LMFDB - Embedded newform 350.4.j.j.149.7

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			149.7
Root			$-5.28099 + 3.04898i$ of defining polynomial
Character	$\chi$	$=$	350.149
Dual form			350.4.j.j.249.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73205 + 1.00000i) q^{2} +(2.69618 - 1.55664i) q^{3} +(2.00000 + 3.46410i) q^{4} +6.22657 q^{6} +(-3.64704 + 18.1576i) q^{7} +8.00000i q^{8} +(-8.65373 + 14.9887i) q^{9} +O(q^{10})$	\(q+(1.73205 + 1.00000i) q^{2} +(2.69618 - 1.55664i) q^{3} +(2.00000 + 3.46410i) q^{4} +6.22657 q^{6} +(-3.64704 + 18.1576i) q^{7} +8.00000i q^{8} +(-8.65373 + 14.9887i) q^{9} +(2.50388 + 4.33685i) q^{11} +(10.7847 + 6.22657i) q^{12} +2.87313i q^{13} +(-24.4745 + 27.8029i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(-40.9643 + 23.6508i) q^{17} +(-29.9774 + 17.3075i) q^{18} +(-11.8450 + 20.5162i) q^{19} +(18.4318 + 54.6334i) q^{21} +10.0155i q^{22} +(-56.9621 - 32.8871i) q^{23} +(12.4531 + 21.5695i) q^{24} +(-2.87313 + 4.97641i) q^{26} +137.942i q^{27} +(-70.1939 + 23.6815i) q^{28} -91.7175 q^{29} +(64.7258 + 112.108i) q^{31} +(-27.7128 + 16.0000i) q^{32} +(13.5018 + 7.79530i) q^{33} -94.6030 q^{34} -69.2299 q^{36} +(321.313 + 185.510i) q^{37} +(-41.0323 + 23.6900i) q^{38} +(4.47243 + 7.74648i) q^{39} -19.0608 q^{41} +(-22.7086 + 113.060i) q^{42} -117.314i q^{43} +(-10.0155 + 17.3474i) q^{44} +(-65.7742 - 113.924i) q^{46} +(519.754 + 300.080i) q^{47} +49.8125i q^{48} +(-316.398 - 132.443i) q^{49} +(-73.6315 + 127.533i) q^{51} +(-9.95282 + 5.74626i) q^{52} +(151.403 - 87.4128i) q^{53} +(-137.942 + 238.922i) q^{54} +(-145.261 - 29.1764i) q^{56} +73.7537i q^{57} +(-158.859 - 91.7175i) q^{58} +(-24.4427 - 42.3359i) q^{59} +(-349.341 + 605.076i) q^{61} +258.903i q^{62} +(-240.599 - 211.796i) q^{63} -64.0000 q^{64} +(15.5906 + 27.0037i) q^{66} +(507.083 - 292.764i) q^{67} +(-163.857 - 94.6030i) q^{68} -204.774 q^{69} -756.468 q^{71} +(-119.910 - 69.2299i) q^{72} +(709.970 - 409.901i) q^{73} +(371.020 + 642.626i) q^{74} -94.7601 q^{76} +(-87.8787 + 29.6479i) q^{77} +17.8897i q^{78} +(240.970 - 417.372i) q^{79} +(-18.9251 - 32.7792i) q^{81} +(-33.0143 - 19.0608i) q^{82} -269.803i q^{83} +(-152.392 + 173.116i) q^{84} +(117.314 - 203.194i) q^{86} +(-247.287 + 142.771i) q^{87} +(-34.6948 + 20.0311i) q^{88} +(73.2952 - 126.951i) q^{89} +(-52.1692 - 10.4784i) q^{91} -263.097i q^{92} +(349.025 + 201.510i) q^{93} +(600.160 + 1039.51i) q^{94} +(-49.8125 + 86.2778i) q^{96} -241.036i q^{97} +(-415.574 - 545.797i) q^{98} -86.6717 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 $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

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

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
$3$	2.69618	−	1.55664i	0.518880	−	0.299576i	−0.217596	−	0.976039i	$-0.569822\pi$
$3$	2.69618	−	1.55664i	0.518880	−	0.299576i	0.736476	+	0.676463i	$0.236488\pi$
$4$	2.00000	+	3.46410i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	6.22657			0.423664
$7$	−3.64704	+	18.1576i	−0.196922	+	0.980419i
$7$	−3.64704	+	18.1576i	−0.196922	+	0.980419i
$8$			8.00000i			0.353553i
$9$	−8.65373	+	14.9887i	−0.320509	+	0.555137i
$10$		0			0
$11$	2.50388	+	4.33685i	0.0686317	+	0.118874i	0.898299	−	0.439384i	$-0.144803\pi$
$11$	2.50388	+	4.33685i	0.0686317	+	0.118874i	−0.829668	+	0.558258i	$0.811470\pi$
$12$	10.7847	+	6.22657i	0.259440	+	0.149788i
$13$			2.87313i			0.0612972i	0.999530	+	0.0306486i	$0.00975727\pi$
$13$			2.87313i			0.0612972i	−0.999530	+	0.0306486i	$0.990243\pi$
$14$	−24.4745	+	27.8029i	−0.467220	+	0.530759i
$15$		0			0
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−40.9643	+	23.6508i	−0.584430	+	0.337421i	−0.762892	−	0.646526i	$-0.776221\pi$
$17$	−40.9643	+	23.6508i	−0.584430	+	0.337421i	0.178462	+	0.983947i	$0.442888\pi$
$18$	−29.9774	+	17.3075i	−0.392541	+	0.226634i
$19$	−11.8450	+	20.5162i	−0.143023	+	0.247723i	−0.928634	−	0.370998i	$-0.879016\pi$
$19$	−11.8450	+	20.5162i	−0.143023	+	0.247723i	0.785611	+	0.618721i	$0.212349\pi$
$20$		0			0
$21$	18.4318	+	54.6334i	0.191531	+	0.567713i
$22$			10.0155i			0.0970599i
$23$	−56.9621	−	32.8871i	−0.516410	−	0.298149i	0.219055	−	0.975713i	$-0.429703\pi$
$23$	−56.9621	−	32.8871i	−0.516410	−	0.298149i	−0.735464	+	0.677563i	$0.763036\pi$
$24$	12.4531	+	21.5695i	0.105916	+	0.183452i
$25$		0			0
$26$	−2.87313	+	4.97641i	−0.0216718	+	0.0375367i
$27$			137.942i			0.983218i
$28$	−70.1939	+	23.6815i	−0.473764	+	0.159835i
$29$	−91.7175			−0.587293			−0.293647	−	0.955914i	$-0.594869\pi$
$29$	−91.7175			−0.587293			−0.293647	+	0.955914i	$0.594869\pi$
$30$		0			0
$31$	64.7258	+	112.108i	0.375003	+	0.649524i	0.990327	−	0.138750i	$-0.0443084\pi$
$31$	64.7258	+	112.108i	0.375003	+	0.649524i	−0.615325	+	0.788274i	$0.710975\pi$
$32$	−27.7128	+	16.0000i	−0.153093	+	0.0883883i
$33$	13.5018	+	7.79530i	0.0712233	+	0.0411208i
$34$	−94.6030			−0.477185
$35$		0			0
$36$	−69.2299			−0.320509
$37$	321.313	+	185.510i	1.42766	+	0.824261i	0.996936	−	0.0782216i	$-0.0249242\pi$
$37$	321.313	+	185.510i	1.42766	+	0.824261i	0.430726	+	0.902483i	$0.358257\pi$
$38$	−41.0323	+	23.6900i	−0.175166	+	0.101132i
$39$	4.47243	+	7.74648i	0.0183631	+	0.0318059i
$40$		0			0
$41$	−19.0608			−0.0726048			−0.0363024	−	0.999341i	$-0.511558\pi$
$41$	−19.0608			−0.0726048			−0.0363024	+	0.999341i	$0.511558\pi$
$42$	−22.7086	+	113.060i	−0.0834287	+	0.415368i
$43$		−	117.314i		−	0.416053i	−0.978123	−	0.208026i	$-0.933296\pi$
$43$		−	117.314i		−	0.416053i	0.978123	−	0.208026i	$-0.0667040\pi$
$44$	−10.0155	+	17.3474i	−0.0343159	+	0.0594368i
$45$		0			0
$46$	−65.7742	−	113.924i	−0.210823	−	0.365157i
$47$	519.754	+	300.080i	1.61306	+	0.931301i	0.988656	+	0.150201i	$0.0479920\pi$
$47$	519.754	+	300.080i	1.61306	+	0.931301i	0.624405	+	0.781100i	$0.285341\pi$
$48$			49.8125i			0.149788i
$49$	−316.398	−	132.443i	−0.922444	−	0.386132i
$50$		0			0
$51$	−73.6315	+	127.533i	−0.202166	+	0.350162i
$52$	−9.95282	+	5.74626i	−0.0265425	+	0.0153243i
$53$	151.403	−	87.4128i	0.392394	−	0.226549i	−0.290803	−	0.956783i	$-0.593922\pi$
$53$	151.403	−	87.4128i	0.392394	−	0.226549i	0.683197	+	0.730234i	$0.260589\pi$
$54$	−137.942	+	238.922i	−0.347620	+	0.602096i
$55$		0			0
$56$	−145.261	−	29.1764i	−0.346631	−	0.0696224i
$57$			73.7537i			0.171385i
$58$	−158.859	−	91.7175i	−0.359642	−	0.207640i
$59$	−24.4427	−	42.3359i	−0.0539350	−	0.0934181i	0.837797	−	0.545981i	$-0.183843\pi$
$59$	−24.4427	−	42.3359i	−0.0539350	−	0.0934181i	−0.891732	+	0.452563i	$0.850510\pi$
$60$		0			0
$61$	−349.341	+	605.076i	−0.733254	+	1.27003i	0.222231	+	0.974994i	$0.428666\pi$
$61$	−349.341	+	605.076i	−0.733254	+	1.27003i	−0.955485	+	0.295040i	$0.904667\pi$
$62$			258.903i			0.530334i
$63$	−240.599	−	211.796i	−0.481152	−	0.423552i
$64$	−64.0000			−0.125000
$65$		0			0
$66$	15.5906	+	27.0037i	0.0290768	+	0.0503625i
$67$	507.083	−	292.764i	0.924627	−	0.533834i	0.0395189	−	0.999219i	$-0.487417\pi$
$67$	507.083	−	292.764i	0.924627	−	0.533834i	0.885108	+	0.465385i	$0.154084\pi$
$68$	−163.857	−	94.6030i	−0.292215	−	0.168710i
$69$	−204.774			−0.357273
$70$		0			0
$71$	−756.468			−1.26445			−0.632227	−	0.774783i	$-0.717859\pi$
$71$	−756.468			−1.26445			−0.632227	+	0.774783i	$0.717859\pi$
$72$	−119.910	−	69.2299i	−0.196271	−	0.113317i
$73$	709.970	−	409.901i	1.13830	−	0.657196i	0.192289	−	0.981338i	$-0.438409\pi$
$73$	709.970	−	409.901i	1.13830	−	0.657196i	0.946008	+	0.324142i	$0.105076\pi$
$74$	371.020	+	642.626i	0.582841	+	1.00951i
$75$		0			0
$76$	−94.7601			−0.143023
$77$	−87.8787	+	29.6479i	−0.130061	+	0.0438790i
$78$			17.8897i			0.0259694i
$79$	240.970	−	417.372i	0.343180	−	0.594405i	−0.641842	−	0.766837i	$-0.721829\pi$
$79$	240.970	−	417.372i	0.343180	−	0.594405i	0.985021	+	0.172433i	$0.0551627\pi$
