LMFDB - Embedded newform 624.4.q.i.289.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,4,Mod(289,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("624.289");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	624.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$36.8171918436$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 29x^{6} + 2x^{5} + 595x^{4} - 288x^{3} + 2526x^{2} + 1872x + 6084 $ x^8 - 2x^7 + 29x^6 + 2x^5 + 595x^4 - 288x^3 + 2526x^2 + 1872*x + 6084
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 3 $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.4
Root			$-0.733051 + 1.26968i$ of defining polynomial
Character	$\chi$	$=$	624.289
Dual form			624.4.q.i.529.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 - 2.59808i) q^{3} +9.85055 q^{5} +(14.9698 - 25.9285i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(-1.50000 - 2.59808i) q^{3} +9.85055 q^{5} +(14.9698 - 25.9285i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(23.4629 + 40.6389i) q^{11} +(3.71050 - 46.7251i) q^{13} +(-14.7758 - 25.5925i) q^{15} +(24.1308 - 41.7958i) q^{17} +(60.1501 - 104.183i) q^{19} -89.8188 q^{21} +(65.3485 + 113.187i) q^{23} -27.9667 q^{25} +27.0000 q^{27} +(97.4729 + 168.828i) q^{29} +32.0123 q^{31} +(70.3886 - 121.917i) q^{33} +(147.461 - 255.409i) q^{35} +(16.2125 + 28.0808i) q^{37} +(-126.961 + 60.4474i) q^{39} +(120.913 + 209.427i) q^{41} +(48.2044 - 83.4924i) q^{43} +(-44.3275 + 76.7774i) q^{45} -539.015 q^{47} +(-276.690 - 479.241i) q^{49} -144.785 q^{51} -152.277 q^{53} +(231.122 + 400.315i) q^{55} -360.901 q^{57} +(163.896 - 283.876i) q^{59} +(49.2090 - 85.2325i) q^{61} +(134.728 + 233.356i) q^{63} +(36.5504 - 460.267i) q^{65} +(-220.575 - 382.048i) q^{67} +(196.046 - 339.561i) q^{69} +(172.524 - 298.821i) q^{71} +773.839 q^{73} +(41.9501 + 72.6597i) q^{75} +1404.94 q^{77} +150.332 q^{79} +(-40.5000 - 70.1481i) q^{81} -337.966 q^{83} +(237.702 - 411.711i) q^{85} +(292.419 - 506.484i) q^{87} +(-84.9567 - 147.149i) q^{89} +(-1155.96 - 795.673i) q^{91} +(-48.0184 - 83.1703i) q^{93} +(592.511 - 1026.26i) q^{95} +(-107.101 + 185.504i) q^{97} -422.332 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{3} - 12 q^{5} - 14 q^{7} - 36 q^{9}+O(q^{10}) $ 8 * q - 12 * q^3 - 12 * q^5 - 14 * q^7 - 36 * q^9	$ 8 q - 12 q^{3} - 12 q^{5} - 14 q^{7} - 36 q^{9} + 40 q^{11} - 60 q^{13} + 18 q^{15} - 98 q^{17} + 124 q^{19} + 84 q^{21} + 104 q^{23} - 116 q^{25} + 216 q^{27} - 194 q^{29} - 52 q^{31} + 120 q^{33} + 88 q^{35} - 102 q^{37} - 342 q^{39} + 1054 q^{41} + 450 q^{43} + 54 q^{45} + 192 q^{47} - 1070 q^{49} + 588 q^{51} + 524 q^{53} + 204 q^{55} - 744 q^{57} + 308 q^{59} + 928 q^{61} - 126 q^{63} + 2346 q^{65} - 1134 q^{67} + 312 q^{69} + 1064 q^{71} + 1904 q^{73} + 174 q^{75} + 5016 q^{77} + 1492 q^{79} - 324 q^{81} + 808 q^{83} + 1394 q^{85} - 582 q^{87} - 1620 q^{89} - 3278 q^{91} + 78 q^{93} + 2204 q^{95} - 2166 q^{97} - 720 q^{99}+O(q^{100}) $ 8 * q - 12 * q^3 - 12 * q^5 - 14 * q^7 - 36 * q^9 + 40 * q^11 - 60 * q^13 + 18 * q^15 - 98 * q^17 + 124 * q^19 + 84 * q^21 + 104 * q^23 - 116 * q^25 + 216 * q^27 - 194 * q^29 - 52 * q^31 + 120 * q^33 + 88 * q^35 - 102 * q^37 - 342 * q^39 + 1054 * q^41 + 450 * q^43 + 54 * q^45 + 192 * q^47 - 1070 * q^49 + 588 * q^51 + 524 * q^53 + 204 * q^55 - 744 * q^57 + 308 * q^59 + 928 * q^61 - 126 * q^63 + 2346 * q^65 - 1134 * q^67 + 312 * q^69 + 1064 * q^71 + 1904 * q^73 + 174 * q^75 + 5016 * q^77 + 1492 * q^79 - 324 * q^81 + 808 * q^83 + 1394 * q^85 - 582 * q^87 - 1620 * q^89 - 3278 * q^91 + 78 * q^93 + 2204 * q^95 - 2166 * q^97 - 720 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$4$		0			0
$5$	9.85055			0.881060			0.440530	−	0.897738i	$-0.354791\pi$
$5$	9.85055			0.881060			0.440530	+	0.897738i	$0.354791\pi$
$6$		0			0
$7$	14.9698	−	25.9285i	0.808293	−	1.40001i	−0.105752	−	0.994393i	$-0.533725\pi$
$7$	14.9698	−	25.9285i	0.808293	−	1.40001i	0.914045	−	0.405613i	$-0.132942\pi$
$8$		0			0
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$		0			0
$11$	23.4629	+	40.6389i	0.643120	+	1.11392i	0.984732	+	0.174076i	$0.0556938\pi$
$11$	23.4629	+	40.6389i	0.643120	+	1.11392i	−0.341612	+	0.939841i	$0.610973\pi$
$12$		0			0
$13$	3.71050	−	46.7251i	0.0791621	−	0.996862i
$13$	3.71050	−	46.7251i	0.0791621	−	0.996862i
$14$		0			0
$15$	−14.7758	−	25.5925i	−0.254340	−	0.440530i
$16$		0			0
$17$	24.1308	−	41.7958i	0.344270	−	0.596292i	−0.640951	−	0.767582i	$-0.721460\pi$
$17$	24.1308	−	41.7958i	0.344270	−	0.596292i	0.985221	+	0.171289i	$0.0547932\pi$
$18$		0			0
$19$	60.1501	−	104.183i	0.726283	−	1.25796i	−0.232161	−	0.972677i	$-0.574579\pi$
$19$	60.1501	−	104.183i	0.726283	−	1.25796i	0.958444	−	0.285282i	$-0.0920872\pi$
$20$		0			0
$21$	−89.8188			−0.933337
$22$		0			0
$23$	65.3485	+	113.187i	0.592440	+	1.02614i	0.993903	+	0.110260i	$0.0351685\pi$
$23$	65.3485	+	113.187i	0.592440	+	1.02614i	−0.401463	+	0.915875i	$0.631498\pi$
$24$		0			0
$25$	−27.9667			−0.223734
$26$		0			0
$27$	27.0000			0.192450
$28$		0			0
$29$	97.4729	+	168.828i	0.624147	+	1.08105i	0.988705	+	0.149874i	$0.0478867\pi$
$29$	97.4729	+	168.828i	0.624147	+	1.08105i	−0.364558	+	0.931181i	$0.618780\pi$
$30$		0			0
$31$	32.0123			0.185470			0.0927351	−	0.995691i	$-0.470439\pi$
$31$	32.0123			0.185470			0.0927351	+	0.995691i	$0.470439\pi$
$32$		0			0
$33$	70.3886	−	121.917i	0.371306	−	0.643120i
$34$		0			0
$35$	147.461	−	255.409i	0.712155	−	1.23349i
$36$		0			0
$37$	16.2125	+	28.0808i	0.0720355	+	0.124769i	0.899793	−	0.436316i	$-0.143717\pi$
$37$	16.2125	+	28.0808i	0.0720355	+	0.124769i	−0.827758	+	0.561086i	$0.810384\pi$
$38$		0			0
$39$	−126.961	+	60.4474i	−0.521283	+	0.248188i
$40$		0			0
$41$	120.913	+	209.427i	0.460570	+	0.797731i	0.998989	−	0.0449461i	$-0.0143116\pi$
$41$	120.913	+	209.427i	0.460570	+	0.797731i	−0.538419	+	0.842677i	$0.680978\pi$
$42$		0			0
$43$	48.2044	−	83.4924i	0.170956	−	0.296104i	−0.767799	−	0.640691i	$-0.778648\pi$
$43$	48.2044	−	83.4924i	0.170956	−	0.296104i	0.938754	+	0.344587i	$0.111981\pi$
$44$		0			0
$45$	−44.3275	+	76.7774i	−0.146843	+	0.254340i
$46$		0			0
$47$	−539.015			−1.67284			−0.836419	−	0.548090i	$-0.815355\pi$
$47$	−539.015			−1.67284			−0.836419	+	0.548090i	$0.815355\pi$
$48$		0			0
$49$	−276.690	−	479.241i	−0.806676	−	1.39720i
$50$		0			0
$51$	−144.785			−0.397528
$52$		0			0
$53$	−152.277			−0.394657			−0.197328	−	0.980337i	$-0.563226\pi$
$53$	−152.277			−0.394657			−0.197328	+	0.980337i	$0.563226\pi$
$54$		0			0
$55$	231.122	+	400.315i	0.566627	+	0.981427i
$56$		0			0
$57$	−360.901			−0.838640
$58$		0			0
$59$	163.896	−	283.876i	0.361652	−	0.626399i	−0.626581	−	0.779356i	$-0.715546\pi$
