LMFDB - Embedded newform 350.4.j.j.249.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,4,Mod(149,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("350.149");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	350.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$20.6506685020$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 66 x^{14} + 3127 x^{12} - 69136 x^{10} + 1110267 x^{8} - 6713681 x^{6} + 29846021 x^{4} + \cdots + 24010000 $ x^16 - 66x^14 + 3127x^12 - 69136x^10 + 1110267x^8 - 6713681x^6 + 29846021x^4 - 29346100*x^2 + 24010000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			249.8
Root			$-0.874749 - 0.505037i$ of defining polynomial
Character	$\chi$	$=$	350.249
Dual form			350.4.j.j.149.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73205 - 1.00000i) q^{2} +(7.32867 + 4.23121i) q^{3} +(2.00000 - 3.46410i) q^{4} +16.9248 q^{6} +(-3.87329 + 18.1107i) q^{7} -8.00000i q^{8} +(22.3062 + 38.6355i) q^{9} +O(q^{10})$	\(q+(1.73205 - 1.00000i) q^{2} +(7.32867 + 4.23121i) q^{3} +(2.00000 - 3.46410i) q^{4} +16.9248 q^{6} +(-3.87329 + 18.1107i) q^{7} -8.00000i q^{8} +(22.3062 + 38.6355i) q^{9} +(-2.80448 + 4.85750i) q^{11} +(29.3147 - 16.9248i) q^{12} -44.1803i q^{13} +(11.4020 + 35.2419i) q^{14} +(-8.00000 - 13.8564i) q^{16} +(94.7578 + 54.7084i) q^{17} +(77.2710 + 44.6125i) q^{18} +(68.3642 + 118.410i) q^{19} +(-105.016 + 116.339i) q^{21} +11.2179i q^{22} +(18.5377 - 10.7027i) q^{23} +(33.8497 - 58.6293i) q^{24} +(-44.1803 - 76.5225i) q^{26} +149.044i q^{27} +(54.9907 + 49.6389i) q^{28} -99.6624 q^{29} +(-8.56690 + 14.8383i) q^{31} +(-27.7128 - 16.0000i) q^{32} +(-41.1062 + 23.7327i) q^{33} +218.834 q^{34} +178.450 q^{36} +(2.77668 - 1.60311i) q^{37} +(236.821 + 136.728i) q^{38} +(186.936 - 323.782i) q^{39} +298.615 q^{41} +(-65.5547 + 306.521i) q^{42} -413.814i q^{43} +(11.2179 + 19.4300i) q^{44} +(21.4055 - 37.0754i) q^{46} +(-508.882 + 293.803i) q^{47} -135.399i q^{48} +(-312.995 - 140.296i) q^{49} +(462.965 + 801.880i) q^{51} +(-153.045 - 88.3605i) q^{52} +(-520.935 - 300.762i) q^{53} +(149.044 + 258.152i) q^{54} +(144.886 + 30.9863i) q^{56} +1157.05i q^{57} +(-172.620 + 99.6624i) q^{58} +(305.985 - 529.982i) q^{59} +(-348.465 - 603.560i) q^{61} +34.2676i q^{62} +(-786.115 + 254.335i) q^{63} -64.0000 q^{64} +(-47.4653 + 82.2123i) q^{66} +(-401.812 - 231.986i) q^{67} +(379.031 - 218.834i) q^{68} +181.142 q^{69} +231.542 q^{71} +(309.084 - 178.450i) q^{72} +(611.386 + 352.984i) q^{73} +(3.20623 - 5.55335i) q^{74} +546.914 q^{76} +(-77.1102 - 69.6056i) q^{77} -747.743i q^{78} +(506.872 + 877.928i) q^{79} +(-28.3674 + 49.1337i) q^{81} +(517.217 - 298.615i) q^{82} +476.913i q^{83} +(192.976 + 596.464i) q^{84} +(-413.814 - 716.747i) q^{86} +(-730.393 - 421.692i) q^{87} +(38.8600 + 22.4358i) q^{88} +(-390.263 - 675.955i) q^{89} +(800.136 + 171.123i) q^{91} -85.6219i q^{92} +(-125.568 + 72.4966i) q^{93} +(-587.606 + 1017.76i) q^{94} +(-135.399 - 234.517i) q^{96} -908.934i q^{97} +(-682.420 + 69.9956i) q^{98} -250.229 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{4} - 8 q^{6} + 146 q^{9}+O(q^{10}) $ 16 * q + 32 * q^4 - 8 * q^6 + 146 * q^9	$ 16 q + 32 q^{4} - 8 q^{6} + 146 q^{9} + 20 q^{11} + 140 q^{14} - 128 q^{16} + 492 q^{19} - 1070 q^{21} - 16 q^{24} - 376 q^{26} + 392 q^{29} - 608 q^{31} - 792 q^{34} + 1168 q^{36} - 428 q^{39} + 1408 q^{41} - 80 q^{44} + 8 q^{46} - 2566 q^{49} + 2874 q^{51} - 784 q^{54} + 112 q^{56} + 1346 q^{59} - 2850 q^{61} - 1024 q^{64} - 2104 q^{66} - 3752 q^{69} - 24 q^{71} - 328 q^{74} + 3936 q^{76} + 3488 q^{79} - 3416 q^{81} - 1744 q^{84} - 524 q^{86} - 1742 q^{89} - 1594 q^{91} - 1964 q^{94} + 64 q^{96} + 21124 q^{99}+O(q^{100}) $ 16 * q + 32 * q^4 - 8 * q^6 + 146 * q^9 + 20 * q^11 + 140 * q^14 - 128 * q^16 + 492 * q^19 - 1070 * q^21 - 16 * q^24 - 376 * q^26 + 392 * q^29 - 608 * q^31 - 792 * q^34 + 1168 * q^36 - 428 * q^39 + 1408 * q^41 - 80 * q^44 + 8 * q^46 - 2566 * q^49 + 2874 * q^51 - 784 * q^54 + 112 * q^56 + 1346 * q^59 - 2850 * q^61 - 1024 * q^64 - 2104 * q^66 - 3752 * q^69 - 24 * q^71 - 328 * q^74 + 3936 * q^76 + 3488 * q^79 - 3416 * q^81 - 1744 * q^84 - 524 * q^86 - 1742 * q^89 - 1594 * q^91 - 1964 * q^94 + 64 * q^96 + 21124 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$3$	7.32867	+	4.23121i	1.41040	+	0.814296i	0.995426	−	0.0955360i	$-0.0304565\pi$
$3$	7.32867	+	4.23121i	1.41040	+	0.814296i	0.414976	+	0.909832i	$0.363790\pi$
$4$	2.00000	−	3.46410i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	16.9248			1.15159
$7$	−3.87329	+	18.1107i	−0.209138	+	0.977886i
$7$	−3.87329	+	18.1107i	−0.209138	+	0.977886i
$8$		−	8.00000i		−	0.353553i
$9$	22.3062	+	38.6355i	0.826157	+	1.43095i
$10$		0			0
$11$	−2.80448	+	4.85750i	−0.0768711	+	0.133145i	−0.901898	−	0.431948i	$-0.857826\pi$
$11$	−2.80448	+	4.85750i	−0.0768711	+	0.133145i	0.825027	+	0.565093i	$0.191160\pi$
$12$	29.3147	−	16.9248i	0.705201	−	0.407148i
$13$		−	44.1803i		−	0.942569i	−0.881981	−	0.471285i	$-0.843790\pi$
$13$		−	44.1803i		−	0.942569i	0.881981	−	0.471285i	$-0.156210\pi$
$14$	11.4020	+	35.2419i	0.217665	+	0.672772i
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	94.7578	+	54.7084i	1.35189	+	0.780514i	0.988514	−	0.151128i	$-0.0482906\pi$
$17$	94.7578	+	54.7084i	1.35189	+	0.780514i	0.363376	+	0.931642i	$0.381624\pi$
$18$	77.2710	+	44.6125i	1.01183	+	0.584181i
$19$	68.3642	+	118.410i	0.825465	+	1.42975i	0.901564	+	0.432647i	$0.142420\pi$
$19$	68.3642	+	118.410i	0.825465	+	1.42975i	−0.0760987	+	0.997100i	$0.524246\pi$
$20$		0			0
$21$	−105.016	+	116.339i	−1.09126	+	1.20891i
$22$			11.2179i			0.108712i
$23$	18.5377	−	10.7027i	0.168060	−	0.0970293i	−0.413611	−	0.910454i	$-0.635733\pi$
$23$	18.5377	−	10.7027i	0.168060	−	0.0970293i	0.581671	+	0.813424i	$0.302399\pi$
$24$	33.8497	−	58.6293i	0.287897	−	0.498653i
$25$		0			0
$26$	−44.1803	−	76.5225i	−0.333249	−	0.577203i
$27$			149.044i			1.06235i
$28$	54.9907	+	49.6389i	0.371153	+	0.335031i
$29$	−99.6624			−0.638167			−0.319084	−	0.947727i	$-0.603375\pi$
$29$	−99.6624			−0.638167			−0.319084	+	0.947727i	$0.603375\pi$
$30$		0			0
$31$	−8.56690	+	14.8383i	−0.0496342	+	0.0859689i	−0.889775	−	0.456399i	$-0.849139\pi$
$31$	−8.56690	+	14.8383i	−0.0496342	+	0.0859689i	0.840141	+	0.542368i	$0.182472\pi$
$32$	−27.7128	−	16.0000i	−0.153093	−	0.0883883i
$33$	−41.1062	+	23.7327i	−0.216838	+	0.125192i
$34$	218.834			1.10381
$35$		0			0
$36$	178.450			0.826157
$37$	2.77668	−	1.60311i	0.0123374	−	0.00712298i	−0.493819	−	0.869565i	$-0.664399\pi$
$37$	2.77668	−	1.60311i	0.0123374	−	0.00712298i	0.506156	+	0.862442i	$0.331066\pi$
$38$	236.821	+	136.728i	1.01098	+	0.583692i
$39$	186.936	−	323.782i	0.767530	−	1.32940i
$40$		0			0
$41$	298.615			1.13746			0.568730	−	0.822524i	$-0.307435\pi$
$41$	298.615			1.13746			0.568730	+	0.822524i	$0.307435\pi$
$42$	−65.5547	+	306.521i	−0.240841	+	1.12612i
$43$		−	413.814i		−	1.46758i	−0.679375	−	0.733791i	$-0.737749\pi$
$43$		−	413.814i		−	1.46758i	0.679375	−	0.733791i	$-0.262251\pi$
$44$	11.2179	+	19.4300i	0.0384356	+	0.0665723i
$45$		0			0
$46$	21.4055	−	37.0754i	0.0686101	−	0.118836i
$47$	−508.882	+	293.803i	−1.57932	+	0.911821i	−0.584365	+	0.811491i	$0.698656\pi$
$47$	−508.882	+	293.803i	−1.57932	+	0.911821i	−0.994954	+	0.100330i	$0.968010\pi$
$48$		−	135.399i		−	0.407148i
$49$	−312.995	−	140.296i	−0.912523	−	0.409026i
$50$		0			0
$51$	462.965	+	801.880i	1.27114	+	2.20168i
$52$	−153.045	−	88.3605i	−0.408144	−	0.235642i
$53$	−520.935	−	300.762i	−1.35011	−	0.779487i	−0.361846	−	0.932238i	$-0.617853\pi$
$53$	−520.935	−	300.762i	−1.35011	−	0.779487i	−0.988265	+	0.152751i	$0.951187\pi$
$54$	149.044	+	258.152i	0.375598	+	0.650555i
$55$		0			0
$56$	144.886	+	30.9863i	0.345735	+	0.0739414i
$57$			1157.05i			2.68869i
$58$	−172.620	+	99.6624i	−0.390796	+	0.225626i
$59$	305.985	−	529.982i	0.675185	−	1.16945i	−0.301230	−	0.953552i	$-0.597397\pi$
$59$	305.985	−	529.982i	0.675185	−	1.16945i	0.976415	−	0.215903i	$-0.0692696\pi$
$60$		0			0
