LMFDB - Embedded newform 153.4.l.b.145.6

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:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			145.6
Character	$\chi$	$=$	153.145
Dual form			153.4.l.b.19.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.56233 - 1.56233i) q^{2} +3.11822i q^{4} +(3.46961 - 8.37637i) q^{5} +(11.4295 + 27.5933i) q^{7} +(17.3704 + 17.3704i) q^{8} +O(q^{10})$	\(q+(1.56233 - 1.56233i) q^{2} +3.11822i q^{4} +(3.46961 - 8.37637i) q^{5} +(11.4295 + 27.5933i) q^{7} +(17.3704 + 17.3704i) q^{8} +(-7.66601 - 18.5074i) q^{10} +(-23.8602 + 9.88321i) q^{11} +13.2897i q^{13} +(60.9668 + 25.2533i) q^{14} +29.3310 q^{16} +(68.9883 - 12.3943i) q^{17} +(35.0810 - 35.0810i) q^{19} +(26.1194 + 10.8190i) q^{20} +(-21.8367 + 52.7185i) q^{22} +(174.438 - 72.2546i) q^{23} +(30.2629 + 30.2629i) q^{25} +(20.7630 + 20.7630i) q^{26} +(-86.0420 + 35.6398i) q^{28} +(-64.2677 + 155.156i) q^{29} +(-292.214 - 121.039i) q^{31} +(-93.1383 + 93.1383i) q^{32} +(88.4188 - 127.147i) q^{34} +270.788 q^{35} +(170.607 + 70.6678i) q^{37} -109.617i q^{38} +(205.769 - 85.2324i) q^{40} +(-35.7638 - 86.3414i) q^{41} +(-209.035 - 209.035i) q^{43} +(-30.8180 - 74.4012i) q^{44} +(159.645 - 385.416i) q^{46} -294.586i q^{47} +(-388.220 + 388.220i) q^{49} +94.5616 q^{50} -41.4403 q^{52} +(-134.660 + 134.660i) q^{53} +234.153i q^{55} +(-280.771 + 677.842i) q^{56} +(141.998 + 342.813i) q^{58} +(-536.061 - 536.061i) q^{59} +(-3.38356 - 8.16864i) q^{61} +(-645.640 + 267.433i) q^{62} +525.674i q^{64} +(111.320 + 46.1102i) q^{65} +635.784 q^{67} +(38.6480 + 215.121i) q^{68} +(423.061 - 423.061i) q^{70} +(-713.040 - 295.351i) q^{71} +(-202.310 + 488.419i) q^{73} +(376.952 - 156.139i) q^{74} +(109.390 + 109.390i) q^{76} +(-545.421 - 545.421i) q^{77} +(-81.6679 + 33.8280i) q^{79} +(101.767 - 245.687i) q^{80} +(-190.769 - 79.0191i) q^{82} +(678.972 - 678.972i) q^{83} +(135.543 - 620.875i) q^{85} -653.164 q^{86} +(-586.135 - 242.785i) q^{88} -3.21092i q^{89} +(-366.708 + 151.895i) q^{91} +(225.306 + 543.936i) q^{92} +(-460.242 - 460.242i) q^{94} +(-172.134 - 415.569i) q^{95} +(135.281 - 326.598i) q^{97} +1213.06i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 80 q^{10} - 128 q^{16} + 128 q^{19} + 280 q^{22} + 16 q^{25} + 184 q^{28} - 192 q^{31} + 24 q^{34} - 416 q^{37} - 488 q^{40} + 672 q^{43} - 384 q^{46} + 944 q^{49} - 4032 q^{52} - 1576 q^{58} + 4816 q^{61} + 2464 q^{67} + 5944 q^{70} + 3024 q^{73} - 3384 q^{76} - 4992 q^{79} - 1176 q^{82} - 2544 q^{85} - 1480 q^{88} - 4016 q^{91} + 4672 q^{94} + 1008 q^{97}+O(q^{100}) $ 32 * q - 80 * q^10 - 128 * q^16 + 128 * q^19 + 280 * q^22 + 16 * q^25 + 184 * q^28 - 192 * q^31 + 24 * q^34 - 416 * q^37 - 488 * q^40 + 672 * q^43 - 384 * q^46 + 944 * q^49 - 4032 * q^52 - 1576 * q^58 + 4816 * q^61 + 2464 * q^67 + 5944 * q^70 + 3024 * q^73 - 3384 * q^76 - 4992 * q^79 - 1176 * q^82 - 2544 * q^85 - 1480 * q^88 - 4016 * q^91 + 4672 * q^94 + 1008 * 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 $

$2$	1.56233	−	1.56233i	0.552369	−	0.552369i	−0.374755	−	0.927124i	$-0.622273\pi$
$2$	1.56233	−	1.56233i	0.552369	−	0.552369i	0.927124	+	0.374755i	$0.122273\pi$
$3$		0			0
$3$		0			0
$4$			3.11822i			0.389777i
$5$	3.46961	−	8.37637i	0.310331	−	0.749206i	−0.689362	−	0.724417i	$-0.742109\pi$
$5$	3.46961	−	8.37637i	0.310331	−	0.749206i	0.999693	−	0.0247881i	$-0.00789112\pi$
$6$		0			0
$7$	11.4295	+	27.5933i	0.617137	+	1.48990i	0.855014	+	0.518604i	$0.173548\pi$
$7$	11.4295	+	27.5933i	0.617137	+	1.48990i	−0.237878	+	0.971295i	$0.576452\pi$
$8$	17.3704	+	17.3704i	0.767670	+	0.767670i
$9$		0			0
$10$	−7.66601	−	18.5074i	−0.242421	−	0.585255i
$11$	−23.8602	+	9.88321i	−0.654010	+	0.270900i	−0.684916	−	0.728622i	$-0.740161\pi$
$11$	−23.8602	+	9.88321i	−0.654010	+	0.270900i	0.0309054	+	0.999522i	$0.490161\pi$
$12$		0			0
$13$			13.2897i			0.283532i	0.989900	+	0.141766i	$0.0452780\pi$
$13$			13.2897i			0.283532i	−0.989900	+	0.141766i	$0.954722\pi$
$14$	60.9668	+	25.2533i	1.16386	+	0.482087i
$15$		0			0
$16$	29.3310			0.458296
$17$	68.9883	−	12.3943i	0.984242	−	0.176826i
$17$	68.9883	−	12.3943i	0.984242	−	0.176826i
$18$		0			0
$19$	35.0810	−	35.0810i	0.423586	−	0.423586i	−0.462850	−	0.886437i	$-0.653173\pi$
$19$	35.0810	−	35.0810i	0.423586	−	0.423586i	0.886437	+	0.462850i	$0.153173\pi$
$20$	26.1194	+	10.8190i	0.292023	+	0.120960i
$21$		0			0
$22$	−21.8367	+	52.7185i	−0.211618	+	0.510892i
$23$	174.438	−	72.2546i	1.58143	−	0.655049i	0.592788	−	0.805358i	$-0.298027\pi$
$23$	174.438	−	72.2546i	1.58143	−	0.655049i	0.988639	+	0.150310i	$0.0480271\pi$
$24$		0			0
$25$	30.2629	+	30.2629i	0.242103	+	0.242103i
$26$	20.7630	+	20.7630i	0.156614	+	0.156614i
$27$		0			0
$28$	−86.0420	+	35.6398i	−0.580729	+	0.240546i
$29$	−64.2677	+	155.156i	−0.411525	+	0.993508i	0.573204	+	0.819413i	$0.305700\pi$
$29$	−64.2677	+	155.156i	−0.411525	+	0.993508i	−0.984729	+	0.174096i	$0.944300\pi$
$30$		0			0
$31$	−292.214	−	121.039i	−1.69301	−	0.701266i	−0.693196	−	0.720749i	$-0.743798\pi$
$31$	−292.214	−	121.039i	−1.69301	−	0.701266i	−0.999810	+	0.0194825i	$0.993798\pi$
$32$	−93.1383	+	93.1383i	−0.514521	+	0.514521i
$33$		0			0
$34$	88.4188	−	127.147i	0.445991	−	0.641338i
$35$	270.788			1.30776
$36$		0			0
$37$	170.607	+	70.6678i	0.758044	+	0.313992i	0.728019	−	0.685557i	$-0.240441\pi$
$37$	170.607	+	70.6678i	0.758044	+	0.313992i	0.0300251	+	0.999549i	$0.490441\pi$
$38$		−	109.617i		−	0.467952i
$39$		0			0
$40$	205.769	−	85.2324i	0.813374	−	0.336911i
$41$	−35.7638	−	86.3414i	−0.136228	−	0.328884i	0.841013	−	0.541015i	$-0.181960\pi$
$41$	−35.7638	−	86.3414i	−0.136228	−	0.328884i	−0.977241	+	0.212131i	$0.931960\pi$
$42$		0			0
$43$	−209.035	−	209.035i	−0.741336	−	0.741336i	0.231499	−	0.972835i	$-0.425637\pi$
$43$	−209.035	−	209.035i	−0.741336	−	0.741336i	−0.972835	+	0.231499i	$0.925637\pi$
$44$	−30.8180	−	74.4012i	−0.105591	−	0.254918i
$45$		0			0
$46$	159.645	−	385.416i	0.511703	−	1.23536i
$47$		−	294.586i		−	0.914252i	−0.889402	−	0.457126i	$-0.848879\pi$
$47$		−	294.586i		−	0.914252i	0.889402	−	0.457126i	$-0.151121\pi$
$48$		0			0
$49$	−388.220	+	388.220i	−1.13184	+	1.13184i
$50$	94.5616			0.267461
$51$		0			0
$52$	−41.4403			−0.110514
$53$	−134.660	+	134.660i	−0.349000	+	0.349000i	−0.859737	−	0.510737i	$-0.829373\pi$
$53$	−134.660	+	134.660i	−0.349000	+	0.349000i	0.510737	+	0.859737i	$0.329373\pi$
$54$		0			0
$55$			234.153i			0.574057i
$56$	−280.771	+	677.842i	−0.669994	+	1.61751i
$57$		0			0
$58$	141.998	+	342.813i	0.321470	+	0.776096i
$59$	−536.061	−	536.061i	−1.18287	−	1.18287i	−0.978998	−	0.203870i	$-0.934648\pi$
$59$	−536.061	−	536.061i	−1.18287	−	1.18287i	−0.203870	−	0.978998i	$-0.565352\pi$
$60$		0			0
$61$	−3.38356	−	8.16864i	−0.00710198	−	0.0171457i	0.920289	−	0.391240i	$-0.127954\pi$
$61$	−3.38356	−	8.16864i	−0.00710198	−	0.0171457i	−0.927391	+	0.374094i	$0.877954\pi$
$62$	−645.640	+	267.433i	−1.32252	+	0.547806i
$63$		0			0
$64$			525.674i			1.02671i
$65$	111.320	+	46.1102i	0.212423	+	0.0879887i
$66$		0			0
$67$	635.784			1.15930			0.579652	−	0.814864i	$-0.303188\pi$
$67$	635.784			1.15930			0.579652	+	0.814864i	$0.303188\pi$
$68$	38.6480	+	215.121i	0.0689229	+	0.383635i
$69$		0			0
$70$	423.061	−	423.061i	0.722364	−	0.722364i
$71$	−713.040	−	295.351i	−1.19186	−	0.493686i	−0.303501	−	0.952831i	$-0.598156\pi$
