LMFDB - Embedded newform 175.4.e.b.151.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,4,Mod(51,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("175.51");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	175.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.3253342510$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	175.151
Dual form			175.4.e.b.51.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 + 2.59808i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} -6.00000 q^{6} +(14.0000 + 12.1244i) q^{7} +21.0000 q^{8} +(11.5000 + 19.9186i) q^{9} +O(q^{10})$	\(q+(1.50000 + 2.59808i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} -6.00000 q^{6} +(14.0000 + 12.1244i) q^{7} +21.0000 q^{8} +(11.5000 + 19.9186i) q^{9} +(22.5000 - 38.9711i) q^{11} +(-1.00000 - 1.73205i) q^{12} -59.0000 q^{13} +(-10.5000 + 54.5596i) q^{14} +(35.5000 + 61.4878i) q^{16} +(-27.0000 + 46.7654i) q^{17} +(-34.5000 + 59.7558i) q^{18} +(60.5000 + 104.789i) q^{19} +(-35.0000 + 12.1244i) q^{21} +135.000 q^{22} +(34.5000 + 59.7558i) q^{23} +(-21.0000 + 36.3731i) q^{24} +(-88.5000 - 153.286i) q^{26} -100.000 q^{27} +(-17.5000 + 6.06218i) q^{28} -162.000 q^{29} +(44.0000 - 76.2102i) q^{31} +(-22.5000 + 38.9711i) q^{32} +(45.0000 + 77.9423i) q^{33} -162.000 q^{34} -23.0000 q^{36} +(-129.500 - 224.301i) q^{37} +(-181.500 + 314.367i) q^{38} +(59.0000 - 102.191i) q^{39} +195.000 q^{41} +(-84.0000 - 72.7461i) q^{42} +286.000 q^{43} +(22.5000 + 38.9711i) q^{44} +(-103.500 + 179.267i) q^{46} +(22.5000 + 38.9711i) q^{47} -142.000 q^{48} +(49.0000 + 339.482i) q^{49} +(-54.0000 - 93.5307i) q^{51} +(29.5000 - 51.0955i) q^{52} +(298.500 - 517.017i) q^{53} +(-150.000 - 259.808i) q^{54} +(294.000 + 254.611i) q^{56} -242.000 q^{57} +(-243.000 - 420.888i) q^{58} +(180.000 - 311.769i) q^{59} +(-196.000 - 339.482i) q^{61} +264.000 q^{62} +(-80.5000 + 418.290i) q^{63} +433.000 q^{64} +(-135.000 + 233.827i) q^{66} +(-140.000 + 242.487i) q^{67} +(-27.0000 - 46.7654i) q^{68} -138.000 q^{69} +48.0000 q^{71} +(241.500 + 418.290i) q^{72} +(334.000 - 578.505i) q^{73} +(388.500 - 672.902i) q^{74} -121.000 q^{76} +(787.500 - 272.798i) q^{77} +354.000 q^{78} +(-391.000 - 677.232i) q^{79} +(-210.500 + 364.597i) q^{81} +(292.500 + 506.625i) q^{82} -768.000 q^{83} +(7.00000 - 36.3731i) q^{84} +(429.000 + 743.050i) q^{86} +(162.000 - 280.592i) q^{87} +(472.500 - 818.394i) q^{88} +(597.000 + 1034.03i) q^{89} +(-826.000 - 715.337i) q^{91} -69.0000 q^{92} +(88.0000 + 152.420i) q^{93} +(-67.5000 + 116.913i) q^{94} +(-45.0000 - 77.9423i) q^{96} -902.000 q^{97} +(-808.500 + 636.529i) q^{98} +1035.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{2} - 2 q^{3} - q^{4} - 12 q^{6} + 28 q^{7} + 42 q^{8} + 23 q^{9}+O(q^{10}) $ 2 * q + 3 * q^2 - 2 * q^3 - q^4 - 12 * q^6 + 28 * q^7 + 42 * q^8 + 23 * q^9	$ 2 q + 3 q^{2} - 2 q^{3} - q^{4} - 12 q^{6} + 28 q^{7} + 42 q^{8} + 23 q^{9} + 45 q^{11} - 2 q^{12} - 118 q^{13} - 21 q^{14} + 71 q^{16} - 54 q^{17} - 69 q^{18} + 121 q^{19} - 70 q^{21} + 270 q^{22} + 69 q^{23} - 42 q^{24} - 177 q^{26} - 200 q^{27} - 35 q^{28} - 324 q^{29} + 88 q^{31} - 45 q^{32} + 90 q^{33} - 324 q^{34} - 46 q^{36} - 259 q^{37} - 363 q^{38} + 118 q^{39} + 390 q^{41} - 168 q^{42} + 572 q^{43} + 45 q^{44} - 207 q^{46} + 45 q^{47} - 284 q^{48} + 98 q^{49} - 108 q^{51} + 59 q^{52} + 597 q^{53} - 300 q^{54} + 588 q^{56} - 484 q^{57} - 486 q^{58} + 360 q^{59} - 392 q^{61} + 528 q^{62} - 161 q^{63} + 866 q^{64} - 270 q^{66} - 280 q^{67} - 54 q^{68} - 276 q^{69} + 96 q^{71} + 483 q^{72} + 668 q^{73} + 777 q^{74} - 242 q^{76} + 1575 q^{77} + 708 q^{78} - 782 q^{79} - 421 q^{81} + 585 q^{82} - 1536 q^{83} + 14 q^{84} + 858 q^{86} + 324 q^{87} + 945 q^{88} + 1194 q^{89} - 1652 q^{91} - 138 q^{92} + 176 q^{93} - 135 q^{94} - 90 q^{96} - 1804 q^{97} - 1617 q^{98} + 2070 q^{99}+O(q^{100}) $ 2 * q + 3 * q^2 - 2 * q^3 - q^4 - 12 * q^6 + 28 * q^7 + 42 * q^8 + 23 * q^9 + 45 * q^11 - 2 * q^12 - 118 * q^13 - 21 * q^14 + 71 * q^16 - 54 * q^17 - 69 * q^18 + 121 * q^19 - 70 * q^21 + 270 * q^22 + 69 * q^23 - 42 * q^24 - 177 * q^26 - 200 * q^27 - 35 * q^28 - 324 * q^29 + 88 * q^31 - 45 * q^32 + 90 * q^33 - 324 * q^34 - 46 * q^36 - 259 * q^37 - 363 * q^38 + 118 * q^39 + 390 * q^41 - 168 * q^42 + 572 * q^43 + 45 * q^44 - 207 * q^46 + 45 * q^47 - 284 * q^48 + 98 * q^49 - 108 * q^51 + 59 * q^52 + 597 * q^53 - 300 * q^54 + 588 * q^56 - 484 * q^57 - 486 * q^58 + 360 * q^59 - 392 * q^61 + 528 * q^62 - 161 * q^63 + 866 * q^64 - 270 * q^66 - 280 * q^67 - 54 * q^68 - 276 * q^69 + 96 * q^71 + 483 * q^72 + 668 * q^73 + 777 * q^74 - 242 * q^76 + 1575 * q^77 + 708 * q^78 - 782 * q^79 - 421 * q^81 + 585 * q^82 - 1536 * q^83 + 14 * q^84 + 858 * q^86 + 324 * q^87 + 945 * q^88 + 1194 * q^89 - 1652 * q^91 - 138 * q^92 + 176 * q^93 - 135 * q^94 - 90 * q^96 - 1804 * q^97 - 1617 * q^98 + 2070 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	1.50000	+	2.59808i	0.530330	+	0.918559i	0.999374	+	0.0353837i	$0.0112653\pi$
$2$	1.50000	+	2.59808i	0.530330	+	0.918559i	−0.469044	+	0.883175i	$0.655401\pi$
$3$	−1.00000	+	1.73205i	−0.192450	+	0.333333i	−0.946062	−	0.323987i	$-0.894977\pi$
$3$	−1.00000	+	1.73205i	−0.192450	+	0.333333i	0.753612	+	0.657320i	$0.228310\pi$
$4$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$5$		0			0
$5$		0			0
$6$	−6.00000			−0.408248
$7$	14.0000	+	12.1244i	0.755929	+	0.654654i
$7$	14.0000	+	12.1244i	0.755929	+	0.654654i
$8$	21.0000			0.928078
$9$	11.5000	+	19.9186i	0.425926	+	0.737725i
$10$		0			0
$11$	22.5000	−	38.9711i	0.616728	−	1.06820i	−0.373351	−	0.927690i	$-0.621791\pi$
$11$	22.5000	−	38.9711i	0.616728	−	1.06820i	0.990079	−	0.140514i	$-0.0448754\pi$
$12$	−1.00000	−	1.73205i	−0.0240563	−	0.0416667i
$13$	−59.0000			−1.25874			−0.629371	−	0.777105i	$-0.716688\pi$
$13$	−59.0000			−1.25874			−0.629371	+	0.777105i	$0.716688\pi$
$14$	−10.5000	+	54.5596i	−0.200446	+	1.04155i
$15$		0			0
$16$	35.5000	+	61.4878i	0.554688	+	0.960747i
$17$	−27.0000	+	46.7654i	−0.385204	+	0.667192i	−0.991797	−	0.127820i	$-0.959202\pi$
$17$	−27.0000	+	46.7654i	−0.385204	+	0.667192i	0.606594	+	0.795012i	$0.292535\pi$
$18$	−34.5000	+	59.7558i	−0.451763	+	0.782476i
$19$	60.5000	+	104.789i	0.730508	+	1.26528i	0.956666	+	0.291186i	$0.0940500\pi$
$19$	60.5000	+	104.789i	0.730508	+	1.26528i	−0.226158	+	0.974091i	$0.572617\pi$
$20$		0			0
$21$	−35.0000	+	12.1244i	−0.363696	+	0.125988i
$22$	135.000			1.30828
$23$	34.5000	+	59.7558i	0.312772	+	0.541736i	0.978961	−	0.204046i	$-0.0654092\pi$
$23$	34.5000	+	59.7558i	0.312772	+	0.541736i	−0.666190	+	0.745782i	$0.732076\pi$
