LMFDB - Embedded newform 153.4.l.a.145.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [153,4,Mod(19,153)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(153, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("153.19");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	153.l (of order $8$, degree $4$, 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:	$9.02729223088$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{8})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 54x^{10} + 1085x^{8} + 9836x^{6} + 38276x^{4} + 49664x^{2} + 16384 $ x^12 + 54x^10 + 1085x^8 + 9836x^6 + 38276x^4 + 49664*x^2 + 16384
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			145.3
Root			$-3.86166i$ of defining polynomial
Character	$\chi$	$=$	153.145
Dual form			153.4.l.a.19.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.43772 - 3.43772i) q^{2} -15.6358i q^{4} +(7.10390 - 17.1503i) q^{5} +(5.36561 + 12.9537i) q^{7} +(-26.2496 - 26.2496i) q^{8} +O(q^{10})$	\(q+(3.43772 - 3.43772i) q^{2} -15.6358i q^{4} +(7.10390 - 17.1503i) q^{5} +(5.36561 + 12.9537i) q^{7} +(-26.2496 - 26.2496i) q^{8} +(-34.5367 - 83.3791i) q^{10} +(-17.9963 + 7.45431i) q^{11} +29.9060i q^{13} +(62.9767 + 26.0858i) q^{14} -55.3912 q^{16} +(56.0566 - 42.0792i) q^{17} +(-32.3771 + 32.3771i) q^{19} +(-268.158 - 111.075i) q^{20} +(-36.2404 + 87.4920i) q^{22} +(-82.5263 + 34.1835i) q^{23} +(-155.280 - 155.280i) q^{25} +(102.808 + 102.808i) q^{26} +(202.542 - 83.8955i) q^{28} +(22.1603 - 53.4998i) q^{29} +(149.621 + 61.9751i) q^{31} +(19.5778 - 19.5778i) q^{32} +(48.0504 - 337.363i) q^{34} +260.277 q^{35} +(125.263 + 51.8855i) q^{37} +222.607i q^{38} +(-636.664 + 263.715i) q^{40} +(21.7716 + 52.5612i) q^{41} +(36.8715 + 36.8715i) q^{43} +(116.554 + 281.386i) q^{44} +(-166.189 + 401.215i) q^{46} +482.699i q^{47} +(103.528 - 103.528i) q^{49} -1067.62 q^{50} +467.603 q^{52} +(374.747 - 374.747i) q^{53} +361.597i q^{55} +(199.185 - 480.875i) q^{56} +(-107.736 - 260.098i) q^{58} +(-198.031 - 198.031i) q^{59} +(224.504 + 542.000i) q^{61} +(727.408 - 301.302i) q^{62} -577.735i q^{64} +(512.897 + 212.449i) q^{65} -367.471 q^{67} +(-657.940 - 876.488i) q^{68} +(894.759 - 894.759i) q^{70} +(55.9406 + 23.1713i) q^{71} +(-140.861 + 340.067i) q^{73} +(608.985 - 252.250i) q^{74} +(506.241 + 506.241i) q^{76} +(-193.122 - 193.122i) q^{77} +(201.148 - 83.3181i) q^{79} +(-393.493 + 949.976i) q^{80} +(255.535 + 105.846i) q^{82} +(-420.131 + 420.131i) q^{83} +(-323.451 - 1260.31i) q^{85} +253.508 q^{86} +(668.069 + 276.723i) q^{88} -887.553i q^{89} +(-387.394 + 160.464i) q^{91} +(534.486 + 1290.36i) q^{92} +(1659.38 + 1659.38i) q^{94} +(325.274 + 785.281i) q^{95} +(338.553 - 817.340i) q^{97} -711.801i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} + 20 q^{5} - 4 q^{7} - 28 q^{8}+O(q^{10}) $ 12 * q + 4 * q^2 + 20 * q^5 - 4 * q^7 - 28 * q^8	$ 12 q + 4 q^{2} + 20 q^{5} - 4 q^{7} - 28 q^{8} - 116 q^{10} - 40 q^{11} + 132 q^{14} + 184 q^{16} - 52 q^{17} - 12 q^{19} - 572 q^{20} - 620 q^{22} + 276 q^{23} - 464 q^{25} + 708 q^{26} + 452 q^{28} - 632 q^{29} + 188 q^{31} - 700 q^{32} + 764 q^{34} + 632 q^{35} + 940 q^{37} - 1864 q^{40} - 176 q^{41} - 1360 q^{43} + 1364 q^{44} + 452 q^{46} + 1044 q^{49} - 2856 q^{50} + 792 q^{52} + 360 q^{53} + 1788 q^{56} - 360 q^{58} + 584 q^{59} - 1052 q^{61} + 380 q^{62} - 404 q^{65} + 1080 q^{67} - 2532 q^{68} + 2072 q^{70} - 28 q^{71} + 824 q^{73} + 2292 q^{74} + 1328 q^{76} + 1252 q^{77} - 196 q^{79} + 904 q^{80} - 1528 q^{82} + 1008 q^{83} - 2824 q^{85} + 1200 q^{86} - 56 q^{88} + 2456 q^{91} - 396 q^{92} + 6360 q^{94} - 2172 q^{95} - 904 q^{97}+O(q^{100}) $ 12 * q + 4 * q^2 + 20 * q^5 - 4 * q^7 - 28 * q^8 - 116 * q^10 - 40 * q^11 + 132 * q^14 + 184 * q^16 - 52 * q^17 - 12 * q^19 - 572 * q^20 - 620 * q^22 + 276 * q^23 - 464 * q^25 + 708 * q^26 + 452 * q^28 - 632 * q^29 + 188 * q^31 - 700 * q^32 + 764 * q^34 + 632 * q^35 + 940 * q^37 - 1864 * q^40 - 176 * q^41 - 1360 * q^43 + 1364 * q^44 + 452 * q^46 + 1044 * q^49 - 2856 * q^50 + 792 * q^52 + 360 * q^53 + 1788 * q^56 - 360 * q^58 + 584 * q^59 - 1052 * q^61 + 380 * q^62 - 404 * q^65 + 1080 * q^67 - 2532 * q^68 + 2072 * q^70 - 28 * q^71 + 824 * q^73 + 2292 * q^74 + 1328 * q^76 + 1252 * q^77 - 196 * q^79 + 904 * q^80 - 1528 * q^82 + 1008 * q^83 - 2824 * q^85 + 1200 * q^86 - 56 * q^88 + 2456 * q^91 - 396 * q^92 + 6360 * q^94 - 2172 * q^95 - 904 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$

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 $

$2$	3.43772	−	3.43772i	1.21542	−	1.21542i	0.246196	−	0.969220i	$-0.420819\pi$
$2$	3.43772	−	3.43772i	1.21542	−	1.21542i	0.969220	−	0.246196i	$-0.0791806\pi$
$3$		0			0
$3$		0			0
$4$		−	15.6358i		−	1.95447i
$5$	7.10390	−	17.1503i	0.635392	−	1.53397i	−0.197364	−	0.980330i	$-0.563238\pi$
$5$	7.10390	−	17.1503i	0.635392	−	1.53397i	0.832755	−	0.553641i	$-0.186762\pi$
$6$		0			0
$7$	5.36561	+	12.9537i	0.289716	+	0.699436i	0.999990	−	0.00448945i	$-0.00142904\pi$
$7$	5.36561	+	12.9537i	0.289716	+	0.699436i	−0.710274	+	0.703925i	$0.751429\pi$
$8$	−26.2496	−	26.2496i	−1.16008	−	1.16008i
$9$		0			0
$10$	−34.5367	−	83.3791i	−1.09215	−	2.63668i
$11$	−17.9963	+	7.45431i	−0.493281	+	0.204324i	−0.615435	−	0.788187i	$-0.711020\pi$
$11$	−17.9963	+	7.45431i	−0.493281	+	0.204324i	0.122154	+	0.992511i	$0.461020\pi$
$12$		0			0
$13$			29.9060i			0.638033i	0.947749	+	0.319016i	$0.103352\pi$
$13$			29.9060i			0.638033i	−0.947749	+	0.319016i	$0.896648\pi$
$14$	62.9767	+	26.0858i	1.20223	+	0.497980i
$15$		0			0
$16$	−55.3912			−0.865487
$17$	56.0566	−	42.0792i	0.799748	−	0.600335i
$17$	56.0566	−	42.0792i	0.799748	−	0.600335i
$18$		0			0
$19$	−32.3771	+	32.3771i	−0.390938	+	0.390938i	−0.875022	−	0.484084i	$-0.839153\pi$
$19$	−32.3771	+	32.3771i	−0.390938	+	0.390938i	0.484084	+	0.875022i	$0.339153\pi$
$20$	−268.158	−	111.075i	−2.99810	−	1.24185i
$21$		0			0
$22$	−36.2404	+	87.4920i	−0.351203	+	0.847880i
$23$	−82.5263	+	34.1835i	−0.748171	+	0.309903i	−0.723995	−	0.689805i	$-0.757696\pi$
$23$	−82.5263	+	34.1835i	−0.748171	+	0.309903i	−0.0241759	+	0.999708i	$0.507696\pi$
$24$		0			0
$25$	−155.280	−	155.280i	−1.24224	−	1.24224i
$26$	102.808	+	102.808i	0.775475	+	0.775475i
$27$		0			0
$28$	202.542	−	83.8955i	1.36703	−	0.566241i
$29$	22.1603	−	53.4998i	0.141899	−	0.342574i	−0.836913	−	0.547336i	$-0.815642\pi$
$29$	22.1603	−	53.4998i	0.141899	−	0.342574i	0.978812	+	0.204762i	$0.0656420\pi$
$30$		0			0
$31$	149.621	+	61.9751i	0.866863	+	0.359067i	0.771388	−	0.636365i	$-0.219563\pi$
$31$	149.621	+	61.9751i	0.866863	+	0.359067i	0.0954754	+	0.995432i	$0.469563\pi$
$32$	19.5778	−	19.5778i	0.108153	−	0.108153i
$33$		0			0
$34$	48.0504	−	337.363i	0.242370	−	1.70168i
$35$	260.277			1.25700
$36$		0			0
$37$	125.263	+	51.8855i	0.556569	+	0.230538i	0.643195	−	0.765702i	$-0.277608\pi$
$37$	125.263	+	51.8855i	0.556569	+	0.230538i	−0.0866259	+	0.996241i	$0.527608\pi$
$38$			222.607i			0.950304i
$39$		0			0
$40$	−636.664	+	263.715i	−2.51663	+	1.04242i
$41$	21.7716	+	52.5612i	0.0829304	+	0.200212i	0.959905	−	0.280324i	$-0.0904421\pi$
$41$	21.7716	+	52.5612i	0.0829304	+	0.200212i	−0.876975	+	0.480536i	$0.840442\pi$
$42$		0			0
$43$	36.8715	+	36.8715i	0.130764	+	0.130764i	0.769460	−	0.638695i	$-0.220526\pi$
$43$	36.8715	+	36.8715i	0.130764	+	0.130764i	−0.638695	+	0.769460i	$0.720526\pi$
$44$	116.554	+	281.386i	0.399345	+	0.964104i
$45$		0			0
$46$	−166.189	+	401.215i	−0.532678	+	1.28600i
$47$			482.699i			1.49806i	0.662536	+	0.749030i	$0.269480\pi$
$47$			482.699i			1.49806i	−0.662536	+	0.749030i	$0.730520\pi$
$48$		0			0
$49$	103.528	−	103.528i	0.301832	−	0.301832i
