LMFDB - Embedded newform 936.2.g.c.469.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(469,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.469"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.399424.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 $ x^6 - 2x^5 + 3x^4 - 6x^3 + 6x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			469.5
Root			$1.40680 + 0.144584i$ of defining polynomial
Character	$\chi$	$=$	936.469
Dual form			936.2.g.c.469.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.40680 - 0.144584i) q^{2} +(1.95819 - 0.406803i) q^{4} -1.00000i q^{5} -2.10278 q^{7} +(2.69597 - 0.855416i) q^{8} +(-0.144584 - 1.40680i) q^{10} -5.62721i q^{11} -1.00000i q^{13} +(-2.95819 + 0.304028i) q^{14} +(3.66902 - 1.59320i) q^{16} -1.00000 q^{17} -4.00000i q^{19} +(-0.406803 - 1.95819i) q^{20} +(-0.813607 - 7.91638i) q^{22} -1.62721 q^{23} +4.00000 q^{25} +(-0.144584 - 1.40680i) q^{26} +(-4.11763 + 0.855416i) q^{28} +7.83276i q^{29} +9.62721 q^{31} +(4.93124 - 2.77180i) q^{32} +(-1.40680 + 0.144584i) q^{34} +2.10278i q^{35} +0.421663i q^{37} +(-0.578337 - 5.62721i) q^{38} +(-0.855416 - 2.69597i) q^{40} -5.83276 q^{41} +0.475562i q^{43} +(-2.28917 - 11.0192i) q^{44} +(-2.28917 + 0.235269i) q^{46} +4.68111 q^{47} -2.57834 q^{49} +(5.62721 - 0.578337i) q^{50} +(-0.406803 - 1.95819i) q^{52} -4.57834i q^{53} -5.62721 q^{55} +(-5.66902 + 1.79875i) q^{56} +(1.13249 + 11.0192i) q^{58} +8.67609i q^{59} +12.6761i q^{61} +(13.5436 - 1.39194i) q^{62} +(6.53653 - 4.61235i) q^{64} -1.00000 q^{65} -12.2056i q^{67} +(-1.95819 + 0.406803i) q^{68} +(0.304028 + 2.95819i) q^{70} +9.15165 q^{71} -2.57834 q^{73} +(0.0609658 + 0.593197i) q^{74} +(-1.62721 - 7.83276i) q^{76} +11.8328i q^{77} -14.3033 q^{79} +(-1.59320 - 3.66902i) q^{80} +(-8.20555 + 0.843326i) q^{82} +8.20555i q^{83} +1.00000i q^{85} +(0.0687588 + 0.669022i) q^{86} +(-4.81361 - 15.1708i) q^{88} -11.2544 q^{89} +2.10278i q^{91} +(-3.18639 + 0.661956i) q^{92} +(6.58540 - 0.676815i) q^{94} -4.00000 q^{95} +10.6761 q^{97} +(-3.62721 + 0.372787i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} - 2 q^{4} + 2 q^{7} + 8 q^{8} - 4 q^{14} + 10 q^{16} - 6 q^{17} + 4 q^{20} + 8 q^{22} + 16 q^{23} + 24 q^{25} - 20 q^{28} + 32 q^{31} + 12 q^{32} - 2 q^{34} - 6 q^{40} + 20 q^{41} - 12 q^{44}+ \cdots + 4 q^{98}+O(q^{100}) $ 6 * q + 2 * q^2 - 2 * q^4 + 2 * q^7 + 8 * q^8 - 4 * q^14 + 10 * q^16 - 6 * q^17 + 4 * q^20 + 8 * q^22 + 16 * q^23 + 24 * q^25 - 20 * q^28 + 32 * q^31 + 12 * q^32 - 2 * q^34 - 6 * q^40 + 20 * q^41 - 12 * q^44 - 12 * q^46 + 10 * q^47 - 12 * q^49 + 8 * q^50 + 4 * q^52 - 8 * q^55 - 22 * q^56 + 12 * q^58 + 28 * q^62 + 22 * q^64 - 6 * q^65 + 2 * q^68 + 10 * q^70 + 18 * q^71 - 12 * q^73 - 28 * q^74 + 16 * q^76 - 12 * q^79 - 16 * q^80 - 20 * q^82 + 18 * q^86 - 16 * q^88 - 16 * q^89 - 32 * q^92 - 24 * q^95 + 16 * q^97 + 4 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$1$	$1$	$-1$	$1$

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 $

$2$	1.40680	−	0.144584i	0.994760	−	0.102237i
$2$	1.40680	−	0.144584i	0.994760	−	0.102237i
$3$		0			0
$3$		0			0
$4$	1.95819	−	0.406803i	0.979095	−	0.203402i
$5$		−	1.00000i		−	0.447214i	−0.974679	−	0.223607i	$-0.928217\pi$
$5$		−	1.00000i		−	0.447214i	0.974679	−	0.223607i	$-0.0717831\pi$
$6$		0			0
$7$	−2.10278			−0.794774			−0.397387	−	0.917651i	$-0.630083\pi$
$7$	−2.10278			−0.794774			−0.397387	+	0.917651i	$0.630083\pi$
$8$	2.69597	−	0.855416i	0.953170	−	0.302435i
$9$		0			0
$10$	−0.144584	−	1.40680i	−0.0457216	−	0.444870i
$11$		−	5.62721i		−	1.69667i	−0.529461	−	0.848334i	$-0.677606\pi$
$11$		−	5.62721i		−	1.69667i	0.529461	−	0.848334i	$-0.322394\pi$
$12$		0			0
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	−2.95819	+	0.304028i	−0.790610	+	0.0812550i
$15$		0			0
$16$	3.66902	−	1.59320i	0.917256	−	0.398299i
$17$	−1.00000			−0.242536			−0.121268	−	0.992620i	$-0.538696\pi$
$17$	−1.00000			−0.242536			−0.121268	+	0.992620i	$0.538696\pi$
$18$		0			0
$19$		−	4.00000i		−	0.917663i	−0.888523	−	0.458831i	$-0.848268\pi$
$19$		−	4.00000i		−	0.917663i	0.888523	−	0.458831i	$-0.151732\pi$
$20$	−0.406803	−	1.95819i	−0.0909640	−	0.437865i
$21$		0			0
$22$	−0.813607	−	7.91638i	−0.173461	−	1.68778i
$23$	−1.62721			−0.339297			−0.169649	−	0.985505i	$-0.554263\pi$
$23$	−1.62721			−0.339297			−0.169649	+	0.985505i	$0.554263\pi$
$24$		0			0
$25$	4.00000			0.800000
$26$	−0.144584	−	1.40680i	−0.0283553	−	0.275897i
$27$		0			0
$28$	−4.11763	+	0.855416i	−0.778160	+	0.161658i
$29$			7.83276i			1.45451i	0.686369	+	0.727254i	$0.259204\pi$
$29$			7.83276i			1.45451i	−0.686369	+	0.727254i	$0.740796\pi$
$30$		0			0
$31$	9.62721			1.72910			0.864549	−	0.502548i	$-0.167604\pi$
$31$	9.62721			1.72910			0.864549	+	0.502548i	$0.167604\pi$
$32$	4.93124	−	2.77180i	0.871729	−	0.489989i
$33$		0			0
$34$	−1.40680	+	0.144584i	−0.241265	+	0.0247960i
$35$			2.10278i			0.355434i
$36$		0			0
$37$			0.421663i			0.0693210i	0.999399	+	0.0346605i	$0.0110350\pi$
$37$			0.421663i			0.0693210i	−0.999399	+	0.0346605i	$0.988965\pi$
$38$	−0.578337	−	5.62721i	−0.0938187	−	0.912854i
$39$		0			0
$40$	−0.855416	−	2.69597i	−0.135253	−	0.426271i
$41$	−5.83276			−0.910925			−0.455462	−	0.890255i	$-0.650526\pi$
$41$	−5.83276			−0.910925			−0.455462	+	0.890255i	$0.650526\pi$
$42$		0			0
$43$			0.475562i			0.0725225i	0.999342	+	0.0362613i	$0.0115449\pi$
$43$			0.475562i			0.0725225i	−0.999342	+	0.0362613i	$0.988455\pi$
$44$	−2.28917	−	11.0192i	−0.345105	−	1.66120i
$45$		0			0
$46$	−2.28917	+	0.235269i	−0.337519	+	0.0346886i
$47$	4.68111			0.682810			0.341405	−	0.939916i	$-0.389097\pi$
$47$	4.68111			0.682810			0.341405	+	0.939916i	$0.389097\pi$
$48$		0			0
$49$	−2.57834			−0.368334
$50$	5.62721	−	0.578337i	0.795808	−	0.0817892i
$51$		0			0
$52$	−0.406803	−	1.95819i	−0.0564135	−	0.271552i
$53$		−	4.57834i		−	0.628883i	−0.949277	−	0.314441i	$-0.898183\pi$
$53$		−	4.57834i		−	0.628883i	0.949277	−	0.314441i	$-0.101817\pi$
$54$		0			0
$55$	−5.62721			−0.758773
$56$	−5.66902	+	1.79875i	−0.757555	+	0.240368i
$57$		0			0
$58$	1.13249	+	11.0192i	0.148704	+	1.44689i
$59$			8.67609i			1.12953i	0.825252	+	0.564765i	$0.191033\pi$
$59$			8.67609i			1.12953i	−0.825252	+	0.564765i	$0.808967\pi$
$60$		0			0
$61$			12.6761i			1.62301i	0.584348	+	0.811503i	$0.301350\pi$
$61$			12.6761i			1.62301i	−0.584348	+	0.811503i	$0.698650\pi$
$62$	13.5436	−	1.39194i	1.72004	−	0.176777i
$63$		0			0
$64$	6.53653	−	4.61235i	0.817066	−	0.576544i
$65$	−1.00000			−0.124035
$66$		0			0
$67$		−	12.2056i		−	1.49115i	−0.666424	−	0.745573i	$-0.732176\pi$
$67$		−	12.2056i		−	1.49115i	0.666424	−	0.745573i	$-0.267824\pi$
