LMFDB - Embedded newform 153.4.l.a.19.1

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			19.1
Root			$-4.15292i$ of defining polynomial
Character	$\chi$	$=$	153.19
Dual form			153.4.l.a.145.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.22945 - 2.22945i) q^{2} +1.94089i q^{4} +(1.91633 + 4.62643i) q^{5} +(1.06584 - 2.57316i) q^{7} +(-13.5085 + 13.5085i) q^{8} +O(q^{10})$	\(q+(-2.22945 - 2.22945i) q^{2} +1.94089i q^{4} +(1.91633 + 4.62643i) q^{5} +(1.06584 - 2.57316i) q^{7} +(-13.5085 + 13.5085i) q^{8} +(6.04203 - 14.5867i) q^{10} +(25.1714 + 10.4263i) q^{11} +59.7352i q^{13} +(-8.11295 + 3.36049i) q^{14} +75.7601 q^{16} +(-70.0883 - 0.790881i) q^{17} +(23.5187 + 23.5187i) q^{19} +(-8.97939 + 3.71938i) q^{20} +(-32.8734 - 79.3634i) q^{22} +(194.831 + 80.7017i) q^{23} +(70.6568 - 70.6568i) q^{25} +(133.177 - 133.177i) q^{26} +(4.99421 + 2.06867i) q^{28} +(-7.67362 - 18.5258i) q^{29} +(123.485 - 51.1492i) q^{31} +(-60.8354 - 60.8354i) q^{32} +(154.495 + 158.022i) q^{34} +13.9470 q^{35} +(141.143 - 58.4634i) q^{37} -104.868i q^{38} +(-88.3827 - 36.6093i) q^{40} +(100.202 - 241.908i) q^{41} +(-224.025 + 224.025i) q^{43} +(-20.2364 + 48.8550i) q^{44} +(-254.446 - 614.286i) q^{46} +329.443i q^{47} +(237.052 + 237.052i) q^{49} -315.052 q^{50} -115.939 q^{52} +(219.585 + 219.585i) q^{53} +136.434i q^{55} +(20.3616 + 49.1573i) q^{56} +(-24.1943 + 58.4102i) q^{58} +(-38.7062 + 38.7062i) q^{59} +(-313.322 + 756.427i) q^{61} +(-389.338 - 161.269i) q^{62} -334.822i q^{64} +(-276.360 + 114.472i) q^{65} -731.181 q^{67} +(1.53501 - 136.034i) q^{68} +(-31.0942 - 31.0942i) q^{70} +(-581.286 + 240.777i) q^{71} +(-189.995 - 458.689i) q^{73} +(-445.012 - 184.330i) q^{74} +(-45.6473 + 45.6473i) q^{76} +(53.6572 - 53.6572i) q^{77} +(83.1733 + 34.4515i) q^{79} +(145.181 + 350.498i) q^{80} +(-762.717 + 315.928i) q^{82} +(257.404 + 257.404i) q^{83} +(-130.653 - 325.774i) q^{85} +998.907 q^{86} +(-480.872 + 199.184i) q^{88} +192.079i q^{89} +(153.708 + 63.6679i) q^{91} +(-156.633 + 378.146i) q^{92} +(734.476 - 734.476i) q^{94} +(-63.7380 + 153.877i) q^{95} +(516.698 + 1247.42i) q^{97} -1056.99i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

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 $

$2$	−2.22945	−	2.22945i	−0.788229	−	0.788229i	0.192974	−	0.981204i	$-0.438187\pi$
$2$	−2.22945	−	2.22945i	−0.788229	−	0.788229i	−0.981204	+	0.192974i	$0.938187\pi$
$3$		0			0
$3$		0			0
$4$			1.94089i			0.242611i
$5$	1.91633	+	4.62643i	0.171402	+	0.413800i	0.986115	−	0.166064i	$-0.0531057\pi$
$5$	1.91633	+	4.62643i	0.171402	+	0.413800i	−0.814713	+	0.579864i	$0.803106\pi$
$6$		0			0
$7$	1.06584	−	2.57316i	0.0575498	−	0.138937i	−0.892489	−	0.451069i	$-0.851043\pi$
$7$	1.06584	−	2.57316i	0.0575498	−	0.138937i	0.950039	+	0.312131i	$0.101043\pi$
$8$	−13.5085	+	13.5085i	−0.596996	+	0.596996i
$9$		0			0
$10$	6.04203	−	14.5867i	0.191066	−	0.461273i
$11$	25.1714	+	10.4263i	0.689952	+	0.285787i	0.699980	−	0.714162i	$-0.253192\pi$
$11$	25.1714	+	10.4263i	0.689952	+	0.285787i	−0.0100284	+	0.999950i	$0.503192\pi$
$12$		0			0
$13$			59.7352i			1.27443i	0.770687	+	0.637214i	$0.219913\pi$
$13$			59.7352i			1.27443i	−0.770687	+	0.637214i	$0.780087\pi$
$14$	−8.11295	+	3.36049i	−0.154877	+	0.0641521i
$15$		0			0
$16$	75.7601			1.18375
$17$	−70.0883	−	0.790881i	−0.999936	−	0.0112833i
$17$	−70.0883	−	0.790881i	−0.999936	−	0.0112833i
$18$		0			0
$19$	23.5187	+	23.5187i	0.283977	+	0.283977i	0.834693	−	0.550716i	$-0.185645\pi$
$19$	23.5187	+	23.5187i	0.283977	+	0.283977i	−0.550716	+	0.834693i	$0.685645\pi$
$20$	−8.97939	+	3.71938i	−0.100393	+	0.0415840i
$21$		0			0
$22$	−32.8734	−	79.3634i	−0.318574	−	0.769106i
$23$	194.831	+	80.7017i	1.76631	+	0.731629i	0.995522	+	0.0945353i	$0.0301365\pi$
$23$	194.831	+	80.7017i	1.76631	+	0.731629i	0.770787	+	0.637093i	$0.219863\pi$
$24$		0			0
$25$	70.6568	−	70.6568i	0.565255	−	0.565255i
$26$	133.177	−	133.177i	1.00454	−	1.00454i
$27$		0			0
$28$	4.99421	+	2.06867i	0.0337078	+	0.0139622i
$29$	−7.67362	−	18.5258i	−0.0491364	−	0.118626i	0.897405	−	0.441207i	$-0.145449\pi$
$29$	−7.67362	−	18.5258i	−0.0491364	−	0.118626i	−0.946542	+	0.322581i	$0.895449\pi$
$30$		0			0
$31$	123.485	−	51.1492i	0.715438	−	0.296344i	0.00488535	−	0.999988i	$-0.498445\pi$
$31$	123.485	−	51.1492i	0.715438	−	0.296344i	0.710553	+	0.703644i	$0.248445\pi$
$32$	−60.8354	−	60.8354i	−0.336071	−	0.336071i
$33$		0			0
$34$	154.495	+	158.022i	0.779285	+	0.797073i
$35$	13.9470			0.0673565
$36$		0			0
$37$	141.143	−	58.4634i	0.627129	−	0.259765i	−0.0464037	−	0.998923i	$-0.514776\pi$
$37$	141.143	−	58.4634i	0.627129	−	0.259765i	0.673533	+	0.739157i	$0.264776\pi$
$38$		−	104.868i		−	0.447678i
$39$		0			0
$40$	−88.3827	−	36.6093i	−0.349363	−	0.144711i
$41$	100.202	−	241.908i	0.381680	−	0.921456i	−0.609962	−	0.792431i	$-0.708815\pi$
$41$	100.202	−	241.908i	0.381680	−	0.921456i	0.991641	−	0.129025i	$-0.0411849\pi$
$42$		0			0
$43$	−224.025	+	224.025i	−0.794501	+	0.794501i	−0.982222	−	0.187721i	$-0.939890\pi$
$43$	−224.025	+	224.025i	−0.794501	+	0.794501i	0.187721	+	0.982222i	$0.439890\pi$
$44$	−20.2364	+	48.8550i	−0.0693352	+	0.167390i
$45$		0			0
$46$	−254.446	−	614.286i	−0.815565	−	1.96895i
$47$			329.443i			1.02243i	0.859453	+	0.511215i	$0.170804\pi$
$47$			329.443i			1.02243i	−0.859453	+	0.511215i	$0.829196\pi$
$48$		0			0
$49$	237.052	+	237.052i	0.691115	+	0.691115i
$50$	−315.052			−0.891101
$51$		0			0
$52$	−115.939			−0.309190
$53$	219.585	+	219.585i	0.569100	+	0.569100i	0.931876	−	0.362776i	$-0.118171\pi$
$53$	219.585	+	219.585i	0.569100	+	0.569100i	−0.362776	+	0.931876i	$0.618171\pi$
$54$		0			0
$55$			136.434i			0.334487i
$56$	20.3616	+	49.1573i	0.0485881	+	0.117302i
$57$		0			0
$58$	−24.1943	+	58.4102i	−0.0547735	+	0.132235i
$59$	−38.7062	+	38.7062i	−0.0854087	+	0.0854087i	−0.748520	−	0.663112i	$-0.769235\pi$
$59$	−38.7062	+	38.7062i	−0.0854087	+	0.0854087i	0.663112	+	0.748520i	$0.269235\pi$
$60$		0			0
$61$	−313.322	+	756.427i	−0.657653	+	1.58771i	0.143767	+	0.989612i	$0.454079\pi$
$61$	−313.322	+	756.427i	−0.657653	+	1.58771i	−0.801419	+	0.598103i	$0.795921\pi$
$62$	−389.338	−	161.269i	−0.797517	−	0.330342i
$63$		0			0
$64$		−	334.822i		−	0.653948i
$65$	−276.360	+	114.472i	−0.527358	+	0.218439i
$66$		0			0
$67$	−731.181			−1.33325			−0.666627	−	0.745392i	$-0.732262\pi$
$67$	−731.181			−1.33325			−0.666627	+	0.745392i	$0.732262\pi$
$68$	1.53501	−	136.034i	0.00273747	−	0.242596i
$69$		0			0
$70$	−31.0942	−	31.0942i	−0.0530923	−	0.0530923i
$71$	−581.286	+	240.777i	−0.971633	+	0.402464i	−0.811320	−	0.584603i	$-0.801250\pi$
$71$	−581.286	+	240.777i	−0.971633	+	0.402464i	−0.160313	+	0.987066i	$0.551250\pi$
$72$		0			0
$73$	−189.995	−	458.689i	−0.304620	−	0.735417i	−0.999862	−	0.0166414i	$-0.994703\pi$
$73$	−189.995	−	458.689i	−0.304620	−	0.735417i	0.695242	−	0.718776i	$-0.255297\pi$
$74$	−445.012	−	184.330i	−0.699076	−	0.289567i
$75$		0			0
$76$	−45.6473	+	45.6473i	−0.0688960	+	0.0688960i
$77$	53.6572	−	53.6572i	0.0794131	−	0.0794131i
$78$		0			0
$79$	83.1733	+	34.4515i	0.118452	+	0.0490646i	0.441122	−	0.897447i	$-0.354580\pi$
$79$	83.1733	+	34.4515i	0.118452	+	0.0490646i	−0.322670	+	0.946511i	$0.604580\pi$