$24$	−21.0000	+	36.3731i	−0.178609	+	0.309359i
$25$		0			0
$26$	−88.5000	−	153.286i	−0.667549	−	1.15623i
$27$	−100.000			−0.712778
$28$	−17.5000	+	6.06218i	−0.118114	+	0.0409159i
$29$	−162.000			−1.03733			−0.518666	−	0.854977i	$-0.673571\pi$
$29$	−162.000			−1.03733			−0.518666	+	0.854977i	$0.673571\pi$
$30$		0			0
$31$	44.0000	−	76.2102i	0.254924	−	0.441541i	−0.709951	−	0.704251i	$-0.751283\pi$
$31$	44.0000	−	76.2102i	0.254924	−	0.441541i	0.964875	+	0.262710i	$0.0846163\pi$
$32$	−22.5000	+	38.9711i	−0.124296	+	0.215287i
$33$	45.0000	+	77.9423i	0.237379	+	0.411152i
$34$	−162.000			−0.817140
$35$		0			0
$36$	−23.0000			−0.106481
$37$	−129.500	−	224.301i	−0.575396	−	0.996616i	−0.995998	−	0.0893706i	$-0.971514\pi$
$37$	−129.500	−	224.301i	−0.575396	−	0.996616i	0.420602	−	0.907245i	$-0.361819\pi$
$38$	−181.500	+	314.367i	−0.774821	+	1.34203i
$39$	59.0000	−	102.191i	0.242245	−	0.419581i
$40$		0			0
$41$	195.000			0.742778			0.371389	−	0.928477i	$-0.378882\pi$
$41$	195.000			0.742778			0.371389	+	0.928477i	$0.378882\pi$
$42$	−84.0000	−	72.7461i	−0.308607	−	0.267261i
$43$	286.000			1.01429			0.507146	−	0.861860i	$-0.330700\pi$
$43$	286.000			1.01429			0.507146	+	0.861860i	$0.330700\pi$
$44$	22.5000	+	38.9711i	0.0770910	+	0.133525i
$45$		0			0
$46$	−103.500	+	179.267i	−0.331744	+	0.574598i
$47$	22.5000	+	38.9711i	0.0698290	+	0.120947i	0.898826	−	0.438306i	$-0.144421\pi$
$47$	22.5000	+	38.9711i	0.0698290	+	0.120947i	−0.828997	+	0.559253i	$0.811088\pi$
$48$	−142.000			−0.426999
$49$	49.0000	+	339.482i	0.142857	+	0.989743i
$50$		0			0
$51$	−54.0000	−	93.5307i	−0.148265	−	0.256802i
$52$	29.5000	−	51.0955i	0.0786714	−	0.136263i
$53$	298.500	−	517.017i	0.773625	−	1.33996i	−0.161939	−	0.986801i	$-0.551775\pi$
$53$	298.500	−	517.017i	0.773625	−	1.33996i	0.935564	−	0.353157i	$-0.114892\pi$
$54$	−150.000	−	259.808i	−0.378008	−	0.654729i
$55$		0			0
$56$	294.000	+	254.611i	0.701561	+	0.607569i
$57$	−242.000			−0.562345
$58$	−243.000	−	420.888i	−0.550129	−	0.952851i
$59$	180.000	−	311.769i	0.397187	−	0.687947i	−0.596191	−	0.802843i	$-0.703320\pi$
$59$	180.000	−	311.769i	0.397187	−	0.687947i	0.993378	+	0.114895i	$0.0366533\pi$
$60$		0			0
$61$	−196.000	−	339.482i	−0.411397	−	0.712561i	0.583646	−	0.812009i	$-0.301626\pi$
$61$	−196.000	−	339.482i	−0.411397	−	0.712561i	−0.995043	+	0.0994477i	$0.968292\pi$
$62$	264.000			0.540775
$63$	−80.5000	+	418.290i	−0.160985	+	0.836502i
$64$	433.000			0.845703
$65$		0			0
$66$	−135.000	+	233.827i	−0.251778	+	0.436092i
$67$	−140.000	+	242.487i	−0.255279	+	0.442157i	−0.964971	−	0.262355i	$-0.915501\pi$
$67$	−140.000	+	242.487i	−0.255279	+	0.442157i	0.709692	+	0.704512i	$0.248834\pi$
$68$	−27.0000	−	46.7654i	−0.0481505	−	0.0833990i
$69$	−138.000			−0.240772
$70$		0			0
$71$	48.0000			0.0802331			0.0401166	−	0.999195i	$-0.487227\pi$
$71$	48.0000			0.0802331			0.0401166	+	0.999195i	$0.487227\pi$
$72$	241.500	+	418.290i	0.395292	+	0.684666i
$73$	334.000	−	578.505i	0.535503	−	0.927519i	−0.463635	−	0.886026i	$-0.653455\pi$
$73$	334.000	−	578.505i	0.535503	−	0.927519i	0.999139	−	0.0414929i	$-0.0132114\pi$
$74$	388.500	−	672.902i	0.610300	−	1.05707i
$75$		0			0
$76$	−121.000			−0.182627
$77$	787.500	−	272.798i	1.16551	−	0.403743i
$78$	354.000			0.513880
$79$	−391.000	−	677.232i	−0.556847	−	0.964488i	−0.997757	−	0.0669365i	$-0.978678\pi$
$79$	−391.000	−	677.232i	−0.556847	−	0.964488i	0.440910	−	0.897551i	$-0.354656\pi$
$80$		0			0
$81$	−210.500	+	364.597i	−0.288752	+	0.500133i
$82$	292.500	+	506.625i	0.393917	+	0.682285i
$83$	−768.000			−1.01565			−0.507825	−	0.861460i	$-0.669550\pi$
$83$	−768.000			−1.01565			−0.507825	+	0.861460i	$0.669550\pi$
$84$	7.00000	−	36.3731i	0.00909241	−	0.0472456i
$85$		0			0
$86$	429.000	+	743.050i	0.537910	+	0.931687i
$87$	162.000	−	280.592i	0.199635	−	0.345778i
$88$	472.500	−	818.394i	0.572371	−	0.991376i
$89$	597.000	+	1034.03i	0.711032	+	1.23154i	0.964470	+	0.264192i	$0.0851054\pi$
$89$	597.000	+	1034.03i	0.711032	+	1.23154i	−0.253438	+	0.967352i	$0.581561\pi$
$90$		0			0
$91$	−826.000	−	715.337i	−0.951520	−	0.824041i
$92$	−69.0000			−0.0781929
$93$	88.0000	+	152.420i	0.0981202	+	0.169949i
$94$	−67.5000	+	116.913i	−0.0740648	+	0.128284i
$95$		0			0
$96$	−45.0000	−	77.9423i	−0.0478416	−	0.0828641i
$97$	−902.000			−0.944167			−0.472084	−	0.881554i	$-0.656498\pi$
$97$	−902.000			−0.944167			−0.472084	+	0.881554i	$0.656498\pi$
$98$	−808.500	+	636.529i	−0.833376	+	0.656113i
$99$	1035.00			1.05072
$100$		0			0
$101$	−342.000	+	592.361i	−0.336933	+	0.583586i	−0.983854	−	0.178971i	$-0.942723\pi$
$101$	−342.000	+	592.361i	−0.336933	+	0.583586i	0.646921	+	0.762557i	$0.276056\pi$
$102$	162.000	−	280.592i	0.157259	−	0.272380i
$103$	−758.000	−	1312.89i	−0.725126	−	1.25595i	−0.958922	−	0.283669i	$-0.908448\pi$
$103$	−758.000	−	1312.89i	−0.725126	−	1.25595i	0.233796	−	0.972286i	$-0.424885\pi$
$104$	−1239.00			−1.16821
$105$		0			0
$106$	1791.00			1.64111
$107$	−366.000	−	633.931i	−0.330678	−	0.572751i	0.651967	−	0.758247i	$-0.273944\pi$
$107$	−366.000	−	633.931i	−0.330678	−	0.572751i	−0.982645	+	0.185496i	$0.940611\pi$
$108$	50.0000	−	86.6025i	0.0445486	−	0.0771605i
$109$	800.000	−	1385.64i	0.702992	−	1.21762i	−0.264420	−	0.964408i	$-0.585180\pi$
$109$	800.000	−	1385.64i	0.702992	−	1.21762i	0.967411	−	0.253210i	$-0.0814863\pi$
$110$		0			0
$111$	518.000			0.442940
$112$	−248.500	+	1291.24i	−0.209652	+	1.08938i
$113$	1392.00			1.15883			0.579417	−	0.815031i	$-0.303280\pi$
$113$	1392.00			1.15883			0.579417	+	0.815031i	$0.303280\pi$
$114$	−363.000	−	628.734i	−0.298229	−	0.516547i
$115$		0			0
$116$	81.0000	−	140.296i	0.0648333	−	0.112295i
$117$	−678.500	−	1175.20i	−0.536131	−	0.928606i
$118$	1080.00			0.842560
$119$	−945.000	+	327.358i	−0.727966	+	0.252175i
$120$		0			0
$121$	−347.000	−	601.022i	−0.260706	−	0.451556i
$122$	588.000	−	1018.45i	0.436353	−	0.755785i
$123$	−195.000	+	337.750i	−0.142948	+	0.247593i
$124$	44.0000	+	76.2102i	0.0318655	+	0.0551926i
$125$		0			0
$126$	−1207.50	+	418.290i	−0.853751	+	0.295748i
$127$	−803.000			−0.561061			−0.280530	−	0.959845i	$-0.590510\pi$
$127$	−803.000			−0.561061			−0.280530	+	0.959845i	$0.590510\pi$
$128$	829.500	+	1436.74i	0.572798	+	0.992115i
$129$	−286.000	+	495.367i	−0.195201	+	0.338098i
$130$		0			0
$131$	−1009.50	−	1748.51i	−0.673286	−	1.16617i	−0.976967	−	0.213391i	$-0.931549\pi$
$131$	−1009.50	−	1748.51i	−0.673286	−	1.16617i	0.303681	−	0.952774i	$-0.401784\pi$
$132$	−90.0000			−0.0593447
$133$	−423.500	+	2200.57i	−0.276106	+	1.43469i
$134$	−840.000			−0.541529
$135$		0			0
