LMFDB - Embedded newform 169.4.c.i.22.1

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			22.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	169.22
Dual form			169.4.c.i.146.1

$q$-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 $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

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

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	0.378467	+	0.925615i	$0.376451\pi$
$2$	−1.73205	+	3.00000i	−0.612372	+	1.06066i	−0.990839	+	0.135045i	$0.956882\pi$
$3$	3.50000	−	6.06218i	0.673575	−	1.16667i	−0.303308	−	0.952893i	$-0.598091\pi$
$3$	3.50000	−	6.06218i	0.673575	−	1.16667i	0.976883	−	0.213774i	$-0.0685756\pi$
$4$	−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	0.991587	+	0.129441i	$0.0413183\pi$
$7$	11.2583	+	19.5000i	0.607893	+	1.05290i	−0.383694	+	0.923460i	$0.625348\pi$
$8$	−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	−0.669462	−	0.742846i	$-0.733475\pi$
$11$	11.2583	−	19.5000i	0.308592	−	0.534497i	0.978055	+	0.208349i	$0.0668088\pi$
$12$	−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	0.946112	−	0.323840i	$-0.104974\pi$
$17$	13.5000	+	23.3827i	0.192602	+	0.333596i	−0.753510	+	0.657437i	$0.771641\pi$
$18$	76.2102			0.997940
$19$	44.1673	+	76.5000i	0.533299	+	0.923700i	0.999244	+	0.0388865i	$0.0123811\pi$
$19$	44.1673	+	76.5000i	0.533299	+	0.923700i	−0.465945	+	0.884814i	$0.654286\pi$
$20$	−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	−0.707431	−	0.706783i	$-0.750146\pi$
$23$	28.5000	−	49.3634i	0.258377	−	0.447521i	0.965807	+	0.259261i	$0.0834791\pi$
$24$	−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	−0.734172	−	0.678963i	$-0.762430\pi$
$29$	34.5000	−	59.7558i	0.220913	−	0.382633i	0.955086	+	0.296330i	$0.0957628\pi$
$30$	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	−0.818376	−	0.574683i	$-0.805125\pi$
$37$	19.9186	−	34.5000i	0.0885026	−	0.153291i	0.906878	+	0.421393i	$0.138459\pi$
$38$	−306.000			−1.30631
$39$		0			0
$40$	−192.000			−0.758947
$41$	−196.588	+	340.500i	−0.748826	+	1.29700i	0.199560	+	0.979886i	$0.436049\pi$
$41$	−196.588	+	340.500i	−0.748826	+	1.29700i	−0.948386	+	0.317118i	$0.897285\pi$
$42$	−273.000	+	472.850i	−1.00297	+	1.73720i
$43$	−42.5000	−	73.6122i	−0.150725	−	0.261064i	0.780769	−	0.624820i	$-0.214828\pi$
$43$	−42.5000	−	73.6122i	−0.150725	−	0.261064i	−0.931494	+	0.363756i	$0.881494\pi$
$44$	−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	0.855324	−	0.518094i	$-0.173358\pi$
$59$	−9.52628	−	16.5000i	−0.0210206	−	0.0364088i	−0.876344	+	0.481685i	$0.840025\pi$
$60$	−387.979			−0.834799
$61$	8.50000	+	14.7224i	0.0178412	+	0.0309019i	0.874808	−	0.484469i	$-0.160987\pi$
$61$	8.50000	+	14.7224i	0.0178412	+	0.0309019i	−0.856967	+	0.515371i	$0.827654\pi$
$62$	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	−0.781216	−	0.624261i	$-0.785400\pi$
$67$	82.2724	−	142.500i	0.150018	−	0.259838i	0.931234	+	0.364423i	$0.118734\pi$
$68$	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	0.512067	−	0.858945i	$-0.328880\pi$
$71$	−291.851	−	505.500i	−0.487835	−	0.844955i	−0.999902	+	0.0139904i	$0.995547\pi$
$72$	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	−0.942753	−	0.333490i	$-0.891774\pi$
