LMFDB - Embedded newform 304.6.i.d.273.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,6,Mod(49,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("304.49");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	304.i (of order $3$, degree $2$, not 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:	$48.7566812231$
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} - 5 x^{17} - 3057 x^{16} + 14564 x^{15} + 3829838 x^{14} - 15907074 x^{13} + \cdots + 66\!\cdots\!83 $ x^18 - 5x^17 - 3057x^16 + 14564x^15 + 3829838x^14 - 15907074x^13 - 2546775754x^12 + 7879525640x^11 + 976140188391x^10 - 1502012839499x^9 - 219575028272723x^8 - 104014033904304x^7 + 28115925509664606x^6 + 76771209356887914x^5 - 1810997176122162810x^4 - 9301294316540690604x^3 + 37701980111568799233x^2 + 354684213311311368351*x + 668276771042404734183
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{3}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 76)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			273.4
Root			$9.90852 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	304.273
Dual form			304.6.i.d.49.4

$q$-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 $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−4.20426	−	7.28199i	−0.269703	−	0.467140i	0.699082	−	0.715042i	$-0.253592\pi$
$3$	−4.20426	−	7.28199i	−0.269703	−	0.467140i	−0.968785	+	0.247902i	$0.920259\pi$
$4$		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	$-0.519504\pi$
$7$	−15.8772			−0.122470			−0.0612349	+	0.998123i	$0.519504\pi$
$8$		0			0
$9$	86.1484	−	149.213i	0.354520	−	0.614047i
$10$		0			0
$11$	325.518			0.811136			0.405568	−	0.914065i	$-0.367074\pi$
$11$	325.518			0.811136			0.405568	+	0.914065i	$0.367074\pi$
$12$		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	−0.978152	−	0.207893i	$-0.933339\pi$
$23$	−784.020	+	1357.96i	−0.309035	+	0.535264i	0.669116	+	0.743158i	$0.266673\pi$
$24$		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	$-0.150359\pi$
$31$	9529.39			1.78099			0.890494	+	0.454995i	$0.150359\pi$
$32$		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	0.523281	−	0.852160i	$-0.324708\pi$
$43$	−5775.62	−	10003.7i	−0.476352	−	0.825066i	−0.999633	+	0.0270946i	$0.991374\pi$
$44$		0			0
$45$	−6427.72			−0.473179
$46$		0			0
$47$	3080.89	−	5336.26i	0.203438	−	0.352365i	−0.746196	−	0.665726i	$-0.768122\pi$
$47$	3080.89	−	5336.26i	0.203438	−	0.352365i	0.949634	+	0.313362i	$0.101455\pi$
$48$		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	0.924197	−	0.381916i	$-0.124736\pi$
$59$	3512.04	+	6083.03i	0.131350	+	0.227504i	−0.792847	+	0.609420i	$0.791402\pi$
$60$		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	$-0.566617\pi$
$67$	27310.0	−	47302.3i	0.743250	−	1.28735i	0.951008	−	0.309167i	$-0.100050\pi$
$68$		0			0
$69$	13184.9			0.333391
$70$		0			0
$71$	−24835.7	−	43016.6i	−0.584696	−	1.01272i	−0.994913	−	0.100735i	$-0.967881\pi$
$71$	−24835.7	−	43016.6i	−0.584696	−	1.01272i	0.410218	−	0.911988i	$-0.365453\pi$
$72$		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	0.982580	−	0.185841i	$-0.0595010\pi$
$79$	18324.7	+	31739.4i	0.330347	+	0.572177i	−0.652233	+	0.758018i	$0.726168\pi$
$80$		0			0
$81$	−6252.66	−	10829.9i	−0.105889	−	0.183406i
$82$		0			0
$83$	−65668.7			−1.04632			−0.523158	−	0.852236i	$-0.675246\pi$
$83$	−65668.7			−1.04632			−0.523158	+	0.852236i	$0.675246\pi$
$84$		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	$-0.799763\pi$
