LMFDB - Embedded newform 175.4.x.a.103.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,4,Mod(3,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([21, 10]))

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

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

chi := DirichletCharacter("175.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, 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:	$928$
Relative dimension:	$58$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			103.16
Character	$\chi$	$=$	175.103
Dual form			175.4.x.a.17.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.05582 - 0.160149i) q^{2} +(-5.77199 - 7.12781i) q^{3} +(1.35619 + 0.142541i) q^{4} +(-5.21720 + 9.88842i) q^{5} +(16.4966 + 22.7057i) q^{6} +(7.73716 - 16.8267i) q^{7} +(20.0573 + 3.17676i) q^{8} +(-11.8762 + 55.8733i) q^{9} +(17.5264 - 29.3817i) q^{10} +(26.7186 - 5.67921i) q^{11} +(-6.81189 - 10.4894i) q^{12} +(30.7491 + 15.6674i) q^{13} +(-26.3381 + 50.1801i) q^{14} +(100.596 - 19.8887i) q^{15} +(-71.4534 - 15.1879i) q^{16} +(18.9810 + 49.4473i) q^{17} +(45.2397 - 168.837i) q^{18} +(1.99005 + 18.9341i) q^{19} +(-8.48500 + 12.6669i) q^{20} +(-164.596 + 41.9743i) q^{21} +(-82.5567 + 13.0757i) q^{22} +(5.72932 - 109.322i) q^{23} +(-93.1269 - 161.301i) q^{24} +(-70.5617 - 103.180i) q^{25} +(-91.4544 - 52.8012i) q^{26} +(246.157 - 125.423i) q^{27} +(12.8915 - 21.7172i) q^{28} +(-142.281 + 195.833i) q^{29} +(-310.589 + 44.6657i) q^{30} +(45.9180 - 103.133i) q^{31} +(58.9935 + 15.8073i) q^{32} +(-194.700 - 157.665i) q^{33} +(-50.0836 - 154.141i) q^{34} +(126.023 + 164.296i) q^{35} +(-24.0707 + 74.0819i) q^{36} +(146.670 - 95.2487i) q^{37} +(-3.04897 - 58.1778i) q^{38} +(-65.8088 - 309.606i) q^{39} +(-136.056 + 181.761i) q^{40} +(190.983 - 62.0541i) q^{41} +(509.697 - 101.906i) q^{42} +(-131.557 - 131.557i) q^{43} +(37.0450 - 3.89358i) q^{44} +(-490.538 - 408.940i) q^{45} +(-35.0155 + 333.150i) q^{46} +(528.718 + 202.956i) q^{47} +(304.172 + 596.971i) q^{48} +(-223.273 - 260.381i) q^{49} +(199.100 + 326.598i) q^{50} +(242.893 - 420.702i) q^{51} +(39.4683 + 25.6310i) q^{52} +(229.008 - 185.447i) q^{53} +(-772.297 + 343.849i) q^{54} +(-83.2378 + 293.834i) q^{55} +(208.640 - 312.917i) q^{56} +(123.472 - 123.472i) q^{57} +(466.146 - 575.643i) q^{58} +(290.775 - 322.938i) q^{59} +(139.263 - 12.6336i) q^{60} +(-50.4413 + 45.4175i) q^{61} +(-156.833 + 307.803i) q^{62} +(848.273 + 632.138i) q^{63} +(378.053 + 122.837i) q^{64} +(-315.350 + 222.320i) q^{65} +(569.717 + 512.976i) q^{66} +(-714.192 + 274.153i) q^{67} +(18.6936 + 69.7653i) q^{68} +(-812.296 + 590.168i) q^{69} +(-358.791 - 522.241i) q^{70} +(-785.349 - 570.590i) q^{71} +(-415.701 + 1082.94i) q^{72} +(-294.759 + 453.889i) q^{73} +(-463.451 + 267.573i) q^{74} +(-328.164 + 1098.50i) q^{75} +25.9618i q^{76} +(111.164 - 493.526i) q^{77} +(151.517 + 956.638i) q^{78} +(289.707 + 650.694i) q^{79} +(522.971 - 627.323i) q^{80} +(-905.865 - 403.317i) q^{81} +(-593.546 + 159.040i) q^{82} +(185.606 - 1171.87i) q^{83} +(-229.206 + 33.4633i) q^{84} +(-587.983 - 70.2837i) q^{85} +(380.946 + 423.083i) q^{86} +(2217.10 - 116.193i) q^{87} +(553.943 - 29.0309i) q^{88} +(560.901 + 622.944i) q^{89} +(1433.50 + 1328.20i) q^{90} +(501.541 - 396.183i) q^{91} +(23.3529 - 147.444i) q^{92} +(-1000.15 + 267.990i) q^{93} +(-1583.16 - 704.869i) q^{94} +(-197.611 - 79.1044i) q^{95} +(-227.839 - 511.734i) q^{96} +(-223.240 - 1409.48i) q^{97} +(640.581 + 831.433i) q^{98} +1560.31i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 928 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 24 q^{7} + 84 q^{8} - 10 q^{9} - 96 q^{10} - 6 q^{11} - 72 q^{12} - 20 q^{14} - 368 q^{15} - 1670 q^{16} + 120 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} - 880 q^{22}+ \cdots - 19478 q^{98}+O(q^{100}) $ 928 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 24 * q^7 + 84 * q^8 - 10 * q^9 - 96 * q^10 - 6 * q^11 - 72 * q^12 - 20 * q^14 - 368 * q^15 - 1670 * q^16 + 120 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 - 880 * q^22 + 296 * q^23 + 32 * q^25 - 48 * q^26 + 226 * q^28 - 200 * q^29 - 38 * q^30 - 18 * q^31 - 964 * q^32 - 1092 * q^33 + 288 * q^35 + 7400 * q^36 - 392 * q^37 + 5424 * q^38 + 2430 * q^39 + 2172 * q^40 - 2098 * q^42 + 1560 * q^43 - 10 * q^44 - 4224 * q^45 - 6 * q^46 + 96 * q^47 + 6232 * q^50 - 16 * q^51 - 8928 * q^52 - 2384 * q^53 - 30 * q^54 + 244 * q^56 + 1556 * q^57 + 640 * q^58 + 4890 * q^59 + 3676 * q^60 - 18 * q^61 + 224 * q^63 - 9700 * q^64 - 1116 * q^65 - 2610 * q^66 - 2404 * q^67 - 13614 * q^68 - 1700 * q^70 - 24 * q^71 - 518 * q^72 - 4200 * q^73 - 16104 * q^75 - 722 * q^77 - 356 * q^78 - 10 * q^79 + 6414 * q^80 - 6810 * q^81 + 1692 * q^82 + 20620 * q^84 + 2712 * q^85 - 6 * q^86 + 9102 * q^87 + 1650 * q^88 + 20370 * q^89 - 12 * q^91 + 1612 * q^92 - 4604 * q^93 - 30 * q^94 + 1652 * q^95 - 2610 * q^96 - 19478 * q^98

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{20}\right)$

Coefficient data

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

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

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

$2$	−3.05582	−	0.160149i	−1.08039	−	0.0566211i	−0.496179	−	0.868220i	$-0.665264\pi$
$2$	−3.05582	−	0.160149i	−1.08039	−	0.0566211i	−0.584215	+	0.811599i	$0.698597\pi$
$3$	−5.77199	−	7.12781i	−1.11082	−	1.37175i	−0.920831	−	0.389962i	$-0.872488\pi$
$3$	−5.77199	−	7.12781i	−1.11082	−	1.37175i	−0.189989	−	0.981786i	$-0.560845\pi$
$4$	1.35619	+	0.142541i	0.169523	+	0.0178176i
$5$	−5.21720	+	9.88842i	−0.466640	+	0.884447i
$5$	−5.21720	+	9.88842i	−0.466640	+	0.884447i
$6$	16.4966	+	22.7057i	1.12245	+	1.54492i
$7$	7.73716	−	16.8267i	0.417767	−	0.908554i
$7$	7.73716	−	16.8267i	0.417767	−	0.908554i
$8$	20.0573	+	3.17676i	0.886414	+	0.140394i
$9$	−11.8762	+	55.8733i	−0.439861	+	2.06938i
$10$	17.5264	−	29.3817i	0.554234	−	0.929130i
$11$	26.7186	−	5.67921i	0.732360	−	0.155668i	0.173387	−	0.984854i	$-0.444529\pi$
$11$	26.7186	−	5.67921i	0.732360	−	0.155668i	0.558973	+	0.829186i	$0.311195\pi$
$12$	−6.81189	−	10.4894i	−0.163869	−	0.252336i
$13$	30.7491	+	15.6674i	0.656020	+	0.334259i	0.750118	−	0.661304i	$-0.229997\pi$
$13$	30.7491	+	15.6674i	0.656020	+	0.334259i	−0.0940979	+	0.995563i	$0.529997\pi$
$14$	−26.3381	+	50.1801i	−0.502796	+	0.957942i
$15$	100.596	−	19.8887i	1.73159	−	0.342349i
$16$	−71.4534	−	15.1879i	−1.11646	−	0.237311i
$17$	18.9810	+	49.4473i	0.270799	+	0.705454i	0.999781	+	0.0209220i	$0.00666017\pi$
$17$	18.9810	+	49.4473i	0.270799	+	0.705454i	−0.728983	+	0.684532i	$0.760006\pi$
$18$	45.2397	−	168.837i	0.592394	−	2.21084i
$19$	1.99005	+	18.9341i	0.0240289	+	0.228620i	0.999945	+	0.0104743i	$0.00333413\pi$
$19$	1.99005	+	18.9341i	0.0240289	+	0.228620i	−0.975916	+	0.218146i	$0.929999\pi$
$20$	−8.48500	+	12.6669i	−0.0948652	+	0.141620i
$21$	−164.596	+	41.9743i	−1.71037	+	0.436169i
$22$	−82.5567	+	13.0757i	−0.800052	+	0.126716i
$23$	5.72932	−	109.322i	0.0519411	−	0.991096i	−0.841032	−	0.540985i	$-0.818051\pi$
$23$	5.72932	−	109.322i	0.0519411	−	0.991096i	0.892973	−	0.450110i	$-0.148615\pi$
$24$	−93.1269	−	161.301i	−0.792061	−	1.37189i
$25$	−70.5617	−	103.180i	−0.564494	−	0.825437i
$26$	−91.4544	−	52.8012i	−0.689834	−	0.398276i
$27$	246.157	−	125.423i	1.75455	−	0.893990i
$28$	12.8915	−	21.7172i	0.0870096	−	0.146578i
$29$	−142.281	+	195.833i	−0.911065	+	1.25397i	0.0557366	+	0.998446i	$0.482249\pi$
$29$	−142.281	+	195.833i	−0.911065	+	1.25397i	−0.966802	+	0.255528i	$0.917751\pi$
$30$	−310.589	+	44.6657i	−1.89019	+	0.271827i
$31$	45.9180	−	103.133i	0.266036	−	0.597526i	−0.730293	−	0.683134i	$-0.760617\pi$
$31$	45.9180	−	103.133i	0.266036	−	0.597526i	0.996329	+	0.0856078i	$0.0272832\pi$
