LMFDB - Embedded newform 572.2.e.b.131.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(131,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("572.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.e (of order $2$, degree $1$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			131.3
Character	$\chi$	$=$	572.131
Dual form			572.2.e.b.131.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40623 - 0.150014i) q^{2} +1.91998i q^{3} +(1.95499 + 0.421910i) q^{4} +1.37022 q^{5} +(0.288024 - 2.69995i) q^{6} -2.10998 q^{7} +(-2.68588 - 0.886580i) q^{8} -0.686333 q^{9} +O(q^{10})$	\(q+(-1.40623 - 0.150014i) q^{2} +1.91998i q^{3} +(1.95499 + 0.421910i) q^{4} +1.37022 q^{5} +(0.288024 - 2.69995i) q^{6} -2.10998 q^{7} +(-2.68588 - 0.886580i) q^{8} -0.686333 q^{9} +(-1.92686 - 0.205553i) q^{10} +(3.18194 - 0.935566i) q^{11} +(-0.810060 + 3.75355i) q^{12} +1.00000i q^{13} +(2.96712 + 0.316526i) q^{14} +2.63081i q^{15} +(3.64398 + 1.64966i) q^{16} +6.80287i q^{17} +(0.965145 + 0.102960i) q^{18} +6.04114 q^{19} +(2.67878 + 0.578111i) q^{20} -4.05112i q^{21} +(-4.61490 + 0.838290i) q^{22} +1.02360i q^{23} +(1.70222 - 5.15685i) q^{24} -3.12248 q^{25} +(0.150014 - 1.40623i) q^{26} +4.44220i q^{27} +(-4.12499 - 0.890220i) q^{28} -1.89393i q^{29} +(0.394658 - 3.69953i) q^{30} -1.84386i q^{31} +(-4.87682 - 2.86646i) q^{32} +(1.79627 + 6.10926i) q^{33} +(1.02053 - 9.56643i) q^{34} -2.89114 q^{35} +(-1.34177 - 0.289571i) q^{36} -4.38660 q^{37} +(-8.49526 - 0.906256i) q^{38} -1.91998 q^{39} +(-3.68027 - 1.21481i) q^{40} +1.45663i q^{41} +(-0.607725 + 5.69683i) q^{42} +2.67659 q^{43} +(6.61538 - 0.486533i) q^{44} -0.940430 q^{45} +(0.153554 - 1.43942i) q^{46} +6.96770i q^{47} +(-3.16732 + 6.99639i) q^{48} -2.54799 q^{49} +(4.39094 + 0.468416i) q^{50} -13.0614 q^{51} +(-0.421910 + 1.95499i) q^{52} +2.57732 q^{53} +(0.666392 - 6.24678i) q^{54} +(4.35997 - 1.28194i) q^{55} +(5.66716 + 1.87066i) q^{56} +11.5989i q^{57} +(-0.284116 + 2.66331i) q^{58} +10.9352i q^{59} +(-1.10996 + 5.14321i) q^{60} +4.69168i q^{61} +(-0.276605 + 2.59290i) q^{62} +1.44815 q^{63} +(6.42795 + 4.76251i) q^{64} +1.37022i q^{65} +(-1.60950 - 8.86052i) q^{66} -13.5610i q^{67} +(-2.87020 + 13.2995i) q^{68} -1.96529 q^{69} +(4.06563 + 0.433712i) q^{70} +1.86586i q^{71} +(1.84341 + 0.608489i) q^{72} +0.383156i q^{73} +(6.16859 + 0.658052i) q^{74} -5.99511i q^{75} +(11.8104 + 2.54882i) q^{76} +(-6.71381 + 1.97402i) q^{77} +(2.69995 + 0.288024i) q^{78} -7.48644 q^{79} +(4.99308 + 2.26041i) q^{80} -10.5879 q^{81} +(0.218514 - 2.04836i) q^{82} -1.39705 q^{83} +(1.70921 - 7.91991i) q^{84} +9.32146i q^{85} +(-3.76391 - 0.401526i) q^{86} +3.63631 q^{87} +(-9.37577 - 0.308221i) q^{88} +6.72129 q^{89} +(1.32247 + 0.141078i) q^{90} -2.10998i q^{91} +(-0.431867 + 2.00113i) q^{92} +3.54018 q^{93} +(1.04525 - 9.79822i) q^{94} +8.27772 q^{95} +(5.50355 - 9.36342i) q^{96} +17.6361 q^{97} +(3.58308 + 0.382235i) q^{98} +(-2.18387 + 0.642109i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9}+O(q^{10}) $ 64 * q + 6 * q^4 + 12 * q^5 - 104 * q^9	$ 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9} - 8 q^{12} - 34 q^{14} + 26 q^{16} + 14 q^{20} - 8 q^{22} + 76 q^{25} + 2 q^{26} - 16 q^{33} + 32 q^{34} - 24 q^{36} - 32 q^{37} - 30 q^{38} + 54 q^{42} + 10 q^{44} + 12 q^{45} + 34 q^{48} - 36 q^{49} - 32 q^{53} - 36 q^{56} + 62 q^{58} + 4 q^{60} - 18 q^{64} - 30 q^{66} - 24 q^{69} - 30 q^{70} + 88 q^{77} - 10 q^{78} - 46 q^{80} + 64 q^{81} - 46 q^{82} + 98 q^{86} + 16 q^{88} + 24 q^{89} + 84 q^{92} + 8 q^{93} - 88 q^{97}+O(q^{100}) $ 64 * q + 6 * q^4 + 12 * q^5 - 104 * q^9 - 8 * q^12 - 34 * q^14 + 26 * q^16 + 14 * q^20 - 8 * q^22 + 76 * q^25 + 2 * q^26 - 16 * q^33 + 32 * q^34 - 24 * q^36 - 32 * q^37 - 30 * q^38 + 54 * q^42 + 10 * q^44 + 12 * q^45 + 34 * q^48 - 36 * q^49 - 32 * q^53 - 36 * q^56 + 62 * q^58 + 4 * q^60 - 18 * q^64 - 30 * q^66 - 24 * q^69 - 30 * q^70 + 88 * q^77 - 10 * q^78 - 46 * q^80 + 64 * q^81 - 46 * q^82 + 98 * q^86 + 16 * q^88 + 24 * q^89 + 84 * q^92 + 8 * q^93 - 88 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−1.40623	−	0.150014i	−0.994358	−	0.106076i
$2$	−1.40623	−	0.150014i	−0.994358	−	0.106076i
$3$			1.91998i			1.10850i	0.832349	+	0.554251i	$0.186995\pi$
$3$			1.91998i			1.10850i	−0.832349	+	0.554251i	$0.813005\pi$
$4$	1.95499	+	0.421910i	0.977496	+	0.210955i
$5$	1.37022			0.612783			0.306392	−	0.951906i	$-0.400878\pi$
$5$	1.37022			0.612783			0.306392	+	0.951906i	$0.400878\pi$
$6$	0.288024	−	2.69995i	0.117585	−	1.10225i
$7$	−2.10998			−0.797497			−0.398748	−	0.917060i	$-0.630555\pi$
$7$	−2.10998			−0.797497			−0.398748	+	0.917060i	$0.630555\pi$
$8$	−2.68588	−	0.886580i	−0.949604	−	0.313454i
$9$	−0.686333			−0.228778
$10$	−1.92686	−	0.205553i	−0.609326	−	0.0650016i
$11$	3.18194	−	0.935566i	0.959390	−	0.282084i
$11$	3.18194	−	0.935566i	0.959390	−	0.282084i
$12$	−0.810060	+	3.75355i	−0.233844	+	1.08356i
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	2.96712	+	0.316526i	0.792997	+	0.0845952i
$15$			2.63081i			0.679272i
$16$	3.64398	+	1.64966i	0.910996	+	0.412415i
$17$			6.80287i			1.64994i	0.565178	+	0.824969i	$0.308807\pi$
$17$			6.80287i			1.64994i	−0.565178	+	0.824969i	$0.691193\pi$
$18$	0.965145	+	0.102960i	0.227487	+	0.0242678i
$19$	6.04114			1.38593			0.692966	−	0.720970i	$-0.256304\pi$
$19$	6.04114			1.38593			0.692966	+	0.720970i	$0.256304\pi$
$20$	2.67878	+	0.578111i	0.598993	+	0.129270i
$21$		−	4.05112i		−	0.884027i
$22$	−4.61490	+	0.838290i	−0.983899	+	0.178724i
$23$			1.02360i			0.213435i	0.994289	+	0.106718i	$0.0340341\pi$
$23$			1.02360i			0.213435i	−0.994289	+	0.106718i	$0.965966\pi$
$24$	1.70222	−	5.15685i	0.347464	−	1.05264i
$25$	−3.12248			−0.624497
$26$	0.150014	−	1.40623i	0.0294202	−	0.275785i
$27$			4.44220i			0.854902i
$28$	−4.12499	−	0.890220i	−0.779550	−	0.168236i
$29$		−	1.89393i		−	0.351694i	−0.984418	−	0.175847i	$-0.943734\pi$
$29$		−	1.89393i		−	0.351694i	0.984418	−	0.175847i	$-0.0562664\pi$
$30$	0.394658	−	3.69953i	0.0720544	−	0.675439i
$31$		−	1.84386i		−	0.331167i	−0.986196	−	0.165583i	$-0.947049\pi$
$31$		−	1.84386i		−	0.331167i	0.986196	−	0.165583i	$-0.0529507\pi$
$32$	−4.87682	−	2.86646i	−0.862109	−	0.506723i
$33$	1.79627	+	6.10926i	0.312690	+	1.06349i
$34$	1.02053	−	9.56643i	0.175019	−	1.64063i
$35$	−2.89114			−0.488693
$36$	−1.34177	−	0.289571i	−0.223629	−	0.0482618i
$37$	−4.38660			−0.721153			−0.360577	−	0.932730i	$-0.617420\pi$
$37$	−4.38660			−0.721153			−0.360577	+	0.932730i	$0.617420\pi$
$38$	−8.49526	−	0.906256i	−1.37811	−	0.147014i
$39$	−1.91998			−0.307443
$40$	−3.68027	−	1.21481i	−0.581901	−	0.192079i
$41$			1.45663i			0.227487i	0.993510	+	0.113743i	$0.0362841\pi$
$41$			1.45663i			0.227487i	−0.993510	+	0.113743i	$0.963716\pi$
$42$	−0.607725	+	5.69683i	−0.0937740	+	0.879039i
$43$	2.67659			0.408176			0.204088	−	0.978953i	$-0.434577\pi$
$43$	2.67659			0.408176			0.204088	+	0.978953i	$0.434577\pi$
$44$	6.61538	−	0.486533i	0.997306	−	0.0733476i
$45$	−0.940430			−0.140191
$46$	0.153554	−	1.43942i	0.0226403	−	0.212231i
$47$			6.96770i			1.01634i	0.861256	+	0.508172i	$0.169678\pi$
$47$			6.96770i			1.01634i	−0.861256	+	0.508172i	$0.830322\pi$
$48$	−3.16732	+	6.99639i	−0.457163	+	1.00984i
$49$	−2.54799			−0.363999
$50$	4.39094	+	0.468416i	0.620973	+	0.0662441i
$51$	−13.0614			−1.82896
$52$	−0.421910	+	1.95499i	−0.0585084	+	0.271109i
$53$	2.57732			0.354022			0.177011	−	0.984209i	$-0.443357\pi$
$53$	2.57732			0.354022			0.177011	+	0.984209i	$0.443357\pi$
$54$	0.666392	−	6.24678i	0.0906845	−	0.850079i
$55$	4.35997	−	1.28194i	0.587898	−	0.172856i
$56$	5.66716	+	1.87066i	0.757306	+	0.249978i
$57$			11.5989i			1.53631i
$58$	−0.284116	+	2.66331i	−0.0373063	+	0.349710i
$59$			10.9352i			1.42364i	0.702361	+	0.711821i	$0.252129\pi$
$59$			10.9352i			1.42364i	−0.702361	+	0.711821i	$0.747871\pi$
$60$	−1.10996	+	5.14321i	−0.143296	+	0.663985i
$61$			4.69168i			0.600708i	0.953828	+	0.300354i	$0.0971047\pi$
$61$			4.69168i			0.600708i	−0.953828	+	0.300354i	$0.902895\pi$
$62$	−0.276605	+	2.59290i	−0.0351288	+	0.329298i
