LMFDB - Embedded newform 1155.2.l.f.1121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(1121,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1155.1121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.l (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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1121.1
Character	$\chi$	$=$	1155.1121
Dual form			1155.2.l.f.1121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.72154 q^{2} +(-1.44946 - 0.948193i) q^{3} +5.40675 q^{4} -1.00000i q^{5} +(3.94475 + 2.58054i) q^{6} -1.00000i q^{7} -9.27160 q^{8} +(1.20186 + 2.74873i) q^{9} +O(q^{10})$	\(q-2.72154 q^{2} +(-1.44946 - 0.948193i) q^{3} +5.40675 q^{4} -1.00000i q^{5} +(3.94475 + 2.58054i) q^{6} -1.00000i q^{7} -9.27160 q^{8} +(1.20186 + 2.74873i) q^{9} +2.72154i q^{10} +(-3.31662 - 0.00239114i) q^{11} +(-7.83687 - 5.12664i) q^{12} -0.172105i q^{13} +2.72154i q^{14} +(-0.948193 + 1.44946i) q^{15} +14.4195 q^{16} +0.805674 q^{17} +(-3.27091 - 7.48077i) q^{18} +2.99512i q^{19} -5.40675i q^{20} +(-0.948193 + 1.44946i) q^{21} +(9.02631 + 0.00650757i) q^{22} +0.277197i q^{23} +(13.4388 + 8.79126i) q^{24} -1.00000 q^{25} +0.468390i q^{26} +(0.864280 - 5.12377i) q^{27} -5.40675i q^{28} +7.75959 q^{29} +(2.58054 - 3.94475i) q^{30} +2.70960 q^{31} -20.6999 q^{32} +(4.80504 + 3.14826i) q^{33} -2.19267 q^{34} -1.00000 q^{35} +(6.49817 + 14.8617i) q^{36} -1.15232 q^{37} -8.15131i q^{38} +(-0.163189 + 0.249459i) q^{39} +9.27160i q^{40} -2.26777 q^{41} +(2.58054 - 3.94475i) q^{42} +9.92713i q^{43} +(-17.9322 - 0.0129283i) q^{44} +(2.74873 - 1.20186i) q^{45} -0.754401i q^{46} +11.2793i q^{47} +(-20.9004 - 13.6724i) q^{48} -1.00000 q^{49} +2.72154 q^{50} +(-1.16779 - 0.763934i) q^{51} -0.930529i q^{52} -10.5607i q^{53} +(-2.35217 + 13.9445i) q^{54} +(-0.00239114 + 3.31662i) q^{55} +9.27160i q^{56} +(2.83995 - 4.34130i) q^{57} -21.1180 q^{58} +5.52208i q^{59} +(-5.12664 + 7.83687i) q^{60} -4.15256i q^{61} -7.37428 q^{62} +(2.74873 - 1.20186i) q^{63} +27.4966 q^{64} -0.172105 q^{65} +(-13.0771 - 8.56811i) q^{66} -8.68588 q^{67} +4.35608 q^{68} +(0.262836 - 0.401785i) q^{69} +2.72154 q^{70} +14.8767i q^{71} +(-11.1432 - 25.4851i) q^{72} -6.17210i q^{73} +3.13608 q^{74} +(1.44946 + 0.948193i) q^{75} +16.1939i q^{76} +(-0.00239114 + 3.31662i) q^{77} +(0.444124 - 0.678912i) q^{78} -3.40257i q^{79} -14.4195i q^{80} +(-6.11106 + 6.60719i) q^{81} +6.17182 q^{82} +18.1415 q^{83} +(-5.12664 + 7.83687i) q^{84} -0.805674i q^{85} -27.0170i q^{86} +(-11.2472 - 7.35759i) q^{87} +(30.7504 + 0.0221697i) q^{88} -14.7270i q^{89} +(-7.48077 + 3.27091i) q^{90} -0.172105 q^{91} +1.49874i q^{92} +(-3.92746 - 2.56922i) q^{93} -30.6970i q^{94} +2.99512 q^{95} +(30.0037 + 19.6275i) q^{96} +15.5799 q^{97} +2.72154 q^{98} +(-3.97955 - 9.11939i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{2} - 4 q^{3} + 44 q^{4} + 4 q^{6} + 12 q^{8} - 2 q^{9}+O(q^{10}) $ 40 * q + 4 * q^2 - 4 * q^3 + 44 * q^4 + 4 * q^6 + 12 * q^8 - 2 * q^9	$ 40 q + 4 q^{2} - 4 q^{3} + 44 q^{4} + 4 q^{6} + 12 q^{8} - 2 q^{9} + 6 q^{11} + 8 q^{12} + 2 q^{15} + 68 q^{16} - 40 q^{18} + 2 q^{21} - 4 q^{22} + 12 q^{24} - 40 q^{25} + 32 q^{27} + 24 q^{29} - 8 q^{31} - 52 q^{32} + 28 q^{33} + 32 q^{34} - 40 q^{35} - 48 q^{37} - 66 q^{39} + 16 q^{41} - 32 q^{44} + 32 q^{48} - 40 q^{49} - 4 q^{50} + 14 q^{51} + 72 q^{54} + 8 q^{55} + 24 q^{57} - 80 q^{58} + 24 q^{60} - 48 q^{62} + 76 q^{64} - 4 q^{65} - 48 q^{67} + 32 q^{68} - 20 q^{69} - 4 q^{70} - 128 q^{72} + 4 q^{75} + 8 q^{77} - 28 q^{78} + 50 q^{81} - 32 q^{82} + 24 q^{83} + 24 q^{84} + 32 q^{87} - 16 q^{88} - 8 q^{90} - 4 q^{91} - 20 q^{93} + 12 q^{95} - 12 q^{96} + 100 q^{97} - 4 q^{98} + 56 q^{99}+O(q^{100}) $ 40 * q + 4 * q^2 - 4 * q^3 + 44 * q^4 + 4 * q^6 + 12 * q^8 - 2 * q^9 + 6 * q^11 + 8 * q^12 + 2 * q^15 + 68 * q^16 - 40 * q^18 + 2 * q^21 - 4 * q^22 + 12 * q^24 - 40 * q^25 + 32 * q^27 + 24 * q^29 - 8 * q^31 - 52 * q^32 + 28 * q^33 + 32 * q^34 - 40 * q^35 - 48 * q^37 - 66 * q^39 + 16 * q^41 - 32 * q^44 + 32 * q^48 - 40 * q^49 - 4 * q^50 + 14 * q^51 + 72 * q^54 + 8 * q^55 + 24 * q^57 - 80 * q^58 + 24 * q^60 - 48 * q^62 + 76 * q^64 - 4 * q^65 - 48 * q^67 + 32 * q^68 - 20 * q^69 - 4 * q^70 - 128 * q^72 + 4 * q^75 + 8 * q^77 - 28 * q^78 + 50 * q^81 - 32 * q^82 + 24 * q^83 + 24 * q^84 + 32 * q^87 - 16 * q^88 - 8 * q^90 - 4 * q^91 - 20 * q^93 + 12 * q^95 - 12 * q^96 + 100 * q^97 - 4 * q^98 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$-1$	$1$	$-1$	$1$

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 $

$2$	−2.72154			−1.92442			−0.962208	−	0.272316i	$-0.912210\pi$
$2$	−2.72154			−1.92442			−0.962208	+	0.272316i	$0.912210\pi$
$3$	−1.44946	−	0.948193i	−0.836845	−	0.547439i
$3$	−1.44946	−	0.948193i	−0.836845	−	0.547439i
$4$	5.40675			2.70338
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	3.94475	+	2.58054i	1.61044	+	1.05350i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−9.27160			−3.27801
$9$	1.20186	+	2.74873i	0.400620	+	0.916244i
$10$			2.72154i			0.860625i
$11$	−3.31662	−	0.00239114i	−1.00000	−	0.000720955i
$11$	−3.31662	−	0.00239114i	−1.00000	−	0.000720955i
$12$	−7.83687	−	5.12664i	−2.26231	−	1.47993i
$13$		−	0.172105i		−	0.0477333i	−0.999715	−	0.0238667i	$-0.992402\pi$
$13$		−	0.172105i		−	0.0477333i	0.999715	−	0.0238667i	$-0.00759772\pi$
$14$			2.72154i			0.727361i
$15$	−0.948193	+	1.44946i	−0.244822	+	0.374249i
$16$	14.4195			3.60487
$17$	0.805674			0.195405			0.0977023	−	0.995216i	$-0.468851\pi$
$17$	0.805674			0.195405			0.0977023	+	0.995216i	$0.468851\pi$
$18$	−3.27091	−	7.48077i	−0.770960	−	1.76323i
$19$			2.99512i			0.687127i	0.939130	+	0.343563i	$0.111634\pi$
$19$			2.99512i			0.687127i	−0.939130	+	0.343563i	$0.888366\pi$
$20$		−	5.40675i		−	1.20899i
$21$	−0.948193	+	1.44946i	−0.206913	+	0.316298i
$22$	9.02631	+	0.00650757i	1.92442	+	0.00138742i
$23$			0.277197i			0.0577995i	0.999582	+	0.0288998i	$0.00920036\pi$
$23$			0.277197i			0.0577995i	−0.999582	+	0.0288998i	$0.990800\pi$
$24$	13.4388	+	8.79126i	2.74318	+	1.79451i
$25$	−1.00000			−0.200000
$26$			0.468390i			0.0918588i
$27$	0.864280	−	5.12377i	0.166331	−	0.986070i
$28$		−	5.40675i		−	1.02178i
$29$	7.75959			1.44092			0.720460	−	0.693497i	$-0.243931\pi$
$29$	7.75959			1.44092			0.720460	+	0.693497i	$0.243931\pi$
$30$	2.58054	−	3.94475i	0.471140	−	0.720210i
$31$	2.70960			0.486659			0.243329	−	0.969944i	$-0.421760\pi$
$31$	2.70960			0.486659			0.243329	+	0.969944i	$0.421760\pi$
$32$	−20.6999			−3.65926
$33$	4.80504	+	3.14826i	0.836450	+	0.548042i
$34$	−2.19267			−0.376040
$35$	−1.00000			−0.169031
$36$	6.49817	+	14.8617i	1.08303	+	2.47695i
$37$	−1.15232			−0.189440			−0.0947202	−	0.995504i	$-0.530196\pi$
$37$	−1.15232			−0.189440			−0.0947202	+	0.995504i	$0.530196\pi$
$38$		−	8.15131i		−	1.32232i
$39$	−0.163189	+	0.249459i	−0.0261311	+	0.0399454i
$40$			9.27160i			1.46597i
$41$	−2.26777			−0.354167			−0.177083	−	0.984196i	$-0.556666\pi$
$41$	−2.26777			−0.354167			−0.177083	+	0.984196i	$0.556666\pi$
$42$	2.58054	−	3.94475i	0.398186	−	0.608689i
$43$			9.92713i			1.51387i	0.653488	+	0.756937i	$0.273305\pi$
$43$			9.92713i			1.51387i	−0.653488	+	0.756937i	$0.726695\pi$
$44$	−17.9322	−	0.0129283i	−2.70338	−	0.00194901i
$45$	2.74873	−	1.20186i	0.409757	−	0.179163i
$46$		−	0.754401i		−	0.111230i
$47$			11.2793i			1.64525i	0.568583	+	0.822626i	$0.307492\pi$
$47$			11.2793i			1.64525i	−0.568583	+	0.822626i	$0.692508\pi$
$48$	−20.9004	−	13.6724i	−3.01672	−	1.97345i
$49$	−1.00000			−0.142857
$50$	2.72154			0.384883
$51$	−1.16779	−	0.763934i	−0.163523	−	0.106972i
$52$		−	0.930529i		−	0.129041i
$53$		−	10.5607i		−	1.45062i	−0.688423	−	0.725310i	$-0.741697\pi$
$53$		−	10.5607i		−	1.45062i	0.688423	−	0.725310i	$-0.258303\pi$
$54$	−2.35217	+	13.9445i	−0.320089	+	1.89761i
