LMFDB - Embedded newform 169.4.c.i.146.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,4,Mod(22,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("169.22");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	169.c (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:	$9.97132279097$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			146.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	169.146
Dual form			169.4.c.i.22.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73205 - 3.00000i) q^{2} +(3.50000 + 6.06218i) q^{3} +(-2.00000 + 3.46410i) q^{4} +13.8564 q^{5} +(12.1244 - 21.0000i) q^{6} +(11.2583 - 19.5000i) q^{7} -13.8564 q^{8} +(-11.0000 + 19.0526i) q^{9} +O(q^{10})$	\(q+(-1.73205 - 3.00000i) q^{2} +(3.50000 + 6.06218i) q^{3} +(-2.00000 + 3.46410i) q^{4} +13.8564 q^{5} +(12.1244 - 21.0000i) q^{6} +(11.2583 - 19.5000i) q^{7} -13.8564 q^{8} +(-11.0000 + 19.0526i) q^{9} +(-24.0000 - 41.5692i) q^{10} +(11.2583 + 19.5000i) q^{11} -28.0000 q^{12} -78.0000 q^{14} +(48.4974 + 84.0000i) q^{15} +(40.0000 + 69.2820i) q^{16} +(13.5000 - 23.3827i) q^{17} +76.2102 q^{18} +(44.1673 - 76.5000i) q^{19} +(-27.7128 + 48.0000i) q^{20} +157.617 q^{21} +(39.0000 - 67.5500i) q^{22} +(28.5000 + 49.3634i) q^{23} +(-48.4974 - 84.0000i) q^{24} +67.0000 q^{25} +35.0000 q^{27} +(45.0333 + 78.0000i) q^{28} +(34.5000 + 59.7558i) q^{29} +(168.000 - 290.985i) q^{30} -72.7461 q^{31} +(83.1384 - 144.000i) q^{32} +(-78.8083 + 136.500i) q^{33} -93.5307 q^{34} +(156.000 - 270.200i) q^{35} +(-44.0000 - 76.2102i) q^{36} +(19.9186 + 34.5000i) q^{37} -306.000 q^{38} -192.000 q^{40} +(-196.588 - 340.500i) q^{41} +(-273.000 - 472.850i) q^{42} +(-42.5000 + 73.6122i) q^{43} -90.0666 q^{44} +(-152.420 + 264.000i) q^{45} +(98.7269 - 171.000i) q^{46} +342.946 q^{47} +(-280.000 + 484.974i) q^{48} +(-82.0000 - 142.028i) q^{49} +(-116.047 - 201.000i) q^{50} +189.000 q^{51} +426.000 q^{53} +(-60.6218 - 105.000i) q^{54} +(156.000 + 270.200i) q^{55} +(-156.000 + 270.200i) q^{56} +618.342 q^{57} +(119.512 - 207.000i) q^{58} +(-9.52628 + 16.5000i) q^{59} -387.979 q^{60} +(8.50000 - 14.7224i) q^{61} +(126.000 + 218.238i) q^{62} +(247.683 + 429.000i) q^{63} +64.0000 q^{64} +546.000 q^{66} +(82.2724 + 142.500i) q^{67} +(54.0000 + 93.5307i) q^{68} +(-199.500 + 345.544i) q^{69} -1080.80 q^{70} +(-291.851 + 505.500i) q^{71} +(152.420 - 264.000i) q^{72} -1004.59 q^{73} +(69.0000 - 119.512i) q^{74} +(234.500 + 406.166i) q^{75} +(176.669 + 306.000i) q^{76} +507.000 q^{77} -1244.00 q^{79} +(554.256 + 960.000i) q^{80} +(419.500 + 726.595i) q^{81} +(-681.000 + 1179.53i) q^{82} -426.084 q^{83} +(-315.233 + 546.000i) q^{84} +(187.061 - 324.000i) q^{85} +294.449 q^{86} +(-241.500 + 418.290i) q^{87} +(-156.000 - 270.200i) q^{88} +(-153.286 - 265.500i) q^{89} +1056.00 q^{90} -228.000 q^{92} +(-254.611 - 441.000i) q^{93} +(-594.000 - 1028.84i) q^{94} +(612.000 - 1060.02i) q^{95} +1163.94 q^{96} +(-617.476 + 1069.50i) q^{97} +(-284.056 + 492.000i) q^{98} -495.367 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 14 q^{3} - 8 q^{4} - 44 q^{9}+O(q^{10}) $ 4 * q + 14 * q^3 - 8 * q^4 - 44 * q^9	$ 4 q + 14 q^{3} - 8 q^{4} - 44 q^{9} - 96 q^{10} - 112 q^{12} - 312 q^{14} + 160 q^{16} + 54 q^{17} + 156 q^{22} + 114 q^{23} + 268 q^{25} + 140 q^{27} + 138 q^{29} + 672 q^{30} + 624 q^{35} - 176 q^{36} - 1224 q^{38} - 768 q^{40} - 1092 q^{42} - 170 q^{43} - 1120 q^{48} - 328 q^{49} + 756 q^{51} + 1704 q^{53} + 624 q^{55} - 624 q^{56} + 34 q^{61} + 504 q^{62} + 256 q^{64} + 2184 q^{66} + 216 q^{68} - 798 q^{69} + 276 q^{74} + 938 q^{75} + 2028 q^{77} - 4976 q^{79} + 1678 q^{81} - 2724 q^{82} - 966 q^{87} - 624 q^{88} + 4224 q^{90} - 912 q^{92} - 2376 q^{94} + 2448 q^{95}+O(q^{100}) $ 4 * q + 14 * q^3 - 8 * q^4 - 44 * q^9 - 96 * q^10 - 112 * q^12 - 312 * q^14 + 160 * q^16 + 54 * q^17 + 156 * q^22 + 114 * q^23 + 268 * q^25 + 140 * q^27 + 138 * q^29 + 672 * q^30 + 624 * q^35 - 176 * q^36 - 1224 * q^38 - 768 * q^40 - 1092 * q^42 - 170 * q^43 - 1120 * q^48 - 328 * q^49 + 756 * q^51 + 1704 * q^53 + 624 * q^55 - 624 * q^56 + 34 * q^61 + 504 * q^62 + 256 * q^64 + 2184 * q^66 + 216 * q^68 - 798 * q^69 + 276 * q^74 + 938 * q^75 + 2028 * q^77 - 4976 * q^79 + 1678 * q^81 - 2724 * q^82 - 966 * q^87 - 624 * q^88 + 4224 * q^90 - 912 * q^92 - 2376 * q^94 + 2448 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.73205	−	3.00000i	−0.612372	−	1.06066i	−0.990839	−	0.135045i	$-0.956882\pi$
$2$	−1.73205	−	3.00000i	−0.612372	−	1.06066i	0.378467	−	0.925615i	$-0.376451\pi$
$3$	3.50000	+	6.06218i	0.673575	+	1.16667i	0.976883	+	0.213774i	$0.0685756\pi$
$3$	3.50000	+	6.06218i	0.673575	+	1.16667i	−0.303308	+	0.952893i	$0.598091\pi$
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	13.8564			1.23935			0.619677	−	0.784857i	$-0.287263\pi$
$5$	13.8564			1.23935			0.619677	+	0.784857i	$0.287263\pi$
$6$	12.1244	−	21.0000i	0.824958	−	1.42887i
$7$	11.2583	−	19.5000i	0.607893	−	1.05290i	−0.383694	−	0.923460i	$-0.625348\pi$
$7$	11.2583	−	19.5000i	0.607893	−	1.05290i	0.991587	−	0.129441i	$-0.0413183\pi$
$8$	−13.8564			−0.612372
$9$	−11.0000	+	19.0526i	−0.407407	+	0.705650i
$10$	−24.0000	−	41.5692i	−0.758947	−	1.31453i
$11$	11.2583	+	19.5000i	0.308592	+	0.534497i	0.978055	−	0.208349i	$-0.0668088\pi$
$11$	11.2583	+	19.5000i	0.308592	+	0.534497i	−0.669462	+	0.742846i	$0.733475\pi$
$12$	−28.0000			−0.673575
$13$		0			0
$13$		0			0
$14$	−78.0000			−1.48903
$15$	48.4974	+	84.0000i	0.834799	+	1.44591i
$16$	40.0000	+	69.2820i	0.625000	+	1.08253i
$17$	13.5000	−	23.3827i	0.192602	−	0.333596i	−0.753510	−	0.657437i	$-0.771641\pi$
$17$	13.5000	−	23.3827i	0.192602	−	0.333596i	0.946112	+	0.323840i	$0.104974\pi$
$18$	76.2102			0.997940
$19$	44.1673	−	76.5000i	0.533299	−	0.923700i	−0.465945	−	0.884814i	$-0.654286\pi$
$19$	44.1673	−	76.5000i	0.533299	−	0.923700i	0.999244	−	0.0388865i	$-0.0123811\pi$
$20$	−27.7128	+	48.0000i	−0.309839	+	0.536656i
$21$	157.617			1.63785
$22$	39.0000	−	67.5500i	0.377947	−	0.654623i
$23$	28.5000	+	49.3634i	0.258377	+	0.447521i	0.965807	−	0.259261i	$-0.0834791\pi$
$23$	28.5000	+	49.3634i	0.258377	+	0.447521i	−0.707431	+	0.706783i	$0.750146\pi$
$24$	−48.4974	−	84.0000i	−0.412479	−	0.714435i
$25$	67.0000			0.536000
$26$		0			0
$27$	35.0000			0.249472
$28$	45.0333	+	78.0000i	0.303946	+	0.526451i
$29$	34.5000	+	59.7558i	0.220913	+	0.382633i	0.955086	−	0.296330i	$-0.0957628\pi$
$29$	34.5000	+	59.7558i	0.220913	+	0.382633i	−0.734172	+	0.678963i	$0.762430\pi$
$30$	168.000	−	290.985i	1.02242	−	1.77088i
$31$	−72.7461			−0.421471			−0.210735	−	0.977543i	$-0.567586\pi$
$31$	−72.7461			−0.421471			−0.210735	+	0.977543i	$0.567586\pi$
$32$	83.1384	−	144.000i	0.459279	−	0.795495i
$33$	−78.8083	+	136.500i	−0.415720	+	0.720048i
$34$	−93.5307			−0.471776
$35$	156.000	−	270.200i	0.753395	−	1.30492i
$36$	−44.0000	−	76.2102i	−0.203704	−	0.352825i
$37$	19.9186	+	34.5000i	0.0885026	+	0.153291i	0.906878	−	0.421393i	$-0.138459\pi$
$37$	19.9186	+	34.5000i	0.0885026	+	0.153291i	−0.818376	+	0.574683i	$0.805125\pi$
$38$	−306.000			−1.30631
$39$		0			0
$40$	−192.000			−0.758947
$41$	−196.588	−	340.500i	−0.748826	−	1.29700i	−0.948386	−	0.317118i	$-0.897285\pi$
$41$	−196.588	−	340.500i	−0.748826	−	1.29700i	0.199560	−	0.979886i	$-0.436049\pi$
$42$	−273.000	−	472.850i	−1.00297	−	1.73720i
$43$	−42.5000	+	73.6122i	−0.150725	+	0.261064i	−0.931494	−	0.363756i	$-0.881494\pi$
$43$	−42.5000	+	73.6122i	−0.150725	+	0.261064i	0.780769	+	0.624820i	$0.214828\pi$
$44$	−90.0666			−0.308592
$45$	−152.420	+	264.000i	−0.504922	+	0.874551i
$46$	98.7269	−	171.000i	0.316445	−	0.548099i
$47$	342.946			1.06434			0.532168	−	0.846639i	$-0.321377\pi$
$47$	342.946			1.06434			0.532168	+	0.846639i	$0.321377\pi$
$48$	−280.000	+	484.974i	−0.841969	+	1.45833i
$49$	−82.0000	−	142.028i	−0.239067	−	0.414076i
$50$	−116.047	−	201.000i	−0.328232	−	0.568514i
$51$	189.000			0.518927
$52$		0			0
$53$	426.000			1.10407			0.552034	−	0.833822i	$-0.313852\pi$
$53$	426.000			1.10407			0.552034	+	0.833822i	$0.313852\pi$
$54$	−60.6218	−	105.000i	−0.152770	−	0.264605i
$55$	156.000	+	270.200i	0.382455	+	0.662432i
$56$	−156.000	+	270.200i	−0.372257	+	0.644768i
$57$	618.342			1.43687
$58$	119.512	−	207.000i	0.270563	−	0.468628i
$59$	−9.52628	+	16.5000i	−0.0210206	+	0.0364088i	−0.876344	−	0.481685i	$-0.840025\pi$
$59$	−9.52628	+	16.5000i	−0.0210206	+	0.0364088i	0.855324	+	0.518094i	$0.173358\pi$
