LMFDB - Embedded newform 225.3.o.b.157.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [225,3,Mod(7,225)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(225, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([8, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("225.7"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	225.o (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.13080594811$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			157.2
Character	$\chi$	$=$	225.157
Dual form			225.3.o.b.43.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.863931 + 3.22423i) q^{2} +(2.79645 + 1.08621i) q^{3} +(-6.18520 - 3.57103i) q^{4} +(-5.91814 + 8.07800i) q^{6} +(-2.35787 + 8.79970i) q^{7} +(7.41620 - 7.41620i) q^{8} +(6.64028 + 6.07508i) q^{9} +(1.02371 + 1.77311i) q^{11} +(-13.4177 - 16.7046i) q^{12} +(1.12075 + 4.18269i) q^{13} +(-26.3352 - 15.2047i) q^{14} +(3.22036 + 5.57783i) q^{16} +(-17.1585 - 17.1585i) q^{17} +(-25.3242 + 16.1614i) q^{18} +18.6363i q^{19} +(-16.1520 + 22.0468i) q^{21} +(-6.60133 + 1.76882i) q^{22} +(-3.08350 - 11.5078i) q^{23} +(28.7946 - 12.6835i) q^{24} -14.4542 q^{26} +(11.9704 + 24.2014i) q^{27} +(46.0079 - 46.0079i) q^{28} +(-19.4918 + 11.2536i) q^{29} +(11.9368 - 20.6752i) q^{31} +(19.7565 - 5.29373i) q^{32} +(0.936770 + 6.07038i) q^{33} +(70.1467 - 40.4992i) q^{34} +(-19.3772 - 61.2882i) q^{36} +(33.2840 + 33.2840i) q^{37} +(-60.0877 - 16.1005i) q^{38} +(-1.40917 + 12.9141i) q^{39} +(2.15756 - 3.73700i) q^{41} +(-57.1297 - 71.1247i) q^{42} +(30.4181 + 8.15051i) q^{43} -14.6227i q^{44} +39.7677 q^{46} +(-0.224807 + 0.838990i) q^{47} +(2.94688 + 19.0961i) q^{48} +(-29.4398 - 16.9971i) q^{49} +(-29.3451 - 66.6207i) q^{51} +(8.00445 - 29.8730i) q^{52} +(3.33316 - 3.33316i) q^{53} +(-88.3727 + 17.6870i) q^{54} +(47.7739 + 82.7467i) q^{56} +(-20.2430 + 52.1155i) q^{57} +(-19.4446 - 72.5684i) q^{58} +(66.3254 + 38.2930i) q^{59} +(35.3623 + 61.2493i) q^{61} +(56.3490 + 56.3490i) q^{62} +(-69.1158 + 44.1082i) q^{63} +94.0358i q^{64} +(-20.3816 - 2.22403i) q^{66} +(20.8965 - 5.59919i) q^{67} +(44.8553 + 167.402i) q^{68} +(3.87703 - 35.5302i) q^{69} -28.6105 q^{71} +(94.2997 - 4.19166i) q^{72} +(-48.1316 + 48.1316i) q^{73} +(-136.071 + 78.5604i) q^{74} +(66.5507 - 115.269i) q^{76} +(-18.0166 + 4.82753i) q^{77} +(-40.4205 - 15.7004i) q^{78} +(0.201686 - 0.116444i) q^{79} +(7.18677 + 80.6805i) q^{81} +(10.1850 + 10.1850i) q^{82} +(153.477 + 41.1240i) q^{83} +(178.633 - 78.6845i) q^{84} +(-52.5583 + 91.0337i) q^{86} +(-66.7316 + 10.2979i) q^{87} +(20.7418 + 5.55774i) q^{88} -103.385i q^{89} -39.4490 q^{91} +(-22.0225 + 82.1891i) q^{92} +(55.8384 - 44.8512i) q^{93} +(-2.51088 - 1.44966i) q^{94} +(60.9981 + 6.65606i) q^{96} +(18.6837 - 69.7287i) q^{97} +(80.2366 - 80.2366i) q^{98} +(-3.97409 + 17.9931i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 2 q^{2} + 6 q^{3} - 24 q^{6} + 2 q^{7} + 24 q^{8} + 8 q^{11} + 30 q^{12} + 2 q^{13} + 28 q^{16} - 28 q^{17} - 48 q^{18} + 12 q^{21} - 14 q^{22} - 82 q^{23} - 112 q^{26} + 198 q^{27} + 88 q^{28} - 4 q^{31}+ \cdots + 1876 q^{98}+O(q^{100}) $ 40 * q + 2 * q^2 + 6 * q^3 - 24 * q^6 + 2 * q^7 + 24 * q^8 + 8 * q^11 + 30 * q^12 + 2 * q^13 + 28 * q^16 - 28 * q^17 - 48 * q^18 + 12 * q^21 - 14 * q^22 - 82 * q^23 - 112 * q^26 + 198 * q^27 + 88 * q^28 - 4 * q^31 + 14 * q^32 - 96 * q^33 + 264 * q^36 + 92 * q^37 - 330 * q^38 - 28 * q^41 - 498 * q^42 + 2 * q^43 - 136 * q^46 - 64 * q^47 + 510 * q^48 - 396 * q^51 + 74 * q^52 + 608 * q^53 - 192 * q^56 + 114 * q^57 - 30 * q^58 + 92 * q^61 + 100 * q^62 - 24 * q^63 + 588 * q^66 + 80 * q^67 - 626 * q^68 + 248 * q^71 + 162 * q^72 + 8 * q^73 - 96 * q^76 - 338 * q^77 - 1062 * q^78 + 204 * q^81 - 104 * q^82 - 370 * q^83 - 328 * q^86 - 534 * q^87 + 210 * q^88 + 152 * q^91 - 388 * q^92 + 1062 * q^93 - 876 * q^96 - 292 * q^97 + 1876 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.863931	+	3.22423i	−0.431965	+	1.61212i	0.316261	+	0.948672i	$0.397573\pi$
$2$	−0.863931	+	3.22423i	−0.431965	+	1.61212i	−0.748226	+	0.663444i	$0.769094\pi$
$3$	2.79645	+	1.08621i	0.932151	+	0.362071i
$3$	2.79645	+	1.08621i	0.932151	+	0.362071i
$4$	−6.18520	−	3.57103i	−1.54630	−	0.892757i
$5$		0			0
$5$		0			0
$6$	−5.91814	+	8.07800i	−0.986357	+	1.34633i
$7$	−2.35787	+	8.79970i	−0.336839	+	1.25710i	0.565023	+	0.825075i	$0.308867\pi$
$7$	−2.35787	+	8.79970i	−0.336839	+	1.25710i	−0.901862	+	0.432024i	$0.857799\pi$
$8$	7.41620	−	7.41620i	0.927025	−	0.927025i
$9$	6.64028	+	6.07508i	0.737809	+	0.675009i
$10$		0			0
$11$	1.02371	+	1.77311i	0.0930642	+	0.161192i	0.908799	−	0.417234i	$-0.137000\pi$
$11$	1.02371	+	1.77311i	0.0930642	+	0.161192i	−0.815735	+	0.578426i	$0.803667\pi$
$12$	−13.4177	−	16.7046i	−1.11814	−	1.39205i
$13$	1.12075	+	4.18269i	0.0862115	+	0.321746i	0.995541	−	0.0943314i	$-0.0300713\pi$
$13$	1.12075	+	4.18269i	0.0862115	+	0.321746i	−0.909329	+	0.416077i	$0.863405\pi$
$14$	−26.3352	−	15.2047i	−1.88109	−	1.08605i
$15$		0			0
$16$	3.22036	+	5.57783i	0.201273	+	0.348615i
$17$	−17.1585	−	17.1585i	−1.00932	−	1.00932i	−0.999956	−	0.00936716i	$-0.997018\pi$
$17$	−17.1585	−	17.1585i	−1.00932	−	1.00932i	−0.00936716	−	0.999956i	$-0.502982\pi$
$18$	−25.3242	+	16.1614i	−1.40690	+	0.897854i
$19$			18.6363i			0.980857i	0.871481	+	0.490428i	$0.163160\pi$
$19$			18.6363i			0.980857i	−0.871481	+	0.490428i	$0.836840\pi$
$20$		0			0
$21$	−16.1520	+	22.0468i	−0.769143	+	1.04985i
$22$	−6.60133	+	1.76882i	−0.300061	+	0.0804010i
$23$	−3.08350	−	11.5078i	−0.134065	−	0.500338i	−1.00000		0.000180980i	$-0.999942\pi$
$23$	−3.08350	−	11.5078i	−0.134065	−	0.500338i	0.865935	−	0.500157i	$-0.166724\pi$
$24$	28.7946	−	12.6835i	1.19978	−	0.528478i
$25$		0			0
$26$	−14.4542			−0.555932
$27$	11.9704	+	24.2014i	0.443348	+	0.896349i
$28$	46.0079	−	46.0079i	1.64314	−	1.64314i
$29$	−19.4918	+	11.2536i	−0.672131	+	0.388055i	−0.796883	−	0.604133i	$-0.793520\pi$
$29$	−19.4918	+	11.2536i	−0.672131	+	0.388055i	0.124753	+	0.992188i	$0.460186\pi$
$30$		0			0
$31$	11.9368	−	20.6752i	0.385059	−	0.666941i	−0.606719	−	0.794917i	$-0.707514\pi$
$31$	11.9368	−	20.6752i	0.385059	−	0.666941i	0.991777	+	0.127975i	$0.0408478\pi$
$32$	19.7565	−	5.29373i	0.617389	−	0.165429i
$33$	0.936770	+	6.07038i	0.0283870	+	0.183951i
$34$	70.1467	−	40.4992i	2.06314	−	1.19115i
$35$		0			0
$36$	−19.3772	−	61.2882i	−0.538256	−	1.70245i
$37$	33.2840	+	33.2840i	0.899568	+	0.899568i	0.995398	−	0.0958294i	$-0.0305503\pi$
$37$	33.2840	+	33.2840i	0.899568	+	0.899568i	−0.0958294	+	0.995398i	$0.530550\pi$
$38$	−60.0877	−	16.1005i	−1.58126	−	0.423696i
$39$	−1.40917	+	12.9141i	−0.0361326	+	0.331130i
$40$		0			0
$41$	2.15756	−	3.73700i	0.0526234	−	0.0911464i	−0.838514	−	0.544880i	$-0.816575\pi$
$41$	2.15756	−	3.73700i	0.0526234	−	0.0911464i	0.891137	+	0.453734i	$0.149908\pi$
$42$	−57.1297	−	71.1247i	−1.36023	−	1.69345i
$43$	30.4181	+	8.15051i	0.707398	+	0.189547i	0.594542	−	0.804065i	$-0.297333\pi$
$43$	30.4181	+	8.15051i	0.707398	+	0.189547i	0.112856	+	0.993611i	$0.464000\pi$
$44$		−	14.6227i		−	0.332335i
$45$		0			0
$46$	39.7677			0.864514
$47$	−0.224807	+	0.838990i	−0.00478312	+	0.0178509i	−0.968276	−	0.249883i	$-0.919608\pi$
$47$	−0.224807	+	0.838990i	−0.00478312	+	0.0178509i	0.963493	+	0.267733i	$0.0862746\pi$
$48$	2.94688	+	19.0961i	0.0613933	+	0.397836i
$49$	−29.4398	−	16.9971i	−0.600813	−	0.346880i
$50$		0			0
$51$	−29.3451	−	66.6207i	−0.575395	−	1.30629i
$52$	8.00445	−	29.8730i	0.153932	−	0.574481i
$53$	3.33316	−	3.33316i	0.0628899	−	0.0628899i	−0.674962	−	0.737852i	$-0.735840\pi$
$53$	3.33316	−	3.33316i	0.0628899	−	0.0628899i	0.737852	+	0.674962i	$0.235840\pi$
$54$	−88.3727	+	17.6870i	−1.63653	+	0.327537i
$55$		0			0
$56$	47.7739	+	82.7467i	0.853105	+	1.47762i
$57$	−20.2430	+	52.1155i	−0.355140	+	0.914306i
$58$	−19.4446	−	72.5684i	−0.335252	−	1.25118i
$59$	66.3254	+	38.2930i	1.12416	+	0.649033i	0.942459	−	0.334321i	$-0.108507\pi$
$59$	66.3254	+	38.2930i	1.12416	+	0.649033i	0.181699	+	0.983354i	$0.441840\pi$
$60$		0			0
$61$	35.3623	+	61.2493i	0.579710	+	1.00409i	0.995512	+	0.0946322i	$0.0301675\pi$
$61$	35.3623	+	61.2493i	0.579710	+	1.00409i	−0.415802	+	0.909455i	$0.636499\pi$
$62$	56.3490	+	56.3490i	0.908855	+	0.908855i
$63$	−69.1158	+	44.1082i	−1.09708	+	0.700131i
$64$			94.0358i			1.46931i
$65$		0			0
$66$	−20.3816	−	2.22403i	−0.308813	−	0.0336974i
