LMFDB - Embedded newform 60.5.c.a.31.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,5,Mod(31,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("60.31");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	60.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.20219778503$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 9 x^{14} + 18 x^{13} + 263 x^{12} - 444 x^{11} - 1732 x^{10} - 832 x^{9} + \cdots + 16777216 $ x^16 - 4x^15 - 9x^14 + 18x^13 + 263x^12 - 444x^11 - 1732x^10 - 832x^9 + 25296x^8 - 6656x^7 - 110848x^6 - 227328x^5 + 1077248x^4 + 589824x^3 - 2359296x^2 - 8388608*x + 16777216
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{32}\cdot 3^{4}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			31.7
Root			$2.70166 + 0.837276i$ of defining polynomial
Character	$\chi$	$=$	60.31
Dual form			60.5.c.a.31.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.08838 - 2.54203i) q^{2} -5.19615i q^{3} +(3.07620 + 15.7015i) q^{4} +11.1803 q^{5} +(-13.2088 + 16.0477i) q^{6} -86.5709i q^{7} +(30.4132 - 56.3120i) q^{8} -27.0000 q^{9} +O(q^{10})$	\(q+(-3.08838 - 2.54203i) q^{2} -5.19615i q^{3} +(3.07620 + 15.7015i) q^{4} +11.1803 q^{5} +(-13.2088 + 16.0477i) q^{6} -86.5709i q^{7} +(30.4132 - 56.3120i) q^{8} -27.0000 q^{9} +(-34.5292 - 28.4207i) q^{10} +97.6947i q^{11} +(81.5874 - 15.9844i) q^{12} -297.644 q^{13} +(-220.066 + 267.364i) q^{14} -58.0948i q^{15} +(-237.074 + 96.6018i) q^{16} -58.8402 q^{17} +(83.3863 + 68.6347i) q^{18} -497.315i q^{19} +(34.3929 + 175.548i) q^{20} -449.835 q^{21} +(248.343 - 301.718i) q^{22} -120.919i q^{23} +(-292.606 - 158.031i) q^{24} +125.000 q^{25} +(919.237 + 756.618i) q^{26} +140.296i q^{27} +(1359.29 - 266.309i) q^{28} -947.079 q^{29} +(-147.678 + 179.419i) q^{30} -559.454i q^{31} +(977.739 + 304.306i) q^{32} +507.636 q^{33} +(181.721 + 149.573i) q^{34} -967.892i q^{35} +(-83.0573 - 423.940i) q^{36} +1163.36 q^{37} +(-1264.19 + 1535.90i) q^{38} +1546.60i q^{39} +(340.030 - 629.587i) q^{40} +3178.56 q^{41} +(1389.26 + 1143.49i) q^{42} -1166.21i q^{43} +(-1533.95 + 300.528i) q^{44} -301.869 q^{45} +(-307.380 + 373.445i) q^{46} -1060.01i q^{47} +(501.958 + 1231.87i) q^{48} -5093.52 q^{49} +(-386.048 - 317.753i) q^{50} +305.743i q^{51} +(-915.610 - 4673.45i) q^{52} +1440.77 q^{53} +(356.637 - 433.288i) q^{54} +1092.26i q^{55} +(-4874.98 - 2632.89i) q^{56} -2584.13 q^{57} +(2924.94 + 2407.50i) q^{58} +2004.76i q^{59} +(912.175 - 178.711i) q^{60} +3522.56 q^{61} +(-1422.15 + 1727.81i) q^{62} +2337.41i q^{63} +(-2246.08 - 3425.25i) q^{64} -3327.76 q^{65} +(-1567.77 - 1290.43i) q^{66} +6169.67i q^{67} +(-181.004 - 923.879i) q^{68} -628.315 q^{69} +(-2460.41 + 2989.22i) q^{70} -882.122i q^{71} +(-821.156 + 1520.42i) q^{72} +1659.75 q^{73} +(-3592.90 - 2957.30i) q^{74} -649.519i q^{75} +(7808.59 - 1529.84i) q^{76} +8457.51 q^{77} +(3931.50 - 4776.50i) q^{78} -7276.52i q^{79} +(-2650.57 + 1080.04i) q^{80} +729.000 q^{81} +(-9816.61 - 8079.99i) q^{82} -5346.39i q^{83} +(-1383.78 - 7063.09i) q^{84} -657.854 q^{85} +(-2964.55 + 3601.72i) q^{86} +4921.17i q^{87} +(5501.38 + 2971.20i) q^{88} +9009.81 q^{89} +(932.287 + 767.360i) q^{90} +25767.3i q^{91} +(1898.61 - 371.971i) q^{92} -2907.01 q^{93} +(-2694.57 + 3273.71i) q^{94} -5560.15i q^{95} +(1581.22 - 5080.48i) q^{96} -9798.06 q^{97} +(15730.7 + 12947.9i) q^{98} -2637.76i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{2} + 26 q^{4} + 18 q^{6} - 180 q^{8} - 432 q^{9}+O(q^{10}) $ 16 * q - 12 * q^2 + 26 * q^4 + 18 * q^6 - 180 * q^8 - 432 * q^9	$ 16 q - 12 q^{2} + 26 q^{4} + 18 q^{6} - 180 q^{8} - 432 q^{9} + 50 q^{10} - 352 q^{13} - 804 q^{14} - 190 q^{16} + 324 q^{18} + 600 q^{20} + 288 q^{21} + 436 q^{22} - 1998 q^{24} + 2000 q^{25} - 852 q^{26} - 1156 q^{28} - 3456 q^{29} + 7668 q^{32} + 4772 q^{34} - 702 q^{36} + 9376 q^{37} - 1320 q^{38} + 550 q^{40} + 1248 q^{41} - 324 q^{42} - 6420 q^{44} - 1112 q^{46} - 4176 q^{48} - 3952 q^{49} - 1500 q^{50} + 12704 q^{52} - 5184 q^{53} - 486 q^{54} - 2604 q^{56} - 11232 q^{57} + 12708 q^{58} + 3150 q^{60} - 3808 q^{61} - 16152 q^{62} - 11902 q^{64} + 2400 q^{65} - 2916 q^{66} - 12312 q^{68} + 9792 q^{69} - 17100 q^{70} + 4860 q^{72} + 11040 q^{73} + 30516 q^{74} - 5160 q^{76} - 27456 q^{77} - 3600 q^{78} + 10800 q^{80} + 11664 q^{81} - 54040 q^{82} - 2052 q^{84} - 11200 q^{85} + 39768 q^{86} - 7220 q^{88} + 7584 q^{89} - 1350 q^{90} + 28848 q^{92} + 19872 q^{93} + 49776 q^{94} + 18882 q^{96} - 14496 q^{97} + 23940 q^{98}+O(q^{100}) $ 16 * q - 12 * q^2 + 26 * q^4 + 18 * q^6 - 180 * q^8 - 432 * q^9 + 50 * q^10 - 352 * q^13 - 804 * q^14 - 190 * q^16 + 324 * q^18 + 600 * q^20 + 288 * q^21 + 436 * q^22 - 1998 * q^24 + 2000 * q^25 - 852 * q^26 - 1156 * q^28 - 3456 * q^29 + 7668 * q^32 + 4772 * q^34 - 702 * q^36 + 9376 * q^37 - 1320 * q^38 + 550 * q^40 + 1248 * q^41 - 324 * q^42 - 6420 * q^44 - 1112 * q^46 - 4176 * q^48 - 3952 * q^49 - 1500 * q^50 + 12704 * q^52 - 5184 * q^53 - 486 * q^54 - 2604 * q^56 - 11232 * q^57 + 12708 * q^58 + 3150 * q^60 - 3808 * q^61 - 16152 * q^62 - 11902 * q^64 + 2400 * q^65 - 2916 * q^66 - 12312 * q^68 + 9792 * q^69 - 17100 * q^70 + 4860 * q^72 + 11040 * q^73 + 30516 * q^74 - 5160 * q^76 - 27456 * q^77 - 3600 * q^78 + 10800 * q^80 + 11664 * q^81 - 54040 * q^82 - 2052 * q^84 - 11200 * q^85 + 39768 * q^86 - 7220 * q^88 + 7584 * q^89 - 1350 * q^90 + 28848 * q^92 + 19872 * q^93 + 49776 * q^94 + 18882 * q^96 - 14496 * q^97 + 23940 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	−3.08838	−	2.54203i	−0.772095	−	0.635507i
$2$	−3.08838	−	2.54203i	−0.772095	−	0.635507i
$3$		−	5.19615i		−	0.577350i
$3$		−	5.19615i		−	0.577350i
$4$	3.07620	+	15.7015i	0.192262	+	0.981344i
$5$	11.1803			0.447214
$5$	11.1803			0.447214
$6$	−13.2088	+	16.0477i	−0.366910	+	0.445769i
$7$		−	86.5709i		−	1.76675i	−0.468665	−	0.883376i	$-0.655265\pi$
$7$		−	86.5709i		−	1.76675i	0.468665	−	0.883376i	$-0.344735\pi$
$8$	30.4132	−	56.3120i	0.475206	−	0.879875i
$9$	−27.0000			−0.333333
$10$	−34.5292	−	28.4207i	−0.345292	−	0.284207i
$11$			97.6947i			0.807394i	0.914893	+	0.403697i	$0.132275\pi$
$11$			97.6947i			0.807394i	−0.914893	+	0.403697i	$0.867725\pi$
$12$	81.5874	−	15.9844i	0.566579	−	0.111003i
$13$	−297.644			−1.76121			−0.880603	−	0.473856i	$-0.842862\pi$
$13$	−297.644			−1.76121			−0.880603	+	0.473856i	$0.842862\pi$
$14$	−220.066	+	267.364i	−1.12278	+	1.36410i
$15$		−	58.0948i		−	0.258199i
$16$	−237.074	+	96.6018i	−0.926070	+	0.377351i
$17$	−58.8402			−0.203599			−0.101800	−	0.994805i	$-0.532460\pi$
$17$	−58.8402			−0.203599			−0.101800	+	0.994805i	$0.532460\pi$
$18$	83.3863	+	68.6347i	0.257365	+	0.211836i
$19$		−	497.315i		−	1.37760i	−0.724949	−	0.688802i	$-0.758137\pi$
$19$		−	497.315i		−	1.37760i	0.724949	−	0.688802i	$-0.241863\pi$
$20$	34.3929	+	175.548i	0.0859823	+	0.438870i
$21$	−449.835			−1.02004
$22$	248.343	−	301.718i	0.513104	−	0.623385i
$23$		−	120.919i		−	0.228581i	−0.993447	−	0.114290i	$-0.963541\pi$
$23$		−	120.919i		−	0.228581i	0.993447	−	0.114290i	$-0.0364594\pi$
$24$	−292.606	−	158.031i	−0.507996	−	0.274360i
$25$	125.000			0.200000
$26$	919.237	+	756.618i	1.35982	+	1.11926i
$27$			140.296i			0.192450i
$28$	1359.29	−	266.309i	1.73379	−	0.339680i
$29$	−947.079			−1.12613			−0.563067	−	0.826411i	$-0.690379\pi$
$29$	−947.079			−1.12613			−0.563067	+	0.826411i	$0.690379\pi$
$30$	−147.678	+	179.419i	−0.164087	+	0.199354i
$31$		−	559.454i		−	0.582158i	−0.956699	−	0.291079i	$-0.905986\pi$
$31$		−	559.454i		−	0.582158i	0.956699	−	0.291079i	$-0.0940142\pi$
$32$	977.739	+	304.306i	0.954824	+	0.297173i
$33$	507.636			0.466149
$34$	181.721	+	149.573i	0.157198	+	0.129389i
$35$		−	967.892i		−	0.790116i
$36$	−83.0573	−	423.940i	−0.0640874	−	0.327115i
$37$	1163.36			0.849789			0.424894	−	0.905243i	$-0.360311\pi$
$37$	1163.36			0.849789			0.424894	+	0.905243i	$0.360311\pi$
$38$	−1264.19	+	1535.90i	−0.875477	+	1.06364i
$39$			1546.60i			1.01683i
$40$	340.030	−	629.587i	0.212518	−	0.393492i
$41$	3178.56			1.89088			0.945438	−	0.325802i	$-0.105634\pi$
$41$	3178.56			1.89088			0.945438	+	0.325802i	$0.105634\pi$
$42$	1389.26	+	1143.49i	0.787564	+	0.648239i
$43$		−	1166.21i		−	0.630727i	−0.948971	−	0.315364i	$-0.897874\pi$
$43$		−	1166.21i		−	0.630727i	0.948971	−	0.315364i	$-0.102126\pi$
