LMFDB - Embedded newform 315.3.ca.b.172.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,3,Mod(37,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("315.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	315.ca (of order $12$, degree $4$, 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:	$8.58312832735$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			172.1
Character	$\chi$	$=$	315.172
Dual form			315.3.ca.b.163.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.955194 + 3.56483i) q^{2} +(-8.33154 - 4.81021i) q^{4} +(3.70210 + 3.36072i) q^{5} +(3.07429 - 6.28878i) q^{7} +(14.6673 - 14.6673i) q^{8} +O(q^{10})$	\(q+(-0.955194 + 3.56483i) q^{2} +(-8.33154 - 4.81021i) q^{4} +(3.70210 + 3.36072i) q^{5} +(3.07429 - 6.28878i) q^{7} +(14.6673 - 14.6673i) q^{8} +(-15.5166 + 9.98725i) q^{10} +(4.09367 - 7.09045i) q^{11} +(14.0569 - 14.0569i) q^{13} +(19.4819 + 16.9663i) q^{14} +(19.0355 + 32.9704i) q^{16} +(6.76150 - 1.81174i) q^{17} +(18.2350 - 10.5280i) q^{19} +(-14.6784 - 45.8079i) q^{20} +(21.3660 + 21.3660i) q^{22} +(-31.4621 - 8.43024i) q^{23} +(2.41116 + 24.8835i) q^{25} +(36.6833 + 63.5374i) q^{26} +(-55.8639 + 37.6072i) q^{28} +22.1129i q^{29} +(13.7286 - 23.7786i) q^{31} +(-55.5730 + 14.8907i) q^{32} +25.8342i q^{34} +(32.5162 - 12.9499i) q^{35} +(-4.01580 + 14.9872i) q^{37} +(20.1126 + 75.0611i) q^{38} +(103.592 - 5.00723i) q^{40} -0.496183 q^{41} +(-33.4554 + 33.4554i) q^{43} +(-68.2132 + 39.3829i) q^{44} +(60.1048 - 104.105i) q^{46} +(6.46488 - 24.1272i) q^{47} +(-30.0975 - 38.6671i) q^{49} +(-91.0085 - 15.1731i) q^{50} +(-184.732 + 49.4987i) q^{52} +(-9.20667 - 34.3598i) q^{53} +(38.9842 - 12.4919i) q^{55} +(-47.1478 - 137.331i) q^{56} +(-78.8289 - 21.1222i) q^{58} +(-15.5949 - 9.00371i) q^{59} +(13.4849 + 23.3565i) q^{61} +(71.6533 + 71.6533i) q^{62} -60.0481i q^{64} +(99.2811 - 4.79884i) q^{65} +(5.37586 - 1.44046i) q^{67} +(-65.0485 - 17.4297i) q^{68} +(15.1050 + 128.284i) q^{70} +105.010 q^{71} +(21.8814 + 81.6625i) q^{73} +(-49.5909 - 28.6313i) q^{74} -202.568 q^{76} +(-32.0051 - 47.5423i) q^{77} +(86.5708 - 49.9817i) q^{79} +(-40.3329 + 186.033i) q^{80} +(0.473951 - 1.76881i) q^{82} +(-95.6303 + 95.6303i) q^{83} +(31.1205 + 16.0162i) q^{85} +(-87.3064 - 151.219i) q^{86} +(-43.9546 - 164.041i) q^{88} +(54.3480 - 31.3778i) q^{89} +(-45.1856 - 131.615i) q^{91} +(221.576 + 221.576i) q^{92} +(79.8344 + 46.0924i) q^{94} +(102.890 + 22.3070i) q^{95} +(59.0158 + 59.0158i) q^{97} +(166.591 - 70.3578i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8}+O(q^{10}) $ 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8	$ 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8} - 16 q^{10} - 16 q^{11} + 80 q^{16} - 56 q^{17} - 96 q^{22} - 72 q^{23} - 4 q^{25} + 288 q^{26} - 380 q^{28} - 136 q^{31} + 48 q^{32} - 76 q^{35} - 28 q^{37} + 68 q^{38} + 164 q^{40} - 128 q^{41} + 344 q^{43} + 240 q^{46} - 412 q^{47} + 72 q^{50} + 388 q^{52} + 40 q^{53} - 8 q^{55} + 864 q^{56} + 56 q^{58} - 216 q^{61} + 912 q^{62} - 20 q^{65} - 368 q^{67} + 492 q^{68} + 416 q^{70} - 784 q^{71} - 316 q^{73} - 32 q^{76} - 844 q^{77} - 908 q^{80} + 556 q^{82} - 1408 q^{83} - 536 q^{85} - 1024 q^{86} + 372 q^{88} - 1064 q^{91} + 1704 q^{92} - 260 q^{95} + 352 q^{97} - 272 q^{98}+O(q^{100}) $ 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8 - 16 * q^10 - 16 * q^11 + 80 * q^16 - 56 * q^17 - 96 * q^22 - 72 * q^23 - 4 * q^25 + 288 * q^26 - 380 * q^28 - 136 * q^31 + 48 * q^32 - 76 * q^35 - 28 * q^37 + 68 * q^38 + 164 * q^40 - 128 * q^41 + 344 * q^43 + 240 * q^46 - 412 * q^47 + 72 * q^50 + 388 * q^52 + 40 * q^53 - 8 * q^55 + 864 * q^56 + 56 * q^58 - 216 * q^61 + 912 * q^62 - 20 * q^65 - 368 * q^67 + 492 * q^68 + 416 * q^70 - 784 * q^71 - 316 * q^73 - 32 * q^76 - 844 * q^77 - 908 * q^80 + 556 * q^82 - 1408 * q^83 - 536 * q^85 - 1024 * q^86 + 372 * q^88 - 1064 * q^91 + 1704 * q^92 - 260 * q^95 + 352 * q^97 - 272 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.955194	+	3.56483i	−0.477597	+	1.78242i	0.133707	+	0.991021i	$0.457312\pi$
$2$	−0.955194	+	3.56483i	−0.477597	+	1.78242i	−0.611304	+	0.791396i	$0.709355\pi$
$3$		0			0
$3$		0			0
$4$	−8.33154	−	4.81021i	−2.08288	−	1.20255i
$5$	3.70210	+	3.36072i	0.740421	+	0.672143i
$5$	3.70210	+	3.36072i	0.740421	+	0.672143i
$6$		0			0
$7$	3.07429	−	6.28878i	0.439185	−	0.898397i
$7$	3.07429	−	6.28878i	0.439185	−	0.898397i
$8$	14.6673	−	14.6673i	1.83341	−	1.83341i
$9$		0			0
$10$	−15.5166	+	9.98725i	−1.55166	+	0.998725i
$11$	4.09367	−	7.09045i	0.372152	−	0.644586i	−0.617744	−	0.786379i	$-0.711953\pi$
$11$	4.09367	−	7.09045i	0.372152	−	0.644586i	0.989896	+	0.141793i	$0.0452866\pi$
$12$		0			0
$13$	14.0569	−	14.0569i	1.08130	−	1.08130i	0.0849086	−	0.996389i	$-0.472940\pi$
$13$	14.0569	−	14.0569i	1.08130	−	1.08130i	0.996389	−	0.0849086i	$-0.0270598\pi$
$14$	19.4819	+	16.9663i	1.39156	+	1.21188i
$15$		0			0
$16$	19.0355	+	32.9704i	1.18972	+	2.06065i
$17$	6.76150	−	1.81174i	0.397735	−	0.106573i	−0.0544067	−	0.998519i	$-0.517327\pi$
$17$	6.76150	−	1.81174i	0.397735	−	0.106573i	0.452142	+	0.891946i	$0.350660\pi$
$18$		0			0
$19$	18.2350	−	10.5280i	0.959739	−	0.554105i	0.0636460	−	0.997973i	$-0.479727\pi$
$19$	18.2350	−	10.5280i	0.959739	−	0.554105i	0.896093	+	0.443867i	$0.146394\pi$
$20$	−14.6784	−	45.8079i	−0.733922	−	2.29039i
$21$		0			0
$22$	21.3660	+	21.3660i	0.971183	+	0.971183i
$23$	−31.4621	−	8.43024i	−1.36792	−	0.366532i	−0.501199	−	0.865332i	$-0.667108\pi$
$23$	−31.4621	−	8.43024i	−1.36792	−	0.366532i	−0.866717	+	0.498800i	$0.833774\pi$
$24$		0			0
$25$	2.41116	+	24.8835i	0.0964464	+	0.995338i
$26$	36.6833	+	63.5374i	1.41090	+	2.44375i
$27$		0			0
$28$	−55.8639	+	37.6072i	−1.99514	+	1.34311i
$29$			22.1129i			0.762515i	0.924469	+	0.381258i	$0.124509\pi$
$29$			22.1129i			0.762515i	−0.924469	+	0.381258i	$0.875491\pi$
$30$		0			0
$31$	13.7286	−	23.7786i	0.442857	−	0.767052i	−0.555043	−	0.831822i	$-0.687298\pi$
$31$	13.7286	−	23.7786i	0.442857	−	0.767052i	0.997900	+	0.0647702i	$0.0206314\pi$
$32$	−55.5730	+	14.8907i	−1.73666	+	0.465335i
$33$		0			0
$34$			25.8342i			0.759829i
$35$	32.5162	−	12.9499i	0.929033	−	0.369997i
$36$		0			0
$37$	−4.01580	+	14.9872i	−0.108535	+	0.405058i	−0.998722	−	0.0505367i	$-0.983907\pi$
$37$	−4.01580	+	14.9872i	−0.108535	+	0.405058i	0.890187	+	0.455595i	$0.150573\pi$
$38$	20.1126	+	75.0611i	0.529278	+	1.97529i
$39$		0			0
$40$	103.592	−	5.00723i	2.58981	−	0.125181i
$41$	−0.496183			−0.0121020			−0.00605101	−	0.999982i	$-0.501926\pi$
$41$	−0.496183			−0.0121020			−0.00605101	+	0.999982i	$0.501926\pi$
$42$		0			0
$43$	−33.4554	+	33.4554i	−0.778032	+	0.778032i	−0.979496	−	0.201464i	$-0.935430\pi$
$43$	−33.4554	+	33.4554i	−0.778032	+	0.778032i	0.201464	+	0.979496i	$0.435430\pi$
$44$	−68.2132	+	39.3829i	−1.55030	+	0.895066i
$45$		0			0
$46$	60.1048	−	104.105i	1.30663	−	2.26314i
$47$	6.46488	−	24.1272i	0.137551	−	0.513346i	−0.862424	−	0.506187i	$-0.831055\pi$
$47$	6.46488	−	24.1272i	0.137551	−	0.513346i	0.999974	−	0.00715874i	$-0.00227872\pi$
$48$		0			0
$49$	−30.0975	−	38.6671i	−0.614234	−	0.789124i
$50$	−91.0085	−	15.1731i	−1.82017	−	0.303463i
$51$		0			0
$52$	−184.732	+	49.4987i	−3.55253	+	0.951899i
$53$	−9.20667	−	34.3598i	−0.173711	−	0.648297i	−0.996768	−	0.0803384i	$-0.974400\pi$
$53$	−9.20667	−	34.3598i	−0.173711	−	0.648297i	0.823057	−	0.567959i	$-0.192267\pi$
$54$		0			0
$55$	38.9842	−	12.4919i	0.708804	−	0.227126i
$56$	−47.1478	−	137.331i	−0.841925	−	2.45234i
$57$		0			0
$58$	−78.8289	−	21.1222i	−1.35912	−	0.364175i
$59$	−15.5949	−	9.00371i	−0.264320	−	0.152605i	0.361984	−	0.932184i	$-0.382100\pi$
$59$	−15.5949	−	9.00371i	−0.264320	−	0.152605i	−0.626304	+	0.779579i	$0.715433\pi$
$60$		0			0
$61$	13.4849	+	23.3565i	0.221064	+	0.382894i	0.955131	−	0.296183i	$-0.0957137\pi$
