LMFDB - Embedded newform 117.4.g.e.100.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,4,Mod(55,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("117.55");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	117.g (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.90322347067$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3 $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.2
Root			$-0.733051 + 1.26968i$ of defining polynomial
Character	$\chi$	$=$	117.100
Dual form			117.4.g.e.55.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.733051 + 1.26968i) q^{2} +(2.92527 + 5.06672i) q^{4} -9.85055 q^{5} +(-14.9698 - 25.9285i) q^{7} -20.3063 q^{8} +O(q^{10})$	\(q+(-0.733051 + 1.26968i) q^{2} +(2.92527 + 5.06672i) q^{4} -9.85055 q^{5} +(-14.9698 - 25.9285i) q^{7} -20.3063 q^{8} +(7.22095 - 12.5071i) q^{10} +(23.4629 - 40.6389i) q^{11} +(3.71050 + 46.7251i) q^{13} +43.8945 q^{14} +(-8.51663 + 14.7512i) q^{16} +(-24.1308 - 41.7958i) q^{17} +(-60.1501 - 104.183i) q^{19} +(-28.8155 - 49.9100i) q^{20} +(34.3990 + 59.5807i) q^{22} +(65.3485 - 113.187i) q^{23} -27.9667 q^{25} +(-62.0459 - 29.5407i) q^{26} +(87.5815 - 151.696i) q^{28} +(-97.4729 + 168.828i) q^{29} -32.0123 q^{31} +(-93.7115 - 162.313i) q^{32} +70.7565 q^{34} +(147.461 + 255.409i) q^{35} +(16.2125 - 28.0808i) q^{37} +176.372 q^{38} +200.028 q^{40} +(-120.913 + 209.427i) q^{41} +(-48.2044 - 83.4924i) q^{43} +274.541 q^{44} +(95.8076 + 165.944i) q^{46} -539.015 q^{47} +(-276.690 + 479.241i) q^{49} +(20.5010 - 35.5088i) q^{50} +(-225.889 + 155.484i) q^{52} +152.277 q^{53} +(-231.122 + 400.315i) q^{55} +(303.981 + 526.511i) q^{56} +(-142.905 - 247.519i) q^{58} +(163.896 + 283.876i) q^{59} +(49.2090 + 85.2325i) q^{61} +(23.4666 - 40.6454i) q^{62} +138.515 q^{64} +(-36.5504 - 460.267i) q^{65} +(220.575 - 382.048i) q^{67} +(141.178 - 244.528i) q^{68} -432.385 q^{70} +(172.524 + 298.821i) q^{71} +773.839 q^{73} +(23.7691 + 41.1694i) q^{74} +(351.911 - 609.528i) q^{76} -1404.94 q^{77} -150.332 q^{79} +(83.8934 - 145.308i) q^{80} +(-177.270 - 307.041i) q^{82} -337.966 q^{83} +(237.702 + 411.711i) q^{85} +141.345 q^{86} +(-476.444 + 825.226i) q^{88} +(84.9567 - 147.149i) q^{89} +(1155.96 - 795.673i) q^{91} +764.649 q^{92} +(395.125 - 684.377i) q^{94} +(592.511 + 1026.26i) q^{95} +(-107.101 - 185.504i) q^{97} +(-405.656 - 702.616i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 22 q^{4} + 12 q^{5} + 14 q^{7} - 108 q^{8}+O(q^{10}) $ 8 * q + 2 * q^2 - 22 * q^4 + 12 * q^5 + 14 * q^7 - 108 * q^8	$ 8 q + 2 q^{2} - 22 q^{4} + 12 q^{5} + 14 q^{7} - 108 q^{8} + 62 q^{10} + 40 q^{11} - 60 q^{13} - 80 q^{14} - 122 q^{16} + 98 q^{17} - 124 q^{19} - 466 q^{20} - 220 q^{22} + 104 q^{23} - 116 q^{25} - 14 q^{26} + 144 q^{28} + 194 q^{29} + 52 q^{31} + 654 q^{32} + 2124 q^{34} + 88 q^{35} - 102 q^{37} - 664 q^{38} - 1996 q^{40} - 1054 q^{41} - 450 q^{43} + 88 q^{44} + 172 q^{46} + 192 q^{47} - 1070 q^{49} + 996 q^{50} + 2280 q^{52} - 524 q^{53} - 204 q^{55} + 2164 q^{56} - 722 q^{58} + 308 q^{59} + 928 q^{61} + 2780 q^{62} + 2052 q^{64} - 2346 q^{65} + 1134 q^{67} + 1786 q^{68} - 4648 q^{70} + 1064 q^{71} + 1904 q^{73} + 1158 q^{74} + 1708 q^{76} - 5016 q^{77} - 1492 q^{79} - 2922 q^{80} - 1734 q^{82} + 808 q^{83} + 1394 q^{85} - 6336 q^{86} - 3060 q^{88} + 1620 q^{89} + 3278 q^{91} - 664 q^{92} + 772 q^{94} + 2204 q^{95} - 2166 q^{97} - 1906 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 - 22 * q^4 + 12 * q^5 + 14 * q^7 - 108 * q^8 + 62 * q^10 + 40 * q^11 - 60 * q^13 - 80 * q^14 - 122 * q^16 + 98 * q^17 - 124 * q^19 - 466 * q^20 - 220 * q^22 + 104 * q^23 - 116 * q^25 - 14 * q^26 + 144 * q^28 + 194 * q^29 + 52 * q^31 + 654 * q^32 + 2124 * q^34 + 88 * q^35 - 102 * q^37 - 664 * q^38 - 1996 * q^40 - 1054 * q^41 - 450 * q^43 + 88 * q^44 + 172 * q^46 + 192 * q^47 - 1070 * q^49 + 996 * q^50 + 2280 * q^52 - 524 * q^53 - 204 * q^55 + 2164 * q^56 - 722 * q^58 + 308 * q^59 + 928 * q^61 + 2780 * q^62 + 2052 * q^64 - 2346 * q^65 + 1134 * q^67 + 1786 * q^68 - 4648 * q^70 + 1064 * q^71 + 1904 * q^73 + 1158 * q^74 + 1708 * q^76 - 5016 * q^77 - 1492 * q^79 - 2922 * q^80 - 1734 * q^82 + 808 * q^83 + 1394 * q^85 - 6336 * q^86 - 3060 * q^88 + 1620 * q^89 + 3278 * q^91 - 664 * q^92 + 772 * q^94 + 2204 * q^95 - 2166 * q^97 - 1906 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.733051	+	1.26968i	−0.259173	+	0.448900i	−0.966021	−	0.258465i	$-0.916783\pi$
$2$	−0.733051	+	1.26968i	−0.259173	+	0.448900i	0.706848	+	0.707366i	$0.250117\pi$
$3$		0			0
$3$		0			0
$4$	2.92527	+	5.06672i	0.365659	+	0.633340i
$5$	−9.85055			−0.881060			−0.440530	−	0.897738i	$-0.645209\pi$
$5$	−9.85055			−0.881060			−0.440530	+	0.897738i	$0.645209\pi$
$6$		0			0
$7$	−14.9698	−	25.9285i	−0.808293	−	1.40001i	−0.914045	−	0.405613i	$-0.867058\pi$
$7$	−14.9698	−	25.9285i	−0.808293	−	1.40001i	0.105752	−	0.994393i	$-0.466275\pi$
$8$	−20.3063			−0.897421
$9$		0			0
$10$	7.22095	−	12.5071i	0.228347	−	0.395508i
$11$	23.4629	−	40.6389i	0.643120	−	1.11392i	−0.341612	−	0.939841i	$-0.610973\pi$
$11$	23.4629	−	40.6389i	0.643120	−	1.11392i	0.984732	−	0.174076i	$-0.0556938\pi$
$12$		0			0
$13$	3.71050	+	46.7251i	0.0791621	+	0.996862i
$13$	3.71050	+	46.7251i	0.0791621	+	0.996862i
$14$	43.8945			0.837950
$15$		0			0
$16$	−8.51663	+	14.7512i	−0.133072	+	0.230488i
$17$	−24.1308	−	41.7958i	−0.344270	−	0.596292i	0.640951	−	0.767582i	$-0.278540\pi$
$17$	−24.1308	−	41.7958i	−0.344270	−	0.596292i	−0.985221	+	0.171289i	$0.945207\pi$
$18$		0			0
$19$	−60.1501	−	104.183i	−0.726283	−	1.25796i	−0.958444	−	0.285282i	$-0.907913\pi$
$19$	−60.1501	−	104.183i	−0.726283	−	1.25796i	0.232161	−	0.972677i	$-0.425421\pi$
$20$	−28.8155	−	49.9100i	−0.322167	−	0.558010i
$21$		0			0
$22$	34.3990	+	59.5807i	0.333358	+	0.577393i
$23$	65.3485	−	113.187i	0.592440	−	1.02614i	−0.401463	−	0.915875i	$-0.631498\pi$
$23$	65.3485	−	113.187i	0.592440	−	1.02614i	0.993903	−	0.110260i	$-0.0351685\pi$
$24$		0			0
$25$	−27.9667			−0.223734
$26$	−62.0459	−	29.5407i	−0.468008	−	0.222823i
$27$		0			0
$28$	87.5815	−	151.696i	0.591120	−	1.02385i
$29$	−97.4729	+	168.828i	−0.624147	+	1.08105i	0.364558	+	0.931181i	$0.381220\pi$
$29$	−97.4729	+	168.828i	−0.624147	+	1.08105i	−0.988705	+	0.149874i	$0.952113\pi$
$30$		0			0
$31$	−32.0123			−0.185470			−0.0927351	−	0.995691i	$-0.529561\pi$
$31$	−32.0123			−0.185470			−0.0927351	+	0.995691i	$0.529561\pi$
$32$	−93.7115	−	162.313i	−0.517688	−	0.896661i
$33$		0			0
$34$	70.7565			0.356901
$35$	147.461	+	255.409i	0.712155	+	1.23349i
$36$		0			0
$37$	16.2125	−	28.0808i	0.0720355	−	0.124769i	−0.827758	−	0.561086i	$-0.810384\pi$
$37$	16.2125	−	28.0808i	0.0720355	−	0.124769i	0.899793	+	0.436316i	$0.143717\pi$
$38$	176.372			0.752931
$39$		0			0
$40$	200.028			0.790681
$41$	−120.913	+	209.427i	−0.460570	+	0.797731i	−0.998989	−	0.0449461i	$-0.985688\pi$
$41$	−120.913	+	209.427i	−0.460570	+	0.797731i	0.538419	+	0.842677i	$0.319022\pi$
$42$		0			0
$43$	−48.2044	−	83.4924i	−0.170956	−	0.296104i	0.767799	−	0.640691i	$-0.221352\pi$
$43$	−48.2044	−	83.4924i	−0.170956	−	0.296104i	−0.938754	+	0.344587i	$0.888019\pi$
$44$	274.541			0.940651
$45$		0			0
$46$	95.8076	+	165.944i	0.307088	+	0.531892i
