LMFDB - Embedded newform 1134.3.q.c.701.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,3,Mod(701,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0]))

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

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

chi := DirichletCharacter("1134.701");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1134.q (of order $6$, degree $2$, not 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:	$30.8992619785$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.12745506816.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 8x^{6} + 55x^{4} - 72x^{2} + 81 $ x^8 - 8x^6 + 55x^4 - 72*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			701.1
Root			$-2.23256 + 1.28897i$ of defining polynomial
Character	$\chi$	$=$	1134.701
Dual form			1134.3.q.c.1079.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 + 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(-7.70549 - 4.44876i) q^{5} +(-1.32288 - 2.29129i) q^{7} +2.82843i q^{8} +O(q^{10})$	\(q+(-1.22474 + 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(-7.70549 - 4.44876i) q^{5} +(-1.32288 - 2.29129i) q^{7} +2.82843i q^{8} +12.5830 q^{10} +(15.4110 - 8.89753i) q^{11} +(-1.29150 + 2.23695i) q^{13} +(3.24037 + 1.87083i) q^{14} +(-2.00000 - 3.46410i) q^{16} -25.8681i q^{17} +20.0000 q^{19} +(-15.4110 + 8.89753i) q^{20} +(-12.5830 + 21.7944i) q^{22} +(-15.4110 - 8.89753i) q^{23} +(27.0830 + 46.9091i) q^{25} -3.65292i q^{26} -5.29150 q^{28} +(10.3087 - 5.95171i) q^{29} +(8.58301 - 14.8662i) q^{31} +(4.89898 + 2.82843i) q^{32} +(18.2915 + 31.6818i) q^{34} +23.5406i q^{35} +38.0000 q^{37} +(-24.4949 + 14.1421i) q^{38} +(12.5830 - 21.7944i) q^{40} +(13.6259 + 7.86691i) q^{41} +(21.7490 + 37.6704i) q^{43} -35.5901i q^{44} +25.1660 q^{46} +(-14.6969 + 8.48528i) q^{47} +(-3.50000 + 6.06218i) q^{49} +(-66.3395 - 38.3012i) q^{50} +(2.58301 + 4.47390i) q^{52} -85.5571i q^{53} -158.332 q^{55} +(6.48074 - 3.74166i) q^{56} +(-8.41699 + 14.5787i) q^{58} +(-1.42807 - 0.824494i) q^{59} +(-50.1660 - 86.8901i) q^{61} +24.2764i q^{62} -8.00000 q^{64} +(19.9033 - 11.4912i) q^{65} +(-18.3320 + 31.7520i) q^{67} +(-44.8048 - 25.8681i) q^{68} +(-16.6458 - 28.8313i) q^{70} +17.7951i q^{71} +28.9150 q^{73} +(-46.5403 + 26.8701i) q^{74} +(20.0000 - 34.6410i) q^{76} +(-40.7736 - 23.5406i) q^{77} +(-59.1660 - 102.479i) q^{79} +35.5901i q^{80} -22.2510 q^{82} +(-104.307 + 60.2215i) q^{83} +(-115.081 + 199.326i) q^{85} +(-53.2740 - 30.7578i) q^{86} +(25.1660 + 43.5888i) q^{88} -139.475i q^{89} +6.83399 q^{91} +(-30.8219 + 17.7951i) q^{92} +(12.0000 - 20.7846i) q^{94} +(-154.110 - 88.9753i) q^{95} +(-22.2065 - 38.4628i) q^{97} -9.89949i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{4}+O(q^{10}) $ 8 * q + 8 * q^4	$ 8 q + 8 q^{4} + 16 q^{10} + 32 q^{13} - 16 q^{16} + 160 q^{19} - 16 q^{22} + 132 q^{25} - 16 q^{31} + 104 q^{34} + 304 q^{37} + 16 q^{40} - 80 q^{43} + 32 q^{46} - 28 q^{49} - 64 q^{52} - 928 q^{55} - 152 q^{58} - 232 q^{61} - 64 q^{64} + 192 q^{67} - 112 q^{70} - 192 q^{73} + 160 q^{76} - 304 q^{79} - 432 q^{82} - 328 q^{85} + 32 q^{88} + 224 q^{91} + 96 q^{94} + 288 q^{97}+O(q^{100}) $ 8 * q + 8 * q^4 + 16 * q^10 + 32 * q^13 - 16 * q^16 + 160 * q^19 - 16 * q^22 + 132 * q^25 - 16 * q^31 + 104 * q^34 + 304 * q^37 + 16 * q^40 - 80 * q^43 + 32 * q^46 - 28 * q^49 - 64 * q^52 - 928 * q^55 - 152 * q^58 - 232 * q^61 - 64 * q^64 + 192 * q^67 - 112 * q^70 - 192 * q^73 + 160 * q^76 - 304 * q^79 - 432 * q^82 - 328 * q^85 + 32 * q^88 + 224 * q^91 + 96 * q^94 + 288 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.22474	+	0.707107i	−0.612372	+	0.353553i
$2$	−1.22474	+	0.707107i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$	−7.70549	−	4.44876i	−1.54110	−	0.889753i	−0.998770	−	0.0495855i	$-0.984210\pi$
$5$	−7.70549	−	4.44876i	−1.54110	−	0.889753i	−0.542327	−	0.840167i	$-0.682457\pi$
$6$		0			0
$7$	−1.32288	−	2.29129i	−0.188982	−	0.327327i
$7$	−1.32288	−	2.29129i	−0.188982	−	0.327327i
$8$			2.82843i			0.353553i
$9$		0			0
$10$	12.5830			1.25830
$11$	15.4110	−	8.89753i	1.40100	−	0.808866i	0.406502	−	0.913650i	$-0.366748\pi$
$11$	15.4110	−	8.89753i	1.40100	−	0.808866i	0.994495	+	0.104784i	$0.0334150\pi$
$12$		0			0
$13$	−1.29150	+	2.23695i	−0.0993464	+	0.172073i	−0.911414	−	0.411490i	$-0.865009\pi$
$13$	−1.29150	+	2.23695i	−0.0993464	+	0.172073i	0.812068	+	0.583563i	$0.198342\pi$
$14$	3.24037	+	1.87083i	0.231455	+	0.133631i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$		−	25.8681i		−	1.52165i	−0.648956	−	0.760826i	$-0.724794\pi$
$17$		−	25.8681i		−	1.52165i	0.648956	−	0.760826i	$-0.275206\pi$
$18$		0			0
$19$	20.0000			1.05263			0.526316	−	0.850289i	$-0.323573\pi$
$19$	20.0000			1.05263			0.526316	+	0.850289i	$0.323573\pi$
$20$	−15.4110	+	8.89753i	−0.770549	+	0.444876i
$21$		0			0
$22$	−12.5830	+	21.7944i	−0.571955	+	0.990655i
$23$	−15.4110	−	8.89753i	−0.670042	−	0.386849i	0.126050	−	0.992024i	$-0.459770\pi$
$23$	−15.4110	−	8.89753i	−0.670042	−	0.386849i	−0.796093	+	0.605175i	$0.793103\pi$
$24$		0			0
$25$	27.0830	+	46.9091i	1.08332	+	1.87637i
$26$		−	3.65292i		−	0.140497i
$27$		0			0
$28$	−5.29150			−0.188982
$29$	10.3087	−	5.95171i	0.355471	−	0.205232i	−0.311621	−	0.950206i	$-0.600872\pi$
$29$	10.3087	−	5.95171i	0.355471	−	0.205232i	0.667092	+	0.744975i	$0.267539\pi$
$30$		0			0
$31$	8.58301	−	14.8662i	0.276871	−	0.479555i	−0.693734	−	0.720231i	$-0.744036\pi$
$31$	8.58301	−	14.8662i	0.276871	−	0.479555i	0.970605	+	0.240676i	$0.0773692\pi$
$32$	4.89898	+	2.82843i	0.153093	+	0.0883883i
$33$		0			0
$34$	18.2915	+	31.6818i	0.537985	+	0.931818i
$35$			23.5406i			0.672590i
$36$		0			0
$37$	38.0000			1.02703			0.513514	−	0.858082i	$-0.328344\pi$
$37$	38.0000			1.02703			0.513514	+	0.858082i	$0.328344\pi$
$38$	−24.4949	+	14.1421i	−0.644603	+	0.372161i
$39$		0			0
$40$	12.5830	−	21.7944i	0.314575	−	0.544860i
$41$	13.6259	+	7.86691i	0.332339	+	0.191876i	0.656879	−	0.753996i	$-0.271876\pi$
$41$	13.6259	+	7.86691i	0.332339	+	0.191876i	−0.324540	+	0.945872i	$0.605210\pi$
$42$		0			0
$43$	21.7490	+	37.6704i	0.505791	+	0.876056i	0.999978	+	0.00669990i	$0.00213266\pi$
$43$	21.7490	+	37.6704i	0.505791	+	0.876056i	−0.494186	+	0.869356i	$0.664534\pi$
$44$		−	35.5901i		−	0.808866i
$45$		0			0
$46$	25.1660			0.547087
$47$	−14.6969	+	8.48528i	−0.312701	+	0.180538i	−0.648134	−	0.761526i	$-0.724451\pi$
$47$	−14.6969	+	8.48528i	−0.312701	+	0.180538i	0.335434	+	0.942064i	$0.391117\pi$
$48$		0			0
$49$	−3.50000	+	6.06218i	−0.0714286	+	0.123718i
$50$	−66.3395	−	38.3012i	−1.32679	−	0.766023i
$51$		0			0
$52$	2.58301	+	4.47390i	0.0496732	+	0.0860365i
$53$		−	85.5571i		−	1.61429i	−0.590356	−	0.807143i	$-0.701013\pi$
$53$		−	85.5571i		−	1.61429i	0.590356	−	0.807143i	$-0.298987\pi$
$54$		0			0
$55$	−158.332			−2.87876
$56$	6.48074	−	3.74166i	0.115728	−	0.0668153i
$57$		0			0
$58$	−8.41699	+	14.5787i	−0.145121	+	0.251356i
$59$	−1.42807	−	0.824494i	−0.0242045	−	0.0139745i	0.487849	−	0.872928i	$-0.337782\pi$
$59$	−1.42807	−	0.824494i	−0.0242045	−	0.0139745i	−0.512053	+	0.858954i	$0.671115\pi$
$60$		0			0
$61$	−50.1660	−	86.8901i	−0.822394	−	1.42443i	−0.903895	−	0.427754i	$-0.859305\pi$
$61$	−50.1660	−	86.8901i	−0.822394	−	1.42443i	0.0815014	−	0.996673i	$-0.474028\pi$
$62$			24.2764i			0.391555i
$63$		0			0
$64$	−8.00000			−0.125000
$65$	19.9033	−	11.4912i	0.306205	−	0.176787i
$66$		0			0