$44$	−1533.95	+	300.528i	−0.792331	+	0.155231i
$45$	−301.869			−0.149071
$46$	−307.380	+	373.445i	−0.145265	+	0.176486i
$47$		−	1060.01i		−	0.479859i	−0.970790	−	0.239930i	$-0.922876\pi$
$47$		−	1060.01i		−	0.479859i	0.970790	−	0.239930i	$-0.0771244\pi$
$48$	501.958	+	1231.87i	0.217863	+	0.534667i
$49$	−5093.52			−2.12141
$50$	−386.048	−	317.753i	−0.154419	−	0.127101i
$51$			305.743i			0.117548i
$52$	−915.610	−	4673.45i	−0.338613	−	1.72835i
$53$	1440.77			0.512911			0.256455	−	0.966556i	$-0.417445\pi$
$53$	1440.77			0.512911			0.256455	+	0.966556i	$0.417445\pi$
$54$	356.637	−	433.288i	0.122303	−	0.148590i
$55$			1092.26i			0.361078i
$56$	−4874.98	−	2632.89i	−1.55452	−	0.839571i
$57$	−2584.13			−0.795360
$58$	2924.94	+	2407.50i	0.869483	+	0.715666i
$59$			2004.76i			0.575914i	0.957643	+	0.287957i	$0.0929760\pi$
$59$			2004.76i			0.575914i	−0.957643	+	0.287957i	$0.907024\pi$
$60$	912.175	−	178.711i	0.253382	−	0.0496419i
$61$	3522.56			0.946671			0.473335	−	0.880882i	$-0.343050\pi$
$61$	3522.56			0.946671			0.473335	+	0.880882i	$0.343050\pi$
$62$	−1422.15	+	1727.81i	−0.369965	+	0.449481i
$63$			2337.41i			0.588917i
$64$	−2246.08	−	3425.25i	−0.548359	−	0.836243i
$65$	−3327.76			−0.787635
$66$	−1567.77	−	1290.43i	−0.359912	−	0.296241i
$67$			6169.67i			1.37440i	0.726470	+	0.687199i	$0.241160\pi$
$67$			6169.67i			1.37440i	−0.726470	+	0.687199i	$0.758840\pi$
$68$	−181.004	−	923.879i	−0.0391445	−	0.199801i
$69$	−628.315			−0.131971
$70$	−2460.41	+	2989.22i	−0.502124	+	0.610045i
$71$		−	882.122i		−	0.174990i	−0.996165	−	0.0874948i	$-0.972114\pi$
$71$		−	882.122i		−	0.174990i	0.996165	−	0.0874948i	$-0.0278861\pi$
$72$	−821.156	+	1520.42i	−0.158402	+	0.293292i
$73$	1659.75			0.311457			0.155728	−	0.987800i	$-0.450228\pi$
$73$	1659.75			0.311457			0.155728	+	0.987800i	$0.450228\pi$
$74$	−3592.90	−	2957.30i	−0.656118	−	0.540047i
$75$		−	649.519i		−	0.115470i
$76$	7808.59	−	1529.84i	1.35190	−	0.264861i
$77$	8457.51			1.42647
$78$	3931.50	−	4776.50i	0.646204	−	0.785091i
$79$		−	7276.52i		−	1.16592i	−0.812500	−	0.582961i	$-0.801894\pi$
$79$		−	7276.52i		−	1.16592i	0.812500	−	0.582961i	$-0.198106\pi$
$80$	−2650.57	+	1080.04i	−0.414151	+	0.168756i
$81$	729.000			0.111111
$82$	−9816.61	−	8079.99i	−1.45994	−	1.20166i
$83$		−	5346.39i		−	0.776076i	−0.921643	−	0.388038i	$-0.873153\pi$
$83$		−	5346.39i		−	0.776076i	0.921643	−	0.388038i	$-0.126847\pi$
$84$	−1383.78	−	7063.09i	−0.196114	−	1.00100i
$85$	−657.854			−0.0910524
$86$	−2964.55	+	3601.72i	−0.400831	+	0.486982i
$87$			4921.17i			0.650174i
$88$	5501.38	+	2971.20i	0.710406	+	0.383678i
$89$	9009.81			1.13746			0.568730	−	0.822525i	$-0.307435\pi$
$89$	9009.81			1.13746			0.568730	+	0.822525i	$0.307435\pi$
$90$	932.287	+	767.360i	0.115097	+	0.0947358i
$91$			25767.3i			3.11161i
$92$	1898.61	−	371.971i	0.224316	−	0.0439475i
$93$	−2907.01			−0.336109
$94$	−2694.57	+	3273.71i	−0.304954	+	0.370497i
$95$		−	5560.15i		−	0.616083i
$96$	1581.22	−	5080.48i	0.171573	−	0.551268i
$97$	−9798.06			−1.04135			−0.520675	−	0.853755i	$-0.674320\pi$
$97$	−9798.06			−1.04135			−0.520675	+	0.853755i	$0.674320\pi$
$98$	15730.7	+	12947.9i	1.63793	+	1.34817i
$99$		−	2637.76i		−	0.269131i
$100$	384.524	+	1962.69i	0.0384524	+	0.196269i
$101$	5404.90			0.529841			0.264920	−	0.964270i	$-0.414654\pi$
$101$	5404.90			0.529841			0.264920	+	0.964270i	$0.414654\pi$
$102$	777.206	−	944.250i	0.0747026	−	0.0907584i
$103$		−	8294.77i		−	0.781862i	−0.920420	−	0.390931i	$-0.872153\pi$
$103$		−	8294.77i		−	0.781862i	0.920420	−	0.390931i	$-0.127847\pi$
$104$	−9052.29	+	16760.9i	−0.836935	+	1.54964i
$105$	−5029.31			−0.456174
$106$	−4449.64	−	3662.47i	−0.396016	−	0.325958i
$107$		−	5744.62i		−	0.501758i	−0.968018	−	0.250879i	$-0.919280\pi$
$107$		−	5744.62i		−	0.501758i	0.968018	−	0.250879i	$-0.0807196\pi$
$108$	−2202.86	+	431.578i	−0.188860	+	0.0370009i
$109$	4709.84			0.396418			0.198209	−	0.980160i	$-0.436488\pi$
$109$	4709.84			0.396418			0.198209	+	0.980160i	$0.436488\pi$
$110$	2776.55	−	3373.31i	0.229467	−	0.278786i
$111$		−	6045.00i		−	0.490626i
$112$	8362.90	+	20523.7i	0.666685	+	1.63614i
$113$	241.555			0.0189173			0.00945864	−	0.999955i	$-0.496989\pi$
$113$	241.555			0.0189173			0.00945864	+	0.999955i	$0.496989\pi$
$114$	7980.76	+	6568.92i	0.614094	+	0.505457i
$115$		−	1351.92i		−	0.102224i
$116$	−2913.40	−	14870.6i	−0.216513	−	1.10513i
$117$	8036.38			0.587068
$118$	5096.14	−	6191.45i	0.365997	−	0.444660i
$119$			5093.85i			0.359710i
$120$	−3271.43	−	1766.85i	−0.227183	−	0.122698i
$121$	5096.75			0.348115
$122$	−10879.0	−	8954.45i	−0.730920	−	0.601616i
$123$		−	16516.3i		−	1.09170i
$124$	8784.26	−	1720.99i	0.571297	−	0.111927i
$125$	1397.54			0.0894427
$126$	5941.77	−	7218.82i	0.374261	−	0.454700i
$127$		−	6882.74i		−	0.426731i	−0.976972	−	0.213365i	$-0.931558\pi$
$127$		−	6882.74i		−	0.426731i	0.976972	−	0.213365i	$-0.0684425\pi$
$128$	−1770.34	+	16288.1i	−0.108053	+	0.994145i
$129$	−6059.83			−0.364151
$130$	10277.4	+	8459.25i	0.608129	+	0.500547i
$131$			1247.82i			0.0727126i	0.999339	+	0.0363563i	$0.0115751\pi$
$131$			1247.82i			0.0727126i	−0.999339	+	0.0363563i	$0.988425\pi$
$132$	1561.59	+	7970.65i	0.0896229	+	0.457452i
$133$	−43053.0			−2.43389
$134$	15683.5	−	19054.3i	0.873439	−	1.06117i
$135$			1568.56i			0.0860663i
$136$	−1789.52	+	3313.41i	−0.0967516	+	0.179142i
$137$	1712.53			0.0912422			0.0456211	−	0.998959i	$-0.485473\pi$
$137$	1712.53			0.0912422			0.0456211	+	0.998959i	$0.485473\pi$
$138$	1940.48	+	1597.19i	0.101894	+	0.0838686i
$139$			6748.58i			0.349287i	0.984632	+	0.174644i	$0.0558773\pi$
$139$			6748.58i			0.349287i	−0.984632	+	0.174644i	$0.944123\pi$
$140$	15197.3	−	2977.42i	0.775375	−	0.151909i
$141$	−5507.97			−0.277047
$142$	−2242.38	+	2724.33i	−0.111207	+	0.135109i
$143$		−	29078.2i		−	1.42199i
$144$	6401.00	−	2608.25i	0.308690	−	0.125784i
$145$	−10588.7			−0.503623
$146$	−5125.95	−	4219.14i	−0.240474	−	0.197933i
$147$			26466.7i			1.22480i
$148$	3578.73	+	18266.5i	0.163382	+	0.833935i
$149$	−38109.7			−1.71657			−0.858287	−	0.513170i	$-0.828471\pi$
$149$	−38109.7			−1.71657			−0.858287	+	0.513170i	$0.828471\pi$
$150$	−1651.10	+	2005.96i	−0.0733820	+	0.0891539i
$151$		−	4383.99i		−	0.192272i	−0.995368	−	0.0961360i	$-0.969352\pi$
$151$		−	4383.99i		−	0.192272i	0.995368	−	0.0961360i	$-0.0306484\pi$
$152$	−28004.8	−	15124.9i	−1.21212	−	0.654645i
$153$	1588.69			0.0678665
$154$	−26120.0	−	21499.2i	−1.10137	−	0.906528i
$155$		−	6254.88i		−	0.260349i
$156$	−24284.0	+	4757.65i	−0.997862	+	0.195498i
$157$	18910.0			0.767173			0.383586	−	0.923505i	$-0.374689\pi$
$157$	18910.0			0.767173			0.383586	+	0.923505i	$0.374689\pi$
$158$	−18497.1	+	22472.7i	−0.740951	+	0.900202i
$159$		−	7486.44i		−	0.296129i
$160$	10931.5	+	3402.24i	0.427010	+	0.132900i
$161$	−10468.1			−0.403846
$162$	−2251.43	−	1853.14i	−0.0857884	−	0.0706119i
$163$		−	2243.95i		−	0.0844575i	−0.999108	−	0.0422288i	$-0.986554\pi$
$163$		−	2243.95i		−	0.0844575i	0.999108	−	0.0422288i	$-0.0134458\pi$
$164$	9777.88	+	49908.2i	0.363544	+	1.85560i
$165$	5675.55			0.208468
$166$	−13590.7	+	16511.7i	−0.493201	+	0.599204i
$167$		−	24011.7i		−	0.860972i	−0.902597	−	0.430486i	$-0.858342\pi$
$167$		−	24011.7i		−	0.860972i	0.902597	−	0.430486i	$-0.141658\pi$
$168$	−13680.9	+	25331.1i	−0.484726	+	0.897503i
$169$	60030.7			2.10184
$170$	2031.70	+	1672.28i	0.0703011	+	0.0578644i
$171$			13427.5i			0.459201i
$172$	18311.3	−	3587.51i	0.618960	−	0.121265i
$173$	−38810.8			−1.29676			−0.648381	−	0.761316i	$-0.724554\pi$
$173$	−38810.8			−1.29676			−0.648381	+	0.761316i	$0.724554\pi$
$174$	12509.7	−	15198.4i	0.413190	−	0.501996i
$175$		−	10821.4i		−	0.353350i
$176$	−9437.48	−	23160.9i	−0.304671	−	0.747704i
$177$	10417.0			0.332504
$178$	−27825.7	−	22903.2i	−0.878227	−	0.722863i
$179$			56139.5i			1.75211i	0.482207	+	0.876057i	$0.339835\pi$
$179$			56139.5i			1.75211i	−0.482207	+	0.876057i	$0.660165\pi$
$180$	−928.609	−	4739.80i	−0.0286608	−	0.146290i
$181$	19958.6			0.609217			0.304609	−	0.952478i	$-0.401474\pi$
$181$	19958.6			0.609217			0.304609	+	0.952478i	$0.401474\pi$
$182$	65501.1	−	79579.2i	1.97745	−	2.40246i
$183$		−	18303.8i		−	0.546561i
$184$	−6809.20	−	3677.54i	−0.201122	−	0.108623i
$185$	13006.8			0.380037
$186$	8977.95	+	7389.69i	0.259508	+	0.213600i