$71$	−713.040	−	295.351i	−1.19186	−	0.493686i	−0.888361	+	0.459146i	$0.848156\pi$
$72$		0			0
$73$	−202.310	+	488.419i	−0.324364	+	0.783083i	0.674627	+	0.738159i	$0.264305\pi$
$73$	−202.310	+	488.419i	−0.324364	+	0.783083i	−0.998990	+	0.0449241i	$0.985695\pi$
$74$	376.952	−	156.139i	0.592159	−	0.245280i
$75$		0			0
$76$	109.390	+	109.390i	0.165104	+	0.165104i
$77$	−545.421	−	545.421i	−0.807227	−	0.807227i
$78$		0			0
$79$	−81.6679	+	33.8280i	−0.116308	+	0.0481765i	−0.440079	−	0.897959i	$-0.645049\pi$
$79$	−81.6679	+	33.8280i	−0.116308	+	0.0481765i	0.323770	+	0.946136i	$0.395049\pi$
$80$	101.767	−	245.687i	0.142224	−	0.343358i
$81$		0			0
$82$	−190.769	−	79.0191i	−0.256914	−	0.106417i
$83$	678.972	−	678.972i	0.897914	−	0.897914i	−0.0973374	−	0.995251i	$-0.531033\pi$
$83$	678.972	−	678.972i	0.897914	−	0.897914i	0.995251	+	0.0973374i	$0.0310326\pi$
$84$		0			0
$85$	135.543	−	620.875i	0.172962	−	0.792274i
$86$	−653.164			−0.818982
$87$		0			0
$88$	−586.135	−	242.785i	−0.710025	−	0.294102i
$89$		−	3.21092i		−	0.00382424i	−0.999998	−	0.00191212i	$-0.999391\pi$
$89$		−	3.21092i		−	0.00382424i	0.999998	−	0.00191212i	$-0.000608646\pi$
$90$		0			0
$91$	−366.708	+	151.895i	−0.422434	+	0.174978i
$92$	225.306	+	543.936i	0.255323	+	0.616404i
$93$		0			0
$94$	−460.242	−	460.242i	−0.505004	−	0.505004i
$95$	−172.134	−	415.569i	−0.185901	−	0.448805i
$96$		0			0
$97$	135.281	−	326.598i	0.141606	−	0.341866i	−0.837126	−	0.547010i	$-0.815766\pi$
$97$	135.281	−	326.598i	0.141606	−	0.341866i	0.978732	+	0.205144i	$0.0657661\pi$
$98$			1213.06i			1.25038i
$99$		0			0
$100$	−94.3664	+	94.3664i	−0.0943664	+	0.0943664i
$101$	−218.648			−0.215409			−0.107704	−	0.994183i	$-0.534350\pi$
$101$	−218.648			−0.215409			−0.107704	+	0.994183i	$0.534350\pi$
$102$		0			0
$103$	841.220			0.804737			0.402368	−	0.915478i	$-0.368187\pi$
$103$	841.220			0.804737			0.402368	+	0.915478i	$0.368187\pi$
$104$	−230.848	+	230.848i	−0.217659	+	0.217659i
$105$		0			0
$106$			420.769i			0.385553i
$107$	−102.923	+	248.479i	−0.0929903	+	0.224498i	−0.963530	−	0.267599i	$-0.913770\pi$
$107$	−102.923	+	248.479i	−0.0929903	+	0.224498i	0.870540	+	0.492098i	$0.163770\pi$
$108$		0			0
$109$	−147.236	−	355.460i	−0.129382	−	0.312357i	0.845892	−	0.533354i	$-0.179069\pi$
$109$	−147.236	−	355.460i	−0.129382	−	0.312357i	−0.975274	+	0.220997i	$0.929069\pi$
$110$	365.825	+	365.825i	0.317091	+	0.317091i
$111$		0			0
$112$	335.239	+	809.339i	0.282831	+	0.682815i
$113$	1428.81	−	591.833i	1.18948	−	0.492699i	0.301894	−	0.953342i	$-0.402381\pi$
$113$	1428.81	−	591.833i	1.18948	−	0.492699i	0.887586	+	0.460643i	$0.152381\pi$
$114$		0			0
$115$		−	1711.85i		−	1.38810i
$116$	−483.810	−	200.401i	−0.387247	−	0.160403i
$117$		0			0
$118$	−1675.01			−1.30676
$119$	1130.50	+	1761.96i	0.870865	+	1.35730i
$120$		0			0
$121$	−469.529	+	469.529i	−0.352764	+	0.352764i
$122$	−18.0484	−	7.47589i	−0.0133937	−	0.00554783i
$123$		0			0
$124$	377.426	−	911.188i	0.273338	−	0.659896i
$125$	1405.54	−	582.194i	1.00572	−	0.416584i
$126$		0			0
$127$	421.143	+	421.143i	0.294255	+	0.294255i	0.838759	−	0.544503i	$-0.183282\pi$
$127$	421.143	+	421.143i	0.294255	+	0.294255i	−0.544503	+	0.838759i	$0.683282\pi$
$128$	76.1728	+	76.1728i	0.0525999	+	0.0525999i
$129$		0			0
$130$	245.958	−	101.879i	0.165938	−	0.0687339i
$131$	344.213	−	831.003i	0.229573	−	0.554237i	−0.766553	−	0.642181i	$-0.778030\pi$
$131$	344.213	−	831.003i	0.229573	−	0.554237i	0.996125	+	0.0879440i	$0.0280297\pi$
$132$		0			0
$133$	1368.96	+	567.043i	0.892512	+	0.369690i
$134$	993.308	−	993.308i	0.640363	−	0.640363i
$135$		0			0
$136$	1413.65	+	983.060i	0.891317	+	0.619829i
$137$	1707.25			1.06468			0.532338	−	0.846532i	$-0.321314\pi$
$137$	1707.25			1.06468			0.532338	+	0.846532i	$0.321314\pi$
$138$		0			0
$139$	−2292.06	−	949.404i	−1.39864	−	0.579334i	−0.449239	−	0.893412i	$-0.648305\pi$
$139$	−2292.06	−	949.404i	−1.39864	−	0.579334i	−0.949397	+	0.314078i	$0.898305\pi$
$140$			844.376i			0.509734i
$141$		0			0
$142$	−1575.44	+	652.570i	−0.931044	+	0.385651i
$143$	−131.345	−	317.096i	−0.0768087	−	0.185433i
$144$		0			0
$145$	1076.66	+	1076.66i	0.616633	+	0.616633i
$146$	446.998	+	1079.15i	0.253382	+	0.611719i
$147$		0			0
$148$	−220.358	+	531.990i	−0.122387	+	0.295468i
$149$		−	2846.73i		−	1.56519i	−0.622530	−	0.782596i	$-0.713895\pi$
$149$		−	2846.73i		−	1.56519i	0.622530	−	0.782596i	$-0.286105\pi$
$150$		0			0
$151$	1371.91	−	1371.91i	0.739365	−	0.739365i	−0.233090	−	0.972455i	$-0.574884\pi$
$151$	1371.91	−	1371.91i	0.739365	−	0.739365i	0.972455	+	0.233090i	$0.0748837\pi$
$152$	1218.74			0.650349
$153$		0			0
$154$	−1704.26			−0.891774
$155$	−2027.74	+	2027.74i	−1.05079	+	1.05079i
$156$		0			0
$157$		−	1943.24i		−	0.987819i	−0.869513	−	0.493909i	$-0.835567\pi$
$157$		−	1943.24i		−	0.987819i	0.869513	−	0.493909i	$-0.164433\pi$
$158$	−74.7420	+	180.443i	−0.0376339	+	0.0908563i
$159$		0			0
$160$	457.008	+	1103.31i	0.225810	+	0.545154i
$161$	3987.49	+	3987.49i	1.95191	+	1.95191i
$162$		0			0
$163$	1495.00	+	3609.24i	0.718387	+	1.73434i	0.677894	+	0.735159i	$0.262893\pi$
$163$	1495.00	+	3609.24i	0.718387	+	1.73434i	0.0404927	+	0.999180i	$0.487107\pi$
$164$	269.231	−	111.519i	0.128192	−	0.0530987i
$165$		0			0
$166$		−	2121.56i		−	0.991959i
$167$	−3673.52	−	1521.62i	−1.70219	−	0.705070i	−0.702213	−	0.711967i	$-0.747805\pi$
$167$	−3673.52	−	1521.62i	−1.70219	−	0.705070i	−0.999976	+	0.00689684i	$0.997805\pi$
$168$		0			0
$169$	2020.38			0.919610
$170$	−758.250	−	1181.78i	−0.342089	−	0.533166i
$171$		0			0
$172$	651.815	−	651.815i	0.288956	−	0.288956i
$173$	−1478.39	−	612.368i	−0.649710	−	0.269119i	0.0333914	−	0.999442i	$-0.489369\pi$
$173$	−1478.39	−	612.368i	−0.649710	−	0.269119i	−0.683101	+	0.730324i	$0.739369\pi$
$174$		0			0
$175$	−489.163	+	1180.94i	−0.211299	+	0.510120i
$176$	−699.842	+	289.884i	−0.299730	+	0.124152i
$177$		0			0
$178$	−5.01653	−	5.01653i	−0.00211239	−	0.00211239i
$179$	530.244	+	530.244i	0.221409	+	0.221409i	0.809092	−	0.587682i	$-0.199960\pi$
$179$	530.244	+	530.244i	0.221409	+	0.221409i	−0.587682	+	0.809092i	$0.699960\pi$
$180$		0			0
$181$	−1043.86	+	432.382i	−0.428672	+	0.177562i	−0.586579	−	0.809892i	$-0.699525\pi$
$181$	−1043.86	+	432.382i	−0.428672	+	0.177562i	0.157907	+	0.987454i	$0.449525\pi$
$182$	−335.609	+	810.233i	−0.136687	+	0.329991i
$183$		0			0
$184$	4285.14	+	1774.96i	1.71687	+	0.711153i
$185$	1183.88	−	1183.88i	0.470489	−	0.470489i
$186$		0			0
$187$	−1523.58	+	977.555i	−0.595802	+	0.382277i
$188$	918.584			0.356355
$189$		0			0
$190$	−918.190	−	380.327i	−0.350592	−	0.145220i
$191$			782.448i			0.296419i	0.988956	+	0.148209i	$0.0473509\pi$
$191$			782.448i			0.296419i	−0.988956	+	0.148209i	$0.952649\pi$
$192$		0			0
$193$	−3264.60	+	1352.24i	−1.21757	+	0.504334i	−0.896637	−	0.442767i	$-0.853997\pi$
$193$	−3264.60	+	1352.24i	−1.21757	+	0.504334i	−0.320934	+	0.947101i	$0.603997\pi$
$194$	−298.901	−	721.610i	−0.110618	−	0.267055i
$195$		0			0
$196$	−1210.55	−	1210.55i	−0.441164	−	0.441164i
$197$	−1615.30	−	3899.68i	−0.584189	−	1.41036i	−0.888984	−	0.457939i	$-0.848588\pi$
$197$	−1615.30	−	3899.68i	−0.584189	−	1.41036i	0.304794	−	0.952418i	$-0.401412\pi$
$198$		0			0
$199$	167.810	−	405.129i	0.0597776	−	0.144316i	−0.891169	−	0.453672i	$-0.850114\pi$
$199$	167.810	−	405.129i	0.0597776	−	0.144316i	0.950946	+	0.309357i	$0.100114\pi$