$59$	163.896	−	283.876i	0.361652	−	0.626399i	0.988233	+	0.152957i	$0.0488796\pi$
$60$		0			0
$61$	49.2090	−	85.2325i	0.103288	−	0.178900i	−0.809749	−	0.586776i	$-0.800397\pi$
$61$	49.2090	−	85.2325i	0.103288	−	0.178900i	0.913037	+	0.407876i	$0.133730\pi$
$62$		0			0
$63$	134.728	+	233.356i	0.269431	+	0.466668i
$64$		0			0
$65$	36.5504	−	460.267i	0.0697465	−	0.878295i
$66$		0			0
$67$	−220.575	−	382.048i	−0.402202	−	0.696635i	0.591789	−	0.806093i	$-0.298422\pi$
$67$	−220.575	−	382.048i	−0.402202	−	0.696635i	−0.993991	+	0.109458i	$0.965089\pi$
$68$		0			0
$69$	196.046	−	339.561i	0.342045	−	0.592440i
$70$		0			0
$71$	172.524	−	298.821i	0.288379	−	0.499486i	−0.685044	−	0.728501i	$-0.740217\pi$
$71$	172.524	−	298.821i	0.288379	−	0.499486i	0.973423	+	0.229015i	$0.0735505\pi$
$72$		0			0
$73$	773.839			1.24070			0.620349	−	0.784326i	$-0.286991\pi$
$73$	773.839			1.24070			0.620349	+	0.784326i	$0.286991\pi$
$74$		0			0
$75$	41.9501	+	72.6597i	0.0645864	+	0.111867i
$76$		0			0
$77$	1404.94			2.07932
$78$		0			0
$79$	150.332			0.214097			0.107049	−	0.994254i	$-0.465860\pi$
$79$	150.332			0.214097			0.107049	+	0.994254i	$0.465860\pi$
$80$		0			0
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−337.966			−0.446947			−0.223473	−	0.974710i	$-0.571740\pi$
$83$	−337.966			−0.446947			−0.223473	+	0.974710i	$0.571740\pi$
$84$		0			0
$85$	237.702	−	411.711i	0.303322	−	0.525369i
$86$		0			0
$87$	292.419	−	506.484i	0.360351	−	0.624147i
$88$		0			0
$89$	−84.9567	−	147.149i	−0.101184	−	0.175256i	0.810989	−	0.585062i	$-0.198930\pi$
$89$	−84.9567	−	147.149i	−0.101184	−	0.175256i	−0.912173	+	0.409806i	$0.865596\pi$
$90$		0			0
$91$	−1155.96	−	795.673i	−1.33163	−	0.916584i
$92$		0			0
$93$	−48.0184	−	83.1703i	−0.0535406	−	0.0927351i
$94$		0			0
$95$	592.511	−	1026.26i	0.639899	−	1.10834i
$96$		0			0
$97$	−107.101	+	185.504i	−0.112107	+	0.194176i	−0.916620	−	0.399760i	$-0.869093\pi$
$97$	−107.101	+	185.504i	−0.112107	+	0.194176i	0.804512	+	0.593936i	$0.202427\pi$
$98$		0			0
$99$	−422.332			−0.428747
$100$		0			0
$101$	−797.556	−	1381.41i	−0.785741	−	1.36094i	−0.928555	−	0.371194i	$-0.878949\pi$
$101$	−797.556	−	1381.41i	−0.785741	−	1.36094i	0.142815	−	0.989749i	$-0.454385\pi$
$102$		0			0
$103$	1570.30			1.50219			0.751096	−	0.660193i	$-0.229525\pi$
$103$	1570.30			1.50219			0.751096	+	0.660193i	$0.229525\pi$
$104$		0			0
$105$	−884.764			−0.822325
$106$		0			0
$107$	−3.36651	−	5.83096i	−0.00304161	−	0.00526823i	0.864501	−	0.502632i	$-0.167635\pi$
$107$	−3.36651	−	5.83096i	−0.00304161	−	0.00526823i	−0.867542	+	0.497364i	$0.834302\pi$
$108$		0			0
$109$	−542.422			−0.476648			−0.238324	−	0.971186i	$-0.576598\pi$
$109$	−542.422			−0.476648			−0.238324	+	0.971186i	$0.576598\pi$
$110$		0			0
$111$	48.6374	−	84.2425i	0.0415897	−	0.0720355i
$112$		0			0
$113$	721.411	−	1249.52i	0.600572	−	1.04022i	−0.392162	−	0.919896i	$-0.628273\pi$
$113$	721.411	−	1249.52i	0.600572	−	1.04022i	0.992735	−	0.120325i	$-0.0383938\pi$
$114$		0			0
$115$	643.719	+	1114.95i	0.521975	+	0.904087i
$116$		0			0
$117$	347.489	+	239.183i	0.274576	+	0.188996i
$118$		0			0
$119$	−722.467	−	1251.35i	−0.556542	−	0.963958i
$120$		0			0
$121$	−435.513	+	754.330i	−0.327207	+	0.566739i
$122$		0			0
$123$	362.738	−	628.280i	0.265910	−	0.460570i
$124$		0			0
$125$	−1506.81			−1.07818
$126$		0			0
$127$	−1246.42	−	2158.86i	−0.870881	−	1.50841i	−0.861087	−	0.508458i	$-0.830216\pi$
$127$	−1246.42	−	2158.86i	−0.870881	−	1.50841i	−0.00979442	−	0.999952i	$-0.503118\pi$
$128$		0			0
$129$	−289.226			−0.197403
$130$		0			0
$131$	−744.561			−0.496585			−0.248292	−	0.968685i	$-0.579869\pi$
$131$	−744.561			−0.496585			−0.248292	+	0.968685i	$0.579869\pi$
$132$		0			0
$133$	−1800.87	−	3119.20i	−1.17410	−	2.03360i
$134$		0			0
$135$	265.965			0.169560
$136$		0			0
$137$	111.083	−	192.402i	0.0692736	−	0.119985i	−0.829308	−	0.558792i	$-0.811265\pi$
$137$	111.083	−	192.402i	0.0692736	−	0.119985i	0.898582	+	0.438806i	$0.144599\pi$
$138$		0			0
$139$	−388.573	+	673.028i	−0.237110	+	0.410687i	−0.959884	−	0.280398i	$-0.909534\pi$
$139$	−388.573	+	673.028i	−0.237110	+	0.410687i	0.722774	+	0.691085i	$0.242867\pi$
$140$		0			0
$141$	808.522	+	1400.40i	0.482907	+	0.836419i
$142$		0			0
$143$	1985.91	−	945.514i	1.16133	−	0.552922i
$144$		0			0
$145$	960.161	+	1663.05i	0.549911	+	0.952473i
$146$		0			0
$147$	−830.070	+	1437.72i	−0.465735	+	0.806676i
$148$		0			0
$149$	−889.147	+	1540.05i	−0.488871	+	0.846750i	−0.999918	−	0.0128032i	$-0.995925\pi$
$149$	−889.147	+	1540.05i	−0.488871	+	0.846750i	0.511047	+	0.859553i	$0.329258\pi$
$150$		0			0
$151$	−1166.00			−0.628394			−0.314197	−	0.949358i	$-0.601735\pi$
$151$	−1166.00			−0.628394			−0.314197	+	0.949358i	$0.601735\pi$
$152$		0			0
$153$	217.177	+	376.162i	0.114757	+	0.198764i
$154$		0			0
$155$	315.338			0.163410
$156$		0			0
$157$	517.628			0.263129			0.131564	−	0.991308i	$-0.458000\pi$
$157$	517.628			0.263129			0.131564	+	0.991308i	$0.458000\pi$
$158$		0			0
$159$	228.415	+	395.626i	0.113928	+	0.197328i
$160$		0			0
$161$	3913.02			1.91546
$162$		0			0
$163$	305.094	−	528.438i	0.146606	−	0.253929i	−0.783365	−	0.621562i	$-0.786498\pi$
$163$	305.094	−	528.438i	0.146606	−	0.253929i	0.929971	+	0.367633i	$0.119832\pi$
$164$		0			0
$165$	693.366	−	1200.95i	0.327142	−	0.566627i
$166$		0			0
$167$	1491.51	+	2583.36i	0.691115	+	1.19705i	0.971473	+	0.237150i	$0.0762133\pi$
$167$	1491.51	+	2583.36i	0.691115	+	1.19705i	−0.280358	+	0.959895i	$0.590453\pi$
$168$		0			0
$169$	−2169.46	−	346.747i	−0.987467	−	0.157827i
$170$		0			0
$171$	541.351	+	937.647i	0.242094	+	0.419320i
$172$		0			0
$173$	−489.106	+	847.157i	−0.214948	+	0.372301i	−0.953257	−	0.302162i	$-0.902292\pi$
$173$	−489.106	+	847.157i	−0.214948	+	0.372301i	0.738308	+	0.674463i	$0.235625\pi$
$174$		0			0
$175$	−418.657	+	725.134i	−0.180843	+	0.313229i
$176$		0			0
$177$	−983.377			−0.417599
$178$		0			0
$179$	926.471	+	1604.69i	0.386858	+	0.670058i	0.992025	−	0.126040i	$-0.0402269\pi$
$179$	926.471	+	1604.69i	0.386858	+	0.670058i	−0.605167	+	0.796099i	$0.706894\pi$
$180$		0			0
$181$	852.777			0.350201			0.175101	−	0.984551i	$-0.443975\pi$
$181$	852.777			0.350201			0.175101	+	0.984551i	$0.443975\pi$
$182$		0			0
$183$	−295.254			−0.119267
$184$		0			0
$185$	159.702	+	276.612i	0.0634676	+	0.109929i
$186$		0			0
$187$	2264.71			0.885627
$188$		0			0
$189$	404.185	−	700.068i	0.155556	−	0.269431i
$190$		0			0
$191$	2220.65	−	3846.27i	0.841258	−	1.45710i	−0.0475730	−	0.998868i	$-0.515149\pi$
$191$	2220.65	−	3846.27i	0.841258	−	1.45710i	0.888831	−	0.458234i	$-0.151518\pi$
$192$		0			0
$193$	1241.21	+	2149.85i	0.462925	+	0.801810i	0.999105	−	0.0422935i	$-0.0134665\pi$
