LMFDB - Embedded newform 175.4.k.b.74.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,4,Mod(74,175)]

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([3, 4]))

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

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

chi := DirichletCharacter("175.74");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	175.k (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.3253342510$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			74.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	175.74
Dual form			175.4.k.b.149.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.59808 + 1.50000i) q^{2} +(1.73205 + 1.00000i) q^{3} +(0.500000 - 0.866025i) q^{4} -6.00000 q^{6} +(-12.1244 + 14.0000i) q^{7} -21.0000i q^{8} +(-11.5000 - 19.9186i) q^{9} +O(q^{10})$	\(q+(-2.59808 + 1.50000i) q^{2} +(1.73205 + 1.00000i) q^{3} +(0.500000 - 0.866025i) q^{4} -6.00000 q^{6} +(-12.1244 + 14.0000i) q^{7} -21.0000i q^{8} +(-11.5000 - 19.9186i) q^{9} +(22.5000 - 38.9711i) q^{11} +(1.73205 - 1.00000i) q^{12} +59.0000i q^{13} +(10.5000 - 54.5596i) q^{14} +(35.5000 + 61.4878i) q^{16} +(-46.7654 - 27.0000i) q^{17} +(59.7558 + 34.5000i) q^{18} +(-60.5000 - 104.789i) q^{19} +(-35.0000 + 12.1244i) q^{21} +135.000i q^{22} +(59.7558 - 34.5000i) q^{23} +(21.0000 - 36.3731i) q^{24} +(-88.5000 - 153.286i) q^{26} -100.000i q^{27} +(6.06218 + 17.5000i) q^{28} +162.000 q^{29} +(44.0000 - 76.2102i) q^{31} +(-38.9711 - 22.5000i) q^{32} +(77.9423 - 45.0000i) q^{33} +162.000 q^{34} -23.0000 q^{36} +(224.301 - 129.500i) q^{37} +(314.367 + 181.500i) q^{38} +(-59.0000 + 102.191i) q^{39} +195.000 q^{41} +(72.7461 - 84.0000i) q^{42} -286.000i q^{43} +(-22.5000 - 38.9711i) q^{44} +(-103.500 + 179.267i) q^{46} +(-38.9711 + 22.5000i) q^{47} +142.000i q^{48} +(-49.0000 - 339.482i) q^{49} +(-54.0000 - 93.5307i) q^{51} +(51.0955 + 29.5000i) q^{52} +(-517.017 - 298.500i) q^{53} +(150.000 + 259.808i) q^{54} +(294.000 + 254.611i) q^{56} -242.000i q^{57} +(-420.888 + 243.000i) q^{58} +(-180.000 + 311.769i) q^{59} +(-196.000 - 339.482i) q^{61} +264.000i q^{62} +(418.290 + 80.5000i) q^{63} -433.000 q^{64} +(-135.000 + 233.827i) q^{66} +(-242.487 - 140.000i) q^{67} +(-46.7654 + 27.0000i) q^{68} +138.000 q^{69} +48.0000 q^{71} +(-418.290 + 241.500i) q^{72} +(-578.505 - 334.000i) q^{73} +(-388.500 + 672.902i) q^{74} -121.000 q^{76} +(272.798 + 787.500i) q^{77} -354.000i q^{78} +(391.000 + 677.232i) q^{79} +(-210.500 + 364.597i) q^{81} +(-506.625 + 292.500i) q^{82} +768.000i q^{83} +(-7.00000 + 36.3731i) q^{84} +(429.000 + 743.050i) q^{86} +(280.592 + 162.000i) q^{87} +(-818.394 - 472.500i) q^{88} +(-597.000 - 1034.03i) q^{89} +(-826.000 - 715.337i) q^{91} -69.0000i q^{92} +(152.420 - 88.0000i) q^{93} +(67.5000 - 116.913i) q^{94} +(-45.0000 - 77.9423i) q^{96} -902.000i q^{97} +(636.529 + 808.500i) q^{98} -1035.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - 24 q^{6} - 46 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 - 24 * q^6 - 46 * q^9	$ 4 q + 2 q^{4} - 24 q^{6} - 46 q^{9} + 90 q^{11} + 42 q^{14} + 142 q^{16} - 242 q^{19} - 140 q^{21} + 84 q^{24} - 354 q^{26} + 648 q^{29} + 176 q^{31} + 648 q^{34} - 92 q^{36} - 236 q^{39} + 780 q^{41} - 90 q^{44} - 414 q^{46} - 196 q^{49} - 216 q^{51} + 600 q^{54} + 1176 q^{56} - 720 q^{59} - 784 q^{61} - 1732 q^{64} - 540 q^{66} + 552 q^{69} + 192 q^{71} - 1554 q^{74} - 484 q^{76} + 1564 q^{79} - 842 q^{81} - 28 q^{84} + 1716 q^{86} - 2388 q^{89} - 3304 q^{91} + 270 q^{94} - 180 q^{96} - 4140 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 - 24 * q^6 - 46 * q^9 + 90 * q^11 + 42 * q^14 + 142 * q^16 - 242 * q^19 - 140 * q^21 + 84 * q^24 - 354 * q^26 + 648 * q^29 + 176 * q^31 + 648 * q^34 - 92 * q^36 - 236 * q^39 + 780 * q^41 - 90 * q^44 - 414 * q^46 - 196 * q^49 - 216 * q^51 + 600 * q^54 + 1176 * q^56 - 720 * q^59 - 784 * q^61 - 1732 * q^64 - 540 * q^66 + 552 * q^69 + 192 * q^71 - 1554 * q^74 - 484 * q^76 + 1564 * q^79 - 842 * q^81 - 28 * q^84 + 1716 * q^86 - 2388 * q^89 - 3304 * q^91 + 270 * q^94 - 180 * q^96 - 4140 * 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 $

$2$	−2.59808	+	1.50000i	−0.918559	+	0.530330i	−0.883175	−	0.469044i	$-0.844599\pi$
$2$	−2.59808	+	1.50000i	−0.918559	+	0.530330i	−0.0353837	+	0.999374i	$0.511265\pi$
$3$	1.73205	+	1.00000i	0.333333	+	0.192450i	0.657320	−	0.753612i	$-0.271690\pi$
$3$	1.73205	+	1.00000i	0.333333	+	0.192450i	−0.323987	+	0.946062i	$0.605023\pi$
$4$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$5$		0			0
$5$		0			0
$6$	−6.00000			−0.408248
$7$	−12.1244	+	14.0000i	−0.654654	+	0.755929i
$7$	−12.1244	+	14.0000i	−0.654654	+	0.755929i
$8$		−	21.0000i		−	0.928078i
$9$	−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	$-0.0448754\pi$
$12$	1.73205	−	1.00000i	0.0416667	−	0.0240563i
$13$			59.0000i			1.25874i	0.777105	+	0.629371i	$0.216688\pi$
$13$			59.0000i			1.25874i	−0.777105	+	0.629371i	$0.783312\pi$
$14$	10.5000	−	54.5596i	0.200446	−	1.04155i
$15$		0			0
$16$	35.5000	+	61.4878i	0.554688	+	0.960747i
$17$	−46.7654	−	27.0000i	−0.667192	−	0.385204i	0.127820	−	0.991797i	$-0.459202\pi$
$17$	−46.7654	−	27.0000i	−0.667192	−	0.385204i	−0.795012	+	0.606594i	$0.792535\pi$
$18$	59.7558	+	34.5000i	0.782476	+	0.451763i
$19$	−60.5000	−	104.789i	−0.730508	−	1.26528i	−0.956666	−	0.291186i	$-0.905950\pi$
$19$	−60.5000	−	104.789i	−0.730508	−	1.26528i	0.226158	−	0.974091i	$-0.427383\pi$
$20$		0			0
$21$	−35.0000	+	12.1244i	−0.363696	+	0.125988i
$22$			135.000i			1.30828i
$23$	59.7558	−	34.5000i	0.541736	−	0.312772i	−0.204046	−	0.978961i	$-0.565409\pi$
$23$	59.7558	−	34.5000i	0.541736	−	0.312772i	0.745782	+	0.666190i	$0.232076\pi$
$24$	21.0000	−	36.3731i	0.178609	−	0.309359i
$25$		0			0
$26$	−88.5000	−	153.286i	−0.667549	−	1.15623i
$27$		−	100.000i		−	0.712778i
$28$	6.06218	+	17.5000i	0.0409159	+	0.118114i
$29$	162.000			1.03733			0.518666	−	0.854977i	$-0.326429\pi$