$80$	145.181	+	350.498i	0.202897	+	0.489836i
$81$		0			0
$82$	−762.717	+	315.928i	−1.02717	+	0.425468i
$83$	257.404	+	257.404i	0.340407	+	0.340407i	0.856520	−	0.516113i	$-0.172622\pi$
$83$	257.404	+	257.404i	0.340407	+	0.340407i	−0.516113	+	0.856520i	$0.672622\pi$
$84$		0			0
$85$	−130.653	−	325.774i	−0.166722	−	0.415708i
$86$	998.907			1.25250
$87$		0			0
$88$	−480.872	+	199.184i	−0.582512	+	0.241285i
$89$			192.079i			0.228767i	0.993437	+	0.114384i	$0.0364893\pi$
$89$			192.079i			0.228767i	−0.993437	+	0.114384i	$0.963511\pi$
$90$		0			0
$91$	153.708	+	63.6679i	0.177066	+	0.0733430i
$92$	−156.633	+	378.146i	−0.177501	+	0.428526i
$93$		0			0
$94$	734.476	−	734.476i	0.805909	−	0.805909i
$95$	−63.7380	+	153.877i	−0.0688356	+	0.166184i
$96$		0			0
$97$	516.698	+	1247.42i	0.540853	+	1.30574i	0.924122	+	0.382098i	$0.124798\pi$
$97$	516.698	+	1247.42i	0.540853	+	1.30574i	−0.383268	+	0.923637i	$0.625202\pi$
$98$		−	1056.99i		−	1.08951i
$99$		0			0
$100$	137.137	+	137.137i	0.137137	+	0.137137i
$101$	−304.020			−0.299516			−0.149758	−	0.988723i	$-0.547850\pi$
$101$	−304.020			−0.299516			−0.149758	+	0.988723i	$0.547850\pi$
$102$		0			0
$103$	988.515			0.945643			0.472822	−	0.881158i	$-0.343236\pi$
$103$	988.515			0.945643			0.472822	+	0.881158i	$0.343236\pi$
$104$	−806.931	−	806.931i	−0.760828	−	0.760828i
$105$		0			0
$106$		−	979.107i		−	0.897163i
$107$	−449.658	−	1085.57i	−0.406263	−	0.980805i	−0.986112	−	0.166081i	$-0.946889\pi$
$107$	−449.658	−	1085.57i	−0.406263	−	0.980805i	0.579849	−	0.814724i	$-0.303111\pi$
$108$		0			0
$109$	321.020	−	775.010i	0.282093	−	0.681032i	−0.717791	−	0.696258i	$-0.754847\pi$
$109$	321.020	−	775.010i	0.282093	−	0.681032i	0.999884	+	0.0152262i	$0.00484683\pi$
$110$	304.173	−	304.173i	0.263652	−	0.263652i
$111$		0			0
$112$	80.7478	−	194.943i	0.0681246	−	0.164467i
$113$	1872.53	+	775.626i	1.55887	+	0.645706i	0.984893	−	0.173164i	$-0.0553992\pi$
$113$	1872.53	+	775.626i	1.55887	+	0.645706i	0.573979	+	0.818870i	$0.305399\pi$
$114$		0			0
$115$			1056.02i			0.856301i
$116$	35.9564	−	14.8936i	0.0287799	−	0.0119210i
$117$		0			0
$118$	172.587			0.134643
$119$	−76.7378	+	179.505i	−0.0591138	+	0.138279i
$120$		0			0
$121$	−416.267	−	416.267i	−0.312748	−	0.312748i
$122$	2384.95	−	987.880i	1.76986	−	0.733102i
$123$		0			0
$124$	99.2750	+	239.671i	0.0718964	+	0.173573i
$125$	1040.59	+	431.028i	0.744588	+	0.308419i
$126$		0			0
$127$	1131.58	−	1131.58i	0.790645	−	0.790645i	−0.190954	−	0.981599i	$-0.561158\pi$
$127$	1131.58	−	1131.58i	0.790645	−	0.790645i	0.981599	+	0.190954i	$0.0611582\pi$
$128$	−1233.15	+	1233.15i	−0.851533	+	0.851533i
$129$		0			0
$130$	871.342	+	360.921i	0.587859	+	0.243499i
$131$	−1000.75	−	2416.01i	−0.667447	−	1.61136i	−0.785867	−	0.618396i	$-0.787783\pi$
$131$	−1000.75	−	2416.01i	−0.667447	−	1.61136i	0.118420	−	0.992964i	$-0.462217\pi$
$132$		0			0
$133$	85.5845	−	35.4502i	0.0557979	−	0.0231122i
$134$	1630.13	+	1630.13i	1.05091	+	1.05091i
$135$		0			0
$136$	957.470	−	936.103i	0.603694	−	0.590222i
$137$	−745.711			−0.465039			−0.232520	−	0.972592i	$-0.574697\pi$
$137$	−745.711			−0.465039			−0.232520	+	0.972592i	$0.574697\pi$
$138$		0			0
$139$	−2339.68	+	969.128i	−1.42769	+	0.591369i	−0.956781	−	0.290811i	$-0.906075\pi$
$139$	−2339.68	+	969.128i	−1.42769	+	0.591369i	−0.470912	+	0.882180i	$0.656075\pi$
$140$			27.0696i			0.0163414i
$141$		0			0
$142$	1832.75	+	759.149i	1.08310	+	0.448636i
$143$	−622.819	+	1503.62i	−0.364215	+	0.879293i
$144$		0			0
$145$	71.0029	−	71.0029i	0.0406653	−	0.0406653i
$146$	−599.039	+	1446.21i	−0.339567	+	0.819788i
$147$		0			0
$148$	113.471	+	273.943i	0.0630220	+	0.152149i
$149$		−	1816.70i		−	0.998858i	−0.866355	−	0.499429i	$-0.833543\pi$
$149$		−	1816.70i		−	0.998858i	0.866355	−	0.499429i	$-0.166457\pi$
$150$		0			0
$151$	1499.42	+	1499.42i	0.808085	+	0.808085i	0.984344	−	0.176259i	$-0.0563996\pi$
$151$	1499.42	+	1499.42i	0.808085	+	0.808085i	−0.176259	+	0.984344i	$0.556400\pi$
$152$	−635.404			−0.339066
$153$		0			0
$154$	−239.252			−0.125191
$155$	473.276	+	473.276i	0.245255	+	0.245255i
$156$		0			0
$157$		−	1607.82i		−	0.817314i	−0.912688	−	0.408657i	$-0.865997\pi$
$157$		−	1607.82i		−	0.817314i	0.912688	−	0.408657i	$-0.134003\pi$
$158$	−108.623	−	262.239i	−0.0546935	−	0.132042i
$159$		0			0
$160$	164.870	−	398.031i	0.0814632	−	0.196670i
$161$	415.316	−	415.316i	0.203301	−	0.203301i
$162$		0			0
$163$	−871.753	+	2104.60i	−0.418902	+	1.01132i	0.563765	+	0.825936i	$0.309353\pi$
$163$	−871.753	+	2104.60i	−0.418902	+	1.01132i	−0.982666	+	0.185383i	$0.940647\pi$
$164$	469.517	+	194.480i	0.223556	+	0.0925998i
$165$		0			0
$166$		−	1147.74i		−	0.536638i
$167$	−1526.36	+	632.239i	−0.707265	+	0.292959i	−0.707172	−	0.707041i	$-0.750029\pi$
$167$	−1526.36	+	632.239i	−0.707265	+	0.292959i	−9.26752e−5		1.00000i	$0.500029\pi$
$168$		0			0
$169$	−1371.29			−0.624165
$170$	−435.012	+	1017.58i	−0.196258	+	0.459088i
$171$		0			0
$172$	−434.809	−	434.809i	−0.192755	−	0.192755i
$173$	−2042.54	+	846.046i	−0.897637	+	0.371813i	−0.783311	−	0.621630i	$-0.786471\pi$
$173$	−2042.54	+	846.046i	−0.897637	+	0.371813i	−0.114326	+	0.993443i	$0.536471\pi$
$174$		0			0
$175$	−106.502	−	257.120i	−0.0460048	−	0.111065i
$176$	1906.99	+	789.900i	0.816731	+	0.338301i
$177$		0			0
$178$	428.230	−	428.230i	0.180321	−	0.180321i
$179$	−14.6759	+	14.6759i	−0.00612807	+	0.00612807i	−0.710164	−	0.704036i	$-0.751379\pi$
$179$	−14.6759	+	14.6759i	−0.00612807	+	0.00612807i	0.704036	+	0.710164i	$0.251379\pi$
$180$		0			0
$181$	403.272	+	167.041i	0.165608	+	0.0685969i	0.463947	−	0.885863i	$-0.346433\pi$
$181$	403.272	+	167.041i	0.165608	+	0.0685969i	−0.298340	+	0.954460i	$0.596433\pi$
$182$	−200.740	−	484.629i	−0.0817572	−	0.197379i
$183$		0			0
$184$	−3722.03	+	1541.71i	−1.49126	+	0.617700i
$185$	540.953	+	540.953i	0.214982	+	0.214982i
$186$		0			0
$187$	−1755.98	−	750.673i	−0.686683	−	0.293554i
$188$	−639.412			−0.248053
$189$		0			0
$190$	485.162	−	200.961i	0.185249	−	0.0767328i
$191$		−	787.808i		−	0.298449i	−0.988803	−	0.149225i	$-0.952322\pi$
$191$		−	787.808i		−	0.298449i	0.988803	−	0.149225i	$-0.0476777\pi$
$192$		0			0
$193$	3443.17	+	1426.21i	1.28417	+	0.531921i	0.917243	−	0.398329i	$-0.130410\pi$
$193$	3443.17	+	1426.21i	1.28417	+	0.531921i	0.366928	+	0.930249i	$0.380410\pi$
$194$	1629.11	−	3933.01i	0.602903	−	1.45554i
$195$		0			0
$196$	−460.093	+	460.093i	−0.167672	+	0.167672i
$197$	−172.929	+	417.488i	−0.0625415	+	0.150989i	−0.952061	−	0.305909i	$-0.901040\pi$
$197$	−172.929	+	417.488i	−0.0625415	+	0.150989i	0.889519	+	0.456898i	$0.151040\pi$
$198$		0			0
$199$	−1331.80	−	3215.25i	−0.474416	−	1.14534i	−0.962192	−	0.272373i	$-0.912191\pi$
$199$	−1331.80	−	3215.25i	−0.474416	−	1.14534i	0.487775	−	0.872969i	$-0.337809\pi$
$200$			1908.93i			0.674910i
$201$		0			0
$202$	677.798	+	677.798i	0.236088	+	0.236088i
$203$	−55.8485			−0.0193093
$204$		0			0
$205$	1311.19			0.446719
$206$	−2203.84	−	2203.84i	−0.745384	−	0.745384i
$207$		0			0
$208$			4525.54i			1.50860i
$209$	346.785	+	837.214i	0.114773	+	0.277088i
$210$		0			0
$211$	695.912	−	1680.08i	0.227055	−	0.548159i	−0.768762	−	0.639535i	$-0.779127\pi$
$211$	695.912	−	1680.08i	0.227055	−	0.548159i	0.995816	+	0.0913768i	$0.0291268\pi$