$200$			1051.36i			0.371711i
$201$		0			0
$202$	−341.601	+	341.601i	−0.118985	+	0.118985i
$203$	−5015.82			−1.73419
$204$		0			0
$205$	−847.314			−0.288678
$206$	1314.27	−	1314.27i	0.444512	−	0.444512i
$207$		0			0
$208$			389.801i			0.129942i
$209$	−490.326	+	1183.75i	−0.162280	+	0.391779i
$210$		0			0
$211$	−180.146	−	434.910i	−0.0587760	−	0.141898i	0.891763	−	0.452502i	$-0.149469\pi$
$211$	−180.146	−	434.910i	−0.0587760	−	0.141898i	−0.950539	+	0.310604i	$0.899469\pi$
$212$	−419.900	−	419.900i	−0.136032	−	0.136032i
$213$		0			0
$214$	227.406	+	549.007i	0.0726410	+	0.175371i
$215$	−2476.22	+	1025.68i	−0.785473	+	0.325354i
$216$		0			0
$217$		−	9446.58i		−	2.95519i
$218$	−785.380	−	325.315i	−0.244003	−	0.101069i
$219$		0			0
$220$	−730.139			−0.223754
$221$	164.717	+	916.836i	0.0501359	+	0.279064i
$222$		0			0
$223$	1561.16	−	1561.16i	0.468803	−	0.468803i	−0.432723	−	0.901527i	$-0.642447\pi$
$223$	1561.16	−	1561.16i	0.468803	−	0.468803i	0.901527	+	0.432723i	$0.142447\pi$
$224$	−3634.52	−	1505.47i	−1.08411	−	0.449055i
$225$		0			0
$226$	1307.64	−	3156.92i	0.384880	−	0.929183i
$227$	478.497	−	198.200i	0.139907	−	0.0579515i	−0.311631	−	0.950203i	$-0.600875\pi$
$227$	478.497	−	198.200i	0.139907	−	0.0579515i	0.451539	+	0.892252i	$0.350875\pi$
$228$		0			0
$229$	1709.44	+	1709.44i	0.493287	+	0.493287i	0.909340	−	0.416053i	$-0.136587\pi$
$229$	1709.44	+	1709.44i	0.493287	+	0.493287i	−0.416053	+	0.909340i	$0.636587\pi$
$230$	−2674.49	−	2674.49i	−0.766741	−	0.766741i
$231$		0			0
$232$	−3811.47	+	1578.76i	−1.07860	+	0.446771i
$233$	−2399.32	+	5792.47i	−0.674613	+	1.62866i	0.0990661	+	0.995081i	$0.468414\pi$
$233$	−2399.32	+	5792.47i	−0.674613	+	1.62866i	−0.773679	+	0.633578i	$0.781586\pi$
$234$		0			0
$235$	−2467.56	−	1022.10i	−0.684962	−	0.283721i
$236$	1671.56	−	1671.56i	0.461055	−	0.461055i
$237$		0			0
$238$	4518.99	+	986.541i	1.23077	+	0.268689i
$239$	−1575.56			−0.426420			−0.213210	−	0.977006i	$-0.568392\pi$
$239$	−1575.56			−0.426420			−0.213210	+	0.977006i	$0.568392\pi$
$240$		0			0
$241$	−1340.71	−	555.342i	−0.358353	−	0.148435i	0.196241	−	0.980556i	$-0.437126\pi$
$241$	−1340.71	−	555.342i	−0.358353	−	0.148435i	−0.554594	+	0.832121i	$0.687126\pi$
$242$			1467.12i			0.389712i
$243$		0			0
$244$	25.4716	−	10.5507i	0.00668300	−	0.00276819i
$245$	1904.90	+	4598.84i	0.496734	+	1.19922i
$246$		0			0
$247$	466.218	+	466.218i	0.120100	+	0.120100i
$248$	−2973.38	−	7178.37i	−0.761329	−	1.83801i
$249$		0			0
$250$	1286.34	−	3105.51i	0.325422	−	0.785638i
$251$		−	1758.27i		−	0.442155i	−0.975256	−	0.221077i	$-0.929043\pi$
$251$		−	1758.27i		−	0.442155i	0.975256	−	0.221077i	$-0.0709573\pi$
$252$		0			0
$253$	−3448.01	+	3448.01i	−0.856817	+	0.856817i
$254$	1315.93			0.325075
$255$		0			0
$256$	−3967.38			−0.968598
$257$	2796.07	−	2796.07i	0.678653	−	0.678653i	−0.281042	−	0.959695i	$-0.590680\pi$
$257$	2796.07	−	2796.07i	0.678653	−	0.678653i	0.959695	+	0.281042i	$0.0906801\pi$
$258$		0			0
$259$			5515.31i			1.32319i
$260$	−143.782	+	347.120i	−0.0342960	+	0.0827979i
$261$		0			0
$262$	−760.530	−	1836.08i	−0.179335	−	0.432952i
$263$	−185.805	−	185.805i	−0.0435636	−	0.0435636i	0.684989	−	0.728553i	$-0.259807\pi$
$263$	−185.805	−	185.805i	−0.0435636	−	0.0435636i	−0.728553	+	0.684989i	$0.759807\pi$
$264$		0			0
$265$	660.746	+	1595.18i	0.153167	+	0.369778i
$266$	3024.69	−	1252.87i	0.697201	−	0.288790i
$267$		0			0
$268$			1982.51i			0.451870i
$269$	769.130	+	318.584i	0.174330	+	0.0722097i	0.468141	−	0.883654i	$-0.344924\pi$
$269$	769.130	+	318.584i	0.174330	+	0.0722097i	−0.293812	+	0.955863i	$0.594924\pi$
$270$		0			0
$271$	8230.30			1.84485			0.922426	−	0.386174i	$-0.126203\pi$
$271$	8230.30			1.84485			0.922426	+	0.386174i	$0.126203\pi$
$272$	2023.49	−	363.536i	0.451074	−	0.0810389i
$273$		0			0
$274$	2667.30	−	2667.30i	0.588094	−	0.588094i
$275$	−1021.17	−	422.984i	−0.223924	−	0.0927523i
$276$		0			0
$277$	−2097.69	+	5064.28i	−0.455011	+	1.09849i	0.515381	+	0.856961i	$0.327650\pi$
$277$	−2097.69	+	5064.28i	−0.455011	+	1.09849i	−0.970393	+	0.241533i	$0.922350\pi$
$278$	−5064.26	+	2097.69i	−1.09257	+	0.452557i
$279$		0			0
$280$	4703.69	+	4703.69i	1.00393	+	1.00393i
$281$	4348.42	+	4348.42i	0.923150	+	0.923150i	0.997251	−	0.0741006i	$-0.0236086\pi$
$281$	4348.42	+	4348.42i	0.923150	+	0.923150i	−0.0741006	+	0.997251i	$0.523609\pi$
$282$		0			0
$283$	−4340.97	+	1798.09i	−0.911816	+	0.377687i	−0.788752	−	0.614712i	$-0.789272\pi$
$283$	−4340.97	+	1798.09i	−0.911816	+	0.377687i	−0.123064	+	0.992399i	$0.539272\pi$
$284$	920.968	−	2223.41i	0.192427	−	0.464561i
$285$		0			0
$286$	−700.615	−	290.204i	−0.144854	−	0.0600005i
$287$	1973.68	−	1973.68i	0.405933	−	0.405933i
$288$		0			0
$289$	4605.76	−	1710.12i	0.937465	−	0.348080i
$290$	3364.21			0.681218
$291$		0			0
$292$	−1523.00	−	630.846i	−0.305228	−	0.126430i
$293$			7969.53i			1.58903i	0.607247	+	0.794513i	$0.292274\pi$
$293$			7969.53i			1.58903i	−0.607247	+	0.794513i	$0.707726\pi$
$294$		0			0
$295$	−6350.17	+	2630.33i	−1.25329	+	0.519130i
$296$	1735.98	+	4191.04i	0.340885	+	0.822970i
$297$		0			0
$298$	−4447.55	−	4447.55i	−0.864563	−	0.864563i
$299$	960.245	+	2318.24i	0.185727	+	0.448385i
$300$		0			0
$301$	3378.79	−	8157.12i	0.647011	−	1.56202i
$302$		−	4286.75i		−	0.816805i
$303$		0			0
$304$	1028.96	−	1028.96i	0.194128	−	0.194128i
$305$	−80.1632			−0.0150496
$306$		0			0
$307$	4245.13			0.789193			0.394596	−	0.918855i	$-0.370884\pi$
$307$	4245.13			0.789193			0.394596	+	0.918855i	$0.370884\pi$
$308$	1700.74	−	1700.74i	0.314639	−	0.314639i
$309$		0			0
$310$			6336.01i			1.16084i
$311$	−3272.44	+	7900.38i	−0.596666	+	1.44048i	0.280292	+	0.959915i	$0.409569\pi$
$311$	−3272.44	+	7900.38i	−0.596666	+	1.44048i	−0.876959	+	0.480566i	$0.840431\pi$
$312$		0			0
$313$	3240.05	+	7822.18i	0.585107	+	1.41257i	0.888131	+	0.459591i	$0.152004\pi$
$313$	3240.05	+	7822.18i	0.585107	+	1.41257i	−0.303023	+	0.952983i	$0.597996\pi$
$314$	−3035.99	−	3035.99i	−0.545640	−	0.545640i
$315$		0			0
$316$	−105.483	−	254.658i	−0.0187781	−	0.0453344i
$317$	−3842.41	+	1591.58i	−0.680793	+	0.281994i	−0.696158	−	0.717888i	$-0.745109\pi$
$317$	−3842.41	+	1591.58i	−0.680793	+	0.281994i	0.0153655	+	0.999882i	$0.495109\pi$
$318$		0			0
$319$		−	4337.22i		−	0.761246i
$320$	4403.24	+	1823.88i	0.769215	+	0.318619i
$321$		0			0
$322$	12459.6			2.15635
$323$	1985.38	−	2854.98i	0.342010	−	0.491813i
$324$		0			0
$325$	−402.186	+	402.186i	−0.0686439	+	0.0686439i
$326$	7974.52	+	3303.15i	1.35481	+	0.561180i
$327$		0			0
$328$	878.552	−	2121.01i	0.147896	−	0.357053i
$329$	8128.61	−	3366.98i	1.36214	−	0.564218i
$330$		0			0
$331$	−3841.52	−	3841.52i	−0.637912	−	0.637912i	0.312128	−	0.950040i	$-0.398958\pi$
$331$	−3841.52	−	3841.52i	−0.637912	−	0.637912i	−0.950040	+	0.312128i	$0.898958\pi$
$332$	2117.18	+	2117.18i	0.349987	+	0.349987i
$333$		0			0
$334$	−8116.56	+	3361.99i	−1.32970	+	0.550778i
$335$	2205.92	−	5325.56i	0.359768	−	0.868557i
$336$		0			0
$337$	−5037.04	−	2086.41i	−0.814199	−	0.337252i	−0.0635710	−	0.997977i	$-0.520249\pi$
$337$	−5037.04	−	2086.41i	−0.814199	−	0.337252i	−0.750628	+	0.660725i	$0.770249\pi$
$338$	3156.51	−	3156.51i	0.507964	−	0.507964i
$339$		0			0
$340$	1936.02	+	422.654i	0.308811	+	0.0674165i
$341$	8168.53			1.29722
$342$		0			0