$55$	−0.00239114	+	3.31662i	−0.000322421	+	0.447213i
$56$			9.27160i			1.23897i
$57$	2.83995	−	4.34130i	0.376160	−	0.575019i
$58$	−21.1180			−2.77293
$59$			5.52208i			0.718913i	0.933162	+	0.359456i	$0.117038\pi$
$59$			5.52208i			0.718913i	−0.933162	+	0.359456i	$0.882962\pi$
$60$	−5.12664	+	7.83687i	−0.661847	+	1.01174i
$61$		−	4.15256i		−	0.531680i	−0.964017	−	0.265840i	$-0.914351\pi$
$61$		−	4.15256i		−	0.531680i	0.964017	−	0.265840i	$-0.0856493\pi$
$62$	−7.37428			−0.936534
$63$	2.74873	−	1.20186i	0.346308	−	0.151420i
$64$	27.4966			3.43707
$65$	−0.172105			−0.0213470
$66$	−13.0771	−	8.56811i	−1.60968	−	1.05466i
$67$	−8.68588			−1.06115			−0.530574	−	0.847638i	$-0.678024\pi$
$67$	−8.68588			−1.06115			−0.530574	+	0.847638i	$0.678024\pi$
$68$	4.35608			0.528252
$69$	0.262836	−	0.401785i	0.0316417	−	0.0483693i
$70$	2.72154			0.325286
$71$			14.8767i			1.76554i	0.469803	+	0.882771i	$0.344325\pi$
$71$			14.8767i			1.76554i	−0.469803	+	0.882771i	$0.655675\pi$
$72$	−11.1432	−	25.4851i	−1.31324	−	3.00345i
$73$		−	6.17210i		−	0.722389i	−0.932490	−	0.361195i	$-0.882369\pi$
$73$		−	6.17210i		−	0.722389i	0.932490	−	0.361195i	$-0.117631\pi$
$74$	3.13608			0.364562
$75$	1.44946	+	0.948193i	0.167369	+	0.109488i
$76$			16.1939i			1.85756i
$77$	−0.00239114	+	3.31662i	−0.000272496	+	0.377964i
$78$	0.444124	−	0.678912i	0.0502871	−	0.0768716i
$79$		−	3.40257i		−	0.382819i	−0.981510	−	0.191410i	$-0.938694\pi$
$79$		−	3.40257i		−	0.382819i	0.981510	−	0.191410i	$-0.0613059\pi$
$80$		−	14.4195i		−	1.61215i
$81$	−6.11106	+	6.60719i	−0.679007	+	0.734132i
$82$	6.17182			0.681564
$83$	18.1415			1.99129			0.995645	−	0.0932273i	$-0.0297183\pi$
$83$	18.1415			1.99129			0.995645	+	0.0932273i	$0.0297183\pi$
$84$	−5.12664	+	7.83687i	−0.559363	+	0.855072i
$85$		−	0.805674i		−	0.0873876i
$86$		−	27.0170i		−	2.91332i
$87$	−11.2472	−	7.35759i	−1.20583	−	0.788816i
$88$	30.7504	+	0.0221697i	3.27800	+	0.00236330i
$89$		−	14.7270i		−	1.56106i	−0.625120	−	0.780529i	$-0.714950\pi$
$89$		−	14.7270i		−	1.56106i	0.625120	−	0.780529i	$-0.285050\pi$
$90$	−7.48077	+	3.27091i	−0.788543	+	0.344784i
$91$	−0.172105			−0.0180415
$92$			1.49874i			0.156254i
$93$	−3.92746	−	2.56922i	−0.407258	−	0.266416i
$94$		−	30.6970i		−	3.16615i
$95$	2.99512			0.307292
$96$	30.0037	+	19.6275i	3.06224	+	2.00322i
$97$	15.5799			1.58190			0.790952	−	0.611878i	$-0.209586\pi$
$97$	15.5799			1.58190			0.790952	+	0.611878i	$0.209586\pi$
$98$	2.72154			0.274917
$99$	−3.97955	−	9.11939i	−0.399960	−	0.916533i
$100$	−5.40675			−0.540675
$101$	0.215897			0.0214826			0.0107413	−	0.999942i	$-0.496581\pi$
$101$	0.215897			0.0214826			0.0107413	+	0.999942i	$0.496581\pi$
$102$	3.17818	+	2.07907i	0.314687	+	0.205859i
$103$	0.488013			0.0480854			0.0240427	−	0.999711i	$-0.492346\pi$
$103$	0.488013			0.0480854			0.0240427	+	0.999711i	$0.492346\pi$
$104$			1.59569i			0.156470i
$105$	1.44946	+	0.948193i	0.141453	+	0.0925341i
$106$			28.7412i			2.79160i
$107$	13.8525			1.33917			0.669585	−	0.742736i	$-0.266472\pi$
$107$	13.8525			1.33917			0.669585	+	0.742736i	$0.266472\pi$
$108$	4.67295	−	27.7030i	0.449655	−	2.66572i
$109$		−	7.99287i		−	0.765578i	−0.923836	−	0.382789i	$-0.874964\pi$
$109$		−	7.99287i		−	0.765578i	0.923836	−	0.382789i	$-0.125036\pi$
$110$	0.00650757	−	9.02631i	0.000620472	−	0.860625i
$111$	1.67024	+	1.09262i	0.158532	+	0.103707i
$112$		−	14.4195i		−	1.36251i
$113$			11.5739i			1.08878i	0.838833	+	0.544389i	$0.183238\pi$
$113$			11.5739i			1.08878i	−0.838833	+	0.544389i	$0.816762\pi$
$114$	−7.72901	+	11.8150i	−0.723889	+	1.10658i
$115$	0.277197			0.0258487
$116$	41.9542			3.89535
$117$	0.473070	−	0.206846i	0.0437354	−	0.0191229i
$118$		−	15.0285i		−	1.38349i
$119$		−	0.805674i		−	0.0738560i
$120$	8.79126	−	13.4388i	0.802529	−	1.22679i
$121$	11.0000	+	0.0158610i	0.999999	+	0.00144191i
$122$			11.3013i			1.02317i
$123$	3.28704	+	2.15029i	0.296383	+	0.193885i
$124$	14.6501			1.31562
$125$			1.00000i			0.0894427i
$126$	−7.48077	+	3.27091i	−0.666440	+	0.291396i
$127$			2.44997i			0.217400i	0.994075	+	0.108700i	$0.0346688\pi$
$127$			2.44997i			0.217400i	−0.994075	+	0.108700i	$0.965331\pi$
$128$	−33.4331			−2.95510
$129$	9.41283	−	14.3890i	0.828754	−	1.26688i
$130$	0.468390			0.0410805
$131$	15.0987			1.31918			0.659590	−	0.751626i	$-0.270730\pi$
$131$	15.0987			1.31918			0.659590	+	0.751626i	$0.270730\pi$
$132$	25.9797	+	17.0219i	2.26124	+	1.48157i
$133$	2.99512			0.259709
$134$	23.6389			2.04209
$135$	−5.12377	−	0.864280i	−0.440984	−	0.0743854i
$136$	−7.46989			−0.640537
$137$		−	3.93608i		−	0.336282i	−0.985763	−	0.168141i	$-0.946224\pi$
$137$		−	3.93608i		−	0.336282i	0.985763	−	0.168141i	$-0.0537764\pi$
$138$	−0.715318	+	1.09347i	−0.0608919	+	0.0930826i
$139$		−	18.7504i		−	1.59039i	−0.606357	−	0.795193i	$-0.707370\pi$
$139$		−	18.7504i		−	1.59039i	0.606357	−	0.795193i	$-0.292630\pi$
$140$	−5.40675			−0.456954
$141$	10.6949	−	16.3489i	0.900676	−	1.37682i
$142$		−	40.4875i		−	3.39764i
$143$	−0.000411527		0.570807i	−3.44136e−5		0.0477333i
$144$	17.3302	+	39.6353i	1.44418	+	3.30294i
$145$		−	7.75959i		−	0.644399i
$146$			16.7976i			1.39018i
$147$	1.44946	+	0.948193i	0.119549	+	0.0782056i
$148$	−6.23031			−0.512129
$149$	−12.4309			−1.01838			−0.509189	−	0.860654i	$-0.670055\pi$
$149$	−12.4309			−1.01838			−0.509189	+	0.860654i	$0.670055\pi$
$150$	−3.94475	−	2.58054i	−0.322088	−	0.210700i
$151$		−	15.2632i		−	1.24210i	−0.783770	−	0.621051i	$-0.786706\pi$
$151$		−	15.2632i		−	1.24210i	0.783770	−	0.621051i	$-0.213294\pi$
$152$		−	27.7695i		−	2.25240i
$153$	0.968308	+	2.21458i	0.0782831	+	0.179038i
$154$	0.00650757	−	9.02631i	0.000524395	−	0.727361i
$155$		−	2.70960i		−	0.217640i
$156$	−0.882321	+	1.34876i	−0.0706422	+	0.107987i
$157$	−9.24609			−0.737918			−0.368959	−	0.929446i	$-0.620286\pi$
$157$	−9.24609			−0.737918			−0.368959	+	0.929446i	$0.620286\pi$
$158$			9.26022i			0.736704i
$159$	−10.0135	+	15.3073i	−0.794126	+	1.21394i
$160$			20.6999i			1.63647i
$161$	0.277197			0.0218462
$162$	16.6315	−	17.9817i	1.30669	−	1.41278i
$163$	−11.9348			−0.934808			−0.467404	−	0.884044i	$-0.654811\pi$
$163$	−11.9348			−0.934808			−0.467404	+	0.884044i	$0.654811\pi$
$164$	−12.2613			−0.957446
$165$	3.14826	−	4.80504i	0.245092	−	0.374072i
$166$	−49.3728			−3.83207
$167$	−6.83831			−0.529164			−0.264582	−	0.964363i	$-0.585234\pi$
$167$	−6.83831			−0.529164			−0.264582	+	0.964363i	$0.585234\pi$
$168$	8.79126	−	13.4388i	0.678261	−	1.03683i
$169$	12.9704			0.997722
$170$			2.19267i			0.168170i
$171$	−8.23277	+	3.59971i	−0.629576	+	0.275277i
$172$			53.6735i			4.09257i
$173$	23.5066			1.78717			0.893587	−	0.448889i	$-0.148180\pi$
$173$	23.5066			1.78717			0.893587	+	0.448889i	$0.148180\pi$
$174$	30.6097	+	20.0239i	2.32051	+	1.51801i
$175$			1.00000i			0.0755929i
$176$	−47.8240	−	0.0344790i	−3.60487	−	0.00259895i
$177$	5.23599	−	8.00402i	0.393561	−	0.601619i
$178$			40.0800i			3.00412i
$179$		−	16.7328i		−	1.25067i	−0.780358	−	0.625333i	$-0.784963\pi$
$179$		−	16.7328i		−	1.25067i	0.780358	−	0.625333i	$-0.215037\pi$
$180$	14.8617	−	6.49817i	1.10773	−	0.484345i
$181$	18.7882			1.39652			0.698259	−	0.715846i	$-0.253959\pi$
$181$	18.7882			1.39652			0.698259	+	0.715846i	$0.253959\pi$
$182$	0.468390			0.0347194
$183$	−3.93742	+	6.01896i	−0.291063	+	0.444934i
$184$		−	2.57006i		−	0.189467i
$185$			1.15232i			0.0847203i
$186$	10.6887	+	6.99224i	0.783734	+	0.512696i
$187$	−2.67212	−	0.00192648i	−0.195405	−	0.000140878i
$188$			60.9843i			4.44774i
$189$	−5.12377	−	0.864280i	−0.372699	−	0.0628671i
$190$	−8.15131			−0.591358
$191$		−	19.9286i		−	1.44198i	−0.692944	−	0.720991i	$-0.743687\pi$
$191$		−	19.9286i		−	1.44198i	0.692944	−	0.720991i	$-0.256313\pi$
$192$	−39.8552	−	26.0721i	−2.87630	−	1.88159i