$29$	162.000			1.03733			0.518666	+	0.854977i	$0.326429\pi$
$30$		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	$0.0846163\pi$
$32$	−38.9711	−	22.5000i	−0.215287	−	0.124296i
$33$	77.9423	−	45.0000i	0.411152	−	0.237379i
$34$	162.000			0.817140
$35$		0			0
$36$	−23.0000			−0.106481
$37$	224.301	−	129.500i	0.996616	−	0.575396i	0.0893706	−	0.995998i	$-0.471514\pi$
$37$	224.301	−	129.500i	0.996616	−	0.575396i	0.907245	+	0.420602i	$0.138181\pi$
$38$	314.367	+	181.500i	1.34203	+	0.774821i
$39$	−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	$0.378882\pi$
$42$	72.7461	−	84.0000i	0.267261	−	0.308607i
$43$		−	286.000i		−	1.01429i	−0.861860	−	0.507146i	$-0.830700\pi$
$43$		−	286.000i		−	1.01429i	0.861860	−	0.507146i	$-0.169300\pi$
$44$	−22.5000	−	38.9711i	−0.0770910	−	0.133525i
$45$		0			0
$46$	−103.500	+	179.267i	−0.331744	+	0.574598i
$47$	−38.9711	+	22.5000i	−0.120947	+	0.0698290i	−0.559253	−	0.828997i	$-0.688912\pi$
$47$	−38.9711	+	22.5000i	−0.120947	+	0.0698290i	0.438306	+	0.898826i	$0.355579\pi$
$48$			142.000i			0.426999i
$49$	−49.0000	−	339.482i	−0.142857	−	0.989743i
$50$		0			0
$51$	−54.0000	−	93.5307i	−0.148265	−	0.256802i
$52$	51.0955	+	29.5000i	0.136263	+	0.0786714i
$53$	−517.017	−	298.500i	−1.33996	−	0.773625i	−0.353157	−	0.935564i	$-0.614892\pi$
$53$	−517.017	−	298.500i	−1.33996	−	0.773625i	−0.986801	+	0.161939i	$0.948225\pi$
$54$	150.000	+	259.808i	0.378008	+	0.654729i
$55$		0			0
$56$	294.000	+	254.611i	0.701561	+	0.607569i
$57$		−	242.000i		−	0.562345i
$58$	−420.888	+	243.000i	−0.952851	+	0.550129i
$59$	−180.000	+	311.769i	−0.397187	+	0.687947i	−0.993378	−	0.114895i	$-0.963347\pi$
$59$	−180.000	+	311.769i	−0.397187	+	0.687947i	0.596191	+	0.802843i	$0.296680\pi$
$60$		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	$0.968292\pi$
$62$			264.000i			0.540775i
$63$	418.290	+	80.5000i	0.836502	+	0.160985i
$64$	−433.000			−0.845703
$65$		0			0
$66$	−135.000	+	233.827i	−0.251778	+	0.436092i
$67$	−242.487	−	140.000i	−0.442157	−	0.255279i	0.262355	−	0.964971i	$-0.415501\pi$
$67$	−242.487	−	140.000i	−0.442157	−	0.255279i	−0.704512	+	0.709692i	$0.748834\pi$
$68$	−46.7654	+	27.0000i	−0.0833990	+	0.0481505i
$69$	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	$0.487227\pi$
$72$	−418.290	+	241.500i	−0.684666	+	0.395292i
$73$	−578.505	−	334.000i	−0.927519	−	0.535503i	−0.0414929	−	0.999139i	$-0.513211\pi$
$73$	−578.505	−	334.000i	−0.927519	−	0.535503i	−0.886026	+	0.463635i	$0.846545\pi$
$74$	−388.500	+	672.902i	−0.610300	+	1.05707i
$75$		0			0
$76$	−121.000			−0.182627
$77$	272.798	+	787.500i	0.403743	+	1.16551i
$78$		−	354.000i		−	0.513880i
$79$	391.000	+	677.232i	0.556847	+	0.964488i	0.997757	+	0.0669365i	$0.0213225\pi$
$79$	391.000	+	677.232i	0.556847	+	0.964488i	−0.440910	+	0.897551i	$0.645344\pi$
$80$		0			0
$81$	−210.500	+	364.597i	−0.288752	+	0.500133i
$82$	−506.625	+	292.500i	−0.682285	+	0.393917i
$83$			768.000i			1.01565i	0.861460	+	0.507825i	$0.169550\pi$
$83$			768.000i			1.01565i	−0.861460	+	0.507825i	$0.830450\pi$
$84$	−7.00000	+	36.3731i	−0.00909241	+	0.0472456i
$85$		0			0
$86$	429.000	+	743.050i	0.537910	+	0.931687i
$87$	280.592	+	162.000i	0.345778	+	0.199635i
$88$	−818.394	−	472.500i	−0.991376	−	0.572371i
$89$	−597.000	−	1034.03i	−0.711032	−	1.23154i	−0.964470	−	0.264192i	$-0.914895\pi$
$89$	−597.000	−	1034.03i	−0.711032	−	1.23154i	0.253438	−	0.967352i	$-0.418439\pi$
$90$		0			0
$91$	−826.000	−	715.337i	−0.951520	−	0.824041i
$92$		−	69.0000i		−	0.0781929i
$93$	152.420	−	88.0000i	0.169949	−	0.0981202i
$94$	67.5000	−	116.913i	0.0740648	−	0.128284i
$95$		0			0
$96$	−45.0000	−	77.9423i	−0.0478416	−	0.0828641i
$97$		−	902.000i		−	0.944167i	−0.881554	−	0.472084i	$-0.843502\pi$
$97$		−	902.000i		−	0.944167i	0.881554	−	0.472084i	$-0.156498\pi$
$98$	636.529	+	808.500i	0.656113	+	0.833376i
$99$	−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	$0.276056\pi$
$102$	280.592	+	162.000i	0.272380	+	0.157259i
$103$	−1312.89	+	758.000i	−1.25595	+	0.725126i	−0.972286	−	0.233796i	$-0.924885\pi$
$103$	−1312.89	+	758.000i	−1.25595	+	0.725126i	−0.283669	+	0.958922i	$0.591552\pi$
$104$	1239.00			1.16821
$105$		0			0
$106$	1791.00			1.64111
$107$	633.931	−	366.000i	0.572751	−	0.330678i	−0.185496	−	0.982645i	$-0.559389\pi$
$107$	633.931	−	366.000i	0.572751	−	0.330678i	0.758247	+	0.651967i	$0.226056\pi$
$108$	−86.6025	−	50.0000i	−0.0771605	−	0.0445486i
$109$	−800.000	+	1385.64i	−0.702992	+	1.21762i	0.264420	+	0.964408i	$0.414820\pi$
$109$	−800.000	+	1385.64i	−0.702992	+	1.21762i	−0.967411	+	0.253210i	$0.918514\pi$
$110$		0			0
$111$	518.000			0.442940
$112$	−1291.24	−	248.500i	−1.08938	−	0.209652i
$113$		−	1392.00i		−	1.15883i	−0.815031	−	0.579417i	$-0.803280\pi$
$113$		−	1392.00i		−	1.15883i	0.815031	−	0.579417i	$-0.196720\pi$
$114$	363.000	+	628.734i	0.298229	+	0.516547i
$115$		0			0
$116$	81.0000	−	140.296i	0.0648333	−	0.112295i
$117$	1175.20	−	678.500i	0.928606	−	0.536131i
$118$		−	1080.00i		−	0.842560i
$119$	945.000	−	327.358i	0.727966	−	0.252175i
$120$		0			0
$121$	−347.000	−	601.022i	−0.260706	−	0.451556i
$122$	1018.45	+	588.000i	0.755785	+	0.436353i
$123$	337.750	+	195.000i	0.247593	+	0.142948i
$124$	−44.0000	−	76.2102i	−0.0318655	−	0.0551926i
$125$		0			0
$126$	−1207.50	+	418.290i	−0.853751	+	0.295748i
$127$		−	803.000i		−	0.561061i	−0.959845	−	0.280530i	$-0.909490\pi$
$127$		−	803.000i		−	0.561061i	0.959845	−	0.280530i	$-0.0905104\pi$
$128$	1436.74	−	829.500i	0.992115	−	0.572798i
$129$	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	$-0.401784\pi$
$132$		−	90.0000i		−	0.0593447i
$133$	2200.57	+	423.500i	1.43469	+	0.276106i
$134$	840.000			0.541529
$135$		0			0
$136$	−567.000	+	982.073i	−0.357499	+	0.619206i
$137$	51.9615	+	30.0000i	0.0324042	+	0.0187086i	0.516115	−	0.856520i	$-0.327378\pi$
$137$	51.9615	+	30.0000i	0.0324042	+	0.0187086i	−0.483710	+	0.875228i	$0.660711\pi$
$138$	−358.535	+	207.000i	−0.221163	+	0.127688i