$103$	−174119.			−1.61716			−0.808579	+	0.588387i	$0.799763\pi$
$104$		0			0
$105$	2490.25	−	4313.24i	0.0220430	−	0.0381795i
$106$		0			0
$107$	24682.3			0.208413			0.104207	−	0.994556i	$-0.466770\pi$
$107$	24682.3			0.208413			0.104207	+	0.994556i	$0.466770\pi$
$108$		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	$0.340650\pi$
$127$	−94476.0	+	163637.i	−0.519771	+	0.900270i	−0.999736	+	0.0229825i	$0.992684\pi$
$128$		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	$-0.873895\pi$
$131$	−156242.	−	270619.i	−0.795462	−	1.37778i	0.127083	−	0.991892i	$-0.459438\pi$
$132$		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	−0.770790	−	0.637089i	$-0.780138\pi$
$139$	37890.7	−	65628.7i	0.166340	−	0.288109i	0.937130	+	0.348980i	$0.113472\pi$
$140$		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	$-0.429505\pi$
$151$	123090.			0.439319			0.219659	+	0.975577i	$0.429505\pi$
$152$		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	$-0.404058\pi$
$163$	201402.			0.593737			0.296868	+	0.954918i	$0.404058\pi$
$164$		0			0
$165$	−51055.7	+	88431.1i	−0.145994	+	0.252869i
$166$		0			0
$167$	84718.2	−	146736.i	0.235064	−	0.407142i	−0.724227	−	0.689561i	$-0.757803\pi$
$167$	84718.2	−	146736.i	0.235064	−	0.407142i	0.959291	+	0.282419i	$0.0911368\pi$
$168$		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	$-0.543212\pi$
$179$	−116034.			−0.270677			−0.135339	+	0.990799i	$0.543212\pi$
$180$		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	$-0.689038\pi$
$191$	−564257.			−1.11916			−0.559582	+	0.828775i	$0.689038\pi$
$192$		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	$0.458816\pi$
$199$	−443715.	+	768537.i	−0.794276	+	1.37573i	−0.923298	+	0.384085i	$0.874517\pi$
$200$		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	0.813484	−	0.581588i	$-0.197568\pi$
$211$	−62683.9	−	108572.i	−0.0969282	−	0.167885i	−0.910412	+	0.413703i	$0.864235\pi$
$212$		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	0.684782	−	0.728748i	$-0.259897\pi$
$223$	−214409.	−	371367.i	−0.288723	−	0.500082i	−0.973505	+	0.228665i	$0.926564\pi$
$224$		0			0
$225$	−149317.	−	258625.i	−0.196632	−	0.340576i
$226$		0			0
$227$	−169489.			−0.218312			−0.109156	−	0.994025i	$-0.534815\pi$
$227$	−169489.			−0.218312			−0.109156	+	0.994025i	$0.534815\pi$
$228$		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	$-0.234641\pi$
$239$	1.30763e6			1.48078			0.740390	+	0.672178i	$0.234641\pi$
$240$		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	$-0.591628\pi$
$251$	687152.	−	1.19018e6i	0.688443	−	1.19242i	0.972341	−	0.233565i	$-0.0750390\pi$
$252$		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	0.802086	−	0.597209i	$-0.203724\pi$
$263$	−130295.	−	225678.i	−0.116155	−	0.201187i	−0.918241	+	0.396022i	$0.870390\pi$
$264$		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	0.744322	−	0.667821i	$-0.232773\pi$
$271$	−249281.	−	431768.i	−0.206189	−	0.357130i	−0.950511	+	0.310691i	$0.899440\pi$
$272$		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	$0.0980724\pi$
$283$	995765.	+	1.72472e6i	0.739079	+	1.28012i	−0.213831	+	0.976871i	$0.568594\pi$
$284$		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	$-0.949649\pi$
$307$	−1.04066e6	−	1.80247e6i	−0.630177	−	1.09150i	0.357339	−	0.933975i	$-0.383684\pi$
$308$		0			0
$309$	732041.	+	1.26793e6i	0.436153	+	0.755439i
$310$		0			0
$311$	2.82534e6			1.65642			0.828208	−	0.560421i	$-0.189361\pi$