$32$	58.9935	+	15.8073i	0.325896	+	0.0873237i
$33$	−194.700	−	157.665i	−1.02706	−	0.831695i
$34$	−50.0836	−	154.141i	−0.252626	−	0.777501i
$35$	126.023	+	164.296i	0.608621	+	0.793461i
$36$	−24.0707	+	74.0819i	−0.111438	+	0.342972i
$37$	146.670	−	95.2487i	0.651687	−	0.423210i	−0.176008	−	0.984389i	$-0.556318\pi$
$37$	146.670	−	95.2487i	0.651687	−	0.423210i	0.827695	+	0.561178i	$0.189652\pi$
$38$	−3.04897	−	58.1778i	−0.0130160	−	0.248360i
$39$	−65.8088	−	309.606i	−0.270201	−	1.27120i
$40$	−136.056	+	181.761i	−0.537808	+	0.718473i
$41$	190.983	−	62.0541i	0.727476	−	0.236371i	0.0782144	−	0.996937i	$-0.475078\pi$
$41$	190.983	−	62.0541i	0.727476	−	0.236371i	0.649261	+	0.760565i	$0.275078\pi$
$42$	509.697	−	101.906i	1.87257	−	0.374391i
$43$	−131.557	−	131.557i	−0.466565	−	0.466565i	0.434235	−	0.900800i	$-0.357019\pi$
$43$	−131.557	−	131.557i	−0.466565	−	0.466565i	−0.900800	+	0.434235i	$0.857019\pi$
$44$	37.0450	−	3.89358i	0.126926	−	0.0133404i
$45$	−490.538	−	408.940i	−1.62500	−	1.35469i
$46$	−35.0155	+	333.150i	−0.112234	+	1.06783i
$47$	528.718	+	202.956i	1.64088	+	0.629875i	0.991443	−	0.130539i	$-0.0416709\pi$
$47$	528.718	+	202.956i	1.64088	+	0.629875i	0.649438	+	0.760415i	$0.275004\pi$
$48$	304.172	+	596.971i	0.914654	+	1.79511i
$49$	−223.273	−	260.381i	−0.650941	−	0.759128i
$50$	199.100	+	326.598i	0.563139	+	0.923760i
$51$	242.893	−	420.702i	0.666897	−	1.15510i
$52$	39.4683	+	25.6310i	0.105255	+	0.0683534i
$53$	229.008	−	185.447i	0.593522	−	0.480625i	−0.284870	−	0.958566i	$-0.591950\pi$
$53$	229.008	−	185.447i	0.593522	−	0.480625i	0.878392	+	0.477942i	$0.158617\pi$
$54$	−772.297	+	343.849i	−1.94623	+	0.866517i
$55$	−83.2378	+	293.834i	−0.204069	+	0.720375i
$56$	208.640	−	312.917i	0.497870	−	0.746703i
$57$	123.472	−	123.472i	0.286917	−	0.286917i
$58$	466.146	−	575.643i	1.05531	−	1.30320i
$59$	290.775	−	322.938i	0.641622	−	0.712593i	−0.331352	−	0.943507i	$-0.607505\pi$
$59$	290.775	−	322.938i	0.641622	−	0.712593i	0.972974	+	0.230914i	$0.0741716\pi$
$60$	139.263	−	12.6336i	0.299645	−	0.0271832i
$61$	−50.4413	+	45.4175i	−0.105875	+	0.0953299i	−0.720368	−	0.693592i	$-0.756027\pi$
$61$	−50.4413	+	45.4175i	−0.105875	+	0.0953299i	0.614493	+	0.788922i	$0.289360\pi$
$62$	−156.833	+	307.803i	−0.321256	+	0.630500i
$63$	848.273	+	632.138i	1.69639	+	1.26416i
$64$	378.053	+	122.837i	0.738385	+	0.239916i
$65$	−315.350	+	222.320i	−0.601760	+	0.424236i
$66$	569.717	+	512.976i	1.06254	+	0.956711i
$67$	−714.192	+	274.153i	−1.30228	+	0.499897i	−0.907952	−	0.419075i	$-0.862354\pi$
$67$	−714.192	+	274.153i	−1.30228	+	0.499897i	−0.394324	+	0.918972i	$0.629021\pi$
$68$	18.6936	+	69.7653i	0.0333372	+	0.124416i
$69$	−812.296	+	590.168i	−1.41723	+	1.02968i
$70$	−358.791	−	522.241i	−0.612624	−	0.891711i
$71$	−785.349	−	570.590i	−1.31273	−	0.953754i	−0.999992	−	0.00391469i	$-0.998754\pi$
$71$	−785.349	−	570.590i	−1.31273	−	0.953754i	−0.312738	−	0.949840i	$-0.601246\pi$
$72$	−415.701	+	1082.94i	−0.680428	+	1.77258i
$73$	−294.759	+	453.889i	−0.472588	+	0.727721i	−0.991922	−	0.126850i	$-0.959513\pi$
$73$	−294.759	+	453.889i	−0.472588	+	0.727721i	0.519334	+	0.854571i	$0.326180\pi$
$74$	−463.451	+	267.573i	−0.728041	+	0.420335i
$75$	−328.164	+	1098.50i	−0.505241	+	1.69126i
$76$			25.9618i			0.0391846i
$77$	111.164	−	493.526i	0.164523	−	0.730422i
$78$	151.517	+	956.638i	0.219947	+	1.38869i
$79$	289.707	+	650.694i	0.412590	+	0.926693i	0.993617	+	0.112808i	$0.0359846\pi$
$79$	289.707	+	650.694i	0.412590	+	0.926693i	−0.581026	+	0.813885i	$0.697349\pi$
$80$	522.971	−	627.323i	0.730874	−	0.876710i
$81$	−905.865	−	403.317i	−1.24261	−	0.553247i
$82$	−593.546	+	159.040i	−0.799344	+	0.214184i
$83$	185.606	−	1171.87i	0.245457	−	1.54976i	−0.489719	−	0.871880i	$-0.662901\pi$
$83$	185.606	−	1171.87i	0.245457	−	1.54976i	0.735176	−	0.677876i	$-0.237099\pi$
$84$	−229.206	+	33.4633i	−0.297720	+	0.0434660i
$85$	−587.983	−	70.2837i	−0.750303	−	0.0896864i
$86$	380.946	+	423.083i	0.477656	+	0.530491i
$87$	2217.10	−	116.193i	2.73217	−	0.143187i
$88$	553.943	−	29.0309i	0.671029	−	0.0351671i
$89$	560.901	+	622.944i	0.668039	+	0.741932i	0.977951	−	0.208833i	$-0.0669665\pi$
$89$	560.901	+	622.944i	0.668039	+	0.741932i	−0.309913	+	0.950765i	$0.600300\pi$
$90$	1433.50	+	1328.20i	1.67894	+	1.55561i
$91$	501.541	−	396.183i	0.577756	−	0.456387i
$92$	23.3529	−	147.444i	0.0264642	−	0.167088i
$93$	−1000.15	+	267.990i	−1.11517	+	0.298810i
$94$	−1583.16	−	704.869i	−1.73713	−	0.773422i
$95$	−197.611	−	79.1044i	−0.213415	−	0.0854310i
$96$	−227.839	−	511.734i	−0.242226	−	0.544049i
$97$	−223.240	−	1409.48i	−0.233677	−	1.47538i	−0.773607	−	0.633666i	$-0.781549\pi$
$97$	−223.240	−	1409.48i	−0.233677	−	1.47538i	0.539930	−	0.841710i	$-0.318451\pi$
$98$	640.581	+	831.433i	0.660290	+	0.857014i
$99$			1560.31i			1.58401i
$100$	−80.9876	−	149.989i	−0.0809876	−	0.149989i
$101$	1570.92	−	906.968i	1.54764	−	0.893532i	0.549321	−	0.835611i	$-0.314886\pi$
$101$	1570.92	−	906.968i	1.54764	−	0.893532i	0.998321	−	0.0579208i	$-0.0184471\pi$
$102$	−809.610	+	1246.69i	−0.785915	+	1.21020i
$103$	675.143	−	1758.81i	0.645862	−	1.68253i	−0.0818497	−	0.996645i	$-0.526083\pi$
$103$	675.143	−	1758.81i	0.645862	−	1.68253i	0.727712	−	0.685883i	$-0.240584\pi$
$104$	566.971	+	411.928i	0.534577	+	0.388393i
$105$	443.671	−	1846.58i	0.412360	−	1.71627i
$106$	−729.505	+	530.017i	−0.668451	+	0.485658i
$107$	−170.806	−	637.456i	−0.154322	−	0.575936i	−0.999162	−	0.0409184i	$-0.986972\pi$
$107$	−170.806	−	637.456i	−0.154322	−	0.575936i	0.844841	−	0.535018i	$-0.179695\pi$
$108$	351.713	−	135.010i	0.313367	−	0.120290i
$109$	−133.824	−	120.495i	−0.117596	−	0.105884i	0.608235	−	0.793757i	$-0.291878\pi$
$109$	−133.824	−	120.495i	−0.117596	−	0.105884i	−0.725831	+	0.687873i	$0.758545\pi$
$110$	301.416	−	884.573i	0.261263	−	0.766734i
$111$	−1525.49	−	495.663i	−1.30444	−	0.423840i
$112$	−808.407	+	1084.81i	−0.682030	+	0.915223i
$113$	164.007	−	321.883i	0.136536	−	0.267966i	−0.812607	−	0.582811i	$-0.801953\pi$
$113$	164.007	−	321.883i	0.136536	−	0.267966i	0.949143	+	0.314845i	$0.101953\pi$
$114$	−397.082	+	357.534i	−0.326229	+	0.293738i
$115$	1051.13	+	627.008i	0.852334	+	0.508424i
$116$	−220.874	+	245.305i	−0.176790	+	0.196345i
$117$	−1240.58	+	1531.98i	−0.980267	+	1.21053i
$118$	−940.273	+	940.273i	−0.733552	+	0.733552i
$119$	978.891	+	63.1939i	0.754074	+	0.0486805i
$120$	2080.87	−	79.3414i	1.58297	−	0.0603571i
$121$	−534.299	+	237.885i	−0.401426	+	0.178727i
$122$	161.413	−	130.710i	0.119784	−	0.0969991i
$123$	−1544.66	−	1003.11i	−1.13234	−	0.735348i
$124$	76.9741	−	133.323i	0.0557458	−	0.0965545i
$125$	1388.42	−	159.435i	0.993471	−	0.114083i
$126$	−2490.93	−	2067.55i	−1.76119	−	1.46184i
$127$	−283.770	−	556.929i	−0.198272	−	0.389130i	0.770368	−	0.637599i	$-0.220072\pi$
$127$	−283.770	−	556.929i	−0.198272	−	0.389130i	−0.968640	+	0.248469i	$0.920072\pi$
$128$	−1591.73	−	611.009i	−1.09915	−	0.421923i
$129$	−178.368	+	1697.06i	−0.121740	+	1.15828i
$130$	999.256	−	628.865i	0.674158	−	0.424270i
$131$	−331.433	+	34.8350i	−0.221049	+	0.0232332i	−0.214406	−	0.976745i	$-0.568781\pi$
$131$	−331.433	+	34.8350i	−0.221049	+	0.0232332i	−0.00664360	+	0.999978i	$0.502115\pi$
$132$	−241.576	−	241.576i	−0.159291	−	0.159291i
$133$	333.995	+	113.010i	0.217752	+	0.0736783i
$134$	2226.34	−	723.383i	1.43527	−	0.466349i
$135$	−44.0116	+	3088.46i	−0.0280586	+	1.96898i
$136$	223.625	+	1052.07i	0.140998	+	0.663343i
$137$	−10.4600	−	199.589i	−0.00652307	−	0.124468i	−0.999950	−	0.00999958i	$-0.996817\pi$
$137$	−10.4600	−	199.589i	−0.00652307	−	0.124468i	0.993427	−	0.114468i	$-0.0365164\pi$
$138$	2576.74	−	1673.36i	1.58947	−	1.03221i
$139$	−504.857	+	1553.79i	−0.308068	+	0.948136i	0.670447	+	0.741958i	$0.266103\pi$