$139$	1708.00			1.04224			0.521118	−	0.853485i	$-0.325515\pi$
$139$	1708.00			1.04224			0.521118	+	0.853485i	$0.325515\pi$
$140$		0			0
$141$	−90.0000			−0.0537544
$142$	−124.708	+	72.0000i	−0.0736988	+	0.0425500i
$143$	2299.30	+	1327.50i	1.34459	+	0.776302i
$144$	816.500	−	1414.22i	0.472512	−	0.818414i
$145$		0			0
$146$	2004.00			1.13597
$147$	254.611	−	637.000i	0.142857	−	0.357407i
$148$		−	259.000i		−	0.143849i
$149$	−543.000	−	940.504i	−0.298552	−	0.517108i	0.677253	−	0.735751i	$-0.263170\pi$
$149$	−543.000	−	940.504i	−0.298552	−	0.517108i	−0.975805	+	0.218643i	$0.929837\pi$
$150$		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	$-0.114222\pi$
$152$	−2200.57	+	1270.50i	−1.17428	+	0.677968i
$153$			1242.00i			0.656273i
$154$	−1890.00	−	1636.79i	−0.988965	−	0.856468i
$155$		0			0
$156$	59.0000	+	102.191i	0.0302806	+	0.0524476i
$157$	−198.320	−	114.500i	−0.100813	−	0.0582044i	0.448746	−	0.893659i	$-0.351871\pi$
$157$	−198.320	−	114.500i	−0.100813	−	0.0582044i	−0.549559	+	0.835455i	$0.685204\pi$
$158$	−2031.70	−	1173.00i	−1.02299	−	0.590626i
$159$	−597.000	−	1034.03i	−0.297768	−	0.515750i
$160$		0			0
$161$	−241.500	+	1254.87i	−0.118217	+	0.614271i
$162$		−	1263.00i		−	0.612535i
$163$	−1063.48	+	614.000i	−0.511031	+	0.295044i	−0.733258	−	0.679951i	$-0.762001\pi$
$163$	−1063.48	+	614.000i	−0.511031	+	0.295044i	0.222226	+	0.974995i	$0.428668\pi$
$164$	97.5000	−	168.875i	0.0464236	−	0.0804080i
$165$		0			0
$166$	−1152.00	−	1995.32i	−0.538630	−	0.932934i
$167$			1929.00i			0.893835i	0.894575	+	0.446918i	$0.147478\pi$
$167$			1929.00i			0.893835i	−0.894575	+	0.446918i	$0.852522\pi$
$168$	254.611	+	735.000i	0.116927	+	0.337539i
$169$	−1284.00			−0.584433
$170$		0			0
$171$	−1391.50	+	2410.15i	−0.622285	+	1.07783i
$172$	−247.683	−	143.000i	−0.109800	−	0.0633933i
$173$	−605.352	+	349.500i	−0.266035	+	0.153595i	−0.627084	−	0.778951i	$-0.715752\pi$
$173$	−605.352	+	349.500i	−0.266035	+	0.153595i	0.361049	+	0.932547i	$0.382419\pi$
$174$	−972.000			−0.423489
$175$		0			0
$176$	3195.00			1.36836
$177$	−623.538	+	360.000i	−0.264791	+	0.152877i
$178$	3102.10	+	1791.00i	1.30625	+	0.754164i
$179$	1558.50	−	2699.40i	0.650770	−	1.12717i	−0.332167	−	0.943221i	$-0.607780\pi$
$179$	1558.50	−	2699.40i	0.650770	−	1.12717i	0.982936	−	0.183945i	$-0.0588870\pi$
$180$		0			0
$181$	−1798.00			−0.738366			−0.369183	−	0.929357i	$-0.620362\pi$
$181$	−1798.00			−0.738366			−0.369183	+	0.929357i	$0.620362\pi$
$182$	3219.02	+	619.500i	1.31104	+	0.252310i
$183$		−	784.000i		−	0.316694i
$184$	−724.500	−	1254.87i	−0.290276	−	0.502773i
$185$		0			0
$186$	−264.000	+	457.261i	−0.104072	+	0.180258i
$187$	−2104.44	+	1215.00i	−0.822952	+	0.475132i
$188$			45.0000i			0.0174572i
$189$	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	$0.683927\pi$
$192$	−749.978	−	433.000i	−0.281901	−	0.162756i
$193$	−235.559	−	136.000i	−0.0878544	−	0.0507228i	0.455429	−	0.890272i	$-0.349486\pi$
$193$	−235.559	−	136.000i	−0.0878544	−	0.0507228i	−0.543284	+	0.839549i	$0.682819\pi$
$194$	1353.00	+	2343.46i	0.500720	+	0.867273i
$195$		0			0
$196$	−318.500	−	127.306i	−0.116071	−	0.0463942i
$197$			2109.00i			0.762741i	0.924422	+	0.381371i	$0.124548\pi$
$197$			2109.00i			0.762741i	−0.924422	+	0.381371i	$0.875452\pi$
$198$	2689.01	−	1552.50i	0.965149	−	0.557229i
$199$	712.000	−	1233.22i	0.253630	−	0.439300i	−0.710893	−	0.703301i	$-0.751709\pi$
$199$	712.000	−	1233.22i	0.253630	−	0.439300i	0.964522	+	0.264001i	$0.0850422\pi$
$200$		0			0
$201$	−280.000	−	484.974i	−0.0982571	−	0.170186i
$202$		−	2052.00i		−	0.714744i
$203$	−1964.15	+	2268.00i	−0.679094	+	0.784150i
$204$	−108.000			−0.0370662
$205$		0			0
$206$	2274.00	−	3938.68i	0.769112	−	1.33214i
$207$	−1374.38	−	793.500i	−0.461479	−	0.266435i
$208$	−3627.78	+	2094.50i	−1.20933	+	0.698209i
$209$	−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	$0.701410\pi$
$212$	−517.017	+	298.500i	−0.167495	+	0.0967031i
$213$	83.1384	+	48.0000i	0.0267444	+	0.0154409i
$214$	−1098.00	+	1901.79i	−0.350737	+	0.607494i
$215$		0			0
$216$	−2100.00			−0.661513
$217$	533.472	+	1540.00i	0.166887	+	0.481760i
$218$		−	4800.00i		−	1.49127i
$219$	−668.000	−	1157.01i	−0.206115	−	0.357002i
$220$		0			0
$221$	1593.00	−	2759.16i	0.484872	−	0.839823i
$222$	−1345.80	+	777.000i	−0.406867	+	0.234905i
$223$		−	4960.00i		−	1.48944i	−0.667374	−	0.744722i	$-0.732582\pi$
$223$		−	4960.00i		−	1.48944i	0.667374	−	0.744722i	$-0.267418\pi$
$224$	787.500	−	272.798i	0.234898	−	0.0813709i
$225$		0			0
$226$	2088.00	+	3616.52i	0.614565	+	1.06446i
$227$	−1299.04	−	750.000i	−0.379825	−	0.219292i	0.297917	−	0.954592i	$-0.403708\pi$
$227$	−1299.04	−	750.000i	−0.379825	−	0.219292i	−0.677742	+	0.735300i	$0.737041\pi$
$228$	−209.578	−	121.000i	−0.0608757	−	0.0351466i
$229$	3046.00	+	5275.83i	0.878975	+	1.52243i	0.852467	+	0.522781i	$0.175106\pi$
$229$	3046.00	+	5275.83i	0.878975	+	1.52243i	0.0265085	+	0.999649i	$0.491561\pi$
$230$		0			0
$231$	−315.000	+	1636.79i	−0.0897207	+	0.466202i
$232$		−	3402.00i		−	0.962725i
$233$	119.512	−	69.0000i	0.0336028	−	0.0194006i	−0.483104	−	0.875563i	$-0.660491\pi$
$233$	119.512	−	69.0000i	0.0336028	−	0.0194006i	0.516707	+	0.856162i	$0.327158\pi$
$234$	−2035.50	+	3525.59i	−0.568653	+	0.984936i
$235$		0			0
$236$	180.000	+	311.769i	0.0496483	+	0.0859934i
$237$			1564.00i			0.428661i
$238$	−1964.15	+	2268.00i	−0.534944	+	0.617700i
$239$	5502.00			1.48910			0.744550	−	0.667567i	$-0.232664\pi$
$239$	5502.00			1.48910			0.744550	+	0.667567i	$0.232664\pi$
$240$		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	$0.324061\pi$
$242$	1803.06	+	1041.00i	0.478948	+	0.276521i
$243$	−3067.46	+	1771.00i	−0.809785	+	0.467530i
$244$	−392.000			−0.102849
$245$		0			0
$246$	−1170.00			−0.303238
$247$	6182.56	−	3569.50i	1.59266	−	0.919522i
$248$	−1600.41	−	924.000i	−0.409784	−	0.236589i
$249$	−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	$0.151870\pi$
$252$	278.860	−	322.000i	0.0697085	−	0.0804924i