$89$	−153.286	+	265.500i	−0.182566	+	0.316213i	0.760188	+	0.649703i	$0.225107\pi$
$90$	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	−0.983990	−	0.178225i	$-0.942965\pi$
$97$	−617.476	−	1069.50i	−0.646342	−	1.11950i	0.337647	−	0.941273i	$-0.390369\pi$
$98$	−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	0.255345	−	0.966850i	$-0.417811\pi$
$101$	979.500	−	1696.54i	0.964989	−	1.67141i	0.709645	−	0.704560i	$-0.248856\pi$
$102$	−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	−0.802663	−	0.596433i	$-0.796584\pi$
$107$	127.500	−	220.836i	0.115195	−	0.199524i	0.917858	+	0.396909i	$0.129917\pi$
$108$	−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	0.767719	−	0.640787i	$-0.221392\pi$
$113$	−205.500	−	355.936i	−0.171078	−	0.296316i	−0.938797	+	0.344471i	$0.888058\pi$
$114$	−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	0.146234	+	0.989250i	$0.453285\pi$
$127$	−1121.50	+	1942.49i	−0.783599	+	1.35723i	−0.929833	+	0.367983i	$0.880049\pi$
$128$	−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	0.618696	−	0.785630i	$-0.287661\pi$
$137$	−594.959	−	1030.50i	−0.371028	−	0.642639i	−0.989724	+	0.142991i	$0.954328\pi$
$138$	1382.18			0.852599
$139$	1272.50	+	2204.03i	0.776490	+	1.34492i	0.933953	+	0.357395i	$0.116335\pi$
$139$	1272.50	+	2204.03i	0.776490	+	1.34492i	−0.157464	+	0.987525i	$0.550332\pi$
$140$	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	0.629171	−	0.777267i	$-0.283394\pi$
$149$	−652.117	−	1129.50i	−0.358547	−	0.621022i	−0.987718	+	0.156245i	$0.950061\pi$
$150$	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	0.600340	−	0.799745i	$-0.295032\pi$
$163$	−816.662	−	1414.50i	−0.392429	−	0.679707i	−0.992769	+	0.120038i	$0.961698\pi$
$164$	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	−0.990596	−	0.136819i	$-0.956312\pi$
$167$	−813.198	+	1408.50i	−0.376809	+	0.652653i	0.613787	+	0.789472i	$0.289645\pi$
$168$	−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	0.754027	−	0.656843i	$-0.228109\pi$
$173$	−436.500	−	756.040i	−0.191829	−	0.332258i	−0.945857	+	0.324585i	$0.894775\pi$
$174$	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	−0.968527	−	0.248910i	$-0.919928\pi$
$179$	−643.500	+	1114.57i	−0.268701	+	0.465403i	0.699826	+	0.714314i	$0.253261\pi$
$180$	−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	0.999005	+	0.0446092i	$0.0142043\pi$
$191$	1420.50	+	2460.38i	0.538135	+	0.932077i	−0.460870	+	0.887468i	$0.652462\pi$
$192$	224.000	−	387.979i	0.0841969	−	0.145833i
$193$	2122.63	−	3676.50i	0.791659	−	1.37119i	−0.133281	−	0.991078i	$-0.542551\pi$
$193$	2122.63	−	3676.50i	0.791659	−	1.37119i	0.924939	−	0.380115i	$-0.124115\pi$
$194$	4278.00			1.58321
$195$		0			0
$196$	656.000			0.239067
$197$	1376.11	−	2383.50i	0.497686	−	0.862017i	−0.502311	−	0.864687i	$-0.667517\pi$
$197$	1376.11	−	2383.50i	0.497686	−	0.862017i	0.999996	+	0.00267023i	$0.000849961\pi$
$198$	858.000	−	1486.10i	0.307957	−	0.533396i
$199$	−842.500	−	1459.25i	−0.300117	−	0.519818i	0.676045	−	0.736860i	$-0.263692\pi$
$199$	−842.500	−	1459.25i	−0.300117	−	0.519818i	−0.976162	+	0.217042i	$0.930359\pi$
$200$	−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	−0.969940	−	0.243343i	$-0.921756\pi$
$211$	−840.500	+	1455.79i	−0.274229	+	0.474979i	0.695711	+	0.718322i	$0.255089\pi$