$193$	1241.21	+	2149.85i	0.462925	+	0.801810i	−0.536180	+	0.844104i	$0.680133\pi$
$194$		0			0
$195$	−1250.64	+	595.440i	−0.459281	+	0.218669i
$196$		0			0
$197$	−630.115	−	1091.39i	−0.227888	−	0.394713i	0.729294	−	0.684200i	$-0.239849\pi$
$197$	−630.115	−	1091.39i	−0.227888	−	0.394713i	−0.957182	+	0.289487i	$0.906515\pi$
$198$		0			0
$199$	−2760.48	+	4781.30i	−0.983344	+	1.70320i	−0.334266	+	0.942479i	$0.608489\pi$
$199$	−2760.48	+	4781.30i	−0.983344	+	1.70320i	−0.649077	+	0.760722i	$0.724845\pi$
$200$		0			0
$201$	−661.726	+	1146.14i	−0.232212	+	0.402202i
$202$		0			0
$203$	5836.60			2.01798
$204$		0			0
$205$	1191.06	+	2062.97i	0.405790	+	0.702849i
$206$		0			0
$207$	−1176.27			−0.394960
$208$		0			0
$209$	5645.18			1.86835
$210$		0			0
$211$	−2263.90	−	3921.18i	−0.738640	−	1.27936i	−0.953108	−	0.302631i	$-0.902135\pi$
$211$	−2263.90	−	3921.18i	−0.738640	−	1.27936i	0.214468	−	0.976731i	$-0.431198\pi$
$212$		0			0
$213$	−1035.15			−0.332991
$214$		0			0
$215$	474.839	−	822.446i	0.150622	−	0.260885i
$216$		0			0
$217$	479.217	−	830.029i	0.149914	−	0.259659i
$218$		0			0
$219$	−1160.76	−	2010.49i	−0.358159	−	0.620349i
$220$		0			0
$221$	−1863.37	−	1282.60i	−0.567168	−	0.390393i
$222$		0			0
$223$	2240.59	+	3880.81i	0.672829	+	1.16537i	0.977099	+	0.212787i	$0.0682542\pi$
$223$	2240.59	+	3880.81i	0.672829	+	1.16537i	−0.304270	+	0.952586i	$0.598412\pi$
$224$		0			0
$225$	125.850	−	217.979i	0.0372890	−	0.0645864i
$226$		0			0
$227$	−2879.88	+	4988.09i	−0.842044	+	1.45846i	0.0461191	+	0.998936i	$0.485315\pi$
$227$	−2879.88	+	4988.09i	−0.842044	+	1.45846i	−0.888163	+	0.459528i	$0.848019\pi$
$228$		0			0
$229$	−4635.08			−1.33753			−0.668766	−	0.743473i	$-0.733177\pi$
$229$	−4635.08			−1.33753			−0.668766	+	0.743473i	$0.733177\pi$
$230$		0			0
$231$	−2107.41	−	3650.14i	−0.600248	−	1.03966i
$232$		0			0
$233$	5886.33			1.65505			0.827524	−	0.561431i	$-0.189749\pi$
$233$	5886.33			1.65505			0.827524	+	0.561431i	$0.189749\pi$
$234$		0			0
$235$	−5309.59			−1.47387
$236$		0			0
$237$	−225.498	−	390.574i	−0.0618046	−	0.107049i
$238$		0			0
$239$	−2135.84			−0.578060			−0.289030	−	0.957320i	$-0.593333\pi$
$239$	−2135.84			−0.578060			−0.289030	+	0.957320i	$0.593333\pi$
$240$		0			0
$241$	−2346.46	+	4064.19i	−0.627173	+	1.08630i	0.360943	+	0.932588i	$0.382455\pi$
$241$	−2346.46	+	4064.19i	−0.627173	+	1.08630i	−0.988116	+	0.153708i	$0.950879\pi$
$242$		0			0
$243$	−121.500	+	210.444i	−0.0320750	+	0.0555556i
$244$		0			0
$245$	−2725.55	−	4720.79i	−0.710730	−	1.23102i
$246$		0			0
$247$	−4644.77	−	3197.09i	−1.19652	−	0.823587i
$248$		0			0
$249$	506.949	+	878.062i	0.129022	+	0.223473i
$250$		0			0
$251$	−1951.44	+	3379.99i	−0.490732	+	0.849973i	−0.999943	−	0.0106687i	$-0.996604\pi$
$251$	−1951.44	+	3379.99i	−0.490732	+	0.849973i	0.509211	+	0.860642i	$0.329937\pi$
$252$		0			0
$253$	−3066.53	+	5311.38i	−0.762020	+	1.31986i
$254$		0			0
$255$	−1426.21			−0.350246
$256$		0			0
$257$	2065.42	+	3577.40i	0.501312	+	0.868297i	0.999999	+	0.00151510i	$0.000482272\pi$
$257$	2065.42	+	3577.40i	0.501312	+	0.868297i	−0.498687	+	0.866782i	$0.666184\pi$
$258$		0			0
$259$	970.790			0.232903
$260$		0			0
$261$	−1754.51			−0.416098
$262$		0			0
$263$	3176.09	+	5501.14i	0.744661	+	1.28979i	0.950353	+	0.311174i	$0.100722\pi$
$263$	3176.09	+	5501.14i	0.744661	+	1.28979i	−0.205692	+	0.978617i	$0.565944\pi$
$264$		0			0
$265$	−1500.01			−0.347716
$266$		0			0
$267$	−254.870	+	441.448i	−0.0584187	+	0.101184i
$268$		0			0
$269$	−90.7619	+	157.204i	−0.0205719	+	0.0356316i	−0.876128	−	0.482078i	$-0.839882\pi$
$269$	−90.7619	+	157.204i	−0.0205719	+	0.0356316i	0.855556	+	0.517710i	$0.173215\pi$
$270$		0			0
$271$	1730.18	+	2996.75i	0.387825	+	0.671733i	0.992157	−	0.125000i	$-0.0398930\pi$
$271$	1730.18	+	2996.75i	0.387825	+	0.671733i	−0.604331	+	0.796733i	$0.706560\pi$
$272$		0			0
$273$	−333.273	+	4196.79i	−0.0738849	+	0.930408i
$274$		0			0
$275$	−656.180	−	1136.54i	−0.143888	−	0.249221i
$276$		0			0
$277$	3218.97	−	5575.42i	0.698228	−	1.20937i	−0.270853	−	0.962621i	$-0.587306\pi$
$277$	3218.97	−	5575.42i	0.698228	−	1.20937i	0.969080	−	0.246745i	$-0.0793611\pi$
$278$		0			0
$279$	−144.055	+	249.511i	−0.0309117	+	0.0535406i
$280$		0			0
$281$	−2974.26			−0.631421			−0.315711	−	0.948855i	$-0.602243\pi$
$281$	−2974.26			−0.631421			−0.315711	+	0.948855i	$0.602243\pi$
$282$		0			0
$283$	1517.86	+	2629.01i	0.318825	+	0.552221i	0.980243	−	0.197797i	$-0.0633785\pi$
$283$	1517.86	+	2629.01i	0.318825	+	0.552221i	−0.661418	+	0.750017i	$0.730045\pi$
$284$		0			0
$285$	−3555.07			−0.738891
$286$		0			0
$287$	7240.15			1.48910
$288$		0			0
$289$	1291.91	+	2237.65i	0.262957	+	0.455455i
$290$		0			0
$291$	642.604			0.129451
$292$		0			0
$293$	977.872	−	1693.72i	0.194976	−	0.337708i	−0.751917	−	0.659258i	$-0.770871\pi$
$293$	977.872	−	1693.72i	0.194976	−	0.337708i	0.946893	+	0.321550i	$0.104204\pi$
$294$		0			0
$295$	1614.47	−	2796.34i	0.318637	−	0.551895i
$296$		0			0
$297$	633.498	+	1097.25i	0.123769	+	0.214373i
$298$		0			0
$299$	5531.15	−	2633.43i	1.06981	−	0.509349i
$300$		0			0
$301$	−1443.22	−	2499.73i	−0.276365	−	0.478678i
$302$		0			0
$303$	−2392.67	+	4144.22i	−0.453648	+	0.785741i
$304$		0			0
$305$	484.735	−	839.586i	0.0910029	−	0.157622i
$306$		0			0
$307$	1027.56			0.191029			0.0955147	−	0.995428i	$-0.469550\pi$
$307$	1027.56			0.191029			0.0955147	+	0.995428i	$0.469550\pi$
$308$		0			0
$309$	−2355.44	−	4079.75i	−0.433646	−	0.751096i
$310$		0			0
$311$	−3405.61			−0.620947			−0.310474	−	0.950582i	$-0.600488\pi$
$311$	−3405.61			−0.620947			−0.310474	+	0.950582i	$0.600488\pi$
$312$		0			0
$313$	4813.20			0.869196			0.434598	−	0.900625i	$-0.356890\pi$
$313$	4813.20			0.869196			0.434598	+	0.900625i	$0.356890\pi$
$314$		0			0
$315$	1327.15	+	2298.69i	0.237385	+	0.411163i
$316$		0			0
$317$	1141.33			0.202219			0.101110	−	0.994875i	$-0.467761\pi$
$317$	1141.33			0.202219			0.101110	+	0.994875i	$0.467761\pi$
$318$		0			0
$319$	−4573.99	+	7922.38i	−0.802803	+	1.39050i
$320$		0			0
$321$	−10.0995	+	17.4929i	−0.00175608	+	0.00304161i
$322$		0			0
$323$	−2902.94	−	5028.04i	−0.500074	−	0.866154i
$324$		0			0
$325$	−103.771	+	1306.75i	−0.0177113	+	0.223032i
$326$		0			0
$327$	813.633	+	1409.25i	0.137596	+	0.238324i
$328$		0			0
$329$	−8068.94	+	13975.8i	−1.35214	+	2.34198i
$330$		0			0
$331$	3826.28	−	6627.32i	0.635382	−	1.10051i	−0.351052	−	0.936356i	$-0.614176\pi$
$331$	3826.28	−	6627.32i	0.635382	−	1.10051i	0.986434	−	0.164158i	$-0.0524908\pi$
$332$		0			0
$333$	−291.825			−0.0480237
$334$		0			0
$335$	−2172.79	−	3763.38i	−0.354364	−	0.613777i
$336$		0			0
$337$	−2503.69			−0.404702			−0.202351	−	0.979313i	$-0.564858\pi$