$63$	1.44815			0.182449
$64$	6.42795	+	4.76251i	0.803494	+	0.595313i
$65$			1.37022i			0.169955i
$66$	−1.60950	−	8.86052i	−0.198116	−	1.09065i
$67$		−	13.5610i		−	1.65673i	−0.560186	−	0.828367i	$-0.689270\pi$
$67$		−	13.5610i		−	1.65673i	0.560186	−	0.828367i	$-0.310730\pi$
$68$	−2.87020	+	13.2995i	−0.348062	+	1.61281i
$69$	−1.96529			−0.236594
$70$	4.06563	+	0.433712i	0.485935	+	0.0518385i
$71$			1.86586i			0.221436i	0.993852	+	0.110718i	$0.0353151\pi$
$71$			1.86586i			0.221436i	−0.993852	+	0.110718i	$0.964685\pi$
$72$	1.84341	+	0.608489i	0.217248	+	0.0717111i
$73$			0.383156i			0.0448450i	0.999749	+	0.0224225i	$0.00713790\pi$
$73$			0.383156i			0.0448450i	−0.999749	+	0.0224225i	$0.992862\pi$
$74$	6.16859	+	0.658052i	0.717084	+	0.0764970i
$75$		−	5.99511i		−	0.692256i
$76$	11.8104	+	2.54882i	1.35474	+	0.292369i
$77$	−6.71381	+	1.97402i	−0.765110	+	0.224961i
$78$	2.69995	+	0.288024i	0.305709	+	0.0326123i
$79$	−7.48644			−0.842291			−0.421145	−	0.906993i	$-0.638372\pi$
$79$	−7.48644			−0.842291			−0.421145	+	0.906993i	$0.638372\pi$
$80$	4.99308	+	2.26041i	0.558243	+	0.252721i
$81$	−10.5879			−1.17644
$82$	0.218514	−	2.04836i	0.0241309	−	0.226203i
$83$	−1.39705			−0.153346			−0.0766729	−	0.997056i	$-0.524430\pi$
$83$	−1.39705			−0.153346			−0.0766729	+	0.997056i	$0.524430\pi$
$84$	1.70921	−	7.91991i	0.186490	−	0.864133i
$85$			9.32146i			1.01105i
$86$	−3.76391	−	0.401526i	−0.405873	−	0.0432977i
$87$	3.63631			0.389854
$88$	−9.37577	−	0.308221i	−0.999460	−	0.0328565i
$89$	6.72129			0.712456			0.356228	−	0.934399i	$-0.384063\pi$
$89$	6.72129			0.712456			0.356228	+	0.934399i	$0.384063\pi$
$90$	1.32247	+	0.141078i	0.139400	+	0.0148709i
$91$		−	2.10998i		−	0.221186i
$92$	−0.431867	+	2.00113i	−0.0450252	+	0.208632i
$93$	3.54018			0.367099
$94$	1.04525	−	9.79822i	0.107810	−	1.01061i
$95$	8.27772			0.849276
$96$	5.50355	−	9.36342i	0.561704	−	0.955650i
$97$	17.6361			1.79067			0.895335	−	0.445393i	$-0.146936\pi$
$97$	17.6361			1.79067			0.895335	+	0.445393i	$0.146936\pi$
$98$	3.58308	+	0.382235i	0.361946	+	0.0386116i
$99$	−2.18387	+	0.642109i	−0.219487	+	0.0645344i
$100$	−6.10443	−	1.31741i	−0.610443	−	0.131741i
$101$			14.6720i			1.45992i	0.683492	+	0.729958i	$0.260461\pi$
$101$			14.6720i			1.45992i	−0.683492	+	0.729958i	$0.739539\pi$
$102$	18.3674	+	1.95939i	1.81864	+	0.194009i
$103$		−	18.5991i		−	1.83262i	−0.400464	−	0.916312i	$-0.631151\pi$
$103$		−	18.5991i		−	1.83262i	0.400464	−	0.916312i	$-0.368849\pi$
$104$	0.886580	−	2.68588i	0.0869364	−	0.263373i
$105$		−	5.55095i		−	0.541717i
$106$	−3.62432	−	0.386634i	−0.352025	−	0.0375533i
$107$	3.10940			0.300597			0.150299	−	0.988641i	$-0.451977\pi$
$107$	3.10940			0.300597			0.150299	+	0.988641i	$0.451977\pi$
$108$	−1.87421	+	8.68446i	−0.180346	+	0.835663i
$109$		−	16.6913i		−	1.59874i	−0.600838	−	0.799371i	$-0.705166\pi$
$109$		−	16.6913i		−	1.59874i	0.600838	−	0.799371i	$-0.294834\pi$
$110$	−6.32345	+	1.14865i	−0.602917	+	0.109519i
$111$		−	8.42220i		−	0.799400i
$112$	−7.68872	−	3.48075i	−0.726516	−	0.328900i
$113$	−2.02981			−0.190948			−0.0954740	−	0.995432i	$-0.530437\pi$
$113$	−2.02981			−0.190948			−0.0954740	+	0.995432i	$0.530437\pi$
$114$	1.73999	−	16.3107i	0.162965	−	1.52764i
$115$			1.40256i			0.130790i
$116$	0.799068	−	3.70262i	0.0741916	−	0.343779i
$117$		−	0.686333i		−	0.0634515i
$118$	1.64043	−	15.3775i	0.151014	−	1.41561i
$119$		−	14.3539i		−	1.31582i
$120$	2.33242	−	7.06605i	0.212920	−	0.645039i
$121$	9.24943	−	5.95382i	0.840858	−	0.541256i
$122$	0.703817	−	6.59760i	0.0637206	−	0.597318i
$123$	−2.79669			−0.252169
$124$	0.777942	−	3.60473i	0.0698613	−	0.323714i
$125$	−11.1296			−0.995464
$126$	−2.03643	−	0.217242i	−0.181420	−	0.0193535i
$127$	6.74262			0.598310			0.299155	−	0.954204i	$-0.403295\pi$
$127$	6.74262			0.598310			0.299155	+	0.954204i	$0.403295\pi$
$128$	−8.32476	−	7.66148i	−0.735812	−	0.677186i
$129$			5.13901i			0.452464i
$130$	0.205553	−	1.92686i	0.0180282	−	0.168997i
$131$	−14.6619			−1.28102			−0.640510	−	0.767950i	$-0.721277\pi$
$131$	−14.6619			−1.28102			−0.640510	+	0.767950i	$0.721277\pi$
$132$	0.934135	+	12.7014i	0.0813060	+	1.10552i
$133$	−12.7467			−1.10528
$134$	−2.03433	+	19.0699i	−0.175740	+	1.64739i
$135$			6.08681i			0.523870i
$136$	6.03129	−	18.2717i	0.517179	−	1.56679i
$137$	16.6808			1.42514			0.712571	−	0.701600i	$-0.247531\pi$
$137$	16.6808			1.42514			0.712571	+	0.701600i	$0.247531\pi$
$138$	2.76366	+	0.294822i	0.235259	+	0.0250969i
$139$	8.58671			0.728316			0.364158	−	0.931337i	$-0.381357\pi$
$139$	8.58671			0.728316			0.364158	+	0.931337i	$0.381357\pi$
$140$	−5.65216	−	1.21980i	−0.477695	−	0.103092i
$141$	−13.3779			−1.12662
$142$	0.279904	−	2.62383i	0.0234891	−	0.220187i
$143$	0.935566	+	3.18194i	0.0782359	+	0.266087i
$144$	−2.50099	−	1.13222i	−0.208415	−	0.0943513i
$145$		−	2.59511i		−	0.215512i
$146$	0.0574787	−	0.538807i	0.00475697	−	0.0445920i
$147$		−	4.89210i		−	0.403494i
$148$	−8.57577	−	1.85075i	−0.704924	−	0.152131i
$149$		−	13.3064i		−	1.09011i	−0.838402	−	0.545053i	$-0.816510\pi$
$149$		−	13.3064i		−	1.09011i	0.838402	−	0.545053i	$-0.183490\pi$
$150$	−0.899351	+	8.43054i	−0.0734317	+	0.688350i
$151$	−7.41237			−0.603210			−0.301605	−	0.953433i	$-0.597522\pi$
$151$	−7.41237			−0.603210			−0.301605	+	0.953433i	$0.597522\pi$
$152$	−16.2258	−	5.35596i	−1.31609	−	0.434425i
$153$		−	4.66903i		−	0.377469i
$154$	9.73733	−	1.76877i	0.784656	−	0.142532i
$155$		−	2.52650i		−	0.202934i
$156$	−3.75355	−	0.810060i	−0.300524	−	0.0648567i
$157$	−10.2894			−0.821181			−0.410590	−	0.911820i	$-0.634677\pi$
$157$	−10.2894			−0.821181			−0.410590	+	0.911820i	$0.634677\pi$
$158$	10.5277	+	1.12307i	0.837539	+	0.0893468i
$159$			4.94841i			0.392435i
$160$	−6.68235	−	3.92769i	−0.528286	−	0.310511i
$161$		−	2.15977i		−	0.170214i
$162$	14.8891	+	1.58834i	1.16980	+	0.124792i
$163$		−	0.907429i		−	0.0710753i	−0.999368	−	0.0355377i	$-0.988686\pi$
$163$		−	0.907429i		−	0.0710753i	0.999368	−	0.0355377i	$-0.0113144\pi$
$164$	−0.614564	+	2.84769i	−0.0479894	+	0.222367i
$165$	2.46129	+	8.37106i	0.191611	+	0.651686i
$166$	1.96458	+	0.209577i	0.152481	+	0.0162663i
$167$	7.99754			0.618868			0.309434	−	0.950921i	$-0.399860\pi$
$167$	7.99754			0.618868			0.309434	+	0.950921i	$0.399860\pi$
$168$	−3.59164	+	10.8808i	−0.277101	+	0.839475i
$169$	−1.00000			−0.0769231
$170$	1.39835	−	13.1082i	0.107248	−	1.00535i
$171$	−4.14623			−0.317070
$172$	5.23271	+	1.12928i	0.398991	+	0.0861068i
$173$		−	10.6713i		−	0.811322i	−0.914024	−	0.405661i	$-0.867041\pi$
$173$		−	10.6713i		−	0.811322i	0.914024	−	0.405661i	$-0.132959\pi$
$174$	−5.11351	−	0.545498i	−0.387654	−	0.0413541i
$175$	6.58837			0.498034
$176$	13.1383	+	1.83993i	0.990336	+	0.138690i
$177$	−20.9954			−1.57811
$178$	−9.45171	−	1.00829i	−0.708436	−	0.0755744i
$179$			22.8203i			1.70567i	0.522180	+	0.852835i	$0.325119\pi$
$179$			22.8203i			1.70567i	−0.522180	+	0.852835i	$0.674881\pi$
$180$	−1.83853	−	0.396777i	−0.137036	−	0.0295740i
$181$	23.7389			1.76450			0.882248	−	0.470784i	$-0.156029\pi$
$181$	23.7389			1.76450			0.882248	+	0.470784i	$0.156029\pi$
$182$	−0.316526	+	2.96712i	−0.0234625	+	0.219938i
$183$	−9.00794			−0.665886
$184$	0.907503	−	2.74927i	0.0669020	−	0.202679i
$185$	−6.01063			−0.441911
$186$	−4.97832	−	0.531076i	−0.365028	−	0.0389404i
$187$	6.36453	+	21.6463i	0.465420	+	1.58293i
$188$	−2.93974	+	13.6218i	−0.214403	+	0.993471i
$189$		−	9.37294i		−	0.681781i
$190$	−11.6404	−	1.24177i	−0.844484	−	0.0900878i
$191$			3.86427i			0.279609i	0.990179	+	0.139804i	$0.0446474\pi$
$191$			3.86427i			0.279609i	−0.990179	+	0.139804i	$0.955353\pi$
$192$	−9.14393	+	12.3416i	−0.659906	+	0.890675i
$193$		−	24.6519i		−	1.77448i	−0.461306	−	0.887241i	$-0.652619\pi$
$193$		−	24.6519i		−	1.77448i	0.461306	−	0.887241i	$-0.347381\pi$
$194$	−24.8004	−	2.64566i	−1.78057	−	0.189947i
$195$	−2.63081			−0.188396
$196$	−4.98131	−	1.07502i	−0.355808	−	0.0767874i
$197$		−	10.4132i		−	0.741907i	−0.928652	−	0.370953i	$-0.879031\pi$
$197$		−	10.4132i		−	0.741907i	0.928652	−	0.370953i	$-0.120969\pi$