$80$		0			0
$81$	−18.9251	−	32.7792i	−0.0259603	−	0.0449646i
$82$	−33.0143	−	19.0608i	−0.0444612	−	0.0256697i
$83$		−	269.803i		−	0.356804i	−0.983958	−	0.178402i	$-0.942907\pi$
$83$		−	269.803i		−	0.356804i	0.983958	−	0.178402i	$-0.0570927\pi$
$84$	−152.392	+	173.116i	−0.197944	+	0.224864i
$85$		0			0
$86$	117.314	−	203.194i	0.147097	−	0.254779i
$87$	−247.287	+	142.771i	−0.304735	+	0.175939i
$88$	−34.6948	+	20.0311i	−0.0420282	+	0.0242650i
$89$	73.2952	−	126.951i	0.0872952	−	0.151200i	−0.819072	−	0.573691i	$-0.805511\pi$
$89$	73.2952	−	126.951i	0.0872952	−	0.151200i	0.906367	+	0.422491i	$0.138844\pi$
$90$		0			0
$91$	−52.1692	−	10.4784i	−0.0600969	−	0.0120708i
$92$		−	263.097i		−	0.298149i
$93$	349.025	+	201.510i	0.389163	+	0.224684i
$94$	600.160	+	1039.51i	0.658529	+	1.14061i
$95$		0			0
$96$	−49.8125	+	86.2778i	−0.0529580	+	0.0917260i
$97$		−	241.036i		−	0.252304i	−0.992011	−	0.126152i	$-0.959737\pi$
$97$		−	241.036i		−	0.252304i	0.992011	−	0.126152i	$-0.0402627\pi$
$98$	−415.574	−	545.797i	−0.428361	−	0.562590i
$99$	−86.6717			−0.0879883
$100$		0			0
$101$	−474.936	−	822.613i	−0.467900	−	0.810426i	0.531428	−	0.847104i	$-0.321656\pi$
$101$	−474.936	−	822.613i	−0.467900	−	0.810426i	−0.999327	+	0.0366778i	$0.988322\pi$
$102$	−255.067	+	147.263i	−0.247602	+	0.142953i
$103$	42.9711	+	24.8094i	0.0411074	+	0.0237334i	0.520413	−	0.853915i	$-0.325778\pi$
$103$	42.9711	+	24.8094i	0.0411074	+	0.0237334i	−0.479305	+	0.877648i	$0.659111\pi$
$104$	−22.9850			−0.0216718
$105$		0			0
$106$	349.651			0.320388
$107$	650.048	+	375.306i	0.587314	+	0.339086i	0.764035	−	0.645175i	$-0.223216\pi$
$107$	650.048	+	375.306i	0.587314	+	0.339086i	−0.176721	+	0.984261i	$0.556549\pi$
$108$	−477.844	+	275.883i	−0.425746	+	0.245805i
$109$	−205.055	−	355.166i	−0.180190	−	0.312098i	0.761755	−	0.647865i	$-0.224338\pi$
$109$	−205.055	−	355.166i	−0.180190	−	0.312098i	−0.941945	+	0.335767i	$0.891005\pi$
$110$		0			0
$111$	1155.09			0.987715
$112$	−222.423	−	195.796i	−0.187652	−	0.165187i
$113$			1885.39i			1.56958i	0.619763	+	0.784789i	$0.287229\pi$
$113$			1885.39i			1.56958i	−0.619763	+	0.784789i	$0.712771\pi$
$114$	−73.7537	+	127.745i	−0.0605936	+	0.104951i
$115$		0			0
$116$	−183.435	−	317.719i	−0.146823	−	0.254305i
$117$	−43.0645	−	24.8633i	−0.0340283	−	0.0196463i
$118$		−	97.7706i		−	0.0762755i
$119$	−280.043	−	830.070i	−0.215727	−	0.639432i
$120$		0			0
$121$	652.961	−	1130.96i	0.490579	−	0.849708i
$122$	−1210.15	+	698.682i	−0.898050	+	0.518489i
$123$	−51.3914	+	29.6708i	−0.0376732	+	0.0217506i
$124$	−258.903	+	448.433i	−0.187501	+	0.324762i
$125$		0			0
$126$	−204.933	−	607.440i	−0.144896	−	0.429484i
$127$		−	2336.23i		−	1.63234i	−0.577814	−	0.816169i	$-0.696094\pi$
$127$		−	2336.23i		−	1.63234i	0.577814	−	0.816169i	$-0.303906\pi$
$128$	−110.851	−	64.0000i	−0.0765466	−	0.0441942i
$129$	−182.616	−	316.301i	−0.124639	−	0.215882i
$130$		0			0
$131$	−939.864	+	1627.89i	−0.626842	+	1.08572i	0.361339	+	0.932434i	$0.382320\pi$
$131$	−939.864	+	1627.89i	−0.626842	+	1.08572i	−0.988182	+	0.153288i	$0.951014\pi$
$132$			62.3624i			0.0411208i
$133$	−329.325	−	289.901i	−0.214708	−	0.189004i
$134$	1171.06			0.754955
$135$		0			0
$136$	−189.206	−	327.714i	−0.119296	−	0.206627i
$137$	705.830	−	407.511i	0.440169	−	0.254132i	−0.263500	−	0.964659i	$-0.584877\pi$
$137$	705.830	−	407.511i	0.440169	−	0.254132i	0.703669	+	0.710528i	$0.251544\pi$
$138$	−354.678	−	204.774i	−0.218784	−	0.126315i
$139$	−10.2265			−0.00624028			−0.00312014	−	0.999995i	$-0.500993\pi$
$139$	−10.2265			−0.00624028			−0.00312014	+	0.999995i	$0.500993\pi$
$140$		0			0
$141$	1868.47			1.11598
$142$	−1310.24	−	756.468i	−0.774316	−	0.447052i
$143$	−12.4603	+	7.19398i	−0.00728662	+	0.00420693i
$144$	−138.460	−	239.819i	−0.0801272	−	0.138784i
$145$		0			0
$146$	1639.61			0.929416
$147$	−1059.23	+	135.427i	−0.594314	+	0.0759854i
$148$			1484.08i			0.824261i
$149$	1768.00	−	3062.27i	0.972084	−	1.68370i	0.282844	−	0.959166i	$-0.408722\pi$
$149$	1768.00	−	3062.27i	0.972084	−	1.68370i	0.689240	−	0.724533i	$-0.257944\pi$
$150$		0			0
$151$	1079.99	+	1870.60i	0.582043	+	1.00813i	0.995237	+	0.0974851i	$0.0310798\pi$
$151$	1079.99	+	1870.60i	0.582043	+	1.00813i	−0.413194	+	0.910643i	$0.635587\pi$
$152$	−164.129	−	94.7601i	−0.0875832	−	0.0505662i
$153$		−	818.669i		−	0.432585i
$154$	−181.858	−	36.5271i	−0.0951594	−	0.0191132i
$155$		0			0
$156$	−17.8897	+	30.9859i	−0.00918157	+	0.0159030i
$157$	−1872.78	+	1081.25i	−0.952003	+	0.549639i	−0.893703	−	0.448660i	$-0.851901\pi$
$157$	−1872.78	+	1081.25i	−0.952003	+	0.549639i	−0.0583005	+	0.998299i	$0.518568\pi$
$158$	834.743	−	481.939i	0.420308	−	0.242665i
$159$	272.141	−	471.362i	0.135737	−	0.235103i
$160$		0			0
$161$	804.895	−	914.356i	0.394004	−	0.447586i
$162$		−	75.7003i		−	0.0367135i
$163$	2080.13	+	1200.96i	0.999560	+	0.577096i	0.908118	−	0.418714i	$-0.137519\pi$
$163$	2080.13	+	1200.96i	0.999560	+	0.577096i	0.0914420	+	0.995810i	$0.470852\pi$
$164$	−38.1216	−	66.0285i	−0.0181512	−	0.0314388i
$165$		0			0
$166$	269.803	−	467.312i	0.126149	−	0.218497i
$167$		−	2844.04i		−	1.31784i	−0.752214	−	0.658919i	$-0.771014\pi$
$167$		−	2844.04i		−	1.31784i	0.752214	−	0.658919i	$-0.228986\pi$
$168$	−437.067	+	147.454i	−0.200717	+	0.0677164i
$169$	2188.75			0.996243
$170$		0			0
$171$	−205.007	−	355.083i	−0.0916801	−	0.158795i
$172$	406.389	−	234.629i	0.180156	−	0.104013i
$173$	1518.15	+	876.505i	0.667185	+	0.385199i	0.795009	−	0.606598i	$-0.207466\pi$
$173$	1518.15	+	876.505i	0.667185	+	0.385199i	−0.127824	+	0.991797i	$0.540799\pi$
$174$	−571.085			−0.248815
$175$		0			0
$176$	−80.1242			−0.0343159
$177$	−131.804	−	76.0969i	−0.0559716	−	0.0323152i
$178$	253.902	−	146.590i	0.106914	−	0.0617270i
$179$	−1074.66	−	1861.36i	−0.448735	−	0.777232i	0.549569	−	0.835448i	$-0.314792\pi$
$179$	−1074.66	−	1861.36i	−0.448735	−	0.777232i	−0.998304	+	0.0582164i	$0.981459\pi$
$180$		0			0
$181$	2403.89			0.987180			0.493590	−	0.869695i	$-0.335684\pi$
$181$	2403.89			0.987180			0.493590	+	0.869695i	$0.335684\pi$
$182$	−79.8813	−	70.3184i	−0.0325340	−	0.0286393i
$183$			2175.19i			0.878661i
$184$	263.097	−	455.697i	0.105412	−	0.182578i
$185$		0			0
$186$	403.019	+	698.050i	0.158875	+	0.275180i
$187$	−205.140	−	118.437i	−0.0802208	−	0.0463155i
$188$			2400.64i			0.931301i
$189$	−2504.69	−	503.079i	−0.963966	−	0.193617i
$190$		0			0
$191$	254.284	−	440.432i	0.0963315	−	0.166851i	−0.813832	−	0.581100i	$-0.802622\pi$
$191$	254.284	−	440.432i	0.0963315	−	0.166851i	0.910164	+	0.414249i	$0.135956\pi$
$192$	−172.556	+	99.6251i	−0.0648601	+	0.0374470i
$193$	1314.17	−	758.738i	0.490136	−	0.282980i	−0.234495	−	0.972117i	$-0.575344\pi$
$193$	1314.17	−	758.738i	0.490136	−	0.282980i	0.724631	+	0.689137i	$0.242010\pi$
$194$	241.036	−	417.487i	0.0892030	−	0.154504i
$195$		0			0
$196$	−173.999	−	1360.92i	−0.0634108	−	0.495963i
$197$			25.9685i			0.00939176i	0.999989	+	0.00469588i	$0.00149475\pi$
$197$			25.9685i			0.00939176i	−0.999989	+	0.00469588i	$0.998505\pi$
$198$	−150.120	−	86.6717i	−0.0538816	−	0.0311085i
$199$	2416.64	+	4185.74i	0.860858	+	1.49105i	0.871102	+	0.491103i	$0.163406\pi$
$199$	2416.64	+	4185.74i	0.860858	+	1.49105i	−0.0102436	+	0.999948i	$0.503261\pi$
$200$		0			0
$201$	911.458	−	1578.69i	0.319847	−	0.553992i
$202$		−	1899.74i		−	0.661710i
$203$	334.498	−	1665.37i	0.115651	−	0.575794i
$204$	−589.052			−0.202166
$205$		0			0
$206$	49.6187	+	85.9421i	0.0167820	+	0.0290673i
$207$	985.870	−	569.192i	0.331028	−	0.191119i
$208$	−39.8113	−	22.9850i	−0.0132712	−	0.00766215i
$209$	−118.634			−0.0392636
$210$		0			0
$211$	−1880.24			−0.613464			−0.306732	−	0.951796i	$-0.599235\pi$
$211$	−1880.24			−0.613464			−0.306732	+	0.951796i	$0.599235\pi$