$212$	−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	0.375336	+	0.926889i	$0.377527\pi$
$223$	−2048.15	+	3547.50i	−0.615042	+	1.06528i	−0.990377	+	0.138394i	$0.955806\pi$
$224$	−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	0.832215	−	0.554454i	$-0.187073\pi$
$227$	−219.104	−	379.500i	−0.0640638	−	0.110962i	−0.896278	+	0.443492i	$0.853739\pi$
$228$	−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	0.970192	−	0.242339i	$-0.0779145\pi$
$241$	1029.70	+	1783.50i	0.275224	+	0.476703i	−0.694967	+	0.719041i	$0.744581\pi$
$242$	−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	0.997079	+	0.0763724i	$0.0243338\pi$
$251$	2245.50	+	3889.32i	0.564680	+	0.978055i	−0.432399	+	0.901682i	$0.642333\pi$
$252$	−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	−0.318690	−	0.947859i	$-0.603243\pi$
$257$	2725.50	−	4720.70i	0.661525	−	1.14580i	0.980215	−	0.197936i	$-0.0634239\pi$
$258$	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	−0.816474	−	0.577382i	$-0.804074\pi$
$263$	391.500	−	678.098i	0.0917906	−	0.158986i	0.908265	+	0.418396i	$0.137408\pi$
$264$	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	0.995901	+	0.0904453i	$0.0288290\pi$
$269$	2542.50	+	4403.74i	0.576279	+	0.998144i	−0.419623	+	0.907699i	$0.637838\pi$
$270$	−840.000	+	1454.92i	−0.189336	+	0.327940i
$271$	662.509	−	1147.50i	0.148504	−	0.257216i	−0.782171	−	0.623064i	$-0.785888\pi$
$271$	662.509	−	1147.50i	0.148504	−	0.257216i	0.930675	+	0.365848i	$0.119221\pi$
$272$	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	0.618698	−	0.785629i	$-0.287660\pi$
$277$	−1710.50	−	2962.67i	−0.371025	−	0.642635i	−0.989724	+	0.142994i	$0.954327\pi$
$278$	−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	−0.192228	−	0.981350i	$-0.561571\pi$
$283$	3588.50	−	6215.46i	0.753760	−	1.30555i	0.945988	−	0.324201i	$-0.105095\pi$
$284$	−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	0.785878	+	0.618381i	$0.212211\pi$
$293$	4656.62	+	8065.50i	0.928473	+	1.60816i	0.142595	+	0.989781i	$0.454456\pi$
$294$	−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	0.997550	−	0.0699590i	$-0.0222869\pi$
$331$	2638.78	+	4570.50i	0.438189	+	0.758965i	−0.559361	+	0.828924i	$0.688954\pi$
$332$	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	−0.999338	−	0.0363875i	$-0.988415\pi$
$347$	−3433.50	−	5947.00i	−0.531181	−	0.920033i	0.468156	−	0.883646i	$-0.344918\pi$
$348$	−966.000	+	1673.16i	−0.148802	+	0.257732i
$349$	−6076.90	+	10525.5i	−0.932060	+	1.61438i	−0.152266	+	0.988340i	$0.548657\pi$
$349$	−6076.90	+	10525.5i	−0.932060	+	1.61438i	−0.779794	+	0.626036i	$0.784676\pi$
$350$	−5226.00			−0.798118
$351$		0			0
$352$	3744.00			0.566920
$353$	2903.78	−	5029.50i	0.437827	−	0.758338i	−0.559695	−	0.828699i	$-0.689082\pi$
$353$	2903.78	−	5029.50i	0.437827	−	0.758338i	0.997522	+	0.0703608i	$0.0224151\pi$
$354$	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	−0.966413	−	0.256995i	$-0.917268\pi$
$367$	−1832.50	+	3173.98i	−0.260642	+	0.451446i	0.705770	+	0.708441i	$0.250601\pi$
$368$	−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	0.617205	−	0.786802i	$-0.288265\pi$
$373$	−2685.50	−	4651.42i	−0.372788	−	0.645688i	−0.989993	+	0.141114i	$0.954931\pi$
$374$	−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	0.152020	+	0.988377i	$0.451422\pi$