$61$	−348.465	−	603.560i	−0.731417	−	1.26685i	−0.956278	−	0.292460i	$-0.905526\pi$
$61$	−348.465	−	603.560i	−0.731417	−	1.26685i	0.224861	−	0.974391i	$-0.427807\pi$
$62$			34.2676i			0.0701934i
$63$	−786.115	+	254.335i	−1.57208	+	0.508622i
$64$	−64.0000			−0.125000
$65$		0			0
$66$	−47.4653	+	82.2123i	−0.0885239	+	0.153328i
$67$	−401.812	−	231.986i	−0.732674	−	0.423010i	0.0867256	−	0.996232i	$-0.472360\pi$
$67$	−401.812	−	231.986i	−0.732674	−	0.423010i	−0.819400	+	0.573223i	$0.805693\pi$
$68$	379.031	−	218.834i	0.675945	−	0.390257i
$69$	181.142			0.316042
$70$		0			0
$71$	231.542			0.387028			0.193514	−	0.981098i	$-0.438011\pi$
$71$	231.542			0.387028			0.193514	+	0.981098i	$0.438011\pi$
$72$	309.084	−	178.450i	0.505915	−	0.292090i
$73$	611.386	+	352.984i	0.980237	+	0.565940i	0.902342	−	0.431021i	$-0.141847\pi$
$73$	611.386	+	352.984i	0.980237	+	0.565940i	0.0778955	+	0.996962i	$0.475180\pi$
$74$	3.20623	−	5.55335i	0.00503671	−	0.00872384i
$75$		0			0
$76$	546.914			0.825465
$77$	−77.1102	−	69.6056i	−0.114124	−	0.103017i
$78$		−	747.743i		−	1.08545i
$79$	506.872	+	877.928i	0.721867	+	1.25031i	0.960250	+	0.279140i	$0.0900493\pi$
$79$	506.872	+	877.928i	0.721867	+	1.25031i	−0.238383	+	0.971171i	$0.576617\pi$
$80$		0			0
$81$	−28.3674	+	49.1337i	−0.0389127	+	0.0673988i
$82$	517.217	−	298.615i	0.696549	−	0.402153i
$83$			476.913i			0.630698i	0.948976	+	0.315349i	$0.102122\pi$
$83$			476.913i			0.630698i	−0.948976	+	0.315349i	$0.897878\pi$
$84$	192.976	+	596.464i	0.250660	+	0.774757i
$85$		0			0
$86$	−413.814	−	716.747i	−0.518868	−	0.898707i
$87$	−730.393	−	421.692i	−0.900072	−	0.519657i
$88$	38.8600	+	22.4358i	0.0470737	+	0.0271780i
$89$	−390.263	−	675.955i	−0.464806	−	0.805068i	0.534386	−	0.845240i	$-0.320543\pi$
$89$	−390.263	−	675.955i	−0.464806	−	0.805068i	−0.999193	+	0.0401720i	$0.987209\pi$
$90$		0			0
$91$	800.136	+	171.123i	0.921725	+	0.197127i
$92$		−	85.6219i		−	0.0970293i
$93$	−125.568	+	72.4966i	−0.140008	+	0.0808339i
$94$	−587.606	+	1017.76i	−0.644754	+	1.11675i
$95$		0			0
$96$	−135.399	−	234.517i	−0.143949	−	0.249326i
$97$		−	908.934i		−	0.951425i	−0.879601	−	0.475713i	$-0.842190\pi$
$97$		−	908.934i		−	0.951425i	0.879601	−	0.475713i	$-0.157810\pi$
$98$	−682.420	+	69.9956i	−0.703416	+	0.0721492i
$99$	−250.229			−0.254030
$100$		0			0
$101$	756.347	−	1310.03i	0.745142	−	1.29062i	−0.204987	−	0.978765i	$-0.565715\pi$
$101$	756.347	−	1310.03i	0.745142	−	1.29062i	0.950129	−	0.311859i	$-0.100952\pi$
$102$	1603.76	+	925.931i	1.55682	+	0.898831i
$103$	962.614	−	555.765i	0.920866	−	0.531662i	0.0369545	−	0.999317i	$-0.488234\pi$
$103$	962.614	−	555.765i	0.920866	−	0.531662i	0.883911	+	0.467655i	$0.154901\pi$
$104$	−353.442			−0.333249
$105$		0			0
$106$	−1203.05			−1.10236
$107$	−463.288	+	267.479i	−0.418577	+	0.241666i	−0.694468	−	0.719523i	$-0.744360\pi$
$107$	−463.288	+	267.479i	−0.418577	+	0.241666i	0.275891	+	0.961189i	$0.411027\pi$
$108$	516.303	+	298.088i	0.460012	+	0.265588i
$109$	299.068	−	518.001i	0.262803	−	0.455188i	−0.704183	−	0.710019i	$-0.748686\pi$
$109$	299.068	−	518.001i	0.262803	−	0.455188i	0.966986	+	0.254831i	$0.0820197\pi$
$110$		0			0
$111$	27.1324			0.0232009
$112$	281.936	−	91.2158i	0.237861	−	0.0769561i
$113$		−	1216.27i		−	1.01254i	−0.862374	−	0.506271i	$-0.831023\pi$
$113$		−	1216.27i		−	1.01254i	0.862374	−	0.506271i	$-0.168977\pi$
$114$	1157.05	+	2004.07i	0.950596	+	1.64648i
$115$		0			0
$116$	−199.325	+	345.241i	−0.159542	+	0.276334i
$117$	1706.93	−	985.495i	1.34876	−	0.778710i
$118$		−	1223.94i		−	0.954856i
$119$	−1357.83	+	1504.23i	−1.04599	+	1.15876i
$120$		0			0
$121$	649.770	+	1125.43i	0.488182	+	0.845555i
$122$	−1207.12	−	696.931i	−0.895799	−	0.517190i
$123$	2188.45	+	1263.50i	1.60428	+	0.926229i
$124$	34.2676	+	59.3532i	0.0248171	+	0.0429845i
$125$		0			0
$126$	−1107.26	+	1226.64i	−0.782875	+	0.867281i
$127$			855.997i			0.598090i	0.954239	+	0.299045i	$0.0966681\pi$
$127$			855.997i			0.598090i	−0.954239	+	0.299045i	$0.903332\pi$
$128$	−110.851	+	64.0000i	−0.0765466	+	0.0441942i
$129$	1750.93	−	3032.70i	1.19505	−	2.06988i
$130$		0			0
$131$	−385.352	−	667.449i	−0.257010	−	0.445155i	0.708429	−	0.705782i	$-0.249404\pi$
$131$	−385.352	−	667.449i	−0.257010	−	0.445155i	−0.965440	+	0.260627i	$0.916071\pi$
$132$			189.861i			0.125192i
$133$	−2409.29	+	779.487i	−1.57077	+	0.508196i
$134$	−927.945			−0.598226
$135$		0			0
$136$	437.667	−	758.062i	0.275953	−	0.477965i
$137$	688.398	+	397.447i	0.429298	+	0.247855i	0.699048	−	0.715075i	$-0.253608\pi$
$137$	688.398	+	397.447i	0.429298	+	0.247855i	−0.269750	+	0.962931i	$0.586941\pi$
$138$	313.747	−	181.142i	0.193536	−	0.111738i
$139$	−502.958			−0.306909			−0.153455	−	0.988156i	$-0.549040\pi$
$139$	−502.958			−0.306909			−0.153455	+	0.988156i	$0.549040\pi$
$140$		0			0
$141$	−4972.56			−2.96997
$142$	401.043	−	231.542i	0.237005	−	0.136835i
$143$	214.606	+	123.903i	0.125498	+	0.0724563i
$144$	356.900	−	618.168i	0.206539	−	0.357736i
$145$		0			0
$146$	1411.94			0.800360
$147$	−1700.22	−	2352.53i	−0.953956	−	1.31996i
$148$		−	12.8249i		−	0.00712298i
$149$	−934.931	−	1619.35i	−0.514044	−	0.890350i	−0.999867	−	0.0162929i	$-0.994814\pi$
$149$	−934.931	−	1619.35i	−0.514044	−	0.890350i	0.485824	−	0.874057i	$-0.338520\pi$
$150$		0			0
$151$	512.863	−	888.305i	0.276399	−	0.478737i	−0.694088	−	0.719890i	$-0.744192\pi$
$151$	512.863	−	888.305i	0.276399	−	0.478737i	0.970487	+	0.241153i	$0.0775256\pi$
$152$	947.283	−	546.914i	0.505492	−	0.291846i
$153$			4881.35i			2.57931i
$154$	−203.164	−	43.4502i	−0.106308	−	0.0227358i
$155$		0			0
$156$	−747.743	−	1295.13i	−0.383765	−	0.664701i
$157$	−2361.26	−	1363.27i	−1.20031	−	0.693000i	−0.239687	−	0.970850i	$-0.577045\pi$
$157$	−2361.26	−	1363.27i	−1.20031	−	0.693000i	−0.960625	+	0.277850i	$0.910378\pi$
$158$	1755.86	+	1013.74i	0.884103	+	0.510437i
$159$	−2545.17	−	4408.36i	−1.26947	−	2.19878i
$160$		0			0
$161$	122.032	+	377.185i	0.0597360	+	0.184636i
$162$			113.469i			0.0550309i
$163$	−1877.41	+	1083.93i	−0.902150	+	0.520857i	−0.877897	−	0.478849i	$-0.841054\pi$
$163$	−1877.41	+	1083.93i	−0.902150	+	0.520857i	−0.0242529	+	0.999706i	$0.507721\pi$
$164$	597.230	−	1034.43i	0.284365	−	0.492535i
$165$		0			0
$166$	476.913	+	826.037i	0.222985	+	0.386222i
$167$			1584.77i			0.734330i	0.930156	+	0.367165i	$0.119672\pi$
$167$			1584.77i			0.734330i	−0.930156	+	0.367165i	$0.880328\pi$
$168$	930.709	+	840.129i	0.427415	+	0.385818i
$169$	245.105			0.111563
$170$		0			0
$171$	−3049.90	+	5282.58i	−1.36393	+	2.36239i
$172$	−1433.49	−	827.628i	−0.635482	−	0.366895i
$173$	−2912.12	+	1681.31i	−1.27980	+	0.738890i	−0.976811	−	0.214105i	$-0.931316\pi$
$173$	−2912.12	+	1681.31i	−1.27980	+	0.738890i	−0.302985	+	0.952995i	$0.597983\pi$
$174$	−1686.77			−0.734906
$175$		0			0
$176$	89.7433			0.0384356
$177$	4484.93	−	2589.38i	1.90457	−	1.09960i
$178$	−1351.91	−	780.526i	−0.569269	−	0.328668i
$179$	−1805.01	+	3126.37i	−0.753702	+	1.30545i	0.192315	+	0.981333i	$0.438400\pi$
$179$	−1805.01	+	3126.37i	−0.753702	+	1.30545i	−0.946017	+	0.324117i	$0.894933\pi$
$180$		0			0
$181$	−1653.09			−0.678856			−0.339428	−	0.940632i	$-0.610234\pi$
$181$	−1653.09			−0.678856			−0.339428	+	0.940632i	$0.610234\pi$
$182$	1557.00	−	503.742i	0.634134	−	0.205164i
$183$		−	5897.72i		−	2.38236i
$184$	−85.6219	−	148.301i	−0.0343050	−	0.0594181i
$185$		0			0
$186$	−144.993	+	251.136i	−0.0571582	+	0.0990009i
$187$	−531.492	+	306.857i	−0.207843	+	0.119998i
$188$			2350.42i			0.911821i
$189$	−2699.29	−	577.290i	−1.03886	−	0.222178i
$190$		0			0
$191$	1467.42	+	2541.64i	0.555909	+	0.962863i	0.997832	+	0.0658097i	$0.0209630\pi$
$191$	1467.42	+	2541.64i	0.555909	+	0.962863i	−0.441923	+	0.897053i	$0.645704\pi$
$192$	−469.035	−	270.797i	−0.176300	−	0.101787i
$193$	−3319.88	−	1916.73i	−1.23819	−	0.714867i	−0.269463	−	0.963011i	$-0.586846\pi$
$193$	−3319.88	−	1916.73i	−1.23819	−	0.714867i	−0.968723	+	0.248144i	$0.920179\pi$
$194$	−908.934	−	1574.32i	−0.336380	−	0.582626i
$195$		0			0
$196$	−1111.99	+	803.656i	−0.405244	+	0.292877i