$337$	−2503.69			−0.404702			−0.202351	+	0.979313i	$0.564858\pi$
$338$		0			0
$339$	−4328.47			−0.693481
$340$		0			0
$341$	751.100	+	1300.94i	0.119280	+	0.206598i
$342$		0			0
$343$	−6298.69			−0.991537
$344$		0			0
$345$	1931.16	−	3344.86i	0.301362	−	0.521975i
$346$		0			0
$347$	2248.06	−	3893.75i	0.347787	−	0.602385i	−0.638069	−	0.769979i	$-0.720267\pi$
$347$	2248.06	−	3893.75i	0.347787	−	0.602385i	0.985856	+	0.167594i	$0.0535999\pi$
$348$		0			0
$349$	−1788.81	−	3098.31i	−0.274363	−	0.475211i	0.695611	−	0.718418i	$-0.255134\pi$
$349$	−1788.81	−	3098.31i	−0.274363	−	0.475211i	−0.969974	+	0.243208i	$0.921800\pi$
$350$		0			0
$351$	100.183	−	1261.58i	0.0152348	−	0.191846i
$352$		0			0
$353$	4022.58	+	6967.32i	0.606517	+	1.05052i	0.991810	+	0.127724i	$0.0407672\pi$
$353$	4022.58	+	6967.32i	0.606517	+	1.05052i	−0.385293	+	0.922794i	$0.625900\pi$
$354$		0			0
$355$	1699.46	−	2943.55i	0.254079	−	0.440077i
$356$		0			0
$357$	−2167.40	+	3754.05i	−0.321319	+	0.556542i
$358$		0			0
$359$	2172.90			0.319447			0.159724	−	0.987162i	$-0.448940\pi$
$359$	2172.90			0.319447			0.159724	+	0.987162i	$0.448940\pi$
$360$		0			0
$361$	−3806.57	−	6593.17i	−0.554974	−	0.961244i
$362$		0			0
$363$	2613.08			0.377826
$364$		0			0
$365$	7622.74			1.09313
$366$		0			0
$367$	3831.38	+	6636.15i	0.544949	+	0.943880i	0.998610	+	0.0527056i	$0.0167845\pi$
$367$	3831.38	+	6636.15i	0.544949	+	0.943880i	−0.453661	+	0.891175i	$0.649882\pi$
$368$		0			0
$369$	−2176.43			−0.307047
$370$		0			0
$371$	−2279.55	+	3948.30i	−0.318998	+	0.552521i
$372$		0			0
$373$	−5271.27	+	9130.10i	−0.731732	+	1.26740i	0.224411	+	0.974495i	$0.427954\pi$
$373$	−5271.27	+	9130.10i	−0.731732	+	1.26740i	−0.956143	+	0.292902i	$0.905379\pi$
$374$		0			0
$375$	2260.21	+	3914.80i	0.311244	+	0.539091i
$376$		0			0
$377$	8250.17	−	3927.99i	1.12707	−	0.536610i
$378$		0			0
$379$	2737.77	+	4741.96i	0.371055	+	0.642686i	0.989728	−	0.142962i	$-0.0456628\pi$
$379$	2737.77	+	4741.96i	0.371055	+	0.642686i	−0.618673	+	0.785648i	$0.712329\pi$
$380$		0			0
$381$	−3739.26	+	6476.59i	−0.502803	+	0.870881i
$382$		0			0
$383$	404.042	−	699.822i	0.0539050	−	0.0933661i	−0.837814	−	0.545956i	$-0.816167\pi$
$383$	404.042	−	699.822i	0.0539050	−	0.0933661i	0.891719	+	0.452590i	$0.149500\pi$
$384$		0			0
$385$	13839.4			1.83200
$386$		0			0
$387$	433.839	+	751.432i	0.0569852	+	0.0987013i
$388$		0			0
$389$	−7060.26			−0.920230			−0.460115	−	0.887859i	$-0.652192\pi$
$389$	−7060.26			−0.920230			−0.460115	+	0.887859i	$0.652192\pi$
$390$		0			0
$391$	6307.65			0.815836
$392$		0			0
$393$	1116.84	+	1934.43i	0.143352	+	0.248292i
$394$		0			0
$395$	1480.85			0.188633
$396$		0			0
$397$	709.947	−	1229.66i	0.0897511	−	0.155453i	−0.817655	−	0.575709i	$-0.804726\pi$
$397$	709.947	−	1229.66i	0.0897511	−	0.155453i	0.907406	+	0.420255i	$0.138060\pi$
$398$		0			0
$399$	−5402.61	+	9357.60i	−0.677867	+	1.17410i
$400$		0			0
$401$	−5335.37	−	9241.13i	−0.664428	−	1.15082i	−0.979440	−	0.201735i	$-0.935342\pi$
$401$	−5335.37	−	9241.13i	−0.664428	−	1.15082i	0.315012	−	0.949088i	$-0.397991\pi$
$402$		0			0
$403$	118.782	−	1495.78i	0.0146822	−	0.184888i
$404$		0			0
$405$	−398.947	−	690.997i	−0.0489478	−	0.0847800i
$406$		0			0
$407$	−760.782	+	1317.71i	−0.0926550	+	0.160483i
$408$		0			0
$409$	−3175.78	+	5500.61i	−0.383942	+	0.665007i	−0.991622	−	0.129175i	$-0.958767\pi$
$409$	−3175.78	+	5500.61i	−0.383942	+	0.665007i	0.607680	+	0.794182i	$0.292100\pi$
$410$		0			0
$411$	−666.500			−0.0799903
$412$		0			0
$413$	−4906.98	−	8499.15i	−0.584641	−	1.01263i
$414$		0			0
$415$	−3329.15			−0.393787
$416$		0			0
$417$	2331.44			0.273791
$418$		0			0
$419$	2808.94	+	4865.22i	0.327507	+	0.567259i	0.982017	−	0.188795i	$-0.0604581\pi$
$419$	2808.94	+	4865.22i	0.327507	+	0.567259i	−0.654509	+	0.756054i	$0.727125\pi$
$420$		0			0
$421$	−1518.29			−0.175765			−0.0878825	−	0.996131i	$-0.528010\pi$
$421$	−1518.29			−0.175765			−0.0878825	+	0.996131i	$0.528010\pi$
$422$		0			0
$423$	2425.57	−	4201.20i	0.278806	−	0.482907i
$424$		0			0
$425$	−674.860	+	1168.89i	−0.0770248	+	0.133411i
$426$		0			0
$427$	−1473.30	−	2551.83i	−0.166974	−	0.289207i
$428$		0			0
$429$	−5435.39	−	3741.28i	−0.611709	−	0.421051i
$430$		0			0
$431$	−2485.07	−	4304.26i	−0.277730	−	0.481042i	0.693091	−	0.720850i	$-0.256249\pi$
$431$	−2485.07	−	4304.26i	−0.277730	−	0.481042i	−0.970820	+	0.239809i	$0.922915\pi$
$432$		0			0
$433$	1649.36	−	2856.77i	0.183055	−	0.317061i	−0.759864	−	0.650082i	$-0.774735\pi$
$433$	1649.36	−	2856.77i	0.183055	−	0.317061i	0.942919	+	0.333021i	$0.108068\pi$
$434$		0			0
$435$	2880.48	−	4989.14i	0.317491	−	0.549911i
$436$		0			0
$437$	15722.9			1.72112
$438$		0			0
$439$	−3024.24	−	5238.13i	−0.328790	−	0.569481i	0.653482	−	0.756942i	$-0.273308\pi$
$439$	−3024.24	−	5238.13i	−0.328790	−	0.569481i	−0.982272	+	0.187461i	$0.939974\pi$
$440$		0			0
$441$	4980.42			0.537784
$442$		0			0
$443$	−6822.62			−0.731722			−0.365861	−	0.930670i	$-0.619225\pi$
$443$	−6822.62			−0.731722			−0.365861	+	0.930670i	$0.619225\pi$
$444$		0			0
$445$	−836.869	−	1449.50i	−0.0891493	−	0.154411i
$446$		0			0
$447$	5334.88			0.564500
$448$		0			0
$449$	−205.205	+	355.426i	−0.0215684	+	0.0373576i	−0.876608	−	0.481205i	$-0.840199\pi$
$449$	−205.205	+	355.426i	−0.0215684	+	0.0373576i	0.855040	+	0.518563i	$0.173533\pi$
$450$		0			0
$451$	−5673.91	+	9827.51i	−0.592404	+	1.02607i
$452$		0			0
$453$	1749.00	+	3029.35i	0.181402	+	0.314197i
$454$		0			0
$455$	−11386.9	−	7837.81i	−1.17324	−	0.807565i
$456$		0			0
$457$	8321.41	+	14413.1i	0.851771	+	1.47531i	0.879609	+	0.475697i	$0.157804\pi$
$457$	8321.41	+	14413.1i	0.851771	+	1.47531i	−0.0278385	+	0.999612i	$0.508862\pi$
$458$		0			0
$459$	651.532	−	1128.49i	0.0662547	−	0.114757i
$460$		0			0
$461$	5864.85	−	10158.2i	0.592523	−	1.02628i	−0.401368	−	0.915917i	$-0.631465\pi$
$461$	5864.85	−	10158.2i	0.592523	−	1.02628i	0.993891	−	0.110364i	$-0.0352015\pi$
$462$		0			0
$463$	3564.93			0.357832			0.178916	−	0.983864i	$-0.442741\pi$
$463$	3564.93			0.357832			0.178916	+	0.983864i	$0.442741\pi$
$464$		0			0
$465$	−473.008	−	819.273i	−0.0471725	−	0.0817051i
$466$		0			0
$467$	−1134.81			−0.112447			−0.0562233	−	0.998418i	$-0.517906\pi$
$467$	−1134.81			−0.112447			−0.0562233	+	0.998418i	$0.517906\pi$
$468$		0			0
$469$	−13207.9			−1.30039
$470$		0			0
$471$	−776.441	−	1344.84i	−0.0759587	−	0.131564i
$472$		0			0
$473$	4524.05			0.439780
$474$		0			0
$475$	−1682.20	+	2913.66i	−0.162494	+	0.281448i
$476$		0			0
$477$	685.245	−	1186.88i	0.0657761	−	0.113928i
$478$		0			0
$479$	−9686.30	−	16777.2i	−0.923963	−	1.60035i	−0.793220	−	0.608935i	$-0.791597\pi$
$479$	−9686.30	−	16777.2i	−0.923963	−	1.60035i	−0.130743	−	0.991416i	$-0.541736\pi$