$68$	−1.95819	+	0.406803i	−0.237466	+	0.0493321i
$69$		0			0
$70$	0.304028	+	2.95819i	0.0363383	+	0.353571i
$71$	9.15165			1.08610			0.543051	−	0.839700i	$-0.317269\pi$
$71$	9.15165			1.08610			0.543051	+	0.839700i	$0.317269\pi$
$72$		0			0
$73$	−2.57834			−0.301772			−0.150886	−	0.988551i	$-0.548213\pi$
$73$	−2.57834			−0.301772			−0.150886	+	0.988551i	$0.548213\pi$
$74$	0.0609658	+	0.593197i	0.00708713	+	0.0689577i
$75$		0			0
$76$	−1.62721	−	7.83276i	−0.186654	−	0.898480i
$77$			11.8328i			1.34847i
$78$		0			0
$79$	−14.3033			−1.60925			−0.804624	−	0.593785i	$-0.797633\pi$
$79$	−14.3033			−1.60925			−0.804624	+	0.593785i	$0.797633\pi$
$80$	−1.59320	−	3.66902i	−0.178125	−	0.410209i
$81$		0			0
$82$	−8.20555	+	0.843326i	−0.906151	+	0.0931298i
$83$			8.20555i			0.900676i	0.892858	+	0.450338i	$0.148697\pi$
$83$			8.20555i			0.900676i	−0.892858	+	0.450338i	$0.851303\pi$
$84$		0			0
$85$			1.00000i			0.108465i
$86$	0.0687588	+	0.669022i	0.00741445	+	0.0721425i
$87$		0			0
$88$	−4.81361	−	15.1708i	−0.513132	−	1.61721i
$89$	−11.2544			−1.19297			−0.596483	−	0.802625i	$-0.703436\pi$
$89$	−11.2544			−1.19297			−0.596483	+	0.802625i	$0.703436\pi$
$90$		0			0
$91$			2.10278i			0.220431i
$92$	−3.18639	+	0.661956i	−0.332204	+	0.0690136i
$93$		0			0
$94$	6.58540	−	0.676815i	0.679233	−	0.0698082i
$95$	−4.00000			−0.410391
$96$		0			0
$97$	10.6761			1.08399			0.541996	−	0.840381i	$-0.317669\pi$
$97$	10.6761			1.08399			0.541996	+	0.840381i	$0.317669\pi$
$98$	−3.62721	+	0.372787i	−0.366404	+	0.0376572i
$99$		0			0
$100$	7.83276	−	1.62721i	0.783276	−	0.162721i
$101$			9.15667i			0.911123i	0.890204	+	0.455562i	$0.150562\pi$
$101$			9.15667i			0.911123i	−0.890204	+	0.455562i	$0.849438\pi$
$102$		0			0
$103$	5.36222			0.528356			0.264178	−	0.964474i	$-0.414899\pi$
$103$	5.36222			0.528356			0.264178	+	0.964474i	$0.414899\pi$
$104$	−0.855416	−	2.69597i	−0.0838804	−	0.264362i
$105$		0			0
$106$	−0.661956	−	6.44082i	−0.0642948	−	0.625588i
$107$		−	6.37279i		−	0.616081i	−0.951373	−	0.308040i	$-0.900327\pi$
$107$		−	6.37279i		−	0.616081i	0.951373	−	0.308040i	$-0.0996732\pi$
$108$		0			0
$109$			14.0872i			1.34931i	0.738134	+	0.674654i	$0.235707\pi$
$109$			14.0872i			1.34931i	−0.738134	+	0.674654i	$0.764293\pi$
$110$	−7.91638	+	0.813607i	−0.754797	+	0.0775743i
$111$		0			0
$112$	−7.71513	+	3.35013i	−0.729011	+	0.316558i
$113$	4.84333			0.455622			0.227811	−	0.973705i	$-0.426843\pi$
$113$	4.84333			0.455622			0.227811	+	0.973705i	$0.426843\pi$
$114$		0			0
$115$			1.62721i			0.151738i
$116$	3.18639	+	15.3380i	0.295849	+	1.42410i
$117$		0			0
$118$	1.25443	+	12.2056i	0.115479	+	1.12361i
$119$	2.10278			0.192761
$120$		0			0
$121$	−20.6655			−1.87868
$122$	1.83276	+	17.8328i	0.165931	+	1.61450i
$123$		0			0
$124$	18.8519	−	3.91638i	1.69295	−	0.351701i
$125$		−	9.00000i		−	0.804984i
$126$		0			0
$127$	10.0383			0.890756			0.445378	−	0.895343i	$-0.353069\pi$
$127$	10.0383			0.890756			0.445378	+	0.895343i	$0.353069\pi$
$128$	8.52873	−	7.43375i	0.753841	−	0.657057i
$129$		0			0
$130$	−1.40680	+	0.144584i	−0.123385	+	0.0126809i
$131$			8.47556i			0.740513i	0.928929	+	0.370257i	$0.120730\pi$
$131$			8.47556i			0.740513i	−0.928929	+	0.370257i	$0.879270\pi$
$132$		0			0
$133$			8.41110i			0.729335i
$134$	−1.76473	−	17.1708i	−0.152450	−	1.48333i
$135$		0			0
$136$	−2.69597	+	0.855416i	−0.231178	+	0.0733513i
$137$	19.0872			1.63073			0.815364	−	0.578948i	$-0.196537\pi$
$137$	19.0872			1.63073			0.815364	+	0.578948i	$0.196537\pi$
$138$		0			0
$139$		−	3.99498i		−	0.338850i	−0.985543	−	0.169425i	$-0.945809\pi$
$139$		−	3.99498i		−	0.338850i	0.985543	−	0.169425i	$-0.0541910\pi$
$140$	0.855416	+	4.11763i	0.0722958	+	0.348004i
$141$		0			0
$142$	12.8746	−	1.32318i	1.08041	−	0.111039i
$143$	−5.62721			−0.470571
$144$		0			0
$145$	7.83276			0.650476
$146$	−3.62721	+	0.372787i	−0.300190	+	0.0308521i
$147$		0			0
$148$	0.171534	+	0.825696i	0.0141000	+	0.0678718i
$149$		−	3.15667i		−	0.258605i	−0.991605	−	0.129302i	$-0.958726\pi$
$149$		−	3.15667i		−	0.258605i	0.991605	−	0.129302i	$-0.0412738\pi$
$150$		0			0
$151$	−2.36776			−0.192686			−0.0963429	−	0.995348i	$-0.530715\pi$
$151$	−2.36776			−0.192686			−0.0963429	+	0.995348i	$0.530715\pi$
$152$	−3.42166	−	10.7839i	−0.277534	−	0.874689i
$153$		0			0
$154$	1.71083	+	16.6464i	0.137863	+	1.34140i
$155$		−	9.62721i		−	0.773276i
$156$		0			0
$157$		−	15.9305i		−	1.27139i	−0.771939	−	0.635697i	$-0.780713\pi$
$157$		−	15.9305i		−	1.27139i	0.771939	−	0.635697i	$-0.219287\pi$
$158$	−20.1219	+	2.06803i	−1.60081	+	0.164524i
$159$		0			0
$160$	−2.77180	−	4.93124i	−0.219130	−	0.389849i
$161$	3.42166			0.269665
$162$		0			0
$163$			3.52946i			0.276449i	0.990401	+	0.138224i	$0.0441395\pi$
$163$			3.52946i			0.276449i	−0.990401	+	0.138224i	$0.955860\pi$
$164$	−11.4217	+	2.37279i	−0.891882	+	0.185284i
$165$		0			0
$166$	1.18639	+	11.5436i	0.0920820	+	0.895957i
$167$	−15.7250			−1.21683			−0.608417	−	0.793617i	$-0.708195\pi$
$167$	−15.7250			−1.21683			−0.608417	+	0.793617i	$0.708195\pi$
$168$		0			0
$169$	−1.00000			−0.0769231
$170$	0.144584	+	1.40680i	0.0110891	+	0.107897i
$171$		0			0
$172$	0.193460	+	0.931241i	0.0147512	+	0.0710065i
$173$			14.4111i			1.09566i	0.836591	+	0.547828i	$0.184545\pi$
$173$			14.4111i			1.09566i	−0.836591	+	0.547828i	$0.815455\pi$
$174$		0			0
$175$	−8.41110			−0.635819
$176$	−8.96526	−	20.6464i	−0.675782	−	1.55628i
$177$		0			0
$178$	−15.8328	+	1.62721i	−1.18672	+	0.121965i
$179$			1.69167i			0.126442i	0.998000	+	0.0632209i	$0.0201373\pi$
$179$			1.69167i			0.126442i	−0.998000	+	0.0632209i	$0.979863\pi$
$180$		0			0
$181$			17.2544i			1.28251i	0.767327	+	0.641256i	$0.221586\pi$
$181$			17.2544i			1.28251i	−0.767327	+	0.641256i	$0.778414\pi$
$182$	0.304028	+	2.95819i	0.0225361	+	0.219276i
$183$		0			0
$184$	−4.38692	+	1.39194i	−0.323408	+	0.102615i
$185$	0.421663			0.0310013
$186$		0			0
$187$			5.62721i			0.411503i
$188$	9.16651	−	1.90429i	0.668536	−	0.138885i
$189$		0			0
$190$	−5.62721	+	0.578337i	−0.408241	+	0.0419570i
$191$	−6.03831			−0.436917			−0.218459	−	0.975846i	$-0.570103\pi$
$191$	−6.03831			−0.436917			−0.218459	+	0.975846i	$0.570103\pi$
$192$		0			0
$193$	13.2544			0.954074			0.477037	−	0.878883i	$-0.341711\pi$
$193$	13.2544			0.954074			0.477037	+	0.878883i	$0.341711\pi$
$194$	15.0192	−	1.54359i	1.07831	−	0.110824i
$195$		0			0
$196$	−5.04888	+	1.04888i	−0.360634	+	0.0749197i
$197$			22.9305i			1.63373i	0.576828	+	0.816866i	$0.304290\pi$
$197$			22.9305i			1.63373i	−0.576828	+	0.816866i	$0.695710\pi$
$198$		0			0
$199$	−0.951124			−0.0674234			−0.0337117	−	0.999432i	$-0.510733\pi$
$199$	−0.951124			−0.0674234			−0.0337117	+	0.999432i	$0.510733\pi$