$60$	−387.979			−0.834799
$61$	8.50000	−	14.7224i	0.0178412	−	0.0309019i	−0.856967	−	0.515371i	$-0.827654\pi$
$61$	8.50000	−	14.7224i	0.0178412	−	0.0309019i	0.874808	+	0.484469i	$0.160987\pi$
$62$	126.000	+	218.238i	0.258097	+	0.447037i
$63$	247.683	+	429.000i	0.495320	+	0.857919i
$64$	64.0000			0.125000
$65$		0			0
$66$	546.000			1.01830
$67$	82.2724	+	142.500i	0.150018	+	0.259838i	0.931234	−	0.364423i	$-0.118734\pi$
$67$	82.2724	+	142.500i	0.150018	+	0.259838i	−0.781216	+	0.624261i	$0.785400\pi$
$68$	54.0000	+	93.5307i	0.0963009	+	0.166798i
$69$	−199.500	+	345.544i	−0.348072	+	0.602879i
$70$	−1080.80			−1.84543
$71$	−291.851	+	505.500i	−0.487835	+	0.844955i	−0.999902	−	0.0139904i	$-0.995547\pi$
$71$	−291.851	+	505.500i	−0.487835	+	0.844955i	0.512067	+	0.858945i	$0.328880\pi$
$72$	152.420	−	264.000i	0.249485	−	0.432121i
$73$	−1004.59			−1.61066			−0.805331	−	0.592826i	$-0.798012\pi$
$73$	−1004.59			−1.61066			−0.805331	+	0.592826i	$0.798012\pi$
$74$	69.0000	−	119.512i	0.108393	−	0.187742i
$75$	234.500	+	406.166i	0.361036	+	0.625333i
$76$	176.669	+	306.000i	0.266649	+	0.461850i
$77$	507.000			0.750364
$78$		0			0
$79$	−1244.00			−1.77166			−0.885829	−	0.464012i	$-0.846409\pi$
$79$	−1244.00			−1.77166			−0.885829	+	0.464012i	$0.846409\pi$
$80$	554.256	+	960.000i	0.774597	+	1.34164i
$81$	419.500	+	726.595i	0.575446	+	0.996701i
$82$	−681.000	+	1179.53i	−0.917120	+	1.58850i
$83$	−426.084			−0.563480			−0.281740	−	0.959491i	$-0.590912\pi$
$83$	−426.084			−0.563480			−0.281740	+	0.959491i	$0.590912\pi$
$84$	−315.233	+	546.000i	−0.409462	+	0.709208i
$85$	187.061	−	324.000i	0.238702	−	0.413444i
$86$	294.449			0.369200
$87$	−241.500	+	418.290i	−0.297604	+	0.515465i
$88$	−156.000	−	270.200i	−0.188973	−	0.327311i
$89$	−153.286	−	265.500i	−0.182566	−	0.316213i	0.760188	−	0.649703i	$-0.225107\pi$
$89$	−153.286	−	265.500i	−0.182566	−	0.316213i	−0.942753	+	0.333490i	$0.891774\pi$
$90$	1056.00			1.23680
$91$		0			0
$92$	−228.000			−0.258377
$93$	−254.611	−	441.000i	−0.283892	−	0.491716i
$94$	−594.000	−	1028.84i	−0.651770	−	1.12890i
$95$	612.000	−	1060.02i	0.660946	−	1.14479i
$96$	1163.94			1.23744
$97$	−617.476	+	1069.50i	−0.646342	+	1.11950i	0.337647	+	0.941273i	$0.390369\pi$
$97$	−617.476	+	1069.50i	−0.646342	+	1.11950i	−0.983990	+	0.178225i	$0.942965\pi$
$98$	−284.056	+	492.000i	−0.292796	+	0.507138i
$99$	−495.367			−0.502891
$100$	−134.000	+	232.095i	−0.134000	+	0.232095i
$101$	979.500	+	1696.54i	0.964989	+	1.67141i	0.709645	+	0.704560i	$0.248856\pi$
$101$	979.500	+	1696.54i	0.964989	+	1.67141i	0.255345	+	0.966850i	$0.417811\pi$
$102$	−327.358	−	567.000i	−0.317777	−	0.550406i
$103$	−1856.00			−1.77551			−0.887753	−	0.460320i	$-0.847735\pi$
$103$	−1856.00			−1.77551			−0.887753	+	0.460320i	$0.847735\pi$
$104$		0			0
$105$	2184.00			2.02987
$106$	−737.854	−	1278.00i	−0.676101	−	1.17104i
$107$	127.500	+	220.836i	0.115195	+	0.199524i	0.917858	−	0.396909i	$-0.129917\pi$
$107$	127.500	+	220.836i	0.115195	+	0.199524i	−0.802663	+	0.596433i	$0.796584\pi$
$108$	−70.0000	+	121.244i	−0.0623681	+	0.108025i
$109$	−609.682			−0.535752			−0.267876	−	0.963453i	$-0.586322\pi$
$109$	−609.682			−0.535752			−0.267876	+	0.963453i	$0.586322\pi$
$110$	540.400	−	936.000i	0.468410	−	0.811310i
$111$	−139.430	+	241.500i	−0.119226	+	0.206506i
$112$	1801.33			1.51973
$113$	−205.500	+	355.936i	−0.171078	+	0.296316i	−0.938797	−	0.344471i	$-0.888058\pi$
$113$	−205.500	+	355.936i	−0.171078	+	0.296316i	0.767719	+	0.640787i	$0.221392\pi$
$114$	−1071.00	−	1855.03i	−0.879898	−	1.52403i
$115$	394.908	+	684.000i	0.320220	+	0.554638i
$116$	−276.000			−0.220913
$117$		0			0
$118$	66.0000			0.0514898
$119$	−303.975	−	526.500i	−0.234162	−	0.405581i
$120$	−672.000	−	1163.94i	−0.511208	−	0.885438i
$121$	412.000	−	713.605i	0.309542	−	0.536142i
$122$	−58.8897			−0.0437018
$123$	1376.11	−	2383.50i	1.00878	−	1.74726i
$124$	145.492	−	252.000i	0.105368	−	0.182502i
$125$	−803.672			−0.575061
$126$	858.000	−	1486.10i	0.606641	−	1.05073i
$127$	−1121.50	−	1942.49i	−0.783599	−	1.35723i	−0.929833	−	0.367983i	$-0.880049\pi$
$127$	−1121.50	−	1942.49i	−0.783599	−	1.35723i	0.146234	−	0.989250i	$-0.453285\pi$
$128$	−775.959	−	1344.00i	−0.535826	−	0.928078i
$129$	−595.000			−0.406099
$130$		0			0
$131$	−372.000			−0.248105			−0.124053	−	0.992276i	$-0.539589\pi$
$131$	−372.000			−0.248105			−0.124053	+	0.992276i	$0.539589\pi$
$132$	−315.233	−	546.000i	−0.207860	−	0.360024i
$133$	−994.500	−	1722.52i	−0.648377	−	1.12302i
$134$	285.000	−	493.634i	0.183733	−	0.318235i
$135$	484.974			0.309185
$136$	−187.061	+	324.000i	−0.117944	+	0.204285i
$137$	−594.959	+	1030.50i	−0.371028	+	0.642639i	−0.989724	−	0.142991i	$-0.954328\pi$
$137$	−594.959	+	1030.50i	−0.371028	+	0.642639i	0.618696	+	0.785630i	$0.287661\pi$
$138$	1382.18			0.852599
$139$	1272.50	−	2204.03i	0.776490	−	1.34492i	−0.157464	−	0.987525i	$-0.550332\pi$
$139$	1272.50	−	2204.03i	0.776490	−	1.34492i	0.933953	−	0.357395i	$-0.116335\pi$
$140$	624.000	+	1080.80i	0.376697	+	0.652459i
$141$	1200.31	+	2079.00i	0.716911	+	1.24173i
$142$	2022.00			1.19495
$143$		0			0
$144$	−1760.00			−1.01852
$145$	478.046	+	828.000i	0.273790	+	0.474218i
$146$	1740.00	+	3013.77i	0.986325	+	1.70836i
$147$	574.000	−	994.197i	0.322059	−	0.557823i
$148$	−159.349			−0.0885026
$149$	−652.117	+	1129.50i	−0.358547	+	0.621022i	−0.987718	−	0.156245i	$-0.950061\pi$
$149$	−652.117	+	1129.50i	−0.358547	+	0.621022i	0.629171	+	0.777267i	$0.283394\pi$
$150$	812.332	−	1407.00i	0.442177	−	0.765874i
$151$	86.6025			0.0466729			0.0233365	−	0.999728i	$-0.492571\pi$
$151$	86.6025			0.0466729			0.0233365	+	0.999728i	$0.492571\pi$
$152$	−612.000	+	1060.02i	−0.326577	+	0.565649i
$153$	297.000	+	514.419i	0.156935	+	0.271819i
$154$	−878.150	−	1521.00i	−0.459502	−	0.795881i
$155$	−1008.00			−0.522352
$156$		0			0
$157$	−1534.00			−0.779787			−0.389893	−	0.920860i	$-0.627488\pi$
$157$	−1534.00			−0.779787			−0.389893	+	0.920860i	$0.627488\pi$
$158$	2154.67	+	3732.00i	1.08491	+	1.87913i
$159$	1491.00	+	2582.49i	0.743673	+	1.28808i
$160$	1152.00	−	1995.32i	0.569210	−	0.985901i
$161$	1283.45			0.628261
$162$	1453.19	−	2517.00i	0.704774	−	1.22070i
$163$	−816.662	+	1414.50i	−0.392429	+	0.679707i	−0.992769	−	0.120038i	$-0.961698\pi$
$163$	−816.662	+	1414.50i	−0.392429	+	0.679707i	0.600340	+	0.799745i	$0.295032\pi$
$164$	1572.70			0.748826
$165$	−1092.00	+	1891.40i	−0.515225	+	0.892395i
$166$	738.000	+	1278.25i	0.345060	+	0.597661i
$167$	−813.198	−	1408.50i	−0.376809	−	0.652653i	0.613787	−	0.789472i	$-0.289645\pi$
$167$	−813.198	−	1408.50i	−0.376809	−	0.652653i	−0.990596	+	0.136819i	$0.956312\pi$
$168$	−2184.00			−1.00297
$169$		0			0
$170$	−1296.00			−0.584698
$171$	971.681	+	1683.00i	0.434540	+	0.752645i
$172$	−170.000	−	294.449i	−0.0753627	−	0.130532i
$173$	−436.500	+	756.040i	−0.191829	+	0.332258i	−0.945857	−	0.324585i	$-0.894775\pi$
$173$	−436.500	+	756.040i	−0.191829	+	0.332258i	0.754027	+	0.656843i	$0.228109\pi$
$174$	1673.16			0.728977
$175$	754.308	−	1306.50i	0.325830	−	0.564355i
$176$	−900.666	+	1560.00i	−0.385740	+	0.668122i
$177$	−133.368			−0.0566359
$178$	−531.000	+	919.719i	−0.223596	+	0.387280i
$179$	−643.500	−	1114.57i	−0.268701	−	0.465403i	0.699826	−	0.714314i	$-0.253261\pi$
$179$	−643.500	−	1114.57i	−0.268701	−	0.465403i	−0.968527	+	0.248910i	$0.919928\pi$
$180$	−609.682	−	1056.00i	−0.252461	−	0.437276i
$181$	−2.00000			−0.000821319			−0.000410660	−	1.00000i	$-0.500131\pi$
$181$	−2.00000			−0.000821319			−0.000410660		1.00000i	$0.500131\pi$
$182$		0			0
$183$	119.000			0.0480696
$184$	−394.908	−	684.000i	−0.158223	−	0.274050i
$185$	276.000	+	478.046i	0.109686	+	0.189982i
$186$	−882.000	+	1527.67i	−0.347696	+	0.602226i
$187$	607.950			0.237742
$188$	−685.892	+	1188.00i	−0.266084	+	0.460871i
$189$	394.042	−	682.500i	0.151652	−	0.262670i
$190$	−4240.06			−1.61898
$191$	1420.50	−	2460.38i	0.538135	−	0.932077i	−0.460870	−	0.887468i	$-0.652462\pi$
$191$	1420.50	−	2460.38i	0.538135	−	0.932077i	0.999005	−	0.0446092i	$-0.0142043\pi$
$192$	224.000	+	387.979i	0.0841969	+	0.145833i
$193$	2122.63	+	3676.50i	0.791659	+	1.37119i	0.924939	+	0.380115i	$0.124115\pi$
$193$	2122.63	+	3676.50i	0.791659	+	1.37119i	−0.133281	+	0.991078i	$0.542551\pi$
$194$	4278.00			1.58321
$195$		0			0
$196$	656.000			0.239067
$197$	1376.11	+	2383.50i	0.497686	+	0.862017i	0.999996	−	0.00267023i	$-0.000849961\pi$
