LMFDB - Embedded newform 225.4.p.b.218.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(32,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 3]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("225.32");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.p (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:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			218.12
Character	$\chi$	$=$	225.218
Dual form			225.4.p.b.32.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.79258 - 0.748271i) q^{2} +(-5.18419 + 0.352314i) q^{3} +(0.310415 - 0.179218i) q^{4} +(-14.2137 + 4.86305i) q^{6} +(-5.03374 - 18.7862i) q^{7} +(-15.6218 + 15.6218i) q^{8} +(26.7517 - 3.65293i) q^{9} +O(q^{10})$	\(q+(2.79258 - 0.748271i) q^{2} +(-5.18419 + 0.352314i) q^{3} +(0.310415 - 0.179218i) q^{4} +(-14.2137 + 4.86305i) q^{6} +(-5.03374 - 18.7862i) q^{7} +(-15.6218 + 15.6218i) q^{8} +(26.7517 - 3.65293i) q^{9} +(49.0377 + 28.3119i) q^{11} +(-1.54611 + 1.03846i) q^{12} +(0.616650 - 2.30137i) q^{13} +(-28.1143 - 48.6954i) q^{14} +(-33.3695 + 57.7977i) q^{16} +(92.5976 + 92.5976i) q^{17} +(71.9731 - 30.2187i) q^{18} +21.7774i q^{19} +(32.7146 + 95.6178i) q^{21} +(158.127 + 42.3700i) q^{22} +(98.8952 + 26.4989i) q^{23} +(75.4824 - 86.4900i) q^{24} -6.88818i q^{26} +(-137.399 + 28.3625i) q^{27} +(-4.92937 - 4.92937i) q^{28} +(-40.6009 + 70.3228i) q^{29} +(4.26447 + 7.38628i) q^{31} +(-4.19518 + 15.6566i) q^{32} +(-264.196 - 129.498i) q^{33} +(327.875 + 189.298i) q^{34} +(7.64946 - 5.92832i) q^{36} +(-8.92697 + 8.92697i) q^{37} +(16.2954 + 60.8153i) q^{38} +(-2.38603 + 12.1480i) q^{39} +(-28.1572 + 16.2566i) q^{41} +(162.906 + 242.541i) q^{42} +(428.714 - 114.874i) q^{43} +20.2960 q^{44} +296.002 q^{46} +(140.159 - 37.5556i) q^{47} +(152.631 - 311.391i) q^{48} +(-30.5356 + 17.6297i) q^{49} +(-512.667 - 447.420i) q^{51} +(-0.221029 - 0.824893i) q^{52} +(-82.9808 + 82.9808i) q^{53} +(-362.476 + 182.017i) q^{54} +(372.109 + 214.837i) q^{56} +(-7.67250 - 112.898i) q^{57} +(-60.7609 + 226.763i) q^{58} +(-129.436 - 224.189i) q^{59} +(-282.613 + 489.500i) q^{61} +(17.4358 + 17.4358i) q^{62} +(-203.286 - 484.175i) q^{63} -487.051i q^{64} +(-834.688 - 163.944i) q^{66} +(-434.879 - 116.526i) q^{67} +(45.3388 + 12.1485i) q^{68} +(-522.028 - 102.533i) q^{69} -16.2978i q^{71} +(-360.844 + 474.974i) q^{72} +(-59.2407 - 59.2407i) q^{73} +(-18.2495 + 31.6091i) q^{74} +(3.90290 + 6.76003i) q^{76} +(285.030 - 1063.75i) q^{77} +(2.42681 + 35.7097i) q^{78} +(472.049 + 272.538i) q^{79} +(702.312 - 195.445i) q^{81} +(-66.4671 + 66.4671i) q^{82} +(260.644 + 972.735i) q^{83} +(27.2915 + 23.8181i) q^{84} +(1111.26 - 641.588i) q^{86} +(185.707 - 378.871i) q^{87} +(-1208.34 + 323.773i) q^{88} -844.831 q^{89} -46.3380 q^{91} +(35.4476 - 9.49816i) q^{92} +(-24.7101 - 36.7895i) q^{93} +(363.305 - 209.754i) q^{94} +(16.2326 - 82.6450i) q^{96} +(105.374 + 393.261i) q^{97} +(-72.0814 + 72.0814i) q^{98} +(1415.27 + 578.262i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7}+O(q^{10}) $ 64 * q + 6 * q^2 - 24 * q^6 + 2 * q^7	$ 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7} - 36 q^{11} + 138 q^{12} + 2 q^{13} + 316 q^{16} + 480 q^{18} + 480 q^{21} + 34 q^{22} - 306 q^{23} - 180 q^{27} + 232 q^{28} - 4 q^{31} + 1770 q^{32} + 294 q^{33} - 216 q^{36} - 136 q^{37} - 114 q^{38} + 1992 q^{41} - 1698 q^{42} + 2 q^{43} - 952 q^{46} - 3462 q^{47} - 4326 q^{48} - 2496 q^{51} + 242 q^{52} - 7128 q^{56} + 2544 q^{57} - 534 q^{58} + 32 q^{61} + 4038 q^{63} + 2892 q^{66} - 610 q^{67} + 2694 q^{68} + 1854 q^{72} + 8 q^{73} + 1368 q^{76} + 6486 q^{77} - 1434 q^{78} + 3012 q^{81} + 3784 q^{82} - 2814 q^{83} + 12480 q^{86} - 4830 q^{87} + 1338 q^{88} + 992 q^{91} - 13152 q^{92} - 8310 q^{93} - 7932 q^{96} - 358 q^{97}+O(q^{100}) $ 64 * q + 6 * q^2 - 24 * q^6 + 2 * q^7 - 36 * q^11 + 138 * q^12 + 2 * q^13 + 316 * q^16 + 480 * q^18 + 480 * q^21 + 34 * q^22 - 306 * q^23 - 180 * q^27 + 232 * q^28 - 4 * q^31 + 1770 * q^32 + 294 * q^33 - 216 * q^36 - 136 * q^37 - 114 * q^38 + 1992 * q^41 - 1698 * q^42 + 2 * q^43 - 952 * q^46 - 3462 * q^47 - 4326 * q^48 - 2496 * q^51 + 242 * q^52 - 7128 * q^56 + 2544 * q^57 - 534 * q^58 + 32 * q^61 + 4038 * q^63 + 2892 * q^66 - 610 * q^67 + 2694 * q^68 + 1854 * q^72 + 8 * q^73 + 1368 * q^76 + 6486 * q^77 - 1434 * q^78 + 3012 * q^81 + 3784 * q^82 - 2814 * q^83 + 12480 * q^86 - 4830 * q^87 + 1338 * q^88 + 992 * q^91 - 13152 * q^92 - 8310 * q^93 - 7932 * q^96 - 358 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	2.79258	−	0.748271i	0.987328	−	0.264554i	0.271200	−	0.962523i	$-0.412580\pi$
$2$	2.79258	−	0.748271i	0.987328	−	0.264554i	0.716128	+	0.697969i	$0.245913\pi$
$3$	−5.18419	+	0.352314i	−0.997699	+	0.0678029i
$3$	−5.18419	+	0.352314i	−0.997699	+	0.0678029i
$4$	0.310415	−	0.179218i	0.0388018	−	0.0224022i
$5$		0			0
$5$		0			0
$6$	−14.2137	+	4.86305i	−0.967118	+	0.330889i
$7$	−5.03374	−	18.7862i	−0.271797	−	1.01436i	−0.957958	−	0.286909i	$-0.907372\pi$
$7$	−5.03374	−	18.7862i	−0.271797	−	1.01436i	0.686161	−	0.727450i	$-0.259294\pi$
$8$	−15.6218	+	15.6218i	−0.690390	+	0.690390i
$9$	26.7517	−	3.65293i	0.990806	−	0.135294i
$10$		0			0
$11$	49.0377	+	28.3119i	1.34413	+	0.776033i	0.987410	−	0.158179i	$-0.0505623\pi$
$11$	49.0377	+	28.3119i	1.34413	+	0.776033i	0.356718	+	0.934212i	$0.383896\pi$
$12$	−1.54611	+	1.03846i	−0.0371936	+	0.0249816i
$13$	0.616650	−	2.30137i	0.0131560	−	0.0490988i	−0.959036	−	0.283285i	$-0.908576\pi$
$13$	0.616650	−	2.30137i	0.0131560	−	0.0490988i	0.972192	+	0.234186i	$0.0752425\pi$
$14$	−28.1143	−	48.6954i	−0.536705	−	0.929600i
$15$		0			0
$16$	−33.3695	+	57.7977i	−0.521399	+	0.903089i
$17$	92.5976	+	92.5976i	1.32107	+	1.32107i	0.912910	+	0.408161i	$0.133830\pi$
$17$	92.5976	+	92.5976i	1.32107	+	1.32107i	0.408161	+	0.912910i	$0.366170\pi$
$18$	71.9731	−	30.2187i	0.942457	−	0.395700i
$19$			21.7774i			0.262952i	0.991319	+	0.131476i	$0.0419716\pi$
$19$			21.7774i			0.262952i	−0.991319	+	0.131476i	$0.958028\pi$
$20$		0			0
$21$	32.7146	+	95.6178i	0.339948	+	0.993596i
$22$	158.127	+	42.3700i	1.53240	+	0.410605i
$23$	98.8952	+	26.4989i	0.896569	+	0.240235i	0.677542	−	0.735484i	$-0.263045\pi$
$23$	98.8952	+	26.4989i	0.896569	+	0.240235i	0.219027	+	0.975719i	$0.429712\pi$
$24$	75.4824	−	86.4900i	0.641991	−	0.735612i
$25$		0			0
$26$		−	6.88818i		−	0.0519571i
$27$	−137.399	+	28.3625i	−0.979352	+	0.202162i
$28$	−4.92937	−	4.92937i	−0.0332701	−	0.0332701i
$29$	−40.6009	+	70.3228i	−0.259979	+	0.450297i	−0.966236	−	0.257659i	$-0.917049\pi$
$29$	−40.6009	+	70.3228i	−0.259979	+	0.450297i	0.706257	+	0.707956i	$0.250382\pi$
$30$		0			0
$31$	4.26447	+	7.38628i	0.0247071	+	0.0427940i	0.878115	−	0.478450i	$-0.158801\pi$
$31$	4.26447	+	7.38628i	0.0247071	+	0.0427940i	−0.853407	+	0.521244i	$0.825468\pi$
$32$	−4.19518	+	15.6566i	−0.0231753	+	0.0864914i
$33$	−264.196	−	129.498i	−1.39365	−	0.683111i
$34$	327.875	+	189.298i	1.65382	+	0.954836i
$35$		0			0
$36$	7.64946	−	5.92832i	0.0354142	−	0.0274459i
$37$	−8.92697	+	8.92697i	−0.0396645	+	0.0396645i	−0.726661	−	0.686996i	$-0.758929\pi$
$37$	−8.92697	+	8.92697i	−0.0396645	+	0.0396645i	0.686996	+	0.726661i	$0.258929\pi$
$38$	16.2954	+	60.8153i	0.0695648	+	0.259619i
$39$	−2.38603	+	12.1480i	−0.00979667	+	0.0498778i
$40$		0			0
$41$	−28.1572	+	16.2566i	−0.107254	+	0.0619232i	−0.552668	−	0.833402i	$-0.686390\pi$
$41$	−28.1572	+	16.2566i	−0.107254	+	0.0619232i	0.445413	+	0.895325i	$0.353057\pi$
$42$	162.906	+	242.541i	0.598499	+	0.891070i
$43$	428.714	−	114.874i	1.52042	−	0.407396i	0.600543	−	0.799593i	$-0.294951\pi$
$43$	428.714	−	114.874i	1.52042	−	0.407396i	0.919882	+	0.392196i	$0.128285\pi$
$44$	20.2960			0.0695395
$45$		0			0
$46$	296.002			0.948762
$47$	140.159	−	37.5556i	0.434986	−	0.116554i	−0.0346799	−	0.999398i	$-0.511041\pi$
$47$	140.159	−	37.5556i	0.434986	−	0.116554i	0.469666	+	0.882844i	$0.344374\pi$
$48$	152.631	−	311.391i	0.458967	−	0.936363i
$49$	−30.5356	+	17.6297i	−0.0890251	+	0.0513987i
$50$		0			0
$51$	−512.667	−	447.420i	−1.40760	−	1.22846i
$52$	−0.221029	−	0.824893i	−0.000589447	−	0.00219985i
$53$	−82.9808	+	82.9808i	−0.215062	+	0.215062i	−0.806414	−	0.591352i	$-0.798595\pi$
$53$	−82.9808	+	82.9808i	−0.215062	+	0.215062i	0.591352	+	0.806414i	$0.298595\pi$
$54$	−362.476	+	182.017i	−0.913459	+	0.458691i
$55$		0			0
$56$	372.109	+	214.837i	0.887950	+	0.512658i
$57$	−7.67250	−	112.898i	−0.0178289	−	0.262347i
$58$	−60.7609	+	226.763i	−0.137557	+	0.513369i
$59$	−129.436	−	224.189i	−0.285612	−	0.494695i	0.687145	−	0.726520i	$-0.258864\pi$