$193$			21.8093i			1.56987i	0.619581	+	0.784933i	$0.287303\pi$
$193$			21.8093i			1.56987i	−0.619581	+	0.784933i	$0.712697\pi$
$194$	−42.4014			−3.04424
$195$	0.249459	+	0.163189i	0.0178641	+	0.0116862i
$196$	−5.40675			−0.386197
$197$	−10.8244			−0.771207			−0.385604	−	0.922665i	$-0.626007\pi$
$197$	−10.8244			−0.771207			−0.385604	+	0.922665i	$0.626007\pi$
$198$	10.8305	+	24.8187i	0.769689	+	1.76379i
$199$	−1.09079			−0.0773243			−0.0386621	−	0.999252i	$-0.512310\pi$
$199$	−1.09079			−0.0773243			−0.0386621	+	0.999252i	$0.512310\pi$
$200$	9.27160			0.655601
$201$	12.5898	+	8.23588i	0.888017	+	0.580914i
$202$	−0.587572			−0.0413414
$203$		−	7.75959i		−	0.544616i
$204$	−6.31396	−	4.13040i	−0.442066	−	0.289186i
$205$			2.26777i			0.158388i
$206$	−1.32815			−0.0925363
$207$	−0.761940	+	0.333152i	−0.0529585	+	0.0231557i
$208$		−	2.48166i		−	0.172072i
$209$	0.00716174	−	9.93367i	0.000495388	−	0.687126i
$210$	−3.94475	−	2.58054i	−0.272214	−	0.178074i
$211$		−	11.9193i		−	0.820561i	−0.911959	−	0.410280i	$-0.865431\pi$
$211$		−	11.9193i		−	0.820561i	0.911959	−	0.410280i	$-0.134569\pi$
$212$		−	57.0989i		−	3.92157i
$213$	14.1060	−	21.5632i	0.966527	−	1.47749i
$214$	−37.7000			−2.57712
$215$	9.92713			0.677025
$216$	−8.01325	+	47.5055i	−0.545233	+	3.23234i
$217$		−	2.70960i		−	0.183940i
$218$			21.7529i			1.47329i
$219$	−5.85234	+	8.94620i	−0.395464	+	0.604528i
$220$	−0.0129283	+	17.9322i	−0.000871626	+	1.20899i
$221$		−	0.138660i		−	0.00932731i
$222$	−4.54562	−	2.97361i	−0.305082	−	0.199576i
$223$	11.9148			0.797873			0.398936	−	0.916979i	$-0.369379\pi$
$223$	11.9148			0.797873			0.398936	+	0.916979i	$0.369379\pi$
$224$			20.6999i			1.38307i
$225$	−1.20186	−	2.74873i	−0.0801241	−	0.183249i
$226$		−	31.4987i		−	2.09526i
$227$	22.8508			1.51666			0.758330	−	0.651871i	$-0.226016\pi$
$227$	22.8508			1.51666			0.758330	+	0.651871i	$0.226016\pi$
$228$	15.3549	−	23.4723i	1.01690	−	1.55449i
$229$	5.49872			0.363365			0.181683	−	0.983357i	$-0.441846\pi$
$229$	5.49872			0.363365			0.181683	+	0.983357i	$0.441846\pi$
$230$	−0.754401			−0.0497437
$231$	3.14826	−	4.80504i	0.207141	−	0.316149i
$232$	−71.9438			−4.72334
$233$	16.6448			1.09043			0.545217	−	0.838295i	$-0.316447\pi$
$233$	16.6448			1.09043			0.545217	+	0.838295i	$0.316447\pi$
$234$	−1.28748	+	0.562939i	−0.0841651	+	0.0368005i
$235$	11.2793			0.735779
$236$			29.8565i			1.94349i
$237$	−3.22629	+	4.93189i	−0.209570	+	0.320361i
$238$			2.19267i			0.142130i
$239$	−10.1506			−0.656586			−0.328293	−	0.944576i	$-0.606473\pi$
$239$	−10.1506			−0.656586			−0.328293	+	0.944576i	$0.606473\pi$
$240$	−13.6724	+	20.9004i	−0.882552	+	1.34912i
$241$			14.9415i			0.962465i	0.876593	+	0.481233i	$0.159811\pi$
$241$			14.9415i			0.962465i	−0.876593	+	0.481233i	$0.840189\pi$
$242$	−29.9369	−	0.0431663i	−1.92441	−	0.00277484i
$243$	15.1226	−	3.78239i	0.970116	−	0.242640i
$244$		−	22.4518i		−	1.43733i
$245$			1.00000i			0.0638877i
$246$	−8.94581	−	5.85208i	−0.570364	−	0.373115i
$247$	0.515474			0.0327988
$248$	−25.1223			−1.59527
$249$	−26.2954	−	17.2016i	−1.66640	−	1.09011i
$250$		−	2.72154i		−	0.172125i
$251$			22.0026i			1.38879i	0.719593	+	0.694397i	$0.244329\pi$
$251$			22.0026i			1.38879i	−0.719593	+	0.694397i	$0.755671\pi$
$252$	14.8617	−	6.49817i	0.936200	−	0.409346i
$253$	0.000662816	−	0.919358i	4.16709e−5	−	0.0577995i
$254$		−	6.66769i		−	0.418368i
$255$	−0.763934	+	1.16779i	−0.0478394	+	0.0731299i
$256$	35.9962			2.24976
$257$		−	3.49330i		−	0.217906i	−0.994047	−	0.108953i	$-0.965250\pi$
$257$		−	3.49330i		−	0.217906i	0.994047	−	0.108953i	$-0.0347498\pi$
$258$	−25.6174	+	39.1601i	−1.59487	+	2.43800i
$259$			1.15232i			0.0716017i
$260$	−0.930529			−0.0577090
$261$	9.32595	+	21.3290i	0.577262	+	1.32023i
$262$	−41.0916			−2.53865
$263$	−9.26286			−0.571172			−0.285586	−	0.958353i	$-0.592188\pi$
$263$	−9.26286			−0.571172			−0.285586	+	0.958353i	$0.592188\pi$
$264$	−44.5504	−	29.1894i	−2.74189	−	1.79649i
$265$	−10.5607			−0.648737
$266$	−8.15131			−0.499789
$267$	−13.9640	+	21.3462i	−0.854585	+	1.30636i
$268$	−46.9624			−2.86868
$269$		−	22.0189i		−	1.34252i	−0.741224	−	0.671258i	$-0.765754\pi$
$269$		−	22.0189i		−	1.34252i	0.741224	−	0.671258i	$-0.234246\pi$
$270$	13.9445	+	2.35217i	0.848636	+	0.143148i
$271$			21.5629i			1.30985i	0.755692	+	0.654927i	$0.227301\pi$
$271$			21.5629i			1.30985i	−0.755692	+	0.654927i	$0.772699\pi$
$272$	11.6174			0.704408
$273$	0.249459	+	0.163189i	0.0150979	+	0.00987663i
$274$			10.7122i			0.647147i
$275$	3.31662	+	0.00239114i	0.200000	+	0.000144191i
$276$	1.42109	−	2.17235i	0.0855396	−	0.130760i
$277$		−	23.1201i		−	1.38915i	−0.719418	−	0.694577i	$-0.755592\pi$
$277$		−	23.1201i		−	1.38915i	0.719418	−	0.694577i	$-0.244408\pi$
$278$			51.0298i			3.06056i
$279$	3.25657	+	7.44797i	0.194965	+	0.445898i
$280$	9.27160			0.554084
$281$	7.75556			0.462658			0.231329	−	0.972876i	$-0.425693\pi$
$281$	7.75556			0.462658			0.231329	+	0.972876i	$0.425693\pi$
$282$	−29.1066	+	44.4940i	−1.73327	+	2.64958i
$283$			19.2362i			1.14347i	0.820437	+	0.571737i	$0.193730\pi$
$283$			19.2362i			1.14347i	−0.820437	+	0.571737i	$0.806270\pi$
$284$			80.4348i			4.77293i
$285$	−4.34130	−	2.83995i	−0.257156	−	0.168224i
$286$	0.00111998	−	1.55347i	6.62261e−5	−	0.0918587i
$287$			2.26777i			0.133862i
$288$	−24.8784	−	56.8985i	−1.46597	−	3.35278i
$289$	−16.3509			−0.961817
$290$			21.1180i			1.24009i
$291$	−22.5825	−	14.7728i	−1.32381	−	0.865997i
$292$		−	33.3710i		−	1.95289i
$293$	1.86080			0.108709			0.0543545	−	0.998522i	$-0.482690\pi$
$293$	1.86080			0.108709			0.0543545	+	0.998522i	$0.482690\pi$
$294$	−3.94475	−	2.58054i	−0.230063	−	0.150500i
$295$	5.52208			0.321508
$296$	10.6839			0.620986
$297$	−2.87874	+	16.9916i	−0.167042	+	0.985950i
$298$	33.8311			1.95978
$299$	0.0477070			0.00275896
$300$	7.83687	+	5.12664i	0.452462	+	0.295987i
$301$	9.92713			0.572190
$302$			41.5393i			2.39032i
$303$	−0.312934	−	0.204712i	−0.0179776	−	0.0117604i
$304$			43.1880i			2.47700i
$305$	−4.15256			−0.237775
$306$	−2.63529	−	6.02706i	−0.150649	−	0.344544i
$307$		−	2.56587i		−	0.146442i	−0.997316	−	0.0732208i	$-0.976672\pi$
$307$		−	2.56587i		−	0.146442i	0.997316	−	0.0732208i	$-0.0233278\pi$
$308$	−0.0129283	+	17.9322i	−0.000736658	+	1.02178i
$309$	−0.707355	−	0.462731i	−0.0402400	−	0.0263238i
$310$			7.37428i			0.418831i
$311$			10.8136i			0.613185i	0.951841	+	0.306593i	$0.0991889\pi$
$311$			10.8136i			0.613185i	−0.951841	+	0.306593i	$0.900811\pi$
$312$	1.51302	−	2.31288i	0.0856579	−	0.130941i
$313$	2.72343			0.153937			0.0769686	−	0.997034i	$-0.475476\pi$
$313$	2.72343			0.153937			0.0769686	+	0.997034i	$0.475476\pi$
$314$	25.1635			1.42006
$315$	−1.20186	−	2.74873i	−0.0677172	−	0.154874i
$316$		−	18.3969i		−	1.03490i
$317$		−	34.4141i		−	1.93289i	−0.256873	−	0.966445i	$-0.582692\pi$
$317$		−	34.4141i		−	1.93289i	0.256873	−	0.966445i	$-0.417308\pi$
$318$	27.2522	−	41.6592i	1.52823	−	2.33613i
$319$	−25.7356	−	0.0185543i	−1.44092	−	0.00103884i
$320$		−	27.4966i		−	1.53711i
$321$	−20.0786	−	13.1348i	−1.12068	−	0.733114i
$322$	−0.754401			−0.0420411
$323$			2.41309i			0.134268i
$324$	−33.0410	+	35.7234i	−1.83561	+	1.98464i
$325$			0.172105i			0.00954667i
$326$	32.4811			1.79896
$327$	−7.57878	+	11.5853i	−0.419107	+	0.640670i
$328$	21.0259			1.16096
$329$	11.2793			0.621847
$330$	−8.56811	+	13.0771i	−0.471659	+	0.719870i
$331$	−2.92456			−0.160749			−0.0803743	−	0.996765i	$-0.525612\pi$
$331$	−2.92456			−0.160749			−0.0803743	+	0.996765i	$0.525612\pi$
$332$	98.0867			5.38321
$333$	−1.38493	−	3.16742i	−0.0758937	−	0.173574i
$334$	18.6107			1.01833
$335$			8.68588i			0.474560i
$336$	−13.6724	+	20.9004i	−0.745893	+	1.14021i
$337$		−	13.0089i		−	0.708640i	−0.935124	−	0.354320i	$-0.884712\pi$
$337$		−	13.0089i		−	0.708640i	0.935124	−	0.354320i	$-0.115288\pi$