$212$	605.614	+	349.651i	0.196197	+	0.113274i
$213$	−2039.57	+	1177.55i	−0.656100	+	0.378800i
$214$	750.611	+	1300.10i	0.239770	+	0.415293i
$215$		0			0
$216$	−1103.53			−0.347620
$217$	−2271.68	+	766.402i	−0.710652	+	0.239755i
$218$		−	820.221i		−	0.254827i
$219$	1276.14	−	2210.34i	0.393760	−	0.682013i
$220$		0			0
$221$	−67.9517	−	117.696i	−0.0206829	−	0.0358239i
$222$	2000.68	+	1155.09i	0.604849	+	0.349210i
$223$		−	5199.43i		−	1.56134i	−0.624942	−	0.780671i	$-0.714877\pi$
$223$		−	5199.43i		−	1.56134i	0.624942	−	0.780671i	$-0.285123\pi$
$224$	−189.452	−	561.551i	−0.0565102	−	0.167501i
$225$		0			0
$226$	−1885.39	+	3265.59i	−0.554930	+	0.961167i
$227$	−3358.21	+	1938.86i	−0.981903	+	0.566902i	−0.902844	−	0.429968i	$-0.858525\pi$
$227$	−3358.21	+	1938.86i	−0.981903	+	0.566902i	−0.0790590	+	0.996870i	$0.525192\pi$
$228$	−255.490	+	147.507i	−0.0742117	+	0.0428461i
$229$	−2380.36	+	4122.90i	−0.686893	+	1.18973i	0.285945	+	0.958246i	$0.407692\pi$
$229$	−2380.36	+	4122.90i	−0.686893	+	1.18973i	−0.972838	+	0.231487i	$0.925641\pi$
$230$		0			0
$231$	−190.786	+	216.732i	−0.0543411	+	0.0617311i
$232$		−	733.740i		−	0.207640i
$233$	495.185	+	285.895i	0.139230	+	0.0803846i	0.567997	−	0.823031i	$-0.307718\pi$
$233$	495.185	+	285.895i	0.139230	+	0.0803846i	−0.428767	+	0.903415i	$0.641052\pi$
$234$	−49.7266	−	86.1290i	−0.0138920	−	0.0240617i
$235$		0			0
$236$	97.7706	−	169.344i	0.0269675	−	0.0467090i
$237$		−	1500.41i		−	0.411233i
$238$	345.021	−	1717.77i	0.0939681	−	0.467841i
$239$	4842.24			1.31054			0.655269	−	0.755396i	$-0.272555\pi$
$239$	4842.24			1.31054			0.655269	+	0.755396i	$0.272555\pi$
$240$		0			0
$241$	−1587.99	−	2750.48i	−0.424445	−	0.735161i	0.571923	−	0.820307i	$-0.306198\pi$
$241$	−1587.99	−	2750.48i	−0.424445	−	0.735161i	−0.996368	+	0.0851464i	$0.972864\pi$
$242$	2261.92	−	1305.92i	0.600835	−	0.346892i
$243$	−3327.50	−	1921.13i	−0.878433	−	0.507163i
$244$	−2794.73			−0.733254
$245$		0			0
$246$	−118.683			−0.0307600
$247$	−58.9456	−	34.0323i	−0.0151847	−	0.00876689i
$248$	−896.866	+	517.806i	−0.229641	+	0.132584i
$249$	−419.986	−	727.438i	−0.106890	−	0.185138i
$250$		0			0
$251$	−6433.53			−1.61785			−0.808926	−	0.587910i	$-0.799951\pi$
$251$	−6433.53			−1.61785			−0.808926	+	0.587910i	$0.799951\pi$
$252$	252.484	−	1257.05i	0.0631152	−	0.314233i
$253$		−	329.382i		−	0.0818500i
$254$	2336.23	−	4046.47i	0.577118	−	0.999598i
$255$		0			0
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	6115.84	+	3530.98i	1.48442	+	0.857030i	0.999843	−	0.0177196i	$-0.00564063\pi$
$257$	6115.84	+	3530.98i	1.48442	+	0.857030i	0.484576	+	0.874749i	$0.338974\pi$
$258$		−	730.466i		−	0.176267i
$259$	−4540.26	+	5157.71i	−1.08926	+	1.23739i
$260$		0			0
$261$	793.699	−	1374.73i	0.188233	−	0.326028i
$262$	−3255.79	+	1879.73i	−0.767722	+	0.443244i
$263$	−4031.21	+	2327.42i	−0.945152	+	0.545684i	−0.891572	−	0.452880i	$-0.850397\pi$
$263$	−4031.21	+	2327.42i	−0.945152	+	0.545684i	−0.0535805	+	0.998564i	$0.517063\pi$
$264$	−62.3624	+	108.015i	−0.0145384	+	0.0251813i
$265$		0			0
$266$	−280.508	−	831.448i	−0.0646580	−	0.191652i
$267$		−	456.377i		−	0.104606i
$268$	2028.33	+	1171.06i	0.462314	+	0.266917i
$269$	2577.99	+	4465.21i	0.584322	+	1.01208i	0.994960	+	0.100277i	$0.0319729\pi$
$269$	2577.99	+	4465.21i	0.584322	+	1.01208i	−0.410637	+	0.911799i	$0.634694\pi$
$270$		0			0
$271$	−2514.12	+	4354.58i	−0.563549	+	0.976095i	0.433635	+	0.901089i	$0.357231\pi$
$271$	−2514.12	+	4354.58i	−0.563549	+	0.976095i	−0.997183	+	0.0750058i	$0.976102\pi$
$272$		−	756.824i		−	0.168710i
$273$	−156.969	+	52.9570i	−0.0347992	+	0.0117403i
$274$	1630.05			0.359397
$275$		0			0
$276$	−409.547	−	709.357i	−0.0893183	−	0.154704i
$277$	99.8881	−	57.6704i	0.0216668	−	0.0125093i	−0.489127	−	0.872212i	$-0.662685\pi$
$277$	99.8881	−	57.6704i	0.0216668	−	0.0125093i	0.510794	+	0.859703i	$0.329351\pi$
$278$	−17.7128	−	10.2265i	−0.00382137	−	0.00220627i
$279$	−2240.48			−0.480767
$280$		0			0
$281$	−977.317			−0.207480			−0.103740	−	0.994604i	$-0.533081\pi$
$281$	−977.317			−0.207480			−0.103740	+	0.994604i	$0.533081\pi$
$282$	3236.28	+	1868.47i	0.683396	+	0.394559i
$283$	−3652.15	+	2108.57i	−0.767131	+	0.442903i	−0.831850	−	0.555000i	$-0.812718\pi$
$283$	−3652.15	+	2108.57i	−0.767131	+	0.442903i	0.0647192	+	0.997904i	$0.479385\pi$
$284$	−1512.94	−	2620.48i	−0.316113	−	0.547524i
$285$		0			0
$286$	−28.7759			−0.00594950
$287$	69.5156	−	346.099i	0.0142975	−	0.0711831i
$288$		−	553.839i		−	0.113317i
$289$	−1337.78	+	2317.11i	−0.272295	+	0.471628i
$290$		0			0
$291$	−375.207	−	649.877i	−0.0755842	−	0.130916i
$292$	2839.88	+	1639.61i	0.569149	+	0.328598i
$293$		−	4064.73i		−	0.810458i	−0.914215	−	0.405229i	$-0.867192\pi$
$293$		−	4064.73i		−	0.810458i	0.914215	−	0.405229i	$-0.132808\pi$
$294$	−1970.07	−	824.667i	−0.390806	−	0.163590i
$295$		0			0
$296$	−1484.08	+	2570.50i	−0.291420	+	0.504755i
$297$	−598.233	+	345.390i	−0.116879	+	0.0674800i
$298$	6124.54	−	3536.01i	1.19055	−	0.687367i
$299$	94.4889	−	163.660i	0.0182757	−	0.0316544i
$300$		0			0
$301$	2130.15	+	427.851i	0.407906	+	0.0819299i
$302$			4319.97i			0.823133i
$303$	−2561.03	−	1478.61i	−0.485568	−	0.280343i
$304$	−189.520	−	328.259i	−0.0357557	−	0.0619307i
$305$		0			0
$306$	818.669	−	1417.98i	0.152942	−	0.264903i
$307$			1650.69i			0.306872i	0.988159	+	0.153436i	$0.0490339\pi$
$307$			1650.69i			0.306872i	−0.988159	+	0.153436i	$0.950966\pi$
$308$	−278.461	−	245.125i	−0.0515155	−	0.0453483i
$309$	154.477			0.0284398
$310$		0			0
$311$	−2143.20	−	3712.13i	−0.390771	−	0.676835i	0.601781	−	0.798661i	$-0.294458\pi$
$311$	−2143.20	−	3712.13i	−0.390771	−	0.676835i	−0.992551	+	0.121827i	$0.961125\pi$
$312$	−61.9719	+	35.7795i	−0.0112451	+	0.00649235i
$313$	6159.68	+	3556.29i	1.11235	+	0.642216i	0.939437	−	0.342721i	$-0.111349\pi$
$313$	6159.68	+	3556.29i	1.11235	+	0.642216i	0.172913	+	0.984937i	$0.444682\pi$
$314$	−4325.01			−0.777307
$315$		0			0
$316$	1927.76			0.343180
$317$	7904.73	+	4563.80i	1.40055	+	0.808607i	0.994449	−	0.105222i	$-0.0335552\pi$
$317$	7904.73	+	4563.80i	1.40055	+	0.808607i	0.406100	+	0.913829i	$0.366889\pi$
$318$	942.723	−	544.282i	0.166243	−	0.0959805i
$319$	−229.650	−	397.765i	−0.0403070	−	0.0698137i
$320$		0			0
$321$	2336.86			0.406327
$322$	2308.47	−	778.816i	0.399522	−	0.134788i
$323$		−	1120.57i		−	0.193035i
$324$	75.7003	−	131.117i	0.0129802	−	0.0224823i
$325$		0			0
$326$	2401.93	+	4160.26i	0.408069	+	0.706796i
$327$	−1105.73	−	638.395i	−0.186994	−	0.107961i
$328$		−	152.486i		−	0.0256697i
$329$	−7344.30	+	8343.08i	−1.23071	+	1.39808i
$330$		0			0
$331$	−4458.65	+	7722.61i	−0.740392	+	1.28240i	0.211925	+	0.977286i	$0.432027\pi$
$331$	−4458.65	+	7722.61i	−0.740392	+	1.28240i	−0.952317	+	0.305110i	$0.901307\pi$
$332$	934.624	−	539.606i	0.154501	−	0.0892009i
$333$	−5561.11	+	3210.71i	−0.915156	+	0.528366i
$334$	2844.04	−	4926.03i	0.465926	−	0.807007i
$335$		0			0
$336$	−904.477	−	181.668i	−0.146855	−	0.0294965i
$337$			9427.08i			1.52382i	0.647685	+	0.761908i	$0.275737\pi$
$337$			9427.08i			1.52382i	−0.647685	+	0.761908i	$0.724263\pi$
$338$	3791.02	+	2188.75i	0.610072	+	0.352225i
$339$	2934.87	+	5083.35i	0.470208	+	0.814424i
$340$		0			0
$341$	−324.131	+	561.412i	−0.0514742	+	0.0891559i
$342$		−	820.029i		−	0.129655i
$343$	3558.77	−	5262.01i	0.560221	−	0.828344i
$344$	938.515			0.147097
$345$		0			0
$346$	1753.01	+	3036.30i	0.272377	+	0.471771i
$347$	−385.004	+	222.282i	−0.0595623	+	0.0343883i	−0.529485	−	0.848319i	$-0.677615\pi$
$347$	−385.004	+	222.282i	−0.0595623	+	0.0343883i	0.469923	+	0.882707i	$0.344282\pi$
$348$	−989.148	−	571.085i	−0.152368	−	0.0879694i
$349$	−8417.98			−1.29113			−0.645565	−	0.763706i	$-0.723378\pi$