$343$	−5684.93	−	2354.77i	−0.894919	−	0.370688i
$344$		−	7262.02i		−	1.13820i
$345$		0			0
$346$	−3266.46	+	1353.01i	−0.507532	+	0.210227i
$347$	−4367.91	−	10545.1i	−0.675740	−	1.63138i	−0.771693	−	0.635995i	$-0.780590\pi$
$347$	−4367.91	−	10545.1i	−0.675740	−	1.63138i	0.0959533	−	0.995386i	$-0.469410\pi$
$348$		0			0
$349$	−4848.94	−	4848.94i	−0.743719	−	0.743719i	0.229573	−	0.973291i	$-0.426267\pi$
$349$	−4848.94	−	4848.94i	−0.743719	−	0.743719i	−0.973291	+	0.229573i	$0.926267\pi$
$350$	1080.79	+	2609.27i	0.165060	+	0.398489i
$351$		0			0
$352$	1301.79	−	3142.80i	0.197118	−	0.475886i
$353$			4779.85i			0.720697i	0.932818	+	0.360348i	$0.117342\pi$
$353$			4779.85i			0.720697i	−0.932818	+	0.360348i	$0.882658\pi$
$354$		0			0
$355$	−4947.93	+	4947.93i	−0.739744	+	0.739744i
$356$	10.0124			0.00149060
$357$		0			0
$358$	1656.84			0.244599
$359$	−5121.94	+	5121.94i	−0.752996	+	0.752996i	−0.975037	−	0.222041i	$-0.928728\pi$
$359$	−5121.94	+	5121.94i	−0.752996	+	0.752996i	0.222041	+	0.975037i	$0.428728\pi$
$360$		0			0
$361$			4397.64i			0.641149i
$362$	−955.337	+	2306.39i	−0.138705	+	0.334865i
$363$		0			0
$364$	−473.643	−	1143.48i	−0.0682024	−	0.164655i
$365$	3389.24	+	3389.24i	0.486030	+	0.486030i
$366$		0			0
$367$	3541.57	+	8550.11i	0.503729	+	1.21611i	0.947438	+	0.319938i	$0.103662\pi$
$367$	3541.57	+	8550.11i	0.503729	+	1.21611i	−0.443710	+	0.896171i	$0.646338\pi$
$368$	5116.43	−	2119.30i	0.724762	−	0.300206i
$369$		0			0
$370$		−	3699.23i		−	0.519767i
$371$	−5254.82	−	2176.62i	−0.735355	−	0.304594i
$372$		0			0
$373$	7825.58			1.08631			0.543154	−	0.839633i	$-0.317230\pi$
$373$	7825.58			1.08631			0.543154	+	0.839633i	$0.317230\pi$
$374$	−853.070	+	3907.61i	−0.117944	+	0.540261i
$375$		0			0
$376$	5117.08	−	5117.08i	0.701843	−	0.701843i
$377$	−2061.98	−	854.101i	−0.281691	−	0.116680i
$378$		0			0
$379$	2984.35	−	7204.86i	0.404474	−	0.976488i	−0.582091	−	0.813123i	$-0.697765\pi$
$379$	2984.35	−	7204.86i	0.404474	−	0.976488i	0.986566	−	0.163364i	$-0.0522346\pi$
$380$	1295.84	−	536.753i	0.174934	−	0.0724601i
$381$		0			0
$382$	1222.45	+	1222.45i	0.163732	+	0.163732i
$383$	489.292	+	489.292i	0.0652785	+	0.0652785i	0.738992	−	0.673714i	$-0.235302\pi$
$383$	489.292	+	489.292i	0.0652785	+	0.0652785i	−0.673714	+	0.738992i	$0.735302\pi$
$384$		0			0
$385$	−6461.05	+	2676.25i	−0.855287	+	0.354271i
$386$	−2987.75	+	7213.06i	−0.393970	+	0.951127i
$387$		0			0
$388$	1018.40	+	421.837i	0.133252	+	0.0551946i
$389$	−7280.49	+	7280.49i	−0.948934	+	0.948934i	−0.998758	−	0.0498240i	$-0.984134\pi$
$389$	−7280.49	+	7280.49i	−0.948934	+	0.948934i	0.0498240	+	0.998758i	$0.484134\pi$
$390$		0			0
$391$	11138.6	−	7146.75i	1.44068	−	0.924364i
$392$	−13487.0			−1.73775
$393$		0			0
$394$	−8616.24	−	3568.96i	−1.10173	−	0.456350i
$395$			801.451i			0.102090i
$396$		0			0
$397$	−1062.97	+	440.297i	−0.134380	+	0.0556621i	−0.448860	−	0.893602i	$-0.648170\pi$
$397$	−1062.97	+	440.297i	−0.134380	+	0.0556621i	0.314480	+	0.949264i	$0.398170\pi$
$398$	−370.772	−	895.123i	−0.0466963	−	0.112735i
$399$		0			0
$400$	887.640	+	887.640i	0.110955	+	0.110955i
$401$	2719.60	+	6565.70i	0.338679	+	0.817645i	0.997843	+	0.0656449i	$0.0209105\pi$
$401$	2719.60	+	6565.70i	0.338679	+	0.817645i	−0.659164	+	0.752000i	$0.729090\pi$
$402$		0			0
$403$	1608.58	−	3883.45i	0.198831	−	0.480021i
$404$		−	681.792i		−	0.0839614i
$405$		0			0
$406$	−7836.39	+	7836.39i	−0.957915	+	0.957915i
$407$	−4769.14			−0.580829
$408$		0			0
$409$	−10098.3			−1.22085			−0.610427	−	0.792073i	$-0.709002\pi$
$409$	−10098.3			−1.22085			−0.610427	+	0.792073i	$0.709002\pi$
$410$	−1323.79	+	1323.79i	−0.159457	+	0.159457i
$411$		0			0
$412$			2623.11i			0.313668i
$413$	8664.78	−	20918.6i	1.03236	−	2.49235i
$414$		0			0
$415$	−3331.56	−	8043.09i	−0.394072	−	0.951373i
$416$	−1237.78	−	1237.78i	−0.145883	−	0.145883i
$417$		0			0
$418$	1083.36	+	2615.47i	0.126768	+	0.306045i
$419$	−4245.28	+	1758.45i	−0.494978	+	0.205026i	−0.616186	−	0.787601i	$-0.711323\pi$
$419$	−4245.28	+	1758.45i	−0.494978	+	0.205026i	0.121208	+	0.992627i	$0.461323\pi$
$420$		0			0
$421$		−	10693.5i		−	1.23793i	−0.785417	−	0.618967i	$-0.787552\pi$
$421$		−	10693.5i		−	1.23793i	0.785417	−	0.618967i	$-0.212448\pi$
$422$	−960.923	−	398.027i	−0.110846	−	0.0459139i
$423$		0			0
$424$	−4678.20			−0.535833
$425$	2462.87	+	1712.70i	0.281098	+	0.195478i
$426$		0			0
$427$	186.727	−	186.727i	0.0211625	−	0.0211625i
$428$	−774.811	−	320.937i	−0.0875044	−	0.0362455i
$429$		0			0
$430$	−2266.22	+	5471.14i	−0.254156	+	0.613586i
$431$	−1238.86	+	513.154i	−0.138455	+	0.0573498i	−0.450835	−	0.892607i	$-0.648874\pi$
$431$	−1238.86	+	513.154i	−0.138455	+	0.0573498i	0.312380	+	0.949957i	$0.398874\pi$
$432$		0			0
$433$	9262.54	+	9262.54i	1.02801	+	1.02801i	0.999596	+	0.0284155i	$0.00904616\pi$
$433$	9262.54	+	9262.54i	1.02801	+	1.02801i	0.0284155	+	0.999596i	$0.490954\pi$
$434$	−14758.7	−	14758.7i	−1.63235	−	1.63235i
$435$		0			0
$436$	1108.40	−	459.115i	0.121750	−	0.0504303i
$437$	3584.70	−	8654.23i	0.392401	−	0.947341i
$438$		0			0
$439$	10133.7	+	4197.51i	1.10172	+	0.456347i	0.858078	−	0.513519i	$-0.171658\pi$
$439$	10133.7	+	4197.51i	1.10172	+	0.456347i	0.243640	+	0.969866i	$0.421658\pi$
$440$	−4067.32	+	4067.32i	−0.440686	+	0.440686i
$441$		0			0
$442$	1689.75	+	1175.06i	0.181840	+	0.126453i
$443$	−5816.55			−0.623821			−0.311910	−	0.950112i	$-0.600969\pi$
$443$	−5816.55			−0.623821			−0.311910	+	0.950112i	$0.600969\pi$
$444$		0			0
$445$	−26.8959	−	11.1406i	−0.00286514	−	0.00118678i
$446$		−	4878.12i		−	0.517905i
$447$		0			0
$448$	−14505.1	+	6008.21i	−1.52969	+	0.633618i
$449$	−813.499	−	1963.96i	−0.0855042	−	0.206425i	0.875344	−	0.483501i	$-0.160635\pi$
$449$	−813.499	−	1963.96i	−0.0855042	−	0.206425i	−0.960848	+	0.277075i	$0.910635\pi$
$450$		0			0
$451$	1706.66	+	1706.66i	0.178189	+	0.178189i
$452$	1845.46	+	4455.34i	0.192043	+	0.463632i
$453$		0			0
$454$	437.918	−	1057.23i	0.0452698	−	0.109291i
$455$			3598.70i			0.370791i
$456$		0			0
$457$	12220.4	−	12220.4i	1.25086	−	1.25086i	0.295528	−	0.955334i	$-0.404505\pi$
$457$	12220.4	−	12220.4i	1.25086	−	1.25086i	0.955334	−	0.295528i	$-0.0954955\pi$
$458$	5341.43			0.544953
$459$		0			0
$460$	5337.93			0.541048
$461$	−3337.05	+	3337.05i	−0.337141	+	0.337141i	−0.855290	−	0.518149i	$-0.826621\pi$
$461$	−3337.05	+	3337.05i	−0.337141	+	0.337141i	0.518149	+	0.855290i	$0.326621\pi$
$462$		0			0
$463$			4035.00i			0.405016i	0.979281	+	0.202508i	$0.0649092\pi$
$463$			4035.00i			0.405016i	−0.979281	+	0.202508i	$0.935091\pi$
$464$	−1885.03	+	4550.87i	−0.188600	+	0.455321i
$465$		0			0
$466$	5301.24	+	12798.3i	0.526985	+	1.27226i
$467$	−7000.76	−	7000.76i	−0.693697	−	0.693697i	0.269347	−	0.963043i	$-0.413192\pi$
$467$	−7000.76	−	7000.76i	−0.693697	−	0.693697i	−0.963043	+	0.269347i	$0.913192\pi$
$468$		0			0
$469$	7266.71	+	17543.4i	0.715449	+	1.72725i
$470$	−5452.02	+	2258.30i	−0.535070	+	0.221633i
$471$		0			0
$472$		−	18623.2i		−	1.81610i
$473$	7053.53	+	2921.67i	0.685670	+	0.284014i
$474$		0			0
$475$	2123.31			0.205103
$476$	−5494.16	+	3525.15i	−0.529043	+	0.339444i
$477$		0			0
$478$	−2461.55	+	2461.55i	−0.235541	+	0.235541i
$479$	−7404.19	−	3066.92i	−0.706276	−	0.292549i	0.000486879	−	1.00000i	$-0.499845\pi$
$479$	−7404.19	−	3066.92i	−0.706276	−	0.292549i	−0.706762	+	0.707451i	$0.749845\pi$
$480$		0			0