$338$	−35.2993			−1.92003
$339$	10.9743	−	16.7758i	0.596040	−	0.911139i
$340$		−	4.35608i		−	0.236242i
$341$	−8.98673	−	0.00647903i	−0.486659	−	0.000350859i
$342$	22.4058	−	9.79675i	1.21157	−	0.529747i
$343$			1.00000i			0.0539949i
$344$		−	92.0404i		−	4.96248i
$345$	−0.401785	−	0.262836i	−0.0216314	−	0.0141506i
$346$	−63.9741			−3.43927
$347$	−8.30106			−0.445624			−0.222812	−	0.974861i	$-0.571524\pi$
$347$	−8.30106			−0.445624			−0.222812	+	0.974861i	$0.571524\pi$
$348$	−60.8109	−	39.7807i	−3.25980	−	2.13247i
$349$			13.4179i			0.718243i	0.933291	+	0.359121i	$0.116924\pi$
$349$			13.4179i			0.718243i	−0.933291	+	0.359121i	$0.883076\pi$
$350$		−	2.72154i		−	0.145472i
$351$	−0.881826	−	0.148747i	−0.0470684	−	0.00793952i
$352$	68.6538	+	0.0494964i	3.65926	+	0.00263816i
$353$			2.79079i			0.148539i	0.997238	+	0.0742693i	$0.0236624\pi$
$353$			2.79079i			0.148539i	−0.997238	+	0.0742693i	$0.976338\pi$
$354$	−14.2499	+	21.7832i	−0.757375	+	1.15777i
$355$	14.8767			0.789575
$356$		−	79.6252i		−	4.22013i
$357$	−0.763934	+	1.16779i	−0.0404317	+	0.0618061i
$358$			45.5388i			2.40680i
$359$	12.6490			0.667591			0.333795	−	0.942646i	$-0.391671\pi$
$359$	12.6490			0.667591			0.333795	+	0.942646i	$0.391671\pi$
$360$	−25.4851	+	11.1432i	−1.34319	+	0.587297i
$361$	10.0293			0.527857
$362$	−51.1328			−2.68748
$363$	−15.9290	−	10.4531i	−0.836055	−	0.548645i
$364$	−0.930529			−0.0487730
$365$	−6.17210			−0.323062
$366$	10.7158	−	16.3808i	0.560126	−	0.856238i
$367$	20.5199			1.07113			0.535566	−	0.844494i	$-0.320098\pi$
$367$	20.5199			1.07113			0.535566	+	0.844494i	$0.320098\pi$
$368$			3.99703i			0.208360i
$369$	−2.72555	−	6.23350i	−0.141886	−	0.324503i
$370$		−	3.13608i		−	0.163037i
$371$	−10.5607			−0.548283
$372$	−21.2348	−	13.8912i	−1.10097	−	0.720223i
$373$			6.46957i			0.334982i	0.985874	+	0.167491i	$0.0535664\pi$
$373$			6.46957i			0.334982i	−0.985874	+	0.167491i	$0.946434\pi$
$374$	7.27226	+	0.00524298i	0.376040	+	0.000271108i
$375$	0.948193	−	1.44946i	0.0489645	−	0.0748497i
$376$		−	104.577i		−	5.39315i
$377$		−	1.33546i		−	0.0687799i
$378$	13.9445	+	2.35217i	0.717229	+	0.120982i
$379$	27.7284			1.42431			0.712155	−	0.702022i	$-0.247719\pi$
$379$	27.7284			1.42431			0.712155	+	0.702022i	$0.247719\pi$
$380$	16.1939			0.830727
$381$	2.32305	−	3.55114i	0.119013	−	0.181930i
$382$			54.2364i			2.77497i
$383$		−	14.3961i		−	0.735607i	−0.929903	−	0.367804i	$-0.880110\pi$
$383$		−	14.3961i		−	0.735607i	0.929903	−	0.367804i	$-0.119890\pi$
$384$	48.4599	+	31.7010i	2.47296	+	1.61774i
$385$	3.31662	+	0.00239114i	0.169031	+	0.000121864i
$386$		−	59.3547i		−	3.02108i
$387$	−27.2870	+	11.9310i	−1.38708	+	0.606489i
$388$	84.2369			4.27648
$389$		−	18.3625i		−	0.931017i	−0.885043	−	0.465508i	$-0.845872\pi$
$389$		−	18.3625i		−	0.931017i	0.885043	−	0.465508i	$-0.154128\pi$
$390$	−0.678912	−	0.444124i	−0.0343780	−	0.0224891i
$391$			0.223330i			0.0112943i
$392$	9.27160			0.468286
$393$	−21.8849	−	14.3165i	−1.10395	−	0.722171i
$394$	29.4590			1.48412
$395$	−3.40257			−0.171202
$396$	−21.5164	−	49.3063i	−1.08124	−	2.47773i
$397$	21.7707			1.09264			0.546320	−	0.837576i	$-0.316028\pi$
$397$	21.7707			1.09264			0.546320	+	0.837576i	$0.316028\pi$
$398$	2.96863			0.148804
$399$	−4.34130	−	2.83995i	−0.217337	−	0.142175i
$400$	−14.4195			−0.720974
$401$			7.26794i			0.362943i	0.983396	+	0.181472i	$0.0580861\pi$
$401$			7.26794i			0.362943i	−0.983396	+	0.181472i	$0.941914\pi$
$402$	−34.2636	−	22.4142i	−1.70891	−	1.11792i
$403$		−	0.466336i		−	0.0232298i
$404$	1.16730			0.0580755
$405$	6.60719	+	6.11106i	0.328314	+	0.303661i
$406$			21.1180i			1.04807i
$407$	3.82181	+	0.00275536i	0.189440	+	0.000136578i
$408$	10.8273	+	7.08289i	0.536031	+	0.350655i
$409$			25.5498i			1.26335i	0.775231	+	0.631677i	$0.217633\pi$
$409$			25.5498i			1.26335i	−0.775231	+	0.631677i	$0.782367\pi$
$410$		−	6.17182i		−	0.304805i
$411$	−3.73216	+	5.70519i	−0.184094	+	0.281416i
$412$	2.63857			0.129993
$413$	5.52208			0.271724
$414$	2.07365	−	0.906685i	0.101914	−	0.0445612i
$415$		−	18.1415i		−	0.890532i
$416$			3.56256i			0.174669i
$417$	−17.7790	+	27.1779i	−0.870639	+	1.33091i
$418$	−0.0194909	+	27.0348i	−0.000953332	+	1.32232i
$419$			0.887405i			0.0433526i	0.999765	+	0.0216763i	$0.00690032\pi$
$419$			0.887405i			0.0433526i	−0.999765	+	0.0216763i	$0.993100\pi$
$420$	7.83687	+	5.12664i	0.382400	+	0.250155i
$421$	19.1695			0.934262			0.467131	−	0.884188i	$-0.345288\pi$
$421$	19.1695			0.934262			0.467131	+	0.884188i	$0.345288\pi$
$422$			32.4389i			1.57910i
$423$	−31.0037	+	13.5561i	−1.50745	+	0.659122i
$424$			97.9143i			4.75514i
$425$	−0.805674			−0.0390809
$426$	−38.3900	+	58.6850i	−1.86000	+	2.84330i
$427$	−4.15256			−0.200956
$428$	74.8969			3.62028
$429$	0.541832	−	0.826972i	0.0261599	−	0.0399266i
$430$	−27.0170			−1.30288
$431$	28.7718			1.38589			0.692945	−	0.720991i	$-0.256313\pi$
$431$	28.7718			1.38589			0.692945	+	0.720991i	$0.256313\pi$
$432$	12.4625	−	73.8821i	0.599600	−	3.55465i
$433$	6.02132			0.289366			0.144683	−	0.989478i	$-0.453784\pi$
$433$	6.02132			0.289366			0.144683	+	0.989478i	$0.453784\pi$
$434$			7.37428i			0.353977i
$435$	−7.35759	+	11.2472i	−0.352769	+	0.539262i
$436$		−	43.2155i		−	2.06965i
$437$	−0.830237			−0.0397156
$438$	15.9273	−	24.3474i	0.761038	−	1.16336i
$439$		−	11.4284i		−	0.545447i	−0.962092	−	0.272723i	$-0.912076\pi$
$439$		−	11.4284i		−	0.545447i	0.962092	−	0.272723i	$-0.0879244\pi$
$440$	0.0221697	−	30.7504i	0.00105690	−	1.46597i
$441$	−1.20186	−	2.74873i	−0.0572315	−	0.130892i
$442$			0.377369i			0.0179496i
$443$			13.9506i			0.662814i	0.943488	+	0.331407i	$0.107523\pi$
$443$			13.9506i			0.662814i	−0.943488	+	0.331407i	$0.892477\pi$
$444$	9.03058	+	5.90754i	0.428572	+	0.280359i
$445$	−14.7270			−0.698126
$446$	−32.4265			−1.53544
$447$	18.0181	+	11.7869i	0.852226	+	0.557501i
$448$		−	27.4966i		−	1.29909i
$449$			20.3223i			0.959070i	0.877523	+	0.479535i	$0.159195\pi$
$449$			20.3223i			0.959070i	−0.877523	+	0.479535i	$0.840805\pi$
$450$	3.27091	+	7.48077i	0.154192	+	0.352647i
$451$	7.52135	+	0.00542256i	0.354167	+	0.000255338i
$452$			62.5770i			2.94338i
$453$	−14.4725	+	22.1234i	−0.679975	+	1.03945i
$454$	−62.1892			−2.91868
$455$			0.172105i			0.00806840i
$456$	−26.3308	+	40.2508i	−1.23305	+	1.88491i
$457$			19.8529i			0.928680i	0.885657	+	0.464340i	$0.153708\pi$
$457$			19.8529i			0.928680i	−0.885657	+	0.464340i	$0.846292\pi$
$458$	−14.9650			−0.699266
$459$	0.696328	−	4.12809i	0.0325018	−	0.192683i
$460$	1.49874			0.0698789
$461$	−14.5172			−0.676134			−0.338067	−	0.941122i	$-0.609773\pi$
$461$	−14.5172			−0.676134			−0.338067	+	0.941122i	$0.609773\pi$
$462$	−8.56811	+	13.0771i	−0.398625	+	0.608401i
$463$	−8.28367			−0.384975			−0.192487	−	0.981299i	$-0.561655\pi$
$463$	−8.28367			−0.384975			−0.192487	+	0.981299i	$0.561655\pi$
$464$	111.889			5.19433
$465$	−2.56922	+	3.92746i	−0.119145	+	0.182131i
$466$	−45.2993			−2.09845
$467$			36.8146i			1.70358i	0.523886	+	0.851788i	$0.324482\pi$
$467$			36.8146i			1.70358i	−0.523886	+	0.851788i	$0.675518\pi$
$468$	2.55778	−	1.11837i	0.118233	−	0.0516965i
$469$			8.68588i			0.401076i
$470$	−30.6970			−1.41595
$471$	13.4018	+	8.76707i	0.617523	+	0.403965i
$472$		−	51.1985i		−	2.35660i
$473$	0.0237371	−	32.9246i	0.00109144	−	1.51387i
$474$	8.78047	−	13.4223i	0.403301	−	0.616507i
$475$		−	2.99512i		−	0.137425i
$476$		−	4.35608i		−	0.199661i
$477$	29.0285	−	12.6925i	1.32912	−	0.581148i
$478$	27.6251			1.26354
$479$	−39.8146			−1.81918			−0.909589	−	0.415510i	$-0.863603\pi$
$479$	−39.8146			−1.81918			−0.909589	+	0.415510i	$0.863603\pi$
$480$	19.6275	−	30.0037i	0.895869	−	1.36947i
$481$			0.198320i			0.00904262i
$482$		−	40.6638i		−	1.85218i
$483$	−0.401785	−	0.262836i	−0.0182819	−	0.0119595i
