LMFDB - Embedded newform 315.3.ca.b.37.16

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			37.16
Character	$\chi$	$=$	315.37
Dual form			315.3.ca.b.298.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.56483 - 0.955194i) q^{2} +(8.33154 - 4.81021i) q^{4} +(1.05941 - 4.88648i) q^{5} +(-6.28878 + 3.07429i) q^{7} +(14.6673 - 14.6673i) q^{8} +O(q^{10})$	\(q+(3.56483 - 0.955194i) q^{2} +(8.33154 - 4.81021i) q^{4} +(1.05941 - 4.88648i) q^{5} +(-6.28878 + 3.07429i) q^{7} +(14.6673 - 14.6673i) q^{8} +(-0.890898 - 18.4314i) q^{10} +(4.09367 + 7.09045i) q^{11} +(14.0569 - 14.0569i) q^{13} +(-19.4819 + 16.9663i) q^{14} +(19.0355 - 32.9704i) q^{16} +(-1.81174 + 6.76150i) q^{17} +(-18.2350 - 10.5280i) q^{19} +(-14.6784 - 45.8079i) q^{20} +(21.3660 + 21.3660i) q^{22} +(8.43024 + 31.4621i) q^{23} +(-22.7553 - 10.3536i) q^{25} +(36.6833 - 63.5374i) q^{26} +(-37.6072 + 55.8639i) q^{28} +22.1129i q^{29} +(13.7286 + 23.7786i) q^{31} +(14.8907 - 55.5730i) q^{32} +25.8342i q^{34} +(8.36003 + 33.9869i) q^{35} +(14.9872 - 4.01580i) q^{37} +(-75.0611 - 20.1126i) q^{38} +(-56.1326 - 87.2101i) q^{40} -0.496183 q^{41} +(-33.4554 + 33.4554i) q^{43} +(68.2132 + 39.3829i) q^{44} +(60.1048 + 104.105i) q^{46} +(-24.1272 + 6.46488i) q^{47} +(30.0975 - 38.6671i) q^{49} +(-91.0085 - 15.1731i) q^{50} +(49.4987 - 184.732i) q^{52} +(34.3598 + 9.20667i) q^{53} +(38.9842 - 12.4919i) q^{55} +(-47.1478 + 137.331i) q^{56} +(21.1222 + 78.8289i) q^{58} +(15.5949 - 9.00371i) q^{59} +(13.4849 - 23.3565i) q^{61} +(71.6533 + 71.6533i) q^{62} -60.0481i q^{64} +(-53.7965 - 83.5806i) q^{65} +(-1.44046 + 5.37586i) q^{67} +(17.4297 + 65.0485i) q^{68} +(62.2662 + 113.172i) q^{70} +105.010 q^{71} +(-81.6625 - 21.8814i) q^{73} +(49.5909 - 28.6313i) q^{74} -202.568 q^{76} +(-47.5423 - 32.0051i) q^{77} +(-86.5708 - 49.9817i) q^{79} +(-140.943 - 127.946i) q^{80} +(-1.76881 + 0.473951i) q^{82} +(-95.6303 + 95.6303i) q^{83} +(31.1205 + 16.0162i) q^{85} +(-87.3064 + 151.219i) q^{86} +(164.041 + 43.9546i) q^{88} +(-54.3480 - 31.3778i) q^{89} +(-45.1856 + 131.615i) q^{91} +(221.576 + 221.576i) q^{92} +(-79.8344 + 46.0924i) q^{94} +(-70.7633 + 77.9515i) q^{95} +(59.0158 + 59.0158i) q^{97} +(70.3578 - 166.591i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

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

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 $

$2$	3.56483	−	0.955194i	1.78242	−	0.477597i	0.791396	−	0.611304i	$-0.209355\pi$
$2$	3.56483	−	0.955194i	1.78242	−	0.477597i	0.991021	+	0.133707i	$0.0426882\pi$
$3$		0			0
$3$		0			0
$4$	8.33154	−	4.81021i	2.08288	−	1.20255i
$5$	1.05941	−	4.88648i	0.211883	−	0.977295i
$5$	1.05941	−	4.88648i	0.211883	−	0.977295i
$6$		0			0
$7$	−6.28878	+	3.07429i	−0.898397	+	0.439185i
$7$	−6.28878	+	3.07429i	−0.898397	+	0.439185i
$8$	14.6673	−	14.6673i	1.83341	−	1.83341i
$9$		0			0
$10$	−0.890898	−	18.4314i	−0.0890898	−	1.84314i
$11$	4.09367	+	7.09045i	0.372152	+	0.644586i	0.989896	−	0.141793i	$-0.0452866\pi$
$11$	4.09367	+	7.09045i	0.372152	+	0.644586i	−0.617744	+	0.786379i	$0.711953\pi$
$12$		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
$17$	−1.81174	+	6.76150i	−0.106573	+	0.397735i	−0.998519	−	0.0544067i	$-0.982673\pi$
$17$	−1.81174	+	6.76150i	−0.106573	+	0.397735i	0.891946	+	0.452142i	$0.149340\pi$
$18$		0			0
$19$	−18.2350	−	10.5280i	−0.959739	−	0.554105i	−0.0636460	−	0.997973i	$-0.520273\pi$
$19$	−18.2350	−	10.5280i	−0.959739	−	0.554105i	−0.896093	+	0.443867i	$0.853606\pi$
$20$	−14.6784	−	45.8079i	−0.733922	−	2.29039i
$21$		0			0
$22$	21.3660	+	21.3660i	0.971183	+	0.971183i
$23$	8.43024	+	31.4621i	0.366532	+	1.36792i	0.865332	+	0.501199i	$0.167108\pi$
$23$	8.43024	+	31.4621i	0.366532	+	1.36792i	−0.498800	+	0.866717i	$0.666226\pi$
$24$		0			0
$25$	−22.7553	−	10.3536i	−0.910211	−	0.414144i
$26$	36.6833	−	63.5374i	1.41090	−	2.44375i
$27$		0			0
$28$	−37.6072	+	55.8639i	−1.34311	+	1.99514i
$29$			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	0.997900	−	0.0647702i	$-0.0206314\pi$
$31$	13.7286	+	23.7786i	0.442857	+	0.767052i	−0.555043	+	0.831822i	$0.687298\pi$
$32$	14.8907	−	55.5730i	0.465335	−	1.73666i
$33$		0			0
$34$			25.8342i			0.759829i
$35$	8.36003	+	33.9869i	0.238858	+	0.971054i
$36$		0			0
$37$	14.9872	−	4.01580i	0.405058	−	0.108535i	−0.0505367	−	0.998722i	$-0.516093\pi$
$37$	14.9872	−	4.01580i	0.405058	−	0.108535i	0.455595	+	0.890187i	$0.349427\pi$
$38$	−75.0611	−	20.1126i	−1.97529	−	0.529278i
$39$		0			0
$40$	−56.1326	−	87.2101i	−1.40332	−	2.18025i
$41$	−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
$47$	−24.1272	+	6.46488i	−0.513346	+	0.137551i	−0.506187	−	0.862424i	$-0.668945\pi$
$47$	−24.1272	+	6.46488i	−0.513346	+	0.137551i	−0.00715874	+	0.999974i	$0.502279\pi$
$48$		0			0
$49$	30.0975	−	38.6671i	0.614234	−	0.789124i
$50$	−91.0085	−	15.1731i	−1.82017	−	0.303463i
$51$		0			0
$52$	49.4987	−	184.732i	0.951899	−	3.55253i
$53$	34.3598	+	9.20667i	0.648297	+	0.173711i	0.567959	−	0.823057i	$-0.307733\pi$
$53$	34.3598	+	9.20667i	0.648297	+	0.173711i	0.0803384	+	0.996768i	$0.474400\pi$
$54$		0			0
$55$	38.9842	−	12.4919i	0.708804	−	0.227126i
$56$	−47.1478	+	137.331i	−0.841925	+	2.45234i
$57$		0			0
$58$	21.1222	+	78.8289i	0.364175	+	1.35912i
$59$	15.5949	−	9.00371i	0.264320	−	0.152605i	−0.361984	−	0.932184i	$-0.617900\pi$
$59$	15.5949	−	9.00371i	0.264320	−	0.152605i	0.626304	+	0.779579i	$0.284567\pi$
$60$		0			0
$61$	13.4849	−	23.3565i	0.221064	−	0.382894i	−0.734067	−	0.679077i	$-0.762380\pi$
$61$	13.4849	−	23.3565i	0.221064	−	0.382894i	0.955131	+	0.296183i	$0.0957137\pi$
$62$	71.6533	+	71.6533i	1.15570	+	1.15570i
$63$		0			0
$64$		−	60.0481i		−	0.938252i
$65$	−53.7965	−	83.5806i	−0.827638	−	1.28585i
$66$		0			0
$67$	−1.44046	+	5.37586i	−0.0214993	+	0.0802367i	−0.975842	−	0.218477i	$-0.929891\pi$
$67$	−1.44046	+	5.37586i	−0.0214993	+	0.0802367i	0.954343	+	0.298714i	$0.0965577\pi$