$349$	−8417.98			−1.29113			−0.645565	+	0.763706i	$0.723378\pi$
$350$		0			0
$351$	−396.325			−0.0602685
$352$	−138.779	−	80.1242i	−0.0210141	−	0.0121325i
$353$	−9652.68	+	5572.98i	−1.45541	+	0.840282i	−0.998780	−	0.0493743i	$-0.984277\pi$
$353$	−9652.68	+	5572.98i	−1.45541	+	0.840282i	−0.456631	+	0.889656i	$0.650944\pi$
$354$	−152.194	−	263.607i	−0.0228503	−	0.0395779i
$355$		0			0
$356$	586.361			0.0872952
$357$	−2047.17	−	1802.09i	−0.303495	−	0.267162i
$358$		−	4298.63i		−	0.634607i
$359$	4939.32	−	8555.15i	0.726148	−	1.25773i	−0.232351	−	0.972632i	$-0.574642\pi$
$359$	4939.32	−	8555.15i	0.726148	−	1.25773i	0.958500	−	0.285094i	$-0.0920247\pi$
$360$		0			0
$361$	3148.89	+	5454.04i	0.459089	+	0.795165i
$362$	4163.66	+	2403.89i	0.604522	+	0.349021i
$363$		−	4065.71i		−	0.587863i
$364$	−68.0401	−	201.676i	−0.00979744	−	0.0290404i
$365$		0			0
$366$	−2175.19	+	3767.55i	−0.310654	+	0.538068i
$367$	−6950.29	+	4012.75i	−0.988561	+	0.570746i	−0.904844	−	0.425743i	$-0.860013\pi$
$367$	−6950.29	+	4012.75i	−0.988561	+	0.570746i	−0.0837174	+	0.996490i	$0.526679\pi$
$368$	911.394	−	526.193i	0.129102	−	0.0745373i
$369$	164.947	−	285.697i	0.0232705	−	0.0403056i
$370$		0			0
$371$	1035.03	+	3067.92i	0.144842	+	0.429323i
$372$			1612.08i			0.224684i
$373$	10465.0	+	6041.97i	1.45270	+	0.838717i	0.998634	−	0.0522510i	$-0.0166396\pi$
$373$	10465.0	+	6041.97i	1.45270	+	0.838717i	0.454066	+	0.890968i	$0.349973\pi$
$374$	−236.875	−	410.279i	−0.0327500	−	0.0567247i
$375$		0			0
$376$	−2400.64	+	4158.03i	−0.329265	+	0.570303i
$377$		−	263.516i		−	0.0359994i
$378$	−3835.18	−	3376.05i	−0.521852	−	0.459379i
$379$	−3034.22			−0.411234			−0.205617	−	0.978633i	$-0.565920\pi$
$379$	−3034.22			−0.411234			−0.205617	+	0.978633i	$0.565920\pi$
$380$		0			0
$381$	−3636.67	−	6298.90i	−0.489009	−	0.846988i
$382$	880.864	−	508.567i	0.117981	−	0.0681166i
$383$	−6887.54	−	3976.52i	−0.918895	−	0.530524i	−0.0356123	−	0.999366i	$-0.511338\pi$
$383$	−6887.54	−	3976.52i	−0.918895	−	0.530524i	−0.883282	+	0.468842i	$0.844671\pi$
$384$	−398.500			−0.0529580
$385$		0			0
$386$	3034.95			0.400194
$387$	1758.39	+	1015.21i	0.230967	+	0.133349i
$388$	834.973	−	482.072i	0.109251	−	0.0630760i
$389$	−1789.65	−	3099.77i	−0.233262	−	0.404022i	0.725504	−	0.688218i	$-0.241607\pi$
$389$	−1789.65	−	3099.77i	−0.233262	−	0.404022i	−0.958766	+	0.284196i	$0.908273\pi$
$390$		0			0
$391$	3111.22			0.402407
$392$	1059.55	−	2531.19i	0.136518	−	0.326133i
$393$			5852.13i			0.751147i
$394$	−25.9685	+	44.9787i	−0.00332049	+	0.00575126i
$395$		0			0
$396$	−173.343	−	300.240i	−0.0219971	−	0.0381000i
$397$	−1604.06	−	926.104i	−0.202785	−	0.117078i	0.395169	−	0.918608i	$-0.370686\pi$
$397$	−1604.06	−	926.104i	−0.202785	−	0.117078i	−0.597954	+	0.801531i	$0.704019\pi$
$398$			9666.54i			1.21744i
$399$	−1339.19	−	268.983i	−0.168029	−	0.0337494i
$400$		0			0
$401$	2992.38	−	5182.96i	0.372649	−	0.645448i	−0.617323	−	0.786710i	$-0.711783\pi$
$401$	2992.38	−	5182.96i	0.372649	−	0.645448i	0.989972	+	0.141262i	$0.0451161\pi$
$402$	3157.38	−	1822.92i	0.391731	−	0.226166i
$403$	−322.102	+	185.966i	−0.0398140	+	0.0229866i
$404$	1899.74	−	3290.45i	0.233950	−	0.405213i
$405$		0			0
$406$	2244.74	−	2550.01i	0.274395	−	0.311711i
$407$			1857.98i			0.226282i
$408$	−1020.27	−	589.052i	−0.123801	−	0.0714765i
$409$	4805.85	+	8323.98i	0.581013	+	1.00634i	0.995360	+	0.0962245i	$0.0306767\pi$
$409$	4805.85	+	8323.98i	0.581013	+	1.00634i	−0.414347	+	0.910119i	$0.635990\pi$
$410$		0			0
$411$	1268.70	−	2197.45i	0.152263	−	0.263728i
$412$			198.475i			0.0237334i
$413$	857.863	−	289.419i	0.102210	−	0.0344828i
$414$	2276.77			0.270283
$415$		0			0
$416$	−45.9701	−	79.6225i	−0.00541796	−	0.00938417i
$417$	−27.5724	+	15.9190i	−0.00323796	+	0.00186944i
$418$	−205.480	−	118.634i	−0.0240439	−	0.0138818i
$419$	2060.89			0.240289			0.120145	−	0.992756i	$-0.461664\pi$
$419$	2060.89			0.240289			0.120145	+	0.992756i	$0.461664\pi$
$420$		0			0
$421$	4670.81			0.540716			0.270358	−	0.962760i	$-0.412858\pi$
$421$	4670.81			0.540716			0.270358	+	0.962760i	$0.412858\pi$
$422$	−3256.67	−	1880.24i	−0.375668	−	0.216892i
$423$	−8995.62	+	5193.62i	−1.03400	+	0.596980i
$424$	699.302	+	1211.23i	0.0800970	+	0.138732i
$425$		0			0
$426$	−4710.20			−0.535704
$427$	−9712.68	−	8549.94i	−1.10077	−	0.968994i
$428$			3002.44i			0.339086i
$429$	−22.3969	+	38.7926i	−0.00252059	+	0.00436579i
$430$		0			0
$431$	−5866.94	−	10161.8i	−0.655686	−	1.13568i	−0.981721	−	0.190324i	$-0.939046\pi$
$431$	−5866.94	−	10161.8i	−0.655686	−	1.13568i	0.326035	−	0.945358i	$-0.394287\pi$
$432$	−1911.38	−	1103.53i	−0.212873	−	0.122902i
$433$		−	3982.03i		−	0.441949i	−0.975280	−	0.220975i	$-0.929076\pi$
$433$		−	3982.03i		−	0.441949i	0.975280	−	0.220975i	$-0.0709238\pi$
$434$	−4701.06	−	944.231i	−0.519950	−	0.104434i
$435$		0			0
$436$	820.221	−	1420.66i	0.0900950	−	0.156049i
$437$	1349.43	−	779.096i	0.147717	−	0.0852842i
$438$	4420.67	−	2552.28i	0.482256	−	0.278430i
$439$	3077.50	−	5330.38i	0.334581	−	0.579511i	−0.648823	−	0.760939i	$-0.724739\pi$
$439$	3077.50	−	5330.38i	0.334581	−	0.579511i	0.983404	+	0.181428i	$0.0580719\pi$
$440$		0			0
$441$	4723.18	−	3596.27i	0.510007	−	0.388324i
$442$		−	271.807i		−	0.0292501i
$443$	2681.24	+	1548.02i	0.287561	+	0.166024i	0.636842	−	0.770995i	$-0.280241\pi$
$443$	2681.24	+	1548.02i	0.287561	+	0.166024i	−0.349280	+	0.937018i	$0.613574\pi$
$444$	2310.18	+	4001.35i	0.246929	+	0.427693i
$445$		0			0
$446$	5199.43	−	9005.67i	0.552018	−	0.956123i
$447$		−	11008.6i		−	1.16485i
$448$	233.411	−	1162.09i	0.0246152	−	0.122552i
$449$	7810.84			0.820972			0.410486	−	0.911867i	$-0.365359\pi$
$449$	7810.84			0.820972			0.410486	+	0.911867i	$0.365359\pi$
$450$		0			0
$451$	−47.7260	−	82.6638i	−0.00498299	−	0.00863079i
$452$	−6531.18	+	3770.78i	−0.679647	+	0.392395i
$453$	5823.71	+	3362.32i	0.604022	+	0.348732i
$454$	−7755.45			−0.801721
$455$		0			0
$456$	−590.030			−0.0605936
$457$	5833.50	+	3367.97i	0.597111	+	0.344742i	0.767904	−	0.640565i	$-0.221300\pi$
$457$	5833.50	+	3367.97i	0.597111	+	0.344742i	−0.170793	+	0.985307i	$0.554633\pi$
$458$	−8245.80	+	4760.71i	−0.841268	+	0.485706i
$459$	−3262.43	−	5650.69i	−0.331758	−	0.574622i
$460$		0			0
$461$	17562.3			1.77431			0.887157	−	0.461468i	$-0.152677\pi$
$461$	17562.3			1.77431			0.887157	+	0.461468i	$0.152677\pi$
$462$	−547.182	+	184.604i	−0.0551022	+	0.0185900i
$463$		−	3575.44i		−	0.358887i	−0.983768	−	0.179444i	$-0.942570\pi$
$463$		−	3575.44i		−	0.358887i	0.983768	−	0.179444i	$-0.0574297\pi$
$464$	733.740	−	1270.87i	0.0734117	−	0.127153i
$465$		0			0
$466$	571.790	+	990.370i	0.0568405	+	0.0984506i
$467$	−15006.8	−	8664.19i	−1.48701	−	0.858524i	−0.487117	−	0.873337i	$-0.661952\pi$
$467$	−15006.8	−	8664.19i	−1.48701	−	0.858524i	−0.999890	+	0.0148125i	$0.995285\pi$
$468$		−	198.906i		−	0.0196463i
$469$	3466.55	+	10275.1i	0.341302	+	1.01165i
$470$		0			0
$471$	−3366.25	+	5830.51i	−0.329317	+	0.570394i
$472$	338.687	−	195.541i	0.0330283	−	0.0190689i
$473$	508.775	−	293.741i	0.0494577	−	0.0285544i
$474$	1500.41	−	2598.79i	0.145393	−	0.251828i
$475$		0			0
$476$	2315.36	−	2630.24i	0.222950	−	0.253270i
$477$			3025.79i			0.290443i
$478$	8387.01	+	4842.24i	0.802537	+	0.463345i
$479$	2625.98	+	4548.33i	0.250488	+	0.433859i	0.963660	−	0.267130i	$-0.0860755\pi$
$479$	2625.98	+	4548.33i	0.250488	+	0.433859i	−0.713172	+	0.700989i	$0.752742\pi$
$480$		0			0
$481$	−532.995	+	923.174i	−0.0505249	+	0.0875116i
$482$		−	6351.95i		−	0.600256i
$483$	746.819	−	3718.20i	0.0703549	−	0.350278i
$484$	5223.69			0.490579
$485$		0			0
$486$	−3842.26	−	6655.00i	−0.358619	−	0.621146i
$487$	757.266	−	437.208i	0.0704620	−	0.0406813i	−0.464355	−	0.885649i	$-0.653714\pi$