$139$	−504.857	+	1553.79i	−0.308068	+	0.948136i	−0.978515	+	0.206178i	$0.933897\pi$
$140$	147.492	+	240.780i	0.0890380	+	0.145354i
$141$	−1605.12	−	4940.06i	−0.958693	−	2.95055i
$142$	2308.50	+	1869.39i	1.36426	+	1.10476i
$143$	910.551	+	243.982i	0.532476	+	0.142677i
$144$	1697.20	−	3811.96i	0.982174	−	2.20600i
$145$	−1194.17	−	2428.63i	−0.683934	−	1.39094i
$146$	973.418	−	1339.80i	0.551785	−	0.759467i
$147$	−567.218	+	3094.36i	−0.318254	+	1.73618i
$148$	212.489	−	108.269i	0.118017	−	0.0601326i
$149$	1059.60	+	611.762i	0.582591	+	0.336359i	0.762162	−	0.647386i	$-0.224138\pi$
$149$	1059.60	+	611.762i	0.582591	+	0.336359i	−0.179572	+	0.983745i	$0.557471\pi$
$150$	1178.73	−	3304.27i	0.641620	−	1.79862i
$151$	−1089.16	−	1886.48i	−0.586984	−	1.01669i	−0.994625	−	0.103544i	$-0.966982\pi$
$151$	−1089.16	−	1886.48i	−0.586984	−	1.01669i	0.407641	−	0.913142i	$-0.366352\pi$
$152$	−20.2340	+	386.088i	−0.0107973	+	0.206025i
$153$	−2988.21	+	473.286i	−1.57897	+	0.250084i
$154$	−418.734	+	1490.32i	−0.219107	+	0.779828i
$155$	780.264	+	992.123i	0.404337	+	0.514124i
$156$	−45.1175	−	429.264i	−0.0231557	−	0.220312i
$157$	554.685	−	2070.11i	0.281966	−	1.05231i	−0.669062	−	0.743207i	$-0.733304\pi$
$157$	554.685	−	2070.11i	0.281966	−	1.05231i	0.951028	−	0.309105i	$-0.100030\pi$
$158$	−781.085	−	2034.80i	−0.393290	−	1.02455i
$159$	−2643.66	−	561.928i	−1.31859	−	0.280275i
$160$	−464.090	+	500.883i	−0.229310	+	0.247489i
$161$	−1795.19	−	942.246i	−0.878765	−	0.461239i
$162$	2703.57	+	1377.54i	1.31119	+	0.668083i
$163$	1329.33	+	2046.99i	0.638780	+	0.983635i	0.998716	+	0.0506583i	$0.0161319\pi$
$163$	1329.33	+	2046.99i	0.638780	+	0.983635i	−0.359936	+	0.932977i	$0.617201\pi$
$164$	267.854	−	56.9341i	0.127536	−	0.0271086i
$165$	2574.84	−	1102.71i	1.21486	−	0.520276i
$166$	−754.853	+	3551.30i	−0.352939	+	1.66045i
$167$	−2484.70	−	393.537i	−1.15133	−	0.182352i	−0.448547	−	0.893759i	$-0.648058\pi$
$167$	−2484.70	−	393.537i	−1.15133	−	0.182352i	−0.702780	+	0.711407i	$0.748058\pi$
$168$	−3434.69	+	319.007i	−1.57733	+	0.146500i
$169$	−591.327	−	813.891i	−0.269152	−	0.370456i
$170$	1785.51	+	308.939i	0.805544	+	0.139380i
$171$	−1081.55	−	113.675i	−0.483672	−	0.0508359i
$172$	−159.664	−	197.168i	−0.0707805	−	0.0874067i
$173$	3288.99	+	172.369i	1.44542	+	0.0757512i	0.758827	−	0.651292i	$-0.225773\pi$
$173$	3288.99	+	172.369i	1.44542	+	0.0757512i	0.686592	+	0.727043i	$0.259106\pi$
$174$	−6793.67			−2.95992
$175$	−2282.12	+	389.001i	−0.985781	+	0.168033i
$176$	−1995.39			−0.854592
$177$	−3980.20	−	208.593i	−1.69022	−	0.0885809i
$178$	−1614.25	−	1993.43i	−0.679736	−	0.839404i
$179$	209.128	+	21.9802i	0.0873238	+	0.00917810i	0.148090	−	0.988974i	$-0.452688\pi$
$179$	209.128	+	21.9802i	0.0873238	+	0.00917810i	−0.0607658	+	0.998152i	$0.519354\pi$
$180$	−606.971	−	624.521i	−0.251339	−	0.258606i
$181$	1993.91	+	2744.38i	0.818819	+	1.12701i	0.989902	+	0.141751i	$0.0452733\pi$
$181$	1993.91	+	2744.38i	0.818819	+	1.12701i	−0.171083	+	0.985257i	$0.554727\pi$
$182$	−1596.07	+	1130.34i	−0.650045	+	0.460365i
$183$	614.874	+	97.3865i	0.248376	+	0.0393389i
$184$	462.204	−	2174.50i	0.185185	−	0.871229i
$185$	176.652	+	1947.27i	0.0702039	+	0.773870i
$186$	3099.20	−	658.756i	1.22175	−	0.259690i
$187$	787.968	+	1213.36i	0.308139	+	0.474492i
$188$	688.111	+	350.610i	0.266945	+	0.136015i
$189$	−205.899	−	5112.42i	−0.0792432	−	1.96759i
$190$	591.194	+	273.376i	0.225735	+	0.104383i
$191$	2883.97	+	613.006i	1.09255	+	0.232228i	0.718740	−	0.695279i	$-0.244719\pi$
$191$	2883.97	+	613.006i	1.09255	+	0.232228i	0.373807	+	0.927507i	$0.378052\pi$
$192$	−1306.56	−	3403.71i	−0.491109	−	1.27938i
$193$	1026.44	−	3830.73i	0.382823	−	1.42871i	−0.458748	−	0.888566i	$-0.651702\pi$
$193$	1026.44	−	3830.73i	0.382823	−	1.42871i	0.841571	−	0.540147i	$-0.181631\pi$
$194$	456.455	+	4342.88i	0.168925	+	1.60722i
$195$	3404.85	+	964.531i	1.25039	+	0.354213i
$196$	−265.685	−	384.951i	−0.0968239	−	0.140288i
$197$	−2206.19	+	349.426i	−0.797890	+	0.126373i	−0.542051	−	0.840346i	$-0.682352\pi$
$197$	−2206.19	+	349.426i	−0.797890	+	0.126373i	−0.255840	+	0.966719i	$0.582352\pi$
$198$	249.881	−	4768.01i	0.0896881	−	1.71135i
$199$	−1251.41	−	2167.51i	−0.445781	−	0.772116i	0.552325	−	0.833629i	$-0.313741\pi$
$199$	−1251.41	−	2167.51i	−0.445781	−	0.772116i	−0.998106	+	0.0615132i	$0.980407\pi$
$200$	−1087.50	−	2293.66i	−0.384488	−	0.810931i
$201$	6076.42	+	3508.22i	2.13233	+	1.23110i
$202$	−4945.68	+	2519.95i	−1.72266	+	0.877737i
$203$	2194.36	+	3909.30i	0.758690	+	1.35162i
$204$	389.375	−	535.929i	0.133636	−	0.183934i
$205$	−382.778	+	2212.27i	−0.130412	+	0.753714i
$206$	−2344.78	+	5266.47i	−0.793052	+	1.78122i
$207$	6040.14	+	1618.45i	2.02811	+	0.543430i
$208$	−1959.17	−	1586.51i	−0.653096	−	0.528867i
$209$	160.702	+	494.591i	0.0531866	+	0.163692i
$210$	−1651.50	+	5571.76i	−0.542688	+	1.83090i
$211$	566.141	−	1742.40i	0.184714	−	0.568492i	−0.815229	−	0.579139i	$-0.803389\pi$
$211$	566.141	−	1742.40i	0.184714	−	0.568492i	0.999943	+	0.0106464i	$0.00338893\pi$
$212$	337.012	−	218.858i	0.109179	−	0.0709020i
$213$	465.971	+	8891.26i	0.149896	+	2.86018i
$214$	419.863	+	1975.30i	0.134118	+	0.630976i
$215$	1987.25	−	614.533i	0.630370	−	0.194934i
$216$	5335.68	−	1733.67i	1.68077	−	0.546116i
$217$	−1380.12	−	1570.60i	−0.431744	−	0.491335i
$218$	389.643	+	389.643i	0.121055	+	0.121055i
$219$	4936.58	−	518.855i	1.52321	−	0.160096i
$220$	−154.769	+	386.630i	−0.0474298	+	0.118484i
$221$	−191.063	+	1817.84i	−0.0581551	+	0.553309i
$222$	4582.25	+	1758.96i	1.38532	+	0.531773i
$223$	352.484	+	691.789i	0.105848	+	0.207738i	0.937856	−	0.347026i	$-0.112808\pi$
$223$	352.484	+	691.789i	0.105848	+	0.207738i	−0.832008	+	0.554764i	$0.812808\pi$
$224$	722.426	−	870.361i	0.215487	−	0.259614i
$225$	6603.00	−	2717.13i	1.95644	−	0.805076i
$226$	−552.726	+	957.349i	−0.162685	+	0.281778i
$227$	−1392.20	−	904.108i	−0.407065	−	0.264351i	0.324825	−	0.945774i	$-0.394695\pi$
$227$	−1392.20	−	904.108i	−0.407065	−	0.264351i	−0.731890	+	0.681423i	$0.761361\pi$
$228$	185.051	−	149.851i	0.0537514	−	0.0435270i
$229$	322.701	−	143.676i	0.0931209	−	0.0414601i	−0.359648	−	0.933088i	$-0.617103\pi$
$229$	322.701	−	143.676i	0.0931209	−	0.0414601i	0.452768	+	0.891628i	$0.350436\pi$
$230$	−3111.65	−	2084.36i	−0.892069	−	0.597559i
$231$	−4159.40	+	2056.27i	−1.18471	+	0.585683i
$232$	−3475.88	+	3475.88i	−0.983631	+	0.983631i
$233$	2314.96	−	2858.73i	0.650892	−	0.803785i	−0.339714	−	0.940529i	$-0.610330\pi$
$233$	2314.96	−	2858.73i	0.650892	−	0.803785i	0.990606	+	0.136744i	$0.0436637\pi$
$234$	4036.32	−	4482.78i	1.12762	−	1.25235i
$235$	−4765.34	+	4169.32i	−1.32279	+	1.15735i
$236$	440.377	−	396.518i	0.121467	−	0.109369i
$237$	2965.83	−	5820.78i	0.812876	−	1.59536i
$238$	−2981.19	−	349.877i	−0.811941	−	0.0952906i
$239$	−1695.61	−	550.937i	−0.458912	−	0.149109i	0.0704327	−	0.997517i	$-0.477562\pi$
$239$	−1695.61	−	550.937i	−0.458912	−	0.149109i	−0.529344	+	0.848407i	$0.677562\pi$
$240$	−7490.02	−	106.735i	−2.01450	−	0.0287072i
$241$	1851.67	+	1667.26i	0.494925	+	0.445632i	0.878405	−	0.477917i	$-0.158608\pi$
$241$	1851.67	+	1667.26i	0.494925	+	0.445632i	−0.383480	+	0.923549i	$0.625275\pi$
$242$	1670.82	−	641.366i	0.443818	−	0.170366i
$243$	423.278	+	1579.70i	0.111742	+	0.417027i
$244$	−74.8817	+	54.4047i	−0.0196468	+	0.0142742i
$245$	3739.61	−	849.357i	0.975164	−	0.221483i
$246$	4559.55	+	3312.71i	1.18173	+	0.858579i
$247$	−235.456	+	613.385i	−0.0606548	+	0.158011i
$248$	1248.62	−	1922.70i	0.319707	−	0.492305i
$249$	−9424.21	+	5441.07i	−2.39853	+	1.38479i
$250$	−4268.28	+	264.852i	−1.07980	+	0.0670028i
$251$			6750.43i			1.69754i	0.528759	+	0.848772i	$0.322658\pi$
$251$			6750.43i			1.69754i	−0.528759	+	0.848772i	$0.677342\pi$