$200$	10.7839	−	3.42166i	0.762536	−	0.241948i
$201$		0			0
$202$	1.32391	+	12.8816i	0.0931501	+	0.906349i
$203$		−	16.4705i		−	1.15601i
$204$		0			0
$205$			5.83276i			0.407378i
$206$	7.54359	−	0.775293i	0.525587	−	0.0540172i
$207$		0			0
$208$	−1.59320	−	3.66902i	−0.110468	−	0.254401i
$209$	−22.5089			−1.55697
$210$		0			0
$211$		−	11.7300i		−	0.807526i	−0.914864	−	0.403763i	$-0.867702\pi$
$211$		−	11.7300i		−	0.807526i	0.914864	−	0.403763i	$-0.132298\pi$
$212$	−1.86248	−	8.96526i	−0.127916	−	0.615736i
$213$		0			0
$214$	−0.921405	−	8.96526i	−0.0629859	−	0.612852i
$215$	0.475562			0.0324331
$216$		0			0
$217$	−20.2439			−1.37424
$218$	2.03679	+	19.8179i	0.137949	+	1.34224i
$219$		0			0
$220$	−11.0192	+	2.28917i	−0.742911	+	0.154336i
$221$			1.00000i			0.0672673i
$222$		0			0
$223$	4.68111			0.313470			0.156735	−	0.987641i	$-0.449903\pi$
$223$	4.68111			0.313470			0.156735	+	0.987641i	$0.449903\pi$
$224$	−10.3693	+	5.82847i	−0.692827	+	0.389431i
$225$		0			0
$226$	6.81361	−	0.700269i	0.453234	−	0.0465812i
$227$			11.7350i			0.778880i	0.921052	+	0.389440i	$0.127331\pi$
$227$			11.7350i			0.778880i	−0.921052	+	0.389440i	$0.872669\pi$
$228$		0			0
$229$			5.84333i			0.386138i	0.981185	+	0.193069i	$0.0618441\pi$
$229$			5.84333i			0.386138i	−0.981185	+	0.193069i	$0.938156\pi$
$230$	0.235269	+	2.28917i	0.0155132	+	0.150943i
$231$		0			0
$232$	6.70027	+	21.1169i	0.439894	+	1.38639i
$233$	25.2439			1.65378			0.826890	−	0.562363i	$-0.190108\pi$
$233$	25.2439			1.65378			0.826890	+	0.562363i	$0.190108\pi$
$234$		0			0
$235$		−	4.68111i		−	0.305362i
$236$	3.52946	+	16.9894i	0.229748	+	1.10592i
$237$		0			0
$238$	2.95819	−	0.304028i	0.191751	−	0.0197072i
$239$	11.4650			0.741609			0.370805	−	0.928711i	$-0.379082\pi$
$239$	11.4650			0.741609			0.370805	+	0.928711i	$0.379082\pi$
$240$		0			0
$241$	−2.09775			−0.135128			−0.0675640	−	0.997715i	$-0.521523\pi$
$241$	−2.09775			−0.135128			−0.0675640	+	0.997715i	$0.521523\pi$
$242$	−29.0723	+	2.98791i	−1.86884	+	0.192070i
$243$		0			0
$244$	5.15667	+	24.8222i	0.330122	+	1.58908i
$245$			2.57834i			0.164724i
$246$		0			0
$247$	−4.00000			−0.254514
$248$	25.9547	−	8.23527i	1.64812	−	0.522940i
$249$		0			0
$250$	−1.30126	−	12.6612i	−0.0822988	−	0.800766i
$251$		−	14.7839i		−	0.933151i	−0.884481	−	0.466575i	$-0.845488\pi$
$251$		−	14.7839i		−	0.933151i	0.884481	−	0.466575i	$-0.154512\pi$
$252$		0			0
$253$			9.15667i			0.575675i
$254$	14.1219	−	1.45138i	0.886089	−	0.0910678i
$255$		0			0
$256$	10.9234	−	11.6909i	0.682716	−	0.730684i
$257$	−3.31335			−0.206681			−0.103340	−	0.994646i	$-0.532953\pi$
$257$	−3.31335			−0.206681			−0.103340	+	0.994646i	$0.532953\pi$
$258$		0			0
$259$		−	0.886662i		−	0.0550945i
$260$	−1.95819	+	0.406803i	−0.121442	+	0.0252289i
$261$		0			0
$262$	1.22543	+	11.9234i	0.0757075	+	0.736633i
$263$	−17.4217			−1.07427			−0.537133	−	0.843498i	$-0.680493\pi$
$263$	−17.4217			−1.07427			−0.537133	+	0.843498i	$0.680493\pi$
$264$		0			0
$265$	−4.57834			−0.281245
$266$	1.21611	+	11.8328i	0.0745647	+	0.725513i
$267$		0			0
$268$	−4.96526	−	23.9008i	−0.303301	−	1.45997i
$269$			3.32391i			0.202662i	0.994853	+	0.101331i	$0.0323102\pi$
$269$			3.32391i			0.202662i	−0.994853	+	0.101331i	$0.967690\pi$
$270$		0			0
$271$	−14.0333			−0.852462			−0.426231	−	0.904614i	$-0.640159\pi$
$271$	−14.0333			−0.852462			−0.426231	+	0.904614i	$0.640159\pi$
$272$	−3.66902	+	1.59320i	−0.222467	+	0.0966017i
$273$		0			0
$274$	26.8519	−	2.75971i	1.62218	−	0.166720i
$275$		−	22.5089i		−	1.35733i
$276$		0			0
$277$		−	1.01056i		−	0.0607188i	−0.999539	−	0.0303594i	$-0.990335\pi$
$277$		−	1.01056i		−	0.0607188i	0.999539	−	0.0303594i	$-0.00966519\pi$
$278$	−0.577611	−	5.62015i	−0.0346428	−	0.337074i
$279$		0			0
$280$	1.79875	+	5.66902i	0.107496	+	0.338789i
$281$	−3.58890			−0.214096			−0.107048	−	0.994254i	$-0.534140\pi$
$281$	−3.58890			−0.214096			−0.107048	+	0.994254i	$0.534140\pi$
$282$		0			0
$283$		−	13.2927i		−	0.790171i	−0.918644	−	0.395086i	$-0.870715\pi$
$283$		−	13.2927i		−	0.790171i	0.918644	−	0.395086i	$-0.129285\pi$
$284$	17.9207	−	3.72292i	1.06340	−	0.220915i
$285$		0			0
$286$	−7.91638	+	0.813607i	−0.468105	+	0.0481096i
$287$	12.2650			0.723979
$288$		0			0
$289$	−16.0000			−0.941176
$290$	11.0192	−	1.13249i	0.647067	−	0.0665024i
$291$		0			0
$292$	−5.04888	+	1.04888i	−0.295463	+	0.0613808i
$293$		−	9.24386i		−	0.540032i	−0.962856	−	0.270016i	$-0.912971\pi$
$293$		−	9.24386i		−	0.540032i	0.962856	−	0.270016i	$-0.0870290\pi$
$294$		0			0
$295$	8.67609			0.505141
$296$	0.360697	+	1.13679i	0.0209651	+	0.0660747i
$297$		0			0
$298$	−0.456405	−	4.44082i	−0.0264389	−	0.257250i
$299$			1.62721i			0.0941042i
$300$		0			0
$301$		−	1.00000i		−	0.0576390i
$302$	−3.33098	+	0.342341i	−0.191676	+	0.0196995i
$303$		0			0
$304$	−6.37279	−	14.6761i	−0.365504	−	0.841731i
$305$	12.6761			0.725831
$306$		0			0
$307$			8.26499i			0.471708i	0.971789	+	0.235854i	$0.0757887\pi$
$307$			8.26499i			0.471708i	−0.971789	+	0.235854i	$0.924211\pi$
$308$	4.81361	+	23.1708i	0.274281	+	1.32028i
$309$		0			0
$310$	−1.39194	−	13.5436i	−0.0790571	−	0.769224i
$311$	23.6655			1.34195			0.670974	−	0.741480i	$-0.265876\pi$
$311$	23.6655			1.34195			0.670974	+	0.741480i	$0.265876\pi$
$312$		0			0
$313$	−0.735011			−0.0415453			−0.0207726	−	0.999784i	$-0.506613\pi$
$313$	−0.735011			−0.0415453			−0.0207726	+	0.999784i	$0.506613\pi$
$314$	−2.30330	−	22.4111i	−0.129983	−	1.26473i
$315$		0			0
$316$	−28.0086	+	5.81863i	−1.57561	+	0.327323i
$317$		−	11.1567i		−	0.626621i	−0.949651	−	0.313311i	$-0.898562\pi$
$317$		−	11.1567i		−	0.626621i	0.949651	−	0.313311i	$-0.101438\pi$
$318$		0			0
$319$	44.0766			2.46782
$320$	−4.61235	−	6.53653i	−0.257838	−	0.365403i
$321$		0			0
$322$	4.81361	−	0.494719i	0.268252	−	0.0275696i
$323$			4.00000i			0.222566i
$324$		0			0
$325$		−	4.00000i		−	0.221880i
$326$	0.510305	+	4.96526i	0.0282632	+	0.275000i
$327$		0			0
$328$	−15.7250	+	4.98944i	−0.868266	+	0.275496i
$329$	−9.84333			−0.542680
$330$		0			0
$331$		−	7.79445i		−	0.428422i	−0.976787	−	0.214211i	$-0.931282\pi$
$331$		−	7.79445i		−	0.428422i	0.976787	−	0.214211i	$-0.0687180\pi$
$332$	3.33804	+	16.0680i	0.183199	+	0.881848i
$333$		0			0
$334$	−22.1219	+	2.27358i	−1.21046	+	0.124405i
$335$	−12.2056			−0.666860
$336$		0			0
$337$	19.2439			1.04828			0.524140	−	0.851632i	$-0.324387\pi$
$337$	19.2439			1.04828			0.524140	+	0.851632i	$0.324387\pi$
$338$	−1.40680	+	0.144584i	−0.0765200	+	0.00786435i
$339$		0			0
$340$	0.406803	+	1.95819i	0.0220620	+	0.106198i
$341$		−	54.1744i		−	2.93371i
$342$		0			0
$343$	20.1411			1.08752
$344$	0.406803	+	1.28210i	0.0219334	+	0.0691263i