$68$	17.4297	+	65.0485i	0.256319	+	0.956596i
$69$		0			0
$70$	62.2662	+	113.172i	0.889517	+	1.61675i
$71$	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
$73$	−81.6625	−	21.8814i	−1.11866	−	0.299745i	−0.348321	−	0.937375i	$-0.613248\pi$
$73$	−81.6625	−	21.8814i	−1.11866	−	0.299745i	−0.770343	+	0.637630i	$0.779915\pi$
$74$	49.5909	−	28.6313i	0.670147	−	0.386909i
$75$		0			0
$76$	−202.568			−2.66537
$77$	−47.5423	−	32.0051i	−0.617433	−	0.415651i
$78$		0			0
$79$	−86.5708	−	49.9817i	−1.09583	−	0.632679i	−0.160710	−	0.987002i	$-0.551378\pi$
$79$	−86.5708	−	49.9817i	−1.09583	−	0.632679i	−0.935123	+	0.354322i	$0.884712\pi$
$80$	−140.943	−	127.946i	−1.76178	−	1.59932i
$81$		0			0
$82$	−1.76881	+	0.473951i	−0.0215708	+	0.00577989i
$83$	−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
$88$	164.041	+	43.9546i	1.86410	+	0.499484i
$89$	−54.3480	−	31.3778i	−0.610651	−	0.352560i	0.162569	−	0.986697i	$-0.448022\pi$
$89$	−54.3480	−	31.3778i	−0.610651	−	0.352560i	−0.773220	+	0.634137i	$0.781355\pi$
$90$		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
$95$	−70.7633	+	77.9515i	−0.744877	+	0.820542i
$96$		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	$0.608439\pi$
$98$	70.3578	−	166.591i	0.717937	−	1.69990i
$99$		0			0
$100$	−239.390	+	23.1964i	−2.39390	+	0.231964i
$101$	−19.3636	−	33.5388i	−0.191719	−	0.332067i	0.754101	−	0.656758i	$-0.228073\pi$
$101$	−19.3636	−	33.5388i	−0.191719	−	0.332067i	−0.945820	+	0.324691i	$0.894740\pi$
$102$		0			0
$103$	−8.01775	−	29.9227i	−0.0778422	−	0.290511i	0.916021	−	0.401131i	$-0.131383\pi$
$103$	−8.01775	−	29.9227i	−0.0778422	−	0.290511i	−0.993863	+	0.110620i	$0.964716\pi$
$104$		−	412.352i		−	3.96493i
$105$		0			0
$106$	131.281			1.23850
$107$	−18.7482	+	5.02357i	−0.175217	+	0.0469492i	−0.345361	−	0.938470i	$-0.612243\pi$
$107$	−18.7482	+	5.02357i	−0.175217	+	0.0469492i	0.170144	+	0.985419i	$0.445577\pi$
$108$		0			0
$109$	−73.5876	+	42.4858i	−0.675116	+	0.389778i	−0.798012	−	0.602641i	$-0.794115\pi$
$109$	−73.5876	+	42.4858i	−0.675116	+	0.389778i	0.122896	+	0.992419i	$0.460782\pi$
$110$	127.040	−	81.7691i	1.15491	−	0.743355i
$111$		0			0
$112$	−18.3492	+	265.864i	−0.163832	+	2.37379i
$113$	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
$115$	162.670	−	7.86279i	1.41452	−	0.0683720i
$116$	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
$122$	25.7614	−	96.1428i	0.211159	−	0.788056i
$123$		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	$-0.553734\pi$
$128$	2.20532	+	8.23036i	0.0172290	+	0.0642997i
$129$		0			0
$130$	−271.611	−	246.565i	−2.08932	−	1.89665i
$131$	57.4723	−	99.5449i	0.438720	−	0.759885i	−0.558871	−	0.829254i	$-0.688765\pi$
$131$	57.4723	−	99.5449i	0.438720	−	0.759885i	0.997591	+	0.0693695i	$0.0220987\pi$
$132$		0			0
$133$	147.042	+	10.1484i	1.10558	+	0.0763041i
$134$			20.5399i			0.153283i
$135$		0			0
$136$	72.5996	+	125.746i	0.533820	+	0.924604i
$137$	28.1594	−	105.092i	0.205543	−	0.767096i	−0.783741	−	0.621088i	$-0.786691\pi$
$137$	28.1594	−	105.092i	0.205543	−	0.767096i	0.989283	−	0.146008i	$-0.0466425\pi$
$138$		0			0
$139$		−	188.782i		−	1.35814i	−0.734071	−	0.679072i	$-0.762382\pi$
$139$		−	188.782i		−	1.35814i	0.734071	−	0.679072i	$-0.237618\pi$
$140$	233.136	+	242.950i	1.66526	+	1.73535i
$141$		0			0
$142$	374.344	−	100.305i	2.63623	−	0.706375i
$143$	157.214	+	42.1253i	1.09940	+	0.294582i
$144$		0			0
$145$	108.054	+	23.4268i	0.745202	+	0.161564i
$146$	−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	$-0.203714\pi$
$149$	102.211	+	59.0115i	0.685979	+	0.396050i	−0.116125	+	0.993235i	$0.537047\pi$
$150$		0			0
$151$	−89.3003	−	154.673i	−0.591393	−	1.02432i	−0.994045	−	0.108969i	$-0.965245\pi$
$151$	−89.3003	−	154.673i	−0.591393	−	1.02432i	0.402653	−	0.915353i	$-0.368088\pi$
$152$	−421.876	+	113.041i	−2.77550	+	0.743693i
$153$		0			0
$154$	−200.052	−	68.6808i	−1.29904	−	0.445979i
$155$	130.738	−	41.8930i	0.843470	−	0.270277i
$156$		0			0
$157$	−15.3559	+	57.3089i	−0.0978081	+	0.365025i	−0.997430	−	0.0716444i	$-0.977175\pi$
$157$	−15.3559	+	57.3089i	−0.0978081	+	0.365025i	0.899622	+	0.436669i	$0.143842\pi$
$158$	−356.353	−	95.4844i	−2.25540	−	0.604332i
$159$		0			0
$160$	−255.780	−	131.638i	−1.59863	−	0.822737i
$161$	−149.740	−	171.941i	−0.930059	−	1.06796i
$162$		0			0
$163$	32.5532	+	121.490i	0.199713	+	0.745338i	0.990996	+	0.133889i	$0.0427466\pi$
$163$	32.5532	+	121.490i	0.199713	+	0.745338i	−0.791284	+	0.611449i	$0.790587\pi$
$164$	−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
$170$	126.238	+	27.3691i	0.742577	+	0.160995i
$171$		0			0
$172$	−117.807	+	439.662i	−0.684925	+	2.55617i
$173$	9.32360	+	34.7961i	0.0538936	+	0.201134i	0.987623	−	0.156846i	$-0.0501325\pi$
$173$	9.32360	+	34.7961i	0.0538936	+	0.201134i	−0.933730	+	0.357979i	$0.883466\pi$
$174$		0			0
$175$	174.933	−	4.84489i	0.999617	−	0.0276851i
$176$	311.700			1.77102
$177$		0			0
$178$	−223.713	−	59.9438i	−1.25682	−	0.336763i
$179$	−65.4777	+	37.8036i	−0.365797	+	0.211193i	−0.671621	−	0.740895i	$-0.734402\pi$
$179$	−65.4777	+	37.8036i	−0.365797	+	0.211193i	0.305823	+	0.952088i	$0.401068\pi$
$180$		0			0
$181$	−182.419			−1.00784			−0.503919	−	0.863751i	$-0.668109\pi$
$181$	−182.419			−1.00784			−0.503919	+	0.863751i	$0.668109\pi$
$182$	−35.3608	+	512.348i	−0.194290	+	2.81510i
$183$		0			0
$184$	585.112	+	337.815i	3.17996	+	1.83595i
$185$	−3.74549	−	77.4888i	−0.0202459	−	0.418858i
$186$		0			0
$187$	−55.3587	+	14.8333i	−0.296036	+	0.0793226i
$188$	−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	−0.845268	−	0.534343i	$-0.820559\pi$
$191$	7.66297	−	13.2727i	0.0401203	−	0.0694904i	0.885388	+	0.464852i	$0.153893\pi$
$192$		0			0
$193$	−217.420	−	58.2576i	−1.12653	−	0.301853i	−0.353007	−	0.935621i	$-0.614841\pi$
$193$	−217.420	−	58.2576i	−1.12653	−	0.301853i	−0.773523	+	0.633768i	$0.781507\pi$
$194$	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	$-0.613689\pi$