$487$	757.266	−	437.208i	0.0704620	−	0.0406813i	0.534817	+	0.844968i	$0.320381\pi$
$488$	−4840.61	−	2794.73i	−0.449025	−	0.259245i
$489$	7477.88			0.691536
$490$		0			0
$491$	−15821.1			−1.45417			−0.727085	−	0.686547i	$-0.759126\pi$
$491$	−15821.1			−1.45417			−0.727085	+	0.686547i	$0.759126\pi$
$492$	−205.565	−	118.683i	−0.0188366	−	0.0108753i
$493$	3757.14	−	2169.19i	0.343232	−	0.198165i
$494$	−68.0645	−	117.891i	−0.00619913	−	0.0107372i
$495$		0			0
$496$	−2071.22			−0.187501
$497$	2758.87	−	13735.6i	0.248999	−	1.23969i
$498$		−	1679.95i		−	0.151165i
$499$	5881.17	−	10186.5i	0.527610	−	0.913847i	−0.471872	−	0.881667i	$-0.656422\pi$
$499$	5881.17	−	10186.5i	0.527610	−	0.913847i	0.999482	−	0.0321800i	$-0.0102450\pi$
$500$		0			0
$501$	−4427.16	−	7668.06i	−0.394792	−	0.683800i
$502$	−11143.2	−	6433.53i	−0.990728	−	0.571997i
$503$		−	14178.9i		−	1.25687i	−0.777863	−	0.628434i	$-0.783696\pi$
$503$		−	14178.9i		−	1.25687i	0.777863	−	0.628434i	$-0.216304\pi$
$504$	1694.37	−	1924.79i	0.149748	−	0.170113i
$505$		0			0
$506$	329.382	−	570.506i	0.0289383	−	0.0501227i
$507$	5901.26	−	3407.09i	0.516931	−	0.298450i
$508$	8092.94	−	4672.46i	0.706823	−	0.408084i
$509$	3701.46	−	6411.11i	0.322327	−	0.558286i	−0.658641	−	0.752457i	$-0.728868\pi$
$509$	3701.46	−	6411.11i	0.322327	−	0.558286i	0.980968	+	0.194171i	$0.0622017\pi$
$510$		0			0
$511$	4853.54	+	14386.3i	0.420172	+	1.24542i
$512$		−	512.000i		−	0.0441942i
$513$	−2830.03	−	1633.92i	−0.243565	−	0.140623i
$514$	7061.96	+	12231.7i	0.606011	+	1.04964i
$515$		0			0
$516$	730.466	−	1265.20i	0.0623197	−	0.107941i
$517$			3005.46i			0.255667i
$518$	−13021.7	+	4393.16i	−1.10452	+	0.372634i
$519$	5457.62			0.461585
$520$		0			0
$521$	−712.532	−	1234.14i	−0.0599167	−	0.103779i	0.834511	−	0.550991i	$-0.185750\pi$
$521$	−712.532	−	1234.14i	−0.0599167	−	0.103779i	−0.894428	+	0.447212i	$0.852417\pi$
$522$	2749.45	−	1587.40i	0.230537	−	0.133101i
$523$	19274.1	+	11127.9i	1.61147	+	0.930380i	0.989031	+	0.147708i	$0.0471896\pi$
$523$	19274.1	+	11127.9i	1.61147	+	0.930380i	0.622435	+	0.782672i	$0.286144\pi$
$524$	−7518.91			−0.626842
$525$		0			0
$526$	−9309.68			−0.771714
$527$	−5302.89	−	3061.63i	−0.438326	−	0.253067i
$528$	−216.030	+	124.725i	−0.0178058	+	0.0102802i
$529$	−3920.38	−	6790.29i	−0.322214	−	0.558091i
$530$		0			0
$531$	846.081			0.0691465
$532$	345.594	−	1720.62i	0.0281643	−	0.140222i
$533$		−	54.7642i		−	0.00445047i
$534$	456.377	−	790.468i	0.0369838	−	0.0640579i
$535$		0			0
$536$	2342.12	+	4056.66i	0.188739	+	0.326905i
$537$	−5794.94	−	3345.71i	−0.465680	−	0.268860i
$538$			10311.9i			0.826356i
$539$	−217.837	−	1703.79i	−0.0174080	−	0.136155i
$540$		0			0
$541$	2661.08	−	4609.13i	0.211477	−	0.366288i	−0.740700	−	0.671836i	$-0.765506\pi$
$541$	2661.08	−	4609.13i	0.211477	−	0.366288i	0.952177	+	0.305547i	$0.0988394\pi$
$542$	−8709.15	+	5028.23i	−0.690203	+	0.398489i
$543$	6481.32	−	3741.99i	0.512228	−	0.295735i
$544$	756.824	−	1310.86i	0.0596481	−	0.103314i
$545$		0			0
$546$	−324.835	−	65.2447i	−0.0254609	−	0.00511395i
$547$		−	10627.6i		−	0.830718i	−0.909658	−	0.415359i	$-0.863656\pi$
$547$		−	10627.6i		−	0.830718i	0.909658	−	0.415359i	$-0.136344\pi$
$548$	2823.32	+	1630.05i	0.220085	+	0.127066i
$549$	−6046.21	−	10472.3i	−0.470029	−	0.814114i
$550$		0			0
$551$	1086.39	−	1881.69i	0.0839963	−	0.145486i
$552$		−	1638.19i		−	0.126315i
$553$	6699.65	+	5897.61i	0.515186	+	0.453511i
$554$	230.682			0.0176908
$555$		0			0
$556$	−20.4529	−	35.4255i	−0.00156007	−	0.00270212i
$557$	17369.4	−	10028.2i	1.32130	−	0.762853i	0.337365	−	0.941374i	$-0.390464\pi$
$557$	17369.4	−	10028.2i	1.32130	−	0.762853i	0.983936	+	0.178521i	$0.0571311\pi$
$558$	−3880.62	−	2240.48i	−0.294408	−	0.169977i
$559$	337.060			0.0255029
$560$		0			0
$561$	−737.458			−0.0555000
$562$	−1692.76	−	977.317i	−0.127055	−	0.0733552i
$563$	1049.30	−	605.816i	0.0785487	−	0.0453501i	−0.460211	−	0.887809i	$-0.652226\pi$
$563$	1049.30	−	605.816i	0.0785487	−	0.0453501i	0.538760	+	0.842459i	$0.318893\pi$
$564$	3736.93	+	6472.56i	0.278995	+	0.483234i
$565$		0			0
$566$	−8434.29			−0.626360
$567$	664.213	−	224.087i	0.0491963	−	0.0165975i
$568$		−	6051.74i		−	0.447052i
$569$	5391.08	−	9337.63i	0.397199	−	0.687968i	−0.596181	−	0.802850i	$-0.703316\pi$
$569$	5391.08	−	9337.63i	0.397199	−	0.687968i	0.993379	+	0.114882i	$0.0366491\pi$
$570$		0			0
$571$	2071.37	+	3587.72i	0.151811	+	0.262944i	0.931893	−	0.362733i	$-0.118156\pi$
$571$	2071.37	+	3587.72i	0.151811	+	0.262944i	−0.780082	+	0.625677i	$0.784823\pi$
$572$	−49.8414	−	28.7759i	−0.00364331	−	0.00210347i
$573$		−	1583.31i		−	0.115434i
$574$	466.503	−	529.945i	0.0339224	−	0.0385357i
$575$		0			0
$576$	553.839	−	959.277i	0.0400636	−	0.0693922i
$577$	−9881.54	+	5705.11i	−0.712953	+	0.411624i	−0.812153	−	0.583444i	$-0.801705\pi$
$577$	−9881.54	+	5705.11i	−0.712953	+	0.411624i	0.0992005	+	0.995067i	$0.468371\pi$
$578$	−4634.22	+	2675.57i	−0.333491	+	0.192541i
$579$	2362.17	−	4091.39i	0.169548	−	0.293666i
$580$		0			0
$581$	4898.98	+	983.983i	0.349817	+	0.0702625i
$582$		−	1500.83i		−	0.106892i
$583$	758.193	+	437.743i	0.0538613	+	0.0310968i
$584$	3279.21	+	5679.76i	0.232354	+	0.402449i
$585$		0			0
$586$	4064.73	−	7040.32i	0.286540	−	0.496302i
$587$			3848.96i			0.270637i	0.990802	+	0.135318i	$0.0432057\pi$
$587$			3848.96i			0.270637i	−0.990802	+	0.135318i	$0.956794\pi$
$588$	−2587.60	−	3398.44i	−0.181481	−	0.238349i
$589$	−3066.71			−0.214536
$590$		0			0
$591$	40.4236	+	70.0157i	0.00281354	+	0.00487320i
$592$	−5141.00	+	2968.16i	−0.356916	+	0.206065i
$593$	7212.04	+	4163.88i	0.499432	+	0.288347i	0.728479	−	0.685068i	$-0.240228\pi$
$593$	7212.04	+	4163.88i	0.499432	+	0.288347i	−0.229047	+	0.973415i	$0.573561\pi$
$594$	−1381.56			−0.0954311
$595$		0			0
$596$	14144.0			0.972084
$597$	13031.4	+	7523.67i	0.893365	+	0.515785i
$598$	327.319	−	188.978i	0.0223831	−	0.0129229i
$599$	−9899.97	−	17147.3i	−0.675295	−	1.16965i	−0.976382	−	0.216049i	$-0.930683\pi$
$599$	−9899.97	−	17147.3i	−0.675295	−	1.16965i	0.301087	−	0.953597i	$-0.402650\pi$
$600$		0			0
$601$	19424.3			1.31836			0.659180	−	0.751985i	$-0.270904\pi$
$601$	19424.3			1.31836			0.659180	+	0.751985i	$0.270904\pi$
$602$	3261.68	+	2871.21i	0.220824	+	0.194388i
$603$			10134.0i			0.684393i
$604$	−4319.97	+	7482.40i	−0.291022	+	0.504064i
$605$		0			0
$606$	−2957.22	−	5122.05i	−0.198232	−	0.343348i
$607$	−348.327	−	201.106i	−0.0232918	−	0.0134475i	0.488309	−	0.872671i	$-0.337614\pi$
$607$	−348.327	−	201.106i	−0.0232918	−	0.0134475i	−0.511601	+	0.859223i	$0.670947\pi$
$608$		−	758.081i		−	0.0505662i
$609$	−1690.52	−	5010.84i	−0.112485	−	0.333414i
$610$		0			0
$611$	−862.169	+	1493.32i	−0.0570861	+	0.0988761i
$612$	2835.95	−	1637.34i	0.187315	−	0.108146i
$613$	10750.4	−	6206.75i	0.708327	−	0.408953i	−0.102114	−	0.994773i	$-0.532561\pi$
$613$	10750.4	−	6206.75i	0.708327	−	0.408953i	0.810441	+	0.585820i	$0.199227\pi$
$614$	−1650.69	+	2859.08i	−0.108496	+	0.187920i
$615$		0			0
$616$	−237.183	−	703.029i	−0.0155136	−	0.0459835i
$617$			12205.8i			0.796412i	0.917296	+	0.398206i	$0.130367\pi$
$617$			12205.8i			0.796412i	−0.917296	+	0.398206i	$0.869633\pi$
$618$	267.562	+	154.477i	0.0174157	+	0.0100550i
$619$	8500.05	+	14722.5i	0.551932	+	0.955974i	0.998135	+	0.0610421i	$0.0194424\pi$
$619$	8500.05	+	14722.5i	0.551932	+	0.955974i	−0.446204	+	0.894931i	$0.647224\pi$
$620$		0			0
$621$	4536.50	−	7857.45i	0.293146	−	0.507743i
$622$		−	8572.80i		−	0.552633i
$623$	2037.82	+	1793.86i	0.131049	+	0.115360i
$624$	−143.118			−0.00918157
$625$		0			0
$626$	7112.59	+	12319.4i	0.454115	+	0.786551i
$627$	−319.859	+	184.671i	−0.0203731	+	0.0117624i
$628$	−7491.14	−	4325.01i	−0.476002	−	0.274820i
$629$	−17549.8			−1.11249