$67$	20.8965	−	5.59919i	0.311888	−	0.0835700i	−0.0994800	−	0.995040i	$-0.531718\pi$
$67$	20.8965	−	5.59919i	0.311888	−	0.0835700i	0.411368	+	0.911470i	$0.365051\pi$
$68$	44.8553	+	167.402i	0.659637	+	2.46180i
$69$	3.87703	−	35.5302i	0.0561888	−	0.514931i
$70$		0			0
$71$	−28.6105			−0.402965			−0.201483	−	0.979492i	$-0.564576\pi$
$71$	−28.6105			−0.402965			−0.201483	+	0.979492i	$0.564576\pi$
$72$	94.2997	−	4.19166i	1.30972	−	0.0582175i
$73$	−48.1316	+	48.1316i	−0.659336	+	0.659336i	−0.955223	−	0.295887i	$-0.904385\pi$
$73$	−48.1316	+	48.1316i	−0.659336	+	0.659336i	0.295887	+	0.955223i	$0.404385\pi$
$74$	−136.071	+	78.5604i	−1.83879	+	1.06163i
$75$		0			0
$76$	66.5507	−	115.269i	0.875667	−	1.51670i
$77$	−18.0166	+	4.82753i	−0.233982	+	0.0626953i
$78$	−40.4205	−	15.7004i	−0.518212	−	0.201287i
$79$	0.201686	−	0.116444i	0.00255299	−	0.00147397i	−0.498723	−	0.866761i	$-0.666197\pi$
$79$	0.201686	−	0.116444i	0.00255299	−	0.00147397i	0.501276	+	0.865287i	$0.332864\pi$
$80$		0			0
$81$	7.18677	+	80.6805i	0.0887255	+	0.996056i
$82$	10.1850	+	10.1850i	0.124207	+	0.124207i
$83$	153.477	+	41.1240i	1.84912	+	0.495470i	0.999491	−	0.0319094i	$-0.0101588\pi$
$83$	153.477	+	41.1240i	1.84912	+	0.495470i	0.849630	+	0.527380i	$0.176825\pi$
$84$	178.633	−	78.6845i	2.12658	−	0.936720i
$85$		0			0
$86$	−52.5583	+	91.0337i	−0.611143	+	1.05853i
$87$	−66.7316	+	10.2979i	−0.767030	+	0.118367i
$88$	20.7418	+	5.55774i	0.235702	+	0.0631561i
$89$		−	103.385i		−	1.16163i	−0.814035	−	0.580816i	$-0.802734\pi$
$89$		−	103.385i		−	1.16163i	0.814035	−	0.580816i	$-0.197266\pi$
$90$		0			0
$91$	−39.4490			−0.433506
$92$	−22.0225	+	82.1891i	−0.239375	+	0.893360i
$93$	55.8384	−	44.8512i	0.600413	−	0.482271i
$94$	−2.51088	−	1.44966i	−0.0267115	−	0.0154219i
$95$		0			0
$96$	60.9981	+	6.65606i	0.635397	+	0.0693340i
$97$	18.6837	−	69.7287i	0.192616	−	0.718852i	−0.800255	−	0.599660i	$-0.795303\pi$
$97$	18.6837	−	69.7287i	0.192616	−	0.718852i	0.992871	−	0.119193i	$-0.0380306\pi$
$98$	80.2366	−	80.2366i	0.818741	−	0.818741i
$99$	−3.97409	+	17.9931i	−0.0401424	+	0.181748i
$100$		0			0
$101$	−31.0086	−	53.7085i	−0.307016	−	0.531767i	0.670692	−	0.741736i	$-0.265997\pi$
$101$	−31.0086	−	53.7085i	−0.307016	−	0.531767i	−0.977708	+	0.209969i	$0.932664\pi$
$102$	240.153	−	37.0599i	2.35444	−	0.363332i
$103$	13.6798	+	51.0537i	0.132813	+	0.495667i	0.999997	−	0.00232157i	$-0.000738981\pi$
$103$	13.6798	+	51.0537i	0.132813	+	0.495667i	−0.867184	+	0.497988i	$0.834072\pi$
$104$	39.3314	+	22.7080i	0.378186	+	0.218346i
$105$		0			0
$106$	7.86727	+	13.6265i	0.0742195	+	0.128552i
$107$	−84.3909	−	84.3909i	−0.788700	−	0.788700i	0.192581	−	0.981281i	$-0.438314\pi$
$107$	−84.3909	−	84.3909i	−0.788700	−	0.788700i	−0.981281	+	0.192581i	$0.938314\pi$
$108$	12.3846	−	192.437i	0.114672	−	1.78183i
$109$			102.481i			0.940190i	0.882616	+	0.470095i	$0.155780\pi$
$109$			102.481i			0.940190i	−0.882616	+	0.470095i	$0.844220\pi$
$110$		0			0
$111$	56.9237	+	129.231i	0.512826	+	1.16424i
$112$	−56.6764	+	15.1864i	−0.506040	+	0.135593i
$113$	10.5178	+	39.2529i	0.0930777	+	0.347371i	0.996721	−	0.0809152i	$-0.0257843\pi$
$113$	10.5178	+	39.2529i	0.0930777	+	0.347371i	−0.903643	+	0.428286i	$0.859118\pi$
$114$	−150.544	−	110.292i	−1.32056	−	0.967475i
$115$		0			0
$116$	160.747			1.38575
$117$	−17.9681	+	34.5829i	−0.153574	+	0.295580i
$118$	−180.766	+	180.766i	−1.53192	+	1.53192i
$119$	191.447	−	110.532i	1.60880	−	0.928840i
$120$		0			0
$121$	58.4041	−	101.159i	0.482678	−	0.836023i
$122$	−228.033	+	61.1012i	−1.86912	+	0.500829i
$123$	10.0927	−	8.10678i	0.0820544	−	0.0659088i
$124$	−147.663	+	85.2534i	−1.19083	+	0.687528i
$125$		0			0
$126$	−82.5039	−	260.952i	−0.654793	−	2.07105i
$127$	81.3527	+	81.3527i	0.640572	+	0.640572i	0.950696	−	0.310124i	$-0.100370\pi$
$127$	81.3527	+	81.3527i	0.640572	+	0.640572i	−0.310124	+	0.950696i	$0.600370\pi$
$128$	−224.167	−	60.0655i	−1.75131	−	0.469261i
$129$	76.2096	+	55.8331i	0.590772	+	0.432814i
$130$		0			0
$131$	−41.3420	+	71.6064i	−0.315588	+	0.546614i	−0.979562	−	0.201141i	$-0.935535\pi$
$131$	−41.3420	+	71.6064i	−0.315588	+	0.546614i	0.663975	+	0.747755i	$0.268868\pi$
$132$	15.8834	−	40.8918i	0.120329	−	0.309786i
$133$	−163.994	−	43.9420i	−1.23303	−	0.330391i
$134$			72.2124i			0.538899i
$135$		0			0
$136$	−254.502			−1.87134
$137$	40.3630	−	150.637i	0.294621	−	1.09954i	−0.646898	−	0.762577i	$-0.723934\pi$
$137$	40.3630	−	150.637i	0.294621	−	1.09954i	0.941518	−	0.336962i	$-0.109399\pi$
$138$	111.208	+	43.1961i	0.805857	+	0.313015i
$139$	−1.35272	−	0.780993i	−0.00973180	−	0.00561866i	0.495126	−	0.868821i	$-0.335122\pi$
$139$	−1.35272	−	0.780993i	−0.00973180	−	0.00561866i	−0.504858	+	0.863202i	$0.668455\pi$
$140$		0			0
$141$	−1.53998	+	2.10201i	−0.0109219	+	0.0149079i
$142$	24.7175	−	92.2470i	0.174067	−	0.649627i
$143$	−6.26906	+	6.26906i	−0.0438396	+	0.0438396i
$144$	−12.5017	+	56.6024i	−0.0868171	+	0.393072i
$145$		0			0
$146$	−113.605	−	196.770i	−0.778117	−	1.34774i
$147$	−63.8646	−	79.5095i	−0.434453	−	0.540881i
$148$	−87.0102	−	324.727i	−0.587907	−	2.19410i
$149$	−87.4092	−	50.4657i	−0.586639	−	0.338696i	0.177128	−	0.984188i	$-0.443319\pi$
$149$	−87.4092	−	50.4657i	−0.586639	−	0.338696i	−0.763767	+	0.645492i	$0.776653\pi$
$150$		0			0
$151$	−109.094	−	188.956i	−0.722477	−	1.25137i	−0.960004	−	0.279986i	$-0.909670\pi$
$151$	−109.094	−	188.956i	−0.722477	−	1.25137i	0.237527	−	0.971381i	$-0.423663\pi$
$152$	138.210	+	138.210i	0.909279	+	0.909279i
$153$	−9.69804	−	218.177i	−0.0633859	−	1.42599i
$154$		−	62.2604i		−	0.404288i
$155$		0			0
$156$	54.8325	−	74.8439i	0.351490	−	0.479769i
$157$	−256.443	+	68.7136i	−1.63339	+	0.437666i	−0.954897	−	0.296937i	$-0.904035\pi$
$157$	−256.443	+	68.7136i	−1.63339	+	0.437666i	−0.678496	+	0.734604i	$0.737368\pi$
$158$	0.201198	+	0.750883i	0.00127341	+	0.00475242i
$159$	12.9416	−	5.70051i	0.0813934	−	0.0358522i
$160$		0			0
$161$	108.535			0.674133
$162$	−266.342	−	46.5306i	−1.64408	−	0.287226i
$163$	161.076	−	161.076i	0.988199	−	0.988199i	−0.0117324	−	0.999931i	$-0.503735\pi$
$163$	161.076	−	161.076i	0.988199	−	0.988199i	0.999931	+	0.0117324i	$0.00373463\pi$
$164$	−26.6899	+	15.4094i	−0.162743	+	0.0939598i
$165$		0			0
$166$	−265.187	+	459.317i	−1.59751	+	2.76697i
$167$	57.6223	−	15.4399i	0.345044	−	0.0924542i	−0.0821354	−	0.996621i	$-0.526174\pi$
$167$	57.6223	−	15.4399i	0.345044	−	0.0924542i	0.427179	+	0.904167i	$0.359507\pi$
$168$	43.7167	+	283.290i	0.260219	+	1.68625i
$169$	130.119	−	75.1245i	0.769938	−	0.444524i
$170$		0			0
$171$	−113.217	+	123.750i	−0.662087	+	0.723685i
$172$	−159.037	−	159.037i	−0.924631	−	0.924631i
$173$	93.6378	+	25.0902i	0.541259	+	0.145030i	0.519083	−	0.854724i	$-0.326274\pi$
$173$	93.6378	+	25.0902i	0.541259	+	0.145030i	0.0221766	+	0.999754i	$0.492940\pi$
$174$	24.4487	−	224.055i	0.140510	−	1.28767i
$175$		0			0
$176$	−6.59341	+	11.4201i	−0.0374626	+	0.0648871i
$177$	143.881	+	179.128i	0.812889	+	1.01202i
$178$	333.338	+	89.3176i	1.87269	+	0.501784i
$179$		−	89.4315i		−	0.499617i	−0.968295	−	0.249809i	$-0.919632\pi$
$179$		−	89.4315i		−	0.499617i	0.968295	−	0.249809i	$-0.0803677\pi$
$180$		0			0
$181$	307.336			1.69799			0.848995	−	0.528401i	$-0.177208\pi$
$181$	307.336			1.69799			0.848995	+	0.528401i	$0.177208\pi$
$182$	34.0812	−	127.193i	0.187259	−	0.698861i
$183$	32.3592	+	209.692i	0.176826	+	1.14586i
$184$	−108.212	−	62.4761i	−0.588107	−	0.339544i
$185$		0			0
$186$	96.3703	+	218.784i	0.518120	+	1.17626i
$187$	12.8587	−	47.9892i	0.0687629	−	0.256627i
$188$	4.38653	−	4.38653i	0.0233326	−	0.0233326i
$189$	−241.190	+	48.2721i	−1.27614	+	0.255408i
$190$		0			0
$191$	81.7990	+	141.680i	0.428267	+	0.741780i	0.996719	−	0.0809360i	$-0.0257910\pi$
$191$	81.7990	+	141.680i	0.428267	+	0.741780i	−0.568452	+	0.822716i	$0.692458\pi$
$192$	−102.143	+	262.966i	−0.531994	+	1.36962i
$193$	65.7869	+	245.520i	0.340865	+	1.27212i	0.897369	+	0.441280i	$0.145476\pi$
$193$	65.7869	+	245.520i	0.340865	+	1.27212i	−0.556504	+	0.830845i	$0.687858\pi$
$194$	208.680	+	120.481i	1.07567	+	0.621039i
$195$		0			0
$196$	121.394	+	210.261i	0.619358	+	1.07276i
$197$	83.9878	+	83.9878i	0.426334	+	0.426334i	0.887377	−	0.461044i	$-0.152525\pi$
$197$	83.9878	+	83.9878i	0.426334	+	0.426334i	−0.461044	+	0.887377i	$0.652525\pi$
$198$	−54.5805	−	28.3582i	−0.275659	−	0.143223i
$199$		−	165.065i		−	0.829471i	−0.909942	−	0.414736i	$-0.863874\pi$
