LMFDB - Embedded newform 234.3.i.b.73.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,3,Mod(73,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("234.73");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	234.i (of order $4$, degree $2$, 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:	$6.37603818603$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			73.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	234.73
Dual form			234.3.i.b.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 - 1.00000i) q^{2} +2.00000i q^{4} +(-1.26795 - 1.26795i) q^{5} +(0.732051 - 0.732051i) q^{7} +(2.00000 - 2.00000i) q^{8} +2.53590i q^{10} +(1.73205 - 1.73205i) q^{11} +(-3.92820 - 12.3923i) q^{13} -1.46410 q^{14} -4.00000 q^{16} -5.32051i q^{17} +(-14.7321 - 14.7321i) q^{19} +(2.53590 - 2.53590i) q^{20} -3.46410 q^{22} -5.32051i q^{23} -21.7846i q^{25} +(-8.46410 + 16.3205i) q^{26} +(1.46410 + 1.46410i) q^{28} -4.14359 q^{29} +(-24.9808 - 24.9808i) q^{31} +(4.00000 + 4.00000i) q^{32} +(-5.32051 + 5.32051i) q^{34} -1.85641 q^{35} +(-3.14359 + 3.14359i) q^{37} +29.4641i q^{38} -5.07180 q^{40} +(-44.4449 - 44.4449i) q^{41} +37.1769i q^{43} +(3.46410 + 3.46410i) q^{44} +(-5.32051 + 5.32051i) q^{46} +(30.8038 - 30.8038i) q^{47} +47.9282i q^{49} +(-21.7846 + 21.7846i) q^{50} +(24.7846 - 7.85641i) q^{52} -57.7128 q^{53} -4.39230 q^{55} -2.92820i q^{56} +(4.14359 + 4.14359i) q^{58} +(66.6218 - 66.6218i) q^{59} +103.426 q^{61} +49.9615i q^{62} -8.00000i q^{64} +(-10.7321 + 20.6936i) q^{65} +(46.6936 + 46.6936i) q^{67} +10.6410 q^{68} +(1.85641 + 1.85641i) q^{70} +(26.9090 + 26.9090i) q^{71} +(5.67949 - 5.67949i) q^{73} +6.28719 q^{74} +(29.4641 - 29.4641i) q^{76} -2.53590i q^{77} +4.21024 q^{79} +(5.07180 + 5.07180i) q^{80} +88.8897i q^{82} +(109.799 + 109.799i) q^{83} +(-6.74613 + 6.74613i) q^{85} +(37.1769 - 37.1769i) q^{86} -6.92820i q^{88} +(19.5167 - 19.5167i) q^{89} +(-11.9474 - 6.19615i) q^{91} +10.6410 q^{92} -61.6077 q^{94} +37.3590i q^{95} +(4.03332 + 4.03332i) q^{97} +(47.9282 - 47.9282i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 12 q^{5} - 4 q^{7} + 8 q^{8} + 12 q^{13} + 8 q^{14} - 16 q^{16} - 52 q^{19} + 24 q^{20} - 20 q^{26} - 8 q^{28} - 72 q^{29} + 4 q^{31} + 16 q^{32} + 48 q^{34} + 48 q^{35} - 68 q^{37} - 48 q^{40}+ \cdots + 164 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 - 12 * q^5 - 4 * q^7 + 8 * q^8 + 12 * q^13 + 8 * q^14 - 16 * q^16 - 52 * q^19 + 24 * q^20 - 20 * q^26 - 8 * q^28 - 72 * q^29 + 4 * q^31 + 16 * q^32 + 48 * q^34 + 48 * q^35 - 68 * q^37 - 48 * q^40 - 60 * q^41 + 48 * q^46 + 144 * q^47 - 4 * q^50 + 16 * q^52 - 120 * q^53 + 24 * q^55 + 72 * q^58 + 24 * q^59 + 192 * q^61 - 36 * q^65 - 28 * q^67 - 96 * q^68 - 48 * q^70 - 24 * q^71 + 92 * q^73 + 136 * q^74 + 104 * q^76 - 288 * q^79 + 48 * q^80 + 72 * q^83 + 264 * q^85 + 24 * q^86 - 12 * q^89 - 124 * q^91 - 96 * q^92 - 288 * q^94 - 164 * q^97 + 164 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$			2.00000i			0.500000i
$5$	−1.26795	−	1.26795i	−0.253590	−	0.253590i	0.568851	−	0.822441i	$-0.307388\pi$
$5$	−1.26795	−	1.26795i	−0.253590	−	0.253590i	−0.822441	+	0.568851i	$0.807388\pi$
$6$		0			0
$7$	0.732051	−	0.732051i	0.104579	−	0.104579i	−0.652881	−	0.757460i	$-0.726440\pi$
$7$	0.732051	−	0.732051i	0.104579	−	0.104579i	0.757460	+	0.652881i	$0.226440\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$		0			0
$10$			2.53590i			0.253590i
$11$	1.73205	−	1.73205i	0.157459	−	0.157459i	−0.623981	−	0.781440i	$-0.714486\pi$
$11$	1.73205	−	1.73205i	0.157459	−	0.157459i	0.781440	+	0.623981i	$0.214486\pi$
$12$		0			0
$13$	−3.92820	−	12.3923i	−0.302169	−	0.953254i
$13$	−3.92820	−	12.3923i	−0.302169	−	0.953254i
$14$	−1.46410			−0.104579
$15$		0			0
$16$	−4.00000			−0.250000
$17$		−	5.32051i		−	0.312971i	−0.987680	−	0.156486i	$-0.949984\pi$
$17$		−	5.32051i		−	0.312971i	0.987680	−	0.156486i	$-0.0500165\pi$
$18$		0			0
$19$	−14.7321	−	14.7321i	−0.775371	−	0.775371i	0.203669	−	0.979040i	$-0.434713\pi$
$19$	−14.7321	−	14.7321i	−0.775371	−	0.775371i	−0.979040	+	0.203669i	$0.934713\pi$
$20$	2.53590	−	2.53590i	0.126795	−	0.126795i
$21$		0			0
$22$	−3.46410			−0.157459
$23$		−	5.32051i		−	0.231326i	−0.993288	−	0.115663i	$-0.963101\pi$
$23$		−	5.32051i		−	0.231326i	0.993288	−	0.115663i	$-0.0368993\pi$
$24$		0			0
$25$		−	21.7846i		−	0.871384i
$26$	−8.46410	+	16.3205i	−0.325542	+	0.627712i
$27$		0			0
$28$	1.46410	+	1.46410i	0.0522893	+	0.0522893i
$29$	−4.14359			−0.142883			−0.0714413	−	0.997445i	$-0.522760\pi$
$29$	−4.14359			−0.142883			−0.0714413	+	0.997445i	$0.522760\pi$
$30$		0			0
$31$	−24.9808	−	24.9808i	−0.805831	−	0.805831i	0.178169	−	0.984000i	$-0.442983\pi$
$31$	−24.9808	−	24.9808i	−0.805831	−	0.805831i	−0.984000	+	0.178169i	$0.942983\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$		0			0
$34$	−5.32051	+	5.32051i	−0.156486	+	0.156486i
$35$	−1.85641			−0.0530402
$36$		0			0
$37$	−3.14359	+	3.14359i	−0.0849620	+	0.0849620i	−0.748311	−	0.663349i	$-0.769135\pi$
$37$	−3.14359	+	3.14359i	−0.0849620	+	0.0849620i	0.663349	+	0.748311i	$0.269135\pi$
$38$			29.4641i			0.775371i
$39$		0			0
$40$	−5.07180			−0.126795
$41$	−44.4449	−	44.4449i	−1.08402	−	1.08402i	−0.996130	−	0.0878910i	$-0.971987\pi$
$41$	−44.4449	−	44.4449i	−1.08402	−	1.08402i	−0.0878910	−	0.996130i	$-0.528013\pi$
$42$		0			0
$43$			37.1769i			0.864579i	0.901735	+	0.432290i	$0.142294\pi$
$43$			37.1769i			0.864579i	−0.901735	+	0.432290i	$0.857706\pi$
$44$	3.46410	+	3.46410i	0.0787296	+	0.0787296i
$45$		0			0
$46$	−5.32051	+	5.32051i	−0.115663	+	0.115663i
$47$	30.8038	−	30.8038i	0.655401	−	0.655401i	−0.298887	−	0.954288i	$-0.596615\pi$
$47$	30.8038	−	30.8038i	0.655401	−	0.655401i	0.954288	+	0.298887i	$0.0966155\pi$
$48$		0			0
$49$			47.9282i			0.978127i
$50$	−21.7846	+	21.7846i	−0.435692	+	0.435692i
$51$		0			0
$52$	24.7846	−	7.85641i	0.476627	−	0.151085i
$53$	−57.7128			−1.08892			−0.544460	−	0.838786i	$-0.683266\pi$
$53$	−57.7128			−1.08892			−0.544460	+	0.838786i	$0.683266\pi$
$54$		0			0
$55$	−4.39230			−0.0798601
$56$		−	2.92820i		−	0.0522893i
$57$		0			0
$58$	4.14359	+	4.14359i	0.0714413	+	0.0714413i
$59$	66.6218	−	66.6218i	1.12918	−	1.12918i	0.138872	−	0.990310i	$-0.455652\pi$
$59$	66.6218	−	66.6218i	1.12918	−	1.12918i	0.990310	−	0.138872i	$-0.0443478\pi$
$60$		0			0
$61$	103.426			1.69550			0.847751	−	0.530394i	$-0.177956\pi$
$61$	103.426			1.69550			0.847751	+	0.530394i	$0.177956\pi$
$62$			49.9615i			0.805831i
$63$		0			0
$64$		−	8.00000i		−	0.125000i
$65$	−10.7321	+	20.6936i	−0.165108	+	0.318363i
$66$		0			0
$67$	46.6936	+	46.6936i	0.696919	+	0.696919i	0.963745	−	0.266826i	$-0.0859748\pi$
$67$	46.6936	+	46.6936i	0.696919	+	0.696919i	−0.266826	+	0.963745i	$0.585975\pi$
$68$	10.6410			0.156486
$69$		0			0
$70$	1.85641	+	1.85641i	0.0265201	+	0.0265201i
$71$	26.9090	+	26.9090i	0.379000	+	0.379000i	0.870741	−	0.491742i	$-0.163640\pi$