$197$		−	168.443i		−	0.0609190i	−0.999536	−	0.0304595i	$-0.990303\pi$
$197$		−	168.443i		−	0.0609190i	0.999536	−	0.0304595i	$-0.00969706\pi$
$198$	−433.410	+	250.229i	−0.155561	+	0.0898133i
$199$	289.238	−	500.975i	0.103033	−	0.178458i	−0.809900	−	0.586568i	$-0.800479\pi$
$199$	289.238	−	500.975i	0.103033	−	0.178458i	0.912933	+	0.408110i	$0.133812\pi$
$200$		0			0
$201$	−1963.16	−	3400.30i	−0.688910	−	1.19323i
$202$		−	3025.39i		−	1.05379i
$203$	386.021	−	1804.96i	0.133465	−	0.624055i
$204$	3703.72			1.27114
$205$		0			0
$206$	1111.53	−	1925.23i	0.375942	−	0.651150i
$207$	827.011	+	477.475i	0.277687	+	0.160323i
$208$	−612.180	+	353.442i	−0.204072	+	0.117821i
$209$	−766.904			−0.253818
$210$		0			0
$211$	4636.03			1.51260			0.756298	−	0.654228i	$-0.227006\pi$
$211$	4636.03			1.51260			0.756298	+	0.654228i	$0.227006\pi$
$212$	−2083.74	+	1203.05i	−0.675055	+	0.389743i
$213$	1696.89	+	979.703i	0.545865	+	0.315156i
$214$	−534.959	+	926.576i	−0.170883	+	0.295979i
$215$		0			0
$216$	1192.35			0.375598
$217$	−235.550	−	212.626i	−0.0736875	−	0.0665160i
$218$		−	1196.27i		−	0.371660i
$219$	2987.10	+	5173.80i	0.921686	+	1.59641i
$220$		0			0
$221$	2417.03	−	4186.42i	0.735689	−	1.27425i
$222$	46.9948	−	27.1324i	0.0142076	−	0.00820275i
$223$			1171.13i			0.351679i	0.984419	+	0.175840i	$0.0562640\pi$
$223$			1171.13i			0.351679i	−0.984419	+	0.175840i	$0.943736\pi$
$224$	397.111	−	439.926i	0.118451	−	0.131222i
$225$		0			0
$226$	−1216.27	−	2106.65i	−0.357988	−	0.620053i
$227$	−3412.97	−	1970.48i	−0.997916	−	0.576147i	−0.0902850	−	0.995916i	$-0.528778\pi$
$227$	−3412.97	−	1970.48i	−0.997916	−	0.576147i	−0.907631	+	0.419769i	$0.862111\pi$
$228$	4008.15	+	2314.11i	1.16424	+	0.672173i
$229$	3139.76	+	5438.22i	0.906031	+	1.56929i	0.819528	+	0.573040i	$0.194236\pi$
$229$	3139.76	+	5438.22i	0.906031	+	1.56929i	0.0865031	+	0.996252i	$0.472431\pi$
$230$		0			0
$231$	−270.599	−	836.385i	−0.0770741	−	0.238226i
$232$			797.299i			0.225626i
$233$	6021.09	−	3476.28i	1.69294	−	0.977418i	0.740813	−	0.671711i	$-0.234441\pi$
$233$	6021.09	−	3476.28i	1.69294	−	0.977418i	0.952126	−	0.305707i	$-0.0988928\pi$
$234$	1970.99	−	3413.85i	0.550631	−	0.953721i
$235$		0			0
$236$	−1223.94	−	2119.93i	−0.337593	−	0.584727i
$237$			8578.72i			2.35126i
$238$	−847.606	+	3963.23i	−0.230849	+	1.07940i
$239$	2139.43			0.579031			0.289516	−	0.957173i	$-0.406506\pi$
$239$	2139.43			0.579031			0.289516	+	0.957173i	$0.406506\pi$
$240$		0			0
$241$	−1816.77	+	3146.73i	−0.485594	+	0.841074i	−0.999863	−	0.0165552i	$-0.994730\pi$
$241$	−1816.77	+	3146.73i	−0.485594	+	0.841074i	0.514269	+	0.857629i	$0.328063\pi$
$242$	2250.87	+	1299.54i	0.597898	+	0.345197i
$243$	3069.26	−	1772.04i	0.810259	−	0.467803i
$244$	−2787.72			−0.731417
$245$		0			0
$246$	5054.01			1.30989
$247$	5231.40	−	3020.35i	1.34764	−	0.778058i
$248$	118.706	+	68.5352i	0.0303946	+	0.0175483i
$249$	−2017.92	+	3495.13i	−0.513575	+	0.889538i
$250$		0			0
$251$	3155.90			0.793620			0.396810	−	0.917901i	$-0.370117\pi$
$251$	3155.90			0.793620			0.396810	+	0.917901i	$0.370117\pi$
$252$	−691.187	+	3231.85i	−0.172781	+	0.807887i
$253$			120.062i			0.0298350i
$254$	855.997	+	1482.63i	0.211457	+	0.366254i
$255$		0			0
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	231.138	−	133.448i	0.0561012	−	0.0323900i	−0.471687	−	0.881766i	$-0.656355\pi$
$257$	231.138	−	133.448i	0.0561012	−	0.0323900i	0.527788	+	0.849376i	$0.323021\pi$
$258$		−	7003.73i		−	1.69005i
$259$	18.2787	+	56.4969i	0.00438526	+	0.0135542i
$260$		0			0
$261$	−2223.09	−	3850.51i	−0.527226	−	0.913182i
$262$	−1334.90	−	770.703i	−0.314772	−	0.181734i
$263$	−4144.37	−	2392.75i	−0.971684	−	0.561002i	−0.0719351	−	0.997409i	$-0.522917\pi$
$263$	−4144.37	−	2392.75i	−0.971684	−	0.561002i	−0.899749	+	0.436407i	$0.856251\pi$
$264$	189.861	+	328.849i	0.0442619	+	0.0766639i
$265$		0			0
$266$	−3393.52	+	3759.40i	−0.782219	+	0.866555i
$267$		−	6605.13i		−	1.51396i
$268$	−1607.25	+	927.945i	−0.366337	+	0.211505i
$269$	−384.209	+	665.470i	−0.0870843	+	0.150834i	−0.906277	−	0.422683i	$-0.861088\pi$
$269$	−384.209	+	665.470i	−0.0870843	+	0.150834i	0.819193	+	0.573518i	$0.194422\pi$
$270$		0			0
$271$	−1099.64	−	1904.63i	−0.246489	−	0.426931i	0.716061	−	0.698038i	$-0.245943\pi$
$271$	−1099.64	−	1904.63i	−0.246489	−	0.426931i	−0.962549	+	0.271107i	$0.912610\pi$
$272$		−	1750.67i		−	0.390257i
$273$	5139.87	+	4639.64i	1.13948	+	1.02859i
$274$	1589.79			0.350520
$275$		0			0
$276$	362.284	−	627.494i	0.0790106	−	0.136850i
$277$	3983.49	+	2299.87i	0.864060	+	0.498866i	0.865370	−	0.501134i	$-0.167083\pi$
$277$	3983.49	+	2299.87i	0.864060	+	0.498866i	−0.00130947	+	0.999999i	$0.500417\pi$
$278$	−871.149	+	502.958i	−0.187943	+	0.108509i
$279$	−764.381			−0.164022
$280$		0			0
$281$	−32.6041			−0.00692170			−0.00346085	−	0.999994i	$-0.501102\pi$
$281$	−32.6041			−0.00692170			−0.00346085	+	0.999994i	$0.501102\pi$
$282$	−8612.73	+	4972.56i	−1.81873	+	1.05004i
$283$	−6900.45	−	3983.98i	−1.44943	−	0.836830i	−0.450984	−	0.892532i	$-0.648927\pi$
$283$	−6900.45	−	3983.98i	−1.44943	−	0.836830i	−0.998447	+	0.0557021i	$0.982260\pi$
$284$	463.084	−	802.085i	0.0967570	−	0.167588i
$285$		0			0
$286$	495.610			0.102469
$287$	−1156.62	+	5408.13i	−0.237886	+	1.11231i
$288$		−	1427.60i		−	0.292090i
$289$	3529.52	+	6113.31i	0.718405	+	1.24431i
$290$		0			0
$291$	3845.89	−	6661.27i	0.774742	−	1.34189i
$292$	2445.54	−	1411.94i	0.490119	−	0.282970i
$293$		−	151.426i		−	0.0301926i	−0.999886	−	0.0150963i	$-0.995195\pi$
$293$		−	151.426i		−	0.0301926i	0.999886	−	0.0150963i	$-0.00480548\pi$
$294$	−5297.39	−	2374.48i	−1.05085	−	0.471030i
$295$		0			0
$296$	−12.8249	−	22.2134i	−0.00251836	−	0.00436192i
$297$	−723.981	−	417.990i	−0.141447	−	0.0816642i
$298$	−3238.70	−	1869.86i	−0.629572	−	0.363484i
$299$	−472.850	−	819.000i	−0.0914569	−	0.158408i
$300$		0			0
$301$	7494.46	+	1602.82i	1.43513	+	0.306927i
$302$		−	2051.45i		−	0.390887i
$303$	11086.0	−	6400.52i	2.10190	−	1.21353i
$304$	1093.83	−	1894.57i	0.206366	−	0.357437i
$305$		0			0
$306$	4881.35	+	8454.75i	0.911923	+	1.57950i
$307$			3177.58i			0.590729i	0.955385	+	0.295365i	$0.0954412\pi$
$307$			3177.58i			0.590729i	−0.955385	+	0.295365i	$0.904559\pi$
$308$	−395.341	+	127.906i	−0.0731385	+	0.0236628i
$309$	9406.23			1.73172
$310$		0			0
$311$	−459.268	+	795.475i	−0.0837386	+	0.145039i	−0.904853	−	0.425724i	$-0.860019\pi$
$311$	−459.268	+	795.475i	−0.0837386	+	0.145039i	0.821114	+	0.570764i	$0.193353\pi$
$312$	−2590.26	−	1495.49i	−0.470015	−	0.271363i
$313$	−2873.23	+	1658.86i	−0.518865	+	0.299567i	−0.736470	−	0.676470i	$-0.763509\pi$
$313$	−2873.23	+	1658.86i	−0.518865	+	0.299567i	0.217605	+	0.976037i	$0.430175\pi$
$314$	−5453.09			−0.980051
$315$		0			0
$316$	4054.97			0.721867
$317$	−5554.84	+	3207.09i	−0.984199	+	0.568227i	−0.903535	−	0.428514i	$-0.859037\pi$
$317$	−5554.84	+	3207.09i	−0.984199	+	0.568227i	−0.0806636	+	0.996741i	$0.525704\pi$
$318$	−8816.73	−	5090.34i	−1.55477	−	0.897648i
$319$	279.501	−	484.110i	0.0490566	−	0.0849685i
$320$		0			0
$321$	−4527.04			−0.787149
$322$	588.551	+	531.272i	0.101859	+	0.0919460i
$323$			14960.4i			2.57715i
$324$	113.469	+	196.535i	0.0194564	+	0.0336994i
$325$		0			0
$326$	−2167.85	+	3754.83i	−0.368301	+	0.637916i
$327$	4383.54	−	2530.84i	0.741316	−	0.427999i
$328$		−	2388.92i		−	0.402153i
$329$	−3349.93	−	10354.2i	−0.561361	−	1.73509i
$330$		0			0
$331$	3387.61	+	5867.52i	0.562538	+	0.974345i	0.997274	+	0.0737867i	$0.0235084\pi$
$331$	3387.61	+	5867.52i	0.562538	+	0.974345i	−0.434736	+	0.900558i	$0.643158\pi$
$332$	1652.07	+	953.825i	0.273100	+	0.157675i
$333$	123.874	+	71.5189i	0.0203852	+	0.0117694i
$334$	1584.77	+	2744.90i	0.259625	+	0.449683i
$335$		0			0
$336$	2452.16	+	524.438i	0.398144	+	0.0851501i
$337$			9890.09i			1.59866i	0.600894	+	0.799329i	$0.294812\pi$
$337$			9890.09i			1.59866i	−0.600894	+	0.799329i	$0.705188\pi$
$338$	424.534	−	245.105i	0.0683183	−	0.0394436i
$339$	5146.30	−	8913.66i	0.824510	−	1.42809i
$340$		0			0