$198$	3.16735	−	0.575346i	0.225094	−	0.0408880i
$199$		−	17.9465i		−	1.27219i	−0.771609	−	0.636097i	$-0.780548\pi$
$199$		−	17.9465i		−	1.27219i	0.771609	−	0.636097i	$-0.219452\pi$
$200$	8.38663	+	2.76833i	0.593024	+	0.195751i
$201$	26.0368			1.83649
$202$	2.20100	−	20.6322i	0.154862	−	1.45168i
$203$			3.99615i			0.280475i
$204$	−25.5349	−	5.51073i	−1.78780	−	0.385828i
$205$			1.99590i			0.139400i
$206$	−2.79013	+	26.1547i	−0.194397	+	1.82229i
$207$		−	0.702530i		−	0.0488292i
$208$	−1.64966	+	3.64398i	−0.114383	+	0.252665i
$209$	19.2225	−	5.65188i	1.32965	−	0.390949i
$210$	−0.832720	+	7.80593i	−0.0574631	+	0.538660i
$211$	21.2278			1.46138			0.730691	−	0.682708i	$-0.239198\pi$
$211$	21.2278			1.46138			0.730691	+	0.682708i	$0.239198\pi$
$212$	5.03864	+	1.08740i	0.346055	+	0.0746828i
$213$	−3.58241			−0.245463
$214$	−4.37255	−	0.466454i	−0.298901	−	0.0318861i
$215$	3.66753			0.250124
$216$	3.93837	−	11.9312i	0.267972	−	0.811818i
$217$			3.89050i			0.264104i
$218$	−2.50394	+	23.4720i	−0.169588	+	1.58972i
$219$	−0.735652			−0.0497108
$220$	9.06456	−	0.666659i	0.611133	−	0.0449462i
$221$	−6.80287			−0.457610
$222$	−1.26345	+	11.8436i	−0.0847971	+	0.794890i
$223$		−	2.44294i		−	0.163592i	−0.996649	−	0.0817958i	$-0.973934\pi$
$223$		−	2.44294i		−	0.163592i	0.996649	−	0.0817958i	$-0.0260655\pi$
$224$	10.2900	+	6.04816i	0.687529	+	0.404110i
$225$	2.14306			0.142871
$226$	2.85438	+	0.304499i	0.189871	+	0.0202550i
$227$	14.8121			0.983113			0.491556	−	0.870846i	$-0.336428\pi$
$227$	14.8121			0.983113			0.491556	+	0.870846i	$0.336428\pi$
$228$	−4.89368	+	22.6757i	−0.324092	+	1.50174i
$229$	−7.66249			−0.506352			−0.253176	−	0.967420i	$-0.581475\pi$
$229$	−7.66249			−0.506352			−0.253176	+	0.967420i	$0.581475\pi$
$230$	0.210404	−	1.97233i	0.0138736	−	0.130052i
$231$	−3.79009	−	12.8904i	−0.249370	−	0.848126i
$232$	−1.67912	+	5.08688i	−0.110240	+	0.333970i
$233$		−	15.0655i		−	0.986977i	−0.869752	−	0.493488i	$-0.835722\pi$
$233$		−	15.0655i		−	0.986977i	0.869752	−	0.493488i	$-0.164278\pi$
$234$	−0.102960	+	0.965145i	−0.00673068	+	0.0630935i
$235$			9.54731i			0.622798i
$236$	−4.61367	+	21.3782i	−0.300324	+	1.39160i
$237$		−	14.3738i		−	0.933681i
$238$	−2.15329	+	20.1849i	−0.139577	+	1.30840i
$239$	14.8991			0.963745			0.481872	−	0.876241i	$-0.339957\pi$
$239$	14.8991			0.963745			0.481872	+	0.876241i	$0.339957\pi$
$240$	−4.33994	+	9.58662i	−0.280142	+	0.618814i
$241$			8.49104i			0.546956i	0.961878	+	0.273478i	$0.0881740\pi$
$241$			8.49104i			0.546956i	−0.961878	+	0.273478i	$0.911826\pi$
$242$	−13.9000	+	6.98492i	−0.893528	+	0.449008i
$243$		−	7.00207i		−	0.449183i
$244$	−1.97946	+	9.17219i	−0.126722	+	0.587189i
$245$	−3.49133			−0.223053
$246$	3.93281	+	0.419543i	0.250747	+	0.0267491i
$247$			6.04114i			0.384388i
$248$	−1.63473	+	4.95239i	−0.103805	+	0.314477i
$249$		−	2.68231i		−	0.169984i
$250$	15.6509	+	1.66960i	0.989848	+	0.105595i
$251$		−	19.2323i		−	1.21393i	−0.794728	−	0.606966i	$-0.792387\pi$
$251$		−	19.2323i		−	1.21393i	0.794728	−	0.606966i	$-0.207613\pi$
$252$	2.83111	+	0.610987i	0.178343	+	0.0384886i
$253$	0.957645	+	3.25703i	0.0602066	+	0.204768i
$254$	−9.48170	−	1.01149i	−0.594935	−	0.0634663i
$255$	−17.8970			−1.12076
$256$	10.5572	+	12.0227i	0.659828	+	0.751417i
$257$	11.5633			0.721299			0.360649	−	0.932701i	$-0.382555\pi$
$257$	11.5633			0.721299			0.360649	+	0.932701i	$0.382555\pi$
$258$	0.770923	−	7.22665i	0.0479956	−	0.449912i
$259$	9.25563			0.575117
$260$	−0.578111	+	2.67878i	−0.0358529	+	0.166131i
$261$			1.29987i			0.0804597i
$262$	20.6181	+	2.19950i	1.27379	+	0.135885i
$263$	13.2998			0.820101			0.410051	−	0.912063i	$-0.365511\pi$
$263$	13.2998			0.820101			0.410051	+	0.912063i	$0.365511\pi$
$264$	0.591779	−	18.0013i	0.0364215	−	1.10790i
$265$	3.53151			0.216939
$266$	17.9248	+	1.91218i	1.09904	+	0.117243i
$267$			12.9048i			0.789759i
$268$	5.72150	−	26.5115i	0.349496	−	1.61945i
$269$	3.42765			0.208987			0.104494	−	0.994526i	$-0.466678\pi$
$269$	3.42765			0.208987			0.104494	+	0.994526i	$0.466678\pi$
$270$	0.913108	−	8.55949i	0.0555700	−	0.520914i
$271$	−16.3143			−0.991024			−0.495512	−	0.868601i	$-0.665020\pi$
$271$	−16.3143			−0.991024			−0.495512	+	0.868601i	$0.665020\pi$
$272$	−11.2224	+	24.7895i	−0.680459	+	1.50309i
$273$	4.05112			0.245185
$274$	−23.4572	−	2.50236i	−1.41710	−	0.151173i
$275$	−9.93554	+	2.92129i	−0.599136	+	0.176160i
$276$	−3.84213	−	0.829177i	−0.231269	−	0.0499106i
$277$			31.5948i			1.89835i	0.314755	+	0.949173i	$0.398078\pi$
$277$			31.5948i			1.89835i	−0.314755	+	0.949173i	$0.601922\pi$
$278$	−12.0749	−	1.28813i	−0.724206	−	0.0772568i
$279$			1.26550i			0.0757636i
$280$	7.76528	+	2.56323i	0.464064	+	0.153182i
$281$		−	12.4376i		−	0.741963i	−0.928640	−	0.370981i	$-0.879021\pi$
$281$		−	12.4376i		−	0.741963i	0.928640	−	0.370981i	$-0.120979\pi$
$282$	18.8124	+	2.00687i	1.12026	+	0.119507i
$283$	−23.6943			−1.40848			−0.704240	−	0.709962i	$-0.748712\pi$
$283$	−23.6943			−1.40848			−0.704240	+	0.709962i	$0.748712\pi$
$284$	−0.787223	+	3.64773i	−0.0467131	+	0.216453i
$285$			15.8931i			0.941425i
$286$	−0.838290	−	4.61490i	−0.0495691	−	0.272885i
$287$		−	3.07345i		−	0.181420i
$288$	3.34712	+	1.96734i	0.197231	+	0.115927i
$289$	−29.2790			−1.72229
$290$	−0.389303	+	3.64933i	−0.0228607	+	0.214296i
$291$			33.8609i			1.98496i
$292$	−0.161657	+	0.749066i	−0.00946027	+	0.0438358i
$293$		−	23.0404i		−	1.34603i	−0.739627	−	0.673017i	$-0.764998\pi$
$293$		−	23.0404i		−	1.34603i	0.739627	−	0.673017i	$-0.235002\pi$
$294$	−0.733884	+	6.87945i	−0.0428010	+	0.401218i
$295$			14.9837i			0.872384i
$296$	11.7819	+	3.88908i	0.684810	+	0.226048i
$297$	4.15597	+	14.1348i	0.241154	+	0.820184i
$298$	−1.99615	+	18.7120i	−0.115634	+	1.08396i
$299$	−1.02360			−0.0591963
$300$	2.52940	−	11.7204i	0.146035	−	0.676677i
$301$	−5.64755			−0.325519
$302$	10.4235	+	1.11196i	0.599807	+	0.0639861i
$303$	−28.1699			−1.61832
$304$	22.0138	+	9.96583i	1.26258	+	0.571579i
$305$			6.42865i			0.368104i
$306$	−0.700420	+	6.56575i	−0.0400403	+	0.375339i
$307$	−18.6198			−1.06269			−0.531344	−	0.847156i	$-0.678313\pi$
$307$	−18.6198			−1.06269			−0.531344	+	0.847156i	$0.678313\pi$
$308$	−13.9583	+	1.02657i	−0.795348	+	0.0584945i
$309$	35.7100			2.03147
$310$	−0.379011	+	3.55285i	−0.0215264	+	0.201789i
$311$		−	32.8262i		−	1.86141i	−0.365777	−	0.930703i	$-0.619197\pi$
$311$		−	32.8262i		−	1.86141i	0.365777	−	0.930703i	$-0.380803\pi$
$312$	5.15685	+	1.70222i	0.291949	+	0.0963692i
$313$	−13.3697			−0.755698			−0.377849	−	0.925867i	$-0.623336\pi$
$313$	−13.3697			−0.755698			−0.377849	+	0.925867i	$0.623336\pi$
$314$	14.4693	+	1.54355i	0.816548	+	0.0871075i
$315$	1.98429			0.111802
$316$	−14.6359	−	3.15860i	−0.823336	−	0.177685i
$317$	16.6820			0.936957			0.468478	−	0.883475i	$-0.344802\pi$
$317$	16.6820			0.936957			0.468478	+	0.883475i	$0.344802\pi$
$318$	0.742331	−	6.95863i	0.0416279	−	0.390221i
$319$	−1.77190	−	6.02636i	−0.0992071	−	0.337412i
$320$	8.80774	+	6.52570i	0.492368	+	0.364798i
$321$			5.96999i			0.333213i
$322$	−0.323996	+	3.03715i	−0.0180556	+	0.169254i
$323$			41.0971i			2.28670i
$324$	−20.6993	−	4.46716i	−1.14996	−	0.248175i
$325$		−	3.12248i		−	0.173204i
$326$	−0.136127	+	1.27606i	−0.00753938	+	0.0706743i
$327$	32.0471			1.77221
$328$	1.29142	−	3.91233i	0.0713065	−	0.216022i
$329$		−	14.7017i		−	0.810530i
$330$	−2.20538	−	12.1409i	−0.121402	−	0.668335i
$331$			3.90114i			0.214426i	0.994236	+	0.107213i	$0.0341927\pi$
$331$			3.90114i			0.214426i	−0.994236	+	0.107213i	$0.965807\pi$
$332$	−2.73122	−	0.589428i	−0.149895	−	0.0323491i
$333$	3.01067			0.164984
$334$	−11.2464	−	1.19974i	−0.615376	−	0.0656470i
$335$		−	18.5816i		−	1.01522i
$336$	6.68297	−	14.7622i	0.364586	−	0.805345i
$337$			3.24032i			0.176512i	0.996098	+	0.0882558i	$0.0281293\pi$
$337$			3.24032i			0.176512i	−0.996098	+	0.0882558i	$0.971871\pi$
$338$	1.40623	+	0.150014i	0.0764891	+	0.00815969i
$339$		−	3.89719i		−	0.211666i
$340$	−3.93281	+	18.2234i	−0.213287	+	0.988301i
$341$	−1.72505	−	5.86704i	−0.0934168	−	0.317718i