$187$		−	5748.38i		−	0.164385i
$188$	16643.7	−	3260.80i	0.470907	−	0.0922588i
$189$	12145.6			0.340012
$190$	−14134.1	+	17171.9i	−0.391525	+	0.475675i
$191$			57207.0i			1.56813i	0.620677	+	0.784066i	$0.286858\pi$
$191$			57207.0i			1.56813i	−0.620677	+	0.784066i	$0.713142\pi$
$192$	−17798.1	+	11671.0i	−0.482805	+	0.316595i
$193$	−4603.04			−0.123575			−0.0617874	−	0.998089i	$-0.519680\pi$
$193$	−4603.04			−0.123575			−0.0617874	+	0.998089i	$0.519680\pi$
$194$	30260.1	+	24906.9i	0.804021	+	0.661785i
$195$			17291.5i			0.454741i
$196$	−15668.7	−	79975.8i	−0.407868	−	2.08184i
$197$	30077.6			0.775017			0.387509	−	0.921866i	$-0.373336\pi$
$197$	30077.6			0.775017			0.387509	+	0.921866i	$0.373336\pi$
$198$	−6705.25	+	8146.40i	−0.171035	+	0.207795i
$199$		−	42243.9i		−	1.06674i	−0.845883	−	0.533369i	$-0.820926\pi$
$199$		−	42243.9i		−	1.06674i	0.845883	−	0.533369i	$-0.179074\pi$
$200$	3801.65	−	7039.00i	0.0950411	−	0.175975i
$201$	32058.5			0.793509
$202$	−16692.4	−	13739.4i	−0.409087	−	0.336717i
$203$			81989.5i			1.98960i
$204$	−4800.62	+	940.525i	−0.115355	+	0.0226001i
$205$	35537.4			0.845625
$206$	−21085.5	+	25617.4i	−0.496878	+	0.603672i
$207$			3264.82i			0.0761936i
$208$	70563.6	−	28752.9i	1.63100	−	0.664592i
$209$	48585.0			1.11227
$210$	15532.4	+	12784.7i	0.352209	+	0.289901i
$211$			3093.80i			0.0694908i	0.999396	+	0.0347454i	$0.0110620\pi$
$211$			3093.80i			0.0694908i	−0.999396	+	0.0347454i	$0.988938\pi$
$212$	4432.08	+	22622.2i	0.0986134	+	0.503342i
$213$	−4583.64			−0.101030
$214$	−14603.0	+	17741.6i	−0.318870	+	0.387405i
$215$		−	13038.7i		−	0.282070i
$216$	7900.35	+	4266.85i	0.169332	+	0.0914534i
$217$	−48432.4			−1.02853
$218$	−14545.8	−	11972.5i	−0.306072	−	0.251926i
$219$		−	8624.33i		−	0.179820i
$220$	−17150.1	+	3360.00i	−0.354341	+	0.0694216i
$221$	17513.4			0.358580
$222$	−15366.6	+	18669.3i	−0.311796	+	0.378810i
$223$		−	43059.5i		−	0.865884i	−0.901422	−	0.432942i	$-0.857475\pi$
$223$		−	43059.5i		−	0.865884i	0.901422	−	0.432942i	$-0.142525\pi$
$224$	26344.0	−	84643.7i	0.525032	−	1.68694i
$225$	−3375.00			−0.0666667
$226$	−746.013	−	614.039i	−0.0146059	−	0.0120221i
$227$			43385.8i			0.841968i	0.907068	+	0.420984i	$0.138315\pi$
$227$			43385.8i			0.841968i	−0.907068	+	0.420984i	$0.861685\pi$
$228$	−7949.28	−	40574.6i	−0.152918	−	0.780522i
$229$	56036.8			1.06857			0.534285	−	0.845305i	$-0.320581\pi$
$229$	56036.8			1.06857			0.534285	+	0.845305i	$0.320581\pi$
$230$	−3436.61	+	4175.24i	−0.0649643	+	0.0789270i
$231$		−	43946.5i		−	0.823570i
$232$	−28803.7	+	53331.9i	−0.535146	+	0.990857i
$233$	−41638.3			−0.766974			−0.383487	−	0.923546i	$-0.625277\pi$
$233$	−41638.3			−0.766974			−0.383487	+	0.923546i	$0.625277\pi$
$234$	−24819.4	−	20428.7i	−0.453273	−	0.373086i
$235$		−	11851.3i		−	0.214600i
$236$	−31477.7	+	6167.02i	−0.565169	+	0.110726i
$237$	−37809.9			−0.673145
$238$	12948.7	−	15731.7i	0.228598	−	0.277730i
$239$			71028.3i			1.24347i	0.783227	+	0.621736i	$0.213572\pi$
$239$			71028.3i			1.24347i	−0.783227	+	0.621736i	$0.786428\pi$
$240$	5612.06	+	13772.8i	0.0974315	+	0.239110i
$241$	−58695.9			−1.01059			−0.505294	−	0.862947i	$-0.668616\pi$
$241$	−58695.9			−1.01059			−0.505294	+	0.862947i	$0.668616\pi$
$242$	−15740.7	−	12956.1i	−0.268778	−	0.221229i
$243$		−	3788.00i		−	0.0641500i
$244$	10836.1	+	55309.5i	0.182009	+	0.929009i
$245$	−56947.2			−0.948725
$246$	−41984.9	+	51008.6i	−0.693781	+	0.842895i
$247$			148023.i			2.42624i
$248$	−31504.0	−	17014.8i	−0.512226	−	0.276645i
$249$	−27780.6			−0.448068
$250$	−4316.14	−	3552.59i	−0.0690583	−	0.0568415i
$251$		−	40236.7i		−	0.638668i	−0.947642	−	0.319334i	$-0.896541\pi$
$251$		−	40236.7i		−	0.638668i	0.947642	−	0.319334i	$-0.103459\pi$
$252$	−36700.9	+	7190.34i	−0.577930	+	0.113227i
$253$	11813.2			0.184555
$254$	−17496.1	+	21256.5i	−0.271190	+	0.329477i
$255$			3418.31i			0.0525691i
$256$	46872.2	−	45803.5i	0.715213	−	0.698907i
$257$	−85304.1			−1.29153			−0.645763	−	0.763538i	$-0.723461\pi$
$257$	−85304.1			−1.29153			−0.645763	+	0.763538i	$0.723461\pi$
$258$	18715.1	+	15404.3i	0.281159	+	0.231420i
$259$		−	100713.i		−	1.50137i
$260$	−10236.8	−	52250.8i	−0.151432	−	0.772940i
$261$	25571.1			0.375378
$262$	3172.00	−	3853.75i	0.0462094	−	0.0561411i
$263$		−	87162.9i		−	1.26014i	−0.776537	−	0.630072i	$-0.783025\pi$
$263$		−	87162.9i		−	1.26014i	0.776537	−	0.630072i	$-0.216975\pi$
$264$	15438.8	−	28586.0i	0.221517	−	0.410153i
$265$	16108.3			0.229381
$266$	132964.	+	109442.i	1.87919	+	1.54675i
$267$		−	46816.4i		−	0.656712i
$268$	−96873.0	+	18979.1i	−1.34876	+	0.264245i
$269$	−125878.			−1.73958			−0.869789	−	0.493424i	$-0.835745\pi$
$269$	−125878.			−1.73958			−0.869789	+	0.493424i	$0.835745\pi$
$270$	3987.32	−	4844.31i	0.0546957	−	0.0664514i
$271$		−	94283.5i		−	1.28380i	−0.766789	−	0.641899i	$-0.778147\pi$
$271$		−	94283.5i		−	1.28380i	0.766789	−	0.641899i	$-0.221853\pi$
$272$	13949.5	−	5684.07i	0.188547	−	0.0768283i
$273$	133891.			1.79649
$274$	−5288.93	−	4353.29i	−0.0704477	−	0.0579850i
$275$			12211.8i			0.161479i
$276$	−1932.82	−	9865.48i	−0.0253731	−	0.129509i
$277$	65798.3			0.857541			0.428771	−	0.903413i	$-0.358947\pi$
$277$	65798.3			0.857541			0.428771	+	0.903413i	$0.358947\pi$
$278$	17155.1	−	20842.2i	0.221974	−	0.269683i
$279$			15105.3i			0.194053i
$280$	−54503.9	−	29436.7i	−0.695203	−	0.375468i
$281$	16122.0			0.204177			0.102088	−	0.994775i	$-0.467448\pi$
$281$	16122.0			0.204177			0.102088	+	0.994775i	$0.467448\pi$
$282$	17010.7	+	14001.4i	0.213907	+	0.176065i
$283$			128462.i			1.60399i	0.597329	+	0.801997i	$0.296229\pi$
$283$			128462.i			1.60399i	−0.597329	+	0.801997i	$0.703771\pi$
$284$	13850.6	−	2713.58i	0.171725	−	0.0336439i
$285$	−28891.4			−0.355696
$286$	−73917.6	+	89804.6i	−0.903682	+	1.09791i
$287$		−	275171.i		−	3.34071i
$288$	−26399.0	−	8216.25i	−0.318275	−	0.0990578i
$289$	−80058.8			−0.958547
$290$	32701.8	+	26916.7i	0.388845	+	0.320056i
$291$			50912.2i			0.601224i
$292$	5105.73	+	26060.6i	0.0598814	+	0.305646i
$293$	161599.			1.88236			0.941180	−	0.337906i	$-0.109718\pi$
$293$	161599.			1.88236			0.941180	+	0.337906i	$0.109718\pi$
$294$	67279.0	−	81739.2i	0.778368	−	0.945662i
$295$			22413.8i			0.257556i
$296$	35381.5	−	65511.2i	0.403825	−	0.747708i
$297$	−13706.2			−0.155383
$298$	117697.	+	96875.8i	1.32536	+	1.09089i
$299$			35990.8i			0.402578i
$300$	10198.4	−	1998.05i	0.113316	−	0.0222005i
$301$	−100960.			−1.11434
$302$	−11144.2	+	13539.4i	−0.122190	+	0.148452i
$303$		−	28084.7i		−	0.305904i
$304$	48041.5	+	117901.i	0.519840	+	1.27576i
$305$	39383.4			0.423364
$306$	−4906.47	−	4038.48i	−0.0523994	−	0.0431296i
$307$			39700.0i			0.421224i	0.977570	+	0.210612i	$0.0675457\pi$
$307$			39700.0i			0.421224i	−0.977570	+	0.210612i	$0.932454\pi$
$308$	26017.0	+	132796.i	0.274255	+	1.39985i
$309$	−43100.9			−0.451408
$310$	−15900.1	+	19317.5i	−0.165454	+	0.201014i
$311$		−	16610.8i		−	0.171739i	−0.996306	−	0.0858696i	$-0.972633\pi$
$311$		−	16610.8i		−	0.171739i	0.996306	−	0.0858696i	$-0.0273669\pi$
$312$	87092.2	+	47037.1i	0.894685	+	0.483205i
$313$	−34354.3			−0.350665			−0.175332	−	0.984509i	$-0.556100\pi$
$313$	−34354.3			−0.350665			−0.175332	+	0.984509i	$0.556100\pi$
$314$	−58401.4	−	48069.8i	−0.592331	−	0.487544i
$315$			26133.1i			0.263372i
$316$	114252.	−	22384.0i	1.14417	−	0.224163i
$317$	−51349.0			−0.510991			−0.255495	−	0.966810i	$-0.582239\pi$
$317$	−51349.0			−0.510991			−0.255495	+	0.966810i	$0.582239\pi$
$318$	−19030.7	+	23121.0i	−0.188192	+	0.228640i
$319$		−	92524.6i		−	0.909234i
$320$	−25111.9	−	38295.5i	−0.245234	−	0.373979i
$321$	−29849.9			−0.289690
$322$	32329.4	+	26610.2i	0.311807	+	0.256647i
$323$			29262.1i			0.280479i
$324$	2242.55	+	11446.4i	0.0213625	+	0.109038i
$325$	−37205.5			−0.352241
$326$	−5704.19	+	6930.18i	−0.0536733	+	0.0652092i
$327$		−	24473.0i		−	0.228872i
$328$	96670.1	−	178991.i	0.898555	−	1.66373i
$329$	−91765.9			−0.847792
$330$	−17528.3	−	14427.4i	−0.160957	−	0.132483i
$331$			28680.3i			0.261775i	0.991397	+	0.130887i	$0.0417826\pi$
$331$			28680.3i			0.261775i	−0.991397	+	0.130887i	$0.958217\pi$
$332$	83946.3	−	16446.5i	0.761597	−	0.149210i
$333$	−31410.7			−0.283263
$334$	−61038.3	+	74157.2i	−0.547154	+	0.664753i
$335$			68979.0i			0.614649i