$341$	−48.0514	−	83.2274i	−0.00763087	−	0.0132171i
$342$			12199.6i			1.92888i
$343$	3753.18	−	5125.16i	0.590824	−	0.806800i
$344$	−3310.51			−0.518868
$345$		0			0
$346$	−3362.63	+	5824.24i	−0.522474	+	0.904952i
$347$	−2790.21	−	1610.93i	−0.431661	−	0.249220i	0.268393	−	0.963310i	$-0.413507\pi$
$347$	−2790.21	−	1610.93i	−0.431661	−	0.249220i	−0.700054	+	0.714090i	$0.746841\pi$
$348$	−2921.57	+	1686.77i	−0.450036	+	0.259829i
$349$	4622.04			0.708917			0.354459	−	0.935072i	$-0.384665\pi$
$349$	4622.04			0.708917			0.354459	+	0.935072i	$0.384665\pi$
$350$		0			0
$351$	6584.80			1.00134
$352$	155.440	−	89.7433i	0.0235369	−	0.0135890i
$353$	−1877.83	−	1084.16i	−0.283135	−	0.163468i	0.351707	−	0.936110i	$-0.385601\pi$
$353$	−1877.83	−	1084.16i	−0.283135	−	0.163468i	−0.634842	+	0.772642i	$0.718935\pi$
$354$	5178.75	−	8969.86i	0.777535	−	1.34673i
$355$		0			0
$356$	−3122.10			−0.464806
$357$	−16315.8	+	5278.72i	−2.41883	+	0.782575i
$358$			7220.03i			1.06590i
$359$	233.014	+	403.592i	0.0342563	+	0.0593336i	0.882645	−	0.470040i	$-0.155760\pi$
$359$	233.014	+	403.592i	0.0342563	+	0.0593336i	−0.848389	+	0.529373i	$0.822427\pi$
$360$		0			0
$361$	−5917.84	+	10250.0i	−0.862784	+	1.49439i
$362$	−2863.23	+	1653.09i	−0.415713	+	0.240012i
$363$			10997.2i			1.59010i
$364$	2193.06	−	2429.51i	0.315790	−	0.349837i
$365$		0			0
$366$	−5897.72	−	10215.1i	−0.842291	−	1.45889i
$367$	2505.25	+	1446.41i	0.356329	+	0.205727i	0.667469	−	0.744637i	$-0.267377\pi$
$367$	2505.25	+	1446.41i	0.356329	+	0.205727i	−0.311140	+	0.950364i	$0.600711\pi$
$368$	−296.603	−	171.244i	−0.0420149	−	0.0242573i
$369$	6660.98	+	11537.2i	0.939720	+	1.62764i
$370$		0			0
$371$	7464.74	−	8269.56i	1.04461	−	1.15723i
$372$			579.973i			0.0808339i
$373$	1567.10	−	904.763i	0.217537	−	0.125595i	−0.387273	−	0.921965i	$-0.626583\pi$
$373$	1567.10	−	904.763i	0.217537	−	0.125595i	0.604809	+	0.796371i	$0.293249\pi$
$374$	−613.714	+	1062.98i	−0.0848514	+	0.146967i
$375$		0			0
$376$	2350.42	+	4071.05i	0.322377	+	0.558374i
$377$			4403.11i			0.601517i
$378$	−5252.60	+	1699.39i	−0.714721	+	0.231237i
$379$	8994.04			1.21898			0.609489	−	0.792794i	$-0.291375\pi$
$379$	8994.04			1.21898			0.609489	+	0.792794i	$0.291375\pi$
$380$		0			0
$381$	−3621.90	+	6273.32i	−0.487023	+	0.843548i
$382$	5083.28	+	2934.84i	0.680847	+	0.393087i
$383$	10705.5	−	6180.82i	1.42826	−	0.824608i	0.431280	−	0.902218i	$-0.358062\pi$
$383$	10705.5	−	6180.82i	1.42826	−	0.824608i	0.996984	+	0.0776096i	$0.0247288\pi$
$384$	−1083.19			−0.143949
$385$		0			0
$386$	−7666.92			−1.01097
$387$	15987.9	−	9230.62i	2.10003	−	1.21245i
$388$	−3148.64	−	1817.87i	−0.411979	−	0.237856i
$389$	−2392.79	+	4144.43i	−0.311875	+	0.540183i	−0.978768	−	0.204970i	$-0.934290\pi$
$389$	−2392.79	+	4144.43i	−0.311875	+	0.540183i	0.666894	+	0.745153i	$0.267624\pi$
$390$		0			0
$391$	2342.12			0.302931
$392$	−1122.37	+	2503.96i	−0.144613	+	0.322625i
$393$		−	6522.01i		−	0.837130i
$394$	−168.443	−	291.751i	−0.0215381	−	0.0373051i
$395$		0			0
$396$	−500.459	+	866.820i	−0.0635076	+	0.109998i
$397$	3463.29	−	1999.53i	0.437827	−	0.252780i	−0.264848	−	0.964290i	$-0.585322\pi$
$397$	3463.29	−	1999.53i	0.437827	−	0.252780i	0.702675	+	0.711510i	$0.251989\pi$
$398$		−	1156.95i		−	0.145711i
$399$	−20955.0	−	4481.60i	−2.62923	−	0.562307i
$400$		0			0
$401$	−2969.96	−	5144.13i	−0.369858	−	0.640612i	0.619685	−	0.784850i	$-0.287260\pi$
$401$	−2969.96	−	5144.13i	−0.369858	−	0.640612i	−0.989543	+	0.144238i	$0.953927\pi$
$402$	−6800.60	−	3926.33i	−0.843739	−	0.487133i
$403$	655.560	+	378.488i	0.0810317	+	0.0467837i
$404$	−3025.39	−	5240.12i	−0.372571	−	0.645312i
$405$		0			0
$406$	−1136.35	−	3512.30i	−0.138906	−	0.429341i
$407$			17.9836i			0.00219021i
$408$	6415.04	−	3703.72i	0.778411	−	0.449416i
$409$	−4634.33	+	8026.90i	−0.560276	+	0.970427i	0.437196	+	0.899366i	$0.355972\pi$
$409$	−4634.33	+	8026.90i	−0.560276	+	0.970427i	−0.997472	+	0.0710603i	$0.977362\pi$
$410$		0			0
$411$	3363.36	+	5825.51i	0.403655	+	0.699151i
$412$		−	4446.12i		−	0.531662i
$413$	8413.19	+	7594.39i	1.00239	+	0.904831i
$414$	1909.90			0.226731
$415$		0			0
$416$	−706.884	+	1224.36i	−0.0833121	+	0.144301i
$417$	−3686.01	−	2128.12i	−0.432865	−	0.249915i
$418$	−1328.32	+	766.904i	−0.155431	+	0.0897381i
$419$	−2058.22			−0.239977			−0.119989	−	0.992775i	$-0.538286\pi$
$419$	−2058.22			−0.239977			−0.119989	+	0.992775i	$0.538286\pi$
$420$		0			0
$421$	−14211.3			−1.64517			−0.822583	−	0.568645i	$-0.807468\pi$
$421$	−14211.3			−1.64517			−0.822583	+	0.568645i	$0.807468\pi$
$422$	8029.84	−	4636.03i	0.926272	−	0.534783i
$423$	−22702.5	−	13107.3i	−2.60953	−	1.50661i
$424$	−2406.09	+	4167.48i	−0.275590	+	0.477336i
$425$		0			0
$426$	3918.81			0.445697
$427$	12280.6	−	3973.19i	1.39180	−	0.450296i
$428$			2139.84i			0.241666i
$429$	1048.52	+	1816.08i	0.118002	+	0.204385i
$430$		0			0
$431$	43.8486	−	75.9479i	0.00490049	−	0.00848789i	−0.863565	−	0.504238i	$-0.831773\pi$
$431$	43.8486	−	75.9479i	0.00490049	−	0.00848789i	0.868465	+	0.495750i	$0.165107\pi$
$432$	2065.21	−	1192.35i	0.230006	−	0.132794i
$433$			10482.6i			1.16342i	0.813397	+	0.581709i	$0.197616\pi$
$433$			10482.6i			1.16342i	−0.813397	+	0.581709i	$0.802384\pi$
$434$	−620.610	−	132.728i	−0.0686411	−	0.0146801i
$435$		0			0
$436$	−1196.27	−	2072.00i	−0.131402	−	0.227594i
$437$	2534.63	+	1463.37i	0.277455	+	0.160189i
$438$	10347.6	+	5974.19i	1.12883	+	0.651730i
$439$	1924.67	+	3333.62i	0.209247	+	0.362426i	0.951478	−	0.307718i	$-0.0995654\pi$
$439$	1924.67	+	3333.62i	0.209247	+	0.362426i	−0.742231	+	0.670145i	$0.766232\pi$
$440$		0			0
$441$	−1561.34	−	15222.2i	−0.168593	−	1.64369i
$442$		−	9668.13i		−	1.04042i
$443$	9103.46	−	5255.89i	0.976340	−	0.563690i	0.0751769	−	0.997170i	$-0.476048\pi$
$443$	9103.46	−	5255.89i	0.976340	−	0.563690i	0.901163	+	0.433480i	$0.142715\pi$
$444$	54.2649	−	93.9895i	0.00580022	−	0.0100463i
$445$		0			0
$446$	1171.13	+	2028.45i	0.124337	+	0.215359i
$447$		−	15823.5i		−	1.67434i
$448$	247.890	−	1159.09i	0.0261422	−	0.122236i
$449$	6500.68			0.683265			0.341633	−	0.939834i	$-0.389020\pi$
$449$	6500.68			0.683265			0.341633	+	0.939834i	$0.389020\pi$
$450$		0			0
$451$	−837.460	+	1450.52i	−0.0874378	+	0.151447i
$452$	−4213.29	−	2432.55i	−0.438444	−	0.253136i
$453$	7517.20	−	4340.06i	0.779667	−	0.450141i
$454$	−7881.92			−0.814795
$455$		0			0
$456$	9256.42			0.950596
$457$	−4332.91	+	2501.60i	−0.443512	+	0.256061i	−0.705086	−	0.709122i	$-0.749092\pi$
$457$	−4332.91	+	2501.60i	−0.443512	+	0.256061i	0.261574	+	0.965183i	$0.415758\pi$
$458$	10876.4	+	6279.52i	1.10966	+	0.640660i
$459$	−8153.96	+	14123.1i	−0.829181	+	1.43618i
$460$		0			0
$461$	−6656.10			−0.672463			−0.336231	−	0.941779i	$-0.609152\pi$
$461$	−6656.10			−0.672463			−0.336231	+	0.941779i	$0.609152\pi$
$462$	−1305.08	−	1178.06i	−0.131424	−	0.118633i
$463$			9725.18i			0.976172i	0.872796	+	0.488086i	$0.162305\pi$
$463$			9725.18i			0.976172i	−0.872796	+	0.488086i	$0.837695\pi$
$464$	797.299	+	1380.96i	0.0797709	+	0.138167i
$465$		0			0
$466$	6952.55	−	12042.2i	0.691139	−	1.19709i
$467$	177.589	−	102.531i	0.0175971	−	0.0101597i	−0.491176	−	0.871061i	$-0.663433\pi$
$467$	177.589	−	102.531i	0.0175971	−	0.0101597i	0.508773	+	0.860901i	$0.330099\pi$
$468$		−	7883.96i		−	0.778710i
$469$	5757.77	−	6378.55i	0.566885	−	0.628004i
$470$		0			0
$471$	−11536.6	−	19982.0i	−1.12862	−	1.95482i
$472$	−4239.86	−	2447.88i	−0.413465	−	0.238714i
$473$	2010.10	+	1160.53i	0.195401	+	0.112815i
$474$	8578.72	+	14858.8i	0.831294	+	1.43984i
$475$		0			0
$476$	2495.14	+	7712.13i	0.240261	+	0.742615i
$477$		−	26835.4i		−	2.57591i
$478$	3705.61	−	2139.43i	0.354583	−	0.204719i
$479$	5476.34	−	9485.29i	0.522380	−	0.904789i	−0.477281	−	0.878751i	$-0.658377\pi$
$479$	5476.34	−	9485.29i	0.522380	−	0.904789i	0.999661	−	0.0260383i	$-0.00828919\pi$
$480$		0			0
$481$	−70.8260	−	122.674i	−0.00671391	−	0.0116288i
$482$			7267.07i			0.686734i
$483$	−701.615	+	3280.61i	−0.0660964	+	0.309054i
$484$	5198.16			0.488182
$485$		0			0