$481$	−939.156	+	2267.32i	−0.0890267	+	0.214929i
$482$	−2962.28	+	1227.01i	−0.279934	+	0.115952i
$483$		0			0
$484$	−1464.09	−	1464.09i	−0.137499	−	0.137499i
$485$	−2266.33	−	2266.33i	−0.212183	−	0.212183i
$486$		0			0
$487$	1413.06	−	585.310i	0.131483	−	0.0544618i	−0.315972	−	0.948768i	$-0.602331\pi$
$487$	1413.06	−	585.310i	0.131483	−	0.0544618i	0.447455	+	0.894307i	$0.352331\pi$
$488$	83.1186	−	200.666i	0.00771025	−	0.0186142i
$489$		0			0
$490$	10161.0	+	4208.84i	0.936793	+	0.388032i
$491$	−12007.8	+	12007.8i	−1.10368	+	1.10368i	−0.109712	+	0.993963i	$0.534993\pi$
$491$	−12007.8	+	12007.8i	−1.10368	+	1.10368i	−0.993963	+	0.109712i	$0.965007\pi$
$492$		0			0
$493$	−2510.67	+	11500.5i	−0.229361	+	1.05062i
$494$	1456.78			0.132679
$495$		0			0
$496$	−8570.92	−	3550.19i	−0.775899	−	0.321388i
$497$		−	23050.8i		−	2.08043i
$498$		0			0
$499$	−6868.39	+	2844.98i	−0.616175	+	0.255228i	−0.668866	−	0.743383i	$-0.733220\pi$
$499$	−6868.39	+	2844.98i	−0.616175	+	0.255228i	0.0526910	+	0.998611i	$0.483220\pi$
$500$	1815.41	+	4382.78i	0.162375	+	0.392008i
$501$		0			0
$502$	−2747.00	−	2747.00i	−0.244232	−	0.244232i
$503$	805.118	+	1943.73i	0.0713687	+	0.172299i	0.955538	−	0.294866i	$-0.0952752\pi$
$503$	805.118	+	1943.73i	0.0713687	+	0.172299i	−0.884170	+	0.467166i	$0.845275\pi$
$504$		0			0
$505$	−758.622	+	1831.47i	−0.0668480	+	0.161385i
$506$			10773.9i			0.946558i
$507$		0			0
$508$	−1313.22	+	1313.22i	−0.114694	+	0.114694i
$509$	18436.6			1.60547			0.802737	−	0.596333i	$-0.203376\pi$
$509$	18436.6			1.60547			0.802737	+	0.596333i	$0.203376\pi$
$510$		0			0
$511$	−15789.4			−1.36689
$512$	−6807.76	+	6807.76i	−0.587623	+	0.587623i
$513$		0			0
$514$		−	8736.79i		−	0.749734i
$515$	2918.70	−	7046.37i	0.249735	−	0.602913i
$516$		0			0
$517$	2911.46	+	7028.88i	0.247671	+	0.597930i
$518$	8616.77	+	8616.77i	0.730886	+	0.730886i
$519$		0			0
$520$	1132.72	+	2734.62i	0.0955248	+	0.230617i
$521$	11134.4	−	4612.01i	0.936288	−	0.387823i	0.138228	−	0.990400i	$-0.455859\pi$
$521$	11134.4	−	4612.01i	0.936288	−	0.387823i	0.798061	+	0.602577i	$0.205859\pi$
$522$		0			0
$523$		−	15689.4i		−	1.31175i	−0.754868	−	0.655877i	$-0.772299\pi$
$523$		−	15689.4i		−	1.31175i	0.754868	−	0.655877i	$-0.227701\pi$
$524$	2591.25	+	1073.33i	0.216029	+	0.0894822i
$525$		0			0
$526$	−580.579			−0.0481263
$527$	−21659.5	−	4728.50i	−1.79033	−	0.390847i
$528$		0			0
$529$	16604.5	−	16604.5i	1.36472	−	1.36472i
$530$	3524.51	+	1459.90i	0.288859	+	0.119649i
$531$		0			0
$532$	−1768.16	+	4268.72i	−0.144097	+	0.347881i
$533$	1147.45	−	475.291i	0.0932491	−	0.0386250i
$534$		0			0
$535$	1724.25	+	1724.25i	0.139338	+	0.139338i
$536$	11043.8	+	11043.8i	0.889963	+	0.889963i
$537$		0			0
$538$	1699.37	−	703.903i	0.136181	−	0.0564079i
$539$	5426.13	−	13099.8i	0.433618	−	1.04685i
$540$		0			0
$541$	5014.78	+	2077.19i	0.398525	+	0.165075i	0.572939	−	0.819598i	$-0.305803\pi$
$541$	5014.78	+	2077.19i	0.398525	+	0.165075i	−0.174414	+	0.984672i	$0.555803\pi$
$542$	12858.5	−	12858.5i	1.01904	−	1.01904i
$543$		0			0
$544$	−5271.07	+	7579.83i	−0.415432	+	0.597394i
$545$	−3488.32			−0.274171
$546$		0			0
$547$	−22776.0	−	9434.12i	−1.78031	−	0.737430i	−0.992606	−	0.121379i	$-0.961268\pi$
$547$	−22776.0	−	9434.12i	−1.78031	−	0.737430i	−0.787706	−	0.616051i	$-0.788732\pi$
$548$			5323.59i			0.414987i
$549$		0			0
$550$	−2256.26	+	934.572i	−0.174922	+	0.0724551i
$551$	3188.45	+	7697.61i	0.246520	+	0.595153i
$552$		0			0
$553$	−1866.85	−	1866.85i	−0.143556	−	0.143556i
$554$	4634.80	+	11189.4i	0.355440	+	0.858108i
$555$		0			0
$556$	2960.45	−	7147.16i	0.225811	−	0.545157i
$557$			1284.08i			0.0976810i	0.998807	+	0.0488405i	$0.0155526\pi$
$557$			1284.08i			0.0976810i	−0.998807	+	0.0488405i	$0.984447\pi$
$558$		0			0
$559$	2778.02	−	2778.02i	0.210192	−	0.210192i
$560$	7942.47			0.599340
$561$		0			0
$562$	13587.4			1.01984
$563$	14548.5	−	14548.5i	1.08907	−	1.08907i	0.0934455	−	0.995624i	$-0.470212\pi$
$563$	14548.5	−	14548.5i	1.08907	−	1.08907i	0.995624	−	0.0934455i	$-0.0297881\pi$
$564$		0			0
$565$		−	14021.7i		−	1.04406i
$566$	−3972.83	+	9591.27i	−0.295036	+	0.712281i
$567$		0			0
$568$	−7255.42	−	17516.1i	−0.535969	−	1.29394i
$569$	−15335.4	−	15335.4i	−1.12987	−	1.12987i	−0.990198	−	0.139667i	$-0.955397\pi$
$569$	−15335.4	−	15335.4i	−1.12987	−	1.12987i	−0.139667	−	0.990198i	$-0.544603\pi$
$570$		0			0
$571$	1076.74	+	2599.48i	0.0789145	+	0.190517i	0.958413	−	0.285386i	$-0.0921217\pi$
$571$	1076.74	+	2599.48i	0.0789145	+	0.190517i	−0.879498	+	0.475902i	$0.842122\pi$
$572$	988.773	−	409.563i	0.0722774	−	0.0299383i
$573$		0			0
$574$		−	6167.10i		−	0.448449i
$575$	7465.63	+	3092.37i	0.541458	+	0.224279i
$576$		0			0
$577$	−21684.6			−1.56454			−0.782272	−	0.622937i	$-0.785939\pi$
$577$	−21684.6			−1.56454			−0.782272	+	0.622937i	$0.785939\pi$
$578$	4523.97	−	9867.52i	0.325558	−	0.710095i
$579$		0			0
$580$	−3357.26	+	3357.26i	−0.240350	+	0.240350i
$581$	26495.4	+	10974.8i	1.89194	+	0.783666i
$582$		0			0
$583$	1882.14	−	4543.89i	0.133705	−	0.322794i
$584$	−11998.2	+	4969.82i	−0.850153	+	0.352145i
$585$		0			0
$586$	12451.1	+	12451.1i	0.877729	+	0.877729i
$587$	11424.4	+	11424.4i	0.803299	+	0.803299i	0.983610	−	0.180310i	$-0.0577102\pi$
$587$	11424.4	+	11424.4i	0.803299	+	0.803299i	−0.180310	+	0.983610i	$0.557710\pi$
$588$		0			0
$589$	−14497.3	+	6005.00i	−1.01418	+	0.420088i
$590$	−5811.64	+	14030.5i	−0.405528	+	0.979031i
$591$		0			0
$592$	5004.07	+	2072.75i	0.347409	+	0.143901i
$593$	−7362.68	+	7362.68i	−0.509863	+	0.509863i	−0.914484	−	0.404621i	$-0.867403\pi$
$593$	−7362.68	+	7362.68i	−0.509863	+	0.509863i	0.404621	+	0.914484i	$0.367403\pi$
$594$		0			0
$595$	18681.2	−	3356.22i	1.28715	−	0.231246i
$596$	8876.74			0.610076
$597$		0			0
$598$	5122.08	+	2121.64i	0.350264	+	0.145084i
$599$			2035.36i			0.138836i	0.997588	+	0.0694179i	$0.0221142\pi$
$599$			2035.36i			0.138836i	−0.997588	+	0.0694179i	$0.977886\pi$
$600$		0			0
$601$	392.473	−	162.567i	0.0266378	−	0.0110337i	−0.369325	−	0.929300i	$-0.620411\pi$
$601$	392.473	−	162.567i	0.0266378	−	0.0110337i	0.395963	+	0.918267i	$0.370411\pi$
$602$	−7465.35	−	18023.0i	−0.505424	−	1.22020i
$603$		0			0
$604$	4277.90	+	4277.90i	0.288188	+	0.288188i
$605$	2303.87	+	5562.03i	0.154819	+	0.373767i
$606$		0			0
$607$	−4784.94	+	11551.9i	−0.319958	+	0.772448i	0.679297	+	0.733863i	$0.262285\pi$
$607$	−4784.94	+	11551.9i	−0.319958	+	0.772448i	−0.999255	+	0.0385842i	$0.987715\pi$
$608$			6534.77i			0.435888i
$609$		0			0
$610$	−125.242	+	125.242i	−0.00831293	+	0.00831293i
$611$	3914.98			0.259219
$612$		0			0
$613$	−18239.5			−1.20177			−0.600886	−	0.799335i	$-0.705185\pi$
$613$	−18239.5			−1.20177			−0.600886	+	0.799335i	$0.705185\pi$
$614$	6632.31	−	6632.31i	0.435925	−	0.435925i
$615$		0			0
$616$		−	18948.3i		−	1.23937i
$617$	3719.17	−	8978.87i	0.242671	−	0.585860i	−0.754875	−	0.655869i	$-0.772303\pi$
$617$	3719.17	−	8978.87i	0.242671	−	0.585860i	0.997546	+	0.0700082i	$0.0223025\pi$
$618$		0			0
$619$	6998.55	+	16896.0i	0.454435	+	1.09710i	0.970618	+	0.240625i	$0.0773525\pi$
$619$	6998.55	+	16896.0i	0.454435	+	1.09710i	−0.516183	+	0.856478i	$0.672648\pi$
$620$	−6322.93	−	6322.93i	−0.409572	−	0.409572i
$621$		0			0
$622$	7230.38	+	17455.7i	0.466096	+	1.12526i
$623$	88.6000	−	36.6993i	0.00569773	−	0.00236008i
$624$		0			0