$67$	−18.3320	+	31.7520i	−0.273612	+	0.473910i	−0.969784	−	0.243965i	$-0.921552\pi$
$67$	−18.3320	+	31.7520i	−0.273612	+	0.473910i	0.696172	+	0.717875i	$0.254885\pi$
$68$	−44.8048	−	25.8681i	−0.658895	−	0.380413i
$69$		0			0
$70$	−16.6458	−	28.8313i	−0.237796	−	0.411876i
$71$			17.7951i			0.250635i	0.992117	+	0.125317i	$0.0399949\pi$
$71$			17.7951i			0.250635i	−0.992117	+	0.125317i	$0.960005\pi$
$72$		0			0
$73$	28.9150			0.396096			0.198048	−	0.980192i	$-0.436540\pi$
$73$	28.9150			0.396096			0.198048	+	0.980192i	$0.436540\pi$
$74$	−46.5403	+	26.8701i	−0.628923	+	0.363109i
$75$		0			0
$76$	20.0000	−	34.6410i	0.263158	−	0.455803i
$77$	−40.7736	−	23.5406i	−0.529527	−	0.305723i
$78$		0			0
$79$	−59.1660	−	102.479i	−0.748937	−	1.29720i	−0.948333	−	0.317278i	$-0.897231\pi$
$79$	−59.1660	−	102.479i	−0.748937	−	1.29720i	0.199396	−	0.979919i	$-0.436102\pi$
$80$			35.5901i			0.444876i
$81$		0			0
$82$	−22.2510			−0.271353
$83$	−104.307	+	60.2215i	−1.25671	+	0.725560i	−0.972433	−	0.233183i	$-0.925086\pi$
$83$	−104.307	+	60.2215i	−1.25671	+	0.725560i	−0.284274	+	0.958743i	$0.591752\pi$
$84$		0			0
$85$	−115.081	+	199.326i	−1.35389	+	2.34501i
$86$	−53.2740	−	30.7578i	−0.619465	−	0.357648i
$87$		0			0
$88$	25.1660	+	43.5888i	0.285977	+	0.495327i
$89$		−	139.475i		−	1.56713i	−0.621309	−	0.783566i	$-0.713399\pi$
$89$		−	139.475i		−	1.56713i	0.621309	−	0.783566i	$-0.286601\pi$
$90$		0			0
$91$	6.83399			0.0750988
$92$	−30.8219	+	17.7951i	−0.335021	+	0.193425i
$93$		0			0
$94$	12.0000	−	20.7846i	0.127660	−	0.221113i
$95$	−154.110	−	88.9753i	−1.62221	−	0.936582i
$96$		0			0
$97$	−22.2065	−	38.4628i	−0.228933	−	0.396524i	0.728559	−	0.684983i	$-0.240190\pi$
$97$	−22.2065	−	38.4628i	−0.228933	−	0.396524i	−0.957492	+	0.288459i	$0.906857\pi$
$98$		−	9.89949i		−	0.101015i
$99$		0			0
$100$	108.332			1.08332
$101$	27.6088	−	15.9399i	0.273354	−	0.157821i	−0.357057	−	0.934083i	$-0.616220\pi$
$101$	27.6088	−	15.9399i	0.273354	−	0.157821i	0.630411	+	0.776261i	$0.282886\pi$
$102$		0			0
$103$	−2.25098	+	3.89882i	−0.0218542	+	0.0378526i	−0.876746	−	0.480954i	$-0.840290\pi$
$103$	−2.25098	+	3.89882i	−0.0218542	+	0.0378526i	0.854891	+	0.518807i	$0.173624\pi$
$104$	−6.32704	−	3.65292i	−0.0608370	−	0.0351242i
$105$		0			0
$106$	60.4980	+	104.786i	0.570736	+	0.988544i
$107$			172.179i			1.60915i	0.593851	+	0.804575i	$0.297607\pi$
$107$			172.179i			1.60915i	−0.593851	+	0.804575i	$0.702393\pi$
$108$		0			0
$109$	−177.830			−1.63147			−0.815734	−	0.578427i	$-0.803667\pi$
$109$	−177.830			−1.63147			−0.815734	+	0.578427i	$0.803667\pi$
$110$	193.916	−	111.958i	1.76288	−	1.01780i
$111$		0			0
$112$	−5.29150	+	9.16515i	−0.0472456	+	0.0818317i
$113$	−27.1477	−	15.6737i	−0.240245	−	0.138706i	0.375044	−	0.927007i	$-0.377628\pi$
$113$	−27.1477	−	15.6737i	−0.240245	−	0.138706i	−0.615289	+	0.788301i	$0.710961\pi$
$114$		0			0
$115$	79.1660	+	137.120i	0.688400	+	1.19234i
$116$		−	23.8069i		−	0.205232i
$117$		0			0
$118$	2.33202			0.0197629
$119$	−59.2712	+	34.2203i	−0.498078	+	0.287565i
$120$		0			0
$121$	97.8320	−	169.450i	0.808529	−	1.40041i
$122$	122.881	+	70.9455i	1.00722	+	0.581520i
$123$		0			0
$124$	−17.1660	−	29.7324i	−0.138436	−	0.239777i
$125$		−	259.505i		−	2.07604i
$126$		0			0
$127$	214.332			1.68765			0.843827	−	0.536616i	$-0.180297\pi$
$127$	214.332			1.68765			0.843827	+	0.536616i	$0.180297\pi$
$128$	9.79796	−	5.65685i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−16.2510	+	28.1475i	−0.125008	+	0.216519i
$131$	−79.1970	−	45.7244i	−0.604557	−	0.349041i	0.166275	−	0.986079i	$-0.446826\pi$
$131$	−79.1970	−	45.7244i	−0.604557	−	0.349041i	−0.770832	+	0.637038i	$0.780159\pi$
$132$		0			0
$133$	−26.4575	−	45.8258i	−0.198929	−	0.344555i
$134$		−	51.8508i		−	0.386946i
$135$		0			0
$136$	73.1660			0.537985
$137$	−92.5699	+	53.4453i	−0.675693	+	0.390111i	−0.798230	−	0.602353i	$-0.794230\pi$
$137$	−92.5699	+	53.4453i	−0.675693	+	0.390111i	0.122537	+	0.992464i	$0.460897\pi$
$138$		0			0
$139$	60.6640	−	105.073i	0.436432	−	0.755922i	−0.560979	−	0.827830i	$-0.689575\pi$
$139$	60.6640	−	105.073i	0.436432	−	0.755922i	0.997411	+	0.0719075i	$0.0229086\pi$
$140$	40.7736	+	23.5406i	0.291240	+	0.168147i
$141$		0			0
$142$	−12.5830	−	21.7944i	−0.0886127	−	0.153482i
$143$			45.9647i			0.321432i
$144$		0			0
$145$	−105.911			−0.730421
$146$	−35.4135	+	20.4460i	−0.242558	+	0.140041i
$147$		0			0
$148$	38.0000	−	65.8179i	0.256757	−	0.444716i
$149$	15.3069	+	8.83744i	0.102731	+	0.0593117i	0.550485	−	0.834845i	$-0.314443\pi$
$149$	15.3069	+	8.83744i	0.102731	+	0.0593117i	−0.447754	+	0.894157i	$0.647776\pi$
$150$		0			0
$151$	25.4170	+	44.0235i	0.168324	+	0.291547i	0.937831	−	0.347093i	$-0.112831\pi$
$151$	25.4170	+	44.0235i	0.168324	+	0.291547i	−0.769506	+	0.638639i	$0.779498\pi$
$152$			56.5685i			0.372161i
$153$		0			0
$154$	66.5830			0.432357
$155$	−132.272	+	76.3675i	−0.853371	+	0.492694i
$156$		0			0
$157$	−34.4980	+	59.7523i	−0.219733	+	0.380588i	−0.954726	−	0.297486i	$-0.903852\pi$
$157$	−34.4980	+	59.7523i	−0.219733	+	0.380588i	0.734994	+	0.678074i	$0.237185\pi$
$158$	144.927	+	83.6734i	0.917257	+	0.529578i
$159$		0			0
$160$	−25.1660	−	43.5888i	−0.157288	−	0.272430i
$161$			47.0813i			0.292430i
$162$		0			0
$163$	−166.996			−1.02452			−0.512258	−	0.858832i	$-0.671191\pi$
$163$	−166.996			−1.02452			−0.512258	+	0.858832i	$0.671191\pi$
$164$	27.2518	−	15.7338i	0.166169	−	0.0959379i
$165$		0			0
$166$	85.1660	−	147.512i	0.513048	−	0.888626i
$167$	−104.307	−	60.2215i	−0.624591	−	0.360608i	0.154064	−	0.988061i	$-0.450764\pi$
$167$	−104.307	−	60.2215i	−0.624591	−	0.360608i	−0.778654	+	0.627453i	$0.784097\pi$
$168$		0			0
$169$	81.1640	+	140.580i	0.480261	+	0.831836i
$170$		−	325.498i		−	1.91470i
$171$		0			0
$172$	86.9961			0.505791
$173$	−79.5540	+	45.9305i	−0.459850	+	0.265494i	−0.711981	−	0.702199i	$-0.752202\pi$
$173$	−79.5540	+	45.9305i	−0.459850	+	0.265494i	0.252131	+	0.967693i	$0.418868\pi$
$174$		0			0
$175$	71.6549	−	124.110i	0.409457	−	0.709200i
$176$	−61.6439	−	35.5901i	−0.350249	−	0.202217i
$177$		0			0
$178$	98.6235	+	170.821i	0.554065	+	0.959668i
$179$			133.291i			0.744643i	0.928104	+	0.372321i	$0.121438\pi$
$179$			133.291i			0.744643i	−0.928104	+	0.372321i	$0.878562\pi$
$180$		0			0
$181$	83.0850			0.459033			0.229517	−	0.973305i	$-0.426286\pi$
$181$	83.0850			0.459033			0.229517	+	0.973305i	$0.426286\pi$
$182$	−8.36989	+	4.83236i	−0.0459884	+	0.0265514i
$183$		0			0
$184$	25.1660	−	43.5888i	0.136772	−	0.236896i
$185$	−292.808	−	169.053i	−1.58275	−	0.913800i
$186$		0			0
$187$	−230.162	−	398.652i	−1.23081	−	2.13183i
$188$			33.9411i			0.180538i
$189$		0			0
$190$	251.660			1.32453
$191$	35.8202	−	20.6808i	0.187540	−	0.108276i	−0.403290	−	0.915072i	$-0.632134\pi$
$191$	35.8202	−	20.6808i	0.187540	−	0.108276i	0.590830	+	0.806796i	$0.298800\pi$
$192$		0			0
$193$	−67.0000	+	116.047i	−0.347150	+	0.601282i	−0.985742	−	0.168264i	$-0.946184\pi$
$193$	−67.0000	+	116.047i	−0.347150	+	0.601282i	0.638592	+	0.769546i	$0.279517\pi$
$194$	54.3947	+	31.4048i	0.280385	+	0.161880i
$195$		0			0
$196$	7.00000	+	12.1244i	0.0357143	+	0.0618590i
$197$		−	68.8269i		−	0.349375i	−0.984624	−	0.174688i	$-0.944108\pi$
$197$		−	68.8269i		−	0.349375i	0.984624	−	0.174688i	$-0.0558916\pi$
$198$		0			0
$199$	−278.494			−1.39947			−0.699734	−	0.714404i	$-0.746698\pi$
$199$	−278.494			−1.39947			−0.699734	+	0.714404i	$0.746698\pi$