$311$	2.82534e6			1.65642			0.828208	+	0.560421i	$0.189361\pi$
$312$		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	$-0.467773\pi$
$331$	402928.			0.202142			0.101071	+	0.994879i	$0.467773\pi$
$332$		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	0.926623	−	0.375991i	$-0.122698\pi$
$347$	308844.	+	534934.i	0.137694	+	0.238493i	−0.788929	+	0.614484i	$0.789364\pi$
$348$		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	0.705579	−	0.708631i	$-0.250687\pi$
$359$	−637110.	−	1.10351e6i	−0.260903	−	0.451897i	−0.966482	+	0.256734i	$0.917353\pi$
$360$		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	−0.942170	−	0.335137i	$-0.891218\pi$
$367$	−466637.	+	808238.i	−0.180848	+	0.313238i	0.761322	+	0.648374i	$0.224551\pi$
$368$		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	$-0.879497\pi$
$379$	−5.19678e6			−1.85839			−0.929193	+	0.369594i	$0.879497\pi$
$380$		0			0
$381$	1.58881e6			0.560736
$382$		0			0
$383$	−1.96378e6	−	3.40136e6i	−0.684062	−	1.18483i	−0.973731	−	0.227703i	$-0.926879\pi$
$383$	−1.96378e6	−	3.40136e6i	−0.684062	−	1.18483i	0.289669	−	0.957127i	$-0.406455\pi$
$384$		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	$-0.392466\pi$
$419$	2.38214e6			0.662877			0.331438	+	0.943477i	$0.392466\pi$
$420$		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	−0.741491	−	0.670963i	$-0.765881\pi$
$431$	811120.	−	1.40490e6i	0.210326	−	0.364295i	0.951816	+	0.306668i	$0.0992142\pi$
$432$		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	0.664009	−	0.747724i	$-0.268854\pi$
$439$	−1.27415e6	−	2.20689e6i	−0.315544	−	0.546538i	−0.979553	+	0.201187i	$0.935520\pi$
$440$		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	$0.346907\pi$
$443$	−2.21590e6	+	3.83805e6i	−0.536463	+	0.929182i	−0.999091	+	0.0426292i	$0.986427\pi$
$444$		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	$-0.355634\pi$
$463$	4.04208e6			0.876299			0.438150	+	0.898902i	$0.355634\pi$
$464$		0			0
$465$	−1.49463e6	+	2.58878e6i	−0.320554	+	0.555217i
$466$		0			0
$467$	8.27237e6			1.75525			0.877623	−	0.479352i	$-0.159128\pi$
$467$	8.27237e6			1.75525			0.877623	+	0.479352i	$0.159128\pi$
$468$		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	−0.832804	−	0.553567i	$-0.813266\pi$
$479$	316364.	−	547958.i	0.0630011	−	0.109121i	0.895806	+	0.444446i	$0.146600\pi$
$480$		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	$-0.716981\pi$
$487$	−6.59560e6			−1.26018			−0.630089	+	0.776523i	$0.716981\pi$
$488$		0			0
$489$	−846745.	−	1.46660e6i	−0.160133	−	0.277358i
$490$		0			0
$491$	−1.84714e6	−	3.19933e6i	−0.345776	−	0.598902i	0.639718	−	0.768610i	$-0.279051\pi$
$491$	−1.84714e6	−	3.19933e6i	−0.345776	−	0.598902i	−0.985494	+	0.169707i	$0.945718\pi$
$492$		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	$-0.780459\pi$
$499$	−5.21061e6	−	9.02504e6i	−0.936779	−	1.62255i	−0.165347	−	0.986235i	$-0.552875\pi$
$500$		0			0
$501$	−1.42471e6			−0.253590
$502$		0			0
$503$	−2.40212e6	+	4.16060e6i	−0.423326	+	0.733222i	−0.996262	−	0.0863777i	$-0.972471\pi$
$503$	−2.40212e6	+	4.16060e6i	−0.423326	+	0.733222i	0.572937	+	0.819600i	$0.305804\pi$
$504$		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	$-0.624886\pi$
$523$	3.80982e6	−	6.59880e6i	0.609046	−	1.05490i	0.991398	−	0.130882i	$-0.0417810\pi$
$524$		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	$0.576846\pi$