$47$	−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
$50$	20.5010	−	35.5088i	0.0579857	−	0.100434i
$51$		0			0
$52$	−225.889	+	155.484i	−0.602406	+	0.414648i
$53$	152.277			0.394657			0.197328	−	0.980337i	$-0.436774\pi$
$53$	152.277			0.394657			0.197328	+	0.980337i	$0.436774\pi$
$54$		0			0
$55$	−231.122	+	400.315i	−0.566627	+	0.981427i
$56$	303.981	+	526.511i	0.725379	+	1.25639i
$57$		0			0
$58$	−142.905	−	247.519i	−0.323524	−	0.560359i
$59$	163.896	+	283.876i	0.361652	+	0.626399i	0.988233	−	0.152957i	$-0.0488796\pi$
$59$	163.896	+	283.876i	0.361652	+	0.626399i	−0.626581	+	0.779356i	$0.715546\pi$
$60$		0			0
$61$	49.2090	+	85.2325i	0.103288	+	0.178900i	0.913037	−	0.407876i	$-0.133730\pi$
$61$	49.2090	+	85.2325i	0.103288	+	0.178900i	−0.809749	+	0.586776i	$0.800397\pi$
$62$	23.4666	−	40.6454i	0.0480688	−	0.0832576i
$63$		0			0
$64$	138.515			0.270537
$65$	−36.5504	−	460.267i	−0.0697465	−	0.878295i
$66$		0			0
$67$	220.575	−	382.048i	0.402202	−	0.696635i	−0.591789	−	0.806093i	$-0.701578\pi$
$67$	220.575	−	382.048i	0.402202	−	0.696635i	0.993991	+	0.109458i	$0.0349115\pi$
$68$	141.178	−	244.528i	0.251771	−	0.436080i
$69$		0			0
$70$	−432.385			−0.738284
$71$	172.524	+	298.821i	0.288379	+	0.499486i	0.973423	−	0.229015i	$-0.0735505\pi$
$71$	172.524	+	298.821i	0.288379	+	0.499486i	−0.685044	+	0.728501i	$0.740217\pi$
$72$		0			0
$73$	773.839			1.24070			0.620349	−	0.784326i	$-0.286991\pi$
$73$	773.839			1.24070			0.620349	+	0.784326i	$0.286991\pi$
$74$	23.7691	+	41.1694i	0.0373393	+	0.0646735i
$75$		0			0
$76$	351.911	−	609.528i	0.531144	−	0.919969i
$77$	−1404.94			−2.07932
$78$		0			0
$79$	−150.332			−0.214097			−0.107049	−	0.994254i	$-0.534140\pi$
$79$	−150.332			−0.214097			−0.107049	+	0.994254i	$0.534140\pi$
$80$	83.8934	−	145.308i	0.117245	−	0.203074i
$81$		0			0
$82$	−177.270	−	307.041i	−0.238734	−	0.413500i
$83$	−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
$86$	141.345			0.177228
$87$		0			0
$88$	−476.444	+	825.226i	−0.577149	+	0.999652i
$89$	84.9567	−	147.149i	0.101184	−	0.175256i	−0.810989	−	0.585062i	$-0.801070\pi$
$89$	84.9567	−	147.149i	0.101184	−	0.175256i	0.912173	+	0.409806i	$0.134404\pi$
$90$		0			0
$91$	1155.96	−	795.673i	1.33163	−	0.916584i
$92$	764.649			0.866524
$93$		0			0
$94$	395.125	−	684.377i	0.433554	−	0.750937i
$95$	592.511	+	1026.26i	0.639899	+	1.10834i
$96$		0			0
$97$	−107.101	−	185.504i	−0.112107	−	0.194176i	0.804512	−	0.593936i	$-0.202427\pi$
$97$	−107.101	−	185.504i	−0.112107	−	0.194176i	−0.916620	+	0.399760i	$0.869093\pi$
$98$	−405.656	−	702.616i	−0.418137	−	0.724234i
$99$		0			0
$100$	−81.8104	−	141.700i	−0.0818104	−	0.141700i
$101$	797.556	−	1381.41i	0.785741	−	1.36094i	−0.142815	−	0.989749i	$-0.545615\pi$
$101$	797.556	−	1381.41i	0.785741	−	1.36094i	0.928555	−	0.371194i	$-0.121051\pi$
$102$		0			0
$103$	−1570.30			−1.50219			−0.751096	−	0.660193i	$-0.770475\pi$
$103$	−1570.30			−1.50219			−0.751096	+	0.660193i	$0.770475\pi$
$104$	−75.3465	−	948.814i	−0.0710417	−	0.894604i
$105$		0			0
$106$	−111.626	+	193.343i	−0.102284	+	0.177161i
$107$	−3.36651	+	5.83096i	−0.00304161	+	0.00526823i	−0.867542	−	0.497364i	$-0.834302\pi$
$107$	−3.36651	+	5.83096i	−0.00304161	+	0.00526823i	0.864501	+	0.502632i	$0.167635\pi$
$108$		0			0
$109$	−542.422			−0.476648			−0.238324	−	0.971186i	$-0.576598\pi$
$109$	−542.422			−0.476648			−0.238324	+	0.971186i	$0.576598\pi$
$110$	−338.848	−	586.903i	−0.293708	−	0.508718i
$111$		0			0
$112$	509.969			0.430246
$113$	−721.411	−	1249.52i	−0.600572	−	1.04022i	−0.992735	−	0.120325i	$-0.961606\pi$
$113$	−721.411	−	1249.52i	−0.600572	−	1.04022i	0.392162	−	0.919896i	$-0.371727\pi$
$114$		0			0
$115$	−643.719	+	1114.95i	−0.521975	+	0.904087i
$116$	−1140.54			−0.912900
$117$		0			0
$118$	−480.577			−0.374921
$119$	−722.467	+	1251.35i	−0.556542	+	0.963958i
$120$		0			0
$121$	−435.513	−	754.330i	−0.327207	−	0.566739i
$122$	−144.291			−0.107078
$123$		0			0
$124$	−93.6446	−	162.197i	−0.0678188	−	0.117466i
$125$	1506.81			1.07818
$126$		0			0
$127$	1246.42	−	2158.86i	0.870881	−	1.50841i	0.00979442	−	0.999952i	$-0.496882\pi$
$127$	1246.42	−	2158.86i	0.870881	−	1.50841i	0.861087	−	0.508458i	$-0.169784\pi$
$128$	648.153	−	1122.63i	0.447572	−	0.775217i
$129$		0			0
$130$	611.186	+	290.992i	0.412343	+	0.196321i
$131$	−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
$134$	323.386	+	560.121i	0.208480	+	0.361097i
$135$		0			0
$136$	490.008	+	848.718i	0.308955	+	0.535125i
$137$	−111.083	−	192.402i	−0.0692736	−	0.119985i	0.829308	−	0.558792i	$-0.188735\pi$
$137$	−111.083	−	192.402i	−0.0692736	−	0.119985i	−0.898582	+	0.438806i	$0.855401\pi$
$138$		0			0
$139$	388.573	+	673.028i	0.237110	+	0.410687i	0.959884	−	0.280398i	$-0.0904665\pi$
$139$	388.573	+	673.028i	0.237110	+	0.410687i	−0.722774	+	0.691085i	$0.757133\pi$
$140$	−862.726	+	1494.28i	−0.520812	+	0.902072i
$141$		0			0
$142$	−505.876			−0.298959
$143$	1985.91	+	945.514i	1.16133	+	0.552922i
$144$		0			0
$145$	960.161	−	1663.05i	0.549911	−	0.952473i
$146$	−567.263	+	982.529i	−0.321555	+	0.556950i
$147$		0			0
$148$	189.704			0.105362
$149$	889.147	+	1540.05i	0.488871	+	0.846750i	0.999918	−	0.0128032i	$-0.00407549\pi$
$149$	889.147	+	1540.05i	0.488871	+	0.846750i	−0.511047	+	0.859553i	$0.670742\pi$
$150$		0			0
$151$	1166.00			0.628394			0.314197	−	0.949358i	$-0.398265\pi$
$151$	1166.00			0.628394			0.314197	+	0.949358i	$0.398265\pi$
$152$	1221.43	+	2115.57i	0.651781	+	1.12892i
$153$		0			0
$154$	1029.89	−	1783.82i	0.538902	−	0.933407i
$155$	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	$0.458000\pi$
$158$	110.201	−	190.874i	0.0554882	−	0.0961083i
$159$		0			0
$160$	923.109	+	1598.87i	0.456114	+	0.790012i
$161$	−3913.02			−1.91546
$162$		0			0
$163$	−305.094	−	528.438i	−0.146606	−	0.253929i	0.783365	−	0.621562i	$-0.213502\pi$
$163$	−305.094	−	528.438i	−0.146606	−	0.253929i	−0.929971	+	0.367633i	$0.880168\pi$
$164$	−1414.81			−0.673647
$165$		0			0
$166$	247.746	−	429.109i	0.115836	−	0.200635i
$167$	1491.51	−	2583.36i	0.691115	−	1.19705i	−0.280358	−	0.959895i	$-0.590453\pi$
$167$	1491.51	−	2583.36i	0.691115	−	1.19705i	0.971473	−	0.237150i	$-0.0762133\pi$
$168$		0			0
$169$	−2169.46	+	346.747i	−0.987467	+	0.157827i
$170$	−696.990			−0.314451
$171$		0			0
$172$	282.022	−	488.476i	0.125023	−	0.216546i
$173$	489.106	+	847.157i	0.214948	+	0.372301i	0.953257	−	0.302162i	$-0.0977084\pi$
$173$	489.106	+	847.157i	0.214948	+	0.372301i	−0.738308	+	0.674463i	$0.764375\pi$
$174$		0			0
$175$	418.657	+	725.134i	0.180843	+	0.313229i
$176$	399.649	+	692.213i	0.171163	+	0.296463i
$177$		0			0
$178$	124.555	+	215.736i	0.0524483	+	0.0908431i
$179$	926.471	−	1604.69i	0.386858	−	0.670058i	−0.605167	−	0.796099i	$-0.706894\pi$
$179$	926.471	−	1604.69i	0.386858	−	0.670058i	0.992025	+	0.126040i	$0.0402269\pi$
$180$		0			0
$181$	852.777			0.350201			0.175101	−	0.984551i	$-0.443975\pi$
$181$	852.777			0.350201			0.175101	+	0.984551i	$0.443975\pi$
$182$	162.871	+	2050.97i	0.0663339	+	0.835320i
$183$		0			0
$184$	−1326.99	+	2298.41i	−0.531668	+	0.920875i
$185$	−159.702	+	276.612i	−0.0634676	+	0.109929i
$186$		0			0
$187$	−2264.71			−0.885627
$188$	−1576.77	−	2731.04i	−0.611689	−	1.05948i
