LMFDB - Embedded newform 234.3.i.b.109.2

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			109.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	234.109
Dual form			234.3.i.b.73.2

$q$-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 $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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	−0.822441	−	0.568851i	$-0.807388\pi$
$5$	−1.26795	+	1.26795i	−0.253590	+	0.253590i	0.568851	+	0.822441i	$0.307388\pi$
$6$		0			0
$7$	0.732051	+	0.732051i	0.104579	+	0.104579i	0.757460	−	0.652881i	$-0.226440\pi$
$7$	0.732051	+	0.732051i	0.104579	+	0.104579i	−0.652881	+	0.757460i	$0.726440\pi$
$8$	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	0.781440	−	0.623981i	$-0.214486\pi$
$11$	1.73205	+	1.73205i	0.157459	+	0.157459i	−0.623981	+	0.781440i	$0.714486\pi$
$12$		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	$0.0500165\pi$
$17$			5.32051i			0.312971i	−0.987680	+	0.156486i	$0.949984\pi$
$18$		0			0
$19$	−14.7321	+	14.7321i	−0.775371	+	0.775371i	−0.979040	−	0.203669i	$-0.934713\pi$
$19$	−14.7321	+	14.7321i	−0.775371	+	0.775371i	0.203669	+	0.979040i	$0.434713\pi$
$20$	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	$0.0368993\pi$
$23$			5.32051i			0.231326i	−0.993288	+	0.115663i	$0.963101\pi$
$24$		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	−0.984000	−	0.178169i	$-0.942983\pi$
$31$	−24.9808	+	24.9808i	−0.805831	+	0.805831i	0.178169	+	0.984000i	$0.442983\pi$
$32$	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	0.663349	−	0.748311i	$-0.269135\pi$
$37$	−3.14359	−	3.14359i	−0.0849620	−	0.0849620i	−0.748311	+	0.663349i	$0.769135\pi$
$38$		−	29.4641i		−	0.775371i
$39$		0			0
$40$	−5.07180			−0.126795
$41$	−44.4449	+	44.4449i	−1.08402	+	1.08402i	−0.0878910	+	0.996130i	$0.528013\pi$
$41$	−44.4449	+	44.4449i	−1.08402	+	1.08402i	−0.996130	+	0.0878910i	$0.971987\pi$
$42$		0			0
$43$		−	37.1769i		−	0.864579i	−0.901735	−	0.432290i	$-0.857706\pi$
$43$		−	37.1769i		−	0.864579i	0.901735	−	0.432290i	$-0.142294\pi$
$44$	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	0.954288	−	0.298887i	$-0.0966155\pi$
$47$	30.8038	+	30.8038i	0.655401	+	0.655401i	−0.298887	+	0.954288i	$0.596615\pi$
$48$		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	0.990310	+	0.138872i	$0.0443478\pi$
$59$	66.6218	+	66.6218i	1.12918	+	1.12918i	0.138872	+	0.990310i	$0.455652\pi$
$60$		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	−0.266826	−	0.963745i	$-0.585975\pi$
$67$	46.6936	−	46.6936i	0.696919	−	0.696919i	0.963745	+	0.266826i	$0.0859748\pi$
$68$	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	−0.491742	−	0.870741i	$-0.663640\pi$
$71$	26.9090	−	26.9090i	0.379000	−	0.379000i	0.870741	+	0.491742i	$0.163640\pi$
$72$		0			0
$73$	5.67949	+	5.67949i	0.0778013	+	0.0778013i	0.744937	−	0.667135i	$-0.232480\pi$
$73$	5.67949	+	5.67949i	0.0778013	+	0.0778013i	−0.667135	+	0.744937i	$0.732480\pi$
$74$	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	0.411438	−	0.911438i	$-0.365027\pi$
$83$	109.799	−	109.799i	1.32288	−	1.32288i	0.911438	−	0.411438i	$-0.134973\pi$
$84$		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	0.808198	−	0.588910i	$-0.200443\pi$
