	0.824818i	$-0.308723\pi$
$787$	1.96481e7			1.13080			0.565398	+	0.824818i	$0.308723\pi$
$788$		0			0
$789$	−1.09559e6	+	1.89762e6i	−0.0626550	+	0.108522i
$790$		0			0
$791$	1.84145e6			0.104645
$792$		0			0
$793$	−4.23478e6	−	7.33486e6i	−0.239138	−	0.414199i
$794$		0			0
$795$	3.50919e6	+	6.07810e6i	0.196920	+	0.341075i
$796$		0			0
$797$	1.00003e7			0.557657			0.278829	−	0.960341i	$-0.410054\pi$
$797$	1.00003e7			0.557657			0.278829	+	0.960341i	$0.410054\pi$
$798$		0			0
$799$	−9.59929e6			−0.531952
$800$		0			0
$801$	3.46382e6	+	5.99952e6i	0.190754	+	0.330396i
$802$		0			0
$803$	9.49526e6	+	1.64463e7i	0.519658	+	0.900075i
$804$		0			0
$805$	−928776.			−0.0505151
$806$		0			0
$807$	−5.46313e6	+	9.46243e6i	−0.295296	+	0.511468i
$808$		0			0
$809$	1.07362e7			0.576742			0.288371	−	0.957519i	$-0.406886\pi$
$809$	1.07362e7			0.576742			0.288371	+	0.957519i	$0.406886\pi$
$810$		0			0
$811$	8.65323e6	−	1.49878e7i	0.461983	−	0.800178i	−0.537077	−	0.843533i	$-0.680471\pi$
$811$	8.65323e6	−	1.49878e7i	0.461983	−	0.800178i	0.999060	+	0.0433553i	$0.0138047\pi$
$812$		0			0
$813$	−2.09609e6	+	3.63053e6i	−0.111220	+	0.192639i
$814$		0			0
$815$	3.75675e6	+	6.50688e6i	0.198115	+	0.343146i
$816$		0			0
$817$	1.75905e7	−	4.57864e6i	0.921983	−	0.239983i
$818$		0			0
$819$	−1.42172e6	−	2.46248e6i	−0.0740633	−	0.128281i
$820$		0			0
$821$	−1.15442e6	+	1.99951e6i	−0.0597729	+	0.103530i	−0.894363	−	0.447341i	$-0.852371\pi$
$821$	−1.15442e6	+	1.99951e6i	−0.0597729	+	0.103530i	0.834590	+	0.550871i	$0.185704\pi$
$822$		0			0
$823$	3.33550e6	−	5.77725e6i	0.171657	−	0.297318i	−0.767342	−	0.641238i	$-0.778421\pi$
$823$	3.33550e6	−	5.77725e6i	0.171657	−	0.297318i	0.938999	+	0.343919i	$0.111755\pi$
$824$		0			0
$825$	−4.74415e6			−0.242674
$826$		0			0
$827$	1.34266e7	−	2.32556e7i	0.682659	−	1.18240i	−0.291507	−	0.956569i	$-0.594157\pi$
$827$	1.34266e7	−	2.32556e7i	0.682659	−	1.18240i	0.974166	−	0.225831i	$-0.0725098\pi$
$828$		0			0
$829$	−2.97779e7			−1.50490			−0.752449	−	0.658650i	$-0.771128\pi$
$829$	−2.97779e7			−1.50490			−0.752449	+	0.658650i	$0.771128\pi$
$830$		0			0
$831$	1.76914e6	+	3.06424e6i	0.0888710	+	0.153929i
$832$		0			0
$833$	−1.28953e7	−	2.23352e7i	−0.643899	−	1.11527i
$834$		0			0
$835$	6.32101e6			0.313740
$836$		0			0
$837$	−3.32769e7			−1.64184
$838$		0			0
$839$	−7.39525e6	−	1.28090e7i	−0.362701	−	0.628216i	0.625704	−	0.780061i	$-0.284812\pi$
$839$	−7.39525e6	−	1.28090e7i	−0.362701	−	0.628216i	−0.988404	+	0.151845i	$0.951479\pi$
$840$		0			0
$841$	−2.21288e7	−	3.83282e7i	−1.07887	−	1.86865i
$842$		0			0
$843$	−2.05772e7			−0.997282
$844$		0			0
$845$	−1.32269e7	+	2.29097e7i	−0.637260	+	1.10377i
$846$		0			0