$50$	−1067.62			−3.01967
$51$		0			0
$52$	467.603			1.24702
$53$	374.747	−	374.747i	0.971234	−	0.971234i	−0.0283638	−	0.999598i	$-0.509030\pi$
$53$	374.747	−	374.747i	0.971234	−	0.971234i	0.999598	+	0.0283638i	$0.00902968\pi$
$54$		0			0
$55$			361.597i			0.886504i
$56$	199.185	−	480.875i	0.475308	−	1.14749i
$57$		0			0
$58$	−107.736	−	260.098i	−0.243904	−	0.588836i
$59$	−198.031	−	198.031i	−0.436973	−	0.436973i	0.454019	−	0.890992i	$-0.349990\pi$
$59$	−198.031	−	198.031i	−0.436973	−	0.436973i	−0.890992	+	0.454019i	$0.849990\pi$
$60$		0			0
$61$	224.504	+	542.000i	0.471226	+	1.13764i	0.963622	+	0.267268i	$0.0861209\pi$
$61$	224.504	+	542.000i	0.471226	+	1.13764i	−0.492397	+	0.870371i	$0.663879\pi$
$62$	727.408	−	301.302i	1.49001	−	0.617184i
$63$		0			0
$64$		−	577.735i		−	1.12839i
$65$	512.897	+	212.449i	0.978724	+	0.405401i
$66$		0			0
$67$	−367.471			−0.670056			−0.335028	−	0.942208i	$-0.608746\pi$
$67$	−367.471			−0.670056			−0.335028	+	0.942208i	$0.608746\pi$
$68$	−657.940	−	876.488i	−1.17334	−	1.56309i
$69$		0			0
$70$	894.759	−	894.759i	1.52777	−	1.52777i
$71$	55.9406	+	23.1713i	0.0935060	+	0.0387314i	0.428946	−	0.903330i	$-0.358885\pi$
$71$	55.9406	+	23.1713i	0.0935060	+	0.0387314i	−0.335440	+	0.942062i	$0.608885\pi$
$72$		0			0
$73$	−140.861	+	340.067i	−0.225842	+	0.545231i	−0.995663	−	0.0930283i	$-0.970345\pi$
$73$	−140.861	+	340.067i	−0.225842	+	0.545231i	0.769821	+	0.638259i	$0.220345\pi$
$74$	608.985	−	252.250i	0.956663	−	0.396263i
$75$		0			0
$76$	506.241	+	506.241i	0.764077	+	0.764077i
$77$	−193.122	−	193.122i	−0.285823	−	0.285823i
$78$		0			0
$79$	201.148	−	83.3181i	0.286467	−	0.118659i	−0.234823	−	0.972038i	$-0.575451\pi$
$79$	201.148	−	83.3181i	0.286467	−	0.118659i	0.521290	+	0.853380i	$0.325451\pi$
$80$	−393.493	+	949.976i	−0.549923	+	1.32763i
$81$		0			0
$82$	255.535	+	105.846i	0.344136	+	0.142546i
$83$	−420.131	+	420.131i	−0.555606	+	0.555606i	−0.928053	−	0.372447i	$-0.878519\pi$
$83$	−420.131	+	420.131i	−0.555606	+	0.555606i	0.372447	+	0.928053i	$0.378519\pi$
$84$		0			0
$85$	−323.451	−	1260.31i	−0.412743	−	1.60824i
$86$	253.508			0.317866
$87$		0			0
$88$	668.069	+	276.723i	0.809277	+	0.335213i
$89$		−	887.553i		−	1.05708i	−0.848907	−	0.528542i	$-0.822739\pi$
$89$		−	887.553i		−	1.05708i	0.848907	−	0.528542i	$-0.177261\pi$
$90$		0			0
$91$	−387.394	+	160.464i	−0.446263	+	0.184848i
$92$	534.486	+	1290.36i	0.605696	+	1.46228i
$93$		0			0
$94$	1659.38	+	1659.38i	1.82077	+	1.82077i
$95$	325.274	+	785.281i	0.351289	+	0.848086i
$96$		0			0
$97$	338.553	−	817.340i	0.354380	−	0.855549i	−0.641688	−	0.766965i	$-0.721766\pi$
$97$	338.553	−	817.340i	0.354380	−	0.855549i	0.996069	−	0.0885841i	$-0.0282342\pi$
$98$		−	711.801i		−	0.733702i
$99$		0			0
$100$	−2427.92	+	2427.92i	−2.42792	+	2.42792i
$101$	−1845.31			−1.81798			−0.908988	−	0.416822i	$-0.863144\pi$
$101$	−1845.31			−1.81798			−0.908988	+	0.416822i	$0.863144\pi$
$102$		0			0
$103$	−1823.07			−1.74400			−0.872002	−	0.489502i	$-0.837178\pi$
$103$	−1823.07			−1.74400			−0.872002	+	0.489502i	$0.837178\pi$
$104$	785.020	−	785.020i	0.740169	−	0.740169i
$105$		0			0
$106$		−	2576.54i		−	2.36091i
$107$	−710.011	+	1714.12i	−0.641490	+	1.54869i	0.183181	+	0.983079i	$0.441361\pi$
$107$	−710.011	+	1714.12i	−0.641490	+	1.54869i	−0.824670	+	0.565613i	$0.808639\pi$
$108$		0			0
$109$	530.959	+	1281.85i	0.466575	+	1.12641i	0.965648	+	0.259852i	$0.0836739\pi$
$109$	530.959	+	1281.85i	0.466575	+	1.12641i	−0.499073	+	0.866560i	$0.666326\pi$
$110$	1243.07	+	1243.07i	1.07747	+	1.07747i
$111$		0			0
$112$	−297.207	−	717.522i	−0.250745	−	0.605352i
$113$	566.444	−	234.629i	0.471563	−	0.195328i	−0.134230	−	0.990950i	$-0.542856\pi$
$113$	566.444	−	234.629i	0.471563	−	0.195328i	0.605793	+	0.795623i	$0.292856\pi$
$114$		0			0
$115$			1658.19i			1.34458i
$116$	−836.510	−	346.494i	−0.669552	−	0.277337i
$117$		0			0
$118$	−1361.55			−1.06221
$119$	845.860	+	500.362i	0.651596	+	0.385446i
$120$		0			0
$121$	−672.859	+	672.859i	−0.505529	+	0.505529i
$122$	2635.02	+	1091.46i	1.95544	+	0.809970i
$123$		0			0
$124$	969.029	−	2339.44i	0.701785	−	1.69426i
$125$	−1622.40	+	672.020i	−1.16089	+	0.480858i
$126$		0			0
$127$	−78.9750	−	78.9750i	−0.0551803	−	0.0551803i	0.678978	−	0.734158i	$-0.262423\pi$
$127$	−78.9750	−	78.9750i	−0.0551803	−	0.0551803i	−0.734158	+	0.678978i	$0.762423\pi$
$128$	−1829.47	−	1829.47i	−1.26331	−	1.26331i
$129$		0			0
$130$	2493.53	−	1032.85i	1.68229	−	0.696826i
$131$	815.895	−	1969.75i	0.544161	−	1.31372i	−0.377602	−	0.925968i	$-0.623251\pi$
$131$	815.895	−	1969.75i	0.544161	−	1.31372i	0.921763	−	0.387753i	$-0.126749\pi$
$132$		0			0
$133$	−593.127	−	245.681i	−0.386697	−	0.160175i
$134$	−1263.26	+	1263.26i	−0.814397	+	0.814397i
$135$		0			0
$136$	−2576.03	−	366.902i	−1.62421	−	0.231335i
$137$	−3087.68			−1.92554			−0.962769	−	0.270327i	$-0.912868\pi$
$137$	−3087.68			−1.92554			−0.962769	+	0.270327i	$0.912868\pi$
$138$		0			0
$139$	434.062	+	179.794i	0.264868	+	0.109712i	0.511165	−	0.859482i	$-0.329214\pi$
$139$	434.062	+	179.794i	0.264868	+	0.109712i	−0.246297	+	0.969194i	$0.579214\pi$
$140$		−	4069.64i		−	2.45677i
$141$		0			0
$142$	271.964	−	112.651i	0.160723	−	0.0665738i
$143$	−222.929	−	538.197i	−0.130365	−	0.314729i
$144$		0			0
$145$	−760.113	−	760.113i	−0.435338	−	0.435338i
$146$	684.816	+	1653.29i	0.388190	+	0.937175i
$147$		0			0
$148$	811.270	−	1958.58i	0.450581	−	1.08780i
$149$			2209.36i			1.21475i	0.794416	+	0.607374i	$0.207777\pi$
$149$			2209.36i			1.21475i	−0.794416	+	0.607374i	$0.792223\pi$
$150$		0			0
$151$	532.003	−	532.003i	0.286714	−	0.286714i	−0.549065	−	0.835779i	$-0.685016\pi$
$151$	532.003	−	532.003i	0.286714	−	0.286714i	0.835779	+	0.549065i	$0.185016\pi$
$152$	1699.77			0.907038
$153$		0			0
$154$	−1327.80			−0.694787
$155$	2125.79	−	2125.79i	1.10160	−	1.10160i
$156$		0			0
$157$		−	579.544i		−	0.294603i	−0.989092	−	0.147301i	$-0.952941\pi$
$157$		−	579.544i		−	0.294603i	0.989092	−	0.147301i	$-0.0470587\pi$
$158$	405.065	−	977.913i	0.203957	−	0.492396i
$159$		0			0
$160$	−196.687	−	474.844i	−0.0971842	−	0.234623i
$161$	−885.609	−	885.609i	−0.433514	−	0.433514i
$162$		0			0
$163$	680.311	+	1642.42i	0.326908	+	0.789227i	0.998819	+	0.0485941i	$0.0154741\pi$
$163$	680.311	+	1642.42i	0.326908	+	0.789227i	−0.671910	+	0.740633i	$0.734526\pi$
$164$	821.835	−	340.415i	0.391308	−	0.162085i
$165$		0			0
$166$			2888.58i			1.35059i
$167$	−2896.21	−	1199.65i	−1.34201	−	0.555879i	−0.407953	−	0.913003i	$-0.633757\pi$
$167$	−2896.21	−	1199.65i	−1.34201	−	0.555879i	−0.934057	+	0.357124i	$0.883757\pi$
$168$		0			0
$169$	1302.63			0.592914
$170$	−5444.54	−	3220.67i	−2.45633	−	1.45302i
$171$		0			0
$172$	576.515	−	576.515i	0.255575	−	0.255575i
$173$	1080.32	+	447.482i	0.474768	+	0.196656i	0.607220	−	0.794534i	$-0.292285\pi$
$173$	1080.32	+	447.482i	0.474768	+	0.196656i	−0.132451	+	0.991190i	$0.542285\pi$
$174$		0			0
$175$	1178.28	−	2844.62i	0.508970	−	1.22876i
$176$	996.836	−	412.903i	0.426928	−	0.176839i
$177$		0			0
$178$	−3051.16	−	3051.16i	−1.28480	−	1.28480i
$179$	1097.81	+	1097.81i	0.458404	+	0.458404i	0.898131	−	0.439727i	$-0.144925\pi$
$179$	1097.81	+	1097.81i	0.458404	+	0.458404i	−0.439727	+	0.898131i	$0.644925\pi$
$180$		0			0
$181$	−1382.05	+	572.462i	−0.567551	+	0.235087i	−0.647960	−	0.761675i	$-0.724377\pi$
$181$	−1382.05	+	572.462i	−0.567551	+	0.235087i	0.0804087	+	0.996762i	$0.474377\pi$
$182$	−780.121	+	1883.38i	−0.317728	+	0.767062i
$183$		0			0
$184$	3063.59	+	1268.98i	1.22745	+	0.508426i
$185$	1779.71	−	1779.71i	0.707279	−	0.707279i
$186$		0			0
$187$	−695.141	+	1175.13i	−0.271838	+	0.459542i
$188$	7547.37			2.92792