$253$		−	3105.00i		−	0.771580i
$254$	1204.50	+	2086.26i	0.297547	+	0.515367i
$255$		0			0
$256$	−756.500	+	1310.30i	−0.184692	+	0.319897i
$257$	3533.38	−	2040.00i	0.857613	−	0.495143i	−0.00559954	−	0.999984i	$-0.501782\pi$
$257$	3533.38	−	2040.00i	0.857613	−	0.495143i	0.863212	+	0.504842i	$0.168449\pi$
$258$			1716.00i			0.414083i
$259$	−906.500	+	4710.31i	−0.217479	+	1.13006i
$260$		0			0
$261$	−1863.00	−	3226.81i	−0.441827	−	0.765267i
$262$	5245.52	+	3028.50i	1.23690	+	0.714127i
$263$	2847.49	+	1644.00i	0.667619	+	0.385450i	0.795174	−	0.606381i	$-0.207380\pi$
$263$	2847.49	+	1644.00i	0.667619	+	0.385450i	−0.127555	+	0.991832i	$0.540713\pi$
$264$	−945.000	−	1636.79i	−0.220306	−	0.381581i
$265$		0			0
$266$	−6352.50	+	2200.57i	−1.46427	+	0.507239i
$267$		−	2388.00i		−	0.547353i
$268$	−242.487	+	140.000i	−0.0552696	+	0.0319099i
$269$	−1632.00	+	2826.71i	−0.369906	+	0.640697i	−0.989551	−	0.144186i	$-0.953944\pi$
$269$	−1632.00	+	2826.71i	−0.369906	+	0.640697i	0.619644	+	0.784883i	$0.287277\pi$
$270$		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	$0.733528\pi$
$272$		−	3834.00i		−	0.854671i
$273$	−715.337	−	2065.00i	−0.158587	−	0.457800i
$274$	−180.000			−0.0396869
$275$		0			0
$276$	69.0000	−	119.512i	0.0150482	−	0.0260643i
$277$	−4061.66	−	2345.00i	−0.881016	−	0.508655i	−0.0100228	−	0.999950i	$-0.503190\pi$
$277$	−4061.66	−	2345.00i	−0.881016	−	0.508655i	−0.870993	+	0.491295i	$0.836524\pi$
$278$	−4437.51	+	2562.00i	−0.957354	+	0.552729i
$279$	−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	$0.188237\pi$
$282$	233.827	−	135.000i	0.0493765	−	0.0285076i
$283$	569.845	+	329.000i	0.119695	+	0.0691061i	0.558652	−	0.829402i	$-0.311319\pi$
$283$	569.845	+	329.000i	0.119695	+	0.0691061i	−0.438957	+	0.898508i	$0.644652\pi$
$284$	24.0000	−	41.5692i	0.00501457	−	0.00868549i
$285$		0			0
$286$	−7965.00			−1.64678
$287$	−2364.25	+	2730.00i	−0.486262	+	0.561487i
$288$			1035.00i			0.211764i
$289$	−998.500	−	1729.45i	−0.203236	−	0.352016i
$290$		0			0
$291$	902.000	−	1562.31i	0.181705	−	0.314722i
$292$	−578.505	+	334.000i	−0.115940	+	0.0669379i
$293$		−	5997.00i		−	1.19573i	−0.801597	−	0.597864i	$-0.796016\pi$
$293$		−	5997.00i		−	1.19573i	0.801597	−	0.597864i	$-0.203984\pi$
$294$	294.000	+	2036.89i	0.0583212	+	0.404061i
$295$		0			0
$296$	−2719.50	−	4710.31i	−0.534013	−	0.924937i
$297$	−3897.11	−	2250.00i	−0.761392	−	0.439590i
$298$	2821.51	+	1629.00i	0.548476	+	0.316663i
$299$	2035.50	+	3525.59i	0.393699	+	0.681907i
$300$		0			0
$301$	4004.00	+	3467.57i	0.766733	+	0.664011i
$302$			8598.00i			1.63828i
$303$	−1184.72	+	684.000i	−0.224622	+	0.129686i
$304$	4295.50	−	7440.02i	0.810407	−	1.40367i
$305$		0			0
$306$	−1863.00	−	3226.81i	−0.348041	−	0.602825i
$307$			6226.00i			1.15745i	0.815523	+	0.578724i	$0.196449\pi$
$307$			6226.00i			1.15745i	−0.815523	+	0.578724i	$0.803551\pi$
$308$	818.394	+	157.500i	0.151404	+	0.0291376i
$309$	−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	$0.306974\pi$
$312$	2146.01	+	1239.00i	0.389404	+	0.224822i
$313$	890.274	−	514.000i	0.160771	−	0.0928211i	−0.417456	−	0.908697i	$-0.637078\pi$
$313$	890.274	−	514.000i	0.160771	−	0.0928211i	0.578227	+	0.815876i	$0.303745\pi$
$314$	687.000			0.123470
$315$		0			0
$316$	782.000			0.139212
$317$	−7466.87	+	4311.00i	−1.32297	+	0.763817i	−0.984201	−	0.177053i	$-0.943344\pi$
$317$	−7466.87	+	4311.00i	−1.32297	+	0.763817i	−0.338768	+	0.940870i	$0.610010\pi$
$318$	3102.10	+	1791.00i	0.547036	+	0.315831i
$319$	3645.00	−	6313.33i	0.639752	−	1.10808i
$320$		0			0
$321$	1464.00			0.254556
$322$	−1254.87	−	3622.50i	−0.217178	−	0.626938i
$323$			6534.00i			1.12558i
$324$	210.500	+	364.597i	0.0360940	+	0.0625166i
$325$		0			0
$326$	1842.00	−	3190.44i	0.312942	−	0.542031i
$327$	−2771.28	+	1600.00i	−0.468661	+	0.270582i
$328$		−	4095.00i		−	0.689355i
$329$	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	$0.780256\pi$
$332$	665.108	+	384.000i	0.109947	+	0.0634781i
$333$	−5158.91	−	2978.50i	−0.848969	−	0.490153i
$334$	−2893.50	−	5011.69i	−0.474028	−	0.821040i
$335$		0			0
$336$	−1988.00	−	1721.66i	−0.322781	−	0.279536i
$337$		−	5114.00i		−	0.826639i	−0.910586	−	0.413319i	$-0.864369\pi$
$337$		−	5114.00i		−	0.826639i	0.910586	−	0.413319i	$-0.135631\pi$
$338$	3335.93	−	1926.00i	0.536836	−	0.309943i
$339$	1392.00	−	2411.01i	0.223018	−	0.386278i
$340$		0			0
$341$	−1980.00	−	3429.46i	−0.314437	−	0.544621i
$342$		−	8349.00i		−	1.32006i
$343$	5346.84	+	3430.00i	0.841698	+	0.539949i
$344$	−6006.00			−0.941342
$345$		0			0
$346$	1048.50	−	1816.06i	0.162912	−	0.282173i
$347$	3741.23	+	2160.00i	0.578789	+	0.334164i	0.760652	−	0.649160i	$-0.224879\pi$
$347$	3741.23	+	2160.00i	0.578789	+	0.334164i	−0.181863	+	0.983324i	$0.558213\pi$
$348$	280.592	−	162.000i	0.0432222	−	0.0249543i
$349$	−7922.00			−1.21506			−0.607529	−	0.794298i	$-0.707839\pi$
$349$	−7922.00			−1.21506			−0.607529	+	0.794298i	$0.707839\pi$
$350$		0			0
$351$	5900.00			0.897204
$352$	−1753.70	+	1012.50i	−0.265547	+	0.153314i
$353$	−717.069	−	414.000i	−0.108118	−	0.0624221i	0.444966	−	0.895548i	$-0.353216\pi$
$353$	−717.069	−	414.000i	−0.108118	−	0.0624221i	−0.553084	+	0.833125i	$0.686549\pi$
$354$	1080.00	−	1870.61i	0.162151	−	0.280853i
$355$		0			0
$356$	−1194.00			−0.177758
$357$	1964.15	+	378.000i	0.291187	+	0.0560389i
$358$			9351.00i			1.38049i
$359$	−675.000	−	1169.13i	−0.0992344	−	0.171879i	0.812134	−	0.583472i	$-0.198306\pi$
$359$	−675.000	−	1169.13i	−0.0992344	−	0.171879i	−0.911368	+	0.411593i	$0.864973\pi$
$360$		0			0
$361$	−3891.00	+	6739.41i	−0.567284	+	0.982564i
$362$	4671.34	−	2697.00i	0.678233	−	0.391578i
$363$		−	1388.00i		−	0.200692i
$364$	−1032.50	+	357.668i	−0.148675	+	0.0515025i
$365$		0			0
$366$	1176.00	+	2036.89i	0.167952	+	0.290902i
$367$	2425.74	+	1400.50i	0.345020	+	0.199198i	0.662490	−	0.749071i	$-0.269500\pi$
$367$	2425.74	+	1400.50i	0.345020	+	0.199198i	−0.317470	+	0.948268i	$0.602833\pi$
$368$	4242.66	+	2449.50i	0.600989	+	0.346981i