$89$	19.5167	+	19.5167i	0.219288	+	0.219288i	−0.588910	+	0.808198i	$0.700443\pi$
$90$		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	−0.686011	−	0.727591i	$-0.740640\pi$
$97$	4.03332	−	4.03332i	0.0415806	−	0.0415806i	0.727591	+	0.686011i	$0.240640\pi$
$98$	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	$-0.813940\pi$
$101$		−	111.464i		−	1.10360i	0.833975	−	0.551802i	$-0.186060\pi$
$102$		0			0
$103$			71.3205i			0.692432i	0.938155	+	0.346216i	$0.112534\pi$
$103$			71.3205i			0.692432i	−0.938155	+	0.346216i	$0.887466\pi$
$104$	−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	−0.00289735	+	0.999996i	$0.500922\pi$
$109$	−109.315	+	109.315i	−1.00289	+	1.00289i	−0.999996	+	0.00289735i	$0.999078\pi$
$110$	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	$-0.911076\pi$
$127$		−	70.0385i		−	0.551484i	0.961232	−	0.275742i	$-0.0889236\pi$
$128$	−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	0.957981	−	0.286832i	$-0.0926021\pi$
$137$	91.9474	+	91.9474i	0.671149	+	0.671149i	−0.286832	+	0.957981i	$0.592602\pi$
$138$		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	−0.989776	−	0.142633i	$-0.954443\pi$
$149$	−126.224	+	126.224i	−0.847143	+	0.847143i	0.142633	+	0.989776i	$0.454443\pi$
$150$		0			0
$151$	124.406	+	124.406i	0.823883	+	0.823883i	0.986663	−	0.162779i	$-0.0520458\pi$
$151$	124.406	+	124.406i	0.823883	+	0.823883i	−0.162779	+	0.986663i	$0.552046\pi$
$152$	−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	0.550137	−	0.835075i	$-0.314576\pi$
$163$	−46.4449	−	46.4449i	−0.284938	−	0.284938i	−0.835075	+	0.550137i	$0.814576\pi$
$164$	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	0.967709	−	0.252071i	$-0.0811116\pi$
$167$	119.512	+	119.512i	0.715638	+	0.715638i	−0.252071	+	0.967709i	$0.581112\pi$
$168$		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	$-0.752664\pi$
$173$		−	242.603i		−	1.40233i	0.713001	−	0.701163i	$-0.247336\pi$
$174$		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	$0.0237780\pi$
$179$			26.7180i			0.149262i	−0.997211	+	0.0746312i	$0.976222\pi$
$180$		0			0
$181$			256.144i			1.41516i	0.706634	+	0.707579i	$0.250213\pi$
$181$			256.144i			1.41516i	−0.706634	+	0.707579i	$0.749787\pi$
$182$	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	0.157105	−	0.987582i	$-0.449784\pi$
$193$	−160.282	−	160.282i	−0.830477	−	0.830477i	−0.987582	+	0.157105i	$0.949784\pi$
$194$			8.06664i			0.0415806i
$195$		0			0
$196$	−95.8564			−0.489063
$197$	109.268	−	109.268i	0.554660	−	0.554660i	−0.373122	−	0.927782i	$-0.621713\pi$
$197$	109.268	−	109.268i	0.554660	−	0.554660i	0.927782	+	0.373122i	$0.121713\pi$
$198$		0			0
$199$			25.1000i			0.126130i	0.998009	+	0.0630652i	$0.0200876\pi$
$199$			25.1000i			0.126130i	−0.998009	+	0.0630652i	$0.979912\pi$
$200$	−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	−0.321683	−	0.946847i	$-0.604249\pi$
$223$	139.412	−	139.412i	0.625164	−	0.625164i	0.946847	+	0.321683i	$0.104249\pi$
$224$	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	−0.459331	−	0.888265i	$-0.651911\pi$
$227$	97.3679	−	97.3679i	0.428934	−	0.428934i	0.888265	+	0.459331i	$0.151911\pi$
$228$		0			0
$229$	204.177	+	204.177i	0.891602	+	0.891602i	0.994674	−	0.103072i	$-0.0328671\pi$