$189$		0			0
$190$	3817.77	+	1581.37i	1.45774	+	0.603815i
$191$			3008.79i			1.13983i	0.821702	+	0.569917i	$0.193025\pi$
$191$			3008.79i			1.13983i	−0.821702	+	0.569917i	$0.806975\pi$
$192$		0			0
$193$	−3597.18	+	1490.00i	−1.34161	+	0.555713i	−0.933945	−	0.357418i	$-0.883657\pi$
$193$	−3597.18	+	1490.00i	−1.34161	+	0.555713i	−0.407666	+	0.913131i	$0.633657\pi$
$194$	−1645.93	−	3973.63i	−0.609129	−	1.47057i
$195$		0			0
$196$	−1618.74	−	1618.74i	−0.589921	−	0.589921i
$197$	362.277	+	874.614i	0.131021	+	0.316313i	0.975752	−	0.218878i	$-0.0702396\pi$
$197$	362.277	+	874.614i	0.131021	+	0.316313i	−0.844731	+	0.535191i	$0.820240\pi$
$198$		0			0
$199$	675.758	−	1631.42i	0.240720	−	0.581149i	−0.756635	−	0.653837i	$-0.773158\pi$
$199$	675.758	−	1631.42i	0.240720	−	0.581149i	0.997355	+	0.0726889i	$0.0231580\pi$
$200$			8152.07i			2.88219i
$201$		0			0
$202$	−6343.66	+	6343.66i	−2.20960	+	2.20960i
$203$	811.925			0.280719
$204$		0			0
$205$	1056.10			0.359812
$206$	−6267.19	+	6267.19i	−2.11969	+	2.11969i
$207$		0			0
$208$		−	1656.53i		−	0.552209i
$209$	341.319	−	824.018i	0.112964	−	0.272720i
$210$		0			0
$211$	−142.128	−	343.127i	−0.0463720	−	0.111952i	0.898996	−	0.437956i	$-0.144298\pi$
$211$	−142.128	−	343.127i	−0.0463720	−	0.111952i	−0.945368	+	0.326004i	$0.894298\pi$
$212$	−5859.45	−	5859.45i	−1.89825	−	1.89825i
$213$		0			0
$214$	3451.84	+	8333.47i	1.10263	+	2.66198i
$215$	894.290	−	370.427i	0.283675	−	0.117502i
$216$		0			0
$217$			2270.69i			0.710342i
$218$	6231.92	+	2581.35i	1.93614	+	0.801976i
$219$		0			0
$220$	5653.85			1.73265
$221$	1258.42	+	1676.43i	0.383033	+	0.510266i
$222$		0			0
$223$	1820.02	−	1820.02i	0.546536	−	0.546536i	−0.378901	−	0.925437i	$-0.623698\pi$
$223$	1820.02	−	1820.02i	0.546536	−	0.546536i	0.925437	+	0.378901i	$0.123698\pi$
$224$	358.653	+	148.559i	0.106980	+	0.0443125i
$225$		0			0
$226$	1140.69	−	2753.86i	0.335740	−	0.810549i
$227$	4808.47	−	1991.73i	1.40594	−	0.582361i	0.454657	−	0.890666i	$-0.349762\pi$
$227$	4808.47	−	1991.73i	1.40594	−	0.582361i	0.951288	+	0.308305i	$0.0997617\pi$
$228$		0			0
$229$	−2261.84	−	2261.84i	−0.652694	−	0.652694i	0.300947	−	0.953641i	$-0.402697\pi$
$229$	−2261.84	−	2261.84i	−0.652694	−	0.652694i	−0.953641	+	0.300947i	$0.902697\pi$
$230$	5700.38	+	5700.38i	1.63423	+	1.63423i
$231$		0			0
$232$	−1986.05	+	822.648i	−0.562027	+	0.232799i
$233$	−326.467	+	788.162i	−0.0917923	+	0.221606i	−0.963107	−	0.269118i	$-0.913268\pi$
$233$	−326.467	+	788.162i	−0.0917923	+	0.221606i	0.871315	+	0.490724i	$0.163268\pi$
$234$		0			0
$235$	8278.44	+	3429.04i	2.29798	+	0.951855i
$236$	−3096.36	+	3096.36i	−0.854051	+	0.854051i
$237$		0			0
$238$	4627.93	−	1187.73i	1.26044	−	0.323482i
$239$	−1892.67			−0.512246			−0.256123	−	0.966644i	$-0.582445\pi$
$239$	−1892.67			−0.512246			−0.256123	+	0.966644i	$0.582445\pi$
$240$		0			0
$241$	1708.64	+	707.742i	0.456694	+	0.189169i	0.599157	−	0.800631i	$-0.295502\pi$
$241$	1708.64	+	707.742i	0.456694	+	0.189169i	−0.142464	+	0.989800i	$0.545502\pi$
$242$			4626.19i			1.22886i
$243$		0			0
$244$	8474.59	−	3510.29i	2.22348	−	0.920997i
$245$	−1040.09	−	2511.00i	−0.271220	−	0.654783i
$246$		0			0
$247$	−968.269	−	968.269i	−0.249431	−	0.249431i
$248$	−2300.67	−	5554.32i	−0.589085	−	1.42218i
$249$		0			0
$250$	−3267.13	+	7887.56i	−0.826527	+	1.99541i
$251$		−	1026.39i		−	0.258109i	−0.991637	−	0.129055i	$-0.958806\pi$
$251$		−	1026.39i		−	0.258109i	0.991637	−	0.129055i	$-0.0411942\pi$
$252$		0			0
$253$	1230.35	−	1230.35i	0.305738	−	0.305738i
$254$	−542.987			−0.134134
$255$		0			0
$256$	−7956.49			−1.94250
$257$	−1849.68	+	1849.68i	−0.448949	+	0.448949i	−0.895005	−	0.446056i	$-0.852828\pi$
$257$	−1849.68	+	1849.68i	−0.448949	+	0.448949i	0.446056	+	0.895005i	$0.352828\pi$
$258$		0			0
$259$			1901.02i			0.456075i
$260$	3321.80	−	8019.54i	0.792344	−	1.91289i
$261$		0			0
$262$	−3966.61	−	9576.24i	−0.935335	−	2.25810i
$263$	−3529.99	−	3529.99i	−0.827637	−	0.827637i	0.159553	−	0.987189i	$-0.448995\pi$
$263$	−3529.99	−	3529.99i	−0.827637	−	0.827637i	−0.987189	+	0.159553i	$0.948995\pi$
$264$		0			0
$265$	−3764.86	−	9089.18i	−0.872731	−	2.10696i
$266$	−2883.59	+	1194.42i	−0.664677	+	0.275318i
$267$		0			0
$268$			5745.70i			1.30961i
$269$	3150.91	+	1305.15i	0.714181	+	0.295823i	0.710033	−	0.704168i	$-0.248680\pi$
$269$	3150.91	+	1305.15i	0.714181	+	0.295823i	0.00414728	+	0.999991i	$0.498680\pi$
$270$		0			0
$271$	−75.0911			−0.0168319			−0.00841597	−	0.999965i	$-0.502679\pi$
$271$	−75.0911			−0.0168319			−0.00841597	+	0.999965i	$0.502679\pi$
$272$	−3105.04	+	2330.81i	−0.692172	+	0.519582i
$273$		0			0
$274$	−10614.6	+	10614.6i	−2.34033	+	2.34033i
$275$	3951.97	+	1636.96i	0.866591	+	0.358954i
$276$		0			0
$277$	−1317.15	+	3179.88i	−0.285704	+	0.689750i	−0.999949	−	0.0101463i	$-0.996770\pi$
$277$	−1317.15	+	3179.88i	−0.285704	+	0.689750i	0.714245	+	0.699896i	$0.246770\pi$
$278$	2110.26	−	874.099i	0.455270	−	0.188579i
$279$		0			0
$280$	−6832.18	−	6832.18i	−1.45822	−	1.45822i
$281$	−1183.03	−	1183.03i	−0.251151	−	0.251151i	0.570291	−	0.821443i	$-0.306830\pi$
$281$	−1183.03	−	1183.03i	−0.251151	−	0.251151i	−0.821443	+	0.570291i	$0.806830\pi$
$282$		0			0
$283$	6275.19	−	2599.27i	1.31810	−	0.545973i	0.390860	−	0.920450i	$-0.372178\pi$
$283$	6275.19	−	2599.27i	1.31810	−	0.545973i	0.927236	+	0.374477i	$0.122178\pi$
$284$	362.302	−	874.674i	0.0756995	−	0.182755i
$285$		0			0
$286$	−2616.53	−	1083.80i	−0.540975	−	0.224079i
$287$	−564.046	+	564.046i	−0.116009	+	0.116009i
$288$		0			0
$289$	1371.69	−	4717.63i	0.279195	−	0.960234i
$290$	−5226.11			−1.05823
$291$		0			0
$292$	5317.22	+	2202.46i	1.06564	+	0.441402i
$293$		−	6436.90i		−	1.28344i	−0.766939	−	0.641720i	$-0.778221\pi$
$293$		−	6436.90i		−	1.28344i	0.766939	−	0.641720i	$-0.221779\pi$
$294$		0			0
$295$	−4803.08	+	1989.50i	−0.947952	+	0.392655i
$296$	−1926.12	−	4650.07i	−0.378221	−	0.913107i
$297$		0			0
$298$	7595.14	+	7595.14i	1.47643	+	1.47643i
$299$	−1022.29	−	2468.03i	−0.197728	−	0.477357i
$300$		0			0
$301$	−279.786	+	675.462i	−0.0535767	+	0.129346i
$302$		−	3657.75i		−	0.696953i
$303$		0			0
$304$	1793.41	−	1793.41i	0.338352	−	0.338352i
$305$	10890.3			2.04452
$306$		0			0
$307$	5129.87			0.953672			0.476836	−	0.878992i	$-0.341784\pi$
$307$	5129.87			0.953672			0.476836	+	0.878992i	$0.341784\pi$
$308$	−3019.62	+	3019.62i	−0.558632	+	0.558632i
$309$		0			0
$310$		−	14615.7i		−	2.67779i
$311$	1309.80	−	3162.14i	0.238816	−	0.576554i	−0.758344	−	0.651854i	$-0.773991\pi$
$311$	1309.80	−	3162.14i	0.238816	−	0.576554i	0.997161	+	0.0753000i	$0.0239915\pi$
$312$		0			0
$313$	−1639.23	−	3957.46i	−0.296022	−	0.714661i	−0.999990	−	0.00442950i	$-0.998590\pi$
$313$	−1639.23	−	3957.46i	−0.296022	−	0.714661i	0.703968	−	0.710232i	$-0.251410\pi$
$314$	−1992.31	−	1992.31i	−0.358065	−	0.358065i
$315$		0			0
$316$	−1302.74	−	3145.10i	−0.231915	−	0.559892i
$317$	−360.637	+	149.381i	−0.0638971	+	0.0264670i	−0.414403	−	0.910093i	$-0.636010\pi$
$317$	−360.637	+	149.381i	−0.0638971	+	0.0264670i	0.350506	+	0.936560i	$0.386010\pi$
$318$		0			0
$319$			1127.99i			0.197979i
$320$	−9908.34	−	4104.17i	−1.73092	−	0.716969i
$321$		0			0
$322$	−6088.94			−1.05380
$323$	−452.549	+	3177.35i	−0.0779582	+	0.547346i
$324$		0			0
$325$	4643.79	−	4643.79i	0.792589	−	0.792589i
$326$	7984.87	+	3307.44i	1.35657	+	0.561909i
$327$		0			0
$328$	808.216	−	1951.21i	0.136056	−	0.328467i
$329$	−6252.75	+	2589.97i	−1.04780	+	0.434012i
$330$		0			0
$331$	−2704.60	−	2704.60i	−0.449119	−	0.449119i	0.445942	−	0.895062i	$-0.352869\pi$
$331$	−2704.60	−	2704.60i	−0.449119	−	0.449119i	−0.895062	+	0.445942i	$0.852869\pi$
$332$	6569.07	+	6569.07i	1.08592	+	1.08592i