$71$	26.9090	+	26.9090i	0.379000	+	0.379000i	−0.491742	+	0.870741i	$0.663640\pi$
$72$		0			0
$73$	5.67949	−	5.67949i	0.0778013	−	0.0778013i	−0.667135	−	0.744937i	$-0.732480\pi$
$73$	5.67949	−	5.67949i	0.0778013	−	0.0778013i	0.744937	+	0.667135i	$0.232480\pi$
$74$	6.28719			0.0849620
$75$		0			0
$76$	29.4641	−	29.4641i	0.387686	−	0.387686i
$77$		−	2.53590i		−	0.0329337i
$78$		0			0
$79$	4.21024			0.0532941			0.0266471	−	0.999645i	$-0.491517\pi$
$79$	4.21024			0.0532941			0.0266471	+	0.999645i	$0.491517\pi$
$80$	5.07180	+	5.07180i	0.0633975	+	0.0633975i
$81$		0			0
$82$			88.8897i			1.08402i
$83$	109.799	+	109.799i	1.32288	+	1.32288i	0.911438	+	0.411438i	$0.134973\pi$
$83$	109.799	+	109.799i	1.32288	+	1.32288i	0.411438	+	0.911438i	$0.365027\pi$
$84$		0			0
$85$	−6.74613	+	6.74613i	−0.0793663	+	0.0793663i
$86$	37.1769	−	37.1769i	0.432290	−	0.432290i
$87$		0			0
$88$		−	6.92820i		−	0.0787296i
$89$	19.5167	−	19.5167i	0.219288	−	0.219288i	−0.588910	−	0.808198i	$-0.700443\pi$
$89$	19.5167	−	19.5167i	0.219288	−	0.219288i	0.808198	+	0.588910i	$0.200443\pi$
$90$		0			0
$91$	−11.9474	−	6.19615i	−0.131291	−	0.0680896i
$92$	10.6410			0.115663
$93$		0			0
$94$	−61.6077			−0.655401
$95$			37.3590i			0.393252i
$96$		0			0
$97$	4.03332	+	4.03332i	0.0415806	+	0.0415806i	0.727591	−	0.686011i	$-0.240640\pi$
$97$	4.03332	+	4.03332i	0.0415806	+	0.0415806i	−0.686011	+	0.727591i	$0.740640\pi$
$98$	47.9282	−	47.9282i	0.489063	−	0.489063i
$99$		0			0
$100$	43.5692			0.435692
$101$			111.464i			1.10360i	0.833975	+	0.551802i	$0.186060\pi$
$101$			111.464i			1.10360i	−0.833975	+	0.551802i	$0.813940\pi$
$102$		0			0
$103$		−	71.3205i		−	0.692432i	−0.938155	−	0.346216i	$-0.887466\pi$
$103$		−	71.3205i		−	0.692432i	0.938155	−	0.346216i	$-0.112534\pi$
$104$	−32.6410	−	16.9282i	−0.313856	−	0.162771i
$105$		0			0
$106$	57.7128	+	57.7128i	0.544460	+	0.544460i
$107$	116.536			1.08912			0.544560	−	0.838722i	$-0.316697\pi$
$107$	116.536			1.08912			0.544560	+	0.838722i	$0.316697\pi$
$108$		0			0
$109$	−109.315	−	109.315i	−1.00289	−	1.00289i	−0.999996	−	0.00289735i	$-0.999078\pi$
$109$	−109.315	−	109.315i	−1.00289	−	1.00289i	−0.00289735	−	0.999996i	$-0.500922\pi$
$110$	4.39230	+	4.39230i	0.0399300	+	0.0399300i
$111$		0			0
$112$	−2.92820	+	2.92820i	−0.0261447	+	0.0261447i
$113$	−148.277			−1.31218			−0.656092	−	0.754681i	$-0.727792\pi$
$113$	−148.277			−1.31218			−0.656092	+	0.754681i	$0.727792\pi$
$114$		0			0
$115$	−6.74613	+	6.74613i	−0.0586620	+	0.0586620i
$116$		−	8.28719i		−	0.0714413i
$117$		0			0
$118$	−133.244			−1.12918
$119$	−3.89488	−	3.89488i	−0.0327301	−	0.0327301i
$120$		0			0
$121$			115.000i			0.950413i
$122$	−103.426	−	103.426i	−0.847751	−	0.847751i
$123$		0			0
$124$	49.9615	−	49.9615i	0.402916	−	0.402916i
$125$	−59.3205	+	59.3205i	−0.474564	+	0.474564i
$126$		0			0
$127$			70.0385i			0.551484i	0.961232	+	0.275742i	$0.0889236\pi$
$127$			70.0385i			0.551484i	−0.961232	+	0.275742i	$0.911076\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	31.4256	−	9.96152i	0.241736	−	0.0766271i
$131$	−238.890			−1.82359			−0.911793	−	0.410650i	$-0.865302\pi$
$131$	−238.890			−1.82359			−0.911793	+	0.410650i	$0.865302\pi$
$132$		0			0
$133$	−21.5692			−0.162175
$134$		−	93.3872i		−	0.696919i
$135$		0			0
$136$	−10.6410	−	10.6410i	−0.0782428	−	0.0782428i
$137$	91.9474	−	91.9474i	0.671149	−	0.671149i	−0.286832	−	0.957981i	$-0.592602\pi$
$137$	91.9474	−	91.9474i	0.671149	−	0.671149i	0.957981	+	0.286832i	$0.0926021\pi$
$138$		0			0
$139$	139.138			1.00100			0.500498	−	0.865738i	$-0.333150\pi$
$139$	139.138			1.00100			0.500498	+	0.865738i	$0.333150\pi$
$140$		−	3.71281i		−	0.0265201i
$141$		0			0
$142$		−	53.8179i		−	0.379000i
$143$	−28.2679	−	14.6603i	−0.197678	−	0.102519i
$144$		0			0
$145$	5.25387	+	5.25387i	0.0362336	+	0.0362336i
$146$	−11.3590			−0.0778013
$147$		0			0
$148$	−6.28719	−	6.28719i	−0.0424810	−	0.0424810i
$149$	−126.224	−	126.224i	−0.847143	−	0.847143i	0.142633	−	0.989776i	$-0.454443\pi$
$149$	−126.224	−	126.224i	−0.847143	−	0.847143i	−0.989776	+	0.142633i	$0.954443\pi$
$150$		0			0
$151$	124.406	−	124.406i	0.823883	−	0.823883i	−0.162779	−	0.986663i	$-0.552046\pi$
$151$	124.406	−	124.406i	0.823883	−	0.823883i	0.986663	+	0.162779i	$0.0520458\pi$
$152$	−58.9282			−0.387686
$153$		0			0
$154$	−2.53590	+	2.53590i	−0.0164669	+	0.0164669i
$155$			63.3487i			0.408701i
$156$		0			0
$157$	−268.785			−1.71200			−0.856002	−	0.516973i	$-0.827059\pi$
$157$	−268.785			−1.71200			−0.856002	+	0.516973i	$0.827059\pi$
$158$	−4.21024	−	4.21024i	−0.0266471	−	0.0266471i
$159$		0			0
$160$		−	10.1436i		−	0.0633975i
$161$	−3.89488	−	3.89488i	−0.0241918	−	0.0241918i
$162$		0			0
$163$	−46.4449	+	46.4449i	−0.284938	+	0.284938i	−0.835075	−	0.550137i	$-0.814576\pi$
$163$	−46.4449	+	46.4449i	−0.284938	+	0.284938i	0.550137	+	0.835075i	$0.314576\pi$
$164$	88.8897	−	88.8897i	0.542011	−	0.542011i
$165$		0			0
$166$		−	219.597i		−	1.32288i
$167$	119.512	−	119.512i	0.715638	−	0.715638i	−0.252071	−	0.967709i	$-0.581112\pi$
$167$	119.512	−	119.512i	0.715638	−	0.715638i	0.967709	+	0.252071i	$0.0811116\pi$
$168$		0			0
$169$	−138.138	+	97.3590i	−0.817387	+	0.576089i
$170$	13.4923			0.0793663
$171$		0			0
$172$	−74.3538			−0.432290
$173$			242.603i			1.40233i	0.713001	+	0.701163i	$0.247336\pi$
$173$			242.603i			1.40233i	−0.713001	+	0.701163i	$0.752664\pi$
$174$		0			0
$175$	−15.9474	−	15.9474i	−0.0911282	−	0.0911282i
$176$	−6.92820	+	6.92820i	−0.0393648	+	0.0393648i
$177$		0			0
$178$	−39.0333			−0.219288
$179$		−	26.7180i		−	0.149262i	−0.997211	−	0.0746312i	$-0.976222\pi$
$179$		−	26.7180i		−	0.149262i	0.997211	−	0.0746312i	$-0.0237780\pi$
$180$		0			0
$181$		−	256.144i		−	1.41516i	−0.706634	−	0.707579i	$-0.749787\pi$
$181$		−	256.144i		−	1.41516i	0.706634	−	0.707579i	$-0.250213\pi$
$182$	5.75129	+	18.1436i	0.0316005	+	0.0996901i
$183$		0			0
$184$	−10.6410	−	10.6410i	−0.0578316	−	0.0578316i
$185$	7.97183			0.0430910
$186$		0			0
$187$	−9.21539	−	9.21539i	−0.0492802	−	0.0492802i
$188$	61.6077	+	61.6077i	0.327701	+	0.327701i
$189$		0			0
$190$	37.3590	−	37.3590i	0.196626	−	0.196626i
$191$	129.282			0.676869			0.338435	−	0.940990i	$-0.390103\pi$
$191$	129.282			0.676869			0.338435	+	0.940990i	$0.390103\pi$
$192$		0			0
$193$	−160.282	+	160.282i	−0.830477	+	0.830477i	−0.987582	−	0.157105i	$-0.949784\pi$
$193$	−160.282	+	160.282i	−0.830477	+	0.830477i	0.157105	+	0.987582i	$0.449784\pi$
$194$		−	8.06664i		−	0.0415806i
$195$		0			0
$196$	−95.8564			−0.489063
$197$	109.268	+	109.268i	0.554660	+	0.554660i	0.927782	−	0.373122i	$-0.121713\pi$
$197$	109.268	+	109.268i	0.554660	+	0.554660i	−0.373122	+	0.927782i	$0.621713\pi$
$198$		0			0
$199$		−	25.1000i		−	0.126130i	−0.998009	−	0.0630652i	$-0.979912\pi$
$199$		−	25.1000i		−	0.126130i	0.998009	−	0.0630652i	$-0.0200876\pi$