$345$		0			0
$346$	2.08362	+	20.2736i	0.112016	+	1.08991i
$347$		−	32.6116i		−	1.75068i	−0.483504	−	0.875342i	$-0.660636\pi$
$347$		−	32.6116i		−	1.75068i	0.483504	−	0.875342i	$-0.339364\pi$
$348$		0			0
$349$			31.8222i			1.70340i	0.524027	+	0.851702i	$0.324429\pi$
$349$			31.8222i			1.70340i	−0.524027	+	0.851702i	$0.675571\pi$
$350$	−11.8328	+	1.21611i	−0.632488	+	0.0650040i
$351$		0			0
$352$	−15.5975	−	27.7491i	−0.831349	−	1.47903i
$353$	−20.0978			−1.06970			−0.534848	−	0.844948i	$-0.679631\pi$
$353$	−20.0978			−1.06970			−0.534848	+	0.844948i	$0.679631\pi$
$354$		0			0
$355$		−	9.15165i		−	0.485719i
$356$	−22.0383	+	4.57834i	−1.16803	+	0.242651i
$357$		0			0
$358$	0.244590	+	2.37985i	0.0129270	+	0.125779i
$359$	−8.68614			−0.458437			−0.229218	−	0.973375i	$-0.573617\pi$
$359$	−8.68614			−0.458437			−0.229218	+	0.973375i	$0.573617\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$	2.49472	+	24.2736i	0.131120	+	1.27579i
$363$		0			0
$364$	0.855416	+	4.11763i	0.0448360	+	0.215823i
$365$			2.57834i			0.134956i
$366$		0			0
$367$	−9.36222			−0.488704			−0.244352	−	0.969687i	$-0.578575\pi$
$367$	−9.36222			−0.488704			−0.244352	+	0.969687i	$0.578575\pi$
$368$	−5.97028	+	2.59247i	−0.311222	+	0.135142i
$369$		0			0
$370$	0.593197	−	0.0609658i	0.0308388	−	0.00316946i
$371$			9.62721i			0.499820i
$372$		0			0
$373$		−	21.9789i		−	1.13802i	−0.822330	−	0.569011i	$-0.807326\pi$
$373$		−	21.9789i		−	1.13802i	0.822330	−	0.569011i	$-0.192674\pi$
$374$	0.813607	+	7.91638i	0.0420706	+	0.409346i
$375$		0			0
$376$	12.6201	−	4.00430i	0.650834	−	0.206506i
$377$	7.83276			0.403408
$378$		0			0
$379$		−	4.05944i		−	0.208519i	−0.994550	−	0.104260i	$-0.966753\pi$
$379$		−	4.05944i		−	0.208519i	0.994550	−	0.104260i	$-0.0332473\pi$
$380$	−7.83276	+	1.62721i	−0.401812	+	0.0834743i
$381$		0			0
$382$	−8.49472	+	0.873045i	−0.434628	+	0.0446689i
$383$	7.39551			0.377893			0.188947	−	0.981987i	$-0.439493\pi$
$383$	7.39551			0.377893			0.188947	+	0.981987i	$0.439493\pi$
$384$		0			0
$385$	11.8328			0.603053
$386$	18.6464	−	1.91638i	0.949075	−	0.0975413i
$387$		0			0
$388$	20.9058	−	4.34307i	1.06133	−	0.220486i
$389$			13.4217i			0.680505i	0.940334	+	0.340253i	$0.110513\pi$
$389$			13.4217i			0.680505i	−0.940334	+	0.340253i	$0.889487\pi$
$390$		0			0
$391$	1.62721			0.0822917
$392$	−6.95112	+	2.20555i	−0.351085	+	0.111397i
$393$		0			0
$394$	3.31539	+	32.2587i	0.167027	+	1.62517i
$395$			14.3033i			0.719677i
$396$		0			0
$397$		−	33.1355i		−	1.66303i	−0.555506	−	0.831513i	$-0.687475\pi$
$397$		−	33.1355i		−	1.66303i	0.555506	−	0.831513i	$-0.312525\pi$
$398$	−1.33804	+	0.137518i	−0.0670701	+	0.00689313i
$399$		0			0
$400$	14.6761	−	6.37279i	0.733804	−	0.318639i
$401$	14.2650			0.712360			0.356180	−	0.934417i	$-0.384079\pi$
$401$	14.2650			0.712360			0.356180	+	0.934417i	$0.384079\pi$
$402$		0			0
$403$		−	9.62721i		−	0.479566i
$404$	3.72496	+	17.9305i	0.185324	+	0.892076i
$405$		0			0
$406$	−2.38138	−	23.1708i	−0.118186	−	1.14995i
$407$	2.37279			0.117615
$408$		0			0
$409$	5.93051			0.293245			0.146623	−	0.989193i	$-0.453160\pi$
$409$	5.93051			0.293245			0.146623	+	0.989193i	$0.453160\pi$
$410$	0.843326	+	8.20555i	0.0416489	+	0.405243i
$411$		0			0
$412$	10.5003	−	2.18137i	0.517311	−	0.107468i
$413$		−	18.2439i		−	0.897722i
$414$		0			0
$415$	8.20555			0.402795
$416$	−2.77180	−	4.93124i	−0.135899	−	0.241774i
$417$		0			0
$418$	−31.6655	+	3.25443i	−1.54881	+	0.159179i
$419$			25.5628i			1.24882i	0.781096	+	0.624411i	$0.214661\pi$
$419$			25.5628i			1.24882i	−0.781096	+	0.624411i	$0.785339\pi$
$420$		0			0
$421$		−	26.6655i		−	1.29960i	−0.760106	−	0.649799i	$-0.774853\pi$
$421$		−	26.6655i		−	1.29960i	0.760106	−	0.649799i	$-0.225147\pi$
$422$	−1.69597	−	16.5018i	−0.0825586	−	0.803294i
$423$		0			0
$424$	−3.91638	−	12.3431i	−0.190196	−	0.599432i
$425$	−4.00000			−0.194029
$426$		0			0
$427$		−	26.6550i		−	1.28992i
$428$	−2.59247	−	12.4791i	−0.125312	−	0.603202i
$429$		0			0
$430$	0.669022	−	0.0687588i	0.0322631	−	0.00331584i
$431$	12.4061			0.597580			0.298790	−	0.954319i	$-0.403417\pi$
$431$	12.4061			0.597580			0.298790	+	0.954319i	$0.403417\pi$
$432$		0			0
$433$	0.108315			0.00520526			0.00260263	−	0.999997i	$-0.499172\pi$
$433$	0.108315			0.00520526			0.00260263	+	0.999997i	$0.499172\pi$
$434$	−28.4791	+	2.92694i	−1.36704	+	0.140498i
$435$		0			0
$436$	5.73071	+	27.5854i	0.274451	+	1.32110i
$437$			6.50885i			0.311361i
$438$		0			0
$439$	−6.24386			−0.298003			−0.149002	−	0.988837i	$-0.547606\pi$
$439$	−6.24386			−0.298003			−0.149002	+	0.988837i	$0.547606\pi$
$440$	−15.1708	+	4.81361i	−0.723240	+	0.229480i
$441$		0			0
$442$	0.144584	+	1.40680i	0.00687717	+	0.0669148i
$443$		−	14.0333i		−	0.666742i	−0.942796	−	0.333371i	$-0.891814\pi$
$443$		−	14.0333i		−	0.666742i	0.942796	−	0.333371i	$-0.108186\pi$
$444$		0			0
$445$			11.2544i			0.533511i
$446$	6.58540	−	0.676815i	0.311828	−	0.0320481i
$447$		0			0
$448$	−13.7448	+	9.69874i	−0.649383	+	0.458222i
$449$	−5.51941			−0.260477			−0.130239	−	0.991483i	$-0.541574\pi$
$449$	−5.51941			−0.260477			−0.130239	+	0.991483i	$0.541574\pi$
$450$		0			0
$451$			32.8222i			1.54554i
$452$	9.48416	−	1.97028i	0.446097	−	0.0926742i
$453$		0			0
$454$	1.69670	+	16.5089i	0.0796300	+	0.774799i
$455$	2.10278			0.0985796
$456$		0			0
$457$	−20.0766			−0.939145			−0.469572	−	0.882894i	$-0.655592\pi$
$457$	−20.0766			−0.939145			−0.469572	+	0.882894i	$0.655592\pi$
$458$	0.844853	+	8.22041i	0.0394774	+	0.384115i
$459$		0			0
$460$	0.661956	+	3.18639i	0.0308638	+	0.148566i
$461$			12.4217i			0.578535i	0.957248	+	0.289267i	$0.0934116\pi$
$461$			12.4217i			0.578535i	−0.957248	+	0.289267i	$0.906588\pi$
$462$		0			0
$463$	−11.1184			−0.516714			−0.258357	−	0.966050i	$-0.583181\pi$
$463$	−11.1184			−0.516714			−0.258357	+	0.966050i	$0.583181\pi$
$464$	12.4791	+	28.7386i	0.579329	+	1.33416i
$465$		0			0
$466$	35.5131	−	3.64987i	1.64511	−	0.169077i
$467$		−	1.09724i		−	0.0507740i	−0.999678	−	0.0253870i	$-0.991918\pi$
$467$		−	1.09724i		−	0.0507740i	0.999678	−	0.0253870i	$-0.00808180\pi$
$468$		0			0
$469$			25.6655i			1.18512i
$470$	−0.676815	−	6.58540i	−0.0312192	−	0.303762i
$471$		0			0
$472$	7.42166	+	23.3905i	0.341610	+	1.07663i
$473$	2.67609			0.123047
$474$		0			0
$475$		−	16.0000i		−	0.734130i
$476$	4.11763	−	0.855416i	0.188731	−	0.0392079i
$477$		0			0
$478$	16.1290	−	1.65766i	0.737723	−	0.0758195i
$479$	−14.9844			−0.684655			−0.342328	−	0.939581i	$-0.611215\pi$
$479$	−14.9844			−0.684655			−0.342328	+	0.939581i	$0.611215\pi$
$480$		0			0
$481$	0.421663			0.0192262
$482$	−2.95112	+	0.303302i	−0.134420	+	0.0138150i
$483$		0			0