$229$	204.177	+	204.177i	0.891602	+	0.891602i	−0.103072	+	0.994674i	$0.532867\pi$
$230$	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	$0.165848\pi$
$233$			231.962i			0.995543i	−0.867308	+	0.497772i	$0.834152\pi$
$234$		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	−0.936462	−	0.350769i	$-0.885920\pi$
$239$	−139.981	+	139.981i	−0.585694	+	0.585694i	0.350769	+	0.936462i	$0.385920\pi$
$240$		0			0
$241$	53.4589	+	53.4589i	0.221821	+	0.221821i	0.809265	−	0.587444i	$-0.199866\pi$
$241$	53.4589	+	53.4589i	0.221821	+	0.221821i	−0.587444	+	0.809265i	$0.699866\pi$
$242$	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	$-0.682909\pi$
$251$		−	421.377i		−	1.67879i	0.543520	−	0.839396i	$-0.317091\pi$
$252$		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	$0.161445\pi$
$257$			249.664i			0.971455i	−0.874110	+	0.485728i	$0.838555\pi$
$258$		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	0.778772	+	0.627307i	$0.215843\pi$
$271$	381.047	+	381.047i	1.40608	+	1.40608i	0.627307	+	0.778772i	$0.284157\pi$
$272$		−	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	$-0.960376\pi$
$277$		−	68.7846i		−	0.248320i	0.992262	−	0.124160i	$-0.0396236\pi$
$278$	−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	0.572288	−	0.820053i	$-0.306056\pi$
$281$	−69.6218	−	69.6218i	−0.247764	−	0.247764i	−0.820053	+	0.572288i	$0.806056\pi$
$282$		0			0
$283$		−	425.808i		−	1.50462i	−0.658809	−	0.752310i	$-0.728939\pi$
$283$		−	425.808i		−	1.50462i	0.658809	−	0.752310i	$-0.271061\pi$
$284$	−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	−0.998962	−	0.0455508i	$-0.985496\pi$
$293$	−306.042	−	306.042i	−1.04451	−	1.04451i	−0.0455508	−	0.998962i	$-0.514504\pi$
$294$		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	0.983559	−	0.180589i	$-0.0578005\pi$
$307$	246.512	+	246.512i	0.802969	+	0.802969i	−0.180589	+	0.983559i	$0.557801\pi$
$308$	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	$0.168073\pi$
$311$			313.377i			1.00764i	−0.863808	+	0.503821i	$0.831927\pi$
$312$		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	−0.431934	−	0.901905i	$-0.642169\pi$
$317$	148.981	−	148.981i	0.469971	−	0.469971i	0.901905	+	0.431934i	$0.142169\pi$
$318$		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	−0.994885	−	0.101016i	$-0.967791\pi$
$331$	−295.870	+	295.870i	−0.893869	+	0.893869i	0.101016	+	0.994885i	$0.467791\pi$
$332$	−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	$0.0231325\pi$
$337$			48.9385i			0.145218i	−0.997360	+	0.0726091i	$0.976867\pi$
$338$	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	0.924159	−	0.382009i	$-0.124768\pi$
$349$	189.210	+	189.210i	0.542150	+	0.542150i	−0.382009	+	0.924159i	$0.624768\pi$
$350$		−	31.8949i		−	0.0911282i
$351$		0			0
$352$	13.8564			0.0393648
$353$	51.8705	−	51.8705i	0.146942	−	0.146942i	−0.629809	−	0.776750i	$-0.716867\pi$
$353$	51.8705	−	51.8705i	0.146942	−	0.146942i	0.776750	+	0.629809i	$0.216867\pi$
$354$		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	0.932509	−	0.361146i	$-0.117615\pi$
$359$	205.119	+	205.119i	0.571363	+	0.571363i	−0.361146	+	0.932509i	$0.617615\pi$
$360$		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	−0.739065	−	0.673634i	$-0.764733\pi$