$200$	−132.679	+	76.6023i	−0.663395	+	0.383012i
$201$		0			0
$202$	−22.5425	+	39.0447i	−0.111596	+	0.193291i
$203$	−27.2742	−	15.7468i	−0.134356	−	0.0775702i
$204$		0			0
$205$	−69.9961	−	121.237i	−0.341444	−	0.591399i
$206$		−	6.36674i		−	0.0309065i
$207$		0			0
$208$	10.3320			0.0496732
$209$	308.219	−	177.951i	1.47473	−	0.851438i
$210$		0			0
$211$	105.749	−	183.163i	0.501180	−	0.868070i	−0.498819	−	0.866706i	$-0.666233\pi$
$211$	105.749	−	183.163i	0.501180	−	0.868070i	0.999999	−	0.00136328i	$-0.000433945\pi$
$212$	−148.189	−	85.5571i	−0.699006	−	0.403571i
$213$		0			0
$214$	−121.749	−	210.875i	−0.568921	−	0.985399i
$215$		−	387.025i		−	1.80012i
$216$		0			0
$217$	−45.4170			−0.209295
$218$	217.796	−	125.745i	0.999066	−	0.576811i
$219$		0			0
$220$	−158.332	+	274.239i	−0.719691	+	1.24654i
$221$	57.8656	+	33.4087i	0.261835	+	0.151171i
$222$		0			0
$223$	−111.247	−	192.686i	−0.498866	−	0.864061i	0.501133	−	0.865370i	$-0.332917\pi$
$223$	−111.247	−	192.686i	−0.498866	−	0.864061i	−0.999999	+	0.00130930i	$0.999583\pi$
$224$		−	14.9666i		−	0.0668153i
$225$		0			0
$226$	44.3320			0.196159
$227$	88.1816	−	50.9117i	0.388465	−	0.224281i	−0.293030	−	0.956103i	$-0.594663\pi$
$227$	88.1816	−	50.9117i	0.388465	−	0.224281i	0.681495	+	0.731823i	$0.261330\pi$
$228$		0			0
$229$	81.5425	−	141.236i	0.356081	−	0.616750i	−0.631222	−	0.775603i	$-0.717446\pi$
$229$	81.5425	−	141.236i	0.356081	−	0.616750i	0.987302	+	0.158853i	$0.0507795\pi$
$230$	−193.916	−	111.958i	−0.843114	−	0.486772i
$231$		0			0
$232$	16.8340	+	29.1573i	0.0725603	+	0.125678i
$233$			362.858i			1.55733i	0.627441	+	0.778664i	$0.284102\pi$
$233$			362.858i			1.55733i	−0.627441	+	0.778664i	$0.715898\pi$
$234$		0			0
$235$	150.996			0.642536
$236$	−2.85613	+	1.64899i	−0.0121022	+	0.00698724i
$237$		0			0
$238$	48.3948	−	83.8222i	0.203339	−	0.352194i
$239$	153.396	+	88.5630i	0.641823	+	0.370557i	0.785316	−	0.619095i	$-0.212500\pi$
$239$	153.396	+	88.5630i	0.641823	+	0.370557i	−0.143493	+	0.989651i	$0.545834\pi$
$240$		0			0
$241$	−76.3765	−	132.288i	−0.316915	−	0.548913i	0.662928	−	0.748683i	$-0.269314\pi$
$241$	−76.3765	−	132.288i	−0.316915	−	0.548913i	−0.979843	+	0.199771i	$0.935980\pi$
$242$			276.711i			1.14343i
$243$		0			0
$244$	−200.664			−0.822394
$245$	53.9384	−	31.1413i	0.220157	−	0.127108i
$246$		0			0
$247$	−25.8301	+	44.7390i	−0.104575	+	0.181129i
$248$	42.0480	+	24.2764i	0.169548	+	0.0978887i
$249$		0			0
$250$	183.498	+	317.828i	0.733992	+	1.27131i
$251$			356.382i			1.41985i	0.704278	+	0.709924i	$0.251271\pi$
$251$			356.382i			1.41985i	−0.704278	+	0.709924i	$0.748729\pi$
$252$		0			0
$253$	−316.664			−1.25164
$254$	−262.502	+	151.556i	−1.03347	+	0.596676i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−51.5882	−	29.7844i	−0.200732	−	0.115893i	0.396265	−	0.918136i	$-0.370306\pi$
$257$	−51.5882	−	29.7844i	−0.200732	−	0.115893i	−0.596997	+	0.802244i	$0.703640\pi$
$258$		0			0
$259$	−50.2693	−	87.0689i	−0.194090	−	0.336174i
$260$		−	45.9647i		−	0.176787i
$261$		0			0
$262$	129.328			0.493619
$263$	−6.42629	+	3.71022i	−0.0244346	+	0.0141073i	−0.512168	−	0.858886i	$-0.671157\pi$
$263$	−6.42629	+	3.71022i	−0.0244346	+	0.0141073i	0.487733	+	0.872993i	$0.337824\pi$
$264$		0			0
$265$	−380.624	+	659.259i	−1.43632	+	2.48777i
$266$	64.8074	+	37.4166i	0.243637	+	0.140664i
$267$		0			0
$268$	36.6640	+	63.5040i	0.136806	+	0.236955i
$269$		−	430.207i		−	1.59928i	−0.600477	−	0.799642i	$-0.705023\pi$
$269$		−	430.207i		−	1.59928i	0.600477	−	0.799642i	$-0.294977\pi$
$270$		0			0
$271$	−41.1660			−0.151904			−0.0759520	−	0.997111i	$-0.524200\pi$
$271$	−41.1660			−0.151904			−0.0759520	+	0.997111i	$0.524200\pi$
$272$	−89.6097	+	51.7362i	−0.329447	+	0.190207i
$273$		0			0
$274$	75.5830	−	130.914i	0.275850	−	0.477787i
$275$	834.751	+	481.944i	3.03546	+	1.75252i
$276$		0			0
$277$	−16.0000	−	27.7128i	−0.0577617	−	0.100046i	0.835699	−	0.549188i	$-0.185063\pi$
$277$	−16.0000	−	27.7128i	−0.0577617	−	0.100046i	−0.893460	+	0.449142i	$0.851730\pi$
$278$			171.584i			0.617208i
$279$		0			0
$280$	−66.5830			−0.237796
$281$	14.8010	−	8.54537i	0.0526726	−	0.0304106i	−0.473432	−	0.880830i	$-0.656985\pi$
$281$	14.8010	−	8.54537i	0.0526726	−	0.0304106i	0.526105	+	0.850420i	$0.323652\pi$
$282$		0			0
$283$	−219.830	+	380.757i	−0.776785	+	1.34543i	0.157001	+	0.987598i	$0.449817\pi$
$283$	−219.830	+	380.757i	−0.776785	+	1.34543i	−0.933786	+	0.357832i	$0.883516\pi$
$284$	30.8219	+	17.7951i	0.108528	+	0.0626587i
$285$		0			0
$286$	−32.5020	−	56.2951i	−0.113643	−	0.196836i
$287$		−	41.6278i		−	0.145045i
$288$		0			0
$289$	−380.158			−1.31543
$290$	129.714	−	74.8904i	0.447290	−	0.258243i
$291$		0			0
$292$	28.9150	−	50.0823i	0.0990241	−	0.171515i
$293$	341.540	+	197.188i	1.16567	+	0.672998i	0.952656	−	0.304051i	$-0.0983395\pi$
$293$	341.540	+	197.188i	1.16567	+	0.672998i	0.213012	+	0.977050i	$0.431673\pi$
$294$		0			0
$295$	7.33596	+	12.7063i	0.0248677	+	0.0430720i
$296$			107.480i			0.363109i
$297$		0			0
$298$	−24.9961			−0.0838794
$299$	39.8066	−	22.9824i	0.133133	−	0.0768641i
$300$		0			0
$301$	57.5425	−	99.6665i	0.191171	−	0.331118i
$302$	−62.2587	−	35.9451i	−0.206155	−	0.119023i
$303$		0			0
$304$	−40.0000	−	69.2820i	−0.131579	−	0.227901i
$305$			892.707i			2.92691i
$306$		0			0
$307$	−23.3360			−0.0760129			−0.0380064	−	0.999277i	$-0.512101\pi$
$307$	−23.3360			−0.0760129			−0.0380064	+	0.999277i	$0.512101\pi$
$308$	−81.5472	+	47.0813i	−0.264764	+	0.152861i
$309$		0			0
$310$	108.000	−	187.061i	0.348387	−	0.603424i
$311$	456.617	+	263.628i	1.46822	+	0.847678i	0.999366	−	0.0355970i	$-0.0113333\pi$
$311$	456.617	+	263.628i	1.46822	+	0.847678i	0.468855	+	0.883275i	$0.344667\pi$
$312$		0			0
$313$	147.664	+	255.762i	0.471770	+	0.817130i	0.999478	−	0.0322959i	$-0.0102819\pi$
$313$	147.664	+	255.762i	0.471770	+	0.817130i	−0.527708	+	0.849426i	$0.676949\pi$
$314$		−	97.5752i		−	0.310749i
$315$		0			0
$316$	−236.664			−0.748937
$317$	93.0758	−	53.7373i	0.293614	−	0.169518i	−0.345956	−	0.938251i	$-0.612445\pi$
$317$	93.0758	−	53.7373i	0.293614	−	0.169518i	0.639571	+	0.768732i	$0.279112\pi$
$318$		0			0
$319$	105.911	−	183.443i	0.332010	−	0.575058i
$320$	61.6439	+	35.5901i	0.192637	+	0.111219i
$321$		0			0
$322$	−33.2915	−	57.6626i	−0.103390	−	0.179076i
$323$		−	517.362i		−	1.60174i
$324$		0			0
$325$	−139.911			−0.430496
$326$	204.528	−	118.084i	0.627385	−	0.362221i
$327$		0			0
$328$	−22.2510	+	38.5398i	−0.0678384	+	0.117499i
$329$	38.8844	+	22.4499i	0.118190	+	0.0682369i
$330$		0			0
$331$	136.745	+	236.849i	0.413127	+	0.715557i	0.995230	−	0.0975581i	$-0.0311032\pi$
$331$	136.745	+	236.849i	0.413127	+	0.715557i	−0.582103	+	0.813115i	$0.697770\pi$
$332$			240.886i			0.725560i
$333$		0			0
$334$	170.332			0.509976
$335$	282.514	−	163.110i	0.843326	−	0.486895i
$336$		0			0
$337$	170.583	−	295.458i	0.506181	−	0.876731i	−0.493793	−	0.869579i	$-0.664390\pi$
$337$	170.583	−	295.458i	0.506181	−	0.876731i	0.999974	−	0.00715200i	$-0.00227657\pi$
$338$	−198.810	−	114.783i	−0.588197	−	0.339596i
$339$		0			0
$340$	230.162	+	398.652i	0.676947	+	1.17251i
$341$		−	305.470i		−	0.895807i
$342$		0			0
$343$	18.5203			0.0539949
$344$	−106.548	+	61.5155i	−0.309733	+	0.178824i
$345$		0			0
$346$	64.9555	−	112.506i	0.187733	−	0.325163i
$347$	−100.736	−	58.1602i	−0.290307	−	0.167609i	0.347773	−	0.937579i	$-0.386938\pi$
$347$	−100.736	−	58.1602i	−0.290307	−	0.167609i	−0.638080	+	0.769970i	$0.720271\pi$