$484$	−40.4670	+	8.40680i	−1.83941	+	0.382127i
$485$		−	10.6761i		−	0.484776i
$486$		0			0
$487$	−23.1950			−1.05107			−0.525533	−	0.850773i	$-0.676134\pi$
$487$	−23.1950			−1.05107			−0.525533	+	0.850773i	$0.676134\pi$
$488$	10.8433	+	34.1744i	0.490854	+	1.54700i
$489$		0			0
$490$	0.372787	+	3.62721i	0.0168408	+	0.163861i
$491$		−	22.9844i		−	1.03727i	−0.854995	−	0.518636i	$-0.826440\pi$
$491$		−	22.9844i		−	1.03727i	0.854995	−	0.518636i	$-0.173560\pi$
$492$		0			0
$493$		−	7.83276i		−	0.352770i
$494$	−5.62721	+	0.578337i	−0.253180	+	0.0260206i
$495$		0			0
$496$	35.3225	−	15.3380i	1.58603	−	0.688699i
$497$	−19.2439			−0.863205
$498$		0			0
$499$		−	13.4983i		−	0.604266i	−0.953266	−	0.302133i	$-0.902301\pi$
$499$		−	13.4983i		−	0.604266i	0.953266	−	0.302133i	$-0.0976987\pi$
$500$	−3.66123	−	17.6237i	−0.163735	−	0.788157i
$501$		0			0
$502$	−2.13752	−	20.7980i	−0.0954021	−	0.928261i
$503$	−17.5678			−0.783308			−0.391654	−	0.920112i	$-0.628097\pi$
$503$	−17.5678			−0.783308			−0.391654	+	0.920112i	$0.628097\pi$
$504$		0			0
$505$	9.15667			0.407467
$506$	1.32391	+	12.8816i	0.0588550	+	0.572659i
$507$		0			0
$508$	19.6569	−	4.08362i	0.872135	−	0.181181i
$509$		−	8.31335i		−	0.368483i	−0.982881	−	0.184241i	$-0.941017\pi$
$509$		−	8.31335i		−	0.368483i	0.982881	−	0.184241i	$-0.0589828\pi$
$510$		0			0
$511$	5.42166			0.239840
$512$	13.6768	−	18.0262i	0.604436	−	0.796654i
$513$		0			0
$514$	−4.66123	+	0.479058i	−0.205598	+	0.0211303i
$515$		−	5.36222i		−	0.236288i
$516$		0			0
$517$		−	26.3416i		−	1.15850i
$518$	−0.128197	−	1.24736i	−0.00563267	−	0.0548058i
$519$		0			0
$520$	−2.69597	+	0.855416i	−0.118226	+	0.0375125i
$521$	−16.0872			−0.704793			−0.352396	−	0.935851i	$-0.614633\pi$
$521$	−16.0872			−0.704793			−0.352396	+	0.935851i	$0.614633\pi$
$522$		0			0
$523$		−	9.09724i		−	0.397794i	−0.980020	−	0.198897i	$-0.936264\pi$
$523$		−	9.09724i		−	0.397794i	0.980020	−	0.198897i	$-0.0637360\pi$
$524$	3.44789	+	16.5968i	0.150622	+	0.725033i
$525$		0			0
$526$	−24.5089	+	2.51890i	−1.06864	+	0.109829i
$527$	−9.62721			−0.419368
$528$		0			0
$529$	−20.3522			−0.884877
$530$	−6.44082	+	0.661956i	−0.279771	+	0.0287535i
$531$		0			0
$532$	3.42166	+	16.4705i	0.148348	+	0.714088i
$533$			5.83276i			0.252645i
$534$		0			0
$535$	−6.37279			−0.275520
$536$	−10.4408	−	32.9058i	−0.450975	−	1.42131i
$537$		0			0
$538$	0.480585	+	4.67609i	0.0207195	+	0.201601i
$539$			14.5089i			0.624940i
$540$		0			0
$541$		−	22.0872i		−	0.949602i	−0.880093	−	0.474801i	$-0.842520\pi$
$541$		−	22.0872i		−	0.949602i	0.880093	−	0.474801i	$-0.157480\pi$
$542$	−19.7421	+	2.02899i	−0.847995	+	0.0871527i
$543$		0			0
$544$	−4.93124	+	2.77180i	−0.211425	+	0.118840i
$545$	14.0872			0.603429
$546$		0			0
$547$			44.2772i			1.89315i	0.322477	+	0.946577i	$0.395484\pi$
$547$			44.2772i			1.89315i	−0.322477	+	0.946577i	$0.604516\pi$
$548$	37.3764	−	7.76473i	1.59664	−	0.331693i
$549$		0			0
$550$	−3.25443	−	31.6655i	−0.138769	−	1.35022i
$551$	31.3311			1.33475
$552$		0			0
$553$	30.0766			1.27899
$554$	−0.146111	−	1.42166i	−0.00620768	−	0.0604007i
$555$		0			0
$556$	−1.62517	−	7.82293i	−0.0689225	−	0.331766i
$557$		−	36.9094i		−	1.56390i	−0.623341	−	0.781951i	$-0.714225\pi$
$557$		−	36.9094i		−	1.56390i	0.623341	−	0.781951i	$-0.285775\pi$
$558$		0			0
$559$	0.475562			0.0201141
$560$	3.35013	+	7.71513i	0.141569	+	0.326024i
$561$		0			0
$562$	−5.04888	+	0.518898i	−0.212974	+	0.0218884i
$563$			1.28057i			0.0539698i	0.999636	+	0.0269849i	$0.00859060\pi$
$563$			1.28057i			0.0539698i	−0.999636	+	0.0269849i	$0.991409\pi$
$564$		0			0
$565$		−	4.84333i		−	0.203760i
$566$	−1.92192	−	18.7003i	−0.0807844	−	0.786031i
$567$		0			0
$568$	24.6726	−	7.82847i	1.03524	−	0.328475i
$569$	37.5089			1.57245			0.786226	−	0.617938i	$-0.212032\pi$
$569$	37.5089			1.57245			0.786226	+	0.617938i	$0.212032\pi$
$570$		0			0
$571$			29.7583i			1.24534i	0.782483	+	0.622672i	$0.213953\pi$
$571$			29.7583i			1.24534i	−0.782483	+	0.622672i	$0.786047\pi$
$572$	−11.0192	+	2.28917i	−0.460734	+	0.0957149i
$573$		0			0
$574$	17.2544	−	1.77332i	0.720186	−	0.0740171i
$575$	−6.50885			−0.271438
$576$		0			0
$577$	−20.4605			−0.851781			−0.425891	−	0.904775i	$-0.640039\pi$
$577$	−20.4605			−0.851781			−0.425891	+	0.904775i	$0.640039\pi$
$578$	−22.5089	+	2.31335i	−0.936245	+	0.0962226i
$579$		0			0
$580$	15.3380	−	3.18639i	0.636878	−	0.132308i
$581$		−	17.2544i		−	0.715834i
$582$		0			0
$583$	−25.7633			−1.06701
$584$	−6.95112	+	2.20555i	−0.287640	+	0.0912663i
$585$		0			0
$586$	−1.33652	−	13.0043i	−0.0552110	−	0.537203i
$587$			9.62721i			0.397358i	0.980065	+	0.198679i	$0.0636651\pi$
$587$			9.62721i			0.397358i	−0.980065	+	0.198679i	$0.936335\pi$
$588$		0			0
$589$		−	38.5089i		−	1.58673i
$590$	12.2056	−	1.25443i	0.502495	−	0.0516439i
$591$		0			0
$592$	0.671792	+	1.54709i	0.0276105	+	0.0635850i
$593$	28.6550			1.17672			0.588359	−	0.808600i	$-0.299774\pi$
$593$	28.6550			1.17672			0.588359	+	0.808600i	$0.299774\pi$
$594$		0			0
$595$		−	2.10278i		−	0.0862054i
$596$	−1.28415	−	6.18137i	−0.0526006	−	0.253199i
$597$		0			0
$598$	0.235269	+	2.28917i	0.00962088	+	0.0936111i
$599$	−39.0661			−1.59620			−0.798098	−	0.602528i	$-0.794160\pi$
$599$	−39.0661			−1.59620			−0.798098	+	0.602528i	$0.794160\pi$
$600$		0			0
$601$	19.8222			0.808564			0.404282	−	0.914634i	$-0.367521\pi$
$601$	19.8222			0.808564			0.404282	+	0.914634i	$0.367521\pi$
$602$	−0.144584	−	1.40680i	−0.00589282	−	0.0573370i
$603$		0			0
$604$	−4.63653	+	0.963214i	−0.188658	+	0.0391926i
$605$			20.6655i			0.840173i
$606$		0			0
$607$	−12.8917			−0.523257			−0.261629	−	0.965169i	$-0.584260\pi$
$607$	−12.8917			−0.523257			−0.261629	+	0.965169i	$0.584260\pi$
$608$	−11.0872	−	19.7250i	−0.449645	−	0.799953i
$609$		0			0
$610$	17.8328	−	1.83276i	0.722027	−	0.0742064i
$611$		−	4.68111i		−	0.189378i
$612$		0			0
$613$		−	0.313348i		−	0.0126560i	−0.999980	−	0.00632801i	$-0.997986\pi$
$613$		−	0.313348i		−	0.0126560i	0.999980	−	0.00632801i	$-0.00201428\pi$
$614$	1.19499	+	11.6272i	0.0482258	+	0.469236i
$615$		0			0
$616$	10.1219	+	31.9008i	0.407824	+	1.28532i
$617$	−6.31335			−0.254166			−0.127083	−	0.991892i	$-0.540561\pi$
$617$	−6.31335			−0.254166			−0.127083	+	0.991892i	$0.540561\pi$
$618$		0			0
$619$			33.1638i			1.33297i	0.745520	+	0.666483i	$0.232201\pi$
$619$			33.1638i			1.33297i	−0.745520	+	0.666483i	$0.767799\pi$
$620$	−3.91638	−	18.8519i	−0.157286	−	0.757111i
$621$		0			0
$622$	33.2927	−	3.42166i	1.33492	−	0.137196i
$623$	23.6655			0.948139
$624$		0			0
$625$	11.0000			0.440000
$626$	−1.03402	+	0.106271i	−0.0413276	+	0.00424745i
$627$		0			0
$628$	−6.48059	−	31.1950i	−0.258604	−	1.24482i