$336$	106644.	−	43454.9i	0.944624	−	0.384911i
$337$	99523.5			0.876326			0.438163	−	0.898895i	$-0.355629\pi$
$337$	99523.5			0.876326			0.438163	+	0.898895i	$0.355629\pi$
$338$	−185398.	−	152600.i	−1.62282	−	1.33574i
$339$		−	1255.16i		−	0.0109219i
$340$	−2023.69	−	10329.3i	−0.0175059	−	0.0893537i
$341$	54655.7			0.470031
$342$	34133.1	−	41469.3i	0.291826	−	0.354547i
$343$			233093.i			1.98126i
$344$	−65671.9	−	35468.3i	−0.554961	−	0.299725i
$345$	−7024.77			−0.0590193
$346$	119863.	+	98658.1i	1.00122	+	0.824102i
$347$			47129.6i			0.391413i	0.980663	+	0.195706i	$0.0626999\pi$
$347$			47129.6i			0.391413i	−0.980663	+	0.195706i	$0.937300\pi$
$348$	−77269.7	+	15138.5i	−0.638044	+	0.125004i
$349$	171932.			1.41158			0.705792	−	0.708419i	$-0.250591\pi$
$349$	171932.			1.41158			0.705792	+	0.708419i	$0.250591\pi$
$350$	−27508.2	+	33420.5i	−0.224557	+	0.272820i
$351$		−	41758.2i		−	0.338944i
$352$	−29729.0	+	95519.9i	−0.239936	+	0.770919i
$353$	210420.			1.68864			0.844321	−	0.535837i	$-0.180004\pi$
$353$	210420.			1.68864			0.844321	+	0.535837i	$0.180004\pi$
$354$	−32171.7	−	26480.3i	−0.256725	−	0.211308i
$355$		−	9862.43i		−	0.0782577i
$356$	27716.0	+	141468.i	0.218690	+	1.11624i
$357$	26468.4			0.207678
$358$	142708.	−	173380.i	1.11348	−	1.35280i
$359$		−	123067.i		−	0.954888i	−0.878662	−	0.477444i	$-0.841563\pi$
$359$		−	123067.i		−	0.954888i	0.878662	−	0.477444i	$-0.158437\pi$
$360$	−9180.80	+	16998.9i	−0.0708395	+	0.131164i
$361$	−117001.			−0.897794
$362$	−61639.6	−	50735.2i	−0.470374	−	0.387162i
$363$		−	26483.5i		−	0.200984i
$364$	−404585.	+	79265.2i	−3.05356	+	0.598246i
$365$	18556.6			0.139288
$366$	−46528.7	+	56529.0i	−0.347343	+	0.421997i
$367$		−	113887.i		−	0.845553i	−0.906234	−	0.422777i	$-0.861056\pi$
$367$		−	113887.i		−	0.845553i	0.906234	−	0.422777i	$-0.138944\pi$
$368$	11681.0	+	28666.8i	0.0862551	+	0.211682i
$369$	−85821.2			−0.630292
$370$	−40169.9	−	33063.6i	−0.293425	−	0.241516i
$371$		−	124728.i		−	0.906187i
$372$	−8942.52	−	45644.4i	−0.0646211	−	0.329838i
$373$	−69712.3			−0.501062			−0.250531	−	0.968109i	$-0.580605\pi$
$373$	−69712.3			−0.501062			−0.250531	+	0.968109i	$0.580605\pi$
$374$	−14612.5	+	17753.2i	−0.104468	+	0.126921i
$375$		−	7261.84i		−	0.0516398i
$376$	−59691.2	−	32238.2i	−0.422216	−	0.228032i
$377$	281892.			1.98335
$378$	−37510.1	−	30874.3i	−0.262521	−	0.216080i
$379$			35367.5i			0.246222i	0.992393	+	0.123111i	$0.0392871\pi$
$379$			35367.5i			0.246222i	−0.992393	+	0.123111i	$0.960713\pi$
$380$	87302.7	−	17104.1i	0.604589	−	0.118450i
$381$	−35763.8			−0.246373
$382$	145422.	−	176677.i	0.996559	−	1.21075i
$383$			256391.i			1.74785i	0.486058	+	0.873926i	$0.338434\pi$
$383$			256391.i			1.74785i	−0.486058	+	0.873926i	$0.661566\pi$
$384$	84635.3	+	9198.93i	0.573970	+	0.0623843i
$385$	94557.9			0.637935
$386$	14215.9	+	11701.1i	0.0954116	+	0.0785327i
$387$			31487.8i			0.210242i
$388$	−30140.8	−	153844.i	−0.200212	−	1.02192i
$389$	55802.7			0.368770			0.184385	−	0.982854i	$-0.440971\pi$
$389$	55802.7			0.368770			0.184385	+	0.982854i	$0.440971\pi$
$390$	43955.5	−	53402.8i	0.288991	−	0.351104i
$391$			7114.91i			0.0465389i
$392$	−154910.	+	286826.i	−1.00811	+	1.86658i
$393$	6483.87			0.0419806
$394$	−92891.2	−	76458.2i	−0.598387	−	0.492529i
$395$		−	81353.9i		−	0.521416i
$396$	41416.7	−	8114.25i	0.264110	−	0.0517438i
$397$	−264607.			−1.67888			−0.839442	−	0.543449i	$-0.817118\pi$
$397$	−264607.			−1.67888			−0.839442	+	0.543449i	$0.817118\pi$
$398$	−107385.	+	130465.i	−0.677919	+	0.823623i
$399$			223710.i			1.40520i
$400$	−29634.3	+	12075.2i	−0.185214	+	0.0754701i
$401$	−232397.			−1.44525			−0.722623	−	0.691243i	$-0.757063\pi$
$401$	−232397.			−1.44525			−0.722623	+	0.691243i	$0.757063\pi$
$402$	−99009.0	−	81493.7i	−0.612664	−	0.504280i
$403$			166518.i			1.02530i
$404$	16626.5	+	84865.1i	0.101868	+	0.519956i
$405$	8150.47			0.0496904
$406$	208419.	−	253215.i	1.26441	−	1.53616i
$407$			113654.i			0.686114i
$408$	17217.0	+	9298.60i	0.103428	+	0.0558596i
$409$	−72108.2			−0.431060			−0.215530	−	0.976497i	$-0.569148\pi$
$409$	−72108.2			−0.431060			−0.215530	+	0.976497i	$0.569148\pi$
$410$	−109753.	−	90337.1i	−0.652903	−	0.537401i
$411$		−	8898.54i		−	0.0526787i
$412$	130240.	−	25516.3i	0.767275	−	0.150322i
$413$	173553.			1.01750
$414$	8299.26	−	10083.0i	0.0484216	−	0.0588287i
$415$		−	59774.4i		−	0.347072i
$416$	−291018.	−	90574.6i	−1.68164	−	0.523383i
$417$	35066.6			0.201661
$418$	−150049.	−	123504.i	−0.858778	−	0.706855i
$419$		−	36120.5i		−	0.205743i	−0.994695	−	0.102872i	$-0.967197\pi$
$419$		−	36120.5i		−	0.205743i	0.994695	−	0.102872i	$-0.0328031\pi$
$420$	−15471.2	−	78967.7i	−0.0877049	−	0.447663i
$421$	218504.			1.23281			0.616405	−	0.787429i	$-0.288589\pi$
$421$	218504.			1.23281			0.616405	+	0.787429i	$0.288589\pi$
$422$	7864.53	−	9554.84i	0.0441619	−	0.0536535i
$423$			28620.2i			0.159953i
$424$	43818.3	−	81132.4i	0.243738	−	0.451297i
$425$	−7355.03			−0.0407199
$426$	14156.0	+	11651.7i	0.0780050	+	0.0642054i
$427$		−	304951.i		−	1.67253i
$428$	90199.2	−	17671.6i	0.492397	−	0.0964691i
$429$	−151095.			−0.820984
$430$	−33144.7	+	40268.4i	−0.179257	+	0.217785i
$431$		−	84359.7i		−	0.454130i	−0.973880	−	0.227065i	$-0.927087\pi$
$431$		−	84359.7i		−	0.454130i	0.973880	−	0.227065i	$-0.0729130\pi$
$432$	−13552.9	−	33260.6i	−0.0726212	−	0.178222i
$433$	−80951.5			−0.431767			−0.215883	−	0.976419i	$-0.569263\pi$
$433$	−80951.5			−0.431767			−0.215883	+	0.976419i	$0.569263\pi$
$434$	149578.	+	123116.i	0.794122	+	0.653637i
$435$			55020.3i			0.290767i
$436$	14488.4	+	73951.5i	0.0762161	+	0.389022i
$437$	−60135.0			−0.314894
$438$	−21923.3	+	26635.2i	−0.114277	+	0.138838i
$439$			31983.1i			0.165955i	0.996551	+	0.0829777i	$0.0264430\pi$
$439$			31983.1i			0.165955i	−0.996551	+	0.0829777i	$0.973557\pi$
$440$	61507.3	+	33219.1i	0.317703	+	0.171586i
$441$	137525.			0.707138
$442$	−54088.1	−	44519.6i	−0.276858	−	0.227880i
$443$		−	376981.i		−	1.92093i	−0.278394	−	0.960467i	$-0.589802\pi$
$443$		−	376981.i		−	1.92093i	0.278394	−	0.960467i	$-0.410198\pi$
$444$	94915.6	−	18595.6i	0.481473	−	0.0943288i
$445$	100733.			0.508687
$446$	−109459.	+	132984.i	−0.550275	+	0.668545i
$447$			198024.i			0.991064i
$448$	−296527.	+	194445.i	−1.47743	+	0.968815i
$449$	−105390.			−0.522767			−0.261384	−	0.965235i	$-0.584179\pi$
$449$	−105390.			−0.522767			−0.261384	+	0.965235i	$0.584179\pi$
$450$	10423.3	+	8579.34i	0.0514730	+	0.0423671i
$451$			310529.i			1.52668i
$452$	743.070	+	3792.77i	0.00363708	+	0.0185644i
$453$	−22779.9			−0.111008
$454$	110288.	−	133992.i	0.535076	−	0.650080i
$455$			288087.i			1.39156i
$456$	−78591.4	+	145517.i	−0.377960	+	0.699817i
$457$	−260309.			−1.24640			−0.623200	−	0.782063i	$-0.714168\pi$
$457$	−260309.			−1.24640			−0.623200	+	0.782063i	$0.714168\pi$
$458$	−173063.	−	142447.i	−0.825037	−	0.679083i
$459$		−	8255.05i		−	0.0391827i
$460$	21227.1	−	4158.77i	0.100317	−	0.0196539i
$461$	112820.			0.530865			0.265433	−	0.964129i	$-0.414485\pi$
$461$	112820.			0.530865			0.265433	+	0.964129i	$0.414485\pi$
$462$	−111713.	+	135724.i	−0.523384	+	0.635875i
$463$		−	188351.i		−	0.878628i	−0.898334	−	0.439314i	$-0.855222\pi$
$463$		−	188351.i		−	0.878628i	0.898334	−	0.439314i	$-0.144778\pi$
$464$	224528.	−	91489.5i	1.04288	−	0.424948i
$465$	−32501.3			−0.150313
$466$	128595.	+	105846.i	0.592177	+	0.487417i
$467$			373875.i			1.71432i	0.515048	+	0.857161i	$0.327774\pi$
$467$			373875.i			1.71432i	−0.515048	+	0.857161i	$0.672226\pi$
$468$	24721.5	+	126183.i	0.112871	+	0.576116i
$469$	534114.			2.42822
$470$	−30126.2	+	36601.2i	−0.136379	+	0.165691i
$471$		−	98259.5i		−	0.442927i
$472$	112892.	+	60971.0i	0.506732	+	0.273677i
$473$	113933.			0.509245
$474$	116771.	+	96113.7i	0.519732	+	0.427788i
$475$		−	62164.4i		−	0.275521i
$476$	−79981.0	+	15669.7i	−0.352999	+	0.0691586i
$477$	−38900.7			−0.170970
$478$	180556.	−	219363.i	0.790235	−	0.960079i
$479$			169326.i			0.737993i	0.929431	+	0.368997i	$0.120299\pi$
$479$			169326.i			0.737993i	−0.929431	+	0.368997i	$0.879701\pi$
$480$	17678.6	−	56801.5i	0.0767298	−	0.246534i
$481$	−346267.			−1.49665
$482$	181275.	+	149207.i	0.780270	+	0.642235i
$483$			54393.8i			0.233160i
$484$	15678.6	+	80026.6i	0.0669294	+	0.341620i
$485$	−109546.			−0.465706