$61$	13.4849	+	23.3565i	0.221064	+	0.382894i	−0.734067	+	0.679077i	$0.762380\pi$
$62$	71.6533	+	71.6533i	1.15570	+	1.15570i
$63$		0			0
$64$		−	60.0481i		−	0.938252i
$65$	99.2811	−	4.79884i	1.52740	−	0.0738283i
$66$		0			0
$67$	5.37586	−	1.44046i	0.0802367	−	0.0214993i	−0.218477	−	0.975842i	$-0.570109\pi$
$67$	5.37586	−	1.44046i	0.0802367	−	0.0214993i	0.298714	+	0.954343i	$0.403442\pi$
$68$	−65.0485	−	17.4297i	−0.956596	−	0.256319i
$69$		0			0
$70$	15.1050	+	128.284i	0.215785	+	1.83263i
$71$	105.010			1.47902			0.739509	−	0.673146i	$-0.235058\pi$
$71$	105.010			1.47902			0.739509	+	0.673146i	$0.235058\pi$
$72$		0			0
$73$	21.8814	+	81.6625i	0.299745	+	1.11866i	0.937375	+	0.348321i	$0.113248\pi$
$73$	21.8814	+	81.6625i	0.299745	+	1.11866i	−0.637630	+	0.770343i	$0.720085\pi$
$74$	−49.5909	−	28.6313i	−0.670147	−	0.386909i
$75$		0			0
$76$	−202.568			−2.66537
$77$	−32.0051	−	47.5423i	−0.415651	−	0.617433i
$78$		0			0
$79$	86.5708	−	49.9817i	1.09583	−	0.632679i	0.160710	−	0.987002i	$-0.448622\pi$
$79$	86.5708	−	49.9817i	1.09583	−	0.632679i	0.935123	+	0.354322i	$0.115288\pi$
$80$	−40.3329	+	186.033i	−0.504161	+	2.32541i
$81$		0			0
$82$	0.473951	−	1.76881i	0.00577989	−	0.0215708i
$83$	−95.6303	+	95.6303i	−1.15217	+	1.15217i	−0.166057	+	0.986116i	$0.553103\pi$
$83$	−95.6303	+	95.6303i	−1.15217	+	1.15217i	−0.986116	+	0.166057i	$0.946897\pi$
$84$		0			0
$85$	31.1205	+	16.0162i	0.366124	+	0.188426i
$86$	−87.3064	−	151.219i	−1.01519	−	1.75836i
$87$		0			0
$88$	−43.9546	−	164.041i	−0.499484	−	1.86410i
$89$	54.3480	−	31.3778i	0.610651	−	0.352560i	−0.162569	−	0.986697i	$-0.551978\pi$
$89$	54.3480	−	31.3778i	0.610651	−	0.352560i	0.773220	+	0.634137i	$0.218645\pi$
$90$		0			0
$91$	−45.1856	−	131.615i	−0.496545	−	1.44632i
$92$	221.576	+	221.576i	2.40844	+	2.40844i
$93$		0			0
$94$	79.8344	+	46.0924i	0.849302	+	0.490345i
$95$	102.890	+	22.3070i	1.08305	+	0.234811i
$96$		0			0
$97$	59.0158	+	59.0158i	0.608410	+	0.608410i	0.942530	−	0.334120i	$-0.108439\pi$
$97$	59.0158	+	59.0158i	0.608410	+	0.608410i	−0.334120	+	0.942530i	$0.608439\pi$
$98$	166.591	−	70.3578i	1.69990	−	0.717937i
$99$		0			0
$100$	99.6061	−	218.916i	0.996061	−	2.18916i
$101$	−19.3636	+	33.5388i	−0.191719	+	0.332067i	−0.945820	−	0.324691i	$-0.894740\pi$
$101$	−19.3636	+	33.5388i	−0.191719	+	0.332067i	0.754101	+	0.656758i	$0.228073\pi$
$102$		0			0
$103$	29.9227	+	8.01775i	0.290511	+	0.0778422i	0.401131	−	0.916021i	$-0.368617\pi$
$103$	29.9227	+	8.01775i	0.290511	+	0.0778422i	−0.110620	+	0.993863i	$0.535284\pi$
$104$		−	412.352i		−	3.96493i
$105$		0			0
$106$	131.281			1.23850
$107$	5.02357	−	18.7482i	0.0469492	−	0.175217i	−0.938470	−	0.345361i	$-0.887757\pi$
$107$	5.02357	−	18.7482i	0.0469492	−	0.175217i	0.985419	+	0.170144i	$0.0544232\pi$
$108$		0			0
$109$	73.5876	+	42.4858i	0.675116	+	0.389778i	0.798012	−	0.602641i	$-0.205885\pi$
$109$	73.5876	+	42.4858i	0.675116	+	0.389778i	−0.122896	+	0.992419i	$0.539218\pi$
$110$	7.29410	+	150.904i	0.0663100	+	1.37186i
$111$		0			0
$112$	265.864	−	18.3492i	2.37379	−	0.163832i
$113$	94.3686	−	94.3686i	0.835120	−	0.835120i	−0.153092	−	0.988212i	$-0.548923\pi$
$113$	94.3686	−	94.3686i	0.835120	−	0.835120i	0.988212	+	0.153092i	$0.0489231\pi$
$114$		0			0
$115$	−88.1443	−	136.945i	−0.766472	−	1.19082i
$116$	106.368	−	184.235i	0.916966	−	1.58823i
$117$		0			0
$118$	46.9929	−	46.9929i	0.398245	−	0.398245i
$119$	9.39320	−	48.0914i	0.0789345	−	0.404129i
$120$		0			0
$121$	26.9837	+	46.7371i	0.223006	+	0.386257i
$122$	−96.1428	+	25.7614i	−0.788056	+	0.211159i
$123$		0			0
$124$	−228.760	+	132.075i	−1.84484	+	1.06512i
$125$	−74.6999	+	100.224i	−0.597599	+	0.801795i
$126$		0			0
$127$	−146.532	−	146.532i	−1.15380	−	1.15380i	−0.985785	−	0.168010i	$-0.946266\pi$
$127$	−146.532	−	146.532i	−1.15380	−	1.15380i	−0.168010	−	0.985785i	$-0.553734\pi$
$128$	−8.23036	−	2.20532i	−0.0642997	−	0.0172290i
$129$		0			0
$130$	−77.7257	+	358.504i	−0.597890	+	2.75773i
$131$	57.4723	+	99.5449i	0.438720	+	0.759885i	0.997591	−	0.0693695i	$-0.0220987\pi$
$131$	57.4723	+	99.5449i	0.438720	+	0.759885i	−0.558871	+	0.829254i	$0.688765\pi$
$132$		0			0
$133$	−10.1484	−	147.042i	−0.0763041	−	1.10558i
$134$			20.5399i			0.153283i
$135$		0			0
$136$	72.5996	−	125.746i	0.533820	−	0.924604i
$137$	−105.092	+	28.1594i	−0.767096	+	0.205543i	−0.621088	−	0.783741i	$-0.713309\pi$
$137$	−105.092	+	28.1594i	−0.767096	+	0.205543i	−0.146008	+	0.989283i	$0.546643\pi$
$138$		0			0
$139$		−	188.782i		−	1.35814i	−0.734071	−	0.679072i	$-0.762382\pi$
$139$		−	188.782i		−	1.35814i	0.734071	−	0.679072i	$-0.237618\pi$
$140$	−333.201	−	48.5172i	−2.38001	−	0.346552i
$141$		0			0
$142$	−100.305	+	374.344i	−0.706375	+	2.63623i
$143$	−42.1253	−	157.214i	−0.294582	−	1.09940i
$144$		0			0
$145$	−74.3154	+	81.8644i	−0.512520	+	0.564582i
$146$	−312.014			−2.13708
$147$		0			0
$148$	105.549	−	105.549i	0.713170	−	0.713170i
$149$	−102.211	+	59.0115i	−0.685979	+	0.396050i	−0.802104	−	0.597184i	$-0.796286\pi$
$149$	−102.211	+	59.0115i	−0.685979	+	0.396050i	0.116125	+	0.993235i	$0.462953\pi$
$150$		0			0
$151$	−89.3003	+	154.673i	−0.591393	+	1.02432i	0.402653	+	0.915353i	$0.368088\pi$
$151$	−89.3003	+	154.673i	−0.591393	+	1.02432i	−0.994045	+	0.108969i	$0.965245\pi$
$152$	113.041	−	421.876i	0.743693	−	2.77550i
$153$		0			0
$154$	200.052	−	68.6808i	1.29904	−	0.445979i
$155$	130.738	−	41.8930i	0.843470	−	0.270277i
$156$		0			0
$157$	57.3089	−	15.3559i	0.365025	−	0.0978081i	−0.0716444	−	0.997430i	$-0.522825\pi$
$157$	57.3089	−	15.3559i	0.365025	−	0.0978081i	0.436669	+	0.899622i	$0.356158\pi$
$158$	95.4844	+	356.353i	0.604332	+	2.25540i
$159$		0			0
$160$	−255.780	−	131.638i	−1.59863	−	0.822737i
$161$	−149.740	+	171.941i	−0.930059	+	1.06796i
$162$		0			0
$163$	−121.490	−	32.5532i	−0.745338	−	0.199713i	−0.133889	−	0.990996i	$-0.542747\pi$
$163$	−121.490	−	32.5532i	−0.745338	−	0.199713i	−0.611449	+	0.791284i	$0.709413\pi$
$164$	4.13396	+	2.38674i	0.0252071	+	0.0145533i
$165$		0			0
$166$	−249.561	−	432.252i	−1.50338	−	2.60393i
$167$	30.2982	+	30.2982i	0.181427	+	0.181427i	0.791977	−	0.610551i	$-0.209052\pi$
$167$	30.2982	+	30.2982i	0.181427	+	0.181427i	−0.610551	+	0.791977i	$0.709052\pi$
$168$		0			0
$169$		−	226.191i		−	1.33841i
$170$	−86.8214	+	95.6408i	−0.510714	+	0.562593i
$171$		0			0
$172$	439.662	−	117.807i	2.55617	−	0.684925i
$173$	−34.7961	−	9.32360i	−0.201134	−	0.0538936i	0.156846	−	0.987623i	$-0.449868\pi$
$173$	−34.7961	−	9.32360i	−0.201134	−	0.0538936i	−0.357979	+	0.933730i	$0.616534\pi$
$174$		0			0
$175$	163.899	+	61.3358i	0.936566	+	0.350490i
$176$	311.700			1.77102
$177$		0			0
$178$	59.9438	+	223.713i	0.336763	+	1.25682i
$179$	65.4777	+	37.8036i	0.365797	+	0.211193i	0.671621	−	0.740895i	$-0.265598\pi$
$179$	65.4777	+	37.8036i	0.365797	+	0.211193i	−0.305823	+	0.952088i	$0.598932\pi$
$180$		0			0
$181$	−182.419			−1.00784			−0.503919	−	0.863751i	$-0.668109\pi$
$181$	−182.419			−1.00784			−0.503919	+	0.863751i	$0.668109\pi$
$182$	512.348	−	35.3608i	2.81510	−	0.194290i
$183$		0			0
$184$	−585.112	+	337.815i	−3.17996	+	1.83595i
$185$	−65.2345	+	41.9881i	−0.352619	+	0.226963i
$186$		0			0
$187$	14.8333	−	55.3587i	0.0793226	−	0.296036i
$188$	−169.920	+	169.920i	−0.903827	+	0.903827i
$189$		0			0
$190$	−177.800	+	345.477i	−0.935792	+	1.81830i
$191$	7.66297	+	13.2727i	0.0401203	+	0.0694904i	0.885388	−	0.464852i	$-0.153893\pi$
$191$	7.66297	+	13.2727i	0.0401203	+	0.0694904i	−0.845268	+	0.534343i	$0.820559\pi$
$192$		0			0
$193$	58.2576	+	217.420i	0.301853	+	1.12653i	0.935621	+	0.353007i	$0.114841\pi$
$193$	58.2576	+	217.420i	0.301853	+	1.12653i	−0.633768	+	0.773523i	$0.718493\pi$
$194$	−266.753	+	154.010i	−1.37502	+	0.793865i
$195$		0			0
$196$	64.7611	+	466.931i	0.330414	+	2.38230i