$199$		−	165.065i		−	0.829471i	0.909942	−	0.414736i	$-0.136126\pi$
$200$		0			0
$201$	64.5179	+	7.04014i	0.320985	+	0.0350256i
$202$	199.958	−	53.5786i	0.989891	−	0.265240i
$203$	−53.0690	−	198.056i	−0.261424	−	0.975647i
$204$	−56.3987	+	516.855i	−0.276464	+	2.53360i
$205$		0			0
$206$	−176.427			−0.856443
$207$	49.4353	−	95.1473i	0.238818	−	0.459649i
$208$	−19.7211	+	19.7211i	−0.0948132	+	0.0948132i
$209$	−33.0442	+	19.0781i	−0.158106	+	0.0912827i
$210$		0			0
$211$	5.87275	−	10.1719i	0.0278329	−	0.0482081i	−0.851773	−	0.523910i	$-0.824473\pi$
$211$	5.87275	−	10.1719i	0.0278329	−	0.0482081i	0.879606	+	0.475702i	$0.157806\pi$
$212$	−32.5191	+	8.71347i	−0.153392	+	0.0411013i
$213$	−80.0080	−	31.0771i	−0.375624	−	0.145902i
$214$	345.004	−	199.188i	1.61217	−	0.930785i
$215$		0			0
$216$	268.258	+	90.7077i	1.24193	+	0.419943i
$217$	153.790	+	153.790i	0.708709	+	0.708709i
$218$	−330.422	−	88.5362i	−1.51570	−	0.406129i
$219$	−186.879	+	82.3165i	−0.853327	+	0.375874i
$220$		0			0
$221$	52.5383	−	90.9991i	0.237730	−	0.411761i
$222$	−465.848	+	71.8888i	−2.09841	+	0.323823i
$223$	−12.3702	−	3.31460i	−0.0554720	−	0.0148637i	0.230976	−	0.972959i	$-0.425808\pi$
$223$	−12.3702	−	3.31460i	−0.0554720	−	0.0148637i	−0.286448	+	0.958096i	$0.592475\pi$
$224$			186.333i			0.831843i
$225$		0			0
$226$	−135.647			−0.600208
$227$	114.563	−	427.557i	0.504685	−	1.88351i	0.0376093	−	0.999293i	$-0.488026\pi$
$227$	114.563	−	427.557i	0.504685	−	1.88351i	0.467076	−	0.884217i	$-0.345308\pi$
$228$	311.313	−	250.056i	1.36541	−	1.09674i
$229$	−164.262	−	94.8369i	−0.717303	−	0.414135i	0.0964562	−	0.995337i	$-0.469249\pi$
$229$	−164.262	−	94.8369i	−0.717303	−	0.414135i	−0.813759	+	0.581202i	$0.802583\pi$
$230$		0			0
$231$	−55.6263	−	6.06989i	−0.240806	−	0.0262766i
$232$	−61.0961	+	228.014i	−0.263345	+	0.982818i
$233$	62.7917	−	62.7917i	0.269492	−	0.269492i	−0.559403	−	0.828896i	$-0.688970\pi$
$233$	62.7917	−	62.7917i	0.269492	−	0.269492i	0.828896	+	0.559403i	$0.188970\pi$
$234$	−95.9802	−	87.8106i	−0.410172	−	0.375259i
$235$		0			0
$236$	−273.491	−	473.699i	−1.15886	−	2.00720i
$237$	0.690489	−	0.106555i	0.00291345	−	0.000449599i
$238$	190.984	+	712.762i	0.802454	+	2.99480i
$239$	−57.9140	−	33.4367i	−0.242318	−	0.139902i	0.373924	−	0.927460i	$-0.378012\pi$
$239$	−57.9140	−	33.4367i	−0.242318	−	0.139902i	−0.616242	+	0.787557i	$0.711346\pi$
$240$		0			0
$241$	29.6700	+	51.3900i	0.123112	+	0.213236i	0.920993	−	0.389578i	$-0.127379\pi$
$241$	29.6700	+	51.3900i	0.123112	+	0.213236i	−0.797881	+	0.602815i	$0.794046\pi$
$242$	275.702	+	275.702i	1.13927	+	1.13927i
$243$	−67.5388	+	233.426i	−0.277937	+	0.960599i
$244$		−	505.119i		−	2.07016i
$245$		0			0
$246$	17.4188	+	39.5449i	0.0708080	+	0.160751i
$247$	−77.9498	+	20.8866i	−0.315586	+	0.0845611i
$248$	−64.8054	−	241.857i	−0.261312	−	0.975230i
$249$	384.522	+	281.710i	1.54426	+	1.13137i
$250$		0			0
$251$	−88.5781			−0.352901			−0.176450	−	0.984310i	$-0.556461\pi$
$251$	−88.5781			−0.352901			−0.176450	+	0.984310i	$0.556461\pi$
$252$	585.007	−	26.0038i	2.32146	−	0.103190i
$253$	17.2480	−	17.2480i	0.0681737	−	0.0681737i
$254$	−332.583	+	192.017i	−1.30938	+	0.755972i
$255$		0			0
$256$	199.259	−	345.126i	0.778354	−	1.34815i
$257$	−151.819	+	40.6797i	−0.590734	+	0.158287i	−0.541789	−	0.840515i	$-0.682253\pi$
$257$	−151.819	+	40.6797i	−0.590734	+	0.158287i	−0.0489452	+	0.998801i	$0.515586\pi$
$258$	−245.859	+	197.482i	−0.952940	+	0.765433i
$259$	−371.369	+	214.410i	−1.43386	+	0.827837i
$260$		0			0
$261$	−197.797	−	43.6872i	−0.757845	−	0.167384i
$262$	−195.159	−	195.159i	−0.744882	−	0.744882i
$263$	−339.020	−	90.8401i	−1.28905	−	0.345400i	−0.451750	−	0.892145i	$-0.649200\pi$
$263$	−339.020	−	90.8401i	−1.28905	−	0.345400i	−0.837299	+	0.546745i	$0.815867\pi$
$264$	51.9664	+	38.0719i	0.196843	+	0.144212i
$265$		0			0
$266$	283.358	−	490.791i	1.06526	−	1.84508i
$267$	112.298	−	289.112i	0.420593	−	1.08282i
$268$	−149.244	−	39.9897i	−0.556880	−	0.149215i
$269$		−	81.1798i		−	0.301784i	−0.988550	−	0.150892i	$-0.951785\pi$
$269$		−	81.1798i		−	0.301784i	0.988550	−	0.150892i	$-0.0482145\pi$
$270$		0			0
$271$	−96.4105			−0.355758			−0.177879	−	0.984052i	$-0.556924\pi$
$271$	−96.4105			−0.355758			−0.177879	+	0.984052i	$0.556924\pi$
$272$	40.4506	−	150.964i	0.148716	−	0.555014i
$273$	−110.317	−	42.8500i	−0.404092	−	0.156960i
$274$	450.817	+	260.280i	1.64532	+	0.949925i
$275$		0			0
$276$	−150.860	+	205.917i	−0.546593	+	0.746075i
$277$	−113.398	+	423.206i	−0.409378	+	1.52782i	0.386458	+	0.922307i	$0.373698\pi$
$277$	−113.398	+	423.206i	−0.409378	+	1.52782i	−0.795836	+	0.605512i	$0.792968\pi$
$278$	3.68676	−	3.68676i	0.0132617	−	0.0132617i
$279$	204.867	−	64.7719i	0.734292	−	0.232157i
$280$		0			0
$281$	−95.5531	−	165.503i	−0.340047	−	0.588978i	0.644394	−	0.764693i	$-0.277110\pi$
$281$	−95.5531	−	165.503i	−0.340047	−	0.588978i	−0.984441	+	0.175715i	$0.943776\pi$
$282$	−5.44693	−	6.78125i	−0.0193153	−	0.0240470i
$283$	−89.6088	−	334.424i	−0.316639	−	1.18171i	−0.922454	−	0.386107i	$-0.873820\pi$
$283$	−89.6088	−	334.424i	−0.316639	−	1.18171i	0.605815	−	0.795605i	$-0.292847\pi$
$284$	176.962	+	102.169i	0.623105	+	0.359750i
$285$		0			0
$286$	−14.7969	−	25.6289i	−0.0517373	−	0.0896117i
$287$	27.7972	+	27.7972i	0.0968545	+	0.0968545i
$288$	163.348	+	84.8702i	0.567182	+	0.294688i
$289$			299.828i			1.03747i
$290$		0			0
$291$	127.988	−	174.698i	0.439822	−	0.600338i
$292$	469.582	−	125.824i	1.60816	−	0.430905i
$293$	77.5588	+	289.453i	0.264706	+	0.987895i	0.962430	+	0.271529i	$0.0875292\pi$
$293$	77.5588	+	289.453i	0.264706	+	0.987895i	−0.697725	+	0.716366i	$0.745804\pi$
$294$	311.532	−	137.224i	1.05963	−	0.466748i
$295$		0			0
$296$	493.682			1.66784
$297$	−30.6576	+	46.0000i	−0.103224	+	0.154882i
$298$	238.229	−	238.229i	0.799426	−	0.799426i
$299$	44.6776	−	25.7946i	0.149423	−	0.0862697i
$300$		0			0
$301$	−143.444	+	248.452i	−0.476558	+	0.825423i
$302$	703.489	−	188.499i	2.32944	−	0.624170i
$303$	−28.3753	−	183.875i	−0.0936477	−	0.606849i
$304$	−103.950	+	60.0156i	−0.341941	+	0.197420i
$305$		0			0
$306$	711.831	+	157.221i	2.32624	+	0.513793i
$307$	−138.397	−	138.397i	−0.450805	−	0.450805i	0.444817	−	0.895622i	$-0.353269\pi$
$307$	−138.397	−	138.397i	−0.450805	−	0.450805i	−0.895622	+	0.444817i	$0.853269\pi$
$308$	128.676	+	34.4785i	0.417778	+	0.111943i
$309$	−17.2003	+	157.628i	−0.0556643	+	0.510124i
$310$		0			0
$311$	53.6367	−	92.9015i	0.172465	−	0.298719i	−0.766816	−	0.641867i	$-0.778160\pi$
$311$	53.6367	−	92.9015i	0.172465	−	0.298719i	0.939281	+	0.343148i	$0.111493\pi$
$312$	85.3226	+	106.224i	0.273470	+	0.340462i
$313$	−528.306	−	141.559i	−1.68788	−	0.452266i	−0.718038	−	0.696004i	$-0.754960\pi$
$313$	−528.306	−	141.559i	−1.68788	−	0.452266i	−0.969841	+	0.243738i	$0.921626\pi$
$314$		−	886.195i		−	2.82228i
$315$		0			0
$316$	−1.66329			−0.00526359
$317$	−112.931	+	421.463i	−0.356248	+	1.32954i	0.522658	+	0.852542i	$0.324941\pi$
$317$	−112.931	+	421.463i	−0.356248	+	1.32954i	−0.878906	+	0.476994i	$0.841726\pi$
$318$	7.19916	+	46.6514i	0.0226389	+	0.146703i
$319$	−39.9077	−	23.0407i	−0.125103	−	0.0722280i
$320$		0			0
$321$	−144.329	−	327.661i	−0.449622	−	1.02075i
$322$	−93.7670	+	349.943i	−0.291202	+	1.08678i
$323$	319.771	−	319.771i	0.990002	−	0.990002i
$324$	243.661	−	524.690i	0.752040	−	1.61941i
$325$		0			0
$326$	380.189	+	658.507i	1.16622	+	2.01996i
$327$	−111.316	+	286.582i	−0.340415	+	0.876398i
$328$	−11.7135	−	43.7152i	−0.0357118	−	0.133278i
$329$	−6.85279	−	3.95646i	−0.0208292	−	0.0120257i
$330$		0			0
$331$	−293.152	−	507.754i	−0.885655	−	1.53400i	−0.844961	−	0.534827i	$-0.820377\pi$
$331$	−293.152	−	507.754i	−0.885655	−	1.53400i	−0.0406933	−	0.999172i	$-0.512957\pi$
$332$	−802.431	−	802.431i	−2.41696	−	2.41696i
$333$	18.8122	+	423.219i	0.0564932	+	1.27093i
$334$			199.127i			0.596188i
$335$		0			0
$336$	−174.989	−	19.0946i	−0.520799	−	0.0568292i
$337$	459.691	−	123.174i	1.36407	−	0.365501i	0.498760	−	0.866740i	$-0.333789\pi$
$337$	459.691	−	123.174i	1.36407	−	0.365501i	0.865309	+	0.501239i	$0.167122\pi$
$338$	129.805	+	484.438i	0.384038	+	1.43325i
$339$	−13.2245	+	121.193i	−0.0390104	+	0.357502i
$340$		0			0
$341$	48.8792			0.143341
$342$	−301.188	−	471.949i	−0.880667	−	1.37997i
$343$	−96.6647	+	96.6647i	−0.281821	+	0.281821i
$344$	286.033	−	165.141i	0.831490	−	0.480061i
$345$		0			0
$346$	−161.793	+	280.234i	−0.467610	+	0.809925i