$369$	−2242.50	−	3884.12i	−0.316368	−	0.547966i
$370$		0			0
$371$	10447.5	−	3619.12i	1.46201	−	0.506456i
$372$		−	176.000i		−	0.0245300i
$373$	5717.50	−	3301.00i	0.793675	−	0.458229i	−0.0475795	−	0.998867i	$-0.515151\pi$
$373$	5717.50	−	3301.00i	0.793675	−	0.458229i	0.841255	+	0.540639i	$0.181817\pi$
$374$	3645.00	−	6313.33i	0.503953	−	0.872872i
$375$		0			0
$376$	472.500	+	818.394i	0.0648067	+	0.112249i
$377$			9558.00i			1.30573i
$378$	−5455.96	−	1050.00i	−0.742392	−	0.142873i
$379$	8305.00			1.12559			0.562796	−	0.826596i	$-0.309726\pi$
$379$	8305.00			1.12559			0.562796	+	0.826596i	$0.309726\pi$
$380$		0			0
$381$	803.000	−	1390.84i	0.107976	−	0.187020i
$382$	−6204.21	−	3582.00i	−0.830981	−	0.479767i
$383$	818.394	−	472.500i	0.109185	−	0.0630382i	−0.444413	−	0.895822i	$-0.646588\pi$
$383$	818.394	−	472.500i	0.109185	−	0.0630382i	0.553598	+	0.832784i	$0.313254\pi$
$384$	3318.00			0.440940
$385$		0			0
$386$	816.000			0.107599
$387$	−5696.72	+	3289.00i	−0.748270	+	0.432014i
$388$	−781.155	−	451.000i	−0.102209	−	0.0590105i
$389$	6018.00	−	10423.5i	0.784382	−	1.35859i	−0.144985	−	0.989434i	$-0.546313\pi$
$389$	6018.00	−	10423.5i	0.784382	−	1.35859i	0.929367	−	0.369156i	$-0.120353\pi$
$390$		0			0
$391$	−3726.00			−0.481923
$392$	−7129.12	+	1029.00i	−0.918559	+	0.132583i
$393$		−	4038.00i		−	0.518296i
$394$	−3163.50	−	5479.34i	−0.404505	−	0.700623i
$395$		0			0
$396$	−517.500	+	896.336i	−0.0656701	+	0.113744i
$397$	2336.54	−	1349.00i	0.295384	−	0.170540i	−0.344983	−	0.938609i	$-0.612115\pi$
$397$	2336.54	−	1349.00i	0.295384	−	0.170540i	0.640367	+	0.768069i	$0.278782\pi$
$398$			4272.00i			0.538030i
$399$	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	$0.978059\pi$
$402$	1454.92	+	840.000i	0.180510	+	0.104217i
$403$	4496.40	+	2596.00i	0.555786	+	0.320883i
$404$	342.000	+	592.361i	0.0421167	+	0.0729482i
$405$		0			0
$406$	1701.00	−	8838.66i	0.207929	−	1.08043i
$407$		−	11655.0i		−	1.41945i
$408$	−1964.15	+	1134.00i	−0.238333	+	0.137601i
$409$	−5435.00	+	9413.70i	−0.657074	+	1.13809i	0.324295	+	0.945956i	$0.394873\pi$
$409$	−5435.00	+	9413.70i	−0.657074	+	1.13809i	−0.981369	+	0.192130i	$0.938460\pi$
$410$		0			0
$411$	60.0000	+	103.923i	0.00720093	+	0.0124724i
$412$			1516.00i			0.181281i
$413$	−2182.38	−	6300.00i	−0.260020	−	0.750612i
$414$	4761.00			0.565194
$415$		0			0
$416$	1327.50	−	2299.30i	0.156457	−	0.270991i
$417$	2958.34	+	1708.00i	0.347412	+	0.200578i
$418$	14146.5	−	8167.50i	1.65533	−	0.955707i
$419$	9729.00			1.13435			0.567175	−	0.823597i	$-0.308036\pi$
$419$	9729.00			1.13435			0.567175	+	0.823597i	$0.308036\pi$
$420$		0			0
$421$	−12550.0			−1.45285			−0.726425	−	0.687246i	$-0.758819\pi$
$421$	−12550.0			−1.45285			−0.726425	+	0.687246i	$0.758819\pi$
$422$	9418.03	−	5437.50i	1.08640	−	0.627235i
$423$	896.336	+	517.500i	0.103029	+	0.0594840i
$424$	−6268.50	+	10857.4i	−0.717984	+	1.24358i
$425$		0			0
$426$	−288.000			−0.0327550
$427$	7129.12	+	1372.00i	0.807968	+	0.155494i
$428$		−	732.000i		−	0.0826695i
$429$	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	$0.220065\pi$
$432$	6148.78	−	3550.00i	0.684799	−	0.395369i
$433$			16616.0i			1.84414i	0.387019	+	0.922072i	$0.373505\pi$
$433$			16616.0i			1.84414i	−0.387019	+	0.922072i	$0.626495\pi$
$434$	−3696.00	−	3200.83i	−0.408787	−	0.354020i
$435$		0			0
$436$	800.000	+	1385.64i	0.0878740	+	0.152202i
$437$	−7230.45	−	4174.50i	−0.791485	−	0.456964i
$438$	3471.03	+	2004.00i	0.378658	+	0.218618i
$439$	3673.00	+	6361.82i	0.399323	+	0.691647i	0.993642	−	0.112581i	$-0.0359119\pi$
$439$	3673.00	+	6361.82i	0.399323	+	0.691647i	−0.594320	+	0.804229i	$0.702579\pi$
$440$		0			0
$441$	−6198.50	+	4880.05i	−0.669312	+	0.526947i
$442$			9558.00i			1.02857i
$443$	10.3923	−	6.00000i	0.00111457	−	0.000643496i	−0.499443	−	0.866347i	$-0.666462\pi$
$443$	10.3923	−	6.00000i	0.00111457	−	0.000643496i	0.500557	+	0.865703i	$0.333129\pi$
$444$	259.000	−	448.601i	0.0276838	−	0.0479497i
$445$		0			0
$446$	7440.00	+	12886.5i	0.789897	+	1.36814i
$447$		−	2172.00i		−	0.229826i
$448$	5249.85	−	6062.00i	0.553643	−	0.639291i
$449$	−9669.00			−1.01628			−0.508138	−	0.861275i	$-0.669666\pi$
$449$	−9669.00			−1.01628			−0.508138	+	0.861275i	$0.669666\pi$
$450$		0			0
$451$	4387.50	−	7599.37i	0.458092	−	0.793438i
$452$	−1205.51	−	696.000i	−0.125448	−	0.0724272i
$453$	4964.06	−	2866.00i	0.514860	−	0.297255i
$454$	4500.00			0.465188
$455$		0			0
$456$	−5082.00			−0.521900
$457$	8343.29	−	4817.00i	0.854010	−	0.493063i	−0.00799181	−	0.999968i	$-0.502544\pi$
$457$	8343.29	−	4817.00i	0.854010	−	0.493063i	0.862002	+	0.506905i	$0.169211\pi$
$458$	−15827.5	−	9138.00i	−1.61478	−	0.932294i
$459$	−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	$0.505499\pi$
$462$	−1636.79	−	4725.00i	−0.164827	−	0.475816i
$463$			2411.00i			0.242006i	0.992652	+	0.121003i	$0.0386110\pi$
$463$			2411.00i			0.242006i	−0.992652	+	0.121003i	$0.961389\pi$
$464$	5751.00	+	9961.02i	0.575395	+	0.996614i
$465$		0			0
$466$	−207.000	+	358.535i	−0.0205774	+	0.0356412i
$467$	1044.43	−	603.000i	0.103491	−	0.0597506i	−0.447361	−	0.894353i	$-0.647636\pi$
$467$	1044.43	−	603.000i	0.103491	−	0.0597506i	0.550852	+	0.834603i	$0.314303\pi$
$468$		−	1357.00i		−	0.134033i
$469$	4900.00	−	1697.41i	0.482433	−	0.167120i
$470$		0			0
$471$	−229.000	−	396.640i	−0.0224029	−	0.0388030i
$472$	6547.15	+	3780.00i	0.638468	+	0.368620i
$473$	−11145.7	−	6435.00i	−1.08347	−	0.625543i
$474$	−2346.00	−	4063.39i	−0.227332	−	0.393751i
$475$		0			0
$476$	189.000	−	982.073i	0.0181992	−	0.0945656i
$477$			13731.0i			1.31803i
$478$	−14294.6	+	8253.00i	−1.36783	+	0.789714i
$479$	−216.000	+	374.123i	−0.0206039	+	0.0356871i	−0.876144	−	0.482050i	$-0.839892\pi$
$479$	−216.000	+	374.123i	−0.0206039	+	0.0356871i	0.855540	+	0.517737i	$0.173226\pi$
$480$		0			0
$481$	7640.50	+	13233.7i	0.724276	+	1.25448i
$482$		−	10653.0i		−	1.00670i
$483$	−1673.16	+	1932.00i	−0.157622	+	0.182006i