$59$	−129.436	−	224.189i	−0.285612	−	0.494695i	−0.972757	+	0.231825i	$0.925530\pi$
$60$		0			0
$61$	−282.613	+	489.500i	−0.593195	+	1.02744i	0.400604	+	0.916251i	$0.368800\pi$
$61$	−282.613	+	489.500i	−0.593195	+	1.02744i	−0.993799	+	0.111192i	$0.964533\pi$
$62$	17.4358	+	17.4358i	0.0357153	+	0.0357153i
$63$	−203.286	−	484.175i	−0.406534	−	0.968260i
$64$		−	487.051i		−	0.951271i
$65$		0			0
$66$	−834.688	−	163.944i	−1.55671	−	0.305759i
$67$	−434.879	−	116.526i	−0.792970	−	0.212476i	−0.160475	−	0.987040i	$-0.551302\pi$
$67$	−434.879	−	116.526i	−0.792970	−	0.212476i	−0.632495	+	0.774564i	$0.717969\pi$
$68$	45.3388	+	12.1485i	0.0808549	+	0.0216650i
$69$	−522.028	−	102.533i	−0.910794	−	0.178892i
$70$		0			0
$71$		−	16.2978i		−	0.0272422i	−0.999907	−	0.0136211i	$-0.995664\pi$
$71$		−	16.2978i		−	0.0272422i	0.999907	−	0.0136211i	$-0.00433587\pi$
$72$	−360.844	+	474.974i	−0.590637	+	0.777448i
$73$	−59.2407	−	59.2407i	−0.0949809	−	0.0949809i	0.658020	−	0.753001i	$-0.271394\pi$
$73$	−59.2407	−	59.2407i	−0.0949809	−	0.0949809i	−0.753001	+	0.658020i	$0.771394\pi$
$74$	−18.2495	+	31.6091i	−0.0286684	+	0.0496552i
$75$		0			0
$76$	3.90290	+	6.76003i	0.00589071	+	0.0102030i
$77$	285.030	−	1063.75i	0.421846	−	1.57435i
$78$	2.42681	+	35.7097i	0.00352284	+	0.0518375i
$79$	472.049	+	272.538i	0.672274	+	0.388138i	0.796938	−	0.604061i	$-0.206452\pi$
$79$	472.049	+	272.538i	0.672274	+	0.388138i	−0.124663	+	0.992199i	$0.539785\pi$
$80$		0			0
$81$	702.312	−	195.445i	0.963391	−	0.268100i
$82$	−66.4671	+	66.4671i	−0.0895129	+	0.0895129i
$83$	260.644	+	972.735i	0.344691	+	1.28640i	0.892973	+	0.450110i	$0.148615\pi$
$83$	260.644	+	972.735i	0.344691	+	1.28640i	−0.548282	+	0.836294i	$0.684718\pi$
$84$	27.2915	+	23.8181i	0.0354494	+	0.0309377i
$85$		0			0
$86$	1111.26	−	641.588i	1.39338	−	0.804467i
$87$	185.707	−	378.871i	0.228849	−	0.466888i
$88$	−1208.34	+	323.773i	−1.46374	+	0.392208i
$89$	−844.831			−1.00620			−0.503101	−	0.864228i	$-0.667808\pi$
$89$	−844.831			−1.00620			−0.503101	+	0.864228i	$0.667808\pi$
$90$		0			0
$91$	−46.3380			−0.0533796
$92$	35.4476	−	9.49816i	0.0401703	−	0.0107636i
$93$	−24.7101	−	36.7895i	−0.0275518	−	0.0410203i
$94$	363.305	−	209.754i	0.398639	−	0.230154i
$95$		0			0
$96$	16.2326	−	82.6450i	0.0172576	−	0.0878637i
$97$	105.374	+	393.261i	0.110300	+	0.411645i	0.998892	−	0.0470524i	$-0.0149828\pi$
$97$	105.374	+	393.261i	0.110300	+	0.411645i	−0.888592	+	0.458698i	$0.848316\pi$
$98$	−72.0814	+	72.0814i	−0.0742992	+	0.0742992i
$99$	1415.27	+	578.262i	1.43676	+	0.587046i
$100$		0			0
$101$	−398.138	−	229.865i	−0.392240	−	0.226460i	0.290890	−	0.956756i	$-0.406049\pi$
$101$	−398.138	−	229.865i	−0.392240	−	0.226460i	−0.683130	+	0.730297i	$0.739382\pi$
$102$	−1766.46	−	865.845i	−1.71476	−	0.840504i
$103$	−360.103	+	1343.92i	−0.344485	+	1.28564i	0.548727	+	0.836001i	$0.315113\pi$
$103$	−360.103	+	1343.92i	−0.344485	+	1.28564i	−0.893212	+	0.449635i	$0.851554\pi$
$104$	26.3182	+	45.5845i	0.0248146	+	0.0429801i
$105$		0			0
$106$	−169.639	+	293.823i	−0.155441	+	0.269232i
$107$	−319.287	−	319.287i	−0.288473	−	0.288473i	0.548003	−	0.836476i	$-0.315388\pi$
$107$	−319.287	−	319.287i	−0.288473	−	0.288473i	−0.836476	+	0.548003i	$0.815388\pi$
$108$	−37.5677	+	33.4286i	−0.0334718	+	0.0297839i
$109$			1126.24i			0.989672i	0.868986	+	0.494836i	$0.164772\pi$
$109$			1126.24i			0.989672i	−0.868986	+	0.494836i	$0.835228\pi$
$110$		0			0
$111$	43.1341	−	49.4243i	0.0368838	−	0.0422625i
$112$	1253.77	+	335.947i	1.05777	+	0.283429i
$113$	1458.69	+	390.853i	1.21435	+	0.325384i	0.808467	−	0.588541i	$-0.200297\pi$
$113$	1458.69	+	390.853i	1.21435	+	0.325384i	0.405883	+	0.913925i	$0.366964\pi$
$114$	−105.905	−	309.537i	−0.0870077	−	0.254305i
$115$		0			0
$116$			29.1056i			0.0232965i
$117$	8.08972	−	63.8182i	0.00639226	−	0.0504273i
$118$	−529.215	−	529.215i	−0.412866	−	0.412866i
$119$	1273.44	−	2205.67i	0.980977	−	1.69910i
$120$		0			0
$121$	937.629	+	1624.02i	0.704455	+	1.22015i
$122$	−422.942	+	1578.44i	−0.313864	+	1.17136i
$123$	140.245	−	94.1974i	0.102809	−	0.0690528i
$124$	2.64751	+	1.52854i	0.00191736	+	0.00110699i
$125$		0			0
$126$	−929.988	−	1199.99i	−0.657539	−	0.848440i
$127$	638.135	−	638.135i	0.445869	−	0.445869i	−0.448110	−	0.893979i	$-0.647903\pi$
$127$	638.135	−	638.135i	0.445869	−	0.445869i	0.893979	+	0.448110i	$0.147903\pi$
$128$	−398.007	−	1485.38i	−0.274837	−	1.02571i
$129$	−2182.06	+	746.569i	−1.48930	+	0.509548i
$130$		0			0
$131$	2261.94	−	1305.93i	1.50860	−	0.870992i	0.508653	−	0.860972i	$-0.330144\pi$
$131$	2261.94	−	1305.93i	1.50860	−	0.870992i	0.999950	−	0.0100207i	$-0.00318975\pi$
$132$	−105.218	+	7.15058i	−0.0693795	+	0.00471498i
$133$	409.115	−	109.622i	0.266727	−	0.0714694i
$134$	−1301.63			−0.839132
$135$		0			0
$136$	−2893.07			−1.82411
$137$	−942.088	+	252.432i	−0.587504	+	0.157421i	−0.540312	−	0.841465i	$-0.681694\pi$
$137$	−942.088	+	252.432i	−0.587504	+	0.157421i	−0.0471916	+	0.998886i	$0.515027\pi$
$138$	−1534.53	+	104.286i	−0.946579	+	0.0643288i
$139$	−1106.34	+	638.748i	−0.675099	+	0.389769i	−0.798006	−	0.602649i	$-0.794112\pi$
$139$	−1106.34	+	638.748i	−0.675099	+	0.389769i	0.122907	+	0.992418i	$0.460778\pi$
$140$		0			0
$141$	−713.382	+	244.075i	−0.426082	+	0.145779i
$142$	−12.1952	−	45.5131i	−0.00720703	−	0.0268970i
$143$	95.3952	−	95.3952i	0.0557856	−	0.0557856i
$144$	−681.562	+	1668.09i	−0.394422	+	0.965327i
$145$		0			0
$146$	−209.763	−	121.107i	−0.118905	−	0.0686497i
$147$	152.091	−	102.154i	0.0853352	−	0.0573165i
$148$	−1.17119	+	4.37094i	−0.000650480	+	0.00242763i
$149$	69.6092	+	120.567i	0.0382725	+	0.0662900i	0.884527	−	0.466489i	$-0.154481\pi$
$149$	69.6092	+	120.567i	0.0382725	+	0.0662900i	−0.846255	+	0.532779i	$0.821148\pi$
$150$		0			0
$151$	706.994	−	1224.55i	0.381022	−	0.659950i	−0.610186	−	0.792258i	$-0.708905\pi$
$151$	706.994	−	1224.55i	0.381022	−	0.659950i	0.991209	+	0.132308i	$0.0422388\pi$
$152$	−340.201	−	340.201i	−0.181539	−	0.181539i
$153$	2815.40	+	2138.89i	1.48766	+	1.13019i
$154$		−	3183.88i		−	1.66600i
$155$		0			0
$156$	1.43648	+	4.19853i	0.000737247	+	0.00215482i
$157$	−2293.99	−	614.674i	−1.16612	−	0.312461i	−0.376712	−	0.926330i	$-0.622945\pi$
$157$	−2293.99	−	614.674i	−1.16612	−	0.312461i	−0.789407	+	0.613870i	$0.789612\pi$
$158$	1522.17	+	407.864i	0.766438	+	0.205367i
$159$	400.953	−	459.424i	0.199985	−	0.229149i
$160$		0			0
$161$		−	1991.25i		−	0.974738i
$162$	1815.02	−	1071.32i	0.880256	−	0.519571i
$163$	−940.543	−	940.543i	−0.451957	−	0.451957i	0.444046	−	0.896004i	$-0.353543\pi$
$163$	−940.543	−	940.543i	−0.451957	−	0.451957i	−0.896004	+	0.444046i	$0.853543\pi$
$164$	−5.82694	+	10.0926i	−0.00277444	+	0.00480547i
$165$		0			0
$166$	1455.74	+	2521.41i	0.680646	+	1.17891i
$167$	973.893	−	3634.62i	0.451270	−	1.68416i	−0.247558	−	0.968873i	$-0.579628\pi$
$167$	973.893	−	3634.62i	0.451270	−	1.68416i	0.698828	−	0.715290i	$-0.253705\pi$
$168$	−2004.78	−	982.659i	−0.920666	−	0.451273i
$169$	1897.74	+	1095.66i	0.863788	+	0.498708i
$170$		0			0
$171$	79.5514	+	582.584i	0.0355757	+	0.260534i
$172$	112.492	−	112.492i	0.0498686	−	0.0498686i
$173$	−1129.62	−	4215.81i	−0.496437	−	1.85273i	−0.521826	−	0.853052i	$-0.674749\pi$
$173$	−1129.62	−	4215.81i	−0.496437	−	1.85273i	0.0253882	−	0.999678i	$-0.491918\pi$
$174$	235.105	−	1196.99i	0.102432	−	0.521515i
$175$		0			0
$176$	−3272.73	+	1889.51i	−1.40165	+	0.809245i
$177$	750.006	+	1116.64i	0.318497	+	0.474191i
$178$	−2359.26	+	632.163i	−0.993451	+	0.266194i
$179$	2857.68			1.19326			0.596628	−	0.802518i	$-0.296507\pi$
$179$	2857.68			1.19326			0.596628	+	0.802518i	$0.296507\pi$
$180$		0			0
$181$	−1459.11			−0.599199			−0.299599	−	0.954065i	$-0.596853\pi$
$181$	−1459.11			−0.599199			−0.299599	+	0.954065i	$0.596853\pi$
$182$	−129.403	+	34.6734i	−0.0527031	+	0.0141218i
$183$	1292.66	−	2637.23i	0.522166	−	1.06530i
$184$	−1958.88	+	1130.96i	−0.784838	+	0.453127i
$185$		0			0
$186$	−96.5336	−	84.2478i	−0.0380548	−	0.0332116i
$187$	1919.15	+	7162.38i	0.750495	+	2.80088i
$188$	36.7768	−	36.7768i	0.0142672	−	0.0142672i
$189$	1224.46	+	2438.44i	0.471249	+	0.938468i
$190$		0			0
$191$	610.123	+	352.255i	0.231136	+	0.133446i	0.611096	−	0.791557i	$-0.290729\pi$
$191$	610.123	+	352.255i	0.231136	+	0.133446i	−0.379960	+	0.925003i	$0.624062\pi$
$192$	171.595	+	2524.96i	0.0644989	+	0.949081i
$193$	−396.828	+	1480.98i	−0.148001	+	0.552349i	0.851602	+	0.524189i	$0.175631\pi$
$193$	−396.828	+	1480.98i	−0.148001	+	0.552349i	−0.999603	+	0.0281599i	$0.991035\pi$
$194$	588.531	+	1019.37i	0.217804	+	0.377248i
$195$		0			0
$196$	−6.31913	+	10.9451i	−0.00230289	+	0.00398872i