$847$	−874655.			−0.0418917
$848$		0			0
$849$	8.37291e6	−	1.45023e7i	0.398664	−	0.690507i
$850$		0			0
$851$	−353703.	+	612632.i	−0.0167423	+	0.0289985i
$852$		0			0
$853$	1.63792e7	+	2.83697e7i	0.770763	+	1.33500i	0.937145	+	0.348939i	$0.113458\pi$
$853$	1.63792e7	+	2.83697e7i	0.770763	+	1.33500i	−0.166382	+	0.986061i	$0.553209\pi$
$854$		0			0
$855$	−2.68768e6	+	9.75078e6i	−0.125737	+	0.456167i
$856$		0			0
$857$	1.80189e7	+	3.12097e7i	0.838063	+	1.45157i	0.891512	+	0.452998i	$0.149645\pi$
$857$	1.80189e7	+	3.12097e7i	0.838063	+	1.45157i	−0.0534483	+	0.998571i	$0.517021\pi$
$858$		0			0
$859$	−2.75980e6	+	4.78012e6i	−0.127613	+	0.221032i	−0.922751	−	0.385396i	$-0.874065\pi$
$859$	−2.75980e6	+	4.78012e6i	−0.127613	+	0.221032i	0.795138	+	0.606428i	$0.207398\pi$
$860$		0			0
$861$	−297861.	+	515910.i	−0.0136932	+	0.0237173i
$862$		0			0
$863$	−2.04317e6			−0.0933852			−0.0466926	−	0.998909i	$-0.514868\pi$
$863$	−2.04317e6			−0.0933852			−0.0466926	+	0.998909i	$0.514868\pi$
$864$		0			0
$865$	1.19133e6	−	2.06344e6i	0.0541366	−	0.0937673i
$866$		0			0
$867$	−8.46841e6			−0.382608
$868$		0			0
$869$	5.96504e6	+	1.03318e7i	0.267956	+	0.464114i
$870$		0			0
$871$	2.83866e7	+	4.91670e7i	1.26785	+	2.19598i
$872$		0			0
$873$	−1.95635e6			−0.0868781
$874$		0			0
$875$	−2.87762e6			−0.127062
$876$		0			0
$877$	−1.34846e7	−	2.33559e7i	−0.592022	−	1.02541i	−0.993960	−	0.109745i	$-0.964997\pi$
$877$	−1.34846e7	−	2.33559e7i	−0.592022	−	1.02541i	0.401938	−	0.915667i	$-0.368337\pi$
$878$		0			0
$879$	7.65826e6	+	1.32645e7i	0.334317	+	0.579053i
$880$		0			0
$881$	2.67933e7			1.16302			0.581509	−	0.813540i	$-0.302462\pi$
$881$	2.67933e7			1.16302			0.581509	+	0.813540i	$0.302462\pi$
$882$		0			0
$883$	1.26523e7	−	2.19145e7i	0.546095	−	0.945865i	−0.452442	−	0.891794i	$-0.649447\pi$
$883$	1.26523e7	−	2.19145e7i	0.546095	−	0.945865i	0.998537	−	0.0540711i	$-0.0172198\pi$
$884$		0			0
$885$	−2.20337e6			−0.0945649
$886$		0			0
$887$	−1.94038e7	+	3.36084e7i	−0.828090	+	1.43429i	0.0714439	+	0.997445i	$0.477239\pi$
$887$	−1.94038e7	+	3.36084e7i	−0.828090	+	1.43429i	−0.899534	+	0.436850i	$0.856094\pi$
$888$		0			0
$889$	1.50002e6	−	2.59810e6i	0.0636563	−	0.110256i
$890$		0			0
$891$	2.03536e6	+	3.52534e6i	0.0858907	+	0.148767i
$892$		0			0
$893$	6.80681e6	+	6.90498e6i	0.285637	+	0.289757i
$894$		0			0
$895$	−2.16438e6	−	3.74882e6i	−0.0903184	−	0.156436i
$896$		0			0
$897$	6.85233e6	−	1.18686e7i	0.284352	−	0.492513i
$898$		0			0
$899$	−3.83458e7	+	6.64169e7i	−1.58241	+	2.74081i
$900$		0			0
$901$	−3.48555e7			−1.43041
$902$		0			0
$903$	−771068.	+	1.33553e6i	−0.0314683	+	0.0545047i
$904$		0			0
$905$	−1.99386e6			−0.0809231
$906$		0			0