$348$		0			0
$349$	79.1621	+	137.113i	0.226825	+	0.392873i	0.956866	−	0.290531i	$-0.0938320\pi$
$349$	79.1621	+	137.113i	0.226825	+	0.392873i	−0.730040	+	0.683404i	$0.760499\pi$
$350$			202.671i			0.579059i
$351$		0			0
$352$	100.664			0.285977
$353$	−199.480	+	115.170i	−0.565098	+	0.326260i	−0.755189	−	0.655507i	$-0.772455\pi$
$353$	−199.480	+	115.170i	−0.565098	+	0.326260i	0.190091	+	0.981766i	$0.439122\pi$
$354$		0			0
$355$	79.1660	−	137.120i	0.223003	−	0.386252i
$356$	−241.577	−	139.475i	−0.678588	−	0.391783i
$357$		0			0
$358$	−94.2510	−	163.247i	−0.263271	−	0.455999i
$359$			171.698i			0.478269i	0.970987	+	0.239134i	$0.0768636\pi$
$359$			171.698i			0.478269i	−0.970987	+	0.239134i	$0.923136\pi$
$360$		0			0
$361$	39.0000			0.108033
$362$	−101.758	+	58.7499i	−0.281099	+	0.162293i
$363$		0			0
$364$	6.83399	−	11.8368i	0.0187747	−	0.0325187i
$365$	−222.804	−	128.636i	−0.610423	−	0.352428i
$366$		0			0
$367$	−258.745	−	448.160i	−0.705027	−	1.22114i	−0.966682	−	0.255982i	$-0.917601\pi$
$367$	−258.745	−	448.160i	−0.705027	−	1.22114i	0.261654	−	0.965162i	$-0.415732\pi$
$368$			71.1802i			0.193425i
$369$		0			0
$370$	478.154			1.29231
$371$	−196.036	+	113.181i	−0.528399	+	0.305071i
$372$		0			0
$373$	116.668	−	202.075i	0.312783	−	0.541756i	−0.666181	−	0.745790i	$-0.732072\pi$
$373$	116.668	−	202.075i	0.312783	−	0.541756i	0.978964	+	0.204035i	$0.0654055\pi$
$374$	563.780	+	325.498i	1.50743	+	0.870316i
$375$		0			0
$376$	−24.0000	−	41.5692i	−0.0638298	−	0.110556i
$377$			30.7466i			0.0815560i
$378$		0			0
$379$	441.166			1.16403			0.582013	−	0.813179i	$-0.302265\pi$
$379$	441.166			1.16403			0.582013	+	0.813179i	$0.302265\pi$
$380$	−308.219	+	177.951i	−0.811104	+	0.468291i
$381$		0			0
$382$	−29.2470	+	50.6574i	−0.0765630	+	0.132611i
$383$	184.515	+	106.530i	0.481763	+	0.278146i	0.721151	−	0.692778i	$-0.243613\pi$
$383$	184.515	+	106.530i	0.481763	+	0.278146i	−0.239388	+	0.970924i	$0.576947\pi$
$384$		0			0
$385$	209.454	+	362.784i	0.544035	+	0.942297i
$386$		−	189.505i		−	0.490945i
$387$		0			0
$388$	−88.8261			−0.228933
$389$	−489.387	+	282.548i	−1.25806	+	0.726344i	−0.972698	−	0.232074i	$-0.925449\pi$
$389$	−489.387	+	282.548i	−1.25806	+	0.726344i	−0.285367	+	0.958418i	$0.592115\pi$
$390$		0			0
$391$	−230.162	+	398.652i	−0.588650	+	1.01957i
$392$	−17.1464	−	9.89949i	−0.0437409	−	0.0252538i
$393$		0			0
$394$	48.6680	+	84.2954i	0.123523	+	0.213948i
$395$			1052.86i			2.66547i
$396$		0			0
$397$	498.324			1.25522			0.627612	−	0.778526i	$-0.284032\pi$
$397$	498.324			1.25522			0.627612	+	0.778526i	$0.284032\pi$
$398$	341.084	−	196.925i	0.856996	−	0.494787i
$399$		0			0
$400$	108.332	−	187.637i	0.270830	−	0.469091i
$401$	167.483	+	96.6962i	0.417662	+	0.241138i	0.694077	−	0.719901i	$-0.255813\pi$
$401$	167.483	+	96.6962i	0.417662	+	0.241138i	−0.276414	+	0.961039i	$0.589146\pi$
$402$		0			0
$403$	22.1699	+	38.3995i	0.0550123	+	0.0952841i
$404$		−	63.7598i		−	0.157821i
$405$		0			0
$406$	44.5385			0.109701
$407$	585.617	−	338.106i	1.43886	−	0.830727i
$408$		0			0
$409$	227.122	−	393.386i	0.555309	−	0.961824i	−0.442570	−	0.896734i	$-0.645933\pi$
$409$	227.122	−	393.386i	0.555309	−	0.961824i	0.997879	−	0.0650902i	$-0.0207335\pi$
$410$	171.455	+	98.9894i	0.418182	+	0.241438i
$411$		0			0
$412$	4.50197	+	7.79764i	0.0109271	+	0.0189263i
$413$			4.36281i			0.0105637i
$414$		0			0
$415$	1071.64			2.58228
$416$	−12.6541	+	7.30584i	−0.0304185	+	0.0175621i
$417$		0			0
$418$	−251.660	+	435.888i	−0.602058	+	1.04279i
$419$	−293.939	−	169.706i	−0.701525	−	0.405025i	0.106390	−	0.994324i	$-0.466071\pi$
$419$	−293.939	−	169.706i	−0.701525	−	0.405025i	−0.807915	+	0.589299i	$0.799404\pi$
$420$		0			0
$421$	−123.660	−	214.186i	−0.293729	−	0.508754i	0.680959	−	0.732321i	$-0.261563\pi$
$421$	−123.660	−	214.186i	−0.293729	−	0.508754i	−0.974689	+	0.223567i	$0.928230\pi$
$422$			299.103i			0.708776i
$423$		0			0
$424$	241.992			0.570736
$425$	1213.45	−	700.586i	2.85518	−	1.64844i
$426$		0			0
$427$	−132.727	+	229.890i	−0.310836	+	0.538383i
$428$	298.223	+	172.179i	0.696783	+	0.402288i
$429$		0			0
$430$	273.668	+	474.007i	0.636437	+	1.10234i
$431$		−	456.419i		−	1.05898i	−0.848317	−	0.529489i	$-0.822384\pi$
$431$		−	456.419i		−	1.05898i	0.848317	−	0.529489i	$-0.177616\pi$
$432$		0			0
$433$	−637.984			−1.47340			−0.736702	−	0.676217i	$-0.763618\pi$
$433$	−637.984			−1.47340			−0.736702	+	0.676217i	$0.763618\pi$
$434$	55.6242	−	32.1147i	0.128166	−	0.0739969i
$435$		0			0
$436$	−177.830	+	308.011i	−0.407867	+	0.706447i
$437$	−308.219	−	177.951i	−0.705308	−	0.407210i
$438$		0			0
$439$	392.073	+	679.091i	0.893105	+	1.54690i	0.836132	+	0.548528i	$0.184812\pi$
$439$	392.073	+	679.091i	0.893105	+	1.54690i	0.0569728	+	0.998376i	$0.481855\pi$
$440$		−	447.831i		−	1.01780i
$441$		0			0
$442$	−94.4941			−0.213788
$443$	−408.956	+	236.111i	−0.923151	+	0.532981i	−0.884639	−	0.466277i	$-0.845595\pi$
$443$	−408.956	+	236.111i	−0.923151	+	0.532981i	−0.0385120	+	0.999258i	$0.512262\pi$
$444$		0			0
$445$	−620.490	+	1074.72i	−1.39436	+	2.41510i
$446$	272.499	+	157.327i	0.610983	+	0.352751i
$447$		0			0
$448$	10.5830	+	18.3303i	0.0236228	+	0.0409159i
$449$			739.852i			1.64778i	0.566752	+	0.823888i	$0.308200\pi$
$449$			739.852i			1.64778i	−0.566752	+	0.823888i	$0.691800\pi$
$450$		0			0
$451$	279.984			0.620808
$452$	−54.2954	+	31.3475i	−0.120123	+	0.0693528i
$453$		0			0
$454$	−72.0000	+	124.708i	−0.158590	+	0.274686i
$455$	−52.6592	−	30.4028i	−0.115735	−	0.0668194i
$456$		0			0
$457$	124.162	+	215.055i	0.271689	+	0.470580i	0.969295	−	0.245903i	$-0.0790843\pi$
$457$	124.162	+	215.055i	0.271689	+	0.470580i	−0.697605	+	0.716482i	$0.745751\pi$
$458$			230.637i			0.503574i
$459$		0			0
$460$	316.664			0.688400
$461$	−308.279	+	177.985i	−0.668717	+	0.386084i	−0.795590	−	0.605835i	$-0.792839\pi$
$461$	−308.279	+	177.985i	−0.668717	+	0.386084i	0.126873	+	0.991919i	$0.459506\pi$
$462$		0			0
$463$	3.16601	−	5.48369i	0.00683804	−	0.0118438i	−0.862586	−	0.505910i	$-0.831157\pi$
$463$	3.16601	−	5.48369i	0.00683804	−	0.0118438i	0.869424	+	0.494066i	$0.164490\pi$
$464$	−41.2347	−	23.8069i	−0.0888679	−	0.0513079i
$465$		0			0
$466$	−256.579	−	444.408i	−0.550599	−	0.953665i
$467$		−	878.691i		−	1.88156i	−0.339011	−	0.940782i	$-0.610093\pi$
$467$		−	878.691i		−	1.88156i	0.339011	−	0.940782i	$-0.389907\pi$
$468$		0			0
$469$	97.0039			0.206831
$470$	−184.932	+	106.770i	−0.393472	+	0.227171i
$471$		0			0
$472$	2.33202	−	4.03918i	0.00494072	−	0.00855758i
$473$	670.347	+	387.025i	1.41722	+	0.818235i
$474$		0			0
$475$	541.660	+	938.183i	1.14034	+	1.97512i
$476$			136.881i			0.287565i
$477$		0			0
$478$	−250.494			−0.524046
$479$	−194.333	+	112.198i	−0.405705	+	0.234234i	−0.688943	−	0.724816i	$-0.741925\pi$
$479$	−194.333	+	112.198i	−0.405705	+	0.234234i	0.283238	+	0.959050i	$0.408591\pi$
$480$		0			0
$481$	−49.0771	+	85.0040i	−0.102031	+	0.176724i
$482$	187.083	+	108.013i	0.388140	+	0.224093i
$483$		0			0
$484$	−195.664	−	338.900i	−0.404265	−	0.700207i
$485$			395.166i			0.814776i
$486$		0			0
$487$	−717.490			−1.47329			−0.736643	−	0.676282i	$-0.763590\pi$
$487$	−717.490			−1.47329			−0.736643	+	0.676282i	$0.763590\pi$
$488$	245.762	−	141.891i	0.503611	−	0.290760i
$489$		0			0
$490$	−44.0405	+	76.2804i	−0.0898786	+	0.155674i
$491$	237.293	+	137.001i	0.483285	+	0.279025i	0.721785	−	0.692118i	$-0.243322\pi$