$136$	−567.000	+	982.073i	−0.357499	+	0.619206i
$137$	30.0000	−	51.9615i	0.0187086	−	0.0324042i	−0.856520	−	0.516115i	$-0.827378\pi$
$137$	30.0000	−	51.9615i	0.0187086	−	0.0324042i	0.875228	+	0.483710i	$0.160711\pi$
$138$	−207.000	−	358.535i	−0.127688	−	0.221163i
$139$	−1708.00			−1.04224			−0.521118	−	0.853485i	$-0.674485\pi$
$139$	−1708.00			−1.04224			−0.521118	+	0.853485i	$0.674485\pi$
$140$		0			0
$141$	−90.0000			−0.0537544
$142$	72.0000	+	124.708i	0.0425500	+	0.0736988i
$143$	−1327.50	+	2299.30i	−0.776302	+	1.34459i
$144$	−816.500	+	1414.22i	−0.472512	+	0.818414i
$145$		0			0
$146$	2004.00			1.13597
$147$	−637.000	−	254.611i	−0.357407	−	0.142857i
$148$	259.000			0.143849
$149$	543.000	+	940.504i	0.298552	+	0.517108i	0.975805	−	0.218643i	$-0.0701629\pi$
$149$	543.000	+	940.504i	0.298552	+	0.517108i	−0.677253	+	0.735751i	$0.736830\pi$
$150$		0			0
$151$	1433.00	−	2482.03i	0.772291	−	1.33765i	−0.164014	−	0.986458i	$-0.552444\pi$
$151$	1433.00	−	2482.03i	0.772291	−	1.33765i	0.936305	−	0.351189i	$-0.114222\pi$
$152$	1270.50	+	2200.57i	0.677968	+	1.17428i
$153$	−1242.00			−0.656273
$154$	1890.00	+	1636.79i	0.988965	+	0.856468i
$155$		0			0
$156$	59.0000	+	102.191i	0.0302806	+	0.0524476i
$157$	−114.500	+	198.320i	−0.0582044	+	0.100813i	−0.893659	−	0.448746i	$-0.851871\pi$
$157$	−114.500	+	198.320i	−0.0582044	+	0.100813i	0.835455	+	0.549559i	$0.185204\pi$
$158$	1173.00	−	2031.70i	0.590626	−	1.02299i
$159$	597.000	+	1034.03i	0.297768	+	0.515750i
$160$		0			0
$161$	−241.500	+	1254.87i	−0.118217	+	0.614271i
$162$	−1263.00			−0.612535
$163$	−614.000	−	1063.48i	−0.295044	−	0.511031i	0.679951	−	0.733258i	$-0.262001\pi$
$163$	−614.000	−	1063.48i	−0.295044	−	0.511031i	−0.974995	+	0.222226i	$0.928668\pi$
$164$	−97.5000	+	168.875i	−0.0464236	+	0.0804080i
$165$		0			0
$166$	−1152.00	−	1995.32i	−0.538630	−	0.932934i
$167$	1929.00			0.893835			0.446918	−	0.894575i	$-0.352522\pi$
$167$	1929.00			0.893835			0.446918	+	0.894575i	$0.352522\pi$
$168$	−735.000	+	254.611i	−0.337539	+	0.116927i
$169$	1284.00			0.584433
$170$		0			0
$171$	−1391.50	+	2410.15i	−0.622285	+	1.07783i
$172$	−143.000	+	247.683i	−0.0633933	+	0.109800i
$173$	−349.500	−	605.352i	−0.153595	−	0.266035i	0.778951	−	0.627084i	$-0.215752\pi$
$173$	−349.500	−	605.352i	−0.153595	−	0.266035i	−0.932547	+	0.361049i	$0.882419\pi$
$174$	972.000			0.423489
$175$		0			0
$176$	3195.00			1.36836
$177$	360.000	+	623.538i	0.152877	+	0.264791i
$178$	−1791.00	+	3102.10i	−0.754164	+	1.30625i
$179$	−1558.50	+	2699.40i	−0.650770	+	1.12717i	0.332167	+	0.943221i	$0.392220\pi$
$179$	−1558.50	+	2699.40i	−0.650770	+	1.12717i	−0.982936	+	0.183945i	$0.941113\pi$
$180$		0			0
$181$	−1798.00			−0.738366			−0.369183	−	0.929357i	$-0.620362\pi$
$181$	−1798.00			−0.738366			−0.369183	+	0.929357i	$0.620362\pi$
$182$	619.500	−	3219.02i	0.252310	−	1.31104i
$183$	784.000			0.316694
$184$	724.500	+	1254.87i	0.290276	+	0.502773i
$185$		0			0
$186$	−264.000	+	457.261i	−0.104072	+	0.180258i
$187$	1215.00	+	2104.44i	0.475132	+	0.822952i
$188$	−45.0000			−0.0174572
$189$	−1400.00	−	1212.44i	−0.538810	−	0.466623i
$190$		0			0
$191$	1194.00	+	2068.07i	0.452329	+	0.783457i	0.998530	−	0.0541974i	$-0.0172600\pi$
$191$	1194.00	+	2068.07i	0.452329	+	0.783457i	−0.546201	+	0.837654i	$0.683927\pi$
$192$	−433.000	+	749.978i	−0.162756	+	0.281901i
$193$	136.000	−	235.559i	0.0507228	−	0.0878544i	−0.839549	−	0.543284i	$-0.817181\pi$
$193$	136.000	−	235.559i	0.0507228	−	0.0878544i	0.890272	+	0.455429i	$0.150514\pi$
$194$	−1353.00	−	2343.46i	−0.500720	−	0.867273i
$195$		0			0
$196$	−318.500	−	127.306i	−0.116071	−	0.0463942i
$197$	2109.00			0.762741			0.381371	−	0.924422i	$-0.375452\pi$
$197$	2109.00			0.762741			0.381371	+	0.924422i	$0.375452\pi$
$198$	1552.50	+	2689.01i	0.557229	+	0.965149i
$199$	−712.000	+	1233.22i	−0.253630	+	0.439300i	−0.964522	−	0.264001i	$-0.914958\pi$
$199$	−712.000	+	1233.22i	−0.253630	+	0.439300i	0.710893	+	0.703301i	$0.248291\pi$
$200$		0			0
$201$	−280.000	−	484.974i	−0.0982571	−	0.170186i
$202$	−2052.00			−0.714744
$203$	−2268.00	−	1964.15i	−0.784150	−	0.679094i
$204$	108.000			0.0370662
$205$		0			0
$206$	2274.00	−	3938.68i	0.769112	−	1.33214i
$207$	−793.500	+	1374.38i	−0.266435	+	0.461479i
$208$	−2094.50	−	3627.78i	−0.698209	−	1.20933i
$209$	5445.00			1.80210
$210$		0			0
$211$	−3625.00			−1.18273			−0.591363	−	0.806405i	$-0.701410\pi$
$211$	−3625.00			−1.18273			−0.591363	+	0.806405i	$0.701410\pi$
$212$	298.500	+	517.017i	0.0967031	+	0.167495i
$213$	−48.0000	+	83.1384i	−0.0154409	+	0.0267444i
$214$	1098.00	−	1901.79i	0.350737	−	0.607494i
$215$		0			0
$216$	−2100.00			−0.661513
$217$	1540.00	−	533.472i	0.481760	−	0.166887i
$218$	4800.00			1.49127
$219$	668.000	+	1157.01i	0.206115	+	0.357002i
$220$		0			0
$221$	1593.00	−	2759.16i	0.484872	−	0.839823i
$222$	777.000	+	1345.80i	0.234905	+	0.406867i
$223$	4960.00			1.48944			0.744722	−	0.667374i	$-0.232582\pi$
$223$	4960.00			1.48944			0.744722	+	0.667374i	$0.232582\pi$
$224$	−787.500	+	272.798i	−0.234898	+	0.0813709i
$225$		0			0
$226$	2088.00	+	3616.52i	0.614565	+	1.06446i
$227$	−750.000	+	1299.04i	−0.219292	+	0.379825i	−0.954592	−	0.297917i	$-0.903708\pi$
$227$	−750.000	+	1299.04i	−0.219292	+	0.379825i	0.735300	+	0.677742i	$0.237041\pi$
$228$	121.000	−	209.578i	0.0351466	−	0.0608757i
$229$	−3046.00	−	5275.83i	−0.878975	−	1.52243i	−0.852467	−	0.522781i	$-0.824894\pi$
$229$	−3046.00	−	5275.83i	−0.878975	−	1.52243i	−0.0265085	−	0.999649i	$-0.508439\pi$
$230$		0			0
$231$	−315.000	+	1636.79i	−0.0897207	+	0.466202i
$232$	−3402.00			−0.962725
$233$	69.0000	+	119.512i	0.0194006	+	0.0336028i	0.875563	−	0.483104i	$-0.160491\pi$
$233$	69.0000	+	119.512i	0.0194006	+	0.0336028i	−0.856162	+	0.516707i	$0.827158\pi$
$234$	2035.50	−	3525.59i	0.568653	−	0.984936i
$235$		0			0
$236$	180.000	+	311.769i	0.0496483	+	0.0859934i
$237$	1564.00			0.428661
$238$	−2268.00	−	1964.15i	−0.617700	−	0.534944i
$239$	−5502.00			−1.48910			−0.744550	−	0.667567i	$-0.767336\pi$
$239$	−5502.00			−1.48910			−0.744550	+	0.667567i	$0.767336\pi$
$240$		0			0
$241$	−1775.50	+	3075.26i	−0.474564	+	0.821970i	−0.999576	−	0.0291256i	$-0.990728\pi$
$241$	−1775.50	+	3075.26i	−0.474564	+	0.821970i	0.525011	+	0.851095i	$0.324061\pi$
$242$	1041.00	−	1803.06i	0.276521	−	0.478948i
$243$	−1771.00	−	3067.46i	−0.467530	−	0.809785i
$244$	392.000			0.102849
$245$		0			0
$246$	−1170.00			−0.303238
$247$	−3569.50	−	6182.56i	−0.919522	−	1.59266i
$248$	924.000	−	1600.41i	0.236589	−	0.409784i
$249$	768.000	−	1330.22i	0.195462	−	0.338550i
$250$		0			0
$251$	7065.00			1.77665			0.888324	−	0.459216i	$-0.151870\pi$