$484$	59.4742	+	0.0857566i	2.70337	+	0.00389803i
$485$		−	15.5799i		−	0.707449i
$486$	−41.1567	+	10.2939i	−1.86691	+	0.466941i
$487$	−25.6257			−1.16121			−0.580606	−	0.814185i	$-0.697184\pi$
$487$	−25.6257			−1.16121			−0.580606	+	0.814185i	$0.697184\pi$
$488$			38.5008i			1.74285i
$489$	17.2990	+	11.3165i	0.782290	+	0.511751i
$490$		−	2.72154i		−	0.122946i
$491$	−4.88356			−0.220392			−0.110196	−	0.993910i	$-0.535148\pi$
$491$	−4.88356			−0.220392			−0.110196	+	0.993910i	$0.535148\pi$
$492$	17.7722	+	11.6261i	0.801234	+	0.524144i
$493$	6.25170			0.281562
$494$	−1.40288			−0.0631186
$495$	−9.11939	+	3.97955i	−0.409886	+	0.178867i
$496$	39.0710			1.75434
$497$	14.8767			0.667312
$498$	71.5638	+	46.8149i	3.20685	+	2.09783i
$499$	19.6421			0.879303			0.439651	−	0.898169i	$-0.355102\pi$
$499$	19.6421			0.879303			0.439651	+	0.898169i	$0.355102\pi$
$500$			5.40675i			0.241797i
$501$	9.91185	+	6.48404i	0.442829	+	0.289685i
$502$		−	59.8809i		−	2.67262i
$503$	−14.6898			−0.654985			−0.327492	−	0.944854i	$-0.606204\pi$
$503$	−14.6898			−0.654985			−0.327492	+	0.944854i	$0.606204\pi$
$504$	−25.4851	+	11.1432i	−1.13520	+	0.496356i
$505$		−	0.215897i		−	0.00960730i
$506$	−0.00180388	+	2.50206i	−8.01921e−5	+	0.111230i
$507$	−18.8000	−	12.2984i	−0.834939	−	0.546192i
$508$			13.2464i			0.587714i
$509$			24.7908i			1.09883i	0.835548	+	0.549417i	$0.185150\pi$
$509$			24.7908i			1.09883i	−0.835548	+	0.549417i	$0.814850\pi$
$510$	2.07907	−	3.17818i	0.0920629	−	0.140732i
$511$	−6.17210			−0.273038
$512$	−31.0987			−1.37438
$513$	15.3463	+	2.58862i	0.677555	+	0.114290i
$514$			9.50713i			0.419342i
$515$		−	0.488013i		−	0.0215044i
$516$	50.8929	−	77.7976i	2.24043	−	3.42485i
$517$	0.0269703	−	37.4091i	0.00118615	−	1.64525i
$518$		−	3.13608i		−	0.137792i
$519$	−34.0719	−	22.2888i	−1.49559	−	0.978370i
$520$	1.59569			0.0699756
$521$		−	9.73355i		−	0.426435i	−0.977005	−	0.213217i	$-0.931606\pi$
$521$		−	9.73355i		−	0.426435i	0.977005	−	0.213217i	$-0.0683942\pi$
$522$	−25.3809	−	58.0477i	−1.11089	−	2.54068i
$523$		−	4.63100i		−	0.202499i	−0.994861	−	0.101250i	$-0.967716\pi$
$523$		−	4.63100i		−	0.202499i	0.994861	−	0.101250i	$-0.0322841\pi$
$524$	81.6349			3.56624
$525$	0.948193	−	1.44946i	0.0413825	−	0.0632596i
$526$	25.2092			1.09917
$527$	2.18306			0.0950954
$528$	69.2862	+	45.3963i	3.01529	+	1.97562i
$529$	22.9232			0.996659
$530$	28.7412			1.24844
$531$	−15.1787	+	6.63677i	−0.658700	+	0.288011i
$532$	16.1939			0.702092
$533$			0.390295i			0.0169056i
$534$	38.0036	−	58.0943i	1.64458	−	2.51399i
$535$		−	13.8525i		−	0.598895i
$536$	80.5320			3.47845
$537$	−15.8659	+	24.2534i	−0.684663	+	1.04661i
$538$			59.9252i			2.58356i
$539$	3.31662	+	0.00239114i	0.142857	+	0.000102994i
$540$	−27.7030	−	4.67295i	−1.19215	−	0.201092i
$541$			33.9406i			1.45922i	0.683863	+	0.729610i	$0.260299\pi$
$541$			33.9406i			1.45922i	−0.683863	+	0.729610i	$0.739701\pi$
$542$		−	58.6843i		−	2.52071i
$543$	−27.2327	−	17.8149i	−1.16867	−	0.764508i
$544$	−16.6774			−0.715037
$545$	−7.99287			−0.342377
$546$	−0.678912	−	0.444124i	−0.0290547	−	0.0190067i
$547$		−	2.35160i		−	0.100547i	−0.998735	−	0.0502735i	$-0.983991\pi$
$547$		−	2.35160i		−	0.100547i	0.998735	−	0.0502735i	$-0.0160093\pi$
$548$		−	21.2814i		−	0.909097i
$549$	11.4143	−	4.99080i	0.487149	−	0.213002i
$550$	−9.02631	−	0.00650757i	−0.384883	−	0.000277484i
$551$			23.2409i			0.990094i
$552$	−2.43691	+	3.72519i	−0.103722	+	0.158555i
$553$	−3.40257			−0.144692
$554$			62.9222i			2.67331i
$555$	1.09262	−	1.67024i	0.0463792	−	0.0708978i
$556$		−	101.379i		−	4.29941i
$557$	−7.96546			−0.337507			−0.168754	−	0.985658i	$-0.553974\pi$
$557$	−7.96546			−0.337507			−0.168754	+	0.985658i	$0.553974\pi$
$558$	−8.86286	−	20.2699i	−0.375195	−	0.858094i
$559$	1.70851			0.0722622
$560$	−14.4195			−0.609334
$561$	3.87130	+	2.53647i	0.163446	+	0.107090i
$562$	−21.1070			−0.890346
$563$	25.1595			1.06035			0.530174	−	0.847889i	$-0.322127\pi$
$563$	25.1595			1.06035			0.530174	+	0.847889i	$0.322127\pi$
$564$	57.8249	−	88.3942i	2.43487	−	3.72207i
$565$	11.5739			0.486916
$566$		−	52.3520i		−	2.20052i
$567$	6.60719	+	6.11106i	0.277476	+	0.256640i
$568$		−	137.931i		−	5.78746i
$569$	−23.6867			−0.992998			−0.496499	−	0.868037i	$-0.665381\pi$
$569$	−23.6867			−0.992998			−0.496499	+	0.868037i	$0.665381\pi$
$570$	11.8150	+	7.72901i	0.494875	+	0.323733i
$571$			16.6368i			0.696227i	0.937452	+	0.348114i	$0.113178\pi$
$571$			16.6368i			0.696227i	−0.937452	+	0.348114i	$0.886822\pi$
$572$	−0.00222502	+	3.08621i	−9.30329e−5	+	0.129041i
$573$	−18.8961	+	28.8857i	−0.789398	+	1.20672i
$574$		−	6.17182i		−	0.257607i
$575$		−	0.277197i		−	0.0115599i
$576$	33.0471	+	75.5807i	1.37696	+	3.14920i
$577$	11.8929			0.495109			0.247554	−	0.968874i	$-0.420373\pi$
$577$	11.8929			0.495109			0.247554	+	0.968874i	$0.420373\pi$
$578$	44.4995			1.85094
$579$	20.6794	−	31.6116i	0.859406	−	1.31374i
$580$		−	41.9542i		−	1.74205i
$581$		−	18.1415i		−	0.752637i
$582$	61.4590	+	40.2047i	2.54756	+	1.66654i
$583$	−0.0252520	+	35.0258i	−0.00104583	+	1.45062i
$584$			57.2252i			2.36800i
$585$	−0.206846	−	0.473070i	−0.00855204	−	0.0195591i
$586$	−5.06423			−0.209201
$587$		−	42.5068i		−	1.75444i	−0.480087	−	0.877221i	$-0.659395\pi$
$587$		−	42.5068i		−	1.75444i	0.480087	−	0.877221i	$-0.340605\pi$
$588$	7.83687	+	5.12664i	0.323187	+	0.211419i
$589$			8.11557i			0.334396i
$590$	−15.0285			−0.618714
$591$	15.6895	+	10.2636i	0.645381	+	0.422189i
$592$	−16.6159			−0.682908
$593$	2.87782			0.118178			0.0590889	−	0.998253i	$-0.481180\pi$
$593$	2.87782			0.118178			0.0590889	+	0.998253i	$0.481180\pi$
$594$	7.83460	−	46.2431i	0.321457	−	1.89738i
$595$	−0.805674			−0.0330294
$596$	−67.2108			−2.75306
$597$	1.58106	+	1.03428i	0.0647085	+	0.0423303i
$598$	−0.129836			−0.00530940
$599$			19.2896i			0.788153i	0.919078	+	0.394076i	$0.128935\pi$
$599$			19.2896i			0.788153i	−0.919078	+	0.394076i	$0.871065\pi$
$600$	−13.4388	−	8.79126i	−0.548637	−	0.358902i
$601$			16.0532i			0.654822i	0.944882	+	0.327411i	$0.106176\pi$
$601$			16.0532i			0.654822i	−0.944882	+	0.327411i	$0.893824\pi$
$602$	−27.0170			−1.10113
$603$	−10.4392	−	23.8751i	−0.425118	−	0.972271i
$604$		−	82.5243i		−	3.35787i
$605$	0.0158610	−	11.0000i	0.000644842	−	0.447213i
$606$	0.851662	+	0.557132i	0.0345964	+	0.0226319i
$607$			18.9219i			0.768015i	0.923330	+	0.384007i	$0.125456\pi$
$607$			18.9219i			0.768015i	−0.923330	+	0.384007i	$0.874544\pi$
$608$		−	61.9986i		−	2.51438i
$609$	−7.35759	+	11.2472i	−0.298144	+	0.455760i
$610$	11.3013			0.457577
$611$	1.94122			0.0785334
$612$	5.23540	+	11.9737i	0.211629	+	0.484008i
$613$			16.2024i			0.654407i	0.944954	+	0.327204i	$0.106106\pi$
$613$			16.2024i			0.654407i	−0.944954	+	0.327204i	$0.893894\pi$
$614$			6.98309i			0.281815i
$615$	2.15029	−	3.28704i	0.0867079	−	0.132546i
$616$	0.0221697	−	30.7504i	0.000893242	−	1.23897i
$617$			28.2745i			1.13829i	0.822238	+	0.569144i	$0.192725\pi$
$617$			28.2745i			1.13829i	−0.822238	+	0.569144i	$0.807275\pi$
$618$	1.92509	+	1.25934i	0.0774385	+	0.0506580i
$619$	−36.7577			−1.47742			−0.738708	−	0.674025i	$-0.764564\pi$
$619$	−36.7577			−1.47742			−0.738708	+	0.674025i	$0.764564\pi$
$620$		−	14.6501i		−	0.588364i
$621$	1.42029	+	0.239576i	0.0569944	+	0.00961384i
$622$		−	29.4297i		−	1.18002i
$623$	−14.7270			−0.590024
$624$	−2.35309	+	3.59707i	−0.0941992	+	0.143998i
$625$	1.00000			0.0400000
$626$	−7.41190			−0.296239
$627$	−9.42942	+	14.3917i	−0.376575	+	0.574747i
$628$	−49.9913			−1.99487
$629$	−0.928395			−0.0370175
$630$	3.27091	+	7.48077i	0.130316	+	0.298041i
$631$	−4.33480			−0.172566			−0.0862829	−	0.996271i	$-0.527499\pi$
$631$	−4.33480			−0.172566			−0.0862829	+	0.996271i	$0.527499\pi$
$632$			31.5473i			1.25488i