$197$	989.475	+	989.475i	0.357854	+	0.357854i	0.863021	−	0.505168i	$-0.168569\pi$
$197$	989.475	+	989.475i	0.357854	+	0.357854i	−0.505168	+	0.863021i	$0.668569\pi$
$198$	4384.94	+	555.844i	1.57386	+	0.199506i
$199$		−	2035.66i		−	0.725146i	−0.931955	−	0.362573i	$-0.881898\pi$
$199$		−	2035.66i		−	0.725146i	0.931955	−	0.362573i	$-0.118102\pi$
$200$		0			0
$201$	2295.55	+	450.877i	0.805551	+	0.158221i
$202$	−1283.84	−	344.003i	−0.447180	−	0.119822i
$203$	1525.47	+	408.749i	0.527424	+	0.141323i
$204$	−239.325	−	47.0066i	−0.0821378	−	0.0161330i
$205$		0			0
$206$			4022.47i			1.36048i
$207$	2742.42	+	347.634i	0.920828	+	0.116726i
$208$	112.436	+	112.436i	0.0374811	+	0.0374811i
$209$	−616.560	+	1067.91i	−0.204059	+	0.353441i
$210$		0			0
$211$	−688.380	−	1192.31i	−0.224597	−	0.389014i	0.731601	−	0.681733i	$-0.238773\pi$
$211$	−688.380	−	1192.31i	−0.224597	−	0.389014i	−0.956199	+	0.292719i	$0.905440\pi$
$212$	−10.8868	+	40.6301i	−0.00352693	+	0.0131627i
$213$	5.74196	+	84.4912i	0.00184710	+	0.0271795i
$214$	−1130.55	−	652.723i	−0.361134	−	0.208501i
$215$		0			0
$216$	1703.35	−	2589.49i	0.536565	−	0.815706i
$217$	117.294	−	117.294i	0.0366932	−	0.0366932i
$218$	842.733	+	3145.12i	0.261821	+	0.977131i
$219$	327.987	+	286.244i	0.101202	+	0.0883223i
$220$		0			0
$221$	270.201	−	156.001i	0.0822430	−	0.0474830i
$222$	83.4728	−	170.297i	0.0252357	−	0.0514847i
$223$	3795.71	−	1017.06i	1.13982	−	0.305413i	0.360940	−	0.932589i	$-0.382456\pi$
$223$	3795.71	−	1017.06i	1.13982	−	0.305413i	0.778878	+	0.627176i	$0.215789\pi$
$224$	315.246			0.0940323
$225$		0			0
$226$	4365.96			1.28504
$227$	872.812	−	233.869i	0.255201	−	0.0683809i	−0.128950	−	0.991651i	$-0.541161\pi$
$227$	872.812	−	233.869i	0.255201	−	0.0683809i	0.384151	+	0.923270i	$0.374494\pi$
$228$	−22.6151	−	33.6703i	−0.00656895	−	0.00978012i
$229$	3128.15	−	1806.04i	0.902682	−	0.521164i	0.0246126	−	0.999697i	$-0.492165\pi$
$229$	3128.15	−	1806.04i	0.902682	−	0.521164i	0.878069	+	0.478533i	$0.158831\pi$
$230$		0			0
$231$	−1102.88	+	5615.09i	−0.314130	+	1.59933i
$232$	−464.308	−	1732.82i	−0.131394	−	0.490368i
$233$	−2992.27	+	2992.27i	−0.841332	+	0.841332i	−0.989032	−	0.147700i	$-0.952813\pi$
$233$	−2992.27	+	2992.27i	−0.841332	+	0.841332i	0.147700	+	0.989032i	$0.452813\pi$
$234$	−25.1621	−	184.271i	−0.00702947	−	0.0514794i
$235$		0			0
$236$	−80.3575	−	46.3945i	−0.0221645	−	0.0127967i
$237$	−2543.21	−	1246.58i	−0.697044	−	0.341662i
$238$	1905.76	−	7112.39i	0.519042	−	1.93709i
$239$	1931.06	+	3344.69i	0.522635	+	0.905230i	0.999653	+	0.0263367i	$0.00838419\pi$
$239$	1931.06	+	3344.69i	0.522635	+	0.905230i	−0.477018	+	0.878893i	$0.658282\pi$
$240$		0			0
$241$	858.250	−	1486.53i	0.229397	−	0.397328i	−0.728232	−	0.685330i	$-0.759658\pi$
$241$	858.250	−	1486.53i	0.229397	−	0.397328i	0.957630	+	0.288003i	$0.0929912\pi$
$242$	3833.62	+	3833.62i	1.01832	+	1.01832i
$243$	−3572.07	+	1260.66i	−0.942996	+	0.332803i
$244$			202.597i			0.0531556i
$245$		0			0
$246$	321.161	−	367.996i	0.0832377	−	0.0953762i
$247$	50.1178	+	13.4290i	0.0129106	+	0.00345939i
$248$	−182.005	−	48.7681i	−0.0466021	−	0.0124870i
$249$	−1693.94	−	4951.02i	−0.431120	−	1.26007i
$250$		0			0
$251$			2285.88i			0.574836i	0.957805	+	0.287418i	$0.0927968\pi$
$251$			2285.88i			0.574836i	−0.957805	+	0.287418i	$0.907203\pi$
$252$	−149.876	−	113.863i	−0.0374655	−	0.0284630i
$253$	4099.36	+	4099.36i	1.01867	+	1.01867i
$254$	1304.55	−	2259.54i	0.322262	−	0.558175i
$255$		0			0
$256$	−274.734	−	475.854i	−0.0670738	−	0.116175i
$257$	−988.996	+	3690.98i	−0.240046	+	0.895865i	0.735763	+	0.677239i	$0.236824\pi$
$257$	−988.996	+	3690.98i	−0.240046	+	0.895865i	−0.975809	+	0.218625i	$0.929843\pi$
$258$	−5534.96	+	3717.63i	−1.33563	+	0.897091i
$259$	212.640	+	122.768i	0.0510147	+	0.0294533i
$260$		0			0
$261$	−829.260	+	2029.57i	−0.196666	+	0.481330i
$262$	5339.48	−	5339.48i	1.25906	−	1.25906i
$263$	−1276.64	−	4764.50i	−0.299320	−	1.11708i	−0.937725	−	0.347378i	$-0.887072\pi$
$263$	−1276.64	−	4764.50i	−0.299320	−	1.11708i	0.638405	−	0.769701i	$-0.279595\pi$
$264$	6150.18	−	2104.21i	1.43378	−	0.490551i
$265$		0			0
$266$	1060.46	−	612.257i	0.244440	−	0.141127i
$267$	4379.77	−	297.646i	1.00389	−	0.0682234i
$268$	−155.876	+	41.7669i	−0.0355286	+	0.00951986i
$269$	−6569.52			−1.48904			−0.744518	−	0.667602i	$-0.767321\pi$
$269$	−6569.52			−1.48904			−0.744518	+	0.667602i	$0.767321\pi$
$270$		0			0
$271$	−1603.65			−0.359465			−0.179733	−	0.983715i	$-0.557523\pi$
$271$	−1603.65			−0.359465			−0.179733	+	0.983715i	$0.557523\pi$
$272$	−8441.86	+	2261.99i	−1.88185	+	0.504240i
$273$	240.225	−	16.3255i	0.0532567	−	0.00361929i
$274$	−2441.97	+	1409.87i	−0.538412	+	0.310852i
$275$		0			0
$276$	−180.421	+	61.7290i	−0.0393481	+	0.0134625i
$277$	−2276.92	−	8497.59i	−0.493888	−	1.84322i	−0.536171	−	0.844109i	$-0.680130\pi$
$277$	−2276.92	−	8497.59i	−0.493888	−	1.84322i	0.0422830	−	0.999106i	$-0.486537\pi$
$278$	−2611.60	+	2611.60i	−0.563430	+	0.563430i
$279$	141.064	+	182.018i	0.0302697	+	0.0390578i
$280$		0			0
$281$	−5805.61	−	3351.87i	−1.23250	−	0.711586i	−0.264953	−	0.964261i	$-0.585356\pi$
$281$	−5805.61	−	3351.87i	−1.23250	−	0.711586i	−0.967551	+	0.252675i	$0.918690\pi$
$282$	−1809.54	+	1215.40i	−0.382116	+	0.256653i
$283$	−295.723	+	1103.65i	−0.0621163	+	0.231821i	−0.990004	−	0.141038i	$-0.954956\pi$
$283$	−295.723	+	1103.65i	−0.0621163	+	0.231821i	0.927888	+	0.372859i	$0.121623\pi$
$284$	−2.92087	−	5.05909i	−0.000610287	−	0.00105705i
$285$		0			0
$286$	195.018	−	337.781i	0.0403204	−	0.0698370i
$287$	447.135	+	447.135i	0.0919636	+	0.0919636i
$288$	−55.0358	+	434.167i	−0.0112605	+	0.0888316i
$289$			12235.6i			2.49046i
$290$		0			0
$291$	−684.830	−	2001.62i	−0.137957	−	0.403219i
$292$	−29.0062	−	7.77218i	−0.00581322	−	0.00155765i
$293$	−6076.51	−	1628.20i	−1.21158	−	0.324642i	−0.404199	−	0.914671i	$-0.632450\pi$
$293$	−6076.51	−	1628.20i	−1.21158	−	0.324642i	−0.807382	+	0.590029i	$0.799116\pi$
$294$	348.289	−	399.080i	0.0690905	−	0.0791660i
$295$		0			0
$296$		−	278.910i		−	0.0547679i
$297$	−7540.74	−	2499.20i	−1.47326	−	0.488278i
$298$	284.606	+	284.606i	0.0553248	+	0.0553248i
$299$	121.967	−	211.254i	0.0235905	−	0.0408599i
$300$		0			0
$301$	−4316.07	−	7475.65i	−0.826492	−	1.43153i
$302$	1058.05	−	3948.68i	0.201602	−	0.752388i
$303$	2145.01	+	1051.40i	0.406692	+	0.199344i
$304$	−1258.68	−	726.702i	−0.237469	−	0.137103i
$305$		0			0
$306$	9462.71	+	3866.36i	1.76780	+	0.722304i
$307$	−4998.67	+	4998.67i	−0.929281	+	0.929281i	−0.997659	−	0.0683782i	$-0.978218\pi$
$307$	−4998.67	+	4998.67i	−0.929281	+	0.929281i	0.0683782	+	0.997659i	$0.478218\pi$
$308$	−102.165	−	381.285i	−0.0189006	−	0.0705380i
$309$	1393.36	−	7094.02i	0.256523	−	1.30603i
$310$		0			0
$311$	−2626.45	+	1516.38i	−0.478882	+	0.276483i	−0.719950	−	0.694025i	$-0.755835\pi$
$311$	−2626.45	+	1516.38i	−0.478882	+	0.276483i	0.241068	+	0.970508i	$0.422502\pi$
$312$	−152.499	−	227.047i	−0.0276717	−	0.0411987i
$313$	4163.08	−	1115.49i	0.751793	−	0.201442i	0.137480	−	0.990505i	$-0.456100\pi$
$313$	4163.08	−	1115.49i	0.751793	−	0.201442i	0.614313	+	0.789062i	$0.289433\pi$
$314$	−6866.12			−1.23400
$315$		0			0
$316$	195.375			0.0347806
$317$	4660.18	−	1248.69i	0.825684	−	0.221241i	0.178854	−	0.983876i	$-0.442761\pi$
$317$	4660.18	−	1248.69i	0.825684	−	0.221241i	0.646830	+	0.762634i	$0.276094\pi$
$318$	775.922	−	1583.00i	0.136829	−	0.279152i
$319$	−3981.95	+	2298.98i	−0.698891	+	0.403505i
$320$		0			0
$321$	1767.74	+	1542.76i	0.307369	+	0.268250i
$322$	−1490.00	−	5560.74i	−0.257870	−	0.962385i
$323$	−2016.54	+	2016.54i	−0.347378	+	0.347378i
$324$	182.981	−	186.536i	0.0313753	−	0.0319849i
$325$		0			0
$326$	−3330.33	−	1922.77i	−0.565797	−	0.326663i
$327$	−396.791	−	5838.65i	−0.0671027	−	0.987395i
$328$	185.909	−	693.821i	0.0312960	−	0.116798i
$329$	−1411.05	−	2444.01i	−0.236455	−	0.409553i
$330$		0			0
$331$	5632.10	−	9755.08i	0.935251	−	1.61990i	0.161065	−	0.986944i	$-0.448507\pi$
$331$	5632.10	−	9755.08i	0.935251	−	1.61990i	0.774186	−	0.632958i	$-0.218160\pi$
$332$	255.239	+	255.239i	0.0421930	+	0.0421930i
$333$	−206.202	+	271.422i	−0.0339334	+	0.0446661i
$334$		−	10878.7i		−	1.78221i
$335$		0			0
$336$	−6618.16	−	1299.89i	−1.07455	−	0.211057i
$337$	−2284.24	−	612.060i	−0.369230	−	0.0989348i	0.0694329	−	0.997587i	$-0.477881\pi$
$337$	−2284.24	−	612.060i	−0.369230	−	0.0989348i	−0.438663	+	0.898652i	$0.644548\pi$
$338$	6119.46	+	1639.70i	0.984777	+	0.263870i
$339$	−7699.81	−	1512.34i	−1.23362	−	0.242299i
$340$		0			0
$341$			482.941i			0.0766942i
$342$	658.085	+	1567.39i	0.104050	+	0.247821i