$379$	−24.7987	+	24.7987i	−0.0654319	+	0.0654319i	0.673634	+	0.739065i	$0.264733\pi$
$380$	−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	−0.897260	−	0.441502i	$-0.854446\pi$
$383$	−174.555	+	174.555i	−0.455758	+	0.455758i	0.441502	+	0.897260i	$0.354446\pi$
$384$		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	$0.310610\pi$
$389$			644.305i			1.65631i	−0.560498	+	0.828156i	$0.689390\pi$
$390$		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	0.995537	+	0.0943673i	$0.0300828\pi$
$397$	432.692	+	432.692i	1.08990	+	1.08990i	0.0943673	+	0.995537i	$0.469917\pi$
$398$	−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	0.961047	−	0.276384i	$-0.0891362\pi$
$401$	274.550	+	274.550i	0.684663	+	0.684663i	−0.276384	+	0.961047i	$0.589136\pi$
$402$		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	−0.607808	−	0.794084i	$-0.707951\pi$
$409$	76.1872	−	76.1872i	0.186277	−	0.186277i	0.794084	+	0.607808i	$0.207951\pi$
$410$	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	−0.553285	−	0.832992i	$-0.686626\pi$
$421$	117.756	−	117.756i	0.279707	−	0.279707i	0.832992	+	0.553285i	$0.186626\pi$
$422$	−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	−0.988991	−	0.147975i	$-0.952725\pi$
$431$	−362.478	+	362.478i	−0.841017	+	0.841017i	0.147975	+	0.988991i	$0.452725\pi$
$432$		0			0
$433$		−	197.292i		−	0.455641i	−0.973703	−	0.227820i	$-0.926840\pi$
$433$		−	197.292i		−	0.455641i	0.973703	−	0.227820i	$-0.0731599\pi$
$434$	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	$0.100351\pi$
$439$			272.238i			0.620133i	−0.950715	+	0.310067i	$0.899649\pi$
$440$	−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	−0.986607	−	0.163113i	$-0.947847\pi$
$449$	−516.224	−	516.224i	−1.14972	−	1.14972i	−0.163113	−	0.986607i	$-0.552153\pi$
$450$		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	−0.760662	−	0.649149i	$-0.775125\pi$
$457$	−50.9615	+	50.9615i	−0.111513	+	0.111513i	0.649149	+	0.760662i	$0.275125\pi$
$458$	−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	−0.891800	−	0.452429i	$-0.850557\pi$
$461$	−202.550	+	202.550i	−0.439371	+	0.439371i	0.452429	+	0.891800i	$0.350557\pi$
$462$		0			0
$463$	−223.247	−	223.247i	−0.482176	−	0.482176i	0.423650	−	0.905826i	$-0.360749\pi$
$463$	−223.247	−	223.247i	−0.482176	−	0.482176i	−0.905826	+	0.423650i	$0.860749\pi$
$464$	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	$-0.944572\pi$
$467$		−	161.818i		−	0.346505i	0.984877	−	0.173253i	$-0.0554277\pi$
$468$		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	0.793996	−	0.607922i	$-0.207997\pi$
$479$	89.1295	+	89.1295i	0.186074	+	0.186074i	−0.607922	+	0.793996i	$0.707997\pi$
$480$		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	−0.0868139	+	0.996225i	$0.527669\pi$
$487$	−527.440	+	527.440i	−1.08304	+	1.08304i	−0.996225	+	0.0868139i	$0.972331\pi$
$488$	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	$-0.747077\pi$
$491$		−	700.726i		−	1.42714i	0.700584	−	0.713570i	$-0.252923\pi$
$492$		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	−0.369845	−	0.929094i	$-0.620589\pi$
$499$	279.065	−	279.065i	0.559249	−	0.559249i	0.929094	+	0.369845i	$0.120589\pi$
$500$	−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	−0.365592	−	0.930775i	$-0.619134\pi$