$197$	1376.11	+	2383.50i	0.497686	+	0.862017i	−0.502311	+	0.864687i	$0.667517\pi$
$198$	858.000	+	1486.10i	0.307957	+	0.533396i
$199$	−842.500	+	1459.25i	−0.300117	+	0.519818i	−0.976162	−	0.217042i	$-0.930359\pi$
$199$	−842.500	+	1459.25i	−0.300117	+	0.519818i	0.676045	+	0.736860i	$0.263692\pi$
$200$	−928.379			−0.328232
$201$	−575.907	+	997.500i	−0.202096	+	0.350041i
$202$	3393.09	−	5877.00i	1.18187	−	2.04705i
$203$	1553.65			0.537167
$204$	−378.000	+	654.715i	−0.129732	+	0.224702i
$205$	−2724.00	−	4718.11i	−0.928061	−	1.60745i
$206$	3214.69	+	5568.00i	1.08727	+	1.88321i
$207$	−1254.00			−0.421058
$208$		0			0
$209$	1989.00			0.658287
$210$	−3782.80	−	6552.00i	−1.24304	−	2.15300i
$211$	−840.500	−	1455.79i	−0.274229	−	0.474979i	0.695711	−	0.718322i	$-0.255089\pi$
$211$	−840.500	−	1455.79i	−0.274229	−	0.474979i	−0.969940	+	0.243343i	$0.921756\pi$
$212$	−852.000	+	1475.71i	−0.276017	+	0.478075i
$213$	−4085.91			−1.31437
$214$	441.673	−	765.000i	0.141085	−	0.244366i
$215$	−588.897	+	1020.00i	−0.186802	+	0.323551i
$216$	−484.974			−0.152770
$217$	−819.000	+	1418.55i	−0.256209	+	0.443767i
$218$	1056.00	+	1829.05i	0.328080	+	0.568250i
$219$	−3516.06	−	6090.00i	−1.08490	−	1.87911i
$220$	−1248.00			−0.382455
$221$		0			0
$222$	966.000			0.292044
$223$	−2048.15	−	3547.50i	−0.615042	−	1.06528i	−0.990377	−	0.138394i	$-0.955806\pi$
$223$	−2048.15	−	3547.50i	−0.615042	−	1.06528i	0.375336	−	0.926889i	$-0.377527\pi$
$224$	−1872.00	−	3242.40i	−0.558385	−	0.967151i
$225$	−737.000	+	1276.52i	−0.218370	+	0.378229i
$226$	1423.75			0.419054
$227$	−219.104	+	379.500i	−0.0640638	+	0.110962i	−0.896278	−	0.443492i	$-0.853739\pi$
$227$	−219.104	+	379.500i	−0.0640638	+	0.110962i	0.832215	+	0.554454i	$0.187073\pi$
$228$	−1236.68	+	2142.00i	−0.359217	+	0.622182i
$229$	−180.133			−0.0519805			−0.0259903	−	0.999662i	$-0.508274\pi$
$229$	−180.133			−0.0519805			−0.0259903	+	0.999662i	$0.508274\pi$
$230$	1368.00	−	2369.45i	0.392188	−	0.679290i
$231$	1774.50	+	3073.52i	0.505427	+	0.875424i
$232$	−478.046	−	828.000i	−0.135281	−	0.234314i
$233$	5778.00			1.62459			0.812295	−	0.583247i	$-0.198218\pi$
$233$	5778.00			1.62459			0.812295	+	0.583247i	$0.198218\pi$
$234$		0			0
$235$	4752.00			1.31909
$236$	−38.1051	−	66.0000i	−0.0105103	−	0.0182044i
$237$	−4354.00	−	7541.35i	−1.19334	−	2.06693i
$238$	−1053.00	+	1823.85i	−0.286789	+	0.496734i
$239$	−1860.22			−0.503464			−0.251732	−	0.967797i	$-0.581000\pi$
$239$	−1860.22			−0.503464			−0.251732	+	0.967797i	$0.581000\pi$
$240$	−3879.79	+	6720.00i	−1.04350	+	1.80739i
$241$	1029.70	−	1783.50i	0.275224	−	0.476703i	−0.694967	−	0.719041i	$-0.744581\pi$
$241$	1029.70	−	1783.50i	0.275224	−	0.476703i	0.970192	+	0.242339i	$0.0779145\pi$
$242$	−2854.42			−0.758219
$243$	−2464.00	+	4267.77i	−0.650476	+	1.12666i
$244$	34.0000	+	58.8897i	0.00892060	+	0.0154509i
$245$	−1136.23	−	1968.00i	−0.296289	−	0.513187i
$246$	−9534.00			−2.47100
$247$		0			0
$248$	1008.00			0.258097
$249$	−1491.30	−	2583.00i	−0.379546	−	0.657393i
$250$	1392.00	+	2411.01i	0.352151	+	0.609944i
$251$	2245.50	−	3889.32i	0.564680	−	0.978055i	−0.432399	−	0.901682i	$-0.642333\pi$
$251$	2245.50	−	3889.32i	0.564680	−	0.978055i	0.997079	−	0.0763724i	$-0.0243338\pi$
$252$	−1981.47			−0.495320
$253$	−641.725	+	1111.50i	−0.159466	+	0.276203i
$254$	−3884.99	+	6729.00i	−0.959708	+	1.66226i
$255$	2618.86			0.643135
$256$	−2432.00	+	4212.35i	−0.593750	+	1.02841i
$257$	2725.50	+	4720.70i	0.661525	+	1.14580i	0.980215	+	0.197936i	$0.0634239\pi$
$257$	2725.50	+	4720.70i	0.661525	+	1.14580i	−0.318690	+	0.947859i	$0.603243\pi$
$258$	1030.57	+	1785.00i	0.248684	+	0.430734i
$259$	897.000			0.215200
$260$		0			0
$261$	−1518.00			−0.360007
$262$	644.323	+	1116.00i	0.151933	+	0.263155i
$263$	391.500	+	678.098i	0.0917906	+	0.158986i	0.908265	−	0.418396i	$-0.137408\pi$
$263$	391.500	+	678.098i	0.0917906	+	0.158986i	−0.816474	+	0.577382i	$0.804074\pi$
$264$	1092.00	−	1891.40i	0.254576	−	0.440938i
$265$	5902.83			1.36833
$266$	−3445.05	+	5967.00i	−0.794096	+	1.37541i
$267$	1073.01	−	1858.50i	0.245943	−	0.425986i
$268$	−658.179			−0.150018
$269$	2542.50	−	4403.74i	0.576279	−	0.998144i	−0.419623	−	0.907699i	$-0.637838\pi$
$269$	2542.50	−	4403.74i	0.576279	−	0.998144i	0.995901	−	0.0904453i	$-0.0288290\pi$
$270$	−840.000	−	1454.92i	−0.189336	−	0.327940i
$271$	662.509	+	1147.50i	0.148504	+	0.257216i	0.930675	−	0.365848i	$-0.119221\pi$
$271$	662.509	+	1147.50i	0.148504	+	0.257216i	−0.782171	+	0.623064i	$0.785888\pi$
$272$	2160.00			0.481505
$273$		0			0
$274$	4122.00			0.908829
$275$	754.308	+	1306.50i	0.165405	+	0.286491i
$276$	−798.000	−	1382.18i	−0.174036	−	0.301439i
$277$	−1710.50	+	2962.67i	−0.371025	+	0.642635i	−0.989724	−	0.142994i	$-0.954327\pi$
$277$	−1710.50	+	2962.67i	−0.371025	+	0.642635i	0.618698	+	0.785629i	$0.287660\pi$
$278$	−8816.14			−1.90200
$279$	800.207	−	1386.00i	0.171710	−	0.297411i
$280$	−2161.60	+	3744.00i	−0.461358	+	0.799096i
$281$	−810.600			−0.172087			−0.0860433	−	0.996291i	$-0.527422\pi$
$281$	−810.600			−0.172087			−0.0860433	+	0.996291i	$0.527422\pi$
$282$	4158.00	−	7201.87i	0.878033	−	1.52080i
$283$	3588.50	+	6215.46i	0.753760	+	1.30555i	0.945988	+	0.324201i	$0.105095\pi$
$283$	3588.50	+	6215.46i	0.753760	+	1.30555i	−0.192228	+	0.981350i	$0.561571\pi$
$284$	−1167.40	−	2022.00i	−0.243918	−	0.422478i
$285$	8568.00			1.78079
$286$		0			0
$287$	−8853.00			−1.82082
$288$	1829.05	+	3168.00i	0.374228	+	0.648181i
$289$	2092.00	+	3623.45i	0.425809	+	0.737523i
$290$	1656.00	−	2868.28i	0.335323	−	0.580796i
$291$	−8644.67			−1.74144
$292$	2009.18	−	3480.00i	0.402665	−	0.697437i
$293$	4656.62	−	8065.50i	0.928473	−	1.60816i	0.142595	−	0.989781i	$-0.454456\pi$
$293$	4656.62	−	8065.50i	0.928473	−	1.60816i	0.785878	−	0.618381i	$-0.212211\pi$
$294$	−3976.79			−0.788881
$295$	−132.000	+	228.631i	−0.0260520	+	0.0451234i
$296$	−276.000	−	478.046i	−0.0541965	−	0.0938712i
$297$	394.042	+	682.500i	0.0769852	+	0.133342i
$298$	4518.00			0.878257
$299$		0			0
$300$	−1876.00			−0.361036
$301$	956.958	+	1657.50i	0.183250	+	0.317398i
$302$	−150.000	−	259.808i	−0.0285812	−	0.0495041i
$303$	−6856.50	+	11875.8i	−1.29999	+	2.25164i
$304$	7066.77			1.33325
$305$	117.779	−	204.000i	0.0221116	−	0.0382984i
$306$	1028.84	−	1782.00i	0.192205	−	0.332909i
$307$	4777.00			0.888070			0.444035	−	0.896009i	$-0.353547\pi$
$307$	4777.00			0.888070			0.444035	+	0.896009i	$0.353547\pi$
$308$	−1014.00	+	1756.30i	−0.187591	+	0.324917i
$309$	−6496.00	−	11251.4i	−1.19594	−	2.07142i
$310$	1745.91	+	3024.00i	0.319874	+	0.554038i
$311$	−6192.00			−1.12899			−0.564495	−	0.825436i	$-0.690929\pi$
$311$	−6192.00			−1.12899			−0.564495	+	0.825436i	$0.690929\pi$
$312$		0			0
$313$	−770.000			−0.139051			−0.0695255	−	0.997580i	$-0.522149\pi$
$313$	−770.000			−0.139051			−0.0695255	+	0.997580i	$0.522149\pi$
$314$	2656.97	+	4602.00i	0.477520	+	0.827089i
$315$	3432.00	+	5944.40i	0.613877	+	1.06327i
$316$	2488.00	−	4309.34i	0.442914	−	0.767150i
$317$	8057.50			1.42762			0.713808	−	0.700341i	$-0.246969\pi$
$317$	8057.50			1.42762			0.713808	+	0.700341i	$0.246969\pi$
$318$	5164.98	−	8946.00i	0.910810	−	1.57757i
$319$	−776.825	+	1345.50i	−0.136344	+	0.236155i
$320$	886.810			0.154919
$321$	−892.500	+	1545.86i	−0.155185	+	0.268789i
$322$	−2223.00	−	3850.35i	−0.384730	−	0.666371i
$323$	−1192.52	−	2065.50i	−0.205429	−	0.355813i
$324$	−3356.00			−0.575446
$325$		0			0
$326$	5658.00			0.961250
$327$	−2133.89	−	3696.00i	−0.360869	−	0.625044i
$328$	2724.00	+	4718.11i	0.458560	+	0.794250i
$329$	3861.00	−	6687.45i	0.647002	−	1.12064i
$330$	7565.60			1.26204
$331$	2638.78	−	4570.50i	0.438189	−	0.758965i	−0.559361	−	0.828924i	$-0.688954\pi$
$331$	2638.78	−	4570.50i	0.438189	−	0.758965i	0.997550	+	0.0699590i	$0.0222869\pi$
$332$	852.169	−	1476.00i	0.140870	−	0.243994i
$333$	−876.418			−0.144226
$334$	−2817.00	+	4879.19i	−0.461495	+	0.799333i
$335$	1140.00	+	1974.54i	0.185925	+	0.322031i
$336$	6304.66	+	10920.0i	1.02365	+	1.77302i
$337$	−8278.00			−1.33808			−0.669038	−	0.743228i	$-0.733294\pi$
$337$	−8278.00			−1.33808			−0.669038	+	0.743228i	$0.733294\pi$
$338$		0			0
$339$	−2877.00			−0.460936
$340$	748.246	+	1296.00i	0.119351	+	0.206722i
$341$	−819.000	−	1418.55i	−0.130063	−	0.225275i
$342$	3366.00	−	5830.08i	0.532200	−	0.921798i
$343$	4030.48			0.634477
$344$	588.897	−	1020.00i	0.0923000	−	0.159868i
$345$	−2764.35	+	4788.00i	−0.431385	+	0.747180i