$547$	−6.72115e6	+	1.16414e7i	−0.960451	+	1.66355i	−0.721370	+	0.692549i	$0.756487\pi$
$548$		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	$-0.338198\pi$
$563$	7.32095e6			0.973412			0.486706	+	0.873566i	$0.338198\pi$
$564$		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	$-0.661499\pi$
$571$	−7.57087e6			−0.971753			−0.485876	+	0.874028i	$0.661499\pi$
$572$		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	$0.0665887\pi$
$587$	5.58455e6	+	9.67272e6i	0.668949	+	1.15865i	−0.309250	+	0.950981i	$0.600078\pi$
$588$		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	−0.940931	−	0.338599i	$-0.890047\pi$
$599$	−1.55634e6	+	2.69567e6i	−0.177231	+	0.306972i	0.763700	+	0.645571i	$0.223380\pi$
$600$		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	$-0.364031\pi$
$607$	7.52150e6			0.828577			0.414288	+	0.910146i	$0.364031\pi$
$608$		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	$-0.277917\pi$
$619$	1.22489e7			1.28491			0.642453	+	0.766325i	$0.277917\pi$
$620$		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	$-0.519737\pi$
$631$	8.33519e6	−	1.44370e7i	0.833378	−	1.44345i	0.895344	−	0.445375i	$-0.146930\pi$
$632$		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	0.968065	−	0.250698i	$-0.0806601\pi$
$643$	2.79841e6	+	4.84699e6i	0.266922	+	0.462322i	−0.701144	+	0.713020i	$0.747327\pi$
$644$		0			0
$645$	3.62350e6			0.342948
$646$		0			0
$647$	8.75822e6			0.822536			0.411268	−	0.911514i	$-0.365086\pi$
$647$	8.75822e6			0.822536			0.411268	+	0.911514i	$0.365086\pi$
$648$		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	−0.678260	−	0.734822i	$-0.737266\pi$
$659$	3.31380e6	−	5.73967e6i	0.297244	−	0.514842i	0.975504	+	0.219980i	$0.0705992\pi$
$660$		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	$-0.443369\pi$
$683$	4.31513e6			0.353951			0.176975	+	0.984215i	$0.443369\pi$
$684$		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	$-0.551389\pi$
$691$	−4.03514e6			−0.321487			−0.160744	+	0.986996i	$0.551389\pi$
$692$		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	0.951964	−	0.306209i	$-0.0990606\pi$
$719$	2.92205e6	+	5.06114e6i	0.210797	+	0.365112i	−0.741167	+	0.671321i	$0.765727\pi$
$720$		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	0.960566	−	0.278052i	$-0.0896888\pi$
$727$	3.41280e6	+	5.91114e6i	0.239483	+	0.414797i	−0.721083	+	0.692849i	$0.756355\pi$
$728$		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	0.834586	−	0.550877i	$-0.185707\pi$
$739$	−887503.	−	1.53720e6i	−0.0597804	−	0.103543i	−0.894367	+	0.447334i	$0.852373\pi$
$740$		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	$-0.935060\pi$
$743$	−1.00081e7	−	1.73345e7i	−0.665089	−	1.15197i	0.314172	−	0.949366i	$-0.398273\pi$
$744$		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	−0.978722	−	0.205190i	$-0.934219\pi$
$751$	−4.81707e6	+	8.34342e6i	−0.311662	+	0.539814i	0.667061	+	0.745004i	$0.267552\pi$
$752$		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	$-0.691277\pi$
$787$	−1.96481e7			−1.13080			−0.565398	+	0.824818i	$0.691277\pi$
$788$		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	−0.999060	−	0.0433553i	$-0.986195\pi$
$811$	−8.65323e6	+	1.49878e7i	−0.461983	+	0.800178i	0.537077	+	0.843533i	$0.319529\pi$
$812$		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	−0.938999	−	0.343919i	$-0.888245\pi$
$823$	−3.33550e6	+	5.77725e6i	−0.171657	+	0.297318i	0.767342	+	0.641238i	$0.221579\pi$
$824$		0			0