$343$	−4232.18	−	4232.18i	−0.666229	−	0.666229i
$344$	−4902.73	+	8491.79i	−0.768424	+	1.33095i
$345$		0			0
$346$	−6309.14	−	10927.7i	−0.980293	−	1.69792i
$347$	266.565	−	994.834i	0.0412391	−	0.153906i	−0.942236	−	0.334950i	$-0.891281\pi$
$347$	266.565	−	994.834i	0.0412391	−	0.153906i	0.983475	+	0.181043i	$0.0579474\pi$
$348$	−10.2543	−	150.889i	−0.00157957	−	0.0232429i
$349$	−4729.47	−	2730.56i	−0.725394	−	0.418807i	0.0913406	−	0.995820i	$-0.470885\pi$
$349$	−4729.47	−	2730.56i	−0.725394	−	0.418807i	−0.816735	+	0.577013i	$0.804218\pi$
$350$		0			0
$351$	−19.4546	+	333.696i	−0.00295843	+	0.0507447i
$352$	−648.991	+	648.991i	−0.0982708	+	0.0982708i
$353$	172.316	+	643.090i	0.0259814	+	0.0969638i	0.977699	−	0.210011i	$-0.0673500\pi$
$353$	172.316	+	643.090i	0.0259814	+	0.0969638i	−0.951718	+	0.306975i	$0.900683\pi$
$354$	2930.00	+	2557.10i	0.439909	+	0.383922i
$355$		0			0
$356$	−262.248	+	151.409i	−0.0390425	+	0.0225412i
$357$	−5824.69	+	11883.3i	−0.863516	+	1.76171i
$358$	7980.30	−	2138.31i	1.17813	−	0.315680i
$359$	6703.88			0.985563			0.492781	−	0.870153i	$-0.335980\pi$
$359$	6703.88			0.985563			0.492781	+	0.870153i	$0.335980\pi$
$360$		0			0
$361$	6384.74			0.930856
$362$	−4074.69	+	1091.81i	−0.591605	+	0.158520i
$363$	−5433.02	−	8088.90i	−0.785563	−	1.16958i
$364$	−14.3840	+	8.30460i	−0.00207122	+	0.00119582i
$365$		0			0
$366$	1636.51	−	8331.95i	0.233720	−	1.18994i
$367$	−845.191	−	3154.29i	−0.120214	−	0.448645i	0.879410	−	0.476065i	$-0.157937\pi$
$367$	−845.191	−	3154.29i	−0.120214	−	0.448645i	−0.999624	+	0.0274202i	$0.991271\pi$
$368$	−4831.66	+	4831.66i	−0.684423	+	0.684423i
$369$	−693.871	+	537.748i	−0.0978901	+	0.0758646i
$370$		0			0
$371$	1976.60	+	1141.19i	0.276603	+	0.159697i
$372$	−14.2637	−	6.99149i	−0.00198801	−	0.000974440i
$373$	−1093.97	+	4082.74i	−0.151859	+	0.566747i	0.847495	+	0.530804i	$0.178110\pi$
$373$	−1093.97	+	4082.74i	−0.151859	+	0.566747i	−0.999354	+	0.0359425i	$0.988557\pi$
$374$	10718.8	+	18565.5i	1.48197	+	2.56684i
$375$		0			0
$376$	−1602.85	+	2776.22i	−0.219842	+	0.380778i
$377$	136.802	+	136.802i	0.0186888	+	0.0186888i
$378$	5244.01	+	5893.32i	0.713553	+	0.801904i
$379$			2005.61i			0.271824i	0.990721	+	0.135912i	$0.0433965\pi$
$379$			2005.61i			0.271824i	−0.990721	+	0.135912i	$0.956604\pi$
$380$		0			0
$381$	−3083.39	+	3533.04i	−0.414612	+	0.475074i
$382$	1967.40	+	527.164i	0.263511	+	0.0706074i
$383$	−1133.16	−	303.630i	−0.151180	−	0.0405085i	0.182435	−	0.983218i	$-0.441602\pi$
$383$	−1133.16	−	303.630i	−0.151180	−	0.0405085i	−0.333615	+	0.942709i	$0.608269\pi$
$384$	2586.67	+	7560.29i	0.343751	+	1.00471i
$385$		0			0
$386$			4432.70i			0.584504i
$387$	11049.2	−	4639.13i	1.45133	−	0.609355i
$388$	103.189	+	103.189i	0.0135016	+	0.0135016i
$389$	5874.10	−	10174.2i	0.765627	−	1.32610i	−0.174288	−	0.984695i	$-0.555762\pi$
$389$	5874.10	−	10174.2i	0.765627	−	1.32610i	0.939915	−	0.341410i	$-0.110904\pi$
$390$		0			0
$391$	6703.72	+	11611.2i	0.867064	+	1.50180i
$392$	201.612	−	752.427i	0.0259769	−	0.0969472i
$393$	−11266.3	+	7567.13i	−1.44608	+	0.971276i
$394$	3503.59	+	2022.80i	0.447990	+	0.258647i
$395$		0			0
$396$	542.954	−	74.1400i	0.0689001	−	0.00940826i
$397$	−10419.9	+	10419.9i	−1.31728	+	1.31728i	−0.401363	+	0.915919i	$0.631463\pi$
$397$	−10419.9	+	10419.9i	−1.31728	+	1.31728i	−0.915919	+	0.401363i	$0.868537\pi$
$398$	−1523.22	−	5684.75i	−0.191840	−	0.715957i
$399$	−2082.31	+	712.439i	−0.261268	+	0.0893898i
$400$		0			0
$401$	−4827.90	+	2787.39i	−0.601231	+	0.347121i	−0.769526	−	0.638616i	$-0.779507\pi$
$401$	−4827.90	+	2787.39i	−0.601231	+	0.347121i	0.168295	+	0.985737i	$0.446174\pi$
$402$	6747.90	−	458.583i	0.837201	−	0.0568956i
$403$	19.6282	−	5.25937i	0.00242618	−	0.000650093i
$404$	−164.784			−0.0202928
$405$		0			0
$406$	4565.86			0.558128
$407$	−690.498	+	185.018i	−0.0840951	+	0.0225332i
$408$	14998.2	−	1019.27i	1.81991	−	0.123680i
$409$	8856.21	−	5113.13i	1.07069	−	0.618162i	0.142318	−	0.989821i	$-0.454544\pi$
$409$	8856.21	−	5113.13i	1.07069	−	0.618162i	0.928369	+	0.371659i	$0.121211\pi$
$410$		0			0
$411$	4795.03	−	1640.57i	0.575478	−	0.196893i
$412$	129.074	+	481.710i	0.0154345	+	0.0576023i
$413$	−3560.12	+	3560.12i	−0.424169	+	0.424169i
$414$	7918.56	−	1081.27i	0.940039	−	0.128362i
$415$		0			0
$416$	33.4447	+	19.3093i	0.00394173	+	0.00227576i
$417$	5510.46	−	3701.17i	0.647118	−	0.434646i
$418$	−922.708	+	3443.59i	−0.107969	+	0.402947i
$419$	−4387.14	−	7598.75i	−0.511517	−	0.885974i	−0.999911	−	0.0133505i	$-0.995750\pi$
$419$	−4387.14	−	7598.75i	−0.511517	−	0.885974i	0.488394	−	0.872623i	$-0.337583\pi$
$420$		0			0
$421$	−6005.42	+	10401.7i	−0.695217	+	1.20415i	0.274891	+	0.961475i	$0.411358\pi$
$421$	−6005.42	+	10401.7i	−0.695217	+	1.20415i	−0.970108	+	0.242675i	$0.921975\pi$
$422$	−2814.53	−	2814.53i	−0.324666	−	0.324666i
$423$	3612.32	−	1516.67i	0.415217	−	0.174333i
$424$		−	2592.61i		−	0.296954i
$425$		0			0
$426$	79.2572	+	231.652i	0.00901414	+	0.0263464i
$427$	10618.4	+	2845.20i	1.20342	+	0.322457i
$428$	−156.333	−	41.8894i	−0.0176557	−	0.00473084i
$429$	−460.938	+	528.156i	−0.0518748	+	0.0594397i
$430$		0			0
$431$			4099.38i			0.458145i	0.973409	+	0.229072i	$0.0735692\pi$
$431$			4099.38i			0.458145i	−0.973409	+	0.229072i	$0.926431\pi$
$432$	2945.66	−	8887.80i	0.328063	−	0.989849i
$433$	−4324.33	−	4324.33i	−0.479940	−	0.479940i	0.425172	−	0.905112i	$-0.360213\pi$
$433$	−4324.33	−	4324.33i	−0.479940	−	0.479940i	−0.905112	+	0.425172i	$0.860213\pi$
$434$	239.785	−	415.320i	0.0265209	−	0.0459355i
$435$		0			0
$436$	201.843	+	349.602i	0.0221709	+	0.0384011i
$437$	−577.078	+	2153.68i	−0.0631702	+	0.235754i
$438$	1130.12	+	553.938i	0.123286	+	0.0604296i
$439$	−10469.7	−	6044.67i	−1.13825	−	0.657167i	−0.192251	−	0.981346i	$-0.561579\pi$
$439$	−10469.7	−	6044.67i	−1.13825	−	0.657167i	−0.945996	+	0.324179i	$0.894912\pi$
$440$		0			0
$441$	−752.481	+	583.171i	−0.0812526	+	0.0629706i
$442$	637.829	−	637.829i	0.0686390	−	0.0686390i
$443$	−2391.39	−	8924.79i	−0.256475	−	0.957177i	−0.967264	−	0.253772i	$-0.918329\pi$
$443$	−2391.39	−	8924.79i	−0.256475	−	0.957177i	0.710789	−	0.703405i	$-0.248338\pi$
$444$	4.53173	−	23.0724i	0.000484383	−	0.00246614i
$445$		0			0
$446$	9838.80	−	5680.43i	1.04458	−	0.603086i
$447$	−403.345	−	600.517i	−0.0426791	−	0.0635424i
$448$	−9149.82	+	2451.69i	−0.964930	+	0.258552i
$449$	−702.553			−0.0738431			−0.0369215	−	0.999318i	$-0.511755\pi$
$449$	−702.553			−0.0738431			−0.0369215	+	0.999318i	$0.511755\pi$
$450$		0			0
$451$	−1841.02			−0.192218
$452$	522.845	−	140.096i	0.0544083	−	0.0145787i
$453$	−3233.77	+	6597.39i	−0.335399	+	0.684266i
$454$	2262.40	−	1306.20i	0.233876	−	0.135029i
$455$		0			0
$456$	1883.53	+	1643.81i	0.193430	+	0.168813i
$457$	1175.37	+	4386.55i	0.120310	+	0.449002i	0.999629	−	0.0272303i	$-0.00866873\pi$
$457$	1175.37	+	4386.55i	0.120310	+	0.449002i	−0.879319	+	0.476232i	$0.842002\pi$
$458$	7384.22	−	7384.22i	0.753367	−	0.753367i
$459$	−15349.1	−	10096.5i	−1.56086	−	1.02672i
$460$		0			0
$461$	−7776.73	−	4489.90i	−0.785680	−	0.453613i	0.0527593	−	0.998607i	$-0.483198\pi$
$461$	−7776.73	−	4489.90i	−0.785680	−	0.453613i	−0.838440	+	0.544995i	$0.816532\pi$
$462$	1121.73	+	16505.9i	0.112960	+	1.66217i
$463$	1770.40	−	6607.21i	0.177705	−	0.663204i	−0.818370	−	0.574691i	$-0.805122\pi$
$463$	1770.40	−	6607.21i	0.177705	−	0.663204i	0.996075	−	0.0885123i	$-0.0282112\pi$
$464$	−2709.66	−	4693.27i	−0.271106	−	0.469569i
$465$		0			0
$466$	−6117.14	+	10595.2i	−0.608093	+	1.05325i
$467$	1646.02	+	1646.02i	0.163102	+	0.163102i	0.783939	−	0.620837i	$-0.213207\pi$
$467$	1646.02	+	1646.02i	0.163102	+	0.163102i	−0.620837	+	0.783939i	$0.713207\pi$
$468$	−8.92620	−	21.2599i	−0.000881653	−	0.00209987i
$469$			8756.28i			0.862106i
$470$		0			0
$471$	12109.1	+	2378.38i	1.18462	+	0.232675i
$472$	5524.25	+	1480.22i	0.538716	+	0.144349i
$473$	24275.4	+	6504.58i	2.35980	+	0.632306i
$474$	−8034.92	−	1578.16i	−0.778599	−	0.152927i
$475$		0			0
$476$		−	912.895i		−	0.0879044i
$477$	−1916.76	+	2523.00i	−0.183988	+	0.242181i
$478$	7895.37	+	7895.37i	0.755494	+	0.755494i
$479$	7066.68	−	12239.8i	0.674081	−	1.16754i	−0.302656	−	0.953100i	$-0.597873\pi$
$479$	7066.68	−	12239.8i	0.674081	−	1.16754i	0.976737	−	0.214442i	$-0.0687933\pi$
$480$		0			0
$481$	15.0394	+	26.0491i	0.00142565	+	0.00246930i
$482$	1284.41	−	4793.47i	0.121376	−	0.452980i
$483$	701.547	+	10323.0i	0.0660901	+	0.972494i
$484$	582.107	+	336.080i	0.0546682	+	0.0315627i
$485$		0			0
$486$	−9031.98	+	6193.36i	−0.843002	+	0.578059i