$346$	3024.16			0.469884
$347$	−3433.50	+	5947.00i	−0.531181	+	0.920033i	0.468156	+	0.883646i	$0.344918\pi$
$347$	−3433.50	+	5947.00i	−0.531181	+	0.920033i	−0.999338	+	0.0363875i	$0.988415\pi$
$348$	−966.000	−	1673.16i	−0.148802	−	0.257732i
$349$	−6076.90	−	10525.5i	−0.932060	−	1.61438i	−0.779794	−	0.626036i	$-0.784676\pi$
$349$	−6076.90	−	10525.5i	−0.932060	−	1.61438i	−0.152266	−	0.988340i	$-0.548657\pi$
$350$	−5226.00			−0.798118
$351$		0			0
$352$	3744.00			0.566920
$353$	2903.78	+	5029.50i	0.437827	+	0.758338i	0.997522	−	0.0703608i	$-0.0224151\pi$
$353$	2903.78	+	5029.50i	0.437827	+	0.758338i	−0.559695	+	0.828699i	$0.689082\pi$
$354$	231.000	+	400.104i	0.0346822	+	0.0600714i
$355$	−4044.00	+	7004.41i	−0.604601	+	1.04720i
$356$	1226.29			0.182566
$357$	2127.82	−	3685.50i	0.315452	−	0.546379i
$358$	−2229.15	+	3861.00i	−0.329090	+	0.570001i
$359$	−1340.61			−0.197088			−0.0985439	−	0.995133i	$-0.531419\pi$
$359$	−1340.61			−0.197088			−0.0985439	+	0.995133i	$0.531419\pi$
$360$	2112.00	−	3658.09i	0.309200	−	0.535551i
$361$	−472.000	−	817.528i	−0.0688147	−	0.119191i
$362$	3.46410	+	6.00000i	0.000502953	+	0.000871141i
$363$	5768.00			0.833999
$364$		0			0
$365$	−13920.0			−1.99618
$366$	−206.114	−	357.000i	−0.0294365	−	0.0509855i
$367$	−1832.50	−	3173.98i	−0.260642	−	0.451446i	0.705770	−	0.708441i	$-0.250601\pi$
$367$	−1832.50	−	3173.98i	−0.260642	−	0.451446i	−0.966413	+	0.256995i	$0.917268\pi$
$368$	−2280.00	+	3949.08i	−0.322971	+	0.559402i
$369$	8649.86			1.22031
$370$	956.092	−	1656.00i	0.134337	−	0.232679i
$371$	4796.05	−	8307.00i	0.671155	−	1.16247i
$372$	2036.89			0.283892
$373$	−2685.50	+	4651.42i	−0.372788	+	0.645688i	−0.989993	−	0.141114i	$-0.954931\pi$
$373$	−2685.50	+	4651.42i	−0.372788	+	0.645688i	0.617205	+	0.786802i	$0.288265\pi$
$374$	−1053.00	−	1823.85i	−0.145586	−	0.252163i
$375$	−2812.85	−	4872.00i	−0.387347	−	0.670904i
$376$	−4752.00			−0.651770
$377$		0			0
$378$	−2730.00			−0.371471
$379$	−5754.74	−	9967.50i	−0.779950	−	1.35091i	−0.931970	−	0.362536i	$-0.881911\pi$
$379$	−5754.74	−	9967.50i	−0.779950	−	1.35091i	0.152020	−	0.988377i	$-0.451422\pi$
$380$	2448.00	+	4240.06i	0.330473	+	0.572396i
$381$	7850.50	−	13597.5i	1.05563	−	1.82840i
$382$	−9841.51			−1.31816
$383$	−1209.84	+	2095.50i	−0.161409	+	0.279569i	−0.935374	−	0.353659i	$-0.884937\pi$
$383$	−1209.84	+	2095.50i	−0.161409	+	0.279569i	0.773965	+	0.633228i	$0.218271\pi$
$384$	5431.71	−	9408.00i	0.721838	−	1.25026i
$385$	7025.20			0.929967
$386$	7353.00	−	12735.8i	0.969580	−	1.67936i
$387$	−935.000	−	1619.47i	−0.122813	−	0.212719i
$388$	−2469.90	−	4278.00i	−0.323171	−	0.559749i
$389$	9858.00			1.28489			0.642443	−	0.766334i	$-0.277921\pi$
$389$	9858.00			1.28489			0.642443	+	0.766334i	$0.277921\pi$
$390$		0			0
$391$	1539.00			0.199055
$392$	1136.23	+	1968.00i	0.146398	+	0.253569i
$393$	−1302.00	−	2255.13i	−0.167118	−	0.289456i
$394$	4767.00	−	8256.69i	0.609538	−	1.05575i
$395$	−17237.4			−2.19571
$396$	990.733	−	1716.00i	0.125723	−	0.217758i
$397$	−4360.44	+	7552.50i	−0.551245	+	0.954784i	0.446941	+	0.894564i	$0.352514\pi$
$397$	−4360.44	+	7552.50i	−0.551245	+	0.954784i	−0.998185	+	0.0602200i	$0.980820\pi$
$398$	5837.01			0.735133
$399$	6961.50	−	12057.7i	0.873461	−	1.51288i
$400$	2680.00	+	4641.90i	0.335000	+	0.580237i
$401$	3792.33	+	6568.50i	0.472269	+	0.817993i	0.999496	−	0.0317308i	$-0.0101019\pi$
$401$	3792.33	+	6568.50i	0.472269	+	0.817993i	−0.527228	+	0.849724i	$0.676769\pi$
$402$	3990.00			0.495033
$403$		0			0
$404$	−7836.00			−0.964989
$405$	5812.76	+	10068.0i	0.713181	+	1.23527i
$406$	−2691.00	−	4660.95i	−0.328946	−	0.569751i
$407$	−448.500	+	776.825i	−0.0546224	+	0.0946088i
$408$	−2618.86			−0.317777
$409$	−2152.07	+	3727.50i	−0.260179	+	0.450643i	−0.966289	−	0.257459i	$-0.917115\pi$
$409$	−2152.07	+	3727.50i	−0.260179	+	0.450643i	0.706110	+	0.708102i	$0.250448\pi$
$410$	−9436.21	+	16344.0i	−1.13664	+	1.96871i
$411$	−8329.43			−0.999661
$412$	3712.00	−	6429.37i	0.443876	−	0.768817i
$413$	214.500	+	371.525i	0.0255565	+	0.0442652i
$414$	2171.99	+	3762.00i	0.257844	+	0.446600i
$415$	−5904.00			−0.698352
$416$		0			0
$417$	17815.0			2.09210
$418$	−3445.05	−	5967.00i	−0.403117	−	0.698219i
$419$	−2698.50	−	4673.94i	−0.314631	−	0.544957i	0.664728	−	0.747085i	$-0.268547\pi$
$419$	−2698.50	−	4673.94i	−0.314631	−	0.544957i	−0.979359	+	0.202129i	$0.935214\pi$
$420$	−4368.00	+	7565.60i	−0.507468	+	0.878960i
$421$	7260.76			0.840541			0.420270	−	0.907399i	$-0.361935\pi$
$421$	7260.76			0.840541			0.420270	+	0.907399i	$0.361935\pi$
$422$	−2911.58	+	5043.00i	−0.335861	+	0.581728i
$423$	−3772.41	+	6534.00i	−0.433619	+	0.751050i
$424$	−5902.83			−0.676101
$425$	904.500	−	1566.64i	0.103235	−	0.178808i
$426$	7077.00	+	12257.7i	0.804887	+	1.39410i
$427$	−191.392	−	331.500i	−0.0216911	−	0.0375700i
$428$	−1020.00			−0.115195
$429$		0			0
$430$	4080.00			0.457570
$431$	−243.353	−	421.500i	−0.0271970	−	0.0471066i	0.852107	−	0.523368i	$-0.175325\pi$
$431$	−243.353	−	421.500i	−0.0271970	−	0.0471066i	−0.879304	+	0.476262i	$0.841991\pi$
$432$	1400.00	+	2424.87i	0.155920	+	0.270062i
$433$	6069.50	−	10512.7i	0.673629	−	1.16676i	−0.303238	−	0.952915i	$-0.598068\pi$
$433$	6069.50	−	10512.7i	0.673629	−	1.16676i	0.976867	−	0.213846i	$-0.0685989\pi$
$434$	5674.20			0.627581
$435$	−3346.32	+	5796.00i	−0.368836	+	0.638844i
$436$	1219.36	−	2112.00i	0.133938	−	0.231987i
$437$	5035.07			0.551167
$438$	−12180.0	+	21096.4i	−1.32873	+	2.30142i
$439$	230.500	+	399.238i	0.0250596	+	0.0434045i	0.878283	−	0.478141i	$-0.158689\pi$
$439$	230.500	+	399.238i	0.0250596	+	0.0434045i	−0.853224	+	0.521545i	$0.825356\pi$
$440$	−2161.60	−	3744.00i	−0.234205	−	0.405655i
$441$	3608.00			0.389591
$442$		0			0
$443$	12156.0			1.30372			0.651861	−	0.758338i	$-0.273988\pi$
$443$	12156.0			1.30372			0.651861	+	0.758338i	$0.273988\pi$
$444$	−557.720	−	966.000i	−0.0596131	−	0.103253i
$445$	−2124.00	−	3678.88i	−0.226263	−	0.391900i
$446$	−7095.00	+	12288.9i	−0.753269	+	1.30470i
$447$	−9129.64			−0.966034
$448$	720.533	−	1248.00i	0.0759866	−	0.131613i
$449$	−148.090	+	256.500i	−0.0155653	+	0.0269599i	−0.873703	−	0.486459i	$-0.838288\pi$
$449$	−148.090	+	256.500i	−0.0155653	+	0.0269599i	0.858138	+	0.513419i	$0.171621\pi$
$450$	5106.09			0.534896
$451$	4426.50	−	7666.92i	0.462164	−	0.800491i
$452$	−822.000	−	1423.75i	−0.0855390	−	0.148158i
$453$	303.109	+	525.000i	0.0314377	+	0.0544518i
$454$	1518.00			0.156924
$455$		0			0
$456$	−8568.00			−0.879898
$457$	305.707	+	529.500i	0.0312918	+	0.0541990i	0.881247	−	0.472656i	$-0.156705\pi$
$457$	305.707	+	529.500i	0.0312918	+	0.0541990i	−0.849955	+	0.526855i	$0.823371\pi$
$458$	312.000	+	540.400i	0.0318314	+	0.0551337i
$459$	472.500	−	818.394i	0.0480488	−	0.0832230i
$460$	−3159.26			−0.320220
$461$	6563.61	−	11368.5i	0.663119	−	1.14855i	−0.316673	−	0.948535i	$-0.602566\pi$
$461$	6563.61	−	11368.5i	0.663119	−	1.14855i	0.979792	−	0.200020i	$-0.0641008\pi$
$462$	6147.05	−	10647.0i	0.619019	−	1.07217i
$463$	834.848			0.0837985			0.0418992	−	0.999122i	$-0.486659\pi$
$463$	834.848			0.0837985			0.0418992	+	0.999122i	$0.486659\pi$
$464$	−2760.00	+	4780.46i	−0.276142	+	0.478292i
$465$	−3528.00	−	6110.68i	−0.351843	−	0.609410i
$466$	−10007.8	−	17334.0i	−0.994854	−	1.72314i
$467$	−14496.0			−1.43639			−0.718196	−	0.695841i	$-0.755032\pi$
$467$	−14496.0			−1.43639			−0.718196	+	0.695841i	$0.755032\pi$
$468$		0			0
$469$	3705.00			0.364778
$470$	−8230.71	−	14256.0i	−0.807775	−	1.39911i
$471$	−5369.00	−	9299.38i	−0.525245	−	0.909751i
$472$	132.000	−	228.631i	0.0128724	−	0.0222957i
$473$	−1913.92			−0.186051
$474$	−15082.7	+	26124.0i	−1.46154	+	2.53147i
$475$	2959.21	−	5125.50i	0.285848	−	0.495103i
$476$	2431.80			0.234162
$477$	−4686.00	+	8116.39i	−0.449805	+	0.779086i
$478$	3222.00	+	5580.67i	0.308307	+	0.534004i
$479$	4448.77	+	7705.50i	0.424362	+	0.735017i	0.996361	−	0.0852376i	$-0.0271649\pi$
$479$	4448.77	+	7705.50i	0.424362	+	0.735017i	−0.571998	+	0.820255i	$0.693832\pi$
$480$	16128.0			1.53362
$481$		0			0
$482$	−7134.00			−0.674159
$483$	4492.07	+	7780.50i	0.423181	+	0.732971i
$484$	1648.00	+	2854.42i	0.154771	+	0.268071i
$485$	−8556.00	+	14819.4i	−0.801047	+	1.38745i
$486$	17071.1			1.59333
$487$	−2377.24	+	4117.50i	−0.221197	+	0.383125i	−0.955172	−	0.296052i	$-0.904330\pi$
$487$	−2377.24	+	4117.50i	−0.221197	+	0.383125i	0.733975	+	0.679177i	$0.237663\pi$