$347$	−169.638	+	45.4544i	−0.488870	+	0.130992i	−0.494830	−	0.868990i	$-0.664770\pi$
$347$	−169.638	+	45.4544i	−0.488870	+	0.130992i	0.00595969	+	0.999982i	$0.498103\pi$
$348$	449.523	+	174.606i	1.29173	+	0.501741i
$349$	−298.148	+	172.136i	−0.854292	+	0.493226i	−0.862097	−	0.506744i	$-0.830849\pi$
$349$	−298.148	+	172.136i	−0.854292	+	0.493226i	0.00780468	+	0.999970i	$0.497516\pi$
$350$		0			0
$351$	−87.8113	+	77.1923i	−0.250175	+	0.219921i
$352$	29.6112	+	29.6112i	0.0841227	+	0.0841227i
$353$	−260.440	−	69.7848i	−0.737792	−	0.197691i	−0.129695	−	0.991554i	$-0.541400\pi$
$353$	−260.440	−	69.7848i	−0.737792	−	0.197691i	−0.608096	+	0.793863i	$0.708067\pi$
$354$	−701.854	+	309.153i	−1.98264	+	0.873314i
$355$		0			0
$356$	−369.191	+	639.458i	−1.03705	+	1.79623i
$357$	655.434	−	101.145i	1.83595	−	0.283320i
$358$	288.348	+	77.2626i	0.805441	+	0.215817i
$359$			411.438i			1.14607i	0.819532	+	0.573033i	$0.194233\pi$
$359$			411.438i			1.14607i	−0.819532	+	0.573033i	$0.805767\pi$
$360$		0			0
$361$	13.6890			0.0379198
$362$	−265.517	+	990.923i	−0.733473	+	2.73736i
$363$	273.204	−	219.446i	0.752628	−	0.604536i
$364$	244.000	+	140.873i	0.670330	+	0.387015i
$365$		0			0
$366$	−704.051	−	76.8255i	−1.92364	−	0.209906i
$367$	167.988	−	626.938i	0.457732	−	1.70828i	−0.222199	−	0.975001i	$-0.571323\pi$
$367$	167.988	−	626.938i	0.457732	−	1.70828i	0.679930	−	0.733277i	$-0.262010\pi$
$368$	54.2584	−	54.2584i	0.147441	−	0.147441i
$369$	37.0294	−	11.7074i	0.100351	−	0.0317274i
$370$		0			0
$371$	21.4716	+	37.1900i	0.0578751	+	0.100243i
$372$	−505.537	+	78.0134i	−1.35897	+	0.209714i
$373$	−28.7295	−	107.220i	−0.0770229	−	0.287453i	0.916662	−	0.399664i	$-0.130873\pi$
$373$	−28.7295	−	107.220i	−0.0770229	−	0.287453i	−0.993684	+	0.112211i	$0.964207\pi$
$374$	143.619	+	82.9186i	0.384009	+	0.221708i
$375$		0			0
$376$	4.55491	+	7.88933i	0.0121141	+	0.0209823i
$377$	−68.9157	−	68.9157i	−0.182800	−	0.182800i
$378$	52.7309	−	819.356i	0.139500	−	2.16761i
$379$		−	317.077i		−	0.836614i	−0.908306	−	0.418307i	$-0.862624\pi$
$379$		−	317.077i		−	0.836614i	0.908306	−	0.418307i	$-0.137376\pi$
$380$		0			0
$381$	139.133	+	315.865i	0.365177	+	0.829043i
$382$	−527.478	+	141.337i	−1.38083	+	0.369993i
$383$	−23.0644	−	86.0774i	−0.0602203	−	0.224745i	0.929257	−	0.369434i	$-0.120448\pi$
$383$	−23.0644	−	86.0774i	−0.0602203	−	0.224745i	−0.989477	+	0.144689i	$0.953782\pi$
$384$	−561.629	−	411.464i	−1.46258	−	1.07152i
$385$		0			0
$386$	−848.449			−2.19806
$387$	152.470	+	238.914i	0.393979	+	0.617350i
$388$	−364.566	+	364.566i	−0.939602	+	0.939602i
$389$	64.0677	−	36.9895i	0.164698	−	0.0950887i	−0.415385	−	0.909646i	$-0.636353\pi$
$389$	64.0677	−	36.9895i	0.164698	−	0.0950887i	0.580084	+	0.814557i	$0.303020\pi$
$390$		0			0
$391$	−144.548	+	250.364i	−0.369687	+	0.640318i
$392$	−344.386	+	92.2778i	−0.878535	+	0.235403i
$393$	−193.391	+	155.338i	−0.492088	+	0.395261i
$394$	−343.356	+	198.237i	−0.871461	+	0.503138i
$395$		0			0
$396$	88.8343	−	97.0991i	0.224329	−	0.245200i
$397$	−331.663	−	331.663i	−0.835422	−	0.835422i	0.152830	−	0.988252i	$-0.451161\pi$
$397$	−331.663	−	331.663i	−0.835422	−	0.835422i	−0.988252	+	0.152830i	$0.951161\pi$
$398$	532.207	+	142.605i	1.33720	+	0.358303i
$399$	−410.870	−	301.013i	−1.02975	−	0.754420i
$400$		0			0
$401$	−324.360	+	561.808i	−0.808877	+	1.40102i	0.104765	+	0.994497i	$0.466591\pi$
$401$	−324.360	+	561.808i	−0.808877	+	1.40102i	−0.913642	+	0.406520i	$0.866742\pi$
$402$	−78.4380	+	201.939i	−0.195119	+	0.502335i
$403$	99.8561	+	26.7564i	0.247782	+	0.0663930i
$404$			442.930i			1.09636i
$405$		0			0
$406$	684.428			1.68578
$407$	−24.9432	+	93.0893i	−0.0612855	+	0.228721i
$408$	−711.702	−	276.443i	−1.74437	−	0.677556i
$409$	−545.487	−	314.937i	−1.33371	−	0.770017i	−0.347842	−	0.937553i	$-0.613086\pi$
$409$	−545.487	−	314.937i	−1.33371	−	0.770017i	−0.985866	+	0.167536i	$0.946419\pi$
$410$		0			0
$411$	276.497	−	377.406i	0.672742	−	0.918262i
$412$	97.7018	−	364.628i	0.237140	−	0.885019i
$413$	−493.353	+	493.353i	−1.19456	+	1.19456i
$414$	264.069	+	241.592i	0.637847	+	0.583555i
$415$		0			0
$416$	44.2841	+	76.7023i	0.106452	+	0.184380i
$417$	−2.93449	−	3.65335i	−0.00703715	−	0.00876103i
$418$	−32.9643	−	123.024i	−0.0788619	−	0.294317i
$419$	−153.113	−	88.3997i	−0.365424	−	0.210978i	0.306033	−	0.952021i	$-0.400998\pi$
$419$	−153.113	−	88.3997i	−0.365424	−	0.210978i	−0.671457	+	0.741043i	$0.734331\pi$
$420$		0			0
$421$	44.6779	+	77.3843i	0.106123	+	0.183811i	0.914197	−	0.405271i	$-0.132823\pi$
$421$	44.6779	+	77.3843i	0.106123	+	0.183811i	−0.808073	+	0.589082i	$0.799490\pi$
$422$	27.7229	+	27.7229i	0.0656941	+	0.0656941i
$423$	−6.58972	+	4.20542i	−0.0155785	+	0.00994188i
$424$		−	49.4388i		−	0.116601i
$425$		0			0
$426$	169.321	−	231.116i	0.397468	−	0.542526i
$427$	−622.355	+	166.760i	−1.45751	+	0.390538i
$428$	220.612	+	823.337i	0.515449	+	1.92368i
$429$	−24.3407	+	10.7216i	−0.0567381	+	0.0249921i
$430$		0			0
$431$	648.364			1.50433			0.752163	−	0.658977i	$-0.229011\pi$
$431$	648.364			1.50433			0.752163	+	0.658977i	$0.229011\pi$
$432$	−96.4425	+	144.706i	−0.223247	+	0.334968i
$433$	481.270	−	481.270i	1.11148	−	1.11148i	0.118526	−	0.992951i	$-0.462183\pi$
$433$	481.270	−	481.270i	1.11148	−	1.11148i	0.992951	−	0.118526i	$-0.0378169\pi$
$434$	−628.718	+	362.991i	−1.44866	+	0.836384i
$435$		0			0
$436$	365.961	−	633.864i	0.839361	−	1.45382i
$437$	214.462	−	57.4649i	0.490760	−	0.131499i
$438$	−103.957	−	673.656i	−0.237345	−	1.53803i
$439$	543.519	−	313.801i	1.23808	−	0.714809i	0.269382	−	0.963033i	$-0.413180\pi$
$439$	543.519	−	313.801i	1.23808	−	0.714809i	0.968702	+	0.248225i	$0.0798471\pi$
$440$		0			0
$441$	−92.2302	−	291.715i	−0.209139	−	0.661485i
$442$	248.013	+	248.013i	0.561115	+	0.561115i
$443$	519.441	+	139.184i	1.17255	+	0.314185i	0.791969	−	0.610562i	$-0.209056\pi$
$443$	519.441	+	139.184i	1.17255	+	0.314185i	0.380584	+	0.924746i	$0.375723\pi$
$444$	109.402	−	1002.59i	0.246401	−	2.25809i
$445$		0			0
$446$	21.3741	−	37.0210i	0.0479239	−	0.0830067i
$447$	−189.619	−	236.070i	−0.424204	−	0.528121i
$448$	−827.486	−	221.724i	−1.84707	−	0.494920i
$449$			252.073i			0.561410i	0.959794	+	0.280705i	$0.0905683\pi$
$449$			252.073i			0.561410i	−0.959794	+	0.280705i	$0.909432\pi$
$450$		0			0
$451$	8.83482			0.0195894
$452$	75.1186	−	280.346i	0.166191	−	0.620235i
$453$	−99.8294	−	646.907i	−0.220374	−	1.42805i
$454$	1279.57	+	738.759i	2.81843	+	1.62722i
$455$		0			0
$456$	236.373	+	536.624i	0.518361	+	1.17681i
$457$	−76.3993	+	285.126i	−0.167176	+	0.623908i	0.830577	+	0.556904i	$0.188011\pi$
$457$	−76.3993	+	285.126i	−0.167176	+	0.623908i	−0.997753	+	0.0670042i	$0.978656\pi$
$458$	447.688	−	447.688i	0.977484	−	0.977484i
$459$	209.866	−	620.654i	0.457224	−	1.35219i
$460$		0			0
$461$	254.881	+	441.467i	0.552887	+	0.957629i	0.998065	+	0.0621865i	$0.0198074\pi$
$461$	254.881	+	441.467i	0.552887	+	0.957629i	−0.445177	+	0.895443i	$0.646859\pi$
$462$	67.6280	−	174.108i	0.146381	−	0.376858i
$463$	76.4168	+	285.192i	0.165047	+	0.615964i	0.998034	+	0.0626719i	$0.0199622\pi$
$463$	76.4168	+	285.192i	0.165047	+	0.615964i	−0.832987	+	0.553293i	$0.813371\pi$
$464$	−125.541	−	72.4813i	−0.270563	−	0.156210i
$465$		0			0
$466$	148.208	+	256.703i	0.318042	+	0.550865i
$467$	375.745	+	375.745i	0.804593	+	0.804593i	0.983810	−	0.179217i	$-0.0573564\pi$
$467$	375.745	+	375.745i	0.804593	+	0.804593i	−0.179217	+	0.983810i	$0.557356\pi$
$468$	234.633	−	149.738i	0.501352	−	0.319952i
$469$			197.085i			0.420223i
$470$		0			0
$471$	−791.767	−	86.3970i	−1.68103	−	0.183433i
$472$	775.871	−	207.894i	1.64379	−	0.440453i
$473$	16.6875	+	62.2784i	0.0352800	+	0.131667i
$474$	−0.252977	+	2.31835i	−0.000533706	+	0.00489104i
$475$		0			0
$476$	−1578.85			−3.31691
$477$	42.3824	−	1.88391i	0.0888520	−	0.00394951i
$478$	157.841	−	157.841i	0.330212	−	0.330212i
$479$	375.237	−	216.643i	0.783376	−	0.452282i	−0.0542492	−	0.998527i	$-0.517277\pi$
$479$	375.237	−	216.643i	0.783376	−	0.452282i	0.837625	+	0.546245i	$0.183943\pi$
$480$		0			0
$481$	−101.914	+	176.520i	−0.211879	+	0.366985i
$482$	−191.326	+	51.2656i	−0.396942	+	0.106360i
$483$	303.514	+	117.892i	0.628393	+	0.244084i
$484$	−722.482	+	417.125i	−1.49273	+	0.861828i
$485$		0			0
$486$	−694.270	−	419.424i	−1.42854	−	0.863013i
$487$	−417.712	−	417.712i	−0.857725	−	0.857725i	0.133345	−	0.991070i	$-0.457428\pi$