$625$		−	8443.54i		−	0.540386i
$626$	17282.9	+	7158.82i	1.10346	+	0.457067i
$627$		0			0
$628$	6059.45			0.385029
$629$	12645.8	+	2760.70i	0.801621	+	0.175002i
$630$		0			0
$631$	−14686.9	+	14686.9i	−0.926587	+	0.926587i	−0.997484	−	0.0708967i	$-0.977414\pi$
$631$	−14686.9	+	14686.9i	−0.926587	+	0.926587i	0.0708967	+	0.997484i	$0.477414\pi$
$632$	−2006.21	−	830.998i	−0.126270	−	0.0523028i
$633$		0			0
$634$	−3516.55	+	8489.71i	−0.220284	+	0.531813i
$635$	4988.85	−	2066.45i	0.311774	−	0.129141i
$636$		0			0
$637$	−5159.34	−	5159.34i	−0.320911	−	0.320911i
$638$	−6776.19	−	6776.19i	−0.420489	−	0.420489i
$639$		0			0
$640$	902.341	−	373.762i	0.0557315	−	0.0230848i
$641$	170.059	−	410.558i	0.0104788	−	0.0252981i	−0.918554	−	0.395297i	$-0.870642\pi$
$641$	170.059	−	410.558i	0.0104788	−	0.0252981i	0.929032	+	0.369999i	$0.120642\pi$
$642$		0			0
$643$	10473.8	+	4338.37i	0.642371	+	0.266079i	0.679999	−	0.733213i	$-0.261980\pi$
$643$	10473.8	+	4338.37i	0.642371	+	0.266079i	−0.0376280	+	0.999292i	$0.511980\pi$
$644$	−12433.9	+	12433.9i	−0.760811	+	0.760811i
$645$		0			0
$646$	−1358.62	−	7562.26i	−0.0827462	−	0.460578i
$647$	−1852.56			−0.112568			−0.0562842	−	0.998415i	$-0.517925\pi$
$647$	−1852.56			−0.112568			−0.0562842	+	0.998415i	$0.517925\pi$
$648$		0			0
$649$	18088.5	+	7492.51i	1.09405	+	0.453169i
$650$			1256.70i			0.0758336i
$651$		0			0
$652$	−11254.4	+	4661.72i	−0.676006	+	0.280011i
$653$	6136.54	+	14814.9i	0.367751	+	0.887829i	0.994118	+	0.108301i	$0.0345411\pi$
$653$	6136.54	+	14814.9i	0.367751	+	0.887829i	−0.626367	+	0.779528i	$0.715459\pi$
$654$		0			0
$655$	−5766.51	−	5766.51i	−0.343994	−	0.343994i
$656$	−1048.99	−	2532.47i	−0.0624329	−	0.150726i
$657$		0			0
$658$	7439.26	−	17960.0i	0.440749	−	1.06406i
$659$		−	24037.4i		−	1.42088i	−0.703755	−	0.710442i	$-0.748495\pi$
$659$		−	24037.4i		−	1.42088i	0.703755	−	0.710442i	$-0.251505\pi$
$660$		0			0
$661$	−14426.9	+	14426.9i	−0.848928	+	0.848928i	−0.989999	−	0.141072i	$-0.954945\pi$
$661$	−14426.9	+	14426.9i	−0.848928	+	0.848928i	0.141072	+	0.989999i	$0.454945\pi$
$662$	−12003.5			−0.704725
$663$		0			0
$664$	23588.0			1.37860
$665$	9499.52	−	9499.52i	0.553948	−	0.553948i
$666$		0			0
$667$			31708.7i			1.84073i
$668$	4744.75	−	11454.8i	0.274820	−	0.663475i
$669$		0			0
$670$	−4873.93	−	11766.7i	−0.281039	−	0.678488i
$671$	161.465	+	161.465i	0.00928953	+	0.00928953i
$672$		0			0
$673$	−3166.73	−	7645.17i	−0.181380	−	0.437889i	0.806872	−	0.590727i	$-0.201159\pi$
$673$	−3166.73	−	7645.17i	−0.181380	−	0.437889i	−0.988251	+	0.152837i	$0.951159\pi$
$674$	−11129.2	+	4609.87i	−0.636026	+	0.263451i
$675$		0			0
$676$			6300.00i			0.358443i
$677$	726.206	+	300.805i	0.0412266	+	0.0170766i	0.403201	−	0.915111i	$-0.367897\pi$
$677$	726.206	+	300.805i	0.0412266	+	0.0170766i	−0.361975	+	0.932188i	$0.617897\pi$
$678$		0			0
$679$	10558.1			0.596736
$680$	13139.3	−	8430.39i	0.740982	−	0.475428i
$681$		0			0
$682$	12762.0	−	12762.0i	0.716542	−	0.716542i
$683$	8241.86	+	3413.89i	0.461736	+	0.191257i	0.601411	−	0.798940i	$-0.294606\pi$
$683$	8241.86	+	3413.89i	0.461736	+	0.191257i	−0.139674	+	0.990197i	$0.544606\pi$
$684$		0			0
$685$	5923.50	−	14300.6i	0.330402	−	0.797661i
$686$	−12560.7	+	5202.82i	−0.699082	+	0.289569i
$687$		0			0
$688$	−6131.18	−	6131.18i	−0.339752	−	0.339752i
$689$	−1789.60	−	1789.60i	−0.0989525	−	0.0989525i
$690$		0			0
$691$	17252.9	−	7146.40i	0.949830	−	0.393432i	0.146663	−	0.989187i	$-0.453147\pi$
$691$	17252.9	−	7146.40i	0.949830	−	0.393432i	0.803167	+	0.595754i	$0.203147\pi$
$692$	1909.50	−	4609.94i	0.104896	−	0.253242i
$693$		0			0
$694$	−23299.1	−	9650.79i	−1.27438	−	0.527866i
$695$	−15905.1	+	15905.1i	−0.868080	+	0.868080i
$696$		0			0
$697$	−3537.42	−	5513.28i	−0.192237	−	0.299613i
$698$	−15151.3			−0.821614
$699$		0			0
$700$	−3682.44	−	1525.32i	−0.198833	−	0.0823595i
$701$			30519.4i			1.64437i	0.569222	+	0.822184i	$0.307245\pi$
$701$			30519.4i			1.64437i	−0.569222	+	0.822184i	$0.692755\pi$
$702$		0			0
$703$	8464.17	−	3505.97i	0.454100	−	0.188094i
$704$	−5195.35	−	12542.7i	−0.278135	−	0.671477i
$705$		0			0
$706$	7467.73	+	7467.73i	0.398090	+	0.398090i
$707$	−2499.04	−	6033.22i	−0.132936	−	0.320937i
$708$		0			0
$709$	−1122.42	+	2709.75i	−0.0594545	+	0.143536i	−0.950815	−	0.309759i	$-0.899752\pi$
$709$	−1122.42	+	2709.75i	−0.0594545	+	0.143536i	0.891361	+	0.453295i	$0.149752\pi$
$710$			15460.7i			0.817223i
$711$		0			0
$712$	55.7749	−	55.7749i	0.00293575	−	0.00293575i
$713$	−59718.8			−3.13673
$714$		0			0
$715$	−3111.83			−0.162763
$716$	−1653.42	+	1653.42i	−0.0863003	+	0.0863003i
$717$		0			0
$718$			16004.4i			0.831863i
$719$	6221.44	−	15019.9i	0.322699	−	0.779064i	−0.676397	−	0.736538i	$-0.736459\pi$
$719$	6221.44	−	15019.9i	0.322699	−	0.779064i	0.999095	−	0.0425261i	$-0.0135406\pi$
$720$		0			0
$721$	9614.75	+	23212.1i	0.496632	+	1.19898i
$722$	6870.59	+	6870.59i	0.354151	+	0.354151i
$723$		0			0
$724$	−1348.26	−	3254.99i	−0.0692095	−	0.167087i
$725$	−6640.40	+	2750.54i	−0.340163	+	0.140900i
$726$		0			0
$727$			36661.3i			1.87028i	0.354282	+	0.935138i	$0.384725\pi$
$727$			36661.3i			1.87028i	−0.354282	+	0.935138i	$0.615275\pi$
$728$	−9008.34	−	3731.38i	−0.458615	−	0.189964i
$729$		0			0
$730$	10590.3			0.536936
$731$	−17011.8	−	11830.1i	−0.860742	−	0.598567i
$732$		0			0
$733$	15483.7	−	15483.7i	0.780222	−	0.780222i	−0.199646	−	0.979868i	$-0.563979\pi$
$733$	15483.7	−	15483.7i	0.780222	−	0.780222i	0.979868	+	0.199646i	$0.0639792\pi$
$734$	18891.3	+	7825.01i	0.949985	+	0.393497i
$735$		0			0
$736$	−9517.18	+	22976.5i	−0.476641	+	1.15071i
$737$	−15169.9	+	6283.58i	−0.758197	+	0.314055i
$738$		0			0
$739$	−5331.30	−	5331.30i	−0.265379	−	0.265379i	0.561856	−	0.827235i	$-0.310087\pi$
$739$	−5331.30	−	5331.30i	−0.265379	−	0.265379i	−0.827235	+	0.561856i	$0.810087\pi$
$740$	3691.59	+	3691.59i	0.183386	+	0.183386i
$741$		0			0
$742$	−11610.4	+	4809.19i	−0.574436	+	0.237939i
$743$	−7333.49	+	17704.6i	−0.362099	+	0.874184i	0.632894	+	0.774238i	$0.281867\pi$
$743$	−7333.49	+	17704.6i	−0.362099	+	0.874184i	−0.994993	+	0.0999456i	$0.968133\pi$
$744$		0			0
$745$	−23845.3	−	9877.05i	−1.17265	−	0.485728i
$746$	12226.2	−	12226.2i	0.600043	−	0.600043i
$747$		0			0
$748$	−3048.23	−	4750.85i	−0.149003	−	0.232230i
$749$	−8032.71			−0.391868
$750$		0			0
$751$	−19531.2	−	8090.10i	−0.949008	−	0.393092i	−0.146150	−	0.989262i	$-0.546688\pi$
$751$	−19531.2	−	8090.10i	−0.949008	−	0.393092i	−0.802858	+	0.596170i	$0.796688\pi$
$752$		−	8640.50i		−	0.418998i
$753$		0			0
$754$	−4555.90	+	1887.12i	−0.220048	+	0.0911468i
$755$	−6731.62	−	16251.6i	−0.324488	−	0.783385i
$756$		0			0
$757$	−17294.1	−	17294.1i	−0.830335	−	0.830335i	0.157227	−	0.987562i	$-0.449745\pi$
$757$	−17294.1	−	17294.1i	−0.830335	−	0.830335i	−0.987562	+	0.157227i	$0.949745\pi$
$758$	−6593.85	−	15919.0i	−0.315962	−	0.762800i
$759$		0			0
$760$	4228.56	−	10208.6i	0.201823	−	0.487245i
$761$		−	12212.8i		−	0.581753i	−0.956761	−	0.290876i	$-0.906053\pi$
$761$		−	12212.8i		−	0.581753i	0.956761	−	0.290876i	$-0.0939468\pi$
$762$		0			0
$763$	8125.48	−	8125.48i	0.385534	−	0.385534i
$764$	−2439.85			−0.115537
$765$		0			0
$766$	1528.88			0.0721156
$767$	7124.11	−	7124.11i	0.335380	−	0.335380i
$768$		0			0
$769$			8061.22i			0.378017i	0.981975	+	0.189009i	$0.0605274\pi$