$488$	−117.779	+	204.000i	−0.0109255	+	0.0189235i
$489$	−11433.3			−1.05732
$490$	−3936.00	+	6817.35i	−0.362878	+	0.628524i
$491$	−817.500	−	1415.95i	−0.0751390	−	0.130145i	0.826008	−	0.563659i	$-0.190607\pi$
$491$	−817.500	−	1415.95i	−0.0751390	−	0.130145i	−0.901147	+	0.433514i	$0.857273\pi$
$492$	5504.46	+	9534.00i	0.504390	+	0.873630i
$493$	1863.00			0.170193
$494$		0			0
$495$	−6864.00			−0.623260
$496$	−2909.85	−	5040.00i	−0.263419	−	0.456255i
$497$	6571.50	+	11382.2i	0.593103	+	1.02728i
$498$	−5166.00	+	8947.77i	−0.464847	+	0.805139i
$499$	−14434.9			−1.29498			−0.647490	−	0.762074i	$-0.724181\pi$
$499$	−14434.9			−1.29498			−0.647490	+	0.762074i	$0.724181\pi$
$500$	1607.34	−	2784.00i	0.143765	−	0.249009i
$501$	5692.38	−	9859.50i	0.507619	−	0.879222i
$502$	−15557.3			−1.38318
$503$	−6343.50	+	10987.3i	−0.562312	+	0.973952i	0.434983	+	0.900439i	$0.356754\pi$
$503$	−6343.50	+	10987.3i	−0.562312	+	0.973952i	−0.997294	+	0.0735133i	$0.976579\pi$
$504$	−3432.00	−	5944.40i	−0.303320	−	0.525366i
$505$	13572.4	+	23508.0i	1.19596	+	2.07147i
$506$	4446.00			0.390610
$507$		0			0
$508$	8972.00			0.783599
$509$	−2874.34	−	4978.50i	−0.250300	−	0.433533i	0.713308	−	0.700850i	$-0.247196\pi$
$509$	−2874.34	−	4978.50i	−0.250300	−	0.433533i	−0.963608	+	0.267318i	$0.913863\pi$
$510$	−4536.00	−	7856.58i	−0.393838	−	0.682148i
$511$	−11310.0	+	19589.5i	−0.979109	+	1.69587i
$512$	4434.05			0.382733
$513$	1545.86	−	2677.50i	0.133043	−	0.230438i
$514$	9441.41	−	16353.0i	0.810200	−	1.40331i
$515$	−25717.5			−2.20048
$516$	1190.00	−	2061.14i	0.101525	−	0.175846i
$517$	3861.00	+	6687.45i	0.328446	+	0.568885i
$518$	−1553.65	−	2691.00i	−0.131783	−	0.228254i
$519$	−6111.00			−0.516846
$520$		0			0
$521$	6054.00			0.509080			0.254540	−	0.967062i	$-0.418076\pi$
$521$	6054.00			0.509080			0.254540	+	0.967062i	$0.418076\pi$
$522$	2629.25	+	4554.00i	0.220458	+	0.381845i
$523$	7401.50	+	12819.8i	0.618824	+	1.07183i	0.989701	+	0.143153i	$0.0457240\pi$
$523$	7401.50	+	12819.8i	0.618824	+	1.07183i	−0.370877	+	0.928682i	$0.620943\pi$
$524$	744.000	−	1288.65i	0.0620263	−	0.107433i
$525$	10560.3			0.877885
$526$	1356.20	−	2349.00i	0.112420	−	0.194717i
$527$	−982.073	+	1701.00i	−0.0811760	+	0.140601i
$528$	−12609.3			−1.03930
$529$	4459.00	−	7723.21i	0.366483	−	0.634767i
$530$	−10224.0	−	17708.5i	−0.837929	−	1.45133i
$531$	−209.578	−	363.000i	−0.0171279	−	0.0296664i
$532$	7956.00			0.648377
$533$		0			0
$534$	−7434.00			−0.602436
$535$	1766.69	+	3060.00i	0.142768	+	0.247281i
$536$	−1140.00	−	1974.54i	−0.0918666	−	0.159118i
$537$	4504.50	−	7802.02i	0.361980	−	0.626969i
$538$	−17615.0			−1.41159
$539$	1846.37	−	3198.00i	0.147548	−	0.255561i
$540$	−969.948	+	1680.00i	−0.0772962	+	0.133881i
$541$	21470.5			1.70626			0.853132	−	0.521695i	$-0.174700\pi$
$541$	21470.5			1.70626			0.853132	+	0.521695i	$0.174700\pi$
$542$	2295.00	−	3975.06i	0.181880	−	0.315025i
$543$	−7.00000	−	12.1244i	−0.000553221	−	0.000958206i
$544$	−2244.74	−	3888.00i	−0.176916	−	0.306428i
$545$	−8448.00			−0.663986
$546$		0			0
$547$	−13516.0			−1.05649			−0.528247	−	0.849091i	$-0.677151\pi$
$547$	−13516.0			−1.05649			−0.528247	+	0.849091i	$0.677151\pi$
$548$	−2379.84	−	4122.00i	−0.185514	−	0.321320i
$549$	187.000	+	323.894i	0.0145373	+	0.0251793i
$550$	2613.00	−	4525.85i	0.202579	−	0.350878i
$551$	6095.09			0.471251
$552$	2764.35	−	4788.00i	0.213150	−	0.369186i
$553$	−14005.4	+	24258.0i	−1.07698	+	1.86538i
$554$	11850.7			0.908822
$555$	−1932.00	+	3346.32i	−0.147764	+	0.255934i
$556$	5090.00	+	8816.14i	0.388245	+	0.672460i
$557$	−1445.40	−	2503.50i	−0.109952	−	0.190443i	0.805798	−	0.592190i	$-0.201736\pi$
$557$	−1445.40	−	2503.50i	−0.109952	−	0.190443i	−0.915751	+	0.401747i	$0.868403\pi$
$558$	−5544.00			−0.420603
$559$		0			0
$560$	24960.0			1.88349
$561$	2127.82	+	3685.50i	0.160137	+	0.277365i
$562$	1404.00	+	2431.80i	0.105381	+	0.182525i
$563$	5791.50	−	10031.2i	0.433539	−	0.750912i	−0.563636	−	0.826023i	$-0.690598\pi$
$563$	5791.50	−	10031.2i	0.433539	−	0.750912i	0.997175	+	0.0751113i	$0.0239312\pi$
$564$	−9602.49			−0.716911
$565$	−2847.49	+	4932.00i	−0.212026	+	0.367240i
$566$	12430.9	−	21531.0i	0.923164	−	1.59897i
$567$	18891.5			1.39924
$568$	4044.00	−	7004.41i	0.298737	−	0.517427i
$569$	6439.50	+	11153.5i	0.474443	+	0.821759i	0.999572	−	0.0292638i	$-0.00931628\pi$
$569$	6439.50	+	11153.5i	0.474443	+	0.821759i	−0.525129	+	0.851023i	$0.675983\pi$
$570$	−14840.2	−	25704.0i	−1.09051	−	1.88881i
$571$	11636.0			0.852805			0.426402	−	0.904534i	$-0.359781\pi$
$571$	11636.0			0.852805			0.426402	+	0.904534i	$0.359781\pi$
$572$		0			0
$573$	19887.0			1.44990
$574$	15333.8	+	26559.0i	1.11502	+	1.93127i
$575$	1909.50	+	3307.35i	0.138490	+	0.239871i
$576$	−704.000	+	1219.36i	−0.0509259	+	0.0882063i
$577$	12311.4			0.888269			0.444134	−	0.895960i	$-0.353511\pi$
$577$	12311.4			0.888269			0.444134	+	0.895960i	$0.353511\pi$
$578$	7246.90	−	12552.0i	0.521507	−	0.903277i
$579$	−14858.4	+	25735.5i	−1.06648	+	1.84720i
$580$	−3824.37			−0.273790
$581$	−4797.00	+	8308.65i	−0.342535	+	0.593289i
$582$	14973.0	+	25934.0i	1.06641	+	1.84708i
$583$	4796.05	+	8307.00i	0.340707	+	0.590121i
$584$	13920.0			0.986325
$585$		0			0
$586$	−32262.0			−2.27428
$587$	−7822.81	−	13549.5i	−0.550054	−	0.952722i	−0.998270	−	0.0587964i	$-0.981274\pi$
$587$	−7822.81	−	13549.5i	−0.550054	−	0.952722i	0.448216	−	0.893925i	$-0.352060\pi$
$588$	2296.00	+	3976.79i	0.161030	+	0.278912i
$589$	−3213.00	+	5565.08i	−0.224770	+	0.389313i
$590$	914.523			0.0638141
$591$	−9632.80	+	16684.5i	−0.670458	+	1.16127i
$592$	−1593.49	+	2760.00i	−0.110628	+	0.191614i
$593$	−25821.4			−1.78813			−0.894063	−	0.447942i	$-0.852157\pi$
$593$	−25821.4			−1.78813			−0.894063	+	0.447942i	$0.852157\pi$
$594$	1365.00	−	2364.25i	0.0942873	−	0.163310i
$595$	−4212.00	−	7295.40i	−0.290210	−	0.502659i
$596$	−2608.47	−	4518.00i	−0.179274	−	0.310511i
$597$	−11795.0			−0.808605
$598$		0			0
$599$	1668.00			0.113777			0.0568887	−	0.998381i	$-0.481882\pi$
$599$	1668.00			0.113777			0.0568887	+	0.998381i	$0.481882\pi$
$600$	−3249.33	−	5628.00i	−0.221089	−	0.382937i
$601$	−6849.50	−	11863.7i	−0.464887	−	0.805207i	0.534310	−	0.845289i	$-0.320572\pi$
$601$	−6849.50	−	11863.7i	−0.464887	−	0.805207i	−0.999196	+	0.0400813i	$0.987238\pi$
$602$	3315.00	−	5741.75i	0.224434	−	0.388731i
$603$	−3619.99			−0.244473
$604$	−173.205	+	300.000i	−0.0116682	+	0.0202100i
$605$	5708.84	−	9888.00i	0.383632	−	0.664470i
$606$	47503.2			3.18430
$607$	11586.5	−	20068.4i	0.774764	−	1.34193i	−0.160164	−	0.987090i	$-0.551202\pi$
$607$	11586.5	−	20068.4i	0.774764	−	1.34193i	0.934927	−	0.354839i	$-0.115464\pi$
$608$	−7344.00	−	12720.2i	−0.489866	−	0.848473i
$609$	5437.77	+	9418.50i	0.361822	+	0.626694i
$610$	−816.000			−0.0541621
$611$		0			0
$612$	−2376.00			−0.156935
$613$	8307.78	+	14389.5i	0.547387	+	0.948102i	0.998453	+	0.0556111i	$0.0177107\pi$
$613$	8307.78	+	14389.5i	0.547387	+	0.948102i	−0.451066	+	0.892491i	$0.648956\pi$
$614$	−8274.00	−	14331.0i	−0.543830	−	0.941941i
$615$	19068.0	−	33026.7i	1.25024	−	2.16547i
$616$	−7025.20			−0.459502
$617$	−14196.8	+	24589.5i	−0.926321	+	1.60443i	−0.136897	+	0.990585i	$0.543713\pi$
$617$	−14196.8	+	24589.5i	−0.926321	+	1.60443i	−0.789423	+	0.613849i	$0.789620\pi$
$618$	−22502.8	+	38976.0i	−1.46472	+	2.53697i
$619$	6245.78			0.405556			0.202778	−	0.979225i	$-0.435003\pi$
$619$	6245.78			0.405556			0.202778	+	0.979225i	$0.435003\pi$
$620$	2016.00	−	3491.81i	0.130588	−	0.226185i
$621$	997.500	+	1727.72i	0.0644578	+	0.111644i
$622$	10724.9	+	18576.0i	0.691363	+	1.19748i
$623$	−6903.00			−0.443921
$624$		0			0
$625$	−19511.0			−1.24870
$626$	1333.68	+	2310.00i	0.0851510	+	0.147486i
$627$	6961.50	+	12057.7i	0.443406	+	0.768002i
$628$	3068.00	−	5313.93i	0.194947	−	0.337658i
$629$	1075.60			0.0681830
$630$	11888.8	−	20592.0i	0.751843	−	1.30223i
$631$	11189.9	−	19381.5i	0.705964	−	1.22277i	−0.260378	−	0.965507i	$-0.583847\pi$
$631$	11189.9	−	19381.5i	0.705964	−	1.22277i	0.966342	−	0.257259i	$-0.0828194\pi$
$632$	17237.4			1.08491
$633$	5883.50	−	10190.5i	0.369428	−	0.639869i
$634$	−13956.0	−	24172.5i	−0.874233	−	1.51422i
$635$	−15540.0	−	26916.0i	−0.971157	−	1.68209i
$636$	−11928.0			−0.743673
$637$		0			0
$638$	5382.00			0.333974
$639$	−6420.71	−	11121.0i	−0.397495	−	0.688482i
$640$	−10752.0	−	18623.0i	−0.664078	−	1.15022i
$641$	9913.50	−	17170.7i	0.610858	−	1.05804i	−0.380239	−	0.924888i	$-0.624158\pi$