$630$		0			0
$631$	−9451.75			−0.596305			−0.298152	−	0.954518i	$-0.596370\pi$
$631$	−9451.75			−0.596305			−0.298152	+	0.954518i	$0.596370\pi$
$632$	3338.97	+	1927.76i	0.210154	+	0.121332i
$633$	−5069.46	+	2926.85i	−0.318314	+	0.183779i
$634$	9127.60	+	15809.5i	0.571772	+	0.990337i
$635$		0			0
$636$	2177.13			0.135737
$637$	380.527	−	909.053i	0.0236688	−	0.0565432i
$638$		−	918.599i		−	0.0570026i
$639$	6546.27	−	11338.5i	0.405268	−	0.701945i
$640$		0			0
$641$	−8356.38	−	14473.7i	−0.514910	−	0.891850i	−0.999850	−	0.0173025i	$-0.994492\pi$
$641$	−8356.38	−	14473.7i	−0.514910	−	0.891850i	0.484941	−	0.874547i	$-0.338841\pi$
$642$	4047.57	+	2336.86i	0.248824	+	0.143658i
$643$		−	4835.69i		−	0.296580i	−0.988944	−	0.148290i	$-0.952623\pi$
$643$		−	4835.69i		−	0.296580i	0.988944	−	0.148290i	$-0.0473769\pi$
$644$	4777.21	+	959.525i	0.292311	+	0.0587121i
$645$		0			0
$646$	1120.57	−	1940.89i	0.0682483	−	0.118209i
$647$	5994.48	−	3460.92i	0.364246	−	0.210298i	−0.306696	−	0.951808i	$-0.599223\pi$
$647$	5994.48	−	3460.92i	0.364246	−	0.210298i	0.670942	+	0.741510i	$0.265890\pi$
$648$	262.234	−	151.401i	0.0158974	−	0.00917836i
$649$	122.403	−	212.008i	0.00740330	−	0.0128229i
$650$		0			0
$651$	−4931.84	+	5602.55i	−0.296919	+	0.337298i
$652$			9607.71i			0.577096i
$653$	−21626.6	−	12486.1i	−1.29604	−	0.748270i	−0.316323	−	0.948651i	$-0.602448\pi$
$653$	−21626.6	−	12486.1i	−1.29604	−	0.748270i	−0.979718	+	0.200382i	$0.935782\pi$
$654$	−1276.79	−	2211.46i	−0.0763401	−	0.132225i
$655$		0			0
$656$	152.486	−	264.114i	0.00907560	−	0.0157194i
$657$			14188.7i			0.842548i
$658$	−21063.8	+	7106.34i	−1.24795	+	0.421025i
$659$	−22380.5			−1.32294			−0.661471	−	0.749971i	$-0.730068\pi$
$659$	−22380.5			−1.32294			−0.661471	+	0.749971i	$0.730068\pi$
$660$		0			0
$661$	11571.4	+	20042.3i	0.680903	+	1.17936i	0.974705	+	0.223493i	$0.0717460\pi$
$661$	11571.4	+	20042.3i	0.680903	+	1.17936i	−0.293802	+	0.955866i	$0.594921\pi$
$662$	−15445.2	+	8917.30i	−0.906791	+	0.523536i
$663$	−366.420	−	211.553i	−0.0214639	−	0.0123922i
$664$	2158.42			0.126149
$665$		0			0
$666$	−12842.8			−0.747222
$667$	5224.42	+	3016.32i	0.303284	+	0.175101i
$668$	9852.06	−	5688.09i	0.570640	−	0.329459i
$669$	−8093.65	−	14018.6i	−0.467741	−	0.810150i
$670$		0			0
$671$	−3498.83			−0.201298
$672$	−1384.93	−	1219.14i	−0.0795013	−	0.0699839i
$673$			17263.9i			0.988820i	0.869229	+	0.494410i	$0.164616\pi$
$673$			17263.9i			0.988820i	−0.869229	+	0.494410i	$0.835384\pi$
$674$	−9427.08	+	16328.2i	−0.538750	+	0.933143i
$675$		0			0
$676$	4377.49	+	7582.04i	0.249061	+	0.431386i
$677$	2390.54	+	1380.18i	0.135711	+	0.0783525i	0.566318	−	0.824187i	$-0.308367\pi$
$677$	2390.54	+	1380.18i	0.135711	+	0.0783525i	−0.430608	+	0.902539i	$0.641701\pi$
$678$			11739.5i			0.664974i
$679$	4376.64	+	879.069i	0.247364	+	0.0496842i
$680$		0			0
$681$	−6036.22	+	10455.0i	−0.339660	+	0.588309i
$682$	−1122.82	+	648.263i	−0.0630428	+	0.0363978i
$683$	−19169.9	+	11067.8i	−1.07396	+	0.620053i	−0.929261	−	0.369423i	$-0.879555\pi$
$683$	−19169.9	+	11067.8i	−1.07396	+	0.620053i	−0.144701	+	0.989475i	$0.546222\pi$
$684$	820.029	−	1420.33i	0.0458400	−	0.0793973i
$685$		0			0
$686$	11426.0	−	5555.30i	0.635927	−	0.309187i
$687$			14821.4i			0.823106i
$688$	1625.56	+	938.515i	0.0900781	+	0.0520066i
$689$	251.148	+	435.002i	0.0138868	+	0.0240526i
$690$		0			0
$691$	−13507.9	+	23396.3i	−0.743653	+	1.28804i	0.207169	+	0.978305i	$0.433575\pi$
$691$	−13507.9	+	23396.3i	−0.743653	+	1.28804i	−0.950822	+	0.309739i	$0.899758\pi$
$692$			7012.04i			0.385199i
$693$	316.096	−	1573.75i	0.0173268	−	0.0862654i
$694$	−889.129			−0.0486324
$695$		0			0
$696$	−1142.17	−	1978.30i	−0.0622038	−	0.107740i
$697$	780.812	−	450.802i	0.0424324	−	0.0244983i
$698$	−14580.4	−	8417.98i	−0.790652	−	0.456483i
$699$	1780.14			0.0963251
$700$		0			0
$701$	−19107.2			−1.02949			−0.514743	−	0.857345i	$-0.672112\pi$
$701$	−19107.2			−1.02949			−0.514743	+	0.857345i	$0.672112\pi$
$702$	−686.454	−	396.325i	−0.0369068	−	0.0213081i
$703$	−7611.91	+	4394.74i	−0.408376	+	0.235776i
$704$	−160.248	−	277.559i	−0.00857897	−	0.0148592i
$705$		0			0
$706$	−22291.9			−1.18834
$707$	16668.8	−	5623.59i	0.886697	−	0.299147i
$708$		−	608.775i		−	0.0323152i
$709$	−6276.78	+	10871.7i	−0.332481	+	0.575875i	−0.982998	−	0.183618i	$-0.941219\pi$
$709$	−6276.78	+	10871.7i	−0.332481	+	0.575875i	0.650516	+	0.759492i	$0.274553\pi$
$710$		0			0
$711$	4170.57	+	7223.65i	0.219984	+	0.381024i
$712$	1015.61	+	586.361i	0.0534572	+	0.0308635i
$713$		−	8514.57i		−	0.447227i
$714$	−1743.70	−	5168.48i	−0.0913957	−	0.270904i
$715$		0			0
$716$	4298.63	−	7445.44i	0.224368	−	0.388616i
$717$	13055.6	−	7537.63i	0.680012	−	0.392605i
$718$	17110.3	−	9878.64i	0.889346	−	0.513464i
$719$	−11122.9	+	19265.4i	−0.576933	+	0.999276i	0.418896	+	0.908034i	$0.362417\pi$
$719$	−11122.9	+	19265.4i	−0.576933	+	0.999276i	−0.995829	+	0.0912423i	$0.970916\pi$
$720$		0			0
$721$	−607.196	+	689.771i	−0.0313636	+	0.0356289i
$722$			12595.6i			0.649250i
$723$	−8563.01	−	4943.86i	−0.440473	−	0.254307i
$724$	4807.78	+	8327.31i	0.246795	+	0.427461i
$725$		0			0
$726$	4065.71	−	7042.01i	0.207841	−	0.359991i
$727$			34604.1i			1.76533i	0.470004	+	0.882665i	$0.344253\pi$
$727$			34604.1i			1.76533i	−0.470004	+	0.882665i	$0.655747\pi$
$728$	83.8275	−	417.354i	0.00426766	−	0.0212475i
$729$	−10940.1			−0.555815
$730$		0			0
$731$	2774.57	+	4805.70i	0.140385	+	0.243154i
$732$	−7535.09	+	4350.39i	−0.380471	+	0.219665i
$733$	11728.4	+	6771.39i	0.590993	+	0.341210i	0.765490	−	0.643448i	$-0.222497\pi$
$733$	11728.4	+	6771.39i	0.590993	+	0.341210i	−0.174497	+	0.984658i	$0.555830\pi$
$734$	−16051.0			−0.807157
$735$		0			0
$736$	2104.77			0.105412
$737$	2539.35	+	1466.10i	0.126918	+	0.0732759i
$738$	571.393	−	329.894i	0.0285004	−	0.0164547i
$739$	8669.99	+	15016.9i	0.431571	+	0.747503i	0.997009	−	0.0772883i	$-0.0246262\pi$
$739$	8669.99	+	15016.9i	0.431571	+	0.747503i	−0.565438	+	0.824791i	$0.691293\pi$
$740$		0			0
$741$	−211.904			−0.0105054
$742$	−1275.19	+	6348.83i	−0.0630914	+	0.314115i
$743$		−	14341.8i		−	0.708142i	−0.935219	−	0.354071i	$-0.884797\pi$
$743$		−	14341.8i		−	0.708142i	0.935219	−	0.354071i	$-0.115203\pi$
$744$	−1612.08	+	2792.20i	−0.0794376	+	0.137590i
$745$		0			0
$746$	12083.9	+	20930.0i	0.593062	+	1.02721i
$747$	4044.00	+	2334.80i	0.198075	+	0.114359i
$748$		−	947.499i		−	0.0463155i
$749$	−9185.41	+	10434.6i	−0.448101	+	0.509040i
$750$		0			0
$751$	3005.17	−	5205.12i	0.146019	−	0.252913i	−0.783734	−	0.621097i	$-0.786687\pi$
$751$	3005.17	−	5205.12i	0.146019	−	0.252913i	0.929753	+	0.368185i	$0.120021\pi$
$752$	−8316.06	+	4801.28i	−0.403265	+	0.232825i
$753$	−17346.0	+	10014.7i	−0.839472	+	0.484669i
$754$	263.516	−	456.424i	0.0127277	−	0.0220451i
$755$		0			0
$756$	−3266.67	−	9682.67i	−0.157153	−	0.465814i
$757$			1057.57i			0.0507767i	0.999678	+	0.0253884i	$0.00808224\pi$
$757$			1057.57i			0.0507767i	−0.999678	+	0.0253884i	$0.991918\pi$
$758$	−5255.43	−	3034.22i	−0.251828	−	0.145393i
$759$	−512.729	−	888.073i	−0.0245203	−	0.0424704i
$760$		0			0
$761$	−2947.79	+	5105.72i	−0.140417	+	0.243209i	−0.927654	−	0.373442i	$-0.878178\pi$
$761$	−2947.79	+	5105.72i	−0.140417	+	0.243209i	0.787237	+	0.616651i	$0.211511\pi$
$762$		−	14546.7i		−	0.691563i
$763$	7196.81	−	2428.01i	0.341471	−	0.115203i
$764$	2034.27			0.0963315
$765$		0			0
$766$	−7953.04	−	13775.1i	−0.375137	−	0.649757i
$767$	121.637	−	70.2269i	0.00572626	−	0.00330606i
$768$	−690.223	−	398.500i	−0.0324300	−	0.0187235i
$769$	25098.6			1.17696			0.588478	−	0.808513i	$-0.299727\pi$
$769$	25098.6			1.17696			0.588478	+	0.808513i	$0.299727\pi$
$770$		0			0
$771$	21985.9			1.02698
$772$	5256.69	+	3034.95i	0.245068	+	0.141490i