$509$	287.678	−	287.678i	0.565183	−	0.565183i	0.930775	+	0.365592i	$0.119134\pi$
$510$		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	0.606780	−	0.794870i	$-0.292461\pi$
$541$	−101.756	−	101.756i	−0.188090	−	0.188090i	−0.794870	+	0.606780i	$0.792461\pi$
$542$	−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	0.915179	−	0.403047i	$-0.132049\pi$
$557$	285.258	+	285.258i	0.512132	+	0.512132i	−0.403047	+	0.915179i	$0.632049\pi$
$558$		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	$-0.721955\pi$
$563$		−	863.174i		−	1.53317i	0.642143	−	0.766585i	$-0.278045\pi$
$564$		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	$-0.910078\pi$
$569$		−	317.223i		−	0.557510i	0.960362	−	0.278755i	$-0.0899217\pi$
$570$		0			0
$571$		−	73.2539i		−	0.128290i	−0.997941	−	0.0641452i	$-0.979568\pi$
$571$		−	73.2539i		−	0.128290i	0.997941	−	0.0641452i	$-0.0204321\pi$
$572$	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	−0.774305	−	0.632813i	$-0.781900\pi$
$577$	−81.6410	+	81.6410i	−0.141492	+	0.141492i	0.632813	+	0.774305i	$0.281900\pi$
$578$	−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	−0.953268	−	0.302128i	$-0.902303\pi$
$587$	−382.219	+	382.219i	−0.651140	+	0.651140i	0.302128	+	0.953268i	$0.402303\pi$
$588$		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	0.547707	−	0.836670i	$-0.315501\pi$
$593$	−171.355	−	171.355i	−0.288963	−	0.288963i	−0.836670	+	0.547707i	$0.815501\pi$
$594$		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	−0.427229	−	0.904144i	$-0.640510\pi$
$613$	292.349	−	292.349i	0.476915	−	0.476915i	0.904144	+	0.427229i	$0.140510\pi$
$614$	−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	−0.341275	−	0.939964i	$-0.610859\pi$
$617$	369.391	−	369.391i	0.598689	−	0.598689i	0.939964	+	0.341275i	$0.110859\pi$
$618$		0			0
$619$	−446.070	−	446.070i	−0.720631	−	0.720631i	0.248103	−	0.968734i	$-0.420193\pi$
$619$	−446.070	−	446.070i	−0.720631	−	0.720631i	−0.968734	+	0.248103i	$0.920193\pi$
$620$	−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	0.0412923	−	0.999147i	$-0.486853\pi$
$631$	−604.406	−	604.406i	−0.957855	−	0.957855i	−0.999147	+	0.0412923i	$0.986853\pi$
$632$	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	$0.395791\pi$
$641$			1213.91i			1.89378i	−0.321565	+	0.946888i	$0.604209\pi$
$642$		0			0
$643$	413.804	−	413.804i	0.643552	−	0.643552i	−0.307875	−	0.951427i	$-0.599618\pi$
$643$	413.804	−	413.804i	0.643552	−	0.643552i	0.951427	+	0.307875i	$0.0996178\pi$
$644$	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	$-0.970954\pi$
$647$		−	117.913i		−	0.182245i	0.995840	−	0.0911227i	$-0.0290455\pi$
$648$		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	−0.999946	−	0.0104193i	$-0.996683\pi$
$661$	−667.851	−	667.851i	−1.01036	−	1.01036i	−0.0104193	−	0.999946i	$-0.503317\pi$
$662$		−	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	$0.0989668\pi$
$673$			411.779i			0.611857i	−0.952055	+	0.305928i	$0.901033\pi$
$674$	−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	0.628637	−	0.777699i	$-0.283613\pi$
$683$	−101.809	−	101.809i	−0.149061	−	0.149061i	−0.777699	+	0.628637i	$0.783613\pi$
$684$		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	−0.782935	−	0.622103i	$-0.786278\pi$