$769$			8061.22i			0.378017i	−0.981975	+	0.189009i	$0.939473\pi$
$770$	−5913.11	+	14275.5i	−0.276745	+	0.668122i
$771$		0			0
$772$	−4216.59	−	10179.7i	−0.196578	−	0.474582i
$773$	−23202.2	−	23202.2i	−1.07959	−	1.07959i	−0.996546	−	0.0830468i	$-0.973535\pi$
$773$	−23202.2	−	23202.2i	−1.07959	−	1.07959i	−0.0830468	−	0.996546i	$-0.526465\pi$
$774$		0			0
$775$	−5180.26	−	12506.2i	−0.240104	−	0.579661i
$776$	8023.02	−	3323.24i	0.371147	−	0.153734i
$777$		0			0
$778$			22749.1i			1.04832i
$779$	−4283.57	−	1774.31i	−0.197015	−	0.0816064i
$780$		0			0
$781$	19932.3			0.913230
$782$	6236.66	−	28567.9i	0.285195	−	1.30638i
$783$		0			0
$784$	−11386.9	+	11386.9i	−0.518716	+	0.518716i
$785$	−16277.3	−	6742.29i	−0.740079	−	0.306551i
$786$		0			0
$787$	12029.4	−	29041.6i	0.544857	−	1.31540i	−0.376403	−	0.926456i	$-0.622839\pi$
$787$	12029.4	−	29041.6i	0.544857	−	1.31540i	0.921260	−	0.388946i	$-0.127161\pi$
$788$	12160.0	−	5036.85i	0.549725	−	0.227704i
$789$		0			0
$790$	1252.13	+	1252.13i	0.0563911	+	0.0563911i
$791$	32661.3	+	32661.3i	1.46814	+	1.46814i
$792$		0			0
$793$	108.559	−	44.9666i	0.00486134	−	0.00201364i
$794$	−972.825	+	2348.61i	−0.0434814	+	0.104973i
$795$		0			0
$796$	1263.28	+	523.268i	0.0562510	+	0.0232999i
$797$	−6105.00	+	6105.00i	−0.271330	+	0.271330i	−0.829636	−	0.558305i	$-0.811452\pi$
$797$	−6105.00	+	6105.00i	−0.271330	+	0.271330i	0.558305	+	0.829636i	$0.311452\pi$
$798$		0			0
$799$	−3651.18	−	20323.0i	−0.161664	−	0.899845i
$800$	−5637.27			−0.249134
$801$		0			0
$802$	14506.8	+	6008.89i	0.638717	+	0.264565i
$803$		−	13653.2i		−	0.600014i
$804$		0			0
$805$	47235.7	−	19565.7i	2.06812	−	0.856645i
$806$	−3554.11	−	8580.39i	−0.155320	−	0.374977i
$807$		0			0
$808$	−3797.99	−	3797.99i	−0.165363	−	0.165363i
$809$	2705.33	+	6531.24i	0.117570	+	0.283840i	0.971699	−	0.236222i	$-0.0759091\pi$
$809$	2705.33	+	6531.24i	0.117570	+	0.283840i	−0.854129	+	0.520061i	$0.825909\pi$
$810$		0			0
$811$	−3353.97	+	8097.20i	−0.145220	+	0.350593i	−0.979707	−	0.200435i	$-0.935764\pi$
$811$	−3353.97	+	8097.20i	−0.145220	+	0.350593i	0.834487	+	0.551028i	$0.185764\pi$
$812$		−	15640.4i		−	0.675950i
$813$		0			0
$814$	−7450.99	+	7450.99i	−0.320832	+	0.320832i
$815$	35419.4			1.52231
$816$		0			0
$817$	−14666.3			−0.628040
$818$	−15776.9	+	15776.9i	−0.674362	+	0.674362i
$819$		0			0
$820$		−	2642.11i		−	0.112520i
$821$	−6434.33	+	15533.8i	−0.273520	+	0.660335i	−0.999629	−	0.0272448i	$-0.991327\pi$
$821$	−6434.33	+	15533.8i	−0.273520	+	0.660335i	0.726109	+	0.687579i	$0.241327\pi$
$822$		0			0
$823$	−3513.88	−	8483.26i	−0.148829	−	0.359305i	0.831830	−	0.555031i	$-0.187294\pi$
$823$	−3513.88	−	8483.26i	−0.148829	−	0.359305i	−0.980659	+	0.195726i	$0.937294\pi$
$824$	14612.3	+	14612.3i	0.617772	+	0.617772i
$825$		0			0
$826$	−19144.6	−	46219.2i	−0.806449	−	1.94694i
$827$	−11800.4	+	4887.90i	−0.496181	+	0.205525i	−0.616718	−	0.787184i	$-0.711538\pi$
$827$	−11800.4	+	4887.90i	−0.496181	+	0.205525i	0.120537	+	0.992709i	$0.461538\pi$
$828$		0			0
$829$		−	2354.91i		−	0.0986604i	−0.998783	−	0.0493302i	$-0.984291\pi$
$829$		−	2354.91i		−	0.0986604i	0.998783	−	0.0493302i	$-0.0157087\pi$
$830$	−17771.0	−	7360.99i	−0.743181	−	0.307836i
$831$		0			0
$832$	−6986.07			−0.291104
$833$	−21970.9	+	31594.3i	−0.913862	+	1.31414i
$834$		0			0
$835$	−25491.4	+	25491.4i	−1.05648	+	1.05648i
$836$	−3691.20	−	1528.94i	−0.152707	−	0.0632532i
$837$		0			0
$838$	−3885.26	+	9379.85i	−0.160160	+	0.386660i
$839$	−27813.1	+	11520.6i	−1.14448	+	0.474057i	−0.872678	−	0.488297i	$-0.837618\pi$
$839$	−27813.1	+	11520.6i	−1.14448	+	0.474057i	−0.271798	+	0.962354i	$0.587618\pi$
$840$		0			0
$841$	−2697.40	−	2697.40i	−0.110599	−	0.110599i
$842$	−16706.9	−	16706.9i	−0.683796	−	0.683796i
$843$		0			0
$844$	1356.14	−	561.734i	0.0553086	−	0.0229096i
$845$	7009.93	−	16923.5i	0.285384	−	0.688977i
$846$		0			0
$847$	−18322.4	−	7589.37i	−0.743287	−	0.307879i
$848$	−3949.71	+	3949.71i	−0.159945	+	0.159945i
$849$		0			0
$850$	6523.64	−	1172.02i	0.263246	−	0.0472941i
$851$	34866.4			1.40447
$852$		0			0
$853$	22839.8	+	9460.55i	0.916787	+	0.379745i	0.790651	−	0.612267i	$-0.209742\pi$
$853$	22839.8	+	9460.55i	0.916787	+	0.379745i	0.126136	+	0.992013i	$0.459742\pi$
$854$		−	583.461i		−	0.0233790i
$855$		0			0
$856$	−6103.98	+	2528.35i	−0.243727	+	0.100955i
$857$	14418.5	+	34809.3i	0.574709	+	1.38747i	0.897506	+	0.441002i	$0.145377\pi$
$857$	14418.5	+	34809.3i	0.574709	+	1.38747i	−0.322797	+	0.946468i	$0.604623\pi$
$858$		0			0
$859$	898.007	+	898.007i	0.0356689	+	0.0356689i	0.724716	−	0.689047i	$-0.241971\pi$
$859$	898.007	+	898.007i	0.0356689	+	0.0356689i	−0.689047	+	0.724716i	$0.741971\pi$
$860$	−3198.30	−	7721.39i	−0.126815	−	0.306160i
$861$		0			0
$862$	−1133.80	+	2737.24i	−0.0447998	+	0.108156i
$863$			39149.8i			1.54423i	0.635480	+	0.772117i	$0.280802\pi$
$863$			39149.8i			1.54423i	−0.635480	+	0.772117i	$0.719198\pi$
$864$		0			0
$865$	−10258.9	+	10258.9i	−0.403250	+	0.403250i
$866$	28942.4			1.13568
$867$		0			0
$868$	29456.5			1.15186
$869$	1614.28	−	1614.28i	0.0630158	−	0.0630158i
$870$		0			0
$871$			8449.41i			0.328699i
$872$	3616.92	−	8732.03i	0.140464	−	0.339110i
$873$		0			0
$874$	−7920.30	−	19121.3i	−0.306531	−	0.740032i
$875$	32129.3	+	32129.3i	1.24134	+	1.24134i
$876$		0			0
$877$	5512.36	+	13308.0i	0.212245	+	0.512406i	0.993768	−	0.111472i	$-0.0355564\pi$
$877$	5512.36	+	13308.0i	0.212245	+	0.512406i	−0.781522	+	0.623877i	$0.785556\pi$
$878$	22390.1	−	9274.29i	0.860626	−	0.356483i
$879$		0			0
$880$			6867.92i			0.263088i
$881$	11269.0	+	4667.78i	0.430945	+	0.178503i	0.587603	−	0.809150i	$-0.300072\pi$
$881$	11269.0	+	4667.78i	0.430945	+	0.178503i	−0.156657	+	0.987653i	$0.550072\pi$
$882$		0			0
$883$	6659.37			0.253800			0.126900	−	0.991915i	$-0.459497\pi$
$883$	6659.37			0.253800			0.126900	+	0.991915i	$0.459497\pi$
$884$	−2858.90	+	513.622i	−0.108773	+	0.0195418i
$885$		0			0
$886$	−9087.40	+	9087.40i	−0.344579	+	0.344579i
$887$	−29891.2	−	12381.3i	−1.13151	−	0.468686i	−0.263215	−	0.964737i	$-0.584783\pi$
$887$	−29891.2	−	12381.3i	−1.13151	−	0.468686i	−0.868293	+	0.496051i	$0.834783\pi$
$888$		0			0
$889$	−6807.27	+	16434.2i	−0.256815	+	0.620006i
$890$	−59.4258	+	24.6150i	−0.00223815	+	0.000927073i
$891$		0			0
$892$	4868.04	+	4868.04i	0.182729	+	0.182729i
$893$	−10334.4	−	10334.4i	−0.387264	−	0.387264i
$894$		0			0
$895$	6281.25	−	2601.78i	0.234591	−	0.0971709i
$896$	−1231.24	+	2972.48i	−0.0459072	+	0.110830i
$897$		0			0
$898$	−4339.32	−	1797.41i	−0.161253	−	0.0667931i
$899$	37559.9	−	37559.9i	1.39343	−	1.39343i
$900$		0			0
$901$	−7620.96	+	10959.0i	−0.281788	+	0.405213i
$902$	5332.75			0.196853
$903$		0			0
$904$	35099.3	+	14538.6i	1.29136	+	0.534898i
$905$			10244.0i			0.376266i
$906$		0			0
$907$	33509.7	−	13880.2i	1.22676	−	0.508140i	0.327207	−	0.944953i	$-0.393893\pi$
$907$	33509.7	−	13880.2i	1.22676	−	0.508140i	0.899553	+	0.436813i	$0.143893\pi$
$908$	618.031	+	1492.06i	0.0225882	+	0.0545327i
$909$		0			0
$910$	5622.38	+	5622.38i	0.204813	+	0.204813i
$911$	7178.63	+	17330.7i	0.261074	+	0.630289i	0.999006	−	0.0445871i	$-0.0141972\pi$
$911$	7178.63	+	17330.7i	0.261074	+	0.630289i	−0.737931	+	0.674876i	$0.764197\pi$
$912$		0			0
$913$	−9489.97	+	22910.8i	−0.344000	+	0.830490i
$914$		−	38184.6i		−	1.38187i
$915$		0			0
$916$	−5330.40	+	5330.40i	−0.192272	+	0.192272i