$197$	−261.191	−	261.191i	−1.32584	−	1.32584i	−0.908960	−	0.416883i	$-0.863122\pi$
$197$	−261.191	−	261.191i	−1.32584	−	1.32584i	−0.416883	−	0.908960i	$-0.636878\pi$
$198$		0			0
$199$	−57.1020	−	32.9678i	−0.286945	−	0.165668i	0.349619	−	0.936892i	$-0.386311\pi$
$199$	−57.1020	−	32.9678i	−0.286945	−	0.165668i	−0.636563	+	0.771225i	$0.719645\pi$
$200$	400.338	+	329.608i	2.00169	+	1.64804i
$201$		0			0
$202$	−101.064	−	101.064i	−0.500317	−	0.500317i
$203$	139.063	+	67.9816i	0.685041	+	0.334885i
$204$		0			0
$205$	−1.83692	−	1.66753i	−0.00896058	−	0.00813429i
$206$	−57.1639	+	99.0107i	−0.277495	+	0.480635i
$207$		0			0
$208$	731.039	+	195.881i	3.51461	+	0.941738i
$209$		−	172.393i		−	0.824846i
$210$		0			0
$211$	408.766			1.93728			0.968639	−	0.248472i	$-0.0799283\pi$
$211$	408.766			1.93728			0.968639	+	0.248472i	$0.0799283\pi$
$212$	−88.5721	+	330.556i	−0.417793	+	1.55922i
$213$		0			0
$214$	62.0357	+	35.8164i	0.289887	+	0.167366i
$215$	−236.289	+	11.4212i	−1.09902	+	0.0531221i
$216$		0			0
$217$	−107.333	−	159.438i	−0.494621	−	0.734739i
$218$	−221.745	+	221.745i	−1.01718	+	1.01718i
$219$		0			0
$220$	−384.887	−	83.4456i	−1.74949	−	0.379298i
$221$	69.5781	−	120.513i	0.314833	−	0.545307i
$222$		0			0
$223$	−180.123	+	180.123i	−0.807725	+	0.807725i	−0.984289	−	0.176564i	$-0.943502\pi$
$223$	−180.123	+	180.123i	−0.807725	+	0.807725i	0.176564	+	0.984289i	$0.443502\pi$
$224$	−77.2030	+	395.264i	−0.344656	+	1.76457i
$225$		0			0
$226$	246.268	+	426.548i	1.08968	+	1.88738i
$227$	−211.989	+	56.8024i	−0.933874	+	0.250231i	−0.693506	−	0.720451i	$-0.743935\pi$
$227$	−211.989	+	56.8024i	−0.933874	+	0.250231i	−0.240368	+	0.970682i	$0.577268\pi$
$228$		0			0
$229$	−292.008	+	168.591i	−1.27515	+	0.736206i	−0.975952	−	0.217986i	$-0.930051\pi$
$229$	−292.008	+	168.591i	−1.27515	+	0.736206i	−0.299194	+	0.954192i	$0.596718\pi$
$230$	572.380	−	183.411i	2.48861	−	0.797438i
$231$		0			0
$232$	324.337	+	324.337i	1.39800	+	1.39800i
$233$	−284.131	−	76.1326i	−1.21945	−	0.326749i	−0.408984	−	0.912542i	$-0.634117\pi$
$233$	−284.131	−	76.1326i	−1.21945	−	0.326749i	−0.810461	+	0.585792i	$0.800783\pi$
$234$		0			0
$235$	105.018	−	67.5950i	0.446887	−	0.287638i
$236$	86.6195	+	150.029i	0.367032	+	0.635718i
$237$		0			0
$238$	162.465	+	79.4218i	0.682628	+	0.333705i
$239$		−	191.663i		−	0.801937i	−0.916092	−	0.400968i	$-0.868674\pi$
$239$		−	191.663i		−	0.801937i	0.916092	−	0.400968i	$-0.131326\pi$
$240$		0			0
$241$	−61.5720	+	106.646i	−0.255486	+	0.442514i	−0.965027	−	0.262149i	$-0.915569\pi$
$241$	−61.5720	+	106.646i	−0.255486	+	0.442514i	0.709542	+	0.704663i	$0.248902\pi$
$242$	−192.385	+	51.5493i	−0.794978	+	0.213014i
$243$		0			0
$244$		−	259.461i		−	1.06337i
$245$	18.5252	−	244.299i	0.0756130	−	0.997137i
$246$		0			0
$247$	108.337	−	404.318i	0.438610	−	1.63692i
$248$	−147.407	−	550.129i	−0.594381	−	2.21826i
$249$		0			0
$250$	−285.930	−	362.026i	−1.14372	−	1.44811i
$251$	21.1349			0.0842027			0.0421014	−	0.999113i	$-0.486595\pi$
$251$	21.1349			0.0842027			0.0421014	+	0.999113i	$0.486595\pi$
$252$		0			0
$253$	−188.570	+	188.570i	−0.745335	+	0.745335i
$254$	662.329	−	382.396i	2.60759	−	1.50549i
$255$		0			0
$256$	135.819	−	235.246i	0.530545	−	0.918930i
$257$	48.9113	−	182.539i	0.190316	−	0.710270i	−0.803114	−	0.595826i	$-0.796825\pi$
$257$	48.9113	−	182.539i	0.190316	−	0.710270i	0.993430	−	0.114444i	$-0.0365086\pi$
$258$		0			0
$259$	81.9052	+	71.3294i	0.316236	+	0.275403i
$260$	−850.248	−	437.582i	−3.27018	−	1.68301i
$261$		0			0
$262$	−409.758	+	109.794i	−1.56396	+	0.419063i
$263$	36.1131	+	134.776i	0.137312	+	0.512457i	0.999978	+	0.00668144i	$0.00212678\pi$
$263$	36.1131	+	134.776i	0.137312	+	0.512457i	−0.862665	+	0.505775i	$0.831207\pi$
$264$		0			0
$265$	81.3894	−	158.144i	0.307130	−	0.596771i
$266$	533.875	+	104.276i	2.00705	+	0.392016i
$267$		0			0
$268$	−51.7180	−	13.8578i	−0.192978	−	0.0517082i
$269$	169.522	+	97.8736i	0.630194	+	0.363842i	0.780827	−	0.624747i	$-0.214798\pi$
$269$	169.522	+	97.8736i	0.630194	+	0.363842i	−0.150634	+	0.988590i	$0.548131\pi$
$270$		0			0
$271$	123.964	+	214.711i	0.457430	+	0.792292i	0.998824	−	0.0484766i	$-0.0154366\pi$
$271$	123.964	+	214.711i	0.457430	+	0.792292i	−0.541394	+	0.840769i	$0.682103\pi$
$272$	188.442	+	188.442i	0.692802	+	0.692802i
$273$		0			0
$274$		−	401.534i		−	1.46545i
$275$	186.305	+	84.7685i	0.677474	+	0.308249i
$276$		0			0
$277$	−263.603	+	70.6321i	−0.951634	+	0.254989i	−0.701055	−	0.713107i	$-0.747287\pi$
$277$	−263.603	+	70.6321i	−0.951634	+	0.254989i	−0.250578	+	0.968096i	$0.580621\pi$
$278$	672.977	+	180.324i	2.42078	+	0.648646i
$279$		0			0
$280$	286.984	−	666.864i	1.02494	−	2.38166i
$281$	426.012			1.51606			0.758028	−	0.652222i	$-0.226163\pi$
$281$	426.012			1.51606			0.758028	+	0.652222i	$0.226163\pi$
$282$		0			0
$283$	−28.5453	−	106.533i	−0.100867	−	0.376440i	0.896977	−	0.442078i	$-0.145759\pi$
$283$	−28.5453	−	106.533i	−0.100867	−	0.376440i	−0.997844	+	0.0656376i	$0.979092\pi$
$284$	−874.897	−	505.122i	−3.08062	−	1.77860i
$285$		0			0
$286$	600.679			2.10027
$287$	−1.52541	+	3.12038i	−0.00531502	+	0.0108724i
$288$		0			0
$289$	−207.846	+	120.000i	−0.719190	+	0.415224i
$290$	−220.847	−	343.118i	−0.761543	−	1.18317i
$291$		0			0
$292$	210.508	−	785.628i	0.720919	−	2.69051i
$293$	−224.196	+	224.196i	−0.765175	+	0.765175i	−0.977253	−	0.212078i	$-0.931977\pi$
$293$	−224.196	+	224.196i	−0.765175	+	0.765175i	0.212078	+	0.977253i	$0.431977\pi$
$294$		0			0
$295$	−27.4750	−	85.7427i	−0.0931355	−	0.290653i
$296$	160.920	+	278.722i	0.543649	+	0.941628i
$297$		0			0
$298$	−112.735	−	420.732i	−0.378305	−	1.41185i
$299$	−560.761	+	323.755i	−1.87545	+	1.08279i
$300$		0			0
$301$	107.542	+	313.245i	0.357282	+	1.04068i
$302$	−466.083	−	466.083i	−1.54332	−	1.54332i
$303$		0			0
$304$	694.225	+	400.811i	2.28363	+	1.31846i
$305$	−28.5722	+	131.787i	−0.0936793	+	0.432089i
$306$		0			0
$307$	348.544	+	348.544i	1.13532	+	1.13532i	0.989278	+	0.146043i	$0.0466539\pi$
$307$	348.544	+	348.544i	1.13532	+	1.13532i	0.146043	+	0.989278i	$0.453346\pi$
$308$	37.9631	+	550.052i	0.123257	+	1.78588i
$309$		0			0
$310$	24.4615	+	506.074i	0.0789082	+	1.63250i
$311$	7.38338	−	12.7884i	0.0237408	−	0.0411202i	−0.853911	−	0.520419i	$-0.825776\pi$
$311$	7.38338	−	12.7884i	0.0237408	−	0.0411202i	0.877652	+	0.479299i	$0.159109\pi$
$312$		0			0
$313$	−116.758	−	31.2853i	−0.373030	−	0.0999530i	0.0674334	−	0.997724i	$-0.478519\pi$
$313$	−116.758	−	31.2853i	−0.373030	−	0.0999530i	−0.440463	+	0.897771i	$0.645186\pi$
$314$			218.964i			0.697339i
$315$		0			0
$316$	−961.690			−3.04332
$317$	−80.4604	+	300.282i	−0.253818	+	0.947262i	0.714926	+	0.699200i	$0.246460\pi$
$317$	−80.4604	+	300.282i	−0.253818	+	0.947262i	−0.968744	+	0.248062i	$0.920206\pi$
$318$		0			0
$319$	156.791	+	90.5232i	0.491507	+	0.283772i
$320$	201.805	−	222.304i	0.630640	−	0.694701i
$321$		0			0
$322$	−469.911	−	698.033i	−1.45935	−	2.16781i
$323$	104.222	−	104.222i	0.322669	−	0.322669i
$324$		0			0
$325$	383.677	+	315.890i	1.18054	+	0.971969i
$326$	232.093	−	401.998i	0.711943	−	1.23312i
$327$		0			0
$328$	−7.27765	+	7.27765i	−0.0221880	+	0.0221880i
$329$	−131.856	−	114.830i	−0.400778	−	0.349028i
$330$		0			0
$331$	64.5929	+	111.878i	0.195145	+	0.338001i	0.946948	−	0.321387i	$-0.104149\pi$
$331$	64.5929	+	111.878i	0.195145	+	0.338001i	−0.751803	+	0.659388i	$0.770816\pi$
$332$	1256.75	−	336.745i	3.78539	−	1.01429i
$333$		0			0
$334$	−136.949	+	79.0675i	−0.410027	+	0.236729i
$335$	24.7429	+	12.7340i	0.0738595	+	0.0380120i
$336$		0			0
$337$	−51.0347	−	51.0347i	−0.151438	−	0.151438i	0.627322	−	0.778760i	$-0.284151\pi$
$337$	−51.0347	−	51.0347i	−0.151438	−	0.151438i	−0.778760	+	0.627322i	$0.784151\pi$
$338$	806.333	+	216.056i	2.38560	+	0.639220i
$339$		0			0