$251$	7065.00			1.77665			0.888324	+	0.459216i	$0.151870\pi$
$252$	−322.000	−	278.860i	−0.0804924	−	0.0697085i
$253$	3105.00			0.771580
$254$	−1204.50	−	2086.26i	−0.297547	−	0.515367i
$255$		0			0
$256$	−756.500	+	1310.30i	−0.184692	+	0.319897i
$257$	−2040.00	−	3533.38i	−0.495143	−	0.857613i	0.504842	−	0.863212i	$-0.331551\pi$
$257$	−2040.00	−	3533.38i	−0.495143	−	0.857613i	−0.999984	+	0.00559954i	$0.998218\pi$
$258$	−1716.00			−0.414083
$259$	906.500	−	4710.31i	0.217479	−	1.13006i
$260$		0			0
$261$	−1863.00	−	3226.81i	−0.441827	−	0.765267i
$262$	3028.50	−	5245.52i	0.714127	−	1.23690i
$263$	−1644.00	+	2847.49i	−0.385450	+	0.667619i	−0.991832	−	0.127555i	$-0.959287\pi$
$263$	−1644.00	+	2847.49i	−0.385450	+	0.667619i	0.606381	+	0.795174i	$0.292620\pi$
$264$	945.000	+	1636.79i	0.220306	+	0.381581i
$265$		0			0
$266$	−6352.50	+	2200.57i	−1.46427	+	0.507239i
$267$	−2388.00			−0.547353
$268$	−140.000	−	242.487i	−0.0319099	−	0.0552696i
$269$	1632.00	−	2826.71i	0.369906	−	0.640697i	−0.619644	−	0.784883i	$-0.712723\pi$
$269$	1632.00	−	2826.71i	0.369906	−	0.640697i	0.989551	+	0.144186i	$0.0460564\pi$
$270$		0			0
$271$	1376.00	+	2383.30i	0.308436	+	0.534226i	0.978020	−	0.208510i	$-0.0668612\pi$
$271$	1376.00	+	2383.30i	0.308436	+	0.534226i	−0.669585	+	0.742736i	$0.733528\pi$
$272$	−3834.00			−0.854671
$273$	2065.00	−	715.337i	0.457800	−	0.158587i
$274$	180.000			0.0396869
$275$		0			0
$276$	69.0000	−	119.512i	0.0150482	−	0.0260643i
$277$	−2345.00	+	4061.66i	−0.508655	+	0.881016i	0.491295	+	0.870993i	$0.336524\pi$
$277$	−2345.00	+	4061.66i	−0.508655	+	0.881016i	−0.999950	+	0.0100228i	$0.996810\pi$
$278$	−2562.00	−	4437.51i	−0.552729	−	0.957354i
$279$	2024.00			0.434314
$280$		0			0
$281$	7821.00			1.66036			0.830181	−	0.557494i	$-0.188237\pi$
$281$	7821.00			1.66036			0.830181	+	0.557494i	$0.188237\pi$
$282$	−135.000	−	233.827i	−0.0285076	−	0.0493765i
$283$	−329.000	+	569.845i	−0.0691061	+	0.119695i	−0.898508	−	0.438957i	$-0.855348\pi$
$283$	−329.000	+	569.845i	−0.0691061	+	0.119695i	0.829402	+	0.558652i	$0.188681\pi$
$284$	−24.0000	+	41.5692i	−0.00501457	+	0.00868549i
$285$		0			0
$286$	−7965.00			−1.64678
$287$	2730.00	+	2364.25i	0.561487	+	0.486262i
$288$	−1035.00			−0.211764
$289$	998.500	+	1729.45i	0.203236	+	0.352016i
$290$		0			0
$291$	902.000	−	1562.31i	0.181705	−	0.314722i
$292$	334.000	+	578.505i	0.0669379	+	0.115940i
$293$	5997.00			1.19573			0.597864	−	0.801597i	$-0.296016\pi$
$293$	5997.00			1.19573			0.597864	+	0.801597i	$0.296016\pi$
$294$	−294.000	−	2036.89i	−0.0583212	−	0.404061i
$295$		0			0
$296$	−2719.50	−	4710.31i	−0.534013	−	0.924937i
$297$	−2250.00	+	3897.11i	−0.439590	+	0.761392i
$298$	−1629.00	+	2821.51i	−0.316663	+	0.548476i
$299$	−2035.50	−	3525.59i	−0.393699	−	0.681907i
$300$		0			0
$301$	4004.00	+	3467.57i	0.766733	+	0.664011i
$302$	8598.00			1.63828
$303$	−684.000	−	1184.72i	−0.129686	−	0.224622i
$304$	−4295.50	+	7440.02i	−0.810407	+	1.40367i
$305$		0			0
$306$	−1863.00	−	3226.81i	−0.348041	−	0.602825i
$307$	6226.00			1.15745			0.578724	−	0.815523i	$-0.303551\pi$
$307$	6226.00			1.15745			0.578724	+	0.815523i	$0.303551\pi$
$308$	−157.500	+	818.394i	−0.0291376	+	0.151404i
$309$	3032.00			0.558202
$310$		0			0
$311$	−2340.00	+	4053.00i	−0.426653	+	0.738985i	−0.996573	−	0.0827149i	$-0.973641\pi$
$311$	−2340.00	+	4053.00i	−0.426653	+	0.738985i	0.569920	+	0.821700i	$0.306974\pi$
$312$	1239.00	−	2146.01i	0.224822	−	0.389404i
$313$	514.000	+	890.274i	0.0928211	+	0.160771i	0.908697	−	0.417456i	$-0.137078\pi$
$313$	514.000	+	890.274i	0.0928211	+	0.160771i	−0.815876	+	0.578227i	$0.803745\pi$
$314$	−687.000			−0.123470
$315$		0			0
$316$	782.000			0.139212
$317$	4311.00	+	7466.87i	0.763817	+	1.32297i	0.940870	+	0.338768i	$0.110010\pi$
$317$	4311.00	+	7466.87i	0.763817	+	1.32297i	−0.177053	+	0.984201i	$0.556656\pi$
$318$	−1791.00	+	3102.10i	−0.315831	+	0.547036i
$319$	−3645.00	+	6313.33i	−0.639752	+	1.10808i
$320$		0			0
$321$	1464.00			0.254556
$322$	−3622.50	+	1254.87i	−0.626938	+	0.217178i
$323$	−6534.00			−1.12558
$324$	−210.500	−	364.597i	−0.0360940	−	0.0625166i
$325$		0			0
$326$	1842.00	−	3190.44i	0.312942	−	0.542031i
$327$	1600.00	+	2771.28i	0.270582	+	0.468661i
$328$	4095.00			0.689355
$329$	−157.500	+	818.394i	−0.0263929	+	0.137141i
$330$		0			0
$331$	999.500	+	1731.18i	0.165974	+	0.287476i	0.937001	−	0.349327i	$-0.113590\pi$
$331$	999.500	+	1731.18i	0.165974	+	0.287476i	−0.771027	+	0.636803i	$0.780256\pi$
$332$	384.000	−	665.108i	0.0634781	−	0.109947i
$333$	2978.50	−	5158.91i	0.490153	−	0.848969i
$334$	2893.50	+	5011.69i	0.474028	+	0.821040i
$335$		0			0
$336$	−1988.00	−	1721.66i	−0.322781	−	0.279536i
$337$	−5114.00			−0.826639			−0.413319	−	0.910586i	$-0.635631\pi$
$337$	−5114.00			−0.826639			−0.413319	+	0.910586i	$0.635631\pi$
$338$	1926.00	+	3335.93i	0.309943	+	0.536836i
$339$	−1392.00	+	2411.01i	−0.223018	+	0.386278i
$340$		0			0
$341$	−1980.00	−	3429.46i	−0.314437	−	0.544621i
$342$	−8349.00			−1.32006
$343$	−3430.00	+	5346.84i	−0.539949	+	0.841698i
$344$	6006.00			0.941342
$345$		0			0
$346$	1048.50	−	1816.06i	0.162912	−	0.282173i
$347$	2160.00	−	3741.23i	0.334164	−	0.578789i	−0.649160	−	0.760652i	$-0.724879\pi$
$347$	2160.00	−	3741.23i	0.334164	−	0.578789i	0.983324	+	0.181863i	$0.0582128\pi$
$348$	162.000	+	280.592i	0.0249543	+	0.0432222i
$349$	7922.00			1.21506			0.607529	−	0.794298i	$-0.292161\pi$
$349$	7922.00			1.21506			0.607529	+	0.794298i	$0.292161\pi$
$350$		0			0
$351$	5900.00			0.897204
$352$	1012.50	+	1753.70i	0.153314	+	0.265547i
$353$	414.000	−	717.069i	0.0624221	−	0.108118i	−0.833125	−	0.553084i	$-0.813451\pi$
$353$	414.000	−	717.069i	0.0624221	−	0.108118i	0.895548	+	0.444966i	$0.146784\pi$
$354$	−1080.00	+	1870.61i	−0.162151	+	0.280853i
$355$		0			0
$356$	−1194.00			−0.177758
$357$	378.000	−	1964.15i	0.0560389	−	0.291187i
$358$	−9351.00			−1.38049
$359$	675.000	+	1169.13i	0.0992344	+	0.171879i	0.911368	−	0.411593i	$-0.135027\pi$
$359$	675.000	+	1169.13i	0.0992344	+	0.171879i	−0.812134	+	0.583472i	$0.801694\pi$
$360$		0			0
$361$	−3891.00	+	6739.41i	−0.567284	+	0.982564i
$362$	−2697.00	−	4671.34i	−0.391578	−	0.678233i
$363$	1388.00			0.200692
$364$	1032.50	−	357.668i	0.148675	−	0.0515025i
$365$		0			0
$366$	1176.00	+	2036.89i	0.167952	+	0.290902i
$367$	1400.50	−	2425.74i	0.199198	−	0.345020i	−0.749071	−	0.662490i	$-0.769500\pi$
$367$	1400.50	−	2425.74i	0.199198	−	0.345020i	0.948268	+	0.317470i	$0.102833\pi$
$368$	−2449.50	+	4242.66i	−0.346981	+	0.600989i
$369$	2242.50	+	3884.12i	0.316368	+	0.547966i
$370$		0			0