$212$	−426.190	+	426.190i	−0.138070	+	0.138070i
$213$		0			0
$214$	−1417.74	+	3422.72i	−0.452871	+	1.09333i
$215$	−1465.74	−	607.131i	−0.464944	−	0.192586i
$216$		0			0
$217$		−	372.263i		−	0.116456i
$218$	−2443.54	+	1012.15i	−0.759163	+	0.314456i
$219$		0			0
$220$	−264.803			−0.0811502
$221$	47.2434	−	4186.74i	0.0143798	−	1.27435i
$222$		0			0
$223$	−4601.73	−	4601.73i	−1.38186	−	1.38186i	−0.841315	−	0.540546i	$-0.818218\pi$
$223$	−4601.73	−	4601.73i	−1.38186	−	1.38186i	−0.540546	−	0.841315i	$-0.681782\pi$
$224$	−221.380	+	91.6984i	−0.0660337	+	0.0273521i
$225$		0			0
$226$	−2445.48	−	5903.92i	−0.719784	−	1.73771i
$227$	2242.41	+	928.835i	0.655655	+	0.271581i	0.685609	−	0.727970i	$-0.259536\pi$
$227$	2242.41	+	928.835i	0.655655	+	0.271581i	−0.0299538	+	0.999551i	$0.509536\pi$
$228$		0			0
$229$	−463.654	+	463.654i	−0.133795	+	0.133795i	−0.770833	−	0.637037i	$-0.780160\pi$
$229$	−463.654	+	463.654i	−0.133795	+	0.133795i	0.637037	+	0.770833i	$0.280160\pi$
$230$	2354.35	−	2354.35i	0.674962	−	0.674962i
$231$		0			0
$232$	353.914	+	146.596i	0.100153	+	0.0414849i
$233$	448.391	+	1082.51i	0.126073	+	0.304368i	0.974296	−	0.225272i	$-0.0723271\pi$
$233$	448.391	+	1082.51i	0.126073	+	0.304368i	−0.848223	+	0.529640i	$0.822327\pi$
$234$		0			0
$235$	−1524.14	+	631.321i	−0.423081	+	0.175246i
$236$	−75.1244	−	75.1244i	−0.0207211	−	0.0207211i
$237$		0			0
$238$	571.281	−	229.115i	0.155591	−	0.0624005i
$239$	5281.06			1.42930			0.714651	−	0.699481i	$-0.246585\pi$
$239$	5281.06			1.42930			0.714651	+	0.699481i	$0.246585\pi$
$240$		0			0
$241$	1226.76	−	508.143i	0.327896	−	0.135819i	−0.212662	−	0.977126i	$-0.568213\pi$
$241$	1226.76	−	508.143i	0.327896	−	0.135819i	0.540558	+	0.841307i	$0.318213\pi$
$242$			1856.09i			0.493034i
$243$		0			0
$244$	−1468.14	−	608.124i	−0.385197	−	0.159554i
$245$	−642.436	+	1550.98i	−0.167525	+	0.404442i
$246$		0			0
$247$	−1404.89	+	1404.89i	−0.361908	+	0.361908i
$248$	−977.148	+	2359.04i	−0.250197	+	0.604030i
$249$		0			0
$250$	−1359.00	−	3280.91i	−0.343802	−	0.830011i
$251$		−	4280.39i		−	1.07640i	−0.842818	−	0.538198i	$-0.819105\pi$
$251$		−	4280.39i		−	1.07640i	0.842818	−	0.538198i	$-0.180895\pi$
$252$		0			0
$253$	4062.75	+	4062.75i	1.00958	+	1.00958i
$254$	−5045.62			−1.24642
$255$		0			0
$256$	2819.92			0.688458
$257$	−171.749	−	171.749i	−0.0416865	−	0.0416865i	0.685956	−	0.727643i	$-0.259384\pi$
$257$	−171.749	−	171.749i	−0.0416865	−	0.0416865i	−0.727643	+	0.685956i	$0.759384\pi$
$258$		0			0
$259$		−	425.496i		−	0.102081i
$260$	−222.178	−	536.385i	−0.0529957	−	0.127943i
$261$		0			0
$262$	−3155.27	+	7617.49i	−0.744020	+	1.79622i
$263$	−2229.86	+	2229.86i	−0.522809	+	0.522809i	−0.918419	−	0.395609i	$-0.870533\pi$
$263$	−2229.86	+	2229.86i	−0.522809	+	0.522809i	0.395609	+	0.918419i	$0.370533\pi$
$264$		0			0
$265$	−595.097	+	1436.69i	−0.137949	+	0.333038i
$266$	−269.841	−	111.772i	−0.0621993	−	0.0257638i
$267$		0			0
$268$		−	1419.14i		−	0.323462i
$269$	194.844	−	80.7072i	0.0441631	−	0.0182930i	−0.360493	−	0.932762i	$-0.617391\pi$
$269$	194.844	−	80.7072i	0.0441631	−	0.0182930i	0.404656	+	0.914469i	$0.367391\pi$
$270$		0			0
$271$	1627.36			0.364780			0.182390	−	0.983226i	$-0.441617\pi$
$271$	1627.36			0.364780			0.182390	+	0.983226i	$0.441617\pi$
$272$	−5309.90	−	59.9172i	−1.18368	−	0.0133567i
$273$		0			0
$274$	1662.52	+	1662.52i	0.366558	+	0.366558i
$275$	2515.23	−	1041.84i	0.551541	−	0.228456i
$276$		0			0
$277$	−1770.63	−	4274.69i	−0.384069	−	0.927224i	−0.991170	−	0.132599i	$-0.957668\pi$
$277$	−1770.63	−	4274.69i	−0.384069	−	0.927224i	0.607101	−	0.794625i	$-0.292332\pi$
$278$	7376.82	+	3055.58i	1.59148	+	0.659214i
$279$		0			0
$280$	−188.403	+	188.403i	−0.0402115	+	0.0402115i
$281$	3589.47	−	3589.47i	0.762029	−	0.762029i	−0.214660	−	0.976689i	$-0.568864\pi$
$281$	3589.47	−	3589.47i	0.762029	−	0.762029i	0.976689	+	0.214660i	$0.0688644\pi$
$282$		0			0
$283$	−2251.53	−	932.616i	−0.472932	−	0.195895i	0.133470	−	0.991053i	$-0.457388\pi$
$283$	−2251.53	−	932.616i	−0.472932	−	0.195895i	−0.606402	+	0.795158i	$0.707388\pi$
$284$	−467.321	−	1128.21i	−0.0976422	−	0.235729i
$285$		0			0
$286$	4740.79	−	1963.70i	0.980170	−	0.406000i
$287$	−515.669	−	515.669i	−0.106059	−	0.106059i
$288$		0			0
$289$	4911.75	+	110.863i	0.999745	+	0.0225653i
$290$	−316.595			−0.0641072
$291$		0			0
$292$	890.265	−	368.760i	0.178421	−	0.0739042i
$293$			3300.30i			0.658041i	0.944323	+	0.329020i	$0.106718\pi$
$293$			3300.30i			0.658041i	−0.944323	+	0.329020i	$0.893282\pi$
$294$		0			0
$295$	−253.245	−	104.898i	−0.0499814	−	0.0207030i
$296$	−1116.88	+	2696.38i	−0.219315	+	0.529472i
$297$		0			0
$298$	−4050.24	+	4050.24i	−0.787329	+	0.787329i
$299$	−4820.73	+	11638.3i	−0.932408	+	2.25103i
$300$		0			0
$301$	337.678	+	815.227i	0.0646626	+	0.156109i
$302$		−	6685.75i		−	1.27391i
$303$		0			0
$304$	1781.78	+	1781.78i	0.336158	+	0.336158i
$305$	−4099.98			−0.769719
$306$		0			0
$307$	−1186.40			−0.220558			−0.110279	−	0.993901i	$-0.535174\pi$
$307$	−1186.40			−0.220558			−0.110279	+	0.993901i	$0.535174\pi$
$308$	104.143	+	104.143i	0.0192665	+	0.0192665i
$309$		0			0
$310$		−	2110.29i		−	0.386634i
$311$	−251.604	−	607.425i	−0.0458751	−	0.110752i	0.899281	−	0.437371i	$-0.144091\pi$
$311$	−251.604	−	607.425i	−0.0458751	−	0.110752i	−0.945156	+	0.326619i	$0.894091\pi$
$312$		0			0
$313$	2324.29	−	5611.33i	0.419733	−	1.01333i	−0.562691	−	0.826667i	$-0.690234\pi$
$313$	2324.29	−	5611.33i	0.419733	−	1.01333i	0.982425	−	0.186659i	$-0.0597659\pi$
$314$	−3584.56	+	3584.56i	−0.644231	+	0.644231i
$315$		0			0
$316$	−66.8666	+	161.430i	−0.0119036	+	0.0287379i
$317$	5315.32	+	2201.68i	0.941761	+	0.390090i	0.800128	−	0.599829i	$-0.204765\pi$
$317$	5315.32	+	2201.68i	0.941761	+	0.390090i	0.141633	+	0.989919i	$0.454765\pi$
$318$		0			0
$319$		−	546.327i		−	0.0958886i
$320$	1549.03	−	641.628i	0.270604	−	0.112088i
$321$		0			0
$322$	−1851.85			−0.320496
$323$	−1629.79	−	1666.99i	−0.280755	−	0.287163i
$324$		0			0
$325$	4220.70	+	4220.70i	0.720376	+	0.720376i
$326$	6635.63	−	2748.57i	1.12734	−	0.466960i
$327$		0			0
$328$	1914.24	+	4621.38i	0.322245	+	0.777967i
$329$	847.708	+	351.132i	0.142054	+	0.0588406i
$330$		0			0
$331$	63.5284	−	63.5284i	0.0105493	−	0.0105493i	−0.701812	−	0.712362i	$-0.747626\pi$
$331$	63.5284	−	63.5284i	0.0105493	−	0.0105493i	0.712362	+	0.701812i	$0.247626\pi$
$332$	−499.594	+	499.594i	−0.0825866	+	0.0825866i
$333$		0			0
$334$	4812.49	+	1993.40i	0.788406	+	0.326568i
$335$	−1401.18	−	3382.75i	−0.228522	−	0.551700i
$336$		0			0
$337$	782.810	−	324.251i	0.126535	−	0.0524126i	−0.318517	−	0.947917i	$-0.603185\pi$
$337$	782.810	−	324.251i	0.126535	−	0.0524126i	0.445053	+	0.895504i	$0.353185\pi$
$338$	3057.22	+	3057.22i	0.491985	+	0.491985i
$339$		0			0
$340$	632.292	−	253.584i	0.100855	−	0.0404486i
$341$	3641.60			0.578309
$342$		0			0
$343$	1745.23	−	722.896i	0.274733	−	0.113798i
$344$		−	6052.48i		−	0.948628i
$345$		0			0
$346$	6439.95	+	2667.51i	1.00062	+	0.414469i
$347$	225.906	−	545.386i	0.0349490	−	0.0843742i	−0.905441	−	0.424471i	$-0.860460\pi$
$347$	225.906	−	545.386i	0.0349490	−	0.0843742i	0.940390	+	0.340097i	$0.110460\pi$
$348$		0			0