$340$	−182.240	−	283.136i	−0.536000	−	0.832754i
$341$	−112.401	−	194.684i	−0.329621	−	0.570920i
$342$		0			0
$343$	−335.697	+	70.4023i	−0.978709	+	0.205255i
$344$			981.399i			2.85290i
$345$		0			0
$346$	66.4741	−	115.137i	0.192122	−	0.332765i
$347$	585.959	−	157.007i	1.68864	−	0.452470i	0.718603	−	0.695420i	$-0.244782\pi$
$347$	585.959	−	157.007i	1.68864	−	0.452470i	0.970039	+	0.242950i	$0.0781151\pi$
$348$		0			0
$349$		−	82.1983i		−	0.235525i	−0.993042	−	0.117763i	$-0.962428\pi$
$349$		−	82.1983i		−	0.235525i	0.993042	−	0.117763i	$-0.0375722\pi$
$350$	−375.207	+	525.685i	−1.07202	+	1.50196i
$351$		0			0
$352$	−121.916	+	454.995i	−0.346351	+	1.29260i
$353$	−38.0031	−	141.830i	−0.107658	−	0.401783i	0.890976	−	0.454051i	$-0.150022\pi$
$353$	−38.0031	−	141.830i	−0.107658	−	0.401783i	−0.998633	+	0.0522678i	$0.983355\pi$
$354$		0			0
$355$	388.759	+	352.910i	1.09510	+	0.994112i
$356$	−603.736			−1.69589
$357$		0			0
$358$	−197.307	+	197.307i	−0.551138	+	0.551138i
$359$	175.063	−	101.073i	0.487641	−	0.281539i	−0.235955	−	0.971764i	$-0.575822\pi$
$359$	175.063	−	101.073i	0.487641	−	0.281539i	0.723595	+	0.690225i	$0.242488\pi$
$360$		0			0
$361$	41.1776	−	71.3218i	0.114065	−	0.197567i
$362$	174.245	−	650.292i	0.481340	−	1.79639i
$363$		0			0
$364$	−256.633	+	1313.91i	−0.705036	+	3.60965i
$365$	−193.437	+	375.860i	−0.529965	+	1.02975i
$366$		0			0
$367$	486.132	−	130.259i	1.32461	−	0.354928i	0.473907	−	0.880575i	$-0.342843\pi$
$367$	486.132	−	130.259i	1.32461	−	0.354928i	0.850703	+	0.525647i	$0.176177\pi$
$368$	−320.947	−	1197.79i	−0.872139	−	3.25487i
$369$		0			0
$370$	−87.3689	−	272.657i	−0.236132	−	0.736911i
$371$	−244.385	−	47.7332i	−0.658719	−	0.128661i
$372$		0			0
$373$	178.568	+	47.8471i	0.478735	+	0.128277i	0.490113	−	0.871659i	$-0.336955\pi$
$373$	178.568	+	47.8471i	0.478735	+	0.128277i	−0.0113788	+	0.999935i	$0.503622\pi$
$374$	183.176	+	105.757i	0.489775	+	0.282772i
$375$		0			0
$376$	−259.059	−	448.703i	−0.688987	−	1.19336i
$377$	310.839	+	310.839i	0.824506	+	0.824506i
$378$		0			0
$379$		−	348.414i		−	0.919299i	−0.888100	−	0.459649i	$-0.847975\pi$
$379$		−	348.414i		−	0.919299i	0.888100	−	0.459649i	$-0.152025\pi$
$380$	−749.927	−	680.773i	−1.97349	−	1.79151i
$381$		0			0
$382$	−54.6344	+	14.6393i	−0.143022	+	0.0383226i
$383$	−436.725	−	117.020i	−1.14028	−	0.305536i	−0.361214	−	0.932483i	$-0.617638\pi$
$383$	−436.725	−	117.020i	−1.14028	−	0.305536i	−0.779062	+	0.626947i	$0.784304\pi$
$384$		0			0
$385$	41.2900	−	283.567i	0.107247	−	0.736537i
$386$	−830.714			−2.15211
$387$		0			0
$388$	−207.814	−	775.571i	−0.535602	−	1.99889i
$389$	565.646	+	326.576i	1.45410	+	0.839527i	0.998711	−	0.0507630i	$-0.0161653\pi$
$389$	565.646	+	326.576i	1.45410	+	0.839527i	0.455393	+	0.890290i	$0.349499\pi$
$390$		0			0
$391$	−228.004			−0.583131
$392$	−1008.59	−	125.693i	−2.57293	−	0.320646i
$393$		0			0
$394$	1180.59	−	681.614i	2.99642	−	1.72999i
$395$	488.468	+	105.903i	1.23663	+	0.268108i
$396$		0			0
$397$	17.0735	−	63.7193i	0.0430064	−	0.160502i	−0.941083	−	0.338175i	$-0.890190\pi$
$397$	17.0735	−	63.7193i	0.0430064	−	0.160502i	0.984090	+	0.177673i	$0.0568570\pi$
$398$	172.068	−	172.068i	0.432333	−	0.432333i
$399$		0			0
$400$	−774.520	+	553.165i	−1.93630	+	1.38291i
$401$	−54.6685	−	94.6886i	−0.136330	−	0.236131i	0.789775	−	0.613397i	$-0.210198\pi$
$401$	−54.6685	−	94.6886i	−0.136330	−	0.236131i	−0.926105	+	0.377266i	$0.876864\pi$
$402$		0			0
$403$	−141.272	−	527.233i	−0.350550	−	1.30827i
$404$	322.657	−	186.286i	0.798657	−	0.461105i
$405$		0			0
$406$	−375.176	+	430.802i	−0.924078	+	1.06109i
$407$	89.8264	+	89.8264i	0.220704	+	0.220704i
$408$		0			0
$409$	−254.528	−	146.952i	−0.622318	−	0.359295i	0.155453	−	0.987843i	$-0.450316\pi$
$409$	−254.528	−	146.952i	−0.622318	−	0.359295i	−0.777771	+	0.628548i	$0.783650\pi$
$410$	7.69908	−	4.95550i	0.0187782	−	0.0120866i
$411$		0			0
$412$	−210.735	−	210.735i	−0.511492	−	0.511492i
$413$	−104.566	+	70.3927i	−0.253185	+	0.170442i
$414$		0			0
$415$	−675.420	+	32.6470i	−1.62752	+	0.0786675i
$416$	−571.865	+	990.499i	−1.37467	+	2.38101i
$417$		0			0
$418$	614.552	+	164.669i	1.47022	+	0.393944i
$419$			234.794i			0.560368i	0.959946	+	0.280184i	$0.0903955\pi$
$419$			234.794i			0.560368i	−0.959946	+	0.280184i	$0.909605\pi$
$420$		0			0
$421$	−124.297			−0.295242			−0.147621	−	0.989044i	$-0.547162\pi$
$421$	−124.297			−0.295242			−0.147621	+	0.989044i	$0.547162\pi$
$422$	−390.451	+	1457.18i	−0.925238	+	3.45304i
$423$		0			0
$424$	−639.001	−	368.928i	−1.50708	−	0.870112i
$425$	61.3854	+	163.881i	0.144436	+	0.385602i
$426$		0			0
$427$	188.341	−	12.9987i	0.441079	−	0.0304420i
$428$	−132.037	+	132.037i	−0.308498	+	0.308498i
$429$		0			0
$430$	184.987	−	853.241i	0.430203	−	1.98428i
$431$	−105.297	+	182.380i	−0.244309	+	0.423155i	−0.961937	−	0.273271i	$-0.911894\pi$
$431$	−105.297	+	182.380i	−0.244309	+	0.423155i	0.717628	+	0.696426i	$0.245228\pi$
$432$		0			0
$433$	−549.109	+	549.109i	−1.26815	+	1.26815i	−0.321109	+	0.947042i	$0.604056\pi$
$433$	−549.109	+	549.109i	−1.26815	+	1.26815i	−0.947042	+	0.321109i	$0.895944\pi$
$434$	670.895	−	230.328i	1.54584	−	0.530711i
$435$		0			0
$436$	−408.732	−	707.944i	−0.937459	−	1.62373i
$437$	−662.466	+	177.507i	−1.51594	+	0.406195i
$438$		0			0
$439$	83.0573	−	47.9532i	0.189197	−	0.109233i	−0.402410	−	0.915460i	$-0.631827\pi$
$439$	83.0573	−	47.9532i	0.189197	−	0.109233i	0.591606	+	0.806227i	$0.298494\pi$
$440$	388.570	−	755.015i	0.883114	−	1.71594i
$441$		0			0
$442$	363.148	+	363.148i	0.821601	+	0.821601i
$443$	96.6633	+	25.9009i	0.218202	+	0.0584670i	0.366264	−	0.930511i	$-0.380637\pi$
$443$	96.6633	+	25.9009i	0.218202	+	0.0584670i	−0.148062	+	0.988978i	$0.547304\pi$
$444$		0			0
$445$	306.654	+	66.4842i	0.689110	+	0.149403i
$446$	−470.055	−	814.159i	−1.05394	−	1.82547i
$447$		0			0
$448$	−377.629	−	184.605i	−0.842922	−	0.412066i
$449$		−	344.308i		−	0.766832i	−0.923576	−	0.383416i	$-0.874748\pi$
$449$		−	344.308i		−	0.766832i	0.923576	−	0.383416i	$-0.125252\pi$
$450$		0			0
$451$	−2.03121	+	3.51816i	−0.00450379	+	0.00780079i
$452$	−1240.17	+	332.302i	−2.74373	+	0.735181i
$453$		0			0
$454$		−	809.964i		−	1.78406i
$455$	275.040	−	639.110i	0.604484	−	1.40464i
$456$		0			0
$457$	−22.3113	+	83.2667i	−0.0488211	+	0.182203i	−0.986031	−	0.166564i	$-0.946733\pi$
$457$	−22.3113	+	83.2667i	−0.0488211	+	0.182203i	0.937210	+	0.348767i	$0.113399\pi$
$458$	−322.074	−	1202.00i	−0.703219	−	2.62445i
$459$		0			0
$460$	75.6434	+	1564.95i	0.164442	+	3.40207i
$461$	618.594			1.34185			0.670926	−	0.741524i	$-0.265897\pi$
$461$	618.594			1.34185			0.670926	+	0.741524i	$0.265897\pi$
$462$		0			0
$463$	113.717	−	113.717i	0.245610	−	0.245610i	−0.573556	−	0.819166i	$-0.694437\pi$
$463$	113.717	−	113.717i	0.245610	−	0.245610i	0.819166	+	0.573556i	$0.194437\pi$
$464$	−729.073	+	420.930i	−1.57128	+	0.907177i
$465$		0			0
$466$	542.800	−	940.157i	1.16481	−	2.01750i
$467$	−13.0497	+	48.7023i	−0.0279438	+	0.104288i	−0.978489	−	0.206298i	$-0.933858\pi$
$467$	−13.0497	+	48.7023i	−0.0279438	+	0.104288i	0.950545	+	0.310585i	$0.100525\pi$
$468$		0			0
$469$	7.46824	−	38.2359i	0.0159238	−	0.0815265i
$470$	140.652	+	438.940i	0.299259	+	0.933914i
$471$		0			0
$472$	−360.795	+	96.6746i	−0.764395	+	0.204819i
$473$	100.258	+	374.169i	0.211963	+	0.791055i
$474$		0			0
$475$	305.941	+	428.366i	0.644086	+	0.901823i
$476$	−309.590	+	355.492i	−0.650398	+	0.746831i
$477$		0			0
$478$	683.246	+	183.075i	1.42938	+	0.383003i
$479$	−152.207	−	87.8766i	−0.317760	−	0.183459i	0.332634	−	0.943056i	$-0.392063\pi$
$479$	−152.207	−	87.8766i	−0.317760	−	0.183459i	−0.650393	+	0.759597i	$0.725396\pi$
$480$		0			0
$481$	154.223	+	267.122i	0.320630	+	0.555347i
$482$	−321.361	−	321.361i	−0.666725	−	0.666725i
$483$		0			0
$484$		−	519.189i		−	1.07270i