$252$	1060.31	+	978.212i	0.265053	+	0.244530i
$253$	−467.783	−	2953.47i	−0.116242	−	0.733925i
$254$	777.956	+	1747.32i	0.192178	+	0.431640i
$255$	2892.86	+	4596.71i	0.710424	+	1.12885i
$256$	1861.05	+	828.594i	0.454359	+	0.202294i
$257$	−6967.30	+	1866.88i	−1.69108	+	0.453124i	−0.970669	−	0.240420i	$-0.922715\pi$
$257$	−6967.30	+	1866.88i	−1.69108	+	0.453124i	−0.720414	+	0.693544i	$0.756048\pi$
$258$	816.843	−	5157.34i	0.197110	−	1.24450i
$259$	−467.907	−	3204.92i	−0.112256	−	0.768896i
$260$	−459.364	+	256.557i	−0.109571	+	0.0611961i
$261$	−9252.07	−	10275.5i	−2.19421	−	2.43692i
$262$	1018.38	−	53.3709i	0.240136	−	0.0125850i
$263$	3008.04	−	157.645i	0.705262	−	0.0369612i	0.303667	−	0.952778i	$-0.401789\pi$
$263$	3008.04	−	157.645i	0.705262	−	0.0369612i	0.401595	+	0.915817i	$0.368456\pi$
$264$	−3404.28	−	3780.84i	−0.793633	−	0.881419i
$265$	638.998	+	3232.04i	0.148126	+	0.749218i
$266$	−1002.53	−	398.827i	−0.231086	−	0.0919310i
$267$	1202.71	−	7593.63i	0.275673	−	1.74053i
$268$	−1007.66	+	270.001i	−0.229673	+	0.0615407i
$269$	6056.55	+	2696.55i	1.37277	+	0.611195i	0.954795	−	0.297265i	$-0.0960746\pi$
$269$	6056.55	+	2696.55i	1.37277	+	0.611195i	0.417971	+	0.908460i	$0.362741\pi$
$270$	629.104	−	9430.73i	0.141800	−	2.12569i
$271$	−1018.60	−	2287.82i	−0.228324	−	0.512824i	0.762661	−	0.646799i	$-0.223893\pi$
$271$	−1018.60	−	2287.82i	−0.228324	−	0.512824i	−0.990985	+	0.133975i	$0.957226\pi$
$272$	−605.259	−	3821.46i	−0.134924	−	0.851874i
$273$	−5718.81	−	1288.13i	−1.26783	−	0.285572i
$274$			611.583i			0.134843i
$275$	−2471.29	−	2356.08i	−0.541907	−	0.516644i
$276$	−1185.75	+	684.592i	−0.258600	+	0.149303i
$277$	3127.09	−	4815.29i	0.678298	−	1.04449i	−0.317075	−	0.948400i	$-0.602701\pi$
$277$	3127.09	−	4815.29i	0.678298	−	1.04449i	0.995373	−	0.0960868i	$-0.0306326\pi$
$278$	1791.59	−	4667.25i	0.386519	−	1.00692i
$279$	5217.08	+	3790.43i	1.11949	+	0.813358i
$280$	2005.74	+	3695.68i	0.428093	+	0.788782i
$281$	736.192	−	534.875i	0.156290	−	0.113551i	−0.506892	−	0.862010i	$-0.669206\pi$
$281$	736.192	−	534.875i	0.156290	−	0.113551i	0.663182	+	0.748458i	$0.269206\pi$
$282$	4113.82	+	15353.0i	0.868703	+	3.24204i
$283$	1659.76	−	637.120i	0.348630	−	0.133826i	−0.177751	−	0.984076i	$-0.556882\pi$
$283$	1659.76	−	637.120i	0.348630	−	0.133826i	0.526380	+	0.850249i	$0.323549\pi$
$284$	−983.749	−	885.771i	−0.205545	−	0.185073i
$285$	576.766	+	1865.12i	0.119876	+	0.387650i
$286$	−2743.40	−	891.386i	−0.567206	−	0.184296i
$287$	433.501	−	3693.72i	0.0891594	−	0.759699i
$288$	−1583.83	+	3108.44i	−0.324055	+	0.635994i
$289$	1566.32	−	1410.32i	0.318811	−	0.287059i
$290$	3260.22	+	7612.69i	0.660161	+	1.54149i
$291$	−8758.00	+	9726.75i	−1.76427	+	1.95942i
$292$	−464.446	+	573.543i	−0.0930810	+	0.114945i
$293$	−3115.70	+	3115.70i	−0.621233	+	0.621233i	−0.945847	−	0.324614i	$-0.894766\pi$
$293$	−3115.70	+	3115.70i	−0.621233	+	0.621233i	0.324614	+	0.945847i	$0.394766\pi$
$294$	2228.87	−	9364.97i	0.442144	−	1.85774i
$295$	1676.32	+	4560.14i	0.330845	+	0.900005i
$296$	3244.38	−	1444.49i	0.637080	−	0.283646i
$297$	5864.67	−	4749.12i	1.14580	−	0.927851i
$298$	−3139.98	−	2039.12i	−0.610382	−	0.396387i
$299$	1888.97	−	3271.79i	0.365357	−	0.632817i
$300$	−601.633	+	1443.00i	−0.115784	+	0.277705i
$301$	−3231.55	+	1195.79i	−0.618814	+	0.228984i
$302$	3026.16	+	5939.17i	0.576608	+	1.13166i
$303$	−15532.0	−	5962.18i	−2.94485	−	1.13042i
$304$	145.373	−	1383.13i	0.0274267	−	0.260947i
$305$	−185.946	−	735.737i	−0.0349089	−	0.138125i
$306$	9207.21	−	967.716i	1.72007	−	0.180786i
$307$	6748.13	+	6748.13i	1.25451	+	1.25451i	0.953675	+	0.300840i	$0.0972670\pi$
$307$	6748.13	+	6748.13i	1.25451	+	1.25451i	0.300840	+	0.953675i	$0.402733\pi$
$308$	221.107	−	653.468i	0.0409049	−	0.120892i
$309$	−16433.4	+	5339.52i	−3.02544	+	0.983025i
$310$	−2225.45	−	3156.70i	−0.407733	−	0.578351i
$311$	965.126	+	4540.56i	0.175972	+	0.827883i	0.974228	+	0.225565i	$0.0724228\pi$
$311$	965.126	+	4540.56i	0.175972	+	0.827883i	−0.798256	+	0.602318i	$0.794244\pi$
$312$	−336.401	−	6418.91i	−0.0610415	−	1.16474i
$313$	5198.64	−	3376.04i	0.938800	−	0.609664i	0.0180586	−	0.999837i	$-0.494251\pi$
$313$	5198.64	−	3376.04i	0.938800	−	0.609664i	0.920742	+	0.390173i	$0.127585\pi$
$314$	−2026.54	+	6237.05i	−0.364218	+	1.12095i
$315$	−10676.5	+	5090.09i	−1.90968	+	0.910458i
$316$	300.147	+	923.758i	0.0534322	+	0.164448i
$317$	3985.32	+	3227.25i	0.706114	+	0.571800i	0.913686	−	0.406420i	$-0.133223\pi$
$317$	3985.32	+	3227.25i	0.706114	+	0.571800i	−0.207573	+	0.978220i	$0.566556\pi$
$318$	7988.56	+	2140.53i	1.40873	+	0.377468i
$319$	−2689.37	+	6040.42i	−0.472024	+	1.06018i
$320$	−3187.04	+	3097.49i	−0.556753	+	0.541108i
$321$	−3557.78	+	4896.86i	−0.618616	+	0.851452i
$322$	5334.88	+	3166.83i	0.923296	+	0.548076i
$323$	−898.466	+	457.791i	−0.154774	+	0.0788612i
$324$	−1171.03	−	676.097i	−0.200795	−	0.115929i
$325$	−553.147	−	4278.20i	−0.0944094	−	0.730191i
$326$	−3734.37	−	6468.11i	−0.634440	−	1.09888i
$327$	−86.4397	+	1649.37i	−0.0146181	+	0.278930i
$328$	4027.72	−	637.928i	0.678030	−	0.107389i
$329$	7505.84	−	7326.25i	1.25778	−	1.22769i
$330$	−8044.85	+	2957.31i	−1.34198	+	0.493317i
$331$	−577.169	−	5491.40i	−0.0958432	−	0.911887i	−0.931771	−	0.363047i	$-0.881736\pi$
$331$	−577.169	−	5491.40i	−0.0958432	−	0.911887i	0.835927	−	0.548840i	$-0.184930\pi$
$332$	418.757	−	1562.82i	0.0692237	−	0.258346i
$333$	3579.97	+	9326.14i	0.589133	+	1.53474i
$334$	7529.75	+	1600.50i	1.23356	+	0.262202i
$335$	1015.14	−	8492.54i	0.165562	−	1.38507i
$336$	12398.4	−	499.339i	2.01307	−	0.0810749i
$337$	−1968.79	−	1003.15i	−0.318240	−	0.162152i	0.287572	−	0.957759i	$-0.407152\pi$
$337$	−1968.79	−	1003.15i	−0.318240	−	0.162152i	−0.605813	+	0.795607i	$0.707152\pi$
$338$	1676.64	+	2581.80i	0.269815	+	0.415478i
$339$	−3240.97	+	688.889i	−0.519249	+	0.110370i
$340$	−787.397	−	179.130i	−0.125596	−	0.0285725i
$341$	641.147	−	3016.36i	0.101818	−	0.479018i
$342$	3286.80	+	520.578i	0.519678	+	0.0823088i
$343$	−6108.84	+	1742.33i	−0.961651	+	0.274277i
$344$	−2220.75	−	3056.60i	−0.348066	−	0.479072i
$345$	−1597.92	−	11111.3i	−0.249359	−	1.73396i
$346$	−10023.0	−	1053.45i	−1.55733	−	0.163682i
$347$	−48.4334	−	59.8103i	−0.00749291	−	0.00925298i	0.773386	−	0.633936i	$-0.218562\pi$
$347$	−48.4334	−	59.8103i	−0.00749291	−	0.00925298i	−0.780879	+	0.624683i	$0.785228\pi$
$348$	3023.37	+	158.448i	0.465717	+	0.0244072i
$349$	−1764.87			−0.270691			−0.135346	−	0.990798i	$-0.543214\pi$
$349$	−1764.87			−0.270691			−0.135346	+	0.990798i	$0.543214\pi$
$350$	7036.02	−	823.237i	1.07455	−	0.125725i
$351$	9534.17			1.44985
$352$	1666.00	+	87.3113i	0.252267	+	0.0132208i
$353$	4446.76	+	5491.30i	0.670474	+	0.827967i	0.992940	−	0.118614i	$-0.0378452\pi$
$353$	4446.76	+	5491.30i	0.670474	+	0.827967i	−0.322466	+	0.946581i	$0.604512\pi$
$354$	12129.3	+	1274.84i	1.82109	+	0.191405i
$355$	9739.55	−	4788.99i	1.45612	−	0.715980i
$356$	671.892	+	924.781i	0.100029	+	0.137678i
$357$	−5199.72	−	7342.11i	−0.770863	−	1.08848i
$358$	−635.536	−	100.659i	−0.0938244	−	0.0148603i
$359$	−1222.57	+	5751.75i	−0.179735	+	0.845587i	0.792186	+	0.610280i	$0.208943\pi$
$359$	−1222.57	+	5751.75i	−0.179735	+	0.845587i	−0.971921	+	0.235307i	$0.924390\pi$
$360$	−8539.75	−	9760.53i	−1.25023	−	1.42896i
$361$	6354.57	−	1350.71i	0.926458	−	0.196925i
$362$	−5653.52	−	8705.65i	−0.820835	−	1.26397i
$363$	4779.57	+	2435.31i	0.691080	+	0.352123i
$364$	736.656	−	465.808i	0.106075	−	0.0670741i
$365$	−2950.43	−	5282.73i	−0.423103	−	0.757563i
$366$	−1863.35	−	396.067i	−0.266117	−	0.0565648i
$367$	−2628.50	−	6847.48i	−0.373860	−	0.973938i	−0.983443	−	0.181216i	$-0.941997\pi$
$367$	−2628.50	−	6847.48i	−0.373860	−	0.973938i	0.609583	−	0.792722i	$-0.291337\pi$