$349$	6638.10	−	6638.10i	1.01813	−	1.01813i	0.0183025	−	0.999832i	$-0.494174\pi$
$349$	6638.10	−	6638.10i	1.01813	−	1.01813i	0.999832	−	0.0183025i	$-0.00582618\pi$
$350$	−335.794	+	810.677i	−0.0512826	+	0.123807i
$351$		0			0
$352$	−897.023	−	2165.60i	−0.135828	−	0.327918i
$353$		−	6176.09i		−	0.931218i	−0.884990	−	0.465609i	$-0.845835\pi$
$353$		−	6176.09i		−	0.931218i	0.884990	−	0.465609i	$-0.154165\pi$
$354$		0			0
$355$	−2227.87	−	2227.87i	−0.333079	−	0.333079i
$356$	−372.804			−0.0555015
$357$		0			0
$358$	65.4382			0.00966066
$359$	−5056.62	−	5056.62i	−0.743393	−	0.743393i	0.229836	−	0.973229i	$-0.426181\pi$
$359$	−5056.62	−	5056.62i	−0.743393	−	0.743393i	−0.973229	+	0.229836i	$0.926181\pi$
$360$		0			0
$361$		−	5752.74i		−	0.838714i
$362$	−526.666	−	1271.48i	−0.0764667	−	0.184607i
$363$		0			0
$364$	−123.572	+	298.330i	−0.0177938	+	0.0429581i
$365$	1758.00	−	1758.00i	0.252104	−	0.252104i
$366$		0			0
$367$	−1285.07	+	3102.43i	−0.182780	+	0.441269i	−0.988537	−	0.150976i	$-0.951758\pi$
$367$	−1285.07	+	3102.43i	−0.182780	+	0.441269i	0.805758	+	0.592245i	$0.201758\pi$
$368$	14760.4	+	6113.96i	2.09087	+	0.866066i
$369$		0			0
$370$		−	2412.05i		−	0.338910i
$371$	799.068	−	330.985i	0.111821	−	0.0463177i
$372$		0			0
$373$	−8379.14			−1.16315			−0.581576	−	0.813492i	$-0.697564\pi$
$373$	−8379.14			−1.16315			−0.581576	+	0.813492i	$0.697564\pi$
$374$	2241.27	+	5588.45i	0.309876	+	0.772652i
$375$		0			0
$376$	−4450.27	−	4450.27i	−0.610386	−	0.610386i
$377$	1106.64	−	458.385i	0.151180	−	0.0626207i
$378$		0			0
$379$	2447.53	+	5908.86i	0.331718	+	0.800839i	0.998456	+	0.0555463i	$0.0176901\pi$
$379$	2447.53	+	5908.86i	0.331718	+	0.800839i	−0.666738	+	0.745292i	$0.732310\pi$
$380$	−298.659	−	123.709i	−0.0403181	−	0.0167003i
$381$		0			0
$382$	−1756.38	+	1756.38i	−0.235246	+	0.235246i
$383$	144.736	−	144.736i	0.0193098	−	0.0193098i	−0.697386	−	0.716696i	$-0.745654\pi$
$383$	144.736	−	144.736i	0.0193098	−	0.0193098i	0.716696	+	0.697386i	$0.245654\pi$
$384$		0			0
$385$	351.066	+	145.416i	0.0464727	+	0.0192496i
$386$	−4496.72	−	10856.0i	−0.592945	−	1.43150i
$387$		0			0
$388$	−2421.11	+	1002.85i	−0.316786	+	0.131217i
$389$	4080.40	+	4080.40i	0.531837	+	0.531837i	0.921119	−	0.389282i	$-0.127277\pi$
$389$	4080.40	+	4080.40i	0.531837	+	0.531837i	−0.389282	+	0.921119i	$0.627277\pi$
$390$		0			0
$391$	−13591.6	−	5810.33i	−1.75794	−	0.751512i
$392$	−6404.44			−0.825186
$393$		0			0
$394$	1316.30	−	545.231i	0.168311	−	0.0697166i
$395$			450.816i			0.0574253i
$396$		0			0
$397$	6600.54	+	2734.03i	0.834437	+	0.345635i	0.758658	−	0.651489i	$-0.225855\pi$
$397$	6600.54	+	2734.03i	0.834437	+	0.345635i	0.0757795	+	0.997125i	$0.475855\pi$
$398$	−4199.06	+	10137.4i	−0.528844	+	1.27674i
$399$		0			0
$400$	5352.97	−	5352.97i	0.669121	−	0.669121i
$401$	2435.60	−	5880.05i	0.303312	−	0.732259i	−0.696579	−	0.717480i	$-0.745296\pi$
$401$	2435.60	−	5880.05i	0.303312	−	0.732259i	0.999891	−	0.0147789i	$-0.00470446\pi$
$402$		0			0
$403$	3055.41	+	7376.40i	0.377669	+	0.911774i
$404$		−	590.070i		−	0.0726660i
$405$		0			0
$406$	124.511	+	124.511i	0.0152202	+	0.0152202i
$407$	4162.33			0.506926
$408$		0			0
$409$	2997.87			0.362433			0.181217	−	0.983443i	$-0.441997\pi$
$409$	2997.87			0.362433			0.181217	+	0.983443i	$0.441997\pi$
$410$	−2923.23	−	2923.23i	−0.352117	−	0.352117i
$411$		0			0
$412$			1918.60i			0.229424i
$413$	58.3426	+	140.852i	0.00695122	+	0.0167817i
$414$		0			0
$415$	−697.591	+	1684.13i	−0.0825142	+	0.199207i
$416$	3634.01	−	3634.01i	0.428298	−	0.428298i
$417$		0			0
$418$	1093.39	−	2639.67i	0.127941	−	0.308876i
$419$	−10853.1	−	4495.49i	−1.26541	−	0.524150i	−0.353844	−	0.935304i	$-0.615126\pi$
$419$	−10853.1	−	4495.49i	−1.26541	−	0.524150i	−0.911566	+	0.411154i	$0.865126\pi$
$420$		0			0
$421$		−	8842.15i		−	1.02361i	−0.859102	−	0.511805i	$-0.828977\pi$
$421$		−	8842.15i		−	1.02361i	0.859102	−	0.511805i	$-0.171023\pi$
$422$	−5297.15	+	2194.15i	−0.611046	+	0.253103i
$423$		0			0
$424$	−5932.52			−0.679501
$425$	−5008.10	+	4896.34i	−0.571597	+	0.558841i
$426$		0			0
$427$	1612.46	+	1612.46i	0.182745	+	0.182745i
$428$	2106.97	−	872.737i	0.237954	−	0.0985639i
$429$		0			0
$430$	1914.23	+	4621.37i	0.214680	+	0.518284i
$431$	−2863.45	−	1186.08i	−0.320018	−	0.132556i	0.216891	−	0.976196i	$-0.430408\pi$
$431$	−2863.45	−	1186.08i	−0.320018	−	0.132556i	−0.536909	+	0.843640i	$0.680408\pi$
$432$		0			0
$433$	−7122.55	+	7122.55i	−0.790503	+	0.790503i	−0.981576	−	0.191073i	$-0.938803\pi$
$433$	−7122.55	+	7122.55i	−0.790503	+	0.790503i	0.191073	+	0.981576i	$0.438803\pi$
$434$	−829.942	+	829.942i	−0.0917938	+	0.0917938i
$435$		0			0
$436$	1504.21	+	623.064i	0.165226	+	0.0684389i
$437$	2684.18	+	6480.18i	0.293825	+	0.709357i
$438$		0			0
$439$	−16036.6	+	6642.57i	−1.74347	+	0.722170i	−0.744992	+	0.667073i	$0.767547\pi$
$439$	−16036.6	+	6642.57i	−1.74347	+	0.722170i	−0.998481	+	0.0550975i	$0.982453\pi$
$440$	−1843.02	−	1843.02i	−0.199687	−	0.199687i
$441$		0			0
$442$	−9439.45	+	9228.79i	−1.01581	+	0.993143i
$443$	−6979.90			−0.748589			−0.374295	−	0.927310i	$-0.622115\pi$
$443$	−6979.90			−0.748589			−0.374295	+	0.927310i	$0.622115\pi$
$444$		0			0
$445$	−888.638	+	368.086i	−0.0946640	+	0.0392111i
$446$			20518.7i			2.17845i
$447$		0			0
$448$	−861.549	−	356.865i	−0.0908579	−	0.0376346i
$449$	3532.36	−	8527.87i	0.371275	−	0.896336i	−0.622260	−	0.782810i	$-0.713785\pi$
$449$	3532.36	−	8527.87i	0.371275	−	0.896336i	0.993535	−	0.113526i	$-0.0362145\pi$
$450$		0			0
$451$	5044.44	−	5044.44i	0.526681	−	0.526681i
$452$	−1505.40	+	3634.37i	−0.156655	+	0.378200i
$453$		0			0
$454$	−2928.54	−	7070.12i	−0.302738	−	0.730875i
$455$			833.127i			0.0858409i
$456$		0			0
$457$	−8662.49	−	8662.49i	−0.886683	−	0.886683i	0.107520	−	0.994203i	$-0.465709\pi$
$457$	−8662.49	−	8662.49i	−0.886683	−	0.886683i	−0.994203	+	0.107520i	$0.965709\pi$
$458$	2067.39			0.210923
$459$		0			0
$460$	−2049.62			−0.207748
$461$	−4426.14	−	4426.14i	−0.447171	−	0.447171i	0.447242	−	0.894413i	$-0.352406\pi$
$461$	−4426.14	−	4426.14i	−0.447171	−	0.447171i	−0.894413	+	0.447242i	$0.852406\pi$
$462$		0			0
$463$			10195.0i			1.02333i	0.859185	+	0.511665i	$0.170971\pi$
$463$			10195.0i			1.02333i	−0.859185	+	0.511665i	$0.829029\pi$
$464$	−581.354	−	1403.51i	−0.0581652	−	0.140423i
$465$		0			0
$466$	1413.74	−	3413.07i	0.140537	−	0.339286i
$467$	−10453.2	+	10453.2i	−1.03579	+	1.03579i	−0.0364587	+	0.999335i	$0.511608\pi$
$467$	−10453.2	+	10453.2i	−1.03579	+	1.03579i	−0.999335	+	0.0364587i	$0.988392\pi$
$468$		0			0
$469$	−779.319	+	1881.44i	−0.0767284	+	0.185239i
$470$	4805.50	+	1990.50i	0.471619	+	0.195351i
$471$		0			0
$472$		−	1045.72i		−	0.101977i
$473$	−7974.80	+	3303.27i	−0.775226	+	0.321109i
$474$		0			0
$475$	3323.52			0.321039
$476$	−348.400	−	148.940i	−0.0335481	−	0.0143417i
$477$		0			0
$478$	−11773.9	−	11773.9i	−1.12662	−	1.12662i
$479$	15123.9	−	6264.54i	1.44265	−	0.597566i	0.482212	−	0.876054i	$-0.339833\pi$
$479$	15123.9	−	6264.54i	1.44265	−	0.597566i	0.960440	+	0.278488i	$0.0898334\pi$
$480$		0			0
$481$	3492.32	+	8431.20i	0.331052	+	0.799230i
$482$	−3867.89	−	1602.13i	−0.365513	−	0.151401i
$483$		0			0
$484$	807.929	−	807.929i	0.0758761	−	0.0758761i
$485$	−4780.93	+	4780.93i	−0.447610	+	0.447610i