$199$	57.1020	−	32.9678i	0.286945	−	0.165668i	0.636563	+	0.771225i	$0.280355\pi$
$200$	−485.618	+	181.899i	−2.42809	+	0.909495i
$201$		0			0
$202$	−101.064	−	101.064i	−0.500317	−	0.500317i
$203$	−67.9816	−	139.063i	−0.334885	−	0.685041i
$204$		0			0
$205$	−0.525663	+	2.42458i	−0.00256421	+	0.0118272i
$206$	−57.1639	−	99.0107i	−0.277495	−	0.480635i
$207$		0			0
$208$	−195.881	−	731.039i	−0.941738	−	3.51461i
$209$		−	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	$0.0799283\pi$
$212$	330.556	−	88.5721i	1.55922	−	0.417793i
$213$		0			0
$214$	−62.0357	+	35.8164i	−0.289887	+	0.167366i
$215$	128.036	+	198.922i	0.595515	+	0.925218i
$216$		0			0
$217$	−159.438	−	107.333i	−0.734739	−	0.494621i
$218$	−221.745	+	221.745i	−1.01718	+	1.01718i
$219$		0			0
$220$	264.710	−	291.599i	1.20323	−	1.32545i
$221$	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
$227$	56.8024	−	211.989i	0.250231	−	0.933874i	−0.720451	−	0.693506i	$-0.756065\pi$
$227$	56.8024	−	211.989i	0.250231	−	0.933874i	0.970682	−	0.240368i	$-0.0772681\pi$
$228$		0			0
$229$	292.008	+	168.591i	1.27515	+	0.736206i	0.975952	−	0.217986i	$-0.0699489\pi$
$229$	292.008	+	168.591i	1.27515	+	0.736206i	0.299194	+	0.954192i	$0.403282\pi$
$230$	572.380	−	183.411i	2.48861	−	0.797438i
$231$		0			0
$232$	324.337	+	324.337i	1.39800	+	1.39800i
$233$	76.1326	+	284.131i	0.326749	+	1.21945i	0.912542	+	0.408984i	$0.134117\pi$
$233$	76.1326	+	284.131i	0.326749	+	1.21945i	−0.585792	+	0.810461i	$0.699217\pi$
$234$		0			0
$235$	6.02971	+	124.746i	0.0256584	+	0.530835i
$236$	86.6195	−	150.029i	0.367032	−	0.635718i
$237$		0			0
$238$	−79.4218	−	162.465i	−0.333705	−	0.682628i
$239$		−	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	0.709542	−	0.704663i	$-0.248902\pi$
$241$	−61.5720	−	106.646i	−0.255486	−	0.442514i	−0.965027	+	0.262149i	$0.915569\pi$
$242$	51.5493	−	192.385i	0.213014	−	0.794978i
$243$		0			0
$244$		−	259.461i		−	1.06337i
$245$	−157.060	−	188.035i	−0.641062	−	0.767490i
$246$		0			0
$247$	−404.318	+	108.337i	−1.63692	+	0.438610i
$248$	550.129	+	147.407i	2.21826	+	0.594381i
$249$		0			0
$250$	−170.559	+	428.636i	−0.682235	+	1.71454i
$251$	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
$257$	−182.539	+	48.9113i	−0.710270	+	0.190316i	−0.595826	−	0.803114i	$-0.703175\pi$
$257$	−182.539	+	48.9113i	−0.710270	+	0.190316i	−0.114444	+	0.993430i	$0.536509\pi$
$258$		0			0
$259$	−81.9052	+	71.3294i	−0.316236	+	0.275403i
$260$	−850.248	−	437.582i	−3.27018	−	1.68301i
$261$		0			0
$262$	109.794	−	409.758i	0.419063	−	1.56396i
$263$	−134.776	−	36.1131i	−0.512457	−	0.137312i	−0.00668144	−	0.999978i	$-0.502127\pi$
$263$	−134.776	−	36.1131i	−0.512457	−	0.137312i	−0.505775	+	0.862665i	$0.668793\pi$
$264$		0			0
$265$	81.3894	−	158.144i	0.307130	−	0.596771i
$266$	533.875	−	104.276i	2.00705	−	0.392016i
$267$		0			0
$268$	13.8578	+	51.7180i	0.0517082	+	0.192978i
$269$	−169.522	+	97.8736i	−0.630194	+	0.363842i	−0.780827	−	0.624747i	$-0.785202\pi$
$269$	−169.522	+	97.8736i	−0.630194	+	0.363842i	0.150634	+	0.988590i	$0.451869\pi$
$270$		0			0
$271$	123.964	−	214.711i	0.457430	−	0.792292i	−0.541394	−	0.840769i	$-0.682103\pi$
$271$	123.964	−	214.711i	0.457430	−	0.792292i	0.998824	+	0.0484766i	$0.0154366\pi$
$272$	188.442	+	188.442i	0.692802	+	0.692802i
$273$		0			0
$274$		−	401.534i		−	1.46545i
$275$	−19.7410	−	203.729i	−0.0717855	−	0.740834i
$276$		0			0
$277$	70.6321	−	263.603i	0.254989	−	0.951634i	−0.713107	−	0.701055i	$-0.752713\pi$
$277$	70.6321	−	263.603i	0.254989	−	0.951634i	0.968096	−	0.250578i	$-0.0806208\pi$
$278$	−180.324	−	672.977i	−0.648646	−	2.42078i
$279$		0			0
$280$	621.115	+	375.877i	2.21827	+	1.34242i
$281$	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
$283$	106.533	+	28.5453i	0.376440	+	0.100867i	0.442078	−	0.896977i	$-0.354241\pi$
$283$	106.533	+	28.5453i	0.376440	+	0.100867i	−0.0656376	+	0.997844i	$0.520908\pi$
$284$	874.897	−	505.122i	3.08062	−	1.77860i
$285$		0			0
$286$	600.679			2.10027
$287$	3.12038	−	1.52541i	0.0108724	−	0.00531502i
$288$		0			0
$289$	207.846	+	120.000i	0.719190	+	0.415224i
$290$	407.573	−	19.7004i	1.40542	−	0.0679324i
$291$		0			0
$292$	−785.628	+	210.508i	−2.69051	+	0.720919i
$293$	−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
$298$	420.732	+	112.735i	1.41185	+	0.378305i
$299$	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
$305$	−99.8450	−	90.6379i	−0.327361	−	0.297173i
$306$		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	$0.453346\pi$
$308$	−550.052	−	37.9631i	−1.78588	−	0.123257i
$309$		0			0
$310$	426.042	−	274.221i	1.37433	−	0.884585i
$311$	7.38338	+	12.7884i	0.0237408	+	0.0411202i	0.877652	−	0.479299i	$-0.159109\pi$
$311$	7.38338	+	12.7884i	0.0237408	+	0.0411202i	−0.853911	+	0.520419i	$0.825776\pi$
$312$		0			0
$313$	31.2853	+	116.758i	0.0999530	+	0.373030i	0.997724	−	0.0674334i	$-0.0214810\pi$
$313$	31.2853	+	116.758i	0.0999530	+	0.373030i	−0.897771	+	0.440463i	$0.854814\pi$
$314$			218.964i			0.697339i
$315$		0			0
$316$	−961.690			−3.04332
$317$	300.282	−	80.4604i	0.947262	−	0.253818i	0.248062	−	0.968744i	$-0.420206\pi$
$317$	300.282	−	80.4604i	0.947262	−	0.253818i	0.699200	+	0.714926i	$0.253540\pi$
$318$		0			0
$319$	−156.791	+	90.5232i	−0.491507	+	0.283772i
$320$	−293.424	−	63.6158i	−0.916949	−	0.198799i
$321$		0			0
$322$	−698.033	−	469.911i	−2.16781	−	1.45935i
$323$	104.222	−	104.222i	0.322669	−	0.322669i
$324$		0			0
$325$	−465.407	+	174.329i	−1.43202	+	0.536396i
$326$	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	−0.751803	−	0.659388i	$-0.770816\pi$
$331$	64.5929	−	111.878i	0.195145	−	0.338001i	0.946948	+	0.321387i	$0.104149\pi$
$332$	−336.745	+	1256.75i	−1.01429	+	3.78539i
$333$		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	$0.784151\pi$
$338$	−216.056	−	806.333i	−0.639220	−	2.38560i
$339$		0			0
$340$	336.323	−	16.2565i	0.989186	−	0.0478132i
$341$	−112.401	+	194.684i	−0.329621	+	0.570920i