$333$		0			0
$334$	−14080.4	+	5832.30i	−2.30672	+	0.955477i
$335$	−2610.48	+	6302.25i	−0.425748	+	1.02785i
$336$		0			0
$337$	2195.97	+	909.601i	0.354962	+	0.147030i	0.553037	−	0.833157i	$-0.313469\pi$
$337$	2195.97	+	909.601i	0.354962	+	0.147030i	−0.198075	+	0.980187i	$0.563469\pi$
$338$	4478.08	−	4478.08i	0.720638	−	0.720638i
$339$		0			0
$340$	−19706.0	+	5057.41i	−3.14326	+	0.806695i
$341$	−3154.61			−0.500973
$342$		0			0
$343$	6339.70	+	2625.99i	0.997993	+	0.413382i
$344$		−	1935.73i		−	0.303394i
$345$		0			0
$346$	5252.13	−	2175.51i	0.816059	−	0.338023i
$347$	4562.82	+	11015.6i	0.705893	+	1.70418i	0.710017	+	0.704184i	$0.248687\pi$
$347$	4562.82	+	11015.6i	0.705893	+	1.70418i	−0.00412480	+	0.999991i	$0.501313\pi$
$348$		0			0
$349$	−5225.48	−	5225.48i	−0.801471	−	0.801471i	0.181854	−	0.983326i	$-0.441790\pi$
$349$	−5225.48	−	5225.48i	−0.801471	−	0.801471i	−0.983326	+	0.181854i	$0.941790\pi$
$350$	−5728.41	−	13829.6i	−0.874847	−	2.11207i
$351$		0			0
$352$	−206.389	+	498.267i	−0.0312516	+	0.0754481i
$353$		−	2966.18i		−	0.447235i	−0.974677	−	0.223617i	$-0.928213\pi$
$353$		−	2966.18i		−	0.447235i	0.974677	−	0.223617i	$-0.0717866\pi$
$354$		0			0
$355$	794.792	−	794.792i	0.118826	−	0.118826i
$356$	−13877.6			−2.06604
$357$		0			0
$358$	7547.93			1.11430
$359$	4614.81	−	4614.81i	0.678441	−	0.678441i	−0.281206	−	0.959647i	$-0.590735\pi$
$359$	4614.81	−	4614.81i	0.678441	−	0.678441i	0.959647	+	0.281206i	$0.0907345\pi$
$360$		0			0
$361$			4762.44i			0.694335i
$362$	−2783.12	+	6719.05i	−0.404082	+	0.975539i
$363$		0			0
$364$	2508.97	+	6057.20i	0.361280	+	0.872208i
$365$	4831.61	+	4831.61i	0.692871	+	0.692871i
$366$		0			0
$367$	2256.50	+	5447.66i	0.320949	+	0.774838i	0.999199	+	0.0400079i	$0.0127383\pi$
$367$	2256.50	+	5447.66i	0.320949	+	0.774838i	−0.678251	+	0.734831i	$0.737262\pi$
$368$	4571.23	−	1893.47i	0.647532	−	0.268217i
$369$		0			0
$370$		−	12236.2i		−	1.71928i
$371$	6865.11	+	2843.62i	0.960697	+	0.397934i
$372$		0			0
$373$	9234.98			1.28195			0.640977	−	0.767560i	$-0.278529\pi$
$373$	9234.98			1.28195			0.640977	+	0.767560i	$0.278529\pi$
$374$	1650.08	+	6429.47i	0.228138	+	0.888930i
$375$		0			0
$376$	12670.6	−	12670.6i	1.73787	−	1.73787i
$377$	1599.96	+	662.726i	0.218574	+	0.0905361i
$378$		0			0
$379$	−554.759	+	1339.31i	−0.0751875	+	0.181519i	−0.957005	−	0.290073i	$-0.906320\pi$
$379$	−554.759	+	1339.31i	−0.0751875	+	0.181519i	0.881817	+	0.471592i	$0.156320\pi$
$380$	12278.5	−	5085.91i	1.65756	−	0.686584i
$381$		0			0
$382$	10343.4	+	10343.4i	1.38537	+	1.38537i
$383$	−5769.34	−	5769.34i	−0.769711	−	0.769711i	0.208344	−	0.978056i	$-0.433192\pi$
$383$	−5769.34	−	5769.34i	−0.769711	−	0.769711i	−0.978056	+	0.208344i	$0.933192\pi$
$384$		0			0
$385$	−4684.03	+	1940.19i	−0.620053	+	0.256834i
$386$	−7243.89	+	17488.3i	−0.955192	+	2.30604i
$387$		0			0
$388$	−12779.7	−	5293.54i	−1.67215	−	0.692626i
$389$	−1037.93	+	1037.93i	−0.135283	+	0.135283i	−0.771506	−	0.636222i	$-0.780496\pi$
$389$	−1037.93	+	1037.93i	−0.135283	+	0.135283i	0.636222	+	0.771506i	$0.280496\pi$
$390$		0			0
$391$	−3187.73	+	5388.85i	−0.412303	+	0.696998i
$392$	−5435.15			−0.700298
$393$		0			0
$394$	4252.08	+	1761.27i	0.543697	+	0.225207i
$395$		−	4041.63i		−	0.514827i
$396$		0			0
$397$	−5560.11	+	2303.07i	−0.702907	+	0.291154i	−0.705366	−	0.708843i	$-0.749217\pi$
$397$	−5560.11	+	2303.07i	−0.702907	+	0.291154i	0.00245887	+	0.999997i	$0.499217\pi$
$398$	−3285.31	−	7931.43i	−0.413763	−	0.998912i
$399$		0			0
$400$	8601.13	+	8601.13i	1.07514	+	1.07514i
$401$	−2257.50	−	5450.08i	−0.281132	−	0.678713i	0.718730	−	0.695289i	$-0.244724\pi$
$401$	−2257.50	−	5450.08i	−0.281132	−	0.678713i	−0.999863	+	0.0165756i	$0.994724\pi$
$402$		0			0
$403$	−1853.43	+	4474.57i	−0.229096	+	0.553087i
$404$			28852.9i			3.55318i
$405$		0			0
$406$	2791.17	−	2791.17i	0.341190	−	0.341190i
$407$	−2641.04			−0.321649
$408$		0			0
$409$	−9261.09			−1.11964			−0.559818	−	0.828616i	$-0.689129\pi$
$409$	−9261.09			−1.11964			−0.559818	+	0.828616i	$0.689129\pi$
$410$	3630.59	−	3630.59i	0.437322	−	0.437322i
$411$		0			0
$412$			28505.1i			3.40861i
$413$	1502.68	−	3627.79i	0.179036	−	0.432232i
$414$		0			0
$415$	4220.81	+	10189.9i	0.499257	+	1.20531i
$416$	585.493	+	585.493i	0.0690052	+	0.0690052i
$417$		0			0
$418$	−1659.38	−	4006.10i	−0.194170	−	0.468767i
$419$	−7888.15	+	3267.38i	−0.919716	+	0.380959i	−0.791768	−	0.610822i	$-0.790839\pi$
$419$	−7888.15	+	3267.38i	−0.919716	+	0.380959i	−0.127948	+	0.991781i	$0.540839\pi$
$420$		0			0
$421$		−	1617.31i		−	0.187228i	−0.995609	−	0.0936140i	$-0.970158\pi$
$421$		−	1617.31i		−	0.187228i	0.995609	−	0.0936140i	$-0.0298420\pi$
$422$	−1668.17	−	690.978i	−0.192429	−	0.0797068i
$423$		0			0
$424$	−19673.9			−2.25342
$425$	−15238.5	−	2170.41i	−1.73924	−	0.247719i
$426$		0			0
$427$	−5816.32	+	5816.32i	−0.659184	+	0.659184i
$428$	26801.6	+	11101.6i	3.02688	+	1.25377i
$429$		0			0
$430$	1800.89	−	4347.74i	0.201969	−	0.487597i
$431$	−2343.97	+	970.905i	−0.261961	+	0.108508i	−0.509799	−	0.860294i	$-0.670280\pi$
$431$	−2343.97	+	970.905i	−0.261961	+	0.108508i	0.247838	+	0.968802i	$0.420280\pi$
$432$		0			0
$433$	−1296.36	−	1296.36i	−0.143878	−	0.143878i	0.631499	−	0.775377i	$-0.282440\pi$
$433$	−1296.36	−	1296.36i	−0.143878	−	0.143878i	−0.775377	+	0.631499i	$0.782440\pi$
$434$	7805.98	+	7805.98i	0.863361	+	0.863361i
$435$		0			0
$436$	20042.7	−	8301.96i	2.20154	−	0.911908i
$437$	1565.20	−	3778.73i	0.171336	−	0.413641i
$438$		0			0
$439$	−9607.00	−	3979.35i	−1.04446	−	0.432629i	−0.206548	−	0.978436i	$-0.566223\pi$
$439$	−9607.00	−	3979.35i	−1.04446	−	0.432629i	−0.837911	+	0.545808i	$0.816223\pi$
$440$	9491.78	−	9491.78i	1.02842	−	1.02842i
$441$		0			0
$442$	10089.2	+	1436.99i	1.08573	+	0.154640i
$443$	3984.14			0.427296			0.213648	−	0.976911i	$-0.431465\pi$
$443$	3984.14			0.427296			0.213648	+	0.976911i	$0.431465\pi$
$444$		0			0
$445$	−15221.8	−	6305.09i	−1.62154	−	0.671662i
$446$		−	12513.4i		−	1.32854i
$447$		0			0
$448$	7483.82	−	3099.90i	0.789235	−	0.326912i
$449$	−5045.33	−	12180.5i	−0.530298	−	1.28025i	−0.931326	−	0.364187i	$-0.881347\pi$
$449$	−5045.33	−	12180.5i	−0.530298	−	1.28025i	0.401027	−	0.916066i	$-0.368653\pi$
$450$		0			0
$451$	−783.616	−	783.616i	−0.0818160	−	0.0818160i
$452$	−3668.60	−	8856.79i	−0.381762	−	0.921656i
$453$		0			0
$454$	9683.14	−	23377.2i	1.00100	−	2.41662i
$455$			7783.85i			0.802005i
$456$		0			0
$457$	11484.8	−	11484.8i	1.17557	−	1.17557i	0.194706	−	0.980862i	$-0.437625\pi$
$457$	11484.8	−	11484.8i	1.17557	−	1.17557i	0.980862	−	0.194706i	$-0.0623754\pi$
$458$	−15551.2			−1.58659
$459$		0			0
$460$	25927.1			2.62795
$461$	−7816.84	+	7816.84i	−0.789732	+	0.789732i	−0.981450	−	0.191718i	$-0.938594\pi$
$461$	−7816.84	+	7816.84i	−0.789732	+	0.789732i	0.191718	+	0.981450i	$0.438594\pi$
$462$		0			0
$463$		−	14185.7i		−	1.42390i	−0.702228	−	0.711952i	$-0.747811\pi$
$463$		−	14185.7i		−	1.42390i	0.702228	−	0.711952i	$-0.252189\pi$
$464$	−1227.49	+	2963.41i	−0.122812	+	0.296494i
$465$		0			0
$466$	1587.18	+	3831.78i	0.157778	+	0.380909i
$467$	6851.43	+	6851.43i	0.678900	+	0.678900i	0.959751	−	0.280851i	$-0.0906167\pi$
$467$	6851.43	+	6851.43i	0.678900	+	0.678900i	−0.280851	+	0.959751i	$0.590617\pi$
$468$		0			0
$469$	−1971.71	−	4760.13i	−0.194126	−	0.468661i
$470$	40247.0	−	16670.8i	3.94990	−	1.63610i
$471$		0			0
$472$			10396.5i			1.01385i
$473$	−938.404	−	388.699i	−0.0912217	−	0.0377852i
$474$		0			0
$475$	10055.0			0.971276
$476$	7823.54	−	13225.7i	0.753343	−	1.27352i
$477$		0			0
$478$	−6506.47	+	6506.47i	−0.622592	+	0.622592i
$479$	−12229.4	−	5065.58i	−1.16655	−	0.483199i	−0.286497	−	0.958081i	$-0.592491\pi$