$486$	3544.07	−	6138.51i	0.330787	−	0.572939i
$487$	10616.9	+	6129.67i	0.987881	+	0.570353i	0.904640	−	0.426176i	$-0.140140\pi$
$487$	10616.9	+	6129.67i	0.987881	+	0.570353i	0.0832406	+	0.996529i	$0.473473\pi$
$488$	−4828.48	+	2787.72i	−0.447899	+	0.258595i
$489$	−18345.3			−1.69653
$490$		0			0
$491$	1917.95			0.176285			0.0881425	−	0.996108i	$-0.471907\pi$
$491$	1917.95			0.176285			0.0881425	+	0.996108i	$0.471907\pi$
$492$	8753.80	−	5054.01i	0.802138	−	0.463115i
$493$	−9443.79	−	5452.37i	−0.862732	−	0.498099i
$494$	6040.70	−	10462.8i	0.550170	−	0.952922i
$495$		0			0
$496$	274.141			0.0248171
$497$	−896.829	+	4193.39i	−0.0809422	+	0.378469i
$498$			8071.66i			0.726305i
$499$	2564.08	+	4441.12i	0.230028	+	0.398421i	0.957816	−	0.287382i	$-0.0927848\pi$
$499$	2564.08	+	4441.12i	0.230028	+	0.398421i	−0.727788	+	0.685802i	$0.759451\pi$
$500$		0			0
$501$	−6705.48	+	11614.2i	−0.597962	+	1.03570i
$502$	5466.18	−	3155.90i	0.485991	−	0.280587i
$503$		−	16093.9i		−	1.42662i	−0.700849	−	0.713310i	$-0.747195\pi$
$503$		−	16093.9i		−	1.42662i	0.700849	−	0.713310i	$-0.252805\pi$
$504$	2034.68	+	6288.92i	0.179825	+	0.555815i
$505$		0			0
$506$	120.062	+	207.954i	0.0105483	+	0.0182701i
$507$	1796.29	+	1037.09i	0.157349	+	0.0908456i
$508$	2965.26	+	1711.99i	0.258981	+	0.149523i
$509$	−2102.76	−	3642.09i	−0.183111	−	0.317157i	0.759827	−	0.650125i	$-0.225283\pi$
$509$	−2102.76	−	3642.09i	−0.183111	−	0.317157i	−0.942938	+	0.332968i	$0.891950\pi$
$510$		0			0
$511$	−8760.86	+	9705.42i	−0.758430	+	0.840201i
$512$			512.000i			0.0441942i
$513$	−17648.3	+	10189.3i	−1.51889	+	0.876934i
$514$	266.895	−	462.276i	0.0229032	−	0.0396695i
$515$		0			0
$516$	−7003.73	−	12130.8i	−0.597523	−	1.03494i
$517$		−	3295.86i		−	0.280371i
$518$	88.1565	+	79.5768i	0.00747755	+	0.00674981i
$519$	−28456.0			−2.40670
$520$		0			0
$521$	−843.022	+	1460.16i	−0.0708896	+	0.122784i	−0.899291	−	0.437350i	$-0.855917\pi$
$521$	−843.022	+	1460.16i	−0.0708896	+	0.122784i	0.828402	+	0.560134i	$0.189250\pi$
$522$	−7701.02	−	4446.18i	−0.645717	−	0.372805i
$523$	−18914.5	+	10920.3i	−1.58140	+	0.913023i	−0.586748	+	0.809770i	$0.699592\pi$
$523$	−18914.5	+	10920.3i	−1.58140	+	0.913023i	−0.994655	+	0.103254i	$0.967075\pi$
$524$	−3082.81			−0.257010
$525$		0			0
$526$	−9571.02			−0.793377
$527$	−1623.56	+	937.363i	−0.134200	+	0.0774804i
$528$	657.699	+	379.723i	0.0542096	+	0.0312979i
$529$	−5854.40	+	10140.1i	−0.481171	+	0.833412i
$530$		0			0
$531$	27301.5			2.23123
$532$	−2118.35	+	9905.00i	−0.172636	+	0.807211i
$533$		−	13192.9i		−	1.07213i
$534$	−6605.13	−	11440.4i	−0.535266	−	0.927108i
$535$		0			0
$536$	−1855.89	+	3214.50i	−0.149556	+	0.259039i
$537$	−26456.6	+	15274.7i	−2.12605	+	1.22747i
$538$			1536.84i			0.123156i
$539$	1559.28	−	1126.92i	0.124606	−	0.0900552i
$540$		0			0
$541$	8286.85	+	14353.3i	0.658558	+	1.14066i	0.980989	+	0.194063i	$0.0621665\pi$
$541$	8286.85	+	14353.3i	0.658558	+	1.14066i	−0.322432	+	0.946593i	$0.604500\pi$
$542$	−3809.27	−	2199.28i	−0.301886	−	0.174294i
$543$	−12114.9	−	6994.55i	−0.957461	−	0.552790i
$544$	−1750.67	−	3032.25i	−0.137977	−	0.238983i
$545$		0			0
$546$	13542.2	+	2896.23i	1.06145	+	0.227009i
$547$		−	11756.1i		−	0.918930i	−0.888196	−	0.459465i	$-0.848041\pi$
$547$		−	11756.1i		−	0.918930i	0.888196	−	0.459465i	$-0.151959\pi$
$548$	2753.59	−	1589.79i	0.214649	−	0.123928i
$549$	15545.9	−	26926.3i	1.20853	−	2.09323i
$550$		0			0
$551$	−6813.34	−	11801.1i	−0.526784	−	0.912417i
$552$		−	1449.14i		−	0.111738i
$553$	−17863.1	+	5779.34i	−1.37363	+	0.444417i
$554$	9199.48			0.705502
$555$		0			0
$556$	−1005.92	+	1742.30i	−0.0767273	+	0.132896i
$557$	1603.26	+	925.643i	0.121961	+	0.0704143i	0.559739	−	0.828669i	$-0.310901\pi$
$557$	1603.26	+	925.643i	0.121961	+	0.0704143i	−0.437778	+	0.899083i	$0.644235\pi$
$558$	−1323.95	+	764.381i	−0.100443	+	0.0579907i
$559$	−18282.4			−1.38330
$560$		0			0
$561$	−5193.51			−0.390856
$562$	−56.4720	+	32.6041i	−0.00423866	+	0.00244719i
$563$	−1449.60	−	836.927i	−0.108514	−	0.0626506i	0.444761	−	0.895649i	$-0.353289\pi$
$563$	−1449.60	−	836.927i	−0.108514	−	0.0626506i	−0.553275	+	0.832999i	$0.686622\pi$
$564$	−9945.13	+	17225.5i	−0.742492	+	1.28603i
$565$		0			0
$566$	−15935.9			−1.18346
$567$	−779.971	−	704.062i	−0.0577702	−	0.0521479i
$568$		−	1852.34i		−	0.136835i
$569$	3112.51	+	5391.02i	0.229320	+	0.397194i	0.957607	−	0.288079i	$-0.0930164\pi$
$569$	3112.51	+	5391.02i	0.229320	+	0.397194i	−0.728287	+	0.685273i	$0.759683\pi$
$570$		0			0
$571$	−5956.98	+	10317.8i	−0.436589	+	0.756194i	−0.997424	−	0.0717339i	$-0.977147\pi$
$571$	−5956.98	+	10317.8i	−0.436589	+	0.756194i	0.560835	+	0.827927i	$0.310480\pi$
$572$	858.422	−	495.610i	0.0627490	−	0.0362282i
$573$			24835.8i			1.81070i
$574$	3404.80	+	10523.8i	0.247585	+	0.765251i
$575$		0			0
$576$	−1427.60	−	2472.67i	−0.103270	−	0.178868i
$577$	544.606	+	314.429i	0.0392933	+	0.0226860i	0.519518	−	0.854460i	$-0.326112\pi$
$577$	544.606	+	314.429i	0.0392933	+	0.0226860i	−0.480225	+	0.877146i	$0.659445\pi$
$578$	12226.6	+	7059.05i	0.879863	+	0.507989i
$579$	−16220.2	−	28094.2i	−1.16423	−	2.01650i
$580$		0			0
$581$	−8637.22	−	1847.22i	−0.616751	−	0.131903i
$582$		−	15383.5i		−	1.09565i
$583$	2921.90	−	1686.96i	0.207569	−	0.119840i
$584$	2823.87	−	4891.09i	0.200090	−	0.346566i
$585$		0			0
$586$	−151.426	−	262.278i	−0.0106747	−	0.0184891i
$587$		−	19553.2i		−	1.37487i	−0.726246	−	0.687434i	$-0.758737\pi$
$587$		−	19553.2i		−	1.37487i	0.726246	−	0.687434i	$-0.241263\pi$
$588$	−11549.8	+	1184.66i	−0.810046	+	0.0830862i
$589$	−2342.68			−0.163885
$590$		0			0
$591$	712.716	−	1234.46i	0.0496061	−	0.0859203i
$592$	−44.4268	−	25.6498i	−0.00308434	−	0.00178075i
$593$	2818.26	−	1627.12i	0.195163	−	0.112678i	−0.399234	−	0.916849i	$-0.630724\pi$
$593$	2818.26	−	1627.12i	0.195163	−	0.112678i	0.594397	+	0.804171i	$0.297391\pi$
$594$	−1671.96			−0.115491
$595$		0			0
$596$	−7479.45			−0.514044
$597$	4239.46	−	2447.65i	0.290636	−	0.167799i
$598$	−1638.00	−	945.699i	−0.112011	−	0.0646698i
$599$	9587.01	−	16605.2i	0.653948	−	1.13267i	−0.328209	−	0.944605i	$-0.606445\pi$
$599$	9587.01	−	16605.2i	0.653948	−	1.13267i	0.982156	−	0.188066i	$-0.0602218\pi$
$600$		0			0
$601$	12137.0			0.823756			0.411878	−	0.911239i	$-0.364873\pi$
$601$	12137.0			0.823756			0.411878	+	0.911239i	$0.364873\pi$
$602$	14583.6	−	4718.29i	0.987348	−	0.319441i
$603$		−	20699.0i		−	1.39789i
$604$	−2051.45	−	3553.22i	−0.138199	−	0.239368i
$605$		0			0
$606$	12801.0	−	22172.1i	0.858097	−	1.48627i
$607$	−17717.8	+	10229.4i	−1.18475	+	0.684017i	−0.957109	−	0.289727i	$-0.906435\pi$
$607$	−17717.8	+	10229.4i	−1.18475	+	0.684017i	−0.227644	+	0.973745i	$0.573102\pi$
$608$		−	4375.31i		−	0.291846i
$609$	10466.2	−	11594.6i	0.696405	−	0.771488i
$610$		0			0
$611$	12980.3	+	22482.5i	0.859454	+	1.48862i
$612$	16909.5	+	9762.71i	1.11687	+	0.644827i
$613$	1068.81	+	617.080i	0.0704225	+	0.0406585i	0.534798	−	0.844980i	$-0.320388\pi$
$613$	1068.81	+	617.080i	0.0704225	+	0.0406585i	−0.464375	+	0.885639i	$0.653721\pi$
$614$	3177.58	+	5503.73i	0.208854	+	0.361746i
$615$		0			0
$616$	−556.845	+	616.881i	−0.0364219	+	0.0403488i
$617$		−	12020.4i		−	0.784314i	−0.919898	−	0.392157i	$-0.871729\pi$
$617$		−	12020.4i		−	0.784314i	0.919898	−	0.392157i	$-0.128271\pi$
$618$	16292.1	−	9406.23i	1.06046	−	0.612256i
$619$	10555.0	−	18281.8i	0.685368	−	1.18709i	−0.287954	−	0.957644i	$-0.592975\pi$
$619$	10555.0	−	18281.8i	0.685368	−	1.18709i	0.973321	−	0.229447i	$-0.0736918\pi$
$620$		0			0
$621$	1595.18	+	2762.93i	0.103079	+	0.178539i
$622$			1837.07i			0.118424i
$623$	13753.6	−	4449.77i	0.884474	−	0.286157i
$624$	−5981.95			−0.383765
$625$		0			0
$626$	−3317.72	+	5746.47i	−0.211826	+	0.366893i
$627$	−5620.38	−	3244.93i	−0.357985	−	0.206683i
$628$	−9445.04	+	5453.09i	−0.600156	+	0.346500i
$629$	350.816			0.0222384
$630$		0			0
$631$	−2345.47			−0.147974			−0.0739872	−	0.997259i	$-0.523572\pi$
$631$	−2345.47			−0.147974			−0.0739872	+	0.997259i	$0.523572\pi$
$632$	7023.42	−	4054.97i	0.442052	−	0.255219i