$486$		0			0
$487$	3793.74	+	1571.42i	0.352999	+	0.146217i	0.552135	−	0.833755i	$-0.313813\pi$
$487$	3793.74	+	1571.42i	0.352999	+	0.146217i	−0.199135	+	0.979972i	$0.563813\pi$
$488$	−5985.67	−	14450.7i	−0.555243	−	1.34048i
$489$		0			0
$490$	4890.10	−	2025.55i	0.450841	−	0.186745i
$491$	−620.841	−	620.841i	−0.0570634	−	0.0570634i	0.677999	−	0.735063i	$-0.262847\pi$
$491$	−620.841	−	620.841i	−0.0570634	−	0.0570634i	−0.735063	+	0.677999i	$0.762847\pi$
$492$		0			0
$493$	523.179	+	1304.51i	0.0477948	+	0.119173i
$494$	6264.28			0.570533
$495$		0			0
$496$	9355.24	−	3875.07i	0.846901	−	0.350798i
$497$			1752.37i			0.158158i
$498$		0			0
$499$	−12767.7	−	5288.55i	−1.14541	−	0.474445i	−0.272419	−	0.962179i	$-0.587824\pi$
$499$	−12767.7	−	5288.55i	−1.14541	−	0.474445i	−0.872992	+	0.487734i	$0.837824\pi$
$500$	−836.578	+	2019.68i	−0.0748258	+	0.180646i
$501$		0			0
$502$	−9542.91	+	9542.91i	−0.848448	+	0.848448i
$503$	−1806.81	+	4362.03i	−0.160163	+	0.386667i	−0.983506	−	0.180877i	$-0.942106\pi$
$503$	−1806.81	+	4362.03i	−0.160163	+	0.386667i	0.823343	+	0.567544i	$0.192106\pi$
$504$		0			0
$505$	−582.603	−	1406.53i	−0.0513376	−	0.123940i
$506$		−	18115.4i		−	1.59156i
$507$		0			0
$508$	2196.28	+	2196.28i	0.191819	+	0.191819i
$509$	−16554.3			−1.44156			−0.720782	−	0.693161i	$-0.756217\pi$
$509$	−16554.3			−1.44156			−0.720782	+	0.693161i	$0.756217\pi$
$510$		0			0
$511$	−1382.78			−0.119708
$512$	3578.33	+	3578.33i	0.308870	+	0.308870i
$513$		0			0
$514$			765.813i			0.0657171i
$515$	1894.32	+	4573.29i	0.162085	+	0.391307i
$516$		0			0
$517$	−3434.88	+	8292.54i	−0.292197	+	0.705427i
$518$	−948.621	+	948.621i	−0.0804633	+	0.0804633i
$519$		0			0
$520$	2186.86	−	5279.55i	0.184424	−	0.445238i
$521$	13632.3	+	5646.69i	1.14634	+	0.474829i	0.873304	−	0.487175i	$-0.161973\pi$
$521$	13632.3	+	5646.69i	1.14634	+	0.474829i	0.273035	+	0.962004i	$0.411973\pi$
$522$		0			0
$523$		−	7800.86i		−	0.652214i	−0.945333	−	0.326107i	$-0.894263\pi$
$523$		−	7800.86i		−	0.652214i	0.945333	−	0.326107i	$-0.105737\pi$
$524$	4689.22	−	1942.34i	0.390934	−	0.161930i
$525$		0			0
$526$	9942.71			0.824188
$527$	−8695.32	+	3487.30i	−0.718736	+	0.288253i
$528$		0			0
$529$	22843.0	+	22843.0i	1.87746	+	1.87746i
$530$	4529.77	−	1876.29i	0.371246	−	0.153775i
$531$		0			0
$532$	68.8050	+	166.110i	0.00560729	+	0.0135372i
$533$	14450.4	+	5985.56i	1.17433	+	0.486423i
$534$		0			0
$535$	4160.62	−	4160.62i	0.336223	−	0.336223i
$536$	9877.14	−	9877.14i	0.795947	−	0.795947i
$537$		0			0
$538$	−614.329	−	254.463i	−0.0492297	−	0.0203916i
$539$	3495.36	+	8438.54i	0.279324	+	0.674348i
$540$		0			0
$541$	21275.5	−	8812.61i	1.69077	−	0.700339i	0.691022	−	0.722834i	$-0.257161\pi$
$541$	21275.5	−	8812.61i	1.69077	−	0.700339i	0.999747	+	0.0224947i	$0.00716090\pi$
$542$	−3628.13	−	3628.13i	−0.287530	−	0.287530i
$543$		0			0
$544$	4215.74	+	4311.97i	0.332258	+	0.339842i
$545$	4200.71			0.330162
$546$		0			0
$547$	−2440.68	+	1010.96i	−0.190779	+	0.0790232i	−0.476028	−	0.879430i	$-0.657924\pi$
$547$	−2440.68	+	1010.96i	−0.190779	+	0.0790232i	0.285249	+	0.958454i	$0.407924\pi$
$548$		−	1447.34i		−	0.112824i
$549$		0			0
$550$	−7930.30	−	3284.84i	−0.614816	−	0.254665i
$551$	255.228	−	616.176i	0.0197334	−	0.0476406i
$552$		0			0
$553$	177.298	−	177.298i	0.0136338	−	0.0136338i
$554$	−5582.66	+	13477.7i	−0.428131	+	1.03360i
$555$		0			0
$556$	−1880.97	−	4541.06i	−0.143473	−	0.346374i
$557$		−	19800.8i		−	1.50626i	−0.657873	−	0.753129i	$-0.728544\pi$
$557$		−	19800.8i		−	1.50626i	0.657873	−	0.753129i	$-0.271456\pi$
$558$		0			0
$559$	−13382.2	−	13382.2i	−1.01253	−	1.01253i
$560$	1056.63			0.0797333
$561$		0			0
$562$	−16005.1			−1.20131
$563$	6882.93	+	6882.93i	0.515241	+	0.515241i	0.916128	−	0.400886i	$-0.131298\pi$
$563$	6882.93	+	6882.93i	0.515241	+	0.515241i	−0.400886	+	0.916128i	$0.631298\pi$
$564$		0			0
$565$			10149.5i			0.755736i
$566$	2940.46	+	7098.90i	0.218369	+	0.527189i
$567$		0			0
$568$	4599.76	−	11104.8i	0.339792	−	0.820330i
$569$	4483.53	−	4483.53i	0.330333	−	0.330333i	−0.522380	−	0.852713i	$-0.674956\pi$
$569$	4483.53	−	4483.53i	0.330333	−	0.330333i	0.852713	+	0.522380i	$0.174956\pi$
$570$		0			0
$571$	4736.75	−	11435.5i	0.347157	−	0.838112i	−0.649796	−	0.760109i	$-0.725146\pi$
$571$	4736.75	−	11435.5i	0.347157	−	0.838112i	0.996953	−	0.0780032i	$-0.0248544\pi$
$572$	−2918.36	−	1208.82i	−0.213326	−	0.0883627i
$573$		0			0
$574$			2299.32i			0.167198i
$575$	19468.3	−	8064.02i	1.41197	−	0.584857i
$576$		0			0
$577$	36.6040			0.00264098			0.00132049	−	0.999999i	$-0.499580\pi$
$577$	36.6040			0.00264098			0.00132049	+	0.999999i	$0.499580\pi$
$578$	−10703.3	−	11197.7i	−0.770242	−	0.805815i
$579$		0			0
$580$	137.809	+	137.809i	0.00986586	+	0.00986586i
$581$	936.693	−	387.991i	0.0668857	−	0.0277049i
$582$		0			0
$583$	3237.80	+	7816.73i	0.230010	+	0.555293i
$584$	8762.74	+	3629.64i	0.620898	+	0.257184i
$585$		0			0
$586$	7357.86	−	7357.86i	0.518687	−	0.518687i
$587$	14389.9	−	14389.9i	1.01182	−	1.01182i	0.0118873	−	0.999929i	$-0.496216\pi$
$587$	14389.9	−	14389.9i	1.01182	−	1.01182i	0.999929	−	0.0118873i	$-0.00378392\pi$
$588$		0			0
$589$	4107.18	+	1701.25i	0.287323	+	0.119013i
$590$	330.733	+	798.461i	0.0230781	+	0.0557155i
$591$		0			0
$592$	10693.0	−	4429.19i	0.742365	−	0.307498i
$593$	−14416.1	−	14416.1i	−0.998308	−	0.998308i	0.00169056	−	0.999999i	$-0.499462\pi$
$593$	−14416.1	−	14416.1i	−0.998308	−	0.998308i	−0.999999	+	0.00169056i	$0.999462\pi$
$594$		0			0
$595$	−977.523	−	11.0304i	−0.0673522	−	0.000760006i
$596$	3526.02			0.242334
$597$		0			0
$598$	36694.5	−	15199.4i	2.50928	−	1.03938i
$599$		−	316.417i		−	0.0215834i	−0.999942	−	0.0107917i	$-0.996565\pi$
$599$		−	316.417i		−	0.0215834i	0.999942	−	0.0107917i	$-0.00343517\pi$
$600$		0			0
$601$	1230.47	+	509.678i	0.0835141	+	0.0345927i	0.424049	−	0.905639i	$-0.360608\pi$
$601$	1230.47	+	509.678i	0.0835141	+	0.0345927i	−0.340535	+	0.940232i	$0.610608\pi$
$602$	1064.67	−	2570.34i	0.0720810	−	0.174019i
$603$		0			0
$604$	−2910.20	+	2910.20i	−0.196050	+	0.196050i
$605$	1128.13	−	2723.54i	0.0758096	−	0.183021i
$606$		0			0
$607$	5309.03	+	12817.1i	0.355003	+	0.857053i	0.995987	+	0.0894989i	$0.0285266\pi$
$607$	5309.03	+	12817.1i	0.355003	+	0.857053i	−0.640984	+	0.767554i	$0.721473\pi$
$608$		−	2861.54i		−	0.190873i
$609$		0			0
$610$	9140.71	+	9140.71i	0.606715	+	0.606715i
$611$	−19679.3			−1.30301
$612$		0			0
$613$	15297.0			1.00790			0.503948	−	0.863734i	$-0.331880\pi$
$613$	15297.0			1.00790			0.503948	+	0.863734i	$0.331880\pi$
$614$	2645.01	+	2645.01i	0.173850	+	0.173850i
$615$		0			0
$616$			1449.66i			0.0948186i
$617$	5784.96	+	13966.1i	0.377461	+	0.911272i	0.992440	+	0.122729i	$0.0391645\pi$
$617$	5784.96	+	13966.1i	0.377461	+	0.911272i	−0.614979	+	0.788544i	$0.710835\pi$
$618$		0			0
$619$	−8576.73	+	20706.0i	−0.556911	+	1.34450i	0.355289	+	0.934756i	$0.384382\pi$
$619$	−8576.73	+	20706.0i	−0.556911	+	1.34450i	−0.912200	+	0.409745i	$0.865618\pi$
$620$	−918.577	+	918.577i	−0.0595015	+	0.0595015i
$621$		0			0
$622$	−793.286	+	1915.16i	−0.0511381	+	0.123458i
$623$	494.249	+	204.724i	0.0317844	+	0.0131655i
$624$		0			0
$625$		−	6850.26i		−	0.438417i