$487$	−417.712	−	417.712i	−0.857725	−	0.857725i	−0.991070	+	0.133345i	$0.957428\pi$
$488$	716.491	+	191.983i	1.46822	+	0.393408i
$489$	625.406	−	275.479i	1.27895	−	0.563352i
$490$		0			0
$491$	385.003	−	666.845i	0.784121	−	1.35814i	−0.145402	−	0.989373i	$-0.546447\pi$
$491$	385.003	−	666.845i	0.784121	−	1.35814i	0.929523	−	0.368765i	$-0.120219\pi$
$492$	−91.3748	+	14.1008i	−0.185721	+	0.0286601i
$493$	527.544	+	141.355i	1.07007	+	0.286724i
$494$		−	269.373i		−	0.545289i
$495$		0			0
$496$	153.764			0.310007
$497$	67.4600	−	251.764i	0.135734	−	0.506567i
$498$	−1240.50	+	996.409i	−2.49096	+	2.00082i
$499$	−84.7687	−	48.9412i	−0.169877	−	0.0980786i	0.412651	−	0.910889i	$-0.364603\pi$
$499$	−84.7687	−	48.9412i	−0.169877	−	0.0980786i	−0.582528	+	0.812811i	$0.697936\pi$
$500$		0			0
$501$	177.909	+	19.4133i	0.355108	+	0.0387491i
$502$	76.5253	−	285.596i	0.152441	−	0.568917i
$503$	−350.849	+	350.849i	−0.697512	+	0.697512i	−0.963873	−	0.266361i	$-0.914179\pi$
$503$	−350.849	+	350.849i	−0.697512	+	0.697512i	0.266361	+	0.963873i	$0.414179\pi$
$504$	−185.461	+	839.692i	−0.367979	+	1.66606i
$505$		0			0
$506$	40.7104	+	70.5125i	0.0804553	+	0.139353i
$507$	445.474	−	68.7447i	0.878647	−	0.135591i
$508$	−212.670	−	793.696i	−0.418642	−	1.56239i
$509$	389.842	+	225.075i	0.765897	+	0.442191i	0.831409	−	0.555661i	$-0.187535\pi$
$509$	389.842	+	225.075i	0.765897	+	0.442191i	−0.0655119	+	0.997852i	$0.520868\pi$
$510$		0			0
$511$	−310.055	−	537.031i	−0.606761	−	1.05094i
$512$	284.213	+	284.213i	0.555104	+	0.555104i
$513$	−451.025	+	223.084i	−0.879190	+	0.434861i
$514$		−	524.643i		−	1.02071i
$515$		0			0
$516$	−271.991	−	617.485i	−0.527113	−	1.19668i
$517$	−1.71776	+	0.460272i	−0.00332255	+	0.000890275i
$518$	−370.470	−	1382.61i	−0.715194	−	2.66914i
$519$	234.600	+	171.874i	0.452024	+	0.331164i
$520$		0			0
$521$	749.947			1.43944			0.719718	−	0.694266i	$-0.244271\pi$
$521$	749.947			1.43944			0.719718	+	0.694266i	$0.244271\pi$
$522$	311.741	−	600.002i	0.597205	−	1.14943i
$523$	−377.284	+	377.284i	−0.721385	+	0.721385i	−0.968887	−	0.247502i	$-0.920390\pi$
$523$	−377.284	+	377.284i	−0.721385	+	0.721385i	0.247502	+	0.968887i	$0.420390\pi$
$524$	511.417	−	295.267i	0.975986	−	0.563486i
$525$		0			0
$526$	585.779	−	1014.60i	1.11365	−	1.92890i
$527$	−559.573	+	149.937i	−1.06181	+	0.284511i
$528$	−30.8428	+	24.7740i	−0.0584145	+	0.0469204i
$529$	335.207	−	193.532i	0.633661	−	0.365844i
$530$		0			0
$531$	207.786	+	657.208i	0.391312	+	1.23768i
$532$	857.415	+	857.415i	1.61168	+	1.61168i
$533$	18.0488	+	4.83616i	0.0338627	+	0.00907348i
$534$	835.146	+	611.848i	1.56394	+	1.14578i
$535$		0			0
$536$	113.448	−	196.497i	0.211656	−	0.366599i
$537$	97.1416	−	250.091i	0.180897	−	0.465719i
$538$	261.743	+	70.1337i	0.486510	+	0.130360i
$539$		−	69.6001i		−	0.129128i
$540$		0			0
$541$	861.919			1.59320			0.796598	−	0.604509i	$-0.206631\pi$
$541$	861.919			1.59320			0.796598	+	0.604509i	$0.206631\pi$
$542$	83.2920	−	310.850i	0.153675	−	0.573524i
$543$	859.451	+	333.832i	1.58278	+	0.614793i
$544$	−429.824	−	248.159i	−0.790117	−	0.456174i
$545$		0			0
$546$	233.465	−	318.669i	0.427591	−	0.583643i
$547$	−103.247	+	385.325i	−0.188752	+	0.704433i	0.805044	+	0.593215i	$0.202142\pi$
$547$	−103.247	+	385.325i	−0.188752	+	0.704433i	−0.993796	+	0.111218i	$0.964525\pi$
$548$	−787.582	+	787.582i	−1.43719	+	1.43719i
$549$	−137.279	+	621.542i	−0.250052	+	1.13213i
$550$		0			0
$551$	−209.725	−	363.254i	−0.380626	−	0.659264i
$552$	−234.747	−	292.252i	−0.425266	−	0.529442i
$553$	0.549118	+	2.04934i	0.000992981	+	0.00370585i
$554$	−1266.55	−	731.241i	−2.28619	−	1.31993i
$555$		0			0
$556$	5.57790	+	9.66120i	0.0100322	+	0.0173763i
$557$	262.321	+	262.321i	0.470954	+	0.470954i	0.902223	−	0.431269i	$-0.141934\pi$
$557$	262.321	+	262.321i	0.470954	+	0.470954i	−0.431269	+	0.902223i	$0.641934\pi$
$558$	31.8487	+	716.499i	0.0570765	+	1.28405i
$559$			136.364i			0.243943i
$560$		0			0
$561$	88.0851	−	120.232i	0.157014	−	0.214318i
$562$	616.171	−	165.102i	1.09639	−	0.293777i
$563$	−235.225	−	877.872i	−0.417806	−	1.55928i	−0.779147	−	0.626841i	$-0.784347\pi$
$563$	−235.225	−	877.872i	−0.417806	−	1.55928i	0.361341	−	0.932434i	$-0.382319\pi$
$564$	17.0314	−	7.50202i	0.0301976	−	0.0133015i
$565$		0			0
$566$	1155.68			2.04183
$567$	−726.910	−	126.993i	−1.28203	−	0.223973i
$568$	−212.181	+	212.181i	−0.373559	+	0.373559i
$569$	−632.780	+	365.336i	−1.11209	+	0.642066i	−0.939370	−	0.342905i	$-0.888589\pi$
$569$	−632.780	+	365.336i	−1.11209	+	0.642066i	−0.172721	+	0.984971i	$0.555256\pi$
$570$		0			0
$571$	−348.293	+	603.262i	−0.609971	+	1.05650i	0.381273	+	0.924462i	$0.375486\pi$
$571$	−348.293	+	603.262i	−0.609971	+	1.05650i	−0.991245	+	0.132039i	$0.957848\pi$
$572$	61.1624	−	16.3884i	0.106927	−	0.0286511i
$573$	74.8523	+	485.052i	0.130632	+	0.846514i
$574$	−113.640	+	65.6099i	−0.197978	+	0.114303i
$575$		0			0
$576$	−571.275	+	624.424i	−0.991797	+	1.08407i
$577$	524.179	+	524.179i	0.908455	+	0.908455i	0.996148	−	0.0876926i	$-0.0279493\pi$
$577$	524.179	+	524.179i	0.908455	+	0.908455i	−0.0876926	+	0.996148i	$0.527949\pi$
$578$	−966.715	−	259.031i	−1.67252	−	0.448150i
$579$	−82.7171	+	758.044i	−0.142862	+	1.30923i
$580$		0			0
$581$	−723.758	+	1253.59i	−1.24571	+	2.15763i
$582$	452.695	+	563.591i	0.777827	+	0.968370i
$583$	9.32225	+	2.49789i	0.0159901	+	0.00428454i
$584$			713.907i			1.22244i
$585$		0			0
$586$	−1000.27			−1.70695
$587$	141.391	−	527.677i	0.240870	−	0.898938i	−0.734545	−	0.678560i	$-0.762604\pi$
$587$	141.391	−	527.677i	0.240870	−	0.898938i	0.975415	−	0.220378i	$-0.0707291\pi$
$588$	111.085	+	719.845i	0.188920	+	1.22423i
$589$	385.309	+	222.458i	0.654174	+	0.377688i
$590$		0			0
$591$	143.639	+	326.096i	0.243044	+	0.551770i
$592$	−78.4661	+	292.839i	−0.132544	+	0.494661i
$593$	61.2676	−	61.2676i	0.103318	−	0.103318i	−0.653558	−	0.756876i	$-0.726725\pi$
$593$	61.2676	−	61.2676i	0.103318	−	0.103318i	0.756876	+	0.653558i	$0.226725\pi$
$594$	−121.829	−	138.588i	−0.205099	−	0.233314i
$595$		0			0
$596$	360.429	+	624.282i	0.604747	+	1.04745i
$597$	179.295	−	461.596i	0.300327	−	0.773192i
$598$	44.5696	+	166.336i	0.0745310	+	0.278154i
$599$	−572.037	−	330.266i	−0.954987	−	0.551362i	−0.0603602	−	0.998177i	$-0.519225\pi$
$599$	−572.037	−	330.266i	−0.954987	−	0.551362i	−0.894626	+	0.446815i	$0.852558\pi$
$600$		0			0
$601$	65.1748	+	112.886i	0.108444	+	0.187830i	0.915140	−	0.403136i	$-0.132080\pi$
$601$	65.1748	+	112.886i	0.108444	+	0.187830i	−0.806696	+	0.590966i	$0.798747\pi$
$602$	−677.143	−	677.143i	−1.12482	−	1.12482i
$603$	172.774	+	89.7675i	0.286524	+	0.148868i
$604$			1558.31i			2.57999i
$605$		0			0
$606$	617.371	+	67.3669i	1.01876	+	0.111167i
$607$	−313.749	+	84.0689i	−0.516885	+	0.138499i	−0.507826	−	0.861460i	$-0.669551\pi$
$607$	−313.749	+	84.0689i	−0.516885	+	0.138499i	−0.00905986	+	0.999959i	$0.502884\pi$
$608$	98.6554	+	368.187i	0.162262	+	0.605571i
$609$	66.7263	−	611.499i	0.109567	−	1.00410i
$610$		0			0
$611$	−3.76119			−0.00615580
$612$	−719.130	+	1384.10i	−1.17505	+	2.26160i
$613$	778.916	−	778.916i	1.27066	−	1.27066i	0.324921	−	0.945741i	$-0.394662\pi$
$613$	778.916	−	778.916i	1.27066	−	1.27066i	0.945741	−	0.324921i	$-0.105338\pi$
$614$	565.790	−	326.659i	0.921482	−	0.532018i
$615$		0			0
$616$	−97.8128	+	169.417i	−0.158787	+	0.275027i
$617$	−331.081	+	88.7130i	−0.536599	+	0.143781i	−0.516934	−	0.856025i	$-0.672927\pi$
$617$	−331.081	+	88.7130i	−0.536599	+	0.143781i	−0.0196651	+	0.999807i	$0.506260\pi$
$618$	−493.370	−	191.637i	−0.798334	−	0.310093i
$619$	448.805	−	259.118i	0.725049	−	0.418607i	−0.0915591	−	0.995800i	$-0.529185\pi$
$619$	448.805	−	259.118i	0.725049	−	0.418607i	0.816608	+	0.577192i	$0.195852\pi$
$620$		0			0
$621$	241.594	−	212.378i	0.389040	−	0.341993i
$622$	253.198	+	253.198i	0.407070	+	0.407070i
$623$	909.758	+	243.769i	1.46029	+	0.391282i
$624$	−76.5706	+	33.7279i	−0.122709	+	0.0540511i
$625$		0			0
$626$	912.840	−	1581.09i	1.45821	−	2.52569i
$627$	−113.129	+	17.4579i	−0.180430	+	0.0278435i
$628$	1831.53	+	490.756i	2.91645	+	0.781459i
$629$		−	1142.21i		−	1.81591i
$630$		0			0
$631$	−48.4016			−0.0767062			−0.0383531	−	0.999264i	$-0.512211\pi$
$631$	−48.4016			−0.0767062			−0.0383531	+	0.999264i	$0.512211\pi$
$632$	0.632177	−	2.35932i	0.00100028	−	0.00373309i
$633$	27.4717	−	22.0662i	0.0433992	−	0.0348597i
$634$	−1261.33	−	728.230i	−1.98948	−	1.14863i
$635$		0			0