$491$	237.293	+	137.001i	0.483285	+	0.279025i	−0.238499	+	0.971143i	$0.576655\pi$
$492$		0			0
$493$	−153.959	−	266.666i	−0.312291	−	0.540904i
$494$		−	73.0584i		−	0.147892i
$495$		0			0
$496$	−68.6640			−0.138436
$497$	40.7736	−	23.5406i	0.0820394	−	0.0473655i
$498$		0			0
$499$	364.405	−	631.168i	0.730271	−	1.26487i	−0.226496	−	0.974012i	$-0.572727\pi$
$499$	364.405	−	631.168i	0.730271	−	1.26487i	0.956767	−	0.290854i	$-0.0939395\pi$
$500$	−449.477	−	259.505i	−0.898953	−	0.519011i
$501$		0			0
$502$	−252.000	−	436.477i	−0.501992	−	0.869476i
$503$			594.657i			1.18222i	0.806590	+	0.591111i	$0.201310\pi$
$503$			594.657i			1.18222i	−0.806590	+	0.591111i	$0.798690\pi$
$504$		0			0
$505$	−283.652			−0.561688
$506$	387.833	−	223.915i	0.766468	−	0.442520i
$507$		0			0
$508$	214.332	−	371.234i	0.421913	−	0.730775i
$509$	−860.842	−	497.007i	−1.69124	−	0.976439i	−0.953518	−	0.301336i	$-0.902568\pi$
$509$	−860.842	−	497.007i	−1.69124	−	0.976439i	−0.737723	−	0.675103i	$-0.764099\pi$
$510$		0			0
$511$	−38.2510	−	66.2526i	−0.0748552	−	0.129653i
$512$		−	22.6274i		−	0.0441942i
$513$		0			0
$514$	84.2431			0.163897
$515$	34.6899	−	20.0282i	0.0673589	−	0.0388897i
$516$		0			0
$517$	−150.996	+	261.533i	−0.292062	+	0.505866i
$518$	123.134	+	71.0915i	0.237711	+	0.137242i
$519$		0			0
$520$	32.5020	+	56.2951i	0.0625038	+	0.108260i
$521$			40.8459i			0.0783990i	0.999231	+	0.0391995i	$0.0124808\pi$
$521$			40.8459i			0.0783990i	−0.999231	+	0.0391995i	$0.987519\pi$
$522$		0			0
$523$	−232.000			−0.443595			−0.221797	−	0.975093i	$-0.571192\pi$
$523$	−232.000			−0.443595			−0.221797	+	0.975093i	$0.571192\pi$
$524$	−158.394	+	91.4488i	−0.302278	+	0.174521i
$525$		0			0
$526$	5.24705	−	9.08815i	0.00997537	−	0.0172779i
$527$	−384.560	−	222.026i	−0.729716	−	0.421302i
$528$		0			0
$529$	−106.168	−	183.888i	−0.200696	−	0.347615i
$530$		−	1076.57i		−	2.03126i
$531$		0			0
$532$	−105.830			−0.198929
$533$	−35.1957	+	20.3203i	−0.0660333	+	0.0381243i
$534$		0			0
$535$	765.984	−	1326.72i	1.43175	−	2.47986i
$536$	−89.8082	−	51.8508i	−0.167553	−	0.0967365i
$537$		0			0
$538$	304.203	+	526.894i	0.565432	+	0.979358i
$539$			124.565i			0.231105i
$540$		0			0
$541$	250.332			0.462721			0.231360	−	0.972868i	$-0.425682\pi$
$541$	250.332			0.462721			0.231360	+	0.972868i	$0.425682\pi$
$542$	50.4179	−	29.1088i	0.0930219	−	0.0537062i
$543$		0			0
$544$	73.1660	−	126.727i	0.134496	−	0.232954i
$545$	1370.27	+	791.124i	2.51425	+	1.45160i
$546$		0			0
$547$	−444.162	−	769.311i	−0.811996	−	1.40642i	−0.911465	−	0.411378i	$-0.865047\pi$
$547$	−444.162	−	769.311i	−0.811996	−	1.40642i	0.0994682	−	0.995041i	$-0.468286\pi$
$548$			213.781i			0.390111i
$549$		0			0
$550$	−1363.14			−2.47844
$551$	206.173	−	119.034i	0.374180	−	0.216033i
$552$		0			0
$553$	−156.539	+	271.133i	−0.283072	+	0.490294i
$554$	39.1918	+	22.6274i	0.0707434	+	0.0408437i
$555$		0			0
$556$	−121.328	−	210.146i	−0.218216	−	0.377961i
$557$			316.309i			0.567879i	0.958842	+	0.283940i	$0.0916415\pi$
$557$			316.309i			0.567879i	−0.958842	+	0.283940i	$0.908358\pi$
$558$		0			0
$559$	−112.356			−0.200994
$560$	81.5472	−	47.0813i	0.145620	−	0.0840737i
$561$		0			0
$562$	−12.0850	+	20.9318i	−0.0215035	+	0.0372452i
$563$	−50.6356	−	29.2345i	−0.0899390	−	0.0519263i	0.454356	−	0.890820i	$-0.349869\pi$
$563$	−50.6356	−	29.2345i	−0.0899390	−	0.0519263i	−0.544295	+	0.838894i	$0.683203\pi$
$564$		0			0
$565$	139.458	+	241.547i	0.246827	+	0.427518i
$566$		−	621.773i		−	1.09854i
$567$		0			0
$568$	−50.3320			−0.0886127
$569$	191.968	−	110.833i	0.337378	−	0.194785i	−0.321734	−	0.946830i	$-0.604266\pi$
$569$	191.968	−	110.833i	0.337378	−	0.194785i	0.659112	+	0.752045i	$0.270932\pi$
$570$		0			0
$571$	243.822	−	422.312i	0.427009	−	0.739601i	−0.569597	−	0.821924i	$-0.692901\pi$
$571$	243.822	−	422.312i	0.427009	−	0.739601i	0.996606	+	0.0823230i	$0.0262339\pi$
$572$	79.6132	+	45.9647i	0.139184	+	0.0803579i
$573$		0			0
$574$	29.4353	+	50.9834i	0.0512810	+	0.0888213i
$575$		−	963.887i		−	1.67633i
$576$		0			0
$577$	−487.328			−0.844589			−0.422295	−	0.906459i	$-0.638775\pi$
$577$	−487.328			−0.844589			−0.422295	+	0.906459i	$0.638775\pi$
$578$	465.597	−	268.812i	0.805531	−	0.465073i
$579$		0			0
$580$	−105.911	+	183.443i	−0.182605	+	0.316282i
$581$	275.969	+	159.331i	0.474990	+	0.274236i
$582$		0			0
$583$	−761.247	−	1318.52i	−1.30574	−	2.26161i
$584$			81.7840i			0.140041i
$585$		0			0
$586$	−557.733			−0.951763
$587$	−385.988	+	222.850i	−0.657561	+	0.379643i	−0.791347	−	0.611367i	$-0.790620\pi$
$587$	−385.988	+	222.850i	−0.657561	+	0.379643i	0.133786	+	0.991010i	$0.457287\pi$
$588$		0			0
$589$	171.660	−	297.324i	0.291443	−	0.504795i
$590$	−17.9694	−	10.3746i	−0.0304565	−	0.0175841i
$591$		0			0
$592$	−76.0000	−	131.636i	−0.128378	−	0.222358i
$593$		−	276.648i		−	0.466523i	−0.972414	−	0.233261i	$-0.925060\pi$
$593$		−	276.648i		−	0.466523i	0.972414	−	0.233261i	$-0.0749397\pi$
$594$		0			0
$595$	608.952			1.02345
$596$	30.6138	−	17.6749i	0.0513654	−	0.0296558i
$597$		0			0
$598$	−32.5020	+	56.2951i	−0.0543511	+	0.0941389i
$599$	71.3426	+	41.1897i	0.119103	+	0.0687641i	0.558368	−	0.829593i	$-0.311428\pi$
$599$	71.3426	+	41.1897i	0.119103	+	0.0687641i	−0.439265	+	0.898358i	$0.644761\pi$
$600$		0			0
$601$	209.000	+	361.999i	0.347754	+	0.602327i	0.985850	−	0.167629i	$-0.0536112\pi$
$601$	209.000	+	361.999i	0.347754	+	0.602327i	−0.638096	+	0.769957i	$0.720278\pi$
$602$			162.755i			0.270357i
$603$		0			0
$604$	101.668			0.168324
$605$	−1507.69	+	870.463i	−2.49204	+	1.43878i
$606$		0			0
$607$	−38.4209	+	66.5470i	−0.0632964	+	0.109633i	−0.895937	−	0.444181i	$-0.853495\pi$
$607$	−38.4209	+	66.5470i	−0.0632964	+	0.109633i	0.832641	+	0.553814i	$0.186828\pi$
$608$	97.9796	+	56.5685i	0.161151	+	0.0930404i
$609$		0			0
$610$	−631.239	−	1093.34i	−1.03482	−	1.79236i
$611$		−	43.8351i		−	0.0717431i
$612$		0			0
$613$	59.3281			0.0967832			0.0483916	−	0.998828i	$-0.484590\pi$
$613$	59.3281			0.0967832			0.0483916	+	0.998828i	$0.484590\pi$
$614$	28.5806	−	16.5010i	0.0465482	−	0.0268746i
$615$		0			0
$616$	66.5830	−	115.325i	0.108089	−	0.187216i
$617$	−25.2138	−	14.5572i	−0.0408651	−	0.0235935i	0.479428	−	0.877581i	$-0.340844\pi$
$617$	−25.2138	−	14.5572i	−0.0408651	−	0.0235935i	−0.520293	+	0.853988i	$0.674177\pi$
$618$		0			0
$619$	−227.822	−	394.600i	−0.368049	−	0.637479i	0.621212	−	0.783643i	$-0.286641\pi$
$619$	−227.822	−	394.600i	−0.368049	−	0.637479i	−0.989260	+	0.146164i	$0.953307\pi$
$620$			305.470i			0.492694i
$621$		0			0
$622$	−745.652			−1.19880
$623$	−319.577	+	184.508i	−0.512964	+	0.296160i
$624$		0			0
$625$	−477.403	+	826.887i	−0.763845	+	1.32302i
$626$	−361.702	−	208.828i	−0.577798	−	0.333592i
$627$		0			0
$628$	68.9961	+	119.505i	0.109866	+	0.190294i
$629$		−	982.987i		−	1.56278i
$630$		0			0
$631$	−45.0039			−0.0713216			−0.0356608	−	0.999364i	$-0.511354\pi$
$631$	−45.0039			−0.0713216			−0.0356608	+	0.999364i	$0.511354\pi$
$632$	289.853	−	167.347i	0.458628	−	0.264789i
$633$		0			0
$634$	−75.9961	+	131.629i	−0.119868	+	0.207617i
$635$	−1651.53	−	953.513i	−2.60084	−	1.50159i
$636$		0			0
$637$	−9.04052	−	15.6586i	−0.0141923	−	0.0245818i
$638$			299.562i			0.469533i
$639$		0			0
$640$	−100.664			−0.157288
$641$	−555.315	+	320.611i	−0.866327	+	0.500174i	−0.866126	−	0.499826i	$-0.833397\pi$
$641$	−555.315	+	320.611i	−0.866327	+	0.500174i	−0.000200774		1.00000i	$0.500064\pi$