$825$	−4.74415e6			−0.242674
$826$		0			0
$827$	−1.34266e7	+	2.32556e7i	−0.682659	+	1.18240i	0.291507	+	0.956569i	$0.405843\pi$
$827$	−1.34266e7	+	2.32556e7i	−0.682659	+	1.18240i	−0.974166	+	0.225831i	$0.927490\pi$
$828$		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	0.988404	−	0.151845i	$-0.0485215\pi$
$839$	7.39525e6	+	1.28090e7i	0.362701	+	0.628216i	−0.625704	+	0.780061i	$0.715188\pi$
$840$		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	−0.795138	−	0.606428i	$-0.792602\pi$
$859$	2.75980e6	−	4.78012e6i	0.127613	−	0.221032i	0.922751	+	0.385396i	$0.125935\pi$
$860$		0			0
$861$	−297861.	+	515910.i	−0.0136932	+	0.0237173i
$862$		0			0
$863$	2.04317e6			0.0933852			0.0466926	−	0.998909i	$-0.485132\pi$
$863$	2.04317e6			0.0933852			0.0466926	+	0.998909i	$0.485132\pi$
$864$		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	$0.350553\pi$
$883$	−1.26523e7	+	2.19145e7i	−0.546095	+	0.945865i	−0.998537	+	0.0540711i	$0.982780\pi$
$884$		0			0
$885$	−2.20337e6			−0.0945649
$886$		0			0
$887$	1.94038e7	−	3.36084e7i	0.828090	−	1.43429i	−0.0714439	−	0.997445i	$-0.522761\pi$
$887$	1.94038e7	−	3.36084e7i	0.828090	−	1.43429i	0.899534	−	0.436850i	$-0.143906\pi$
$888$		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	0.526906	−	0.849924i	$-0.323352\pi$
$907$	−1.17089e7	−	2.02803e7i	−0.472603	−	0.818572i	−0.999508	+	0.0313519i	$0.990019\pi$
$908$		0			0
$909$	−1.66031e7	−	2.87574e7i	−0.666467	−	1.15435i
$910$		0			0
$911$	2.20141e7			0.878829			0.439415	−	0.898284i	$-0.355186\pi$
$911$	2.20141e7			0.878829			0.439415	+	0.898284i	$0.355186\pi$
$912$		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	$-0.620079\pi$
$919$	−1.88619e7			−0.736709			−0.368355	+	0.929685i	$0.620079\pi$
$920$		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	0.909299	−	0.416143i	$-0.136618\pi$
$947$	2.60136e6	+	4.50569e6i	0.0942596	+	0.163262i	−0.815040	+	0.579405i	$0.803285\pi$
$948$		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	$0.198770\pi$
$967$	2.65183e7	+	4.59310e7i	0.911966	+	1.57957i	0.100683	+	0.994919i	$0.467897\pi$
$968$		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	$0.0631678\pi$
$971$	1.94177e7	+	3.36325e7i	0.660922	+	1.14475i	−0.319452	+	0.947602i	$0.603499\pi$
$972$		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	0.859463	−	0.511197i	$-0.170798\pi$
$983$	−393185.	−	681016.i	−0.0129782	−	0.0224788i	−0.872442	+	0.488718i	$0.837465\pi$
$984$		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	0.957680	−	0.287835i	$-0.0929355\pi$
$991$	7.09732e6	+	1.22929e7i	0.229568	+	0.397623i	−0.728112	+	0.685458i	$0.759602\pi$
$992$		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	304.6.i.d.273.4		18
4.3	odd	2		76.6.e.a.45.6	✓	18
12.11	even	2		684.6.k.f.577.7		18
19.11	even	3	inner	304.6.i.d.49.4		18
76.11	odd	6		76.6.e.a.49.6	yes	18
228.11	even	6		684.6.k.f.505.7		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.6.e.a.45.6	✓	18	4.3	odd	2
76.6.e.a.49.6	yes	18	76.11	odd	6
304.6.i.d.49.4		18	19.11	even	3	inner
304.6.i.d.273.4		18	1.1	even	1	trivial
684.6.k.f.505.7		18	228.11	even	6
684.6.k.f.577.7		18	12.11	even	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:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	304.i (of order \(3\), degree \(2\), not 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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Database

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