$636$	−100.403	−	10.9559i	−0.157866	−	0.0172262i
$637$	38.0990	−	142.187i	0.0598100	−	0.223214i
$638$	108.766	−	108.766i	0.170480	−	0.170480i
$639$	−189.982	−	173.811i	−0.297312	−	0.272005i
$640$		0			0
$641$	−313.217	−	542.507i	−0.488637	−	0.846345i	0.511277	−	0.859416i	$-0.329173\pi$
$641$	−313.217	−	542.507i	−0.488637	−	0.846345i	−0.999915	+	0.0130711i	$0.995839\pi$
$642$	1181.15	−	182.272i	1.83979	−	0.283913i
$643$	−125.261	−	467.479i	−0.194807	−	0.727028i	−0.992317	−	0.123723i	$-0.960517\pi$
$643$	−125.261	−	467.479i	−0.194807	−	0.727028i	0.797510	−	0.603305i	$-0.206150\pi$
$644$	−671.313	−	387.583i	−1.04241	−	0.601836i
$645$		0			0
$646$	754.755	+	1307.27i	1.16835	+	2.02364i
$647$	388.357	+	388.357i	0.600242	+	0.600242i	0.940377	−	0.340135i	$-0.110473\pi$
$647$	388.357	+	388.357i	0.600242	+	0.600242i	−0.340135	+	0.940377i	$0.610473\pi$
$648$	651.642	+	545.045i	1.00562	+	0.841118i
$649$			156.803i			0.241607i
$650$		0			0
$651$	263.017	+	597.114i	0.404021	+	0.917226i
$652$	−1571.50	+	421.082i	−2.41027	+	0.645831i
$653$	−51.2298	−	191.192i	−0.0784530	−	0.292791i	0.915541	−	0.402225i	$-0.131763\pi$
$653$	−51.2298	−	191.192i	−0.0784530	−	0.292791i	−0.993994	+	0.109434i	$0.965096\pi$
$654$	−827.839	−	606.495i	−1.26581	−	0.927363i
$655$		0			0
$656$	27.7925			0.0423666
$657$	−612.010	+	27.2041i	−0.931523	+	0.0414066i
$658$	18.6769	−	18.6769i	0.0283843	−	0.0283843i
$659$	−97.2838	+	56.1668i	−0.147623	+	0.0852304i	−0.571992	−	0.820259i	$-0.693829\pi$
$659$	−97.2838	+	56.1668i	−0.147623	+	0.0852304i	0.424369	+	0.905489i	$0.360496\pi$
$660$		0			0
$661$	55.4873	−	96.1067i	0.0839444	−	0.145396i	−0.820997	−	0.570933i	$-0.806582\pi$
$661$	55.4873	−	96.1067i	0.0839444	−	0.145396i	0.904941	+	0.425537i	$0.139915\pi$
$662$	1890.38	−	506.525i	2.85556	−	0.765144i
$663$	245.765	−	197.407i	0.370687	−	0.297748i
$664$	1443.20	−	833.232i	2.17349	−	1.25487i
$665$		0			0
$666$	−1380.81	−	304.976i	−2.07329	−	0.457923i
$667$	189.607	+	189.607i	0.284268	+	0.284268i
$668$	−411.542	−	110.272i	−0.616081	−	0.165078i
$669$	−30.9924	−	22.7058i	−0.0463265	−	0.0339400i
$670$		0			0
$671$	−72.4012	+	125.403i	−0.107900	+	0.186889i
$672$	−202.397	+	521.071i	−0.301186	+	0.775403i
$673$	202.929	+	54.3747i	0.301529	+	0.0807945i	0.406412	−	0.913690i	$-0.366780\pi$
$673$	202.929	+	54.3747i	0.301529	+	0.0807945i	−0.104882	+	0.994485i	$0.533447\pi$
$674$			1588.56i			2.35692i
$675$		0			0
$676$	−1073.09			−1.58741
$677$	−193.957	+	723.857i	−0.286495	+	1.06921i	0.661246	+	0.750169i	$0.270028\pi$
$677$	−193.957	+	723.857i	−0.286495	+	1.06921i	−0.947740	+	0.319043i	$0.896639\pi$
$678$	−379.331	−	147.342i	−0.559485	−	0.217318i
$679$	569.537	+	328.822i	0.838788	+	0.484275i
$680$		0			0
$681$	784.789	−	1071.20i	1.15241	−	1.57298i
$682$	−42.2282	+	157.598i	−0.0619182	+	0.231082i
$683$	−441.268	+	441.268i	−0.646074	+	0.646074i	−0.952042	−	0.305968i	$-0.901020\pi$
$683$	−441.268	+	441.268i	−0.646074	+	0.646074i	0.305968	+	0.952042i	$0.401020\pi$
$684$	1142.18	−	361.119i	1.66986	−	0.527952i
$685$		0			0
$686$	−228.158	−	395.181i	−0.332592	−	0.576066i
$687$	−356.339	−	443.631i	−0.518688	−	0.645751i
$688$	52.4952	+	195.915i	0.0763012	+	0.284760i
$689$	17.6772	+	10.2060i	0.0256564	+	0.0148127i
$690$		0			0
$691$	396.083	+	686.036i	0.573202	+	0.992816i	0.996234	+	0.0867010i	$0.0276325\pi$
$691$	396.083	+	686.036i	0.573202	+	0.992816i	−0.423032	+	0.906115i	$0.639034\pi$
$692$	−489.571	−	489.571i	−0.707473	−	0.707473i
$693$	−148.963	−	77.3961i	−0.214954	−	0.111683i
$694$		−	586.222i		−	0.844700i
$695$		0			0
$696$	−418.524	+	571.266i	−0.601327	+	0.820785i
$697$	−101.142	+	27.1009i	−0.145110	+	0.0388822i
$698$	−297.427	−	1110.01i	−0.426113	−	1.59027i
$699$	243.799	−	107.389i	0.348783	−	0.153632i
$700$		0			0
$701$	−1185.25			−1.69080			−0.845401	−	0.534133i	$-0.820638\pi$
$701$	−1185.25			−1.69080			−0.845401	+	0.534133i	$0.820638\pi$
$702$	−173.023	−	349.813i	−0.246471	−	0.498309i
$703$	−620.290	+	620.290i	−0.882348	+	0.882348i
$704$	−166.736	+	96.2650i	−0.236841	+	0.136740i
$705$		0			0
$706$	450.005	−	779.431i	0.637401	−	1.10401i
$707$	545.733	−	146.229i	0.771899	−	0.206830i
$708$	−250.265	−	1621.75i	−0.353481	−	2.29060i
$709$	237.674	−	137.221i	0.335224	−	0.193542i	−0.322934	−	0.946421i	$-0.604669\pi$
$709$	237.674	−	137.221i	0.335224	−	0.193542i	0.658158	+	0.752880i	$0.271336\pi$
$710$		0			0
$711$	2.04666	+	0.452042i	0.00287856	+	0.000635783i
$712$	−766.725	−	766.725i	−1.07686	−	1.07686i
$713$	−274.732	−	73.6143i	−0.385319	−	0.103246i
$714$	−240.133	+	2200.65i	−0.336321	+	3.08215i
$715$		0			0
$716$	−319.362	+	553.152i	−0.446037	+	0.772558i
$717$	−125.634	−	156.411i	−0.175222	−	0.218146i
$718$	−1326.57	−	355.454i	−1.84759	−	0.495061i
$719$			1409.12i			1.95983i	0.199416	+	0.979915i	$0.436096\pi$
$719$			1409.12i			1.95983i	−0.199416	+	0.979915i	$0.563904\pi$
$720$		0			0
$721$	−481.512			−0.667839
$722$	−11.8264	+	44.1367i	−0.0163800	+	0.0611311i
$723$	27.1503	+	175.937i	0.0375523	+	0.243344i
$724$	−1900.94	−	1097.51i	−2.62560	−	1.51589i
$725$		0			0
$726$	471.517	+	1070.46i	0.649473	+	1.47446i
$727$	184.607	−	688.962i	0.253930	−	0.947678i	−0.714753	−	0.699377i	$-0.753461\pi$
$727$	184.607	−	688.962i	0.253930	−	0.947678i	0.968683	−	0.248302i	$-0.0798724\pi$
$728$	−292.562	+	292.562i	−0.401870	+	0.401870i
$729$	−442.419	+	579.402i	−0.606884	+	0.794790i
$730$		0			0
$731$	−382.079	−	661.780i	−0.522680	−	0.905308i
$732$	548.667	−	1412.54i	0.749545	−	1.92970i
$733$	230.005	+	858.390i	0.313786	+	1.17106i	0.925115	+	0.379688i	$0.123969\pi$
$733$	230.005	+	858.390i	0.313786	+	1.17106i	−0.611329	+	0.791377i	$0.709365\pi$
$734$	1876.26	+	1083.26i	2.55622	+	1.47583i
$735$		0			0
$736$	−121.838	−	211.030i	−0.165541	−	0.286725i
$737$	31.3198	+	31.3198i	0.0424964	+	0.0424964i
$738$	5.75659	+	129.506i	0.00780025	+	0.175482i
$739$		−	719.160i		−	0.973153i	−0.873638	−	0.486577i	$-0.838245\pi$
$739$		−	719.160i		−	0.973153i	0.873638	−	0.486577i	$-0.161755\pi$
$740$		0			0
$741$	−240.670	−	26.2617i	−0.324791	−	0.0354409i
$742$	−138.459	+	37.1000i	−0.186603	+	0.0500000i
$743$	43.1096	+	160.887i	0.0580210	+	0.216537i	0.988849	−	0.148919i	$-0.0475795\pi$
$743$	43.1096	+	160.887i	0.0580210	+	0.216537i	−0.930828	+	0.365457i	$0.880913\pi$
$744$	81.4830	−	746.734i	0.109520	−	1.00368i
$745$		0			0
$746$	370.523			0.496679
$747$	769.299	+	1205.46i	1.02985	+	1.61374i
$748$	−250.904	+	250.904i	−0.335433	+	0.335433i
$749$	941.597	−	543.631i	1.25714	−	0.725809i
$750$		0			0
$751$	241.781	−	418.776i	0.321945	−	0.557625i	−0.658945	−	0.752192i	$-0.728997\pi$
$751$	241.781	−	418.776i	0.321945	−	0.557625i	0.980889	+	0.194567i	$0.0623301\pi$
$752$	−5.40371	+	1.44792i	−0.00718578	+	0.00192542i
$753$	−247.704	−	96.2146i	−0.328957	−	0.127775i
$754$	281.739	−	162.662i	0.373659	−	0.215732i
$755$		0			0
$756$	1664.19	+	562.723i	2.20131	+	0.744343i
$757$	−144.792	−	144.792i	−0.191270	−	0.191270i	0.604974	−	0.796245i	$-0.293183\pi$
$757$	−144.792	−	144.792i	−0.191270	−	0.191270i	−0.796245	+	0.604974i	$0.793183\pi$
$758$	1022.33	+	273.932i	1.34872	+	0.361388i
$759$	66.9680	−	29.4981i	0.0882319	−	0.0388645i
$760$		0			0
$761$	149.929	−	259.685i	0.197016	−	0.341241i	−0.750544	−	0.660821i	$-0.770208\pi$
$761$	149.929	−	259.685i	0.197016	−	0.341241i	0.947559	+	0.319580i	$0.103542\pi$
$762$	−1138.62	+	175.710i	−1.49426	+	0.230591i
$763$	−901.799	−	241.636i	−1.18191	−	0.316692i
$764$		−	1168.43i		−	1.52935i
$765$		0			0
$766$	297.459			0.388328
$767$	−85.8336	+	320.335i	−0.111908	+	0.417647i
$768$	932.097	−	748.691i	1.21367	−	0.974858i
$769$	−96.6554	−	55.8040i	−0.125690	−	0.0725670i	0.435837	−	0.900026i	$-0.356452\pi$
$769$	−96.6554	−	55.8040i	−0.125690	−	0.0725670i	−0.561527	+	0.827459i	$0.689786\pi$
$770$		0			0
$771$	−468.740	−	51.1485i	−0.607964	−	0.0663405i
$772$	469.854	−	1753.52i	0.608619	−	2.27140i
$773$	43.6287	−	43.6287i	0.0564408	−	0.0564408i	−0.678323	−	0.734764i	$-0.737293\pi$
$773$	43.6287	−	43.6287i	0.0564408	−	0.0564408i	0.734764	+	0.678323i	$0.237293\pi$
$774$	−902.039	+	285.193i	−1.16543	+	0.368467i
$775$		0			0
$776$	−378.559	−	655.684i	−0.487834	−	0.844954i
$777$	−1271.41	+	196.201i	−1.63631	+	0.252512i
$778$	63.9127	+	238.526i	0.0821500	+	0.306588i
$779$	69.6438	+	40.2089i	0.0894015	+	0.0516160i
$780$		0			0
$781$	−29.2888	−	50.7297i	−0.0375016	−	0.0649547i
$782$	−682.353	−	682.353i	−0.872574	−	0.872574i