$485$	20.1473	+	416.818i	0.0415408	+	0.859419i
$486$		0			0
$487$	−245.352	+	65.7419i	−0.503803	+	0.134994i	−0.501765	−	0.865004i	$-0.667316\pi$
$487$	−245.352	+	65.7419i	−0.503803	+	0.134994i	−0.00203876	+	0.999998i	$0.500649\pi$
$488$	540.364	+	144.790i	1.10730	+	0.296701i
$489$		0			0
$490$	853.189	+	299.392i	1.74120	+	0.611004i
$491$	−275.796			−0.561704			−0.280852	−	0.959751i	$-0.590617\pi$
$491$	−275.796			−0.561704			−0.280852	+	0.959751i	$0.590617\pi$
$492$		0			0
$493$	40.0629	+	149.517i	0.0812634	+	0.303279i
$494$	1337.84	+	772.405i	2.70819	+	1.56357i
$495$		0			0
$496$	1045.32			2.10750
$497$	322.832	−	660.386i	0.649562	−	1.32875i
$498$		0			0
$499$	−520.379	+	300.441i	−1.04284	+	0.602086i	−0.920637	−	0.390419i	$-0.872330\pi$
$499$	−520.379	+	300.441i	−1.04284	+	0.602086i	−0.122206	+	0.992505i	$0.538997\pi$
$500$	1104.47	−	475.701i	2.20893	−	0.951401i
$501$		0			0
$502$	−20.1879	+	75.3423i	−0.0402150	+	0.150084i
$503$	513.924	−	513.924i	1.02172	−	1.02172i	0.0219593	−	0.999759i	$-0.493010\pi$
$503$	513.924	−	513.924i	1.02172	−	1.02172i	0.999759	−	0.0219593i	$-0.00699042\pi$
$504$		0			0
$505$	−184.401	+	59.0884i	−0.365150	+	0.117007i
$506$	−492.099	−	852.340i	−0.972527	−	1.68447i
$507$		0			0
$508$	515.986	+	1925.69i	1.01572	+	3.79072i
$509$	406.687	−	234.801i	0.798993	−	0.461299i	−0.0441259	−	0.999026i	$-0.514050\pi$
$509$	406.687	−	234.801i	0.798993	−	0.461299i	0.843119	+	0.537727i	$0.180717\pi$
$510$		0			0
$511$	580.827	+	113.447i	1.13665	+	0.222010i
$512$	684.779	+	684.779i	1.33746	+	1.33746i
$513$		0			0
$514$	604.002	+	348.721i	1.17510	+	0.678446i
$515$	83.8314	+	130.244i	0.162779	+	0.252901i
$516$		0			0
$517$	−144.608	−	144.608i	−0.279706	−	0.279706i
$518$	−332.513	+	223.845i	−0.641916	+	0.432133i
$519$		0			0
$520$	1385.80	−	1526.57i	2.66500	−	2.93571i
$521$	−72.5876	+	125.725i	−0.139324	+	0.241316i	−0.927241	−	0.374466i	$-0.877826\pi$
$521$	−72.5876	+	125.725i	−0.139324	+	0.241316i	0.787917	+	0.615781i	$0.211160\pi$
$522$		0			0
$523$	−809.900	−	217.012i	−1.54857	−	0.414937i	−0.619543	−	0.784962i	$-0.712682\pi$
$523$	−809.900	−	217.012i	−1.54857	−	0.414937i	−0.929022	+	0.370026i	$0.879349\pi$
$524$		−	1105.82i		−	2.11034i
$525$		0			0
$526$	−514.949			−0.978991
$527$	49.7452	−	185.652i	0.0943932	−	0.352280i
$528$		0			0
$529$	460.666	+	265.966i	0.870824	+	0.502770i
$530$	486.016	+	441.198i	0.917011	+	0.832449i
$531$		0			0
$532$	−622.753	+	1273.90i	−1.17059	+	2.39456i
$533$	−6.97477	+	6.97477i	−0.0130859	+	0.0130859i
$534$		0			0
$535$	81.6052	−	52.5250i	0.152533	−	0.0981777i
$536$	57.7216	−	99.9768i	0.107690	−	0.186524i
$537$		0			0
$538$	−510.829	+	510.829i	−0.949497	+	0.949497i
$539$	−397.376	+	55.1141i	−0.737247	+	0.102253i
$540$		0			0
$541$	−225.980	−	391.408i	−0.417708	−	0.723491i	0.578001	−	0.816036i	$-0.303833\pi$
$541$	−225.980	−	391.408i	−0.417708	−	0.723491i	−0.995708	+	0.0925455i	$0.970500\pi$
$542$	−883.819	+	236.819i	−1.63066	+	0.436935i
$543$		0			0
$544$	−348.778	+	201.367i	−0.641137	+	0.370160i
$545$	129.646	+	404.594i	0.237883	+	0.742375i
$546$		0			0
$547$	389.492	+	389.492i	0.712051	+	0.712051i	0.966964	−	0.254913i	$-0.0820469\pi$
$547$	389.492	+	389.492i	0.712051	+	0.712051i	−0.254913	+	0.966964i	$0.582047\pi$
$548$	1011.03	+	270.905i	1.84495	+	0.494353i
$549$		0			0
$550$	−480.143	+	583.177i	−0.872988	+	1.06032i
$551$	232.805	+	403.230i	0.422514	+	0.731815i
$552$		0			0
$553$	−48.1797	−	698.083i	−0.0871243	−	1.26236i
$554$		−	1007.17i		−	1.81799i
$555$		0			0
$556$	−908.083	+	1572.85i	−1.63324	+	2.82886i
$557$	950.780	−	254.761i	1.70697	−	0.457380i	0.732288	−	0.680995i	$-0.238453\pi$
$557$	950.780	−	254.761i	1.70697	−	0.457380i	0.974678	+	0.223615i	$0.0717859\pi$
$558$		0			0
$559$			940.555i			1.68257i
$560$	1045.92	+	825.563i	1.86772	+	1.47422i
$561$		0			0
$562$	−406.924	+	1518.66i	−0.724064	+	2.70224i
$563$	222.762	+	831.358i	0.395669	+	1.47666i	0.820637	+	0.571450i	$0.193619\pi$
$563$	222.762	+	831.358i	0.395669	+	1.47666i	−0.424968	+	0.905208i	$0.639715\pi$
$564$		0			0
$565$	666.508	−	32.2163i	1.17966	−	0.0570199i
$566$	407.037			0.719147
$567$		0			0
$568$	1540.22	−	1540.22i	2.71165	−	2.71165i
$569$	−343.723	+	198.449i	−0.604083	+	0.348768i	−0.770646	−	0.637263i	$-0.780066\pi$
$569$	−343.723	+	198.449i	−0.604083	+	0.348768i	0.166563	+	0.986031i	$0.446733\pi$
$570$		0			0
$571$	402.947	−	697.924i	0.705686	−	1.22228i	−0.260757	−	0.965404i	$-0.583972\pi$
$571$	402.947	−	697.924i	0.705686	−	1.22228i	0.966443	−	0.256880i	$-0.0826944\pi$
$572$	−405.263	+	1512.46i	−0.708502	+	2.64417i
$573$		0			0
$574$	−9.66658	−	8.41840i	−0.0168407	−	0.0146662i
$575$	133.913	−	803.212i	0.232893	−	1.39689i
$576$		0			0
$577$	−1000.77	+	268.157i	−1.73445	+	0.464743i	−0.981200	−	0.192996i	$-0.938180\pi$
$577$	−1000.77	+	268.157i	−1.73445	+	0.464743i	−0.753246	+	0.657739i	$0.771513\pi$
$578$	−229.246	−	855.559i	−0.396620	−	1.48021i
$579$		0			0
$580$	1012.95	−	324.584i	1.74646	−	0.559627i
$581$	307.402	+	895.394i	0.529092	+	1.54113i
$582$		0			0
$583$	−281.315	−	75.3782i	−0.482530	−	0.129294i
$584$	1518.71	+	876.826i	2.60053	+	1.50141i
$585$		0			0
$586$	−585.071	−	1013.37i	−0.998415	−	1.72930i
$587$	−541.901	−	541.901i	−0.923170	−	0.923170i	0.0740817	−	0.997252i	$-0.476397\pi$
$587$	−541.901	−	541.901i	−0.923170	−	0.923170i	−0.997252	+	0.0740817i	$0.976397\pi$
$588$		0			0
$589$		−	578.138i		−	0.981559i
$590$	331.902	−	16.0428i	0.562546	−	0.0271912i
$591$		0			0
$592$	−570.575	+	152.885i	−0.963810	+	0.258252i
$593$	−767.912	−	205.761i	−1.29496	−	0.346984i	−0.455419	−	0.890277i	$-0.650510\pi$
$593$	−767.912	−	205.761i	−1.29496	−	0.346984i	−0.839543	+	0.543293i	$0.817177\pi$
$594$		0			0
$595$	196.396	−	146.471i	0.330078	−	0.246170i
$596$	1135.43			1.90509
$597$		0			0
$598$	−618.499	−	2308.27i	−1.03428	−	3.85998i
$599$	−357.782	−	206.565i	−0.597299	−	0.344850i	0.170680	−	0.985327i	$-0.445404\pi$
$599$	−357.782	−	206.565i	−0.597299	−	0.344850i	−0.767978	+	0.640476i	$0.778737\pi$
$600$		0			0
$601$	−439.370			−0.731066			−0.365533	−	0.930798i	$-0.619113\pi$
$601$	−439.370			−0.731066			−0.365533	+	0.930798i	$0.619113\pi$
$602$	−1219.39	+	84.1588i	−2.02556	+	0.139799i
$603$		0			0
$604$	1488.02	−	859.107i	2.46360	−	1.42236i
$605$	−57.1738	+	263.710i	−0.0945021	+	0.435884i
$606$		0			0
$607$	56.8754	−	212.262i	0.0936991	−	0.349690i	−0.903120	−	0.429388i	$-0.858729\pi$
$607$	56.8754	−	212.262i	0.0936991	−	0.349690i	0.996819	+	0.0796986i	$0.0253958\pi$
$608$	−856.605	+	856.605i	−1.40889	+	1.40889i
$609$		0			0
$610$	−442.508	−	227.738i	−0.725422	−	0.373340i
$611$	−248.278	−	430.029i	−0.406346	−	0.703812i
$612$		0			0
$613$	253.466	+	945.946i	0.413484	+	1.54314i	0.787853	+	0.615863i	$0.211192\pi$
$613$	253.466	+	945.946i	0.413484	+	1.54314i	−0.374370	+	0.927280i	$0.622141\pi$
$614$	−1575.43	+	909.573i	−2.56584	+	1.48139i
$615$		0			0
$616$	−1166.75	−	227.889i	−1.89407	−	0.369949i
$617$	56.3252	+	56.3252i	0.0912887	+	0.0912887i	0.751276	−	0.659988i	$-0.229439\pi$
$617$	56.3252	+	56.3252i	0.0912887	+	0.0912887i	−0.659988	+	0.751276i	$0.729439\pi$
$618$		0			0
$619$	451.442	+	260.640i	0.729309	+	0.421067i	0.818169	−	0.574977i	$-0.194989\pi$
$619$	451.442	+	260.640i	0.729309	+	0.421067i	−0.0888604	+	0.996044i	$0.528323\pi$
$620$	−1290.76	−	279.844i	−2.08187	−	0.451361i
$621$		0			0
$622$	38.5359	+	38.5359i	0.0619548	+	0.0619548i
$623$	−30.2466	−	438.247i	−0.0485499	−	0.703446i
$624$		0			0
$625$	−613.373	+	119.996i	−0.981396	+	0.191994i
$626$	223.054	−	386.340i	0.356316	−	0.617157i
$627$		0			0
$628$	−551.336	−	147.730i	−0.877924	−	0.235239i
$629$			108.611i			0.172673i
$630$		0			0
$631$	606.021			0.960413			0.480207	−	0.877155i	$-0.340562\pi$
$631$	606.021			0.960413			0.480207	+	0.877155i	$0.340562\pi$