$773$	32283.7	−	18639.0i	1.50215	−	0.867268i	0.502156	−	0.864777i	$-0.332540\pi$
$773$	32283.7	−	18639.0i	1.50215	−	0.867268i	0.999997	−	0.00249151i	$-0.000793072\pi$
$774$	2030.42	+	3516.78i	0.0942917	+	0.163318i
$775$		0			0
$776$	1928.29			0.0892030
$777$	−4212.67	+	20973.7i	−0.194503	+	0.968374i
$778$		−	7158.61i		−	0.329883i
$779$	225.775	−	391.054i	0.0103841	−	0.0179858i
$780$		0			0
$781$	−1894.11	−	3280.69i	−0.0867816	−	0.150310i
$782$	5388.79	+	3111.22i	0.246423	+	0.142272i
$783$		−	12651.7i		−	0.577437i
$784$	4366.37	−	3324.60i	0.198905	−	0.151448i
$785$		0			0
$786$	−5852.13	+	10136.2i	−0.265571	+	0.459982i
$787$	11670.4	−	6737.93i	0.528597	−	0.305186i	−0.211848	−	0.977303i	$-0.567948\pi$
$787$	11670.4	−	6737.93i	0.528597	−	0.305186i	0.740445	+	0.672117i	$0.234615\pi$
$788$	−89.9574	+	51.9369i	−0.00406675	+	0.00234794i
$789$	−7245.92	+	12550.3i	−0.326947	+	0.566289i
$790$		0			0
$791$	−34234.2	−	6876.09i	−1.53884	−	0.309084i
$792$		−	693.374i		−	0.0311085i
$793$	−1738.46	−	1003.70i	−0.0778495	−	0.0449464i
$794$	−1852.21	−	3208.12i	−0.0827864	−	0.143390i
$795$		0			0
$796$	−9666.54	+	16742.9i	−0.430429	+	0.745525i
$797$		−	10414.0i		−	0.462839i	−0.972854	−	0.231420i	$-0.925663\pi$
$797$		−	10414.0i		−	0.462839i	0.972854	−	0.231420i	$-0.0743371\pi$
$798$	−2050.57	−	1805.08i	−0.0909640	−	0.0800743i
$799$	−28388.5			−1.25696
$800$		0			0
$801$	1268.55	+	2197.20i	0.0559577	+	0.0969216i
$802$	10365.9	−	5984.76i	0.456400	−	0.263503i
$803$	3555.36	+	2052.69i	0.156247	+	0.0902090i
$804$	7291.67			0.319847
$805$		0			0
$806$	−743.862			−0.0325080
$807$	13901.4	+	8026.00i	0.606387	+	0.350098i
$808$	6580.90	−	3799.49i	0.286529	−	0.165428i
$809$	10167.0	+	17609.7i	0.441843	+	0.765295i	0.997826	−	0.0658988i	$-0.0209914\pi$
$809$	10167.0	+	17609.7i	0.441843	+	0.765295i	−0.555983	+	0.831194i	$0.687658\pi$
$810$		0			0
$811$	16769.3			0.726081			0.363040	−	0.931773i	$-0.381739\pi$
$811$	16769.3			0.726081			0.363040	+	0.931773i	$0.381739\pi$
$812$	6438.01	−	2172.01i	0.278239	−	0.0938701i
$813$			15654.3i			0.675302i
$814$	−1857.98	+	3218.12i	−0.0800027	+	0.138569i
$815$		0			0
$816$	−1178.10	−	2040.54i	−0.0505415	−	0.0875405i
$817$	2406.84	+	1389.59i	0.103066	+	0.0595050i
$818$			19223.4i			0.821676i
$819$	608.517	−	691.271i	0.0259625	−	0.0294933i
$820$		0			0
$821$	3510.97	−	6081.17i	0.149249	−	0.258507i	−0.781701	−	0.623653i	$-0.785648\pi$
$821$	3510.97	−	6081.17i	0.149249	−	0.258507i	0.930950	+	0.365146i	$0.118981\pi$
$822$	4394.90	−	2537.40i	0.186484	−	0.107667i
$823$	−727.886	+	420.245i	−0.0308293	+	0.0177993i	−0.515335	−	0.856989i	$-0.672333\pi$
$823$	−727.886	+	420.245i	−0.0308293	+	0.0177993i	0.484506	+	0.874788i	$0.338999\pi$
$824$	−198.475	+	343.769i	−0.00839102	+	0.0145337i
$825$		0			0
$826$	1775.28	+	356.574i	0.0747820	+	0.0150203i
$827$		−	30133.0i		−	1.26702i	−0.773735	−	0.633510i	$-0.781614\pi$
$827$		−	30133.0i		−	1.26702i	0.773735	−	0.633510i	$-0.218386\pi$
$828$	3943.48	+	2276.77i	0.165514	+	0.0955594i
$829$	−23055.0	−	39932.5i	−0.965903	−	1.67299i	−0.707168	−	0.707045i	$-0.750028\pi$
$829$	−23055.0	−	39932.5i	−0.965903	−	1.67299i	−0.258735	−	0.965948i	$-0.583306\pi$
$830$		0			0
$831$	179.544	−	310.980i	0.00749497	−	0.0129817i
$832$		−	183.880i		−	0.00766215i
$833$	16093.4	−	2057.61i	0.669392	−	0.0855845i
$834$	−63.6758			−0.00264378
$835$		0			0
$836$	−237.268	−	410.960i	−0.00981590	−	0.0170016i
$837$	−15464.4	+	8928.38i	−0.638624	+	0.368710i
$838$	3569.57	+	2060.89i	0.147147	+	0.0849551i
$839$	34470.7			1.41843			0.709214	−	0.704993i	$-0.249050\pi$
$839$	34470.7			1.41843			0.709214	+	0.704993i	$0.249050\pi$
$840$		0			0
$841$	−15976.9			−0.655087
$842$	8090.09	+	4670.81i	0.331120	+	0.191172i
$843$	−2635.03	+	1521.33i	−0.107657	+	0.0621560i
$844$	−3760.47	−	6513.33i	−0.153366	−	0.265638i
$845$		0			0
$846$	−20774.5			−0.844258
$847$	18154.2	+	15980.9i	0.736465	+	0.648300i
$848$			2797.21i			0.113274i
$849$	−6564.58	+	11370.2i	−0.265366	+	0.459628i
$850$		0			0
$851$	−12201.8	−	21134.1i	−0.491506	−	0.851313i
$852$	−8158.30	−	4710.20i	−0.328050	−	0.189400i
$853$		−	28159.1i		−	1.13031i	−0.824986	−	0.565153i	$-0.808817\pi$
$853$		−	28159.1i		−	1.13031i	0.824986	−	0.565153i	$-0.191183\pi$
$854$	−8272.92	−	24521.6i	−0.331491	−	0.982567i
$855$		0			0
$856$	−3002.44	+	5200.39i	−0.119885	+	0.207647i
$857$	−1141.95	+	659.305i	−0.0455172	+	0.0262794i	−0.522586	−	0.852587i	$-0.675033\pi$
$857$	−1141.95	+	659.305i	−0.0455172	+	0.0262794i	0.477069	+	0.878866i	$0.341699\pi$
$858$	−77.5851	+	44.7938i	−0.00308708	+	0.00178233i
$859$	2269.32	−	3930.57i	0.0901374	−	0.156123i	−0.817431	−	0.576026i	$-0.804603\pi$
$859$	2269.32	−	3930.57i	0.0901374	−	0.156123i	0.907569	+	0.419903i	$0.137936\pi$
$860$		0			0
$861$	−351.325	−	1041.36i	−0.0139061	−	0.0412187i
$862$		−	23467.8i		−	0.927280i
$863$	−24902.0	−	14377.2i	−0.982240	−	0.567096i	−0.0792943	−	0.996851i	$-0.525267\pi$
$863$	−24902.0	−	14377.2i	−0.982240	−	0.567096i	−0.902946	+	0.429755i	$0.858600\pi$
$864$	−2207.07	−	3822.75i	−0.0869050	−	0.150524i
$865$		0			0
$866$	3982.03	−	6897.08i	0.156253	−	0.270638i
$867$			8329.80i			0.326292i
$868$	−7198.25	−	6336.52i	−0.281480	−	0.247783i
$869$	2413.44			0.0942121
$870$		0			0
$871$	841.150	+	1456.92i	0.0327225	+	0.0566770i
$872$	2841.33	−	1640.44i	0.110343	−	0.0637068i
$873$	3612.82	+	2085.86i	0.140063	+	0.0808657i
$874$	3116.38			0.120610
$875$		0			0
$876$	10209.1			0.393760
$877$	−37453.6	−	21623.9i	−1.44210	−	0.832595i	−0.444107	−	0.895974i	$-0.646479\pi$
$877$	−37453.6	−	21623.9i	−1.44210	−	0.832595i	−0.997990	+	0.0633789i	$0.979812\pi$
$878$	10660.8	−	6155.00i	0.409776	−	0.236584i
$879$	−6327.33	−	10959.3i	−0.242794	−	0.420531i
$880$		0			0
$881$	−43971.7			−1.68155			−0.840775	−	0.541385i	$-0.817900\pi$
$881$	−43971.7			−1.68155			−0.840775	+	0.541385i	$0.817900\pi$
$882$	11777.1	−	1505.74i	0.449608	−	0.0574842i
$883$			2936.92i			0.111931i	0.998433	+	0.0559656i	$0.0178237\pi$
$883$			2936.92i			0.111931i	−0.998433	+	0.0559656i	$0.982176\pi$
$884$	271.807	−	470.783i	0.0103415	−	0.0179119i
$885$		0			0
$886$	3096.03	+	5362.48i	0.117396	+	0.203337i
$887$	−3721.73	−	2148.74i	−0.140883	−	0.0813390i	0.427902	−	0.903825i	$-0.359253\pi$
$887$	−3721.73	−	2148.74i	−0.140883	−	0.0813390i	−0.568785	+	0.822486i	$0.692586\pi$
$888$			9240.72i			0.349210i
$889$	42420.4	+	8520.33i	1.60037	+	0.321443i
$890$		0			0
$891$	94.7724	−	164.151i	0.00356341	−	0.00617200i
$892$	18011.3	−	10398.9i	0.676081	−	0.390336i
$893$	−12313.0	+	7108.90i	−0.461409	+	0.266394i
$894$	11008.6	−	19067.4i	0.411837	−	0.713323i
$895$		0			0
$896$	1566.37	−	1779.38i	0.0584025	−	0.0663449i
$897$		−	588.342i		−	0.0218998i
$898$	13528.8	+	7810.84i	0.502741	+	0.290257i
$899$	−5936.48	−	10282.3i	−0.220237	−	0.381461i
$900$		0			0
$901$	−4134.76	+	7161.61i	−0.152884	+	0.264803i
$902$		−	190.904i		−	0.00704701i
$903$	6409.28	−	2162.32i	0.236199	−	0.0796870i
$904$	−15083.1			−0.554930
$905$		0			0
$906$	6724.64	+	11647.4i	0.246591	+	0.427108i
$907$	6705.54	−	3871.45i	0.245484	−	0.141730i	−0.372211	−	0.928148i	$-0.621400\pi$
$907$	6705.54	−	3871.45i	0.245484	−	0.141730i	0.617695	+	0.786418i	$0.288067\pi$
$908$	−13432.8	−	7755.45i	−0.490952	−	0.283451i
$909$	16439.9			0.599864
$910$		0			0
$911$	27691.3			1.00709			0.503543	−	0.863970i	$-0.332030\pi$
$911$	27691.3			1.00709			0.503543	+	0.863970i	$0.332030\pi$
$912$	−1021.96	−	590.030i	−0.0371059	−	0.0214231i
$913$	1170.09	−	675.555i	0.0424146	−	0.0244881i
$914$	6735.95	+	11667.0i	0.243770	+	0.422221i
$915$		0			0
$916$	−19042.9			−0.686893
$917$	−26130.9	−	23002.7i	−0.941024	−	0.828371i
$918$		−	13049.7i		−	0.469177i
$919$	−2233.76	+	3868.99i	−0.0801796	+	0.138875i	−0.903327	−	0.428953i	$-0.858883\pi$