$641$	9913.50	−	17170.7i	0.610858	−	1.05804i	0.991096	−	0.133148i	$-0.0425085\pi$
$642$	6183.42			0.380125
$643$	4225.34	−	7318.50i	0.259146	−	0.448855i	−0.706867	−	0.707346i	$-0.749892\pi$
$643$	4225.34	−	7318.50i	0.259146	−	0.448855i	0.966013	+	0.258492i	$0.0832255\pi$
$644$	−2566.90	+	4446.00i	−0.157065	+	0.272045i
$645$	−8244.56			−0.503301
$646$	−4131.00	+	7155.10i	−0.251598	+	0.435780i
$647$	1474.50	+	2553.91i	0.0895959	+	0.155185i	0.907340	−	0.420397i	$-0.138109\pi$
$647$	1474.50	+	2553.91i	0.0895959	+	0.155185i	−0.817744	+	0.575581i	$0.804776\pi$
$648$	−5812.76	−	10068.0i	−0.352387	−	0.610352i
$649$	−429.000			−0.0259472
$650$		0			0
$651$	−11466.0			−0.690304
$652$	−3266.65	−	5658.00i	−0.196214	−	0.339853i
$653$	−6019.50	−	10426.1i	−0.360737	−	0.624815i	0.627345	−	0.778741i	$-0.284141\pi$
$653$	−6019.50	−	10426.1i	−0.360737	−	0.624815i	−0.988082	+	0.153926i	$0.950808\pi$
$654$	−7392.00	+	12803.3i	−0.441973	+	0.765519i
$655$	−5154.58			−0.307490
$656$	15727.0	−	27240.0i	0.936032	−	1.62126i
$657$	11050.5	−	19140.0i	0.656196	−	1.13656i
$658$	−26749.8			−1.58483
$659$	−1681.50	+	2912.44i	−0.0993960	+	0.172159i	−0.911435	−	0.411445i	$-0.865024\pi$
$659$	−1681.50	+	2912.44i	−0.0993960	+	0.172159i	0.812039	+	0.583603i	$0.198358\pi$
$660$	−4368.00	−	7565.60i	−0.257612	−	0.446198i
$661$	−5079.24	−	8797.50i	−0.298880	−	0.517675i	0.677000	−	0.735983i	$-0.263280\pi$
$661$	−5079.24	−	8797.50i	−0.298880	−	0.517675i	−0.975880	+	0.218308i	$0.929946\pi$
$662$	−18282.0			−1.07334
$663$		0			0
$664$	5904.00			0.345060
$665$	−13780.2	−	23868.0i	−0.803569	−	1.39182i
$666$	1518.00	+	2629.25i	0.0883203	+	0.152975i
$667$	−1966.50	+	3406.08i	−0.114158	+	0.197727i
$668$	6505.58			0.376809
$669$	14337.1	−	24832.5i	0.828554	−	1.43510i
$670$	3949.08	−	6840.00i	0.227711	−	0.394406i
$671$	382.783			0.0220226
$672$	13104.0	−	22696.8i	0.752229	−	1.30290i
$673$	−9084.50	−	15734.8i	−0.520329	−	0.901237i	−0.999721	−	0.0236358i	$-0.992476\pi$
$673$	−9084.50	−	15734.8i	−0.520329	−	0.901237i	0.479391	−	0.877601i	$-0.340858\pi$
$674$	14337.9	+	24834.0i	0.819400	+	1.41924i
$675$	2345.00			0.133717
$676$		0			0
$677$	9042.00			0.513312			0.256656	−	0.966503i	$-0.417379\pi$
$677$	9042.00			0.513312			0.256656	+	0.966503i	$0.417379\pi$
$678$	4983.11	+	8631.00i	0.282264	+	0.488896i
$679$	13903.5	+	24081.6i	0.785813	+	1.36107i
$680$	−2592.00	+	4489.48i	−0.146175	+	0.253182i
$681$	−3067.46			−0.172607
$682$	−2837.10	+	4914.00i	−0.159293	+	0.275904i
$683$	−6231.05	+	10792.5i	−0.349084	+	0.604632i	−0.986087	−	0.166230i	$-0.946841\pi$
$683$	−6231.05	+	10792.5i	−0.349084	+	0.604632i	0.637003	+	0.770862i	$0.280174\pi$
$684$	−7773.44			−0.434540
$685$	−8244.00	+	14279.0i	−0.459835	+	0.796458i
$686$	−6981.00	−	12091.4i	−0.388536	−	0.672964i
$687$	−630.466	−	1092.00i	−0.0350128	−	0.0606440i
$688$	−6800.00			−0.376813
$689$		0			0
$690$	19152.0			1.05667
$691$	−2159.00	−	3739.50i	−0.118860	−	0.205872i	0.800456	−	0.599391i	$-0.204591\pi$
$691$	−2159.00	−	3739.50i	−0.118860	−	0.205872i	−0.919316	+	0.393520i	$0.871257\pi$
$692$	−1746.00	−	3024.16i	−0.0959147	−	0.166129i
$693$	−5577.00	+	9659.65i	−0.305704	+	0.529494i
$694$	23788.0			1.30112
$695$	17632.3	−	30540.0i	0.962346	−	1.66683i
$696$	3346.32	−	5796.00i	0.182244	−	0.315656i
$697$	−10615.7			−0.576901
$698$	−21051.0	+	36461.4i	−1.14154	+	1.97720i
$699$	20223.0	+	35027.3i	1.09428	+	1.89535i
$700$	3017.23	+	5226.00i	0.162915	+	0.282177i
$701$	18270.0			0.984377			0.492189	−	0.870489i	$-0.336197\pi$
$701$	18270.0			0.984377			0.492189	+	0.870489i	$0.336197\pi$
$702$		0			0
$703$	3519.00			0.188793
$704$	720.533	+	1248.00i	0.0385740	+	0.0668122i
$705$	16632.0	+	28807.5i	0.888507	+	1.53894i
$706$	10059.0	−	17422.7i	0.536226	−	0.928770i
$707$	44110.1			2.34644
$708$	266.736	−	462.000i	0.0141590	−	0.0245240i
$709$	814.930	−	1411.50i	0.0431669	−	0.0747673i	−0.843635	−	0.536918i	$-0.819589\pi$
$709$	814.930	−	1411.50i	0.0431669	−	0.0747673i	0.886802	+	0.462150i	$0.152922\pi$
$710$	28017.7			1.48096
$711$	13684.0	−	23701.4i	0.721786	−	1.25017i
$712$	2124.00	+	3678.88i	0.111798	+	0.193640i
$713$	−2073.26	−	3591.00i	−0.108898	−	0.188617i
$714$	−14742.0			−0.772697
$715$		0			0
$716$	5148.00			0.268701
$717$	−6510.78	−	11277.0i	−0.339121	−	0.587374i
$718$	2322.00	+	4021.82i	0.120691	+	0.209043i
$719$	4915.50	−	8513.90i	0.254961	−	0.441606i	−0.709924	−	0.704279i	$-0.751271\pi$
$719$	4915.50	−	8513.90i	0.254961	−	0.441606i	0.964885	+	0.262673i	$0.0846039\pi$
$720$	−24387.3			−1.26231
$721$	−20895.5	+	36192.0i	−1.07932	+	1.86943i
$722$	−1635.06	+	2832.00i	−0.0842804	+	0.145978i
$723$	14415.9			0.741537
$724$	4.00000	−	6.92820i	0.000205330	−	0.000355642i
$725$	2311.50	+	4003.64i	0.118410	+	0.205091i
$726$	−9990.47	−	17304.0i	−0.510718	−	0.884589i
$727$	15464.0			0.788897			0.394448	−	0.918918i	$-0.370936\pi$
$727$	15464.0			0.788897			0.394448	+	0.918918i	$0.370936\pi$
$728$		0			0
$729$	−11843.0			−0.601687
$730$	24110.1	+	41760.0i	1.22241	+	2.11727i
$731$	1147.50	+	1987.53i	0.0580599	+	0.100563i
$732$	−238.000	+	412.228i	−0.0120174	+	0.0208147i
$733$	−12616.3			−0.635733			−0.317866	−	0.948136i	$-0.602966\pi$
$733$	−12616.3			−0.635733			−0.317866	+	0.948136i	$0.602966\pi$
$734$	−6347.97	+	10995.0i	−0.319220	+	0.552906i
$735$	7953.58	−	13776.0i	0.399146	−	0.691341i
$736$	9477.78			0.474668
$737$	−1852.50	+	3208.62i	−0.0925885	+	0.160368i
$738$	−14982.0	−	25949.6i	−0.747283	−	1.29433i
$739$	8141.50	+	14101.5i	0.405264	+	0.701938i	0.994352	−	0.106131i	$-0.0338463\pi$
$739$	8141.50	+	14101.5i	0.405264	+	0.701938i	−0.589088	+	0.808069i	$0.700513\pi$
$740$	−2208.00			−0.109686
$741$		0			0
$742$	−33228.0			−1.64399
$743$	5403.13	+	9358.50i	0.266786	+	0.462086i	0.968030	−	0.250835i	$-0.0807051\pi$
$743$	5403.13	+	9358.50i	0.266786	+	0.462086i	−0.701244	+	0.712921i	$0.747372\pi$
$744$	3528.00	+	6110.68i	0.173848	+	0.301113i
$745$	−9036.00	+	15650.8i	−0.444367	+	0.769666i
$746$	18605.7			0.913140
$747$	4686.93	−	8118.00i	0.229566	−	0.397620i
$748$	−1215.90	+	2106.00i	−0.0594354	+	0.102945i
$749$	5741.75			0.280105
$750$	−9744.00	+	16877.1i	−0.474401	+	0.821686i
$751$	−6807.50	−	11790.9i	−0.330771	−	0.572913i	0.651892	−	0.758312i	$-0.273976\pi$
$751$	−6807.50	−	11790.9i	−0.330771	−	0.572913i	−0.982663	+	0.185399i	$0.940642\pi$
$752$	13717.8	+	23760.0i	0.665210	+	1.15218i
$753$	31437.0			1.52142
$754$		0			0
$755$	1200.00			0.0578443
$756$	1576.17	+	2730.00i	0.0758262	+	0.131335i
$757$	−2775.50	−	4807.31i	−0.133259	−	0.230812i	0.791672	−	0.610947i	$-0.209211\pi$
$757$	−2775.50	−	4807.31i	−0.133259	−	0.230812i	−0.924931	+	0.380135i	$0.875878\pi$
$758$	−19935.0	+	34528.4i	−0.955240	+	1.65452i
$759$	−8984.15			−0.429649
$760$	−8480.12	+	14688.0i	−0.404745	+	0.701039i
$761$	5041.13	−	8731.50i	0.240133	−	0.415922i	−0.720619	−	0.693331i	$-0.756142\pi$
$761$	5041.13	−	8731.50i	0.240133	−	0.415922i	0.960752	+	0.277409i	$0.0894757\pi$
$762$	−54389.9			−2.58574
$763$	−6864.00	+	11888.8i	−0.325680	+	0.564093i
$764$	5682.00	+	9841.51i	0.269067	+	0.466039i
$765$	4115.35	+	7128.00i	0.194498	+	0.336880i
$766$	8382.00			0.395371
$767$		0			0
$768$	−34048.0			−1.59974
$769$	14879.2	+	25771.5i	0.697733	+	1.20851i	0.969250	+	0.246076i	$0.0791413\pi$
$769$	14879.2	+	25771.5i	0.697733	+	1.20851i	−0.271517	+	0.962434i	$0.587525\pi$
$770$	−12168.0	−	21075.6i	−0.569486	−	0.986379i
$771$	−19078.5	+	33044.9i	−0.891174	+	1.54356i
$772$	−16981.0			−0.791659
$773$	−13867.7	+	24019.5i	−0.645259	+	1.11762i	0.338983	+	0.940793i	$0.389917\pi$
$773$	−13867.7	+	24019.5i	−0.645259	+	1.11762i	−0.984242	+	0.176829i	$0.943416\pi$
$774$	−3238.94	+	5610.00i	−0.150415	+	0.260526i
$775$	−4873.99			−0.225908
$776$	8556.00	−	14819.4i	0.395802	−	0.685550i
$777$	3139.50	+	5437.77i	0.144954	+	0.251067i
$778$	−17074.6	−	29574.0i	−0.786828	−	1.36283i
$779$	−34731.0			−1.59739
$780$		0			0
$781$	−13143.0			−0.602168
$782$	−2665.63	−	4617.00i	−0.121896	−	0.211130i
$783$	1207.50	+	2091.45i	0.0551118	+	0.0954564i
$784$	6560.00	−	11362.3i	0.298834	−	0.517595i
$785$	−21255.7			−0.966432
$786$	−4510.26	+	7812.00i	−0.204676	+	0.354510i
$787$	−15774.7	+	27322.5i	−0.714493	+	1.23754i	0.248662	+	0.968590i	$0.420009\pi$
$787$	−15774.7	+	27322.5i	−0.714493	+	1.23754i	−0.963155	+	0.268947i	$0.913324\pi$
$788$	−11008.9			−0.497686
$789$	−2740.50	+	4746.69i	−0.123656	+	0.214178i