$200$	−43.5692	−	43.5692i	−0.217846	−	0.217846i
$201$		0			0
$202$	111.464	−	111.464i	0.551802	−	0.551802i
$203$	−3.03332	+	3.03332i	−0.0149425	+	0.0149425i
$204$		0			0
$205$			112.708i			0.549793i
$206$	−71.3205	+	71.3205i	−0.346216	+	0.346216i
$207$		0			0
$208$	15.7128	+	49.5692i	0.0755424	+	0.238314i
$209$	−51.0333			−0.244179
$210$		0			0
$211$	206.718			0.979706			0.489853	−	0.871805i	$-0.337050\pi$
$211$	206.718			0.979706			0.489853	+	0.871805i	$0.337050\pi$
$212$		−	115.426i		−	0.544460i
$213$		0			0
$214$	−116.536	−	116.536i	−0.544560	−	0.544560i
$215$	47.1384	−	47.1384i	0.219249	−	0.219249i
$216$		0			0
$217$	−36.5744			−0.168546
$218$			218.631i			1.00289i
$219$		0			0
$220$		−	8.78461i		−	0.0399300i
$221$	−65.9334	+	20.9000i	−0.298341	+	0.0945703i
$222$		0			0
$223$	139.412	+	139.412i	0.625164	+	0.625164i	0.946847	−	0.321683i	$-0.104249\pi$
$223$	139.412	+	139.412i	0.625164	+	0.625164i	−0.321683	+	0.946847i	$0.604249\pi$
$224$	5.85641			0.0261447
$225$		0			0
$226$	148.277	+	148.277i	0.656092	+	0.656092i
$227$	97.3679	+	97.3679i	0.428934	+	0.428934i	0.888265	−	0.459331i	$-0.151911\pi$
$227$	97.3679	+	97.3679i	0.428934	+	0.428934i	−0.459331	+	0.888265i	$0.651911\pi$
$228$		0			0
$229$	204.177	−	204.177i	0.891602	−	0.891602i	−0.103072	−	0.994674i	$-0.532867\pi$
$229$	204.177	−	204.177i	0.891602	−	0.891602i	0.994674	+	0.103072i	$0.0328671\pi$
$230$	13.4923			0.0586620
$231$		0			0
$232$	−8.28719	+	8.28719i	−0.0357206	+	0.0357206i
$233$		−	231.962i		−	0.995543i	−0.867308	−	0.497772i	$-0.834152\pi$
$233$		−	231.962i		−	0.995543i	0.867308	−	0.497772i	$-0.165848\pi$
$234$		0			0
$235$	−78.1154			−0.332406
$236$	133.244	+	133.244i	0.564591	+	0.564591i
$237$		0			0
$238$			7.78976i			0.0327301i
$239$	−139.981	−	139.981i	−0.585694	−	0.585694i	0.350769	−	0.936462i	$-0.385920\pi$
$239$	−139.981	−	139.981i	−0.585694	−	0.585694i	−0.936462	+	0.350769i	$0.885920\pi$
$240$		0			0
$241$	53.4589	−	53.4589i	0.221821	−	0.221821i	−0.587444	−	0.809265i	$-0.699866\pi$
$241$	53.4589	−	53.4589i	0.221821	−	0.221821i	0.809265	+	0.587444i	$0.199866\pi$
$242$	115.000	−	115.000i	0.475207	−	0.475207i
$243$		0			0
$244$			206.851i			0.847751i
$245$	60.7705	−	60.7705i	0.248043	−	0.248043i
$246$		0			0
$247$	−124.694	+	240.435i	−0.504832	+	0.973419i
$248$	−99.9230			−0.402916
$249$		0			0
$250$	118.641			0.474564
$251$			421.377i			1.67879i	0.543520	+	0.839396i	$0.317091\pi$
$251$			421.377i			1.67879i	−0.543520	+	0.839396i	$0.682909\pi$
$252$		0			0
$253$	−9.21539	−	9.21539i	−0.0364245	−	0.0364245i
$254$	70.0385	−	70.0385i	0.275742	−	0.275742i
$255$		0			0
$256$	16.0000			0.0625000
$257$		−	249.664i		−	0.971455i	−0.874110	−	0.485728i	$-0.838555\pi$
$257$		−	249.664i		−	0.971455i	0.874110	−	0.485728i	$-0.161445\pi$
$258$		0			0
$259$			4.60254i			0.0177704i
$260$	−41.3872	−	21.4641i	−0.159181	−	0.0825542i
$261$		0			0
$262$	238.890	+	238.890i	0.911793	+	0.911793i
$263$	94.8897			0.360797			0.180399	−	0.983594i	$-0.442261\pi$
$263$	94.8897			0.360797			0.180399	+	0.983594i	$0.442261\pi$
$264$		0			0
$265$	73.1769	+	73.1769i	0.276139	+	0.276139i
$266$	21.5692	+	21.5692i	0.0810873	+	0.0810873i
$267$		0			0
$268$	−93.3872	+	93.3872i	−0.348460	+	0.348460i
$269$	208.774			0.776113			0.388056	−	0.921636i	$-0.373147\pi$
$269$	208.774			0.776113			0.388056	+	0.921636i	$0.373147\pi$
$270$		0			0
$271$	381.047	−	381.047i	1.40608	−	1.40608i	0.627307	−	0.778772i	$-0.284157\pi$
$271$	381.047	−	381.047i	1.40608	−	1.40608i	0.778772	−	0.627307i	$-0.215843\pi$
$272$			21.2820i			0.0782428i
$273$		0			0
$274$	−183.895			−0.671149
$275$	−37.7321	−	37.7321i	−0.137207	−	0.137207i
$276$		0			0
$277$			68.7846i			0.248320i	0.992262	+	0.124160i	$0.0396236\pi$
$277$			68.7846i			0.248320i	−0.992262	+	0.124160i	$0.960376\pi$
$278$	−139.138	−	139.138i	−0.500498	−	0.500498i
$279$		0			0
$280$	−3.71281	+	3.71281i	−0.0132600	+	0.0132600i
$281$	−69.6218	+	69.6218i	−0.247764	+	0.247764i	−0.820053	−	0.572288i	$-0.806056\pi$
$281$	−69.6218	+	69.6218i	−0.247764	+	0.247764i	0.572288	+	0.820053i	$0.306056\pi$
$282$		0			0
$283$			425.808i			1.50462i	0.658809	+	0.752310i	$0.271061\pi$
$283$			425.808i			1.50462i	−0.658809	+	0.752310i	$0.728939\pi$
$284$	−53.8179	+	53.8179i	−0.189500	+	0.189500i
$285$		0			0
$286$	13.6077	+	42.9282i	0.0475794	+	0.150099i
$287$	−65.0718			−0.226731
$288$		0			0
$289$	260.692			0.902049
$290$		−	10.5077i		−	0.0362336i
$291$		0			0
$292$	11.3590	+	11.3590i	0.0389006	+	0.0389006i
$293$	−306.042	+	306.042i	−1.04451	+	1.04451i	−0.0455508	+	0.998962i	$0.514504\pi$
$293$	−306.042	+	306.042i	−1.04451	+	1.04451i	−0.998962	+	0.0455508i	$0.985496\pi$
$294$		0			0
$295$	−168.946			−0.572699
$296$			12.5744i			0.0424810i
$297$		0			0
$298$			252.449i			0.847143i
$299$	−65.9334	+	20.9000i	−0.220513	+	0.0698998i
$300$		0			0
$301$	27.2154	+	27.2154i	0.0904166	+	0.0904166i
$302$	−248.813			−0.823883
$303$		0			0
$304$	58.9282	+	58.9282i	0.193843	+	0.193843i
$305$	−131.138	−	131.138i	−0.429962	−	0.429962i
$306$		0			0
$307$	246.512	−	246.512i	0.802969	−	0.802969i	−0.180589	−	0.983559i	$-0.557801\pi$
$307$	246.512	−	246.512i	0.802969	−	0.802969i	0.983559	+	0.180589i	$0.0578005\pi$
$308$	5.07180			0.0164669
$309$		0			0
$310$	63.3487	−	63.3487i	0.204351	−	0.204351i
$311$		−	313.377i		−	1.00764i	−0.863808	−	0.503821i	$-0.831927\pi$
$311$		−	313.377i		−	1.00764i	0.863808	−	0.503821i	$-0.168073\pi$
$312$		0			0
$313$	−262.841			−0.839747			−0.419874	−	0.907583i	$-0.637926\pi$
$313$	−262.841			−0.839747			−0.419874	+	0.907583i	$0.637926\pi$
$314$	268.785	+	268.785i	0.856002	+	0.856002i
$315$		0			0
$316$			8.42047i			0.0266471i
$317$	148.981	+	148.981i	0.469971	+	0.469971i	0.901905	−	0.431934i	$-0.142169\pi$
$317$	148.981	+	148.981i	0.469971	+	0.469971i	−0.431934	+	0.901905i	$0.642169\pi$
$318$		0			0
$319$	−7.17691	+	7.17691i	−0.0224982	+	0.0224982i
$320$	−10.1436	+	10.1436i	−0.0316987	+	0.0316987i
$321$		0			0
$322$			7.78976i			0.0241918i
$323$	−78.3820	+	78.3820i	−0.242669	+	0.242669i
$324$		0			0
$325$	−269.962	+	85.5744i	−0.830651	+	0.263306i
$326$	92.8897			0.284938
$327$		0			0
$328$	−177.779			−0.542011
$329$		−	45.1000i		−	0.137082i
$330$		0			0
$331$	−295.870	−	295.870i	−0.893869	−	0.893869i	0.101016	−	0.994885i	$-0.467791\pi$
$331$	−295.870	−	295.870i	−0.893869	−	0.893869i	−0.994885	+	0.101016i	$0.967791\pi$
$332$	−219.597	+	219.597i	−0.661438	+	0.661438i
$333$		0			0
$334$	−239.023			−0.715638
$335$		−	118.410i		−	0.353463i
$336$		0			0
$337$		−	48.9385i		−	0.145218i	−0.997360	−	0.0726091i	$-0.976867\pi$
$337$		−	48.9385i		−	0.145218i	0.997360	−	0.0726091i	$-0.0231325\pi$
$338$	235.497	+	40.7795i	0.696738	+	0.120649i
$339$		0			0
$340$	−13.4923	−	13.4923i	−0.0396831	−	0.0396831i
$341$	−86.5359			−0.253771
$342$		0			0
$343$	70.9564	+	70.9564i	0.206870	+	0.206870i
$344$	74.3538	+	74.3538i	0.216145	+	0.216145i