$486$	−9629.19	+	11698.8i	−0.0407678	+	0.0495299i
$487$		−	27221.0i		−	0.114774i	−0.998352	−	0.0573872i	$-0.981723\pi$
$487$		−	27221.0i		−	0.114774i	0.998352	−	0.0573872i	$-0.0182770\pi$
$488$	107132.	−	198362.i	0.449863	−	0.832952i
$489$	−11659.9			−0.0487616
$490$	175875.	+	144761.i	0.732506	+	0.602921i
$491$		−	437686.i		−	1.81552i	−0.419495	−	0.907758i	$-0.637793\pi$
$491$		−	437686.i		−	1.81552i	0.419495	−	0.907758i	$-0.362207\pi$
$492$	259331.	−	50807.4i	1.07133	−	0.209892i
$493$	55726.3			0.229280
$494$	376278.	−	457151.i	1.54189	−	1.87329i
$495$		−	29491.0i		−	0.120359i
$496$	54044.2	+	132632.i	0.219678	+	0.539119i
$497$	−76366.1			−0.309163
$498$	85797.2	+	70619.1i	0.345951	+	0.284750i
$499$		−	347647.i		−	1.39617i	−0.716016	−	0.698084i	$-0.754036\pi$
$499$		−	347647.i		−	1.39617i	0.716016	−	0.698084i	$-0.245964\pi$
$500$	4299.11	+	21943.5i	0.0171965	+	0.0877740i
$501$	−124768.			−0.497083
$502$	−102283.	+	124266.i	−0.405878	+	0.493112i
$503$		−	262758.i		−	1.03853i	−0.854612	−	0.519267i	$-0.826205\pi$
$503$		−	262758.i		−	1.03853i	0.854612	−	0.519267i	$-0.173795\pi$
$504$	131624.	+	71088.1i	0.518174	+	0.279857i
$505$	60428.7			0.236952
$506$	−36483.6	−	30029.4i	−0.142494	−	0.117286i
$507$		−	311929.i		−	1.21350i
$508$	108069.	−	21172.7i	0.418769	−	0.0820442i
$509$	192747.			0.743963			0.371981	−	0.928240i	$-0.378679\pi$
$509$	192747.			0.743963			0.371981	+	0.928240i	$0.378679\pi$
$510$	8689.43	−	10557.0i	0.0334080	−	0.0405884i
$511$		−	143686.i		−	0.550267i
$512$	−261193.	+	22308.4i	−0.996372	+	0.0850998i
$513$	69771.4			0.265120
$514$	263451.	+	216845.i	0.997182	+	0.820774i
$515$		−	92738.4i		−	0.349659i
$516$	−18641.2	−	95148.4i	−0.0700124	−	0.357357i
$517$	103557.			0.387435
$518$	−256016.	+	311041.i	−0.954129	+	1.15920i
$519$			201667.i			0.748686i
$520$	−101208.	+	187393.i	−0.374289	+	0.693020i
$521$	377715.			1.39152			0.695760	−	0.718275i	$-0.255068\pi$
$521$	377715.			1.39152			0.695760	+	0.718275i	$0.255068\pi$
$522$	−78973.4	−	65002.5i	−0.289828	−	0.238555i
$523$			234085.i			0.855798i	0.903827	+	0.427899i	$0.140746\pi$
$523$			234085.i			0.855798i	−0.903827	+	0.427899i	$0.859254\pi$
$524$	−19592.7	+	3838.54i	−0.0713561	+	0.0139799i
$525$	−56229.4			−0.204007
$526$	−221570.	+	269192.i	−0.800830	+	0.972951i
$527$			32918.4i			0.118527i
$528$	−120347.	+	49038.6i	−0.431687	+	0.175902i
$529$	265220.			0.947751
$530$	−49748.4	−	40947.6i	−0.177104	−	0.145773i
$531$		−	54128.4i		−	0.191971i
$532$	−132439.	−	675997.i	−0.467944	−	2.38848i
$533$	−946079.			−3.33022
$534$	−119008.	+	144587.i	−0.417345	+	0.507044i
$535$		−	64226.8i		−	0.224393i
$536$	347426.	+	187639.i	1.20930	+	0.653121i
$537$	291709.			1.01158
$538$	388758.	+	319984.i	1.34312	+	1.10551i
$539$		−	497609.i		−	1.71282i
$540$	−24628.7	+	4825.19i	−0.0844606	+	0.0165473i
$541$	−27230.3			−0.0930374			−0.0465187	−	0.998917i	$-0.514813\pi$
$541$	−27230.3			−0.0930374			−0.0465187	+	0.998917i	$0.514813\pi$
$542$	−239671.	+	291183.i	−0.815863	+	0.991215i
$543$		−	103708.i		−	0.351732i
$544$	−57530.4	−	17905.4i	−0.194401	−	0.0605043i
$545$	52657.6			0.177283
$546$	−413505.	−	340354.i	−1.38706	−	1.14168i
$547$		−	219088.i		−	0.732225i	−0.930571	−	0.366112i	$-0.880689\pi$
$547$		−	219088.i		−	0.732225i	0.930571	−	0.366112i	$-0.119311\pi$
$548$	5268.06	+	26889.2i	0.0175424	+	0.0895400i
$549$	−95109.2			−0.315557
$550$	31042.8	−	37714.8i	0.102621	−	0.124677i
$551$			470997.i			1.55137i
$552$	−19109.0	+	35381.7i	−0.0627135	+	0.116118i
$553$	−629934.			−2.05989
$554$	−203210.	−	167261.i	−0.662104	−	0.544973i
$555$		−	67585.2i		−	0.219415i
$556$	−105963.	+	20759.9i	−0.342771	+	0.0671547i
$557$	−507368.			−1.63536			−0.817678	−	0.575675i	$-0.804739\pi$
$557$	−507368.			−1.63536			−0.817678	+	0.575675i	$0.804739\pi$
$558$	38398.0	−	46650.8i	0.123322	−	0.149827i
$559$			347116.i			1.11084i
$560$	93500.1	+	229462.i	0.298151	+	0.731703i
$561$	−29869.4			−0.0949077
$562$	−49790.9	−	40982.6i	−0.157644	−	0.129756i
$563$			165410.i			0.521850i	0.965359	+	0.260925i	$0.0840276\pi$
$563$			165410.i			0.521850i	−0.965359	+	0.260925i	$0.915972\pi$
$564$	−16943.6	−	86483.3i	−0.0532656	−	0.271878i
$565$	2700.67			0.00846007
$566$	326554.	−	396740.i	1.01935	−	1.23844i
$567$		−	63110.2i		−	0.196306i
$568$	−49674.1	−	26828.1i	−0.153969	−	0.0831561i
$569$	59830.4			0.184798			0.0923990	−	0.995722i	$-0.470546\pi$
$569$	59830.4			0.184798			0.0923990	+	0.995722i	$0.470546\pi$
$570$	89227.7	+	73442.7i	0.274631	+	0.226047i
$571$			149969.i			0.459969i	0.973194	+	0.229984i	$0.0738675\pi$
$571$			149969.i			0.459969i	−0.973194	+	0.229984i	$0.926132\pi$
$572$	456571.	−	89450.2i	1.39546	−	0.273394i
$573$	297256.			0.905361
$574$	−699492.	+	849833.i	−2.12304	+	2.57935i
$575$		−	15114.9i		−	0.0457162i
$576$	60644.1	+	92481.8i	0.182786	+	0.278748i
$577$	−195679.			−0.587750			−0.293875	−	0.955844i	$-0.594945\pi$
$577$	−195679.			−0.587750			−0.293875	+	0.955844i	$0.594945\pi$
$578$	247252.	+	203512.i	0.740090	+	0.609163i
$579$			23918.1i			0.0713460i
$580$	−32572.8	−	166258.i	−0.0968276	−	0.494227i
$581$	−462841.			−1.37113
$582$	129420.	−	157236.i	0.382082	−	0.464202i
$583$			140755.i			0.414121i
$584$	50478.4	−	93464.0i	0.148006	−	0.274043i
$585$	89849.4			0.262545
$586$	−499078.	−	410788.i	−1.45336	−	1.19625i
$587$			273284.i			0.793119i	0.918009	+	0.396559i	$0.129796\pi$
$587$			273284.i			0.793119i	−0.918009	+	0.396559i	$0.870204\pi$
$588$	−415567.	+	81416.7i	−1.20195	+	0.235483i
$589$	−278225.			−0.801983
$590$	56976.6	−	69222.5i	0.163679	−	0.198858i
$591$		−	156288.i		−	0.447456i
$592$	−275803.	+	112383.i	−0.786964	+	0.320668i
$593$	151488.			0.430794			0.215397	−	0.976527i	$-0.430895\pi$
$593$	151488.			0.430794			0.215397	+	0.976527i	$0.430895\pi$
$594$	42329.9	+	34841.5i	0.119971	+	0.0987470i
$595$			56951.0i			0.160867i
$596$	−117233.	−	598379.i	−0.330032	−	1.68455i
$597$	−219506.			−0.615881
$598$	91489.7	−	111153.i	0.255841	−	0.310828i
$599$			371626.i			1.03575i	0.855458	+	0.517873i	$0.173276\pi$
$599$			371626.i			1.03575i	−0.855458	+	0.517873i	$0.826724\pi$
$600$	−36575.7	−	19753.9i	−0.101599	−	0.0548720i
$601$	368841.			1.02115			0.510575	−	0.859833i	$-0.329433\pi$
$601$	368841.			1.02115			0.510575	+	0.859833i	$0.329433\pi$
$602$	311804.	+	256644.i	0.860376	+	0.708170i
$603$		−	166581.i		−	0.458132i
$604$	68835.2	−	13486.0i	0.188685	−	0.0369666i
$605$	56983.4			0.155682
$606$	−71392.1	+	86736.3i	−0.194404	+	0.236187i
$607$			511656.i			1.38868i	0.719649	+	0.694338i	$0.244303\pi$
$607$			511656.i			1.38868i	−0.719649	+	0.694338i	$0.755697\pi$
$608$	151336.	−	486245.i	0.409387	−	1.31537i
$609$	426030.			1.14870
$610$	−121631.	−	100114.i	−0.326877	−	0.269051i
$611$			315505.i			0.845130i
$612$	4887.11	+	24944.7i	0.0130482	+	0.0666003i
$613$	−384682.			−1.02372			−0.511859	−	0.859069i	$-0.671043\pi$
$613$	−384682.			−1.02372			−0.511859	+	0.859069i	$0.671043\pi$
$614$	100918.	−	122609.i	0.267691	−	0.325225i
$615$		−	184658.i		−	0.488222i
$616$	257220.	−	476259.i	0.677864	−	1.25511i
$617$	326231.			0.856949			0.428475	−	0.903554i	$-0.359051\pi$
$617$	326231.			0.856949			0.428475	+	0.903554i	$0.359051\pi$
$618$	133112.	+	109564.i	0.348530	+	0.286873i
$619$		−	752595.i		−	1.96417i	−0.188428	−	0.982087i	$-0.560339\pi$
$619$		−	752595.i		−	1.96417i	0.188428	−	0.982087i	$-0.439661\pi$
$620$	98211.0	−	19241.2i	0.255492	−	0.0500553i
$621$	16964.5			0.0439904
$622$	−42225.1	+	51300.5i	−0.109141	+	0.132599i
$623$		−	779987.i		−	2.00961i
$624$	−149404.	−	366659.i	−0.383702	−	0.941658i
$625$	15625.0			0.0400000
$626$	106099.	+	87329.5i	0.270746	+	0.222850i
$627$		−	252455.i		−	0.642169i
$628$	58171.0	+	296916.i	0.147498	+	0.752860i
$629$	−68452.4			−0.173016
$630$	66431.0	−	80708.9i	0.167375	−	0.203348i
$631$			514641.i			1.29255i	0.763106	+	0.646273i	$0.223673\pi$
$631$			514641.i			1.29255i	−0.763106	+	0.646273i	$0.776327\pi$
$632$	−409755.	−	221302.i	−1.02586	−	0.554053i
$633$	16075.9			0.0401206
$634$	158585.	+	130530.i	0.394534	+	0.324738i
$635$		−	76951.4i		−	0.190840i
$636$	117548.	−	23029.8i	0.290605	−	0.0569345i
$637$	1.51605e6			3.73625
$638$	−235200.	+	285751.i	−0.577825	+	0.702016i
$639$			23817.3i			0.0583299i
$640$	−19793.0	+	182106.i	−0.0483226	+	0.444595i