$480$		0			0
$481$	1372.24	−	653.335i	0.130080	−	0.0619325i
$482$		0			0
$483$	−5869.53	−	10166.3i	−0.552946	−	0.957730i
$484$		0			0
$485$	−1055.00	+	1827.31i	−0.0987733	+	0.171080i
$486$		0			0
$487$	−4522.98	+	7834.02i	−0.420853	+	0.728939i	−0.996023	−	0.0890946i	$-0.971603\pi$
$487$	−4522.98	+	7834.02i	−0.420853	+	0.728939i	0.575170	+	0.818034i	$0.304936\pi$
$488$		0			0
$489$	−1830.56			−0.169286
$490$		0			0
$491$	7201.66	+	12473.6i	0.661927	+	1.14649i	0.980109	+	0.198462i	$0.0635947\pi$
$491$	7201.66	+	12473.6i	0.661927	+	1.14649i	−0.318181	+	0.948030i	$0.603072\pi$
$492$		0			0
$493$	9408.40			0.859499
$494$		0			0
$495$	−4160.20			−0.377751
$496$		0			0
$497$	−5165.31	−	8946.58i	−0.466189	−	0.807463i
$498$		0			0
$499$	9319.75			0.836091			0.418045	−	0.908426i	$-0.362715\pi$
$499$	9319.75			0.836091			0.418045	+	0.908426i	$0.362715\pi$
$500$		0			0
$501$	4474.52	−	7750.09i	0.399015	−	0.691115i
$502$		0			0
$503$	1372.99	−	2378.09i	0.121707	−	0.210802i	−0.798734	−	0.601684i	$-0.794497\pi$
$503$	1372.99	−	2378.09i	0.121707	−	0.210802i	0.920441	+	0.390882i	$0.127830\pi$
$504$		0			0
$505$	−7856.37	−	13607.6i	−0.692285	−	1.19907i
$506$		0			0
$507$	2353.32	+	6156.55i	0.206143	+	0.539294i
$508$		0			0
$509$	591.055	+	1023.74i	0.0514697	+	0.0891481i	0.890612	−	0.454763i	$-0.150276\pi$
$509$	591.055	+	1023.74i	0.0514697	+	0.0891481i	−0.839143	+	0.543911i	$0.816943\pi$
$510$		0			0
$511$	11584.2	−	20064.5i	1.00285	−	1.73698i
$512$		0			0
$513$	1624.05	−	2812.94i	0.139773	−	0.242094i
$514$		0			0
$515$	15468.3			1.32352
$516$		0			0
$517$	−12646.8	−	21905.0i	−1.07584	−	1.86340i
$518$		0			0
$519$	2934.64			0.248201
$520$		0			0
$521$	10858.8			0.913115			0.456558	−	0.889694i	$-0.349082\pi$
$521$	10858.8			0.913115			0.456558	+	0.889694i	$0.349082\pi$
$522$		0			0
$523$	−5080.87	−	8800.33i	−0.424801	−	0.735777i	0.571601	−	0.820532i	$-0.306323\pi$
$523$	−5080.87	−	8800.33i	−0.424801	−	0.735777i	−0.996402	+	0.0847546i	$0.972989\pi$
$524$		0			0
$525$	2511.94			0.208819
$526$		0			0
$527$	772.482	−	1337.98i	0.0638517	−	0.110594i
$528$		0			0
$529$	−2457.36	+	4256.28i	−0.201970	+	0.349821i
$530$		0			0
$531$	1475.06	+	2554.89i	0.120551	+	0.208800i
$532$		0			0
$533$	10234.1	−	4872.57i	0.831687	−	0.395975i
$534$		0			0
$535$	−33.1620	−	57.4382i	−0.00267984	−	0.00464162i
$536$		0			0
$537$	2779.41	−	4814.08i	0.223353	−	0.386858i
$538$		0			0
$539$	12983.9	−	22488.7i	1.03758	−	1.79714i
$540$		0			0
$541$	−9573.04			−0.760771			−0.380386	−	0.924828i	$-0.624209\pi$
$541$	−9573.04			−0.760771			−0.380386	+	0.924828i	$0.624209\pi$
$542$		0			0
$543$	−1279.16	−	2215.58i	−0.101094	−	0.175101i
$544$		0			0
$545$	−5343.15			−0.419955
$546$		0			0
$547$	−15958.9			−1.24745			−0.623724	−	0.781645i	$-0.714381\pi$
$547$	−15958.9			−1.24745			−0.623724	+	0.781645i	$0.714381\pi$
$548$		0			0
$549$	442.881	+	767.092i	0.0344293	+	0.0596333i
$550$		0			0
$551$	23452.0			1.81323
$552$		0			0
$553$	2250.44	−	3897.88i	0.173053	−	0.299737i
$554$		0			0
$555$	479.105	−	829.835i	0.0366430	−	0.0634676i
$556$		0			0
$557$	1072.55	+	1857.70i	0.0815892	+	0.141317i	0.903933	−	0.427675i	$-0.140667\pi$
$557$	1072.55	+	1857.70i	0.0815892	+	0.141317i	−0.822344	+	0.568991i	$0.807334\pi$
$558$		0			0
$559$	−3722.33	−	2562.15i	−0.281642	−	0.193859i
$560$		0			0
$561$	−3397.07	−	5883.90i	−0.255658	−	0.442813i
$562$		0			0
$563$	−11159.3	+	19328.5i	−0.835362	+	1.44689i	0.0583740	+	0.998295i	$0.481408\pi$
$563$	−11159.3	+	19328.5i	−0.835362	+	1.44689i	−0.893736	+	0.448594i	$0.851925\pi$
$564$		0			0
$565$	7106.29	−	12308.5i	0.529140	−	0.916497i
$566$		0			0
$567$	−2425.11			−0.179621
$568$		0			0
$569$	9876.51	+	17106.6i	0.727671	+	1.26036i	0.957865	+	0.287218i	$0.0927304\pi$
$569$	9876.51	+	17106.6i	0.727671	+	1.26036i	−0.230194	+	0.973145i	$0.573936\pi$
$570$		0			0
$571$	10640.6			0.779850			0.389925	−	0.920847i	$-0.372501\pi$
$571$	10640.6			0.779850			0.389925	+	0.920847i	$0.372501\pi$
$572$		0			0
$573$	−13323.9			−0.971401
$574$		0			0
$575$	−1827.59	−	3165.47i	−0.132549	−	0.229581i
$576$		0			0
$577$	6547.89			0.472430			0.236215	−	0.971701i	$-0.424093\pi$
$577$	6547.89			0.472430			0.236215	+	0.971701i	$0.424093\pi$
$578$		0			0
$579$	3723.64	−	6449.54i	0.267270	−	0.462925i
$580$		0			0
$581$	−5059.29	+	8762.94i	−0.361264	+	0.625728i
$582$		0			0
$583$	−3572.85	−	6188.35i	−0.253812	−	0.439615i
$584$		0			0
$585$	3422.95	+	2356.09i	0.241917	+	0.166517i
$586$		0			0
$587$	2950.17	+	5109.84i	0.207439	+	0.359294i	0.950907	−	0.309477i	$-0.100154\pi$
$587$	2950.17	+	5109.84i	0.207439	+	0.359294i	−0.743468	+	0.668771i	$0.766821\pi$
$588$		0			0
$589$	1925.54	−	3335.14i	0.134704	−	0.233314i
$590$		0			0
$591$	−1890.35	+	3274.18i	−0.131571	+	0.227888i
$592$		0			0
$593$	−15261.5			−1.05686			−0.528428	−	0.848978i	$-0.677218\pi$
$593$	−15261.5			−1.05686			−0.528428	+	0.848978i	$0.677218\pi$
$594$		0			0
$595$	−7116.70	−	12326.5i	−0.490346	−	0.849305i
$596$		0			0
$597$	16562.9			1.13547
$598$		0			0
$599$	18900.6			1.28925			0.644623	−	0.764501i	$-0.277014\pi$
$599$	18900.6			1.28925			0.644623	+	0.764501i	$0.277014\pi$
$600$		0			0
$601$	9253.48	+	16027.5i	0.628049	+	1.08781i	0.987943	+	0.154819i	$0.0494794\pi$
$601$	9253.48	+	16027.5i	0.628049	+	1.08781i	−0.359894	+	0.932993i	$0.617187\pi$
$602$		0			0
$603$	3970.36			0.268135
$604$		0			0
$605$	−4290.04	+	7430.56i	−0.288289	+	0.499331i
$606$		0			0
$607$	−3204.25	+	5549.92i	−0.214261	+	0.371111i	−0.953044	−	0.302833i	$-0.902068\pi$
$607$	−3204.25	+	5549.92i	−0.214261	+	0.371111i	0.738783	+	0.673944i	$0.235401\pi$
$608$		0			0
$609$	−8754.90	−	15163.9i	−0.582539	−	1.00899i
$610$		0			0
$611$	−2000.01	+	25185.5i	−0.132425	+	1.66759i
$612$		0			0
$613$	1753.63	+	3037.38i	0.115544	+	0.200128i	0.917997	−	0.396587i	$-0.129806\pi$
$613$	1753.63	+	3037.38i	0.115544	+	0.200128i	−0.802453	+	0.596715i	$0.796472\pi$
$614$		0			0
$615$	3573.17	−	6188.91i	0.234283	−	0.405790i
$616$		0			0
$617$	−7253.89	+	12564.1i	−0.473307	+	0.819792i	−0.999533	−	0.0305526i	$-0.990273\pi$
$617$	−7253.89	+	12564.1i	−0.473307	+	0.819792i	0.526226	+	0.850345i	$0.323607\pi$
$618$		0			0
$619$	−4750.85			−0.308486			−0.154243	−	0.988033i	$-0.549294\pi$
$619$	−4750.85			−0.308486			−0.154243	+	0.988033i	$0.549294\pi$
$620$		0			0
$621$	1764.41	+	3056.05i	0.114015	+	0.197480i
$622$		0			0
$623$	−5087.14			−0.327146
$624$		0			0
$625$	−11347.0			−0.726209
$626$		0			0
$627$	−8467.76	−	14666.6i	−0.539346	−	0.934175i
$628$		0			0
$629$	1564.88			0.0991986
$630$		0			0
$631$	2412.60	−	4178.74i	0.152209	−	0.263634i	−0.779830	−	0.625991i	$-0.784695\pi$
$631$	2412.60	−	4178.74i	0.152209	−	0.263634i	0.932039	+	0.362357i	$0.118028\pi$