$487$	6660.19	−	6660.19i	0.619717	−	0.619717i	−0.325742	−	0.945459i	$-0.605614\pi$
$487$	6660.19	−	6660.19i	0.619717	−	0.619717i	0.945459	+	0.325742i	$0.105614\pi$
$488$	−3231.94	−	12061.8i	−0.299801	−	1.11887i
$489$	5207.33	+	4544.59i	0.481561	+	0.420273i
$490$		0			0
$491$	−4778.58	+	2758.92i	−0.439215	+	0.253581i	−0.703264	−	0.710928i	$-0.748275\pi$
$491$	−4778.58	+	2758.92i	−0.439215	+	0.253581i	0.264050	+	0.964509i	$0.414942\pi$
$492$	26.6522	−	54.3747i	0.00244223	−	0.00498252i
$493$	−10271.3	+	2752.18i	−0.938325	+	0.251424i
$494$	150.007			0.0136622
$495$		0			0
$496$	−569.213			−0.0515291
$497$	−306.174	+	82.0392i	−0.0276334	+	0.00740435i
$498$	−8435.16	−	12558.6i	−0.759013	−	1.13005i
$499$	4628.28	−	2672.14i	0.415211	−	0.239722i	−0.277816	−	0.960634i	$-0.589610\pi$
$499$	4628.28	−	2672.14i	0.415211	−	0.239722i	0.693026	+	0.720913i	$0.256277\pi$
$500$		0			0
$501$	−3768.32	+	19185.7i	−0.336040	+	1.71088i
$502$	1710.46	+	6383.52i	0.152075	+	0.567551i
$503$	3380.78	−	3380.78i	0.299685	−	0.299685i	−0.541205	−	0.840890i	$-0.682032\pi$
$503$	3380.78	−	3380.78i	0.299685	−	0.299685i	0.840890	+	0.541205i	$0.182032\pi$
$504$	10739.4	+	4387.98i	0.949145	+	0.387810i
$505$		0			0
$506$	14515.2	+	8380.37i	1.27526	+	0.736271i
$507$	−10224.3	−	5011.52i	−0.895614	−	0.438993i
$508$	83.7212	−	312.452i	0.00731206	−	0.0272890i
$509$	6234.51	+	10798.5i	0.542908	+	0.940344i	0.998735	+	0.0502756i	$0.0160100\pi$
$509$	6234.51	+	10798.5i	0.542908	+	0.940344i	−0.455828	+	0.890068i	$0.650657\pi$
$510$		0			0
$511$	−814.705	+	1411.11i	−0.0705292	+	0.122160i
$512$	7575.72	+	7575.72i	0.653911	+	0.653911i
$513$	−617.663	−	2992.20i	−0.0531588	−	0.257522i
$514$			11047.4i			0.948017i
$515$		0			0
$516$	−543.546	+	622.811i	−0.0463726	+	0.0531351i
$517$	7936.35	+	2126.54i	0.675127	+	0.180900i
$518$	685.678	+	183.727i	0.0581602	+	0.0155840i
$519$	7341.48	+	21457.6i	0.620916	+	1.81481i
$520$		0			0
$521$		−	16543.1i		−	1.39111i	−0.718473	−	0.695555i	$-0.755159\pi$
$521$		−	16543.1i		−	1.39111i	0.718473	−	0.695555i	$-0.244841\pi$
$522$	−797.112	+	6288.26i	−0.0668365	+	0.527260i
$523$	937.744	+	937.744i	0.0784029	+	0.0784029i	0.745221	−	0.666818i	$-0.232344\pi$
$523$	937.744	+	937.744i	0.0784029	+	0.0784029i	−0.666818	+	0.745221i	$0.732344\pi$
$524$	468.094	−	810.762i	0.0390244	−	0.0675922i
$525$		0			0
$526$	−7130.27	−	12350.0i	−0.591054	−	1.02374i
$527$	−289.072	+	1078.83i	−0.0238940	+	0.0891738i
$528$	16300.7	−	10948.6i	1.34356	−	0.902419i
$529$	−1458.85	−	842.270i	−0.119903	−	0.0692258i
$530$		0			0
$531$	−4281.58	−	5524.64i	−0.349915	−	0.451505i
$532$	107.349	−	107.349i	0.00874843	−	0.00874843i
$533$	20.0492	+	74.8247i	0.00162932	+	0.00608071i
$534$	12008.2	−	4108.46i	0.973116	−	0.332941i
$535$		0			0
$536$	8613.91	−	4973.24i	0.694150	−	0.400768i
$537$	−14814.7	+	1006.80i	−1.19051	+	0.0809062i
$538$	−18345.9	+	4915.78i	−1.47017	+	0.393930i
$539$	−1996.53			−0.159548
$540$		0			0
$541$	−946.946			−0.0752540			−0.0376270	−	0.999292i	$-0.511980\pi$
$541$	−946.946			−0.0752540			−0.0376270	+	0.999292i	$0.511980\pi$
$542$	−4478.34	+	1199.97i	−0.354910	+	0.0950979i
$543$	7564.32	−	514.066i	0.597820	−	0.0406274i
$544$	−1838.23	+	1061.30i	−0.144878	+	0.0836451i
$545$		0			0
$546$	658.633	−	225.344i	0.0516243	−	0.0176627i
$547$	3015.33	+	11253.3i	0.235697	+	0.879631i	0.977834	+	0.209383i	$0.0671456\pi$
$547$	3015.33	+	11253.3i	0.235697	+	0.879631i	−0.742137	+	0.670248i	$0.766188\pi$
$548$	−247.198	+	247.198i	−0.0192696	+	0.0192696i
$549$	−5772.28	+	14127.3i	−0.448734	+	1.09825i
$550$		0			0
$551$	−1531.45	−	884.183i	−0.118406	−	0.0683620i
$552$	9756.74	−	6553.25i	0.752309	−	0.505298i
$553$	2743.77	−	10239.9i	0.210989	−	0.787422i
$554$	−12717.0	−	22026.5i	−0.975259	−	1.68920i
$555$		0			0
$556$	−228.950	+	396.553i	−0.0174634	+	0.0302475i
$557$	1609.11	+	1609.11i	0.122406	+	0.122406i	0.765656	−	0.643250i	$-0.222414\pi$
$557$	1609.11	+	1609.11i	0.122406	+	0.122406i	−0.643250	+	0.765656i	$0.722414\pi$
$558$	530.131	+	402.747i	0.0402190	+	0.0305549i
$559$		−	1057.46i		−	0.0800107i
$560$		0			0
$561$	−12472.7	−	36455.0i	−0.938676	−	2.74355i
$562$	−18720.8	−	5016.21i	−1.40514	−	0.376506i
$563$	−17547.6	−	4701.86i	−1.31357	−	0.351971i	−0.467008	−	0.884253i	$-0.654668\pi$
$563$	−17547.6	−	4701.86i	−1.31357	−	0.351971i	−0.846567	+	0.532282i	$0.821335\pi$
$564$	−177.701	+	203.615i	−0.0132670	+	0.0152017i
$565$		0			0
$566$			3303.33i			0.245317i
$567$	−7206.92	−	12210.0i	−0.533796	−	0.904356i
$568$	254.601	+	254.601i	0.0188078	+	0.0188078i
$569$	−149.738	+	259.354i	−0.0110322	+	0.0191084i	−0.871489	−	0.490415i	$-0.836845\pi$
$569$	−149.738	+	259.354i	−0.0110322	+	0.0191084i	0.860457	+	0.509524i	$0.170178\pi$
$570$		0			0
$571$	10802.7	+	18710.8i	0.791732	+	1.37132i	0.924894	+	0.380226i	$0.124154\pi$
$571$	10802.7	+	18710.8i	0.791732	+	1.37132i	−0.133162	+	0.991094i	$0.542513\pi$
$572$	12.5155	−	46.7086i	0.000914861	−	0.00341431i
$573$	−3287.10	−	1611.20i	−0.239652	−	0.117468i
$574$	1583.24	+	914.085i	0.115128	+	0.0664689i
$575$		0			0
$576$	−1779.16	−	13029.5i	−0.128701	−	0.942524i
$577$	6073.88	−	6073.88i	0.438231	−	0.438231i	−0.453186	−	0.891416i	$-0.649712\pi$
$577$	6073.88	−	6073.88i	0.438231	−	0.438231i	0.891416	+	0.453186i	$0.149712\pi$
$578$	9155.55	+	34169.0i	0.658859	+	2.45890i
$579$	1535.46	−	7817.50i	0.110210	−	0.561113i
$580$		0			0
$581$	16962.0	−	9793.00i	1.21119	−	0.699281i
$582$	−3410.20	−	5077.24i	−0.242882	−	0.361613i
$583$	−6418.53	+	1719.84i	−0.455966	+	0.122176i
$584$	1850.89			0.131148
$585$		0			0
$586$	−18187.5			−1.28211
$587$	10872.4	−	2913.25i	0.764484	−	0.204843i	0.144551	−	0.989497i	$-0.453826\pi$
$587$	10872.4	−	2913.25i	0.764484	−	0.204843i	0.619933	+	0.784654i	$0.287160\pi$
$588$	28.9035	−	58.9676i	0.00202714	−	0.00413569i
$589$	−160.854	+	92.8691i	−0.0112528	+	0.00649678i
$590$		0			0
$591$	−5478.24	−	4781.02i	−0.381294	−	0.332767i
$592$	−218.070	−	813.847i	−0.0151395	−	0.0565015i
$593$	19651.0	−	19651.0i	1.36082	−	1.36082i	0.487953	−	0.872870i	$-0.337744\pi$
$593$	19651.0	−	19651.0i	1.36082	−	1.36082i	0.872870	−	0.487953i	$-0.162256\pi$
$594$	−22928.2	−	1336.72i	−1.58377	−	0.0923341i
$595$		0			0
$596$	43.2154	+	24.9504i	0.00297009	+	0.00171478i
$597$	717.192	+	10553.3i	0.0491670	+	0.723478i
$598$	182.529	−	681.209i	0.0124819	−	0.0465831i
$599$	−1419.69	−	2458.97i	−0.0968396	−	0.167731i	0.813535	−	0.581516i	$-0.197540\pi$
$599$	−1419.69	−	2458.97i	−0.0968396	−	0.167731i	−0.910375	+	0.413784i	$0.864207\pi$
$600$		0			0
$601$	−254.777	+	441.286i	−0.0172921	+	0.0299508i	−0.874542	−	0.484950i	$-0.838838\pi$
$601$	−254.777	+	441.286i	−0.0172921	+	0.0299508i	0.857250	+	0.514901i	$0.172171\pi$
$602$	−17646.8	−	17646.8i	−1.19473	−	1.19473i
$603$	−12059.4	−	1528.68i	−0.814425	−	0.103238i
$604$		−	506.824i		−	0.0341430i
$605$		0			0
$606$	6776.85	+	1331.06i	0.454275	+	0.0892257i
$607$	−3306.40	−	885.947i	−0.221092	−	0.0592413i	0.146573	−	0.989200i	$-0.453176\pi$
$607$	−3306.40	−	885.947i	−0.221092	−	0.0592413i	−0.367664	+	0.929959i	$0.619842\pi$
$608$	−340.961	−	91.3602i	−0.0227431	−	0.00609399i
$609$	−8052.35	−	1581.59i	−0.535793	−	0.105237i
$610$		0			0
$611$		−	345.717i		−	0.0228907i
$612$	1257.27	+	159.374i	0.0830426	+	0.0105266i
$613$	6435.77	+	6435.77i	0.424043	+	0.424043i	0.886593	−	0.462550i	$-0.153066\pi$
$613$	6435.77	+	6435.77i	0.424043	+	0.424043i	−0.462550	+	0.886593i	$0.653066\pi$
$614$	−10218.9	+	17699.6i	−0.671660	+	1.16335i
$615$		0			0
$616$	12164.9	+	21070.2i	0.795679	+	1.37816i
$617$	−556.352	+	2076.34i	−0.0363013	+	0.135478i	−0.981698	−	0.190443i	$-0.939008\pi$
$617$	−556.352	+	2076.34i	−0.0363013	+	0.135478i	0.945397	+	0.325921i	$0.105674\pi$
$618$	−1417.17	−	20853.3i	−0.0922444	−	1.35735i
$619$	16359.4	+	9445.11i	1.06226	+	0.613297i	0.926057	−	0.377383i	$-0.123176\pi$
$619$	16359.4	+	9445.11i	1.06226	+	0.613297i	0.136205	+	0.990681i	$0.456509\pi$
$620$		0			0
$621$	−14339.7	−	836.011i	−0.926623	−	0.0540225i
$622$	−6199.92	+	6199.92i	−0.399669	+	0.399669i
$623$	4252.66	+	15871.2i	0.273482	+	1.02065i
$624$	−622.505	−	543.279i	−0.0399361	−	0.0348535i
$625$		0			0
$626$	10791.1	−	6230.22i	0.688974	−	0.397779i
$627$	2820.13	−	5753.50i	0.179625	−	0.366463i
$628$	−822.250	+	220.321i	−0.0522474	+	0.0139996i
$629$	−1653.23			−0.104799
$630$		0			0
$631$	865.068			0.0545766			0.0272883	−	0.999628i	$-0.491313\pi$
$631$	865.068			0.0545766			0.0272883	+	0.999628i	$0.491313\pi$
$632$	−11631.8	+	3116.72i	−0.732099	+	0.196165i
$633$	3988.77	+	5938.64i	0.250457	+	0.372891i
$634$	12079.6	−	6974.16i	0.756691	−	0.436876i
$635$		0			0