$345$		0			0
$346$	242.603	−	242.603i	0.701163	−	0.701163i
$347$	552.133			1.59116			0.795581	−	0.605847i	$-0.207166\pi$
$347$	552.133			1.59116			0.795581	+	0.605847i	$0.207166\pi$
$348$		0			0
$349$	189.210	−	189.210i	0.542150	−	0.542150i	−0.382009	−	0.924159i	$-0.624768\pi$
$349$	189.210	−	189.210i	0.542150	−	0.542150i	0.924159	+	0.382009i	$0.124768\pi$
$350$			31.8949i			0.0911282i
$351$		0			0
$352$	13.8564			0.0393648
$353$	51.8705	+	51.8705i	0.146942	+	0.146942i	0.776750	−	0.629809i	$-0.216867\pi$
$353$	51.8705	+	51.8705i	0.146942	+	0.146942i	−0.629809	+	0.776750i	$0.716867\pi$
$354$		0			0
$355$		−	68.2384i		−	0.192221i
$356$	39.0333	+	39.0333i	0.109644	+	0.109644i
$357$		0			0
$358$	−26.7180	+	26.7180i	−0.0746312	+	0.0746312i
$359$	205.119	−	205.119i	0.571363	−	0.571363i	−0.361146	−	0.932509i	$-0.617615\pi$
$359$	205.119	−	205.119i	0.571363	−	0.571363i	0.932509	+	0.361146i	$0.117615\pi$
$360$		0			0
$361$			73.0666i			0.202401i
$362$	−256.144	+	256.144i	−0.707579	+	0.707579i
$363$		0			0
$364$	12.3923	−	23.8949i	0.0340448	−	0.0656453i
$365$	−14.4026			−0.0394592
$366$		0			0
$367$	−351.292			−0.957200			−0.478600	−	0.878033i	$-0.658856\pi$
$367$	−351.292			−0.957200			−0.478600	+	0.878033i	$0.658856\pi$
$368$			21.2820i			0.0578316i
$369$		0			0
$370$	−7.97183	−	7.97183i	−0.0215455	−	0.0215455i
$371$	−42.2487	+	42.2487i	−0.113878	+	0.113878i
$372$		0			0
$373$	−131.836			−0.353447			−0.176724	−	0.984261i	$-0.556550\pi$
$373$	−131.836			−0.353447			−0.176724	+	0.984261i	$0.556550\pi$
$374$			18.4308i			0.0492802i
$375$		0			0
$376$		−	123.215i		−	0.327701i
$377$	16.2769	+	51.3487i	0.0431747	+	0.136203i
$378$		0			0
$379$	−24.7987	−	24.7987i	−0.0654319	−	0.0654319i	0.673634	−	0.739065i	$-0.264733\pi$
$379$	−24.7987	−	24.7987i	−0.0654319	−	0.0654319i	−0.739065	+	0.673634i	$0.764733\pi$
$380$	−74.7180			−0.196626
$381$		0			0
$382$	−129.282	−	129.282i	−0.338435	−	0.338435i
$383$	−174.555	−	174.555i	−0.455758	−	0.455758i	0.441502	−	0.897260i	$-0.354446\pi$
$383$	−174.555	−	174.555i	−0.455758	−	0.455758i	−0.897260	+	0.441502i	$0.854446\pi$
$384$		0			0
$385$	−3.21539	+	3.21539i	−0.00835166	+	0.00835166i
$386$	320.564			0.830477
$387$		0			0
$388$	−8.06664	+	8.06664i	−0.0207903	+	0.0207903i
$389$		−	644.305i		−	1.65631i	−0.560498	−	0.828156i	$-0.689390\pi$
$389$		−	644.305i		−	1.65631i	0.560498	−	0.828156i	$-0.310610\pi$
$390$		0			0
$391$	−28.3078			−0.0723985
$392$	95.8564	+	95.8564i	0.244532	+	0.244532i
$393$		0			0
$394$		−	218.536i		−	0.554660i
$395$	−5.33836	−	5.33836i	−0.0135148	−	0.0135148i
$396$		0			0
$397$	432.692	−	432.692i	1.08990	−	1.08990i	0.0943673	−	0.995537i	$-0.469917\pi$
$397$	432.692	−	432.692i	1.08990	−	1.08990i	0.995537	−	0.0943673i	$-0.0300828\pi$
$398$	−25.1000	+	25.1000i	−0.0630652	+	0.0630652i
$399$		0			0
$400$			87.1384i			0.217846i
$401$	274.550	−	274.550i	0.684663	−	0.684663i	−0.276384	−	0.961047i	$-0.589136\pi$
$401$	274.550	−	274.550i	0.684663	−	0.684663i	0.961047	+	0.276384i	$0.0891362\pi$
$402$		0			0
$403$	−211.440	+	407.699i	−0.524664	+	1.01166i
$404$	−222.928			−0.551802
$405$		0			0
$406$	6.06664			0.0149425
$407$			10.8897i			0.0267561i
$408$		0			0
$409$	76.1872	+	76.1872i	0.186277	+	0.186277i	0.794084	−	0.607808i	$-0.207951\pi$
$409$	76.1872	+	76.1872i	0.186277	+	0.186277i	−0.607808	+	0.794084i	$0.707951\pi$
$410$	112.708	−	112.708i	0.274897	−	0.274897i
$411$		0			0
$412$	142.641			0.346216
$413$		−	97.5411i		−	0.236177i
$414$		0			0
$415$		−	278.438i		−	0.670936i
$416$	33.8564	−	65.2820i	0.0813856	−	0.156928i
$417$		0			0
$418$	51.0333	+	51.0333i	0.122089	+	0.122089i
$419$	−76.8231			−0.183349			−0.0916743	−	0.995789i	$-0.529222\pi$
$419$	−76.8231			−0.183349			−0.0916743	+	0.995789i	$0.529222\pi$
$420$		0			0
$421$	117.756	+	117.756i	0.279707	+	0.279707i	0.832992	−	0.553285i	$-0.186626\pi$
$421$	117.756	+	117.756i	0.279707	+	0.279707i	−0.553285	+	0.832992i	$0.686626\pi$
$422$	−206.718	−	206.718i	−0.489853	−	0.489853i
$423$		0			0
$424$	−115.426	+	115.426i	−0.272230	+	0.272230i
$425$	−115.905			−0.272718
$426$		0			0
$427$	75.7128	−	75.7128i	0.177313	−	0.177313i
$428$			233.072i			0.544560i
$429$		0			0
$430$	−94.2769			−0.219249
$431$	−362.478	−	362.478i	−0.841017	−	0.841017i	0.147975	−	0.988991i	$-0.452725\pi$
$431$	−362.478	−	362.478i	−0.841017	−	0.841017i	−0.988991	+	0.147975i	$0.952725\pi$
$432$		0			0
$433$			197.292i			0.455641i	0.973703	+	0.227820i	$0.0731599\pi$
$433$			197.292i			0.455641i	−0.973703	+	0.227820i	$0.926840\pi$
$434$	36.5744	+	36.5744i	0.0842728	+	0.0842728i
$435$		0			0
$436$	218.631	−	218.631i	0.501447	−	0.501447i
$437$	−78.3820	+	78.3820i	−0.179364	+	0.179364i
$438$		0			0
$439$		−	272.238i		−	0.620133i	−0.950715	−	0.310067i	$-0.899649\pi$
$439$		−	272.238i		−	0.620133i	0.950715	−	0.310067i	$-0.100351\pi$
$440$	−8.78461	+	8.78461i	−0.0199650	+	0.0199650i
$441$		0			0
$442$	86.8334	+	45.0333i	0.196456	+	0.101885i
$443$	−74.7358			−0.168704			−0.0843519	−	0.996436i	$-0.526882\pi$
$443$	−74.7358			−0.168704			−0.0843519	+	0.996436i	$0.526882\pi$
$444$		0			0
$445$	−49.4923			−0.111219
$446$		−	278.823i		−	0.625164i
$447$		0			0
$448$	−5.85641	−	5.85641i	−0.0130723	−	0.0130723i
$449$	−516.224	+	516.224i	−1.14972	+	1.14972i	−0.163113	+	0.986607i	$0.552153\pi$
$449$	−516.224	+	516.224i	−1.14972	+	1.14972i	−0.986607	+	0.163113i	$0.947847\pi$
$450$		0			0
$451$	−153.962			−0.341378
$452$		−	296.554i		−	0.656092i
$453$		0			0
$454$		−	194.736i		−	0.428934i
$455$	7.29234	+	23.0052i	0.0160271	+	0.0505608i
$456$		0			0
$457$	−50.9615	−	50.9615i	−0.111513	−	0.111513i	0.649149	−	0.760662i	$-0.275125\pi$
$457$	−50.9615	−	50.9615i	−0.111513	−	0.111513i	−0.760662	+	0.649149i	$0.775125\pi$
$458$	−408.354			−0.891602
$459$		0			0
$460$	−13.4923	−	13.4923i	−0.0293310	−	0.0293310i
$461$	−202.550	−	202.550i	−0.439371	−	0.439371i	0.452429	−	0.891800i	$-0.350557\pi$
$461$	−202.550	−	202.550i	−0.439371	−	0.439371i	−0.891800	+	0.452429i	$0.850557\pi$
$462$		0			0
$463$	−223.247	+	223.247i	−0.482176	+	0.482176i	−0.905826	−	0.423650i	$-0.860749\pi$
$463$	−223.247	+	223.247i	−0.482176	+	0.482176i	0.423650	+	0.905826i	$0.360749\pi$
$464$	16.5744			0.0357206
$465$		0			0
$466$	−231.962	+	231.962i	−0.497772	+	0.497772i
$467$			161.818i			0.346505i	0.984877	+	0.173253i	$0.0554277\pi$
$467$			161.818i			0.346505i	−0.984877	+	0.173253i	$0.944572\pi$
$468$		0			0
$469$	68.3641			0.145766
$470$	78.1154	+	78.1154i	0.166203	+	0.166203i
$471$		0			0
$472$		−	266.487i		−	0.564591i
$473$	64.3923	+	64.3923i	0.136136	+	0.136136i
$474$		0			0
$475$	−320.932	+	320.932i	−0.675646	+	0.675646i
$476$	7.78976	−	7.78976i	0.0163651	−	0.0163651i
$477$		0			0
$478$			279.962i			0.585694i
$479$	89.1295	−	89.1295i	0.186074	−	0.186074i	−0.607922	−	0.793996i	$-0.707997\pi$
$479$	89.1295	−	89.1295i	0.186074	−	0.186074i	0.793996	+	0.607922i	$0.207997\pi$