$342$	5.83057	+	0.621993i	0.315281	+	0.0336335i
$343$	20.1461			1.08778
$344$	−7.18901	−	2.37301i	−0.387606	−	0.127944i
$345$	−2.69289			−0.144981
$346$	−1.60084	+	15.0063i	−0.0860617	+	0.806744i
$347$	−28.2415			−1.51608			−0.758041	−	0.652207i	$-0.773843\pi$
$347$	−28.2415			−1.51608			−0.758041	+	0.652207i	$0.773843\pi$
$348$	7.10896	+	1.53420i	0.381080	+	0.0822415i
$349$			11.9537i			0.639867i	0.947440	+	0.319934i	$0.103661\pi$
$349$			11.9537i			0.639867i	−0.947440	+	0.319934i	$0.896339\pi$
$350$	−9.26479	−	0.988348i	−0.495224	−	0.0528294i
$351$	−4.44220			−0.237107
$352$	−18.1995	−	4.55830i	−0.970037	−	0.242958i
$353$	−13.1876			−0.701904			−0.350952	−	0.936394i	$-0.614142\pi$
$353$	−13.1876			−0.701904			−0.350952	+	0.936394i	$0.614142\pi$
$354$	29.5245	+	3.14960i	1.56921	+	0.167400i
$355$			2.55664i			0.135692i
$356$	13.1401	+	2.83578i	0.696422	+	0.150296i
$357$	27.5592			1.45859
$358$	3.42337	−	32.0907i	0.180931	−	1.69605i
$359$	−14.1979			−0.749337			−0.374669	−	0.927159i	$-0.622244\pi$
$359$	−14.1979			−0.749337			−0.374669	+	0.927159i	$0.622244\pi$
$360$	2.52589	+	0.833767i	0.133126	+	0.0439434i
$361$	17.4954			0.920808
$362$	−33.3824	−	3.56116i	−1.75454	−	0.187171i
$363$	11.4312	+	17.7588i	0.599984	+	0.932093i
$364$	0.890220	−	4.12499i	0.0466602	−	0.216208i
$365$			0.525010i			0.0274803i
$366$	12.6673	+	1.35132i	0.662129	+	0.0706345i
$367$			20.8904i			1.09047i	0.838284	+	0.545234i	$0.183559\pi$
$367$			20.8904i			1.09047i	−0.838284	+	0.545234i	$0.816441\pi$
$368$	−1.68859	+	3.72998i	−0.0880239	+	0.194439i
$369$		−	0.999729i		−	0.0520438i
$370$	8.45236	+	0.901679i	0.439417	+	0.0468761i
$371$	−5.43809			−0.282332
$372$	6.92102	+	1.49364i	0.358838	+	0.0774414i
$373$		−	26.8728i		−	1.39142i	−0.718322	−	0.695711i	$-0.755090\pi$
$373$		−	26.8728i		−	1.39142i	0.718322	−	0.695711i	$-0.244910\pi$
$374$	−5.70277	−	31.3945i	−0.294883	−	1.62337i
$375$		−	21.3687i		−	1.10347i
$376$	6.17742	−	18.7144i	0.318576	−	0.965123i
$377$	1.89393			0.0975424
$378$	−1.40607	+	13.1806i	−0.0723206	+	0.677935i
$379$		−	11.1090i		−	0.570632i	−0.958433	−	0.285316i	$-0.907901\pi$
$379$		−	11.1090i		−	0.570632i	0.958433	−	0.285316i	$-0.0920986\pi$
$380$	16.1829	+	3.49245i	0.830164	+	0.179159i
$381$			12.9457i			0.663228i
$382$	0.579695	−	5.43407i	0.0296598	−	0.278031i
$383$			10.2623i			0.524379i	0.965016	+	0.262190i	$0.0844446\pi$
$383$			10.2623i			0.524379i	−0.965016	+	0.262190i	$0.915555\pi$
$384$	14.7099	−	15.9834i	0.750662	−	0.815649i
$385$	−9.19944	+	2.70486i	−0.468847	+	0.137852i
$386$	−3.69813	+	34.6663i	−0.188230	+	1.76447i
$387$	−1.83703			−0.0933816
$388$	34.4783	+	7.44083i	1.75037	+	0.377751i
$389$	−0.437609			−0.0221877			−0.0110938	−	0.999938i	$-0.503531\pi$
$389$	−0.437609			−0.0221877			−0.0110938	+	0.999938i	$0.503531\pi$
$390$	3.69953	+	0.394658i	0.187333	+	0.0199843i
$391$	−6.96341			−0.352155
$392$	6.84362	+	2.25900i	0.345655	+	0.114097i
$393$		−	28.1507i		−	1.42001i
$394$	−1.56212	+	14.6433i	−0.0786984	+	0.737721i
$395$	−10.2581			−0.516142
$396$	−4.54035	+	0.333923i	−0.228161	+	0.0167803i
$397$	−28.6458			−1.43769			−0.718845	−	0.695171i	$-0.755329\pi$
$397$	−28.6458			−1.43769			−0.718845	+	0.695171i	$0.755329\pi$
$398$	−2.69223	+	25.2370i	−0.134949	+	1.26502i
$399$		−	24.4734i		−	1.22520i
$400$	−11.3783	−	5.15104i	−0.568914	−	0.257552i
$401$	−30.6330			−1.52974			−0.764870	−	0.644185i	$-0.777197\pi$
$401$	−30.6330			−1.52974			−0.764870	+	0.644185i	$0.777197\pi$
$402$	−36.6138	−	3.90588i	−1.82613	−	0.194808i
$403$	1.84386			0.0918492
$404$	−6.19025	+	28.6836i	−0.307977	+	1.42706i
$405$	−14.5079			−0.720902
$406$	0.599479	−	5.61952i	0.0297516	−	0.278892i
$407$	−13.9579	+	4.10396i	−0.691867	+	0.203426i
$408$	35.0814	+	11.5800i	1.73679	+	0.573294i
$409$			21.8056i			1.07822i	0.842236	+	0.539109i	$0.181239\pi$
$409$			21.8056i			1.07822i	−0.842236	+	0.539109i	$0.818761\pi$
$410$	0.299414	−	2.80671i	0.0147870	−	0.138613i
$411$			32.0269i			1.57977i
$412$	7.84715	−	36.3611i	0.386601	−	1.79138i
$413$		−	23.0730i		−	1.13535i
$414$	−0.105389	+	0.987922i	−0.00517960	+	0.0485537i
$415$	−1.91427			−0.0939678
$416$	2.86646	−	4.87682i	0.140540	−	0.239106i
$417$			16.4863i			0.807339i
$418$	−27.8792	+	5.06422i	−1.36362	+	0.247699i
$419$		−	18.6047i		−	0.908900i	−0.890772	−	0.454450i	$-0.849836\pi$
$419$		−	18.6047i		−	0.908900i	0.890772	−	0.454450i	$-0.150164\pi$
$420$	2.34200	−	10.8521i	0.114278	−	0.529526i
$421$	−9.03468			−0.440323			−0.220162	−	0.975463i	$-0.570658\pi$
$421$	−9.03468			−0.440323			−0.220162	+	0.975463i	$0.570658\pi$
$422$	−29.8513	−	3.18447i	−1.45314	−	0.155018i
$423$		−	4.78216i		−	0.232517i
$424$	−6.92239	−	2.28500i	−0.336181	−	0.110970i
$425$		−	21.2418i		−	1.03038i
$426$	5.03771	+	0.537412i	0.244078	+	0.0260377i
$427$		−	9.89933i		−	0.479062i
$428$	6.07885	+	1.31189i	0.293832	+	0.0634124i
$429$	−6.10926	+	1.79627i	−0.294958	+	0.0867247i
$430$	−5.15741	−	0.550181i	−0.248712	−	0.0265321i
$431$	−3.55362			−0.171172			−0.0855859	−	0.996331i	$-0.527276\pi$
$431$	−3.55362			−0.171172			−0.0855859	+	0.996331i	$0.527276\pi$
$432$	−7.32812	+	16.1873i	−0.352574	+	0.778812i
$433$	−3.16179			−0.151946			−0.0759730	−	0.997110i	$-0.524206\pi$
$433$	−3.16179			−0.151946			−0.0759730	+	0.997110i	$0.524206\pi$
$434$	0.583630	−	5.47096i	0.0280151	−	0.262614i
$435$	4.98257			0.238896
$436$	7.04224	−	32.6314i	0.337262	−	1.56276i
$437$			6.18371i			0.295807i
$438$	1.03450	+	0.110358i	0.0494303	+	0.00527312i
$439$	20.4729			0.977117			0.488559	−	0.872531i	$-0.337523\pi$
$439$	20.4729			0.977117			0.488559	+	0.872531i	$0.337523\pi$
$440$	−12.8469	−	0.422332i	−0.612452	−	0.0201339i
$441$	1.74877			0.0832749
$442$	9.56643	+	1.02053i	0.455028	+	0.0485414i
$443$			12.3547i			0.586990i	0.955961	+	0.293495i	$0.0948184\pi$
$443$			12.3547i			0.586990i	−0.955961	+	0.293495i	$0.905182\pi$
$444$	3.55341	−	16.4653i	0.168637	−	0.781410i
$445$	9.20968			0.436581
$446$	−0.366476	+	3.43535i	−0.0173531	+	0.162669i
$447$	25.5481			1.20838
$448$	−13.5628	−	10.0488i	−0.640784	−	0.474760i
$449$	9.75034			0.460147			0.230074	−	0.973173i	$-0.426103\pi$
$449$	9.75034			0.460147			0.230074	+	0.973173i	$0.426103\pi$
$450$	−3.01365	−	0.321489i	−0.142065	−	0.0151552i
$451$	1.36277	+	4.63489i	0.0641703	+	0.218248i
$452$	−3.96825	−	0.856395i	−0.186651	−	0.0402814i
$453$		−	14.2316i		−	0.668660i
$454$	−20.8293	−	2.22202i	−0.977566	−	0.104285i
$455$		−	2.89114i		−	0.135539i
$456$	10.2833	−	31.1533i	0.481562	−	1.45888i
$457$		−	11.3721i		−	0.531962i	−0.963978	−	0.265981i	$-0.914304\pi$
$457$		−	11.3721i		−	0.531962i	0.963978	−	0.265981i	$-0.0856959\pi$
$458$	10.7753	+	1.14948i	0.503495	+	0.0537117i
$459$	−30.2197			−1.41053
$460$	−0.591755	+	2.74200i	−0.0275907	+	0.127846i
$461$			3.35014i			0.156032i	0.996952	+	0.0780158i	$0.0248585\pi$
$461$			3.35014i			0.156032i	−0.996952	+	0.0780158i	$0.975142\pi$
$462$	3.39601	+	18.6955i	0.157997	+	0.869793i
$463$		−	22.8052i		−	1.05985i	−0.848046	−	0.529923i	$-0.822221\pi$
$463$		−	22.8052i		−	1.05985i	0.848046	−	0.529923i	$-0.177779\pi$
$464$	3.12434	−	6.90145i	0.145044	−	0.320392i
$465$	4.85084			0.224952
$466$	−2.26004	+	21.1857i	−0.104694	+	0.981408i
$467$			23.2393i			1.07538i	0.843141	+	0.537692i	$0.180704\pi$
$467$			23.2393i			1.07538i	−0.843141	+	0.537692i	$0.819296\pi$
$468$	0.289571	−	1.34177i	0.0133854	−	0.0620236i
$469$			28.6133i			1.32124i
$470$	1.43223	−	13.4258i	0.0660639	−	0.619284i
$471$		−	19.7554i		−	0.910281i
$472$	9.69494	−	29.3707i	0.446246	−	1.35190i
$473$	8.51674	−	2.50413i	0.391600	−	0.115140i
$474$	−2.15628	+	20.2130i	−0.0990411	+	0.928413i
$475$	−18.8634			−0.865510
$476$	6.05605	−	28.0617i	0.277579	−	1.28621i
$477$	−1.76890			−0.0809924
$478$	−20.9517	−	2.23508i	−0.958308	−	0.102230i
$479$	19.1239			0.873791			0.436896	−	0.899512i	$-0.356078\pi$
$479$	19.1239			0.873791			0.436896	+	0.899512i	$0.356078\pi$
$480$	7.54110	−	12.8300i	0.344203	−	0.585606i
$481$		−	4.38660i		−	0.200012i
$482$	1.27377	−	11.9404i	0.0580189	−	0.543870i
$483$	4.14673			0.188683