$636$	42.1247	−	214.470i	0.00262634	−	0.0133715i
$637$	21.7427	+	81.1450i	0.00135240	+	0.00504723i
$638$	−9399.66	+	9399.66i	−0.583286	+	0.583286i
$639$	−59.5349	−	435.996i	−0.00368570	−	0.0269917i
$640$		0			0
$641$	6830.18	+	3943.41i	0.420867	+	0.242988i	0.695448	−	0.718576i	$-0.255206\pi$
$641$	6830.18	+	3943.41i	0.420867	+	0.242988i	−0.274581	+	0.961564i	$0.588539\pi$
$642$	6090.95	+	2985.53i	0.374440	+	0.183535i
$643$	−1839.94	+	6866.75i	−0.112846	+	0.421148i	−0.999117	−	0.0420200i	$-0.986621\pi$
$643$	−1839.94	+	6866.75i	−0.112846	+	0.421148i	0.886270	+	0.463168i	$0.153287\pi$
$644$	−356.868	−	618.114i	−0.0218363	−	0.0378216i
$645$		0			0
$646$	−4122.43	+	7140.26i	−0.251076	+	0.434876i
$647$	1933.74	+	1933.74i	0.117501	+	0.117501i	0.763412	−	0.645911i	$-0.223522\pi$
$647$	1933.74	+	1933.74i	0.117501	+	0.117501i	−0.645911	+	0.763412i	$0.723522\pi$
$648$	−7918.16	+	14024.5i	−0.480023	+	0.850210i
$649$		−	14658.3i		−	0.886578i
$650$		0			0
$651$	−566.749	+	649.398i	−0.0341208	+	0.0390966i
$652$	−460.521	−	123.396i	−0.0276616	−	0.00741191i
$653$	6232.28	+	1669.93i	0.373488	+	0.100076i	0.440680	−	0.897664i	$-0.354737\pi$
$653$	6232.28	+	1669.93i	0.373488	+	0.100076i	−0.0671918	+	0.997740i	$0.521404\pi$
$654$	−5476.96	−	16008.0i	−0.327471	−	0.957130i
$655$		0			0
$656$		−	2169.90i		−	0.129147i
$657$	−1801.20	−	1368.39i	−0.106958	−	0.0812572i
$658$	−5769.26	−	5769.26i	−0.341807	−	0.341807i
$659$	−3849.42	+	6667.40i	−0.227545	+	0.394120i	−0.957080	−	0.289824i	$-0.906403\pi$
$659$	−3849.42	+	6667.40i	−0.227545	+	0.394120i	0.729535	+	0.683944i	$0.239737\pi$
$660$		0			0
$661$	−1130.78	−	1958.57i	−0.0665392	−	0.115249i	0.830837	−	0.556517i	$-0.187862\pi$
$661$	−1130.78	−	1958.57i	−0.0665392	−	0.115249i	−0.897376	+	0.441267i	$0.854529\pi$
$662$	8428.67	−	31456.2i	0.494848	−	1.84680i
$663$	−1345.81	+	903.934i	−0.0788343	+	0.0529501i
$664$	−19267.5	−	11124.1i	−1.12609	−	0.650150i
$665$		0			0
$666$	−372.741	+	912.263i	−0.0216868	+	0.0530773i
$667$	−5878.71	+	5878.71i	−0.341266	+	0.341266i
$668$	−349.078	−	1302.78i	−0.0202189	−	0.0754581i
$669$	−19319.4	+	6609.90i	−1.11649	+	0.381993i
$670$		0			0
$671$	−27717.4	+	16002.6i	−1.59466	+	0.920678i
$672$	−1634.29	+	111.066i	−0.0938159	+	0.00637566i
$673$	8335.28	−	2233.43i	0.477417	−	0.127923i	−0.0120828	−	0.999927i	$-0.503846\pi$
$673$	8335.28	−	2233.43i	0.477417	−	0.127923i	0.489499	+	0.872004i	$0.337180\pi$
$674$	−6836.92			−0.390724
$675$		0			0
$676$	785.449			0.0446887
$677$	12923.2	−	3462.76i	0.733646	−	0.196580i	0.127394	−	0.991852i	$-0.459339\pi$
$677$	12923.2	−	3462.76i	0.733646	−	0.196580i	0.606252	+	0.795272i	$0.292672\pi$
$678$	−22634.0	+	1538.19i	−1.28209	+	0.0871297i
$679$	6857.45	−	3959.15i	0.387577	−	0.223768i
$680$		0			0
$681$	−4442.43	+	1519.93i	−0.249977	+	0.0855269i
$682$	361.371	+	1348.65i	0.0202897	+	0.0757223i
$683$	−14959.7	+	14959.7i	−0.838091	+	0.838091i	−0.988608	−	0.150516i	$-0.951906\pi$
$683$	−14959.7	+	14959.7i	−0.838091	+	0.838091i	0.150516	+	0.988608i	$0.451906\pi$
$684$	129.103	+	166.586i	0.00721695	+	0.00931222i
$685$		0			0
$686$	−14985.6	−	8651.91i	−0.834039	−	0.481533i
$687$	−15580.7	+	10465.0i	−0.865268	+	0.581169i
$688$	−7666.54	+	28611.9i	−0.424832	+	1.58549i
$689$	139.799	+	242.139i	0.00772994	+	0.0133886i
$690$		0			0
$691$	14446.2	−	25021.6i	0.795311	−	1.37752i	−0.127331	−	0.991860i	$-0.540641\pi$
$691$	14446.2	−	25021.6i	0.795311	−	1.37752i	0.922642	−	0.385658i	$-0.126026\pi$
$692$	−1106.20	−	1106.20i	−0.0607680	−	0.0607680i
$693$	3739.26	−	29498.3i	0.204968	−	1.61695i
$694$		−	2977.62i		−	0.162866i
$695$		0			0
$696$	3017.56	+	8819.71i	0.164340	+	0.480331i
$697$	−4112.61	−	1101.97i	−0.223495	−	0.0598854i
$698$	−15250.6	−	4086.39i	−0.826999	−	0.221594i
$699$	14458.3	−	16566.7i	0.782351	−	0.896440i
$700$		0			0
$701$		−	4479.63i		−	0.241360i	−0.992691	−	0.120680i	$-0.961493\pi$
$701$		−	4479.63i		−	0.241360i	0.992691	−	0.120680i	$-0.0385075\pi$
$702$	195.366	+	946.432i	0.0105037	+	0.0508843i
$703$	−194.406	−	194.406i	−0.0104298	−	0.0104298i
$704$	13789.3	−	23883.8i	0.738217	−	1.27863i
$705$		0			0
$706$	962.411	+	1666.94i	0.0513043	+	0.0888616i
$707$	−2314.17	+	8636.58i	−0.123102	+	0.459423i
$708$	432.935	+	212.207i	0.0229812	+	0.0112644i
$709$	25712.6	+	14845.2i	1.36200	+	0.786351i	0.989890	−	0.141837i	$-0.0453009\pi$
$709$	25712.6	+	14845.2i	1.36200	+	0.786351i	0.372110	+	0.928188i	$0.378634\pi$
$710$		0			0
$711$	13623.7	+	5566.50i	0.718606	+	0.293615i
$712$	13197.7	−	13197.7i	0.694672	−	0.694672i
$713$	226.007	+	843.471i	0.0118710	+	0.0443033i
$714$	−7374.03	+	37543.5i	−0.386507	+	1.96783i
$715$		0			0
$716$	887.064	−	512.147i	0.0463005	−	0.0267316i
$717$	−11189.4	−	16659.2i	−0.582809	−	0.867711i
$718$	18721.1	−	5016.31i	0.973073	−	0.260734i
$719$	17740.3			0.920171			0.460085	−	0.887875i	$-0.347819\pi$
$719$	17740.3			0.920171			0.460085	+	0.887875i	$0.347819\pi$
$720$		0			0
$721$	27059.8			1.39773
$722$	17829.9	−	4777.52i	0.919060	−	0.246261i
$723$	−3925.61	+	8008.85i	−0.201929	+	0.411967i
$724$	−452.930	+	261.499i	−0.0232500	+	0.0134234i
$725$		0			0
$726$	−21224.8	−	18523.6i	−1.08502	−	0.946934i
$727$	−7841.69	−	29265.6i	−0.400044	−	1.49299i	−0.813016	−	0.582242i	$-0.802176\pi$
$727$	−7841.69	−	29265.6i	−0.400044	−	1.49299i	0.412972	−	0.910744i	$-0.364491\pi$
$728$	723.881	−	723.881i	0.0368527	−	0.0368527i
$729$	18074.1	−	7793.98i	0.918261	−	0.395975i
$730$		0			0
$731$	50334.8	+	29060.8i	2.54679	+	1.47039i
$732$	−71.3779	−	1050.30i	−0.00360410	−	0.0530333i
$733$	−6548.68	+	24440.0i	−0.329988	+	1.23153i	0.579214	+	0.815175i	$0.303359\pi$
$733$	−6548.68	+	24440.0i	−0.329988	+	1.23153i	−0.909202	+	0.416355i	$0.863307\pi$
$734$	−4720.53	−	8176.20i	−0.237381	−	0.411157i
$735$		0			0
$736$	−829.766	+	1437.20i	−0.0415565	+	0.0719780i
$737$	−18026.4	−	18026.4i	−0.900965	−	0.900965i
$738$	−1535.31	+	2020.91i	−0.0765794	+	0.100800i
$739$			27310.7i			1.35946i	0.733463	+	0.679730i	$0.237903\pi$
$739$			27310.7i			1.35946i	−0.733463	+	0.679730i	$0.762097\pi$
$740$		0			0
$741$	−264.552	−	51.9615i	−0.0131155	−	0.00257605i
$742$	6373.73	+	1707.84i	0.315346	+	0.0844968i
$743$	9929.86	+	2660.70i	0.490298	+	0.131375i	0.495494	−	0.868612i	$-0.334987\pi$
$743$	9929.86	+	2660.70i	0.490298	+	0.131375i	−0.00519568	+	0.999987i	$0.501654\pi$
$744$	960.731	+	188.700i	0.0473416	+	0.00929851i
$745$		0			0
$746$			12220.0i			0.599739i
$747$	10526.0	+	25070.2i	0.515564	+	1.22794i
$748$	1879.36	+	1879.36i	0.0918666	+	0.0918666i
$749$	−4390.98	+	7605.39i	−0.214209	+	0.371021i
$750$		0			0
$751$	−12313.5	−	21327.6i	−0.598302	−	1.03629i	−0.993072	−	0.117509i	$-0.962509\pi$
$751$	−12313.5	−	21327.6i	−0.598302	−	1.03629i	0.394770	−	0.918780i	$-0.370824\pi$
$752$	−2506.42	+	9354.09i	−0.121542	+	0.453602i
$753$	−805.350	−	11850.5i	−0.0389755	−	0.573513i
$754$	484.396	+	279.666i	0.0233961	+	0.0135078i
$755$		0			0
$756$	817.101	+	537.483i	0.0393091	+	0.0258572i
$757$	−3491.44	+	3491.44i	−0.167633	+	0.167633i	−0.785938	−	0.618305i	$-0.787820\pi$
$757$	−3491.44	+	3491.44i	−0.167633	+	0.167633i	0.618305	+	0.785938i	$0.287820\pi$
$758$	1500.74	+	5600.84i	0.0719121	+	0.268380i
$759$	−22696.1	−	19807.6i	−1.08540	−	0.947260i
$760$		0			0
$761$	1927.71	−	1112.96i	0.0918256	−	0.0530155i	−0.453384	−	0.891315i	$-0.649783\pi$
$761$	1927.71	−	1112.96i	0.0918256	−	0.0530155i	0.545210	+	0.838300i	$0.316450\pi$
$762$	−5966.96	+	12173.5i	−0.283675	+	0.578741i
$763$	21157.8	−	5669.21i	1.00388	−	0.268990i
$764$	252.521			0.0119580
$765$		0			0
$766$	−3391.65			−0.159981
$767$	−595.759	+	159.633i	−0.0280464	+	0.00751502i
$768$	1591.93	+	2370.13i	0.0747965	+	0.111360i
$769$	−28584.4	+	16503.2i	−1.34042	+	0.773890i	−0.986868	−	0.161526i	$-0.948358\pi$
$769$	−28584.4	+	16503.2i	−1.34042	+	0.773890i	−0.353548	+	0.935416i	$0.615025\pi$
$770$		0			0
$771$	3826.76	−	19483.2i	0.178752	−	0.910079i
$772$	142.237	+	530.837i	0.00663113	+	0.0247477i
$773$	−9771.76	+	9771.76i	−0.454677	+	0.454677i	−0.896904	−	0.442226i	$-0.854189\pi$
$773$	−9771.76	+	9771.76i	−0.454677	+	0.454677i	0.442226	+	0.896904i	$0.354189\pi$
$774$	27384.5	−	21223.0i	1.27173	−	0.985586i
$775$		0			0
$776$	−7789.55	−	4497.30i	−0.360346	−	0.208046i
$777$	−1145.62	−	561.535i	−0.0528943	−	0.0259266i
$778$	8790.84	−	32807.8i	0.405099	−	1.51185i
$779$	−354.026	−	613.192i	−0.0162828	−	0.0282027i
$780$		0			0
$781$	461.423	−	799.208i	0.0211409	−	0.0366171i
$782$	27409.0	+	27409.0i	1.25338	+	1.25338i
$783$	3584.00	−	10813.8i	0.163578	−	0.493557i
$784$		−	2353.18i		−	0.107197i
$785$		0			0
$786$	−25799.7	+	29562.1i	−1.17080	+	1.34153i