$642$		0			0
$643$	302.000	−	523.079i	0.469673	−	0.813498i	−0.529725	−	0.848169i	$-0.677705\pi$
$643$	302.000	−	523.079i	0.469673	−	0.813498i	0.999399	+	0.0346710i	$0.0110383\pi$
$644$	81.5472	+	47.0813i	0.126626	+	0.0731076i
$645$		0			0
$646$	365.830	+	633.636i	0.566300	+	0.980861i
$647$		−	179.600i		−	0.277588i	−0.990321	−	0.138794i	$-0.955677\pi$
$647$		−	179.600i		−	0.277588i	0.990321	−	0.138794i	$-0.0443226\pi$
$648$		0			0
$649$	−29.3438			−0.0452139
$650$	171.355	−	98.9321i	0.263624	−	0.152203i
$651$		0			0
$652$	−166.996	+	289.246i	−0.256129	+	0.443628i
$653$	−339.562	−	196.046i	−0.520003	−	0.300224i	0.216933	−	0.976186i	$-0.430395\pi$
$653$	−339.562	−	196.046i	−0.520003	−	0.300224i	−0.736936	+	0.675963i	$0.763728\pi$
$654$		0			0
$655$	406.834	+	704.657i	0.621121	+	1.07581i
$656$		−	62.9353i		−	0.0959379i
$657$		0			0
$658$	−63.4980			−0.0965016
$659$	1096.86	−	633.270i	1.66442	−	0.960956i	0.693862	−	0.720108i	$-0.255908\pi$
$659$	1096.86	−	633.270i	1.66442	−	0.960956i	0.970563	−	0.240848i	$-0.0774255\pi$
$660$		0			0
$661$	−458.822	+	794.703i	−0.694133	+	1.20227i	0.276339	+	0.961060i	$0.410879\pi$
$661$	−458.822	+	794.703i	−0.694133	+	1.20227i	−0.970472	+	0.241214i	$0.922454\pi$
$662$	−334.956	−	193.387i	−0.505975	−	0.292125i
$663$		0			0
$664$	−170.332	−	295.024i	−0.256524	−	0.444313i
$665$			470.813i			0.707989i
$666$		0			0
$667$	−211.822			−0.317574
$668$	−208.613	+	120.443i	−0.312295	+	0.180304i
$669$		0			0
$670$	−230.672	+	399.535i	−0.344286	+	0.596322i
$671$	−1546.21	−	892.707i	−2.30434	−	1.33041i
$672$		0			0
$673$	76.0039	+	131.643i	0.112933	+	0.195606i	0.916952	−	0.398998i	$-0.130642\pi$
$673$	76.0039	+	131.643i	0.112933	+	0.195606i	−0.804019	+	0.594604i	$0.797309\pi$
$674$			482.482i			0.715848i
$675$		0			0
$676$	324.656			0.480261
$677$	141.316	−	81.5891i	0.208739	−	0.120516i	−0.391986	−	0.919971i	$-0.628212\pi$
$677$	141.316	−	81.5891i	0.208739	−	0.120516i	0.600725	+	0.799456i	$0.294879\pi$
$678$		0			0
$679$	−58.7530	+	101.763i	−0.0865286	+	0.149872i
$680$	−563.780	−	325.498i	−0.829088	−	0.478674i
$681$		0			0
$682$	216.000	+	374.123i	0.316716	+	0.548567i
$683$		−	324.914i		−	0.475716i	−0.971300	−	0.237858i	$-0.923555\pi$
$683$		−	324.914i		−	0.475716i	0.971300	−	0.237858i	$-0.0764453\pi$
$684$		0			0
$685$	951.061			1.38841
$686$	−22.6826	+	13.0958i	−0.0330650	+	0.0190901i
$687$		0			0
$688$	86.9961	−	150.682i	0.126448	−	0.219014i
$689$	191.387	+	110.497i	0.277775	+	0.160373i
$690$		0			0
$691$	−609.490	−	1055.67i	−0.882041	−	1.52774i	−0.849068	−	0.528283i	$-0.822836\pi$
$691$	−609.490	−	1055.67i	−0.882041	−	1.52774i	−0.0329725	−	0.999456i	$-0.510497\pi$
$692$			183.722i			0.265494i
$693$		0			0
$694$	164.502			0.237035
$695$	−934.892	+	539.760i	−1.34517	+	0.776633i
$696$		0			0
$697$	203.502	−	352.476i	0.291968	−	0.505704i
$698$	−193.907	−	111.952i	−0.277803	−	0.160390i
$699$		0			0
$700$	−143.310	−	248.220i	−0.204728	−	0.354600i
$701$		−	427.202i		−	0.609417i	−0.952446	−	0.304709i	$-0.901441\pi$
$701$		−	427.202i		−	0.609417i	0.952446	−	0.304709i	$-0.0985591\pi$
$702$		0			0
$703$	760.000			1.08108
$704$	−123.288	+	71.1802i	−0.175125	+	0.101108i
$705$		0			0
$706$	162.875	−	282.107i	0.230700	−	0.399585i
$707$	−73.0460	−	42.1731i	−0.103318	−	0.0596508i
$708$		0			0
$709$	−35.7490	−	61.9191i	−0.0504217	−	0.0873330i	0.839713	−	0.543031i	$-0.182723\pi$
$709$	−35.7490	−	61.9191i	−0.0504217	−	0.0873330i	−0.890135	+	0.455697i	$0.849390\pi$
$710$			223.915i			0.315374i
$711$		0			0
$712$	394.494			0.554065
$713$	−264.545	+	152.735i	−0.371031	+	0.214215i
$714$		0			0
$715$	204.486	−	354.181i	0.285995	−	0.495357i
$716$	230.867	+	133.291i	0.322440	+	0.186161i
$717$		0			0
$718$	−121.409	−	210.287i	−0.169093	−	0.292879i
$719$		−	111.030i		−	0.154422i	−0.997015	−	0.0772112i	$-0.975398\pi$
$719$		−	111.030i		−	0.154422i	0.997015	−	0.0772112i	$-0.0246016\pi$
$720$		0			0
$721$	11.9111			0.0165202
$722$	−47.7650	+	27.5772i	−0.0661566	+	0.0381955i
$723$		0			0
$724$	83.0850	−	143.907i	0.114758	−	0.198767i
$725$	558.380	+	322.381i	0.770179	+	0.444663i
$726$		0			0
$727$	669.409	+	1159.45i	0.920783	+	1.59484i	0.798207	+	0.602384i	$0.205782\pi$
$727$	669.409	+	1159.45i	0.920783	+	1.59484i	0.122576	+	0.992459i	$0.460884\pi$
$728$			19.3294i			0.0265514i
$729$		0			0
$730$	363.838			0.498408
$731$	974.461	−	562.606i	1.33305	−	0.769638i
$732$		0			0
$733$	−24.5385	+	42.5020i	−0.0334769	+	0.0579836i	−0.882278	−	0.470728i	$-0.843991\pi$
$733$	−24.5385	+	42.5020i	−0.0334769	+	0.0579836i	0.848802	+	0.528712i	$0.177325\pi$
$734$	633.793	+	365.921i	0.863479	+	0.498530i
$735$		0			0
$736$	−50.3320	−	87.1776i	−0.0683859	−	0.118448i
$737$			652.439i			0.885263i
$738$		0			0
$739$	1430.32			1.93548			0.967738	−	0.251960i	$-0.0810751\pi$
$739$	1430.32			1.93548			0.967738	+	0.251960i	$0.0810751\pi$
$740$	−585.617	+	338.106i	−0.791374	+	0.456900i
$741$		0			0
$742$	160.063	−	277.237i	0.215718	−	0.373635i
$743$	−758.410	−	437.868i	−1.02074	−	0.589325i	−0.106422	−	0.994321i	$-0.533939\pi$
$743$	−758.410	−	437.868i	−1.02074	−	0.589325i	−0.914318	+	0.404996i	$0.867273\pi$
$744$		0			0
$745$	−78.6314	−	136.194i	−0.105546	−	0.182810i
$746$			329.987i			0.442342i
$747$		0			0
$748$	−920.648			−1.23081
$749$	394.512	−	227.772i	0.526718	−	0.304101i
$750$		0			0
$751$	−160.413	+	277.844i	−0.213599	+	0.369965i	−0.952838	−	0.303478i	$-0.901852\pi$
$751$	−160.413	+	277.844i	−0.213599	+	0.369965i	0.739239	+	0.673443i	$0.235185\pi$
$752$	58.7878	+	33.9411i	0.0781752	+	0.0451345i
$753$		0			0
$754$	−21.7411	−	37.6568i	−0.0288344	−	0.0499427i
$755$		−	452.297i		−	0.599069i
$756$		0			0
$757$	289.830			0.382867			0.191433	−	0.981506i	$-0.438686\pi$
$757$	289.830			0.382867			0.191433	+	0.981506i	$0.438686\pi$
$758$	−540.316	+	311.951i	−0.712818	+	0.411545i
$759$		0			0
$760$	251.660	−	435.888i	0.331132	−	0.573537i
$761$	610.251	+	352.329i	0.801907	+	0.462981i	0.844137	−	0.536127i	$-0.180113\pi$
$761$	610.251	+	352.329i	0.801907	+	0.462981i	−0.0422307	+	0.999108i	$0.513446\pi$
$762$		0			0
$763$	235.247	+	407.460i	0.308319	+	0.534023i
$764$		−	82.7231i		−	0.108276i
$765$		0			0
$766$	−301.312			−0.393358
$767$	3.68870	−	2.12967i	0.00480926	−	0.00277663i
$768$		0			0
$769$	58.6601	−	101.602i	0.0762810	−	0.132123i	−0.825362	−	0.564604i	$-0.809029\pi$
$769$	58.6601	−	101.602i	0.0762810	−	0.132123i	0.901643	+	0.432482i	$0.142362\pi$
$770$	−513.054	−	296.212i	−0.666304	−	0.384691i
$771$		0			0
$772$	134.000	+	232.095i	0.173575	+	0.300641i
$773$			658.005i			0.851235i	0.904903	+	0.425618i	$0.139943\pi$
$773$			658.005i			0.851235i	−0.904903	+	0.425618i	$0.860057\pi$
$774$		0			0
$775$	929.814			1.19976
$776$	108.789	−	62.8095i	0.140192	−	0.0809401i
$777$		0			0
$778$	399.583	−	692.098i	0.513603	−	0.889586i
$779$	272.518	+	157.338i	0.349830	+	0.201975i
$780$		0			0
$781$	158.332	+	274.239i	0.202730	+	0.351138i
$782$		−	650.997i		−	0.832477i
$783$		0			0
$784$	28.0000			0.0357143
$785$	531.648	−	306.947i	0.677259	−	0.391016i
$786$		0			0
$787$	600.324	−	1039.79i	0.762801	−	1.32121i	−0.178601	−	0.983922i	$-0.557157\pi$
$787$	600.324	−	1039.79i	0.762801	−	1.32121i	0.941402	−	0.337288i	$-0.109510\pi$
$788$	−119.212	−	68.8269i	−0.151284	−	0.0873438i
$789$		0			0
$790$	−744.486	−	1289.49i	−0.942388	−	1.63226i
$791$			82.9376i			0.104852i
$792$		0			0
$793$	259.158			0.326807
$794$	−610.320	+	352.368i	−0.768665	+	0.443789i