$917$	26864.3			0.967435
$918$		0			0
$919$	11376.0			0.408333			0.204167	−	0.978936i	$-0.434552\pi$
$919$	11376.0			0.408333			0.204167	+	0.978936i	$0.434552\pi$
$920$	29735.5	−	29735.5i	1.06560	−	1.06560i
$921$		0			0
$922$			10427.2i			0.372452i
$923$	3925.13	−	9476.11i	0.139975	−	0.337931i
$924$		0			0
$925$	3024.45	+	7301.68i	0.107506	+	0.259543i
$926$	6304.02	+	6304.02i	0.223718	+	0.223718i
$927$		0			0
$928$	−8465.17	−	20436.7i	−0.299443	−	0.722919i
$929$	41908.4	−	17359.0i	1.48005	−	0.613059i	0.510928	−	0.859623i	$-0.329302\pi$
$929$	41908.4	−	17359.0i	1.48005	−	0.613059i	0.969126	+	0.246565i	$0.0793018\pi$
$930$		0			0
$931$			27238.3i			0.958860i
$932$	−18062.2	−	7481.61i	−0.634814	−	0.262949i
$933$		0			0
$934$	−21875.0			−0.766353
$935$	2902.15	+	16153.8i	0.101508	+	0.565011i
$936$		0			0
$937$	16226.8	−	16226.8i	0.565747	−	0.565747i	−0.365187	−	0.930934i	$-0.618995\pi$
$937$	16226.8	−	16226.8i	0.565747	−	0.565747i	0.930934	+	0.365187i	$0.118995\pi$
$938$	38761.7	+	16055.6i	1.34927	+	0.558885i
$939$		0			0
$940$	3187.13	−	7694.40i	0.110588	−	0.266983i
$941$	7646.34	−	3167.22i	0.264892	−	0.109722i	−0.246284	−	0.969198i	$-0.579210\pi$
$941$	7646.34	−	3167.22i	0.264892	−	0.109722i	0.511177	+	0.859476i	$0.329210\pi$
$942$		0			0
$943$	−12477.1	−	12477.1i	−0.430870	−	0.430870i
$944$	−15723.2	−	15723.2i	−0.542104	−	0.542104i
$945$		0			0
$946$	15584.6	−	6455.35i	0.535623	−	0.221862i
$947$	2645.45	−	6386.69i	0.0907769	−	0.219155i	−0.871970	−	0.489560i	$-0.837158\pi$
$947$	2645.45	−	6386.69i	0.0907769	−	0.219155i	0.962747	+	0.270405i	$0.0871576\pi$
$948$		0			0
$949$	−6490.96	−	2688.64i	−0.222029	−	0.0919674i
$950$	3317.32	−	3317.32i	0.113293	−	0.113293i
$951$		0			0
$952$	−10968.6	+	50243.1i	−0.373418	+	1.71049i
$953$	−12830.8			−0.436129			−0.218064	−	0.975934i	$-0.569974\pi$
$953$	−12830.8			−0.436129			−0.218064	+	0.975934i	$0.569974\pi$
$954$		0			0
$955$	6554.08	+	2714.79i	0.222079	+	0.0919879i
$956$		−	4912.93i		−	0.166209i
$957$		0			0
$958$	−16359.4	+	6776.27i	−0.551719	+	0.228530i
$959$	19513.1	+	47108.8i	0.657050	+	1.58626i
$960$		0			0
$961$	49673.2	+	49673.2i	1.66739	+	1.66739i
$962$	2075.04	+	5009.60i	0.0695448	+	0.167896i
$963$		0			0
$964$	1731.68	−	4180.64i	0.0578564	−	0.139678i
$965$			32037.3i			1.06872i
$966$		0			0
$967$	31340.0	−	31340.0i	1.04222	−	1.04222i	0.0431503	−	0.999069i	$-0.486261\pi$
$967$	31340.0	−	31340.0i	1.04222	−	1.04222i	0.999069	−	0.0431503i	$-0.0137394\pi$
$968$	−16311.8			−0.541613
$969$		0			0
$970$	−7081.54			−0.234407
$971$	−27830.0	+	27830.0i	−0.919779	+	0.919779i	−0.997013	−	0.0772337i	$-0.975391\pi$
$971$	−27830.0	+	27830.0i	−0.919779	+	0.919779i	0.0772337	+	0.997013i	$0.475391\pi$
$972$		0			0
$973$		−	74096.9i		−	2.44135i
$974$	1293.23	−	3122.13i	0.0425438	−	0.102710i
$975$		0			0
$976$	−99.2431	−	239.594i	−0.00325481	−	0.00785780i
$977$	−1700.94	−	1700.94i	−0.0556991	−	0.0556991i	0.678709	−	0.734408i	$-0.262540\pi$
$977$	−1700.94	−	1700.94i	−0.0556991	−	0.0556991i	−0.734408	+	0.678709i	$0.762540\pi$
$978$		0			0
$979$	31.7342	+	76.6131i	0.00103598	+	0.00250109i
$980$	−14340.2	+	5939.90i	−0.467429	+	0.193616i
$981$		0			0
$982$			37520.4i			1.21927i
$983$	21397.8	+	8863.27i	0.694287	+	0.287583i	0.701785	−	0.712389i	$-0.252387\pi$
$983$	21397.8	+	8863.27i	0.694287	+	0.287583i	−0.00749789	+	0.999972i	$0.502387\pi$
$984$		0			0
$985$	−38269.6			−1.23794
$986$	14045.1	+	21890.1i	0.453638	+	0.707022i
$987$		0			0
$988$	−1453.77	+	1453.77i	−0.0468123	+	0.0468123i
$989$	−51567.2	−	21359.9i	−1.65798	−	0.686758i
$990$		0			0
$991$	6050.40	−	14607.0i	0.193943	−	0.468219i	−0.796755	−	0.604303i	$-0.793452\pi$
$991$	6050.40	−	14607.0i	0.193943	−	0.468219i	0.990697	+	0.136084i	$0.0434517\pi$
$992$	38489.7	−	15942.9i	1.23190	−	0.510271i
$993$		0			0
$994$	−36013.1	−	36013.1i	−1.14916	−	1.14916i
$995$	−2811.28	−	2811.28i	−0.0895714	−	0.0895714i
$996$		0			0
$997$	−6937.23	+	2873.50i	−0.220366	+	0.0912784i	−0.490135	−	0.871647i	$-0.663053\pi$
$997$	−6937.23	+	2873.50i	−0.220366	+	0.0912784i	0.269769	+	0.962925i	$0.413053\pi$
$998$	−6285.92	+	15175.5i	−0.199376	+	0.481336i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.4.l.b.145.6	yes	32
3.2	odd	2	inner	153.4.l.b.145.3	yes	32
17.2	even	8	inner	153.4.l.b.19.6	yes	32
51.2	odd	8	inner	153.4.l.b.19.3	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.4.l.b.19.3	✓	32	51.2	odd	8	inner
153.4.l.b.19.6	yes	32	17.2	even	8	inner
153.4.l.b.145.3	yes	32	3.2	odd	2	inner
153.4.l.b.145.6	yes	32	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(1.56233 - 1.56233i) q^{2} +3.11822i q^{4} +(3.46961 - 8.37637i) q^{5} +(11.4295 + 27.5933i) q^{7} +(17.3704 + 17.3704i) q^{8} +O(q^{10})\)	\(q+(1.56233 - 1.56233i) q^{2} +3.11822i q^{4} +(3.46961 - 8.37637i) q^{5} +(11.4295 + 27.5933i) q^{7} +(17.3704 + 17.3704i) q^{8} +(-7.66601 - 18.5074i) q^{10} +(-23.8602 + 9.88321i) q^{11} +13.2897i q^{13} +(60.9668 + 25.2533i) q^{14} +29.3310 q^{16} +(68.9883 - 12.3943i) q^{17} +(35.0810 - 35.0810i) q^{19} +(26.1194 + 10.8190i) q^{20} +(-21.8367 + 52.7185i) q^{22} +(174.438 - 72.2546i) q^{23} +(30.2629 + 30.2629i) q^{25} +(20.7630 + 20.7630i) q^{26} +(-86.0420 + 35.6398i) q^{28} +(-64.2677 + 155.156i) q^{29} +(-292.214 - 121.039i) q^{31} +(-93.1383 + 93.1383i) q^{32} +(88.4188 - 127.147i) q^{34} +270.788 q^{35} +(170.607 + 70.6678i) q^{37} -109.617i q^{38} +(205.769 - 85.2324i) q^{40} +(-35.7638 - 86.3414i) q^{41} +(-209.035 - 209.035i) q^{43} +(-30.8180 - 74.4012i) q^{44} +(159.645 - 385.416i) q^{46} -294.586i q^{47} +(-388.220 + 388.220i) q^{49} +94.5616 q^{50} -41.4403 q^{52} +(-134.660 + 134.660i) q^{53} +234.153i q^{55} +(-280.771 + 677.842i) q^{56} +(141.998 + 342.813i) q^{58} +(-536.061 - 536.061i) q^{59} +(-3.38356 - 8.16864i) q^{61} +(-645.640 + 267.433i) q^{62} +525.674i q^{64} +(111.320 + 46.1102i) q^{65} +635.784 q^{67} +(38.6480 + 215.121i) q^{68} +(423.061 - 423.061i) q^{70} +(-713.040 - 295.351i) q^{71} +(-202.310 + 488.419i) q^{73} +(376.952 - 156.139i) q^{74} +(109.390 + 109.390i) q^{76} +(-545.421 - 545.421i) q^{77} +(-81.6679 + 33.8280i) q^{79} +(101.767 - 245.687i) q^{80} +(-190.769 - 79.0191i) q^{82} +(678.972 - 678.972i) q^{83} +(135.543 - 620.875i) q^{85} -653.164 q^{86} +(-586.135 - 242.785i) q^{88} -3.21092i q^{89} +(-366.708 + 151.895i) q^{91} +(225.306 + 543.936i) q^{92} +(-460.242 - 460.242i) q^{94} +(-172.134 - 415.569i) q^{95} +(135.281 - 326.598i) q^{97} +1213.06i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 80 q^{10} - 128 q^{16} + 128 q^{19} + 280 q^{22} + 16 q^{25} + 184 q^{28} - 192 q^{31} + 24 q^{34} - 416 q^{37} - 488 q^{40} + 672 q^{43} - 384 q^{46} + 944 q^{49} - 4032 q^{52} - 1576 q^{58} + 4816 q^{61} + 2464 q^{67} + 5944 q^{70} + 3024 q^{73} - 3384 q^{76} - 4992 q^{79} - 1176 q^{82} - 2544 q^{85} - 1480 q^{88} - 4016 q^{91} + 4672 q^{94} + 1008 q^{97}+O(q^{100}) \) 32 * q - 80 * q^10 - 128 * q^16 + 128 * q^19 + 280 * q^22 + 16 * q^25 + 184 * q^28 - 192 * q^31 + 24 * q^34 - 416 * q^37 - 488 * q^40 + 672 * q^43 - 384 * q^46 + 944 * q^49 - 4032 * q^52 - 1576 * q^58 + 4816 * q^61 + 2464 * q^67 + 5944 * q^70 + 3024 * q^73 - 3384 * q^76 - 4992 * q^79 - 1176 * q^82 - 2544 * q^85 - 1480 * q^88 - 4016 * q^91 + 4672 * q^94 + 1008 * q^97

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