$787$	−2450.58	−	656.630i	−0.110996	−	0.0297412i	0.202894	−	0.979201i	$-0.434965\pi$
$787$	−2450.58	−	656.630i	−0.110996	−	0.0297412i	−0.313889	+	0.949460i	$0.601632\pi$
$788$	484.479	+	129.816i	0.0219021	+	0.00586865i
$789$	8296.97	+	24250.3i	0.374373	+	1.09421i
$790$		0			0
$791$		−	29370.6i		−	1.32022i
$792$	−31142.4	+	13075.5i	−1.39722	+	0.586637i
$793$	952.246	+	952.246i	0.0426422	+	0.0426422i
$794$	−21301.6	+	36895.4i	−0.952097	+	1.64908i
$795$		0			0
$796$	−364.827	−	631.899i	−0.0162449	−	0.0281370i
$797$	−7132.77	+	26619.9i	−0.317009	+	1.18309i	0.605096	+	0.796152i	$0.293135\pi$
$797$	−7132.77	+	26619.9i	−0.317009	+	1.18309i	−0.922105	+	0.386940i	$0.873532\pi$
$798$	−5281.93	+	3547.68i	−0.234308	+	0.157376i
$799$	16456.0	+	9500.85i	0.728623	+	0.420671i
$800$		0			0
$801$	−22600.7	+	3086.11i	−0.996950	+	0.136133i
$802$	−11396.6	+	11396.6i	−0.501780	+	0.501780i
$803$	−1227.81	−	4582.25i	−0.0539582	−	0.201375i
$804$	793.378	−	271.445i	0.0348014	−	0.0119069i
$805$		0			0
$806$	50.8780	−	29.3744i	0.00222345	−	0.00128371i
$807$	34057.7	−	2314.54i	1.48561	−	0.100961i
$808$	9810.51	−	2628.72i	0.427144	−	0.114453i
$809$	−28707.4			−1.24759			−0.623794	−	0.781589i	$-0.714409\pi$
$809$	−28707.4			−1.24759			−0.623794	+	0.781589i	$0.714409\pi$
$810$		0			0
$811$	−38280.7			−1.65748			−0.828741	−	0.559632i	$-0.810943\pi$
$811$	−38280.7			−1.65748			−0.828741	+	0.559632i	$0.810943\pi$
$812$	546.784	−	146.510i	0.0236310	−	0.00633190i
$813$	8313.66	−	564.991i	0.358638	−	0.0243728i
$814$	−1789.83	+	1033.36i	−0.0770681	+	0.0444953i
$815$		0			0
$816$	42967.3	−	14700.8i	1.84333	−	0.630674i
$817$	2501.65	+	9336.28i	0.107126	+	0.399798i
$818$	20905.7	−	20905.7i	0.893582	−	0.893582i
$819$	−1239.62	+	169.270i	−0.0528888	+	0.00722192i
$820$		0			0
$821$	−16524.5	−	9540.43i	−0.702447	−	0.405558i	0.105811	−	0.994386i	$-0.466256\pi$
$821$	−16524.5	−	9540.43i	−0.702447	−	0.405558i	−0.808258	+	0.588828i	$0.799589\pi$
$822$	12162.9	−	8169.40i	0.516096	−	0.346643i
$823$	8758.95	−	32688.8i	0.370982	−	1.38452i	−0.488147	−	0.872762i	$-0.662327\pi$
$823$	8758.95	−	32688.8i	0.370982	−	1.38452i	0.859128	−	0.511760i	$-0.171006\pi$
$824$	−15369.0	−	26619.8i	−0.649762	−	1.12542i
$825$		0			0
$826$	−7278.00	+	12605.9i	−0.306579	+	0.531010i
$827$	20140.3	+	20140.3i	0.846854	+	0.846854i	0.989739	−	0.142885i	$-0.0456380\pi$
$827$	20140.3	+	20140.3i	0.846854	+	0.846854i	−0.142885	+	0.989739i	$0.545638\pi$
$828$	913.589	−	383.580i	0.0383447	−	0.0160994i
$829$		−	28979.3i		−	1.21410i	−0.794662	−	0.607052i	$-0.792352\pi$
$829$		−	28979.3i		−	1.21410i	0.794662	−	0.607052i	$-0.207648\pi$
$830$		0			0
$831$	14797.8	+	43251.0i	0.617727	+	1.80549i
$832$	−1120.88	−	300.340i	−0.0467063	−	0.0125149i
$833$	−4459.99	−	1195.05i	−0.185510	−	0.0497072i
$834$	12618.9	−	14459.2i	0.523931	−	0.600335i
$835$		0			0
$836$			441.995i			0.0182855i
$837$	−795.428	−	893.918i	−0.0328483	−	0.0369156i
$838$	−17937.4	−	17937.4i	−0.739423	−	0.739423i
$839$	1123.38	−	1945.74i	0.0462255	−	0.0800650i	−0.841987	−	0.539498i	$-0.818614\pi$
$839$	1123.38	−	1945.74i	0.0462255	−	0.0800650i	0.888212	+	0.459433i	$0.151947\pi$
$840$		0			0
$841$	8897.63	+	15411.2i	0.364822	+	0.631890i
$842$	−8987.36	+	33541.3i	−0.367844	+	1.37281i
$843$	31278.3	+	15331.3i	1.27792	+	0.626381i
$844$	−427.367	−	246.740i	−0.0174296	−	0.0100630i
$845$		0			0
$846$	8952.82	−	6938.42i	0.363835	−	0.281971i
$847$	25789.4	−	25789.4i	1.04620	−	1.04620i
$848$	−2027.07	−	7565.12i	−0.0820871	−	0.306353i
$849$	1144.25	−	5825.74i	0.0462552	−	0.235499i
$850$		0			0
$851$	−1119.39	+	646.280i	−0.0450907	+	0.0260331i
$852$	16.9247	+	25.1982i	0.000680553	+	0.00101324i
$853$	−2144.34	+	574.575i	−0.0860738	+	0.0230634i	−0.301599	−	0.953435i	$-0.597520\pi$
$853$	−2144.34	+	574.575i	−0.0860738	+	0.0230634i	0.215525	+	0.976498i	$0.430854\pi$
$854$	31781.9			1.27348
$855$		0			0
$856$	9975.64			0.398318
$857$	−5332.98	+	1428.97i	−0.212568	+	0.0569576i	−0.363532	−	0.931582i	$-0.618429\pi$
$857$	−5332.98	+	1428.97i	−0.212568	+	0.0569576i	0.150963	+	0.988539i	$0.451762\pi$
$858$	−892.005	+	1819.83i	−0.0354925	+	0.0724101i
$859$	1162.53	−	671.184i	0.0461756	−	0.0266595i	−0.476734	−	0.879047i	$-0.658180\pi$
$859$	1162.53	−	671.184i	0.0461756	−	0.0266595i	0.522910	+	0.852388i	$0.324846\pi$
$860$		0			0
$861$	−2475.57	−	2160.50i	−0.0979874	−	0.0855166i
$862$	3067.45	+	11447.9i	0.121204	+	0.452339i
$863$	18896.7	−	18896.7i	0.745365	−	0.745365i	−0.228240	−	0.973605i	$-0.573297\pi$
$863$	18896.7	−	18896.7i	0.745365	−	0.745365i	0.973605	+	0.228240i	$0.0732971\pi$
$864$	132.353	−	2270.19i	0.00521151	−	0.0893907i
$865$		0			0
$866$	−15311.8	−	8840.29i	−0.600828	−	0.346888i
$867$	−4310.78	−	63431.8i	−0.168860	−	2.48473i
$868$	15.3885	−	57.4308i	0.000601753	−	0.00224577i
$869$	15432.1	+	26729.2i	0.602416	+	1.04341i
$870$		0			0
$871$	−536.336	+	928.962i	−0.0208646	+	0.0361385i
$872$	−17593.9	−	17593.9i	−0.683260	−	0.683260i
$873$	4255.49	+	10135.5i	0.164979	+	0.392937i
$874$			6446.15i			0.249479i
$875$		0			0
$876$	153.112	+	30.0732i	0.00590545	+	0.00115991i
$877$	47507.6	+	12729.6i	1.82921	+	0.490136i	0.997847	−	0.0655906i	$-0.0208931\pi$
$877$	47507.6	+	12729.6i	1.82921	+	0.490136i	0.831365	+	0.555726i	$0.187560\pi$
$878$	−33760.5	−	9046.10i	−1.29768	−	0.347712i
$879$	32075.4	+	6300.04i	1.23080	+	0.241746i
$880$		0			0
$881$			29831.9i			1.14082i	0.821360	+	0.570410i	$0.193216\pi$
$881$			29831.9i			1.14082i	−0.821360	+	0.570410i	$0.806784\pi$
$882$	−1665.00	+	2191.61i	−0.0635639	+	0.0836683i
$883$	−12536.7	−	12536.7i	−0.477796	−	0.477796i	0.426630	−	0.904426i	$-0.359701\pi$
$883$	−12536.7	−	12536.7i	−0.477796	−	0.477796i	−0.904426	+	0.426630i	$0.859701\pi$
$884$	55.9163	−	96.8498i	0.00212745	−	0.00368486i
$885$		0			0
$886$	−13356.3	−	23133.8i	−0.506449	−	0.877196i
$887$	−828.995	+	3093.85i	−0.0313810	+	0.117115i	−0.979840	−	0.199785i	$-0.935976\pi$
$887$	−828.995	+	3093.85i	−0.0313810	+	0.117115i	0.948459	+	0.316901i	$0.102642\pi$
$888$	98.2639	+	1445.92i	0.00371343	+	0.0546419i
$889$	−15200.3	−	8775.92i	−0.573457	−	0.331085i
$890$		0			0
$891$	39973.2	+	10299.7i	1.50298	+	0.387263i
$892$	995.968	−	995.968i	0.0373851	−	0.0373851i
$893$	817.863	+	3052.31i	0.0306481	+	0.114380i
$894$	−1575.72	−	1375.18i	−0.0589487	−	0.0514463i
$895$		0			0
$896$	−25901.2	+	14954.1i	−0.965735	+	0.557568i
$897$	−557.875	+	1138.15i	−0.0207658	+	0.0423654i
$898$	−1961.94	+	525.700i	−0.0729073	+	0.0195355i
$899$	−692.565			−0.0256934
$900$		0			0
$901$	−15367.6			−0.568224
$902$	−5141.20	+	1377.58i	−0.189782	+	0.0508519i
$903$	25009.1	+	37234.6i	0.921652	+	1.37219i
$904$	−28893.0	+	16681.4i	−1.06302	+	0.613734i
$905$		0			0
$906$	−4093.94	+	20843.5i	−0.150124	+	0.764326i
$907$	−4492.30	−	16765.5i	−0.164459	−	0.613769i	−0.998109	−	0.0614756i	$-0.980419\pi$
$907$	−4492.30	−	16765.5i	−0.164459	−	0.613769i	0.833650	−	0.552294i	$-0.186247\pi$
$908$	229.020	−	229.020i	0.00837037	−	0.00837037i
$909$	−11490.6	−	4694.92i	−0.419272	−	0.171310i
$910$		0			0
$911$	−3395.10	−	1960.16i	−0.123474	−	0.0712877i	0.436991	−	0.899466i	$-0.356044\pi$
$911$	−3395.10	−	1960.16i	−0.123474	−	0.0712877i	−0.560465	+	0.828178i	$0.689378\pi$
$912$	6781.29	+	3323.91i	0.246218	+	0.120686i
$913$	−14758.6	+	55080.0i	−0.534983	+	1.99658i
$914$	6564.65	+	11370.3i	0.237570	+	0.411484i
$915$		0			0
$916$	647.349	−	1121.24i	0.0233505	−	0.0404442i
$917$	−35919.6	−	35919.6i	−1.29353	−	1.29353i
$918$	−50418.7	−	16710.1i	−1.81271	−	0.600780i
$919$		−	28637.0i		−	1.02791i	−0.857818	−	0.513954i	$-0.828180\pi$
$919$		−	28637.0i		−	1.02791i	0.857818	−	0.513954i	$-0.171820\pi$
$920$		0			0
$921$	24153.0	−	27675.2i	0.864135	−	0.990151i
$922$	−25076.8	−	6719.32i	−0.895729	−	0.240010i
$923$	−37.5073	−	10.0501i	−0.00133756	−	0.000358398i
$924$	663.975	+	1940.66i	0.0236398	+	0.0690942i
$925$		0			0
$926$		−	19775.9i		−	0.701812i
$927$	−4724.12	+	37267.7i	−0.167379	+	1.32042i
$928$	−930.689	−	930.689i	−0.0329217	−	0.0329217i
$929$	4966.44	−	8602.13i	0.175397	−	0.303796i	−0.764902	−	0.644147i	$-0.777213\pi$
$929$	4966.44	−	8602.13i	0.175397	−	0.303796i	0.940299	+	0.340351i	$0.110546\pi$
$930$		0			0
$931$	−383.930	−	664.987i	−0.0135154	−	0.0234093i
$932$	−392.576	+	1465.11i	−0.0137975	+	0.0514929i
$933$	13081.8	−	8786.55i	0.459034	−	0.308316i
$934$	5828.32	+	3364.98i	0.204185	+	0.117886i
$935$		0			0
$936$	870.576	+	1123.33i	0.0304014	+	0.0392277i
$937$	−13440.3	+	13440.3i	−0.468597	+	0.468597i	−0.901460	−	0.432863i	$-0.857503\pi$
$937$	−13440.3	+	13440.3i	−0.468597	+	0.468597i	0.432863	+	0.901460i	$0.357503\pi$