$484$	−694.000			−0.0651766
$485$		0			0
$486$	5313.00	−	9202.39i	0.495890	−	0.858907i
$487$	−10302.2	−	5948.00i	−0.958602	−	0.553449i	−0.0628592	−	0.998022i	$-0.520022\pi$
$487$	−10302.2	−	5948.00i	−0.958602	−	0.553449i	−0.895742	+	0.444574i	$0.853355\pi$
$488$	−7129.12	+	4116.00i	−0.661312	+	0.381809i
$489$	−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	$0.690801\pi$
$492$	337.750	−	195.000i	0.0309491	−	0.0178685i
$493$	−7575.99	−	4374.00i	−0.692100	−	0.399584i
$494$	−10708.5	+	18547.7i	−0.975300	+	1.68927i
$495$		0			0
$496$	6248.00			0.565612
$497$	−581.969	+	672.000i	−0.0525249	+	0.0606505i
$498$		−	4608.00i		−	0.414637i
$499$	−5438.00	−	9418.89i	−0.487852	−	0.844985i	0.512050	−	0.858956i	$-0.328886\pi$
$499$	−5438.00	−	9418.89i	−0.487852	−	0.844985i	−0.999902	+	0.0139706i	$0.995553\pi$
$500$		0			0
$501$	−1929.00	+	3341.13i	−0.172019	+	0.297945i
$502$	−18355.4	+	10597.5i	−1.63196	+	0.942210i
$503$			12000.0i			1.06372i	0.846831	+	0.531862i	$0.178508\pi$
$503$			12000.0i			1.06372i	−0.846831	+	0.531862i	$0.821492\pi$
$504$	1690.50	−	8784.10i	0.149406	−	0.776339i
$505$		0			0
$506$	4657.50	+	8067.03i	0.409192	+	0.708741i
$507$	−2223.95	−	1284.00i	−0.194811	−	0.112474i
$508$	−695.418	−	401.500i	−0.0607366	−	0.0350663i
$509$	−5841.00	−	10116.9i	−0.508640	−	0.880990i	−0.999950	−	0.0100055i	$-0.996815\pi$
$509$	−5841.00	−	10116.9i	−0.508640	−	0.880990i	0.491310	−	0.870985i	$-0.336518\pi$
$510$		0			0
$511$	11690.0	−	4049.53i	1.01201	−	0.350569i
$512$			8733.00i			0.753804i
$513$	−10478.9	+	6050.00i	−0.901862	+	0.520690i
$514$	−6120.00	+	10600.2i	−0.525178	+	0.909635i
$515$		0			0
$516$	−286.000	−	495.367i	−0.0244001	−	0.0422622i
$517$			2025.00i			0.172262i
$518$	−4710.31	−	13597.5i	−0.399535	−	1.15336i
$519$	−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	$0.299050\pi$
$522$	9680.43	+	5589.00i	0.811688	+	0.468628i
$523$	18349.3	−	10594.0i	1.53415	−	0.885742i	0.534987	−	0.844860i	$-0.320317\pi$
$523$	18349.3	−	10594.0i	1.53415	−	0.885742i	0.999164	−	0.0408820i	$-0.0130168\pi$
$524$	−2019.00			−0.168321
$525$		0			0
$526$	−9864.00			−0.817663
$527$	−4115.35	+	2376.00i	−0.340166	+	0.196395i
$528$	5533.90	+	3195.00i	0.456122	+	0.263342i
$529$	−3703.00	+	6413.78i	−0.304348	+	0.527146i
$530$		0			0
$531$	8280.00			0.676688
$532$	1467.05	−	1694.00i	0.119557	−	0.138053i
$533$			11505.0i			0.934966i
$534$	3582.00	+	6204.21i	0.290278	+	0.502776i
$535$		0			0
$536$	−2940.00	+	5092.23i	−0.236919	+	0.410356i
$537$	5398.80	−	3117.00i	0.433846	−	0.250481i
$538$		−	9792.00i		−	0.784690i
$539$	−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	$0.937265\pi$
$542$	−7149.91	−	4128.00i	−0.566632	−	0.327145i
$543$	−3114.23	−	1798.00i	−0.246122	−	0.142099i
$544$	1215.00	+	2104.44i	0.0957586	+	0.165859i
$545$		0			0
$546$	4956.00	+	4292.02i	0.388456	+	0.336413i
$547$		−	344.000i		−	0.0268892i	−0.999910	−	0.0134446i	$-0.995720\pi$
$547$		−	344.000i		−	0.0268892i	0.999910	−	0.0134446i	$-0.00427967\pi$
$548$	51.9615	−	30.0000i	0.00405052	−	0.00233857i
$549$	−4508.00	+	7808.09i	−0.350449	+	0.606996i
$550$		0			0
$551$	−9801.00	−	16975.8i	−0.757780	−	1.31251i
$552$		−	2898.00i		−	0.223455i
$553$	−14221.9	−	2737.00i	−1.09363	−	0.210468i
$554$	14070.0			1.07902
$555$		0			0
$556$	854.000	−	1479.17i	0.0651397	−	0.112825i
$557$	15902.8	+	9181.50i	1.20974	+	0.698443i	0.962702	−	0.270563i	$-0.0872100\pi$
$557$	15902.8	+	9181.50i	1.20974	+	0.698443i	0.247036	+	0.969006i	$0.420543\pi$
$558$	5258.51	−	3036.00i	0.398943	−	0.230330i
$559$	16874.0			1.27673
$560$		0			0
$561$	−4860.00			−0.365756
$562$	−20319.6	+	11731.5i	−1.52514	+	0.880540i
$563$	5450.76	+	3147.00i	0.408033	+	0.235578i	0.689944	−	0.723863i	$-0.257635\pi$
$563$	5450.76	+	3147.00i	0.408033	+	0.235578i	−0.281912	+	0.959440i	$0.590968\pi$
$564$	−45.0000	+	77.9423i	−0.00335965	+	0.00581908i
$565$		0			0
$566$	−1974.00			−0.146596
$567$	−2552.18	−	7367.50i	−0.189032	−	0.545689i
$568$		−	1008.00i		−	0.0744626i
$569$	5866.50	+	10161.1i	0.432226	+	0.748637i	0.997065	−	0.0765642i	$-0.0243950\pi$
$569$	5866.50	+	10161.1i	0.432226	+	0.748637i	−0.564839	+	0.825201i	$0.691062\pi$
$570$		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	$0.178941\pi$
$572$	2299.30	−	1327.50i	0.168074	−	0.0970377i
$573$			4776.00i			0.348203i
$574$	2047.50	−	10639.1i	0.148887	−	0.773638i
$575$		0			0
$576$	4979.50	+	8624.75i	0.360207	+	0.623897i
$577$	−11393.4	−	6578.00i	−0.822036	−	0.474603i	0.0290821	−	0.999577i	$-0.490742\pi$
$577$	−11393.4	−	6578.00i	−0.822036	−	0.474603i	−0.851118	+	0.524974i	$0.824075\pi$
$578$	5188.36	+	2995.50i	0.373369	+	0.215565i
$579$	−272.000	−	471.118i	−0.0195232	−	0.0338152i
$580$		0			0
$581$	−10752.0	−	9311.51i	−0.767759	−	0.664899i
$582$			5412.00i			0.385455i
$583$	−23265.8	+	13432.5i	−1.65278	+	0.954232i
$584$	−7014.00	+	12148.6i	−0.496989	+	0.860810i
$585$		0			0
$586$	8995.50	+	15580.7i	0.634131	+	1.09835i
$587$			13368.0i			0.939960i	0.882677	+	0.469980i	$0.155739\pi$
$587$			13368.0i			0.939960i	−0.882677	+	0.469980i	$0.844261\pi$
$588$	−424.352	−	539.000i	−0.0297619	−	0.0378027i
$589$	−10648.0			−0.744895
$590$		0			0
$591$	−2109.00	+	3652.90i	−0.146790	+	0.254247i
$592$	15925.3	+	9194.50i	1.10562	+	0.638330i
$593$	23091.7	−	13332.0i	1.59909	−	0.923237i	0.607431	−	0.794372i	$-0.292200\pi$
$593$	23091.7	−	13332.0i	1.59909	−	0.923237i	0.991662	−	0.128865i	$-0.0411334\pi$
$594$	13500.0			0.932511
$595$		0			0
$596$	−1086.00			−0.0746381
$597$	2466.44	−	1424.00i	0.169087	−	0.0976222i
$598$	−10576.8	−	6106.50i	−0.723271	−	0.417581i
$599$	3807.00	−	6593.92i	0.259682	−	0.449783i	−0.706474	−	0.707739i	$-0.749715\pi$
$599$	3807.00	−	6593.92i	0.259682	−	0.449783i	0.966157	+	0.257955i	$0.0830488\pi$
$600$		0			0
$601$	6410.00			0.435057			0.217529	−	0.976054i	$-0.430200\pi$
$601$	6410.00			0.435057			0.217529	+	0.976054i	$0.430200\pi$
$602$	−15604.0	−	3003.00i	−1.05643	−	0.203311i
$603$			6440.00i			0.434921i