$342$		0			0
$343$	−70.4023	+	335.697i	−0.205255	+	0.978709i
$344$			981.399i			2.85290i
$345$		0			0
$346$	66.4741	+	115.137i	0.192122	+	0.332765i
$347$	−157.007	+	585.959i	−0.452470	+	1.68864i	0.242950	+	0.970039i	$0.421885\pi$
$347$	−157.007	+	585.959i	−0.452470	+	1.68864i	−0.695420	+	0.718603i	$0.744782\pi$
$348$		0			0
$349$		−	82.1983i		−	0.235525i	−0.993042	−	0.117763i	$-0.962428\pi$
$349$		−	82.1983i		−	0.235525i	0.993042	−	0.117763i	$-0.0375722\pi$
$350$	618.979	−	184.366i	1.76851	−	0.526760i
$351$		0			0
$352$	454.995	−	121.916i	1.29260	−	0.346351i
$353$	141.830	+	38.0031i	0.401783	+	0.107658i	0.454051	−	0.890976i	$-0.349978\pi$
$353$	141.830	+	38.0031i	0.401783	+	0.107658i	−0.0522678	+	0.998633i	$0.516645\pi$
$354$		0			0
$355$	111.249	−	513.130i	0.313379	−	1.44544i
$356$	−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	$-0.424178\pi$
$359$	−175.063	−	101.073i	−0.487641	−	0.281539i	−0.723595	+	0.690225i	$0.757512\pi$
$360$		0			0
$361$	41.1776	+	71.3218i	0.114065	+	0.197567i
$362$	−650.292	+	174.245i	−1.79639	+	0.481340i
$363$		0			0
$364$	256.633	+	1313.91i	0.705036	+	3.60965i
$365$	−193.437	+	375.860i	−0.529965	+	1.02975i
$366$		0			0
$367$	−130.259	+	486.132i	−0.354928	+	1.32461i	0.525647	+	0.850703i	$0.323823\pi$
$367$	−130.259	+	486.132i	−0.354928	+	1.32461i	−0.880575	+	0.473907i	$0.842843\pi$
$368$	1197.79	+	320.947i	3.25487	+	0.872139i
$369$		0			0
$370$	−87.3689	−	272.657i	−0.236132	−	0.736911i
$371$	−244.385	+	47.7332i	−0.658719	+	0.128661i
$372$		0			0
$373$	−47.8471	−	178.568i	−0.128277	−	0.478735i	0.871659	−	0.490113i	$-0.163045\pi$
$373$	−47.8471	−	178.568i	−0.128277	−	0.478735i	−0.999935	+	0.0113788i	$0.996378\pi$
$374$	−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	$-0.152025\pi$
$380$	−214.603	+	989.842i	−0.564745	+	2.60485i
$381$		0			0
$382$	14.6393	−	54.6344i	0.0383226	−	0.143022i
$383$	117.020	+	436.725i	0.305536	+	1.14028i	0.932483	+	0.361214i	$0.117638\pi$
$383$	117.020	+	436.725i	0.305536	+	1.14028i	−0.626947	+	0.779062i	$0.715696\pi$
$384$		0			0
$385$	−206.759	+	198.408i	−0.537037	+	0.515345i
$386$	−830.714			−2.15211
$387$		0			0
$388$	775.571	+	207.814i	1.99889	+	0.535602i
$389$	−565.646	+	326.576i	−1.45410	+	0.839527i	−0.998711	−	0.0507630i	$-0.983835\pi$
$389$	−565.646	+	326.576i	−1.45410	+	0.839527i	−0.455393	+	0.890290i	$0.650501\pi$
$390$		0			0
$391$	−228.004			−0.583131
$392$	−125.693	−	1008.59i	−0.320646	−	2.57293i
$393$		0			0
$394$	−1180.59	−	681.614i	−2.99642	−	1.72999i
$395$	−335.949	+	370.075i	−0.850503	+	0.936898i
$396$		0			0
$397$	−63.7193	+	17.0735i	−0.160502	+	0.0430064i	−0.338175	−	0.941083i	$-0.609810\pi$
$397$	−63.7193	+	17.0735i	−0.160502	+	0.0430064i	0.177673	+	0.984090i	$0.443143\pi$
$398$	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	−0.926105	−	0.377266i	$-0.876864\pi$
$401$	−54.6685	+	94.6886i	−0.136330	+	0.236131i	0.789775	+	0.613397i	$0.210198\pi$
$402$		0			0
$403$	527.233	+	141.272i	1.30827	+	0.350550i
$404$	−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	$-0.549684\pi$
$409$	254.528	−	146.952i	0.622318	−	0.359295i	0.777771	+	0.628548i	$0.216350\pi$
$410$	0.442048	+	9.14535i	0.00107817	+	0.0223057i
$411$		0			0
$412$	−210.735	−	210.735i	−0.511492	−	0.511492i
$413$	−70.3927	+	104.566i	−0.170442	+	0.253185i
$414$		0			0
$415$	365.983	+	568.607i	0.881887	+	1.37014i
$416$	−571.865	−	990.499i	−1.37467	−	2.38101i
$417$		0			0
$418$	−164.669	−	614.552i	−0.393944	−	1.47022i
$419$			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	$0.547162\pi$
$422$	1457.18	−	390.451i	3.45304	−	0.925238i
$423$		0			0
$424$	639.001	−	368.928i	1.50708	−	0.870112i
$425$	111.232	−	135.102i	0.261723	−	0.317887i
$426$		0			0
$427$	−12.9987	+	188.341i	−0.0304420	+	0.441079i
$428$	−132.037	+	132.037i	−0.308498	+	0.308498i
$429$		0			0
$430$	646.435	+	586.824i	1.50334	+	1.36471i
$431$	−105.297	−	182.380i	−0.244309	−	0.423155i	0.717628	−	0.696426i	$-0.245228\pi$
$431$	−105.297	−	182.380i	−0.244309	−	0.423155i	−0.961937	+	0.273271i	$0.911894\pi$
$432$		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
$437$	177.507	−	662.466i	0.406195	−	1.51594i
$438$		0			0
$439$	−83.0573	−	47.9532i	−0.189197	−	0.109233i	0.402410	−	0.915460i	$-0.368173\pi$
$439$	−83.0573	−	47.9532i	−0.189197	−	0.109233i	−0.591606	+	0.806227i	$0.701506\pi$
$440$	388.570	−	755.015i	0.883114	−	1.71594i
$441$		0			0
$442$	363.148	+	363.148i	0.821601	+	0.821601i
$443$	−25.9009	−	96.6633i	−0.0584670	−	0.218202i	0.930511	−	0.366264i	$-0.119363\pi$
$443$	−25.9009	−	96.6633i	−0.0584670	−	0.218202i	−0.988978	+	0.148062i	$0.952696\pi$
$444$		0			0
$445$	−210.904	+	232.328i	−0.473941	+	0.522085i
$446$	−470.055	+	814.159i	−1.05394	+	1.82547i
$447$		0			0
$448$	184.605	+	377.629i	0.412066	+	0.842922i
$449$		−	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
$452$	332.302	−	1240.17i	0.735181	−	2.74373i
$453$		0			0
$454$		−	809.964i		−	1.78406i
$455$	595.265	+	360.234i	1.30828	+	0.791722i
$456$		0			0
$457$	83.2667	−	22.3113i	0.182203	−	0.0488211i	−0.166564	−	0.986031i	$-0.553267\pi$
$457$	83.2667	−	22.3113i	0.182203	−	0.0488211i	0.348767	+	0.937210i	$0.386601\pi$
$458$	1202.00	+	322.074i	2.62445	+	0.703219i
$459$		0			0
$460$	1317.47	−	847.986i	2.86406	−	1.84345i
$461$	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
$467$	48.7023	−	13.0497i	0.104288	−	0.0279438i	−0.206298	−	0.978489i	$-0.566142\pi$
$467$	48.7023	−	13.0497i	0.104288	−	0.0279438i	0.310585	+	0.950545i	$0.399475\pi$
$468$		0			0
$469$	−7.46824	−	38.2359i	−0.0159238	−	0.0815265i
$470$	140.652	+	438.940i	0.299259	+	0.933914i
$471$		0			0
$472$	96.6746	−	360.795i	0.204819	−	0.764395i
$473$	−374.169	−	100.258i	−0.791055	−	0.211963i
$474$		0			0
$475$	305.941	+	428.366i	0.644086	+	0.901823i
$476$	−309.590	−	355.492i	−0.650398	−	0.746831i
$477$		0			0
$478$	−183.075	−	683.246i	−0.383003	−	1.42938i