$626$	−17692.1	+	7328.29i	−1.12958	+	0.467887i
$627$		0			0
$628$	3120.61			0.198290
$629$	−9938.72	+	3985.97i	−0.630020	+	0.252673i
$630$		0			0
$631$	−3415.99	−	3415.99i	−0.215513	−	0.215513i	0.591092	−	0.806604i	$-0.298697\pi$
$631$	−3415.99	−	3415.99i	−0.215513	−	0.215513i	−0.806604	+	0.591092i	$0.798697\pi$
$632$	−1588.93	+	658.158i	−0.100007	+	0.0414242i
$633$		0			0
$634$	−6941.71	−	16758.8i	−0.434843	−	1.04980i
$635$	7403.68	+	3066.70i	0.462687	+	0.191651i
$636$		0			0
$637$	−14160.4	+	14160.4i	−0.880776	+	0.880776i
$638$	−1218.01	+	1218.01i	−0.0755822	+	0.0755822i
$639$		0			0
$640$	−8068.21	−	3341.96i	−0.498319	−	0.206410i
$641$	8804.50	+	21255.9i	0.542522	+	1.30976i	0.922938	+	0.384949i	$0.125781\pi$
$641$	8804.50	+	21255.9i	0.542522	+	1.30976i	−0.380416	+	0.924816i	$0.624219\pi$
$642$		0			0
$643$	−5256.78	+	2177.43i	−0.322406	+	0.133545i	−0.538016	−	0.842935i	$-0.680826\pi$
$643$	−5256.78	+	2177.43i	−0.322406	+	0.133545i	0.215610	+	0.976480i	$0.430826\pi$
$644$	806.083	+	806.083i	0.0493232	+	0.0493232i
$645$		0			0
$646$	−82.9378	+	7350.00i	−0.00505131	+	0.447650i
$647$	15949.0			0.969122			0.484561	−	0.874758i	$-0.338979\pi$
$647$	15949.0			0.969122			0.484561	+	0.874758i	$0.338979\pi$
$648$		0			0
$649$	−1377.85	+	570.726i	−0.0833366	+	0.0345192i
$650$		−	18819.7i		−	1.13564i
$651$		0			0
$652$	−4084.79	−	1691.98i	−0.245357	−	0.101630i
$653$	−4119.43	+	9945.18i	−0.246869	+	0.595995i	−0.997935	−	0.0642322i	$-0.979540\pi$
$653$	−4119.43	+	9945.18i	−0.246869	+	0.595995i	0.751066	+	0.660228i	$0.229540\pi$
$654$		0			0
$655$	9259.75	−	9259.75i	0.552379	−	0.552379i
$656$	7591.28	−	18327.0i	0.451814	−	1.09078i
$657$		0			0
$658$	−1107.09	−	2672.75i	−0.0655910	−	0.158351i
$659$			25208.2i			1.49010i	0.667011	+	0.745048i	$0.267573\pi$
$659$			25208.2i			1.49010i	−0.667011	+	0.745048i	$0.732427\pi$
$660$		0			0
$661$	−10196.1	−	10196.1i	−0.599975	−	0.599975i	0.340331	−	0.940306i	$-0.389461\pi$
$661$	−10196.1	−	10196.1i	−0.599975	−	0.599975i	−0.940306	+	0.340331i	$0.889461\pi$
$662$	−283.267			−0.0166306
$663$		0			0
$664$	−6954.28			−0.406444
$665$	328.016	+	328.016i	0.0191277	+	0.0191277i
$666$		0			0
$667$		−	4228.67i		−	0.245479i
$668$	−1227.11	−	2962.50i	−0.0710751	−	0.171590i
$669$		0			0
$670$	−4417.81	+	10665.5i	−0.254739	+	0.614994i
$671$	−15773.5	+	15773.5i	−0.907497	+	0.907497i
$672$		0			0
$673$	−807.706	+	1949.97i	−0.0462627	+	0.111688i	−0.945322	−	0.326140i	$-0.894252\pi$
$673$	−807.706	+	1949.97i	−0.0462627	+	0.111688i	0.899059	+	0.437828i	$0.144252\pi$
$674$	−2468.14	−	1022.34i	−0.141052	−	0.0584256i
$675$		0			0
$676$		−	2661.52i		−	0.151429i
$677$	11035.3	−	4570.96i	0.626470	−	0.259493i	−0.0467822	−	0.998905i	$-0.514897\pi$
$677$	11035.3	−	4570.96i	0.626470	−	0.259493i	0.673253	+	0.739413i	$0.264897\pi$
$678$		0			0
$679$	3760.52			0.212541
$680$	6165.64	+	2635.79i	0.347708	+	0.148644i
$681$		0			0
$682$	−8118.75	−	8118.75i	−0.455840	−	0.455840i
$683$	−17633.0	+	7303.83i	−0.987859	+	0.409185i	−0.817331	−	0.576168i	$-0.804547\pi$
$683$	−17633.0	+	7303.83i	−0.987859	+	0.409185i	−0.170528	+	0.985353i	$0.554547\pi$
$684$		0			0
$685$	−1429.03	−	3449.98i	−0.0797085	−	0.192433i
$686$	−5502.55	−	2279.23i	−0.306251	−	0.126853i
$687$		0			0
$688$	−16972.2	+	16972.2i	−0.940492	+	0.940492i
$689$	−13116.9	+	13116.9i	−0.725277	+	0.725277i
$690$		0			0
$691$	26161.3	+	10836.4i	1.44026	+	0.596577i	0.959862	−	0.280471i	$-0.0904908\pi$
$691$	26161.3	+	10836.4i	1.44026	+	0.596577i	0.480402	+	0.877048i	$0.340491\pi$
$692$	−1642.08	−	3964.34i	−0.0902061	−	0.217777i
$693$		0			0
$694$	−1719.56	+	712.264i	−0.0940540	+	0.0389585i
$695$	−8967.20	−	8967.20i	−0.489418	−	0.489418i
$696$		0			0
$697$	−7214.29	+	16875.7i	−0.392053	+	0.917091i
$698$	−29598.6			−1.60505
$699$		0			0
$700$	499.041	−	206.710i	0.0269457	−	0.0111613i
$701$			5916.75i			0.318791i	0.987215	+	0.159396i	$0.0509545\pi$
$701$			5916.75i			0.318791i	−0.987215	+	0.159396i	$0.949045\pi$
$702$		0			0
$703$	4694.49	+	1944.52i	0.251858	+	0.104323i
$704$	3490.97	−	8427.94i	0.186890	−	0.451193i
$705$		0			0
$706$	−13769.3	+	13769.3i	−0.734014	+	0.734014i
$707$	−324.036	+	782.292i	−0.0172371	+	0.0416140i
$708$		0			0
$709$	−7079.57	−	17091.6i	−0.375005	−	0.905343i	−0.992886	−	0.119071i	$-0.962008\pi$
$709$	−7079.57	−	17091.6i	−0.375005	−	0.905343i	0.617880	−	0.786272i	$-0.287992\pi$
$710$			9933.85i			0.525085i
$711$		0			0
$712$	−2594.69	−	2594.69i	−0.136573	−	0.136573i
$713$	28186.6			1.48050
$714$		0			0
$715$	−8149.91			−0.426279
$716$	−28.4842	−	28.4842i	−0.00148674	−	0.00148674i
$717$		0			0
$718$			22546.9i			1.17193i
$719$	−8498.05	−	20516.1i	−0.440784	−	1.06415i	−0.975674	−	0.219226i	$-0.929647\pi$
$719$	−8498.05	−	20516.1i	−0.440784	−	1.06415i	0.534890	−	0.844922i	$-0.320353\pi$
$720$		0			0
$721$	1053.60	−	2543.60i	0.0544215	−	0.131385i
$722$	−12825.4	+	12825.4i	−0.661099	+	0.661099i
$723$		0			0
$724$	−324.208	+	782.706i	−0.0166424	+	0.0401783i
$725$	−1851.16	−	766.778i	−0.0948283	−	0.0392792i
$726$		0			0
$727$		−	3777.02i		−	0.192685i	−0.995348	−	0.0963424i	$-0.969286\pi$
$727$		−	3777.02i		−	0.192685i	0.995348	−	0.0963424i	$-0.0307144\pi$
$728$	−2936.42	+	1216.30i	−0.149493	+	0.0619220i
$729$		0			0
$730$	−7838.73			−0.397431
$731$	15878.7	−	15524.4i	0.803415	−	0.785486i
$732$		0			0
$733$	−14111.3	−	14111.3i	−0.711068	−	0.711068i	0.255690	−	0.966759i	$-0.417697\pi$
$733$	−14111.3	−	14111.3i	−0.711068	−	0.711068i	−0.966759	+	0.255690i	$0.917697\pi$
$734$	9781.72	−	4051.72i	0.491894	−	0.203749i
$735$		0			0
$736$	−6943.11	−	16762.1i	−0.347726	−	0.839485i
$737$	−18404.9	−	7623.54i	−0.919880	−	0.381027i
$738$		0			0
$739$	−16453.2	+	16453.2i	−0.819001	+	0.819001i	−0.985963	−	0.166962i	$-0.946604\pi$
$739$	−16453.2	+	16453.2i	−0.819001	+	0.819001i	0.166962	+	0.985963i	$0.446604\pi$
$740$	−1049.93	+	1049.93i	−0.0521570	+	0.0521570i
$741$		0			0
$742$	−2519.40	−	1043.57i	−0.124649	−	0.0516315i
$743$	−4816.87	−	11629.0i	−0.237838	−	0.574193i	0.759220	−	0.650834i	$-0.225580\pi$
$743$	−4816.87	−	11629.0i	−0.237838	−	0.574193i	−0.997059	+	0.0766410i	$0.975580\pi$
$744$		0			0
$745$	8404.83	−	3481.39i	0.413328	−	0.171206i
$746$	18680.9	+	18680.9i	0.916830	+	0.916830i
$747$		0			0
$748$	1456.97	−	3408.16i	0.0712195	−	0.166597i
$749$	−3272.61			−0.159651
$750$		0			0
$751$	2460.10	−	1019.01i	0.119534	−	0.0495127i	−0.322115	−	0.946701i	$-0.604394\pi$
$751$	2460.10	−	1019.01i	0.119534	−	0.0495127i	0.441649	+	0.897188i	$0.354394\pi$
$752$			24958.6i			1.21030i
$753$		0			0
$754$	−3489.14	−	1445.25i	−0.168524	−	0.0698049i
$755$	−4063.57	+	9810.32i	−0.195879	+	0.472893i
$756$		0			0
$757$	18689.0	−	18689.0i	0.897308	−	0.897308i	−0.0978891	−	0.995197i	$-0.531209\pi$
$757$	18689.0	−	18689.0i	0.897308	−	0.897308i	0.995197	+	0.0978891i	$0.0312090\pi$
$758$	7716.86	−	18630.2i	0.369775	−	0.892715i
$759$		0			0
$760$	−1217.64	−	2939.65i	−0.0581166	−	0.140306i
$761$		−	8469.75i		−	0.403454i	−0.979442	−	0.201727i	$-0.935345\pi$
$761$		−	8469.75i		−	0.403454i	0.979442	−	0.201727i	$-0.0646553\pi$
$762$		0			0
$763$	−1652.07	−	1652.07i	−0.0783865	−	0.0783865i
$764$	1529.05			0.0724071
$765$		0			0
$766$	−645.361			−0.0304410
$767$	−2312.12	−	2312.12i	−0.108847	−	0.108847i