$691$	−111.135	+	111.135i	−0.160832	+	0.160832i	0.622103	+	0.782935i	$0.286278\pi$
$692$	−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	$0.187667\pi$
$701$			779.520i			1.11201i	−0.831178	+	0.556006i	$0.812333\pi$
$702$		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	0.736793	−	0.676119i	$-0.236339\pi$
$709$	43.0179	+	43.0179i	0.0606740	+	0.0606740i	−0.676119	+	0.736793i	$0.736339\pi$
$710$	−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	$0.0749078\pi$
$719$			335.290i			0.466328i	−0.972437	+	0.233164i	$0.925092\pi$
$720$		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	$0.120547\pi$
$727$			537.577i			0.739445i	−0.929142	+	0.369723i	$0.879453\pi$
$728$	−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	−0.954138	−	0.299368i	$-0.903224\pi$
$733$	−479.946	+	479.946i	−0.654770	+	0.654770i	0.299368	+	0.954138i	$0.403224\pi$
$734$	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	0.963087	−	0.269192i	$-0.0867565\pi$
$739$	512.788	+	512.788i	0.693895	+	0.693895i	−0.269192	+	0.963087i	$0.586757\pi$
$740$		−	15.9437i		−	0.0215455i
$741$		0			0
$742$	84.4974			0.113878
$743$	−801.509	+	801.509i	−1.07875	+	1.07875i	−0.0821246	+	0.996622i	$0.526171\pi$
$743$	−801.509	+	801.509i	−1.07875	+	1.07875i	−0.996622	+	0.0821246i	$0.973829\pi$
$744$		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	$0.373218\pi$
$751$			1384.43i			1.84345i	−0.387849	+	0.921723i	$0.626782\pi$
$752$	−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	0.709439	−	0.704767i	$-0.248949\pi$
$761$	3.55514	+	3.55514i	0.00467166	+	0.00467166i	−0.704767	+	0.709439i	$0.748949\pi$
$762$		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	−0.288959	+	0.957342i	$0.593309\pi$
$769$	−958.405	+	958.405i	−1.24630	+	1.24630i	−0.957342	+	0.288959i	$0.906691\pi$
$770$	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	−0.755046	−	0.655672i	$-0.772386\pi$
$773$	−76.8165	+	76.8165i	−0.0993746	+	0.0993746i	0.655672	+	0.755046i	$0.272386\pi$
$774$		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	0.326530	−	0.945187i	$-0.394121\pi$
$787$	−486.883	−	486.883i	−0.618657	−	0.618657i	−0.945187	+	0.326530i	$0.894121\pi$
$788$	−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	$0.147746\pi$
$797$			713.587i			0.895341i	−0.894198	+	0.447671i	$0.852254\pi$
$798$		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	−0.781198	−	0.624283i	$-0.785391\pi$
$811$	−127.258	+	127.258i	−0.156914	+	0.156914i	0.624283	+	0.781198i	$0.285391\pi$
$812$	−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	−0.486953	+	0.873428i	$0.661892\pi$
$821$	−1116.87	+	1116.87i	−1.36038	+	1.36038i	−0.873428	+	0.486953i	$0.838108\pi$
$822$		0			0
$823$			617.920i			0.750814i	0.926860	+	0.375407i	$0.122497\pi$
$823$			617.920i			0.750814i	−0.926860	+	0.375407i	$0.877503\pi$
$824$	−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	0.463214	−	0.886246i	$-0.346696\pi$
$827$	−349.847	−	349.847i	−0.423032	−	0.423032i	−0.886246	+	0.463214i	$0.846696\pi$
$828$		0			0
$829$		−	247.646i		−	0.298729i	−0.988782	−	0.149364i	$-0.952277\pi$
$829$		−	247.646i		−	0.298729i	0.988782	−	0.149364i	$-0.0477227\pi$