$604$	−1433.00	−	2482.03i	−0.0965363	−	0.167206i
$605$		0			0
$606$	2052.00	−	3554.17i	0.137552	−	0.238248i
$607$	18592.7	−	10734.5i	1.24325	−	0.717792i	0.273498	−	0.961873i	$-0.411819\pi$
$607$	18592.7	−	10734.5i	1.24325	−	0.717792i	0.969755	+	0.244080i	$0.0784861\pi$
$608$			5445.00i			0.363197i
$609$	−5670.00	+	1964.15i	−0.377274	+	0.130692i
$610$		0			0
$611$	−1327.50	−	2299.30i	−0.0878967	−	0.152242i
$612$	1075.60	+	621.000i	0.0710436	+	0.0410171i
$613$	−3236.34	−	1868.50i	−0.213237	−	0.123113i	0.389578	−	0.920994i	$-0.372621\pi$
$613$	−3236.34	−	1868.50i	−0.213237	−	0.123113i	−0.602815	+	0.797881i	$0.705954\pi$
$614$	−9339.00	−	16175.6i	−0.613830	−	1.06318i
$615$		0			0
$616$	16537.5	−	5728.76i	1.08168	−	0.374705i
$617$		−	18078.0i		−	1.17957i	−0.807561	−	0.589784i	$-0.799213\pi$
$617$		−	18078.0i		−	1.17957i	0.807561	−	0.589784i	$-0.200787\pi$
$618$	7877.37	−	4548.00i	0.512741	−	0.296031i
$619$	6143.50	−	10640.9i	0.398915	−	0.690940i	−0.594678	−	0.803964i	$-0.702720\pi$
$619$	6143.50	−	10640.9i	0.398915	−	0.690940i	0.993592	+	0.113024i	$0.0360537\pi$
$620$		0			0
$621$	−3450.00	−	5975.58i	−0.222937	−	0.386138i
$622$		−	14040.0i		−	0.905069i
$623$	21714.7	+	4179.00i	1.39644	+	0.268745i
$624$	−8378.00			−0.537481
$625$		0			0
$626$	−1542.00	+	2670.82i	−0.0984516	+	0.170523i
$627$	−9431.02	−	5445.00i	−0.600699	−	0.346814i
$628$	−198.320	+	114.500i	−0.0126016	+	0.00727555i
$629$	−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	$0.597720\pi$
$632$	14221.9	−	8211.00i	0.895120	−	0.516798i
$633$	−6278.68	−	3625.00i	−0.394242	−	0.227616i
$634$	12933.0	−	22400.6i	0.810150	−	1.40322i
$635$		0			0
$636$	−1194.00			−0.0744421
$637$	20029.4	−	2891.00i	1.24583	−	0.179820i
$638$			21870.0i			1.35712i
$639$	−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	$0.274422\pi$
$642$	−3803.58	+	2196.00i	−0.233825	+	0.134999i
$643$			8882.00i			0.544746i	0.962192	+	0.272373i	$0.0878085\pi$
$643$			8882.00i			0.544746i	−0.962192	+	0.272373i	$0.912191\pi$
$644$	966.000	+	836.581i	0.0591083	+	0.0511893i
$645$		0			0
$646$	−9801.00	−	16975.8i	−0.596928	−	1.03391i
$647$	−9542.73	−	5509.50i	−0.579851	−	0.334777i	0.181223	−	0.983442i	$-0.441994\pi$
$647$	−9542.73	−	5509.50i	−0.579851	−	0.334777i	−0.761074	+	0.648665i	$0.775328\pi$
$648$	7656.53	+	4420.50i	0.464162	+	0.267984i
$649$	8100.00	+	14029.6i	0.489912	+	0.848552i
$650$		0			0
$651$	−616.000	+	3200.83i	−0.0370859	+	0.192704i
$652$			1228.00i			0.0737610i
$653$	19332.3	−	11161.5i	1.15855	−	0.668887i	0.207591	−	0.978216i	$-0.433438\pi$
$653$	19332.3	−	11161.5i	1.15855	−	0.668887i	0.950955	+	0.309329i	$0.100104\pi$
$654$	4800.00	−	8313.84i	0.286995	−	0.497090i
$655$		0			0
$656$	6922.50	+	11990.1i	0.412009	+	0.713621i
$657$			15364.0i			0.912339i
$658$	818.394	+	2362.50i	0.0484868	+	0.139969i
$659$	11856.0			0.700826			0.350413	−	0.936595i	$-0.386041\pi$
$659$	11856.0			0.700826			0.350413	+	0.936595i	$0.386041\pi$
$660$		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	$-0.266586\pi$
$662$	−5193.55	−	2998.50i	−0.304914	−	0.176042i
$663$	5518.31	−	3186.00i	0.323248	−	0.186627i
$664$	16128.0			0.942602
$665$		0			0
$666$	17871.0			1.03977
$667$	9680.43	−	5589.00i	0.561961	−	0.324448i
$668$	1670.56	+	964.500i	0.0967605	+	0.0558647i
$669$	4960.00	−	8590.97i	0.286644	−	0.496482i
$670$		0			0
$671$	−17640.0			−1.01488
$672$	1636.79	+	315.000i	0.0939590	+	0.0180824i
$673$		−	12322.0i		−	0.705763i	−0.935668	−	0.352881i	$-0.885202\pi$
$673$		−	12322.0i		−	0.705763i	0.935668	−	0.352881i	$-0.114798\pi$
$674$	7671.00	+	13286.6i	0.438392	+	0.759316i
$675$		0			0
$676$	−642.000	+	1111.98i	−0.0365271	+	0.0632668i
$677$	10909.3	−	6298.50i	0.619320	−	0.357564i	−0.157285	−	0.987553i	$-0.550274\pi$
$677$	10909.3	−	6298.50i	0.619320	−	0.357564i	0.776604	+	0.629989i	$0.216941\pi$
$678$			8352.00i			0.473092i
$679$	12628.0	+	10936.2i	0.713723	+	0.618103i
$680$		0			0
$681$	−1500.00	−	2598.08i	−0.0844055	−	0.146195i
$682$	10288.4	+	5940.00i	0.577658	+	0.333511i
$683$	7222.65	+	4170.00i	0.404637	+	0.233617i	0.688483	−	0.725253i	$-0.258277\pi$
$683$	7222.65	+	4170.00i	0.404637	+	0.233617i	−0.283846	+	0.958870i	$0.591610\pi$
$684$	1391.50	+	2410.15i	0.0777856	+	0.134729i
$685$		0			0
$686$	−19036.5	−	891.140i	−1.05950	−	0.0495975i
$687$			12184.0i			0.676636i
$688$	17585.5	−	10153.0i	0.974479	−	0.562616i
$689$	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	$0.645654\pi$
$692$			699.000i			0.0383988i
$693$	12548.7	−	14490.0i	0.687859	−	0.794271i
$694$	−12960.0			−0.708869
$695$		0			0
$696$	3402.00	−	5892.44i	0.185277	−	0.320908i
$697$	−9119.25	−	5265.00i	−0.495576	−	0.286121i
$698$	20582.0	−	11883.0i	1.11610	−	0.644381i
$699$	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	$0.495935\pi$
$702$	−15328.6	+	8850.00i	−0.824135	+	0.475814i
$703$	−27140.4	−	15669.5i	−1.45607	−	0.840663i
$704$	−9742.50	+	16874.5i	−0.521569	+	0.903383i
$705$		0			0
$706$	2484.00			0.132417
$707$	−4146.53	−	11970.0i	−0.220575	−	0.636744i
$708$			720.000i			0.0382193i
$709$	−12563.0	−	21759.8i	−0.665463	−	1.15262i	−0.979160	−	0.203093i	$-0.934901\pi$
$709$	−12563.0	−	21759.8i	−0.665463	−	1.15262i	0.313696	−	0.949523i	$-0.398433\pi$
$710$		0			0
$711$	8993.00	−	15576.3i	0.474351	−	0.821601i
$712$	−21714.7	+	12537.0i	−1.14297	+	0.659893i
$713$		−	6072.00i		−	0.318932i
$714$	−5670.00	+	1964.15i	−0.297191	+	0.102950i
$715$		0			0
$716$	−1558.50	−	2699.40i	−0.0813462	−	0.140896i
$717$	9529.74	+	5502.00i	0.496367	+	0.286577i
$718$	3507.40	+	2025.00i	0.182305	+	0.105254i
$719$	−3648.00	−	6318.52i	−0.189218	−	0.327734i	0.755772	−	0.654835i	$-0.227262\pi$
$719$	−3648.00	−	6318.52i	−0.189218	−	0.327734i	−0.944990	+	0.327100i	$0.893928\pi$
$720$		0			0
$721$	5306.00	−	27570.8i	0.274072	−	1.42412i
$722$		−	23346.0i		−	1.20339i
$723$	−6150.51	+	3551.00i	−0.316376	+	0.182660i
$724$	−899.000	+	1557.11i	−0.0461479	+	0.0799305i
$725$		0			0
$726$	2082.00	+	3606.13i	0.106433	+	0.184347i