$479$	−12229.4	−	5065.58i	−1.16655	−	0.483199i	−0.880049	+	0.474882i	$0.842491\pi$
$480$		0			0
$481$	−1551.69	+	3746.10i	−0.147091	+	0.355109i
$482$	8306.83	−	3440.80i	0.784992	−	0.325154i
$483$		0			0
$484$	10520.7	+	10520.7i	0.988042	+	0.988042i
$485$	−11612.6	−	11612.6i	−1.08722	−	1.08722i
$486$		0			0
$487$	17831.1	−	7385.89i	1.65915	−	0.687242i	0.661136	−	0.750266i	$-0.270075\pi$
$487$	17831.1	−	7385.89i	1.65915	−	0.687242i	0.998012	+	0.0630247i	$0.0200747\pi$
$488$	8334.15	−	20120.4i	0.773093	−	1.86641i
$489$		0			0
$490$	−12207.6	−	5056.56i	−1.12548	−	0.466188i
$491$	−51.1031	+	51.1031i	−0.00469705	+	0.00469705i	−0.709451	−	0.704754i	$-0.751057\pi$
$491$	−51.1031	+	51.1031i	−0.00469705	+	0.00469705i	0.704754	+	0.709451i	$0.251057\pi$
$492$		0			0
$493$	−1008.99	−	3931.50i	−0.0921760	−	0.359160i
$494$	−6657.27			−0.606325
$495$		0			0
$496$	−8287.69	−	3432.87i	−0.750259	−	0.310767i
$497$			848.967i			0.0766225i
$498$		0			0
$499$	−13678.5	+	5665.84i	−1.22713	+	0.508292i	−0.899668	−	0.436574i	$-0.856192\pi$
$499$	−13678.5	+	5665.84i	−1.22713	+	0.508292i	−0.327457	+	0.944866i	$0.606192\pi$
$500$	10507.5	+	25367.5i	0.939824	+	2.26894i
$501$		0			0
$502$	−3528.45	−	3528.45i	−0.313710	−	0.313710i
$503$	−2561.65	−	6184.36i	−0.227074	−	0.548205i	0.768745	−	0.639555i	$-0.220882\pi$
$503$	−2561.65	−	6184.36i	−0.227074	−	0.548205i	−0.995819	+	0.0913508i	$0.970882\pi$
$504$		0			0
$505$	−13108.9	+	31647.7i	−1.15513	+	2.78872i
$506$		−	8459.22i		−	0.743198i
$507$		0			0
$508$	−1234.84	+	1234.84i	−0.107848	+	0.107848i
$509$	4414.17			0.384390			0.192195	−	0.981357i	$-0.438439\pi$
$509$	4414.17			0.384390			0.192195	+	0.981357i	$0.438439\pi$
$510$		0			0
$511$	−5160.94			−0.446784
$512$	−12716.4	+	12716.4i	−1.09764	+	1.09764i
$513$		0			0
$514$			12717.4i			1.09132i
$515$	−12950.9	+	31266.2i	−1.10813	+	2.67525i
$516$		0			0
$517$	−3598.19	−	8686.79i	−0.306089	−	0.738965i
$518$	6535.15	+	6535.15i	0.554321	+	0.554321i
$519$		0			0
$520$	−7886.64	−	19040.0i	−0.665100	−	1.60569i
$521$	1064.38	−	440.882i	0.0895037	−	0.0370736i	−0.337482	−	0.941332i	$-0.609575\pi$
$521$	1064.38	−	440.882i	0.0895037	−	0.0370736i	0.426986	+	0.904258i	$0.359575\pi$
$522$		0			0
$523$			8548.79i			0.714747i	0.933962	+	0.357373i	$0.116328\pi$
$523$			8548.79i			0.714747i	−0.933962	+	0.357373i	$0.883672\pi$
$524$	−30798.5	−	12757.2i	−2.56763	−	1.06355i
$525$		0			0
$526$	−24270.2			−2.01185
$527$	10995.1	−	2821.82i	0.908833	−	0.233246i
$528$		0			0
$529$	−2961.28	+	2961.28i	−0.243387	+	0.243387i
$530$	−44188.5	−	18303.5i	−3.62156	−	1.50010i
$531$		0			0
$532$	−3841.42	+	9274.00i	−0.313058	+	0.755788i
$533$	−1571.89	+	651.100i	−0.127742	+	0.0529123i
$534$		0			0
$535$	24353.8	+	24353.8i	1.96805	+	1.96805i
$536$	9645.98	+	9645.98i	0.777319	+	0.777319i
$537$		0			0
$538$	15318.7	−	6345.20i	1.22757	−	0.508478i
$539$	−1091.39	+	2634.86i	−0.0872165	+	0.210559i
$540$		0			0
$541$	−1681.96	−	696.690i	−0.133666	−	0.0553661i	0.314848	−	0.949142i	$-0.398046\pi$
$541$	−1681.96	−	696.690i	−0.133666	−	0.0553661i	−0.448514	+	0.893776i	$0.648046\pi$
$542$	−258.142	+	258.142i	−0.0204578	+	0.0204578i
$543$		0			0
$544$	273.647	−	1921.28i	0.0215672	−	0.151423i
$545$	25756.0			2.02434
$546$		0			0
$547$	−76.4832	−	31.6804i	−0.00597840	−	0.00247633i	0.379692	−	0.925113i	$-0.376030\pi$
$547$	−76.4832	−	31.6804i	−0.00597840	−	0.00247633i	−0.385671	+	0.922637i	$0.626030\pi$
$548$			48278.3i			3.76341i
$549$		0			0
$550$	19213.1	−	7958.34i	1.48955	−	0.616991i
$551$	1014.68	+	2449.65i	0.0784516	+	0.189399i
$552$		0			0
$553$	2158.56	+	2158.56i	0.165988	+	0.165988i
$554$	6403.54	+	15459.5i	0.491084	+	1.18558i
$555$		0			0
$556$	2811.22	−	6786.89i	0.214429	−	0.517677i
$557$			12671.9i			0.963963i	0.876181	+	0.481981i	$0.160083\pi$
$557$			12671.9i			0.963963i	−0.876181	+	0.481981i	$0.839917\pi$
$558$		0			0
$559$	−1102.68	+	1102.68i	−0.0834318	+	0.0834318i
$560$	−14417.1			−1.08791
$561$		0			0
$562$	−8133.82			−0.610506
$563$	−3329.39	+	3329.39i	−0.249231	+	0.249231i	−0.820655	−	0.571424i	$-0.806391\pi$
$563$	−3329.39	+	3329.39i	−0.249231	+	0.249231i	0.571424	+	0.820655i	$0.306391\pi$
$564$		0			0
$565$		−	11381.5i		−	0.847473i
$566$	12636.8	−	30507.9i	0.938451	−	2.26562i
$567$		0			0
$568$	−860.179	−	2076.66i	−0.0635428	−	0.153406i
$569$	6005.28	+	6005.28i	0.442450	+	0.442450i	0.892835	−	0.450384i	$-0.148713\pi$
$569$	6005.28	+	6005.28i	0.442450	+	0.442450i	−0.450384	+	0.892835i	$0.648713\pi$
$570$		0			0
$571$	431.903	+	1042.71i	0.0316543	+	0.0764202i	0.938916	−	0.344146i	$-0.111831\pi$
$571$	431.903	+	1042.71i	0.0316543	+	0.0764202i	−0.907262	+	0.420566i	$0.861831\pi$
$572$	−8415.13	+	3485.66i	−0.615129	+	0.254795i
$573$		0			0
$574$			3878.06i			0.281998i
$575$	18122.7	+	7506.66i	1.31438	+	0.544434i
$576$		0			0
$577$	−18288.9			−1.31955			−0.659773	−	0.751465i	$-0.729348\pi$
$577$	−18288.9			−1.31955			−0.659773	+	0.751465i	$0.729348\pi$
$578$	−11502.4	−	20933.3i	−0.827746	−	1.50642i
$579$		0			0
$580$	−11885.0	+	11885.0i	−0.850855	+	0.850855i
$581$	−7696.52	−	3188.00i	−0.549579	−	0.227643i
$582$		0			0
$583$	−3950.58	+	9537.53i	−0.280645	+	0.677537i
$584$	12624.2	−	5229.10i	0.894506	−	0.370517i
$585$		0			0
$586$	−22128.2	−	22128.2i	−1.55991	−	1.55991i
$587$	−7997.50	−	7997.50i	−0.562338	−	0.562338i	0.367633	−	0.929971i	$-0.380168\pi$
$587$	−7997.50	−	7997.50i	−0.562338	−	0.562338i	−0.929971	+	0.367633i	$0.880168\pi$
$588$		0			0
$589$	−6850.88	+	2837.73i	−0.479262	+	0.198517i
$590$	−9672.28	+	23350.9i	−0.674918	+	1.62940i
$591$		0			0
$592$	−6938.44	−	2874.00i	−0.481703	−	0.199528i
$593$	3735.98	−	3735.98i	0.258715	−	0.258715i	−0.565816	−	0.824532i	$-0.691439\pi$
$593$	3735.98	−	3735.98i	0.258715	−	0.258715i	0.824532	+	0.565816i	$0.191439\pi$
$594$		0			0
$595$	14590.3	−	10952.3i	1.00528	−	0.754620i
$596$	34545.0			2.37419
$597$		0			0
$598$	−11998.7	−	4970.04i	−0.820509	−	0.339866i
$599$		−	22287.6i		−	1.52028i	−0.649762	−	0.760138i	$-0.725131\pi$
$599$		−	22287.6i		−	1.52028i	0.649762	−	0.760138i	$-0.274869\pi$
$600$		0			0
$601$	13901.4	−	5758.15i	0.943511	−	0.390815i	0.142723	−	0.989763i	$-0.454414\pi$
$601$	13901.4	−	5758.15i	0.943511	−	0.390815i	0.800788	+	0.598947i	$0.204414\pi$
$602$	1360.22	+	3283.87i	0.0920907	+	0.222326i
$603$		0			0
$604$	−8318.28	−	8318.28i	−0.560374	−	0.560374i
$605$	6759.83	+	16319.7i	0.454258	+	1.09668i
$606$		0			0
$607$	−4319.98	+	10429.4i	−0.288868	+	0.697388i	−0.999984	−	0.00568627i	$-0.998190\pi$
$607$	−4319.98	+	10429.4i	−0.288868	+	0.697388i	0.711116	+	0.703075i	$0.248190\pi$
$608$			1267.75i			0.0845623i
$609$		0			0
$610$	37437.8	−	37437.8i	2.48494	−	2.48494i
$611$	−14435.6			−0.955811
$612$		0			0
$613$	14753.0			0.972054			0.486027	−	0.873944i	$-0.338446\pi$
$613$	14753.0			0.972054			0.486027	+	0.873944i	$0.338446\pi$
$614$	17635.0	−	17635.0i	1.15911	−	1.15911i
$615$		0			0
$616$			10138.8i			0.663154i
$617$	−2561.52	+	6184.04i	−0.167136	+	0.403501i	−0.985150	−	0.171697i	$-0.945075\pi$
$617$	−2561.52	+	6184.04i	−0.167136	+	0.403501i	0.818014	+	0.575198i	$0.195075\pi$
$618$		0			0
$619$	491.884	+	1187.51i	0.0319394	+	0.0771085i	0.939044	−	0.343796i	$-0.111713\pi$
$619$	491.884	+	1187.51i	0.0319394	+	0.0771085i	−0.907105	+	0.420904i	$0.861713\pi$
$620$	−33238.3	−	33238.3i	−2.15304	−	2.15304i
$621$		0			0
$622$	−6367.81	−	15373.2i	−0.410492	−	0.991014i
$623$	11497.1	−	4762.27i	0.739362	−	0.306254i
$624$		0			0
$625$			5148.78i			0.329522i
$626$	−19239.9	−	7969.41i	−1.22840	−	0.508820i
$627$		0			0
$628$	−9061.61			−0.575792
$629$	9205.10	−	2362.42i	0.583516	−	0.149755i