$633$	−11.3018	+	17.2766i	−0.449207	+	0.686682i
$634$			93.6593i			3.71968i
$635$	2.44997			0.0972243
$636$	−54.1408	+	82.7625i	−2.14682	+	3.28175i
$637$			0.172105i			0.00681905i
$638$	70.0405	+	0.0504961i	2.77293	+	0.00199916i
$639$	−40.8921	+	17.8798i	−1.61767	+	0.707312i
$640$			33.4331i			1.32156i
$641$			44.7866i			1.76896i	0.466576	+	0.884481i	$0.345488\pi$
$641$			44.7866i			1.76896i	−0.466576	+	0.884481i	$0.654512\pi$
$642$	54.6446	+	35.7469i	2.15665	+	1.41082i
$643$	−28.3896			−1.11958			−0.559789	−	0.828635i	$-0.689118\pi$
$643$	−28.3896			−1.11958			−0.559789	+	0.828635i	$0.689118\pi$
$644$	1.49874			0.0590584
$645$	−14.3890	−	9.41283i	−0.566565	−	0.370630i
$646$		−	6.56730i		−	0.258387i
$647$			39.9059i			1.56886i	0.620215	+	0.784432i	$0.287045\pi$
$647$			39.9059i			1.56886i	−0.620215	+	0.784432i	$0.712955\pi$
$648$	56.6593	−	61.2592i	2.22579	−	2.40649i
$649$	0.0132040	−	18.3146i	0.000518304	−	0.718913i
$650$		−	0.468390i		−	0.0183718i
$651$	−2.56922	+	3.92746i	−0.100696	+	0.153929i
$652$	−64.5287			−2.52714
$653$		−	23.0556i		−	0.902236i	−0.892464	−	0.451118i	$-0.851025\pi$
$653$		−	23.0556i		−	0.902236i	0.892464	−	0.451118i	$-0.148975\pi$
$654$	20.6259	−	31.5299i	0.806537	−	1.23292i
$655$		−	15.0987i		−	0.589955i
$656$	−32.7001			−1.27672
$657$	16.9654	−	7.41801i	0.661885	−	0.289404i
$658$	−30.6970			−1.19669
$659$	−15.9548			−0.621512			−0.310756	−	0.950490i	$-0.600582\pi$
$659$	−15.9548			−0.621512			−0.310756	+	0.950490i	$0.600582\pi$
$660$	17.0219	−	25.9797i	0.662576	−	1.01126i
$661$	16.3665			0.636584			0.318292	−	0.947993i	$-0.396891\pi$
$661$	16.3665			0.636584			0.318292	+	0.947993i	$0.396891\pi$
$662$	7.95930			0.309347
$663$	−0.131477	+	0.200983i	−0.00510614	+	0.00780552i
$664$	−168.201			−6.52746
$665$		−	2.99512i		−	0.116146i
$666$	3.76913	+	8.62025i	0.146051	+	0.334028i
$667$			2.15093i			0.0832845i
$668$	−36.9731			−1.43053
$669$	−17.2700	−	11.2975i	−0.667696	−	0.436787i
$670$		−	23.6389i		−	0.913251i
$671$	−0.00992934	+	13.7725i	−0.000383318	+	0.531680i
$672$	19.6275	−	30.0037i	0.757147	−	1.15742i
$673$			10.5404i			0.406302i	0.979147	+	0.203151i	$0.0651182\pi$
$673$			10.5404i			0.406302i	−0.979147	+	0.203151i	$0.934882\pi$
$674$			35.4042i			1.36372i
$675$	−0.864280	+	5.12377i	−0.0332661	+	0.197214i
$676$	70.1276			2.69722
$677$	−23.5251			−0.904142			−0.452071	−	0.891982i	$-0.649315\pi$
$677$	−23.5251			−0.904142			−0.452071	+	0.891982i	$0.649315\pi$
$678$	−29.8668	+	45.6560i	−1.14703	+	1.75341i
$679$		−	15.5799i		−	0.597904i
$680$			7.46989i			0.286457i
$681$	−33.1213	−	21.6669i	−1.26921	−	0.830279i
$682$	24.4577	+	0.0176329i	0.936534	+	0.000675199i
$683$		−	11.0546i		−	0.422993i	−0.977379	−	0.211497i	$-0.932166\pi$
$683$		−	11.0546i		−	0.422993i	0.977379	−	0.211497i	$-0.0678338\pi$
$684$	−44.5126	+	19.4628i	−1.70198	+	0.744177i
$685$	−3.93608			−0.150390
$686$		−	2.72154i		−	0.103909i
$687$	−7.97016	−	5.21384i	−0.304081	−	0.198921i
$688$			143.144i			5.45731i
$689$	−1.81754			−0.0692429
$690$	1.09347	+	0.715318i	0.0416278	+	0.0272317i
$691$	32.9085			1.25190			0.625949	−	0.779864i	$-0.284712\pi$
$691$	32.9085			1.25190			0.625949	+	0.779864i	$0.284712\pi$
$692$	127.094			4.83141
$693$	−9.11939	+	3.97955i	−0.346417	+	0.151171i
$694$	22.5916			0.857566
$695$	−18.7504			−0.711242
$696$	104.280	+	68.2166i	3.95271	+	2.58574i
$697$	−1.82709			−0.0692058
$698$		−	36.5172i		−	1.38220i
$699$	−24.1259	−	15.7824i	−0.912525	−	0.596947i
$700$			5.40675i			0.204356i
$701$	14.4987			0.547607			0.273804	−	0.961786i	$-0.411718\pi$
$701$	14.4987			0.547607			0.273804	+	0.961786i	$0.411718\pi$
$702$	2.39992	+	0.404820i	0.0905792	+	0.0152789i
$703$		−	3.45133i		−	0.130170i
$704$	−91.1958	−	0.0657481i	−3.43707	−	0.00247798i
$705$	−16.3489	−	10.6949i	−0.615733	−	0.402794i
$706$		−	7.59522i		−	0.285850i
$707$		−	0.215897i		−	0.00811965i
$708$	28.3097	−	43.2758i	1.06394	−	1.62640i
$709$	1.60433			0.0602520			0.0301260	−	0.999546i	$-0.490409\pi$
$709$	1.60433			0.0602520			0.0301260	+	0.999546i	$0.490409\pi$
$710$	−40.4875			−1.51947
$711$	9.35276	−	4.08942i	0.350756	−	0.153365i
$712$			136.543i			5.11716i
$713$			0.751093i			0.0281287i
$714$	2.07907	−	3.17818i	0.0778074	−	0.118941i
$715$	0.570807		0.000411527i	0.0213470		1.53902e-5i
$716$		−	90.4699i		−	3.38102i
$717$	14.7128	+	9.62470i	0.549461	+	0.359441i
$718$	−34.4248			−1.28472
$719$			5.47717i			0.204264i	0.994771	+	0.102132i	$0.0325664\pi$
$719$			5.47717i			0.204264i	−0.994771	+	0.102132i	$0.967434\pi$
$720$	39.6353	−	17.3302i	1.47712	−	0.645859i
$721$		−	0.488013i		−	0.0181746i
$722$	−27.2950			−1.01582
$723$	14.1674	−	21.6571i	0.526891	−	0.805435i
$724$	101.583			3.77531
$725$	−7.75959			−0.288184
$726$	43.3513	+	28.4485i	1.60892	+	1.05582i
$727$	33.8318			1.25475			0.627376	−	0.778716i	$-0.284129\pi$
$727$	33.8318			1.25475			0.627376	+	0.778716i	$0.284129\pi$
$728$	1.59569			0.0591401
$729$	−25.5060	−	8.85674i	−0.944668	−	0.328027i
$730$	16.7976			0.621706
$731$			7.99803i			0.295818i
$732$	−21.2887	+	32.5430i	−0.786852	+	1.20282i
$733$		−	4.52984i		−	0.167313i	−0.996495	−	0.0836567i	$-0.973340\pi$
$733$		−	4.52984i		−	0.167313i	0.996495	−	0.0836567i	$-0.0266599\pi$
$734$	−55.8457			−2.06130
$735$	0.948193	−	1.44946i	0.0349746	−	0.0534641i
$736$		−	5.73795i		−	0.211504i
$737$	28.8078	+	0.0207691i	1.06115	+	0.000765041i
$738$	7.41768	+	16.9647i	0.273048	+	0.624479i
$739$		−	24.2918i		−	0.893590i	−0.894636	−	0.446795i	$-0.852565\pi$
$739$		−	24.2918i		−	0.893590i	0.894636	−	0.446795i	$-0.147435\pi$
$740$			6.23031i			0.229031i
$741$	−0.747159	−	0.488769i	−0.0274476	−	0.0179554i
$742$	28.7412			1.05512
$743$	−25.4167			−0.932448			−0.466224	−	0.884667i	$-0.654386\pi$
$743$	−25.4167			−0.932448			−0.466224	+	0.884667i	$0.654386\pi$
$744$	36.4138	+	23.8208i	1.33499	+	0.873314i
$745$			12.4309i			0.455433i
$746$		−	17.6072i		−	0.644644i
$747$	21.8036	+	49.8662i	0.797751	+	1.82451i
$748$	−14.4475	−	0.0104160i	−0.528252	−	0.000380846i
$749$		−	13.8525i		−	0.506159i
$750$	−2.58054	+	3.94475i	−0.0942280	+	0.144042i
$751$	−50.1560			−1.83022			−0.915109	−	0.403206i	$-0.867896\pi$
$751$	−50.1560			−1.83022			−0.915109	+	0.403206i	$0.867896\pi$
$752$			162.641i			5.93092i
$753$	20.8627	−	31.8919i	0.760280	−	1.16221i
$754$			3.63451i			0.132361i
$755$	−15.2632			−0.555485
$756$	−27.7030	−	4.67295i	−1.00755	−	0.169953i
$757$	−2.78449			−0.101204			−0.0506020	−	0.998719i	$-0.516114\pi$
$757$	−2.78449			−0.101204			−0.0506020	+	0.998719i	$0.516114\pi$
$758$	−75.4637			−2.74097
$759$	−0.872689	+	1.33194i	−0.0316766	+	0.0483465i
$760$	−27.7695			−1.00731
$761$	3.42022			0.123983			0.0619915	−	0.998077i	$-0.480255\pi$
$761$	3.42022			0.123983			0.0619915	+	0.998077i	$0.480255\pi$
$762$	−6.32226	+	9.66454i	−0.229031	+	0.350109i
$763$	−7.99287			−0.289361
$764$		−	107.749i		−	3.89822i
$765$	2.21458	−	0.968308i	0.0800684	−	0.0350093i
$766$			39.1795i			1.41561i
$767$	0.950376			0.0343161
$768$	−52.1750	−	34.1313i	−1.88270	−	1.23161i
$769$		−	17.5485i		−	0.632816i	−0.948623	−	0.316408i	$-0.897523\pi$
$769$		−	17.5485i		−	0.632816i	0.948623	−	0.316408i	$-0.102477\pi$
$770$	−9.02631	−	0.00650757i	−0.325286	−	0.000234516i
$771$	−3.31232	+	5.06339i	−0.119290	+	0.182354i
$772$			117.917i			4.24394i
$773$			1.59689i			0.0574360i	0.999588	+	0.0287180i	$0.00914249\pi$
$773$			1.59689i			0.0574360i	−0.999588	+	0.0287180i	$0.990858\pi$
$774$	74.2626	−	32.4707i	2.66931	−	1.16714i
$775$	−2.70960			−0.0973318
$776$	−144.451			−5.18549
$777$	1.09262	−	1.67024i	0.0391976	−	0.0599196i
$778$			49.9742i			1.79166i
$779$		−	6.79224i		−	0.243357i
$780$	1.34876	+	0.882321i	0.0482935	+	0.0315922i
$781$	0.0355723	−	49.3405i	0.00127288	−	1.76554i
$782$		−	0.607801i		−	0.0217349i
$783$	6.70646	−	39.7584i	0.239669	−	1.42085i