$189$		0			0
$190$	−1737.36			−0.663377
$191$	2220.65	+	3846.27i	0.841258	+	1.45710i	0.888831	+	0.458234i	$0.151518\pi$
$191$	2220.65	+	3846.27i	0.841258	+	1.45710i	−0.0475730	+	0.998868i	$0.515149\pi$
$192$		0			0
$193$	1241.21	−	2149.85i	0.462925	−	0.801810i	−0.536180	−	0.844104i	$-0.680133\pi$
$193$	1241.21	−	2149.85i	0.462925	−	0.801810i	0.999105	+	0.0422935i	$0.0134665\pi$
$194$	314.041			0.116221
$195$		0			0
$196$	−3237.57			−1.17987
$197$	630.115	−	1091.39i	0.227888	−	0.394713i	−0.729294	−	0.684200i	$-0.760151\pi$
$197$	630.115	−	1091.39i	0.227888	−	0.394713i	0.957182	+	0.289487i	$0.0934848\pi$
$198$		0			0
$199$	2760.48	+	4781.30i	0.983344	+	1.70320i	0.649077	+	0.760722i	$0.275155\pi$
$199$	2760.48	+	4781.30i	0.983344	+	1.70320i	0.334266	+	0.942479i	$0.391511\pi$
$200$	567.901			0.200783
$201$		0			0
$202$	1169.30	+	2025.28i	0.407285	+	0.705438i
$203$	5836.60			2.01798
$204$		0			0
$205$	1191.06	−	2062.97i	0.405790	−	0.702849i
$206$	1151.11	−	1993.78i	0.389327	−	0.674334i
$207$		0			0
$208$	−720.853	−	343.206i	−0.240299	−	0.114409i
$209$	−5645.18			−1.86835
$210$		0			0
$211$	2263.90	−	3921.18i	0.738640	−	1.27936i	−0.214468	−	0.976731i	$-0.568802\pi$
$211$	2263.90	−	3921.18i	0.738640	−	1.27936i	0.953108	−	0.302631i	$-0.0978649\pi$
$212$	445.451	+	771.543i	0.144310	+	0.249952i
$213$		0			0
$214$	−4.93564	−	8.54879i	−0.00157661	−	0.00273076i
$215$	474.839	+	822.446i	0.150622	+	0.260885i
$216$		0			0
$217$	479.217	+	830.029i	0.149914	+	0.259659i
$218$	397.623	−	688.703i	0.123534	−	0.213967i
$219$		0			0
$220$	−2704.38			−0.828770
$221$	1863.37	−	1282.60i	0.567168	−	0.390393i
$222$		0			0
$223$	−2240.59	+	3880.81i	−0.672829	+	1.16537i	0.304270	+	0.952586i	$0.401588\pi$
$223$	−2240.59	+	3880.81i	−0.672829	+	1.16537i	−0.977099	+	0.212787i	$0.931746\pi$
$224$	−2805.68	+	4859.59i	−0.836887	+	1.44953i
$225$		0			0
$226$	2115.32			0.622607
$227$	−2879.88	−	4988.09i	−0.842044	−	1.45846i	−0.888163	−	0.459528i	$-0.848019\pi$
$227$	−2879.88	−	4988.09i	−0.842044	−	1.45846i	0.0461191	−	0.998936i	$-0.485315\pi$
$228$		0			0
$229$	−4635.08			−1.33753			−0.668766	−	0.743473i	$-0.733177\pi$
$229$	−4635.08			−1.33753			−0.668766	+	0.743473i	$0.733177\pi$
$230$	−943.757	−	1634.64i	−0.270563	−	0.468629i
$231$		0			0
$232$	1979.31	−	3428.27i	0.560122	−	0.970160i
$233$	−5886.33			−1.65505			−0.827524	−	0.561431i	$-0.810251\pi$
$233$	−5886.33			−1.65505			−0.827524	+	0.561431i	$0.810251\pi$
$234$		0			0
$235$	5309.59			1.47387
$236$	−958.882	+	1660.83i	−0.264483	+	0.458097i
$237$		0			0
$238$	−1059.21	−	1834.61i	−0.288481	−	0.499663i
$239$	−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	−0.988116	−	0.153708i	$-0.950879\pi$
$241$	−2346.46	−	4064.19i	−0.627173	−	1.08630i	0.360943	−	0.932588i	$-0.382455\pi$
$242$	1277.01			0.339212
$243$		0			0
$244$	−287.899	+	498.656i	−0.0755364	+	0.130833i
$245$	2725.55	−	4720.79i	0.710730	−	1.23102i
$246$		0			0
$247$	4644.77	−	3197.09i	1.19652	−	0.823587i
$248$	650.051			0.166445
$249$		0			0
$250$	−1104.57	+	1913.16i	−0.279435	+	0.483996i
$251$	−1951.44	−	3379.99i	−0.490732	−	0.849973i	0.509211	−	0.860642i	$-0.329937\pi$
$251$	−1951.44	−	3379.99i	−0.490732	−	0.849973i	−0.999943	+	0.0106687i	$0.996604\pi$
$252$		0			0
$253$	−3066.53	−	5311.38i	−0.762020	−	1.31986i
$254$	1827.38	+	3165.11i	0.451417	+	0.781877i
$255$		0			0
$256$	1504.32	+	2605.56i	0.367265	+	0.636122i
$257$	−2065.42	+	3577.40i	−0.501312	+	0.868297i	0.498687	+	0.866782i	$0.333816\pi$
$257$	−2065.42	+	3577.40i	−0.501312	+	0.868297i	−0.999999	+	0.00151510i	$0.999518\pi$
$258$		0			0
$259$	−970.790			−0.232903
$260$	2225.13	−	1531.60i	0.530756	−	0.365330i
$261$		0			0
$262$	545.801	−	945.356i	0.128701	−	0.222917i
$263$	3176.09	−	5501.14i	0.744661	−	1.28979i	−0.205692	−	0.978617i	$-0.565944\pi$
$263$	3176.09	−	5501.14i	0.744661	−	1.28979i	0.950353	−	0.311174i	$-0.100722\pi$
$264$		0			0
$265$	−1500.01			−0.347716
$266$	−2640.26	−	4573.06i	−0.608589	−	1.05411i
$267$		0			0
$268$	2580.97			0.588276
$269$	90.7619	+	157.204i	0.0205719	+	0.0356316i	0.876128	−	0.482078i	$-0.160118\pi$
$269$	90.7619	+	157.204i	0.0205719	+	0.0356316i	−0.855556	+	0.517710i	$0.826785\pi$
$270$		0			0
$271$	−1730.18	+	2996.75i	−0.387825	+	0.671733i	−0.992157	−	0.125000i	$-0.960107\pi$
$271$	−1730.18	+	2996.75i	−0.387825	+	0.671733i	0.604331	+	0.796733i	$0.293440\pi$
$272$	822.053			0.183251
$273$		0			0
$274$	325.719			0.0718153
$275$	−656.180	+	1136.54i	−0.143888	+	0.249221i
$276$		0			0
$277$	3218.97	+	5575.42i	0.698228	+	1.20937i	0.969080	+	0.246745i	$0.0793611\pi$
$277$	3218.97	+	5575.42i	0.698228	+	1.20937i	−0.270853	+	0.962621i	$0.587306\pi$
$278$	−1139.37			−0.245810
$279$		0			0
$280$	−2994.38	−	5186.42i	−0.639102	−	1.10696i
$281$	2974.26			0.631421			0.315711	−	0.948855i	$-0.397757\pi$
$281$	2974.26			0.631421			0.315711	+	0.948855i	$0.397757\pi$
$282$		0			0
$283$	−1517.86	+	2629.01i	−0.318825	+	0.552221i	−0.980243	−	0.197797i	$-0.936621\pi$
$283$	−1517.86	+	2629.01i	−0.318825	+	0.552221i	0.661418	+	0.750017i	$0.269955\pi$
$284$	−1009.36	+	1748.27i	−0.210896	+	0.365283i
$285$		0			0
$286$	−2656.28	+	1828.37i	−0.549192	+	0.378020i
$287$	7240.15			1.48910
$288$		0			0
$289$	1291.91	−	2237.65i	0.262957	−	0.455455i
$290$	1407.69	+	2438.20i	0.285044	+	0.493710i
$291$		0			0
$292$	2263.69	+	3920.83i	0.453673	+	0.785784i
$293$	−977.872	−	1693.72i	−0.194976	−	0.337708i	0.751917	−	0.659258i	$-0.229129\pi$
$293$	−977.872	−	1693.72i	−0.194976	−	0.337708i	−0.946893	+	0.321550i	$0.895796\pi$
$294$		0			0
$295$	−1614.47	−	2796.34i	−0.318637	−	0.551895i
$296$	−329.216	+	570.218i	−0.0646462	+	0.111970i
$297$		0			0
$298$	−2607.16			−0.506808
$299$	5531.15	+	2633.43i	1.06981	+	0.509349i
$300$		0			0
$301$	−1443.22	+	2499.73i	−0.276365	+	0.478678i
$302$	−854.736	+	1480.45i	−0.162863	+	0.282086i
$303$		0			0
$304$	2049.10			0.386593
$305$	−484.735	−	839.586i	−0.0910029	−	0.157622i
$306$		0			0
$307$	−1027.56			−0.191029			−0.0955147	−	0.995428i	$-0.530450\pi$
$307$	−1027.56			−0.191029			−0.0955147	+	0.995428i	$0.530450\pi$
$308$	−4109.83	−	7118.43i	−0.760322	−	1.31692i
$309$		0			0
$310$	−231.159	+	400.379i	−0.0423515	+	0.0733549i
$311$	−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	$0.356890\pi$
$314$	−379.447	+	657.222i	−0.0681957	+	0.118118i
$315$		0			0
$316$	−439.763	−	761.691i	−0.0782866	−	0.135596i
$317$	−1141.33			−0.202219			−0.101110	−	0.994875i	$-0.532239\pi$
$317$	−1141.33			−0.202219			−0.101110	+	0.994875i	$0.532239\pi$
$318$		0			0
$319$	4573.99	+	7922.38i	0.802803	+	1.39050i
$320$	−1364.45			−0.238359
$321$		0			0
$322$	2868.44	−	4968.29i	0.496435	−	0.859850i
$323$	−2902.94	+	5028.04i	−0.500074	+	0.866154i
$324$		0			0
$325$	−103.771	−	1306.75i	−0.0177113	−	0.223032i
$326$	894.597			0.151985
$327$		0			0
$328$	2455.29	−	4252.69i	0.413325	−	0.715900i
$329$	8068.94	+	13975.8i	1.35214	+	2.34198i
$330$		0			0
$331$	−3826.28	−	6627.32i	−0.635382	−	1.10051i	−0.986434	−	0.164158i	$-0.947509\pi$
$331$	−3826.28	−	6627.32i	−0.635382	−	1.10051i	0.351052	−	0.936356i	$-0.385824\pi$
$332$	−988.643	−	1712.38i	−0.163430	−	0.283069i
$333$		0			0
$334$	2186.70	+	3787.47i	0.358236	+	0.620483i