$480$		0			0
$481$	51.3050	+	26.6077i	0.106663	+	0.0553175i
$482$	−106.918			−0.221821
$483$		0			0
$484$	−230.000			−0.475207
$485$		−	10.2281i		−	0.0210888i
$486$		0			0
$487$	−527.440	−	527.440i	−1.08304	−	1.08304i	−0.996225	−	0.0868139i	$-0.972331\pi$
$487$	−527.440	−	527.440i	−1.08304	−	1.08304i	−0.0868139	−	0.996225i	$-0.527669\pi$
$488$	206.851	−	206.851i	0.423876	−	0.423876i
$489$		0			0
$490$	−121.541			−0.248043
$491$			700.726i			1.42714i	0.700584	+	0.713570i	$0.252923\pi$
$491$			700.726i			1.42714i	−0.700584	+	0.713570i	$0.747077\pi$
$492$		0			0
$493$			22.0460i			0.0447181i
$494$	365.128	−	115.741i	0.739126	−	0.234293i
$495$		0			0
$496$	99.9230	+	99.9230i	0.201458	+	0.201458i
$497$	39.3975			0.0792705
$498$		0			0
$499$	279.065	+	279.065i	0.559249	+	0.559249i	0.929094	−	0.369845i	$-0.120589\pi$
$499$	279.065	+	279.065i	0.559249	+	0.559249i	−0.369845	+	0.929094i	$0.620589\pi$
$500$	−118.641	−	118.641i	−0.237282	−	0.237282i
$501$		0			0
$502$	421.377	−	421.377i	0.839396	−	0.839396i
$503$	23.9821			0.0476782			0.0238391	−	0.999716i	$-0.492411\pi$
$503$	23.9821			0.0476782			0.0238391	+	0.999716i	$0.492411\pi$
$504$		0			0
$505$	141.331	−	141.331i	0.279863	−	0.279863i
$506$			18.4308i			0.0364245i
$507$		0			0
$508$	−140.077			−0.275742
$509$	287.678	+	287.678i	0.565183	+	0.565183i	0.930775	−	0.365592i	$-0.119134\pi$
$509$	287.678	+	287.678i	0.565183	+	0.565183i	−0.365592	+	0.930775i	$0.619134\pi$
$510$		0			0
$511$		−	8.31535i		−	0.0162727i
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$		0			0
$514$	−249.664	+	249.664i	−0.485728	+	0.485728i
$515$	−90.4308	+	90.4308i	−0.175594	+	0.175594i
$516$		0			0
$517$		−	106.708i		−	0.206398i
$518$	4.60254	−	4.60254i	0.00888521	−	0.00888521i
$519$		0			0
$520$	19.9230	+	62.8513i	0.0383136	+	0.120868i
$521$	921.349			1.76842			0.884212	−	0.467086i	$-0.154696\pi$
$521$	921.349			1.76842			0.884212	+	0.467086i	$0.154696\pi$
$522$		0			0
$523$	−558.677			−1.06822			−0.534108	−	0.845416i	$-0.679352\pi$
$523$	−558.677			−1.06822			−0.534108	+	0.845416i	$0.679352\pi$
$524$		−	477.779i		−	0.911793i
$525$		0			0
$526$	−94.8897	−	94.8897i	−0.180399	−	0.180399i
$527$	−132.910	+	132.910i	−0.252202	+	0.252202i
$528$		0			0
$529$	500.692			0.946488
$530$		−	146.354i		−	0.276139i
$531$		0			0
$532$		−	43.1384i		−	0.0810873i
$533$	−376.186	+	725.363i	−0.705790	+	1.36091i
$534$		0			0
$535$	−147.762	−	147.762i	−0.276190	−	0.276190i
$536$	186.774			0.348460
$537$		0			0
$538$	−208.774	−	208.774i	−0.388056	−	0.388056i
$539$	83.0141	+	83.0141i	0.154015	+	0.154015i
$540$		0			0
$541$	−101.756	+	101.756i	−0.188090	+	0.188090i	−0.794870	−	0.606780i	$-0.792461\pi$
$541$	−101.756	+	101.756i	−0.188090	+	0.188090i	0.606780	+	0.794870i	$0.292461\pi$
$542$	−762.095			−1.40608
$543$		0			0
$544$	21.2820	−	21.2820i	0.0391214	−	0.0391214i
$545$			277.213i			0.508647i
$546$		0			0
$547$	301.800			0.551737			0.275868	−	0.961195i	$-0.411035\pi$
$547$	301.800			0.551737			0.275868	+	0.961195i	$0.411035\pi$
$548$	183.895	+	183.895i	0.335575	+	0.335575i
$549$		0			0
$550$			75.4641i			0.137207i
$551$	61.0436	+	61.0436i	0.110787	+	0.110787i
$552$		0			0
$553$	3.08211	−	3.08211i	0.00557343	−	0.00557343i
$554$	68.7846	−	68.7846i	0.124160	−	0.124160i
$555$		0			0
$556$			278.277i			0.500498i
$557$	285.258	−	285.258i	0.512132	−	0.512132i	−0.403047	−	0.915179i	$-0.632049\pi$
$557$	285.258	−	285.258i	0.512132	−	0.512132i	0.915179	+	0.403047i	$0.132049\pi$
$558$		0			0
$559$	460.708	−	146.038i	0.824164	−	0.261250i
$560$	7.42563			0.0132600
$561$		0			0
$562$	139.244			0.247764
$563$			863.174i			1.53317i	0.642143	+	0.766585i	$0.278045\pi$
$563$			863.174i			1.53317i	−0.642143	+	0.766585i	$0.721955\pi$
$564$		0			0
$565$	188.008	+	188.008i	0.332757	+	0.332757i
$566$	425.808	−	425.808i	0.752310	−	0.752310i
$567$		0			0
$568$	107.636			0.189500
$569$			317.223i			0.557510i	0.960362	+	0.278755i	$0.0899217\pi$
$569$			317.223i			0.557510i	−0.960362	+	0.278755i	$0.910078\pi$
$570$		0			0
$571$			73.2539i			0.128290i	0.997941	+	0.0641452i	$0.0204321\pi$
$571$			73.2539i			0.128290i	−0.997941	+	0.0641452i	$0.979568\pi$
$572$	29.3205	−	56.5359i	0.0512596	−	0.0988390i
$573$		0			0
$574$	65.0718	+	65.0718i	0.113365	+	0.113365i
$575$	−115.905			−0.201574
$576$		0			0
$577$	−81.6410	−	81.6410i	−0.141492	−	0.141492i	0.632813	−	0.774305i	$-0.281900\pi$
$577$	−81.6410	−	81.6410i	−0.141492	−	0.141492i	−0.774305	+	0.632813i	$0.781900\pi$
$578$	−260.692	−	260.692i	−0.451025	−	0.451025i
$579$		0			0
$580$	−10.5077	+	10.5077i	−0.0181168	+	0.0181168i
$581$	160.756			0.276689
$582$		0			0
$583$	−99.9615	+	99.9615i	−0.171461	+	0.171461i
$584$		−	22.7180i		−	0.0389006i
$585$		0			0
$586$	612.084			1.04451
$587$	−382.219	−	382.219i	−0.651140	−	0.651140i	0.302128	−	0.953268i	$-0.402303\pi$
$587$	−382.219	−	382.219i	−0.651140	−	0.651140i	−0.953268	+	0.302128i	$0.902303\pi$
$588$		0			0
$589$			736.036i			1.24964i
$590$	168.946	+	168.946i	0.286349	+	0.286349i
$591$		0			0
$592$	12.5744	−	12.5744i	0.0212405	−	0.0212405i
$593$	−171.355	+	171.355i	−0.288963	+	0.288963i	−0.836670	−	0.547707i	$-0.815501\pi$
$593$	−171.355	+	171.355i	−0.288963	+	0.288963i	0.547707	+	0.836670i	$0.315501\pi$
$594$		0			0
$595$			9.87703i			0.0166000i
$596$	252.449	−	252.449i	0.423572	−	0.423572i
$597$		0			0
$598$	86.8334	+	45.0333i	0.145206	+	0.0753066i
$599$	109.608			0.182984			0.0914922	−	0.995806i	$-0.470836\pi$
$599$	109.608			0.182984			0.0914922	+	0.995806i	$0.470836\pi$
$600$		0			0
$601$	779.108			1.29635			0.648176	−	0.761491i	$-0.275532\pi$
$601$	779.108			1.29635			0.648176	+	0.761491i	$0.275532\pi$
$602$		−	54.4308i		−	0.0904166i
$603$		0			0
$604$	248.813	+	248.813i	0.411942	+	0.411942i
$605$	145.814	−	145.814i	0.241015	−	0.241015i
$606$		0			0
$607$	1144.40			1.88534			0.942669	−	0.333730i	$-0.108307\pi$
$607$	1144.40			1.88534			0.942669	+	0.333730i	$0.108307\pi$
$608$		−	117.856i		−	0.193843i
$609$		0			0
$610$			262.277i			0.429962i
$611$	−502.734	−	260.727i	−0.822806	−	0.426722i
$612$		0			0
$613$	292.349	+	292.349i	0.476915	+	0.476915i	0.904144	−	0.427229i	$-0.140510\pi$
$613$	292.349	+	292.349i	0.476915	+	0.476915i	−0.427229	+	0.904144i	$0.640510\pi$
$614$	−493.023			−0.802969
$615$		0			0
$616$	−5.07180	−	5.07180i	−0.00823344	−	0.00823344i
$617$	369.391	+	369.391i	0.598689	+	0.598689i	0.939964	−	0.341275i	$-0.110859\pi$
$617$	369.391	+	369.391i	0.598689	+	0.598689i	−0.341275	+	0.939964i	$0.610859\pi$
$618$		0			0
$619$	−446.070	+	446.070i	−0.720631	+	0.720631i	−0.968734	−	0.248103i	$-0.920193\pi$
$619$	−446.070	+	446.070i	−0.720631	+	0.720631i	0.248103	+	0.968734i	$0.420193\pi$
$620$	−126.697			−0.204351
$621$		0			0
$622$	−313.377	+	313.377i	−0.503821	+	0.503821i
$623$		−	28.5744i		−	0.0458658i
$624$		0			0
$625$	−394.184			−0.630695