$630$		0			0
$631$	19224.0	−	19224.0i	1.21283	−	1.21283i	0.242734	−	0.970093i	$-0.421956\pi$
$631$	19224.0	−	19224.0i	1.21283	−	1.21283i	0.970093	−	0.242734i	$-0.0780442\pi$
$632$	−7467.12	−	3092.98i	−0.469978	−	0.194671i
$633$		0			0
$634$	−726.238	+	1753.29i	−0.0454931	+	0.109830i
$635$	−1915.48	+	793.417i	−0.119706	+	0.0495839i
$636$		0			0
$637$	3096.11	+	3096.11i	0.192578	+	0.192578i
$638$	3877.70	+	3877.70i	0.240626	+	0.240626i
$639$		0			0
$640$	−44372.3	+	18379.6i	−2.74057	+	1.13518i
$641$	4715.24	−	11383.6i	0.290547	−	0.701442i	−0.709448	−	0.704758i	$-0.751055\pi$
$641$	4715.24	−	11383.6i	0.290547	−	0.701442i	0.999995	+	0.00331580i	$0.00105545\pi$
$642$		0			0
$643$	−23630.2	−	9787.93i	−1.44927	−	0.600308i	−0.487246	−	0.873265i	$-0.661999\pi$
$643$	−23630.2	−	9787.93i	−1.44927	−	0.600308i	−0.962026	+	0.272956i	$0.911999\pi$
$644$	−13847.2	+	13847.2i	−0.847290	+	0.847290i
$645$		0			0
$646$	9367.10	+	12478.6i	0.570501	+	0.760004i
$647$	28275.5			1.71812			0.859062	−	0.511872i	$-0.171048\pi$
$647$	28275.5			1.71812			0.859062	+	0.511872i	$0.171048\pi$
$648$		0			0
$649$	5040.00	+	2087.64i	0.304834	+	0.126266i
$650$		−	31928.1i		−	1.92665i
$651$		0			0
$652$	25680.4	−	10637.2i	1.54252	−	0.638933i
$653$	−900.910	−	2174.99i	−0.0539898	−	0.130343i	0.894583	−	0.446902i	$-0.147473\pi$
$653$	−900.910	−	2174.99i	−0.0539898	−	0.130343i	−0.948573	+	0.316559i	$0.897473\pi$
$654$		0			0
$655$	−27985.7	−	27985.7i	−1.66945	−	1.66945i
$656$	−1205.95	−	2911.43i	−0.0717752	−	0.173281i
$657$		0			0
$658$	−12591.6	+	30398.8i	−0.746004	+	1.80101i
$659$		−	21272.6i		−	1.25745i	−0.777626	−	0.628727i	$-0.783576\pi$
$659$		−	21272.6i		−	1.25745i	0.777626	−	0.628727i	$-0.216424\pi$
$660$		0			0
$661$	11753.0	−	11753.0i	0.691587	−	0.691587i	−0.270994	−	0.962581i	$-0.587352\pi$
$661$	11753.0	−	11753.0i	0.691587	−	0.691587i	0.962581	+	0.270994i	$0.0873525\pi$
$662$	−18595.3			−1.09173
$663$		0			0
$664$	22056.5			1.28910
$665$	−8427.03	+	8427.03i	−0.491408	+	0.491408i
$666$		0			0
$667$			5172.66i			0.300279i
$668$	−18757.5	+	45284.5i	−1.08645	+	2.62292i
$669$		0			0
$670$	12691.3	+	30639.4i	0.731801	+	1.76672i
$671$	−8080.48	−	8080.48i	−0.464893	−	0.464893i
$672$		0			0
$673$	−87.5115	−	211.271i	−0.00501236	−	0.0121009i	0.921354	−	0.388726i	$-0.127085\pi$
$673$	−87.5115	−	211.271i	−0.00501236	−	0.0121009i	−0.926366	+	0.376625i	$0.877085\pi$
$674$	10676.1	−	4422.17i	0.610129	−	0.252724i
$675$		0			0
$676$		−	20367.7i		−	1.15883i
$677$	−9216.32	−	3817.52i	−0.523208	−	0.216720i	0.105417	−	0.994428i	$-0.466382\pi$
$677$	−9216.32	−	3817.52i	−0.523208	−	0.216720i	−0.628625	+	0.777708i	$0.716382\pi$
$678$		0			0
$679$	12404.1			0.701071
$680$	−24592.3	+	41573.2i	−1.38687	+	2.34450i
$681$		0			0
$682$	−10844.7	+	10844.7i	−0.608890	+	0.608890i
$683$	28742.6	+	11905.6i	1.61026	+	0.666990i	0.992819	−	0.119630i	$-0.0381709\pi$
$683$	28742.6	+	11905.6i	1.61026	+	0.666990i	0.617437	+	0.786620i	$0.288171\pi$
$684$		0			0
$685$	−21934.6	+	52954.8i	−1.22347	+	2.95372i
$686$	30821.5	−	12766.7i	1.71541	−	0.710545i
$687$		0			0
$688$	−2042.36	−	2042.36i	−0.113175	−	0.113175i
$689$	11207.2	+	11207.2i	0.619679	+	0.619679i
$690$		0			0
$691$	−4720.02	+	1955.10i	−0.259852	+	0.107634i	−0.508807	−	0.860881i	$-0.669913\pi$
$691$	−4720.02	+	1955.10i	−0.259852	+	0.107634i	0.248954	+	0.968515i	$0.419913\pi$
$692$	6996.72	−	16891.6i	0.384358	−	0.927921i
$693$		0			0
$694$	53554.2	+	22182.9i	2.92924	+	1.21333i
$695$	6167.06	−	6167.06i	0.336590	−	0.336590i
$696$		0			0
$697$	3432.17	+	2030.27i	0.186518	+	0.110333i
$698$	−35927.4			−1.94824
$699$		0			0
$700$	−44477.9	−	18423.3i	−2.40158	−	0.994767i
$701$			11204.5i			0.603691i	0.953357	+	0.301846i	$0.0976027\pi$
$701$			11204.5i			0.603691i	−0.953357	+	0.301846i	$0.902397\pi$
$702$		0			0
$703$	−5735.55	+	2375.74i	−0.307710	+	0.127458i
$704$	4306.62	+	10397.1i	0.230557	+	0.556613i
$705$		0			0
$706$	−10196.9	−	10196.9i	−0.543576	−	0.543576i
$707$	−9901.24	−	23903.7i	−0.526696	−	1.27156i
$708$		0			0
$709$	12992.1	−	31365.7i	0.688193	−	1.66144i	−0.0601983	−	0.998186i	$-0.519173\pi$
$709$	12992.1	−	31365.7i	0.688193	−	1.66144i	0.748391	−	0.663258i	$-0.230827\pi$
$710$		−	5464.54i		−	0.288846i
$711$		0			0
$712$	−23297.9	+	23297.9i	−1.22630	+	1.22630i
$713$	−14466.2			−0.759838
$714$		0			0
$715$	−10813.9			−0.565619
$716$	17165.1	−	17165.1i	0.895937	−	0.895937i
$717$		0			0
$718$		−	31728.8i		−	1.64918i
$719$	−2384.53	+	5756.76i	−0.123683	+	0.298596i	−0.973578	−	0.228355i	$-0.926665\pi$
$719$	−2384.53	+	5756.76i	−0.123683	+	0.298596i	0.849895	+	0.526952i	$0.176665\pi$
$720$		0			0
$721$	−9781.88	−	23615.6i	−0.505265	−	1.21982i
$722$	16371.9	+	16371.9i	0.843906	+	0.843906i
$723$		0			0
$724$	8950.89	+	21609.4i	0.459471	+	1.10926i
$725$	−11748.5	+	4866.38i	−0.601831	+	0.249287i
$726$		0			0
$727$		−	5206.88i		−	0.265629i	−0.991141	−	0.132815i	$-0.957598\pi$
$727$		−	5206.88i		−	0.265629i	0.991141	−	0.132815i	$-0.0424015\pi$
$728$	14381.0	+	5956.82i	0.732139	+	0.303262i
$729$		0			0
$730$	33219.4			1.68425
$731$	3618.42	+	515.369i	0.183081	+	0.0260761i
$732$		0			0
$733$	2699.43	−	2699.43i	0.136024	−	0.136024i	−0.635816	−	0.771840i	$-0.719336\pi$
$733$	2699.43	−	2699.43i	0.136024	−	0.136024i	0.771840	+	0.635816i	$0.219336\pi$
$734$	26484.7	+	10970.3i	1.33184	+	0.551665i
$735$		0			0
$736$	−946.446	+	2284.92i	−0.0474001	+	0.114434i
$737$	6613.13	−	2739.25i	0.330526	−	0.136908i
$738$		0			0
$739$	6513.44	+	6513.44i	0.324223	+	0.324223i	0.850385	−	0.526162i	$-0.176369\pi$
$739$	6513.44	+	6513.44i	0.324223	+	0.324223i	−0.526162	+	0.850385i	$0.676369\pi$
$740$	−27827.1	−	27827.1i	−1.38236	−	1.38236i
$741$		0			0
$742$	33375.9	−	13824.7i	1.65130	−	0.683992i
$743$	−8854.88	+	21377.6i	−0.437219	+	1.05554i	0.539686	+	0.841867i	$0.318543\pi$
$743$	−8854.88	+	21377.6i	−0.437219	+	1.05554i	−0.976905	+	0.213674i	$0.931457\pi$
$744$		0			0
$745$	37891.2	+	15695.0i	1.86339	+	0.771841i
$746$	31747.2	−	31747.2i	1.55811	−	1.55811i
$747$		0			0
$748$	18374.1	+	10869.1i	0.898161	+	0.531300i
$749$	−26013.9			−1.26906
$750$		0			0
$751$	28770.9	+	11917.3i	1.39796	+	0.579053i	0.949221	−	0.314612i	$-0.101874\pi$
$751$	28770.9	+	11917.3i	1.39796	+	0.579053i	0.448736	+	0.893664i	$0.351874\pi$
$752$		−	26737.2i		−	1.29655i
$753$		0			0
$754$	7778.48	−	3221.95i	0.375697	−	0.155619i
$755$	−5344.73	−	12903.3i	−0.257635	−	0.621986i
$756$		0			0
$757$	21914.1	+	21914.1i	1.05216	+	1.05216i	0.998563	+	0.0535946i	$0.0170679\pi$
$757$	21914.1	+	21914.1i	1.05216	+	1.05216i	0.0535946	+	0.998563i	$0.482932\pi$
$758$	2697.05	+	6511.26i	0.129237	+	0.312005i
$759$		0			0
$760$	12075.0	−	29151.6i	0.576324	−	1.39137i
$761$			14150.5i			0.674053i	0.941495	+	0.337026i	$0.109421\pi$
$761$			14150.5i			0.674053i	−0.941495	+	0.337026i	$0.890579\pi$
$762$		0			0
$763$	−13755.8	+	13755.8i	−0.652679	+	0.652679i
$764$	47044.7			2.22777
$765$		0			0
$766$	−39666.7			−1.87104
$767$	5922.30	−	5922.30i	0.278803	−	0.278803i
$768$		0			0
$769$			619.823i			0.0290655i	0.999894	+	0.0145328i	$0.00462608\pi$
$769$			619.823i			0.0290655i	−0.999894	+	0.0145328i	$0.995374\pi$
$770$	−9432.55	+	22772.2i	−0.441462	+	1.06578i
$771$		0			0
$772$	23297.3	+	56244.7i	1.08613	+	2.62214i
$773$	7209.95	+	7209.95i	0.335477	+	0.335477i	0.854662	−	0.519185i	$-0.173764\pi$
$773$	7209.95	+	7209.95i	0.335477	+	0.335477i	−0.519185	+	0.854662i	$0.673764\pi$
$774$		0			0
$775$	−13609.7	−	32856.6i	−0.630805	−	1.52290i
$776$	−30341.7	+	12568.0i	−1.40361	+	0.581396i
$777$		0			0
$778$			7136.23i			0.328851i
$779$	−2406.68	−	996.880i	−0.110691	−	0.0458497i
$780$		0			0
$781$	−1179.45			−0.0540385