$484$	20.5945	−	7.73724i	0.936115	−	0.351693i
$485$	24.1654			1.09729
$486$	−1.05041	+	9.84655i	−0.0476475	+	0.446649i
$487$		−	27.6905i		−	1.25477i	−0.778707	−	0.627387i	$-0.784124\pi$
$487$		−	27.6905i		−	1.25477i	0.778707	−	0.627387i	$-0.215876\pi$
$488$	4.15955	−	12.6013i	0.188294	−	0.570434i
$489$	1.74225			0.0787872
$490$	4.90962	+	0.523748i	0.221794	+	0.0236605i
$491$	6.41203			0.289371			0.144685	−	0.989478i	$-0.453783\pi$
$491$	6.41203			0.289371			0.144685	+	0.989478i	$0.453783\pi$
$492$	−5.46751	−	1.17995i	−0.246495	−	0.0531964i
$493$	12.8842			0.580273
$494$	0.906256	−	8.49526i	0.0407744	−	0.382220i
$495$	−2.99239	+	0.879834i	−0.134498	+	0.0395456i
$496$	3.04174	−	6.71899i	0.136578	−	0.301692i
$497$		−	3.93691i		−	0.176595i
$498$	−0.402384	+	3.77195i	−0.0180312	+	0.169025i
$499$		−	33.7304i		−	1.50998i	−0.655735	−	0.754991i	$-0.727641\pi$
$499$		−	33.7304i		−	1.50998i	0.655735	−	0.754991i	$-0.272359\pi$
$500$	−21.7583	−	4.69570i	−0.973062	−	0.209998i
$501$			15.3551i			0.686017i
$502$	−2.88511	+	27.0451i	−0.128769	+	1.20708i
$503$	−22.3190			−0.995154			−0.497577	−	0.867420i	$-0.665777\pi$
$503$	−22.3190			−0.995154			−0.497577	+	0.867420i	$0.665777\pi$
$504$	−3.88955	−	1.28390i	−0.173255	−	0.0571894i
$505$			20.1039i			0.894612i
$506$	−0.858073	−	4.72381i	−0.0381460	−	0.209999i
$507$		−	1.91998i		−	0.0852694i
$508$	13.1818	+	2.84478i	0.584846	+	0.126217i
$509$	−37.6551			−1.66903			−0.834515	−	0.550985i	$-0.814252\pi$
$509$	−37.6551			−1.66903			−0.834515	+	0.550985i	$0.814252\pi$
$510$	25.1674	+	2.68481i	1.11443	+	0.118885i
$511$		−	0.808450i		−	0.0357637i
$512$	−13.0424	−	18.4904i	−0.576398	−	0.817169i
$513$			26.8359i			1.18484i
$514$	−16.2607	−	1.73466i	−0.717229	−	0.0765124i
$515$		−	25.4850i		−	1.12300i
$516$	−2.16820	+	10.0467i	−0.0954496	+	0.442282i
$517$	6.51874	+	22.1708i	0.286694	+	0.975069i
$518$	−13.0156	−	1.38848i	−0.571872	−	0.0610061i
$519$	20.4887			0.899352
$520$	1.21481	−	3.68027i	0.0532731	−	0.161390i
$521$	26.2080			1.14819			0.574096	−	0.818788i	$-0.305354\pi$
$521$	26.2080			1.14819			0.574096	+	0.818788i	$0.305354\pi$
$522$	0.194998	−	1.82792i	0.00853484	−	0.0800057i
$523$	26.8549			1.17428			0.587140	−	0.809485i	$-0.300254\pi$
$523$	26.8549			1.17428			0.587140	+	0.809485i	$0.300254\pi$
$524$	−28.6640	−	6.18602i	−1.25219	−	0.270237i
$525$			12.6496i			0.552072i
$526$	−18.7027	−	1.99516i	−0.815474	−	0.0869930i
$527$	12.5435			0.546405
$528$	−3.53263	+	25.2253i	−0.153738	+	1.09779i
$529$	21.9522			0.954445
$530$	−4.96613	−	0.529776i	−0.215715	−	0.0230120i
$531$		−	7.50519i		−	0.325697i
$532$	−24.9196	−	5.37794i	−1.08040	−	0.233163i
$533$	−1.45663			−0.0630934
$534$	1.93590	−	18.1471i	0.0837744	−	0.785303i
$535$	4.26058			0.184201
$536$	−12.0229	+	36.4231i	−0.519309	+	1.57324i
$537$	−43.8146			−1.89074
$538$	−4.82008	−	0.514195i	−0.207808	−	0.0221685i
$539$	−8.10756	+	2.38382i	−0.349217	+	0.102678i
$540$	−2.56809	+	11.8997i	−0.110513	+	0.512080i
$541$			18.7974i			0.808164i	0.914723	+	0.404082i	$0.132409\pi$
$541$			18.7974i			0.808164i	−0.914723	+	0.404082i	$0.867591\pi$
$542$	22.9418	+	2.44738i	0.985433	+	0.105124i
$543$			45.5782i			1.95595i
$544$	19.5001	−	33.1764i	0.836061	−	1.42243i
$545$		−	22.8709i		−	0.979682i
$546$	−5.69683	−	0.607725i	−0.243802	−	0.0260082i
$547$	21.4466			0.916990			0.458495	−	0.888697i	$-0.348389\pi$
$547$	21.4466			0.916990			0.458495	+	0.888697i	$0.348389\pi$
$548$	32.6109	+	7.03781i	1.39307	+	0.300641i
$549$		−	3.22005i		−	0.137428i
$550$	14.4099	−	2.61755i	0.614442	−	0.111613i
$551$		−	11.4415i		−	0.487424i
$552$	5.27855	+	1.74239i	0.224670	+	0.0741611i
$553$	15.7962			0.671724
$554$	4.73966	−	44.4297i	0.201369	−	1.88764i
$555$		−	11.5403i		−	0.489859i
$556$	16.7870	+	3.62282i	0.711925	+	0.153642i
$557$		−	12.9358i		−	0.548109i	−0.961714	−	0.274054i	$-0.911635\pi$
$557$		−	12.9358i		−	0.548109i	0.961714	−	0.274054i	$-0.0883648\pi$
$558$	0.189843	−	1.77959i	0.00803669	−	0.0753361i
$559$			2.67659i			0.113208i
$560$	−10.5353	−	4.76941i	−0.445197	−	0.201544i
$561$	−41.5605	+	12.2198i	−1.75469	+	0.515920i
$562$	−1.86581	+	17.4901i	−0.0787044	+	0.737776i
$563$	7.15445			0.301524			0.150762	−	0.988570i	$-0.451827\pi$
$563$	7.15445			0.301524			0.150762	+	0.988570i	$0.451827\pi$
$564$	−26.1536	−	5.64425i	−1.10127	−	0.237666i
$565$	−2.78129			−0.117010
$566$	33.3197	+	3.55448i	1.40053	+	0.149406i
$567$	22.3403			0.938206
$568$	1.65423	−	5.01147i	0.0694100	−	0.210277i
$569$			3.29200i			0.138008i	0.997616	+	0.0690039i	$0.0219821\pi$
$569$			3.29200i			0.138008i	−0.997616	+	0.0690039i	$0.978018\pi$
$570$	2.38418	−	22.3494i	0.0998625	−	0.936113i
$571$	−23.0361			−0.964033			−0.482016	−	0.876162i	$-0.660095\pi$
$571$	−23.0361			−0.964033			−0.482016	+	0.876162i	$0.660095\pi$
$572$	0.486533	+	6.61538i	0.0203430	+	0.276603i
$573$	−7.41933			−0.309947
$574$	−0.461060	+	4.32199i	−0.0192443	+	0.180396i
$575$		−	3.19617i		−	0.133290i
$576$	−4.41171	−	3.26866i	−0.183821	−	0.136194i
$577$	−46.8020			−1.94839			−0.974197	−	0.225700i	$-0.927533\pi$
$577$	−46.8020			−1.94839			−0.974197	+	0.225700i	$0.927533\pi$
$578$	41.1731	+	4.39226i	1.71258	+	0.182694i
$579$	47.3312			1.96702
$580$	1.09490	−	5.07342i	0.0454634	−	0.210662i
$581$	2.94774			0.122293
$582$	5.07961	−	47.6164i	0.210557	−	1.97376i
$583$	8.20087	−	2.41125i	0.339646	−	0.0998639i
$584$	0.339698	−	1.02911i	0.0140568	−	0.0425850i
$585$		−	0.940430i		−	0.0388820i
$586$	−3.45638	+	32.4002i	−0.142782	+	1.33844i
$587$			24.1267i			0.995817i	0.867229	+	0.497909i	$0.165899\pi$
$587$			24.1267i			0.995817i	−0.867229	+	0.497909i	$0.834101\pi$
$588$	2.06403	−	9.56402i	0.0851191	−	0.394414i
$589$		−	11.1390i		−	0.458975i
$590$	2.24776	−	21.0706i	0.0925390	−	0.867462i
$591$	19.9931			0.822405
$592$	−15.9847	−	7.23641i	−0.656968	−	0.297414i
$593$		−	2.75924i		−	0.113308i	−0.998394	−	0.0566541i	$-0.981957\pi$
$593$		−	2.75924i		−	0.113308i	0.998394	−	0.0566541i	$-0.0180432\pi$
$594$	−3.72385	−	20.5003i	−0.152791	−	0.841137i
$595$		−	19.6681i		−	0.806312i
$596$	5.61412	−	26.0140i	0.229963	−	1.06557i
$597$	34.4570			1.41023
$598$	1.43942	+	0.153554i	0.0588623	+	0.00627930i
$599$		−	10.5396i		−	0.430636i	−0.976544	−	0.215318i	$-0.930921\pi$
$599$		−	10.5396i		−	0.430636i	0.976544	−	0.215318i	$-0.0690789\pi$
$600$	−5.31515	+	16.1022i	−0.216990	+	0.657369i
$601$			39.3690i			1.60589i	0.596050	+	0.802947i	$0.296736\pi$
$601$			39.3690i			1.60589i	−0.596050	+	0.802947i	$0.703264\pi$
$602$	7.94177	+	0.847211i	0.323683	+	0.0345297i
$603$			9.30732i			0.379024i
$604$	−14.4911	−	3.12735i	−0.589635	−	0.127250i
$605$	12.6738	−	8.15807i	0.515263	−	0.331673i
$606$	39.6135	+	4.22589i	1.60919	+	0.171665i
$607$	44.2068			1.79430			0.897150	−	0.441726i	$-0.145634\pi$
$607$	44.2068			1.79430			0.897150	+	0.441726i	$0.145634\pi$
$608$	−29.4616	−	17.3167i	−1.19482	−	0.702284i
$609$	−7.67254			−0.310907
$610$	0.964388	−	9.04019i	0.0390469	−	0.366027i
$611$	−6.96770			−0.281883
$612$	1.96991	−	9.12791i	0.0796289	−	0.368974i
$613$			33.2627i			1.34347i	0.740793	+	0.671734i	$0.234450\pi$
$613$			33.2627i			1.34347i	−0.740793	+	0.671734i	$0.765550\pi$
$614$	26.1838	+	2.79323i	1.05669	+	0.112726i
$615$	−3.83210			−0.154525
$616$	19.7827	+	0.650339i	0.797066	+	0.0262029i
$617$	4.66469			0.187793			0.0938967	−	0.995582i	$-0.470068\pi$
$617$	4.66469			0.187793			0.0938967	+	0.995582i	$0.470068\pi$
$618$	−50.2166	−	5.35700i	−2.02001	−	0.215490i
$619$		−	15.6150i		−	0.627619i	−0.949486	−	0.313810i	$-0.898395\pi$
$619$		−	15.6150i		−	0.627619i	0.949486	−	0.313810i	$-0.101605\pi$
$620$	1.06596	−	4.93929i	0.0428098	−	0.198367i
$621$	−4.54704			−0.182466
$622$	−4.92440	+	46.1614i	−0.197450	+	1.85090i
$623$	−14.1818			−0.568181
$624$	−6.99639	−	3.16732i	−0.280080	−	0.126794i
$625$	0.362322			0.0144929
$626$	18.8009	+	2.00564i	0.751434	+	0.0801614i
$627$	10.8515	+	36.9069i	0.433368	+	1.47392i
$628$	−20.1156	−	4.34119i	−0.802701	−	0.173232i
$629$		−	29.8415i		−	1.18986i
$630$	−2.79037	−	0.297671i	−0.111171	−	0.0118595i