$795$		0			0
$796$	−278.494	+	482.366i	−0.349867	+	0.605987i
$797$	−690.578	−	398.706i	−0.866472	−	0.500258i	−0.000297855	−	1.00000i	$-0.500095\pi$
$797$	−690.578	−	398.706i	−0.866472	−	0.500258i	−0.866174	+	0.499742i	$0.833428\pi$
$798$		0			0
$799$	219.498	+	380.182i	0.274716	+	0.475822i
$800$			306.409i			0.383012i
$801$		0			0
$802$	−273.498			−0.341020
$803$	445.609	−	257.272i	0.554930	−	0.320389i
$804$		0			0
$805$	209.454	−	362.784i	0.260191	−	0.450664i
$806$	−54.3051	−	31.3530i	−0.0673760	−	0.0388996i
$807$		0			0
$808$	45.0850	+	78.0895i	0.0557982	+	0.0966454i
$809$		−	156.016i		−	0.192851i	−0.995340	−	0.0964254i	$-0.969259\pi$
$809$		−	156.016i		−	0.192851i	0.995340	−	0.0964254i	$-0.0307409\pi$
$810$		0			0
$811$	−598.316			−0.737751			−0.368876	−	0.929479i	$-0.620257\pi$
$811$	−598.316			−0.737751			−0.368876	+	0.929479i	$0.620257\pi$
$812$	−54.5484	+	31.4935i	−0.0671778	+	0.0387851i
$813$		0			0
$814$	−478.154	+	828.187i	−0.587413	+	1.01743i
$815$	1286.79	+	742.926i	1.57888	+	0.911566i
$816$		0			0
$817$	434.980	+	753.408i	0.532412	+	0.922164i
$818$			642.397i			0.785326i
$819$		0			0
$820$	−279.984			−0.341444
$821$	−849.552	+	490.489i	−1.03478	+	0.597429i	−0.918349	−	0.395770i	$-0.870478\pi$
$821$	−849.552	+	490.489i	−1.03478	+	0.597429i	−0.116427	+	0.993199i	$0.537144\pi$
$822$		0			0
$823$	215.668	−	373.548i	0.262051	−	0.453886i	−0.704736	−	0.709470i	$-0.748934\pi$
$823$	215.668	−	373.548i	0.262051	−	0.453886i	0.966787	+	0.255584i	$0.0822678\pi$
$824$	−11.0275	−	6.36674i	−0.0133829	−	0.00772663i
$825$		0			0
$826$	−3.08497	−	5.34333i	−0.00373484	−	0.00646892i
$827$		−	1219.41i		−	1.47449i	−0.675623	−	0.737247i	$-0.736125\pi$
$827$		−	1219.41i		−	1.47449i	0.675623	−	0.737247i	$-0.263875\pi$
$828$		0			0
$829$	−770.081			−0.928928			−0.464464	−	0.885592i	$-0.653753\pi$
$829$	−770.081			−0.928928			−0.464464	+	0.885592i	$0.653753\pi$
$830$	−1312.49	+	757.767i	−1.58131	+	0.912972i
$831$		0			0
$832$	10.3320	−	17.8956i	0.0124183	−	0.0215091i
$833$	156.817	+	90.5383i	0.188256	+	0.108689i
$834$		0			0
$835$	535.822	+	928.071i	0.641703	+	1.11146i
$836$		−	711.802i		−	0.851438i
$837$		0			0
$838$	480.000			0.572792
$839$	1134.52	−	655.016i	1.35223	−	0.780710i	0.363668	−	0.931529i	$-0.381524\pi$
$839$	1134.52	−	655.016i	1.35223	−	0.780710i	0.988561	+	0.150819i	$0.0481910\pi$
$840$		0			0
$841$	−349.654	+	605.619i	−0.415760	+	0.720118i
$842$	302.904	+	174.882i	0.359744	+	0.207698i
$843$		0			0
$844$	−211.498	−	366.325i	−0.250590	−	0.434035i
$845$		−	1444.32i		−	1.70925i
$846$		0			0
$847$	−517.678			−0.611191
$848$	−296.379	+	171.114i	−0.349503	+	0.201786i
$849$		0			0
$850$	−990.778	+	1716.08i	−1.16562	+	2.01891i
$851$	−585.617	−	338.106i	−0.688151	−	0.397304i
$852$		0			0
$853$	−449.494	−	778.547i	−0.526957	−	0.912716i	−0.999507	−	0.0314119i	$-0.990000\pi$
$853$	−449.494	−	778.547i	−0.526957	−	0.912716i	0.472550	−	0.881304i	$-0.343334\pi$
$854$		−	375.408i		−	0.439588i
$855$		0			0
$856$	−486.996			−0.568921
$857$	−646.190	+	373.078i	−0.754014	+	0.435330i	−0.827142	−	0.561993i	$-0.810035\pi$
$857$	−646.190	+	373.078i	−0.754014	+	0.435330i	0.0731286	+	0.997323i	$0.476702\pi$
$858$		0			0
$859$	495.992	−	859.084i	0.577406	−	1.00010i	−0.418369	−	0.908277i	$-0.637398\pi$
$859$	495.992	−	859.084i	0.577406	−	1.00010i	0.995776	−	0.0918202i	$-0.0292685\pi$
$860$	−670.347	−	387.025i	−0.779473	−	0.450029i
$861$		0			0
$862$	322.737	+	558.997i	0.374405	+	0.648489i
$863$		−	209.418i		−	0.242663i	−0.992612	−	0.121332i	$-0.961284\pi$
$863$		−	209.418i		−	0.242663i	0.992612	−	0.121332i	$-0.0387164\pi$
$864$		0			0
$865$	817.336			0.944897
$866$	781.368	−	451.123i	0.902272	−	0.520927i
$867$		0			0
$868$	−45.4170	+	78.6645i	−0.0523237	+	0.0906274i
$869$	−1823.61	−	1052.86i	−2.09852	−	1.21158i
$870$		0			0
$871$	−47.3517	−	82.0156i	−0.0543648	−	0.0941625i
$872$		−	502.979i		−	0.576811i
$873$		0			0
$874$	503.320			0.575881
$875$	−594.602	+	343.293i	−0.679545	+	0.392335i
$876$		0			0
$877$	432.652	−	749.376i	0.493332	−	0.854476i	−0.506638	−	0.862159i	$-0.669112\pi$
$877$	432.652	−	749.376i	0.493332	−	0.854476i	0.999970	+	0.00768242i	$0.00244541\pi$
$878$	−960.379	−	554.475i	−1.09383	−	0.631521i
$879$		0			0
$880$	316.664	+	548.478i	0.359846	+	0.623271i
$881$		−	995.046i		−	1.12945i	−0.825279	−	0.564725i	$-0.808982\pi$
$881$		−	995.046i		−	1.12945i	0.825279	−	0.564725i	$-0.191018\pi$
$882$		0			0
$883$	101.474			0.114920			0.0574600	−	0.998348i	$-0.481700\pi$
$883$	101.474			0.114920			0.0574600	+	0.998348i	$0.481700\pi$
$884$	115.731	−	66.8174i	0.130918	−	0.0755853i
$885$		0			0
$886$	333.911	−	578.351i	0.376875	−	0.652766i
$887$	930.191	+	537.046i	1.04869	+	0.605464i	0.922283	−	0.386514i	$-0.126321\pi$
$887$	930.191	+	537.046i	1.04869	+	0.605464i	0.126410	+	0.991978i	$0.459654\pi$
$888$		0			0
$889$	−283.535	−	491.096i	−0.318937	−	0.552414i
$890$		−	1755.01i		−	1.97192i
$891$		0			0
$892$	−444.988			−0.498866
$893$	−293.939	+	169.706i	−0.329159	+	0.190040i
$894$		0			0
$895$	592.980	−	1027.07i	0.662548	−	1.14757i
$896$	−25.9230	−	14.9666i	−0.0289319	−	0.0167038i
$897$		0			0
$898$	−523.154	−	906.130i	−0.582577	−	1.00905i
$899$		−	204.334i		−	0.227291i
$900$		0			0
$901$	−2213.20			−2.45638
$902$	−342.909	+	197.979i	−0.380165	+	0.219489i
$903$		0			0
$904$	44.3320	−	76.7853i	0.0490398	−	0.0849395i
$905$	−640.210	−	369.625i	−0.707414	−	0.408426i
$906$		0			0
$907$	216.081	+	374.263i	0.238237	+	0.412639i	0.960209	−	0.279284i	$-0.0900971\pi$
$907$	216.081	+	374.263i	0.238237	+	0.412639i	−0.721971	+	0.691923i	$0.756764\pi$
$908$		−	203.647i		−	0.224281i
$909$		0			0
$910$	85.9921			0.0944968
$911$	90.9192	−	52.4922i	0.0998016	−	0.0576205i	−0.449268	−	0.893397i	$-0.648315\pi$
$911$	90.9192	−	52.4922i	0.0998016	−	0.0576205i	0.549070	+	0.835776i	$0.314982\pi$
$912$		0			0
$913$	−1071.64	+	1856.14i	−1.17376	+	2.03301i
$914$	−304.134	−	175.592i	−0.332750	−	0.192113i
$915$		0			0
$916$	−163.085	−	282.471i	−0.178040	−	0.308375i
$917$			241.951i			0.263850i
$918$		0			0
$919$	−91.8379			−0.0999325			−0.0499662	−	0.998751i	$-0.515911\pi$
$919$	−91.8379			−0.0999325			−0.0499662	+	0.998751i	$0.515911\pi$
$920$	−387.833	+	223.915i	−0.421557	+	0.243386i
$921$		0			0
$922$	251.708	−	435.972i	0.273003	−	0.472855i
$923$	−39.8066	−	22.9824i	−0.0431274	−	0.0248996i
$924$		0			0
$925$	1029.15	+	1782.55i	1.11260	+	1.92708i
$926$			8.95483i			0.00967044i
$927$		0			0
$928$	67.3360			0.0725603
$929$	1133.63	−	654.501i	1.22027	−	0.704522i	0.255293	−	0.966864i	$-0.417828\pi$
$929$	1133.63	−	654.501i	1.22027	−	0.704522i	0.964975	+	0.262342i	$0.0844949\pi$
$930$		0			0
$931$	−70.0000	+	121.244i	−0.0751880	+	0.130229i
$932$	628.488	+	362.858i	0.674343	+	0.389332i
$933$		0			0
$934$	621.328	+	1076.17i	0.665233	+	1.15222i
$935$			4095.75i			4.38048i
$936$		0			0
$937$	1262.00			1.34685			0.673426	−	0.739255i	$-0.264822\pi$
$937$	1262.00			1.34685			0.673426	+	0.739255i	$0.264822\pi$
$938$	−118.805	+	68.5921i	−0.126658	+	0.0731260i
$939$		0			0
$940$	150.996	−	261.533i	0.160634	−	0.278226i
$941$	−1139.67	−	657.987i	−1.21112	−	0.699243i	−0.248120	−	0.968729i	$-0.579813\pi$
$941$	−1139.67	−	657.987i	−1.21112	−	0.699243i	−0.963004	+	0.269487i	$0.913146\pi$
$942$		0			0
$943$	−139.992	−	242.473i	−0.148454	−	0.257130i
$944$			6.59595i			0.00698724i
$945$		0			0
$946$	−1094.67			−1.15716