$641$	417472.			1.01604			0.508021	−	0.861345i	$-0.330377\pi$
$641$	417472.			1.01604			0.508021	+	0.861345i	$0.330377\pi$
$642$	92188.0	+	75879.4i	0.223668	+	0.184100i
$643$		−	347739.i		−	0.841070i	−0.907276	−	0.420535i	$-0.861842\pi$
$643$		−	347739.i		−	0.841070i	0.907276	−	0.420535i	$-0.138158\pi$
$644$	−32201.9	−	164365.i	−0.0776443	−	0.396311i
$645$	−67751.0			−0.162853
$646$	74385.1	−	90372.6i	0.178247	−	0.216557i
$647$			451372.i			1.07827i	0.842221	+	0.539133i	$0.181248\pi$
$647$			451372.i			1.07827i	−0.842221	+	0.539133i	$0.818752\pi$
$648$	22171.2	−	41051.4i	0.0528006	−	0.0977639i
$649$	−195854.			−0.464989
$650$	114905.	+	94577.3i	0.271964	+	0.223852i
$651$			251662.i			0.593821i
$652$	35233.4	−	6902.83i	0.0828818	−	0.0162380i
$653$	378215.			0.886977			0.443489	−	0.896280i	$-0.353741\pi$
$653$	378215.			0.886977			0.443489	+	0.896280i	$0.353741\pi$
$654$	−62211.1	+	75582.1i	−0.145450	+	0.176711i
$655$			13951.1i			0.0325181i
$656$	−753555.	+	307055.i	−1.75108	+	0.713523i
$657$	−44813.4			−0.103819
$658$	283408.	+	233271.i	0.654576	+	0.538778i
$659$			625044.i			1.43926i	0.694357	+	0.719631i	$0.255689\pi$
$659$			625044.i			1.43926i	−0.694357	+	0.719631i	$0.744311\pi$
$660$	17459.1	+	89114.6i	0.0400806	+	0.204579i
$661$	576980.			1.32056			0.660280	−	0.751020i	$-0.270438\pi$
$661$	576980.			1.32056			0.660280	+	0.751020i	$0.270438\pi$
$662$	72906.1	−	88575.7i	0.166360	−	0.202115i
$663$		−	91002.4i		−	0.207026i
$664$	−301066.	−	162601.i	−0.682849	−	0.368796i
$665$	−481347.			−1.08847
$666$	97008.4	+	79847.0i	0.218706	+	0.180016i
$667$			114520.i			0.257413i
$668$	377019.	−	73864.6i	0.844910	−	0.165532i
$669$	−223744.			−0.499918
$670$	175346.	−	213033.i	0.390614	−	0.474568i
$671$			344136.i			0.764336i
$672$	−439822.	−	136887.i	−0.973953	−	0.303127i
$673$	411758.			0.909101			0.454550	−	0.890721i	$-0.349800\pi$
$673$	411758.			0.909101			0.454550	+	0.890721i	$0.349800\pi$
$674$	−307367.	−	252991.i	−0.676607	−	0.556911i
$675$			17537.0i			0.0384900i
$676$	184666.	+	942573.i	0.404105	+	2.06263i
$677$	628737.			1.37180			0.685902	−	0.727694i	$-0.259408\pi$
$677$	628737.			1.37180			0.685902	+	0.727694i	$0.259408\pi$
$678$	−3190.64	+	3876.40i	−0.00694094	+	0.00843275i
$679$			848227.i			1.83981i
$680$	−20007.4	+	37045.0i	−0.0432686	+	0.0801147i
$681$	225439.			0.486110
$682$	−168797.	−	138936.i	−0.362909	−	0.298708i
$683$			531547.i			1.13946i	0.821831	+	0.569731i	$0.192953\pi$
$683$			531547.i			1.13946i	−0.821831	+	0.569731i	$0.807047\pi$
$684$	−210832.	+	41305.7i	−0.450634	+	0.0882871i
$685$	19146.6			0.0408048
$686$	592530.	−	719881.i	1.25911	−	1.52972i
$687$		−	291176.i		−	0.616939i
$688$	112658.	+	276479.i	0.238005	+	0.584098i
$689$	−428835.			−0.903341
$690$	21695.2	+	17857.2i	0.0455685	+	0.0375072i
$691$		−	157186.i		−	0.329198i	−0.986361	−	0.164599i	$-0.947367\pi$
$691$		−	157186.i		−	0.329198i	0.986361	−	0.164599i	$-0.0526330\pi$
$692$	−119390.	−	609388.i	−0.249319	−	1.27257i
$693$	−228353.			−0.475488
$694$	119805.	−	145554.i	0.248745	−	0.302208i
$695$			75451.4i			0.156206i
$696$	277121.	+	149668.i	0.572072	+	0.308967i
$697$	−187027.			−0.384981
$698$	−530993.	−	437057.i	−1.08988	−	0.897071i
$699$			216359.i			0.442813i
$700$	169912.	−	33288.6i	0.346758	−	0.0679360i
$701$	−194246.			−0.395290			−0.197645	−	0.980274i	$-0.563329\pi$
$701$	−194246.			−0.395290			−0.197645	+	0.980274i	$0.563329\pi$
$702$	−106151.	+	128965.i	−0.215401	+	0.261697i
$703$		−	578557.i		−	1.17067i
$704$	334629.	−	219430.i	0.675178	−	0.442742i
$705$	−61581.0			−0.123899
$706$	−649857.	−	534893.i	−1.30379	−	1.07314i
$707$		−	467907.i		−	0.936097i
$708$	32044.8	+	163563.i	0.0639279	+	0.326301i
$709$	−455572.			−0.906285			−0.453142	−	0.891438i	$-0.649697\pi$
$709$	−455572.			−0.906285			−0.453142	+	0.891438i	$0.649697\pi$
$710$	−25070.6	+	30458.9i	−0.0497333	+	0.0604224i
$711$			196466.i			0.388640i
$712$	274017.	−	507360.i	0.540527	−	1.00082i
$713$	−67648.7			−0.133070
$714$	−81744.5	−	67283.4i	−0.160348	−	0.131981i
$715$		−	325104.i		−	0.635932i
$716$	−881474.	+	172696.i	−1.71943	+	0.336865i
$717$	369074.			0.717919
$718$	−312839.	+	380077.i	−0.606838	+	0.737264i
$719$		−	561316.i		−	1.08580i	−0.839797	−	0.542900i	$-0.817326\pi$
$719$		−	561316.i		−	1.08580i	0.839797	−	0.542900i	$-0.182674\pi$
$720$	71565.3	−	29161.1i	0.138050	−	0.0562521i
$721$	−718086.			−1.38136
$722$	361345.	+	297421.i	0.693182	+	0.570554i
$723$			304993.i			0.583463i
$724$	61396.4	+	313379.i	0.117129	+	0.597851i
$725$	−118385.			−0.225227
$726$	−67321.8	+	81791.1i	−0.127727	+	0.155179i
$727$		−	155857.i		−	0.294889i	−0.989070	−	0.147444i	$-0.952895\pi$
$727$		−	155857.i		−	0.294889i	0.989070	−	0.147444i	$-0.0471047\pi$
$728$	1.45101e6	+	783664.i	2.73783	+	1.47866i
$729$	−19683.0			−0.0370370
$730$	−57309.9	−	47171.4i	−0.107543	−	0.0885183i
$731$			68620.3i			0.128416i
$732$	287397.	−	56306.0i	0.536364	−	0.105083i
$733$	744418.			1.38551			0.692754	−	0.721174i	$-0.256397\pi$
$733$	744418.			1.38551			0.692754	+	0.721174i	$0.256397\pi$
$734$	−289503.	+	351726.i	−0.537355	+	0.652848i
$735$			295907.i			0.547747i
$736$	36796.4	−	118227.i	0.0679281	−	0.218254i
$737$	−602744.			−1.10968
$738$	265049.	+	218160.i	0.486645	+	0.400555i
$739$		−	200689.i		−	0.367480i	−0.982975	−	0.183740i	$-0.941180\pi$
$739$		−	200689.i		−	0.367480i	0.982975	−	0.183740i	$-0.0588205\pi$
$740$	40011.4	+	204226.i	0.0730668	+	0.372947i
$741$	769149.			1.40079
$742$	−317063.	+	385209.i	−0.575888	+	0.699662i
$743$		−	20434.2i		−	0.0370152i	−0.999829	−	0.0185076i	$-0.994109\pi$
$743$		−	20434.2i		−	0.0370152i	0.999829	−	0.0185076i	$-0.00589149\pi$
$744$	−88411.3	+	163699.i	−0.159721	+	0.295734i
$745$	−426079.			−0.767675
$746$	215298.	+	177210.i	0.386868	+	0.318428i
$747$			144352.i			0.258692i
$748$	90258.1	−	17683.1i	0.161318	−	0.0316050i
$749$	−497317.			−0.886482
$750$	−18459.8	+	22427.3i	−0.0328174	+	0.0398708i
$751$		−	60228.7i		−	0.106788i	−0.998574	−	0.0533941i	$-0.982996\pi$
$751$		−	60228.7i		−	0.106788i	0.998574	−	0.0533941i	$-0.0170040\pi$
$752$	102399.	+	251301.i	0.181075	+	0.444383i
$753$	−209076.			−0.368735
$754$	−870590.	−	716578.i	−1.53134	−	1.26044i
$755$		−	49014.5i		−	0.0859866i
$756$	37362.1	+	190703.i	0.0653714	+	0.333668i
$757$	−554160.			−0.967037			−0.483519	−	0.875334i	$-0.660641\pi$
$757$	−554160.			−0.967037			−0.483519	+	0.875334i	$0.660641\pi$
$758$	89905.2	−	109228.i	0.156475	−	0.190107i
$759$		−	61383.0i		−	0.106553i
$760$	−313103.	−	169102.i	−0.542076	−	0.292766i
$761$	62269.4			0.107524			0.0537620	−	0.998554i	$-0.482879\pi$
$761$	62269.4			0.107524			0.0537620	+	0.998554i	$0.482879\pi$
$762$	110452.	+	90912.5i	0.190224	+	0.156572i
$763$		−	407735.i		−	0.700372i
$764$	−898236.	+	175980.i	−1.53888	+	0.301493i
$765$	17762.0			0.0303508
$766$	651752.	−	791833.i	1.11077	−	1.34951i
$767$		−	596703.i		−	1.01430i
$768$	−238002.	−	243555.i	−0.403514	−	0.412928i
$769$	547774.			0.926295			0.463147	−	0.886281i	$-0.346720\pi$
$769$	547774.			0.926295			0.463147	+	0.886281i	$0.346720\pi$
$770$	−292031.	−	240369.i	−0.492546	−	0.405412i
$771$			443253.i			0.745663i
$772$	−14159.9	−	72274.6i	−0.0237588	−	0.121269i
$773$	−23192.7			−0.0388144			−0.0194072	−	0.999812i	$-0.506178\pi$
$773$	−23192.7			−0.0388144			−0.0194072	+	0.999812i	$0.506178\pi$
$774$	80042.8	−	97246.3i	0.133610	−	0.162327i
$775$		−	69931.7i		−	0.116432i
$776$	−297990.	+	551748.i	−0.494855	+	0.916257i
$777$	−523321.			−0.866814
$778$	−172340.	−	141852.i	−0.284726	−	0.234356i
$779$		−	1.58075e6i		−	2.60488i
$780$	−271503.	+	53192.1i	−0.446257	+	0.0874296i
$781$	86178.7			0.141286
$782$	18086.3	−	21973.6i	0.0295758	−	0.0359325i
$783$		−	132872.i		−	0.216725i
$784$	1.20754e6	−	492043.i	1.96458	−	0.800517i
$785$	211421.			0.343090
$786$	−20024.7	−	16482.2i	−0.0324131	−	0.0266790i
$787$			642178.i			1.03683i	0.855130	+	0.518413i	$0.173477\pi$
$787$			642178.i			1.03683i	−0.855130	+	0.518413i	$0.826523\pi$
$788$	92524.7	+	472264.i	0.149007	+	0.760558i
$789$	−452912.			−0.727544
$790$	−206804.	+	251252.i	−0.331363	+	0.402583i
$791$		−	20911.6i		−	0.0334222i
$792$	−148537.	−	80222.5i	−0.236802	−	0.127893i
$793$	−1.04847e6			−1.66728
$794$	817208.	+	672639.i	1.29626	+	1.06694i
$795$		−	83701.0i		−	0.132433i