$633$	33975.9	+	19616.0i	2.13337	+	1.23170i
$634$	−6414.18	+	11109.7i	−0.401797	+	0.695934i
$635$		0			0
$636$	−20361.4			−1.26947
$637$	−6198.31	+	13828.2i	−0.385535	+	0.860116i
$638$		−	1118.00i		−	0.0693765i
$639$	5164.83	+	8945.75i	0.319746	+	0.553816i
$640$		0			0
$641$	10759.8	−	18636.5i	0.663005	−	1.14836i	−0.316817	−	0.948487i	$-0.602614\pi$
$641$	10759.8	−	18636.5i	0.663005	−	1.14836i	0.979822	−	0.199872i	$-0.0640527\pi$
$642$	−7841.07	+	4527.04i	−0.482029	+	0.278299i
$643$			29827.7i			1.82937i	0.404162	+	0.914687i	$0.367563\pi$
$643$			29827.7i			1.82937i	−0.404162	+	0.914687i	$0.632437\pi$
$644$	1550.67	+	331.638i	0.0948836	+	0.0202925i
$645$		0			0
$646$	14960.4	+	25912.2i	0.911159	+	1.57817i
$647$	−24184.7	−	13963.1i	−1.46955	−	0.848446i	−0.470134	−	0.882595i	$-0.655794\pi$
$647$	−24184.7	−	13963.1i	−1.46955	−	0.848446i	−0.999417	+	0.0341494i	$0.989128\pi$
$648$	393.070	+	226.939i	0.0238291	+	0.0137577i
$649$	1716.26	+	2972.65i	0.103804	+	0.179795i
$650$		0			0
$651$	−826.605	−	2554.92i	−0.0497653	−	0.153818i
$652$			8671.41i			0.520857i
$653$	−26134.8	+	15089.0i	−1.56621	+	0.904252i	−0.569605	+	0.821918i	$0.692904\pi$
$653$	−26134.8	+	15089.0i	−1.56621	+	0.904252i	−0.996605	+	0.0823334i	$0.973763\pi$
$654$	5061.68	−	8767.08i	0.302641	−	0.524190i
$655$		0			0
$656$	−2388.92	−	4137.73i	−0.142182	−	0.246267i
$657$			31495.0i			1.87022i
$658$	−16156.4	−	14584.0i	−0.957209	−	0.864051i
$659$	−11978.1			−0.708044			−0.354022	−	0.935237i	$-0.615186\pi$
$659$	−11978.1			−0.708044			−0.354022	+	0.935237i	$0.615186\pi$
$660$		0			0
$661$	−1009.47	+	1748.45i	−0.0594005	+	0.102885i	−0.894196	−	0.447675i	$-0.852252\pi$
$661$	−1009.47	+	1748.45i	−0.0594005	+	0.102885i	0.834796	+	0.550559i	$0.185586\pi$
$662$	11735.0	+	6775.23i	0.688966	+	0.397775i
$663$	35427.2	−	20453.9i	2.07523	−	1.19814i
$664$	3815.30			0.222985
$665$		0			0
$666$	286.075			0.0166444
$667$	−1847.51	+	1066.66i	−0.107250	+	0.0619209i
$668$	5489.80	+	3169.54i	0.317974	+	0.183582i
$669$	−4955.28	+	8582.79i	−0.286371	+	0.496009i
$670$		0			0
$671$	3909.05			0.224899
$672$	4771.71	−	1543.81i	0.273918	−	0.0886218i
$673$		−	11029.5i		−	0.631733i	−0.948804	−	0.315867i	$-0.897705\pi$
$673$		−	11029.5i		−	0.631733i	0.948804	−	0.315867i	$-0.102295\pi$
$674$	9890.09	+	17130.1i	0.565211	+	0.978974i
$675$		0			0
$676$	490.209	−	849.068i	0.0278908	−	0.0483084i
$677$	3911.86	−	2258.51i	0.222075	−	0.128215i	−0.384836	−	0.922985i	$-0.625742\pi$
$677$	3911.86	−	2258.51i	0.222075	−	0.128215i	0.606911	+	0.794770i	$0.292409\pi$
$678$		−	20585.2i		−	1.16603i
$679$	16461.4	+	3520.56i	0.930385	+	0.198979i
$680$		0			0
$681$	−16675.0	−	28882.0i	−0.938309	−	1.62520i
$682$	−166.455	−	96.1027i	−0.00934587	−	0.00539584i
$683$	6718.64	+	3879.01i	0.376400	+	0.217315i	0.676251	−	0.736671i	$-0.263603\pi$
$683$	6718.64	+	3879.01i	0.376400	+	0.217315i	−0.299851	+	0.953986i	$0.596937\pi$
$684$	12199.6	+	21130.3i	0.681963	+	1.18119i
$685$		0			0
$686$	1375.54	−	12630.2i	0.0765573	−	0.702950i
$687$			53139.9i			2.95111i
$688$	−5733.97	+	3310.51i	−0.317741	+	0.183448i
$689$	−13287.7	+	23015.0i	−0.734720	+	1.27257i
$690$		0			0
$691$	6569.03	+	11377.9i	0.361646	+	0.626390i	0.988232	−	0.152963i	$-0.0488815\pi$
$691$	6569.03	+	11377.9i	0.361646	+	0.626390i	−0.626586	+	0.779353i	$0.715548\pi$
$692$			13450.5i			0.738890i
$693$	969.210	−	4531.83i	0.0531273	−	0.248413i
$694$	−6443.72			−0.352450
$695$		0			0
$696$	−3373.54	+	5843.14i	−0.183727	+	0.318224i
$697$	28296.1	+	16336.8i	1.53772	+	0.887804i
$698$	8005.61	−	4622.04i	0.434121	−	0.250640i
$699$	58835.4			3.18363
$700$		0			0
$701$	−26118.1			−1.40723			−0.703614	−	0.710583i	$-0.748431\pi$
$701$	−26118.1			−1.40723			−0.703614	+	0.710583i	$0.748431\pi$
$702$	11405.2	−	6584.80i	0.613193	−	0.354027i
$703$	379.651	+	219.191i	0.0203681	+	0.0117595i
$704$	179.487	−	310.880i	0.00960889	−	0.0166431i
$705$		0			0
$706$	−4336.66			−0.231179
$707$	20796.0	+	18772.1i	1.10625	+	0.998582i
$708$		−	20715.0i		−	1.09960i
$709$	−3567.68	−	6179.41i	−0.188980	−	0.327324i	0.755930	−	0.654652i	$-0.227185\pi$
$709$	−3567.68	−	6179.41i	−0.188980	−	0.327324i	−0.944911	+	0.327329i	$0.893852\pi$
$710$		0			0
$711$	−22612.8	+	39166.5i	−1.19275	+	2.06591i
$712$	−5407.64	+	3122.10i	−0.284635	+	0.164334i
$713$			366.757i			0.0192639i
$714$	−22981.1	+	25458.8i	−1.20455	+	1.33441i
$715$		0			0
$716$	7220.03	+	12505.5i	0.376851	+	0.652725i
$717$	15679.2	+	9052.39i	0.816667	+	0.471503i
$718$	807.184	+	466.028i	0.0419552	+	0.0242229i
$719$	6569.92	+	11379.4i	0.340774	+	0.590238i	0.984577	−	0.174954i	$-0.0559776\pi$
$719$	6569.92	+	11379.4i	0.340774	+	0.590238i	−0.643803	+	0.765192i	$0.722644\pi$
$720$		0			0
$721$	6336.82	+	19586.3i	0.327317	+	1.01169i
$722$			23671.3i			1.22016i
$723$	−26628.9	+	15374.2i	−1.36977	+	0.790835i
$724$	−3306.17	+	5726.46i	−0.169714	+	0.293953i
$725$		0			0
$726$	10997.2	+	19047.8i	0.562184	+	0.973732i
$727$		−	29182.7i		−	1.48876i	−0.667757	−	0.744379i	$-0.732746\pi$
$727$		−	29182.7i		−	1.48876i	0.667757	−	0.744379i	$-0.267254\pi$
$728$	1368.98	−	6401.09i	0.0696949	−	0.325879i
$729$	31523.2			1.60155
$730$		0			0
$731$	22639.1	−	39212.1i	1.14547	−	1.98401i
$732$	−20430.3	−	11795.4i	−1.03159	−	0.595590i
$733$	15181.9	−	8765.30i	0.765018	−	0.441683i	−0.0660767	−	0.997815i	$-0.521048\pi$
$733$	15181.9	−	8765.30i	0.765018	−	0.441683i	0.831094	+	0.556131i	$0.187715\pi$
$734$	5785.62			0.290942
$735$		0			0
$736$	−684.975			−0.0343050
$737$	2253.75	−	1301.20i	0.112643	−	0.0650344i
$738$	23074.3	+	13322.0i	1.15092	+	0.664482i
$739$	4394.22	−	7611.01i	0.218733	−	0.378857i	−0.735688	−	0.677321i	$-0.763141\pi$
$739$	4394.22	−	7611.01i	0.218733	−	0.378857i	0.954421	+	0.298464i	$0.0964742\pi$
$740$		0			0
$741$	51118.9			2.53428
$742$	4659.75	−	21788.0i	0.230545	−	1.07798i
$743$		−	23553.9i		−	1.16300i	−0.813546	−	0.581500i	$-0.802466\pi$
$743$		−	23553.9i		−	1.16300i	0.813546	−	0.581500i	$-0.197534\pi$
$744$	579.973	+	1004.54i	0.0285791	+	0.0495004i
$745$		0			0
$746$	1809.53	−	3134.19i	0.0888089	−	0.153822i
$747$	−18425.8	+	10638.1i	−0.902494	+	0.521055i
$748$			2454.86i			0.119998i
$749$	−3049.79	−	9426.50i	−0.148781	−	0.459862i
$750$		0			0
$751$	−1430.02	−	2476.87i	−0.0694836	−	0.120349i	0.829191	−	0.558966i	$-0.188802\pi$
$751$	−1430.02	−	2476.87i	−0.0694836	−	0.120349i	−0.898674	+	0.438617i	$0.855468\pi$
$752$	8142.11	+	4700.85i	0.394830	+	0.227955i
$753$	23128.5	+	13353.3i	1.11932	+	0.646242i
$754$	4403.11	+	7626.41i	0.212668	+	0.368352i
$755$		0			0
$756$	−7398.37	+	8196.03i	−0.355921	+	0.394295i
$757$			11181.8i			0.536866i	0.963298	+	0.268433i	$0.0865058\pi$
$757$			11181.8i			0.536866i	−0.963298	+	0.268433i	$0.913494\pi$
$758$	15578.1	−	8994.04i	0.746469	−	0.430974i
$759$	−508.009	+	879.897i	−0.0242945	+	0.0420794i
$760$		0			0
$761$	−1620.53	−	2806.84i	−0.0771935	−	0.133703i	0.824845	−	0.565360i	$-0.191263\pi$
$761$	−1620.53	−	2806.84i	−0.0771935	−	0.133703i	−0.902038	+	0.431657i	$0.857929\pi$
$762$			14487.6i			0.688754i
$763$	8222.99	+	7422.70i	0.390160	+	0.352189i
$764$	11739.3			0.555909
$765$		0			0
$766$	12361.6	−	21411.0i	0.583086	−	1.00994i
$767$	−23414.8	−	13518.5i	−1.10229	−	0.636409i
$768$	−1876.14	+	1083.19i	−0.0881501	+	0.0508935i
$769$	5261.79			0.246743			0.123371	−	0.992361i	$-0.460629\pi$
$769$	5261.79			0.246743			0.123371	+	0.992361i	$0.460629\pi$
$770$		0			0
$771$	2258.58			0.105500
$772$	−13279.5	+	7666.92i	−0.619093	+	0.357433i
$773$	−3804.92	−	2196.77i	−0.177042	−	0.102215i	0.408860	−	0.912597i	$-0.365926\pi$
$773$	−3804.92	−	2196.77i	−0.177042	−	0.102215i	−0.585902	+	0.810382i	$0.699260\pi$
$774$	18461.2	−	31975.8i	0.857333	−	1.48494i
$775$		0			0
$776$	−7271.47			−0.336380
$777$	−105.092	+	491.388i	−0.00485218	+	0.0226878i
$778$			9571.15i			0.441057i
$779$	20414.6	+	35359.1i	0.938933	+	1.62628i
$780$		0			0
$781$	−649.355	+	1124.72i	−0.0297513	+	0.0515307i
$782$	4056.67	−	2342.12i	0.185507	−	0.107102i
$783$		−	14854.1i		−	0.677958i