$479$	152.207	−	87.8766i	0.317760	−	0.183459i	−0.332634	−	0.943056i	$-0.607937\pi$
$479$	152.207	−	87.8766i	0.317760	−	0.183459i	0.650393	+	0.759597i	$0.274604\pi$
$480$		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
$485$	350.901	−	225.857i	0.723508	−	0.465685i
$486$		0			0
$487$	65.7419	−	245.352i	0.134994	−	0.503803i	−0.865004	−	0.501765i	$-0.832684\pi$
$487$	65.7419	−	245.352i	0.134994	−	0.503803i	0.999998	−	0.00203876i	$-0.000648959\pi$
$488$	−144.790	−	540.364i	−0.296701	−	1.10730i
$489$		0			0
$490$	−739.503	−	520.290i	−1.50919	−	1.06182i
$491$	−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
$493$	−149.517	−	40.0629i	−0.303279	−	0.0812634i
$494$	−1337.84	+	772.405i	−2.70819	+	1.56357i
$495$		0			0
$496$	1045.32			2.10750
$497$	−660.386	+	322.832i	−1.32875	+	0.649562i
$498$		0			0
$499$	520.379	+	300.441i	1.04284	+	0.602086i	0.920637	−	0.390419i	$-0.127670\pi$
$499$	520.379	+	300.441i	1.04284	+	0.602086i	0.122206	+	0.992505i	$0.461003\pi$
$500$	−140.264	+	1194.35i	−0.280528	+	2.38869i
$501$		0			0
$502$	75.3423	−	20.1879i	0.150084	−	0.0402150i
$503$	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
$508$	−1925.69	−	515.986i	−3.79072	−	1.01572i
$509$	−406.687	−	234.801i	−0.798993	−	0.461299i	0.0441259	−	0.999026i	$-0.485950\pi$
$509$	−406.687	−	234.801i	−0.798993	−	0.461299i	−0.843119	+	0.537727i	$0.819283\pi$
$510$		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
$515$	−154.710	+	7.47806i	−0.300409	+	0.0145205i
$516$		0			0
$517$	−144.608	−	144.608i	−0.279706	−	0.279706i
$518$	−223.845	+	332.513i	−0.432133	+	0.641916i
$519$		0			0
$520$	−2014.95	−	436.852i	−3.87490	−	0.840099i
$521$	−72.5876	−	125.725i	−0.139324	−	0.241316i	0.787917	−	0.615781i	$-0.211160\pi$
$521$	−72.5876	−	125.725i	−0.139324	−	0.241316i	−0.927241	+	0.374466i	$0.877826\pi$
$522$		0			0
$523$	217.012	+	809.900i	0.414937	+	1.54857i	0.784962	+	0.619543i	$0.212682\pi$
$523$	217.012	+	809.900i	0.414937	+	1.54857i	−0.370026	+	0.929022i	$0.620651\pi$
$524$		−	1105.82i		−	2.11034i
$525$		0			0
$526$	−514.949			−0.978991
$527$	−185.652	+	49.7452i	−0.352280	+	0.0943932i
$528$		0			0
$529$	−460.666	+	265.966i	−0.870824	+	0.502770i
$530$	139.081	−	641.501i	0.262417	−	1.21038i
$531$		0			0
$532$	1273.90	−	622.753i	2.39456	−	1.17059i
$533$	−6.97477	+	6.97477i	−0.0130859	+	0.0130859i
$534$		0			0
$535$	4.68542	+	96.9347i	0.00875780	+	0.181186i
$536$	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	−0.995708	−	0.0925455i	$-0.970500\pi$
$541$	−225.980	+	391.408i	−0.417708	+	0.723491i	0.578001	+	0.816036i	$0.303833\pi$
$542$	236.819	−	883.819i	0.436935	−	1.63066i
$543$		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	$0.582047\pi$
$548$	−270.905	−	1011.03i	−0.494353	−	1.84495i
$549$		0			0
$550$	−264.975	−	707.405i	−0.481772	−	1.28619i
$551$	232.805	−	403.230i	0.422514	−	0.731815i
$552$		0			0
$553$	698.083	+	48.1797i	1.26236	+	0.0871243i
$554$		−	1007.17i		−	1.81799i
$555$		0			0
$556$	−908.083	−	1572.85i	−1.63324	−	2.82886i
$557$	−254.761	+	950.780i	−0.457380	+	1.70697i	0.223615	+	0.974678i	$0.428214\pi$
$557$	−254.761	+	950.780i	−0.457380	+	1.70697i	−0.680995	+	0.732288i	$0.738453\pi$
$558$		0			0
$559$			940.555i			1.68257i
$560$	1279.70	+	371.323i	2.28518	+	0.663077i
$561$		0			0
$562$	1518.66	−	406.924i	2.70224	−	0.724064i
$563$	−831.358	−	222.762i	−1.47666	−	0.395669i	−0.571450	−	0.820637i	$-0.693619\pi$
$563$	−831.358	−	222.762i	−1.47666	−	0.395669i	−0.905208	+	0.424968i	$0.860285\pi$
$564$		0			0
$565$	−361.154	−	561.105i	−0.639211	−	0.993106i
$566$	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	$-0.219934\pi$
$569$	343.723	+	198.449i	0.604083	+	0.348768i	−0.166563	+	0.986031i	$0.553267\pi$
$570$		0			0
$571$	402.947	+	697.924i	0.705686	+	1.22228i	0.966443	+	0.256880i	$0.0826944\pi$
$571$	402.947	+	697.924i	0.705686	+	1.22228i	−0.260757	+	0.965404i	$0.583972\pi$
$572$	1512.46	−	405.263i	2.64417	−	0.708502i
$573$		0			0
$574$	9.66658	−	8.41840i	0.0168407	−	0.0146662i
$575$	133.913	−	803.212i	0.232893	−	1.39689i
$576$		0			0
$577$	268.157	−	1000.77i	0.464743	−	1.73445i	−0.192996	−	0.981200i	$-0.561820\pi$
$577$	268.157	−	1000.77i	0.464743	−	1.73445i	0.657739	−	0.753246i	$-0.271513\pi$
$578$	855.559	+	229.246i	1.48021	+	0.396620i
$579$		0			0
$580$	1012.95	−	324.584i	1.74646	−	0.559627i
$581$	307.402	−	895.394i	0.529092	−	1.54113i
$582$		0			0
$583$	75.3782	+	281.315i	0.129294	+	0.482530i
$584$	−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
$590$	−179.845	−	279.414i	−0.304821	−	0.473584i
$591$		0			0
$592$	152.885	−	570.575i	0.258252	−	0.963810i
$593$	205.761	+	767.912i	0.346984	+	1.29496i	0.890277	+	0.455419i	$0.150510\pi$
$593$	205.761	+	767.912i	0.346984	+	1.29496i	−0.543293	+	0.839543i	$0.682823\pi$
$594$		0			0
$595$	−244.949	−	5.04902i	−0.411678	−	0.00848576i
$596$	1135.43			1.90509
$597$		0			0
$598$	2308.27	+	618.499i	3.85998	+	1.03428i
$599$	357.782	−	206.565i	0.597299	−	0.344850i	−0.170680	−	0.985327i	$-0.554596\pi$
$599$	357.782	−	206.565i	0.597299	−	0.344850i	0.767978	+	0.640476i	$0.221263\pi$
$600$		0			0
$601$	−439.370			−0.731066			−0.365533	−	0.930798i	$-0.619113\pi$
$601$	−439.370			−0.731066			−0.365533	+	0.930798i	$0.619113\pi$
$602$	84.1588	−	1219.39i	0.139799	−	2.02556i
$603$		0			0
$604$	−1488.02	−	859.107i	−2.46360	−	1.42236i
$605$	−199.793	−	181.369i	−0.330236	−	0.299783i
$606$		0			0
$607$	−212.262	+	56.8754i	−0.349690	+	0.0936991i	−0.429388	−	0.903120i	$-0.641271\pi$
$607$	−212.262	+	56.8754i	−0.349690	+	0.0936991i	0.0796986	+	0.996819i	$0.474604\pi$
$608$	−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
$613$	−945.946	−	253.466i	−1.54314	−	0.413484i	−0.615863	−	0.787853i	$-0.711192\pi$
$613$	−945.946	−	253.466i	−1.54314	−	0.413484i	−0.927280	+	0.374370i	$0.877859\pi$
$614$	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	$-0.805011\pi$
$619$	−451.442	+	260.640i	−0.729309	+	0.421067i	0.0888604	+	0.996044i	$0.471677\pi$