$783$	−505.678	−	337.019i	−0.645821	−	0.430420i
$784$		−	218.947i		−	0.279270i
$785$		0			0
$786$	−333.769	−	757.737i	−0.424642	−	0.964042i
$787$	1190.57	−	319.011i	1.51279	−	0.405351i	0.595430	−	0.803407i	$-0.296982\pi$
$787$	1190.57	−	319.011i	1.51279	−	0.405351i	0.917361	+	0.398056i	$0.130315\pi$
$788$	−219.559	−	819.404i	−0.278628	−	1.03985i
$789$	−849.381	−	622.277i	−1.07653	−	0.788691i
$790$		0			0
$791$	−370.213			−0.468032
$792$	103.967	+	162.913i	0.131272	+	0.205698i
$793$	−216.555	+	216.555i	−0.273083	+	0.273083i
$794$	1355.89	−	782.824i	1.70767	−	0.985925i
$795$		0			0
$796$	−589.451	+	1020.96i	−0.740516	+	1.28261i
$797$	−735.470	+	197.069i	−0.922799	+	0.247263i	−0.688781	−	0.724969i	$-0.741854\pi$
$797$	−735.470	+	197.069i	−0.922799	+	0.247263i	−0.234017	+	0.972232i	$0.575187\pi$
$798$	1325.50	−	1064.69i	1.66103	−	1.33419i
$799$	18.2532	−	10.5385i	0.0228450	−	0.0131896i
$800$		0			0
$801$	628.073	−	686.507i	0.784112	−	0.857063i
$802$	−1531.17	−	1531.17i	−1.90920	−	1.90920i
$803$	−134.615	−	36.0700i	−0.167640	−	0.0449191i
$804$	−373.916	−	273.940i	−0.465069	−	0.340721i
$805$		0			0
$806$	−172.538	+	298.844i	−0.214066	+	0.370774i
$807$	88.1785	−	227.015i	0.109267	−	0.281308i
$808$	−628.279	−	168.347i	−0.777573	−	0.208350i
$809$			225.758i			0.279058i	0.990218	+	0.139529i	$0.0445589\pi$
$809$			225.758i			0.279058i	−0.990218	+	0.139529i	$0.955441\pi$
$810$		0			0
$811$	−149.469			−0.184303			−0.0921513	−	0.995745i	$-0.529374\pi$
$811$	−149.469			−0.184303			−0.0921513	+	0.995745i	$0.529374\pi$
$812$	−379.022	+	1414.53i	−0.466776	+	1.74203i
$813$	−269.607	−	104.722i	−0.331620	−	0.128810i
$814$	−278.593	−	160.845i	−0.342251	−	0.197599i
$815$		0			0
$816$	277.097	−	378.225i	0.339580	−	0.463511i
$817$	−151.895	+	566.881i	−0.185918	+	0.693856i
$818$	1486.69	−	1486.69i	1.81747	−	1.81747i
$819$	−261.953	−	239.656i	−0.319844	−	0.292620i
$820$		0			0
$821$	2.78890	+	4.83052i	0.00339696	+	0.00588370i	0.867719	−	0.497055i	$-0.165585\pi$
$821$	2.78890	+	4.83052i	0.00339696	+	0.00588370i	−0.864322	+	0.502939i	$0.832252\pi$
$822$	977.970	+	1217.54i	1.18974	+	1.48120i
$823$	167.604	+	625.506i	0.203650	+	0.760032i	0.989857	+	0.142069i	$0.0453754\pi$
$823$	167.604	+	625.506i	0.203650	+	0.760032i	−0.786207	+	0.617963i	$0.787958\pi$
$824$	480.076	+	277.172i	0.582617	+	0.336374i
$825$		0			0
$826$	−1164.46	−	2016.91i	−1.40976	−	2.44178i
$827$	−230.120	−	230.120i	−0.278258	−	0.278258i	0.554155	−	0.832413i	$-0.313041\pi$
$827$	−230.120	−	230.120i	−0.278258	−	0.278258i	−0.832413	+	0.554155i	$0.813041\pi$
$828$	−645.541	+	411.971i	−0.779639	+	0.497549i
$829$			1504.68i			1.81505i	0.419994	+	0.907527i	$0.362032\pi$
$829$			1504.68i			1.81505i	−0.419994	+	0.907527i	$0.637968\pi$
$830$		0			0
$831$	−776.803	+	1060.30i	−0.934781	+	1.27593i
$832$	−393.323	+	105.390i	−0.472744	+	0.126671i
$833$	213.499	+	796.788i	0.256301	+	0.956528i
$834$	14.3145	−	6.30524i	0.0171636	−	0.00756024i
$835$		0			0
$836$	272.513			0.325973
$837$	643.258	+	41.3979i	0.768528	+	0.0494598i
$838$	417.300	−	417.300i	0.497971	−	0.497971i
$839$	−915.370	+	528.489i	−1.09103	+	0.629904i	−0.933849	−	0.357667i	$-0.883572\pi$
$839$	−915.370	+	528.489i	−1.09103	+	0.629904i	−0.157176	+	0.987571i	$0.550239\pi$
$840$		0			0
$841$	−167.214	+	289.622i	−0.198827	+	0.344378i
$842$	−288.104	+	77.1972i	−0.342166	+	0.0916831i
$843$	−87.4384	−	566.612i	−0.103723	−	0.672137i
$844$	−72.6483	+	41.9435i	−0.0860762	+	0.0496961i
$845$		0			0
$846$	−7.86618	−	24.8800i	−0.00929809	−	0.0294089i
$847$	752.457	+	752.457i	0.888379	+	0.888379i
$848$	29.3258	+	7.85783i	0.0345823	+	0.00926631i
$849$	112.669	−	1032.54i	0.132708	−	1.21618i
$850$		0			0
$851$	280.394	−	485.656i	0.329487	−	0.570689i
$852$	383.888	+	477.929i	0.450573	+	0.560949i
$853$	715.340	+	191.675i	0.838617	+	0.224707i	0.652469	−	0.757815i	$-0.273733\pi$
$853$	715.340	+	191.675i	0.838617	+	0.224707i	0.186148	+	0.982522i	$0.440400\pi$
$854$		−	2150.69i		−	2.51837i
$855$		0			0
$856$	−1251.72			−1.46229
$857$	326.446	−	1218.31i	0.380918	−	1.42160i	−0.463585	−	0.886052i	$-0.653437\pi$
$857$	326.446	−	1218.31i	0.380918	−	1.42160i	0.844503	−	0.535551i	$-0.179896\pi$
$858$	−13.5403	−	87.7427i	−0.0157812	−	0.102264i
$859$	37.7603	+	21.8009i	0.0439584	+	0.0253794i	0.521818	−	0.853057i	$-0.325254\pi$
$859$	37.7603	+	21.8009i	0.0439584	+	0.0253794i	−0.477860	+	0.878436i	$0.658587\pi$
$860$		0			0
$861$	47.5399	+	107.927i	0.0552148	+	0.125351i
$862$	−560.142	+	2090.48i	−0.649817	+	2.42515i
$863$	274.423	−	274.423i	0.317988	−	0.317988i	−0.530006	−	0.847994i	$-0.677810\pi$
$863$	274.423	−	274.423i	0.317988	−	0.317988i	0.847994	+	0.530006i	$0.177810\pi$
$864$	364.609	+	414.767i	0.422001	+	0.480054i
$865$		0			0
$866$	1135.94	+	1967.51i	1.31171	+	2.27195i
$867$	−325.677	+	838.454i	−0.375637	+	0.967075i
$868$	−402.033	−	1500.41i	−0.463172	−	1.72858i
$869$	0.412935	+	0.238408i	0.000475184	+	0.000274348i
$870$		0			0
$871$	46.8394	+	81.1282i	0.0537766	+	0.0931438i
$872$	760.017	+	760.017i	0.871579	+	0.871579i
$873$	547.673	−	349.513i	0.627346	−	0.400359i
$874$			741.121i			0.847965i
$875$		0			0
$876$	1449.84	+	158.205i	1.65506	+	0.180599i
$877$	−171.710	+	46.0094i	−0.195792	+	0.0524623i	−0.355382	−	0.934721i	$-0.615649\pi$
$877$	−171.710	+	46.0094i	−0.195792	+	0.0524623i	0.159590	+	0.987183i	$0.448983\pi$
$878$	542.205	+	2023.53i	0.617545	+	2.30471i
$879$	−97.5184	+	893.687i	−0.110942	+	1.01671i
$880$		0			0
$881$	−1000.82			−1.13600			−0.568000	−	0.823029i	$-0.692282\pi$
$881$	−1000.82			−1.13600			−0.568000	+	0.823029i	$0.692282\pi$
$882$	1020.24	−	45.3500i	1.15673	−	0.0514172i
$883$	−766.494	+	766.494i	−0.868057	+	0.868057i	−0.992257	−	0.124201i	$-0.960363\pi$
$883$	−766.494	+	766.494i	−0.868057	+	0.868057i	0.124201	+	0.992257i	$0.460363\pi$
$884$	−649.920	+	375.232i	−0.735204	+	0.424470i
$885$		0			0
$886$	−897.522	+	1554.55i	−1.01300	+	1.75457i
$887$	621.429	−	166.511i	0.700596	−	0.187724i	0.109099	−	0.994031i	$-0.465204\pi$
$887$	621.429	−	166.511i	0.700596	−	0.187724i	0.591498	+	0.806307i	$0.298537\pi$
$888$	1380.56	+	536.244i	1.55468	+	0.603878i
$889$	−907.698	+	524.060i	−1.02103	+	0.589494i
$890$		0			0
$891$	−135.698	+	95.3361i	−0.152299	+	0.106999i
$892$	64.6759	+	64.6759i	0.0725067	+	0.0725067i
$893$	−15.6357	−	4.18956i	−0.0175091	−	0.00469156i
$894$	924.963	−	407.428i	1.03463	−	0.455736i
$895$		0			0
$896$	1057.12	−	1830.98i	1.17982	−	2.04350i
$897$	152.957	−	23.6041i	0.170521	−	0.0263145i
$898$	−812.743	−	217.774i	−0.905058	−	0.242510i
$899$			537.328i			0.597696i
$900$		0			0
$901$	−114.384			−0.126952
$902$	−7.63268	+	28.4855i	−0.00846195	+	0.0315804i
$903$	−671.006	+	538.974i	−0.743086	+	0.596871i
$904$	369.109	+	213.105i	0.408307	+	0.235736i
$905$		0			0
$906$	2172.02	+	237.009i	2.39738	+	0.261600i
$907$	170.993	−	638.156i	0.188526	−	0.703589i	−0.805322	−	0.592838i	$-0.798008\pi$
$907$	170.993	−	638.156i	0.188526	−	0.703589i	0.993848	−	0.110752i	$-0.0353258\pi$
$908$	−2235.42	+	2235.42i	−2.46191	+	2.46191i
$909$	120.377	−	545.019i	0.132428	−	0.599581i
$910$		0			0
$911$	536.476	+	929.204i	0.588887	+	1.01998i	0.994379	+	0.105884i	$0.0337671\pi$
$911$	536.476	+	929.204i	0.588887	+	1.01998i	−0.405491	+	0.914099i	$0.632900\pi$
$912$	−355.881	+	54.9189i	−0.390221	+	0.0602181i
$913$	84.1979	+	314.231i	0.0922211	+	0.344174i
$914$	−853.309	−	492.658i	−0.933598	−	0.539013i
$915$		0			0
$916$	677.331	+	1173.17i	0.739444	+	1.28075i
$917$	−532.635	−	532.635i	−0.580846	−	0.580846i
$918$	1819.82	+	1212.86i	1.98238	+	1.32120i
$919$			728.665i			0.792889i	0.918059	+	0.396444i	$0.129756\pi$
$919$			728.665i			0.792889i	−0.918059	+	0.396444i	$0.870244\pi$
$920$		0			0
$921$	−236.692	−	537.349i	−0.256995	−	0.583441i
$922$	−1643.59	+	440.399i	−1.78264	+	0.477656i
$923$	−32.0652	−	119.669i	−0.0347402	−	0.129652i
$924$	322.384	+	236.187i	0.348901	+	0.255613i
$925$		0			0
$926$	−985.543			−1.06430
$927$	−219.317	+	422.117i	−0.236588	+	0.455358i
$928$	−325.515	+	325.515i	−0.350771	+	0.350771i
$929$	−844.876	+	487.790i	−0.909447	+	0.525070i	−0.880253	−	0.474504i	$-0.842627\pi$
$929$	−844.876	+	487.790i	−0.909447	+	0.525070i	−0.0291940	+	0.999574i	$0.509294\pi$
$930$		0			0
$931$	316.763	−	548.649i	0.340239	−	0.589312i
$932$	−612.611	+	164.149i	−0.657308	+	0.176125i
$933$	250.903	−	201.534i	0.268921	−	0.216006i
$934$	−1536.11	+	886.871i	−1.64465	+	0.949541i