$368$	−2069.75	+	7724.41i	−0.293188	+	1.09419i
$369$	1199.01	+	11407.8i	0.169154	+	1.60940i
$370$	−227.965	−	5978.78i	−0.0320306	−	0.840059i
$371$	−1348.58	−	5288.27i	−0.188719	−	0.740036i
$372$	−1394.60	+	220.882i	−0.194372	+	0.0307855i
$373$	−287.231	+	5480.70i	−0.0398720	+	0.760804i	0.903403	+	0.428792i	$0.141061\pi$
$373$	−287.231	+	5480.70i	−0.0398720	+	0.760804i	−0.943275	+	0.332012i	$0.892273\pi$
$374$	−2213.57	−	3834.01i	−0.306045	−	0.530085i
$375$	−9150.36	−	8976.13i	−1.26006	−	1.23607i
$376$	9959.89	+	5750.34i	1.36607	+	0.788700i
$377$	−7443.20	+	3792.50i	−1.01683	+	0.518100i
$378$	−189.556	+	15655.6i	−0.0257929	+	2.13026i
$379$	4603.39	−	6336.02i	0.623905	−	0.858732i	−0.373724	−	0.927540i	$-0.621919\pi$
$379$	4603.39	−	6336.02i	0.623905	−	0.858732i	0.997630	+	0.0688075i	$0.0219194\pi$
$380$	−256.722	−	135.448i	−0.0346567	−	0.0182851i
$381$	−2331.77	+	5237.25i	−0.313544	+	0.704232i
$382$	−8714.70	−	2335.10i	−1.16723	−	0.312759i
$383$	−3909.36	−	3165.73i	−0.521563	−	0.422354i	0.332049	−	0.943262i	$-0.392260\pi$
$383$	−3909.36	−	3165.73i	−0.521563	−	0.422354i	−0.853613	+	0.520908i	$0.825593\pi$
$384$	4832.31	+	14872.3i	0.642182	+	1.97643i
$385$	4300.23	+	3674.06i	0.569246	+	0.486356i
$386$	−3750.10	+	11541.6i	−0.494495	+	1.52190i
$387$	8912.94	−	5788.13i	1.17072	−	0.760277i
$388$	−101.846	−	1943.35i	−0.0133260	−	0.254274i
$389$	1750.90	+	8237.35i	0.228212	+	1.07365i	0.931780	+	0.363023i	$0.118255\pi$
$389$	1750.90	+	8237.35i	0.228212	+	1.07365i	−0.703569	+	0.710627i	$0.748411\pi$
$390$	−10250.1	−	3492.71i	−1.33086	−	0.453488i
$391$	5514.42	−	1791.74i	0.713238	−	0.231745i
$392$	−3651.07	−	5931.81i	−0.470426	−	0.764290i
$393$	2161.33	+	2161.33i	0.277416	+	0.277416i
$394$	6797.66	−	714.463i	0.869191	−	0.0913557i
$395$	−7945.79	−	530.047i	−1.01214	−	0.0675179i
$396$	−222.408	+	2116.07i	−0.0282232	+	0.268526i
$397$	−7743.50	−	2972.45i	−0.978929	−	0.375776i	−0.184300	−	0.982870i	$-0.559002\pi$
$397$	−7743.50	−	2972.45i	−0.978929	−	0.375776i	−0.794630	+	0.607094i	$0.792335\pi$
$398$	3476.97	+	6823.94i	0.437901	+	0.859430i
$399$	−1122.30	−	3032.95i	−0.140815	−	0.380544i
$400$	3474.79	+	8444.22i	0.434349	+	1.05553i
$401$	6898.24	−	11948.1i	0.859056	−	1.48793i	−0.0137742	−	0.999905i	$-0.504385\pi$
$401$	6898.24	−	11948.1i	0.859056	−	1.48793i	0.872830	−	0.488024i	$-0.162282\pi$
$402$	−18006.6	−	11693.6i	−2.23405	−	1.45081i
$403$	3027.77	−	2451.84i	0.374253	−	0.303064i
$404$	2259.74	−	1006.10i	0.278282	−	0.123899i
$405$	8714.25	−	6853.39i	1.06917	−	0.840859i
$406$	−6079.50	−	12297.5i	−0.743154	−	1.50324i
$407$	3377.88	−	3377.88i	0.411389	−	0.411389i
$408$	6208.23	−	7666.52i	0.753316	−	0.930268i
$409$	2544.18	−	2825.60i	0.307583	−	0.341606i	−0.569458	−	0.822020i	$-0.692847\pi$
$409$	2544.18	−	2825.60i	0.307583	−	0.341606i	0.877042	+	0.480414i	$0.159514\pi$
$410$	1523.99	−	6698.98i	0.183572	−	0.806924i
$411$	−1362.26	+	1226.58i	−0.163492	+	0.147209i
$412$	1166.32	−	2289.04i	0.139467	−	0.273720i
$413$	−3184.20	−	7391.40i	−0.379381	−	0.880646i
$414$	−18198.4	−	5913.01i	−2.16039	−	0.701953i
$415$	10619.6	+	7949.25i	1.25614	+	0.940273i
$416$	1566.34	+	1410.34i	0.184606	+	0.166220i
$417$	13989.2	−	5369.94i	1.64281	−	0.630616i
$418$	−411.868	−	1537.11i	−0.0481941	−	0.179863i
$419$	5512.16	−	4004.82i	0.642689	−	0.466941i	−0.218084	−	0.975930i	$-0.569981\pi$
$419$	5512.16	−	4004.82i	0.642689	−	0.466941i	0.860773	+	0.508989i	$0.169981\pi$
$420$	864.914	−	2441.07i	0.100485	−	0.283600i
$421$	3390.32	+	2463.21i	0.392479	+	0.285153i	0.766471	−	0.642279i	$-0.222011\pi$
$421$	3390.32	+	2463.21i	0.392479	+	0.285153i	−0.373991	+	0.927432i	$0.622011\pi$
$422$	−2009.06	+	5233.79i	−0.231753	+	0.603737i
$423$	−17619.0	+	27130.9i	−2.02521	+	3.11855i
$424$	5182.39	−	2992.05i	0.593583	−	0.342705i
$425$	3762.62	−	5447.54i	0.429444	−	0.621752i
$426$		−	27244.7i		−	3.09861i
$427$	373.953	+	1200.16i	0.0423814	+	0.136018i
$428$	−140.781	−	888.856i	−0.0158993	−	0.100384i
$429$	−3516.64	−	7898.50i	−0.395769	−	0.888912i
$430$	−6171.09	+	1559.64i	−0.692085	+	0.174913i
$431$	−7787.85	−	3467.37i	−0.870366	−	0.387512i	−0.0775610	−	0.996988i	$-0.524713\pi$
$431$	−7787.85	−	3467.37i	−0.870366	−	0.387512i	−0.792805	+	0.609476i	$0.791380\pi$
$432$	−19493.7	+	5223.32i	−2.17104	+	0.581729i
$433$	−835.023	+	5272.13i	−0.0926759	+	0.585133i	0.897025	+	0.441980i	$0.145724\pi$
$433$	−835.023	+	5272.13i	−0.0926759	+	0.585133i	−0.989701	+	0.143152i	$0.954276\pi$
$434$	3965.85	+	5020.50i	0.438634	+	0.555281i
$435$	−10418.1	+	22529.9i	−1.14830	+	2.48327i
$436$	−164.314	−	182.490i	−0.0180487	−	0.0200451i
$437$	2081.31	−	109.077i	0.227832	−	0.0119402i
$438$	−15168.4	+	794.941i	−1.65473	+	0.0867208i
$439$	−3543.03	−	3934.94i	−0.385193	−	0.427800i	0.519099	−	0.854714i	$-0.326268\pi$
$439$	−3543.03	−	3934.94i	−0.385193	−	0.427800i	−0.904292	+	0.426914i	$0.859601\pi$
$440$	−2602.96	+	5629.08i	−0.282026	+	0.609900i
$441$	17200.0	−	9382.65i	1.85725	−	1.01314i
$442$	874.978	−	5524.39i	0.0941594	−	0.594499i
$443$	−3738.89	+	1001.83i	−0.400993	+	0.107446i	−0.453679	−	0.891165i	$-0.649889\pi$
$443$	−3738.89	+	1001.83i	−0.400993	+	0.107446i	0.0526853	+	0.998611i	$0.483222\pi$
$444$	−1998.20	−	889.657i	−0.213582	−	0.0950929i
$445$	−9086.27	+	2296.41i	−0.967933	+	0.244630i
$446$	−966.338	−	2170.43i	−0.102595	−	0.230432i
$447$	−1755.49	−	11083.7i	−0.185754	−	1.17280i
$448$	4991.99	−	5410.96i	0.526450	−	0.570634i
$449$		−	7849.27i		−	0.825011i	−0.910955	−	0.412506i	$-0.864654\pi$
$449$		−	7849.27i		−	0.825011i	0.910955	−	0.412506i	$-0.135346\pi$
$450$	−20612.7	+	7245.59i	−2.15932	+	0.759024i
$451$	4750.38	−	2742.63i	0.495979	−	0.286354i
$452$	268.306	−	413.156i	0.0279205	−	0.0429938i
$453$	−7159.86	+	18652.1i	−0.742604	+	1.93455i
$454$	4109.53	+	2985.75i	0.424823	+	0.308652i
$455$	1300.98	+	7026.41i	0.134046	+	0.723963i
$456$	2868.75	−	2084.27i	0.294609	−	0.214046i
$457$	1134.10	+	4232.53i	0.116085	+	0.433237i	0.999366	−	0.0356084i	$-0.0113369\pi$
$457$	1134.10	+	4232.53i	0.116085	+	0.433237i	−0.883280	+	0.468845i	$0.844670\pi$
$458$	−1009.12	+	387.367i	−0.102955	+	0.0395206i
$459$	10874.2	+	9791.13i	1.10580	+	0.995667i
$460$	1336.16	+	1000.17i	0.135432	+	0.101376i
$461$	−13749.4	−	4467.45i	−1.38909	−	0.451344i	−0.483446	−	0.875374i	$-0.660615\pi$
$461$	−13749.4	−	4467.45i	−1.38909	−	0.451344i	−0.905648	+	0.424030i	$0.860615\pi$
$462$	13039.7	−	5617.46i	1.31312	−	0.565688i
$463$	1904.54	−	3737.88i	0.191170	−	0.375192i	−0.775449	−	0.631410i	$-0.782477\pi$
$463$	1904.54	−	3737.88i	0.191170	−	0.375192i	0.966619	+	0.256218i	$0.0824765\pi$
$464$	13140.7	−	11832.0i	1.31475	−	1.18380i
$465$	2568.00	−	11288.1i	0.256103	−	1.12575i
$466$	−7531.90	+	8365.03i	−0.748731	+	0.831550i
$467$	−5329.51	+	6581.40i	−0.528095	+	0.652143i	−0.969479	−	0.245175i	$-0.921154\pi$
$467$	−5329.51	+	6581.40i	−0.528095	+	0.652143i	0.441384	+	0.897319i	$0.354488\pi$
$468$	−1900.82	+	1900.82i	−0.187747	+	0.187747i
$469$	−912.742	+	14138.6i	−0.0898647	+	1.39203i
$470$	15229.7	−	11977.5i	1.49467	−	1.17549i
$471$	−17957.0	+	7994.98i	−1.75672	+	0.782143i
$472$	6858.05	−	5553.54i	0.668786	−	0.541572i
$473$	−4262.16	−	2767.88i	−0.414322	−	0.269064i
$474$	−9995.23	+	17312.2i	−0.968557	+	1.67759i
$475$	1813.19	−	1541.36i	0.175147	−	0.148889i
$476$	1318.55	+	225.235i	0.126966	+	0.0216883i
$477$	7641.79	+	14997.9i	0.733529	+	1.43963i
$478$	5093.24	+	1955.11i	0.487363	+	0.187081i
$479$	846.886	−	8057.58i	0.0807833	−	0.768602i	−0.876880	−	0.480710i	$-0.840379\pi$
$479$	846.886	−	8057.58i	0.0807833	−	0.768602i	0.957663	−	0.287892i	$-0.0929543\pi$
$480$	6248.92	+	416.853i	0.594215	+	0.0396388i
$481$	6002.27	−	630.864i	0.568982	−	0.0598024i