$620$	887.732	−	977.910i	1.43183	−	1.57727i
$621$		0			0
$622$	38.5359	+	38.5359i	0.0619548	+	0.0619548i
$623$	438.247	+	30.2466i	0.703446	+	0.0485499i
$624$		0			0
$625$	410.606	+	471.198i	0.656969	+	0.753917i
$626$	223.054	+	386.340i	0.356316	+	0.617157i
$627$		0			0
$628$	147.730	+	551.336i	0.235239	+	0.877924i
$629$			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	$0.340562\pi$
$632$	−2002.85	+	536.663i	−3.16907	+	0.849151i
$633$		0			0
$634$	993.601	−	573.656i	1.56719	−	0.904819i
$635$	−871.263	+	560.787i	−1.37207	+	0.883129i
$636$		0			0
$637$	−120.462	−	966.614i	−0.189108	−	1.51745i
$638$	−472.466	+	472.466i	−0.740542	+	0.740542i
$639$		0			0
$640$	42.5538	−	2.05687i	0.0664903	−	0.00321387i
$641$	−552.914	−	957.675i	−0.862580	−	1.49403i	−0.869430	−	0.494056i	$-0.835514\pi$
$641$	−552.914	−	957.675i	−0.862580	−	1.49403i	0.00685032	−	0.999977i	$-0.497819\pi$
$642$		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
$647$	−200.190	+	747.117i	−0.309412	+	1.15474i	0.619669	+	0.784864i	$0.287267\pi$
$647$	−200.190	+	747.117i	−0.309412	+	1.15474i	−0.929081	+	0.369877i	$0.879400\pi$
$648$		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
$653$	280.108	+	1045.38i	0.428956	+	1.60089i	0.755129	+	0.655576i	$0.227574\pi$
$653$	280.108	+	1045.38i	0.428956	+	1.60089i	−0.326172	+	0.945310i	$0.605759\pi$
$654$		0			0
$655$	−425.537	−	386.296i	−0.649675	−	0.589765i
$656$	−9.44507	+	16.3593i	−0.0143980	+	0.0249380i
$657$		0			0
$658$	360.359	−	535.299i	0.547658	−	0.813524i
$659$			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	0.531036	−	0.847350i	$-0.321803\pi$
$661$	−309.552	−	536.160i	−0.468308	−	0.811134i	−0.999344	+	0.0362155i	$0.988470\pi$
$662$	123.398	−	460.526i	0.186401	−	0.695658i
$663$		0			0
$664$			2805.28i			4.22481i
$665$	205.369	−	707.767i	0.308825	−	1.06431i
$666$		0			0
$667$	−695.719	+	186.417i	−1.04306	+	0.279486i
$668$	398.172	+	106.690i	0.596066	+	0.159715i
$669$		0			0
$670$	100.368	+	21.7603i	0.149803	+	0.0324781i
$671$	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
$677$	713.136	−	191.084i	1.05338	−	0.282252i	0.309731	−	0.950824i	$-0.399761\pi$
$677$	713.136	−	191.084i	1.05338	−	0.282252i	0.743647	+	0.668573i	$0.233094\pi$
$678$		0			0
$679$	−552.569	−	189.705i	−0.813798	−	0.279389i
$680$	691.368	−	221.539i	1.01672	−	0.325792i
$681$		0			0
$682$	−214.729	+	801.379i	−0.314852	+	1.17504i
$683$	−504.707	−	135.236i	−0.738957	−	0.198003i	−0.130342	−	0.991469i	$-0.541608\pi$
$683$	−504.707	−	135.236i	−0.738957	−	0.198003i	−0.608614	+	0.793466i	$0.708274\pi$
$684$		0			0
$685$	−483.698	−	248.936i	−0.706129	−	0.363411i
$686$	69.6833	+	1263.95i	0.101579	+	1.84250i
$687$		0			0
$688$	466.198	+	1739.88i	0.677614	+	2.52889i
$689$	612.407	−	353.574i	0.888835	−	0.513169i
$690$		0			0
$691$	−301.546	+	522.293i	−0.436391	+	0.755851i	−0.997408	−	0.0719534i	$-0.977077\pi$
$691$	−301.546	+	522.293i	−0.436391	+	0.755851i	0.561017	+	0.827804i	$0.310410\pi$
$692$	245.057	+	245.057i	0.354128	+	0.354128i
$693$		0			0
$694$			2238.82i			3.22596i
$695$	−922.479	−	199.998i	−1.32731	−	0.287768i
$696$		0			0
$697$	0.898953	−	3.35494i	0.00128975	−	0.00481340i
$698$	−78.5153	−	293.023i	−0.112486	−	0.419804i
$699$		0			0
$700$	1434.15	−	881.830i	2.04879	−	1.25976i
$701$	−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
$703$	−315.570	−	84.5567i	−0.448890	−	0.120280i
$704$	425.768	−	245.817i	0.604784	−	0.349172i
$705$		0			0
$706$	541.899			0.767562
$707$	224.882	+	151.389i	0.318079	+	0.214128i
$708$		0			0
$709$	−339.531	−	196.029i	−0.478888	−	0.276486i	0.241065	−	0.970509i	$-0.422503\pi$
$709$	−339.531	−	196.029i	−0.478888	−	0.276486i	−0.719953	+	0.694023i	$0.755837\pi$
$710$	−93.5535	−	1935.49i	−0.131766	−	2.72604i
$711$		0			0
$712$	−1257.36	+	336.910i	−1.76596	+	0.473188i
$713$	−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
$718$	−720.614	−	193.088i	−1.00364	−	0.268925i
$719$	1001.31	+	578.104i	1.39264	+	0.804039i	0.993607	−	0.112898i	$-0.0360134\pi$
$719$	1001.31	+	578.104i	1.39264	+	0.804039i	0.399031	+	0.916938i	$0.369347\pi$
$720$		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
$725$	228.949	−	503.186i	0.315791	−	0.694050i
$726$		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	$0.758638\pi$
$728$	1267.69	+	2593.19i	1.74133	+	3.56208i
$729$		0			0
$730$	−330.552	+	1524.65i	−0.452811	+	2.08856i
$731$	−165.596	−	286.821i	−0.226534	−	0.392368i
$732$		0			0
$733$	−209.185	−	780.690i	−0.285382	−	1.06506i	−0.948559	−	0.316599i	$-0.897459\pi$
$733$	−209.185	−	780.690i	−0.285382	−	1.06506i	0.663177	−	0.748463i	$-0.269208\pi$
$734$			1857.40i			2.53052i
$735$		0			0
$736$	1873.97			2.54616
$737$	−44.0140	+	11.7935i	−0.0597205	+	0.0160021i
$738$		0			0
$739$	452.698	−	261.365i	0.612582	−	0.353674i	−0.161393	−	0.986890i	$-0.551599\pi$
$739$	452.698	−	261.365i	0.612582	−	0.353674i	0.773975	+	0.633216i	$0.218265\pi$
$740$	−403.943	−	627.584i	−0.545869	−	0.848086i
$741$		0			0
$742$	−825.597	+	403.596i	−1.11266	+	0.543930i
$743$	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
$745$	396.642	−	436.934i	0.532405	−	0.586488i
$746$	−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	−0.529614	−	0.848239i	$-0.677663\pi$
$751$	352.812	−	611.088i	0.469790	−	0.813700i	0.999403	+	0.0345394i	$0.0109964\pi$
$752$	−246.124	+	918.547i	−0.327292	+	1.22147i
$753$		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	$0.629490\pi$
$758$	−332.803	−	1242.04i	−0.439054	−	1.63857i
$759$		0			0
$760$	105.432	+	2181.24i	0.138727	+	2.87006i
$761$	692.529	−	1199.50i	0.910025	−	1.57621i	0.0959984	−	0.995381i	$-0.469396\pi$
$761$	692.529	−	1199.50i	0.910025	−	1.57621i	0.814026	−	0.580828i	$-0.197271\pi$
$762$		0			0
$763$	332.162	−	493.414i	0.435337	−	0.646676i
$764$		−	147.442i		−	0.192987i
$765$		0			0
$766$	834.315	+	1445.08i	1.08918	+	1.88652i
$767$	92.6512	−	345.779i	0.120797	−	0.450820i