$784$	−14.4195			−0.514981
$785$			9.24609i			0.330007i
$786$	59.5606	+	38.9628i	2.12446	+	1.38976i
$787$		−	34.2362i		−	1.22039i	−0.792252	−	0.610194i	$-0.791092\pi$
$787$		−	34.2362i		−	1.22039i	0.792252	−	0.610194i	$-0.208908\pi$
$788$	−58.5249			−2.08486
$789$	13.4261	+	8.78298i	0.477983	+	0.312682i
$790$	9.26022			0.329464
$791$	11.5739			0.411519
$792$	36.8968	+	84.5513i	1.31107	+	3.00440i
$793$	−0.714675			−0.0253789
$794$	−59.2497			−2.10269
$795$	15.3073	+	10.0135i	0.542892	+	0.355144i
$796$	−5.89765			−0.209037
$797$		−	44.0963i		−	1.56197i	−0.624549	−	0.780986i	$-0.714717\pi$
$797$		−	44.0963i		−	1.56197i	0.624549	−	0.780986i	$-0.285283\pi$
$798$	11.8150	+	7.72901i	0.418246	+	0.273604i
$799$			9.08742i			0.321490i
$800$	20.6999			0.731852
$801$	40.4806	−	17.6998i	1.43031	−	0.625392i
$802$		−	19.7799i		−	0.698454i
$803$	−0.0147583	+	20.4705i	−0.000520811	+	0.722389i
$804$	68.0700	+	44.5294i	2.40065	+	1.57043i
$805$		−	0.277197i		−	0.00976991i
$806$			1.26915i			0.0447039i
$807$	−20.8782	+	31.9155i	−0.734946	+	1.12348i
$808$	−2.00171			−0.0704200
$809$	−8.76247			−0.308072			−0.154036	−	0.988065i	$-0.549227\pi$
$809$	−8.76247			−0.308072			−0.154036	+	0.988065i	$0.549227\pi$
$810$	−17.9817	−	16.6315i	−0.631812	−	0.584370i
$811$			30.8999i			1.08504i	0.840043	+	0.542520i	$0.182530\pi$
$811$			30.8999i			1.08504i	−0.840043	+	0.542520i	$0.817470\pi$
$812$		−	41.9542i		−	1.47230i
$813$	20.4458	−	31.2546i	0.717066	−	1.09615i
$814$	−10.4012	−	0.00749881i	−0.364562	−	0.000262833i
$815$			11.9348i			0.418059i
$816$	−16.8389	−	11.0155i	−0.589481	−	0.385621i
$817$	−29.7329			−1.04022
$818$		−	69.5346i		−	2.43122i
$819$	−0.206846	−	0.473070i	−0.00722779	−	0.0165304i
$820$			12.2613i			0.428183i
$821$	50.3975			1.75889			0.879443	−	0.476005i	$-0.157916\pi$
$821$	50.3975			1.75889			0.879443	+	0.476005i	$0.157916\pi$
$822$	10.1572	−	15.5269i	0.354273	−	0.541562i
$823$	39.5308			1.37796			0.688978	−	0.724782i	$-0.258060\pi$
$823$	39.5308			1.37796			0.688978	+	0.724782i	$0.258060\pi$
$824$	−4.52466			−0.157624
$825$	−4.80504	−	3.14826i	−0.167290	−	0.109608i
$826$	−15.0285			−0.522909
$827$	−28.3617			−0.986234			−0.493117	−	0.869963i	$-0.664143\pi$
$827$	−28.3617			−0.986234			−0.493117	+	0.869963i	$0.664143\pi$
$828$	−4.11962	+	1.80127i	−0.143167	+	0.0625985i
$829$	−33.8527			−1.17575			−0.587877	−	0.808950i	$-0.700036\pi$
$829$	−33.8527			−1.17575			−0.587877	+	0.808950i	$0.700036\pi$
$830$			49.3728i			1.71375i
$831$	−21.9223	+	33.5117i	−0.760477	+	1.16251i
$832$		−	4.73230i		−	0.164063i
$833$	−0.805674			−0.0279150
$834$	48.3861	−	73.9655i	1.67547	−	2.56122i
$835$			6.83831i			0.236650i
$836$	0.0387217	−	53.7089i	0.00133922	−	1.85756i
$837$	2.34185	−	13.8834i	0.0809463	−	0.479880i
$838$		−	2.41510i		−	0.0834284i
$839$			19.2183i			0.663490i	0.943369	+	0.331745i	$0.107637\pi$
$839$			19.2183i			0.663490i	−0.943369	+	0.331745i	$0.892363\pi$
$840$	−13.4388	−	8.79126i	−0.463683	−	0.303327i
$841$	31.2112			1.07625
$842$	−52.1704			−1.79791
$843$	−11.2414	−	7.35376i	−0.387173	−	0.253277i
$844$		−	64.4449i		−	2.21828i
$845$		−	12.9704i		−	0.446195i
$846$	84.3777	−	36.8935i	2.90097	−	1.26842i
$847$	0.0158610	−	11.0000i	0.000544991	−	0.377964i
$848$		−	152.279i		−	5.22929i
$849$	18.2396	−	27.8821i	0.625982	−	0.956911i
$850$	2.19267			0.0752080
$851$		−	0.319420i		−	0.0109496i
$852$	76.2677	−	116.587i	2.61289	−	3.99420i
$853$			45.2402i			1.54900i	0.632577	+	0.774498i	$0.281997\pi$
$853$			45.2402i			1.54900i	−0.632577	+	0.774498i	$0.718003\pi$
$854$	11.3013			0.386723
$855$	3.59971	+	8.23277i	0.123108	+	0.281555i
$856$	−128.435			−4.38981
$857$	39.4057			1.34607			0.673037	−	0.739609i	$-0.264990\pi$
$857$	39.4057			1.34607			0.673037	+	0.739609i	$0.264990\pi$
$858$	−1.47461	+	2.25063i	−0.0503425	+	0.0768353i
$859$	−0.570560			−0.0194673			−0.00973363	−	0.999953i	$-0.503098\pi$
$859$	−0.570560			−0.0194673			−0.00973363	+	0.999953i	$0.503098\pi$
$860$	53.6735			1.83025
$861$	2.15029	−	3.28704i	0.0732816	−	0.112022i
$862$	−78.3035			−2.66703
$863$		−	37.9106i		−	1.29049i	−0.763975	−	0.645246i	$-0.776755\pi$
$863$		−	37.9106i		−	1.29049i	0.763975	−	0.645246i	$-0.223245\pi$
$864$	−17.8905	+	106.062i	−0.608648	+	3.60829i
$865$		−	23.5066i		−	0.799249i
$866$	−16.3872			−0.556861
$867$	23.6999	+	15.5038i	0.804892	+	0.526536i
$868$		−	14.6501i		−	0.497258i
$869$	−0.00813602	+	11.2851i	−0.000275996	+	0.382819i
$870$	20.0239	−	30.6097i	0.678875	−	1.03776i
$871$			1.49488i			0.0506521i
$872$			74.1067i			2.50957i
$873$	18.7249	+	42.8251i	0.633743	+	1.44941i
$874$	2.25952			0.0764293
$875$	1.00000			0.0338062
$876$	−31.6421	+	48.3699i	−1.06909	+	1.63427i
$877$		−	37.1560i		−	1.25467i	−0.778750	−	0.627335i	$-0.784146\pi$
$877$		−	37.1560i		−	1.25467i	0.778750	−	0.627335i	$-0.215854\pi$
$878$			31.1027i			1.04967i
$879$	−2.69715	−	1.76440i	−0.0909726	−	0.0595116i
$880$	−0.0344790	+	47.8240i	−0.00116229	+	1.61215i
$881$			47.0403i			1.58483i	0.609983	+	0.792414i	$0.291176\pi$
$881$			47.0403i			1.58483i	−0.609983	+	0.792414i	$0.708824\pi$
$882$	3.27091	+	7.48077i	0.110137	+	0.251891i
$883$	−32.0167			−1.07745			−0.538724	−	0.842482i	$-0.681093\pi$
$883$	−32.0167			−1.07745			−0.538724	+	0.842482i	$0.681093\pi$
$884$		−	0.749703i		−	0.0252152i
$885$	−8.00402	−	5.23599i	−0.269052	−	0.176006i
$886$		−	37.9671i		−	1.27553i
$887$	23.7893			0.798767			0.399384	−	0.916784i	$-0.369224\pi$
$887$	23.7893			0.798767			0.399384	+	0.916784i	$0.369224\pi$
$888$	−15.4858	−	10.1304i	−0.519670	−	0.339952i
$889$	2.44997			0.0821695
$890$	40.0800			1.34349
$891$	20.2839	−	21.8990i	0.679536	−	0.733642i
$892$	64.4203			2.15695
$893$	−33.7827			−1.13050
$894$	−49.0368	−	32.0784i	−1.64004	−	1.07286i
$895$	−16.7328			−0.559314
$896$			33.4331i			1.11692i
$897$	−0.0691493	−	0.0452354i	−0.00230883	−	0.00151037i
$898$		−	55.3080i		−	1.84565i
$899$	21.0254			0.701236
$900$	−6.49817	−	14.8617i	−0.216606	−	0.495391i
$901$		−	8.50846i		−	0.283458i
$902$	−20.4696	−	0.0147577i	−0.681564	−	0.000491377i
$903$	−14.3890	−	9.41283i	−0.478835	−	0.313239i
$904$		−	107.308i		−	3.56902i
$905$		−	18.7882i		−	0.624541i
$906$	39.3873	−	60.2095i	1.30855	−	2.00033i
$907$	37.6602			1.25049			0.625244	−	0.780430i	$-0.285000\pi$
$907$	37.6602			1.25049			0.625244	+	0.780430i	$0.285000\pi$
$908$	123.549			4.10010
$909$	0.259479	+	0.593444i	0.00860636	+	0.0196833i
$910$		−	0.468390i		−	0.0155270i
$911$			11.4298i			0.378687i	0.981911	+	0.189343i	$0.0606359\pi$
$911$			11.4298i			0.378687i	−0.981911	+	0.189343i	$0.939364\pi$
$912$	40.9505	−	62.5992i	1.35601	−	2.07287i
$913$	−60.1686	−	0.0433789i	−1.99129	−	0.00143563i
$914$		−	54.0304i		−	1.78717i
$915$	6.01896	+	3.93742i	0.198981	+	0.130167i
$916$	29.7302			0.982314
$917$		−	15.0987i		−	0.498603i
$918$	−1.89508	+	11.2347i	−0.0625470	+	0.370802i
$919$			27.9845i			0.923123i	0.887108	+	0.461561i	$0.152711\pi$
$919$			27.9845i			0.923123i	−0.887108	+	0.461561i	$0.847289\pi$
$920$	−2.57006			−0.0847323
$921$	−2.43293	+	3.71912i	−0.0801679	+	0.122549i
$922$	39.5091			1.30116
$923$	2.56036			0.0842752
$924$	17.0219	−	25.9797i	0.559979	−	0.854669i
$925$	1.15232			0.0378881
$926$	22.5443			0.740852
$927$	0.586524	+	1.34142i	0.0192640	+	0.0440579i
$928$	−160.623			−5.27270
$929$			20.1572i			0.661337i	0.943747	+	0.330668i	$0.107274\pi$
$929$			20.1572i			0.661337i	−0.943747	+	0.330668i	$0.892726\pi$
$930$	6.99224	−	10.6887i	0.229284	−	0.350497i
$931$		−	2.99512i		−	0.0981609i
$932$	89.9941			2.94786
$933$	10.2534	−	15.6739i	0.335682	−	0.513141i
$934$		−	100.192i		−	3.27839i
$935$	−0.00192648	+	2.67212i	−6.30026e−5	+	0.0873876i
$936$	−4.38612	+	1.91780i	−0.143365	+	0.0626851i
$937$			7.22869i			0.236151i	0.993005	+	0.118076i	$0.0376725\pi$