$632$	536.663	−	2002.85i	0.849151	−	3.16907i
$633$		0			0
$634$	−993.601	−	573.656i	−1.56719	−	0.904819i
$635$	−50.0242	−	1034.93i	−0.0787783	−	1.62981i
$636$		0			0
$637$	−966.614	−	120.462i	−1.51745	−	0.189108i
$638$	−472.466	+	472.466i	−0.740542	+	0.740542i
$639$		0			0
$640$	−23.0582	−	35.8242i	−0.0360284	−	0.0559753i
$641$	−552.914	+	957.675i	−0.862580	+	1.49403i	0.00685032	+	0.999977i	$0.497819\pi$
$641$	−552.914	+	957.675i	−0.862580	+	1.49403i	−0.869430	+	0.494056i	$0.835514\pi$
$642$		0			0
$643$	495.423	−	495.423i	0.770487	−	0.770487i	−0.207704	−	0.978192i	$-0.566599\pi$
$643$	495.423	−	495.423i	0.770487	−	0.770487i	0.978192	+	0.207704i	$0.0665992\pi$
$644$	2074.63	−	712.253i	3.22148	−	1.10598i
$645$		0			0
$646$	271.982	+	471.087i	0.421025	+	0.729237i
$647$	747.117	−	200.190i	1.15474	−	0.309412i	0.369877	−	0.929081i	$-0.379400\pi$
$647$	747.117	−	200.190i	1.15474	−	0.309412i	0.784864	+	0.619669i	$0.212733\pi$
$648$		0			0
$649$	−127.681	+	73.7165i	−0.196735	+	0.113585i
$650$	−1492.58	+	1066.01i	−2.29628	+	1.64001i
$651$		0			0
$652$	855.612	+	855.612i	1.31229	+	1.31229i
$653$	−1045.38	−	280.108i	−1.60089	−	0.428956i	−0.655576	−	0.755129i	$-0.727574\pi$
$653$	−1045.38	−	280.108i	−1.60089	−	0.428956i	−0.945310	+	0.326172i	$0.894241\pi$
$654$		0			0
$655$	−121.774	+	561.674i	−0.185914	+	0.857517i
$656$	−9.44507	−	16.3593i	−0.0143980	−	0.0249380i
$657$		0			0
$658$	535.299	−	360.359i	0.813524	−	0.547658i
$659$			388.022i			0.588805i	0.955682	+	0.294402i	$0.0951206\pi$
$659$			388.022i			0.588805i	−0.955682	+	0.294402i	$0.904879\pi$
$660$		0			0
$661$	−309.552	+	536.160i	−0.468308	+	0.811134i	−0.999344	−	0.0362155i	$-0.988470\pi$
$661$	−309.552	+	536.160i	−0.468308	+	0.811134i	0.531036	+	0.847350i	$0.321803\pi$
$662$	−460.526	+	123.398i	−0.695658	+	0.186401i
$663$		0			0
$664$			2805.28i			4.22481i
$665$	456.597	−	578.472i	0.686612	−	0.869882i
$666$		0			0
$667$	186.417	−	695.719i	0.279486	−	1.04306i
$668$	−106.690	−	398.172i	−0.159715	−	0.596066i
$669$		0			0
$670$	−69.0289	+	76.0410i	−0.103028	+	0.113494i
$671$	220.811			0.329078
$672$		0			0
$673$	185.772	−	185.772i	0.276036	−	0.276036i	−0.555488	−	0.831524i	$-0.687469\pi$
$673$	185.772	−	185.772i	0.276036	−	0.276036i	0.831524	+	0.555488i	$0.187469\pi$
$674$	230.678	−	133.182i	0.342253	−	0.197600i
$675$		0			0
$676$	−1088.03	+	1884.52i	−1.60951	+	2.78775i
$677$	−191.084	+	713.136i	−0.282252	+	1.05338i	0.668573	+	0.743647i	$0.266906\pi$
$677$	−191.084	+	713.136i	−0.282252	+	1.05338i	−0.950824	+	0.309731i	$0.899761\pi$
$678$		0			0
$679$	552.569	−	189.705i	0.813798	−	0.279389i
$680$	691.368	−	221.539i	1.01672	−	0.325792i
$681$		0			0
$682$	801.379	−	214.729i	1.17504	−	0.314852i
$683$	135.236	+	504.707i	0.198003	+	0.738957i	0.991469	+	0.130342i	$0.0416077\pi$
$683$	135.236	+	504.707i	0.198003	+	0.738957i	−0.793466	+	0.608614i	$0.791726\pi$
$684$		0			0
$685$	−483.698	−	248.936i	−0.706129	−	0.363411i
$686$	69.6833	−	1263.95i	0.101579	−	1.84250i
$687$		0			0
$688$	−1739.88	−	466.198i	−2.52889	−	0.677614i
$689$	−612.407	−	353.574i	−0.888835	−	0.513169i
$690$		0			0
$691$	−301.546	−	522.293i	−0.436391	−	0.755851i	0.561017	−	0.827804i	$-0.310410\pi$
$691$	−301.546	−	522.293i	−0.436391	−	0.755851i	−0.997408	+	0.0719534i	$0.977077\pi$
$692$	245.057	+	245.057i	0.354128	+	0.354128i
$693$		0			0
$694$			2238.82i			3.22596i
$695$	634.443	−	698.891i	0.912868	−	1.00560i
$696$		0			0
$697$	−3.35494	+	0.898953i	−0.00481340	+	0.00128975i
$698$	293.023	+	78.5153i	0.419804	+	0.112486i
$699$		0			0
$700$	−1070.49	−	1299.41i	−1.52928	−	1.85630i
$701$	−100.279			−0.143052			−0.0715259	−	0.997439i	$-0.522787\pi$
$701$	−100.279			−0.143052			−0.0715259	+	0.997439i	$0.522787\pi$
$702$		0			0
$703$	84.5567	+	315.570i	0.120280	+	0.448890i
$704$	−425.768	−	245.817i	−0.604784	−	0.349172i
$705$		0			0
$706$	541.899			0.767562
$707$	151.389	+	224.882i	0.214128	+	0.318079i
$708$		0			0
$709$	339.531	−	196.029i	0.478888	−	0.276486i	−0.241065	−	0.970509i	$-0.577497\pi$
$709$	339.531	−	196.029i	0.478888	−	0.276486i	0.719953	+	0.694023i	$0.244163\pi$
$710$	−1629.41	+	1048.76i	−2.29494	+	1.47713i
$711$		0			0
$712$	336.910	−	1257.36i	0.473188	−	1.76596i
$713$	−632.389	+	632.389i	−0.886941	+	0.886941i
$714$		0			0
$715$	372.399	−	723.593i	0.520837	−	1.01202i
$716$	−363.687	−	629.924i	−0.507942	−	0.879782i
$717$		0			0
$718$	193.088	+	720.614i	0.268925	+	1.00364i
$719$	−1001.31	+	578.104i	−1.39264	+	0.804039i	−0.993607	−	0.112898i	$-0.963987\pi$
$719$	−1001.31	+	578.104i	−1.39264	+	0.804039i	−0.399031	+	0.916938i	$0.630653\pi$
$720$		0			0
$721$	142.413	−	163.528i	0.197521	−	0.226807i
$722$	214.918	+	214.918i	0.297670	+	0.297670i
$723$		0			0
$724$	1519.83	+	877.472i	2.09921	+	1.21198i
$725$	−550.246	+	53.3179i	−0.758961	+	0.0735419i
$726$		0			0
$727$	−27.8958	−	27.8958i	−0.0383712	−	0.0383712i	0.687661	−	0.726032i	$-0.258638\pi$
$727$	−27.8958	−	27.8958i	−0.0383712	−	0.0383712i	−0.726032	+	0.687661i	$0.758638\pi$
$728$	−2593.19	−	1267.69i	−3.56208	−	1.74133i
$729$		0			0
$730$	−1155.11	−	1048.59i	−1.58234	−	1.43643i
$731$	−165.596	+	286.821i	−0.226534	+	0.392368i
$732$		0			0
$733$	780.690	+	209.185i	1.06506	+	0.285382i	0.748463	−	0.663177i	$-0.230792\pi$
$733$	780.690	+	209.185i	1.06506	+	0.285382i	0.316599	+	0.948559i	$0.397459\pi$
$734$			1857.40i			2.53052i
$735$		0			0
$736$	1873.97			2.54616
$737$	11.7935	−	44.0140i	0.0160021	−	0.0597205i
$738$		0			0
$739$	−452.698	−	261.365i	−0.612582	−	0.353674i	0.161393	−	0.986890i	$-0.448401\pi$
$739$	−452.698	−	261.365i	−0.612582	−	0.353674i	−0.773975	+	0.633216i	$0.781735\pi$
$740$	745.475	−	36.0332i	1.00740	−	0.0486935i
$741$		0			0
$742$	403.596	−	825.597i	0.543930	−	1.11266i
$743$	34.1788	−	34.1788i	0.0460011	−	0.0460011i	−0.683732	−	0.729733i	$-0.739644\pi$
$743$	34.1788	−	34.1788i	0.0460011	−	0.0460011i	0.729733	+	0.683732i	$0.239644\pi$
$744$		0			0
$745$	−576.717	−	125.035i	−0.774116	−	0.167833i
$746$	−341.134	+	590.862i	−0.457284	+	0.792040i
$747$		0			0
$748$	−389.872	+	389.872i	−0.521219	+	0.521219i
$749$	−102.459	−	89.2296i	−0.136795	−	0.119132i
$750$		0			0
$751$	352.812	+	611.088i	0.469790	+	0.813700i	0.999403	−	0.0345394i	$-0.0109964\pi$
$751$	352.812	+	611.088i	0.469790	+	0.813700i	−0.529614	+	0.848239i	$0.677663\pi$
$752$	918.547	−	246.124i	1.22147	−	0.327292i
$753$		0			0
$754$	−1405.00	+	811.177i	−1.86339	+	1.07583i
$755$	−850.410	+	272.501i	−1.12637	+	0.360929i
$756$		0			0
$757$	395.694	+	395.694i	0.522713	+	0.522713i	0.918390	−	0.395677i	$-0.129490\pi$
$757$	395.694	+	395.694i	0.522713	+	0.522713i	−0.395677	+	0.918390i	$0.629490\pi$
$758$	1242.04	+	332.803i	1.63857	+	0.439054i
$759$		0			0
$760$	1836.30	−	1181.93i	2.41618	−	1.55517i
$761$	692.529	+	1199.50i	0.910025	+	1.57621i	0.814026	+	0.580828i	$0.197271\pi$
$761$	692.529	+	1199.50i	0.910025	+	1.57621i	0.0959984	+	0.995381i	$0.469396\pi$
$762$		0			0
$763$	493.414	−	332.162i	0.646676	−	0.435337i
$764$		−	147.442i		−	0.192987i
$765$		0			0
$766$	834.315	−	1445.08i	1.08918	−	1.88652i
$767$	−345.779	+	92.6512i	−0.450820	+	0.120797i
$768$		0			0
$769$		−	907.238i		−	1.17976i	−0.807490	−	0.589882i	$-0.799174\pi$
$769$		−	907.238i		−	1.17976i	0.807490	−	0.589882i	$-0.200826\pi$
$770$	971.428	+	418.053i	1.26160	+	0.542926i
$771$		0			0
$772$	560.463	−	2091.68i	0.725988	−	2.70942i
$773$	−161.404	−	602.366i	−0.208802	−	0.779258i	−0.988257	−	0.152800i	$-0.951171\pi$
$773$	−161.404	−	602.366i	−0.208802	−	0.779258i	0.779456	−	0.626458i	$-0.215496\pi$
$774$		0			0
$775$	624.796	+	284.281i	0.806188	+	0.366814i
$776$	1731.20			2.23093
$777$		0			0
$778$	−1704.49	+	1704.49i	−2.19086	+	2.19086i
$779$	−9.04791	+	5.22381i	−0.0116148	+	0.00670579i
$780$		0			0
$781$	429.878	−	744.570i	0.550420	−	0.953355i