$768$		0			0
$769$		−	8452.54i		−	0.396367i	−0.980165	−	0.198184i	$-0.936496\pi$
$769$		−	8452.54i		−	0.396367i	0.980165	−	0.198184i	$-0.0635043\pi$
$770$	−458.486	−	1106.88i	−0.0214580	−	0.0518043i
$771$		0			0
$772$	−2768.11	+	6682.82i	−0.129050	+	0.311554i
$773$	23996.5	−	23996.5i	1.11655	−	1.11655i	0.124307	−	0.992244i	$-0.460329\pi$
$773$	23996.5	−	23996.5i	1.11655	−	1.11655i	0.992244	−	0.124307i	$-0.0396707\pi$
$774$		0			0
$775$	5111.03	−	12339.1i	0.236895	−	0.571915i
$776$	−23830.6	−	9870.94i	−1.10241	−	0.456632i
$777$		0			0
$778$		−	18194.1i		−	0.838419i
$779$	8045.99	−	3332.76i	0.370061	−	0.153284i
$780$		0			0
$781$	−17142.2			−0.785399
$782$	17347.8	+	43255.5i	0.793296	+	1.97802i
$783$		0			0
$784$	17959.1	+	17959.1i	0.818108	+	0.818108i
$785$	7438.48	−	3081.12i	0.338205	−	0.140089i
$786$		0			0
$787$	13156.3	+	31762.1i	0.595898	+	1.43863i	0.877727	+	0.479161i	$0.159059\pi$
$787$	13156.3	+	31762.1i	0.595898	+	1.43863i	−0.281829	+	0.959465i	$0.590941\pi$
$788$	−810.297	−	335.636i	−0.0366315	−	0.0151733i
$789$		0			0
$790$	1005.07	−	1005.07i	0.0452643	−	0.0452643i
$791$	3991.61	−	3991.61i	0.179425	−	0.179425i
$792$		0			0
$793$	−45185.3	−	18716.4i	−2.02343	−	0.838131i
$794$	−8620.18	−	20811.0i	−0.385288	−	0.930168i
$795$		0			0
$796$	6240.45	−	2584.88i	0.277873	−	0.115099i
$797$	−2354.14	−	2354.14i	−0.104627	−	0.104627i	0.652855	−	0.757483i	$-0.273571\pi$
$797$	−2354.14	−	2354.14i	−0.104627	−	0.104627i	−0.757483	+	0.652855i	$0.773571\pi$
$798$		0			0
$799$	260.550	−	23090.1i	0.0115364	−	1.02236i
$800$	−8596.87			−0.379932
$801$		0			0
$802$	−18539.3	+	7679.24i	−0.816267	+	0.338109i
$803$		−	13526.8i		−	0.594459i
$804$		0			0
$805$	2717.31	+	1125.55i	0.118972	+	0.0492799i
$806$	9633.45	−	23257.2i	0.420997	−	1.01638i
$807$		0			0
$808$	4106.85	−	4106.85i	0.178810	−	0.178810i
$809$	2762.07	−	6668.23i	0.120036	−	0.289793i	−0.852428	−	0.522844i	$-0.824871\pi$
$809$	2762.07	−	6668.23i	0.120036	−	0.289793i	0.972464	+	0.233051i	$0.0748710\pi$
$810$		0			0
$811$	13992.5	+	33780.9i	0.605848	+	1.46265i	0.867476	+	0.497478i	$0.165741\pi$
$811$	13992.5	+	33780.9i	0.605848	+	1.46265i	−0.261628	+	0.965169i	$0.584259\pi$
$812$		−	108.396i		−	0.00468466i
$813$		0			0
$814$	−9279.70	−	9279.70i	−0.399574	−	0.399574i
$815$	−11407.3			−0.490284
$816$		0			0
$817$	−10537.6			−0.451240
$818$	−6683.60	−	6683.60i	−0.285680	−	0.285680i
$819$		0			0
$820$			2544.88i			0.108379i
$821$	8855.50	+	21379.1i	0.376442	+	0.908812i	0.992627	+	0.121210i	$0.0386775\pi$
$821$	8855.50	+	21379.1i	0.376442	+	0.908812i	−0.616185	+	0.787602i	$0.711323\pi$
$822$		0			0
$823$	15800.2	−	38145.0i	0.669210	−	1.61562i	−0.113725	−	0.993512i	$-0.536278\pi$
$823$	15800.2	−	38145.0i	0.669210	−	1.61562i	0.782935	−	0.622103i	$-0.213722\pi$
$824$	−13353.3	+	13353.3i	−0.564545	+	0.564545i
$825$		0			0
$826$	183.949	−	444.093i	0.00774869	−	0.0187070i
$827$	−9246.14	−	3829.88i	−0.388779	−	0.161037i	0.179727	−	0.983716i	$-0.442478\pi$
$827$	−9246.14	−	3829.88i	−0.388779	−	0.161037i	−0.568506	+	0.822679i	$0.692478\pi$
$828$		0			0
$829$			44643.6i			1.87037i	0.354159	+	0.935185i	$0.384767\pi$
$829$			44643.6i			1.87037i	−0.354159	+	0.935185i	$0.615233\pi$
$830$	5309.94	−	2199.45i	0.222061	−	0.0919806i
$831$		0			0
$832$	20000.6			0.833410
$833$	−16427.1	−	16802.1i	−0.683273	−	0.698869i
$834$		0			0
$835$	−5850.01	−	5850.01i	−0.242453	−	0.242453i
$836$	−1624.94	+	673.072i	−0.0672246	+	0.0278453i
$837$		0			0
$838$	14173.9	+	34218.8i	0.584283	+	1.41058i
$839$	−13151.7	−	5447.61i	−0.541176	−	0.224163i	0.0953141	−	0.995447i	$-0.469614\pi$
$839$	−13151.7	−	5447.61i	−0.541176	−	0.224163i	−0.636490	+	0.771285i	$0.719614\pi$
$840$		0			0
$841$	16961.3	−	16961.3i	0.695449	−	0.695449i
$842$	−19713.1	+	19713.1i	−0.806840	+	0.806840i
$843$		0			0
$844$	3260.85	+	1350.69i	0.132989	+	0.0550860i
$845$	−2627.84	−	6344.17i	−0.106983	−	0.258280i
$846$		0			0
$847$	−1514.79	+	627.448i	−0.0614509	+	0.0254538i
$848$	16635.8	+	16635.8i	0.673673	+	0.673673i
$849$		0			0
$850$	22081.4	+	249.168i	0.891044	+	0.0100546i
$851$	32217.1			1.29775
$852$		0			0
$853$	−25618.2	+	10611.4i	−1.02831	+	0.425942i	−0.832104	−	0.554620i	$-0.812864\pi$
$853$	−25618.2	+	10611.4i	−1.02831	+	0.425942i	−0.196211	+	0.980562i	$0.562864\pi$
$854$		−	7189.78i		−	0.288090i
$855$		0			0
$856$	20738.6	+	8590.22i	0.828074	+	0.342999i
$857$	−11970.6	+	28899.6i	−0.477138	+	1.15191i	0.483807	+	0.875175i	$0.339254\pi$
$857$	−11970.6	+	28899.6i	−0.477138	+	1.15191i	−0.960945	+	0.276739i	$0.910746\pi$
$858$		0			0
$859$	−39.0952	+	39.0952i	−0.00155287	+	0.00155287i	−0.707883	−	0.706330i	$-0.750350\pi$
$859$	−39.0952	+	39.0952i	−0.00155287	+	0.00155287i	0.706330	+	0.707883i	$0.250350\pi$
$860$	1178.37	−	2844.85i	0.0467235	−	0.112801i
$861$		0			0
$862$	3739.62	+	9028.23i	0.147763	+	0.356732i
$863$		−	22900.4i		−	0.903291i	−0.892197	−	0.451646i	$-0.850837\pi$
$863$		−	22900.4i		−	0.903291i	0.892197	−	0.451646i	$-0.149163\pi$
$864$		0			0
$865$	−7828.34	−	7828.34i	−0.307713	−	0.307713i
$866$	31758.7			1.24620
$867$		0			0
$868$	722.522			0.0282535
$869$	1734.39	+	1734.39i	0.0677043	+	0.0677043i
$870$		0			0
$871$		−	43677.2i		−	1.69913i
$872$	6132.72	+	14805.7i	0.238165	+	0.574982i
$873$		0			0
$874$	8462.99	−	20431.5i	0.327534	−	0.790738i
$875$	2218.21	−	2218.21i	0.0857018	−	0.0857018i
$876$		0			0
$877$	−682.134	+	1646.82i	−0.0262646	+	0.0634083i	−0.936468	−	0.350754i	$-0.885925\pi$
$877$	−682.134	+	1646.82i	−0.0262646	+	0.0634083i	0.910203	+	0.414162i	$0.135925\pi$
$878$	50562.1	+	20943.5i	1.94349	+	0.805021i
$879$		0			0
$880$			10336.3i			0.395949i
$881$	−15920.8	+	6594.62i	−0.608838	+	0.252189i	−0.665731	−	0.746191i	$-0.731880\pi$
$881$	−15920.8	+	6594.62i	−0.608838	+	0.252189i	0.0568939	+	0.998380i	$0.481880\pi$
$882$		0			0
$883$	−10188.2			−0.388291			−0.194145	−	0.980973i	$-0.562193\pi$
$883$	−10188.2			−0.388291			−0.194145	+	0.980973i	$0.562193\pi$
$884$	8126.00	+	91.6943i	0.309171	+	0.00348870i
$885$		0			0
$886$	15561.3	+	15561.3i	0.590060	+	0.590060i
$887$	14478.7	−	5997.28i	0.548081	−	0.227022i	−0.0914208	−	0.995812i	$-0.529141\pi$
$887$	14478.7	−	5997.28i	0.548081	−	0.227022i	0.639501	+	0.768790i	$0.279141\pi$
$888$		0			0
$889$	−1705.66	−	4117.83i	−0.0643487	−	0.155352i
$890$	2801.80	+	1160.54i	0.105524	+	0.0437096i
$891$		0			0
$892$	8931.46	−	8931.46i	0.335255	−	0.335255i
$893$	−7748.07	+	7748.07i	−0.290347	+	0.290347i
$894$		0			0
$895$	−96.0206	−	39.7730i	−0.00358616	−	0.00148544i
$896$	1858.75	+	4487.43i	0.0693042	+	0.167315i
$897$		0			0
$898$	−26887.7	+	11137.2i	−0.999168	+	0.413869i
$899$	−1895.16	−	1895.16i	−0.0703081	−	0.0703081i
$900$		0			0
$901$	−15216.7	−	15564.0i	−0.562643	−	0.575485i
$902$	−22492.6			−0.830291
$903$		0			0
$904$	−35772.5	+	14817.5i	−1.31612	+	0.545156i
$905$			2185.81i			0.0802861i
$906$		0			0
$907$	15621.3	+	6470.54i	0.571881	+	0.236881i	0.649834	−	0.760076i	$-0.274838\pi$
$907$	15621.3	+	6470.54i	0.571881	+	0.236881i	−0.0779531	+	0.996957i	$0.524838\pi$
$908$	−1802.77	+	4352.26i	−0.0658887	+	0.159069i
$909$		0			0
$910$	1857.42	−	1857.42i	0.0676623	−	0.0676623i
$911$	−13815.1	+	33352.6i	−0.502431	+	1.21298i	0.445724	+	0.895170i	$0.352946\pi$