$629$		−	0.421663i		−	0.0168128i
$630$		0			0
$631$	−9.42669			−0.375270			−0.187635	−	0.982239i	$-0.560082\pi$
$631$	−9.42669			−0.375270			−0.187635	+	0.982239i	$0.560082\pi$
$632$	−38.5613	+	12.2353i	−1.53389	+	0.486693i
$633$		0			0
$634$	−1.61308	−	15.6952i	−0.0640636	−	0.623338i
$635$		−	10.0383i		−	0.398358i
$636$		0			0
$637$			2.57834i			0.102157i
$638$	62.0071	−	6.37279i	2.45489	−	0.252301i
$639$		0			0
$640$	−7.43375	−	8.52873i	−0.293845	−	0.337128i
$641$	3.68665			0.145614			0.0728070	−	0.997346i	$-0.476804\pi$
$641$	3.68665			0.145614			0.0728070	+	0.997346i	$0.476804\pi$
$642$		0			0
$643$		−	10.3033i		−	0.406323i	−0.979145	−	0.203161i	$-0.934878\pi$
$643$		−	10.3033i		−	0.406323i	0.979145	−	0.203161i	$-0.0651216\pi$
$644$	6.70027	−	1.39194i	0.264028	−	0.0548503i
$645$		0			0
$646$	0.578337	+	5.62721i	0.0227544	+	0.221400i
$647$	29.8328			1.17285			0.586423	−	0.810005i	$-0.300535\pi$
$647$	29.8328			1.17285			0.586423	+	0.810005i	$0.300535\pi$
$648$		0			0
$649$	48.8222			1.91644
$650$	−0.578337	−	5.62721i	−0.0226842	−	0.220717i
$651$		0			0
$652$	1.43580	+	6.91136i	0.0562301	+	0.270670i
$653$			7.47002i			0.292325i	0.989261	+	0.146162i	$0.0466922\pi$
$653$			7.47002i			0.292325i	−0.989261	+	0.146162i	$0.953308\pi$
$654$		0			0
$655$	8.47556			0.331168
$656$	−21.4005	+	9.29274i	−0.835551	+	0.362821i
$657$		0			0
$658$	−13.8476	+	1.42319i	−0.539837	+	0.0554817i
$659$			9.09724i			0.354378i	0.984177	+	0.177189i	$0.0567004\pi$
$659$			9.09724i			0.354378i	−0.984177	+	0.177189i	$0.943300\pi$
$660$		0			0
$661$		−	42.6832i		−	1.66019i	−0.557626	−	0.830093i	$-0.688287\pi$
$661$		−	42.6832i		−	1.66019i	0.557626	−	0.830093i	$-0.311713\pi$
$662$	−1.12695	−	10.9653i	−0.0438003	−	0.426177i
$663$		0			0
$664$	7.01916	+	22.1219i	0.272396	+	0.858497i
$665$	8.41110			0.326168
$666$		0			0
$667$		−	12.7456i		−	0.493511i
$668$	−30.7925	+	6.39697i	−1.19140	+	0.247506i
$669$		0			0
$670$	−17.1708	+	1.76473i	−0.663366	+	0.0681775i
$671$	71.3311			2.75370
$672$		0			0
$673$	−18.6655			−0.719503			−0.359752	−	0.933048i	$-0.617139\pi$
$673$	−18.6655			−0.719503			−0.359752	+	0.933048i	$0.617139\pi$
$674$	27.0723	−	2.78236i	1.04279	−	0.107173i
$675$		0			0
$676$	−1.95819	+	0.406803i	−0.0753150	+	0.0156463i
$677$			11.9022i			0.457441i	0.973492	+	0.228720i	$0.0734541\pi$
$677$			11.9022i			0.457441i	−0.973492	+	0.228720i	$0.926546\pi$
$678$		0			0
$679$	−22.4494			−0.861529
$680$	0.855416	+	2.69597i	0.0328037	+	0.103386i
$681$		0			0
$682$	−7.83276	−	76.2127i	−0.299932	−	2.91833i
$683$			4.95112i			0.189449i	0.995504	+	0.0947247i	$0.0301971\pi$
$683$			4.95112i			0.189449i	−0.995504	+	0.0947247i	$0.969803\pi$
$684$		0			0
$685$		−	19.0872i		−	0.729284i
$686$	28.3345	−	2.91208i	1.08182	−	0.111184i
$687$		0			0
$688$	0.757664	+	1.74485i	0.0288857	+	0.0665217i
$689$	−4.57834			−0.174421
$690$		0			0
$691$			34.7244i			1.32098i	0.750835	+	0.660490i	$0.229651\pi$
$691$			34.7244i			1.32098i	−0.750835	+	0.660490i	$0.770349\pi$
$692$	5.86248	+	28.2197i	0.222858	+	1.07275i
$693$		0			0
$694$	−4.71513	−	45.8781i	−0.178984	−	1.74151i
$695$	−3.99498			−0.151538
$696$		0			0
$697$	5.83276			0.220932
$698$	4.60099	+	44.7676i	0.174150	+	1.69448i
$699$		0			0
$700$	−16.4705	+	3.42166i	−0.622528	+	0.129327i
$701$		−	30.2650i		−	1.14309i	−0.820570	−	0.571546i	$-0.806344\pi$
$701$		−	30.2650i		−	1.14309i	0.820570	−	0.571546i	$-0.193656\pi$
$702$		0			0
$703$	1.68665			0.0636133
$704$	−25.9547	−	36.7824i	−0.978204	−	1.38629i
$705$		0			0
$706$	−28.2736	+	2.90582i	−1.06409	+	0.109362i
$707$		−	19.2544i		−	0.724137i
$708$		0			0
$709$			49.3311i			1.85267i	0.376705	+	0.926333i	$0.377057\pi$
$709$			49.3311i			1.85267i	−0.376705	+	0.926333i	$0.622943\pi$
$710$	−1.32318	−	12.8746i	−0.0496582	−	0.483174i
$711$		0			0
$712$	−30.3416	+	9.62721i	−1.13710	+	0.360795i
$713$	−15.6655			−0.586679
$714$		0			0
$715$			5.62721i			0.210446i
$716$	0.688179	+	3.31262i	0.0257185	+	0.123799i
$717$		0			0
$718$	−12.2197	+	1.25588i	−0.456035	+	0.0468690i
$719$	−39.3411			−1.46718			−0.733588	−	0.679595i	$-0.762156\pi$
$719$	−39.3411			−1.46718			−0.733588	+	0.679595i	$0.762156\pi$
$720$		0			0
$721$	−11.2756			−0.419923
$722$	4.22041	−	0.433753i	0.157067	−	0.0161426i
$723$		0			0
$724$	7.01916	+	33.7875i	0.260865	+	1.25570i
$725$			31.3311i			1.16361i
$726$		0			0
$727$	38.4494			1.42601			0.713005	−	0.701159i	$-0.247334\pi$
$727$	38.4494			1.42601			0.713005	+	0.701159i	$0.247334\pi$
$728$	1.79875	+	5.66902i	0.0666660	+	0.210108i
$729$		0			0
$730$	0.372787	+	3.62721i	0.0137975	+	0.134249i
$731$		−	0.475562i		−	0.0175893i
$732$		0			0
$733$			42.3522i			1.56431i	0.623082	+	0.782157i	$0.285880\pi$
$733$			42.3522i			1.56431i	−0.623082	+	0.782157i	$0.714120\pi$
$734$	−13.1708	+	1.35363i	−0.486143	+	0.0499634i
$735$		0			0
$736$	−8.02418	+	4.51030i	−0.295775	+	0.166252i
$737$	−68.6832			−2.52998
$738$		0			0
$739$			14.5783i			0.536273i	0.963381	+	0.268136i	$0.0864078\pi$
$739$			14.5783i			0.536273i	−0.963381	+	0.268136i	$0.913592\pi$
$740$	0.825696	−	0.171534i	0.0303532	−	0.00630571i
$741$		0			0
$742$	1.39194	+	13.5436i	0.0510999	+	0.497201i
$743$	2.78891			0.102315			0.0511576	−	0.998691i	$-0.483709\pi$
$743$	2.78891			0.102315			0.0511576	+	0.998691i	$0.483709\pi$
$744$		0			0
$745$	−3.15667			−0.115652
$746$	−3.17780	−	30.9200i	−0.116348	−	1.13206i
$747$		0			0
$748$	2.28917	+	11.0192i	0.0837003	+	0.402900i
$749$			13.4005i			0.489645i
$750$		0			0
$751$	−34.2439			−1.24958			−0.624788	−	0.780794i	$-0.714815\pi$
$751$	−34.2439			−1.24958			−0.624788	+	0.780794i	$0.714815\pi$
$752$	17.1751	−	7.45793i	0.626312	−	0.271963i
$753$		0			0
$754$	11.0192	−	1.13249i	0.401294	−	0.0412430i
$755$			2.36776i			0.0861717i
$756$		0			0
$757$		−	18.4605i		−	0.670958i	−0.942048	−	0.335479i	$-0.891102\pi$
$757$		−	18.4605i		−	0.670958i	0.942048	−	0.335479i	$-0.108898\pi$
$758$	−0.586931	−	5.71083i	−0.0213183	−	0.207427i
$759$		0			0
$760$	−10.7839	+	3.42166i	−0.391173	+	0.124117i
$761$	−17.6172			−0.638622			−0.319311	−	0.947650i	$-0.603451\pi$
$761$	−17.6172			−0.638622			−0.319311	+	0.947650i	$0.603451\pi$
$762$		0			0
$763$		−	29.6222i		−	1.07240i
$764$	−11.8242	+	2.45641i	−0.427783	+	0.0888696i
$765$		0			0
$766$	10.4040	−	1.06928i	0.375913	−	0.0386345i
$767$	8.67609			0.313275
$768$		0			0
$769$	−41.3522			−1.49120			−0.745599	−	0.666395i	$-0.767836\pi$
$769$	−41.3522			−1.49120			−0.745599	+	0.666395i	$0.767836\pi$
$770$	16.6464	−	1.71083i	0.599894	−	0.0616541i
$771$		0			0
$772$	25.9547	−	5.39194i	0.934130	−	0.194060i
$773$		−	22.6867i		−	0.815982i	−0.912986	−	0.407991i	$-0.866229\pi$
$773$		−	22.6867i		−	0.815982i	0.912986	−	0.407991i	$-0.133771\pi$