$782$	217.788	−	812.797i	0.278502	−	1.03938i
$783$		0			0
$784$	701.950	−	1728.37i	0.895344	−	2.20455i
$785$	263.770	+	135.750i	0.336013	+	0.172930i
$786$		0			0
$787$	−647.269	+	173.435i	−0.822451	+	0.220375i	−0.645418	−	0.763830i	$-0.723317\pi$
$787$	−647.269	+	173.435i	−0.822451	+	0.220375i	−0.177033	+	0.984205i	$0.556650\pi$
$788$	919.738	+	3432.51i	1.16718	+	4.35598i
$789$		0			0
$790$	−844.107	+	1640.15i	−1.06849	+	2.07614i
$791$	−303.346	−	883.579i	−0.383497	−	1.11704i
$792$		0			0
$793$	517.875	+	138.764i	0.653058	+	0.174986i
$794$	210.840	+	121.729i	0.265542	+	0.153311i
$795$		0			0
$796$	317.165	+	549.346i	0.398448	+	0.690133i
$797$	−499.339	−	499.339i	−0.626524	−	0.626524i	0.320668	−	0.947192i	$-0.396093\pi$
$797$	−499.339	−	499.339i	−0.626524	−	0.626524i	−0.947192	+	0.320668i	$0.896093\pi$
$798$		0			0
$799$		−	174.849i		−	0.218835i
$800$	−504.528	−	1346.94i	−0.630660	−	1.68368i
$801$		0			0
$802$	389.768	−	104.438i	0.485995	−	0.130222i
$803$	668.599	+	179.151i	0.832626	+	0.223102i
$804$		0			0
$805$	−1132.20	+	133.311i	−1.40646	+	0.165604i
$806$	2014.44			2.49931
$807$		0			0
$808$	207.911	+	775.935i	0.257316	+	0.960315i
$809$	−1117.27	−	645.054i	−1.38105	−	0.797347i	−0.388763	−	0.921338i	$-0.627097\pi$
$809$	−1117.27	−	645.054i	−1.38105	−	0.797347i	−0.992283	+	0.123990i	$0.960431\pi$
$810$		0			0
$811$	−1511.76			−1.86407			−0.932036	−	0.362364i	$-0.881970\pi$
$811$	−1511.76			−1.86407			−0.932036	+	0.362364i	$0.881970\pi$
$812$	−831.605	−	1235.32i	−1.02414	−	1.52133i
$813$		0			0
$814$	−406.018	+	234.414i	−0.498793	+	0.287978i
$815$	−340.367	−	528.809i	−0.417629	−	0.648846i
$816$		0			0
$817$	−257.842	+	962.278i	−0.315596	+	1.17782i
$818$	766.982	−	766.982i	0.937631	−	0.937631i
$819$		0			0
$820$	7.28319	+	22.7291i	0.00888194	+	0.0277184i
$821$	480.446	+	832.156i	0.585196	+	1.01359i	0.994851	+	0.101348i	$0.0323156\pi$
$821$	480.446	+	832.156i	0.585196	+	1.01359i	−0.409656	+	0.912240i	$0.634351\pi$
$822$		0			0
$823$	−6.71404	−	25.0572i	−0.00815801	−	0.0304461i	0.961727	−	0.274010i	$-0.0883501\pi$
$823$	−6.71404	−	25.0572i	−0.00815801	−	0.0304461i	−0.969885	+	0.243564i	$0.921683\pi$
$824$	556.483	−	321.286i	0.675343	−	0.389910i
$825$		0			0
$826$	−151.058	−	439.997i	−0.182879	−	0.532684i
$827$	−471.697	−	471.697i	−0.570371	−	0.570371i	0.361861	−	0.932232i	$-0.382141\pi$
$827$	−471.697	−	471.697i	−0.570371	−	0.570371i	−0.932232	+	0.361861i	$0.882141\pi$
$828$		0			0
$829$	33.2384	+	19.1902i	0.0400945	+	0.0231486i	0.519913	−	0.854219i	$-0.325964\pi$
$829$	33.2384	+	19.1902i	0.0400945	+	0.0231486i	−0.479819	+	0.877368i	$0.659298\pi$
$830$	528.776	−	2438.94i	0.637080	−	2.93849i
$831$		0			0
$832$	−844.088	−	844.088i	−1.01453	−	1.01453i
$833$	−273.559	−	206.919i	−0.328402	−	0.248402i
$834$		0			0
$835$	10.3434	+	213.991i	0.0123874	+	0.256277i
$836$	−829.246	+	1436.30i	−0.991922	+	1.71806i
$837$		0			0
$838$	−837.002	−	224.274i	−0.998809	−	0.267630i
$839$		−	641.866i		−	0.765037i	−0.923948	−	0.382519i	$-0.875057\pi$
$839$		−	641.866i		−	0.765037i	0.923948	−	0.382519i	$-0.124943\pi$
$840$		0			0
$841$	352.018			0.418570
$842$	118.728	−	443.097i	0.141007	−	0.526244i
$843$		0			0
$844$	−3405.65	−	1966.25i	−4.03513	−	2.32968i
$845$	760.164	−	837.383i	0.899602	−	0.990985i
$846$		0			0
$847$	376.875	−	26.0109i	0.444953	−	0.0307094i
$848$	957.602	−	957.602i	1.12925	−	1.12925i
$849$		0			0
$850$	−642.844	+	62.2903i	−0.756286	+	0.0732828i
$851$	252.691	−	437.673i	0.296934	−	0.514304i
$852$		0			0
$853$	873.730	−	873.730i	1.02430	−	1.02430i	0.0246050	−	0.999697i	$-0.492167\pi$
$853$	873.730	−	873.730i	1.02430	−	1.02430i	0.999697	−	0.0246050i	$-0.00783282\pi$
$854$	−133.563	+	683.819i	−0.156398	+	0.800725i
$855$		0			0
$856$	−201.303	−	348.668i	−0.235167	−	0.407322i
$857$	−218.566	+	58.5645i	−0.255036	+	0.0683367i	−0.384072	−	0.923303i	$-0.625478\pi$
$857$	−218.566	+	58.5645i	−0.255036	+	0.0683367i	0.129036	+	0.991640i	$0.458812\pi$
$858$		0			0
$859$	−54.8471	+	31.6660i	−0.0638499	+	0.0368638i	−0.531585	−	0.847005i	$-0.678403\pi$
$859$	−54.8471	+	31.6660i	−0.0638499	+	0.0368638i	0.467735	+	0.883869i	$0.345070\pi$
$860$	2023.59	+	1041.45i	2.35301	+	1.21098i
$861$		0			0
$862$	−549.575	−	549.575i	−0.637558	−	0.637558i
$863$	−705.658	−	189.081i	−0.817680	−	0.219097i	−0.174348	−	0.984684i	$-0.555782\pi$
$863$	−705.658	−	189.081i	−0.817680	−	0.219097i	−0.643332	+	0.765587i	$0.722449\pi$
$864$		0			0
$865$	−97.4850	−	151.457i	−0.112699	−	0.175095i
$866$	−1432.98	−	2481.99i	−1.65471	−	2.86604i
$867$		0			0
$868$	127.313	+	1844.66i	0.146674	+	2.12518i
$869$		−	818.435i		−	0.941812i
$870$		0			0
$871$	55.3194	−	95.8160i	0.0635125	−	0.110007i
$872$	1702.48	−	456.179i	1.95239	−	0.523141i
$873$		0			0
$874$		−	2531.13i		−	2.89603i
$875$	400.640	+	777.890i	0.457874	+	0.889017i
$876$		0			0
$877$	136.821	−	510.621i	0.156010	−	0.582236i	−0.843007	−	0.537903i	$-0.819217\pi$
$877$	136.821	−	510.621i	0.156010	−	0.582236i	0.999017	−	0.0443338i	$-0.0141165\pi$
$878$	91.6092	+	341.890i	0.104338	+	0.389396i
$879$		0			0
$880$	1153.95	+	1047.54i	1.31130	+	1.19038i
$881$	−956.484			−1.08568			−0.542840	−	0.839836i	$-0.682651\pi$
$881$	−956.484			−1.08568			−0.542840	+	0.839836i	$0.682651\pi$
$882$		0			0
$883$	883.412	−	883.412i	1.00047	−	1.00047i	0.000466858	−	1.00000i	$-0.499851\pi$
$883$	883.412	−	883.412i	1.00047	−	1.00047i	1.00000		0.000466858i	$-0.000148605\pi$
$884$	−1159.39	+	669.371i	−1.31152	+	0.757207i
$885$		0			0
$886$	−184.664	+	319.848i	−0.208425	+	0.361003i
$887$	5.96195	−	22.2503i	0.00672148	−	0.0250849i	−0.962484	−	0.271340i	$-0.912533\pi$
$887$	5.96195	−	22.2503i	0.00672148	−	0.0250849i	0.969205	+	0.246255i	$0.0792000\pi$
$888$		0			0
$889$	−1371.99	+	471.025i	−1.54330	+	0.529837i
$890$	−529.919	+	1029.66i	−0.595415	+	1.15693i
$891$		0			0
$892$	2367.13	−	634.270i	2.65373	−	0.711065i
$893$	−136.124	−	508.023i	−0.152435	−	0.568895i
$894$		0			0
$895$	115.358	+	360.005i	0.128892	+	0.402240i
$896$	−39.1713	+	44.9791i	−0.0437179	+	0.0501999i
$897$		0			0
$898$	1227.40	+	328.881i	1.36681	+	0.366237i
$899$	525.815	+	303.579i	0.584889	+	0.337686i
$900$		0			0
$901$	−124.502	−	215.643i	−0.138182	−	0.239338i
$902$	−10.6014	−	10.6014i	−0.0117533	−	0.0117533i
$903$		0			0
$904$		−	2768.26i		−	3.06224i
$905$	−675.333	−	613.057i	−0.746224	−	0.677411i
$906$		0			0
$907$	−783.082	+	209.826i	−0.863376	+	0.231341i	−0.663221	−	0.748424i	$-0.730811\pi$
$907$	−783.082	+	209.826i	−0.863376	+	0.231341i	−0.200155	+	0.979764i	$0.564144\pi$
$908$	2039.43	+	546.463i	2.24607	+	0.601832i
$909$		0			0
$910$	2015.60	+	1590.95i	2.21495	+	1.74829i
$911$	302.928			0.332523			0.166261	−	0.986082i	$-0.446830\pi$
$911$	302.928			0.332523			0.166261	+	0.986082i	$0.446830\pi$
$912$		0			0
$913$	286.583	+	1069.54i	0.313891	+	1.17146i
$914$	−275.520	−	159.072i	−0.301445	−	0.174039i
$915$		0			0
$916$	3243.84			3.54131
$917$	802.703	−	55.4003i	0.875357	−	0.0604147i
$918$		0			0
$919$	−838.092	+	483.873i	−0.911961	+	0.526521i	−0.881061	−	0.473002i	$-0.843170\pi$
$919$	−838.092	+	483.873i	−0.911961	+	0.526521i	−0.0308992	+	0.999523i	$0.509837\pi$
$920$	−3301.45	−	715.771i	−3.58853	−	0.778012i
$921$		0			0
$922$	−590.877	+	2205.18i	−0.640864	+	2.39174i
$923$	1476.12	−	1476.12i	1.59926	−	1.59926i
$924$		0			0
$925$	−382.615	−	63.7905i	−0.413638	−	0.0689627i
$926$	296.762	+	514.006i	0.320477	+	0.555082i
$927$		0			0
$928$	−329.278	−	1228.88i	−0.354825	−	1.32423i
$929$	985.363	−	568.900i	1.06067	−	0.612379i	0.135053	−	0.990838i	$-0.456879\pi$
$929$	985.363	−	568.900i	1.06067	−	0.612379i	0.925618	+	0.378460i	$0.123546\pi$
$930$		0			0
$931$	−955.915	−	388.229i	−1.02676	−	0.417003i
$932$	2001.03	+	2001.03i	2.14703	+	2.14703i
$933$		0			0
$934$	−161.150	−	93.0402i	−0.172538	−	0.0996148i