$335$	−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	$0.564858\pi$
$338$	1150.07	−	3008.71i	0.185076	−	0.484178i
$339$		0			0
$340$	−1390.68	+	2408.74i	−0.221825	+	0.384212i
$341$	−751.100	+	1300.94i	−0.119280	+	0.206598i
$342$		0			0
$343$	6298.69			0.991537
$344$	978.853	+	1695.42i	0.153419	+	0.265730i
$345$		0			0
$346$	−1434.16			−0.222835
$347$	2248.06	+	3893.75i	0.347787	+	0.602385i	0.985856	−	0.167594i	$-0.0535999\pi$
$347$	2248.06	+	3893.75i	0.347787	+	0.602385i	−0.638069	+	0.769979i	$0.720267\pi$
$348$		0			0
$349$	−1788.81	+	3098.31i	−0.274363	+	0.475211i	−0.969974	−	0.243208i	$-0.921800\pi$
$349$	−1788.81	+	3098.31i	−0.274363	+	0.475211i	0.695611	+	0.718418i	$0.255134\pi$
$350$	−1227.59			−0.187478
$351$		0			0
$352$	−8794.96			−1.33174
$353$	−4022.58	+	6967.32i	−0.606517	+	1.05052i	0.385293	+	0.922794i	$0.374100\pi$
$353$	−4022.58	+	6967.32i	−0.606517	+	1.05052i	−0.991810	+	0.127724i	$0.959233\pi$
$354$		0			0
$355$	−1699.46	−	2943.55i	−0.254079	−	0.440077i
$356$	994.086			0.147996
$357$		0			0
$358$	1358.30	+	2352.64i	0.200526	+	0.347322i
$359$	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
$362$	−625.129	+	1082.75i	−0.0907625	+	0.157205i
$363$		0			0
$364$	7412.96	+	3529.39i	1.06743	+	0.508215i
$365$	−7622.74			−1.09313
$366$		0			0
$367$	−3831.38	+	6636.15i	−0.544949	+	0.943880i	0.453661	+	0.891175i	$0.350118\pi$
$367$	−3831.38	+	6636.15i	−0.544949	+	0.943880i	−0.998610	+	0.0527056i	$0.983216\pi$
$368$	1113.10	+	1927.94i	0.157675	+	0.273100i
$369$		0			0
$370$	−234.139	−	405.541i	−0.0328981	−	0.0569812i
$371$	−2279.55	−	3948.30i	−0.318998	−	0.552521i
$372$		0			0
$373$	−5271.27	−	9130.10i	−0.731732	−	1.26740i	−0.956143	−	0.292902i	$-0.905379\pi$
$373$	−5271.27	−	9130.10i	−0.731732	−	1.26740i	0.224411	−	0.974495i	$-0.427954\pi$
$374$	1660.15	−	2875.46i	0.229530	−	0.397558i
$375$		0			0
$376$	10945.4			1.50124
$377$	−8250.17	−	3927.99i	−1.12707	−	0.536610i
$378$		0			0
$379$	−2737.77	+	4741.96i	−0.371055	+	0.642686i	−0.989728	−	0.142962i	$-0.954337\pi$
$379$	−2737.77	+	4741.96i	−0.371055	+	0.642686i	0.618673	+	0.785648i	$0.287671\pi$
$380$	−3466.51	+	6004.18i	−0.467970	+	0.810547i
$381$		0			0
$382$	−6511.39			−0.872124
$383$	404.042	+	699.822i	0.0539050	+	0.0933661i	0.891719	−	0.452590i	$-0.149500\pi$
$383$	404.042	+	699.822i	0.0539050	+	0.0933661i	−0.837814	+	0.545956i	$0.816167\pi$
$384$		0			0
$385$	13839.4			1.83200
$386$	1819.75	+	3151.89i	0.239955	+	0.415614i
$387$		0			0
$388$	626.597	−	1085.30i	0.0819862	−	0.142004i
$389$	7060.26			0.920230			0.460115	−	0.887859i	$-0.347808\pi$
$389$	7060.26			0.920230			0.460115	+	0.887859i	$0.347808\pi$
$390$		0			0
$391$	−6307.65			−0.815836
$392$	5618.55	−	9731.62i	0.723928	−	1.25388i
$393$		0			0
$394$	923.813	+	1600.09i	0.118124	+	0.204598i
$395$	1480.85			0.188633
$396$		0			0
$397$	709.947	+	1229.66i	0.0897511	+	0.155453i	0.907406	−	0.420255i	$-0.138060\pi$
$397$	709.947	+	1229.66i	0.0897511	+	0.155453i	−0.817655	+	0.575709i	$0.804726\pi$
$398$	−8094.29			−1.01942
$399$		0			0
$400$	238.182	−	412.544i	0.0297728	−	0.0515680i
$401$	5335.37	−	9241.13i	0.664428	−	1.15082i	−0.315012	−	0.949088i	$-0.602009\pi$
$401$	5335.37	−	9241.13i	0.664428	−	1.15082i	0.979440	−	0.201735i	$-0.0646580\pi$
$402$		0			0
$403$	−118.782	−	1495.78i	−0.0146822	−	0.184888i
$404$	9332.28			1.14925
$405$		0			0
$406$	−4278.52	+	7410.62i	−0.523004	+	0.905869i
$407$	−760.782	−	1317.71i	−0.0926550	−	0.160483i
$408$		0			0
$409$	−3175.78	−	5500.61i	−0.383942	−	0.665007i	0.607680	−	0.794182i	$-0.292100\pi$
$409$	−3175.78	−	5500.61i	−0.383942	−	0.665007i	−0.991622	+	0.129175i	$0.958767\pi$
$410$	1746.21	+	3024.52i	0.210339	+	0.364318i
$411$		0			0
$412$	−4593.54	−	7956.25i	−0.549290	−	0.951399i
$413$	4906.98	−	8499.15i	0.584641	−	1.01263i
$414$		0			0
$415$	3329.15			0.393787
$416$	7236.37	−	4980.94i	0.852866	−	0.587045i
$417$		0			0
$418$	4138.20	−	7167.57i	0.484225	−	0.838702i
$419$	2808.94	−	4865.22i	0.327507	−	0.567259i	−0.654509	−	0.756054i	$-0.727125\pi$
$419$	2808.94	−	4865.22i	0.327507	−	0.567259i	0.982017	+	0.188795i	$0.0604581\pi$
$420$		0			0
$421$	−1518.29			−0.175765			−0.0878825	−	0.996131i	$-0.528010\pi$
$421$	−1518.29			−0.175765			−0.0878825	+	0.996131i	$0.528010\pi$
$422$	3319.10	+	5748.85i	0.382870	+	0.663151i
$423$		0			0
$424$	−3092.17			−0.354173
$425$	674.860	+	1168.89i	0.0770248	+	0.133411i
$426$		0			0
$427$	1473.30	−	2551.83i	0.166974	−	0.289207i
$428$	−39.3918			−0.00444878
$429$		0			0
$430$	−1392.33			−0.156149
$431$	−2485.07	+	4304.26i	−0.277730	+	0.481042i	−0.970820	−	0.239809i	$-0.922915\pi$
$431$	−2485.07	+	4304.26i	−0.277730	+	0.481042i	0.693091	+	0.720850i	$0.256249\pi$
$432$		0			0
$433$	1649.36	+	2856.77i	0.183055	+	0.317061i	0.942919	−	0.333021i	$-0.108068\pi$
$433$	1649.36	+	2856.77i	0.183055	+	0.317061i	−0.759864	+	0.650082i	$0.774735\pi$
$434$	−1405.16			−0.155415
$435$		0			0
$436$	−1586.73	−	2748.30i	−0.174291	−	0.301880i
$437$	−15722.9			−1.72112
$438$		0			0
$439$	3024.24	−	5238.13i	0.328790	−	0.569481i	−0.653482	−	0.756942i	$-0.726692\pi$
$439$	3024.24	−	5238.13i	0.328790	−	0.569481i	0.982272	+	0.187461i	$0.0600257\pi$
$440$	4693.24	−	8128.92i	0.508503	−	0.880753i
$441$		0			0
$442$	262.542	+	3306.10i	0.0282530	+	0.355781i
$443$	−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
$446$	−3284.93	−	5689.66i	−0.348757	−	0.604066i
$447$		0			0
$448$	−2073.54	−	3591.48i	−0.218673	−	0.378753i
$449$	205.205	+	355.426i	0.0215684	+	0.0373576i	0.876608	−	0.481205i	$-0.159801\pi$
$449$	205.205	+	355.426i	0.0215684	+	0.0373576i	−0.855040	+	0.518563i	$0.826467\pi$
$450$		0			0
$451$	5673.91	+	9827.51i	0.592404	+	1.02607i
$452$	4220.65	−	7310.38i	0.439209	−	0.760733i
$453$		0			0
$454$	8444.38			0.872939
$455$	−11386.9	+	7837.81i	−1.17324	+	0.807565i
$456$		0			0
$457$	8321.41	−	14413.1i	0.851771	−	1.47531i	−0.0278385	−	0.999612i	$-0.508862\pi$
$457$	8321.41	−	14413.1i	0.851771	−	1.47531i	0.879609	−	0.475697i	$-0.157804\pi$
$458$	3397.75	−	5885.07i	0.346651	−	0.600418i
$459$		0			0
$460$	−7532.21			−0.763459
$461$	−5864.85	−	10158.2i	−0.592523	−	1.02628i	−0.993891	−	0.110364i	$-0.964798\pi$
$461$	−5864.85	−	10158.2i	−0.592523	−	1.02628i	0.401368	−	0.915917i	$-0.368535\pi$
$462$		0			0
$463$	−3564.93			−0.357832			−0.178916	−	0.983864i	$-0.557259\pi$
$463$	−3564.93			−0.357832			−0.178916	+	0.983864i	$0.557259\pi$
$464$	−1660.28	−	2875.69i	−0.166113	−	0.287717i
$465$		0			0
$466$	4314.98	−	7473.76i	0.428943	−	0.742951i
$467$	−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
$470$	−3892.20	+	6741.49i	−0.381987	+	0.661620i
$471$		0			0
$472$	−3328.12	−	5764.48i	−0.324554	−	0.562144i
$473$	−4524.05			−0.439780
$474$		0			0
$475$	1682.20	+	2913.66i	0.162494	+	0.281448i
$476$	−8453.65			−0.814018
$477$		0			0
$478$	1565.68	−	2711.84i	0.149817	−	0.259491i
$479$	−9686.30	+	16777.2i	−0.923963	+	1.60035i	−0.130743	+	0.991416i	$0.541736\pi$
$479$	−9686.30	+	16777.2i	−0.923963	+	1.60035i	−0.793220	+	0.608935i	$0.791597\pi$
$480$		0			0
$481$	1372.24	+	653.335i	0.130080	+	0.0619325i
$482$	6880.29			0.650184
$483$		0			0
$484$	2547.99	−	4413.24i	0.239293	−	0.414467i