$774$		0			0
$775$	38.5089			1.38328
$776$	28.7824	−	9.13249i	1.03323	−	0.327837i
$777$		0			0
$778$	1.94056	+	18.8816i	0.0695725	+	0.676940i
$779$			23.3311i			0.835922i
$780$		0			0
$781$		−	51.4983i		−	1.84275i
$782$	2.28917	−	0.235269i	0.0818605	−	0.00841322i
$783$		0			0
$784$	−9.45998	+	4.10780i	−0.337856	+	0.146707i
$785$	−15.9305			−0.568584
$786$		0			0
$787$			15.5194i			0.553207i	0.960984	+	0.276604i	$0.0892089\pi$
$787$			15.5194i			0.553207i	−0.960984	+	0.276604i	$0.910791\pi$
$788$	9.32821	+	44.9023i	0.332304	+	1.59958i
$789$		0			0
$790$	2.06803	+	20.1219i	0.0735773	+	0.715906i
$791$	−10.1844			−0.362116
$792$		0			0
$793$	12.6761			0.450141
$794$	−4.79088	−	46.6152i	−0.170022	−	1.65431i
$795$		0			0
$796$	−1.86248	+	0.386920i	−0.0660139	+	0.0137140i
$797$		−	1.56777i		−	0.0555334i	−0.999614	−	0.0277667i	$-0.991160\pi$
$797$		−	1.56777i		−	0.0555334i	0.999614	−	0.0277667i	$-0.00883955\pi$
$798$		0			0
$799$	−4.68111			−0.165606
$800$	19.7250	−	11.0872i	0.697383	−	0.391991i
$801$		0			0
$802$	20.0680	−	2.06249i	0.708627	−	0.0728292i
$803$			14.5089i			0.512006i
$804$		0			0
$805$		−	3.42166i		−	0.120598i
$806$	−1.39194	−	13.5436i	−0.0490291	−	0.477053i
$807$		0			0
$808$	7.83276	+	24.6861i	0.275556	+	0.868455i
$809$	44.4005			1.56104			0.780520	−	0.625131i	$-0.214954\pi$
$809$	44.4005			1.56104			0.780520	+	0.625131i	$0.214954\pi$
$810$		0			0
$811$		−	32.9411i		−	1.15672i	−0.815782	−	0.578359i	$-0.803693\pi$
$811$		−	32.9411i		−	1.15672i	0.815782	−	0.578359i	$-0.196307\pi$
$812$	−6.70027	−	32.2525i	−0.235133	−	1.13184i
$813$		0			0
$814$	3.33804	−	0.343068i	0.116998	−	0.0120245i
$815$	3.52946			0.123632
$816$		0			0
$817$	1.90225			0.0665512
$818$	8.34307	−	0.857459i	0.291709	−	0.0299804i
$819$		0			0
$820$	2.37279	+	11.4217i	0.0828613	+	0.398862i
$821$		−	30.3522i		−	1.05930i	−0.848217	−	0.529649i	$-0.822324\pi$
$821$		−	30.3522i		−	1.05930i	0.848217	−	0.529649i	$-0.177676\pi$
$822$		0			0
$823$	−34.5783			−1.20533			−0.602663	−	0.797996i	$-0.705893\pi$
$823$	−34.5783			−1.20533			−0.602663	+	0.797996i	$0.705893\pi$
$824$	14.4564	−	4.58693i	0.503613	−	0.159793i
$825$		0			0
$826$	−2.63778	−	25.6655i	−0.0917800	−	0.893018i
$827$			14.1744i			0.492891i	0.969157	+	0.246446i	$0.0792627\pi$
$827$			14.1744i			0.492891i	−0.969157	+	0.246446i	$0.920737\pi$
$828$		0			0
$829$			33.1355i			1.15085i	0.817856	+	0.575423i	$0.195162\pi$
$829$			33.1355i			1.15085i	−0.817856	+	0.575423i	$0.804838\pi$
$830$	11.5436	−	1.18639i	0.400684	−	0.0411803i
$831$		0			0
$832$	−4.61235	−	6.53653i	−0.159905	−	0.226613i
$833$	2.57834			0.0893341
$834$		0			0
$835$			15.7250i			0.544185i
$836$	−44.0766	+	9.15667i	−1.52442	+	0.316690i
$837$		0			0
$838$	3.69597	+	35.9618i	0.127675	+	1.24228i
$839$	34.4494			1.18933			0.594663	−	0.803975i	$-0.297286\pi$
$839$	34.4494			1.18933			0.594663	+	0.803975i	$0.297286\pi$
$840$		0			0
$841$	−32.3522			−1.11559
$842$	−3.85542	−	37.5131i	−0.132866	−	1.29279i
$843$		0			0
$844$	−4.77180	−	22.9696i	−0.164252	−	0.790645i
$845$			1.00000i			0.0344010i
$846$		0			0
$847$	43.4550			1.49313
$848$	−7.29419	−	16.7980i	−0.250484	−	0.576846i
$849$		0			0
$850$	−5.62721	+	0.578337i	−0.193012	+	0.0198368i
$851$		−	0.686135i		−	0.0235204i
$852$		0			0
$853$			17.1744i			0.588040i	0.955799	+	0.294020i	$0.0949931\pi$
$853$			17.1744i			0.588040i	−0.955799	+	0.294020i	$0.905007\pi$
$854$	−3.85389	−	37.4983i	−0.131877	−	1.28317i
$855$		0			0
$856$	−5.45138	−	17.1809i	−0.186324	−	0.587230i
$857$	34.4877			1.17808			0.589039	−	0.808104i	$-0.299506\pi$
$857$	34.4877			1.17808			0.589039	+	0.808104i	$0.299506\pi$
$858$		0			0
$859$		−	5.29274i		−	0.180586i	−0.995915	−	0.0902930i	$-0.971220\pi$
$859$		−	5.29274i		−	0.180586i	0.995915	−	0.0902930i	$-0.0287803\pi$
$860$	0.931241	−	0.193460i	0.0317551	−	0.00659694i
$861$		0			0
$862$	17.4529	−	1.79372i	0.594448	−	0.0610945i
$863$	−11.5939			−0.394662			−0.197331	−	0.980337i	$-0.563227\pi$
$863$	−11.5939			−0.394662			−0.197331	+	0.980337i	$0.563227\pi$
$864$		0			0
$865$	14.4111			0.489992
$866$	0.152377	−	0.0156606i	0.00517799	−	0.000532168i
$867$		0			0
$868$	−39.6413	+	8.23527i	−1.34551	+	0.279523i
$869$			80.4877i			2.73036i
$870$		0			0
$871$	−12.2056			−0.413569
$872$	12.0504	+	37.9787i	0.408078	+	1.28612i
$873$		0			0
$874$	0.941078	+	9.15667i	0.0318324	+	0.309729i
$875$			18.9250i			0.639781i
$876$		0			0
$877$			10.3522i			0.349568i	0.984607	+	0.174784i	$0.0559227\pi$
$877$			10.3522i			0.349568i	−0.984607	+	0.174784i	$0.944077\pi$
$878$	−8.78389	+	0.902764i	−0.296442	+	0.0304668i
$879$		0			0
$880$	−20.6464	+	8.96526i	−0.695989	+	0.302219i
$881$	−39.7044			−1.33767			−0.668837	−	0.743409i	$-0.733208\pi$
$881$	−39.7044			−1.33767			−0.668837	+	0.743409i	$0.733208\pi$
$882$		0			0
$883$			42.2388i			1.42145i	0.703470	+	0.710725i	$0.251633\pi$
$883$			42.2388i			1.42145i	−0.703470	+	0.710725i	$0.748367\pi$
$884$	0.406803	+	1.95819i	0.0136823	+	0.0658611i
$885$		0			0
$886$	−2.02899	−	19.7421i	−0.0681654	−	0.663248i
$887$	−36.1461			−1.21367			−0.606834	−	0.794829i	$-0.707561\pi$
$887$	−36.1461			−1.21367			−0.606834	+	0.794829i	$0.707561\pi$
$888$		0			0
$889$	−21.1083			−0.707950
$890$	1.62721	+	15.8328i	0.0545443	+	0.530715i
$891$		0			0
$892$	9.16651	−	1.90429i	0.306917	−	0.0637604i
$893$		−	18.7244i		−	0.626590i
$894$		0			0
$895$	1.69167			0.0565465
$896$	−17.9340	+	15.6315i	−0.599133	+	0.522212i
$897$		0			0
$898$	−7.76473	+	0.798021i	−0.259112	+	0.0266303i
$899$			75.4077i			2.51499i
$900$		0			0
$901$			4.57834i			0.152527i
$902$	4.74557	+	46.1744i	0.158010	+	1.53744i
$903$		0			0
$904$	13.0575	−	4.14306i	0.434285	−	0.137796i
$905$	17.2544			0.573557
$906$		0			0
$907$			43.5910i			1.44742i	0.690106	+	0.723708i	$0.257564\pi$
$907$			43.5910i			1.44742i	−0.690106	+	0.723708i	$0.742436\pi$
$908$	4.77384	+	22.9794i	0.158425	+	0.762598i
$909$		0			0
$910$	2.95819	−	0.304028i	0.0980631	−	0.0100784i
$911$	−53.8993			−1.78576			−0.892882	−	0.450290i	$-0.851321\pi$
$911$	−53.8993			−1.78576			−0.892882	+	0.450290i	$0.851321\pi$
$912$		0			0
$913$	46.1744			1.52815
$914$	−28.2439	+	2.90276i	−0.934224	+	0.0960149i
$915$		0			0
$916$	2.37708	+	11.4423i	0.0785411	+	0.378066i
$917$		−	17.8222i		−	0.588541i
$918$		0			0
$919$	6.64782			0.219291			0.109646	−	0.993971i	$-0.465028\pi$
$919$	6.64782			0.219291			0.109646	+	0.993971i	$0.465028\pi$
$920$	1.39194	+	4.38692i	0.0458910	+	0.144632i
$921$		0			0
$922$	1.79598	+	17.4748i	0.0591474	+	0.575503i
$923$		−	9.15165i		−	0.301230i
$924$		0			0
$925$			1.68665i			0.0554568i
$926$	−15.6413	+	1.60754i	−0.514007	+	0.0528270i