$907$	1.17089e7	+	2.02803e7i	0.472603	+	0.818572i	0.999508	−	0.0313519i	$-0.00998126\pi$
$907$	1.17089e7	+	2.02803e7i	0.472603	+	0.818572i	−0.526906	+	0.849924i	$0.676648\pi$
$908$		0			0
$909$	−1.66031e7	−	2.87574e7i	−0.666467	−	1.15435i
$910$		0			0
$911$	−2.20141e7			−0.878829			−0.439415	−	0.898284i	$-0.644814\pi$
$911$	−2.20141e7			−0.878829			−0.439415	+	0.898284i	$0.644814\pi$
$912$		0			0
$913$	−2.13764e7			−0.848705
$914$		0			0
$915$	−1.27802e6	−	2.21360e6i	−0.0504645	−	0.0874071i
$916$		0			0
$917$	2.48069e6	+	4.29668e6i	0.0974201	+	0.168737i
$918$		0			0
$919$	1.88619e7			0.736709			0.368355	−	0.929685i	$-0.379921\pi$
$919$	1.88619e7			0.736709			0.368355	+	0.929685i	$0.379921\pi$
$920$		0			0
$921$	−8.75040e6	+	1.51561e7i	−0.339921	+	0.588761i
$922$		0			0
$923$	5.16294e7			1.99477
$924$		0			0
$925$	−390971.	+	677182.i	−0.0150242	+	0.0260226i
$926$		0			0
$927$	1.50001e7	−	2.59809e7i	0.573315	−	0.993011i
$928$		0			0
$929$	1.56363e7	+	2.70828e7i	0.594421	+	1.02957i	0.993628	+	0.112706i	$0.0359519\pi$
$929$	1.56363e7	+	2.70828e7i	0.594421	+	1.02957i	−0.399208	+	0.916861i	$0.630715\pi$
$930$		0			0
$931$	−6.92226e6	+	2.51136e7i	−0.261742	+	0.949589i
$932$		0			0
$933$	−1.18785e7	−	2.05741e7i	−0.446741	−	0.773778i
$934$		0			0
$935$	−9.45928e6	+	1.63840e7i	−0.353858	+	0.612900i
$936$		0			0
$937$	−7.79382e6	+	1.34993e7i	−0.290002	+	0.502299i	−0.973810	−	0.227364i	$-0.926989\pi$
$937$	−7.79382e6	+	1.34993e7i	−0.290002	+	0.502299i	0.683808	+	0.729662i	$0.260323\pi$
$938$		0			0
$939$	−3.89979e6			−0.144337
$940$		0			0
$941$	868339.	−	1.50401e6i	0.0319680	−	0.0553702i	−0.849599	−	0.527430i	$-0.823156\pi$
$941$	868339.	−	1.50401e6i	0.0319680	−	0.0553702i	0.881567	+	0.472059i	$0.156489\pi$
$942$		0			0
$943$	6.99692e6			0.256228
$944$		0			0
$945$	−1.03419e6	−	1.79128e6i	−0.0376723	−	0.0652503i
$946$		0			0
$947$	−2.60136e6	−	4.50569e6i	−0.0942596	−	0.163262i	0.815040	−	0.579405i	$-0.196715\pi$
$947$	−2.60136e6	−	4.50569e6i	−0.0942596	−	0.163262i	−0.909299	+	0.416143i	$0.863382\pi$
$948$		0			0
$949$	−6.06391e7			−2.18568
$950$		0			0
$951$	2.30729e7			0.827277
$952$		0			0
$953$	7.54288e6	+	1.30647e7i	0.269033	+	0.465978i	0.968612	−	0.248576i	$-0.0799627\pi$
$953$	7.54288e6	+	1.30647e7i	0.269033	+	0.465978i	−0.699580	+	0.714555i	$0.746629\pi$
$954$		0			0
$955$	−1.05251e7	−	1.82300e7i	−0.373438	−	0.646813i
$956$		0			0
$957$	−2.20281e7			−0.777496
$958$		0			0
$959$	132648.	−	229753.i	0.00465752	−	0.00806706i
$960$		0			0
$961$	6.21802e7			2.17192
$962$		0			0
$963$	−2.12634e6	+	3.68293e6i	−0.0738868	+	0.127976i
$964$		0			0
$965$	5.46664e6	−	9.46850e6i	0.188974	−	0.327313i
$966$		0			0