$947$	−421.392	+	243.291i	−0.444976	+	0.256907i	−0.705706	−	0.708505i	$-0.749370\pi$
$947$	−421.392	+	243.291i	−0.444976	+	0.256907i	0.260730	+	0.965412i	$0.416037\pi$
$948$		0			0
$949$	−37.3438	+	64.6814i	−0.0393507	+	0.0681574i
$950$	−1326.79	−	766.023i	−1.39662	−	0.806340i
$951$		0			0
$952$	−96.7895	−	167.644i	−0.101670	−	0.176097i
$953$		−	43.3711i		−	0.0455100i	−0.999741	−	0.0227550i	$-0.992756\pi$
$953$		−	43.3711i		−	0.0455100i	0.999741	−	0.0227550i	$-0.00724377\pi$
$954$		0			0
$955$	−368.016			−0.385357
$956$	306.791	−	177.126i	0.320911	−	0.185278i
$957$		0			0
$958$	158.672	−	274.828i	0.165628	−	0.286877i
$959$	244.917	+	141.403i	0.255388	+	0.147448i
$960$		0			0
$961$	333.164	+	577.057i	0.346685	+	0.600476i
$962$		−	138.811i		−	0.144294i
$963$		0			0
$964$	−305.506			−0.316915
$965$	1032.54	−	596.134i	1.06998	−	0.617756i
$966$		0			0
$967$	−824.494	+	1428.07i	−0.852631	+	1.47680i	0.0261946	+	0.999657i	$0.491661\pi$
$967$	−824.494	+	1428.07i	−0.852631	+	1.47680i	−0.878826	+	0.477143i	$0.841672\pi$
$968$	479.277	+	276.711i	0.495121	+	0.285858i
$969$		0			0
$970$	−279.425	−	483.978i	−0.288067	−	0.498946i
$971$		−	518.323i		−	0.533803i	−0.963724	−	0.266902i	$-0.914000\pi$
$971$		−	518.323i		−	0.533803i	0.963724	−	0.266902i	$-0.0859999\pi$
$972$		0			0
$973$	−321.004			−0.329912
$974$	878.742	−	507.342i	0.902200	−	0.520885i
$975$		0			0
$976$	−200.664	+	347.560i	−0.205598	+	0.356107i
$977$	95.2179	+	54.9741i	0.0974595	+	0.0562682i	0.547938	−	0.836519i	$-0.315413\pi$
$977$	95.2179	+	54.9741i	0.0974595	+	0.0562682i	−0.450478	+	0.892787i	$0.648746\pi$
$978$		0			0
$979$	−1240.98	−	2149.44i	−1.26760	−	2.19555i
$980$		−	124.565i		−	0.127108i
$981$		0			0
$982$	−387.498			−0.394601
$983$	510.704	−	294.855i	0.519536	−	0.299954i	−0.217209	−	0.976125i	$-0.569695\pi$
$983$	510.704	−	294.855i	0.519536	−	0.299954i	0.736745	+	0.676171i	$0.236362\pi$
$984$		0			0
$985$	−306.195	+	530.345i	−0.310858	+	0.538421i
$986$	377.122	+	217.732i	0.382477	+	0.220823i
$987$		0			0
$988$	51.6601	+	89.4779i	0.0522876	+	0.0905647i
$989$		−	774.050i		−	0.782659i
$990$		0			0
$991$	713.474			0.719954			0.359977	−	0.932961i	$-0.382785\pi$
$991$	713.474			0.719954			0.359977	+	0.932961i	$0.382785\pi$
$992$	84.0959	−	48.5528i	0.0847741	−	0.0489444i
$993$		0			0
$994$	−33.2915	+	57.6626i	−0.0334925	+	0.0580106i
$995$	2145.93	+	1238.95i	2.15672	+	1.24518i
$996$		0			0
$997$	−611.494	−	1059.14i	−0.613334	−	1.06233i	−0.990674	−	0.136251i	$-0.956495\pi$
$997$	−611.494	−	1059.14i	−0.613334	−	1.06233i	0.377340	−	0.926075i	$-0.376839\pi$
$998$			1030.69i			1.03276i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.3.q.c.701.1		8
3.2	odd	2	inner	1134.3.q.c.701.4		8
9.2	odd	6	inner	1134.3.q.c.1079.1		8
9.4	even	3		126.3.b.a.71.2	✓	4
9.5	odd	6		126.3.b.a.71.3	yes	4
9.7	even	3	inner	1134.3.q.c.1079.4		8
36.23	even	6		1008.3.d.a.449.1		4
36.31	odd	6		1008.3.d.a.449.4		4
45.4	even	6		3150.3.e.e.701.3		4
45.13	odd	12		3150.3.c.b.449.2		8
45.14	odd	6		3150.3.e.e.701.1		4
45.22	odd	12		3150.3.c.b.449.8		8
45.23	even	12		3150.3.c.b.449.5		8
45.32	even	12		3150.3.c.b.449.3		8
63.4	even	3		882.3.s.e.863.3		8
63.5	even	6		882.3.s.i.557.4		8
63.13	odd	6		882.3.b.f.197.1		4
63.23	odd	6		882.3.s.e.557.3		8
63.31	odd	6		882.3.s.i.863.4		8
63.32	odd	6		882.3.s.e.863.2		8
63.40	odd	6		882.3.s.i.557.1		8
63.41	even	6		882.3.b.f.197.4		4
63.58	even	3		882.3.s.e.557.2		8
63.59	even	6		882.3.s.i.863.1		8
72.5	odd	6		4032.3.d.i.449.4		4
72.13	even	6		4032.3.d.i.449.1		4
72.59	even	6		4032.3.d.j.449.4		4
72.67	odd	6		4032.3.d.j.449.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.b.a.71.2	✓	4	9.4	even	3
126.3.b.a.71.3	yes	4	9.5	odd	6
882.3.b.f.197.1		4	63.13	odd	6
882.3.b.f.197.4		4	63.41	even	6
882.3.s.e.557.2		8	63.58	even	3
882.3.s.e.557.3		8	63.23	odd	6
882.3.s.e.863.2		8	63.32	odd	6
882.3.s.e.863.3		8	63.4	even	3
882.3.s.i.557.1		8	63.40	odd	6
882.3.s.i.557.4		8	63.5	even	6
882.3.s.i.863.1		8	63.59	even	6
882.3.s.i.863.4		8	63.31	odd	6
1008.3.d.a.449.1		4	36.23	even	6
1008.3.d.a.449.4		4	36.31	odd	6
1134.3.q.c.701.1		8	1.1	even	1	trivial
1134.3.q.c.701.4		8	3.2	odd	2	inner
1134.3.q.c.1079.1		8	9.2	odd	6	inner
1134.3.q.c.1079.4		8	9.7	even	3	inner
3150.3.c.b.449.2		8	45.13	odd	12
3150.3.c.b.449.3		8	45.32	even	12
3150.3.c.b.449.5		8	45.23	even	12
3150.3.c.b.449.8		8	45.22	odd	12
3150.3.e.e.701.1		4	45.14	odd	6
3150.3.e.e.701.3		4	45.4	even	6
4032.3.d.i.449.1		4	72.13	even	6
4032.3.d.i.449.4		4	72.5	odd	6
4032.3.d.j.449.1		4	72.67	odd	6
4032.3.d.j.449.4		4	72.59	even	6

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:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1134.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(-7.70549 - 4.44876i) q^{5} +(-1.32288 - 2.29129i) q^{7} +2.82843i q^{8} +O(q^{10})\)	\(q+(-1.22474 + 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(-7.70549 - 4.44876i) q^{5} +(-1.32288 - 2.29129i) q^{7} +2.82843i q^{8} +12.5830 q^{10} +(15.4110 - 8.89753i) q^{11} +(-1.29150 + 2.23695i) q^{13} +(3.24037 + 1.87083i) q^{14} +(-2.00000 - 3.46410i) q^{16} -25.8681i q^{17} +20.0000 q^{19} +(-15.4110 + 8.89753i) q^{20} +(-12.5830 + 21.7944i) q^{22} +(-15.4110 - 8.89753i) q^{23} +(27.0830 + 46.9091i) q^{25} -3.65292i q^{26} -5.29150 q^{28} +(10.3087 - 5.95171i) q^{29} +(8.58301 - 14.8662i) q^{31} +(4.89898 + 2.82843i) q^{32} +(18.2915 + 31.6818i) q^{34} +23.5406i q^{35} +38.0000 q^{37} +(-24.4949 + 14.1421i) q^{38} +(12.5830 - 21.7944i) q^{40} +(13.6259 + 7.86691i) q^{41} +(21.7490 + 37.6704i) q^{43} -35.5901i q^{44} +25.1660 q^{46} +(-14.6969 + 8.48528i) q^{47} +(-3.50000 + 6.06218i) q^{49} +(-66.3395 - 38.3012i) q^{50} +(2.58301 + 4.47390i) q^{52} -85.5571i q^{53} -158.332 q^{55} +(6.48074 - 3.74166i) q^{56} +(-8.41699 + 14.5787i) q^{58} +(-1.42807 - 0.824494i) q^{59} +(-50.1660 - 86.8901i) q^{61} +24.2764i q^{62} -8.00000 q^{64} +(19.9033 - 11.4912i) q^{65} +(-18.3320 + 31.7520i) q^{67} +(-44.8048 - 25.8681i) q^{68} +(-16.6458 - 28.8313i) q^{70} +17.7951i q^{71} +28.9150 q^{73} +(-46.5403 + 26.8701i) q^{74} +(20.0000 - 34.6410i) q^{76} +(-40.7736 - 23.5406i) q^{77} +(-59.1660 - 102.479i) q^{79} +35.5901i q^{80} -22.2510 q^{82} +(-104.307 + 60.2215i) q^{83} +(-115.081 + 199.326i) q^{85} +(-53.2740 - 30.7578i) q^{86} +(25.1660 + 43.5888i) q^{88} -139.475i q^{89} +6.83399 q^{91} +(-30.8219 + 17.7951i) q^{92} +(12.0000 - 20.7846i) q^{94} +(-154.110 - 88.9753i) q^{95} +(-22.2065 - 38.4628i) q^{97} -9.89949i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4}+O(q^{10}) \) 8 * q + 8 * q^4	\( 8 q + 8 q^{4} + 16 q^{10} + 32 q^{13} - 16 q^{16} + 160 q^{19} - 16 q^{22} + 132 q^{25} - 16 q^{31} + 104 q^{34} + 304 q^{37} + 16 q^{40} - 80 q^{43} + 32 q^{46} - 28 q^{49} - 64 q^{52} - 928 q^{55} - 152 q^{58} - 232 q^{61} - 64 q^{64} + 192 q^{67} - 112 q^{70} - 192 q^{73} + 160 q^{76} - 304 q^{79} - 432 q^{82} - 328 q^{85} + 32 q^{88} + 224 q^{91} + 96 q^{94} + 288 q^{97}+O(q^{100}) \) 8 * q + 8 * q^4 + 16 * q^10 + 32 * q^13 - 16 * q^16 + 160 * q^19 - 16 * q^22 + 132 * q^25 - 16 * q^31 + 104 * q^34 + 304 * q^37 + 16 * q^40 - 80 * q^43 + 32 * q^46 - 28 * q^49 - 64 * q^52 - 928 * q^55 - 152 * q^58 - 232 * q^61 - 64 * q^64 + 192 * q^67 - 112 * q^70 - 192 * q^73 + 160 * q^76 - 304 * q^79 - 432 * q^82 - 328 * q^85 + 32 * q^88 + 224 * q^91 + 96 * q^94 + 288 * q^97

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