$379$	−5754.74	+	9967.50i	−0.779950	+	1.35091i	−0.931970	+	0.362536i	$0.881911\pi$
$380$	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	0.773965	−	0.633228i	$-0.218271\pi$
$383$	−1209.84	−	2095.50i	−0.161409	−	0.279569i	−0.935374	+	0.353659i	$0.884937\pi$
$384$	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	−0.998185	−	0.0602200i	$-0.980820\pi$
$397$	−4360.44	−	7552.50i	−0.551245	−	0.954784i	0.446941	−	0.894564i	$-0.352514\pi$
$398$	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	−0.527228	−	0.849724i	$-0.676769\pi$
$401$	3792.33	−	6568.50i	0.472269	−	0.817993i	0.999496	+	0.0317308i	$0.0101019\pi$
$402$	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	0.706110	−	0.708102i	$-0.250448\pi$
$409$	−2152.07	−	3727.50i	−0.260179	−	0.450643i	−0.966289	+	0.257459i	$0.917115\pi$
$410$	−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	−0.979359	−	0.202129i	$-0.935214\pi$
$419$	−2698.50	+	4673.94i	−0.314631	+	0.544957i	0.664728	+	0.747085i	$0.268547\pi$
$420$	−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	−0.879304	−	0.476262i	$-0.841991\pi$
$431$	−243.353	+	421.500i	−0.0271970	+	0.0471066i	0.852107	+	0.523368i	$0.175325\pi$
$432$	1400.00	−	2424.87i	0.155920	−	0.270062i
$433$	6069.50	+	10512.7i	0.673629	+	1.16676i	0.976867	+	0.213846i	$0.0685989\pi$
$433$	6069.50	+	10512.7i	0.673629	+	1.16676i	−0.303238	+	0.952915i	$0.598068\pi$
$434$	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	−0.853224	−	0.521545i	$-0.825356\pi$
$439$	230.500	−	399.238i	0.0250596	−	0.0434045i	0.878283	+	0.478141i	$0.158689\pi$
$440$	−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	0.858138	−	0.513419i	$-0.171621\pi$
$449$	−148.090	−	256.500i	−0.0155653	−	0.0269599i	−0.873703	+	0.486459i	$0.838288\pi$
$450$	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	−0.849955	−	0.526855i	$-0.823371\pi$
$457$	305.707	−	529.500i	0.0312918	−	0.0541990i	0.881247	+	0.472656i	$0.156705\pi$
$458$	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	0.979792	+	0.200020i	$0.0641008\pi$
$461$	6563.61	+	11368.5i	0.663119	+	1.14855i	−0.316673	+	0.948535i	$0.602566\pi$
$462$	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	−0.571998	−	0.820255i	$-0.693832\pi$
$479$	4448.77	−	7705.50i	0.424362	−	0.735017i	0.996361	+	0.0852376i	$0.0271649\pi$
$480$	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	0.733975	−	0.679177i	$-0.237663\pi$
$487$	−2377.24	−	4117.50i	−0.221197	−	0.383125i	−0.955172	+	0.296052i	$0.904330\pi$
$488$	−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	−0.901147	−	0.433514i	$-0.857273\pi$
$491$	−817.500	+	1415.95i	−0.0751390	+	0.130145i	0.826008	+	0.563659i	$0.190607\pi$
$492$	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	−0.997294	−	0.0735133i	$-0.976579\pi$
$503$	−6343.50	−	10987.3i	−0.562312	−	0.973952i	0.434983	−	0.900439i	$-0.356754\pi$
$504$	−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	−0.963608	−	0.267318i	$-0.913863\pi$
$509$	−2874.34	+	4978.50i	−0.250300	+	0.433533i	0.713308	+	0.700850i	$0.247196\pi$
$510$	−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	−0.370877	−	0.928682i	$-0.620943\pi$
$523$	7401.50	−	12819.8i	0.618824	−	1.07183i	0.989701	−	0.143153i	$-0.0457240\pi$