$790$	29856.0	+	51712.1i	1.34459	+	2.32890i
$791$	4627.17	+	8014.50i	0.207994	+	0.360256i
$792$	6864.00			0.307957
$793$		0			0
$794$	30210.0			1.35027
$795$	20659.9	+	35784.0i	0.921674	+	1.59639i
$796$	−3370.00	−	5837.01i	−0.150058	−	0.259909i
$797$	727.500	−	1260.07i	0.0323330	−	0.0560023i	−0.849406	−	0.527740i	$-0.823040\pi$
$797$	727.500	−	1260.07i	0.0323330	−	0.0560023i	0.881739	+	0.471737i	$0.156373\pi$
$798$	−48230.7			−2.13953
$799$	4629.77	−	8019.00i	0.204993	−	0.355059i
$800$	5570.28	−	9648.00i	0.246174	−	0.426385i
$801$	6744.61			0.297514
$802$	13137.0	−	22754.0i	0.578408	−	1.00183i
$803$	−11310.0	−	19589.5i	−0.497038	−	0.860894i
$804$	−2303.63	−	3990.00i	−0.101048	−	0.175020i
$805$	17784.0			0.778638
$806$		0			0
$807$	35595.0			1.55267
$808$	−13572.4	−	23508.0i	−0.590933	−	1.02353i
$809$	−829.500	−	1436.74i	−0.0360490	−	0.0624388i	0.847438	−	0.530894i	$-0.178144\pi$
$809$	−829.500	−	1436.74i	−0.0360490	−	0.0624388i	−0.883487	+	0.468456i	$0.844811\pi$
$810$	20136.0	−	34876.6i	0.873465	−	1.51289i
$811$	4402.87			0.190636			0.0953180	−	0.995447i	$-0.469613\pi$
$811$	4402.87			0.190636			0.0953180	+	0.995447i	$0.469613\pi$
$812$	−3107.30	+	5382.00i	−0.134292	+	0.232600i
$813$	−4637.57	+	8032.50i	−0.200057	+	0.346509i
$814$	3107.30			0.133797
$815$	−11316.0	+	19599.9i	−0.486359	+	0.842398i
$816$	7560.00	+	13094.3i	0.324330	+	0.561755i
$817$	3754.22	+	6502.50i	0.160763	+	0.278450i
$818$	14910.0			0.637306
$819$		0			0
$820$	21792.0			0.928061
$821$	−14350.9	−	24856.5i	−0.610049	−	1.05664i	−0.991232	−	0.132136i	$-0.957816\pi$
$821$	−14350.9	−	24856.5i	−0.610049	−	1.05664i	0.381183	−	0.924500i	$-0.375517\pi$
$822$	14427.0	+	24988.3i	0.612165	+	1.06030i
$823$	7889.50	−	13665.0i	0.334156	−	0.578776i	−0.649166	−	0.760647i	$-0.724882\pi$
$823$	7889.50	−	13665.0i	0.334156	−	0.578776i	0.983322	+	0.181871i	$0.0582153\pi$
$824$	25717.5			1.08727
$825$	−5280.16	+	9145.50i	−0.222826	+	0.385946i
$826$	743.050	−	1287.00i	0.0313003	−	0.0542136i
$827$	7354.29			0.309231			0.154615	−	0.987975i	$-0.450586\pi$
$827$	7354.29			0.309231			0.154615	+	0.987975i	$0.450586\pi$
$828$	2508.00	−	4343.98i	0.105265	−	0.182324i
$829$	8685.50	+	15043.7i	0.363884	+	0.630266i	0.988596	−	0.150589i	$-0.0481171\pi$
$829$	8685.50	+	15043.7i	0.363884	+	0.630266i	−0.624712	+	0.780855i	$0.714784\pi$
$830$	10226.0	+	17712.0i	0.427651	+	0.740714i
$831$	−23947.0			−0.999654
$832$		0			0
$833$	−4428.00			−0.184179
$834$	−30856.5	−	53445.0i	−1.28114	−	2.21900i
$835$	−11268.0	−	19516.7i	−0.467000	−	0.808868i
$836$	−3978.00	+	6890.10i	−0.164572	+	0.285047i
$837$	−2546.11			−0.105145
$838$	−9347.88	+	16191.0i	−0.385343	+	0.667433i
$839$	14737.2	−	25525.5i	0.606416	−	1.05034i	−0.385410	−	0.922745i	$-0.625940\pi$
$839$	14737.2	−	25525.5i	0.606416	−	1.05034i	0.991826	−	0.127598i	$-0.0407267\pi$
$840$	−30262.4			−1.24304
$841$	9814.00	−	16998.3i	0.402395	−	0.696968i
$842$	−12576.0	−	21782.3i	−0.514724	−	0.891528i
$843$	−2837.10	−	4914.00i	−0.115913	−	0.200768i
$844$	6724.00			0.274229
$845$		0			0
$846$	26136.0			1.06214
$847$	−9276.86	−	16068.0i	−0.376336	−	0.651834i
$848$	17040.0	+	29514.1i	0.690042	+	1.19519i
$849$	−25119.5	+	43508.3i	−1.01543	+	1.75877i
$850$	−6266.56			−0.252872
$851$	−1135.36	+	1966.50i	−0.0457340	+	0.0792136i
$852$	8171.82	−	14154.0i	0.328594	−	0.569141i
$853$	−2909.85			−0.116801			−0.0584005	−	0.998293i	$-0.518600\pi$
$853$	−2909.85			−0.116801			−0.0584005	+	0.998293i	$0.518600\pi$
$854$	−663.000	+	1148.35i	−0.0265660	+	0.0460137i
$855$	13464.0	+	23320.3i	0.538549	+	0.932794i
$856$	−1766.69	−	3060.00i	−0.0705424	−	0.122183i
$857$	5346.00			0.213087			0.106544	−	0.994308i	$-0.466022\pi$
$857$	5346.00			0.213087			0.106544	+	0.994308i	$0.466022\pi$
$858$		0			0
$859$	24244.0			0.962974			0.481487	−	0.876453i	$-0.340097\pi$
$859$	24244.0			0.962974			0.481487	+	0.876453i	$0.340097\pi$
$860$	−2355.59	−	4080.00i	−0.0934011	−	0.161775i
$861$	−30985.5	−	53668.5i	−1.22646	−	2.12429i
$862$	−843.000	+	1460.12i	−0.0333094	+	0.0576936i
$863$	32780.8			1.29301			0.646507	−	0.762908i	$-0.276229\pi$
$863$	32780.8			1.29301			0.646507	+	0.762908i	$0.276229\pi$
$864$	2909.85	−	5040.00i	0.114577	−	0.198454i
$865$	−6048.32	+	10476.0i	−0.237745	+	0.411786i
$866$	−42050.7			−1.65005
$867$	−14644.0	+	25364.2i	−0.573629	+	0.993555i
$868$	−3276.00	−	5674.20i	−0.128104	−	0.221883i
$869$	−14005.4	−	24258.0i	−0.546720	−	0.946946i
$870$	23184.0			0.903461
$871$		0			0
$872$	8448.00			0.328080
$873$	−13584.5	−	23529.0i	−0.526649	−	0.912183i
$874$	−8721.00	−	15105.2i	−0.337520	−	0.584601i
$875$	−9048.00	+	15671.6i	−0.349575	+	0.605482i
$876$	28128.5			1.08490
$877$	2271.58	−	3934.50i	0.0874640	−	0.151492i	−0.818974	−	0.573830i	$-0.805457\pi$
$877$	2271.58	−	3934.50i	0.0874640	−	0.151492i	0.906439	+	0.422338i	$0.138790\pi$
$878$	798.475	−	1383.00i	0.0306916	−	0.0531594i
$879$	65192.7			2.50159
$880$	−12480.0	+	21616.0i	−0.478069	+	0.828040i
$881$	−10258.5	−	17768.2i	−0.392302	−	0.679486i	0.600451	−	0.799661i	$-0.294988\pi$
$881$	−10258.5	−	17768.2i	−0.392302	−	0.679486i	−0.992753	+	0.120175i	$0.961654\pi$
$882$	−6249.24	−	10824.0i	−0.238575	−	0.413223i
$883$	23852.0			0.909042			0.454521	−	0.890736i	$-0.349811\pi$
$883$	23852.0			0.909042			0.454521	+	0.890736i	$0.349811\pi$
$884$		0			0
$885$	−1848.00			−0.0701919
$886$	−21054.8	−	36468.0i	−0.798364	−	1.38281i
$887$	−19378.5	−	33564.5i	−0.733558	−	1.27056i	−0.955353	−	0.295467i	$-0.904525\pi$
$887$	−19378.5	−	33564.5i	−0.733558	−	1.27056i	0.221794	−	0.975093i	$-0.428809\pi$
$888$	1932.00	−	3346.32i	0.0730109	−	0.126459i
$889$	−50504.9			−1.90538
$890$	−7357.75	+	12744.0i	−0.277115	+	0.479977i
$891$	−9445.74	+	16360.5i	−0.355156	+	0.615149i
$892$	16385.2			0.615042
$893$	15147.0	−	26235.4i	0.567609	−	0.983128i
$894$	15813.0	+	27388.9i	0.591573	+	1.02463i
$895$	−8916.60	−	15444.0i	−0.333016	−	0.576800i
$896$	−34944.0			−1.30290
$897$		0			0
$898$	1026.00			0.0381270
$899$	−2509.74	−	4347.00i	−0.0931085	−	0.161269i
$900$	−2948.00	−	5106.09i	−0.109185	−	0.189114i
$901$	5751.00	−	9961.02i	0.212645	−	0.368313i
$902$	−30667.7			−1.13206
$903$	−6698.71	+	11602.5i	−0.246865	+	0.427583i
$904$	2847.49	−	4932.00i	0.104763	−	0.181456i
$905$	−27.7128			−0.00101791
$906$	1050.00	−	1818.65i	0.0385032	−	0.0666895i
$907$	−19535.5	−	33836.5i	−0.715177	−	1.23872i	−0.962891	−	0.269890i	$-0.913013\pi$
$907$	−19535.5	−	33836.5i	−0.715177	−	1.23872i	0.247714	−	0.968833i	$-0.420321\pi$
$908$	−876.418	−	1518.00i	−0.0320319	−	0.0554808i
$909$	−43098.0			−1.57257
$910$		0			0
$911$	−53040.0			−1.92897			−0.964486	−	0.264134i	$-0.914914\pi$
$911$	−53040.0			−1.92897			−0.964486	+	0.264134i	$0.914914\pi$
$912$	24733.7	+	42840.0i	0.898042	+	1.55545i
$913$	−4797.00	−	8308.65i	−0.173886	−	0.301179i
$914$	1059.00	−	1834.24i	0.0383245	−	0.0663800i
$915$	1648.91			0.0595753
$916$	360.267	−	624.000i	0.0129951	−	0.0225082i
$917$	−4188.10	+	7254.00i	−0.150821	+	0.261230i
$918$	−3273.58			−0.117695
$919$	−183.500	+	317.831i	−0.00658662	+	0.0114084i	−0.869300	−	0.494285i	$-0.835430\pi$
$919$	−183.500	+	317.831i	−0.00658662	+	0.0114084i	0.862713	+	0.505693i	$0.168763\pi$
$920$	−5472.00	−	9477.78i	−0.196094	−	0.339645i
$921$	16719.5	+	28959.0i	0.598182	+	1.03608i
$922$	−45474.0			−1.62430
$923$		0			0
$924$	−14196.0			−0.505427
$925$	1334.55	+	2311.50i	0.0474374	+	0.0821639i
$926$	−1446.00	−	2504.55i	−0.0513159	−	0.0888817i
$927$	20416.0	−	35361.5i	0.723354	−	1.25289i
$928$	11473.1			0.405844
$929$	14967.5	−	25924.5i	0.528599	−	0.915560i	−0.470845	−	0.882216i	$-0.656051\pi$
$929$	14967.5	−	25924.5i	0.528599	−	0.915560i	0.999444	−	0.0333441i	$-0.0106157\pi$
$930$	−12221.4	+	21168.0i	−0.430918	+	0.746372i
$931$	−14486.9			−0.509976
$932$	−11556.0	+	20015.6i	−0.406147	+	0.703468i
$933$	−21672.0	−	37537.0i	−0.760460	−	1.31716i
$934$	25107.8	+	43488.0i	0.879607	+	1.52352i
$935$	8424.00			0.294646
$936$		0			0
$937$	42166.0			1.47012			0.735060	−	0.678002i	$-0.237154\pi$
$937$	42166.0			1.47012			0.735060	+	0.678002i	$0.237154\pi$
$938$	−6417.25	−	11115.0i	−0.223380	−	0.386906i
$939$	−2695.00	−	4667.88i	−0.0936613	−	0.162226i
$940$	−9504.00	+	16461.4i	−0.329773	+	0.571183i
$941$	−35022.1			−1.21327			−0.606635	−	0.794981i	$-0.707481\pi$
$941$	−35022.1			−1.21327			−0.606635	+	0.794981i	$0.707481\pi$
$942$	−18598.8	+	32214.0i	−0.643291	+	1.11421i
$943$	11205.5	−	19408.5i	0.386958	−	0.670231i