$784$	559.965	+	5459.36i	0.0255086	+	0.248695i
$785$		0			0
$786$	−6522.01	−	11296.5i	−0.295970	−	0.512635i
$787$	−18024.2	−	10406.2i	−0.816381	−	0.471338i	0.0327861	−	0.999462i	$-0.489562\pi$
$787$	−18024.2	−	10406.2i	−0.816381	−	0.471338i	−0.849167	+	0.528125i	$0.822895\pi$
$788$	−583.503	−	336.885i	−0.0263787	−	0.0152298i
$789$	−20248.5	−	35071.4i	−0.913644	−	1.58248i
$790$		0			0
$791$	22027.6	+	4710.97i	0.990151	+	0.211761i
$792$			2001.83i			0.0898133i
$793$	−26665.4	+	15395.3i	−1.19409	+	0.689411i
$794$	3999.06	−	6926.57i	0.178742	−	0.309591i
$795$		0			0
$796$	−1156.95	−	2003.90i	−0.0515165	−	0.0892291i
$797$		−	27138.1i		−	1.20612i	−0.797694	−	0.603062i	$-0.793947\pi$
$797$		−	27138.1i		−	1.20612i	0.797694	−	0.603062i	$-0.206053\pi$
$798$	−40776.8	+	13192.7i	−1.80888	+	0.585233i
$799$	−64294.0			−2.84676
$800$		0			0
$801$	17410.6	−	30156.0i	0.768006	−	1.33022i
$802$	−10288.3	−	5939.93i	−0.452981	−	0.261529i
$803$	−3429.24	+	1979.87i	−0.150704	+	0.0870089i
$804$	−15705.3			−0.688910
$805$		0			0
$806$	1513.95			0.0661621
$807$	−5631.49	+	3251.34i	−0.245648	+	0.141825i
$808$	−10480.2	−	6050.77i	−0.456304	−	0.263447i
$809$	6696.51	−	11598.7i	0.291022	−	0.504065i	−0.683030	−	0.730391i	$-0.739338\pi$
$809$	6696.51	−	11598.7i	0.291022	−	0.504065i	0.974052	+	0.226326i	$0.0726714\pi$
$810$		0			0
$811$	7438.93			0.322092			0.161046	−	0.986947i	$-0.448513\pi$
$811$	7438.93			0.322092			0.161046	+	0.986947i	$0.448513\pi$
$812$	−5480.51	−	4947.13i	−0.236857	−	0.213806i
$813$		−	18611.2i		−	0.802859i
$814$	17.9836	+	31.1485i	0.000774355	+	0.00134122i
$815$		0			0
$816$	7407.45	−	12830.1i	0.317785	−	0.550420i
$817$	48999.8	−	28290.1i	2.09827	−	1.21144i
$818$			18537.3i			0.792350i
$819$	11236.6	+	34730.8i	0.479412	+	1.48180i
$820$		0			0
$821$	−794.496	−	1376.11i	−0.0337736	−	0.0584976i	0.848645	−	0.528964i	$-0.177419\pi$
$821$	−794.496	−	1376.11i	−0.0337736	−	0.0584976i	−0.882418	+	0.470466i	$0.844086\pi$
$822$	11651.0	+	6726.72i	0.494375	+	0.285427i
$823$	−18742.4	−	10821.0i	−0.793828	−	0.458317i	0.0474804	−	0.998872i	$-0.484881\pi$
$823$	−18742.4	−	10821.0i	−0.793828	−	0.458317i	−0.841308	+	0.540555i	$0.818214\pi$
$824$	−4446.12	−	7700.91i	−0.187971	−	0.325575i
$825$		0			0
$826$	22166.5	+	4740.68i	0.933740	+	0.199697i
$827$			16078.0i			0.676041i	0.941139	+	0.338021i	$0.109757\pi$
$827$			16078.0i			0.676041i	−0.941139	+	0.338021i	$0.890243\pi$
$828$	3308.05	−	1909.90i	0.138844	−	0.0801614i
$829$	−14131.2	+	24475.9i	−0.592033	+	1.02543i	0.401925	+	0.915672i	$0.368341\pi$
$829$	−14131.2	+	24475.9i	−0.592033	+	1.02543i	−0.993958	+	0.109759i	$0.964992\pi$
$830$		0			0
$831$	19462.4	+	33709.9i	0.812449	+	1.40720i
$832$			2827.54i			0.117821i
$833$	−21983.4	−	30417.6i	−0.914380	−	1.26520i
$834$	−8512.48			−0.353433
$835$		0			0
$836$	−1533.81	+	2656.63i	−0.0634544	+	0.109906i
$837$	−2211.56	−	1276.84i	−0.0913293	−	0.0527290i
$838$	−3564.94	+	2058.22i	−0.146956	+	0.0848448i
$839$	−1240.80			−0.0510576			−0.0255288	−	0.999674i	$-0.508127\pi$
$839$	−1240.80			−0.0510576			−0.0255288	+	0.999674i	$0.508127\pi$
$840$		0			0
$841$	−14456.4			−0.592743
$842$	−24614.6	+	14211.3i	−1.00745	+	0.581654i
$843$	−238.945	−	137.955i	−0.00976239	−	0.00563632i
$844$	9272.07	−	16059.7i	0.378149	−	0.654973i
$845$		0			0
$846$	−52429.1			−2.13067
$847$	−22899.2	+	7408.66i	−0.928954	+	0.300548i
$848$			9624.38i			0.389743i
$849$	−33714.1	−	58394.5i	−1.36285	−	2.36053i
$850$		0			0
$851$	34.3154	−	59.4361i	0.00138228	−	0.00239417i
$852$	6787.58	−	3918.81i	0.272933	−	0.157578i
$853$		−	23806.6i		−	0.955595i	−0.878470	−	0.477797i	$-0.841435\pi$
$853$		−	23806.6i		−	0.955595i	0.878470	−	0.477797i	$-0.158565\pi$
$854$	17297.4	−	19162.4i	0.693098	−	0.767825i
$855$		0			0
$856$	2139.84	+	3706.30i	0.0854417	+	0.147989i
$857$	−25900.7	−	14953.8i	−1.03238	−	0.596045i	−0.114715	−	0.993398i	$-0.536596\pi$
$857$	−25900.7	−	14953.8i	−1.03238	−	0.596045i	−0.917666	+	0.397353i	$0.869929\pi$
$858$	3632.16	+	2097.03i	0.144522	+	0.0834399i
$859$	6146.48	+	10646.0i	0.244139	+	0.422861i	0.961889	−	0.273440i	$-0.0881615\pi$
$859$	6146.48	+	10646.0i	0.244139	+	0.422861i	−0.717750	+	0.696300i	$0.754828\pi$
$860$		0			0
$861$	−31359.4	+	34740.5i	−1.24126	+	1.37509i
$862$		−	175.394i		−	0.00693034i
$863$	−22633.8	+	13067.6i	−0.892774	+	0.515444i	−0.874849	−	0.484396i	$-0.839039\pi$
$863$	−22633.8	+	13067.6i	−0.892774	+	0.515444i	−0.0179254	+	0.999839i	$0.505706\pi$
$864$	2384.70	−	4130.42i	0.0938995	−	0.162639i
$865$		0			0
$866$	10482.6	+	18156.3i	0.411330	+	0.712445i
$867$			59736.6i			2.33998i
$868$	−1207.66	+	390.718i	−0.0472241	+	0.0152786i
$869$	−5686.04			−0.221963
$870$		0			0
$871$	−10249.2	+	17752.2i	−0.398716	+	0.690596i
$872$	−4144.01	−	2392.54i	−0.160933	−	0.0929149i
$873$	35117.1	−	20274.9i	1.36144	−	0.786026i
$874$	5853.47			0.226541
$875$		0			0
$876$	23896.8			0.921686
$877$	−31617.6	+	18254.4i	−1.21739	+	0.702861i	−0.964359	−	0.264597i	$-0.914761\pi$
$877$	−31617.6	+	18254.4i	−1.21739	+	0.702861i	−0.253031	+	0.967458i	$0.581428\pi$
$878$	6667.25	+	3849.34i	0.256274	+	0.147960i
$879$	640.716	−	1109.75i	0.0245857	−	0.0425836i
$880$		0			0
$881$	−250.978			−0.00959780			−0.00479890	−	0.999988i	$-0.501528\pi$
$881$	−250.978			−0.00959780			−0.00479890	+	0.999988i	$0.501528\pi$
$882$	−17926.5	−	24804.3i	−0.684374	−	0.946944i
$883$			35300.9i			1.34538i	0.739924	+	0.672690i	$0.234861\pi$
$883$			35300.9i			1.34538i	−0.739924	+	0.672690i	$0.765139\pi$
$884$	−9668.13	−	16745.7i	−0.367844	−	0.637125i
$885$		0			0
$886$	10511.8	−	18206.9i	0.398589	−	0.690377i
$887$	−226.821	+	130.955i	−0.00858615	+	0.00495722i	−0.504287	−	0.863536i	$-0.668245\pi$
$887$	−226.821	+	130.955i	−0.00858615	+	0.00495722i	0.495701	+	0.868493i	$0.334911\pi$
$888$		−	217.060i		−	0.00820275i
$889$	−15502.7	−	3315.52i	−0.584864	−	0.125083i
$890$		0			0
$891$	−159.111	−	275.589i	−0.00598253	−	0.0103620i
$892$	4056.90	+	2342.25i	0.152282	+	0.0879198i
$893$	−69578.6	−	40171.2i	−2.60735	−	1.50535i
$894$	−15823.5	−	27407.2i	−0.591967	−	1.02532i
$895$		0			0
$896$	−729.726	−	2255.48i	−0.0272081	−	0.0840965i
$897$		−	8002.90i		−	0.297892i
$898$	11259.5	−	6500.68i	0.418413	−	0.241571i
$899$	853.798	−	1478.82i	0.0316749	−	0.0548626i
$900$		0			0
$901$	−32908.4	−	56999.0i	−1.21680	−	2.10756i
$902$			3349.84i			0.123656i
$903$	48142.5	+	43457.1i	1.77418	+	1.60151i
$904$	−9730.18			−0.357988
$905$		0			0
$906$	8680.12	−	15034.4i	0.318298	−	0.551308i
$907$	−3789.94	−	2188.12i	−0.138746	−	0.0801052i	0.429020	−	0.903295i	$-0.358859\pi$
$907$	−3789.94	−	2188.12i	−0.138746	−	0.0801052i	−0.567766	+	0.823190i	$0.692192\pi$
$908$	−13651.9	+	7881.92i	−0.498958	+	0.288074i
$909$	67485.0			2.46241
$910$		0			0
$911$	12958.0			0.471261			0.235630	−	0.971843i	$-0.424285\pi$
$911$	12958.0			0.471261			0.235630	+	0.971843i	$0.424285\pi$
$912$	16032.6	−	9256.42i	0.582119	−	0.336086i
$913$	−2316.60	−	1337.49i	−0.0839741	−	0.0484825i
$914$	−5003.21	+	8665.81i	−0.181063	+	0.313610i
$915$		0			0
$916$	25118.1			0.906031
$917$	13580.5	−	4393.77i	0.489061	−	0.158228i
$918$			32615.8i			1.17264i
$919$	20396.0	+	35326.9i	0.732101	+	1.26804i	0.955983	+	0.293420i	$0.0947936\pi$
$919$	20396.0	+	35326.9i	0.732101	+	1.26804i	−0.223882	+	0.974616i	$0.571873\pi$
$920$		0			0
$921$	−13445.0	+	23287.4i	−0.481029	+	0.833166i
$922$	−11528.7	+	6656.10i	−0.411798	+	0.237752i
$923$		−	10229.6i		−	0.364801i
$924$	−3438.52	−	735.387i	−0.122423	−	0.0261823i
$925$		0			0
$926$	9725.18	+	16844.5i	0.345129	+	0.597781i
$927$	42944.6	+	24794.1i	1.52156	+	0.878472i
$928$	2761.93	+	1594.60i	0.0976990	+	0.0564065i
$929$	−2607.12	−	4515.66i	−0.0920740	−	0.159477i	0.816310	−	0.577615i	$-0.196016\pi$
$929$	−2607.12	−	4515.66i	−0.0920740	−	0.159477i	−0.908384	+	0.418138i	$0.862683\pi$
$930$		0			0
$931$	−4785.19	−	46653.1i	−0.168452	−	1.64231i
$932$		−	27810.2i		−	0.977418i
$933$	−6731.64	+	3886.52i	−0.236210	+	0.136376i
$934$	205.062	−	355.177i	0.00718397	−	0.0124430i
$935$		0			0