$371$	10447.5	−	3619.12i	1.46201	−	0.506456i
$372$	−176.000			−0.0245300
$373$	3301.00	+	5717.50i	0.458229	+	0.793675i	0.998867	−	0.0475795i	$-0.0151507\pi$
$373$	3301.00	+	5717.50i	0.458229	+	0.793675i	−0.540639	+	0.841255i	$0.681817\pi$
$374$	−3645.00	+	6313.33i	−0.503953	+	0.872872i
$375$		0			0
$376$	472.500	+	818.394i	0.0648067	+	0.112249i
$377$	9558.00			1.30573
$378$	1050.00	−	5455.96i	0.142873	−	0.742392i
$379$	−8305.00			−1.12559			−0.562796	−	0.826596i	$-0.690274\pi$
$379$	−8305.00			−1.12559			−0.562796	+	0.826596i	$0.690274\pi$
$380$		0			0
$381$	803.000	−	1390.84i	0.107976	−	0.187020i
$382$	−3582.00	+	6204.21i	−0.479767	+	0.830981i
$383$	472.500	+	818.394i	0.0630382	+	0.109185i	0.895822	−	0.444413i	$-0.146588\pi$
$383$	472.500	+	818.394i	0.0630382	+	0.109185i	−0.832784	+	0.553598i	$0.813254\pi$
$384$	−3318.00			−0.440940
$385$		0			0
$386$	816.000			0.107599
$387$	3289.00	+	5696.72i	0.432014	+	0.748270i
$388$	451.000	−	781.155i	0.0590105	−	0.102209i
$389$	−6018.00	+	10423.5i	−0.784382	+	1.35859i	0.144985	+	0.989434i	$0.453687\pi$
$389$	−6018.00	+	10423.5i	−0.784382	+	1.35859i	−0.929367	+	0.369156i	$0.879647\pi$
$390$		0			0
$391$	−3726.00			−0.481923
$392$	1029.00	+	7129.12i	0.132583	+	0.918559i
$393$	4038.00			0.518296
$394$	3163.50	+	5479.34i	0.404505	+	0.700623i
$395$		0			0
$396$	−517.500	+	896.336i	−0.0656701	+	0.113744i
$397$	−1349.00	−	2336.54i	−0.170540	−	0.295384i	0.768069	−	0.640367i	$-0.221218\pi$
$397$	−1349.00	−	2336.54i	−0.170540	−	0.295384i	−0.938609	+	0.344983i	$0.887885\pi$
$398$	−4272.00			−0.538030
$399$	−3388.00	−	2934.09i	−0.425093	−	0.368141i
$400$		0			0
$401$	−3526.50	−	6108.08i	−0.439165	−	0.760655i	0.558461	−	0.829531i	$-0.311392\pi$
$401$	−3526.50	−	6108.08i	−0.439165	−	0.760655i	−0.997625	+	0.0688756i	$0.978059\pi$
$402$	840.000	−	1454.92i	0.104217	−	0.180510i
$403$	−2596.00	+	4496.40i	−0.320883	+	0.555786i
$404$	−342.000	−	592.361i	−0.0421167	−	0.0729482i
$405$		0			0
$406$	1701.00	−	8838.66i	0.207929	−	1.08043i
$407$	−11655.0			−1.41945
$408$	−1134.00	−	1964.15i	−0.137601	−	0.238333i
$409$	5435.00	−	9413.70i	0.657074	−	1.13809i	−0.324295	−	0.945956i	$-0.605127\pi$
$409$	5435.00	−	9413.70i	0.657074	−	1.13809i	0.981369	−	0.192130i	$-0.0615396\pi$
$410$		0			0
$411$	60.0000	+	103.923i	0.00720093	+	0.0124724i
$412$	1516.00			0.181281
$413$	6300.00	−	2182.38i	0.750612	−	0.260020i
$414$	−4761.00			−0.565194
$415$		0			0
$416$	1327.50	−	2299.30i	0.156457	−	0.270991i
$417$	1708.00	−	2958.34i	0.200578	−	0.347412i
$418$	8167.50	+	14146.5i	0.955707	+	1.65533i
$419$	−9729.00			−1.13435			−0.567175	−	0.823597i	$-0.691964\pi$
$419$	−9729.00			−1.13435			−0.567175	+	0.823597i	$0.691964\pi$
$420$		0			0
$421$	−12550.0			−1.45285			−0.726425	−	0.687246i	$-0.758819\pi$
$421$	−12550.0			−1.45285			−0.726425	+	0.687246i	$0.758819\pi$
$422$	−5437.50	−	9418.03i	−0.627235	−	1.08640i
$423$	−517.500	+	896.336i	−0.0594840	+	0.103029i
$424$	6268.50	−	10857.4i	0.717984	−	1.24358i
$425$		0			0
$426$	−288.000			−0.0327550
$427$	1372.00	−	7129.12i	0.155494	−	0.807968i
$428$	732.000			0.0826695
$429$	−2655.00	−	4598.59i	−0.298799	−	0.517534i
$430$		0			0
$431$	−1494.00	+	2587.68i	−0.166969	+	0.289198i	−0.937353	−	0.348382i	$-0.886731\pi$
$431$	−1494.00	+	2587.68i	−0.166969	+	0.289198i	0.770384	+	0.637580i	$0.220065\pi$
$432$	−3550.00	−	6148.78i	−0.395369	−	0.684799i
$433$	−16616.0			−1.84414			−0.922072	−	0.387019i	$-0.873505\pi$
$433$	−16616.0			−1.84414			−0.922072	+	0.387019i	$0.873505\pi$
$434$	3696.00	+	3200.83i	0.408787	+	0.354020i
$435$		0			0
$436$	800.000	+	1385.64i	0.0878740	+	0.152202i
$437$	−4174.50	+	7230.45i	−0.456964	+	0.791485i
$438$	−2004.00	+	3471.03i	−0.218618	+	0.378658i
$439$	−3673.00	−	6361.82i	−0.399323	−	0.691647i	0.594320	−	0.804229i	$-0.297421\pi$
$439$	−3673.00	−	6361.82i	−0.399323	−	0.691647i	−0.993642	+	0.112581i	$0.964088\pi$
$440$		0			0
$441$	−6198.50	+	4880.05i	−0.669312	+	0.526947i
$442$	9558.00			1.02857
$443$	6.00000	+	10.3923i	0.000643496	+	0.00111457i	0.866347	−	0.499443i	$-0.166462\pi$
$443$	6.00000	+	10.3923i	0.000643496	+	0.00111457i	−0.865703	+	0.500557i	$0.833129\pi$
$444$	−259.000	+	448.601i	−0.0276838	+	0.0479497i
$445$		0			0
$446$	7440.00	+	12886.5i	0.789897	+	1.36814i
$447$	−2172.00			−0.229826
$448$	6062.00	+	5249.85i	0.639291	+	0.553643i
$449$	9669.00			1.01628			0.508138	−	0.861275i	$-0.330334\pi$
$449$	9669.00			1.01628			0.508138	+	0.861275i	$0.330334\pi$
$450$		0			0
$451$	4387.50	−	7599.37i	0.458092	−	0.793438i
$452$	−696.000	+	1205.51i	−0.0724272	+	0.125448i
$453$	2866.00	+	4964.06i	0.297255	+	0.514860i
$454$	−4500.00			−0.465188
$455$		0			0
$456$	−5082.00			−0.521900
$457$	−4817.00	−	8343.29i	−0.493063	−	0.854010i	0.506905	−	0.862002i	$-0.330789\pi$
$457$	−4817.00	−	8343.29i	−0.493063	−	0.854010i	−0.999968	+	0.00799181i	$0.997456\pi$
$458$	9138.00	−	15827.5i	0.932294	−	1.61478i
$459$	2700.00	−	4676.54i	0.274565	−	0.475560i
$460$		0			0
$461$	−342.000			−0.0345521			−0.0172761	−	0.999851i	$-0.505499\pi$
$461$	−342.000			−0.0345521			−0.0172761	+	0.999851i	$0.505499\pi$
$462$	−4725.00	+	1636.79i	−0.475816	+	0.164827i
$463$	−2411.00			−0.242006			−0.121003	−	0.992652i	$-0.538611\pi$
$463$	−2411.00			−0.242006			−0.121003	+	0.992652i	$0.538611\pi$
$464$	−5751.00	−	9961.02i	−0.575395	−	0.996614i
$465$		0			0
$466$	−207.000	+	358.535i	−0.0205774	+	0.0356412i
$467$	−603.000	−	1044.43i	−0.0597506	−	0.103491i	0.834603	−	0.550852i	$-0.185697\pi$
$467$	−603.000	−	1044.43i	−0.0597506	−	0.103491i	−0.894353	+	0.447361i	$0.852364\pi$
$468$	1357.00			0.134033
$469$	−4900.00	+	1697.41i	−0.482433	+	0.167120i
$470$		0			0
$471$	−229.000	−	396.640i	−0.0224029	−	0.0388030i
$472$	3780.00	−	6547.15i	0.368620	−	0.638468i
$473$	6435.00	−	11145.7i	0.625543	−	1.08347i
$474$	2346.00	+	4063.39i	0.227332	+	0.393751i
$475$		0			0
$476$	189.000	−	982.073i	0.0181992	−	0.0945656i
$477$	13731.0			1.31803
$478$	−8253.00	−	14294.6i	−0.789714	−	1.36783i
$479$	216.000	−	374.123i	0.0206039	−	0.0356871i	−0.855540	−	0.517737i	$-0.826774\pi$
$479$	216.000	−	374.123i	0.0206039	−	0.0356871i	0.876144	+	0.482050i	$0.160108\pi$
$480$		0			0
$481$	7640.50	+	13233.7i	0.724276	+	1.25448i
$482$	−10653.0			−1.00670
$483$	−1932.00	−	1673.16i	−0.182006	−	0.157622i
$484$	694.000			0.0651766
$485$		0			0
$486$	5313.00	−	9202.39i	0.495890	−	0.858907i
$487$	−5948.00	+	10302.2i	−0.553449	+	0.958602i	0.444574	+	0.895742i	$0.353355\pi$
$487$	−5948.00	+	10302.2i	−0.553449	+	0.958602i	−0.998022	+	0.0628592i	$0.979978\pi$
$488$	−4116.00	−	7129.12i	−0.381809	−	0.661312i