$937$			7.22869i			0.236151i	−0.993005	+	0.118076i	$0.962328\pi$
$938$		−	23.6389i		−	0.771838i
$939$	−3.94750	−	2.58233i	−0.128822	−	0.0842713i
$940$	60.9843			1.98909
$941$	−17.3978			−0.567153			−0.283577	−	0.958950i	$-0.591521\pi$
$941$	−17.3978			−0.567153			−0.283577	+	0.958950i	$0.591521\pi$
$942$	−36.4735	−	23.8599i	−1.18837	−	0.777397i
$943$		−	0.628620i		−	0.0204707i
$944$			79.6254i			2.59159i
$945$	−0.864280	+	5.12377i	−0.0281150	+	0.166676i
$946$	−0.0646015	+	89.6053i	−0.00210038	+	2.91332i
$947$		−	1.01917i		−	0.0331185i	−0.999863	−	0.0165593i	$-0.994729\pi$
$947$		−	1.01917i		−	0.0331185i	0.999863	−	0.0165593i	$-0.00527122\pi$
$948$	−17.4438	+	26.6655i	−0.566548	+	0.866055i
$949$	−1.06225			−0.0344820
$950$			8.15131i			0.264463i
$951$	−32.6312	+	49.8819i	−1.05814	+	1.61753i
$952$			7.46989i			0.242100i
$953$	17.8608			0.578569			0.289285	−	0.957243i	$-0.406583\pi$
$953$	17.8608			0.578569			0.289285	+	0.957243i	$0.406583\pi$
$954$	−79.0020	+	34.5430i	−2.55778	+	1.11837i
$955$	−19.9286			−0.644874
$956$	−54.8817			−1.77500
$957$	37.2852	+	24.4292i	1.20526	+	0.789685i
$958$	108.357			3.50085
$959$	−3.93608			−0.127103
$960$	−26.0721	+	39.8552i	−0.841472	+	1.28632i
$961$	−23.6581			−0.763163
$962$		−	0.539735i		−	0.0174018i
$963$	16.6488	+	38.0768i	0.536499	+	1.22701i
$964$			80.7849i			2.60191i
$965$	21.8093			0.702065
$966$	1.09347	+	0.715318i	0.0351819	+	0.0230150i
$967$			40.5262i			1.30323i	0.758548	+	0.651617i	$0.225909\pi$
$967$			40.5262i			1.30323i	−0.758548	+	0.651617i	$0.774091\pi$
$968$	−101.987	−	0.147057i	−3.27800	−	0.00472659i
$969$	2.28807	−	3.49767i	0.0735034	−	0.112361i
$970$			42.4014i			1.36143i
$971$			13.4067i			0.430241i	0.976588	+	0.215120i	$0.0690144\pi$
$971$			13.4067i			0.430241i	−0.976588	+	0.215120i	$0.930986\pi$
$972$	81.7643	−	20.4504i	2.62259	−	0.655948i
$973$	−18.7504			−0.601109
$974$	69.7413			2.23465
$975$	0.163189	−	0.249459i	0.00522622	−	0.00798908i
$976$		−	59.8777i		−	1.91664i
$977$		−	26.3879i		−	0.844225i	−0.906544	−	0.422112i	$-0.861289\pi$
$977$		−	26.3879i		−	0.844225i	0.906544	−	0.422112i	$-0.138711\pi$
$978$	−47.0800	−	30.7983i	−1.50545	−	0.984821i
$979$	−0.0352143	+	48.8439i	−0.00112545	+	1.56106i
$980$			5.40675i			0.172712i
$981$	21.9703	−	9.60632i	0.701456	−	0.306706i
$982$	13.2908			0.424126
$983$		−	19.6862i		−	0.627893i	−0.949441	−	0.313947i	$-0.898349\pi$
$983$		−	19.6862i		−	0.627893i	0.949441	−	0.313947i	$-0.101651\pi$
$984$	−30.4762	−	19.9366i	−0.971544	−	0.635555i
$985$			10.8244i			0.344894i
$986$	−17.0142			−0.541843
$987$	−16.3489	−	10.6949i	−0.520390	−	0.340423i
$988$	2.78704			0.0886676
$989$	−2.75177			−0.0875012
$990$	24.8187	−	10.8305i	0.788791	−	0.344215i
$991$	−39.8882			−1.26709			−0.633546	−	0.773705i	$-0.718401\pi$
$991$	−39.8882			−1.26709			−0.633546	+	0.773705i	$0.718401\pi$
$992$	−56.0885			−1.78081
$993$	4.23903	+	2.77305i	0.134522	+	0.0880001i
$994$	−40.4875			−1.28419
$995$			1.09079i			0.0345805i
$996$	−142.173	−	93.0051i	−4.50491	−	2.94698i
$997$			19.5278i			0.618453i	0.950988	+	0.309226i	$0.100070\pi$
$997$			19.5278i			0.618453i	−0.950988	+	0.309226i	$0.899930\pi$
$998$	−53.4568			−1.69214
$999$	−0.995927	+	5.90423i	−0.0315097	+	0.186801i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.l.f.1121.1	yes	40
3.2	odd	2		1155.2.l.e.1121.40	yes	40
11.10	odd	2		1155.2.l.e.1121.39	✓	40
33.32	even	2	inner	1155.2.l.f.1121.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.l.e.1121.39	✓	40	11.10	odd	2
1155.2.l.e.1121.40	yes	40	3.2	odd	2
1155.2.l.f.1121.1	yes	40	1.1	even	1	trivial
1155.2.l.f.1121.2	yes	40	33.32	even	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:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.72154 q^{2} +(-1.44946 - 0.948193i) q^{3} +5.40675 q^{4} -1.00000i q^{5} +(3.94475 + 2.58054i) q^{6} -1.00000i q^{7} -9.27160 q^{8} +(1.20186 + 2.74873i) q^{9} +O(q^{10})\)	\(q-2.72154 q^{2} +(-1.44946 - 0.948193i) q^{3} +5.40675 q^{4} -1.00000i q^{5} +(3.94475 + 2.58054i) q^{6} -1.00000i q^{7} -9.27160 q^{8} +(1.20186 + 2.74873i) q^{9} +2.72154i q^{10} +(-3.31662 - 0.00239114i) q^{11} +(-7.83687 - 5.12664i) q^{12} -0.172105i q^{13} +2.72154i q^{14} +(-0.948193 + 1.44946i) q^{15} +14.4195 q^{16} +0.805674 q^{17} +(-3.27091 - 7.48077i) q^{18} +2.99512i q^{19} -5.40675i q^{20} +(-0.948193 + 1.44946i) q^{21} +(9.02631 + 0.00650757i) q^{22} +0.277197i q^{23} +(13.4388 + 8.79126i) q^{24} -1.00000 q^{25} +0.468390i q^{26} +(0.864280 - 5.12377i) q^{27} -5.40675i q^{28} +7.75959 q^{29} +(2.58054 - 3.94475i) q^{30} +2.70960 q^{31} -20.6999 q^{32} +(4.80504 + 3.14826i) q^{33} -2.19267 q^{34} -1.00000 q^{35} +(6.49817 + 14.8617i) q^{36} -1.15232 q^{37} -8.15131i q^{38} +(-0.163189 + 0.249459i) q^{39} +9.27160i q^{40} -2.26777 q^{41} +(2.58054 - 3.94475i) q^{42} +9.92713i q^{43} +(-17.9322 - 0.0129283i) q^{44} +(2.74873 - 1.20186i) q^{45} -0.754401i q^{46} +11.2793i q^{47} +(-20.9004 - 13.6724i) q^{48} -1.00000 q^{49} +2.72154 q^{50} +(-1.16779 - 0.763934i) q^{51} -0.930529i q^{52} -10.5607i q^{53} +(-2.35217 + 13.9445i) q^{54} +(-0.00239114 + 3.31662i) q^{55} +9.27160i q^{56} +(2.83995 - 4.34130i) q^{57} -21.1180 q^{58} +5.52208i q^{59} +(-5.12664 + 7.83687i) q^{60} -4.15256i q^{61} -7.37428 q^{62} +(2.74873 - 1.20186i) q^{63} +27.4966 q^{64} -0.172105 q^{65} +(-13.0771 - 8.56811i) q^{66} -8.68588 q^{67} +4.35608 q^{68} +(0.262836 - 0.401785i) q^{69} +2.72154 q^{70} +14.8767i q^{71} +(-11.1432 - 25.4851i) q^{72} -6.17210i q^{73} +3.13608 q^{74} +(1.44946 + 0.948193i) q^{75} +16.1939i q^{76} +(-0.00239114 + 3.31662i) q^{77} +(0.444124 - 0.678912i) q^{78} -3.40257i q^{79} -14.4195i q^{80} +(-6.11106 + 6.60719i) q^{81} +6.17182 q^{82} +18.1415 q^{83} +(-5.12664 + 7.83687i) q^{84} -0.805674i q^{85} -27.0170i q^{86} +(-11.2472 - 7.35759i) q^{87} +(30.7504 + 0.0221697i) q^{88} -14.7270i q^{89} +(-7.48077 + 3.27091i) q^{90} -0.172105 q^{91} +1.49874i q^{92} +(-3.92746 - 2.56922i) q^{93} -30.6970i q^{94} +2.99512 q^{95} +(30.0037 + 19.6275i) q^{96} +15.5799 q^{97} +2.72154 q^{98} +(-3.97955 - 9.11939i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{2} - 4 q^{3} + 44 q^{4} + 4 q^{6} + 12 q^{8} - 2 q^{9}+O(q^{10}) \) 40 * q + 4 * q^2 - 4 * q^3 + 44 * q^4 + 4 * q^6 + 12 * q^8 - 2 * q^9	\( 40 q + 4 q^{2} - 4 q^{3} + 44 q^{4} + 4 q^{6} + 12 q^{8} - 2 q^{9} + 6 q^{11} + 8 q^{12} + 2 q^{15} + 68 q^{16} - 40 q^{18} + 2 q^{21} - 4 q^{22} + 12 q^{24} - 40 q^{25} + 32 q^{27} + 24 q^{29} - 8 q^{31} - 52 q^{32} + 28 q^{33} + 32 q^{34} - 40 q^{35} - 48 q^{37} - 66 q^{39} + 16 q^{41} - 32 q^{44} + 32 q^{48} - 40 q^{49} - 4 q^{50} + 14 q^{51} + 72 q^{54} + 8 q^{55} + 24 q^{57} - 80 q^{58} + 24 q^{60} - 48 q^{62} + 76 q^{64} - 4 q^{65} - 48 q^{67} + 32 q^{68} - 20 q^{69} - 4 q^{70} - 128 q^{72} + 4 q^{75} + 8 q^{77} - 28 q^{78} + 50 q^{81} - 32 q^{82} + 24 q^{83} + 24 q^{84} + 32 q^{87} - 16 q^{88} - 8 q^{90} - 4 q^{91} - 20 q^{93} + 12 q^{95} - 12 q^{96} + 100 q^{97} - 4 q^{98} + 56 q^{99}+O(q^{100}) \) 40 * q + 4 * q^2 - 4 * q^3 + 44 * q^4 + 4 * q^6 + 12 * q^8 - 2 * q^9 + 6 * q^11 + 8 * q^12 + 2 * q^15 + 68 * q^16 - 40 * q^18 + 2 * q^21 - 4 * q^22 + 12 * q^24 - 40 * q^25 + 32 * q^27 + 24 * q^29 - 8 * q^31 - 52 * q^32 + 28 * q^33 + 32 * q^34 - 40 * q^35 - 48 * q^37 - 66 * q^39 + 16 * q^41 - 32 * q^44 + 32 * q^48 - 40 * q^49 - 4 * q^50 + 14 * q^51 + 72 * q^54 + 8 * q^55 + 24 * q^57 - 80 * q^58 + 24 * q^60 - 48 * q^62 + 76 * q^64 - 4 * q^65 - 48 * q^67 + 32 * q^68 - 20 * q^69 - 4 * q^70 - 128 * q^72 + 4 * q^75 + 8 * q^77 - 28 * q^78 + 50 * q^81 - 32 * q^82 + 24 * q^83 + 24 * q^84 + 32 * q^87 - 16 * q^88 - 8 * q^90 - 4 * q^91 - 20 * q^93 + 12 * q^95 - 12 * q^96 + 100 * q^97 - 4 * q^98 + 56 * q^99

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