$927$		0			0
$928$	21.7108	+	38.6252i	0.712693	+	1.26794i
$929$	17.9789			0.589868			0.294934	−	0.955518i	$-0.404702\pi$
$929$	17.9789			0.589868			0.294934	+	0.955518i	$0.404702\pi$
$930$		0			0
$931$			10.3133i			0.338006i
$932$	49.4323	−	10.2693i	1.61921	−	0.336382i
$933$		0			0
$934$	−0.158643	−	1.54359i	−0.00519096	−	0.0505080i
$935$	5.62721			0.184030
$936$		0			0
$937$	−22.4877			−0.734642			−0.367321	−	0.930094i	$-0.619725\pi$
$937$	−22.4877			−0.734642			−0.367321	+	0.930094i	$0.619725\pi$
$938$	3.71083	+	36.1063i	0.121163	+	1.17891i
$939$		0			0
$940$	−1.90429	−	9.16651i	−0.0621111	−	0.298979i
$941$			15.1955i			0.495359i	0.968842	+	0.247680i	$0.0796680\pi$
$941$			15.1955i			0.495359i	−0.968842	+	0.247680i	$0.920332\pi$
$942$		0			0
$943$	9.49115			0.309074
$944$	13.8227	+	31.8328i	0.449891	+	1.03607i
$945$		0			0
$946$	3.76473	−	0.386920i	0.122402	−	0.0125799i
$947$			32.0594i			1.04179i	0.853620	+	0.520896i	$0.174402\pi$
$947$			32.0594i			1.04179i	−0.853620	+	0.520896i	$0.825598\pi$
$948$		0			0
$949$			2.57834i			0.0836964i
$950$	−2.31335	−	22.5089i	−0.0750549	−	0.730284i
$951$		0			0
$952$	5.66902	−	1.79875i	0.183734	−	0.0582977i
$953$	−31.5089			−1.02067			−0.510336	−	0.859975i	$-0.670479\pi$
$953$	−31.5089			−1.02067			−0.510336	+	0.859975i	$0.670479\pi$
$954$		0			0
$955$			6.03831i			0.195395i
$956$	22.4507	−	4.66400i	0.726106	−	0.150845i
$957$		0			0
$958$	−21.0801	+	2.16651i	−0.681068	+	0.0699968i
$959$	−40.1361			−1.29606
$960$		0			0
$961$	61.6832			1.98978
$962$	0.593197	−	0.0609658i	0.0191254	−	0.00196562i
$963$		0			0
$964$	−4.10780	+	0.853372i	−0.132303	+	0.0274853i
$965$		−	13.2544i		−	0.426675i
$966$		0			0
$967$	44.3960			1.42768			0.713840	−	0.700309i	$-0.246954\pi$
$967$	44.3960			1.42768			0.713840	+	0.700309i	$0.246954\pi$
$968$	−55.7137	+	17.6776i	−1.79071	+	0.568180i
$969$		0			0
$970$	−1.54359	−	15.0192i	−0.0495618	−	0.482236i
$971$			49.2978i			1.58204i	0.611790	+	0.791020i	$0.290450\pi$
$971$			49.2978i			1.58204i	−0.611790	+	0.791020i	$0.709550\pi$
$972$		0			0
$973$			8.40054i			0.269309i
$974$	−32.6308	+	3.35363i	−1.04556	+	0.107457i
$975$		0			0
$976$	20.1955	+	46.5089i	0.646442	+	1.48871i
$977$	3.35218			0.107246			0.0536228	−	0.998561i	$-0.482923\pi$
$977$	3.35218			0.107246			0.0536228	+	0.998561i	$0.482923\pi$
$978$		0			0
$979$			63.3311i			2.02407i
$980$	1.04888	+	5.04888i	0.0335051	+	0.161280i
$981$		0			0
$982$	−3.32318	−	32.3345i	−0.106047	−	1.03184i
$983$	−21.8972			−0.698413			−0.349207	−	0.937046i	$-0.613549\pi$
$983$	−21.8972			−0.698413			−0.349207	+	0.937046i	$0.613549\pi$
$984$		0			0
$985$	22.9305			0.730627
$986$	−1.13249	−	11.0192i	−0.0360660	−	0.350921i
$987$		0			0
$988$	−7.83276	+	1.62721i	−0.249193	+	0.0517685i
$989$		−	0.773841i		−	0.0246067i
$990$		0			0
$991$	−59.7422			−1.89777			−0.948886	−	0.315619i	$-0.897788\pi$
$991$	−59.7422			−1.89777			−0.948886	+	0.315619i	$0.897788\pi$
$992$	47.4741	−	26.6847i	1.50730	−	0.847240i
$993$		0			0
$994$	−27.0723	+	2.78236i	−0.858682	+	0.0882511i
$995$			0.951124i			0.0301527i
$996$		0			0
$997$			38.3416i			1.21429i	0.794591	+	0.607146i	$0.207686\pi$
$997$			38.3416i			1.21429i	−0.794591	+	0.607146i	$0.792314\pi$
$998$	−1.95164	−	18.9894i	−0.0617781	−	0.601100i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.g.c.469.5		6
3.2	odd	2		104.2.b.c.53.2	yes	6
4.3	odd	2		3744.2.g.c.1873.3		6
8.3	odd	2		3744.2.g.c.1873.6		6
8.5	even	2	inner	936.2.g.c.469.6		6
12.11	even	2		416.2.b.c.209.2		6
24.5	odd	2		104.2.b.c.53.1	✓	6
24.11	even	2		416.2.b.c.209.5		6
48.5	odd	4		3328.2.a.be.1.3		3
48.11	even	4		3328.2.a.bg.1.1		3
48.29	odd	4		3328.2.a.bh.1.1		3
48.35	even	4		3328.2.a.bf.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.b.c.53.1	✓	6	24.5	odd	2
104.2.b.c.53.2	yes	6	3.2	odd	2
416.2.b.c.209.2		6	12.11	even	2
416.2.b.c.209.5		6	24.11	even	2
936.2.g.c.469.5		6	1.1	even	1	trivial
936.2.g.c.469.6		6	8.5	even	2	inner
3328.2.a.be.1.3		3	48.5	odd	4
3328.2.a.bf.1.3		3	48.35	even	4
3328.2.a.bg.1.1		3	48.11	even	4
3328.2.a.bh.1.1		3	48.29	odd	4
3744.2.g.c.1873.3		6	4.3	odd	2
3744.2.g.c.1873.6		6	8.3	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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40680 - 0.144584i) q^{2} +(1.95819 - 0.406803i) q^{4} -1.00000i q^{5} -2.10278 q^{7} +(2.69597 - 0.855416i) q^{8} +(-0.144584 - 1.40680i) q^{10} -5.62721i q^{11} -1.00000i q^{13} +(-2.95819 + 0.304028i) q^{14} +(3.66902 - 1.59320i) q^{16} -1.00000 q^{17} -4.00000i q^{19} +(-0.406803 - 1.95819i) q^{20} +(-0.813607 - 7.91638i) q^{22} -1.62721 q^{23} +4.00000 q^{25} +(-0.144584 - 1.40680i) q^{26} +(-4.11763 + 0.855416i) q^{28} +7.83276i q^{29} +9.62721 q^{31} +(4.93124 - 2.77180i) q^{32} +(-1.40680 + 0.144584i) q^{34} +2.10278i q^{35} +0.421663i q^{37} +(-0.578337 - 5.62721i) q^{38} +(-0.855416 - 2.69597i) q^{40} -5.83276 q^{41} +0.475562i q^{43} +(-2.28917 - 11.0192i) q^{44} +(-2.28917 + 0.235269i) q^{46} +4.68111 q^{47} -2.57834 q^{49} +(5.62721 - 0.578337i) q^{50} +(-0.406803 - 1.95819i) q^{52} -4.57834i q^{53} -5.62721 q^{55} +(-5.66902 + 1.79875i) q^{56} +(1.13249 + 11.0192i) q^{58} +8.67609i q^{59} +12.6761i q^{61} +(13.5436 - 1.39194i) q^{62} +(6.53653 - 4.61235i) q^{64} -1.00000 q^{65} -12.2056i q^{67} +(-1.95819 + 0.406803i) q^{68} +(0.304028 + 2.95819i) q^{70} +9.15165 q^{71} -2.57834 q^{73} +(0.0609658 + 0.593197i) q^{74} +(-1.62721 - 7.83276i) q^{76} +11.8328i q^{77} -14.3033 q^{79} +(-1.59320 - 3.66902i) q^{80} +(-8.20555 + 0.843326i) q^{82} +8.20555i q^{83} +1.00000i q^{85} +(0.0687588 + 0.669022i) q^{86} +(-4.81361 - 15.1708i) q^{88} -11.2544 q^{89} +2.10278i q^{91} +(-3.18639 + 0.661956i) q^{92} +(6.58540 - 0.676815i) q^{94} -4.00000 q^{95} +10.6761 q^{97} +(-3.62721 + 0.372787i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} - 2 q^{4} + 2 q^{7} + 8 q^{8} - 4 q^{14} + 10 q^{16} - 6 q^{17} + 4 q^{20} + 8 q^{22} + 16 q^{23} + 24 q^{25} - 20 q^{28} + 32 q^{31} + 12 q^{32} - 2 q^{34} - 6 q^{40} + 20 q^{41} - 12 q^{44}+ \cdots + 4 q^{98}+O(q^{100}) \) 6 * q + 2 * q^2 - 2 * q^4 + 2 * q^7 + 8 * q^8 - 4 * q^14 + 10 * q^16 - 6 * q^17 + 4 * q^20 + 8 * q^22 + 16 * q^23 + 24 * q^25 - 20 * q^28 + 32 * q^31 + 12 * q^32 - 2 * q^34 - 6 * q^40 + 20 * q^41 - 12 * q^44 - 12 * q^46 + 10 * q^47 - 12 * q^49 + 8 * q^50 + 4 * q^52 - 8 * q^55 - 22 * q^56 + 12 * q^58 + 28 * q^62 + 22 * q^64 - 6 * q^65 + 2 * q^68 + 10 * q^70 + 18 * q^71 - 12 * q^73 - 28 * q^74 + 16 * q^76 - 12 * q^79 - 16 * q^80 - 20 * q^82 + 18 * q^86 - 16 * q^88 - 16 * q^89 - 32 * q^92 - 24 * q^95 + 16 * q^97 + 4 * q^98

Introduction

L-functions

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