$524$	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	−0.915751	−	0.401747i	$-0.868403\pi$
$557$	−1445.40	+	2503.50i	−0.109952	+	0.190443i	0.805798	+	0.592190i	$0.201736\pi$
$558$	−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	0.997175	−	0.0751113i	$-0.0239312\pi$
$563$	5791.50	+	10031.2i	0.433539	+	0.750912i	−0.563636	+	0.826023i	$0.690598\pi$
$564$	−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	−0.525129	−	0.851023i	$-0.675983\pi$
$569$	6439.50	−	11153.5i	0.474443	−	0.821759i	0.999572	+	0.0292638i	$0.00931628\pi$
$570$	−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	0.448216	+	0.893925i	$0.352060\pi$
$587$	−7822.81	+	13549.5i	−0.550054	+	0.952722i	−0.998270	+	0.0587964i	$0.981274\pi$
$588$	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	−0.999196	−	0.0400813i	$-0.987238\pi$
$601$	−6849.50	+	11863.7i	−0.464887	+	0.805207i	0.534310	+	0.845289i	$0.320572\pi$
$602$	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	0.934927	+	0.354839i	$0.115464\pi$
$607$	11586.5	+	20068.4i	0.774764	+	1.34193i	−0.160164	+	0.987090i	$0.551202\pi$
$608$	−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	−0.451066	−	0.892491i	$-0.648956\pi$
$613$	8307.78	−	14389.5i	0.547387	−	0.948102i	0.998453	−	0.0556111i	$-0.0177107\pi$
$614$	−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	−0.789423	−	0.613849i	$-0.789620\pi$
$617$	−14196.8	−	24589.5i	−0.926321	−	1.60443i	−0.136897	−	0.990585i	$-0.543713\pi$
$618$	−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	0.966342	+	0.257259i	$0.0828194\pi$
$631$	11189.9	+	19381.5i	0.705964	+	1.22277i	−0.260378	+	0.965507i	$0.583847\pi$
$632$	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	0.991096	+	0.133148i	$0.0425085\pi$
$641$	9913.50	+	17170.7i	0.610858	+	1.05804i	−0.380239	+	0.924888i	$0.624158\pi$
$642$	6183.42			0.380125
$643$	4225.34	+	7318.50i	0.259146	+	0.448855i	0.966013	−	0.258492i	$-0.0832255\pi$
$643$	4225.34	+	7318.50i	0.259146	+	0.448855i	−0.706867	+	0.707346i	$0.749892\pi$
$644$	−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	−0.817744	−	0.575581i	$-0.804776\pi$
$647$	1474.50	−	2553.91i	0.0895959	−	0.155185i	0.907340	+	0.420397i	$0.138109\pi$
$648$	−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	−0.988082	−	0.153926i	$-0.950808\pi$
$653$	−6019.50	+	10426.1i	−0.360737	+	0.624815i	0.627345	+	0.778741i	$0.284141\pi$
$654$	−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	0.812039	−	0.583603i	$-0.198358\pi$
$659$	−1681.50	−	2912.44i	−0.0993960	−	0.172159i	−0.911435	+	0.411445i	$0.865024\pi$
$660$	−4368.00	+	7565.60i	−0.257612	+	0.446198i
$661$	−5079.24	+	8797.50i	−0.298880	+	0.517675i	−0.975880	−	0.218308i	$-0.929946\pi$
$661$	−5079.24	+	8797.50i	−0.298880	+	0.517675i	0.677000	+	0.735983i	$0.263280\pi$
$662$	−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	0.479391	+	0.877601i	$0.340858\pi$
$673$	−9084.50	+	15734.8i	−0.520329	+	0.901237i	−0.999721	+	0.0236358i	$0.992476\pi$
$674$	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	0.637003	−	0.770862i	$-0.280174\pi$
$683$	−6231.05	−	10792.5i	−0.349084	−	0.604632i	−0.986087	+	0.166230i	$0.946841\pi$
$684$	−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	−0.919316	−	0.393520i	$-0.871257\pi$
$691$	−2159.00	+	3739.50i	−0.118860	+	0.205872i	0.800456	+	0.599391i	$0.204591\pi$