$485$	1055.00	+	1827.31i	0.0987733	+	0.171080i
$486$		0			0
$487$	4522.98	+	7834.02i	0.420853	+	0.728939i	0.996023	−	0.0890946i	$-0.0283973\pi$
$487$	4522.98	+	7834.02i	0.420853	+	0.728939i	−0.575170	+	0.818034i	$0.695064\pi$
$488$	−999.253	−	1730.76i	−0.0926927	−	0.160549i
$489$		0			0
$490$	3995.93	+	6921.15i	0.368403	+	0.638093i
$491$	7201.66	−	12473.6i	0.661927	−	1.14649i	−0.318181	−	0.948030i	$-0.603072\pi$
$491$	7201.66	−	12473.6i	0.661927	−	1.14649i	0.980109	−	0.198462i	$-0.0635947\pi$
$492$		0			0
$493$	9408.40			0.859499
$494$	654.429	+	8241.01i	0.0596036	+	0.750568i
$495$		0			0
$496$	272.637	−	472.221i	0.0246809	−	0.0427486i
$497$	5165.31	−	8946.58i	0.466189	−	0.807463i
$498$		0			0
$499$	−9319.75			−0.836091			−0.418045	−	0.908426i	$-0.637285\pi$
$499$	−9319.75			−0.836091			−0.418045	+	0.908426i	$0.637285\pi$
$500$	4407.82	+	7634.57i	0.394247	+	0.682856i
$501$		0			0
$502$	5722.02			0.508737
$503$	1372.99	+	2378.09i	0.121707	+	0.210802i	0.920441	−	0.390882i	$-0.127830\pi$
$503$	1372.99	+	2378.09i	0.121707	+	0.210802i	−0.798734	+	0.601684i	$0.794497\pi$
$504$		0			0
$505$	−7856.37	+	13607.6i	−0.692285	+	1.19907i
$506$	8991.69			0.789979
$507$		0			0
$508$	14584.5			1.27378
$509$	−591.055	+	1023.74i	−0.0514697	+	0.0891481i	−0.890612	−	0.454763i	$-0.849724\pi$
$509$	−591.055	+	1023.74i	−0.0514697	+	0.0891481i	0.839143	+	0.543911i	$0.183057\pi$
$510$		0			0
$511$	−11584.2	−	20064.5i	−1.00285	−	1.73698i
$512$	5959.48			0.514403
$513$		0			0
$514$	−3028.11	−	5244.84i	−0.259852	−	0.450078i
$515$	15468.3			1.32352
$516$		0			0
$517$	−12646.8	+	21905.0i	−1.07584	+	1.86340i
$518$	711.639	−	1232.59i	0.0603622	−	0.104550i
$519$		0			0
$520$	742.205	+	9346.33i	0.0625920	+	0.788200i
$521$	−10858.8			−0.913115			−0.456558	−	0.889694i	$-0.650918\pi$
$521$	−10858.8			−0.913115			−0.456558	+	0.889694i	$0.650918\pi$
$522$		0			0
$523$	5080.87	−	8800.33i	0.424801	−	0.735777i	−0.571601	−	0.820532i	$-0.693677\pi$
$523$	5080.87	−	8800.33i	0.424801	−	0.735777i	0.996402	+	0.0847546i	$0.0270106\pi$
$524$	−2178.05	−	3772.48i	−0.181581	−	0.314507i
$525$		0			0
$526$	4656.47	+	8065.23i	0.385992	+	0.668557i
$527$	772.482	+	1337.98i	0.0638517	+	0.110594i
$528$		0			0
$529$	−2457.36	−	4256.28i	−0.201970	−	0.349821i
$530$	1099.58	−	1904.53i	0.0901184	−	0.156090i
$531$		0			0
$532$	−21072.1			−1.71728
$533$	−10234.1	−	4872.57i	−0.831687	−	0.395975i
$534$		0			0
$535$	33.1620	−	57.4382i	0.00267984	−	0.00464162i
$536$	−4479.07	+	7757.98i	−0.360945	+	0.625175i
$537$		0			0
$538$	−266.132			−0.0213267
$539$	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	$0.624209\pi$
$542$	−2536.61	−	4393.54i	−0.201027	−	0.348190i
$543$		0			0
$544$	−4522.67	+	7833.49i	−0.356448	+	0.617386i
$545$	5343.15			0.419955
$546$		0			0
$547$	15958.9			1.24745			0.623724	−	0.781645i	$-0.285619\pi$
$547$	15958.9			1.24745			0.623724	+	0.781645i	$0.285619\pi$
$548$	649.898	−	1125.66i	0.0506611	−	0.0877475i
$549$		0			0
$550$	−962.027	−	1666.28i	−0.0745836	−	0.129183i
$551$	23452.0			1.81323
$552$		0			0
$553$	2250.44	+	3897.88i	0.173053	+	0.299737i
$554$	−9438.67			−0.723846
$555$		0			0
$556$	−2273.36	+	3937.58i	−0.173403	+	0.300343i
$557$	−1072.55	+	1857.70i	−0.0815892	+	0.141317i	−0.903933	−	0.427675i	$-0.859333\pi$
$557$	−1072.55	+	1857.70i	−0.0815892	+	0.141317i	0.822344	+	0.568991i	$0.192666\pi$
$558$		0			0
$559$	3722.33	−	2562.15i	0.281642	−	0.193859i
$560$	−5023.47			−0.379072
$561$		0			0
$562$	−2180.28	+	3776.36i	−0.163647	+	0.283445i
$563$	−11159.3	−	19328.5i	−0.835362	−	1.44689i	−0.893736	−	0.448594i	$-0.851925\pi$
$563$	−11159.3	−	19328.5i	−0.835362	−	1.44689i	0.0583740	−	0.998295i	$-0.481408\pi$
$564$		0			0
$565$	7106.29	+	12308.5i	0.529140	+	0.916497i
$566$	−2225.34	−	3854.40i	−0.165261	−	0.286241i
$567$		0			0
$568$	−3503.33	−	6067.95i	−0.258797	−	0.448249i
$569$	−9876.51	+	17106.6i	−0.727671	+	1.26036i	0.230194	+	0.973145i	$0.426064\pi$
$569$	−9876.51	+	17106.6i	−0.727671	+	1.26036i	−0.957865	+	0.287218i	$0.907270\pi$
$570$		0			0
$571$	−10640.6			−0.779850			−0.389925	−	0.920847i	$-0.627499\pi$
$571$	−10640.6			−0.779850			−0.389925	+	0.920847i	$0.627499\pi$
$572$	1018.69	+	12828.0i	0.0744639	+	0.937699i
$573$		0			0
$574$	−5307.40	+	9192.69i	−0.385935	+	0.668459i
$575$	−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	$0.424093\pi$
$578$	1894.07	+	3280.62i	0.136302	+	0.236083i
$579$		0			0
$580$	11234.9			0.804319
$581$	5059.29	+	8762.94i	0.361264	+	0.625728i
$582$		0			0
$583$	3572.85	−	6188.35i	0.253812	−	0.439615i
$584$	−15713.8			−1.11343
$585$		0			0
$586$	2867.32			0.202130
$587$	2950.17	−	5109.84i	0.207439	−	0.359294i	−0.743468	−	0.668771i	$-0.766821\pi$
$587$	2950.17	−	5109.84i	0.207439	−	0.359294i	0.950907	+	0.309477i	$0.100154\pi$
$588$		0			0
$589$	1925.54	+	3335.14i	0.134704	+	0.233314i
$590$	4733.94			0.330328
$591$		0			0
$592$	276.151	+	478.308i	0.0191719	+	0.0332067i
$593$	15261.5			1.05686			0.528428	−	0.848978i	$-0.322782\pi$
$593$	15261.5			1.05686			0.528428	+	0.848978i	$0.322782\pi$
$594$		0			0
$595$	7116.70	−	12326.5i	0.490346	−	0.849305i
$596$	−5202.00	+	9010.13i	−0.357520	+	0.619243i
$597$		0			0
$598$	−7398.23	+	5092.35i	−0.505913	+	0.348230i
$599$	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	−0.359894	−	0.932993i	$-0.617187\pi$
$601$	9253.48	−	16027.5i	0.628049	−	1.08781i	0.987943	−	0.154819i	$-0.0494794\pi$
$602$	−2115.91	−	3664.86i	−0.143252	−	0.248120i
$603$		0			0
$604$	3410.86	+	5907.79i	0.229778	+	0.397987i
$605$	4290.04	+	7430.56i	0.288289	+	0.499331i
$606$		0			0
$607$	3204.25	+	5549.92i	0.214261	+	0.371111i	0.953044	−	0.302833i	$-0.0979324\pi$
$607$	3204.25	+	5549.92i	0.214261	+	0.371111i	−0.738783	+	0.673944i	$0.764599\pi$
$608$	−11273.5	+	19526.3i	−0.751976	+	1.30246i
$609$		0			0
$610$	1421.34			0.0943418
$611$	−2000.01	−	25185.5i	−0.132425	−	1.66759i
$612$		0			0
$613$	1753.63	−	3037.38i	0.115544	−	0.200128i	−0.802453	−	0.596715i	$-0.796472\pi$
$613$	1753.63	−	3037.38i	0.115544	−	0.200128i	0.917997	+	0.396587i	$0.129806\pi$
$614$	753.255	−	1304.68i	0.0495096	−	0.0857532i
$615$		0			0
$616$	28529.1			1.86602
$617$	7253.89	+	12564.1i	0.473307	+	0.819792i	0.999533	−	0.0305526i	$-0.00972671\pi$
$617$	7253.89	+	12564.1i	0.473307	+	0.819792i	−0.526226	+	0.850345i	$0.676393\pi$
$618$		0			0
$619$	4750.85			0.308486			0.154243	−	0.988033i	$-0.450706\pi$
$619$	4750.85			0.308486			0.154243	+	0.988033i	$0.450706\pi$
$620$	922.451	+	1597.73i	0.0597525	+	0.103494i
$621$		0			0
$622$	2496.49	−	4324.04i	0.160933	−	0.278743i
$623$	−5087.14			−0.327146
$624$		0			0
$625$	−11347.0			−0.726209
$626$	−3528.32	+	6111.23i	−0.225272	+	0.390182i
$627$		0			0
$628$	1514.20	+	2622.68i	0.0962154	+	0.166650i
$629$	−1564.88			−0.0991986
$630$		0			0
$631$	−2412.60	−	4178.74i	−0.152209	−	0.263634i	0.779830	−	0.625991i	$-0.215305\pi$
$631$	−2412.60	−	4178.74i	−0.152209	−	0.263634i	−0.932039	+	0.362357i	$0.881972\pi$
$632$	3052.69			0.192135
$633$		0			0
$634$	836.652	−	1449.12i	0.0524096	−	0.0907762i
$635$	−12277.9	+	21266.0i	−0.767298	+	1.32900i
$636$		0			0
$637$	−23419.2	−	11150.1i	−1.45668	−	0.693539i
$638$	−13411.9			−0.832258
$639$		0			0
$640$	−6384.66	+	11058.6i	−0.394337	+	0.683013i