$936$	−7883.96	−	13655.4i	−0.275315	−	0.476860i
$937$		−	52538.8i		−	1.83177i	−0.401441	−	0.915885i	$-0.631491\pi$
$937$		−	52538.8i		−	1.83177i	0.401441	−	0.915885i	$-0.368509\pi$
$938$	3594.20	−	16805.7i	0.125112	−	0.584997i
$939$	−28075.9			−0.975744
$940$		0			0
$941$	8941.67	−	15487.4i	0.309766	−	0.536531i	−0.668545	−	0.743672i	$-0.733082\pi$
$941$	8941.67	−	15487.4i	0.309766	−	0.536531i	0.978311	+	0.207141i	$0.0664158\pi$
$942$	−39963.9	−	23073.2i	−1.38227	−	0.798052i
$943$	5535.63	−	3196.00i	0.191161	−	0.110367i
$944$	−9791.54			−0.337593
$945$		0			0
$946$	4642.13			0.159544
$947$	−17658.5	+	10195.1i	−0.605937	+	0.349838i	−0.771374	−	0.636382i	$-0.780430\pi$
$947$	−17658.5	+	10195.1i	−0.605937	+	0.349838i	0.165436	+	0.986220i	$0.447097\pi$
$948$	29717.5	+	17157.4i	1.01812	+	0.587814i
$949$	15594.9	−	27011.2i	0.533438	−	0.923941i
$950$		0			0
$951$	−54279.4			−1.85082
$952$	12033.8	+	10862.7i	0.409683	+	0.369812i
$953$			616.922i			0.0209696i	0.999945	+	0.0104848i	$0.00333748\pi$
$953$			616.922i			0.0209696i	−0.999945	+	0.0104848i	$0.996663\pi$
$954$	−26835.4	−	46480.3i	−0.910723	−	1.57742i
$955$		0			0
$956$	4278.87	−	7411.22i	0.144758	−	0.250728i
$957$	4096.74	−	2365.25i	0.138379	−	0.0798932i
$958$		−	21905.3i		−	0.738757i
$959$	−9864.41	+	10927.9i	−0.332157	+	0.367969i
$960$		0			0
$961$	14748.7	+	25545.5i	0.495073	+	0.857491i
$962$	−245.349	−	141.652i	−0.00822282	−	0.00474745i
$963$	−20668.4	−	11932.9i	−0.691620	−	0.399307i
$964$	7267.07	+	12586.9i	0.242797	+	0.420537i
$965$		0			0
$966$	2065.38	+	6383.80i	0.0687913	+	0.212624i
$967$			16415.7i			0.545910i	0.962027	+	0.272955i	$0.0880010\pi$
$967$			16415.7i			0.545910i	−0.962027	+	0.272955i	$0.911999\pi$
$968$	9003.47	−	5198.16i	0.298949	−	0.172598i
$969$	−63300.5	+	109640.i	−2.09856	+	3.63482i
$970$		0			0
$971$	−10586.8	−	18336.8i	−0.349892	−	0.606031i	0.636338	−	0.771410i	$-0.280448\pi$
$971$	−10586.8	−	18336.8i	−0.349892	−	0.606031i	−0.986230	+	0.165380i	$0.947115\pi$
$972$		−	14176.3i		−	0.467803i
$973$	1948.10	−	9108.93i	0.0641863	−	0.300122i
$974$	24518.7			0.806601
$975$		0			0
$976$	−5575.45	+	9656.96i	−0.182854	+	0.316713i
$977$	40001.3	+	23094.8i	1.30988	+	0.756261i	0.982076	−	0.188483i	$-0.0603571\pi$
$977$	40001.3	+	23094.8i	1.30988	+	0.756261i	0.327807	+	0.944745i	$0.393690\pi$
$978$	−31774.9	+	18345.3i	−1.03891	+	0.599812i
$979$	4377.93			0.142921
$980$		0			0
$981$	26684.3			0.868466
$982$	3321.99	−	1917.95i	0.107952	−	0.0623262i
$983$	38248.9	+	22083.0i	1.24105	+	0.716520i	0.969308	−	0.245850i	$-0.0790670\pi$
$983$	38248.9	+	22083.0i	1.24105	+	0.716520i	0.271742	+	0.962370i	$0.412400\pi$
$984$	10108.0	−	17507.6i	0.327471	−	0.567197i
$985$		0			0
$986$	−21809.5			−0.704418
$987$	19260.2	−	90056.7i	0.621133	−	2.90429i
$988$		−	24162.8i		−	0.778058i
$989$	−4428.94	−	7671.15i	−0.142398	−	0.246641i
$990$		0			0
$991$	16303.1	−	28237.9i	0.522590	−	0.905152i	−0.477065	−	0.878868i	$-0.658299\pi$
$991$	16303.1	−	28237.9i	0.522590	−	0.905152i	0.999655	−	0.0262838i	$-0.00836735\pi$
$992$	474.826	−	274.141i	0.0151973	−	0.00877417i
$993$			57334.8i			1.83229i
$994$	2640.04	+	8160.00i	0.0842424	+	0.260382i
$995$		0			0
$996$	8071.66	+	13980.5i	0.256788	+	0.444769i
$997$	24476.1	+	14131.3i	0.777497	+	0.448888i	0.835542	−	0.549426i	$-0.185154\pi$
$997$	24476.1	+	14131.3i	0.777497	+	0.448888i	−0.0580455	+	0.998314i	$0.518487\pi$
$998$	8882.24	+	5128.16i	0.281726	+	0.162654i
$999$	238.934	+	413.847i	0.00756712	+	0.0131066i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.4.j.j.249.8		16
5.2	odd	4		350.4.e.m.151.4	yes	8
5.3	odd	4		350.4.e.l.151.1	yes	8
5.4	even	2	inner	350.4.j.j.249.1		16
7.2	even	3	inner	350.4.j.j.149.1		16
35.2	odd	12		350.4.e.m.51.4	yes	8
35.3	even	12		2450.4.a.cu.1.1		4
35.9	even	6	inner	350.4.j.j.149.8		16
35.17	even	12		2450.4.a.ck.1.4		4
35.18	odd	12		2450.4.a.cq.1.4		4
35.23	odd	12		350.4.e.l.51.1	✓	8
35.32	odd	12		2450.4.a.co.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.4.e.l.51.1	✓	8	35.23	odd	12
350.4.e.l.151.1	yes	8	5.3	odd	4
350.4.e.m.51.4	yes	8	35.2	odd	12
350.4.e.m.151.4	yes	8	5.2	odd	4
350.4.j.j.149.1		16	7.2	even	3	inner
350.4.j.j.149.8		16	35.9	even	6	inner
350.4.j.j.249.1		16	5.4	even	2	inner
350.4.j.j.249.8		16	1.1	even	1	trivial
2450.4.a.ck.1.4		4	35.17	even	12
2450.4.a.co.1.1		4	35.32	odd	12
2450.4.a.cq.1.4		4	35.18	odd	12
2450.4.a.cu.1.1		4	35.3	even	12

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	350.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.73205 - 1.00000i) q^{2} +(7.32867 + 4.23121i) q^{3} +(2.00000 - 3.46410i) q^{4} +16.9248 q^{6} +(-3.87329 + 18.1107i) q^{7} -8.00000i q^{8} +(22.3062 + 38.6355i) q^{9} +O(q^{10})\)	\(q+(1.73205 - 1.00000i) q^{2} +(7.32867 + 4.23121i) q^{3} +(2.00000 - 3.46410i) q^{4} +16.9248 q^{6} +(-3.87329 + 18.1107i) q^{7} -8.00000i q^{8} +(22.3062 + 38.6355i) q^{9} +(-2.80448 + 4.85750i) q^{11} +(29.3147 - 16.9248i) q^{12} -44.1803i q^{13} +(11.4020 + 35.2419i) q^{14} +(-8.00000 - 13.8564i) q^{16} +(94.7578 + 54.7084i) q^{17} +(77.2710 + 44.6125i) q^{18} +(68.3642 + 118.410i) q^{19} +(-105.016 + 116.339i) q^{21} +11.2179i q^{22} +(18.5377 - 10.7027i) q^{23} +(33.8497 - 58.6293i) q^{24} +(-44.1803 - 76.5225i) q^{26} +149.044i q^{27} +(54.9907 + 49.6389i) q^{28} -99.6624 q^{29} +(-8.56690 + 14.8383i) q^{31} +(-27.7128 - 16.0000i) q^{32} +(-41.1062 + 23.7327i) q^{33} +218.834 q^{34} +178.450 q^{36} +(2.77668 - 1.60311i) q^{37} +(236.821 + 136.728i) q^{38} +(186.936 - 323.782i) q^{39} +298.615 q^{41} +(-65.5547 + 306.521i) q^{42} -413.814i q^{43} +(11.2179 + 19.4300i) q^{44} +(21.4055 - 37.0754i) q^{46} +(-508.882 + 293.803i) q^{47} -135.399i q^{48} +(-312.995 - 140.296i) q^{49} +(462.965 + 801.880i) q^{51} +(-153.045 - 88.3605i) q^{52} +(-520.935 - 300.762i) q^{53} +(149.044 + 258.152i) q^{54} +(144.886 + 30.9863i) q^{56} +1157.05i q^{57} +(-172.620 + 99.6624i) q^{58} +(305.985 - 529.982i) q^{59} +(-348.465 - 603.560i) q^{61} +34.2676i q^{62} +(-786.115 + 254.335i) q^{63} -64.0000 q^{64} +(-47.4653 + 82.2123i) q^{66} +(-401.812 - 231.986i) q^{67} +(379.031 - 218.834i) q^{68} +181.142 q^{69} +231.542 q^{71} +(309.084 - 178.450i) q^{72} +(611.386 + 352.984i) q^{73} +(3.20623 - 5.55335i) q^{74} +546.914 q^{76} +(-77.1102 - 69.6056i) q^{77} -747.743i q^{78} +(506.872 + 877.928i) q^{79} +(-28.3674 + 49.1337i) q^{81} +(517.217 - 298.615i) q^{82} +476.913i q^{83} +(192.976 + 596.464i) q^{84} +(-413.814 - 716.747i) q^{86} +(-730.393 - 421.692i) q^{87} +(38.8600 + 22.4358i) q^{88} +(-390.263 - 675.955i) q^{89} +(800.136 + 171.123i) q^{91} -85.6219i q^{92} +(-125.568 + 72.4966i) q^{93} +(-587.606 + 1017.76i) q^{94} +(-135.399 - 234.517i) q^{96} -908.934i q^{97} +(-682.420 + 69.9956i) q^{98} -250.229 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{4} - 8 q^{6} + 146 q^{9}+O(q^{10}) \) 16 * q + 32 * q^4 - 8 * q^6 + 146 * q^9	\( 16 q + 32 q^{4} - 8 q^{6} + 146 q^{9} + 20 q^{11} + 140 q^{14} - 128 q^{16} + 492 q^{19} - 1070 q^{21} - 16 q^{24} - 376 q^{26} + 392 q^{29} - 608 q^{31} - 792 q^{34} + 1168 q^{36} - 428 q^{39} + 1408 q^{41} - 80 q^{44} + 8 q^{46} - 2566 q^{49} + 2874 q^{51} - 784 q^{54} + 112 q^{56} + 1346 q^{59} - 2850 q^{61} - 1024 q^{64} - 2104 q^{66} - 3752 q^{69} - 24 q^{71} - 328 q^{74} + 3936 q^{76} + 3488 q^{79} - 3416 q^{81} - 1744 q^{84} - 524 q^{86} - 1742 q^{89} - 1594 q^{91} - 1964 q^{94} + 64 q^{96} + 21124 q^{99}+O(q^{100}) \) 16 * q + 32 * q^4 - 8 * q^6 + 146 * q^9 + 20 * q^11 + 140 * q^14 - 128 * q^16 + 492 * q^19 - 1070 * q^21 - 16 * q^24 - 376 * q^26 + 392 * q^29 - 608 * q^31 - 792 * q^34 + 1168 * q^36 - 428 * q^39 + 1408 * q^41 - 80 * q^44 + 8 * q^46 - 2566 * q^49 + 2874 * q^51 - 784 * q^54 + 112 * q^56 + 1346 * q^59 - 2850 * q^61 - 1024 * q^64 - 2104 * q^66 - 3752 * q^69 - 24 * q^71 - 328 * q^74 + 3936 * q^76 + 3488 * q^79 - 3416 * q^81 - 1744 * q^84 - 524 * q^86 - 1742 * q^89 - 1594 * q^91 - 1964 * q^94 + 64 * q^96 + 21124 * q^99

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