$626$	262.841	+	262.841i	0.419874	+	0.419874i
$627$		0			0
$628$		−	537.569i		−	0.856002i
$629$	16.7255	+	16.7255i	0.0265906	+	0.0265906i
$630$		0			0
$631$	−604.406	+	604.406i	−0.957855	+	0.957855i	−0.999147	−	0.0412923i	$-0.986853\pi$
$631$	−604.406	+	604.406i	−0.957855	+	0.957855i	0.0412923	+	0.999147i	$0.486853\pi$
$632$	8.42047	−	8.42047i	0.0133235	−	0.0133235i
$633$		0			0
$634$		−	297.962i		−	0.469971i
$635$	88.8052	−	88.8052i	0.139851	−	0.139851i
$636$		0			0
$637$	593.941	−	188.272i	0.932403	−	0.295560i
$638$	14.3538			0.0224982
$639$		0			0
$640$	20.2872			0.0316987
$641$		−	1213.91i		−	1.89378i	−0.321565	−	0.946888i	$-0.604209\pi$
$641$		−	1213.91i		−	1.89378i	0.321565	−	0.946888i	$-0.395791\pi$
$642$		0			0
$643$	413.804	+	413.804i	0.643552	+	0.643552i	0.951427	−	0.307875i	$-0.0996178\pi$
$643$	413.804	+	413.804i	0.643552	+	0.643552i	−0.307875	+	0.951427i	$0.599618\pi$
$644$	7.78976	−	7.78976i	0.0120959	−	0.0120959i
$645$		0			0
$646$	156.764			0.242669
$647$			117.913i			0.182245i	0.995840	+	0.0911227i	$0.0290455\pi$
$647$			117.913i			0.182245i	−0.995840	+	0.0911227i	$0.970954\pi$
$648$		0			0
$649$		−	230.785i		−	0.355600i
$650$	355.536	+	184.387i	0.546978	+	0.283673i
$651$		0			0
$652$	−92.8897	−	92.8897i	−0.142469	−	0.142469i
$653$	1088.62			1.66711			0.833553	−	0.552439i	$-0.186303\pi$
$653$	1088.62			1.66711			0.833553	+	0.552439i	$0.186303\pi$
$654$		0			0
$655$	302.900	+	302.900i	0.462443	+	0.462443i
$656$	177.779	+	177.779i	0.271005	+	0.271005i
$657$		0			0
$658$	−45.1000	+	45.1000i	−0.0685410	+	0.0685410i
$659$	−1222.68			−1.85535			−0.927676	−	0.373387i	$-0.878196\pi$
$659$	−1222.68			−1.85535			−0.927676	+	0.373387i	$0.878196\pi$
$660$		0			0
$661$	−667.851	+	667.851i	−1.01036	+	1.01036i	−0.0104193	+	0.999946i	$0.503317\pi$
$661$	−667.851	+	667.851i	−1.01036	+	1.01036i	−0.999946	+	0.0104193i	$0.996683\pi$
$662$			591.741i			0.893869i
$663$		0			0
$664$	439.195			0.661438
$665$	27.3487	+	27.3487i	0.0411258	+	0.0411258i
$666$		0			0
$667$			22.0460i			0.0330525i
$668$	239.023	+	239.023i	0.357819	+	0.357819i
$669$		0			0
$670$	−118.410	+	118.410i	−0.176732	+	0.176732i
$671$	179.138	−	179.138i	0.266972	−	0.266972i
$672$		0			0
$673$		−	411.779i		−	0.611857i	−0.952055	−	0.305928i	$-0.901033\pi$
$673$		−	411.779i		−	0.611857i	0.952055	−	0.305928i	$-0.0989668\pi$
$674$	−48.9385	+	48.9385i	−0.0726091	+	0.0726091i
$675$		0			0
$676$	−194.718	−	276.277i	−0.288044	−	0.408694i
$677$	948.600			1.40118			0.700591	−	0.713563i	$-0.252920\pi$
$677$	948.600			1.40118			0.700591	+	0.713563i	$0.252920\pi$
$678$		0			0
$679$	5.90519			0.00869690
$680$			26.9845i			0.0396831i
$681$		0			0
$682$	86.5359	+	86.5359i	0.126885	+	0.126885i
$683$	−101.809	+	101.809i	−0.149061	+	0.149061i	−0.777699	−	0.628637i	$-0.783613\pi$
$683$	−101.809	+	101.809i	−0.149061	+	0.149061i	0.628637	+	0.777699i	$0.283613\pi$
$684$		0			0
$685$	−233.169			−0.340393
$686$		−	141.913i		−	0.206870i
$687$		0			0
$688$		−	148.708i		−	0.216145i
$689$	226.708	+	715.195i	0.329039	+	1.03802i
$690$		0			0
$691$	−111.135	−	111.135i	−0.160832	−	0.160832i	0.622103	−	0.782935i	$-0.286278\pi$
$691$	−111.135	−	111.135i	−0.160832	−	0.160832i	−0.782935	+	0.622103i	$0.786278\pi$
$692$	−485.205			−0.701163
$693$		0			0
$694$	−552.133	−	552.133i	−0.795581	−	0.795581i
$695$	−176.420	−	176.420i	−0.253842	−	0.253842i
$696$		0			0
$697$	−236.469	+	236.469i	−0.339267	+	0.339267i
$698$	−378.420			−0.542150
$699$		0			0
$700$	31.8949	−	31.8949i	0.0455641	−	0.0455641i
$701$		−	779.520i		−	1.11201i	−0.831178	−	0.556006i	$-0.812333\pi$
$701$		−	779.520i		−	1.11201i	0.831178	−	0.556006i	$-0.187667\pi$
$702$		0			0
$703$	92.6232			0.131754
$704$	−13.8564	−	13.8564i	−0.0196824	−	0.0196824i
$705$		0			0
$706$		−	103.741i		−	0.146942i
$707$	81.5974	+	81.5974i	0.115414	+	0.115414i
$708$		0			0
$709$	43.0179	−	43.0179i	0.0606740	−	0.0606740i	−0.676119	−	0.736793i	$-0.736339\pi$
$709$	43.0179	−	43.0179i	0.0606740	−	0.0606740i	0.736793	+	0.676119i	$0.236339\pi$
$710$	−68.2384	+	68.2384i	−0.0961104	+	0.0961104i
$711$		0			0
$712$		−	78.0666i		−	0.109644i
$713$	−132.910	+	132.910i	−0.186410	+	0.186410i
$714$		0			0
$715$	17.2539	+	54.4308i	0.0241313	+	0.0761270i
$716$	53.4359			0.0746312
$717$		0			0
$718$	−410.238			−0.571363
$719$		−	335.290i		−	0.466328i	−0.972437	−	0.233164i	$-0.925092\pi$
$719$		−	335.290i		−	0.466328i	0.972437	−	0.233164i	$-0.0749078\pi$
$720$		0			0
$721$	−52.2102	−	52.2102i	−0.0724136	−	0.0724136i
$722$	73.0666	−	73.0666i	0.101200	−	0.101200i
$723$		0			0
$724$	512.287			0.707579
$725$			90.2666i			0.124506i
$726$		0			0
$727$		−	537.577i		−	0.739445i	−0.929142	−	0.369723i	$-0.879453\pi$
$727$		−	537.577i		−	0.739445i	0.929142	−	0.369723i	$-0.120547\pi$
$728$	−36.2872	+	11.5026i	−0.0498450	+	0.0158002i
$729$		0			0
$730$	14.4026	+	14.4026i	0.0197296	+	0.0197296i
$731$	197.800			0.270588
$732$		0			0
$733$	−479.946	−	479.946i	−0.654770	−	0.654770i	0.299368	−	0.954138i	$-0.403224\pi$
$733$	−479.946	−	479.946i	−0.654770	−	0.654770i	−0.954138	+	0.299368i	$0.903224\pi$
$734$	351.292	+	351.292i	0.478600	+	0.478600i
$735$		0			0
$736$	21.2820	−	21.2820i	0.0289158	−	0.0289158i
$737$	161.751			0.219473
$738$		0			0
$739$	512.788	−	512.788i	0.693895	−	0.693895i	−0.269192	−	0.963087i	$-0.586757\pi$
$739$	512.788	−	512.788i	0.693895	−	0.693895i	0.963087	+	0.269192i	$0.0867565\pi$
$740$			15.9437i			0.0215455i
$741$		0			0
$742$	84.4974			0.113878
$743$	−801.509	−	801.509i	−1.07875	−	1.07875i	−0.996622	−	0.0821246i	$-0.973829\pi$
$743$	−801.509	−	801.509i	−1.07875	−	1.07875i	−0.0821246	−	0.996622i	$-0.526171\pi$
$744$		0			0
$745$			320.092i			0.429654i
$746$	131.836	+	131.836i	0.176724	+	0.176724i
$747$		0			0
$748$	18.4308	−	18.4308i	0.0246401	−	0.0246401i
$749$	85.3102	−	85.3102i	0.113899	−	0.113899i
$750$		0			0
$751$		−	1384.43i		−	1.84345i	−0.387849	−	0.921723i	$-0.626782\pi$
$751$		−	1384.43i		−	1.84345i	0.387849	−	0.921723i	$-0.373218\pi$
$752$	−123.215	+	123.215i	−0.163850	+	0.163850i
$753$		0			0
$754$	35.0718	−	67.6256i	0.0465143	−	0.0896891i
$755$	−315.482			−0.417857
$756$		0			0
$757$	−125.836			−0.166230			−0.0831148	−	0.996540i	$-0.526487\pi$
$757$	−125.836			−0.166230			−0.0831148	+	0.996540i	$0.526487\pi$
$758$			49.5974i			0.0654319i
$759$		0			0
$760$	74.7180	+	74.7180i	0.0983131	+	0.0983131i
$761$	3.55514	−	3.55514i	0.00467166	−	0.00467166i	−0.704767	−	0.709439i	$-0.748949\pi$
$761$	3.55514	−	3.55514i	0.00467166	−	0.00467166i	0.709439	+	0.704767i	$0.248949\pi$
$762$		0			0
$763$	−160.049			−0.209762
$764$			258.564i			0.338435i
$765$		0			0
$766$			349.110i			0.455758i
$767$	−1087.30	−	563.894i	−1.41760	−	0.735194i
$768$		0			0
$769$	−958.405	−	958.405i	−1.24630	−	1.24630i	−0.957342	−	0.288959i	$-0.906691\pi$
$769$	−958.405	−	958.405i	−1.24630	−	1.24630i	−0.288959	−	0.957342i	$-0.593309\pi$