$692$	−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	0.886802	−	0.462150i	$-0.152922\pi$
$709$	814.930	+	1411.50i	0.0431669	+	0.0747673i	−0.843635	+	0.536918i	$0.819589\pi$
$710$	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	0.964885	−	0.262673i	$-0.0846039\pi$
$719$	4915.50	+	8513.90i	0.254961	+	0.441606i	−0.709924	+	0.704279i	$0.751271\pi$
$720$	−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	−0.589088	−	0.808069i	$-0.700513\pi$
$739$	8141.50	−	14101.5i	0.405264	−	0.701938i	0.994352	+	0.106131i	$0.0338463\pi$
$740$	−2208.00			−0.109686
$741$		0			0
$742$	−33228.0			−1.64399
$743$	5403.13	−	9358.50i	0.266786	−	0.462086i	−0.701244	−	0.712921i	$-0.747372\pi$
$743$	5403.13	−	9358.50i	0.266786	−	0.462086i	0.968030	+	0.250835i	$0.0807051\pi$
$744$	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	−0.982663	−	0.185399i	$-0.940642\pi$
$751$	−6807.50	+	11790.9i	−0.330771	+	0.572913i	0.651892	+	0.758312i	$0.273976\pi$
$752$	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	−0.924931	−	0.380135i	$-0.875878\pi$
$757$	−2775.50	+	4807.31i	−0.133259	+	0.230812i	0.791672	+	0.610947i	$0.209211\pi$
$758$	−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	0.960752	−	0.277409i	$-0.0894757\pi$
$761$	5041.13	+	8731.50i	0.240133	+	0.415922i	−0.720619	+	0.693331i	$0.756142\pi$
$762$	−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	−0.271517	−	0.962434i	$-0.587525\pi$
$769$	14879.2	−	25771.5i	0.697733	−	1.20851i	0.969250	−	0.246076i	$-0.0791413\pi$
$770$	−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	−0.984242	−	0.176829i	$-0.943416\pi$
$773$	−13867.7	−	24019.5i	−0.645259	−	1.11762i	0.338983	−	0.940793i	$-0.389917\pi$
$774$	−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	−0.963155	−	0.268947i	$-0.913324\pi$
$787$	−15774.7	−	27322.5i	−0.714493	−	1.23754i	0.248662	−	0.968590i	$-0.420009\pi$
$788$	−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	0.881739	−	0.471737i	$-0.156373\pi$
$797$	727.500	+	1260.07i	0.0323330	+	0.0560023i	−0.849406	+	0.527740i	$0.823040\pi$
$798$	−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	−0.883487	−	0.468456i	$-0.844811\pi$
$809$	−829.500	+	1436.74i	−0.0360490	+	0.0624388i	0.847438	+	0.530894i	$0.178144\pi$
$810$	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	0.381183	+	0.924500i	$0.375517\pi$
$821$	−14350.9	+	24856.5i	−0.610049	+	1.05664i	−0.991232	+	0.132136i	$0.957816\pi$
$822$	14427.0	−	24988.3i	0.612165	−	1.06030i
$823$	7889.50	+	13665.0i	0.334156	+	0.578776i	0.983322	−	0.181871i	$-0.0582153\pi$
$823$	7889.50	+	13665.0i	0.334156	+	0.578776i	−0.649166	+	0.760647i	$0.724882\pi$
$824$	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	−0.624712	−	0.780855i	$-0.714784\pi$
$829$	8685.50	−	15043.7i	0.363884	−	0.630266i	0.988596	+	0.150589i	$0.0481171\pi$
$830$	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	0.991826	+	0.127598i	$0.0407267\pi$
$839$	14737.2	+	25525.5i	0.606416	+	1.05034i	−0.385410	+	0.922745i	$0.625940\pi$
$840$	−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	0.906439	−	0.422338i	$-0.138790\pi$
$877$	2271.58	+	3934.50i	0.0874640	+	0.151492i	−0.818974	+	0.573830i	$0.805457\pi$
$878$	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	−0.992753	−	0.120175i	$-0.961654\pi$