$489$	2456.00			0.227125
$490$		0			0
$491$	−12276.0			−1.12833			−0.564163	−	0.825663i	$-0.690801\pi$
$491$	−12276.0			−1.12833			−0.564163	+	0.825663i	$0.690801\pi$
$492$	−195.000	−	337.750i	−0.0178685	−	0.0309491i
$493$	4374.00	−	7575.99i	0.399584	−	0.692100i
$494$	10708.5	−	18547.7i	0.975300	−	1.68927i
$495$		0			0
$496$	6248.00			0.565612
$497$	672.000	+	581.969i	0.0606505	+	0.0525249i
$498$	4608.00			0.414637
$499$	5438.00	+	9418.89i	0.487852	+	0.844985i	0.999902	−	0.0139706i	$-0.00444712\pi$
$499$	5438.00	+	9418.89i	0.487852	+	0.844985i	−0.512050	+	0.858956i	$0.671114\pi$
$500$		0			0
$501$	−1929.00	+	3341.13i	−0.172019	+	0.297945i
$502$	10597.5	+	18355.4i	0.942210	+	1.63196i
$503$	−12000.0			−1.06372			−0.531862	−	0.846831i	$-0.678508\pi$
$503$	−12000.0			−1.06372			−0.531862	+	0.846831i	$0.678508\pi$
$504$	−1690.50	+	8784.10i	−0.149406	+	0.776339i
$505$		0			0
$506$	4657.50	+	8067.03i	0.409192	+	0.708741i
$507$	−1284.00	+	2223.95i	−0.112474	+	0.194811i
$508$	401.500	−	695.418i	0.0350663	−	0.0607366i
$509$	5841.00	+	10116.9i	0.508640	+	0.880990i	0.999950	+	0.0100055i	$0.00318492\pi$
$509$	5841.00	+	10116.9i	0.508640	+	0.880990i	−0.491310	+	0.870985i	$0.663482\pi$
$510$		0			0
$511$	11690.0	−	4049.53i	1.01201	−	0.350569i
$512$	8733.00			0.753804
$513$	−6050.00	−	10478.9i	−0.520690	−	0.901862i
$514$	6120.00	−	10600.2i	0.525178	−	0.909635i
$515$		0			0
$516$	−286.000	−	495.367i	−0.0244001	−	0.0422622i
$517$	2025.00			0.172262
$518$	13597.5	−	4710.31i	1.15336	−	0.399535i
$519$	1398.00			0.118238
$520$		0			0
$521$	−4804.50	+	8321.64i	−0.404010	+	0.699765i	−0.994206	−	0.107495i	$-0.965717\pi$
$521$	−4804.50	+	8321.64i	−0.404010	+	0.699765i	0.590196	+	0.807260i	$0.299050\pi$
$522$	5589.00	−	9680.43i	0.468628	−	0.811688i
$523$	10594.0	+	18349.3i	0.885742	+	1.53415i	0.844860	+	0.534987i	$0.179683\pi$
$523$	10594.0	+	18349.3i	0.885742	+	1.53415i	0.0408820	+	0.999164i	$0.486983\pi$
$524$	2019.00			0.168321
$525$		0			0
$526$	−9864.00			−0.817663
$527$	2376.00	+	4115.35i	0.196395	+	0.340166i
$528$	−3195.00	+	5533.90i	−0.263342	+	0.456122i
$529$	3703.00	−	6413.78i	0.304348	−	0.527146i
$530$		0			0
$531$	8280.00			0.676688
$532$	−1694.00	−	1467.05i	−0.138053	−	0.119557i
$533$	−11505.0			−0.934966
$534$	−3582.00	−	6204.21i	−0.290278	−	0.502776i
$535$		0			0
$536$	−2940.00	+	5092.23i	−0.236919	+	0.410356i
$537$	−3117.00	−	5398.80i	−0.250481	−	0.433846i
$538$	9792.00			0.784690
$539$	14332.5	+	5728.76i	1.14535	+	0.457802i
$540$		0			0
$541$	−4036.00	−	6990.56i	−0.320742	−	0.555541i	0.659900	−	0.751354i	$-0.270599\pi$
$541$	−4036.00	−	6990.56i	−0.320742	−	0.555541i	−0.980641	+	0.195813i	$0.937265\pi$
$542$	−4128.00	+	7149.91i	−0.327145	+	0.566632i
$543$	1798.00	−	3114.23i	0.142099	−	0.246122i
$544$	−1215.00	−	2104.44i	−0.0957586	−	0.165859i
$545$		0			0
$546$	4956.00	+	4292.02i	0.388456	+	0.336413i
$547$	−344.000			−0.0268892			−0.0134446	−	0.999910i	$-0.504280\pi$
$547$	−344.000			−0.0268892			−0.0134446	+	0.999910i	$0.504280\pi$
$548$	30.0000	+	51.9615i	0.00233857	+	0.00405052i
$549$	4508.00	−	7808.09i	0.350449	−	0.606996i
$550$		0			0
$551$	−9801.00	−	16975.8i	−0.757780	−	1.31251i
$552$	−2898.00			−0.223455
$553$	2737.00	−	14221.9i	0.210468	−	1.09363i
$554$	−14070.0			−1.07902
$555$		0			0
$556$	854.000	−	1479.17i	0.0651397	−	0.112825i
$557$	9181.50	−	15902.8i	0.698443	−	1.20974i	−0.270563	−	0.962702i	$-0.587210\pi$
$557$	9181.50	−	15902.8i	0.698443	−	1.20974i	0.969006	−	0.247036i	$-0.0794567\pi$
$558$	3036.00	+	5258.51i	0.230330	+	0.398943i
$559$	−16874.0			−1.27673
$560$		0			0
$561$	−4860.00			−0.365756
$562$	11731.5	+	20319.6i	0.880540	+	1.52514i
$563$	−3147.00	+	5450.76i	−0.235578	+	0.408033i	−0.959440	−	0.281912i	$-0.909032\pi$
$563$	−3147.00	+	5450.76i	−0.235578	+	0.408033i	0.723863	+	0.689944i	$0.242365\pi$
$564$	45.0000	−	77.9423i	0.00335965	−	0.00581908i
$565$		0			0
$566$	−1974.00			−0.146596
$567$	−7367.50	+	2552.18i	−0.545689	+	0.189032i
$568$	1008.00			0.0744626
$569$	−5866.50	−	10161.1i	−0.432226	−	0.748637i	0.564839	−	0.825201i	$-0.308938\pi$
$569$	−5866.50	−	10161.1i	−0.432226	−	0.748637i	−0.997065	+	0.0765642i	$0.975605\pi$
$570$		0			0
$571$	−526.000	+	911.059i	−0.0385506	+	0.0667717i	−0.884657	−	0.466242i	$-0.845607\pi$
$571$	−526.000	+	911.059i	−0.0385506	+	0.0667717i	0.846106	+	0.533014i	$0.178941\pi$
$572$	−1327.50	−	2299.30i	−0.0970377	−	0.168074i
$573$	−4776.00			−0.348203
$574$	−2047.50	+	10639.1i	−0.148887	+	0.773638i
$575$		0			0
$576$	4979.50	+	8624.75i	0.360207	+	0.623897i
$577$	−6578.00	+	11393.4i	−0.474603	+	0.822036i	−0.999577	−	0.0290821i	$-0.990742\pi$
$577$	−6578.00	+	11393.4i	−0.474603	+	0.822036i	0.524974	+	0.851118i	$0.324075\pi$
$578$	−2995.50	+	5188.36i	−0.215565	+	0.373369i
$579$	272.000	+	471.118i	0.0195232	+	0.0338152i
$580$		0			0
$581$	−10752.0	−	9311.51i	−0.767759	−	0.664899i
$582$	5412.00			0.385455
$583$	−13432.5	−	23265.8i	−0.954232	−	1.65278i
$584$	7014.00	−	12148.6i	0.496989	−	0.860810i
$585$		0			0
$586$	8995.50	+	15580.7i	0.634131	+	1.09835i
$587$	13368.0			0.939960			0.469980	−	0.882677i	$-0.344261\pi$
$587$	13368.0			0.939960			0.469980	+	0.882677i	$0.344261\pi$
$588$	539.000	−	424.352i	0.0378027	−	0.0297619i
$589$	10648.0			0.744895
$590$		0			0
$591$	−2109.00	+	3652.90i	−0.146790	+	0.254247i
$592$	9194.50	−	15925.3i	0.638330	−	1.10562i
$593$	13332.0	+	23091.7i	0.923237	+	1.59909i	0.794372	+	0.607431i	$0.207800\pi$
$593$	13332.0	+	23091.7i	0.923237	+	1.59909i	0.128865	+	0.991662i	$0.458867\pi$
$594$	−13500.0			−0.932511
$595$		0			0
$596$	−1086.00			−0.0746381
$597$	−1424.00	−	2466.44i	−0.0976222	−	0.169087i
$598$	6106.50	−	10576.8i	0.417581	−	0.723271i
$599$	−3807.00	+	6593.92i	−0.259682	+	0.449783i	−0.966157	−	0.257955i	$-0.916951\pi$
$599$	−3807.00	+	6593.92i	−0.259682	+	0.449783i	0.706474	+	0.707739i	$0.250285\pi$
$600$		0			0
$601$	6410.00			0.435057			0.217529	−	0.976054i	$-0.430200\pi$
$601$	6410.00			0.435057			0.217529	+	0.976054i	$0.430200\pi$
$602$	−3003.00	+	15604.0i	−0.203311	+	1.05643i
$603$	−6440.00			−0.434921
$604$	1433.00	+	2482.03i	0.0965363	+	0.167206i
$605$		0			0
$606$	2052.00	−	3554.17i	0.137552	−	0.238248i
$607$	−10734.5	−	18592.7i	−0.717792	−	1.24325i	−0.961873	−	0.273498i	$-0.911819\pi$
$607$	−10734.5	−	18592.7i	−0.717792	−	1.24325i	0.244080	−	0.969755i	$-0.421514\pi$
$608$	−5445.00			−0.363197
$609$	5670.00	−	1964.15i	0.377274	−	0.130692i
$610$		0			0
$611$	−1327.50	−	2299.30i	−0.0878967	−	0.152242i
$612$	621.000	−	1075.60i	0.0410171	−	0.0710436i
$613$	1868.50	−	3236.34i	0.123113	−	0.213237i	−0.797881	−	0.602815i	$-0.794046\pi$