$944$	−1524.20			−0.0525515
$945$	5460.00	−	9457.00i	0.187951	−	0.325541i
$946$	3315.00	+	5741.75i	0.113932	+	0.197337i
$947$	1299.90	+	2251.50i	0.0446053	+	0.0772586i	0.887466	−	0.460873i	$-0.152464\pi$
$947$	1299.90	+	2251.50i	0.0446053	+	0.0772586i	−0.842861	+	0.538132i	$0.819130\pi$
$948$	34832.0			1.19334
$949$		0			0
$950$	−20502.0			−0.700182
$951$	28201.3	+	48846.0i	0.961607	+	1.66555i
$952$	4212.00	+	7295.40i	0.143395	+	0.248367i
$953$	5311.50	−	9199.79i	0.180542	−	0.312708i	−0.761523	−	0.648137i	$-0.775548\pi$
$953$	5311.50	−	9199.79i	0.180542	−	0.312708i	0.942065	+	0.335430i	$0.108882\pi$
$954$	32465.6			1.10179
$955$	19683.0	−	34092.0i	0.666940	−	1.15517i
$956$	3720.45	−	6444.00i	0.125866	−	0.218006i
$957$	−10875.5			−0.367353
$958$	15411.0	−	26692.6i	0.519736	−	0.900209i
$959$	13396.5	+	23203.4i	0.451090	+	0.781311i
$960$	3103.84	+	5376.00i	0.104350	+	0.180739i
$961$	−24499.0			−0.822362
$962$		0			0
$963$	−5610.00			−0.187726
$964$	4118.82	+	7134.00i	0.137612	+	0.238351i
$965$	29412.0	+	50943.1i	0.981146	+	1.69939i
$966$	15561.0	−	26952.4i	0.518289	−	0.897703i
$967$	20199.2			0.671729			0.335864	−	0.941910i	$-0.390972\pi$
$967$	20199.2			0.671729			0.335864	+	0.941910i	$0.390972\pi$
$968$	−5708.84	+	9888.00i	−0.189555	+	0.328319i
$969$	8347.62	−	14458.5i	0.276743	−	0.479333i
$970$	59277.7			1.96216
$971$	1162.50	−	2013.51i	0.0384206	−	0.0665464i	−0.846176	−	0.532904i	$-0.821101\pi$
$971$	1162.50	−	2013.51i	0.0384206	−	0.0665464i	0.884596	+	0.466358i	$0.154434\pi$
$972$	−9856.00	−	17071.1i	−0.325238	−	0.563329i
$973$	−28652.5	−	49627.5i	−0.944045	−	1.63513i
$974$	16470.0			0.541820
$975$		0			0
$976$	1360.00			0.0446030
$977$	16469.2	+	28525.5i	0.539300	+	0.934096i	0.998942	+	0.0459912i	$0.0146446\pi$
$977$	16469.2	+	28525.5i	0.539300	+	0.934096i	−0.459641	+	0.888105i	$0.652022\pi$
$978$	19803.0	+	34299.8i	0.647475	+	1.12146i
$979$	3451.50	−	5978.17i	0.112677	−	0.195162i
$980$	9089.80			0.296289
$981$	6706.50	−	11616.0i	0.218269	−	0.378053i
$982$	−2831.90	+	4905.00i	−0.0920261	+	0.159394i
$983$	−42702.0			−1.38554			−0.692768	−	0.721161i	$-0.743609\pi$
$983$	−42702.0			−1.38554			−0.692768	+	0.721161i	$0.743609\pi$
$984$	−19068.0	+	33026.7i	−0.617750	+	1.06997i
$985$	19068.0	+	33026.7i	0.616809	+	1.06834i
$986$	−3226.81	−	5589.00i	−0.104222	−	0.180517i
$987$	54054.0			1.74322
$988$		0			0
$989$	−4845.00			−0.155776
$990$	11888.8	+	20592.0i	0.381667	+	0.661067i
$991$	2421.50	+	4194.16i	0.0776201	+	0.134442i	0.902223	−	0.431271i	$-0.141935\pi$
$991$	2421.50	+	4194.16i	0.0776201	+	0.134442i	−0.824603	+	0.565712i	$0.808601\pi$
$992$	−6048.00	+	10475.4i	−0.193573	+	0.335278i
$993$	36942.9			1.18061
$994$	22764.3	−	39429.0i	0.726400	−	1.25816i
$995$	−11674.0	+	20220.0i	−0.371951	+	0.644238i
$996$	11930.4			0.379546
$997$	−5471.50	+	9476.92i	−0.173806	+	0.301040i	−0.939747	−	0.341870i	$-0.888940\pi$
$997$	−5471.50	+	9476.92i	−0.173806	+	0.301040i	0.765942	+	0.642910i	$0.222273\pi$
$998$	25002.0	+	43304.7i	0.793011	+	1.37353i
$999$	697.150	+	1207.50i	0.0220789	+	0.0382419i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.4.c.i.146.1		4
13.2	odd	12		169.4.b.b.168.1		2
13.3	even	3		169.4.a.h.1.2		2
13.4	even	6	inner	169.4.c.i.22.2		4
13.5	odd	4		13.4.e.a.10.1	yes	2
13.6	odd	12		169.4.e.b.147.1		2
13.7	odd	12		13.4.e.a.4.1	✓	2
13.8	odd	4		169.4.e.b.23.1		2
13.9	even	3	inner	169.4.c.i.22.1		4
13.10	even	6		169.4.a.h.1.1		2
13.11	odd	12		169.4.b.b.168.2		2
13.12	even	2	inner	169.4.c.i.146.2		4
39.5	even	4		117.4.q.c.10.1		2
39.20	even	12		117.4.q.c.82.1		2
39.23	odd	6		1521.4.a.q.1.2		2
39.29	odd	6		1521.4.a.q.1.1		2
52.7	even	12		208.4.w.a.17.1		2
52.31	even	4		208.4.w.a.49.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.4.e.a.4.1	✓	2	13.7	odd	12
13.4.e.a.10.1	yes	2	13.5	odd	4
117.4.q.c.10.1		2	39.5	even	4
117.4.q.c.82.1		2	39.20	even	12
169.4.a.h.1.1		2	13.10	even	6
169.4.a.h.1.2		2	13.3	even	3
169.4.b.b.168.1		2	13.2	odd	12
169.4.b.b.168.2		2	13.11	odd	12
169.4.c.i.22.1		4	13.9	even	3	inner
169.4.c.i.22.2		4	13.4	even	6	inner
169.4.c.i.146.1		4	1.1	even	1	trivial
169.4.c.i.146.2		4	13.12	even	2	inner
169.4.e.b.23.1		2	13.8	odd	4
169.4.e.b.147.1		2	13.6	odd	12
208.4.w.a.17.1		2	52.7	even	12
208.4.w.a.49.1		2	52.31	even	4
1521.4.a.q.1.1		2	39.29	odd	6
1521.4.a.q.1.2		2	39.23	odd	6

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	169.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.73205 - 3.00000i) q^{2} +(3.50000 + 6.06218i) q^{3} +(-2.00000 + 3.46410i) q^{4} +13.8564 q^{5} +(12.1244 - 21.0000i) q^{6} +(11.2583 - 19.5000i) q^{7} -13.8564 q^{8} +(-11.0000 + 19.0526i) q^{9} +O(q^{10})\)	\(q+(-1.73205 - 3.00000i) q^{2} +(3.50000 + 6.06218i) q^{3} +(-2.00000 + 3.46410i) q^{4} +13.8564 q^{5} +(12.1244 - 21.0000i) q^{6} +(11.2583 - 19.5000i) q^{7} -13.8564 q^{8} +(-11.0000 + 19.0526i) q^{9} +(-24.0000 - 41.5692i) q^{10} +(11.2583 + 19.5000i) q^{11} -28.0000 q^{12} -78.0000 q^{14} +(48.4974 + 84.0000i) q^{15} +(40.0000 + 69.2820i) q^{16} +(13.5000 - 23.3827i) q^{17} +76.2102 q^{18} +(44.1673 - 76.5000i) q^{19} +(-27.7128 + 48.0000i) q^{20} +157.617 q^{21} +(39.0000 - 67.5500i) q^{22} +(28.5000 + 49.3634i) q^{23} +(-48.4974 - 84.0000i) q^{24} +67.0000 q^{25} +35.0000 q^{27} +(45.0333 + 78.0000i) q^{28} +(34.5000 + 59.7558i) q^{29} +(168.000 - 290.985i) q^{30} -72.7461 q^{31} +(83.1384 - 144.000i) q^{32} +(-78.8083 + 136.500i) q^{33} -93.5307 q^{34} +(156.000 - 270.200i) q^{35} +(-44.0000 - 76.2102i) q^{36} +(19.9186 + 34.5000i) q^{37} -306.000 q^{38} -192.000 q^{40} +(-196.588 - 340.500i) q^{41} +(-273.000 - 472.850i) q^{42} +(-42.5000 + 73.6122i) q^{43} -90.0666 q^{44} +(-152.420 + 264.000i) q^{45} +(98.7269 - 171.000i) q^{46} +342.946 q^{47} +(-280.000 + 484.974i) q^{48} +(-82.0000 - 142.028i) q^{49} +(-116.047 - 201.000i) q^{50} +189.000 q^{51} +426.000 q^{53} +(-60.6218 - 105.000i) q^{54} +(156.000 + 270.200i) q^{55} +(-156.000 + 270.200i) q^{56} +618.342 q^{57} +(119.512 - 207.000i) q^{58} +(-9.52628 + 16.5000i) q^{59} -387.979 q^{60} +(8.50000 - 14.7224i) q^{61} +(126.000 + 218.238i) q^{62} +(247.683 + 429.000i) q^{63} +64.0000 q^{64} +546.000 q^{66} +(82.2724 + 142.500i) q^{67} +(54.0000 + 93.5307i) q^{68} +(-199.500 + 345.544i) q^{69} -1080.80 q^{70} +(-291.851 + 505.500i) q^{71} +(152.420 - 264.000i) q^{72} -1004.59 q^{73} +(69.0000 - 119.512i) q^{74} +(234.500 + 406.166i) q^{75} +(176.669 + 306.000i) q^{76} +507.000 q^{77} -1244.00 q^{79} +(554.256 + 960.000i) q^{80} +(419.500 + 726.595i) q^{81} +(-681.000 + 1179.53i) q^{82} -426.084 q^{83} +(-315.233 + 546.000i) q^{84} +(187.061 - 324.000i) q^{85} +294.449 q^{86} +(-241.500 + 418.290i) q^{87} +(-156.000 - 270.200i) q^{88} +(-153.286 - 265.500i) q^{89} +1056.00 q^{90} -228.000 q^{92} +(-254.611 - 441.000i) q^{93} +(-594.000 - 1028.84i) q^{94} +(612.000 - 1060.02i) q^{95} +1163.94 q^{96} +(-617.476 + 1069.50i) q^{97} +(-284.056 + 492.000i) q^{98} -495.367 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 14 q^{3} - 8 q^{4} - 44 q^{9}+O(q^{10}) \) 4 * q + 14 * q^3 - 8 * q^4 - 44 * q^9	\( 4 q + 14 q^{3} - 8 q^{4} - 44 q^{9} - 96 q^{10} - 112 q^{12} - 312 q^{14} + 160 q^{16} + 54 q^{17} + 156 q^{22} + 114 q^{23} + 268 q^{25} + 140 q^{27} + 138 q^{29} + 672 q^{30} + 624 q^{35} - 176 q^{36} - 1224 q^{38} - 768 q^{40} - 1092 q^{42} - 170 q^{43} - 1120 q^{48} - 328 q^{49} + 756 q^{51} + 1704 q^{53} + 624 q^{55} - 624 q^{56} + 34 q^{61} + 504 q^{62} + 256 q^{64} + 2184 q^{66} + 216 q^{68} - 798 q^{69} + 276 q^{74} + 938 q^{75} + 2028 q^{77} - 4976 q^{79} + 1678 q^{81} - 2724 q^{82} - 966 q^{87} - 624 q^{88} + 4224 q^{90} - 912 q^{92} - 2376 q^{94} + 2448 q^{95}+O(q^{100}) \) 4 * q + 14 * q^3 - 8 * q^4 - 44 * q^9 - 96 * q^10 - 112 * q^12 - 312 * q^14 + 160 * q^16 + 54 * q^17 + 156 * q^22 + 114 * q^23 + 268 * q^25 + 140 * q^27 + 138 * q^29 + 672 * q^30 + 624 * q^35 - 176 * q^36 - 1224 * q^38 - 768 * q^40 - 1092 * q^42 - 170 * q^43 - 1120 * q^48 - 328 * q^49 + 756 * q^51 + 1704 * q^53 + 624 * q^55 - 624 * q^56 + 34 * q^61 + 504 * q^62 + 256 * q^64 + 2184 * q^66 + 216 * q^68 - 798 * q^69 + 276 * q^74 + 938 * q^75 + 2028 * q^77 - 4976 * q^79 + 1678 * q^81 - 2724 * q^82 - 966 * q^87 - 624 * q^88 + 4224 * q^90 - 912 * q^92 - 2376 * q^94 + 2448 * q^95

Introduction

L-functions

Modular forms

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