$482$	−5391.37	−	5391.37i	−0.509482	−	0.509482i
$483$	3645.69	+	18234.4i	0.343446	+	1.71780i
$484$	−758.517	+	246.457i	−0.0712357	+	0.0231459i
$485$	15102.3	+	5146.06i	1.41394	+	0.481795i
$486$	−1040.47	−	4895.05i	−0.0971129	−	0.456880i
$487$	−256.785	−	4899.75i	−0.0238933	−	0.455911i	−0.984211	−	0.177001i	$-0.943360\pi$
$487$	−256.785	−	4899.75i	−0.0238933	−	0.455911i	0.960317	−	0.278910i	$-0.0899730\pi$
$488$	−1155.99	+	750.712i	−0.107232	+	0.0696375i
$489$	6917.68	−	21290.4i	0.639730	−	1.96889i
$490$	−11563.6	+	1996.59i	−1.06610	+	0.184075i
$491$	2152.10	+	6623.47i	0.197806	+	0.608785i	0.999932	+	0.0116301i	$0.00370206\pi$
$491$	2152.10	+	6623.47i	0.197806	+	0.608785i	−0.802126	+	0.597154i	$0.796298\pi$
$492$	−1951.86	−	1580.59i	−0.178855	−	0.144834i
$493$	−12384.0	−	3318.29i	−1.13134	−	0.303141i
$494$	817.744	−	1836.68i	0.0744778	−	0.167280i
$495$	−15429.0	−	8140.42i	−1.40097	−	0.739161i
$496$	−4847.37	+	6671.84i	−0.438817	+	0.603980i
$497$	−15677.5	+	8800.06i	−1.41495	+	0.794239i
$498$	29670.0	−	15117.6i	2.66977	−	1.36032i
$499$	3544.05	+	2046.16i	0.317943	+	0.183564i	0.650475	−	0.759528i	$-0.274570\pi$
$499$	3544.05	+	2046.16i	0.317943	+	0.183564i	−0.332533	+	0.943092i	$0.607903\pi$
$500$	1905.68	−	18.3176i	0.170449	−	0.00163838i
$501$	11536.6	+	19982.0i	1.02878	+	1.78189i
$502$	1081.07	−	20628.1i	0.0961167	−	1.83402i
$503$	−2257.20	+	357.506i	−0.200087	+	0.0316907i	−0.255673	−	0.966763i	$-0.582297\pi$
$503$	−2257.20	+	357.506i	−0.200087	+	0.0316907i	0.0555864	+	0.998454i	$0.482297\pi$
$504$	15005.9	+	15373.7i	1.32622	+	1.35873i
$505$	772.711	+	20265.7i	0.0680894	+	1.78577i
$506$	956.466	+	9100.17i	0.0840318	+	0.799510i
$507$	−2388.13	+	8912.64i	−0.209193	+	0.780718i
$508$	−305.460	−	795.749i	−0.0266783	−	0.0694994i
$509$	21318.3	+	4531.34i	1.85642	+	0.394594i	0.993792	−	0.111250i	$-0.0354854\pi$
$509$	21318.3	+	4531.34i	1.85642	+	0.394594i	0.862625	+	0.505844i	$0.168819\pi$
$510$	−8103.90	−	14510.0i	−0.703621	−	1.25983i
$511$	5356.84	+	8471.61i	0.463743	+	0.733390i
$512$	6598.83	+	3362.27i	0.569589	+	0.290220i
$513$	2864.64	+	4411.16i	0.246544	+	0.379645i
$514$	21589.8	−	4589.05i	1.85269	−	0.393802i
$515$	13869.5	+	15852.1i	1.18672	+	1.35637i
$516$	−483.802	+	2276.11i	−0.0412755	+	0.194186i
$517$	15279.2	+	2419.99i	1.29977	+	0.205863i
$518$	916.576	+	9868.58i	0.0777452	+	0.837067i
$519$	−17755.4	−	24438.2i	−1.50169	−	2.06690i
$520$	−7031.32	+	3457.33i	−0.592968	+	0.291566i
$521$	−4687.92	−	492.720i	−0.394206	−	0.0414327i	−0.0946480	−	0.995511i	$-0.530173\pi$
$521$	−4687.92	−	492.720i	−0.394206	−	0.0414327i	−0.299558	+	0.954078i	$0.596839\pi$
$522$	26627.0	+	32881.6i	2.23263	+	2.75707i
$523$	7067.30	+	370.382i	0.590882	+	0.0309668i	0.345434	−	0.938443i	$-0.387732\pi$
$523$	7067.30	+	370.382i	0.590882	+	0.0309668i	0.245448	+	0.969410i	$0.421065\pi$
$524$	−454.451			−0.0378870
$525$	15945.1	+	14021.2i	1.32552	+	1.16559i
$526$	−9217.27			−0.764054
$527$	5971.23	+	312.939i	0.493569	+	0.0258669i
$528$	11517.4	+	14222.8i	0.949298	+	1.17229i
$529$	181.888	+	19.1171i	0.0149492	+	0.00157123i
$530$	−1435.05	−	9978.85i	−0.117613	−	0.817837i
$531$	14590.3	+	20081.9i	1.19240	+	1.64120i
$532$	436.851	+	200.871i	0.0356013	+	0.0163700i
$533$	6844.78	+	1084.11i	0.556248	+	0.0881010i
$534$	−4891.38	+	23012.1i	−0.396387	+	1.86485i
$535$	7194.56	+	1636.73i	0.581398	+	0.132266i
$536$	−15195.6	+	3229.93i	−1.22454	+	0.260283i
$537$	−1050.41	−	1617.49i	−0.0844109	−	0.129981i
$538$	−18075.8	−	9210.10i	−1.44852	−	0.738059i
$539$	−7444.30	−	5689.00i	−0.594895	−	0.454625i
$540$	−499.921	+	4182.26i	−0.0398392	+	0.333289i
$541$	−10708.6	−	2276.19i	−0.851015	−	0.180889i	−0.238299	−	0.971192i	$-0.576590\pi$
$541$	−10708.6	−	2276.19i	−0.851015	−	0.180889i	−0.612716	+	0.790303i	$0.709923\pi$
$542$	2746.27	+	7154.29i	0.217643	+	0.566980i
$543$	8052.62	−	30052.8i	0.636411	−	2.37512i
$544$	338.132	+	3217.11i	0.0266494	+	0.253552i
$545$	1889.69	−	694.656i	0.148524	−	0.0545978i
$546$	17269.3	+	4852.14i	1.35359	+	0.380316i
$547$	−1042.25	+	165.077i	−0.0814690	+	0.0129034i	−0.197036	−	0.980396i	$-0.563132\pi$
$547$	−1042.25	+	165.077i	−0.0814690	+	0.0129034i	0.115567	+	0.993300i	$0.463132\pi$
$548$	14.2639	−	272.171i	0.00111190	−	0.0212164i
$549$	−1938.58	−	3357.71i	−0.150704	−	0.261027i
$550$	7174.48	+	7595.53i	0.556220	+	0.588862i
$551$	−3991.06	−	2304.24i	−0.308575	−	0.178156i
$552$	−18167.2	+	9256.67i	−1.40081	+	0.713750i
$553$	13190.5	+	159.709i	1.01432	+	0.0122813i
$554$	−10327.0	+	14213.9i	−0.791969	+	1.09005i
$555$	12860.1	−	12498.7i	0.983570	−	0.955932i
$556$	−906.160	+	2035.27i	−0.0691183	+	0.155242i
$557$	−5717.86	−	1532.09i	−0.434961	−	0.116547i	0.0346929	−	0.999398i	$-0.488955\pi$
$557$	−5717.86	−	1532.09i	−0.434961	−	0.116547i	−0.469654	+	0.882851i	$0.655621\pi$
$558$	−15335.4	−	12418.4i	−1.16344	−	0.942134i
$559$	−1984.10	−	6106.43i	−0.150122	−	0.462029i
$560$	−6509.44	−	13653.5i	−0.491204	−	1.03030i
$561$	4100.49	−	12620.0i	0.308597	−	0.949764i
$562$	−2335.33	+	1516.58i	−0.175284	+	0.113831i
$563$	−499.818	−	9537.10i	−0.0374153	−	0.713927i	−0.951359	−	0.308085i	$-0.900312\pi$
$563$	−499.818	−	9537.10i	−0.0374153	−	0.713927i	0.913943	−	0.405842i	$-0.133022\pi$
$564$	−1472.69	−	6928.44i	−0.109949	−	0.517270i
$565$	2327.25	+	3301.10i	0.173289	+	0.245802i
$566$	−5173.94	+	1681.12i	−0.384235	+	0.124845i
$567$	−13795.3	+	12122.2i	−1.02178	+	0.897853i
$568$	−13939.3	−	13939.3i	−1.02972	−	1.02972i
$569$	−21223.8	+	2230.71i	−1.56370	+	0.164352i	−0.846453	−	0.532464i	$-0.821266\pi$
$569$	−21223.8	+	2230.71i	−1.56370	+	0.164352i	−0.717250	+	0.696816i	$0.754599\pi$
$570$	−1463.79	−	5791.84i	−0.107564	−	0.425603i
$571$	−1596.34	+	15188.2i	−0.116996	+	1.11315i	0.765699	+	0.643199i	$0.222393\pi$
$571$	−1596.34	+	15188.2i	−0.116996	+	1.11315i	−0.882695	+	0.469946i	$0.844273\pi$
$572$	1200.10	+	460.676i	0.0877251	+	0.0336745i
$573$	−12276.8	−	24094.6i	−0.895064	−	1.75666i
$574$	−1916.24	+	11217.9i	−0.139342	+	0.815726i
$575$	−11684.1	+	7122.79i	−0.847408	+	0.516593i
$576$	−11353.2	+	19664.3i	−0.821265	+	1.42247i
$577$	3072.65	+	1995.40i	0.221692	+	0.143968i	0.650707	−	0.759329i	$-0.274473\pi$
$577$	3072.65	+	1995.40i	0.221692	+	0.143968i	−0.429015	+	0.903297i	$0.641139\pi$
$578$	−5012.24	+	4058.83i	−0.360695	+	0.292085i
$579$	−33229.3	+	14794.6i	−2.38508	+	1.06191i
$580$	−1273.34	−	3463.90i	−0.0911595	−	0.247984i
$581$	−18282.6	−	12190.1i	−1.30549	−	0.870448i
$582$	28320.6	−	28320.6i	2.01705	−	2.01705i
$583$	5065.58	−	6255.47i	0.359854	−	0.444383i
$584$	−7353.95	+	8167.38i	−0.521076	+	0.578714i
$585$	−8676.57	−	20260.0i	−0.613217	−	1.43188i
$586$	10020.0	−	9022.04i	0.706351	−	0.636002i
$587$	−3265.42	+	6408.75i	−0.229605	+	0.450626i	−0.976851	−	0.213923i	$-0.931376\pi$
$587$	−3265.42	+	6408.75i	−0.229605	+	0.450626i	0.747245	+	0.664548i	$0.231376\pi$
$588$	−1210.33	+	4115.68i	−0.0848862	+	0.288653i
$589$	2044.12	+	664.174i	0.142999	+	0.0464632i
$590$	−4392.23	−	14203.4i	−0.306483	−	0.991093i
$591$	15224.7	+	13708.4i	1.05967	+	0.954127i
$592$	−11926.7	+	4578.23i	−0.828014	+	0.317845i
$593$	3258.87	+	12162.3i	0.225676	+	0.842233i	0.982133	+	0.188189i	$0.0602619\pi$
$593$	3258.87	+	12162.3i	0.225676	+	0.842233i	−0.756457	+	0.654043i	$0.773071\pi$
$594$	−18681.9	+	13573.2i	−1.29045	+	0.937568i
$595$	−5731.96	+	9349.99i	−0.394937	+	0.644222i
$596$	1349.82	+	980.700i	0.0927696	+	0.0674011i
$597$	−8226.48	+	21430.7i	−0.563966	+	1.46918i
$598$	−6296.30	+	9695.46i	−0.430560	+	0.663005i
$599$	−11590.3	+	6691.66i	−0.790596	+	0.456451i	−0.840172	−	0.542320i	$-0.817546\pi$
$599$	−11590.3	+	6691.66i	−0.790596	+	0.456451i	0.0495765	+	0.998770i	$0.484213\pi$
$600$	−10071.7	+	20990.5i	−0.685295	+	1.42822i