$727$			15421.0i			0.786703i	0.919388	+	0.393352i	$0.128684\pi$
$727$			15421.0i			0.786703i	−0.919388	+	0.393352i	$0.871316\pi$
$728$	−15022.1	+	17346.0i	−0.764774	+	0.883085i
$729$	4283.00			0.217599
$730$		0			0
$731$	−7722.00	+	13374.9i	−0.390709	+	0.676728i
$732$	−678.964	−	392.000i	−0.0342831	−	0.0197934i
$733$	−25259.4	+	14583.5i	−1.27282	+	0.734862i	−0.975517	−	0.219922i	$-0.929420\pi$
$733$	−25259.4	+	14583.5i	−1.27282	+	0.734862i	−0.297301	+	0.954784i	$0.596086\pi$
$734$	−8403.00			−0.422562
$735$		0			0
$736$	−3105.00			−0.155505
$737$	−10911.9	+	6300.00i	−0.545381	+	0.314876i
$738$	11652.4	+	6727.50i	0.581206	+	0.335559i
$739$	−6690.50	+	11588.3i	−0.333037	+	0.576836i	−0.983106	−	0.183039i	$-0.941407\pi$
$739$	−6690.50	+	11588.3i	−0.333037	+	0.576836i	0.650069	+	0.759875i	$0.274740\pi$
$740$		0			0
$741$	14278.0			0.707848
$742$	−21714.7	+	25074.0i	−1.07436	+	1.24056i
$743$			5487.00i			0.270927i	0.990782	+	0.135463i	$0.0432523\pi$
$743$			5487.00i			0.270927i	−0.990782	+	0.135463i	$0.956748\pi$
$744$	−1848.00	−	3200.83i	−0.0910631	−	0.157726i
$745$		0			0
$746$	−9903.00	+	17152.5i	−0.486025	+	0.841820i
$747$	15297.5	−	8832.00i	0.749271	−	0.432592i
$748$			2430.00i			0.118783i
$749$	−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	$0.884892\pi$
$752$	−2766.95	−	1597.50i	−0.134176	−	0.0774665i
$753$	12236.9	+	7065.00i	0.592216	+	0.341916i
$754$	−14337.0	−	24832.4i	−0.692470	−	1.19939i
$755$		0			0
$756$	1750.00	−	606.218i	0.0841890	−	0.0291639i
$757$		−	14846.0i		−	0.712797i	−0.934334	−	0.356398i	$-0.884005\pi$
$757$		−	14846.0i		−	0.712797i	0.934334	−	0.356398i	$-0.115995\pi$
$758$	−21577.0	+	12457.5i	−1.03392	+	0.596935i
$759$	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	$0.805619\pi$
$762$			4818.00i			0.229052i
$763$	−9699.48	−	28000.0i	−0.460216	−	1.32853i
$764$	2388.00			0.113082
$765$		0			0
$766$	−1417.50	+	2455.18i	−0.0668621	+	0.115809i
$767$	−18394.4	−	10620.0i	−0.865949	−	0.499956i
$768$	−2620.59	+	1513.00i	−0.123128	+	0.0710881i
$769$	−29855.0			−1.40000			−0.699999	−	0.714144i	$-0.746816\pi$
$769$	−29855.0			−1.40000			−0.699999	+	0.714144i	$0.746816\pi$
$770$		0			0
$771$	8160.00			0.381161
$772$	−235.559	+	136.000i	−0.0109818	+	0.00634035i
$773$	5645.62	+	3259.50i	0.262689	+	0.151664i	0.625561	&

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.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.59808 + 1.50000i) q^{2} +(1.73205 + 1.00000i) q^{3} +(0.500000 - 0.866025i) q^{4} -6.00000 q^{6} +(-12.1244 + 14.0000i) q^{7} -21.0000i q^{8} +(-11.5000 - 19.9186i) q^{9} +O(q^{10})\)	\(q+(-2.59808 + 1.50000i) q^{2} +(1.73205 + 1.00000i) q^{3} +(0.500000 - 0.866025i) q^{4} -6.00000 q^{6} +(-12.1244 + 14.0000i) q^{7} -21.0000i q^{8} +(-11.5000 - 19.9186i) q^{9} +(22.5000 - 38.9711i) q^{11} +(1.73205 - 1.00000i) q^{12} +59.0000i q^{13} +(10.5000 - 54.5596i) q^{14} +(35.5000 + 61.4878i) q^{16} +(-46.7654 - 27.0000i) q^{17} +(59.7558 + 34.5000i) q^{18} +(-60.5000 - 104.789i) q^{19} +(-35.0000 + 12.1244i) q^{21} +135.000i q^{22} +(59.7558 - 34.5000i) q^{23} +(21.0000 - 36.3731i) q^{24} +(-88.5000 - 153.286i) q^{26} -100.000i q^{27} +(6.06218 + 17.5000i) q^{28} +162.000 q^{29} +(44.0000 - 76.2102i) q^{31} +(-38.9711 - 22.5000i) q^{32} +(77.9423 - 45.0000i) q^{33} +162.000 q^{34} -23.0000 q^{36} +(224.301 - 129.500i) q^{37} +(314.367 + 181.500i) q^{38} +(-59.0000 + 102.191i) q^{39} +195.000 q^{41} +(72.7461 - 84.0000i) q^{42} -286.000i q^{43} +(-22.5000 - 38.9711i) q^{44} +(-103.500 + 179.267i) q^{46} +(-38.9711 + 22.5000i) q^{47} +142.000i q^{48} +(-49.0000 - 339.482i) q^{49} +(-54.0000 - 93.5307i) q^{51} +(51.0955 + 29.5000i) q^{52} +(-517.017 - 298.500i) q^{53} +(150.000 + 259.808i) q^{54} +(294.000 + 254.611i) q^{56} -242.000i q^{57} +(-420.888 + 243.000i) q^{58} +(-180.000 + 311.769i) q^{59} +(-196.000 - 339.482i) q^{61} +264.000i q^{62} +(418.290 + 80.5000i) q^{63} -433.000 q^{64} +(-135.000 + 233.827i) q^{66} +(-242.487 - 140.000i) q^{67} +(-46.7654 + 27.0000i) q^{68} +138.000 q^{69} +48.0000 q^{71} +(-418.290 + 241.500i) q^{72} +(-578.505 - 334.000i) q^{73} +(-388.500 + 672.902i) q^{74} -121.000 q^{76} +(272.798 + 787.500i) q^{77} -354.000i q^{78} +(391.000 + 677.232i) q^{79} +(-210.500 + 364.597i) q^{81} +(-506.625 + 292.500i) q^{82} +768.000i q^{83} +(-7.00000 + 36.3731i) q^{84} +(429.000 + 743.050i) q^{86} +(280.592 + 162.000i) q^{87} +(-818.394 - 472.500i) q^{88} +(-597.000 - 1034.03i) q^{89} +(-826.000 - 715.337i) q^{91} -69.0000i q^{92} +(152.420 - 88.0000i) q^{93} +(67.5000 - 116.913i) q^{94} +(-45.0000 - 77.9423i) q^{96} -902.000i q^{97} +(636.529 + 808.500i) q^{98} -1035.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 24 q^{6} - 46 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 - 24 * q^6 - 46 * q^9	\( 4 q + 2 q^{4} - 24 q^{6} - 46 q^{9} + 90 q^{11} + 42 q^{14} + 142 q^{16} - 242 q^{19} - 140 q^{21} + 84 q^{24} - 354 q^{26} + 648 q^{29} + 176 q^{31} + 648 q^{34} - 92 q^{36} - 236 q^{39} + 780 q^{41} - 90 q^{44} - 414 q^{46} - 196 q^{49} - 216 q^{51} + 600 q^{54} + 1176 q^{56} - 720 q^{59} - 784 q^{61} - 1732 q^{64} - 540 q^{66} + 552 q^{69} + 192 q^{71} - 1554 q^{74} - 484 q^{76} + 1564 q^{79} - 842 q^{81} - 28 q^{84} + 1716 q^{86} - 2388 q^{89} - 3304 q^{91} + 270 q^{94} - 180 q^{96} - 4140 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 - 24 * q^6 - 46 * q^9 + 90 * q^11 + 42 * q^14 + 142 * q^16 - 242 * q^19 - 140 * q^21 + 84 * q^24 - 354 * q^26 + 648 * q^29 + 176 * q^31 + 648 * q^34 - 92 * q^36 - 236 * q^39 + 780 * q^41 - 90 * q^44 - 414 * q^46 - 196 * q^49 - 216 * q^51 + 600 * q^54 + 1176 * q^56 - 720 * q^59 - 784 * q^61 - 1732 * q^64 - 540 * q^66 + 552 * q^69 + 192 * q^71 - 1554 * q^74 - 484 * q^76 + 1564 * q^79 - 842 * q^81 - 28 * q^84 + 1716 * q^86 - 2388 * q^89 - 3304 * q^91 + 270 * q^94 - 180 * q^96 - 4140 * q^99

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