$631$			25.2350i			1.00459i	0.864697	+	0.502294i	$0.167511\pi$
$631$			25.2350i			1.00459i	−0.864697	+	0.502294i	$0.832489\pi$
$632$	20.1077	+	6.63733i	0.799842	+	0.264019i
$633$			40.7570i			1.61995i
$634$	−23.4589	−	2.50254i	−0.931671	−	0.0993886i
$635$	9.23890			0.366635
$636$	−2.08778	+	9.67411i	−0.0827860	+	0.383603i
$637$		−	2.54799i		−	0.100955i
$638$	1.58766	+	8.74029i	0.0628561	+	0.346031i
$639$		−	1.28060i		−	0.0506597i
$640$	−11.4068	−	10.4980i	−0.450893	−	0.414968i
$641$	−24.0489			−0.949876			−0.474938	−	0.880019i	$-0.657529\pi$
$641$	−24.0489			−0.949876			−0.474938	+	0.880019i	$0.657529\pi$
$642$	0.895583	−	8.39521i	0.0353458	−	0.331333i
$643$			10.7306i			0.423173i	0.977359	+	0.211587i	$0.0678631\pi$
$643$			10.7306i			0.423173i	−0.977359	+	0.211587i	$0.932137\pi$
$644$	0.911229	−	4.22234i	0.0359075	−	0.166383i
$645$			7.04159i			0.277263i
$646$	6.16514	−	57.7921i	0.242564	−	2.27380i
$647$		−	35.3407i		−	1.38938i	−0.719307	−	0.694692i	$-0.755541\pi$
$647$		−	35.3407i		−	1.38938i	0.719307	−	0.694692i	$-0.244459\pi$
$648$	28.4380	+	9.38707i	1.11715	+	0.368759i
$649$	10.2306	+	34.7951i	0.401586	+	1.36583i
$650$	−0.468416	+	4.39094i	−0.0183728	+	0.172227i
$651$	−7.46970			−0.292760
$652$	0.382853	−	1.77402i	0.0149937	−	0.0694758i
$653$	40.5513			1.58689			0.793447	−	0.608639i	$-0.208284\pi$
$653$	40.5513			1.58689			0.793447	+	0.608639i	$0.208284\pi$
$654$	−45.0657	−	4.80751i	−1.76221	−	0.187989i
$655$	−20.0902			−0.784987
$656$	−2.40294	+	5.30792i	−0.0938189	+	0.207239i
$657$		−	0.262972i		−	0.0102595i
$658$	−2.20546	+	20.6740i	−0.0859778	+	0.805957i
$659$	−25.4942			−0.993113			−0.496557	−	0.868004i	$-0.665402\pi$
$659$	−25.4942			−0.993113			−0.496557	+	0.868004i	$0.665402\pi$
$660$	1.27997	+	17.4038i	0.0498229	+	0.677442i
$661$	7.48246			0.291034			0.145517	−	0.989356i	$-0.453515\pi$
$661$	7.48246			0.291034			0.145517	+	0.989356i	$0.453515\pi$
$662$	0.585225	−	5.48591i	0.0227454	−	0.213216i
$663$		−	13.0614i		−	0.507262i
$664$	3.75231	+	1.23859i	0.145618	+	0.0480668i
$665$	−17.4658			−0.677295
$666$	−4.23371	−	0.451643i	−0.164053	−	0.0175008i
$667$	1.93863			0.0750639
$668$	15.6351	+	3.37424i	0.604941	+	0.130553i
$669$	4.69041			0.181342
$670$	−2.78749	+	26.1300i	−0.107690	+	1.00949i
$671$	4.38937	+	14.9286i	0.169450	+	0.576313i
$672$	−11.6124	+	19.7566i	−0.447957	+	0.762127i
$673$			1.11688i			0.0430524i	0.999768	+	0.0215262i	$0.00685253\pi$
$673$			1.11688i			0.0430524i	−0.999768	+	0.0215262i	$0.993147\pi$
$674$	0.486094	−	4.55665i	0.0187236	−	0.175516i
$675$		−	13.8707i		−	0.533883i
$676$	−1.95499	−	0.421910i	−0.0751920	−	0.0162273i
$677$			22.2995i			0.857041i	0.903532	+	0.428521i	$0.140965\pi$
$677$			22.2995i			0.857041i	−0.903532	+	0.428521i	$0.859035\pi$
$678$	−0.584633	+	5.48036i	−0.0224527	+	0.210472i
$679$	−37.2117			−1.42805
$680$	8.26422	−	25.0364i	0.316918	−	0.960100i
$681$			28.4390i			1.08978i
$682$	1.54569	+	8.50922i	0.0591875	+	0.325835i
$683$			30.7095i			1.17507i	0.809200	+	0.587534i	$0.199901\pi$
$683$			30.7095i			1.17507i	−0.809200	+	0.587534i	$0.800099\pi$
$684$	−8.10585	−	1.74934i	−0.309935	−	0.0668875i
$685$	22.8565			0.873303
$686$	−28.3301	−	3.02219i	−1.08165	−	0.115388i
$687$		−	14.7119i		−	0.561292i
$688$	9.75345	+	4.41547i	0.371847	+	0.168338i
$689$			2.57732i			0.0981882i
$690$	3.78684	+	0.403972i	0.144163	+	0.0153789i
$691$			16.9196i			0.643650i	0.946799	+	0.321825i	$0.104296\pi$
$691$			16.9196i			0.643650i	−0.946799	+	0.321825i	$0.895704\pi$
$692$	4.50231	−	20.8622i	0.171152	−	0.793064i
$693$	4.60791	−	1.35484i	0.175040	−	0.0514660i
$694$	39.7141	+	4.23662i	1.50753	+	0.160820i
$695$	11.7657			0.446300
$696$	−9.76671	−	3.22388i	−0.370206	−	0.122201i
$697$	−9.90923			−0.375339
$698$	1.79322	−	16.8097i	0.0678745	−	0.636257i
$699$	28.9256			1.09407
$700$	12.8802	+	2.77970i	0.486826	+	0.105063i
$701$			26.8611i			1.01453i	0.861790	+	0.507265i	$0.169343\pi$
$701$			26.8611i			1.01453i	−0.861790	+	0.507265i	$0.830657\pi$
$702$	6.24678	+	0.666392i	0.235769	+	0.0251514i
$703$	−26.5001			−0.999469
$704$	24.9090	+	9.14022i	0.938792	+	0.344485i
$705$	−18.3307			−0.690373
$706$	18.5448	+	1.97832i	0.697944	+	0.0744551i
$707$		−	30.9575i		−	1.16428i
$708$	−41.0458	−	8.85817i	−1.54260	−	0.332910i
$709$	−43.4641			−1.63233			−0.816164	−	0.577820i	$-0.803904\pi$
$709$	−43.4641			−1.63233			−0.816164	+	0.577820i	$0.803904\pi$
$710$	0.383532	−	3.59524i	0.0143937	−	0.134927i
$711$	5.13819			0.192697
$712$	−18.0526	−	5.95897i	−0.676550	−	0.223322i
$713$	1.88737			0.0706827
$714$	−38.7547	−	4.13427i	−1.45036	−	0.154721i
$715$	1.28194	+	4.35997i	0.0479417	+	0.163054i
$716$	−9.62812	+	44.6135i	−0.359820	+	1.66729i
$717$			28.6061i			1.06831i
$718$	19.9656	+	2.12989i	0.745109	+	0.0794867i
$719$			8.20274i			0.305910i	0.988233	+	0.152955i	$0.0488790\pi$
$719$			8.20274i			0.305910i	−0.988233	+	0.152955i	$0.951121\pi$
$720$	−3.42691	−	1.55139i	−0.127714	−	0.0578169i
$721$			39.2437i			1.46151i
$722$	−24.6026	−	2.62455i	−0.915613	−	0.0976756i
$723$	−16.3026			−0.606302
$724$	46.4093	+	10.0157i	1.72479	+	0.372229i
$725$			5.91377i			0.219632i
$726$	−13.4109	−	26.6878i	−0.497726	−	0.990478i
$727$		−	23.4590i		−	0.870045i	−0.900420	−	0.435022i	$-0.856740\pi$
$727$		−	23.4590i		−	0.870045i	0.900420	−	0.435022i	$-0.143260\pi$
$728$	−1.87066	+	5.66716i	−0.0693315	+	0.210039i
$729$	−18.3200			−0.678518
$730$	0.0787588	−	0.738287i	0.00291499	−	0.0273252i
$731$			18.2085i			0.673465i
$732$	−17.6104	−	3.80054i	−0.650901	−	0.140472i
$733$		−	38.2802i		−	1.41391i	−0.707258	−	0.706955i	$-0.750068\pi$
$733$		−	38.2802i		−	1.41391i	0.707258	−	0.706955i	$-0.249932\pi$
$734$	3.13385	−	29.3768i	0.115672	−	1.08432i
$735$		−	6.70328i		−	0.247254i
$736$	2.93411	−	4.99192i	0.108153	−	0.184004i
$737$	−12.6872	−	43.1501i	−0.467338	−	1.58945i
$738$	−0.149973	+	1.40585i	−0.00552060	+	0.0517502i
$739$	−12.1272			−0.446108			−0.223054	−	0.974806i	$-0.571603\pi$
$739$	−12.1272			−0.446108			−0.223054	+	0.974806i	$0.571603\pi$
$740$	−11.7507	−	2.53595i	−0.431966	−	0.0932232i
$741$	−11.5989			−0.426096
$742$	7.64723	+	0.815790i	0.280739	+	0.0299486i
$743$	−10.0245			−0.367764			−0.183882	−	0.982948i	$-0.558866\pi$
$743$	−10.0245			−0.367764			−0.183882	+	0.982948i	$0.558866\pi$
$744$	−9.50851	−	3.13865i	−0.348599	−	0.115069i
$745$		−	18.2328i		−	0.667998i
$746$	−4.03130	+	37.7895i	−0.147596	+	1.38357i
$747$	0.958839			0.0350821
$748$	3.30982	+	45.0036i	0.121019	+	1.64549i
$749$	−6.56076			−0.239725
$750$	−3.20560	+	30.0494i	−0.117052	+	1.09725i
$751$			9.74418i			0.355570i	0.984069	+	0.177785i	$0.0568932\pi$
$751$			9.74418i			0.355570i	−0.984069	+	0.177785i	$0.943107\pi$
$752$	−11.4943	+	25.3902i	−0.419155	+	0.925885i
$753$	36.9257			1.34565
$754$	−2.66331	−	0.284116i	−0.0969920	−	0.0103469i
$755$	−10.1566			−0.369637
$756$	3.95454	−	18.3240i	0.143825	−	0.666438i
$757$	−46.2142			−1.67968			−0.839841	−	0.542832i	$-0.817352\pi$
$757$	−46.2142			−1.67968			−0.839841	+	0.542832i	$0.817352\pi$
$758$	−1.66651	+	15.6219i	−0.0605303	+	0.567413i
$759$	−6.25344	+	1.83866i	−0.226985	+	0.0667392i
$760$	−22.2330	−	7.33886i	−0.806476	−	0.266209i
$761$		−	10.7711i		−	0.390453i	−0.980758	−	0.195226i	$-0.937456\pi$
$761$		−	10.7711i		−	0.390453i	0.980758	−	0.195226i	$-0.0625442\pi$
$762$	1.94204	−	18.2047i	0.0703526	−	0.659487i
$763$			35.2184i			1.27499i
$764$	−1.63037	+	7.55462i	−0.0589849	+	0.273317i
$765$		−	6.39762i		−	0.231306i
$766$	1.53949	−	14.4312i	0.0556240	−	0.521421i
$767$	−10.9352			−0.394847
$768$	−23.0833	+	20.2697i	−0.832948	+	0.731420i
$769$		−	45.4118i		−	1.63759i	−0.574084	−	0.818797i	$-0.694642\pi$
$769$		−	45.4118i		−	1.63759i	0.574084	−	0.818797i	$-0.305358\pi$
$770$	13.3423	−	2.42362i	0.480824	−	0.0873411i
$771$			22.2013i			0.799561i
$772$	10.4009	−	48.1942i	0.374336	−	1.73455i
$773$	38.7850			1.39500			0.697500	−	0.716585i	$-0.254296\pi$
$773$	38.7850			1.39500			0.697500	+	0.716585i	$0.254296\pi$
$774$	2.58330	+	0.275581i	0.0928547	+	0.00990554i
$775$			5.75742i			0.206813i
$776$	−47.3684	−	15.6358i	−1.70043	−	0.561292i