$782$	7566.83	+	29483.9i	0.346022	+	1.34826i
$783$		0			0
$784$	−5734.55	+	5734.55i	−0.261231	+	0.261231i
$785$	−9939.36	−	4117.02i	−0.451912	−	0.187188i
$786$		0			0
$787$	12707.6	−	30679.0i	0.575577	−	1.38956i	−0.321171	−	0.947021i	$-0.604076\pi$
$787$	12707.6	−	30679.0i	0.575577	−	1.38956i	0.896747	−	0.442543i	$-0.145924\pi$
$788$	13675.3	−	5664.48i	0.618225	−	0.256077i
$789$		0			0
$790$	−13894.0	−	13894.0i	−0.625729	−	0.625729i
$791$	6078.64	+	6078.64i	0.273238	+	0.273238i
$792$		0			0
$793$	−16209.0	+	6714.00i	−0.725851	+	0.300657i
$794$	−11196.8	+	27031.4i	−0.500452	+	1.20820i
$795$		0			0
$796$	−25508.6	−	10566.0i	−1.13584	−	0.470480i
$797$	−3077.08	+	3077.08i	−0.136757	+	0.136757i	−0.772172	−	0.635414i	$-0.780829\pi$
$797$	−3077.08	+	3077.08i	−0.136757	+	0.136757i	0.635414	+	0.772172i	$0.280829\pi$
$798$		0			0
$799$	20311.6	+	27058.4i	0.899338	+	1.19807i
$800$	−6080.08			−0.268704
$801$		0			0
$802$	−26496.5	−	10975.2i	−1.16661	−	0.483226i
$803$		−	7169.98i		−	0.315097i
$804$		0			0
$805$	−21479.7	+	8897.20i	−0.940449	+	0.389547i
$806$	9010.73	+	21753.8i	0.393784	+	0.950678i
$807$		0			0
$808$	48438.8	+	48438.8i	2.10900	+	2.10900i
$809$	5172.06	+	12486.4i	0.224771	+	0.542645i	0.995526	−	0.0944862i	$-0.0301208\pi$
$809$	5172.06	+	12486.4i	0.224771	+	0.542645i	−0.770755	+	0.637132i	$0.780121\pi$
$810$		0			0
$811$	−2203.64	+	5320.06i	−0.0954135	+	0.230348i	−0.964379	−	0.264524i	$-0.914785\pi$
$811$	−2203.64	+	5320.06i	−0.0954135	+	0.230348i	0.868966	+	0.494872i	$0.164785\pi$
$812$		−	12695.1i		−	0.548657i
$813$		0			0
$814$	−9079.13	+	9079.13i	−0.390938	+	0.390938i
$815$	33000.8			1.41837
$816$		0			0
$817$	−2387.59			−0.102241
$818$	−31837.0	+	31837.0i	−1.36082	+	1.36082i
$819$		0			0
$820$		−	16513.0i		−	0.703243i
$821$	10698.4	−	25828.3i	0.454783	−	1.09794i	−0.515699	−	0.856770i	$-0.672468\pi$
$821$	10698.4	−	25828.3i	0.454783	−	1.09794i	0.970482	−	0.241174i	$-0.0775325\pi$
$822$		0			0
$823$	−14557.5	−	35144.9i	−0.616576	−	1.48855i	−0.855655	−	0.517547i	$-0.826845\pi$
$823$	−14557.5	−	35144.9i	−0.616576	−	1.48855i	0.239078	−	0.971000i	$-0.423155\pi$
$824$	47854.9	+	47854.9i	2.02318	+	2.02318i
$825$		0			0
$826$	−7305.52	−	17637.1i	−0.307738	−	0.742946i
$827$	−13366.2	+	5536.47i	−0.562018	+	0.232795i	−0.645561	−	0.763709i	$-0.723376\pi$
$827$	−13366.2	+	5536.47i	−0.562018	+	0.232795i	0.0835432	+	0.996504i	$0.473376\pi$
$828$		0			0
$829$		−	24519.4i		−	1.02726i	−0.858013	−	0.513628i	$-0.828301\pi$
$829$		−	24519.4i		−	1.02726i	0.858013	−	0.513628i	$-0.171699\pi$
$830$	49540.1	+	20520.2i	2.07176	+	0.858151i
$831$		0			0
$832$	17277.7			0.719949
$833$	1447.06	−	10159.8i	0.0601892	−	0.422590i
$834$		0			0
$835$	−41148.8	+	41148.8i	−1.70540	+	1.70540i
$836$	−12884.2	−	5336.79i	−0.533024	−	0.220786i
$837$		0			0
$838$	−15884.9	+	38349.5i	−0.654814	+	1.58086i
$839$	−35168.5	+	14567.3i	−1.44714	+	0.599426i	−0.961518	−	0.274741i	$-0.911408\pi$
$839$	−35168.5	+	14567.3i	−1.44714	+	0.599426i	−0.485625	+	0.874167i	$0.661408\pi$
$840$		0			0
$841$	14874.5	+	14874.5i	0.609885	+	0.609885i
$842$	−5559.86	−	5559.86i	−0.227560	−	0.227560i
$843$		0			0
$844$	−5365.06	+	2222.28i	−0.218807	+	0.0906327i
$845$	9253.77	−	22340.6i	0.376733	−	0.909514i
$846$		0			0
$847$	−12326.3	−	5105.73i	−0.500045	−	0.207125i
$848$	−20757.6	+	20757.6i	−0.840590	+	0.840590i
$849$		0			0
$850$	−59846.9	+	44924.4i	−2.41498	+	1.81282i
$851$	−12111.1			−0.487853
$852$		0			0
$853$	34565.1	+	14317.3i	1.38744	+	0.574696i	0.946460	−	0.322821i	$-0.104631\pi$
$853$	34565.1	+	14317.3i	1.38744	+	0.574696i	0.440979	+	0.897517i	$0.354631\pi$
$854$			39989.7i			1.60237i
$855$		0			0
$856$	63632.5	−	26357.4i	2.54079	−	1.05243i
$857$	−11132.3	−	26875.7i	−0.443723	−	1.07124i	−0.974632	−	0.223814i	$-0.928149\pi$
$857$	−11132.3	−	26875.7i	−0.443723	−	1.07124i	0.530908	−	0.847429i	$-0.321851\pi$
$858$		0			0
$859$	−30775.9	−	30775.9i	−1.22242	−	1.22242i	−0.966769	−	0.255651i	$-0.917710\pi$
$859$	−30775.9	−	30775.9i	−1.22242	−	1.22242i	−0.255651	−	0.966769i	$-0.582290\pi$
$860$	−5791.91	−	13982.9i	−0.229654	−	0.554434i
$861$		0			0
$862$	−4720.21	+	11395.6i	−0.186509	+	0.450274i
$863$		−	15659.4i		−	0.617672i	−0.951115	−	0.308836i	$-0.900061\pi$
$863$		−	15659.4i		−	0.617672i	0.951115	−	0.308836i	$-0.0999394\pi$
$864$		0			0
$865$	15348.9	−	15348.9i	0.603328	−	0.603328i
$866$	−8913.05			−0.349743
$867$		0			0
$868$	35503.9			1.38834
$869$	−2998.84	+	2998.84i	−0.117064	+	0.117064i
$870$		0			0
$871$		−	10989.6i		−	0.427518i
$872$	19710.6	−	47585.5i	0.765463	−	1.84799i
$873$		0			0
$874$	−7609.48	−	18370.9i	−0.294502	−	0.710990i
$875$	−17410.3	−	17410.3i	−0.672659	−	0.672659i
$876$		0			0
$877$	11056.4	+	26692.6i	0.425712	+	1.02776i	0.980633	+	0.195856i	$0.0627485\pi$
$877$	11056.4	+	26692.6i	0.425712	+	1.02776i	−0.554921	+	0.831903i	$0.687252\pi$
$878$	−46706.0	+	19346.3i	−1.79528	+	0.743627i
$879$		0			0
$880$		−	20029.3i		−	0.767258i
$881$	−20413.0	−	8455.34i	−0.780625	−	0.323346i	−0.0434576	−	0.999055i	$-0.513837\pi$
$881$	−20413.0	−	8455.34i	−0.780625	−	0.323346i	−0.737168	+	0.675710i	$0.763837\pi$
$882$		0			0
$883$	−40158.3			−1.53050			−0.765252	−	0.643731i	$-0.777385\pi$
$883$	−40158.3			−1.53050			−0.765252	+	0.643731i	$0.777385\pi$
$884$	26212.2	−	19676.3i	0.997299	−	0.748628i
$885$		0			0
$886$	13696.3	−	13696.3i	0.519343	−	0.519343i
$887$	25685.4	+	10639.3i	0.972303	+	0.402741i	0.811569	−	0.584257i	$-0.198614\pi$
$887$	25685.4	+	10639.3i	0.972303	+	0.402741i	0.160734	+	0.986998i	$0.448614\pi$
$888$		0			0
$889$	599.272	−	1446.77i	0.0226085	−	0.0545817i
$890$	−74003.4	+	30653.2i	−2.78719	+	1.15449i
$891$		0			0
$892$	−28457.4	−	28457.4i	−1.06819	−	1.06819i
$893$	−15628.4	−	15628.4i	−0.585648	−	0.585648i
$894$		0			0
$895$	26626.6	−	11029.1i	0.994444	−	0.411912i
$896$	13882.2	−	33514.6i	0.517603	−	1.24960i
$897$		0			0
$898$	−59217.5	−	24528.7i	−2.20057	−	0.911507i
$899$	6631.31	−	6631.31i	0.246014	−	0.246014i
$900$		0			0
$901$	5237.99	−	36776.0i	0.193677	−	1.35981i
$902$	−5387.70			−0.198881
$903$		0			0
$904$	−21027.8	−	8710.02i	−0.773646	−	0.320455i
$905$			27769.3i			1.01998i
$906$		0			0
$907$	−17011.7	+	7046.48i	−0.622783	+	0.257965i	−0.671683	−	0.740839i	$-0.734428\pi$
$907$	−17011.7	+	7046.48i	−0.622783	+	0.257965i	0.0489002	+	0.998804i	$0.484428\pi$
$908$	−31142.3	−	75184.2i	−1.13821	−	2.74788i
$909$		0			0
$910$	26758.6	+	26758.6i	0.974770	+	0.974770i
$911$	12349.9	+	29815.2i	0.449143	+	1.08433i	0.972644	+	0.232302i	$0.0746258\pi$
$911$	12349.9	+	29815.2i	0.449143	+	1.08433i	−0.523501	+	0.852025i	$0.675374\pi$
$912$		0			0
$913$	4429.01	−	10692.6i	0.160547	−	0.387594i
$914$		−	78962.7i		−	2.85761i
$915$		0			0
$916$	−35365.7	+	35365.7i	−1.27567	+	1.27567i
$917$	29893.3			1.07652
$918$		0			0
$919$	19185.3			0.688643			0.344322	−	0.938852i	$-0.388109\pi$
$919$	19185.3			0.688643			0.344322	+	0.938852i	$0.388109\pi$
$920$	43526.8	−	43526.8i	1.55982	−	1.55982i
$921$		0			0
$922$			53744.2i			1.91971i
$923$	−692.961	+	1672.96i	−0.0247119	+	0.0596599i
$924$		0			0
$925$	−11394.0	−	27507.5i	−0.405008	−	0.977775i
$926$	−48766.6	−	48766.6i	−1.73064	−	1.73064i
$927$		0			0
$928$	−613.557	−	1481.26i	−0.0217037	−	0.0523973i
$929$	19238.6	−	7968.89i	0.679438	−	0.281433i	−0.0161538	−	0.999870i	$-0.505142\pi$
$929$	19238.6	−	7968.89i	0.679438	−	0.281433i	0.695592	+	0.718437i	$0.255142\pi$
$930$		0			0
$931$			6703.89i			0.235995i
$932$	12323.5	+	5104.57i	0.433123	+	0.179405i
$933$		0			0
$934$	47106.5			1.65029
$935$	15215.7	+	20269.9i	0.532200	+	0.708981i
$936$		0			0
$937$	14900.1	−	14900.1i	0.519495	−	0.519495i	−0.397924	−	0.917418i	$-0.630269\pi$