$613$	1868.50	−	3236.34i	0.123113	−	0.213237i	0.920994	+	0.389578i	$0.127379\pi$
$614$	9339.00	+	16175.6i	0.613830	+	1.06318i
$615$		0			0
$616$	16537.5	−	5728.76i	1.08168	−	0.374705i
$617$	−18078.0			−1.17957			−0.589784	−	0.807561i	$-0.700787\pi$
$617$	−18078.0			−1.17957			−0.589784	+	0.807561i	$0.700787\pi$
$618$	4548.00	+	7877.37i	0.296031	+	0.512741i
$619$	−6143.50	+	10640.9i	−0.398915	+	0.690940i	−0.993592	−	0.113024i	$-0.963946\pi$
$619$	−6143.50	+	10640.9i	−0.398915	+	0.690940i	0.594678	+	0.803964i	$0.297280\pi$
$620$		0			0
$621$	−3450.00	−	5975.58i	−0.222937	−	0.386138i
$622$	−14040.0			−0.905069
$623$	−4179.00	+	21714.7i	−0.268745	+	1.39644i
$624$	8378.00			0.537481
$625$		0			0
$626$	−1542.00	+	2670.82i	−0.0984516	+	0.170523i
$627$	−5445.00	+	9431.02i	−0.346814	+	0.600699i
$628$	−114.500	−	198.320i	−0.00727555	−	0.0126016i
$629$	13986.0			0.886579
$630$		0			0
$631$	−9580.00			−0.604396			−0.302198	−	0.953245i	$-0.597720\pi$
$631$	−9580.00			−0.604396			−0.302198	+	0.953245i	$0.597720\pi$
$632$	−8211.00	−	14221.9i	−0.516798	−	0.895120i
$633$	3625.00	−	6278.68i	0.227616	−	0.394242i
$634$	−12933.0	+	22400.6i	−0.810150	+	1.40322i
$635$		0			0
$636$	−1194.00			−0.0744421
$637$	−2891.00	−	20029.4i	−0.179820	−	1.24583i
$638$	−21870.0			−1.35712
$639$	552.000	+	956.092i	0.0341734	+	0.0591900i
$640$		0			0
$641$	−5389.50	+	9334.89i	−0.332094	+	0.575204i	−0.982922	−	0.184021i	$-0.941089\pi$
$641$	−5389.50	+	9334.89i	−0.332094	+	0.575204i	0.650828	+	0.759225i	$0.274422\pi$
$642$	2196.00	+	3803.58i	0.134999	+	0.233825i
$643$	−8882.00			−0.544746			−0.272373	−	0.962192i	$-0.587809\pi$
$643$	−8882.00			−0.544746			−0.272373	+	0.962192i	$0.587809\pi$
$644$	−966.000	−	836.581i	−0.0591083	−	0.0511893i
$645$		0			0
$646$	−9801.00	−	16975.8i	−0.596928	−	1.03391i
$647$	−5509.50	+	9542.73i	−0.334777	+	0.579851i	−0.983442	−	0.181223i	$-0.941994\pi$
$647$	−5509.50	+	9542.73i	−0.334777	+	0.579851i	0.648665	+	0.761074i	$0.275328\pi$
$648$	−4420.50	+	7656.53i	−0.267984	+	0.464162i
$649$	−8100.00	−	14029.6i	−0.489912	−	0.848552i
$650$		0			0
$651$	−616.000	+	3200.83i	−0.0370859	+	0.192704i
$652$	1228.00			0.0737610
$653$	11161.5	+	19332.3i	0.668887	+	1.15855i	0.978216	+	0.207591i	$0.0665624\pi$
$653$	11161.5	+	19332.3i	0.668887	+	1.15855i	−0.309329	+	0.950955i	$0.600104\pi$
$654$	−4800.00	+	8313.84i	−0.286995	+	0.497090i
$655$		0			0
$656$	6922.50	+	11990.1i	0.412009	+	0.713621i
$657$	15364.0			0.912339
$658$	−2362.50	+	818.394i	−0.139969	+	0.0484868i
$659$	−11856.0			−0.700826			−0.350413	−	0.936595i	$-0.613959\pi$
$659$	−11856.0			−0.700826			−0.350413	+	0.936595i	$0.613959\pi$
$660$		0			0
$661$	16622.0	−	28790.1i	0.978095	−	1.69411i	0.308777	−	0.951134i	$-0.400080\pi$
$661$	16622.0	−	28790.1i	0.978095	−	1.69411i	0.669318	−	0.742976i	$-0.266586\pi$
$662$	−2998.50	+	5193.55i	−0.176042	+	0.304914i
$663$	3186.00	+	5518.31i	0.186627	+	0.323248i
$664$	−16128.0			−0.942602
$665$		0			0
$666$	17871.0			1.03977
$667$	−5589.00	−	9680.43i	−0.324448	−	0.561961i
$668$	−964.500	+	1670.56i	−0.0558647	+	0.0967605i
$669$	−4960.00	+	8590.97i	−0.286644	+	0.496482i
$670$		0			0
$671$	−17640.0			−1.01488
$672$	315.000	−	1636.79i	0.0180824	−	0.0939590i
$673$	12322.0			0.705763			0.352881	−	0.935668i	$-0.385202\pi$
$673$	12322.0			0.705763			0.352881	+	0.935668i	$0.385202\pi$
$674$	−7671.00	−	13286.6i	−0.438392	−	0.759316i
$675$		0			0
$676$	−642.000	+	1111.98i	−0.0365271	+	0.0632668i
$677$	−6298.50	−	10909.3i	−0.357564	−	0.619320i	0.629989	−	0.776604i	$-0.283059\pi$
$677$	−6298.50	−	10909.3i	−0.357564	−	0.619320i	−0.987553	+	0.157285i	$0.949726\pi$
$678$	−8352.00			−0.473092
$679$	−12628.0	−	10936.2i	−0.713723	−	0.618103i
$680$		0			0
$681$	−1500.00	−	2598.08i	−0.0844055	−	0.146195i
$682$	5940.00	−	10288.4i	0.333511	−	0.577658i
$683$	−4170.00	+	7222.65i	−0.233617	+	0.404637i	−0.958870	−	0.283846i	$-0.908390\pi$
$683$	−4170.00	+	7222.65i	−0.233617	+	0.404637i	0.725253	+	0.688483i	$0.241723\pi$
$684$	−1391.50	−	2410.15i	−0.0777856	−	0.134729i
$685$		0			0
$686$	−19036.5	−	891.140i	−1.05950	−	0.0495975i
$687$	12184.0			0.676636
$688$	10153.0	+	17585.5i	0.562616	+	0.974479i
$689$	−17611.5	+	30504.0i	−0.973795	+	1.68666i
$690$		0			0
$691$	10100.0	+	17493.7i	0.556038	+	0.963086i	0.997822	+	0.0659643i	$0.0210124\pi$
$691$	10100.0	+	17493.7i	0.556038	+	0.963086i	−0.441784	+	0.897121i	$0.645654\pi$
$692$	699.000			0.0383988
$693$	14490.0	+	12548.7i	0.794271	+	0.687859i
$694$	12960.0			0.708869
$695$		0			0
$696$	3402.00	−	5892.44i	0.185277	−	0.320908i
$697$	−5265.00	+	9119.25i	−0.286121	+	0.495576i
$698$	11883.0	+	20582.0i	0.644381	+	1.11610i
$699$	−276.000			−0.0149346
$700$		0			0
$701$	474.000			0.0255388			0.0127694	−	0.999918i	$-0.495935\pi$
$701$	474.000			0.0255388			0.0127694	+	0.999918i	$0.495935\pi$
$702$	8850.00	+	15328.6i	0.475814	+	0.824135i
$703$	15669.5	−	27140.4i	0.840663	−	1.45607i
$704$	9742.50	−	16874.5i	0.521569	−	0.903383i
$705$		0			0
$706$	2484.00			0.132417
$707$	−11970.0	+	4146.53i	−0.636744	+	0.220575i
$708$	−720.000			−0.0382193
$709$	12563.0	+	21759.8i	0.665463	+	1.15262i	0.979160	+	0.203093i	$0.0650993\pi$
$709$	12563.0	+	21759.8i	0.665463	+	1.15262i	−0.313696	+	0.949523i	$0.601567\pi$
$710$		0			0
$711$	8993.00	−	15576.3i	0.474351	−	0.821601i
$712$	12537.0	+	21714.7i	0.659893	+	1.14297i
$713$	6072.00			0.318932
$714$	5670.00	−	1964.15i	0.297191	−	0.102950i
$715$		0			0
$716$	−1558.50	−	2699.40i	−0.0813462	−	0.140896i
$717$	5502.00	−	9529.74i	0.286577	−	0.496367i
$718$	−2025.00	+	3507.40i	−0.105254	+	0.182305i
$719$	3648.00	+	6318.52i	0.189218	+	0.327734i	0.944990	−	0.327100i	$-0.106072\pi$
$719$	3648.00	+	6318.52i	0.189218	+	0.327734i	−0.755772	+	0.654835i	$0.772738\pi$
$720$		0			0
$721$	5306.00	−	27570.8i	0.274072	−	1.42412i
$722$	−23346.0			−1.20339
$723$	−3551.00	−	6150.51i	−0.182660	−	0.316376i
$724$	899.000	−	1557.11i	0.0461479	−	0.0799305i
$725$		0			0
$726$	2082.00	+	3606.13i	0.106433	+	0.184347i
$727$	15421.0			0.786703			0.393352	−	0.919388i	$-0.371316\pi$
$727$	15421.0			0.786703			0.393352	+	0.919388i	$0.371316\pi$
$728$	−17346.0	−	15022.1i	−0.883085	−	0.764774i
$729$	−4283.00			−0.217599
$730$		0			0
$731$	−7722.00	+	13374.9i	−0.390709	+	0.676728i
$732$	−392.000	+	678.964i	−0.0197934	+	0.0342831i
$733$	−14583.5	−	25259.4i	−0.734862	−	1.27282i	−0.954784	−	0.297301i	$-0.903914\pi$
$733$	−14583.5	−	25259.4i	−0.734862	−	1.27282i	0.219922	−	0.975517i	$-0.429420\pi$
$734$	8403.00			0.422562
$735$		0			0
$736$	−3105.00			−0.155505