$641$	−2955.95	−	5119.85i	−0.182142	−	0.315479i	0.760468	−	0.649376i	$-0.224970\pi$
$641$	−2955.95	−	5119.85i	−0.182142	−	0.315479i	−0.942610	+	0.333897i	$0.891636\pi$
$642$		0			0
$643$	−11704.1	−	20272.2i	−0.717833	−	1.24332i	−0.961857	−	0.273554i	$-0.911801\pi$
$643$	−11704.1	−	20272.2i	−0.717833	−	1.24332i	0.244024	−	0.969769i	$-0.421532\pi$
$644$	−11446.6	−	19826.2i	−0.700405	−	1.21314i
$645$		0			0
$646$	−4256.01	−	7371.62i	−0.259211	−	0.448967i
$647$	−8199.33	+	14201.7i	−0.498221	+	0.862944i	−0.999998	−	0.00205298i	$-0.999347\pi$
$647$	−8199.33	+	14201.7i	−0.498221	+	0.862944i	0.501777	+	0.864997i	$0.332680\pi$
$648$		0			0
$649$	15381.9			0.930342
$650$	1735.22	+	826.157i	0.104709	+	0.0498532i
$651$		0			0
$652$	1784.97	−	3091.65i	0.107216	−	0.185703i
$653$	13764.8	−	23841.3i	0.824897	−	1.42876i	−0.0771005	−	0.997023i	$-0.524566\pi$
$653$	13764.8	−	23841.3i	0.824897	−	1.42876i	0.901998	−	0.431741i	$-0.142100\pi$
$654$		0			0
$655$	7334.34			0.437521
$656$	−2059.54	−	3567.22i	−0.122578	−	0.212312i
$657$		0			0
$658$	−23659.8			−1.40175
$659$	−12089.9	−	20940.3i	−0.714650	−	1.23781i	−0.963094	−	0.269164i	$-0.913253\pi$
$659$	−12089.9	−	20940.3i	−0.714650	−	1.23781i	0.248444	−	0.968646i	$-0.420081\pi$
$660$		0			0
$661$	−2262.52	+	3918.80i	−0.133134	+	0.230595i	−0.924883	−	0.380251i	$-0.875838\pi$
$661$	−2262.52	+	3918.80i	−0.133134	+	0.230595i	0.791749	+	0.610847i	$0.209171\pi$
$662$	11219.4			0.658695
$663$		0			0
$664$	6862.84			0.401099
$665$	17739.6	−	30725.8i	1.03445	−	1.79172i
$666$		0			0
$667$	12739.4	+	22065.3i	0.739539	+	1.28092i
$668$	17452.2			1.01085
$669$		0			0
$670$	−3185.53	−	5517.49i	−0.183683	−	0.318148i
$671$	4618.34			0.265706
$672$		0			0
$673$	−1643.59	+	2846.78i	−0.0941393	+	0.163054i	−0.909249	−	0.416253i	$-0.863343\pi$
$673$	−1643.59	+	2846.78i	−0.0941393	+	0.163054i	0.815110	+	0.579307i	$0.196677\pi$
$674$	1835.33	−	3178.89i	0.104888	−	0.181671i
$675$		0			0
$676$	−8103.14	−	9977.74i	−0.461035	−	0.567691i
$677$	9724.21			0.552041			0.276020	−	0.961152i	$-0.410984\pi$
$677$	9724.21			0.552041			0.276020	+	0.961152i	$0.410984\pi$
$678$		0			0
$679$	−3206.55	+	5553.91i	−0.181231	+	0.313902i
$680$	−4826.84	−	8360.34i	−0.272207	−	0.471477i
$681$		0			0
$682$	−1101.19	−	1907.31i	−0.0618280	−	0.107089i
$683$	7274.33	+	12599.5i	0.407532	+	0.705867i	0.994613	−	0.103662i	$-0.0330560\pi$
$683$	7274.33	+	12599.5i	0.407532	+	0.705867i	−0.587080	+	0.809529i	$0.699723\pi$
$684$		0			0
$685$	1094.23	+	1895.26i	0.0610342	+	0.105714i
$686$	−4617.26	+	7997.33i	−0.256979	+	0.445101i
$687$		0			0
$688$	1642.15			0.0909979
$689$	565.022	+	7115.13i	0.0312418	+	0.393418i
$690$		0			0
$691$	−3364.48	+	5827.45i	−0.185226	+	0.320820i	−0.943653	−	0.330938i	$-0.892635\pi$
$691$	−3364.48	+	5827.45i	−0.185226	+	0.320820i	0.758427	+	0.651758i	$0.225968\pi$
$692$	−2861.54	+	4956.33i	−0.157196	+	0.272271i
$693$		0			0
$694$	−6591.76			−0.360548
$695$	−3827.65	−	6629.69i	−0.208908	−	0.361839i
$696$		0			0
$697$	11670.9			0.634241
$698$	−2622.57	−	4542.43i	−0.142215	−	0.246323i
$699$		0			0
$700$	−2449.37	+	4242.43i	−0.132254	+	0.229070i
$701$	29159.8			1.57111			0.785557	−	0.618789i	$-0.212376\pi$
$701$	29159.8			1.57111			0.785557	+	0.618789i	$0.212376\pi$
$702$		0			0
$703$	−3900.73			−0.209273
$704$	3249.96	−	5629.10i	0.173988	−	0.301356i
$705$		0			0
$706$	−5897.52	−	10214.8i	−0.314385	−	0.544531i
$707$	−47757.0			−2.54044
$708$		0			0
$709$	10244.5	+	17744.0i	0.542653	+	0.939903i	0.998751	+	0.0499730i	$0.0159135\pi$
$709$	10244.5	+	17744.0i	0.542653	+	0.939903i	−0.456097	+	0.889930i	$0.650753\pi$
$710$	4983.16			0.263401
$711$		0			0
$712$	−1725.16	+	2988.06i	−0.0908047	+	0.157278i
$713$	−2091.96	+	3623.37i	−0.109880	+	0.190318i
$714$		0			0
$715$	−19562.3	−	9313.83i	−1.02320	−	0.487157i
$716$	10840.7			0.565833
$717$		0			0
$718$	−1592.85	+	2758.90i	−0.0827919	+	0.143400i
$719$	−8995.06	−	15579.9i	−0.466563	−	0.808111i	0.532707	−	0.846300i	$-0.321175\pi$
$719$	−8995.06	−	15579.9i	−0.466563	−	0.808111i	−0.999271	+	0.0381883i	$0.987841\pi$
$720$		0			0
$721$	23507.0	+	40715.3i	1.21421	+	2.10308i
$722$	−5580.82	−	9666.26i	−0.287668	−	0.498256i
$723$		0			0
$724$	2494.60	+	4320.78i	0.128054	+	0.221796i
$725$	2726.00	−	4721.57i	0.139643	−	0.241869i
$726$		0			0
$727$	−37652.7			−1.92086			−0.960428	−	0.278528i	$-0.910153\pi$
$727$	−37652.7			−1.92086			−0.960428	+	0.278528i	$0.910153\pi$
$728$	−23473.4	+	16157.2i	−1.19503	+	0.822561i
$729$		0			0
$730$	5587.85	−	9678.45i	0.283309	−	0.490706i
$731$	−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	$0.463637\pi$
$734$	−5617.19	−	9729.26i	−0.282472	−	0.489256i
$735$		0			0
$736$	−24495.6			−1.22679
$737$	−10350.7	−	17927.9i	−0.517329	−	0.896040i
$738$		0			0
$739$	−409.151	+	708.671i	−0.0203665	+	0.0352759i	−0.876029	−	0.482258i	$-0.839817\pi$
$739$	−409.151	+	708.671i	−0.0203665	+	0.0352759i	0.855663	+	0.517534i	$0.173150\pi$
$740$	−1868.68			−0.0928300
$741$		0			0
$742$	6684.10			0.330702
$743$	19501.1	−	33776.9i	0.962888	−	1.66777i	0.247702	−	0.968836i	$-0.420324\pi$
$743$	19501.1	−	33776.9i	0.962888	−	1.66777i	0.715185	−	0.698935i	$-0.246342\pi$
$744$		0			0
$745$	−8758.59	−	15170.3i	−0.430725	−	0.746037i
$746$	15456.4			0.758579
$747$		0			0
$748$	−6624.90	−	11474.7i	−0.323838	−	0.560903i
$749$	201.584			0.00983407
$750$		0			0
$751$	11188.8	−	19379.7i	0.543658	−	0.941643i	−0.455032	−	0.890475i	$-0.650372\pi$
$751$	11188.8	−	19379.7i	0.543658	−	0.941643i	0.998690	−	0.0511678i	$-0.0162943\pi$
$752$	4590.59	−	7951.13i	0.222608	−	0.385569i
$753$		0			0
$754$	11035.1	−	7595.67i	0.532990	−	0.366868i
$755$	−11485.7			−0.553653
$756$		0			0
$757$	17256.3	−	29888.8i	0.828521	−	1.43504i	−0.0706770	−	0.997499i	$-0.522516\pi$
$757$	17256.3	−	29888.8i	0.828521	−	1.43504i	0.899198	−	0.437542i	$-0.144151\pi$
$758$	−4013.85	−	6952.19i	−0.192335	−	0.333133i
$759$		0			0
$760$	−12031.7	−	20839.5i	−0.574258	−	0.994645i
$761$	9987.78	+	17299.3i	0.475764	+	0.824048i	0.999615	−	0.0277624i	$-0.00883820\pi$
$761$	9987.78	+	17299.3i	0.475764	+	0.824048i	−0.523850	+	0.851810i	$0.675505\pi$
$762$		0			0
$763$	8119.95	+	14064.2i	0.385271	+	0.667309i
$764$	−12992.0	+	22502.8i	−0.615228	+	1.06561i
$765$		0			0
$766$	−1184.73			−0.0558827
$767$	−12656.0	+	8711.38i	−0.595804	+	0.410104i
$768$		0			0
$769$	16532.4	−	28635.0i	0.775260	−	1.34279i	−0.159388	−	0.987216i	$-0.550952\pi$
$769$	16532.4	−	28635.0i	0.775260	−	1.34279i	0.934648	−	0.355574i	$-0.115715\pi$
$770$	−10145.0	+	17571.6i	−0.474805	+	0.822387i
$771$		0			0
$772$	14523.6			0.677091
$773$	−9282.01	−	16076.9i	−0.431890	−	0.748055i	0.565146	−	0.824991i	$-0.308820\pi$
$773$	−9282.01	−	16076.9i	−0.431890	−	0.748055i	−0.997036	+	0.0769359i	$0.975486\pi$
$774$		0			0
$775$	895.279			0.0414960
$776$	2174.82	+	3766.90i	0.100608	+	0.174257i
$777$		0			0
$778$	−5175.53	+	8964.28i	−0.238498	+	0.413091i
$779$	29091.6			1.33802
$780$		0			0
$781$	16191.7			0.741848
$782$	4623.83	−	8008.71i	0.211442	−	0.366229i
$783$		0			0
$784$	−4712.93	−	8163.04i	−0.214693	−	0.371858i
$785$	−5098.91			−0.231832
$786$		0			0
$787$	−18218.4	−	31555.2i	−0.825179	−	1.42925i	−0.901782	−	0.432190i	$-0.857741\pi$