$632$		0			0
$633$	−6791.69	+	11763.5i	−0.426454	+	0.738640i
$634$		0			0
$635$	−12277.9	−	21266.0i	−0.767298	−	1.32900i
$636$		0			0
$637$	−23419.2	+	11150.1i	−1.45668	+	0.693539i
$638$		0			0
$639$	1552.72	+	2689.39i	0.0961262	+	0.166495i
$640$		0			0
$641$	2955.95	−	5119.85i	0.182142	−	0.315479i	−0.760468	−	0.649376i	$-0.775030\pi$
$641$	2955.95	−	5119.85i	0.182142	−	0.315479i	0.942610	+	0.333897i	$0.108364\pi$
$642$		0			0
$643$	11704.1	−	20272.2i	0.717833	−	1.24332i	−0.244024	−	0.969769i	$-0.578468\pi$
$643$	11704.1	−	20272.2i	0.717833	−	1.24332i	0.961857	−	0.273554i	$-0.0881991\pi$
$644$		0			0
$645$	−2849.04			−0.173924
$646$		0			0
$647$	−8199.33	−	14201.7i	−0.498221	−	0.862944i	0.501777	−	0.864997i	$-0.332680\pi$
$647$	−8199.33	−	14201.7i	−0.498221	−	0.862944i	−0.999998	+	0.00205298i	$0.999347\pi$
$648$		0			0
$649$	15381.9			0.930342
$650$		0			0
$651$	−2875.30			−0.173106
$652$		0			0
$653$	−13764.8	−	23841.3i	−0.824897	−	1.42876i	−0.901998	−	0.431741i	$-0.857900\pi$
$653$	−13764.8	−	23841.3i	−0.824897	−	1.42876i	0.0771005	−	0.997023i	$-0.475434\pi$
$654$		0			0
$655$	−7334.34			−0.437521
$656$		0			0
$657$	−3482.28	+	6031.48i	−0.206783	+	0.358159i
$658$		0			0
$659$	−12089.9	+	20940.3i	−0.714650	+	1.23781i	0.248444	+	0.968646i	$0.420081\pi$
$659$	−12089.9	+	20940.3i	−0.714650	+	1.23781i	−0.963094	+	0.269164i	$0.913253\pi$
$660$		0			0
$661$	−2262.52	−	3918.80i	−0.133134	−	0.230595i	0.791749	−	0.610847i	$-0.209171\pi$
$661$	−2262.52	−	3918.80i	−0.133134	−	0.230595i	−0.924883	+	0.380251i	$0.875838\pi$
$662$		0			0
$663$	−537.224	+	6765.08i	−0.0314692	+	0.396281i
$664$		0			0
$665$	−17739.6	−	30725.8i	−1.03445	−	1.79172i
$666$		0			0
$667$	−12739.4	+	22065.3i	−0.739539	+	1.28092i
$668$		0			0
$669$	6721.76	−	11642.4i	0.388458	−	0.672829i
$670$		0			0
$671$	4618.34			0.265706
$672$		0			0
$673$	−1643.59	−	2846.78i	−0.0941393	−	0.163054i	0.815110	−	0.579307i	$-0.196677\pi$
$673$	−1643.59	−	2846.78i	−0.0941393	−	0.163054i	−0.909249	+	0.416253i	$0.863343\pi$
$674$		0			0
$675$	−755.102			−0.0430576
$676$		0			0
$677$	−9724.21			−0.552041			−0.276020	−	0.961152i	$-0.589016\pi$
$677$	−9724.21			−0.552041			−0.276020	+	0.961152i	$0.589016\pi$
$678$		0			0
$679$	3206.55	+	5553.91i	0.181231	+	0.313902i
$680$		0			0
$681$	17279.3			0.972309
$682$		0			0
$683$	7274.33	−	12599.5i	0.407532	−	0.705867i	−0.587080	−	0.809529i	$-0.699723\pi$
$683$	7274.33	−	12599.5i	0.407532	−	0.705867i	0.994613	+	0.103662i	$0.0330560\pi$
$684$		0			0
$685$	1094.23	−	1895.26i	0.0610342	−	0.105714i
$686$		0			0
$687$	6952.62	+	12042.3i	0.386112	+	0.668766i
$688$		0			0
$689$	−565.022	+	7115.13i	−0.0312418	+	0.393418i
$690$		0			0
$691$	3364.48	+	5827.45i	0.185226	+	0.320820i	0.943653	−	0.330938i	$-0.107365\pi$
$691$	3364.48	+	5827.45i	0.185226	+	0.320820i	−0.758427	+	0.651758i	$0.774032\pi$
$692$		0			0
$693$	−6322.22	+	10950.4i	−0.346553	+	0.600248i
$694$		0			0
$695$	−3827.65	+	6629.69i	−0.208908	+	0.361839i
$696$		0			0
$697$	11670.9			0.634241
$698$		0			0
$699$	−8829.49	−	15293.1i	−0.477771	−	0.827524i
$700$		0			0
$701$	−29159.8			−1.57111			−0.785557	−	0.618789i	$-0.787624\pi$
$701$	−29159.8			−1.57111			−0.785557	+	0.618789i	$0.787624\pi$
$702$		0			0
$703$	3900.73			0.209273
$704$		0			0
$705$	7964.39	+	13794.7i	0.425470	+	0.736935i
$706$		0			0
$707$	−47757.0			−2.54044
$708$		0			0
$709$	10244.5	−	17744.0i	0.542653	−	0.939903i	−0.456097	−	0.889930i	$-0.650753\pi$
$709$	10244.5	−	17744.0i	0.542653	−	0.939903i	0.998751	−	0.0499730i	$-0.0159135\pi$
$710$		0			0
$711$	−676.495	+	1171.72i	−0.0356829	+	0.0618046i
$712$		0			0
$713$	2091.96	+	3623.37i	0.109880	+	0.190318i
$714$		0			0
$715$	19562.3	−	9313.83i	1.02320	−	0.487157i
$716$		0			0
$717$	3203.77	+	5549.09i	0.166871	+	0.289030i
$718$		0			0
$719$	−8995.06	+	15579.9i	−0.466563	+	0.808111i	−0.999271	−	0.0381883i	$-0.987841\pi$
$719$	−8995.06	+	15579.9i	−0.466563	+	0.808111i	0.532707	+	0.846300i	$0.321175\pi$
$720$		0			0
$721$	23507.0	−	40715.3i	1.21421	−	2.10308i
$722$		0			0
$723$	14078.8			0.724197
$724$		0			0
$725$	−2726.00	−	4721.57i	−0.139643	−	0.241869i
$726$		0			0
$727$	37652.7			1.92086			0.960428	−	0.278528i	$-0.0898465\pi$
$727$	37652.7			1.92086			0.960428	+	0.278528i	$0.0898465\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	−2326.42	−	4029.48i	−0.117710	−	0.203879i
$732$		0			0
$733$	4524.26			0.227977			0.113989	−	0.993482i	$-0.463637\pi$
$733$	4524.26			0.227977			0.113989	+	0.993482i	$0.463637\pi$
$734$		0			0
$735$	−8176.64	+	14162.4i	−0.410340	+	0.710730i
$736$		0			0
$737$	10350.7	−	17927.9i	0.517329	−	0.896040i
$738$		0			0
$739$	409.151	+	708.671i	0.0203665	+	0.0352759i	0.876029	−	0.482258i	$-0.160183\pi$
$739$	409.151	+	708.671i	0.0203665	+	0.0352759i	−0.855663	+	0.517534i	$0.826850\pi$
$740$		0			0
$741$	−1339.12	+	16863.1i	−0.0663885	+	0.836008i
$742$		0			0
$743$	19501.1	+	33776.9i	0.962888	+	1.66777i	0.715185	+	0.698935i	$0.246342\pi$
$743$	19501.1	+	33776.9i	0.962888	+	1.66777i	0.247702	+	0.968836i	$0.420324\pi$
$744$		0			0
$745$	−8758.59	+	15170.3i	−0.430725	+	0.746037i
$746$		0			0
$747$	1520.85	−	2634.19i	0.0744912	−	0.129022i
$748$		0			0
$749$	−201.584			−0.00983407
$750$		0			0
$751$	−11188.8	−	19379.7i	−0.543658	−	0.941643i	−0.998690	−	0.0511678i	$-0.983706\pi$
$751$	−11188.8	−	19379.7i	−0.543658	−	0.941643i	0.455032	−	0.890475i	$-0.349628\pi$
$752$		0			0
$753$	11708.6			0.566649
$754$		0			0
$755$	−11485.7			−0.553653
$756$		0			0
$757$	17256.3	+	29888.8i	0.828521	+	1.43504i	0.899198	+	0.437542i	$0.144151\pi$
$757$	17256.3	+	29888.8i	0.828521	+	1.43504i	−0.0706770	+	0.997499i	$0.522516\pi$
$758$		0			0
$759$	18399.2			0.879905
$760$		0			0
$761$	−9987.78	+	17299.3i	−0.475764	+	0.824048i	−0.999615	−	0.0277624i	$-0.991162\pi$
$761$	−9987.78	+	17299.3i	−0.475764	+	0.824048i	0.523850	+	0.851810i	$0.324495\pi$
$762$		0			0
$763$	−8119.95	+	14064.2i	−0.385271	+	0.667309i
$764$		0			0
$765$	2139.32	+	3705.40i	0.101107	+	0.175123i
$766$		0			0
$767$	−12656.0	−	8711.38i	−0.595804	−	0.410104i
$768$		0			0
$769$	16532.4	+	28635.0i	0.775260	+	1.34279i	0.934648	+	0.355574i	$0.115715\pi$
$769$	16532.4	+	28635.0i	0.775260	+	1.34279i	−0.159388	+	0.987216i	$0.550952\pi$
$770$		0			0
$771$	6196.25	−	10732.2i	0.289432	−	0.501312i
$772$		0			0
$773$	9282.01	−	16076.9i	0.431890	−	0.748055i	−0.565146	−	0.824991i	$-0.691180\pi$
$773$	9282.01	−	16076.9i	0.431890	−	0.748055i	0.997036	+	0.0769359i	$0.0245137\pi$
$774$		0			0
$775$	−895.279			−0.0414960
$776$		0			0
$777$	−1456.19	−	2522.19i	−0.0672334	−	0.116452i
$778$		0			0
$779$	29091.6			1.33802
$780$		0			0
$781$	16191.7			0.741848