$935$	240.960	−	155.093i	0.257711	−	0.165875i
$936$		0			0
$937$	695.689	+	695.689i	0.742465	+	0.742465i	0.973052	−	0.230587i	$-0.0740646\pi$
$937$	695.689	+	695.689i	0.742465	+	0.742465i	−0.230587	+	0.973052i	$0.574065\pi$
$938$	129.171	+	63.1458i	0.137709	+	0.0673196i
$939$		0			0
$940$	−1200.11	+	58.0084i	−1.27671	+	0.0617111i
$941$	−175.936	+	304.730i	−0.186967	+	0.323836i	−0.944238	−	0.329265i	$-0.893199\pi$
$941$	−175.936	+	304.730i	−0.186967	+	0.323836i	0.757271	+	0.653101i	$0.226532\pi$
$942$		0			0
$943$	15.6109	+	4.18294i	0.0165545	+	0.00443578i
$944$		−	685.559i		−	0.726228i
$945$		0			0
$946$	−1429.62			−1.51122
$947$	−411.444	+	1535.53i	−0.434471	+	1.62147i	0.307859	+	0.951432i	$0.400387\pi$
$947$	−411.444	+	1535.53i	−0.434471	+	1.62147i	−0.742330	+	0.670034i	$0.766279\pi$
$948$		0			0
$949$	1455.50	+	840.334i	1.53372	+	0.885495i
$950$	−1819.29	+	681.455i	−1.91504	+	0.717321i
$951$		0			0
$952$	−567.597	−	843.143i	−0.596216	−	0.885654i
$953$	808.505	−	808.505i	0.848379	−	0.848379i	−0.141552	−	0.989931i	$-0.545209\pi$
$953$	808.505	−	808.505i	0.848379	−	0.848379i	0.989931	+	0.141552i	$0.0452093\pi$
$954$		0			0
$955$	−16.2365	+	74.8899i	−0.0170016	+	0.0784187i
$956$	−921.939	+	1596.85i	−0.964372	+	1.67034i
$957$		0			0
$958$	458.653	−	458.653i	0.478761	−	0.478761i
$959$	−145.996	+	747.472i	−0.152238	+	0.779428i
$960$		0			0
$961$	103.552	+	179.357i	0.107755	+	0.186636i
$962$	−1099.56	+	294.626i	−1.14299	+	0.306264i
$963$		0			0
$964$	1025.98	−	592.349i	1.06429	−	0.614470i
$965$	−515.012	+	1000.70i	−0.533691	+	1.03699i
$966$		0			0
$967$	−412.298	−	412.298i	−0.426369	−	0.426369i	0.461021	−	0.887389i	$-0.347483\pi$
$967$	−412.298	−	412.298i	−0.426369	−	0.426369i	−0.887389	+	0.461021i	$0.847483\pi$
$968$	1081.28	+	289.729i	1.11703	+	0.299307i
$969$		0			0
$970$	−1505.13	−	326.321i	−1.55168	−	0.336413i
$971$	281.316	+	487.254i	0.289718	+	0.501806i	0.973742	−	0.227653i	$-0.0731052\pi$
$971$	281.316	+	487.254i	0.289718	+	0.501806i	−0.684024	+	0.729459i	$0.739772\pi$
$972$		0			0
$973$	−1187.21	−	580.371i	−1.22015	−	0.596476i
$974$		−	937.436i		−	0.962460i
$975$		0			0
$976$	−513.383	+	889.205i	−0.526007	+	0.911071i
$977$	1661.12	−	445.096i	1.70023	−	0.455575i	0.727231	−	0.686393i	$-0.240807\pi$
$977$	1661.12	−	445.096i	1.70023	−	0.455575i	0.972997	+	0.230818i	$0.0741403\pi$
$978$		0			0
$979$		−	513.802i		−	0.524823i
$980$	−1329.47	+	1946.27i	−1.35660	+	1.98599i
$981$		0			0
$982$	263.439	−	983.168i	0.268268	−	1.00119i
$983$	91.6612	+	342.084i	0.0932463	+	0.348000i	0.996748	−	0.0805851i	$-0.0256789\pi$
$983$	91.6612	+	342.084i	0.0932463	+	0.348000i	−0.903501	+	0.428585i	$0.859012\pi$
$984$		0			0
$985$	−89.1674	−	1844.75i	−0.0905253	−	1.87284i
$986$	−571.270			−0.579381
$987$		0			0
$988$	−2847.47	+	2847.47i	−2.88205	+	2.88205i
$989$	1334.61	−	770.539i	1.34946	−	0.779109i
$990$		0			0
$991$	−433.964	+	751.647i	−0.437905	+	0.758473i	−0.997528	−	0.0702740i	$-0.977613\pi$
$991$	−433.964	+	751.647i	−0.437905	+	0.758473i	0.559623	+	0.828747i	$0.310946\pi$
$992$	−408.857	+	1525.88i	−0.412154	+	1.53818i
$993$		0			0
$994$	2045.80	+	1781.64i	2.05815	+	1.79239i
$995$	−100.602	−	313.954i	−0.101107	−	0.315532i
$996$		0			0
$997$	1418.75	−	380.153i	1.42302	−	0.381297i	0.536466	−	0.843922i	$-0.319759\pi$
$997$	1418.75	−	380.153i	1.42302	−	0.381297i	0.886554	+	0.462625i	$0.153092\pi$
$998$	−573.959	−	2142.04i	−0.575109	−	2.14634i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.3.ca.b.172.1		64
3.2	odd	2		105.3.v.a.67.16	yes	64
5.3	odd	4	inner	315.3.ca.b.298.16		64
7.2	even	3	inner	315.3.ca.b.37.16		64
15.8	even	4		105.3.v.a.88.1	yes	64
21.2	odd	6		105.3.v.a.37.1	✓	64
35.23	odd	12	inner	315.3.ca.b.163.1		64
105.23	even	12		105.3.v.a.58.16	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.v.a.37.1	✓	64	21.2	odd	6
105.3.v.a.58.16	yes	64	105.23	even	12
105.3.v.a.67.16	yes	64	3.2	odd	2
105.3.v.a.88.1	yes	64	15.8	even	4
315.3.ca.b.37.16		64	7.2	even	3	inner
315.3.ca.b.163.1		64	35.23	odd	12	inner
315.3.ca.b.172.1		64	1.1	even	1	trivial
315.3.ca.b.298.16		64	5.3	odd	4	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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	315.ca (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.955194 + 3.56483i) q^{2} +(-8.33154 - 4.81021i) q^{4} +(3.70210 + 3.36072i) q^{5} +(3.07429 - 6.28878i) q^{7} +(14.6673 - 14.6673i) q^{8} +O(q^{10})\)	\(q+(-0.955194 + 3.56483i) q^{2} +(-8.33154 - 4.81021i) q^{4} +(3.70210 + 3.36072i) q^{5} +(3.07429 - 6.28878i) q^{7} +(14.6673 - 14.6673i) q^{8} +(-15.5166 + 9.98725i) q^{10} +(4.09367 - 7.09045i) q^{11} +(14.0569 - 14.0569i) q^{13} +(19.4819 + 16.9663i) q^{14} +(19.0355 + 32.9704i) q^{16} +(6.76150 - 1.81174i) q^{17} +(18.2350 - 10.5280i) q^{19} +(-14.6784 - 45.8079i) q^{20} +(21.3660 + 21.3660i) q^{22} +(-31.4621 - 8.43024i) q^{23} +(2.41116 + 24.8835i) q^{25} +(36.6833 + 63.5374i) q^{26} +(-55.8639 + 37.6072i) q^{28} +22.1129i q^{29} +(13.7286 - 23.7786i) q^{31} +(-55.5730 + 14.8907i) q^{32} +25.8342i q^{34} +(32.5162 - 12.9499i) q^{35} +(-4.01580 + 14.9872i) q^{37} +(20.1126 + 75.0611i) q^{38} +(103.592 - 5.00723i) q^{40} -0.496183 q^{41} +(-33.4554 + 33.4554i) q^{43} +(-68.2132 + 39.3829i) q^{44} +(60.1048 - 104.105i) q^{46} +(6.46488 - 24.1272i) q^{47} +(-30.0975 - 38.6671i) q^{49} +(-91.0085 - 15.1731i) q^{50} +(-184.732 + 49.4987i) q^{52} +(-9.20667 - 34.3598i) q^{53} +(38.9842 - 12.4919i) q^{55} +(-47.1478 - 137.331i) q^{56} +(-78.8289 - 21.1222i) q^{58} +(-15.5949 - 9.00371i) q^{59} +(13.4849 + 23.3565i) q^{61} +(71.6533 + 71.6533i) q^{62} -60.0481i q^{64} +(99.2811 - 4.79884i) q^{65} +(5.37586 - 1.44046i) q^{67} +(-65.0485 - 17.4297i) q^{68} +(15.1050 + 128.284i) q^{70} +105.010 q^{71} +(21.8814 + 81.6625i) q^{73} +(-49.5909 - 28.6313i) q^{74} -202.568 q^{76} +(-32.0051 - 47.5423i) q^{77} +(86.5708 - 49.9817i) q^{79} +(-40.3329 + 186.033i) q^{80} +(0.473951 - 1.76881i) q^{82} +(-95.6303 + 95.6303i) q^{83} +(31.1205 + 16.0162i) q^{85} +(-87.3064 - 151.219i) q^{86} +(-43.9546 - 164.041i) q^{88} +(54.3480 - 31.3778i) q^{89} +(-45.1856 - 131.615i) q^{91} +(221.576 + 221.576i) q^{92} +(79.8344 + 46.0924i) q^{94} +(102.890 + 22.3070i) q^{95} +(59.0158 + 59.0158i) q^{97} +(166.591 - 70.3578i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8}+O(q^{10}) \) 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8	\( 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8} - 16 q^{10} - 16 q^{11} + 80 q^{16} - 56 q^{17} - 96 q^{22} - 72 q^{23} - 4 q^{25} + 288 q^{26} - 380 q^{28} - 136 q^{31} + 48 q^{32} - 76 q^{35} - 28 q^{37} + 68 q^{38} + 164 q^{40} - 128 q^{41} + 344 q^{43} + 240 q^{46} - 412 q^{47} + 72 q^{50} + 388 q^{52} + 40 q^{53} - 8 q^{55} + 864 q^{56} + 56 q^{58} - 216 q^{61} + 912 q^{62} - 20 q^{65} - 368 q^{67} + 492 q^{68} + 416 q^{70} - 784 q^{71} - 316 q^{73} - 32 q^{76} - 844 q^{77} - 908 q^{80} + 556 q^{82} - 1408 q^{83} - 536 q^{85} - 1024 q^{86} + 372 q^{88} - 1064 q^{91} + 1704 q^{92} - 260 q^{95} + 352 q^{97} - 272 q^{98}+O(q^{100}) \) 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8 - 16 * q^10 - 16 * q^11 + 80 * q^16 - 56 * q^17 - 96 * q^22 - 72 * q^23 - 4 * q^25 + 288 * q^26 - 380 * q^28 - 136 * q^31 + 48 * q^32 - 76 * q^35 - 28 * q^37 + 68 * q^38 + 164 * q^40 - 128 * q^41 + 344 * q^43 + 240 * q^46 - 412 * q^47 + 72 * q^50 + 388 * q^52 + 40 * q^53 - 8 * q^55 + 864 * q^56 + 56 * q^58 - 216 * q^61 + 912 * q^62 - 20 * q^65 - 368 * q^67 + 492 * q^68 + 416 * q^70 - 784 * q^71 - 316 * q^73 - 32 * q^76 - 844 * q^77 - 908 * q^80 + 556 * q^82 - 1408 * q^83 - 536 * q^85 - 1024 * q^86 + 372 * q^88 - 1064 * q^91 + 1704 * q^92 - 260 * q^95 + 352 * q^97 - 272 * q^98

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