$787$	−18218.4	−	31555.2i	−0.825179	−	1.42925i	0.0766032	−	0.997062i	$-0.475593\pi$
$788$	7373.04			0.333317
$789$		0			0
$790$	−1085.54	+	1880.21i	−0.0488884	+	0.0846772i
$791$	−21598.8	+	37410.2i	−0.970877	+	1.68161i
$792$		0			0
$793$	−3799.90	+	2615.55i	−0.170162	+	0.117126i
$794$	−2081.71			−0.0930441
$795$		0			0
$796$	−16150.3	+	27973.2i	−0.719137	+	1.24558i
$797$	6182.80	+	10708.9i	0.274788	+	0.475947i	0.970082	−	0.242779i	$-0.0780590\pi$
$797$	6182.80	+	10708.9i	0.274788	+	0.475947i	−0.695294	+	0.718726i	$0.744726\pi$
$798$		0			0
$799$	13006.9	+	22528.6i	0.575907	+	0.997501i
$800$	2620.80	+	4539.37i	0.115824	+	0.200614i
$801$		0			0
$802$	7822.19	+	13548.4i	0.344403	+	0.596523i
$803$	18156.5	−	31448.0i	0.797918	−	1.38204i
$804$		0			0
$805$	38545.4			1.68763
$806$	1986.23	+	945.665i	0.0868015	+	0.0413271i
$807$		0			0
$808$	−16195.4	+	28051.3i	−0.705140	+	1.22134i
$809$	−4046.87	+	7009.39i	−0.175872	+	0.304619i	−0.940463	−	0.339897i	$-0.889608\pi$
$809$	−4046.87	+	7009.39i	−0.175872	+	0.304619i	0.764591	+	0.644516i	$0.222941\pi$
$810$		0			0
$811$	15984.7			0.692105			0.346052	−	0.938215i	$-0.387522\pi$
$811$	15984.7			0.692105			0.346052	+	0.938215i	$0.387522\pi$
$812$	17073.6	+	29572.4i	0.737891	+	1.27806i
$813$		0			0
$814$	2230.77			0.0960546
$815$	3005.34	+	5205.40i	0.129169	+	0.223727i
$816$		0			0
$817$	−5798.99	+	10044.2i	−0.248325	+	0.430111i
$818$	9312.03			0.398029
$819$		0			0
$820$	13936.6			0.593523
$821$	−13430.9	+	23263.1i	−0.570942	+	0.988900i	0.425528	+	0.904945i	$0.360089\pi$
$821$	−13430.9	+	23263.1i	−0.570942	+	0.988900i	−0.996470	+	0.0839550i	$0.973245\pi$
$822$		0			0
$823$	2602.97	+	4508.48i	0.110248	+	0.190955i	0.915870	−	0.401475i	$-0.131502\pi$
$823$	2602.97	+	4508.48i	0.110248	+	0.190955i	−0.805622	+	0.592429i	$0.798169\pi$
$824$	31886.9			1.34810
$825$		0			0
$826$	7194.14	+	12460.6i	0.303046	+	0.524891i
$827$	−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	0.0208053	−	0.999784i	$-0.493377\pi$
$829$	20914.9	−	36225.6i	0.876241	−	1.51769i	0.855435	−	0.517910i	$-0.173290\pi$
$830$	−2440.44	+	4226.96i	−0.102059	+	0.176771i
$831$		0			0
$832$	513.960	+	6472.12i	0.0214163	+	0.269688i
$833$	26707.0			1.11086
$834$		0			0
$835$	−14692.1	+	25447.5i	−0.608913	+	1.05467i
$836$	−16513.7	−	28602.5i	−0.683179	−	1.18330i
$837$		0			0
$838$	4118.19	+	7132.91i	0.169762	+	0.294036i
$839$	6342.54	+	10985.6i	0.260988	+	0.452044i	0.966505	−	0.256649i	$-0.0826185\pi$
$839$	6342.54	+	10985.6i	0.260988	+	0.452044i	−0.705517	+	0.708693i	$0.749285\pi$
$840$		0			0
$841$	−6807.43	−	11790.8i	−0.279119	−	0.483448i
$842$	1112.99	−	1927.75i	0.0455535	−	0.0789009i
$843$		0			0
$844$	26490.1			1.08036
$845$	21370.4	−	3415.64i	0.870017	−	0.139055i
$846$		0			0
$847$	−13039.1	+	22584.3i	−0.528959	+	0.916183i
$848$	−1296.88	+	2246.27i	−0.0525179	+	0.0909636i
$849$		0			0
$850$	−1978.83			−0.0798509
$851$	−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	$0.771146\pi$
$854$	2160.00	+	3741.24i	0.0865501	+	0.149909i
$855$		0			0
$856$	68.3614	−	118.405i	0.00272961	−	0.00472782i
$857$	11826.3			0.471386			0.235693	−	0.971828i	$-0.424264\pi$
$857$	11826.3			0.471386			0.235693	+	0.971828i	$0.424264\pi$
$858$		0			0
$859$	−36498.7			−1.44973			−0.724866	−	0.688890i	$-0.758099\pi$
$859$	−36498.7			−1.44973			−0.724866	+	0.688890i	$0.758099\pi$
$860$	−2778.07	+	4811.76i	−0.110153	+	0.190790i
$861$		0			0
$862$	−3643.36	−	6310.48i	−0.143960	−	0.249346i
$863$	−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
$866$	−4836.24			−0.189772
$867$		0			0
$868$	−2803.68	+	4856.12i	−0.109635	+	0.189893i
$869$	−3527.22	+	6109.33i	−0.137690	+	0.238487i
$870$		0			0
$871$	18669.6	+	8888.81i	0.726288	+	0.345793i
$872$	11014.6			0.427753
$873$		0			0
$874$	11525.7	−	19963.1i	0.446066	−	0.772609i
$875$	−22556.6	−	39069.2i	−0.871488	−	1.50946i
$876$		0			0
$877$	10400.1	+	18013.6i	0.400442	+	0.693587i	0.993779	−	0.111368i	$-0.0355231\pi$
$877$	10400.1	+	18013.6i	0.400442	+	0.693587i	−0.593337	+	0.804954i	$0.702190\pi$
$878$	4433.84	+	7679.63i	0.170427	+	0.295188i
$879$		0			0
$880$	−3936.76	−	6818.67i	−0.150805	−	0.261202i
$881$	−9627.95	+	16676.1i	−0.368188	+	0.637721i	−0.989282	−	0.146015i	$-0.953355\pi$
$881$	−9627.95	+	16676.1i	−0.368188	+	0.637721i	0.621094	+	0.783736i	$0.286689\pi$
$882$		0			0
$883$	1744.49			0.0664857			0.0332429	−	0.999447i	$-0.489417\pi$
$883$	1744.49			0.0664857			0.0332429	+	0.999447i	$0.489417\pi$
$884$	11949.4	+	5689.25i	0.454642	+	0.216460i
$885$		0			0
$886$	5001.33	−	8662.56i	0.189642	−	0.328470i
$887$	1485.35	−	2572.70i	0.0562268	−	0.0973877i	−0.836542	−	0.547903i	$-0.815426\pi$
$887$	1485.35	−	2572.70i	0.0562268	−	0.0973877i	0.892769	+	0.450515i	$0.148760\pi$
$888$		0			0
$889$	−74634.6			−2.81571
$890$	−1226.94	−	2125.11i	−0.0462101	−	0.0800382i
$891$		0			0
$892$	−26217.3			−0.984104
$893$	32421.8	+	56156.2i	1.21495	+	2.10436i
$894$		0			0
$895$	−9126.24	+	15807.1i	−0.340845	+	0.590361i
$896$	−38810.9			−1.44708
$897$		0			0
$898$	−601.703			−0.0223598
$899$	3120.33	−	5404.57i	0.115761	−	0.200503i
$900$		0			0
$901$	−3674.56	−	6364.52i	−0.135868	−	0.235331i
$902$	−16637.1			−0.614140
$903$		0			0
$904$	14649.2	+	25373.2i	0.538966	+	0.933516i
$905$	−8400.32			−0.308548
$906$		0			0
$907$	−16501.7	+	28581.7i	−0.604111	+	1.04635i	0.388080	+	0.921626i	$0.373138\pi$
$907$	−16501.7	+	28581.7i	−0.604111	+	1.04635i	−0.992191	+	0.124726i	$0.960195\pi$
$908$	16848.8	−	29183.1i	0.615802	−	1.06660i
$909$		0			0
$910$	−1604.36	−	20203.2i	−0.0584441	−	0.735967i
$911$	−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
$914$	12200.0	+	21131.1i	0.441511	+	0.764720i
$915$		0			0
$916$	−13558.9	−	23484.7i	−0.489080	−	0.847112i
$917$	11145.9	+	19305.3i	0.401386	+	0.695221i
$918$		0			0
$919$	−5712.69	−	9894.67i	−0.205054	−	0.355163i	0.745096	−	0.666957i	$-0.232404\pi$
$919$	−5712.69	−	9894.67i	−0.205054	−	0.355163i	−0.950150	+	0.311794i	$0.899070\pi$
$920$	13071.6	−	22640.6i	0.468431	−	0.811346i
$921$		0			0
$922$	17196.9			0.614263
$923$	−13322.3	+	9169.99i	−0.475090	+	0.327014i
$924$		0			0
$925$	−453.410	+	785.329i	−0.0161168	+	0.0279151i
$926$	2613.27	−	4526.32i	0.0927403	−	0.160631i
$927$		0			0
$928$	36537.3			1.29245
$929$	5977.10	+	10352.6i	0.211090	+	0.365618i	0.952056	−	0.305924i	$-0.0989655\pi$
$929$	5977.10	+	10352.6i	0.211090	+	0.365618i	−0.740966	+	0.671542i	$0.765632\pi$
$930$		0			0
$931$	66571.7			2.34350
$932$	−17219.1	−	29824.4i	−0.605183	−	1.04821i
$933$		0			0
$934$	831.870	−	1440.84i	0.0291431	−	0.0504773i
$935$	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	$0.234024\pi$
$938$	9682.04	−	16769.8i	0.337025	−	0.583745i
$939$		0			0
$940$	15532.0	+	26902.2i	0.538934	+	0.933461i
$941$	−20665.1			−0.715903			−0.357951	−	0.933740i	$-0.616525\pi$
$941$	−20665.1			−0.715903			−0.357951	+	0.933740i	$0.616525\pi$
$942$		0			0
$943$	15802.9	+	27371.5i	0.545720	+	0.945215i
$944$	−5583.37			−0.192503
$945$		0			0
$946$	3316.36	−	5744.10i	0.113979	−	0.197417i
$947$	−4746.87	+	8221.81i	−0.162885	+	0.282126i	−0.935902	−	0.352260i	$-0.885413\pi$
$947$	−4746.87	+	8221.81i	−0.162885	+	0.282126i	0.773017	+	0.634385i	$0.218747\pi$