$777$			17.7707i			0.637519i
$778$	0.615381	+	0.0656475i	0.0220625	+	0.00235358i
$779$			8.79967i			0.315281i
$780$	−5.14321	−	1.10996i	−0.184156	−	0.0397431i
$781$	1.74563	+	5.93703i	0.0624636	+	0.212444i
$782$	9.79219	+	1.04461i	0.350168	+	0.0373552i
$783$	8.41322			0.300664
$784$	−9.28485	−	4.20333i	−0.331602	−	0.150119i
$785$	−14.0987			−0.503206
$786$	−4.22299	+	39.5864i	−0.150629	+	1.41200i
$787$	−10.3411			−0.368620			−0.184310	−	0.982868i	$-0.559005\pi$
$787$	−10.3411			−0.368620			−0.184310	+	0.982868i	$0.559005\pi$
$788$	4.39341	−	20.3576i	0.156509	−	0.725211i
$789$			25.5354i			0.909084i
$790$	14.4253	+	1.53886i	0.513230	+	0.0547502i
$791$	4.28284			0.152280
$792$	6.43490	+	0.211542i	0.228654	+	0.00751682i
$793$	−4.69168			−0.166606
$794$	40.2827	+	4.29727i	1.42958	+	0.152504i
$795$			6.78044i			0.240477i
$796$	7.57181	−	35.0853i	0.268376	−	1.24357i
$797$	−8.03442			−0.284594			−0.142297	−	0.989824i	$-0.545449\pi$
$797$	−8.03442			−0.284594			−0.142297	+	0.989824i	$0.545449\pi$
$798$	−3.67135	+	34.4153i	−0.129964	+	1.21829i
$799$	−47.4003			−1.67690
$800$	15.2278	+	8.95047i	0.538384	+	0.316447i
$801$	−4.61304			−0.162994
$802$	43.0772	+	4.59538i	1.52111	+	0.162269i
$803$	0.358467	+	1.21918i	0.0126500	+	0.0430238i
$804$	50.9017	+	10.9852i	1.79516	+	0.387417i
$805$		−	2.95937i		−	0.104304i
$806$	−2.59290	−	0.276605i	−0.0913310	−	0.00974299i
$807$			6.58102i			0.231663i
$808$	13.0079	−	39.4072i	0.457616	−	1.38634i
$809$			14.1766i			0.498424i	0.968449	+	0.249212i	$0.0801716\pi$
$809$			14.1766i			0.498424i	−0.968449	+	0.249212i	$0.919828\pi$
$810$	20.4015	+	2.17638i	0.716834	+	0.0764703i
$811$	16.2403			0.570275			0.285137	−	0.958487i	$-0.407961\pi$
$811$	16.2403			0.570275			0.285137	+	0.958487i	$0.407961\pi$
$812$	−1.68601	+	7.81244i	−0.0591675	+	0.274163i
$813$		−	31.3232i		−	1.09855i
$814$	20.2437	−	3.67724i	0.709542	−	0.128887i
$815$		−	1.24338i		−	0.0435538i
$816$	−47.5955	−	21.5468i	−1.66617	−	0.754291i
$817$	16.1697			0.565705
$818$	3.27115	−	30.6638i	0.114373	−	1.07213i
$819$			1.44815i			0.0506023i
$820$	−0.842092	+	3.90198i	−0.0294071	+	0.136263i
$821$		−	53.9498i		−	1.88286i	−0.337209	−	0.941430i	$-0.609483\pi$
$821$		−	53.9498i		−	1.88286i	0.337209	−	0.941430i	$-0.390517\pi$
$822$	4.80449	−	45.0374i	0.167576	−	1.57086i
$823$			29.5289i			1.02931i	0.857396	+	0.514657i	$0.172081\pi$
$823$			29.5289i			1.02931i	−0.857396	+	0.514657i	$0.827919\pi$
$824$	−16.4896	+	49.9551i	−0.574443	+	1.74027i
$825$	−5.60882	−	19.0761i	−0.195274	−	0.664143i
$826$	−3.46128	+	32.4461i	−0.120433	+	1.12894i
$827$	−9.55271			−0.332180			−0.166090	−	0.986111i	$-0.553114\pi$
$827$	−9.55271			−0.332180			−0.166090	+	0.986111i	$0.553114\pi$
$828$	0.296404	−	1.37344i	0.0103008	−	0.0477303i
$829$	40.7568			1.41554			0.707771	−	0.706442i	$-0.249701\pi$
$829$	40.7568			1.41554			0.707771	+	0.706442i	$0.249701\pi$
$830$	2.69191	+	0.287167i	0.0934376	+	0.00996772i
$831$	−60.6614			−2.10432
$832$	−4.76251	+	6.42795i	−0.165110	+	0.222849i
$833$		−	17.3337i		−	0.600576i
$834$	2.47318	−	23.1837i	0.0856393	−	0.802785i
$835$	10.9584			0.379232
$836$	39.9644	−	2.93921i	1.38220	−	0.101655i
$837$	8.19079			0.283115
$838$	−2.79097	+	26.1626i	−0.0964124	+	0.903772i
$839$		−	36.6407i		−	1.26498i	−0.774569	−	0.632489i	$-0.782033\pi$
$839$		−	36.6407i		−	1.26498i	0.774569	−	0.632489i	$-0.217967\pi$
$840$	−4.92136	+	14.9092i	−0.169803	+	0.514416i
$841$	25.4130			0.876311
$842$	12.7049	+	1.35533i	0.437839	+	0.0467077i
$843$	23.8799			0.822467
$844$	41.5002	+	8.95622i	1.42850	+	0.308286i
$845$	−1.37022			−0.0471372
$846$	−0.717391	+	6.72484i	−0.0246644	+	0.231205i
$847$	−19.5161	+	12.5624i	−0.670581	+	0.431650i
$848$	9.39172	+	4.25171i	0.322513	+	0.146004i
$849$		−	45.4926i		−	1.56130i
$850$	−3.18657	+	29.8710i	−0.109299	+	1.02457i
$851$		−	4.49013i		−	0.153920i
$852$	−7.00358	−	1.51145i	−0.239939	−	0.0517816i
$853$			4.79732i			0.164257i	0.996622	+	0.0821285i	$0.0261718\pi$
$853$			4.79732i			0.164257i	−0.996622	+	0.0821285i	$0.973828\pi$
$854$	−1.48504	+	13.9208i	−0.0508170	+	0.476359i
$855$	−5.68127			−0.194295
$856$	−8.35149	−	2.75673i	−0.285448	−	0.0942232i
$857$			21.0856i			0.720271i	0.932900	+	0.360136i	$0.117270\pi$
$857$			21.0856i			0.720271i	−0.932900	+	0.360136i	$0.882730\pi$
$858$	8.86052	−	1.60950i	0.302493	−	0.0549475i
$859$		−	12.8670i		−	0.439017i	−0.975611	−	0.219509i	$-0.929555\pi$
$859$		−	12.8670i		−	0.439017i	0.975611	−	0.219509i	$-0.0704454\pi$
$860$	7.16999	+	1.54737i	0.244495	+	0.0527648i
$861$	5.90096			0.201104
$862$	4.99722	+	0.533092i	0.170206	+	0.0181572i
$863$			17.2988i			0.588857i	0.955674	+	0.294428i	$0.0951293\pi$
$863$			17.2988i			0.588857i	−0.955674	+	0.294428i	$0.904871\pi$
$864$	12.7334	−	21.6638i	0.433198	−	0.737019i
$865$		−	14.6220i		−	0.497164i
$866$	4.44622	+	0.474313i	0.151089	+	0.0161178i
$867$		−	56.2151i		−	1.90917i
$868$	−1.64144	+	7.60590i	−0.0557141	+	0.258161i
$869$	−23.8214	+	7.00406i	−0.808085	+	0.237596i
$870$	−7.00666	−	0.747455i	−0.237548	−	0.0253411i
$871$	13.5610			0.459495
$872$	−14.7982	+	44.8310i	−0.501131	+	1.51817i
$873$	−12.1042			−0.409665
$874$	0.927643	−	8.69574i	0.0313780	−	0.294138i
$875$	23.4833			0.793879
$876$	−1.43819	−	0.310379i	−0.0485921	−	0.0104867i
$877$		−	48.0246i		−	1.62168i	−0.585270	−	0.810838i	$-0.699012\pi$
$877$		−	48.0246i		−	1.62168i	0.585270	−	0.810838i	$-0.300988\pi$
$878$	−28.7897	−	3.07122i	−0.971604	−	0.103649i
$879$	44.2371			1.49208
$880$	18.0024	+	2.52111i	0.606861	+	0.0849868i
$881$	32.7713			1.10409			0.552047	−	0.833813i	$-0.313847\pi$
$881$	32.7713			1.10409			0.552047	+	0.833813i	$0.313847\pi$
$882$	−2.45918	−	0.262340i	−0.0828050	−	0.00883346i
$883$		−	7.74338i		−	0.260585i	−0.991476	−	0.130293i	$-0.958408\pi$
$883$		−	7.74338i		−	0.260585i	0.991476	−	0.130293i	$-0.0415917\pi$
$884$	−13.2995	−	2.87020i	−0.447312	−	0.0965351i
$885$	−28.7684			−0.967040
$886$	1.85338	−	17.3736i	0.0622655	−	0.583678i
$887$	−45.6386			−1.53239			−0.766197	−	0.642606i	$-0.777853\pi$
$887$	−45.6386			−1.53239			−0.766197	+	0.642606i	$0.777853\pi$
$888$	−7.46696	+	22.6211i	−0.250575	+	0.759113i
$889$	−14.2268			−0.477150
$890$	−12.9510	−	1.38158i	−0.434118	−	0.0463107i
$891$	−33.6902	+	9.90572i	−1.12866	+	0.331854i
$892$	1.03070	−	4.77593i	0.0345105	−	0.159910i
$893$			42.0928i			1.40858i
$894$	−35.9267	−	3.83258i	−1.20157	−	0.128181i
$895$			31.2690i			1.04521i
$896$	17.5651	+	16.1656i	0.586808	+	0.540053i
$897$		−	1.96529i		−	0.0656192i
$898$	−13.7113	−	1.46269i	−0.457551	−	0.0488105i
$899$	−3.49214			−0.116469
$900$	4.18967	+	0.904179i	0.139656	+	0.0301393i
$901$			17.5332i			0.584115i
$902$	−1.22107	−	6.72217i	−0.0406573	−	0.223824i
$903$		−	10.8432i		−	0.360839i
$904$	5.45182	+	1.79959i	0.181325	+	0.0598533i
$905$	32.5276			1.08125
$906$	−2.13494	+	20.0130i	−0.0709287	+	0.664887i
$907$		−	10.1360i		−	0.336560i	−0.985739	−	0.168280i	$-0.946179\pi$
$907$		−	10.1360i		−	0.336560i	0.985739	−	0.168280i	$-0.0538213\pi$
$908$	28.9575	+	6.24937i	0.960989	+	0.207393i
$909$		−	10.0699i		−	0.333996i
$910$	−0.433712	+	4.06563i	−0.0143774	+	0.134774i
$911$		−	44.7816i		−	1.48368i	−0.670577	−	0.741840i	$-0.733954\pi$
$911$		−	44.7816i		−	1.48368i	0.670577	−	0.741840i	$-0.266046\pi$
$912$	−19.1342	+	42.2661i	−0.633597	+	1.39957i
$913$	−4.44532	+	1.30703i	−0.147118	+	0.0432564i
$914$	−1.70597	+	15.9918i	−0.0564284	+	0.528961i
$915$	−12.3429			−0.408044
$916$	−14.9801	−	3.23288i	−0.494957	−	0.106817i
$917$	30.9364			1.02161
$918$	42.4960	+	4.53338i	1.40258	+	0.149624i
$919$	31.0232			1.02336			0.511680	−	0.859176i	$-0.329023\pi$
$919$	31.0232			1.02336			0.511680	+	0.859176i	$0.329023\pi$
$920$	1.24348	−	3.76712i	0.0409964	−	0.124198i
$921$		−	35.7497i		−	1.17799i
$922$	0.502568	−	4.71108i	0.0165512	−	0.155151i
$923$	−1.86586			−0.0614154
$924$	−1.97100	−	26.7997i	−0.0648412	−	0.881646i
$925$	13.6971			0.450358
$926$	−3.42110	+	32.0694i	−0.112424	+	1.05387i
$927$			12.7652i			0.419264i
$928$	−5.42887	+	9.23636i	−0.178211	+	0.303198i