$782$		0			0
$783$	2631.77	+	4558.36i	0.120117	+	0.208049i
$784$		0			0
$785$	5098.91			0.231832
$786$		0			0
$787$	18218.4	−	31555.2i	0.825179	−	1.42925i	−0.0766032	−	0.997062i	$-0.524407\pi$
$787$	18218.4	−	31555.2i	0.825179	−	1.42925i	0.901782	−	0.432190i	$-0.142259\pi$
$788$		0			0
$789$	9528.26	−	16503.4i	0.429930	−	0.744661i
$790$		0			0
$791$	−21598.8	−	37410.2i	−0.970877	−	1.68161i
$792$		0			0
$793$	−3799.90	−	2615.55i	−0.170162	−	0.117126i
$794$		0			0
$795$	2250.01	+	3897.13i	0.100377	+	0.173858i
$796$		0			0
$797$	−6182.80	+	10708.9i	−0.274788	+	0.475947i	−0.970082	−	0.242779i	$-0.921941\pi$
$797$	−6182.80	+	10708.9i	−0.274788	+	0.475947i	0.695294	+	0.718726i	$0.255274\pi$
$798$		0			0
$799$	−13006.9	+	22528.6i	−0.575907	+	0.997501i
$800$		0			0
$801$	1529.22			0.0674561
$802$		0			0
$803$	18156.5	+	31448.0i	0.797918	+	1.38204i
$804$		0			0
$805$	38545.4			1.68763
$806$		0			0
$807$	544.571			0.0237544
$808$		0			0
$809$	4046.87	+	7009.39i	0.175872	+	0.304619i	0.940463	−	0.339897i	$-0.110392\pi$
$809$	4046.87	+	7009.39i	0.175872	+	0.304619i	−0.764591	+	0.644516i	$0.777059\pi$
$810$		0			0
$811$	−15984.7			−0.692105			−0.346052	−	0.938215i	$-0.612478\pi$
$811$	−15984.7			−0.692105			−0.346052	+	0.938215i	$0.612478\pi$
$812$		0			0
$813$	5190.53	−	8990.26i	0.223911	−	0.387825i
$814$		0			0
$815$	3005.34	−	5205.40i	0.129169	−	0.223727i
$816$		0			0
$817$	−5798.99	−	10044.2i	−0.248325	−	0.430111i
$818$		0			0
$819$	11403.5	−	5429.32i	0.486533	−	0.231643i
$820$		0			0
$821$	13430.9	+	23263.1i	0.570942	+	0.988900i	0.996470	+	0.0839550i	$0.0267552\pi$
$821$	13430.9	+	23263.1i	0.570942	+	0.988900i	−0.425528	+	0.904945i	$0.639911\pi$
$822$		0			0
$823$	−2602.97	+	4508.48i	−0.110248	+	0.190955i	−0.915870	−	0.401475i	$-0.868498\pi$
$823$	−2602.97	+	4508.48i	−0.110248	+	0.190955i	0.805622	+	0.592429i	$0.201831\pi$
$824$		0			0
$825$	−1968.54	+	3409.61i	−0.0830737	+	0.143888i
$826$		0			0
$827$	−46621.5			−1.96032			−0.980162	−	0.198200i	$-0.936491\pi$
$827$	−46621.5			−1.96032			−0.980162	+	0.198200i	$0.936491\pi$
$828$		0			0
$829$	20914.9	+	36225.6i	0.876241	+	1.51769i	0.855435	+	0.517910i	$0.173290\pi$
$829$	20914.9	+	36225.6i	0.876241	+	1.51769i	0.0208053	+	0.999784i	$0.493377\pi$
$830$		0			0
$831$	−19313.8			−0.806244
$832$		0			0
$833$	−26707.0			−1.11086
$834$		0			0
$835$	14692.1	+	25447.5i	0.608913	+	1.05467i
$836$		0			0
$837$	864.331			0.0356937
$838$		0			0
$839$	6342.54	−	10985.6i	0.260988	−	0.452044i	−0.705517	−	0.708693i	$-0.749285\pi$
$839$	6342.54	−	10985.6i	0.260988	−	0.452044i	0.966505	+	0.256649i	$0.0826185\pi$
$840$		0			0
$841$	−6807.43	+	11790.8i	−0.279119	+	0.483448i
$842$		0			0
$843$	4461.39	+	7727.35i	0.182276	+	0.315711i
$844$		0			0
$845$	−21370.4	−	3415.64i	−0.870017	−	0.139055i
$846$		0			0
$847$	13039.1	+	22584.3i	0.528959	+	0.916183i
$848$		0			0
$849$	4553.58	−	7887.03i	0.184074	−	0.318825i
$850$		0			0
$851$	−2118.92	+	3670.08i	−0.0853534	+	0.147836i
$852$		0			0
$853$	−37493.3			−1.50498			−0.752488	−	0.658606i	$-0.771146\pi$
$853$	−37493.3			−1.50498			−0.752488	+	0.658606i	$0.771146\pi$
$854$		0			0
$855$	5332.60	+	9236.34i	0.213300	+	0.369446i
$856$		0			0
$857$	−11826.3			−0.471386			−0.235693	−	0.971828i	$-0.575736\pi$
$857$	−11826.3			−0.471386			−0.235693	+	0.971828i	$0.575736\pi$
$858$		0			0
$859$	36498.7			1.44973			0.724866	−	0.688890i	$-0.241901\pi$
$859$	36498.7			1.44973			0.724866	+	0.688890i	$0.241901\pi$
$860$		0			0
$861$	−10860.2	−	18810.5i	−0.429867	−	0.744552i
$862$		0			0
$863$	−2292.79			−0.0904372			−0.0452186	−	0.998977i	$-0.514398\pi$
$863$	−2292.79			−0.0904372			−0.0452186	+	0.998977i	$0.514398\pi$
$864$		0			0
$865$	−4817.96	+	8344.95i	−0.189382	+	0.328020i
$866$		0			0
$867$	3875.72	−	6712.95i	0.151818	−	0.262957i
$868$		0			0
$869$	3527.22	+	6109.33i	0.137690	+	0.238487i
$870$		0			0
$871$	−18669.6	+	8888.81i	−0.726288	+	0.345793i
$872$		0			0
$873$	−963.906	−	1669.53i	−0.0373691	−	0.0647253i
$874$		0			0
$875$	−22556.6	+	39069.2i	−0.871488	+	1.50946i
$876$		0			0
$877$	10400.1	−	18013.6i	0.400442	−	0.693587i	−0.593337	−	0.804954i	$-0.702190\pi$
$877$	10400.1	−	18013.6i	0.400442	−	0.693587i	0.993779	+	0.111368i	$0.0355231\pi$
$878$		0			0
$879$	−5867.23			−0.225139
$880$		0			0
$881$	9627.95	+	16676.1i	0.368188	+	0.637721i	0.989282	−	0.146015i	$-0.0466448\pi$
$881$	9627.95	+	16676.1i	0.368188	+	0.637721i	−0.621094	+	0.783736i	$0.713311\pi$
$882$		0			0
$883$	−1744.49			−0.0664857			−0.0332429	−	0.999447i	$-0.510583\pi$
$883$	−1744.49			−0.0664857			−0.0332429	+	0.999447i	$0.510583\pi$
$884$		0			0
$885$	−9686.80			−0.367930
$886$		0			0
$887$	1485.35	+	2572.70i	0.0562268	+	0.0973877i	0.892769	−	0.450515i	$-0.148760\pi$
$887$	1485.35	+	2572.70i	0.0562268	+	0.0973877i	−0.836542	+	0.547903i	$0.815426\pi$
$888$		0			0
$889$	−74634.6			−2.81571
$890$		0			0
$891$	1900.49	−	3291.75i	0.0714578	−	0.123769i
$892$		0			0
$893$	−32421.8	+	56156.2i	−1.21495	+	2.10436i
$894$		0			0
$895$	9126.24	+	15807.1i	0.340845	+	0.590361i
$896$		0			0
$897$	−15138.6	−	10420.2i	−0.563503	−	0.387871i
$898$		0			0
$899$	3120.33	+	5404.57i	0.115761	+	0.200503i
$900$		0			0
$901$	−3674.56	+	6364.52i	−0.135868	+	0.235331i
$902$		0			0
$903$	−4329.66	+	7499.19i	−0.159559	+	0.276365i
$904$		0			0
$905$	8400.32			0.308548
$906$		0			0
$907$	16501.7	+	28581.7i	0.604111	+	1.04635i	0.992191	+	0.124726i	$0.0398051\pi$
$907$	16501.7	+	28581.7i	0.604111	+	1.04635i	−0.388080	+	0.921626i	$0.626862\pi$
$908$		0			0
$909$	14356.0			0.523827
$910$		0			0
$911$	−14977.0			−0.544686			−0.272343	−	0.962200i	$-0.587799\pi$
$911$	−14977.0			−0.544686			−0.272343	+	0.962200i	$0.587799\pi$
$912$		0			0
$913$	−7929.66	−	13734.6i	−0.287441	−	0.497862i
$914$		0			0
$915$	−2908.41			−0.105081
$916$		0			0
$917$	−11145.9	+	19305.3i	−0.401386	+	0.695221i
$918$		0			0
$919$	5712.69	−	9894.67i	0.205054	−	0.355163i	−0.745096	−	0.666957i	$-0.767596\pi$
$919$	5712.69	−	9894.67i	0.205054	−	0.355163i	0.950150	+	0.311794i	$0.100930\pi$
$920$		0			0
$921$	−1541.34	−	2669.68i	−0.0551455	−	0.0955147i
$922$		0			0
$923$	−13322.3	−	9169.99i	−0.475090	−	0.327014i
$924$		0			0
$925$	−453.410	−	785.329i	−0.0161168	−	0.0279151i
$926$		0			0
$927$	−7066.33	+	12239.2i	−0.250365	+	0.433646i
$928$		0			0
$929$	−5977.10	+	10352.6i	−0.211090	+	0.365618i	−0.952056	−	0.305924i	$-0.901035\pi$
$929$	−5977.10	+	10352.6i	−0.211090	+	0.365618i	0.740966	+	0.671542i	$0.234368\pi$
$930$		0			0
$931$	−66571.7			−2.34350
$932$		0			0
$933$	5108.42	+	8848.04i	0.179252	+	0.310474i
$934$		0			0
$935$	22308.7			0.780290
$936$		0			0
$937$	42546.4			1.48338			0.741692	−	0.670740i	$-0.234024\pi$