$770$	6.43078			0.00835166
$771$		0			0
$772$	−320.564	−	320.564i	−0.415238	−	0.415238i
$773$	−76.8165	−	76.8165i	−0.0993746	−	0.0993746i	0.655672	−	0.755046i	$-0.272386\pi$
$773$	−76.8165	−	76.8165i	−0.0993746	−	0.0993746i	−0.755046	+	0.655672i	$0.772386\pi$
$774$		0			0
$775$	−544.196	+	544.196i	−0.702189	+	0.702189i
$776$	16.1333			0.0207903
$777$		0			0
$778$	−644.305	+	644.305i	−0.828156	+	0.828156i
$779$			1309.53i			1.68104i
$780$		0			0
$781$	93.2154			0.119354
$782$	28.3078	+	28.3078i	0.0361992	+	0.0361992i
$783$		0			0
$784$		−	191.713i		−	0.244532i
$785$	340.805	+	340.805i	0.434147	+	0.434147i
$786$		0			0
$787$	−486.883	+	486.883i	−0.618657	+	0.618657i	−0.945187	−	0.326530i	$-0.894121\pi$
$787$	−486.883	+	486.883i	−0.618657	+	0.618657i	0.326530	+	0.945187i	$0.394121\pi$
$788$	−218.536	+	218.536i	−0.277330	+	0.277330i
$789$		0			0
$790$			10.6767i			0.0135148i
$791$	−108.546	+	108.546i	−0.137227	+	0.137227i
$792$		0			0
$793$	−406.277	−	1281.68i	−0.512329	−	1.61624i
$794$	−865.384			−1.08990
$795$		0			0
$796$	50.1999			0.0630652
$797$		−	713.587i		−	0.895341i	−0.894198	−	0.447671i	$-0.852254\pi$
$797$		−	713.587i		−	0.895341i	0.894198	−	0.447671i	$-0.147746\pi$
$798$		0			0
$799$	−163.892	−	163.892i	−0.205122	−	0.205122i
$800$	87.1384	−	87.1384i	0.108923	−	0.108923i
$801$		0			0
$802$	−549.100			−0.684663
$803$		−	19.6743i		−	0.0245010i
$804$		0			0
$805$			9.87703i			0.0122696i
$806$	619.138	−	196.259i	0.768162	−	0.243498i
$807$		0			0
$808$	222.928	+	222.928i	0.275901	+	0.275901i
$809$	257.600			0.318418			0.159209	−	0.987245i	$-0.449106\pi$
$809$	257.600			0.318418			0.159209	+	0.987245i	$0.449106\pi$
$810$		0			0
$811$	−127.258	−	127.258i	−0.156914	−	0.156914i	0.624283	−	0.781198i	$-0.285391\pi$
$811$	−127.258	−	127.258i	−0.156914	−	0.156914i	−0.781198	+	0.624283i	$0.785391\pi$
$812$	−6.06664	−	6.06664i	−0.00747123	−	0.00747123i
$813$		0			0
$814$	10.8897	−	10.8897i	0.0133780	−	0.0133780i
$815$	117.779			0.144515
$816$		0			0
$817$	547.692	−	547.692i	0.670370	−	0.670370i
$818$		−	152.374i		−	0.186277i
$819$		0			0
$820$	−225.415			−0.274897
$821$	−1116.87	−	1116.87i	−1.36038	−	1.36038i	−0.873428	−	0.486953i	$-0.838108\pi$
$821$	−1116.87	−	1116.87i	−1.36038	−	1.36038i	−0.486953	−	0.873428i	$-0.661892\pi$
$822$		0			0
$823$		−	617.920i		−	0.750814i	−0.926860	−	0.375407i	$-0.877503\pi$
$823$		−	617.920i		−	0.750814i	0.926860	−	0.375407i	$-0.122497\pi$
$824$	−142.641	−	142.641i	−0.173108	−	0.173108i
$825$		0			0
$826$	−97.5411	+	97.5411i	−0.118088	+	0.118088i
$827$	−349.847	+	349.847i	−0.423032	+	0.423032i	−0.886246	−	0.463214i	$-0.846696\pi$
$827$	−349.847	+	349.847i	−0.423032	+	0.423032i	0.463214	+	0.886246i	$0.346696\pi$
$828$		0			0
$829$			247.646i			0.298729i	0.988782	+	0.149364i	$0.0477227\pi$
$829$			247.646i			0.298729i	−0.988782	+	0.149364i	$0.952277\pi$
$830$	−278.438	+	278.438i	−0.335468	+	0.335468i
$831$		0			0
$832$	−99.1384	+	31.4256i	−0.119157	+	0.0377712i
$833$	255.002			0.306125
$834$		0			0
$835$	−303.069			−0.362957
$836$		−	102.067i		−	0.122089i
$837$		0			0
$838$	76.8231	+	76.8231i	0.0916743	+	0.0916743i
$839$	598.868	−	598.868i	0.713788	−	0.713788i	−0.253538	−	0.967325i	$-0.581594\pi$
$839$	598.868	−	598.868i	0.713788	−	0.713788i	0.967325	+	0.253538i	$0.0815943\pi$
$840$		0			0
$841$	−823.831			−0.979585
$842$		−	235.513i		−	0.279707i
$843$		0			0
$844$			413.436i			0.489853i
$845$	298.599	+	51.7063i	0.353371	+	0.0611909i
$846$		0			0
$847$	84.1858	+	84.1858i	0.0993930	+	0.0993930i
$848$	230.851			0.272230
$849$		0			0
$850$	115.905	+	115.905i	0.136359	+	0.136359i
$851$	16.7255	+	16.7255i	0.0196540	+	0.0196540i
$852$		0			0
$853$	−519.210	+	519.210i	−0.608687	+	0.608687i	−0.942603	−	0.333916i	$-0.891630\pi$
$853$	−519.210	+	519.210i	−0.608687	+	0.608687i	0.333916	+	0.942603i	$0.391630\pi$
$854$	−151.426			−0.177313
$855$		0			0
$856$	233.072	−	233.072i	0.272280	−	0.272280i
$857$			226.756i			0.264593i	0.991210	+	0.132297i	$0.0422351\pi$
$857$			226.756i			0.264593i	−0.991210	+	0.132297i	$0.957765\pi$
$858$		0			0
$859$	950.656			1.10670			0.553350	−	0.832949i	$-0.313349\pi$
$859$	950.656			1.10670			0.553350	+	0.832949i	$0.313349\pi$
$860$	94.2769	+	94.2769i	0.109624	+	0.109624i
$861$		0			0
$862$			724.956i			0.841017i
$863$	−773.711	−	773.711i	−0.896537	−	0.896537i	0.0985910	−	0.995128i	$-0.468566\pi$
$863$	−773.711	−	773.711i	−0.896537	−	0.896537i	−0.995128	+	0.0985910i	$0.968566\pi$
$864$		0			0
$865$	307.608	−	307.608i	0.355616	−	0.355616i
$866$	197.292	−	197.292i	0.227820	−	0.227820i
$867$		0			0
$868$		−	73.1487i		−	0.0842728i
$869$	7.29234	−	7.29234i	0.00839165	−	0.00839165i
$870$		0			0
$871$	395.219	−	762.063i	0.453753	−	0.874929i
$872$	−437.261			−0.501447
$873$		0			0
$874$	156.764			0.179364
$875$			86.8513i			0.0992586i
$876$		0			0
$877$	646.713	+	646.713i	0.737415	+	0.737415i	0.972077	−	0.234662i	$-0.0753984\pi$
$877$	646.713	+	646.713i	0.737415	+	0.737415i	−0.234662	+	0.972077i	$0.575398\pi$
$878$	−272.238	+	272.238i	−0.310067	+	0.310067i
$879$		0			0
$880$	17.5692			0.0199650
$881$		−	783.997i		−	0.889895i	−0.895557	−	0.444947i	$-0.853222\pi$
$881$		−	783.997i		−	0.889895i	0.895557	−	0.444947i	$-0.146778\pi$
$882$		0			0
$883$			1089.81i			1.23421i	0.786881	+	0.617105i	$0.211695\pi$
$883$			1089.81i			1.23421i	−0.786881	+	0.617105i	$0.788305\pi$
$884$	−41.8001	−	131.867i	−0.0472852	−	0.149170i
$885$		0			0
$886$	74.7358	+	74.7358i	0.0843519	+	0.0843519i
$887$	1057.03			1.19169			0.595846	−	0.803099i	$-0.296817\pi$
$887$	1057.03			1.19169			0.595846	+	0.803099i	$0.296817\pi$
$888$		0			0
$889$	51.2717	+	51.2717i	0.0576735	+	0.0576735i
$890$	49.4923	+	49.4923i	0.0556093	+	0.0556093i
$891$		0			0
$892$	−278.823	+	278.823i	−0.312582	+	0.312582i
$893$	−907.608			−1.01636
$894$		0			0
$895$	−33.8770	+	33.8770i	−0.0378514	+	0.0378514i
$896$			11.7128i			0.0130723i
$897$		0			0
$898$	1032.45			1.14972
$899$	103.510	+	103.510i	0.115139	+	0.115139i
$900$		0			0
$901$			307.061i			0.340801i
$902$	153.962	+	153.962i	0.170689	+	0.170689i
$903$		0			0
$904$	−296.554	+	296.554i	−0.328046	+	0.328046i
$905$	−324.777	+	324.777i	−0.358870	+	0.358870i
$906$		0			0
$907$		−	546.669i		−	0.602722i	−0.953510	−	0.301361i	$-0.902559\pi$
$907$		−	546.669i		−	0.602722i	0.953510	−	0.301361i	$-0.0974410\pi$
$908$	−194.736	+	194.736i	−0.214467	+	0.214467i
$909$		0			0
$910$	15.7128	−	30.2975i	0.0172668	−	0.0332940i
$911$	−724.743			−0.795547			−0.397774	−	0.917484i	$-0.630217\pi$
$911$	−724.743			−0.795547			−0.397774	+	0.917484i	$0.630217\pi$
$912$		0			0
$913$	380.354			0.416598
$914$			101.923i			0.111513i
$915$		0			0
$916$	408.354	+	408.354i	0.445801	+	0.445801i
$917$	−174.879	+	174.879i	−0.190708	+	0.190708i
$918$		0			0
$919$	−941.108			−1.02406			−0.512028	−	0.858969i	$-0.671106\pi$
$919$	−941.108			−1.02406			−0.512028	+	0.858969i	$0.671106\pi$