$768$		0			0
$769$		−	907.238i		−	1.17976i	−0.807490	−	0.589882i	$-0.799174\pi$
$769$		−	907.238i		−	1.17976i	0.807490	−	0.589882i	$-0.200826\pi$
$770$	−547.544	+	904.786i	−0.711096	+	1.17505i
$771$		0			0
$772$	−2091.68	+	560.463i	−2.70942	+	0.725988i
$773$	602.366	+	161.404i	0.779258	+	0.208802i	0.626458	−	0.779456i	$-0.284504\pi$
$773$	602.366	+	161.404i	0.779258	+	0.208802i	0.152800	+	0.988257i	$0.451171\pi$
$774$		0			0
$775$	−66.2036	−	683.229i	−0.0854240	−	0.881586i
$776$	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
$782$	−812.797	+	217.788i	−1.03938	+	0.278502i
$783$		0			0
$784$	−701.950	−	1728.37i	−0.895344	−	2.20455i
$785$	263.770	+	135.750i	0.336013	+	0.172930i
$786$		0			0
$787$	173.435	−	647.269i	0.220375	−	0.822451i	−0.763830	−	0.645418i	$-0.776683\pi$
$787$	173.435	−	647.269i	0.220375	−	0.822451i	0.984205	−	0.177033i	$-0.0566500\pi$
$788$	−3432.51	−	919.738i	−4.35598	−	1.16718i
$789$		0			0
$790$	−844.107	+	1640.15i	−1.06849	+	2.07614i
$791$	−303.346	+	883.579i	−0.383497	+	1.11704i
$792$		0			0
$793$	−138.764	−	517.875i	−0.174986	−	0.653058i
$794$	−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
$800$	−914.223	+	1110.41i	−1.14278	+	1.38801i
$801$		0			0
$802$	−104.438	+	389.768i	−0.130222	+	0.485995i
$803$	−179.151	−	668.599i	−0.223102	−	0.832626i
$804$		0			0
$805$	−998.822	+	549.542i	−1.24077	+	0.682661i
$806$	2014.44			2.49931
$807$		0			0
$808$	−775.935	−	207.911i	−0.960315	−	0.257316i
$809$	1117.27	−	645.054i	1.38105	−	0.797347i	0.388763	−	0.921338i	$-0.372903\pi$
$809$	1117.27	−	645.054i	1.38105	−	0.797347i	0.992283	+	0.123990i	$0.0395692\pi$
$810$		0			0
$811$	−1511.76			−1.86407			−0.932036	−	0.362364i	$-0.881970\pi$
$811$	−1511.76			−1.86407			−0.932036	+	0.362364i	$0.881970\pi$
$812$	−1235.32	−	831.605i	−1.52133	−	1.02414i
$813$		0			0
$814$	406.018	+	234.414i	0.498793	+	0.287978i
$815$	628.146	−	30.3620i	0.770731	−	0.0372540i
$816$		0			0
$817$	962.278	−	257.842i	1.17782	−	0.315596i
$818$	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	−0.409656	−	0.912240i	$-0.634351\pi$
$821$	480.446	−	832.156i	0.585196	−	1.01359i	0.994851	−	0.101348i	$-0.0323156\pi$
$822$		0			0
$823$	25.0572	+	6.71404i	0.0304461	+	0.00815801i	0.274010	−	0.961727i	$-0.411650\pi$
$823$	25.0572	+	6.71404i	0.0304461	+	0.00815801i	−0.243564	+	0.969885i	$0.578317\pi$
$824$	−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	$-0.674036\pi$
$829$	−33.2384	+	19.1902i	−0.0400945	+	0.0231486i	0.479819	+	0.877368i	$0.340702\pi$
$830$	1847.80	+	1677.41i	2.22626	+	2.02097i
$831$		0			0
$832$	−844.088	−	844.088i	−1.01453	−	1.01453i
$833$	206.919	+	273.559i	0.248402	+	0.328402i
$834$		0			0
$835$	180.150	−	115.953i	0.215748	−	0.138866i
$836$	−829.246	−	1436.30i	−0.991922	−	1.71806i
$837$		0			0
$838$	224.274	+	837.002i	0.267630	+	0.998809i
$839$		−	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
$842$	−443.097	+	118.728i	−0.526244	+	0.141007i
$843$		0			0
$844$	3405.65	−	1966.25i	4.03513	−	2.32968i
$845$	−1105.28	−	239.630i	−1.30802	−	0.283586i
$846$		0			0
$847$	−26.0109	+	376.875i	−0.0307094	+	0.444953i
$848$	957.602	−	957.602i	1.12925	−	1.12925i
$849$		0			0
$850$	267.477	−	587.864i	0.314679	−	0.691605i
$851$	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
$857$	58.5645	−	218.566i	0.0683367	−	0.255036i	−0.923303	−	0.384072i	$-0.874522\pi$
$857$	58.5645	−	218.566i	0.0683367	−	0.255036i	0.991640	+	0.129036i	$0.0411882\pi$
$858$		0			0
$859$	54.8471	+	31.6660i	0.0638499	+	0.0368638i	0.531585	−	0.847005i	$-0.321597\pi$
$859$	54.8471	+	31.6660i	0.0638499	+	0.0368638i	−0.467735	+	0.883869i	$0.654930\pi$
$860$	2023.59	+	1041.45i	2.35301	+	1.21098i
$861$		0			0
$862$	−549.575	−	549.575i	−0.637558	−	0.637558i
$863$	189.081	+	705.658i	0.219097	+	0.817680i	0.984684	+	0.174348i	$0.0557819\pi$
$863$	189.081	+	705.658i	0.219097	+	0.817680i	−0.765587	+	0.643332i	$0.777551\pi$
$864$		0			0
$865$	179.908	−	8.69601i	0.207986	−	0.0100532i
$866$	−1432.98	+	2481.99i	−1.65471	+	2.86604i
$867$		0			0
$868$	−1844.66	−	127.313i	−2.12518	−	0.146674i
$869$		−	818.435i		−	0.941812i
$870$		0			0
$871$	55.3194	+	95.8160i	0.0635125	+	0.110007i
$872$	−456.179	+	1702.48i	−0.523141	+	1.95239i
$873$		0			0
$874$		−	2531.13i		−	2.89603i
$875$	161.652	−	859.938i	0.184745	−	0.982786i
$876$		0			0
$877$	−510.621	+	136.821i	−0.582236	+	0.156010i	−0.537903	−	0.843007i	$-0.680783\pi$
$877$	−510.621	+	136.821i	−0.582236	+	0.156010i	−0.0443338	+	0.999017i	$0.514117\pi$
$878$	−341.890	−	91.6092i	−0.389396	−	0.104338i
$879$		0			0
$880$	330.219	−	1523.11i	0.375249	−	1.73081i
$881$	−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
$887$	−22.2503	+	5.96195i	−0.0250849	+	0.00672148i	−0.271340	−	0.962484i	$-0.587467\pi$
$887$	−22.2503	+	5.96195i	−0.0250849	+	0.00672148i	0.246255	+	0.969205i	$0.420800\pi$
$888$		0			0
$889$	1371.99	+	471.025i	1.54330	+	0.529837i
$890$	−529.919	+	1029.66i	−0.595415	+	1.15693i
$891$		0			0
$892$	−634.270	+	2367.13i	−0.711065	+	2.65373i
$893$	508.023	+	136.124i	0.568895	+	0.152435i
$894$		0			0
$895$	115.358	+	360.005i	0.128892	+	0.402240i
$896$	−39.1713	−	44.9791i	−0.0437179	−	0.0501999i
$897$		0			0
$898$	−328.881	−	1227.40i	−0.366237	−	1.36681i
$899$	−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
$905$	−193.257	+	891.384i	−0.213543	+	0.984954i
$906$		0			0
$907$	209.826	−	783.082i	0.231341	−	0.863376i	−0.748424	−	0.663221i	$-0.769189\pi$
$907$	209.826	−	783.082i	0.231341	−	0.863376i	0.979764	−	0.200155i	$-0.0641444\pi$
$908$	−546.463	−	2039.43i	−0.601832	−	2.24607i
$909$		0			0
$910$	2466.11	+	715.578i	2.71002	+	0.786350i
$911$	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
$913$	−1069.54	−	286.583i	−1.17146	−	0.313891i
$914$	275.520	−	159.072i	0.301445	−	0.174039i
$915$		0			0
$916$	3243.84			3.54131
$917$	−55.4003	+	802.703i	−0.0604147	+	0.875357i
$918$		0			0