$919$	−2233.76	+	3868.99i	−0.0801796	+	0.138875i	0.823147	+	0.567828i	$0.192216\pi$
$920$		0			0
$921$	2569.53	+	4450.56i	0.0919315	+	0.159230i
$922$	30418.8	+	17562.3i	1.08654	+	0.627315i
$923$		−	2173.43i		−	0.0775074i
$924$	−1132.35	−	227.438i	−0.0403156	−	0.00809759i
$925$		0			0
$926$	3575.44	−	6192.84i	0.126886	−	0.219773i
$927$	−743.721	+	429.387i	−0.0263506	+	0.0152135i
$928$	2541.75	−	1467.48i	0.0899106	−	0.0519099i
$929$	−4526.82	+	7840.67i	−0.159871	+	0.276904i	−0.934822	−	0.355117i	$-0.884441\pi$
$929$	−4526.82	+	7840.67i	−0.159871	+	0.276904i	0.774951	+	0.632021i	$0.217774\pi$
$930$		0			0
$931$	6464.97	−	4922.48i	0.227584	−	0.173284i
$932$			2287.16i			0.0803846i
$933$	−11556.9	−	6672.38i	−0.405526	−	0.234131i
$934$	−17328.4	−	30013.6i	−0.607068	−	1.05147i
$935$		0			0
$936$	198.906	−	344.516i	0.00694601	−	0.0120308i
$937$			4004.41i			0.139614i	0.997561	+	0.0698071i	$0.0222384\pi$
$937$			4004.41i			0.139614i	−0.997561	+	0.0698071i	$0.977762\pi$
$938$	−4270.90	+	21263.6i	−0.148667	+	0.740172i
$939$	22143.5			0.769569
$940$		0			0
$941$	−8569.25	−	14842.4i	−0.296865	−	0.514185i	0.678552	−	0.734552i	$-0.262608\pi$
$941$	−8569.25	−	14842.4i	−0.296865	−	0.514185i	−0.975417	+	0.220367i	$0.929274\pi$
$942$	−11661.0	+	6732.49i	−0.403330	+	0.232862i
$943$	1085.74	+	626.854i	0.0374938	+	0.0216471i
$944$	782.165			0.0269675
$945$		0			0
$946$	1174.97			0.0403821
$947$	−34381.9	−	19850.4i	−1.17979	−	0.681153i	−0.223825	−	0.974629i	$-0.571854\pi$
$947$	−34381.9	−	19850.4i	−1.17979	−	0.681153i	−0.955966	+	0.293477i	$0.905188\pi$
$948$	5197.58	−	3000.83i	0.178069	−	0.102808i
$949$	1177.70	+	2039.84i	0.0402843	+	0.0697744i
$950$		0			0
$951$	28416.8			0.968956
$952$	6640.56	−	2240.34i	0.226073	−	0.0762709i
$953$			4918.22i			0.167174i	0.996500	+	0.0835870i	$0.0266376\pi$
$953$			4918.22i			0.167174i	−0.996500	+	0.0835870i	$0.973362\pi$
$954$	−3025.79	+	5240.82i	−0.102687	+	0.177859i
$955$		0			0
$956$	9684.48	+	16774.0i	0.327634	+	0.567479i
$957$	−1238.36	−	714.965i	−0.0418290	−	0.0241500i
$958$			10503.9i			0.354244i
$959$	4825.24	+	14302.4i	0.162477	+	0.481594i
$960$		0			0
$961$	6516.65	−	11287.2i	0.218746	−	0.378879i
$962$	−1846.35	+	1065.99i	−0.0618801	+	0.0357265i
$963$	−11250.7	+	6495.59i	−0.376478	+	0.217360i
$964$	6351.95	−	11001.9i	0.212223	−	0.367580i
$965$		0			0
$966$	5011.73	−	5693.30i	0.166925	−	0.189626i
$967$		−	39789.7i		−	1.32322i	−0.749850	−	0.661608i	$-0.769874\pi$
$967$		−	39789.7i		−	1.32322i	0.749850	−	0.661608i	$-0.230126\pi$
$968$	9047.69	+	5223.69i	0.300417	+	0.173446i
$969$	−1744.33	−	3021.27i	−0.0578287	−	0.100162i
$970$		0			0
$971$	15427.5	−	26721.2i	0.509879	−	0.883136i	−0.490056	−	0.871691i	$-0.663024\pi$
$971$	15427.5	−	26721.2i	0.509879	−	0.883136i	0.999935	−	0.0114448i	$-0.00364307\pi$
$972$		−	15369.1i		−	0.507163i
$973$	37.2964	−	185.688i	0.00122885	−	0.00611809i
$974$	1748.83			0.0575320
$975$		0			0
$976$	−5589.45	−	9681.22i	−0.183314	−	0.317508i
$977$	−2911.01	+	1680.67i	−0.0953239	+	0.0550353i	−0.546904	−	0.837195i	$-0.684194\pi$
$977$	−2911.01	+	1680.67i	−0.0953239	+	0.0550353i	0.451580	+	0.892230i	$0.350860\pi$
$978$	12952.1	+	7477.88i	0.423478	+	0.244495i
$979$	734.090			0.0239649
$980$		0			0
$981$	7097.97			0.231010
$982$	−27403.0	−	15821.1i	−0.890494	−	0.514127i
$983$	7497.42	−	4328.64i	0.243266	−	0.140450i	−0.373411	−	0.927666i	$-0.621812\pi$
$983$	7497.42	−	4328.64i	0.243266	−	0.140450i	0.616677	+	0.787216i	$0.288478\pi$
$984$	−237.367	−	411.131i	−0.00769001	−	0.0133195i
$985$		0			0
$986$	8676.75			0.280247
$987$	−6814.38	+	33926.9i	−0.219761	+	1.09413i
$988$		−	272.258i		−	0.00876689i
$989$	−3858.13	+	6682.48i	−0.124046	+	0.214854i
$990$		0			0
$991$	−13322.8	−	23075.7i	−0.427055	−	0.739680i	0.569555	−	0.821953i	$-0.307116\pi$
$991$	−13322.8	−	23075.7i	−0.427055	−	0.739680i	−0.996610	+	0.0822726i	$0.973782\pi$
$992$	−3587.47	−	2071.22i	−0.114821	−	0.0662918i
$993$			27762.1i			0.887214i
$994$	18514.2	−	21032.0i	0.590778	−	0.671120i
$995$		0			0
$996$	1679.95	−	2909.75i	0.0534449	−	0.0925692i
$997$	−11359.3	+	6558.28i	−0.360834	+	0.208328i	−0.669447	−	0.742860i	$-0.733469\pi$
$997$	−11359.3	+	6558.28i	−0.360834	+	0.208328i	0.308612	+	0.951188i	$0.400135\pi$
$998$	20373.0	−	11762.3i	0.646187	−	0.373076i
$999$	−25589.6	+	44322.4i	−0.810428	+	1.40370i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.4.j.j.149.7		16
5.2	odd	4		350.4.e.l.51.2	✓	8
5.3	odd	4		350.4.e.m.51.3	yes	8
5.4	even	2	inner	350.4.j.j.149.2		16
7.4	even	3	inner	350.4.j.j.249.2		16
35.2	odd	12		2450.4.a.cq.1.3		4
35.4	even	6	inner	350.4.j.j.249.7		16
35.12	even	12		2450.4.a.cu.1.2		4
35.18	odd	12		350.4.e.m.151.3	yes	8
35.23	odd	12		2450.4.a.co.1.2		4
35.32	odd	12		350.4.e.l.151.2	yes	8
35.33	even	12		2450.4.a.ck.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.4.e.l.51.2	✓	8	5.2	odd	4
350.4.e.l.151.2	yes	8	35.32	odd	12
350.4.e.m.51.3	yes	8	5.3	odd	4
350.4.e.m.151.3	yes	8	35.18	odd	12
350.4.j.j.149.2		16	5.4	even	2	inner
350.4.j.j.149.7		16	1.1	even	1	trivial
350.4.j.j.249.2		16	7.4	even	3	inner
350.4.j.j.249.7		16	35.4	even	6	inner
2450.4.a.ck.1.3		4	35.33	even	12
2450.4.a.co.1.2		4	35.23	odd	12
2450.4.a.cq.1.3		4	35.2	odd	12
2450.4.a.cu.1.2		4	35.12	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)

\(f(q)\)	\(=\)	\(q+(1.73205 + 1.00000i) q^{2} +(2.69618 - 1.55664i) q^{3} +(2.00000 + 3.46410i) q^{4} +6.22657 q^{6} +(-3.64704 + 18.1576i) q^{7} +8.00000i q^{8} +(-8.65373 + 14.9887i) q^{9} +O(q^{10})\)	\(q+(1.73205 + 1.00000i) q^{2} +(2.69618 - 1.55664i) q^{3} +(2.00000 + 3.46410i) q^{4} +6.22657 q^{6} +(-3.64704 + 18.1576i) q^{7} +8.00000i q^{8} +(-8.65373 + 14.9887i) q^{9} +(2.50388 + 4.33685i) q^{11} +(10.7847 + 6.22657i) q^{12} +2.87313i q^{13} +(-24.4745 + 27.8029i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(-40.9643 + 23.6508i) q^{17} +(-29.9774 + 17.3075i) q^{18} +(-11.8450 + 20.5162i) q^{19} +(18.4318 + 54.6334i) q^{21} +10.0155i q^{22} +(-56.9621 - 32.8871i) q^{23} +(12.4531 + 21.5695i) q^{24} +(-2.87313 + 4.97641i) q^{26} +137.942i q^{27} +(-70.1939 + 23.6815i) q^{28} -91.7175 q^{29} +(64.7258 + 112.108i) q^{31} +(-27.7128 + 16.0000i) q^{32} +(13.5018 + 7.79530i) q^{33} -94.6030 q^{34} -69.2299 q^{36} +(321.313 + 185.510i) q^{37} +(-41.0323 + 23.6900i) q^{38} +(4.47243 + 7.74648i) q^{39} -19.0608 q^{41} +(-22.7086 + 113.060i) q^{42} -117.314i q^{43} +(-10.0155 + 17.3474i) q^{44} +(-65.7742 - 113.924i) q^{46} +(519.754 + 300.080i) q^{47} +49.8125i q^{48} +(-316.398 - 132.443i) q^{49} +(-73.6315 + 127.533i) q^{51} +(-9.95282 + 5.74626i) q^{52} +(151.403 - 87.4128i) q^{53} +(-137.942 + 238.922i) q^{54} +(-145.261 - 29.1764i) q^{56} +73.7537i q^{57} +(-158.859 - 91.7175i) q^{58} +(-24.4427 - 42.3359i) q^{59} +(-349.341 + 605.076i) q^{61} +258.903i q^{62} +(-240.599 - 211.796i) q^{63} -64.0000 q^{64} +(15.5906 + 27.0037i) q^{66} +(507.083 - 292.764i) q^{67} +(-163.857 - 94.6030i) q^{68} -204.774 q^{69} -756.468 q^{71} +(-119.910 - 69.2299i) q^{72} +(709.970 - 409.901i) q^{73} +(371.020 + 642.626i) q^{74} -94.7601 q^{76} +(-87.8787 + 29.6479i) q^{77} +17.8897i q^{78} +(240.970 - 417.372i) q^{79} +(-18.9251 - 32.7792i) q^{81} +(-33.0143 - 19.0608i) q^{82} -269.803i q^{83} +(-152.392 + 173.116i) q^{84} +(117.314 - 203.194i) q^{86} +(-247.287 + 142.771i) q^{87} +(-34.6948 + 20.0311i) q^{88} +(73.2952 - 126.951i) q^{89} +(-52.1692 - 10.4784i) q^{91} -263.097i q^{92} +(349.025 + 201.510i) q^{93} +(600.160 + 1039.51i) q^{94} +(-49.8125 + 86.2778i) q^{96} -241.036i q^{97} +(-415.574 - 545.797i) q^{98} -86.6717 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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