$796$	663292.	−	129950.i	1.04684	−	0.205093i
$797$	−385649.			−0.607122			−0.303561	−	0.952812i	$-0.598176\pi$
$797$	−385649.			−0.607122			−0.303561	+	0.952812i	$0.598176\pi$
$798$	568677.	−	690902.i	0.893017	−	1.08495i
$799$			62371.1i			0.0976990i
$800$	122217.	+	38038.2i	0.190965	+	0.0594347i
$801$	−243265.			−0.379153
$802$	717730.	+	590759.i	1.11587	+	0.918463i
$803$			162149.i			0.251468i
$804$	98618.4	+	503367.i	0.152562	+	0.778705i
$805$	−117037.			−0.180605
$806$	423293.	−	514271.i	0.651585	−	0.791629i
$807$			654079.i			1.00435i
$808$	164380.	−	304361.i	0.251783	−	0.466193i
$809$	404473.			0.618006			0.309003	−	0.951061i	$-0.400005\pi$
$809$	404473.			0.618006			0.309003	+	0.951061i	$0.400005\pi$
$810$	−25171.8	−	20718.7i	−0.0383657	−	0.0315786i
$811$		−	740872.i		−	1.12642i	−0.826313	−	0.563212i	$-0.809566\pi$
$811$		−	740872.i		−	1.12642i	0.826313	−	0.563212i	$-0.190434\pi$
$812$	−1.28736e6	+	252216.i	−1.95248	+	0.382525i
$813$	−489911.			−0.741202
$814$	288912.	−	351007.i	0.436030	−	0.529746i
$815$		−	25088.1i		−	0.0377705i
$816$	−29535.3	−	72483.7i	−0.0443569	−	0.108858i
$817$	−579976.			−0.868893
$818$	222698.	+	183301.i	0.332820	+	0.273942i
$819$		−	695716.i		−	1.03720i
$820$	109320.	+	557991.i	0.162582	+	0.829849i
$821$	326364.			0.484190			0.242095	−	0.970253i	$-0.422165\pi$
$821$	326364.			0.484190			0.242095	+	0.970253i	$0.422165\pi$
$822$	−22620.3	+	27482.1i	−0.0334777	+	0.0406730i
$823$			6015.58i			0.00888132i	0.999990	+	0.00444066i	$0.00141351\pi$
$823$			6015.58i			0.00888132i	−0.999990	+	0.00444066i	$0.998586\pi$
$824$	−467095.	−	252270.i	−0.687940	−	0.371545i
$825$	63454.6			0.0932298
$826$	−535999.	−	441177.i	−0.785604	−	0.646626i
$827$			489341.i			0.715485i	0.933820	+	0.357742i	$0.116453\pi$
$827$			489341.i			0.715485i	−0.933820	+	0.357742i	$0.883547\pi$
$828$	−51262.6	+	10043.2i	−0.0747721	+	0.0146492i
$829$	−92567.3			−0.134694			−0.0673470	−	0.997730i	$-0.521453\pi$
$829$	−92567.3			−0.134694			−0.0673470	+	0.997730i	$0.521453\pi$
$830$	−151948.	+	184606.i	−0.220566	+	0.267972i
$831$		−	341898.i		−	0.495102i
$832$	668531.	+	1.01950e6i	0.965773	+	1.47280i
$833$	299704.			0.431919
$834$	−108299.	−	89140.4i	−0.155702	−	0.128157i
$835$		−	268458.i		−	0.385039i
$836$	149457.	+	762858.i	0.213847	+	1.09152i
$837$	78489.2			0.112036
$838$	−91819.2	+	111554.i	−0.130751	+	0.158853i
$839$			1.34655e6i			1.91293i	0.291847	+	0.956465i	$0.405730\pi$
$839$			1.34655e6i			1.91293i	−0.291847	+	0.956465i	$0.594270\pi$
$840$	−152957.	+	283211.i	−0.216776	+	0.401376i
$841$	189678.			0.268179
$842$	−674825.	−	555444.i	−0.951846	−	0.783459i
$843$		−	83772.5i		−	0.117882i
$844$	−48577.3	+	9517.14i	−0.0681944	+	0.0133605i
$845$	671164.			0.939973
$846$	72753.4	−	88390.2i	0.101651	−	0.123499i
$847$		−	441230.i		−	0.615033i
$848$	−341568.	+	139181.i	−0.474992	+	0.193547i
$849$	667509.			0.926066
$850$	22715.1	+	18696.7i	0.0314396	+	0.0258778i
$851$		−	140673.i		−	0.194245i
$852$	−14100.2	−	71970.1i	−0.0194243	−	0.0991454i
$853$	1.23563e6			1.69820			0.849101	−	0.528230i	$-0.177144\pi$
$853$	1.23563e6			1.69820			0.849101	+	0.528230i	$0.177144\pi$
$854$	−775194.	+	941806.i	−1.06291	+	1.29135i
$855$			150124.i			0.205361i
$856$	−323491.	−	174712.i	−0.441484	−	0.238438i
$857$	496036.			0.675385			0.337693	−	0.941256i	$-0.390354\pi$
$857$	496036.			0.675385			0.337693	+	0.941256i	$0.390354\pi$
$858$	466638.	+	384087.i	0.633878	+	0.521741i
$859$			74255.5i			0.100633i	0.998733	+	0.0503167i	$0.0160231\pi$
$859$			74255.5i			0.100633i	−0.998733	+	0.0503167i	$0.983977\pi$
$860$	204727.	−	40109.5i	0.276807	−	0.0542314i
$861$	−1.42983e6			−1.92876
$862$	−214445.	+	260535.i	−0.288603	+	0.350632i
$863$		−	28282.1i		−	0.0379743i	−0.999820	−	0.0189872i	$-0.993956\pi$
$863$		−	28282.1i		−	0.0379743i	0.999820	−	0.0189872i	$-0.00604417\pi$
$864$	−42692.9	+	137173.i	−0.0571910	+	0.183756i
$865$	−433918.			−0.579930
$866$	250009.	+	205781.i	0.333365	+	0.274391i
$867$			415998.i			0.553418i
$868$	−148988.	−	760461.i	−0.197747	−	1.00934i
$869$	710877.			0.941358
$870$	139863.	−	169924.i	0.184784	−	0.224500i
$871$		−	1.83636e6i		−	2.42060i
$872$	143241.	−	265220.i	0.188380	−	0.348798i
$873$	264548.			0.347117
$874$	185720.	+	152865.i	0.243128	+	0.200117i
$875$		−	120986.i		−	0.158023i
$876$	135415.	−	26530.1i	0.176465	−	0.0345725i
$877$	−345796.			−0.449594			−0.224797	−	0.974406i	$-0.572172\pi$
$877$	−345796.			−0.449594			−0.224797	+	0.974406i	$0.572172\pi$
$878$	81301.9	−	98776.0i	0.105466	−	0.128133i
$879$		−	839692.i		−	1.08678i
$880$	−105514.	−	258946.i	−0.136253	−	0.334383i
$881$	756432.			0.974581			0.487290	−	0.873240i	$-0.337985\pi$
$881$	756432.			0.974581			0.487290	+	0.873240i	$0.337985\pi$
$882$	−424729.	−	349592.i	−0.545978	−	0.449391i
$883$			1.37291e6i			1.76084i	0.474195	+	0.880420i	$0.342739\pi$
$883$			1.37291e6i			1.76084i	−0.474195	+	0.880420i	$0.657261\pi$
$884$	53874.7	+	274987.i	0.0689414	+	0.351890i
$885$	116466.			0.148700
$886$	−958297.	+	1.16426e6i	−1.22077	+	1.48314i
$887$		−	240951.i		−	0.306254i	−0.988207	−	0.153127i	$-0.951066\pi$
$887$		−	240951.i		−	0.306254i	0.988207	−	0.153127i	$-0.0489344\pi$
$888$	−340406.	−	183848.i	−0.431689	−	0.233148i
$889$	−595845.			−0.753928
$890$	−311101.	−	256065.i	−0.392755	−	0.323274i
$891$			71219.4i			0.0897104i
$892$	676099.	−	132460.i	0.849730	−	0.166477i
$893$	−527158.			−0.661056
$894$	503381.	−	611572.i	0.629828	−	0.765196i
$895$			627659.i			0.783569i
$896$	1.41007e6	+	153259.i	1.75641	+	0.190902i
$897$	187014.			0.232428
$898$	325486.	+	267905.i	0.403626	+	0.332222i
$899$			529847.i			0.655588i
$900$	−10382.2	−	52992.6i	−0.0128175	−	0.0654229i
$901$	−84775.0			−0.104428
$902$	789372.	−	959031.i	0.970217	−	1.17874i
$903$			524605.i			0.643364i
$904$	7346.45	−	13602.4i	0.00898960	−	0.0166448i
$905$	223143.			0.272450
$906$	70353.0	+	57907.1i	0.0857089	+	0.0705465i
$907$			125297.i			0.152310i	0.997096	+	0.0761549i	$0.0242643\pi$
$907$			125297.i			0.152310i	−0.997096	+	0.0761549i	$0.975736\pi$
$908$	−681222.	+	133463.i	−0.826260	+	0.161879i
$909$	−145932.			−0.176614
$910$	732325.	−	889722.i	0.884343	−	1.07441i
$911$		−	1.15679e6i		−	1.39386i	−0.717140	−	0.696929i	$-0.754549\pi$
$911$		−	1.15679e6i		−	1.39386i	0.717140	−	0.696929i	$-0.245451\pi$
$912$	612629.	−	249631.i	0.736560	−	0.300130i
$913$	522313.			0.626599
$914$	803934.	+	661713.i	0.962339	+	0.792095i
$915$		−	204642.i		−	0.244429i
$916$	172380.	+	879862.i	0.205445	+	1.04863i
$917$	108025.			0.128465
$918$	−20984.6	+	25494.8i	−0.0249009	+	0.0302528i
$919$			1.27592e6i			1.51076i	0.655290	+	0.755378i	$0.272547\pi$
$919$			1.27592e6i			1.51076i	−0.655290	+	0.755378i	$0.727453\pi$
$920$	−76129.2	−	41116.1i	−0.0899447	−	0.0485776i
$921$	206287.			0.243194
$922$	−348431.	−	286792.i	−0.409879	−	0.337369i
$923$			262558.i			0.308193i
$924$	690026.	−	135188.i	0.808205	−	0.158341i
$925$	145420.			0.169958
$926$	−478792.	+	581698.i	−0.558374	+	0.678384i
$927$			223959.i			0.260621i
$928$	−925997.	−	288202.i	−1.07526	−	0.334657i
$929$	829467.			0.961098			0.480549	−	0.876968i	$-0.340437\pi$
$929$	829467.			0.961098			0.480549	+	0.876968i	$0.340437\pi$
$930$	100376.	+	82619.3i	0.116056	+	0.0955246i
$931$			2.53308e6i			2.92247i
$932$	−128087.	−	653783.i	−0.147460	−	0.752665i
$933$	−86312.2			−0.0991537
$934$	950400.	−	1.15467e6i	1.08946	−	1.32362i
$935$		−	64268.8i		−	0.0735152i
$936$	244412.	−	452544.i	0.278978	−	0.516547i
$937$	448946.			0.511346			0.255673	−	0.966763i	$-0.417703\pi$
$937$	448946.			0.511346			0.255673	+	0.966763i	$0.417703\pi$
$938$	−1.64955e6	−	1.35773e6i	−1.87482	−	1.54315i
$939$			178510.i			0.202456i
$940$	186083.	−	36456.8i	0.210596	−	0.0412594i
$941$	37415.5			0.0422544			0.0211272	−	0.999777i	$-0.493275\pi$
$941$	37415.5			0.0422544			0.0211272	+	0.999777i	$0.493275\pi$
$942$	−249778.	+	303463.i	−0.281483	+	0.341982i
$943$		−	384349.i		−	0.432218i
$944$	−193663.	−	475275.i	−0.217321	−	0.533337i
$945$	135791.			0.152058
$946$	−351868.	−	289621.i	−0.393186	−	0.323629i
$947$		−	1.58481e6i		−	1.76717i	−0.468275	−	0.883583i	$-0.655124\pi$
$947$		−	1.58481e6i		−	1.76717i	0.468275	−	0.883583i	$-0.344876\pi$
$948$	−116311.	−	593672.i	−0.129420	−	0.660587i
$949$	−494015.			−0.548539