$737$	6300.00	+	10911.9i	0.314876	+	0.545381i
$738$	−6727.50	+	11652.4i	−0.335559	+	0.581206i
$739$	6690.50	−	11588.3i	0.333037	−	0.576836i	−0.650069	−	0.759875i	$-0.725260\pi$
$739$	6690.50	−	11588.3i	0.333037	−	0.576836i	0.983106	+	0.183039i	$0.0585934\pi$
$740$		0			0
$741$	14278.0			0.707848
$742$	25074.0	+	21714.7i	1.24056	+	1.07436i
$743$	−5487.00			−0.270927			−0.135463	−	0.990782i	$-0.543252\pi$
$743$	−5487.00			−0.270927			−0.135463	+	0.990782i	$0.543252\pi$
$744$	1848.00	+	3200.83i	0.0910631	+	0.157726i
$745$		0			0
$746$	−9903.00	+	17152.5i	−0.486025	+	0.841820i
$747$	−8832.00	−	15297.5i	−0.432592	−	0.749271i
$748$	−2430.00			−0.118783
$749$	2562.00	−	13312.5i	0.124985	−	0.649439i
$750$		0			0
$751$	−3319.00	−	5748.68i	−0.161268	−	0.279324i	0.774056	−	0.633117i	$-0.218225\pi$
$751$	−3319.00	−	5748.68i	−0.161268	−	0.279324i	−0.935324	+	0.353793i	$0.884892\pi$
$752$	−1597.50	+	2766.95i	−0.0774665	+	0.134176i
$753$	−7065.00	+	12236.9i	−0.341916	+	0.592216i
$754$	14337.0	+	24832.4i	0.692470	+	1.19939i
$755$		0			0
$756$	1750.00	−	606.218i	0.0841890	−	0.0291639i
$757$	−14846.0			−0.712797			−0.356398	−	0.934334i	$-0.615995\pi$
$757$	−14846.0			−0.712797			−0.356398	+	0.934334i	$0.615995\pi$
$758$	−12457.5	−	21577.0i	−0.596935	−	1.03392i
$759$	−3105.00	+	5378.02i	−0.148491	+	0.257193i
$760$		0			0
$761$	1825.50	+	3161.86i	0.0869571	+	0.150614i	0.906223	−	0.422799i	$-0.138952\pi$
$761$	1825.50	+	3161.86i	0.0869571	+	0.150614i	−0.819266	+	0.573413i	$0.805619\pi$
$762$	4818.00			0.229052
$763$	28000.0	−	9699.48i	1.32853	−	0.460216i
$764$	−2388.00			−0.113082
$765$		0			0
$766$	−1417.50	+	2455.18i	−0.0668621	+	0.115809i
$767$	−10620.0	+	18394.4i	−0.499956	+	0.865949i
$768$	−1513.00	−	2620.59i	−0.0710881	−	0.123128i
$769$	29855.0			1.40000			0.699999	−	0.714144i	$-0.253184\pi$
$769$	29855.0			1.40000			0.699999	+	0.714144i	$0.253184\pi$
$770$		0			0
$771$	8160.00			0.381161
$772$	136.000	+	235.559i	0.00634035	+	0.0109818i

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	175.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 2.59808i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} -6.00000 q^{6} +(14.0000 + 12.1244i) q^{7} +21.0000 q^{8} +(11.5000 + 19.9186i) q^{9} +O(q^{10})\)	\(q+(1.50000 + 2.59808i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} -6.00000 q^{6} +(14.0000 + 12.1244i) q^{7} +21.0000 q^{8} +(11.5000 + 19.9186i) q^{9} +(22.5000 - 38.9711i) q^{11} +(-1.00000 - 1.73205i) q^{12} -59.0000 q^{13} +(-10.5000 + 54.5596i) q^{14} +(35.5000 + 61.4878i) q^{16} +(-27.0000 + 46.7654i) q^{17} +(-34.5000 + 59.7558i) q^{18} +(60.5000 + 104.789i) q^{19} +(-35.0000 + 12.1244i) q^{21} +135.000 q^{22} +(34.5000 + 59.7558i) q^{23} +(-21.0000 + 36.3731i) q^{24} +(-88.5000 - 153.286i) q^{26} -100.000 q^{27} +(-17.5000 + 6.06218i) q^{28} -162.000 q^{29} +(44.0000 - 76.2102i) q^{31} +(-22.5000 + 38.9711i) q^{32} +(45.0000 + 77.9423i) q^{33} -162.000 q^{34} -23.0000 q^{36} +(-129.500 - 224.301i) q^{37} +(-181.500 + 314.367i) q^{38} +(59.0000 - 102.191i) q^{39} +195.000 q^{41} +(-84.0000 - 72.7461i) q^{42} +286.000 q^{43} +(22.5000 + 38.9711i) q^{44} +(-103.500 + 179.267i) q^{46} +(22.5000 + 38.9711i) q^{47} -142.000 q^{48} +(49.0000 + 339.482i) q^{49} +(-54.0000 - 93.5307i) q^{51} +(29.5000 - 51.0955i) q^{52} +(298.500 - 517.017i) q^{53} +(-150.000 - 259.808i) q^{54} +(294.000 + 254.611i) q^{56} -242.000 q^{57} +(-243.000 - 420.888i) q^{58} +(180.000 - 311.769i) q^{59} +(-196.000 - 339.482i) q^{61} +264.000 q^{62} +(-80.5000 + 418.290i) q^{63} +433.000 q^{64} +(-135.000 + 233.827i) q^{66} +(-140.000 + 242.487i) q^{67} +(-27.0000 - 46.7654i) q^{68} -138.000 q^{69} +48.0000 q^{71} +(241.500 + 418.290i) q^{72} +(334.000 - 578.505i) q^{73} +(388.500 - 672.902i) q^{74} -121.000 q^{76} +(787.500 - 272.798i) q^{77} +354.000 q^{78} +(-391.000 - 677.232i) q^{79} +(-210.500 + 364.597i) q^{81} +(292.500 + 506.625i) q^{82} -768.000 q^{83} +(7.00000 - 36.3731i) q^{84} +(429.000 + 743.050i) q^{86} +(162.000 - 280.592i) q^{87} +(472.500 - 818.394i) q^{88} +(597.000 + 1034.03i) q^{89} +(-826.000 - 715.337i) q^{91} -69.0000 q^{92} +(88.0000 + 152.420i) q^{93} +(-67.5000 + 116.913i) q^{94} +(-45.0000 - 77.9423i) q^{96} -902.000 q^{97} +(-808.500 + 636.529i) q^{98} +1035.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{2} - 2 q^{3} - q^{4} - 12 q^{6} + 28 q^{7} + 42 q^{8} + 23 q^{9}+O(q^{10}) \) 2 * q + 3 * q^2 - 2 * q^3 - q^4 - 12 * q^6 + 28 * q^7 + 42 * q^8 + 23 * q^9	\( 2 q + 3 q^{2} - 2 q^{3} - q^{4} - 12 q^{6} + 28 q^{7} + 42 q^{8} + 23 q^{9} + 45 q^{11} - 2 q^{12} - 118 q^{13} - 21 q^{14} + 71 q^{16} - 54 q^{17} - 69 q^{18} + 121 q^{19} - 70 q^{21} + 270 q^{22} + 69 q^{23} - 42 q^{24} - 177 q^{26} - 200 q^{27} - 35 q^{28} - 324 q^{29} + 88 q^{31} - 45 q^{32} + 90 q^{33} - 324 q^{34} - 46 q^{36} - 259 q^{37} - 363 q^{38} + 118 q^{39} + 390 q^{41} - 168 q^{42} + 572 q^{43} + 45 q^{44} - 207 q^{46} + 45 q^{47} - 284 q^{48} + 98 q^{49} - 108 q^{51} + 59 q^{52} + 597 q^{53} - 300 q^{54} + 588 q^{56} - 484 q^{57} - 486 q^{58} + 360 q^{59} - 392 q^{61} + 528 q^{62} - 161 q^{63} + 866 q^{64} - 270 q^{66} - 280 q^{67} - 54 q^{68} - 276 q^{69} + 96 q^{71} + 483 q^{72} + 668 q^{73} + 777 q^{74} - 242 q^{76} + 1575 q^{77} + 708 q^{78} - 782 q^{79} - 421 q^{81} + 585 q^{82} - 1536 q^{83} + 14 q^{84} + 858 q^{86} + 324 q^{87} + 945 q^{88} + 1194 q^{89} - 1652 q^{91} - 138 q^{92} + 176 q^{93} - 135 q^{94} - 90 q^{96} - 1804 q^{97} - 1617 q^{98} + 2070 q^{99}+O(q^{100}) \) 2 * q + 3 * q^2 - 2 * q^3 - q^4 - 12 * q^6 + 28 * q^7 + 42 * q^8 + 23 * q^9 + 45 * q^11 - 2 * q^12 - 118 * q^13 - 21 * q^14 + 71 * q^16 - 54 * q^17 - 69 * q^18 + 121 * q^19 - 70 * q^21 + 270 * q^22 + 69 * q^23 - 42 * q^24 - 177 * q^26 - 200 * q^27 - 35 * q^28 - 324 * q^29 + 88 * q^31 - 45 * q^32 + 90 * q^33 - 324 * q^34 - 46 * q^36 - 259 * q^37 - 363 * q^38 + 118 * q^39 + 390 * q^41 - 168 * q^42 + 572 * q^43 + 45 * q^44 - 207 * q^46 + 45 * q^47 - 284 * q^48 + 98 * q^49 - 108 * q^51 + 59 * q^52 + 597 * q^53 - 300 * q^54 + 588 * q^56 - 484 * q^57 - 486 * q^58 + 360 * q^59 - 392 * q^61 + 528 * q^62 - 161 * q^63 + 866 * q^64 - 270 * q^66 - 280 * q^67 - 54 * q^68 - 276 * q^69 + 96 * q^71 + 483 * q^72 + 668 * q^73 + 777 * q^74 - 242 * q^76 + 1575 * q^77 + 708 * q^78 - 782 * q^79 - 421 * q^81 + 585 * q^82 - 1536 * q^83 + 14 * q^84 + 858 * q^86 + 324 * q^87 + 945 * q^88 + 1194 * q^89 - 1652 * q^91 - 138 * q^92 + 176 * q^93 - 135 * q^94 - 90 * q^96 - 1804 * q^97 - 1617 * q^98 + 2070 * q^99

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