$938$	6552.07	+	24452.7i	0.228073	+	0.851181i
$939$	−21189.2	+	7249.65i	−0.736404	+	0.251952i
$940$		0			0
$941$	−33110.5	+	19116.4i	−1.14705	+	0.662249i	−0.948166	−	0.317775i	$-0.897064\pi$
$941$	−33110.5	+	19116.4i	−1.14705	+	0.662249i	−0.198882	+	0.980023i	$0.563731\pi$
$942$	35595.3	−	2419.03i	1.23116	−	0.0836691i
$943$	−3215.40	+	861.563i	−0.111037	+	0.0297522i
$944$	17276.8			0.595671
$945$		0			0
$946$	72658.3			2.49717
$947$	53216.4	−	14259.3i	1.82608	−	0.489297i	0.828575	−	0.559878i	$-0.189152\pi$
$947$	53216.4	−	14259.3i	1.82608	−	0.489297i	0.997506	+	0.0705807i	$0.0224852\pi$
$948$	−1012.86	+	68.8333i	−0.0347006	+	0.00235823i
$949$	−172.865	+	99.8039i	−0.00591301	+	0.00341388i
$950$		0			0
$951$	−23719.4	+	8115.31i	−0.808784	+	0.276716i
$952$	14563.0	+	54349.8i	0.495787	+	1.85030i
$953$	14081.7	−	14081.7i	0.478647	−	0.478647i	−0.426052	−	0.904699i	$-0.640096\pi$
$953$	14081.7	−	14081.7i	0.478647	−	0.478647i	0.904699	+	0.426052i	$0.140096\pi$
$954$	−3464.82	+	8479.96i	−0.117587	+	0.287787i
$955$		0			0
$956$	1198.86	+	692.160i	0.0405584	+	0.0234164i
$957$	19833.2	−	13321.2i	0.669924	−	0.449963i
$958$	10575.6	−	39468.6i	0.356661	−	1.33108i
$959$	9484.46	+	16427.6i	0.319363	+	0.553153i
$960$		0			0
$961$	14859.1	−	25736.8i	0.498779	−	0.863911i
$962$	61.4906	+	61.4906i	0.00206085	+	0.00206085i
$963$	−9707.82	−	7375.15i	−0.324850	−	0.246792i
$964$		−	615.255i		−	0.0205560i
$965$		0			0
$966$	9683.56	+	28303.0i	0.322529	+	0.942686i
$967$	−47533.1	−	12736.5i	−1.58073	−	0.423554i	−0.641575	−	0.767060i	$-0.721719\pi$
$967$	−47533.1	−	12736.5i	−1.58073	−	0.423554i	−0.939151	+	0.343506i	$0.888385\pi$
$968$	−40017.5	−	10722.6i	−1.32873	−	0.356032i
$969$	9743.66	−	11164.6i	0.323025	−	0.370132i
$970$		0			0
$971$			38812.1i			1.28274i	0.767232	+	0.641369i	$0.221633\pi$
$971$			38812.1i			1.28274i	−0.767232	+	0.641369i	$0.778367\pi$
$972$	−882.889	+	1031.50i	−0.0291344	+	0.0340386i
$973$	17568.7	+	17568.7i	0.578855	+	0.578855i
$974$	13615.5	−	23582.8i	0.447915	−	0.775812i
$975$		0			0
$976$	−18861.3	−	32668.7i	−0.618582	−	1.07142i
$977$	4683.10	−	17477.6i	0.153353	−	0.572320i	−0.845888	−	0.533360i	$-0.820929\pi$
$977$	4683.10	−	17477.6i	0.153353	−	0.572320i	0.999241	−	0.0389597i	$-0.0124044\pi$
$978$	17942.5	+	8794.67i	0.586644	+	0.287549i
$979$	−41428.6	−	23918.8i	−1.35246	−	0.780846i
$980$		0			0
$981$	4114.08	+	30128.9i	0.133897	+	0.980573i
$982$	−11280.2	+	11280.2i	−0.366563	+	0.366563i
$983$	−5531.33	−	20643.2i	−0.179473	−	0.669802i	−0.995746	−	0.0921365i	$-0.970630\pi$
$983$	−5531.33	−	20643.2i	−0.179473	−	0.669802i	0.816273	−	0.577666i	$-0.196036\pi$
$984$	−719.345	+	3662.40i	−0.0233047	+	0.118652i
$985$		0			0
$986$	−26624.0	+	15371.4i	−0.859920	+	0.496475i
$987$	8176.23	+	12173.1i	0.263680	+	0.392578i
$988$	17.9640	−	4.81345i	0.000578454	−	0.000154996i
$989$	45441.8			1.46104
$990$		0			0
$991$	−21254.8			−0.681314			−0.340657	−	0.940188i	$-0.610650\pi$
$991$	−21254.8			−0.681314			−0.340657	+	0.940188i	$0.610650\pi$
$992$	−133.534	+	35.7804i	−0.00427391	+	0.00114519i
$993$	−25761.0	+	52556.5i	−0.823265	+	1.67959i
$994$	−793.630	+	458.203i	−0.0253244	+	0.0146210i
$995$		0			0
$996$	−1413.13	−	1233.28i	−0.0449567	−	0.0392351i
$997$	−1350.75	−	5041.09i	−0.0429076	−	0.160133i	0.941148	−	0.337995i	$-0.109749\pi$
$997$	−1350.75	−	5041.09i	−0.0429076	−	0.160133i	−0.984055	+	0.177862i	$0.943082\pi$
$998$	10925.4	−	10925.4i	0.346530	−	0.346530i
$999$	973.368	−	1479.75i	0.0308268	−	0.0468641i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.p.b.218.12		64
5.2	odd	4	inner	225.4.p.b.182.12		64
5.3	odd	4		45.4.l.a.2.5	✓	64
5.4	even	2		45.4.l.a.38.5	yes	64
9.5	odd	6	inner	225.4.p.b.68.12		64
15.8	even	4		135.4.m.a.62.12		64
15.14	odd	2		135.4.m.a.8.12		64
45.4	even	6		135.4.m.a.98.12		64
45.13	odd	12		135.4.m.a.17.12		64
45.14	odd	6		45.4.l.a.23.5	yes	64
45.23	even	12		45.4.l.a.32.5	yes	64
45.32	even	12	inner	225.4.p.b.32.12		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.l.a.2.5	✓	64	5.3	odd	4
45.4.l.a.23.5	yes	64	45.14	odd	6
45.4.l.a.32.5	yes	64	45.23	even	12
45.4.l.a.38.5	yes	64	5.4	even	2
135.4.m.a.8.12		64	15.14	odd	2
135.4.m.a.17.12		64	45.13	odd	12
135.4.m.a.62.12		64	15.8	even	4
135.4.m.a.98.12		64	45.4	even	6
225.4.p.b.32.12		64	45.32	even	12	inner
225.4.p.b.68.12		64	9.5	odd	6	inner
225.4.p.b.182.12		64	5.2	odd	4	inner
225.4.p.b.218.12		64	1.1	even	1	trivial

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

\(f(q)\)	\(=\)	\(q+(2.79258 - 0.748271i) q^{2} +(-5.18419 + 0.352314i) q^{3} +(0.310415 - 0.179218i) q^{4} +(-14.2137 + 4.86305i) q^{6} +(-5.03374 - 18.7862i) q^{7} +(-15.6218 + 15.6218i) q^{8} +(26.7517 - 3.65293i) q^{9} +O(q^{10})\)	\(q+(2.79258 - 0.748271i) q^{2} +(-5.18419 + 0.352314i) q^{3} +(0.310415 - 0.179218i) q^{4} +(-14.2137 + 4.86305i) q^{6} +(-5.03374 - 18.7862i) q^{7} +(-15.6218 + 15.6218i) q^{8} +(26.7517 - 3.65293i) q^{9} +(49.0377 + 28.3119i) q^{11} +(-1.54611 + 1.03846i) q^{12} +(0.616650 - 2.30137i) q^{13} +(-28.1143 - 48.6954i) q^{14} +(-33.3695 + 57.7977i) q^{16} +(92.5976 + 92.5976i) q^{17} +(71.9731 - 30.2187i) q^{18} +21.7774i q^{19} +(32.7146 + 95.6178i) q^{21} +(158.127 + 42.3700i) q^{22} +(98.8952 + 26.4989i) q^{23} +(75.4824 - 86.4900i) q^{24} -6.88818i q^{26} +(-137.399 + 28.3625i) q^{27} +(-4.92937 - 4.92937i) q^{28} +(-40.6009 + 70.3228i) q^{29} +(4.26447 + 7.38628i) q^{31} +(-4.19518 + 15.6566i) q^{32} +(-264.196 - 129.498i) q^{33} +(327.875 + 189.298i) q^{34} +(7.64946 - 5.92832i) q^{36} +(-8.92697 + 8.92697i) q^{37} +(16.2954 + 60.8153i) q^{38} +(-2.38603 + 12.1480i) q^{39} +(-28.1572 + 16.2566i) q^{41} +(162.906 + 242.541i) q^{42} +(428.714 - 114.874i) q^{43} +20.2960 q^{44} +296.002 q^{46} +(140.159 - 37.5556i) q^{47} +(152.631 - 311.391i) q^{48} +(-30.5356 + 17.6297i) q^{49} +(-512.667 - 447.420i) q^{51} +(-0.221029 - 0.824893i) q^{52} +(-82.9808 + 82.9808i) q^{53} +(-362.476 + 182.017i) q^{54} +(372.109 + 214.837i) q^{56} +(-7.67250 - 112.898i) q^{57} +(-60.7609 + 226.763i) q^{58} +(-129.436 - 224.189i) q^{59} +(-282.613 + 489.500i) q^{61} +(17.4358 + 17.4358i) q^{62} +(-203.286 - 484.175i) q^{63} -487.051i q^{64} +(-834.688 - 163.944i) q^{66} +(-434.879 - 116.526i) q^{67} +(45.3388 + 12.1485i) q^{68} +(-522.028 - 102.533i) q^{69} -16.2978i q^{71} +(-360.844 + 474.974i) q^{72} +(-59.2407 - 59.2407i) q^{73} +(-18.2495 + 31.6091i) q^{74} +(3.90290 + 6.76003i) q^{76} +(285.030 - 1063.75i) q^{77} +(2.42681 + 35.7097i) q^{78} +(472.049 + 272.538i) q^{79} +(702.312 - 195.445i) q^{81} +(-66.4671 + 66.4671i) q^{82} +(260.644 + 972.735i) q^{83} +(27.2915 + 23.8181i) q^{84} +(1111.26 - 641.588i) q^{86} +(185.707 - 378.871i) q^{87} +(-1208.34 + 323.773i) q^{88} -844.831 q^{89} -46.3380 q^{91} +(35.4476 - 9.49816i) q^{92} +(-24.7101 - 36.7895i) q^{93} +(363.305 - 209.754i) q^{94} +(16.2326 - 82.6450i) q^{96} +(105.374 + 393.261i) q^{97} +(-72.0814 + 72.0814i) q^{98} +(1415.27 + 578.262i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7}+O(q^{10}) \) 64 * q + 6 * q^2 - 24 * q^6 + 2 * q^7	\( 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7} - 36 q^{11} + 138 q^{12} + 2 q^{13} + 316 q^{16} + 480 q^{18} + 480 q^{21} + 34 q^{22} - 306 q^{23} - 180 q^{27} + 232 q^{28} - 4 q^{31} + 1770 q^{32} + 294 q^{33} - 216 q^{36} - 136 q^{37} - 114 q^{38} + 1992 q^{41} - 1698 q^{42} + 2 q^{43} - 952 q^{46} - 3462 q^{47} - 4326 q^{48} - 2496 q^{51} + 242 q^{52} - 7128 q^{56} + 2544 q^{57} - 534 q^{58} + 32 q^{61} + 4038 q^{63} + 2892 q^{66} - 610 q^{67} + 2694 q^{68} + 1854 q^{72} + 8 q^{73} + 1368 q^{76} + 6486 q^{77} - 1434 q^{78} + 3012 q^{81} + 3784 q^{82} - 2814 q^{83} + 12480 q^{86} - 4830 q^{87} + 1338 q^{88} + 992 q^{91} - 13152 q^{92} - 8310 q^{93} - 7932 q^{96} - 358 q^{97}+O(q^{100}) \) 64 * q + 6 * q^2 - 24 * q^6 + 2 * q^7 - 36 * q^11 + 138 * q^12 + 2 * q^13 + 316 * q^16 + 480 * q^18 + 480 * q^21 + 34 * q^22 - 306 * q^23 - 180 * q^27 + 232 * q^28 - 4 * q^31 + 1770 * q^32 + 294 * q^33 - 216 * q^36 - 136 * q^37 - 114 * q^38 + 1992 * q^41 - 1698 * q^42 + 2 * q^43 - 952 * q^46 - 3462 * q^47 - 4326 * q^48 - 2496 * q^51 + 242 * q^52 - 7128 * q^56 + 2544 * q^57 - 534 * q^58 + 32 * q^61 + 4038 * q^63 + 2892 * q^66 - 610 * q^67 + 2694 * q^68 + 1854 * q^72 + 8 * q^73 + 1368 * q^76 + 6486 * q^77 - 1434 * q^78 + 3012 * q^81 + 3784 * q^82 - 2814 * q^83 + 12480 * q^86 - 4830 * q^87 + 1338 * q^88 + 992 * q^91 - 13152 * q^92 - 8310 * q^93 - 7932 * q^96 - 358 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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