$937$	42546.4			1.48338			0.741692	+	0.670740i	$0.234024\pi$
$938$		0			0
$939$	−7219.81	−	12505.1i	−0.250915	−	0.434598i
$940$		0			0
$941$	20665.1			0.715903			0.357951	−	0.933740i	$-0.383475\pi$
$941$	20665.1			0.715903			0.357951	+	0.933740i	$0.383475\pi$
$942$		0			0
$943$	−15802.9	+	27371.5i	−0.545720	+	0.945215i
$944$		0			0
$945$	3981.44	−	6896.06i	0.137054	−	0.237385i
$946$		0			0
$947$	−4746.87	−	8221.81i	−0.162885	−	0.282126i	0.773017	−	0.634385i	$-0.218747\pi$
$947$	−4746.87	−	8221.81i	−0.162885	−	0.282126i	−0.935902	+	0.352260i	$0.885413\pi$
$948$		0			0
$949$	2871.33	−	36157.7i	0.0982163	−	1.23681i
$950$		0			0
$951$	−1711.99	−	2965.26i	−0.0583756	−	0.101110i
$952$		0			0
$953$	−26667.1	+	46188.7i	−0.906433	+	1.56999i	−0.0874512	+	0.996169i	$0.527872\pi$
$953$	−26667.1	+	46188.7i	−0.906433	+	1.56999i	−0.818982	+	0.573819i	$0.805461\pi$
$954$		0			0
$955$	21874.6	−	37887.9i	0.741199	−	1.28379i
$956$		0			0
$957$	27443.9			0.926997
$958$		0			0
$959$	−3325.79	−	5760.44i	−0.111987	−	0.193967i
$960$		0			0
$961$	−28766.2			−0.965601
$962$		0			0
$963$	60.5972			0.00202774
$964$		0			0
$965$	12226.6	+	21177.2i	0.407865	+	0.706443i
$966$		0			0
$967$	42110.1			1.40038			0.700191	−	0.713956i	$-0.253098\pi$
$967$	42110.1			1.40038			0.700191	+	0.713956i	$0.253098\pi$
$968$		0			0
$969$	−8708.83	+	15084.1i	−0.288718	+	0.500074i
$970$		0			0
$971$	−6913.86	+	11975.2i	−0.228503	+	0.395779i	−0.957365	−	0.288882i	$-0.906716\pi$
$971$	−6913.86	+	11975.2i	−0.228503	+	0.395779i	0.728862	+	0.684661i	$0.240050\pi$
$972$		0			0
$973$	11633.7	+	20150.2i	0.383309	+	0.663911i
$974$		0			0
$975$	3550.69	−	1690.52i	0.116629	−	0.0555281i
$976$		0			0
$977$	−566.943	−	981.973i	−0.0185651	−	0.0321557i	0.856594	−	0.515992i	$-0.172576\pi$
$977$	−566.943	−	981.973i	−0.0185651	−	0.0321557i	−0.875159	+	0.483836i	$0.839243\pi$
$978$		0			0
$979$	3986.65	−	6905.09i	0.130147	−	0.225421i
$980$		0			0
$981$	2440.90	−	4227.76i	0.0794413	−	0.137596i
$982$		0			0
$983$	−26250.2			−0.851729			−0.425865	−	0.904787i	$-0.640030\pi$
$983$	−26250.2			−0.851729			−0.425865	+	0.904787i	$0.640030\pi$
$984$		0			0
$985$	−6206.98	−	10750.8i	−0.200783	−	0.347766i
$986$		0			0
$987$	48413.7			1.56132
$988$		0			0
$989$	12600.3			0.405124
$990$		0			0
$991$	−14680.2	−	25426.8i	−0.470566	−	0.815045i	0.528867	−	0.848705i	$-0.322617\pi$
$991$	−14680.2	−	25426.8i	−0.470566	−	0.815045i	−0.999433	+	0.0336599i	$0.989284\pi$
$992$		0			0
$993$	−22957.7			−0.733676
$994$		0			0
$995$	−27192.3	+	47098.4i	−0.866384	+	1.50062i
$996$		0			0
$997$	−8417.95	+	14580.3i	−0.267401	+	0.463153i	−0.968190	−	0.250216i	$-0.919498\pi$
$997$	−8417.95	+	14580.3i	−0.267401	+	0.463153i	0.700789	+	0.713369i	$0.252832\pi$
$998$		0			0
$999$	437.737	+	758.182i	0.0138632	+	0.0240118i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.4.q.i.289.4		8
4.3	odd	2		39.4.e.c.16.3	✓	8
12.11	even	2		117.4.g.e.55.2		8
13.9	even	3	inner	624.4.q.i.529.4		8
52.3	odd	6		507.4.a.m.1.2		4
52.11	even	12		507.4.b.h.337.4		8
52.15	even	12		507.4.b.h.337.5		8
52.23	odd	6		507.4.a.i.1.3		4
52.35	odd	6		39.4.e.c.22.3	yes	8
156.23	even	6		1521.4.a.bb.1.2		4
156.35	even	6		117.4.g.e.100.2		8
156.107	even	6		1521.4.a.v.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.e.c.16.3	✓	8	4.3	odd	2
39.4.e.c.22.3	yes	8	52.35	odd	6
117.4.g.e.55.2		8	12.11	even	2
117.4.g.e.100.2		8	156.35	even	6
507.4.a.i.1.3		4	52.23	odd	6
507.4.a.m.1.2		4	52.3	odd	6
507.4.b.h.337.4		8	52.11	even	12
507.4.b.h.337.5		8	52.15	even	12
624.4.q.i.289.4		8	1.1	even	1	trivial
624.4.q.i.529.4		8	13.9	even	3	inner
1521.4.a.v.1.3		4	156.107	even	6
1521.4.a.bb.1.2		4	156.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	624.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 2.59808i) q^{3} +9.85055 q^{5} +(14.9698 - 25.9285i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(-1.50000 - 2.59808i) q^{3} +9.85055 q^{5} +(14.9698 - 25.9285i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(23.4629 + 40.6389i) q^{11} +(3.71050 - 46.7251i) q^{13} +(-14.7758 - 25.5925i) q^{15} +(24.1308 - 41.7958i) q^{17} +(60.1501 - 104.183i) q^{19} -89.8188 q^{21} +(65.3485 + 113.187i) q^{23} -27.9667 q^{25} +27.0000 q^{27} +(97.4729 + 168.828i) q^{29} +32.0123 q^{31} +(70.3886 - 121.917i) q^{33} +(147.461 - 255.409i) q^{35} +(16.2125 + 28.0808i) q^{37} +(-126.961 + 60.4474i) q^{39} +(120.913 + 209.427i) q^{41} +(48.2044 - 83.4924i) q^{43} +(-44.3275 + 76.7774i) q^{45} -539.015 q^{47} +(-276.690 - 479.241i) q^{49} -144.785 q^{51} -152.277 q^{53} +(231.122 + 400.315i) q^{55} -360.901 q^{57} +(163.896 - 283.876i) q^{59} +(49.2090 - 85.2325i) q^{61} +(134.728 + 233.356i) q^{63} +(36.5504 - 460.267i) q^{65} +(-220.575 - 382.048i) q^{67} +(196.046 - 339.561i) q^{69} +(172.524 - 298.821i) q^{71} +773.839 q^{73} +(41.9501 + 72.6597i) q^{75} +1404.94 q^{77} +150.332 q^{79} +(-40.5000 - 70.1481i) q^{81} -337.966 q^{83} +(237.702 - 411.711i) q^{85} +(292.419 - 506.484i) q^{87} +(-84.9567 - 147.149i) q^{89} +(-1155.96 - 795.673i) q^{91} +(-48.0184 - 83.1703i) q^{93} +(592.511 - 1026.26i) q^{95} +(-107.101 + 185.504i) q^{97} -422.332 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{3} - 12 q^{5} - 14 q^{7} - 36 q^{9}+O(q^{10}) \) 8 * q - 12 * q^3 - 12 * q^5 - 14 * q^7 - 36 * q^9	\( 8 q - 12 q^{3} - 12 q^{5} - 14 q^{7} - 36 q^{9} + 40 q^{11} - 60 q^{13} + 18 q^{15} - 98 q^{17} + 124 q^{19} + 84 q^{21} + 104 q^{23} - 116 q^{25} + 216 q^{27} - 194 q^{29} - 52 q^{31} + 120 q^{33} + 88 q^{35} - 102 q^{37} - 342 q^{39} + 1054 q^{41} + 450 q^{43} + 54 q^{45} + 192 q^{47} - 1070 q^{49} + 588 q^{51} + 524 q^{53} + 204 q^{55} - 744 q^{57} + 308 q^{59} + 928 q^{61} - 126 q^{63} + 2346 q^{65} - 1134 q^{67} + 312 q^{69} + 1064 q^{71} + 1904 q^{73} + 174 q^{75} + 5016 q^{77} + 1492 q^{79} - 324 q^{81} + 808 q^{83} + 1394 q^{85} - 582 q^{87} - 1620 q^{89} - 3278 q^{91} + 78 q^{93} + 2204 q^{95} - 2166 q^{97} - 720 q^{99}+O(q^{100}) \) 8 * q - 12 * q^3 - 12 * q^5 - 14 * q^7 - 36 * q^9 + 40 * q^11 - 60 * q^13 + 18 * q^15 - 98 * q^17 + 124 * q^19 + 84 * q^21 + 104 * q^23 - 116 * q^25 + 216 * q^27 - 194 * q^29 - 52 * q^31 + 120 * q^33 + 88 * q^35 - 102 * q^37 - 342 * q^39 + 1054 * q^41 + 450 * q^43 + 54 * q^45 + 192 * q^47 - 1070 * q^49 + 588 * q^51 + 524 * q^53 + 204 * q^55 - 744 * q^57 + 308 * q^59 + 928 * q^61 - 126 * q^63 + 2346 * q^65 - 1134 * q^67 + 312 * q^69 + 1064 * q^71 + 1904 * q^73 + 174 * q^75 + 5016 * q^77 + 1492 * q^79 - 324 * q^81 + 808 * q^83 + 1394 * q^85 - 582 * q^87 - 1620 * q^89 - 3278 * q^91 + 78 * q^93 + 2204 * q^95 - 2166 * q^97 - 720 * q^99

Introduction

L-functions

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