$929$	44.8235			1.47061			0.735306	−	0.677736i	$-0.237039\pi$
$929$	44.8235			1.47061			0.735306	+	0.677736i	$0.237039\pi$
$930$	−6.82142	−	0.727694i	−0.223683	−	0.0238620i
$931$	−15.3928			−0.504478
$932$	6.35630	−	29.4530i	0.208208	−	0.964765i
$933$	63.0258			2.06337
$934$	3.48622	−	32.6799i	0.114072	−	1.06932i
$935$	8.72084	+	29.6603i	0.285202	+	0.969995i
$936$	−0.608489	+	1.84341i	−0.0198891	+	0.0602538i
$937$		−	7.50219i		−	0.245086i	−0.992463	−	0.122543i	$-0.960895\pi$
$937$		−	7.50219i		−	0.245086i	0.992463	−	0.122543i	$-0.0391049\pi$
$938$	4.29240	−	40.2370i	0.140152	−	1.31379i
$939$		−	25.6695i		−	0.837693i
$940$	−4.02811	+	18.6649i	−0.131382	+	0.608782i
$941$			29.9611i			0.976704i	0.872647	+	0.488352i	$0.162402\pi$
$941$			29.9611i			0.976704i	−0.872647	+	0.488352i	$0.837598\pi$
$942$	−2.96359	+	27.7807i	−0.0965589	+	0.905145i
$943$	−1.49100			−0.0485537
$944$	−18.0394	+	39.8477i	−0.587132	+	1.29693i
$945$		−	12.8430i		−	0.417784i
$946$	−12.3522	+	2.24376i	−0.401604	+	0.0729509i
$947$			28.6101i			0.929702i	0.885389	+	0.464851i	$0.153892\pi$
$947$			28.6101i			0.929702i	−0.885389	+	0.464851i	$0.846108\pi$
$948$	6.06446	−	28.1007i	0.196965	−	0.912669i
$949$	−0.383156			−0.0124378
$950$	26.5263	+	2.82977i	0.860627	+	0.0918098i
$951$			32.0292i			1.03862i
$952$	−12.7259	+	38.5529i	−0.412448	+	1.24951i
$953$		−	1.26562i		−	0.0409973i	−0.999790	−	0.0204987i	$-0.993475\pi$
$953$		−	1.26562i		−	0.0409973i	0.999790	−	0.0204987i	$-0.00652539\pi$
$954$	2.48749	+	0.265360i	0.0805354	+	0.00859134i
$955$			5.29492i			0.171340i
$956$	29.1277	+	6.28609i	0.942057	+	0.203307i
$957$	11.5705	−	3.40201i	0.374022	−	0.109971i
$958$	−26.8926	−	2.86885i	−0.868861	−	0.0926882i
$959$	−35.1962			−1.13655
$960$	−12.5292	+	16.9107i	−0.404379	+	0.545791i
$961$	27.6002			0.890328
$962$	−0.658052	+	6.16859i	−0.0212164	+	0.198883i
$963$	−2.13408			−0.0687699
$964$	−3.58245	+	16.5999i	−0.115383	+	0.534647i
$965$		−	33.7786i		−	1.08737i
$966$	−5.83127	−	0.622067i	−0.187618	−	0.0200147i
$967$	20.1052			0.646539			0.323270	−	0.946307i	$-0.395218\pi$
$967$	20.1052			0.646539			0.323270	+	0.946307i	$0.395218\pi$
$968$	−30.1215	+	7.79091i	−0.968140	+	0.250409i
$969$	−78.9056			−2.53481
$970$	−33.9822	−	3.62514i	−1.09110	−	0.116396i
$971$			32.0663i			1.02906i	0.857473	+	0.514528i	$0.172033\pi$
$971$			32.0663i			1.02906i	−0.857473	+	0.514528i	$0.827967\pi$
$972$	2.95424	−	13.6890i	0.0947573	−	0.439074i
$973$	−18.1178			−0.580829
$974$	−4.15396	+	38.9393i	−0.133101	+	1.24770i
$975$	5.99511			0.191997
$976$	−7.73967	+	17.0964i	−0.247741	+	0.547242i
$977$	−30.4393			−0.973839			−0.486920	−	0.873447i	$-0.661880\pi$
$977$	−30.4393			−0.973839			−0.486920	+	0.873447i	$0.661880\pi$
$978$	−2.45001	−	0.261362i	−0.0783427	−	0.00835742i
$979$	21.3867	−	6.28821i	0.683523	−	0.200972i
$980$	−6.82551	−	1.47302i	−0.218033	−	0.0470540i
$981$			11.4558i			0.365756i
$982$	−9.01682	−	0.961894i	−0.287738	−	0.0306953i
$983$		−	49.1042i		−	1.56618i	−0.621908	−	0.783090i	$-0.713642\pi$
$983$		−	49.1042i		−	1.56618i	0.621908	−	0.783090i	$-0.286358\pi$
$984$	7.51160	+	2.47949i	0.239461	+	0.0790434i
$985$		−	14.2684i		−	0.454628i
$986$	−18.1181	−	1.93280i	−0.576999	−	0.0615530i
$987$	28.2270			0.898475
$988$	−2.54882	+	11.8104i	−0.0810886	+	0.375738i
$989$			2.73976i			0.0871192i
$990$	4.33999	−	0.788353i	0.137934	−	0.0250555i
$991$			14.3413i			0.455566i	0.973712	+	0.227783i	$0.0731477\pi$
$991$			14.3413i			0.455566i	−0.973712	+	0.227783i	$0.926852\pi$
$992$	−5.28535	+	8.99218i	−0.167810	+	0.285502i
$993$	−7.49011			−0.237692
$994$	−0.590592	+	5.53622i	−0.0187324	+	0.175598i
$995$		−	24.5908i		−	0.779580i
$996$	1.13169	−	5.24389i	0.0358590	−	0.166159i
$997$			3.75566i			0.118943i	0.998230	+	0.0594715i	$0.0189415\pi$
$997$			3.75566i			0.118943i	−0.998230	+	0.0594715i	$0.981058\pi$
$998$	−5.06004	+	47.4329i	−0.160173	+	1.50146i
$999$		−	19.4862i		−	0.616515i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.e.b.131.3	✓	64
4.3	odd	2	inner	572.2.e.b.131.61	yes	64
11.10	odd	2	inner	572.2.e.b.131.62	yes	64
44.43	even	2	inner	572.2.e.b.131.4	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.e.b.131.3	✓	64	1.1	even	1	trivial
572.2.e.b.131.4	yes	64	44.43	even	2	inner
572.2.e.b.131.61	yes	64	4.3	odd	2	inner
572.2.e.b.131.62	yes	64	11.10	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40623 - 0.150014i) q^{2} +1.91998i q^{3} +(1.95499 + 0.421910i) q^{4} +1.37022 q^{5} +(0.288024 - 2.69995i) q^{6} -2.10998 q^{7} +(-2.68588 - 0.886580i) q^{8} -0.686333 q^{9} +O(q^{10})\)	\(q+(-1.40623 - 0.150014i) q^{2} +1.91998i q^{3} +(1.95499 + 0.421910i) q^{4} +1.37022 q^{5} +(0.288024 - 2.69995i) q^{6} -2.10998 q^{7} +(-2.68588 - 0.886580i) q^{8} -0.686333 q^{9} +(-1.92686 - 0.205553i) q^{10} +(3.18194 - 0.935566i) q^{11} +(-0.810060 + 3.75355i) q^{12} +1.00000i q^{13} +(2.96712 + 0.316526i) q^{14} +2.63081i q^{15} +(3.64398 + 1.64966i) q^{16} +6.80287i q^{17} +(0.965145 + 0.102960i) q^{18} +6.04114 q^{19} +(2.67878 + 0.578111i) q^{20} -4.05112i q^{21} +(-4.61490 + 0.838290i) q^{22} +1.02360i q^{23} +(1.70222 - 5.15685i) q^{24} -3.12248 q^{25} +(0.150014 - 1.40623i) q^{26} +4.44220i q^{27} +(-4.12499 - 0.890220i) q^{28} -1.89393i q^{29} +(0.394658 - 3.69953i) q^{30} -1.84386i q^{31} +(-4.87682 - 2.86646i) q^{32} +(1.79627 + 6.10926i) q^{33} +(1.02053 - 9.56643i) q^{34} -2.89114 q^{35} +(-1.34177 - 0.289571i) q^{36} -4.38660 q^{37} +(-8.49526 - 0.906256i) q^{38} -1.91998 q^{39} +(-3.68027 - 1.21481i) q^{40} +1.45663i q^{41} +(-0.607725 + 5.69683i) q^{42} +2.67659 q^{43} +(6.61538 - 0.486533i) q^{44} -0.940430 q^{45} +(0.153554 - 1.43942i) q^{46} +6.96770i q^{47} +(-3.16732 + 6.99639i) q^{48} -2.54799 q^{49} +(4.39094 + 0.468416i) q^{50} -13.0614 q^{51} +(-0.421910 + 1.95499i) q^{52} +2.57732 q^{53} +(0.666392 - 6.24678i) q^{54} +(4.35997 - 1.28194i) q^{55} +(5.66716 + 1.87066i) q^{56} +11.5989i q^{57} +(-0.284116 + 2.66331i) q^{58} +10.9352i q^{59} +(-1.10996 + 5.14321i) q^{60} +4.69168i q^{61} +(-0.276605 + 2.59290i) q^{62} +1.44815 q^{63} +(6.42795 + 4.76251i) q^{64} +1.37022i q^{65} +(-1.60950 - 8.86052i) q^{66} -13.5610i q^{67} +(-2.87020 + 13.2995i) q^{68} -1.96529 q^{69} +(4.06563 + 0.433712i) q^{70} +1.86586i q^{71} +(1.84341 + 0.608489i) q^{72} +0.383156i q^{73} +(6.16859 + 0.658052i) q^{74} -5.99511i q^{75} +(11.8104 + 2.54882i) q^{76} +(-6.71381 + 1.97402i) q^{77} +(2.69995 + 0.288024i) q^{78} -7.48644 q^{79} +(4.99308 + 2.26041i) q^{80} -10.5879 q^{81} +(0.218514 - 2.04836i) q^{82} -1.39705 q^{83} +(1.70921 - 7.91991i) q^{84} +9.32146i q^{85} +(-3.76391 - 0.401526i) q^{86} +3.63631 q^{87} +(-9.37577 - 0.308221i) q^{88} +6.72129 q^{89} +(1.32247 + 0.141078i) q^{90} -2.10998i q^{91} +(-0.431867 + 2.00113i) q^{92} +3.54018 q^{93} +(1.04525 - 9.79822i) q^{94} +8.27772 q^{95} +(5.50355 - 9.36342i) q^{96} +17.6361 q^{97} +(3.58308 + 0.382235i) q^{98} +(-2.18387 + 0.642109i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9}+O(q^{10}) \) 64 * q + 6 * q^4 + 12 * q^5 - 104 * q^9	\( 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9} - 8 q^{12} - 34 q^{14} + 26 q^{16} + 14 q^{20} - 8 q^{22} + 76 q^{25} + 2 q^{26} - 16 q^{33} + 32 q^{34} - 24 q^{36} - 32 q^{37} - 30 q^{38} + 54 q^{42} + 10 q^{44} + 12 q^{45} + 34 q^{48} - 36 q^{49} - 32 q^{53} - 36 q^{56} + 62 q^{58} + 4 q^{60} - 18 q^{64} - 30 q^{66} - 24 q^{69} - 30 q^{70} + 88 q^{77} - 10 q^{78} - 46 q^{80} + 64 q^{81} - 46 q^{82} + 98 q^{86} + 16 q^{88} + 24 q^{89} + 84 q^{92} + 8 q^{93} - 88 q^{97}+O(q^{100}) \) 64 * q + 6 * q^4 + 12 * q^5 - 104 * q^9 - 8 * q^12 - 34 * q^14 + 26 * q^16 + 14 * q^20 - 8 * q^22 + 76 * q^25 + 2 * q^26 - 16 * q^33 + 32 * q^34 - 24 * q^36 - 32 * q^37 - 30 * q^38 + 54 * q^42 + 10 * q^44 + 12 * q^45 + 34 * q^48 - 36 * q^49 - 32 * q^53 - 36 * q^56 + 62 * q^58 + 4 * q^60 - 18 * q^64 - 30 * q^66 - 24 * q^69 - 30 * q^70 + 88 * q^77 - 10 * q^78 - 46 * q^80 + 64 * q^81 - 46 * q^82 + 98 * q^86 + 16 * q^88 + 24 * q^89 + 84 * q^92 + 8 * q^93 - 88 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more