$830$	−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	0.967325	−	0.253538i	$-0.0815943\pi$
$839$	598.868	+	598.868i	0.713788	+	0.713788i	−0.253538	+	0.967325i	$0.581594\pi$
$840$		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	0.333916	−	0.942603i	$-0.391630\pi$
$853$	−519.210	−	519.210i	−0.608687	−	0.608687i	−0.942603	+	0.333916i	$0.891630\pi$
$854$	−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	$-0.957765\pi$
$857$		−	226.756i		−	0.264593i	0.991210	−	0.132297i	$-0.0422351\pi$
$858$		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	−0.995128	−	0.0985910i	$-0.968566\pi$
$863$	−773.711	+	773.711i	−0.896537	+	0.896537i	0.0985910	+	0.995128i	$0.468566\pi$
$864$		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	−0.234662	−	0.972077i	$-0.575398\pi$
$877$	646.713	−	646.713i	0.737415	−	0.737415i	0.972077	+	0.234662i	$0.0753984\pi$
$878$	−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	$0.146778\pi$
$881$			783.997i			0.889895i	−0.895557	+	0.444947i	$0.853222\pi$
$882$		0			0
$883$		−	1089.81i		−	1.23421i	−0.786881	−	0.617105i	$-0.788305\pi$
$883$		−	1089.81i		−	1.23421i	0.786881	−	0.617105i	$-0.211695\pi$
$884$	−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	$0.0974410\pi$
$907$			546.669i			0.602722i	−0.953510	+	0.301361i	$0.902559\pi$
$908$	−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	−0.553103	−	0.833113i	$-0.686556\pi$
$929$	260.130	−	260.130i	0.280010	−	0.280010i	0.833113	+	0.553103i	$0.186556\pi$
$930$		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	−0.673617	−	0.739081i	$-0.735260\pi$
$941$	61.6012	−	61.6012i	0.0654635	−	0.0654635i	0.739081	+	0.673617i	$0.235260\pi$
$942$		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	0.677742	−	0.735299i	$-0.262958\pi$
$947$	−54.5064	−	54.5064i	−0.0575569	−	0.0575569i	−0.735299	+	0.677742i	$0.762958\pi$
$948$		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	$-0.808336\pi$
$953$		−	1079.56i		−	1.13280i	0.824131	−	0.566399i	$-0.191664\pi$
$954$		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	−0.404114	−	0.914709i	$-0.632420\pi$
$967$	493.745	−	493.745i	0.510594	−	0.510594i	0.914709	+	0.404114i	$0.132420\pi$
$968$	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	−0.478723	−	0.877966i	$-0.658900\pi$
$977$	390.060	−	390.060i	0.399243	−	0.399243i	0.877966	+	0.478723i	$0.158900\pi$
$978$		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	0.987984	+	0.154559i	$0.0493956\pi$
$983$	1123.12	+	1123.12i	1.14254	+	1.14254i	0.154559	+	0.987984i	$0.450604\pi$
$984$		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.109.2		4
3.2	odd	2		78.3.f.a.31.2	✓	4
12.11	even	2		624.3.ba.a.577.1		4
13.8	odd	4	inner	234.3.i.b.73.2		4
39.5	even	4		1014.3.f.a.775.2		4
39.8	even	4		78.3.f.a.73.2	yes	4
39.38	odd	2		1014.3.f.a.577.2		4
156.47	odd	4		624.3.ba.a.385.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.3.f.a.31.2	✓	4	3.2	odd	2
78.3.f.a.73.2	yes	4	39.8	even	4
234.3.i.b.73.2		4	13.8	odd	4	inner
234.3.i.b.109.2		4	1.1	even	1	trivial
624.3.ba.a.385.1		4	156.47	odd	4
624.3.ba.a.577.1		4	12.11	even	2
1014.3.f.a.577.2		4	39.38	odd	2
1014.3.f.a.775.2		4	39.5	even	4

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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