$601$		−	6732.60i		−	0.456953i	−0.973549	−	0.228476i	$-0.926626\pi$
$601$		−	6732.60i		−	0.456953i	0.973549	−	0.228476i	$-0.0733743\pi$
$602$	10066.5	−	3136.58i	0.681529	−	0.212355i
$603$	−6835.90	−	43160.2i	−0.461658	−	2.91479i
$604$	−1208.20	−	2713.67i	−0.0813926	−	0.182811i
$605$	435.233	−	6524.46i	0.0292475	−	0.438442i
$606$	46508.1	+	20706.7i	3.11760	+	1.38804i
$607$	8861.55	−	2374.44i	0.592552	−	0.158774i	0.0499327	−	0.998753i	$-0.484099\pi$
$607$	8861.55	−	2374.44i	0.592552	−	0.158774i	0.542619	+	0.839979i	$0.317433\pi$
$608$	−181.896	+	1148.45i	−0.0121330	+	0.0766047i
$609$	15198.9	−	38205.4i	1.01132	−	2.54214i
$610$	450.388	+	2278.06i	0.0298946	+	0.151206i
$611$	13077.8	+	14524.4i	0.865910	+	0.961690i
$612$	−4120.03	+	215.922i	−0.272128	+	0.0142616i
$613$	−26741.5	+	1401.46i	−1.76196	+	0.0923402i	−0.905623	−	0.424083i	$-0.860596\pi$
$613$	−26741.5	+	1401.46i	−1.76196	+	0.0923402i	−0.856333	+	0.516423i	$0.827263\pi$
$614$	−19540.3	−	21701.7i	−1.28434	−	1.42640i
$615$	17978.0	−	10040.8i	1.17877	−	0.658349i
$616$	3797.45	−	9545.63i	0.248383	−	0.624358i
$617$	3086.90	−	19489.9i	0.201417	−	1.27169i	−0.655087	−	0.755553i	$-0.727368\pi$
$617$	3086.90	−	19489.9i	0.201417	−	1.27169i	0.856504	−	0.516141i	$-0.172632\pi$
$618$	51072.4	−	13684.8i	3.32433	−	0.890751i
$619$	−9073.65	−	4039.85i	−0.589177	−	0.262319i	0.0904205	−	0.995904i	$-0.471179\pi$
$619$	−9073.65	−	4039.85i	−0.589177	−	0.262319i	−0.679598	+	0.733585i	$0.737846\pi$
$620$	916.765	+	1456.72i	0.0593842	+	0.0943604i
$621$	−12301.2	−	27629.0i	−0.794896	−	1.78537i
$622$	−2222.08	−	14029.7i	−0.143243	−	0.904404i
$623$	14821.9	−	4618.28i	0.953170	−	0.296994i
$624$			23121.9i			1.48336i
$625$	−5667.09	+	14561.1i	−0.362694	+	0.931908i
$626$	−16426.8	+	9483.99i	−1.04879	+	0.605521i
$627$	2597.78	−	4000.23i	0.165463	−	0.254791i
$628$	1047.33	−	2728.40i	0.0665496	−	0.173368i
$629$	7493.73	+	5444.52i	0.475031	+	0.345131i
$630$	33440.5	−	13844.6i	2.11476	−	0.875525i
$631$	−4423.85	+	3214.12i	−0.279098	+	0.202777i	−0.718524	−	0.695502i	$-0.755182\pi$
$631$	−4423.85	+	3214.12i	−0.279098	+	0.202777i	0.439426	+	0.898279i	$0.355182\pi$
$632$	3743.64	+	13971.5i	0.235623	+	0.879359i
$633$	−15687.3	+	6021.78i	−0.985013	+	0.378111i
$634$	−11661.6	−	10500.1i	−0.730505	−	0.657750i
$635$	6987.63	+	99.5760i	0.436686	+	0.00622292i
$636$	−3505.20	−	1138.91i	−0.218538	−	0.0710074i
$637$	−2785.93	−	11504.6i	−0.173285	−	0.715586i
$638$	9185.58	−	18027.7i	0.570001	−	1.11869i
$639$	41207.8	−	37103.6i	2.55110	−	2.29702i
$640$	14346.3	−	12552.0i	0.886074	−	0.775251i
$641$	3967.60	−	4406.47i	0.244479	−	0.271521i	−0.608400	−	0.793631i	$-0.708188\pi$
$641$	3967.60	−	4406.47i	0.244479	−	0.271521i	0.852878	+	0.522110i	$0.174855\pi$
$642$	11656.1	−	14394.1i	0.716559	−	0.884877i
$643$	6638.15	−	6638.15i	0.407128	−	0.407128i	−0.473608	−	0.880736i	$-0.657049\pi$
$643$	6638.15	−	6638.15i	0.407128	−	0.407128i	0.880736	+	0.473608i	$0.157049\pi$
$644$	−2300.31	−	1533.75i	−0.140753	−	0.0938482i
$645$	−15850.7	−	10617.7i	−0.967627	−	0.648172i
$646$	2818.86	−	1255.04i	0.171682	−	0.0764378i
$647$	−13061.4	+	10576.9i	−0.793658	+	0.642691i	−0.937921	−	0.346848i	$-0.887252\pi$
$647$	−13061.4	+	10576.9i	−0.793658	+	0.642691i	0.144264	+	0.989539i	$0.453919\pi$
$648$	−16887.9	−	10967.1i	−1.02380	−	0.664862i
$649$	5935.07	−	10279.8i	0.358970	−	0.621755i
$650$	1005.17	+	13162.0i	0.0606552	+	0.794239i
$651$	−3228.96	+	18902.7i	−0.194398	+	1.13803i
$652$	1511.04	+	2965.58i	0.0907622	+	0.178131i
$653$	−15771.0	−	6053.91i	−0.945124	−	0.362799i	−0.163496	−	0.986544i	$-0.552277\pi$
$653$	−15771.0	−	6053.91i	−0.945124	−	0.362799i	−0.781628	+	0.623745i	$0.785610\pi$
$654$	528.287	−	5026.32i	0.0315866	−	0.300527i
$655$	1384.69	−	3459.09i	0.0826019	−	0.206348i
$656$	−14588.8	+	1533.35i	−0.868290	+	0.0912610i
$657$	−21859.7	−	21859.7i	−1.29806	−	1.29806i
$658$	−24109.7	+	21185.6i	−1.42841	+	1.25517i
$659$	20563.7	−	6681.56i	1.21555	−	0.394957i	0.370092	−	0.928995i	$-0.379326\pi$
$659$	20563.7	−	6681.56i	1.21555	−	0.394957i	0.845460	+	0.534038i	$0.179326\pi$
$660$	3649.15	−	1128.45i	0.215217	−	0.0665531i
$661$	−4667.96	−	21961.0i	−0.274679	−	1.29226i	−0.871701	−	0.490038i	$-0.836983\pi$
$661$	−4667.96	−	21961.0i	−0.274679	−	1.29226i	0.597022	−	0.802225i	$-0.296350\pi$
$662$	884.284	+	16873.1i	0.0519164	+	0.990624i
$663$	14060.1	−	9130.70i	0.823601	−	0.534852i
$664$	7445.51	−	22914.9i	0.435153	−	1.33926i
$665$	−2860.01	+	2713.09i	−0.166776	+	0.158209i
$666$	−9446.17	−	29072.3i	−0.549597	−	1.69149i
$667$	20593.6	+	16676.4i	1.19549	+	0.968085i
$668$	−3313.62	−	887.882i	−0.191928	−	0.0514269i
$669$	2896.41	−	6505.44i	0.167387	−	0.375957i
$670$	−4462.16	+	25789.1i	−0.257296	+	1.48704i
$671$	−1089.79	+	1499.96i	−0.0626985	+	0.0862971i
$672$	−10373.6	−	125.603i	−0.595492	−	0.00721016i
$673$	−25098.1	+	12788.1i	−1.43754	+	0.732462i	−0.987064	−	0.160328i	$-0.948745\pi$
$673$	−25098.1	+	12788.1i	−1.43754	+	0.732462i	−0.450473	+	0.892790i	$0.648745\pi$
$674$	5855.61	+	3380.74i	0.334644	+	0.193207i
$675$	−30310.4	−	16548.3i	−1.72837	−	0.943623i
$676$	−685.937	−	1188.08i	−0.0390269	−	0.0675966i
$677$	−646.325	+	12332.6i	−0.0366917	+	0.700120i	0.916918	+	0.399075i	$0.130669\pi$
$677$	−646.325	+	12332.6i	−0.0366917	+	0.700120i	−0.953610	+	0.301045i	$0.902665\pi$
$678$	10014.1	−	1586.08i	0.567242	−	0.0898424i
$679$	−25444.2	−	7149.01i	−1.43808	−	0.404056i
$680$	−11570.1	−	3277.58i	−0.652487	−	0.184837i
$681$	1591.47	+	15141.9i	0.0895528	+	0.852038i
$682$	−2442.29	+	9114.76i	−0.137126	+	0.511763i
$683$	10078.8	+	26256.0i	0.564645	+	1.47095i	0.857343	+	0.514746i	$0.172114\pi$
$683$	10078.8	+	26256.0i	0.564645	+	1.47095i	−0.292698	+	0.956205i	$0.594553\pi$
$684$	−1450.58	−	308.329i	−0.0810879	−	0.0172358i
$685$	2028.19	+	937.863i	0.113129	+	0.0523123i
$686$	18946.5	−	4345.91i	1.05449	−	0.241877i
$687$	−2886.72	−	1470.86i	−0.160313	−	0.0816838i
$688$	7402.13	+	11398.3i	0.410180	+	0.631621i
$689$	9947.26	−	2114.36i	0.550015	−	0.116909i
$690$	3103.48	+	34210.1i	0.171228	+	1.88747i
$691$	−3237.92	+	15233.2i	−0.178258	+	0.838638i	0.794581	+	0.607158i	$0.207690\pi$
$691$	−3237.92	+	15233.2i	−0.178258	+	0.838638i	−0.972840	+	0.231481i	$0.925643\pi$
$692$	4435.92	+	702.581i	0.243683	+	0.0385956i
$693$	26254.7	+	12072.3i	1.43916	+	0.661746i
$694$	138.425	+	190.526i	0.00757138	+	0.0104211i
$695$	−12730.6	−	13098.7i	−0.694819	−	0.714908i
$696$	44838.1	+	4712.68i	2.44193	+	0.256657i
$697$	6693.45	+	8265.73i	0.363748	+	0.449192i
$698$	5393.11	+	282.641i	0.292453	+	0.0153268i
$699$	−33738.4			−1.82561
$700$	−3150.43	+	202.263i	−0.170107	+	0.0109212i
$701$	660.516			0.0355882			0.0177941	−	0.999842i	$-0.494336\pi$
$701$	660.516			0.0355882			0.0177941	+	0.999842i	$0.494336\pi$
$702$	−29134.7	−	1526.88i	−1.56641	−	0.0820919i
$703$	2095.33	+	2587.52i	0.112414	+	0.138819i
$704$	10798.7	+	1134.99i	0.578111	+	0.0607619i
$705$	57223.6	+	9901.14i	3.05697	+	0.528934i
$706$	−12709.1	−	17492.5i	−0.677496	−	0.932493i
$707$	−3106.83	−	33450.6i	−0.165268	−	1.77941i
$708$	−5368.16	−	850.233i	−0.284954	−	0.0451323i
$709$	509.984	−	2399.29i	0.0270139	−	0.127090i	−0.962574	−	0.271018i	$-0.912640\pi$
$709$	509.984	−	2399.29i	0.0270139	−	0.127090i	0.989588	+	0.143927i	$0.0459731\pi$
$710$	−30529.2	+	13074.5i	−1.61372	+	0.691094i
$711$	−39797.1	+	8459.13i	−2.09917	+	0.446191i
$712$	9271.20	+	14276.4i	0.487996	+	0.751447i
$713$	−11011.7	−	5610.72i	−0.578387	−	0.294703i
$714$	14713.5	+	23268.9i	0.771205	+	1.21963i
$715$	−7163.12	+	7731.02i	−0.374665	+	0.404369i
$716$	280.484	+	59.6186i	0.0146399	+	0.00311180i
$717$	5860.06	+	15266.0i	0.305227	+	0.795145i
$718$	4657.09	−	17380.5i	0.242063	−	0.903391i
$719$	−3085.34	−	29355.0i	−0.160033	−	1.52261i	−0.719928	−	0.694049i	$-0.755825\pi$