$948$		0			0
$949$	2871.33	+	36157.7i	0.0982163	+	1.23681i
$950$	−4932.56			−0.168456
$951$		0			0
$952$	14670.6	−	25410.3i	0.499452	−	0.865076i
$953$	26667.1	+	46188.7i	0.906433	+	1.56999i	0.818982	+	0.573819i	$0.194539\pi$
$953$	26667.1	+	46188.7i	0.906433	+	1.56999i	0.0874512	+	0.996169i	$0.472128\pi$
$954$		0			0
$955$	−21874.6	−	37887.9i	−0.741199	−	1.28379i
$956$	−6247.93	−	10821.7i	−0.211373	−	0.366108i
$957$		0			0
$958$	−14201.1	−	24597.0i	−0.478932	−	0.829534i
$959$	−3325.79	+	5760.44i	−0.111987	+	0.193967i
$960$		0			0
$961$	−28766.2			−0.965601
$962$	−1835.45	+	1263.37i	−0.0615147	+	0.0423418i
$963$		0			0
$964$	13728.1	−	23777.7i	0.458663	−	0.794428i
$965$	−12226.6	+	21177.2i	−0.407865	+	0.706443i
$966$		0			0
$967$	−42110.1			−1.40038			−0.700191	−	0.713956i	$-0.746902\pi$
$967$	−42110.1			−1.40038			−0.700191	+	0.713956i	$0.746902\pi$
$968$	8843.65	+	15317.7i	0.293642	+	0.508604i
$969$		0			0
$970$	−3093.47			−0.102397
$971$	−6913.86	−	11975.2i	−0.228503	−	0.395779i	0.728862	−	0.684661i	$-0.240050\pi$
$971$	−6913.86	−	11975.2i	−0.228503	−	0.395779i	−0.957365	+	0.288882i	$0.906716\pi$
$972$		0			0
$973$	11633.7	−	20150.2i	0.383309	−	0.663911i
$974$	−13262.3			−0.436295
$975$		0			0
$976$	−1676.38			−0.0549791
$977$	566.943	−	981.973i	0.0185651	−	0.0321557i	−0.856594	−	0.515992i	$-0.827424\pi$
$977$	566.943	−	981.973i	0.0185651	−	0.0321557i	0.875159	+	0.483836i	$0.160757\pi$
$978$		0			0
$979$	−3986.65	−	6905.09i	−0.130147	−	0.225421i
$980$	31891.9			1.03954
$981$		0			0
$982$	10558.4	+	18287.6i	0.343107	+	0.594279i
$983$	−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
$986$	−6896.84	+	11945.7i	−0.222759	+	0.385829i
$987$		0			0
$988$	29786.0	+	14181.4i	0.959128	+	0.456651i
$989$	−12600.3			−0.405124
$990$		0			0
$991$	14680.2	−	25426.8i	0.470566	−	0.815045i	−0.528867	−	0.848705i	$-0.677383\pi$
$991$	14680.2	−	25426.8i	0.470566	−	0.815045i	0.999433	+	0.0336599i	$0.0107163\pi$
$992$	2999.92	+	5196.01i	0.0960156	+	0.166304i
$993$		0			0
$994$	7572.87	+	13116.6i	0.241647	+	0.418544i
$995$	−27192.3	−	47098.4i	−0.866384	−	1.50062i
$996$		0			0
$997$	−8417.95	−	14580.3i	−0.267401	−	0.463153i	0.700789	−	0.713369i	$-0.252832\pi$
$997$	−8417.95	−	14580.3i	−0.267401	−	0.463153i	−0.968190	+	0.250216i	$0.919498\pi$
$998$	6831.85	−	11833.1i	0.216692	−	0.375321i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.4.g.e.100.2		8
3.2	odd	2		39.4.e.c.22.3	yes	8
12.11	even	2		624.4.q.i.529.4		8
13.3	even	3	inner	117.4.g.e.55.2		8
13.4	even	6		1521.4.a.bb.1.2		4
13.9	even	3		1521.4.a.v.1.3		4
39.17	odd	6		507.4.a.i.1.3		4
39.20	even	12		507.4.b.h.337.4		8
39.29	odd	6		39.4.e.c.16.3	✓	8
39.32	even	12		507.4.b.h.337.5		8
39.35	odd	6		507.4.a.m.1.2		4
156.107	even	6		624.4.q.i.289.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.e.c.16.3	✓	8	39.29	odd	6
39.4.e.c.22.3	yes	8	3.2	odd	2
117.4.g.e.55.2		8	13.3	even	3	inner
117.4.g.e.100.2		8	1.1	even	1	trivial
507.4.a.i.1.3		4	39.17	odd	6
507.4.a.m.1.2		4	39.35	odd	6
507.4.b.h.337.4		8	39.20	even	12
507.4.b.h.337.5		8	39.32	even	12
624.4.q.i.289.4		8	156.107	even	6
624.4.q.i.529.4		8	12.11	even	2
1521.4.a.v.1.3		4	13.9	even	3
1521.4.a.bb.1.2		4	13.4	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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	117.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.733051 + 1.26968i) q^{2} +(2.92527 + 5.06672i) q^{4} -9.85055 q^{5} +(-14.9698 - 25.9285i) q^{7} -20.3063 q^{8} +O(q^{10})\)	\(q+(-0.733051 + 1.26968i) q^{2} +(2.92527 + 5.06672i) q^{4} -9.85055 q^{5} +(-14.9698 - 25.9285i) q^{7} -20.3063 q^{8} +(7.22095 - 12.5071i) q^{10} +(23.4629 - 40.6389i) q^{11} +(3.71050 + 46.7251i) q^{13} +43.8945 q^{14} +(-8.51663 + 14.7512i) q^{16} +(-24.1308 - 41.7958i) q^{17} +(-60.1501 - 104.183i) q^{19} +(-28.8155 - 49.9100i) q^{20} +(34.3990 + 59.5807i) q^{22} +(65.3485 - 113.187i) q^{23} -27.9667 q^{25} +(-62.0459 - 29.5407i) q^{26} +(87.5815 - 151.696i) q^{28} +(-97.4729 + 168.828i) q^{29} -32.0123 q^{31} +(-93.7115 - 162.313i) q^{32} +70.7565 q^{34} +(147.461 + 255.409i) q^{35} +(16.2125 - 28.0808i) q^{37} +176.372 q^{38} +200.028 q^{40} +(-120.913 + 209.427i) q^{41} +(-48.2044 - 83.4924i) q^{43} +274.541 q^{44} +(95.8076 + 165.944i) q^{46} -539.015 q^{47} +(-276.690 + 479.241i) q^{49} +(20.5010 - 35.5088i) q^{50} +(-225.889 + 155.484i) q^{52} +152.277 q^{53} +(-231.122 + 400.315i) q^{55} +(303.981 + 526.511i) q^{56} +(-142.905 - 247.519i) q^{58} +(163.896 + 283.876i) q^{59} +(49.2090 + 85.2325i) q^{61} +(23.4666 - 40.6454i) q^{62} +138.515 q^{64} +(-36.5504 - 460.267i) q^{65} +(220.575 - 382.048i) q^{67} +(141.178 - 244.528i) q^{68} -432.385 q^{70} +(172.524 + 298.821i) q^{71} +773.839 q^{73} +(23.7691 + 41.1694i) q^{74} +(351.911 - 609.528i) q^{76} -1404.94 q^{77} -150.332 q^{79} +(83.8934 - 145.308i) q^{80} +(-177.270 - 307.041i) q^{82} -337.966 q^{83} +(237.702 + 411.711i) q^{85} +141.345 q^{86} +(-476.444 + 825.226i) q^{88} +(84.9567 - 147.149i) q^{89} +(1155.96 - 795.673i) q^{91} +764.649 q^{92} +(395.125 - 684.377i) q^{94} +(592.511 + 1026.26i) q^{95} +(-107.101 - 185.504i) q^{97} +(-405.656 - 702.616i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 22 q^{4} + 12 q^{5} + 14 q^{7} - 108 q^{8}+O(q^{10}) \) 8 * q + 2 * q^2 - 22 * q^4 + 12 * q^5 + 14 * q^7 - 108 * q^8	\( 8 q + 2 q^{2} - 22 q^{4} + 12 q^{5} + 14 q^{7} - 108 q^{8} + 62 q^{10} + 40 q^{11} - 60 q^{13} - 80 q^{14} - 122 q^{16} + 98 q^{17} - 124 q^{19} - 466 q^{20} - 220 q^{22} + 104 q^{23} - 116 q^{25} - 14 q^{26} + 144 q^{28} + 194 q^{29} + 52 q^{31} + 654 q^{32} + 2124 q^{34} + 88 q^{35} - 102 q^{37} - 664 q^{38} - 1996 q^{40} - 1054 q^{41} - 450 q^{43} + 88 q^{44} + 172 q^{46} + 192 q^{47} - 1070 q^{49} + 996 q^{50} + 2280 q^{52} - 524 q^{53} - 204 q^{55} + 2164 q^{56} - 722 q^{58} + 308 q^{59} + 928 q^{61} + 2780 q^{62} + 2052 q^{64} - 2346 q^{65} + 1134 q^{67} + 1786 q^{68} - 4648 q^{70} + 1064 q^{71} + 1904 q^{73} + 1158 q^{74} + 1708 q^{76} - 5016 q^{77} - 1492 q^{79} - 2922 q^{80} - 1734 q^{82} + 808 q^{83} + 1394 q^{85} - 6336 q^{86} - 3060 q^{88} + 1620 q^{89} + 3278 q^{91} - 664 q^{92} + 772 q^{94} + 2204 q^{95} - 2166 q^{97} - 1906 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 - 22 * q^4 + 12 * q^5 + 14 * q^7 - 108 * q^8 + 62 * q^10 + 40 * q^11 - 60 * q^13 - 80 * q^14 - 122 * q^16 + 98 * q^17 - 124 * q^19 - 466 * q^20 - 220 * q^22 + 104 * q^23 - 116 * q^25 - 14 * q^26 + 144 * q^28 + 194 * q^29 + 52 * q^31 + 654 * q^32 + 2124 * q^34 + 88 * q^35 - 102 * q^37 - 664 * q^38 - 1996 * q^40 - 1054 * q^41 - 450 * q^43 + 88 * q^44 + 172 * q^46 + 192 * q^47 - 1070 * q^49 + 996 * q^50 + 2280 * q^52 - 524 * q^53 - 204 * q^55 + 2164 * q^56 - 722 * q^58 + 308 * q^59 + 928 * q^61 + 2780 * q^62 + 2052 * q^64 - 2346 * q^65 + 1134 * q^67 + 1786 * q^68 - 4648 * q^70 + 1064 * q^71 + 1904 * q^73 + 1158 * q^74 + 1708 * q^76 - 5016 * q^77 - 1492 * q^79 - 2922 * q^80 - 1734 * q^82 + 808 * q^83 + 1394 * q^85 - 6336 * q^86 - 3060 * q^88 + 1620 * q^89 + 3278 * q^91 - 664 * q^92 + 772 * q^94 + 2204 * q^95 - 2166 * q^97 - 1906 * q^98

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