$881$	−10258.5	+	17768.2i	−0.392302	+	0.679486i	0.600451	+	0.799661i	$0.294988\pi$
$882$	−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	0.221794	+	0.975093i	$0.428809\pi$
$887$	−19378.5	+	33564.5i	−0.733558	+	1.27056i	−0.955353	+	0.295467i	$0.904525\pi$
$888$	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	0.247714	+	0.968833i	$0.420321\pi$
$907$	−19535.5	+	33836.5i	−0.715177	+	1.23872i	−0.962891	+	0.269890i	$0.913013\pi$
$908$	−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	0.862713	−	0.505693i	$-0.168763\pi$
$919$	−183.500	−	317.831i	−0.00658662	−	0.0114084i	−0.869300	+	0.494285i	$0.835430\pi$
$920$	−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	0.999444	+	0.0333441i	$0.0106157\pi$
$929$	14967.5	+	25924.5i	0.528599	+	0.915560i	−0.470845	+	0.882216i	$0.656051\pi$
$930$	−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	−0.842861	−	0.538132i	$-0.819130\pi$
$947$	1299.90	−	2251.50i	0.0446053	−	0.0772586i	0.887466	+	0.460873i	$0.152464\pi$
$948$	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	0.942065	−	0.335430i	$-0.108882\pi$
$953$	5311.50	+	9199.79i	0.180542	+	0.312708i	−0.761523	+	0.648137i	$0.775548\pi$
$954$	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	0.884596	−	0.466358i	$-0.154434\pi$
$971$	1162.50	+	2013.51i	0.0384206	+	0.0665464i	−0.846176	+	0.532904i	$0.821101\pi$
$972$	−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	−0.459641	−	0.888105i	$-0.652022\pi$
$977$	16469.2	−	28525.5i	0.539300	−	0.934096i	0.998942	−	0.0459912i	$-0.0146446\pi$
$978$	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	−0.824603	−	0.565712i	$-0.808601\pi$
$991$	2421.50	−	4194.16i	0.0776201	−	0.134442i	0.902223	+	0.431271i	$0.141935\pi$
$992$	−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	0.765942	−	0.642910i	$-0.222273\pi$
$997$	−5471.50	−	9476.92i	−0.173806	−	0.301040i	−0.939747	+	0.341870i	$0.888940\pi$
$998$	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.22.1		4
13.2	odd	12		13.4.e.a.10.1	yes	2
13.3	even	3	inner	169.4.c.i.146.1		4
13.4	even	6		169.4.a.h.1.1		2
13.5	odd	4		169.4.e.b.147.1		2
13.6	odd	12		169.4.b.b.168.1		2
13.7	odd	12		169.4.b.b.168.2		2
13.8	odd	4		13.4.e.a.4.1	✓	2
13.9	even	3		169.4.a.h.1.2		2
13.10	even	6	inner	169.4.c.i.146.2		4
13.11	odd	12		169.4.e.b.23.1		2
13.12	even	2	inner	169.4.c.i.22.2		4
39.2	even	12		117.4.q.c.10.1		2
39.8	even	4		117.4.q.c.82.1		2
39.17	odd	6		1521.4.a.q.1.2		2
39.35	odd	6		1521.4.a.q.1.1		2
52.15	even	12		208.4.w.a.49.1		2
52.47	even	4		208.4.w.a.17.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.4.e.a.4.1	✓	2	13.8	odd	4
13.4.e.a.10.1	yes	2	13.2	odd	12
117.4.q.c.10.1		2	39.2	even	12
117.4.q.c.82.1		2	39.8	even	4
169.4.a.h.1.1		2	13.4	even	6
169.4.a.h.1.2		2	13.9	even	3
169.4.b.b.168.1		2	13.6	odd	12
169.4.b.b.168.2		2	13.7	odd	12
169.4.c.i.22.1		4	1.1	even	1	trivial
169.4.c.i.22.2		4	13.12	even	2	inner
169.4.c.i.146.1		4	13.3	even	3	inner
169.4.c.i.146.2		4	13.10	even	6	inner
169.4.e.b.23.1		2	13.11	odd	12
169.4.e.b.147.1		2	13.5	odd	4
208.4.w.a.17.1		2	52.47	even	4
208.4.w.a.49.1		2	52.15	even	12
1521.4.a.q.1.1		2	39.35	odd	6
1521.4.a.q.1.2		2	39.17	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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