$950$	−158024.	+	191987.i	−0.175095	+	0.212728i
$951$			266817.i			0.295021i
$952$	286845.	+	154920.i	0.316499	+	0.170936i
$953$	−166901.			−0.183769			−0.0918846	−	0.995770i	$-0.529289\pi$
$953$	−166901.			−0.183769			−0.0918846	+	0.995770i	$0.529289\pi$
$954$	120140.	+	98886.6i	0.132005	+	0.108653i
$955$			639594.i			0.701290i
$956$	−1.11525e6	+	218497.i	−1.22027	+	0.239073i
$957$	−480772.			−0.524947
$958$	430431.	−	522943.i	0.469000	−	0.569801i
$959$		−	148255.i		−	0.161202i
$960$	−198989.	+	130485.i	−0.215917	+	0.141586i
$961$	610532.			0.661092
$962$	1.06940e6	+	880220.i	1.15556	+	0.951133i
$963$			155105.i			0.167253i
$964$	−180560.	−	921614.i	−0.194298	−	0.991734i
$965$	−51463.5			−0.0552644
$966$	138270.	−	167989.i	0.148175	−	0.180022i
$967$		−	873454.i		−	0.934087i	−0.884234	−	0.467043i	$-0.845319\pi$
$967$		−	873454.i		−	0.934087i	0.884234	−	0.467043i	$-0.154681\pi$
$968$	155008.	−	287008.i	0.165426	−	0.306298i
$969$	152050.			0.161935
$970$	338319.	+	278468.i	0.359569	+	0.295959i
$971$			1.16584e6i			1.23651i	0.785976	+	0.618257i	$0.212161\pi$
$971$			1.16584e6i			1.23651i	−0.785976	+	0.618257i	$0.787839\pi$
$972$	59477.2	−	11652.6i	0.0629532	−	0.0123336i
$973$	584230.			0.617104
$974$	−69196.4	+	84068.7i	−0.0729400	+	0.0886168i
$975$			193325.i			0.203366i
$976$	−835108.	+	340286.i	−0.876684	+	0.357227i
$977$	885391.			0.927569			0.463784	−	0.885948i	$-0.346491\pi$
$977$	885391.			0.927569			0.463784	+	0.885948i	$0.346491\pi$
$978$	36010.3	+	29639.8i	0.0376486	+	0.0309883i
$979$			880211.i			0.918378i
$980$	−175181.	−	894157.i	−0.182404	−	0.931025i
$981$	−127166.			−0.132139
$982$	−1.11261e6	+	1.35174e6i	−1.15377	+	1.40175i
$983$		−	671668.i		−	0.695101i	−0.937661	−	0.347550i	$-0.887014\pi$
$983$		−	671668.i		−	0.695101i	0.937661	−	0.347550i	$-0.112986\pi$
$984$	−930065.	−	502313.i	−0.960557	−	0.518781i
$985$	336278.			0.346598
$986$	−172104.	−	141658.i	−0.177026	−	0.145709i
$987$			476830.i			0.489473i
$988$	−2.32418e6	+	455347.i	−2.38098	+	0.466475i
$989$	−141018.			−0.144172
$990$	−74966.9	+	91079.5i	−0.0764891	+	0.0929288i
$991$		−	417477.i		−	0.425094i	−0.977151	−	0.212547i	$-0.931824\pi$
$991$		−	417477.i		−	0.425094i	0.977151	−	0.212547i	$-0.0681759\pi$
$992$	170245.	−	547000.i	0.173002	−	0.555858i
$993$	149027.			0.151136
$994$	235848.	+	194125.i	0.238703	+	0.196475i
$995$		−	472301.i		−	0.477059i
$996$	−85458.7	−	436198.i	−0.0861465	−	0.439708i
$997$	−129166.			−0.129945			−0.0649724	−	0.997887i	$-0.520696\pi$
$997$	−129166.			−0.129945			−0.0649724	+	0.997887i	$0.520696\pi$
$998$	−883729.	+	1.07367e6i	−0.887274	+	1.07798i
$999$			163215.i			0.163542i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.5.c.a.31.7	✓	16
3.2	odd	2		180.5.c.c.91.10		16
4.3	odd	2	inner	60.5.c.a.31.8	yes	16
5.2	odd	4		300.5.f.b.199.25		32
5.3	odd	4		300.5.f.b.199.8		32
5.4	even	2		300.5.c.d.151.10		16
8.3	odd	2		960.5.e.f.511.4		16
8.5	even	2		960.5.e.f.511.9		16
12.11	even	2		180.5.c.c.91.9		16
20.3	even	4		300.5.f.b.199.26		32
20.7	even	4		300.5.f.b.199.7		32
20.19	odd	2		300.5.c.d.151.9		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.5.c.a.31.7	✓	16	1.1	even	1	trivial
60.5.c.a.31.8	yes	16	4.3	odd	2	inner
180.5.c.c.91.9		16	12.11	even	2
180.5.c.c.91.10		16	3.2	odd	2
300.5.c.d.151.9		16	20.19	odd	2
300.5.c.d.151.10		16	5.4	even	2
300.5.f.b.199.7		32	20.7	even	4
300.5.f.b.199.8		32	5.3	odd	4
300.5.f.b.199.25		32	5.2	odd	4
300.5.f.b.199.26		32	20.3	even	4
960.5.e.f.511.4		16	8.3	odd	2
960.5.e.f.511.9		16	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	60.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.08838 - 2.54203i) q^{2} -5.19615i q^{3} +(3.07620 + 15.7015i) q^{4} +11.1803 q^{5} +(-13.2088 + 16.0477i) q^{6} -86.5709i q^{7} +(30.4132 - 56.3120i) q^{8} -27.0000 q^{9} +O(q^{10})\)	\(q+(-3.08838 - 2.54203i) q^{2} -5.19615i q^{3} +(3.07620 + 15.7015i) q^{4} +11.1803 q^{5} +(-13.2088 + 16.0477i) q^{6} -86.5709i q^{7} +(30.4132 - 56.3120i) q^{8} -27.0000 q^{9} +(-34.5292 - 28.4207i) q^{10} +97.6947i q^{11} +(81.5874 - 15.9844i) q^{12} -297.644 q^{13} +(-220.066 + 267.364i) q^{14} -58.0948i q^{15} +(-237.074 + 96.6018i) q^{16} -58.8402 q^{17} +(83.3863 + 68.6347i) q^{18} -497.315i q^{19} +(34.3929 + 175.548i) q^{20} -449.835 q^{21} +(248.343 - 301.718i) q^{22} -120.919i q^{23} +(-292.606 - 158.031i) q^{24} +125.000 q^{25} +(919.237 + 756.618i) q^{26} +140.296i q^{27} +(1359.29 - 266.309i) q^{28} -947.079 q^{29} +(-147.678 + 179.419i) q^{30} -559.454i q^{31} +(977.739 + 304.306i) q^{32} +507.636 q^{33} +(181.721 + 149.573i) q^{34} -967.892i q^{35} +(-83.0573 - 423.940i) q^{36} +1163.36 q^{37} +(-1264.19 + 1535.90i) q^{38} +1546.60i q^{39} +(340.030 - 629.587i) q^{40} +3178.56 q^{41} +(1389.26 + 1143.49i) q^{42} -1166.21i q^{43} +(-1533.95 + 300.528i) q^{44} -301.869 q^{45} +(-307.380 + 373.445i) q^{46} -1060.01i q^{47} +(501.958 + 1231.87i) q^{48} -5093.52 q^{49} +(-386.048 - 317.753i) q^{50} +305.743i q^{51} +(-915.610 - 4673.45i) q^{52} +1440.77 q^{53} +(356.637 - 433.288i) q^{54} +1092.26i q^{55} +(-4874.98 - 2632.89i) q^{56} -2584.13 q^{57} +(2924.94 + 2407.50i) q^{58} +2004.76i q^{59} +(912.175 - 178.711i) q^{60} +3522.56 q^{61} +(-1422.15 + 1727.81i) q^{62} +2337.41i q^{63} +(-2246.08 - 3425.25i) q^{64} -3327.76 q^{65} +(-1567.77 - 1290.43i) q^{66} +6169.67i q^{67} +(-181.004 - 923.879i) q^{68} -628.315 q^{69} +(-2460.41 + 2989.22i) q^{70} -882.122i q^{71} +(-821.156 + 1520.42i) q^{72} +1659.75 q^{73} +(-3592.90 - 2957.30i) q^{74} -649.519i q^{75} +(7808.59 - 1529.84i) q^{76} +8457.51 q^{77} +(3931.50 - 4776.50i) q^{78} -7276.52i q^{79} +(-2650.57 + 1080.04i) q^{80} +729.000 q^{81} +(-9816.61 - 8079.99i) q^{82} -5346.39i q^{83} +(-1383.78 - 7063.09i) q^{84} -657.854 q^{85} +(-2964.55 + 3601.72i) q^{86} +4921.17i q^{87} +(5501.38 + 2971.20i) q^{88} +9009.81 q^{89} +(932.287 + 767.360i) q^{90} +25767.3i q^{91} +(1898.61 - 371.971i) q^{92} -2907.01 q^{93} +(-2694.57 + 3273.71i) q^{94} -5560.15i q^{95} +(1581.22 - 5080.48i) q^{96} -9798.06 q^{97} +(15730.7 + 12947.9i) q^{98} -2637.76i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{2} + 26 q^{4} + 18 q^{6} - 180 q^{8} - 432 q^{9}+O(q^{10}) \) 16 * q - 12 * q^2 + 26 * q^4 + 18 * q^6 - 180 * q^8 - 432 * q^9	\( 16 q - 12 q^{2} + 26 q^{4} + 18 q^{6} - 180 q^{8} - 432 q^{9} + 50 q^{10} - 352 q^{13} - 804 q^{14} - 190 q^{16} + 324 q^{18} + 600 q^{20} + 288 q^{21} + 436 q^{22} - 1998 q^{24} + 2000 q^{25} - 852 q^{26} - 1156 q^{28} - 3456 q^{29} + 7668 q^{32} + 4772 q^{34} - 702 q^{36} + 9376 q^{37} - 1320 q^{38} + 550 q^{40} + 1248 q^{41} - 324 q^{42} - 6420 q^{44} - 1112 q^{46} - 4176 q^{48} - 3952 q^{49} - 1500 q^{50} + 12704 q^{52} - 5184 q^{53} - 486 q^{54} - 2604 q^{56} - 11232 q^{57} + 12708 q^{58} + 3150 q^{60} - 3808 q^{61} - 16152 q^{62} - 11902 q^{64} + 2400 q^{65} - 2916 q^{66} - 12312 q^{68} + 9792 q^{69} - 17100 q^{70} + 4860 q^{72} + 11040 q^{73} + 30516 q^{74} - 5160 q^{76} - 27456 q^{77} - 3600 q^{78} + 10800 q^{80} + 11664 q^{81} - 54040 q^{82} - 2052 q^{84} - 11200 q^{85} + 39768 q^{86} - 7220 q^{88} + 7584 q^{89} - 1350 q^{90} + 28848 q^{92} + 19872 q^{93} + 49776 q^{94} + 18882 q^{96} - 14496 q^{97} + 23940 q^{98}+O(q^{100}) \) 16 * q - 12 * q^2 + 26 * q^4 + 18 * q^6 - 180 * q^8 - 432 * q^9 + 50 * q^10 - 352 * q^13 - 804 * q^14 - 190 * q^16 + 324 * q^18 + 600 * q^20 + 288 * q^21 + 436 * q^22 - 1998 * q^24 + 2000 * q^25 - 852 * q^26 - 1156 * q^28 - 3456 * q^29 + 7668 * q^32 + 4772 * q^34 - 702 * q^36 + 9376 * q^37 - 1320 * q^38 + 550 * q^40 + 1248 * q^41 - 324 * q^42 - 6420 * q^44 - 1112 * q^46 - 4176 * q^48 - 3952 * q^49 - 1500 * q^50 + 12704 * q^52 - 5184 * q^53 - 486 * q^54 - 2604 * q^56 - 11232 * q^57 + 12708 * q^58 + 3150 * q^60 - 3808 * q^61 - 16152 * q^62 - 11902 * q^64 + 2400 * q^65 - 2916 * q^66 - 12312 * q^68 + 9792 * q^69 - 17100 * q^70 + 4860 * q^72 + 11040 * q^73 + 30516 * q^74 - 5160 * q^76 - 27456 * q^77 - 3600 * q^78 + 10800 * q^80 + 11664 * q^81 - 54040 * q^82 - 2052 * q^84 - 11200 * q^85 + 39768 * q^86 - 7220 * q^88 + 7584 * q^89 - 1350 * q^90 + 28848 * q^92 + 19872 * q^93 + 49776 * q^94 + 18882 * q^96 - 14496 * q^97 + 23940 * q^98

Introduction

L-functions

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