$937$	14900.1	−	14900.1i	0.519495	−	0.519495i	0.917418	+	0.397924i	$0.130269\pi$
$938$	−23142.1	−	9585.78i	−0.805562	−	0.333675i
$939$		0			0
$940$	53615.7	−	129440.i	1.86037	−	4.49134i
$941$	10307.2	−	4269.37i	0.357071	−	0.147904i	−0.196935	−	0.980417i	$-0.563099\pi$
$941$	10307.2	−	4269.37i	0.357071	−	0.147904i	0.554006	+	0.832513i	$0.313099\pi$
$942$		0			0
$943$	−3593.46	−	3593.46i	−0.124092	−	0.124092i
$944$	10969.1	+	10969.1i	0.378194	+	0.378194i
$945$		0			0
$946$	−4562.20	+	1889.73i	−0.156797	+	0.0649475i
$947$	1165.49	−	2813.74i	0.0399929	−	0.0965514i	−0.902621	−	0.430436i	$-0.858360\pi$
$947$	1165.49	−	2813.74i	0.0399929	−	0.0965514i	0.942614	+	0.333885i	$0.108360\pi$
$948$		0			0
$949$	−10170.0	−	4212.57i	−0.347875	−	0.144095i
$950$	34566.3	−	34566.3i	1.18050	−	1.18050i
$951$		0			0
$952$	−9069.20	−	35337.8i	−0.308755	−	1.20305i
$953$	−6037.53			−0.205220			−0.102610	−	0.994722i	$-0.532719\pi$
$953$	−6037.53			−0.205220			−0.102610	+	0.994722i	$0.532719\pi$
$954$		0			0
$955$	51601.7	+	21374.1i	1.74847	+	0.724241i
$956$			29593.4i			1.00117i
$957$		0			0
$958$	−59455.2	+	24627.2i	−2.00513	+	0.830551i
$959$	−16567.3	−	39997.0i	−0.557858	−	1.34679i
$960$		0			0
$961$	−2519.83	−	2519.83i	−0.0845836	−	0.0845836i
$962$	7543.77	+	18212.3i	0.252829	+	0.610382i
$963$		0			0
$964$	11066.1	−	26715.9i	0.369725	−	0.892595i
$965$			72277.6i			2.41109i
$966$		0			0
$967$	7884.94	−	7884.94i	0.262216	−	0.262216i	−0.563738	−	0.825954i	$-0.690637\pi$
$967$	7884.94	−	7884.94i	0.262216	−	0.262216i	0.825954	+	0.563738i	$0.190637\pi$
$968$	35324.6			1.17291
$969$		0			0
$970$	−79841.6			−2.64284
$971$	−20542.5	+	20542.5i	−0.678930	+	0.678930i	−0.959758	−	0.280828i	$-0.909391\pi$
$971$	−20542.5	+	20542.5i	−0.678930	+	0.678930i	0.280828	+	0.959758i	$0.409391\pi$
$972$		0			0
$973$			6587.43i			0.217043i
$974$	35907.7	−	86688.9i	1.18127	−	2.85184i
$975$		0			0
$976$	−12435.5	−	30022.0i	−0.407839	−	0.984612i
$977$	1718.38	+	1718.38i	0.0562700	+	0.0562700i	0.734682	−	0.678412i	$-0.237331\pi$
$977$	1718.38	+	1718.38i	0.0562700	+	0.0562700i	−0.678412	+	0.734682i	$0.737331\pi$
$978$		0			0
$979$	6616.10	+	15972.7i	0.215987	+	0.521439i
$980$	−39261.4	+	16262.6i	−1.27975	+	0.530091i
$981$		0			0
$982$			351.356i			0.0114177i
$983$	2002.34	+	829.397i	0.0649693	+	0.0269112i	0.414931	−	0.909853i	$-0.363806\pi$
$983$	2002.34	+	829.397i	0.0649693	+	0.0269112i	−0.349962	+	0.936764i	$0.613806\pi$
$984$		0			0
$985$	17573.5			0.568465
$986$	−16984.0	−	10046.8i	−0.548561	−	0.324497i
$987$		0			0
$988$	−15139.6	+	15139.6i	−0.487506	+	0.487506i
$989$	−4303.27	−	1782.47i	−0.138358	−	0.0573098i
$990$		0			0
$991$	7474.99	−	18046.2i	0.239607	−	0.578463i	−0.757635	−	0.652679i	$-0.773645\pi$
$991$	7474.99	−	18046.2i	0.239607	−	0.578463i	0.997242	+	0.0742153i	$0.0236452\pi$
$992$	4142.59	−	1715.92i	0.132588	−	0.0549198i
$993$		0			0
$994$	2918.51	+	2918.51i	0.0931282	+	0.0931282i
$995$	−23178.9	−	23178.9i	−0.738514	−	0.738514i
$996$		0			0
$997$	−8215.19	+	3402.84i	−0.260961	+	0.108093i	−0.509328	−	0.860572i	$-0.670106\pi$
$997$	−8215.19	+	3402.84i	−0.260961	+	0.108093i	0.248367	+	0.968666i	$0.420106\pi$
$998$	−27545.4	+	66500.5i	−0.873682	+	2.10925i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.4.l.a.145.3		12
3.2	odd	2		17.4.d.a.9.1	yes	12
17.2	even	8	inner	153.4.l.a.19.3		12
51.2	odd	8		17.4.d.a.2.1	✓	12
51.11	even	16		289.4.a.g.1.2		12
51.23	even	16		289.4.a.g.1.1		12
51.41	even	16		289.4.b.e.288.12		12
51.44	even	16		289.4.b.e.288.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.d.a.2.1	✓	12	51.2	odd	8
17.4.d.a.9.1	yes	12	3.2	odd	2
153.4.l.a.19.3		12	17.2	even	8	inner
153.4.l.a.145.3		12	1.1	even	1	trivial
289.4.a.g.1.1		12	51.23	even	16
289.4.a.g.1.2		12	51.11	even	16
289.4.b.e.288.11		12	51.44	even	16
289.4.b.e.288.12		12	51.41	even	16

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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	153.l (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.43772 - 3.43772i) q^{2} -15.6358i q^{4} +(7.10390 - 17.1503i) q^{5} +(5.36561 + 12.9537i) q^{7} +(-26.2496 - 26.2496i) q^{8} +O(q^{10})\)	\(q+(3.43772 - 3.43772i) q^{2} -15.6358i q^{4} +(7.10390 - 17.1503i) q^{5} +(5.36561 + 12.9537i) q^{7} +(-26.2496 - 26.2496i) q^{8} +(-34.5367 - 83.3791i) q^{10} +(-17.9963 + 7.45431i) q^{11} +29.9060i q^{13} +(62.9767 + 26.0858i) q^{14} -55.3912 q^{16} +(56.0566 - 42.0792i) q^{17} +(-32.3771 + 32.3771i) q^{19} +(-268.158 - 111.075i) q^{20} +(-36.2404 + 87.4920i) q^{22} +(-82.5263 + 34.1835i) q^{23} +(-155.280 - 155.280i) q^{25} +(102.808 + 102.808i) q^{26} +(202.542 - 83.8955i) q^{28} +(22.1603 - 53.4998i) q^{29} +(149.621 + 61.9751i) q^{31} +(19.5778 - 19.5778i) q^{32} +(48.0504 - 337.363i) q^{34} +260.277 q^{35} +(125.263 + 51.8855i) q^{37} +222.607i q^{38} +(-636.664 + 263.715i) q^{40} +(21.7716 + 52.5612i) q^{41} +(36.8715 + 36.8715i) q^{43} +(116.554 + 281.386i) q^{44} +(-166.189 + 401.215i) q^{46} +482.699i q^{47} +(103.528 - 103.528i) q^{49} -1067.62 q^{50} +467.603 q^{52} +(374.747 - 374.747i) q^{53} +361.597i q^{55} +(199.185 - 480.875i) q^{56} +(-107.736 - 260.098i) q^{58} +(-198.031 - 198.031i) q^{59} +(224.504 + 542.000i) q^{61} +(727.408 - 301.302i) q^{62} -577.735i q^{64} +(512.897 + 212.449i) q^{65} -367.471 q^{67} +(-657.940 - 876.488i) q^{68} +(894.759 - 894.759i) q^{70} +(55.9406 + 23.1713i) q^{71} +(-140.861 + 340.067i) q^{73} +(608.985 - 252.250i) q^{74} +(506.241 + 506.241i) q^{76} +(-193.122 - 193.122i) q^{77} +(201.148 - 83.3181i) q^{79} +(-393.493 + 949.976i) q^{80} +(255.535 + 105.846i) q^{82} +(-420.131 + 420.131i) q^{83} +(-323.451 - 1260.31i) q^{85} +253.508 q^{86} +(668.069 + 276.723i) q^{88} -887.553i q^{89} +(-387.394 + 160.464i) q^{91} +(534.486 + 1290.36i) q^{92} +(1659.38 + 1659.38i) q^{94} +(325.274 + 785.281i) q^{95} +(338.553 - 817.340i) q^{97} -711.801i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + 20 q^{5} - 4 q^{7} - 28 q^{8}+O(q^{10}) \) 12 * q + 4 * q^2 + 20 * q^5 - 4 * q^7 - 28 * q^8	\( 12 q + 4 q^{2} + 20 q^{5} - 4 q^{7} - 28 q^{8} - 116 q^{10} - 40 q^{11} + 132 q^{14} + 184 q^{16} - 52 q^{17} - 12 q^{19} - 572 q^{20} - 620 q^{22} + 276 q^{23} - 464 q^{25} + 708 q^{26} + 452 q^{28} - 632 q^{29} + 188 q^{31} - 700 q^{32} + 764 q^{34} + 632 q^{35} + 940 q^{37} - 1864 q^{40} - 176 q^{41} - 1360 q^{43} + 1364 q^{44} + 452 q^{46} + 1044 q^{49} - 2856 q^{50} + 792 q^{52} + 360 q^{53} + 1788 q^{56} - 360 q^{58} + 584 q^{59} - 1052 q^{61} + 380 q^{62} - 404 q^{65} + 1080 q^{67} - 2532 q^{68} + 2072 q^{70} - 28 q^{71} + 824 q^{73} + 2292 q^{74} + 1328 q^{76} + 1252 q^{77} - 196 q^{79} + 904 q^{80} - 1528 q^{82} + 1008 q^{83} - 2824 q^{85} + 1200 q^{86} - 56 q^{88} + 2456 q^{91} - 396 q^{92} + 6360 q^{94} - 2172 q^{95} - 904 q^{97}+O(q^{100}) \) 12 * q + 4 * q^2 + 20 * q^5 - 4 * q^7 - 28 * q^8 - 116 * q^10 - 40 * q^11 + 132 * q^14 + 184 * q^16 - 52 * q^17 - 12 * q^19 - 572 * q^20 - 620 * q^22 + 276 * q^23 - 464 * q^25 + 708 * q^26 + 452 * q^28 - 632 * q^29 + 188 * q^31 - 700 * q^32 + 764 * q^34 + 632 * q^35 + 940 * q^37 - 1864 * q^40 - 176 * q^41 - 1360 * q^43 + 1364 * q^44 + 452 * q^46 + 1044 * q^49 - 2856 * q^50 + 792 * q^52 + 360 * q^53 + 1788 * q^56 - 360 * q^58 + 584 * q^59 - 1052 * q^61 + 380 * q^62 - 404 * q^65 + 1080 * q^67 - 2532 * q^68 + 2072 * q^70 - 28 * q^71 + 824 * q^73 + 2292 * q^74 + 1328 * q^76 + 1252 * q^77 - 196 * q^79 + 904 * q^80 - 1528 * q^82 + 1008 * q^83 - 2824 * q^85 + 1200 * q^86 - 56 * q^88 + 2456 * q^91 - 396 * q^92 + 6360 * q^94 - 2172 * q^95 - 904 * q^97

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