$919$	838.092	+	483.873i	0.911961	+	0.526521i	0.881061	−	0.473002i	$-0.156830\pi$
$919$	838.092	+	483.873i	0.911961	+	0.526521i	0.0308992	+	0.999523i	$0.490163\pi$
$920$	2270.60	−	2501.25i	2.46804	−	2.71875i
$921$		0			0
$922$	2205.18	−	590.877i	2.39174	−	0.640864i
$923$	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
$928$	1228.88	+	329.278i	1.32423	+	0.354825i
$929$	−985.363	−	568.900i	−1.06067	−	0.612379i	−0.135053	−	0.990838i	$-0.543121\pi$
$929$	−985.363	−	568.900i	−1.06067	−	0.612379i	−0.925618	+	0.378460i	$0.876454\pi$
$930$		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
$935$	13.8349	+	286.224i	0.0147967	+	0.306122i
$936$		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	$0.574065\pi$
$938$	−63.1458	−	129.171i	−0.0673196	−	0.137709i
$939$		0			0
$940$	650.293	+	1010.32i	0.691801	+	1.07481i
$941$	−175.936	−	304.730i	−0.186967	−	0.323836i	0.757271	−	0.653101i	$-0.226532\pi$
$941$	−175.936	−	304.730i	−0.186967	−	0.323836i	−0.944238	+	0.329265i	$0.893199\pi$
$942$		0			0
$943$	−4.18294	−	15.6109i	−0.00443578	−	0.0165545i
$944$		−	685.559i		−	0.726228i
$945$		0			0
$946$	−1429.62			−1.51122
$947$	1535.53	−	411.444i	1.62147	−	0.434471i	0.670034	−	0.742330i	$-0.266279\pi$
$947$	1535.53	−	411.444i	1.62147	−	0.434471i	0.951432	+	0.307859i	$0.0996126\pi$
$948$		0			0
$949$	−1455.50	+	840.334i	−1.53372	+	0.885495i
$950$	1499.80	+	1234.82i	1.57874	+	1.29981i
$951$		0			0
$952$	−843.143	−	567.597i	−0.885654	−	0.596216i
$953$	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
$955$	−56.7383	−	51.5062i	−0.0594118	−	0.0539332i
$956$	−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
$962$	294.626	−	1099.56i	0.306264	−	1.14299i
$963$		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	$0.847483\pi$
$968$	−289.729	−	1081.28i	−0.299307	−	1.11703i
$969$		0			0
$970$	1035.17	−	1140.32i	1.06718	−	1.17559i
$971$	281.316	−	487.254i	0.289718	−	0.501806i	−0.684024	−	0.729459i	$-0.739772\pi$
$971$	281.316	−	487.254i	0.289718	−	0.501806i	0.973742	+	0.227653i	$0.0731052\pi$
$972$		0			0
$973$	580.371	+	1187.21i	0.596476	+	1.22015i
$974$		−	937.436i		−	0.962460i
$975$		0			0
$976$	−513.383	−	889.205i	−0.526007	−	0.911071i
$977$	−445.096	+	1661.12i	−0.455575	+	1.70023i	0.230818	+	0.972997i	$0.425860\pi$
$977$	−445.096	+	1661.12i	−0.455575	+	1.70023i	−0.686393	+	0.727231i	$0.740807\pi$
$978$		0			0
$979$		−	513.802i		−	0.524823i
$980$	−2213.04	−	811.127i	−2.25820	−	0.827681i
$981$		0			0
$982$	−983.168	+	263.439i	−1.00119	+	0.268268i
$983$	−342.084	−	91.6612i	−0.348000	−	0.0932463i	0.0805851	−	0.996748i	$-0.474321\pi$
$983$	−342.084	−	91.6612i	−0.348000	−	0.0932463i	−0.428585	+	0.903501i	$0.640988\pi$
$984$		0			0
$985$	−1553.01	+	999.594i	−1.57666	+	1.01482i
$986$	−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	0.559623	−	0.828747i	$-0.310946\pi$
$991$	−433.964	−	751.647i	−0.437905	−	0.758473i	−0.997528	+	0.0702740i	$0.977613\pi$
$992$	1525.88	−	408.857i	1.53818	−	0.412154i
$993$		0			0
$994$	−2045.80	+	1781.64i	−2.05815	+	1.79239i
$995$	−100.602	−	313.954i	−0.101107	−	0.315532i
$996$		0			0
$997$	−380.153	+	1418.75i	−0.381297	+	1.42302i	0.462625	+	0.886554i	$0.346908\pi$
$997$	−380.153	+	1418.75i	−0.381297	+	1.42302i	−0.843922	+	0.536466i	$0.819759\pi$
$998$	2142.04	+	573.959i	2.14634	+	0.575109i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.v.a.37.1	✓	64	3.2	odd	2
105.3.v.a.58.16	yes	64	15.8	even	4
105.3.v.a.67.16	yes	64	21.11	odd	6
105.3.v.a.88.1	yes	64	105.53	even	12
315.3.ca.b.37.16		64	1.1	even	1	trivial
315.3.ca.b.163.1		64	5.3	odd	4	inner
315.3.ca.b.172.1		64	7.4	even	3	inner
315.3.ca.b.298.16		64	35.18	odd	12	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)

\(f(q)\)	\(=\)	\(q+(3.56483 - 0.955194i) q^{2} +(8.33154 - 4.81021i) q^{4} +(1.05941 - 4.88648i) q^{5} +(-6.28878 + 3.07429i) q^{7} +(14.6673 - 14.6673i) q^{8} +O(q^{10})\)	\(q+(3.56483 - 0.955194i) q^{2} +(8.33154 - 4.81021i) q^{4} +(1.05941 - 4.88648i) q^{5} +(-6.28878 + 3.07429i) q^{7} +(14.6673 - 14.6673i) q^{8} +(-0.890898 - 18.4314i) q^{10} +(4.09367 + 7.09045i) q^{11} +(14.0569 - 14.0569i) q^{13} +(-19.4819 + 16.9663i) q^{14} +(19.0355 - 32.9704i) q^{16} +(-1.81174 + 6.76150i) q^{17} +(-18.2350 - 10.5280i) q^{19} +(-14.6784 - 45.8079i) q^{20} +(21.3660 + 21.3660i) q^{22} +(8.43024 + 31.4621i) q^{23} +(-22.7553 - 10.3536i) q^{25} +(36.6833 - 63.5374i) q^{26} +(-37.6072 + 55.8639i) q^{28} +22.1129i q^{29} +(13.7286 + 23.7786i) q^{31} +(14.8907 - 55.5730i) q^{32} +25.8342i q^{34} +(8.36003 + 33.9869i) q^{35} +(14.9872 - 4.01580i) q^{37} +(-75.0611 - 20.1126i) q^{38} +(-56.1326 - 87.2101i) q^{40} -0.496183 q^{41} +(-33.4554 + 33.4554i) q^{43} +(68.2132 + 39.3829i) q^{44} +(60.1048 + 104.105i) q^{46} +(-24.1272 + 6.46488i) q^{47} +(30.0975 - 38.6671i) q^{49} +(-91.0085 - 15.1731i) q^{50} +(49.4987 - 184.732i) q^{52} +(34.3598 + 9.20667i) q^{53} +(38.9842 - 12.4919i) q^{55} +(-47.1478 + 137.331i) q^{56} +(21.1222 + 78.8289i) q^{58} +(15.5949 - 9.00371i) q^{59} +(13.4849 - 23.3565i) q^{61} +(71.6533 + 71.6533i) q^{62} -60.0481i q^{64} +(-53.7965 - 83.5806i) q^{65} +(-1.44046 + 5.37586i) q^{67} +(17.4297 + 65.0485i) q^{68} +(62.2662 + 113.172i) q^{70} +105.010 q^{71} +(-81.6625 - 21.8814i) q^{73} +(49.5909 - 28.6313i) q^{74} -202.568 q^{76} +(-47.5423 - 32.0051i) q^{77} +(-86.5708 - 49.9817i) q^{79} +(-140.943 - 127.946i) q^{80} +(-1.76881 + 0.473951i) q^{82} +(-95.6303 + 95.6303i) q^{83} +(31.1205 + 16.0162i) q^{85} +(-87.3064 + 151.219i) q^{86} +(164.041 + 43.9546i) q^{88} +(-54.3480 - 31.3778i) q^{89} +(-45.1856 + 131.615i) q^{91} +(221.576 + 221.576i) q^{92} +(-79.8344 + 46.0924i) q^{94} +(-70.7633 + 77.9515i) q^{95} +(59.0158 + 59.0158i) q^{97} +(70.3578 - 166.591i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8}+O(q^{10}) \) 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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