$935$		0			0
$936$	123.219	+	389.729i	0.131644	+	0.416377i
$937$	141.251	+	141.251i	0.150749	+	0.150749i	0.778452	−	0.627704i	$-0.216005\pi$
$937$	141.251	+	141.251i	0.150749	+	0.150749i	−0.627704	+	0.778452i	$0.716005\pi$
$938$	−635.447	−	170.268i	−0.677449	−	0.181522i
$939$	−1323.62	−	969.716i	−1.40961	−	1.03271i
$940$		0			0
$941$	557.909	−	966.326i	0.592889	−	1.02691i	−0.400952	−	0.916099i	$-0.631321\pi$
$941$	557.909	−	966.326i	0.592889	−	1.02691i	0.993841	−	0.110815i	$-0.0353461\pi$
$942$	962.596	−	2478.20i	1.02186	−	2.63079i
$943$	−49.6574	−	13.3057i	−0.0526589	−	0.0141099i
$944$			493.269i			0.522531i
$945$		0			0
$946$	−215.217			−0.227502
$947$	−205.274	+	766.094i	−0.216763	+	0.808969i	0.768776	+	0.639518i	$0.220866\pi$
$947$	−205.274	+	766.094i	−0.216763	+	0.808969i	−0.985539	+	0.169451i	$0.945801\pi$
$948$	−4.65132	−	1.80669i	−0.00490646	−	0.00190579i
$949$	−255.263	−	147.376i	−0.268981	−	0.155296i
$950$		0			0
$951$	−773.604	+	1055.93i	−0.813464	+	1.11034i
$952$	600.082	−	2239.54i	0.630338	−	2.35245i
$953$	80.4623	−	80.4623i	0.0844305	−	0.0844305i	−0.663630	−	0.748061i	$-0.730985\pi$
$953$	80.4623	−	80.4623i	0.0844305	−	0.0844305i	0.748061	+	0.663630i	$0.230985\pi$
$954$	−30.5413	+	138.278i	−0.0320139	+	0.144946i
$955$		0			0
$956$	238.807	+	413.625i	0.249798	+	0.432662i
$957$	−86.5729	−	107.781i	−0.0904628	−	0.112623i
$958$	374.330	+	1397.02i	0.390741	+	1.45826i
$959$	1230.39	+	710.365i	1.28299	+	0.740735i
$960$		0			0
$961$	195.525	+	338.658i	0.203459	+	0.352402i
$962$	−481.095	−	481.095i	−0.500099	−	0.500099i
$963$	−47.6980	−	1073.06i	−0.0495306	−	1.11429i
$964$		−	423.810i		−	0.439636i
$965$		0			0
$966$	−642.328	+	876.748i	−0.664935	+	0.907607i
$967$	328.164	−	87.9314i	0.339363	−	0.0909322i	−0.0851126	−	0.996371i	$-0.527125\pi$
$967$	328.164	−	87.9314i	0.339363	−	0.0909322i	0.424476	+	0.905439i	$0.360458\pi$
$968$	−317.078	−	1183.35i	−0.327560	−	1.22247i
$969$	1241.56	−	546.884i	1.28128	−	0.564380i
$970$		0			0
$971$	1786.19			1.83954			0.919769	−	0.392460i	$-0.128376\pi$
$971$	1786.19			1.83954			0.919769	+	0.392460i	$0.128376\pi$
$972$	1251.31	−	1202.60i	1.28736	−	1.23724i
$973$	10.0620	−	10.0620i	0.0103413	−	0.0103413i
$974$	1707.67	−	985.926i	1.75326	−	1.01224i
$975$		0			0
$976$	−227.759	+	394.490i	−0.233360	+	0.404191i
$977$	−743.412	+	199.197i	−0.760913	+	0.203886i	−0.618353	−	0.785900i	$-0.712200\pi$
$977$	−743.412	+	199.197i	−0.760913	+	0.203886i	−0.142560	+	0.989786i	$0.545533\pi$
$978$	347.902	+	2254.45i	0.355728	+	2.30516i
$979$	183.313	−	105.836i	0.187246	−	0.108106i
$980$		0			0
$981$	−622.578	+	680.501i	−0.634637	+	0.693681i
$982$	1817.45	+	1817.45i	1.85076	+	1.85076i
$983$	−79.2948	−	21.2470i	−0.0806661	−	0.0216144i	0.218260	−	0.975891i	$-0.429962\pi$
$983$	−79.2948	−	21.2470i	−0.0806661	−	0.0216144i	−0.298926	+	0.954276i	$0.596629\pi$
$984$	14.7279	−	134.971i	0.0149674	−	0.137166i
$985$		0			0
$986$	−911.523	+	1578.80i	−0.924466	+	1.60122i
$987$	−14.8660	−	18.5076i	−0.0150618	−	0.0187514i
$988$	556.722	+	149.173i	0.563484	+	0.150985i
$989$		−	375.177i		−	0.379350i
$990$		0			0
$991$	−515.156			−0.519835			−0.259917	−	0.965631i	$-0.583695\pi$
$991$	−515.156			−0.519835			−0.259917	+	0.965631i	$0.583695\pi$
$992$	126.381	−	471.659i	0.127400	−	0.475462i
$993$	−268.256	−	1738.33i	−0.270147	−	1.75059i
$994$	753.465	+	435.013i	0.758013	+	0.437639i
$995$		0			0
$996$	−1372.35	−	3115.57i	−1.37786	−	3.12808i
$997$	96.0965	−	358.637i	0.0963856	−	0.359716i	−0.900840	−	0.434151i	$-0.857049\pi$
$997$	96.0965	−	358.637i	0.0963856	−	0.359716i	0.997226	+	0.0744346i	$0.0237152\pi$
$998$	231.032	−	231.032i	0.231495	−	0.231495i
$999$	−407.098	+	1203.94i	−0.407505	+	1.20515i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.3.o.b.157.2		40
5.2	odd	4		45.3.k.a.13.2	yes	40
5.3	odd	4	inner	225.3.o.b.193.9		40
5.4	even	2		45.3.k.a.22.9	yes	40
9.7	even	3	inner	225.3.o.b.7.9		40
15.2	even	4		135.3.l.a.118.9		40
15.14	odd	2		135.3.l.a.37.2		40
45.2	even	12		135.3.l.a.73.2		40
45.4	even	6		405.3.g.h.82.9		20
45.7	odd	12		45.3.k.a.43.9	yes	40
45.14	odd	6		405.3.g.g.82.2		20
45.22	odd	12		405.3.g.h.163.9		20
45.29	odd	6		135.3.l.a.127.9		40
45.32	even	12		405.3.g.g.163.2		20
45.34	even	6		45.3.k.a.7.2	✓	40
45.43	odd	12	inner	225.3.o.b.43.2		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.k.a.7.2	✓	40	45.34	even	6
45.3.k.a.13.2	yes	40	5.2	odd	4
45.3.k.a.22.9	yes	40	5.4	even	2
45.3.k.a.43.9	yes	40	45.7	odd	12
135.3.l.a.37.2		40	15.14	odd	2
135.3.l.a.73.2		40	45.2	even	12
135.3.l.a.118.9		40	15.2	even	4
135.3.l.a.127.9		40	45.29	odd	6
225.3.o.b.7.9		40	9.7	even	3	inner
225.3.o.b.43.2		40	45.43	odd	12	inner
225.3.o.b.157.2		40	1.1	even	1	trivial
225.3.o.b.193.9		40	5.3	odd	4	inner
405.3.g.g.82.2		20	45.14	odd	6
405.3.g.g.163.2		20	45.32	even	12
405.3.g.h.82.9		20	45.4	even	6
405.3.g.h.163.9		20	45.22	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	225.o (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.863931 + 3.22423i) q^{2} +(2.79645 + 1.08621i) q^{3} +(-6.18520 - 3.57103i) q^{4} +(-5.91814 + 8.07800i) q^{6} +(-2.35787 + 8.79970i) q^{7} +(7.41620 - 7.41620i) q^{8} +(6.64028 + 6.07508i) q^{9} +(1.02371 + 1.77311i) q^{11} +(-13.4177 - 16.7046i) q^{12} +(1.12075 + 4.18269i) q^{13} +(-26.3352 - 15.2047i) q^{14} +(3.22036 + 5.57783i) q^{16} +(-17.1585 - 17.1585i) q^{17} +(-25.3242 + 16.1614i) q^{18} +18.6363i q^{19} +(-16.1520 + 22.0468i) q^{21} +(-6.60133 + 1.76882i) q^{22} +(-3.08350 - 11.5078i) q^{23} +(28.7946 - 12.6835i) q^{24} -14.4542 q^{26} +(11.9704 + 24.2014i) q^{27} +(46.0079 - 46.0079i) q^{28} +(-19.4918 + 11.2536i) q^{29} +(11.9368 - 20.6752i) q^{31} +(19.7565 - 5.29373i) q^{32} +(0.936770 + 6.07038i) q^{33} +(70.1467 - 40.4992i) q^{34} +(-19.3772 - 61.2882i) q^{36} +(33.2840 + 33.2840i) q^{37} +(-60.0877 - 16.1005i) q^{38} +(-1.40917 + 12.9141i) q^{39} +(2.15756 - 3.73700i) q^{41} +(-57.1297 - 71.1247i) q^{42} +(30.4181 + 8.15051i) q^{43} -14.6227i q^{44} +39.7677 q^{46} +(-0.224807 + 0.838990i) q^{47} +(2.94688 + 19.0961i) q^{48} +(-29.4398 - 16.9971i) q^{49} +(-29.3451 - 66.6207i) q^{51} +(8.00445 - 29.8730i) q^{52} +(3.33316 - 3.33316i) q^{53} +(-88.3727 + 17.6870i) q^{54} +(47.7739 + 82.7467i) q^{56} +(-20.2430 + 52.1155i) q^{57} +(-19.4446 - 72.5684i) q^{58} +(66.3254 + 38.2930i) q^{59} +(35.3623 + 61.2493i) q^{61} +(56.3490 + 56.3490i) q^{62} +(-69.1158 + 44.1082i) q^{63} +94.0358i q^{64} +(-20.3816 - 2.22403i) q^{66} +(20.8965 - 5.59919i) q^{67} +(44.8553 + 167.402i) q^{68} +(3.87703 - 35.5302i) q^{69} -28.6105 q^{71} +(94.2997 - 4.19166i) q^{72} +(-48.1316 + 48.1316i) q^{73} +(-136.071 + 78.5604i) q^{74} +(66.5507 - 115.269i) q^{76} +(-18.0166 + 4.82753i) q^{77} +(-40.4205 - 15.7004i) q^{78} +(0.201686 - 0.116444i) q^{79} +(7.18677 + 80.6805i) q^{81} +(10.1850 + 10.1850i) q^{82} +(153.477 + 41.1240i) q^{83} +(178.633 - 78.6845i) q^{84} +(-52.5583 + 91.0337i) q^{86} +(-66.7316 + 10.2979i) q^{87} +(20.7418 + 5.55774i) q^{88} -103.385i q^{89} -39.4490 q^{91} +(-22.0225 + 82.1891i) q^{92} +(55.8384 - 44.8512i) q^{93} +(-2.51088 - 1.44966i) q^{94} +(60.9981 + 6.65606i) q^{96} +(18.6837 - 69.7287i) q^{97} +(80.2366 - 80.2366i) q^{98} +(-3.97409 + 17.9931i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 2 q^{2} + 6 q^{3} - 24 q^{6} + 2 q^{7} + 24 q^{8} + 8 q^{11} + 30 q^{12} + 2 q^{13} + 28 q^{16} - 28 q^{17} - 48 q^{18} + 12 q^{21} - 14 q^{22} - 82 q^{23} - 112 q^{26} + 198 q^{27} + 88 q^{28} - 4 q^{31}+ \cdots + 1876 q^{98}+O(q^{100}) \) 40 * q + 2 * q^2 + 6 * q^3 - 24 * q^6 + 2 * q^7 + 24 * q^8 + 8 * q^11 + 30 * q^12 + 2 * q^13 + 28 * q^16 - 28 * q^17 - 48 * q^18 + 12 * q^21 - 14 * q^22 - 82 * q^23 - 112 * q^26 + 198 * q^27 + 88 * q^28 - 4 * q^31 + 14 * q^32 - 96 * q^33 + 264 * q^36 + 92 * q^37 - 330 * q^38 - 28 * q^41 - 498 * q^42 + 2 * q^43 - 136 * q^46 - 64 * q^47 + 510 * q^48 - 396 * q^51 + 74 * q^52 + 608 * q^53 - 192 * q^56 + 114 * q^57 - 30 * q^58 + 92 * q^61 + 100 * q^62 - 24 * q^63 + 588 * q^66 + 80 * q^67 - 626 * q^68 + 248 * q^71 + 162 * q^72 + 8 * q^73 - 96 * q^76 - 338 * q^77 - 1062 * q^78 + 204 * q^81 - 104 * q^82 - 370 * q^83 - 328 * q^86 - 534 * q^87 + 210 * q^88 + 152 * q^91 - 388 * q^92 + 1062 * q^93 - 876 * q^96 - 292 * q^97 + 1876 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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