$911$	−13815.1	+	33352.6i	−0.502431	+	1.21298i	−0.948156	+	0.317806i	$0.897054\pi$
$912$		0			0
$913$	3795.45	+	9163.02i	0.137580	+	0.332149i
$914$			38625.1i			1.39782i
$915$		0			0
$916$	−899.902	−	899.902i	−0.0324603	−	0.0324603i
$917$	−7283.41			−0.262290
$918$		0			0
$919$	20016.2			0.718470			0.359235	−	0.933247i	$-0.383038\pi$
$919$	20016.2			0.718470			0.359235	+	0.933247i	$0.383038\pi$
$920$	−14265.3	−	14265.3i	−0.511208	−	0.511208i
$921$		0			0
$922$			19735.7i			0.704947i
$923$	−14382.8	−	34723.2i	−0.512911	−	1.23828i
$924$		0			0
$925$	5841.88	−	14103.6i	0.207654	−	0.501321i
$926$	22729.2	−	22729.2i	0.806618	−	0.806618i
$927$		0			0
$928$	−660.194	+	1593.85i	−0.0233534	+	0.0563800i
$929$	−28298.7	−	11721.7i	−0.999407	−	0.413968i	−0.177828	−	0.984062i	$-0.556907\pi$
$929$	−28298.7	−	11721.7i	−0.999407	−	0.413968i	−0.821580	+	0.570094i	$0.806907\pi$
$930$		0			0
$931$			11150.3i			0.392522i
$932$	−2101.04	+	870.278i	−0.0738431	+	0.0305868i
$933$		0			0
$934$	46609.7			1.63289
$935$	107.903	−	9562.43i	0.00377413	−	0.334465i
$936$		0			0
$937$	2746.18	+	2746.18i	0.0957458	+	0.0957458i	0.753357	−	0.657611i	$-0.228433\pi$
$937$	2746.18	+	2746.18i	0.0957458	+	0.0957458i	−0.657611	+	0.753357i	$0.728433\pi$
$938$	5932.03	−	2457.13i	0.206490	−	0.0855310i
$939$		0			0
$940$	−1225.32	−	2958.19i	−0.0425167	−	0.102644i
$941$	−20044.5	−	8302.68i	−0.694400	−	0.287630i	0.00743202	−	0.999972i	$-0.497634\pi$
$941$	−20044.5	−	8302.68i	−0.694400	−	0.287630i	−0.701832	+	0.712342i	$0.747634\pi$
$942$		0			0
$943$	39044.8	−	39044.8i	1.34833	−	1.34833i
$944$	−2932.38	+	2932.38i	−0.101103	+	0.101103i
$945$		0			0
$946$	25143.9	+	10414.9i	0.864163	+	0.357948i
$947$	6086.52	+	14694.2i	0.208855	+	0.504220i	0.993243	−	0.116050i	$-0.0370233\pi$
$947$	6086.52	+	14694.2i	0.208855	+	0.504220i	−0.784389	+	0.620269i	$0.787023\pi$
$948$		0			0
$949$	27399.9	−	11349.4i	0.937236	−	0.388216i
$950$	−7409.61	−	7409.61i	−0.253052	−	0.253052i
$951$		0			0
$952$	−1388.23	−	3461.45i	−0.0472615	−	0.117843i
$953$	81.8493			0.00278212			0.00139106	−	0.999999i	$-0.499557\pi$
$953$	81.8493			0.00278212			0.00139106	+	0.999999i	$0.499557\pi$
$954$		0			0
$955$	3644.74	−	1509.70i	0.123498	−	0.0511547i
$956$			10250.0i			0.346765i
$957$		0			0
$958$	−47684.5	−	19751.6i	−1.60816	−	0.666122i
$959$	−794.806	+	1918.83i	−0.0267629	+	0.0646113i
$960$		0			0
$961$	−8433.08	+	8433.08i	−0.283075	+	0.283075i
$962$	11011.0	−	26582.9i	0.369032	−	0.890922i
$963$		0			0
$964$	986.249	+	2381.02i	0.0329512	+	0.0795512i
$965$			18662.7i			0.622562i
$966$		0			0
$967$	13632.8	+	13632.8i	0.453363	+	0.453363i	0.896469	−	0.443106i	$-0.146124\pi$
$967$	13632.8	+	13632.8i	0.453363	+	0.453363i	−0.443106	+	0.896469i	$0.646124\pi$
$968$	11246.3			0.373419
$969$		0			0
$970$	21317.7			0.705639
$971$	38025.6	+	38025.6i	1.25674	+	1.25674i	0.952638	+	0.304107i	$0.0983579\pi$
$971$	38025.6	+	38025.6i	1.25674	+	1.25674i	0.304107	+	0.952638i	$0.401642\pi$
$972$		0			0
$973$			7053.30i			0.232393i
$974$	−4954.55	−	11961.3i	−0.162992	−	0.393497i
$975$		0			0
$976$	−23737.3	+	57307.0i	−0.778497	+	1.87946i
$977$	38705.7	−	38705.7i	1.26746	−	1.26746i	0.320061	−	0.947397i	$-0.396297\pi$
$977$	38705.7	−	38705.7i	1.26746	−	1.26746i	0.947397	−	0.320061i	$-0.103703\pi$
$978$		0			0
$979$	−2002.68	+	4834.89i	−0.0653788	+	0.157838i
$980$	−3010.27	−	1246.90i	−0.0981221	−	0.0406435i
$981$		0			0
$982$			2768.27i			0.0899581i
$983$	3146.11	−	1303.16i	0.102081	−	0.0422832i	−0.331059	−	0.943610i	$-0.607406\pi$
$983$	3146.11	−	1303.16i	0.102081	−	0.0422832i	0.433139	+	0.901327i	$0.357406\pi$
$984$		0			0
$985$	−2262.86			−0.0731988
$986$	1741.93	−	4074.74i	0.0562621	−	0.131609i
$987$		0			0
$988$	−2726.75	−	2726.75i	−0.0878030	−	0.0878030i
$989$	−61726.3	+	25567.9i	−1.98461	+	0.822054i
$990$		0			0
$991$	−11452.1	−	27647.8i	−0.367091	−	0.886237i	−0.994224	−	0.107324i	$-0.965772\pi$
$991$	−11452.1	−	27647.8i	−0.367091	−	0.886237i	0.627133	−	0.778912i	$-0.284228\pi$
$992$	−10624.0	−	4400.58i	−0.340031	−	0.140845i
$993$		0			0
$994$	3906.82	−	3906.82i	0.124665	−	0.124665i
$995$	12323.0	−	12323.0i	0.392627	−	0.392627i
$996$		0			0
$997$	−30224.2	−	12519.3i	−0.960092	−	0.397683i	−0.153077	−	0.988214i	$-0.548918\pi$
$997$	−30224.2	−	12519.3i	−0.960092	−	0.397683i	−0.807015	+	0.590531i	$0.798918\pi$
$998$	16674.4	+	40255.5i	0.528875	+	1.27682i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.4.l.a.19.1		12
3.2	odd	2		17.4.d.a.2.3	✓	12
17.9	even	8	inner	153.4.l.a.145.1		12
51.5	even	16		289.4.b.e.288.1		12
51.14	even	16		289.4.a.g.1.12		12
51.20	even	16		289.4.a.g.1.11		12
51.26	odd	8		17.4.d.a.9.3	yes	12
51.29	even	16		289.4.b.e.288.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.d.a.2.3	✓	12	3.2	odd	2
17.4.d.a.9.3	yes	12	51.26	odd	8
153.4.l.a.19.1		12	1.1	even	1	trivial
153.4.l.a.145.1		12	17.9	even	8	inner
289.4.a.g.1.11		12	51.20	even	16
289.4.a.g.1.12		12	51.14	even	16
289.4.b.e.288.1		12	51.5	even	16
289.4.b.e.288.2		12	51.29	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)

\(f(q)\)	\(=\)	\(q+(-2.22945 - 2.22945i) q^{2} +1.94089i q^{4} +(1.91633 + 4.62643i) q^{5} +(1.06584 - 2.57316i) q^{7} +(-13.5085 + 13.5085i) q^{8} +O(q^{10})\)	\(q+(-2.22945 - 2.22945i) q^{2} +1.94089i q^{4} +(1.91633 + 4.62643i) q^{5} +(1.06584 - 2.57316i) q^{7} +(-13.5085 + 13.5085i) q^{8} +(6.04203 - 14.5867i) q^{10} +(25.1714 + 10.4263i) q^{11} +59.7352i q^{13} +(-8.11295 + 3.36049i) q^{14} +75.7601 q^{16} +(-70.0883 - 0.790881i) q^{17} +(23.5187 + 23.5187i) q^{19} +(-8.97939 + 3.71938i) q^{20} +(-32.8734 - 79.3634i) q^{22} +(194.831 + 80.7017i) q^{23} +(70.6568 - 70.6568i) q^{25} +(133.177 - 133.177i) q^{26} +(4.99421 + 2.06867i) q^{28} +(-7.67362 - 18.5258i) q^{29} +(123.485 - 51.1492i) q^{31} +(-60.8354 - 60.8354i) q^{32} +(154.495 + 158.022i) q^{34} +13.9470 q^{35} +(141.143 - 58.4634i) q^{37} -104.868i q^{38} +(-88.3827 - 36.6093i) q^{40} +(100.202 - 241.908i) q^{41} +(-224.025 + 224.025i) q^{43} +(-20.2364 + 48.8550i) q^{44} +(-254.446 - 614.286i) q^{46} +329.443i q^{47} +(237.052 + 237.052i) q^{49} -315.052 q^{50} -115.939 q^{52} +(219.585 + 219.585i) q^{53} +136.434i q^{55} +(20.3616 + 49.1573i) q^{56} +(-24.1943 + 58.4102i) q^{58} +(-38.7062 + 38.7062i) q^{59} +(-313.322 + 756.427i) q^{61} +(-389.338 - 161.269i) q^{62} -334.822i q^{64} +(-276.360 + 114.472i) q^{65} -731.181 q^{67} +(1.53501 - 136.034i) q^{68} +(-31.0942 - 31.0942i) q^{70} +(-581.286 + 240.777i) q^{71} +(-189.995 - 458.689i) q^{73} +(-445.012 - 184.330i) q^{74} +(-45.6473 + 45.6473i) q^{76} +(53.6572 - 53.6572i) q^{77} +(83.1733 + 34.4515i) q^{79} +(145.181 + 350.498i) q^{80} +(-762.717 + 315.928i) q^{82} +(257.404 + 257.404i) q^{83} +(-130.653 - 325.774i) q^{85} +998.907 q^{86} +(-480.872 + 199.184i) q^{88} +192.079i q^{89} +(153.708 + 63.6679i) q^{91} +(-156.633 + 378.146i) q^{92} +(734.476 - 734.476i) q^{94} +(-63.7380 + 153.877i) q^{95} +(516.698 + 1247.42i) q^{97} -1056.99i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + 20 q^{5} - 4 q^{7} - 28 q^{8}+O(q^{10}) \) 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

Introduction

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