$719$	−3085.34	−	29355.0i	−0.160033	−	1.52261i	0.559895	−	0.828564i	$-0.310842\pi$
$720$	28839.7	+	36670.4i	1.49277	+	1.89809i
$721$	−24371.2	−	24968.6i	−1.25885	−	1.28971i
$722$	−19634.7	+	3109.83i	−1.01209	+	0.160299i
$723$	1196.04	−	22821.8i	0.0615230	−	1.17393i
$724$	2312.93	+	4006.11i	0.118728	+	0.205644i
$725$	30245.5	+	862.192i	1.54937	+	0.0441669i
$726$	−14215.5	−	8207.30i	−0.726702	−	0.419561i
$727$	4828.87	−	2460.43i	0.246345	−	0.125519i	−0.326459	−	0.945211i	$-0.605856\pi$
$727$	4828.87	−	2460.43i	0.246345	−	0.125519i	0.572804	+	0.819692i	$0.305856\pi$
$728$	11318.1	−	6353.07i	0.576205	−	0.323435i
$729$	−6920.16	+	9524.78i	−0.351581	+	0.483909i
$730$	8169.94	+	16615.5i	0.414224	+	0.842423i
$731$	4008.05	−	9002.23i	0.202795	−	0.455485i
$732$	820.003	+	219.719i	0.0414046	+	0.0110943i
$733$	−16751.5	−	13565.1i	−0.844105	−	0.683543i	0.106376	−	0.994326i	$-0.466075\pi$
$733$	−16751.5	−	13565.1i	−0.844105	−	0.683543i	−0.950481	+	0.310783i	$0.899409\pi$
$734$	6935.60	+	21345.6i	0.348771	+	1.07341i
$735$	−27639.1	−	21752.8i	−1.38705	−	1.09165i
$736$	2066.07	−	6358.72i	0.103474	−	0.318459i
$737$	−17525.2	+	11381.0i	−0.875917	+	0.568827i
$738$	−1837.01	−	35052.2i	−0.0916277	−	1.74836i
$739$	−2790.71	−	13129.3i	−0.138915	−	0.653542i	−0.991408	−	0.130804i	$-0.958244\pi$
$739$	−2790.71	−	13129.3i	−0.138915	−	0.653542i	0.852493	−	0.522738i	$-0.175089\pi$
$740$	−37.9919	+	2666.04i	−0.00188731	+	0.132440i
$741$	5731.15	−	1862.16i	0.284128	−	0.0923188i
$742$	3274.11	+	16376.0i	0.161990	+	0.810216i
$743$	21516.3	+	21516.3i	1.06239	+	1.06239i	0.997919	+	0.0644734i	$0.0205368\pi$
$743$	21516.3	+	21516.3i	1.06239	+	1.06239i	0.0644734	+	0.997919i	$0.479463\pi$
$744$	−20911.7	+	2197.91i	−1.03046	+	0.108305i
$745$	−11577.5	+	7286.11i	−0.569352	+	0.358312i
$746$	1755.45	−	16702.0i	0.0861550	−	0.819710i
$747$	63272.1	+	24287.9i	3.09907	+	1.18962i
$748$	895.678	+	1757.87i	0.0437824	+	0.0859278i
$749$	−12047.8	−	2058.00i	−0.587740	−	0.100398i
$750$	26524.3	+	28894.8i	1.29137	+	1.40679i
$751$	10099.6	−	17493.1i	0.490734	−	0.849976i	−0.509209	−	0.860643i	$-0.670062\pi$
$751$	10099.6	−	17493.1i	0.490734	−	0.849976i	0.999943	+	0.0106666i	$0.00339534\pi$
$752$	−34696.2	−	22532.0i	−1.68250	−	1.09263i
$753$	48115.8	−	38963.4i	2.32860	−	1.88567i
$754$	23352.4	−	10397.2i	1.12791	−	0.502178i
$755$	24336.7	−	927.933i	1.17312	−	0.0447297i
$756$	449.492	−	6962.75i	0.0216242	−	0.334964i
$757$	−7588.97	+	7588.97i	−0.364367	+	0.364367i	−0.865418	−	0.501051i	$-0.832947\pi$
$757$	−7588.97	+	7588.97i	−0.364367	+	0.364367i	0.501051	+	0.865418i	$0.332947\pi$
$758$	−15081.8	+	18624.5i	−0.722686	+	0.892443i
$759$	−18351.7	+	20381.7i	−0.877636	+	0.974713i
$760$	−3712.23	−	2214.38i	−0.177180	−	0.105689i
$761$	−1334.80	+	1201.86i	−0.0635826	+	0.0572500i	−0.700309	−	0.713840i	$-0.746955\pi$
$761$	−1334.80	+	1201.86i	−0.0635826	+	0.0572500i	0.636727	+	0.771090i	$0.280288\pi$
$762$	7964.21	−	15630.6i	0.378626	−	0.743095i
$763$	−3062.95	+	1319.51i	−0.145329	+	0.0626076i
$764$	3823.82	+	1242.43i	0.181075	+	0.0588347i
$765$	10910.0	−	32017.9i	0.515624	−	1.51321i
$766$	11439.3	+	10300.0i	0.539580	+	0.485840i
$767$	14000.7	−	5374.36i	0.659107	−	0.253008i
$768$

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.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.05582 - 0.160149i) q^{2} +(-5.77199 - 7.12781i) q^{3} +(1.35619 + 0.142541i) q^{4} +(-5.21720 + 9.88842i) q^{5} +(16.4966 + 22.7057i) q^{6} +(7.73716 - 16.8267i) q^{7} +(20.0573 + 3.17676i) q^{8} +(-11.8762 + 55.8733i) q^{9} +(17.5264 - 29.3817i) q^{10} +(26.7186 - 5.67921i) q^{11} +(-6.81189 - 10.4894i) q^{12} +(30.7491 + 15.6674i) q^{13} +(-26.3381 + 50.1801i) q^{14} +(100.596 - 19.8887i) q^{15} +(-71.4534 - 15.1879i) q^{16} +(18.9810 + 49.4473i) q^{17} +(45.2397 - 168.837i) q^{18} +(1.99005 + 18.9341i) q^{19} +(-8.48500 + 12.6669i) q^{20} +(-164.596 + 41.9743i) q^{21} +(-82.5567 + 13.0757i) q^{22} +(5.72932 - 109.322i) q^{23} +(-93.1269 - 161.301i) q^{24} +(-70.5617 - 103.180i) q^{25} +(-91.4544 - 52.8012i) q^{26} +(246.157 - 125.423i) q^{27} +(12.8915 - 21.7172i) q^{28} +(-142.281 + 195.833i) q^{29} +(-310.589 + 44.6657i) q^{30} +(45.9180 - 103.133i) q^{31} +(58.9935 + 15.8073i) q^{32} +(-194.700 - 157.665i) q^{33} +(-50.0836 - 154.141i) q^{34} +(126.023 + 164.296i) q^{35} +(-24.0707 + 74.0819i) q^{36} +(146.670 - 95.2487i) q^{37} +(-3.04897 - 58.1778i) q^{38} +(-65.8088 - 309.606i) q^{39} +(-136.056 + 181.761i) q^{40} +(190.983 - 62.0541i) q^{41} +(509.697 - 101.906i) q^{42} +(-131.557 - 131.557i) q^{43} +(37.0450 - 3.89358i) q^{44} +(-490.538 - 408.940i) q^{45} +(-35.0155 + 333.150i) q^{46} +(528.718 + 202.956i) q^{47} +(304.172 + 596.971i) q^{48} +(-223.273 - 260.381i) q^{49} +(199.100 + 326.598i) q^{50} +(242.893 - 420.702i) q^{51} +(39.4683 + 25.6310i) q^{52} +(229.008 - 185.447i) q^{53} +(-772.297 + 343.849i) q^{54} +(-83.2378 + 293.834i) q^{55} +(208.640 - 312.917i) q^{56} +(123.472 - 123.472i) q^{57} +(466.146 - 575.643i) q^{58} +(290.775 - 322.938i) q^{59} +(139.263 - 12.6336i) q^{60} +(-50.4413 + 45.4175i) q^{61} +(-156.833 + 307.803i) q^{62} +(848.273 + 632.138i) q^{63} +(378.053 + 122.837i) q^{64} +(-315.350 + 222.320i) q^{65} +(569.717 + 512.976i) q^{66} +(-714.192 + 274.153i) q^{67} +(18.6936 + 69.7653i) q^{68} +(-812.296 + 590.168i) q^{69} +(-358.791 - 522.241i) q^{70} +(-785.349 - 570.590i) q^{71} +(-415.701 + 1082.94i) q^{72} +(-294.759 + 453.889i) q^{73} +(-463.451 + 267.573i) q^{74} +(-328.164 + 1098.50i) q^{75} +25.9618i q^{76} +(111.164 - 493.526i) q^{77} +(151.517 + 956.638i) q^{78} +(289.707 + 650.694i) q^{79} +(522.971 - 627.323i) q^{80} +(-905.865 - 403.317i) q^{81} +(-593.546 + 159.040i) q^{82} +(185.606 - 1171.87i) q^{83} +(-229.206 + 33.4633i) q^{84} +(-587.983 - 70.2837i) q^{85} +(380.946 + 423.083i) q^{86} +(2217.10 - 116.193i) q^{87} +(553.943 - 29.0309i) q^{88} +(560.901 + 622.944i) q^{89} +(1433.50 + 1328.20i) q^{90} +(501.541 - 396.183i) q^{91} +(23.3529 - 147.444i) q^{92} +(-1000.15 + 267.990i) q^{93} +(-1583.16 - 704.869i) q^{94} +(-197.611 - 79.1044i) q^{95} +(-227.839 - 511.734i) q^{96} +(-223.240 - 1409.48i) q^{97} +(640.581 + 831.433i) q^{98} +1560.31i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 928 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 24 q^{7} + 84 q^{8} - 10 q^{9} - 96 q^{10} - 6 q^{11} - 72 q^{12} - 20 q^{14} - 368 q^{15} - 1670 q^{16} + 120 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} - 880 q^{22}+ \cdots - 19478 q^{98}+O(q^{100}) \) 928 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 24 * q^7 + 84 * q^8 - 10 * q^9 - 96 * q^10 - 6 * q^11 - 72 * q^12 - 20 * q^14 - 368 * q^15 - 1670 * q^16 + 120 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 - 880 * q^22 + 296 * q^23 + 32 * q^25 - 48 * q^26 + 226 * q^28 - 200 * q^29 - 38 * q^30 - 18 * q^31 - 964 * q^32 - 1092 * q^33 + 288 * q^35 + 7400 * q^36 - 392 * q^37 + 5424 * q^38 + 2430 * q^39 + 2172 * q^40 - 2098 * q^42 + 1560 * q^43 - 10 * q^44 - 4224 * q^45 - 6 * q^46 + 96 * q^47 + 6232 * q^50 - 16 * q^51 - 8928 * q^52 - 2384 * q^53 - 30 * q^54 + 244 * q^56 + 1556 * q^57 + 640 * q^58 + 4890 * q^59 + 3676 * q^60 - 18 * q^61 + 224 * q^63 - 9700 * q^64 - 1116 * q^65 - 2610 * q^66 - 2404 * q^67 - 13614 * q^68 - 1700 * q^70 - 24 * q^71 - 518 * q^72 - 4200 * q^73 - 16104 * q^75 - 722 * q^77 - 356 * q^78 - 10 * q^79 + 6414 * q^80 - 6810 * q^81 + 1692 * q^82 + 20620 * q^84 + 2712 * q^85 - 6 * q^86 + 9102 * q^87 + 1650 * q^88 + 20370 * q^89 - 12 * q^91 + 1612 * q^92 - 4604 * q^93 - 30 * q^94 + 1652 * q^95 - 2610 * q^96 - 19478 * q^98

Introduction

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