$967$	−2.65183e7	−	4.59310e7i	−0.911966	−	1.57957i	−0.811283	−	0.584654i	$-0.801230\pi$
$967$	−2.65183e7	−	4.59310e7i	−0.911966	−	1.57957i	−0.100683	−	0.994919i	$-0.532103\pi$
$968$		0			0
$969$	1.44707e7	+	1.46794e7i	0.495086	+	0.502226i
$970$		0			0
$971$	−1.94177e7	−	3.36325e7i	−0.660922	−	1.14475i	−0.980374	−	0.197148i	$-0.936832\pi$
$971$	−1.94177e7	−	3.36325e7i	−0.660922	−	1.14475i	0.319452	−	0.947602i	$-0.396501\pi$
$972$		0			0
$973$	−601599.	+	1.04200e6i	−0.0203716	+	0.0352846i
$974$		0			0
$975$	7.57432e6	−	1.31191e7i	0.255172	−	0.441970i
$976$		0			0
$977$	−7.05567e6			−0.236484			−0.118242	−	0.992985i	$-0.537726\pi$
$977$	−7.05567e6			−0.236484			−0.118242	+	0.992985i	$0.537726\pi$
$978$		0			0
$979$	6.54416e6	−	1.13348e7i	0.218221	−	0.377970i
$980$		0			0
$981$	5.54606e6			0.183998
$982$		0			0
$983$	393185.	+	681016.i	0.0129782	+	0.0224788i	0.872442	−	0.488718i	$-0.162535\pi$
$983$	393185.	+	681016.i	0.0129782	+	0.0224788i	−0.859463	+	0.511197i	$0.829202\pi$
$984$		0			0
$985$	−7.04913e6	−	1.22094e7i	−0.231497	−	0.400964i
$986$		0			0
$987$	−822621.			−0.0268786
$988$		0			0
$989$	1.81128e7			0.588838
$990$		0			0
$991$	−7.09732e6	−	1.22929e7i	−0.229568	−	0.397623i	0.728112	−	0.685458i	$-0.240398\pi$
$991$	−7.09732e6	−	1.22929e7i	−0.229568	−	0.397623i	−0.957680	+	0.287835i	$0.907065\pi$
$992$		0			0
$993$	−1.69401e6	−	2.93412e6i	−0.0545185	−	0.0944288i
$994$		0			0
$995$	−3.31065e7			−1.06012
$996$		0			0
$997$	−377295.	+	653495.i	−0.0120211	+	0.0208211i	−0.871973	−	0.489553i	$-0.837160\pi$
$997$	−377295.	+	653495.i	−0.0120211	+	0.0208211i	0.859952	+	0.510374i	$0.170493\pi$
$998$		0			0
$999$	−1.57540e6			−0.0499432

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.6.e.a.45.6	✓	18
3.2	odd	2		684.6.k.f.577.7		18
4.3	odd	2		304.6.i.d.273.4		18
19.11	even	3	inner	76.6.e.a.49.6	yes	18
57.11	odd	6		684.6.k.f.505.7		18
76.11	odd	6		304.6.i.d.49.4		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.6.e.a.45.6	✓	18	1.1	even	1	trivial
76.6.e.a.49.6	yes	18	19.11	even	3	inner
304.6.i.d.49.4		18	76.11	odd	6
304.6.i.d.273.4		18	4.3	odd	2
684.6.k.f.505.7		18	57.11	odd	6
684.6.k.f.577.7		18	3.2	odd	2

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.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.20426 + 7.28199i) q^{3} +(-18.6530 - 32.3080i) q^{5} +15.8772 q^{7} +(86.1484 - 149.213i) q^{9} +O(q^{10})\)	\(q+(4.20426 + 7.28199i) q^{3} +(-18.6530 - 32.3080i) q^{5} +15.8772 q^{7} +(86.1484 - 149.213i) q^{9} -325.518 q^{11} +(519.710 - 900.165i) q^{13} +(156.844 - 271.662i) q^{15} +(778.938 + 1349.16i) q^{17} +(418.139 - 1516.99i) q^{19} +(66.7519 + 115.618i) q^{21} +(784.020 - 1357.96i) q^{23} +(866.629 - 1501.04i) q^{25} +3492.03 q^{27} +(4023.95 - 6969.69i) q^{29} -9529.39 q^{31} +(-1368.56 - 2370.42i) q^{33} +(-296.158 - 512.961i) q^{35} -451.140 q^{37} +8739.99 q^{39} +(2231.10 + 3864.38i) q^{41} +(5775.62 + 10003.7i) q^{43} -6427.72 q^{45} +(-3080.89 + 5336.26i) q^{47} -16554.9 q^{49} +(-6549.72 + 11344.4i) q^{51} +(-11186.9 + 19376.2i) q^{53} +(6071.91 + 10516.9i) q^{55} +(12804.7 - 3332.94i) q^{57} +(-3512.04 - 6083.03i) q^{59} +(4074.18 - 7056.68i) q^{61} +(1367.80 - 2369.09i) q^{63} -38776.7 q^{65} +(-27310.0 + 47302.3i) q^{67} +13184.9 q^{69} +(24835.7 + 43016.6i) q^{71} +(-29169.7 - 50523.3i) q^{73} +14574.1 q^{75} -5168.32 q^{77} +(-18324.7 - 31739.4i) q^{79} +(-6252.66 - 10829.9i) q^{81} +65668.7 q^{83} +(29059.1 - 50331.9i) q^{85} +67670.9 q^{87} +(-20103.8 + 34820.8i) q^{89} +(8251.55 - 14292.1i) q^{91} +(-40064.0 - 69393.0i) q^{93} +(-56810.5 + 14787.2i) q^{95} +(-5677.26 - 9833.30i) q^{97} +(-28042.9 + 48571.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 11 q^{3} + 11 q^{5} + 336 q^{7} - 902 q^{9}+O(q^{10}) \) 18 * q - 11 * q^3 + 11 * q^5 + 336 * q^7 - 902 * q^9	\( 18 q - 11 q^{3} + 11 q^{5} + 336 q^{7} - 902 q^{9} - 320 q^{11} + 227 q^{13} - 101 q^{15} + 179 q^{17} - 868 q^{19} - 5700 q^{21} - 3425 q^{23} - 7054 q^{25} + 14722 q^{27} - 7349 q^{29} - 9960 q^{31} - 2998 q^{33} + 15888 q^{35} + 26444 q^{37} - 30246 q^{39} - 7311 q^{41} - 8283 q^{43} - 62164 q^{45} + 37603 q^{47} + 124738 q^{49} + 47227 q^{51} - 20337 q^{53} + 716 q^{55} - 57555 q^{57} - 74455 q^{59} - 7569 q^{61} - 52544 q^{63} + 188998 q^{65} - 26177 q^{67} + 116282 q^{69} - 53463 q^{71} - 14103 q^{73} + 120912 q^{75} - 31960 q^{77} + 31825 q^{79} - 21137 q^{81} + 82600 q^{83} - 50787 q^{85} - 339766 q^{87} - 155197 q^{89} - 2800 q^{91} - 46460 q^{93} + 49315 q^{95} + 111241 q^{97} - 193544 q^{99}+O(q^{100}) \) 18 * q - 11 * q^3 + 11 * q^5 + 336 * q^7 - 902 * q^9 - 320 * q^11 + 227 * q^13 - 101 * q^15 + 179 * q^17 - 868 * q^19 - 5700 * q^21 - 3425 * q^23 - 7054 * q^25 + 14722 * q^27 - 7349 * q^29 - 9960 * q^31 - 2998 * q^33 + 15888 * q^35 + 26444 * q^37 - 30246 * q^39 - 7311 * q^41 - 8283 * q^43 - 62164 * q^45 + 37603 * q^47 + 124738 * q^49 + 47227 * q^51 - 20337 * q^53 + 716 * q^55 - 57555 * q^57 - 74455 * q^59 - 7569 * q^61 - 52544 * q^63 + 188998 * q^65 - 26177 * q^67 + 116282 * q^69 - 53463 * q^71 - 14103 * q^73 + 120912 * q^75 - 31960 * q^77 + 31825 * q^79 - 21137 * q^81 + 82600 * q^83 - 50787 * q^85 - 339766 * q^87 - 155197 * q^89 - 2800 * q^91 - 46460 * q^93 + 49315 * q^95 + 111241 * q^97 - 193544 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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