$920$			26.9845i			0.0293310i
$921$		0			0
$922$			405.100i			0.439371i
$923$	227.760	−	439.168i	0.246761	−	0.475805i
$924$		0			0
$925$	68.4820	+	68.4820i	0.0740345	+	0.0740345i
$926$	446.495			0.482176
$927$		0			0
$928$	−16.5744	−	16.5744i	−0.0178603	−	0.0178603i
$929$	260.130	+	260.130i	0.280010	+	0.280010i	0.833113	−	0.553103i	$-0.186556\pi$
$929$	260.130	+	260.130i	0.280010	+	0.280010i	−0.553103	+	0.833113i	$0.686556\pi$
$930$		0			0
$931$	706.081	−	706.081i	0.758411	−	0.758411i
$932$	463.923			0.497772
$933$		0			0
$934$	161.818	−	161.818i	0.173253	−	0.173253i
$935$			23.3693i			0.0249939i
$936$		0			0
$937$	1387.56			1.48085			0.740426	−	0.672138i	$-0.234624\pi$
$937$	1387.56			1.48085			0.740426	+	0.672138i	$0.234624\pi$
$938$	−68.3641	−	68.3641i	−0.0728829	−	0.0728829i
$939$		0			0
$940$		−	156.231i		−	0.166203i
$941$	61.6012	+	61.6012i	0.0654635	+	0.0654635i	0.739081	−	0.673617i	$-0.235260\pi$
$941$	61.6012	+	61.6012i	0.0654635	+	0.0654635i	−0.673617	+	0.739081i	$0.735260\pi$
$942$		0			0
$943$	−236.469	+	236.469i	−0.250763	+	0.250763i
$944$	−266.487	+	266.487i	−0.282296	+	0.282296i
$945$		0			0
$946$		−	128.785i		−	0.136136i
$947$	−54.5064	+	54.5064i	−0.0575569	+	0.0575569i	−0.735299	−	0.677742i	$-0.762958\pi$
$947$	−54.5064	+	54.5064i	−0.0575569	+	0.0575569i	0.677742	+	0.735299i	$0.262958\pi$
$948$		0			0
$949$	−92.6922	−	48.0718i	−0.0976735	−	0.0506552i
$950$	641.864			0.675646
$951$		0			0
$952$	−15.5795			−0.0163651
$953$			1079.56i			1.13280i	0.824131	+	0.566399i	$0.191664\pi$
$953$			1079.56i			1.13280i	−0.824131	+	0.566399i	$0.808336\pi$
$954$		0			0
$955$	−163.923	−	163.923i	−0.171647	−	0.171647i
$956$	279.962	−	279.962i	0.292847	−	0.292847i
$957$		0			0
$958$	−178.259			−0.186074
$959$		−	134.620i		−	0.140376i
$960$		0			0
$961$			287.077i			0.298727i
$962$	−24.6973	−	77.9127i	−0.0256729	−	0.0809904i
$963$		0			0
$964$	106.918	+	106.918i	0.110911	+	0.110911i
$965$	406.459			0.421201
$966$		0			0
$967$	493.745	+	493.745i	0.510594	+	0.510594i	0.914709	−	0.404114i	$-0.132420\pi$
$967$	493.745	+	493.745i	0.510594	+	0.510594i	−0.404114	+	0.914709i	$0.632420\pi$
$968$	230.000	+	230.000i	0.237603	+	0.237603i
$969$		0			0
$970$	−10.2281	+	10.2281i	−0.0105444	+	0.0105444i
$971$	1694.52			1.74513			0.872566	−	0.488497i	$-0.162455\pi$
$971$	1694.52			1.74513			0.872566	+	0.488497i	$0.162455\pi$
$972$		0			0
$973$	101.856	−	101.856i	0.104683	−	0.104683i
$974$			1054.88i			1.08304i
$975$		0			0
$976$	−413.703			−0.423876
$977$	390.060	+	390.060i	0.399243	+	0.399243i	0.877966	−	0.478723i	$-0.158900\pi$
$977$	390.060	+	390.060i	0.399243	+	0.399243i	−0.478723	+	0.877966i	$0.658900\pi$
$978$		0			0
$979$		−	67.6077i		−	0.0690579i
$980$	121.541	+	121.541i	0.124021	+	0.124021i
$981$		0			0
$982$	700.726	−	700.726i	0.713570	−	0.713570i
$983$	1123.12	−	1123.12i	1.14254	−	1.14254i	0.154559	−	0.987984i	$-0.450604\pi$
$983$	1123.12	−	1123.12i	1.14254	−	1.14254i	0.987984	−	0.154559i	$-0.0493956\pi$
$984$		0			0
$985$		−	277.092i		−	0.281312i
$986$	22.0460	−	22.0460i	0.0223590	−	0.0223590i
$987$		0			0
$988$	−480.869	−	249.387i	−0.486710	−	0.252416i
$989$	197.800			0.200000
$990$		0			0
$991$	610.985			0.616533			0.308267	−	0.951300i	$-0.400251\pi$
$991$	610.985			0.616533			0.308267	+	0.951300i	$0.400251\pi$
$992$		−	199.846i		−	0.201458i
$993$		0			0
$994$	−39.3975	−	39.3975i	−0.0396353	−	0.0396353i
$995$	−31.8255	+	31.8255i	−0.0319854	+	0.0319854i
$996$		0			0
$997$	−412.123			−0.413363			−0.206682	−	0.978408i	$-0.566266\pi$
$997$	−412.123			−0.413363			−0.206682	+	0.978408i	$0.566266\pi$
$998$		−	558.131i		−	0.559249i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.3.i.b.73.2		4
3.2	odd	2		78.3.f.a.73.2	yes	4
12.11	even	2		624.3.ba.a.385.1		4
13.5	odd	4	inner	234.3.i.b.109.2		4
39.5	even	4		78.3.f.a.31.2	✓	4
39.8	even	4		1014.3.f.a.577.2		4
39.38	odd	2		1014.3.f.a.775.2		4
156.83	odd	4		624.3.ba.a.577.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.3.f.a.31.2	✓	4	39.5	even	4
78.3.f.a.73.2	yes	4	3.2	odd	2
234.3.i.b.73.2		4	1.1	even	1	trivial
234.3.i.b.109.2		4	13.5	odd	4	inner
624.3.ba.a.385.1		4	12.11	even	2
624.3.ba.a.577.1		4	156.83	odd	4
1014.3.f.a.577.2		4	39.8	even	4
1014.3.f.a.775.2		4	39.38	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	234.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +2.00000i q^{4} +(-1.26795 - 1.26795i) q^{5} +(0.732051 - 0.732051i) q^{7} +(2.00000 - 2.00000i) q^{8} +2.53590i q^{10} +(1.73205 - 1.73205i) q^{11} +(-3.92820 - 12.3923i) q^{13} -1.46410 q^{14} -4.00000 q^{16} -5.32051i q^{17} +(-14.7321 - 14.7321i) q^{19} +(2.53590 - 2.53590i) q^{20} -3.46410 q^{22} -5.32051i q^{23} -21.7846i q^{25} +(-8.46410 + 16.3205i) q^{26} +(1.46410 + 1.46410i) q^{28} -4.14359 q^{29} +(-24.9808 - 24.9808i) q^{31} +(4.00000 + 4.00000i) q^{32} +(-5.32051 + 5.32051i) q^{34} -1.85641 q^{35} +(-3.14359 + 3.14359i) q^{37} +29.4641i q^{38} -5.07180 q^{40} +(-44.4449 - 44.4449i) q^{41} +37.1769i q^{43} +(3.46410 + 3.46410i) q^{44} +(-5.32051 + 5.32051i) q^{46} +(30.8038 - 30.8038i) q^{47} +47.9282i q^{49} +(-21.7846 + 21.7846i) q^{50} +(24.7846 - 7.85641i) q^{52} -57.7128 q^{53} -4.39230 q^{55} -2.92820i q^{56} +(4.14359 + 4.14359i) q^{58} +(66.6218 - 66.6218i) q^{59} +103.426 q^{61} +49.9615i q^{62} -8.00000i q^{64} +(-10.7321 + 20.6936i) q^{65} +(46.6936 + 46.6936i) q^{67} +10.6410 q^{68} +(1.85641 + 1.85641i) q^{70} +(26.9090 + 26.9090i) q^{71} +(5.67949 - 5.67949i) q^{73} +6.28719 q^{74} +(29.4641 - 29.4641i) q^{76} -2.53590i q^{77} +4.21024 q^{79} +(5.07180 + 5.07180i) q^{80} +88.8897i q^{82} +(109.799 + 109.799i) q^{83} +(-6.74613 + 6.74613i) q^{85} +(37.1769 - 37.1769i) q^{86} -6.92820i q^{88} +(19.5167 - 19.5167i) q^{89} +(-11.9474 - 6.19615i) q^{91} +10.6410 q^{92} -61.6077 q^{94} +37.3590i q^{95} +(4.03332 + 4.03332i) q^{97} +(47.9282 - 47.9282i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 12 q^{5} - 4 q^{7} + 8 q^{8} + 12 q^{13} + 8 q^{14} - 16 q^{16} - 52 q^{19} + 24 q^{20} - 20 q^{26} - 8 q^{28} - 72 q^{29} + 4 q^{31} + 16 q^{32} + 48 q^{34} + 48 q^{35} - 68 q^{37} - 48 q^{40}+ \cdots + 164 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 - 12 * q^5 - 4 * q^7 + 8 * q^8 + 12 * q^13 + 8 * q^14 - 16 * q^16 - 52 * q^19 + 24 * q^20 - 20 * q^26 - 8 * q^28 - 72 * q^29 + 4 * q^31 + 16 * q^32 + 48 * q^34 + 48 * q^35 - 68 * q^37 - 48 * q^40 - 60 * q^41 + 48 * q^46 + 144 * q^47 - 4 * q^50 + 16 * q^52 - 120 * q^53 + 24 * q^55 + 72 * q^58 + 24 * q^59 + 192 * q^61 - 36 * q^65 - 28 * q^67 - 96 * q^68 - 48 * q^70 - 24 * q^71 + 92 * q^73 + 136 * q^74 + 104 * q^76 - 288 * q^79 + 48 * q^80 + 72 * q^83 + 264 * q^85 + 24 * q^86 - 12 * q^89 - 124 * q^91 - 96 * q^92 - 288 * q^94 - 164 * q^97 + 164 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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