LMFDB - Embedded newform 37.7.d.a.6.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,7,Mod(6,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("37.6");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	37.d (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.51200109393$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			6.12
Character	$\chi$	$=$	37.6
Dual form			37.7.d.a.31.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.77875 - 2.77875i) q^{2} -27.0135i q^{3} +48.5571i q^{4} +(96.7657 + 96.7657i) q^{5} +(-75.0636 - 75.0636i) q^{6} +312.208 q^{7} +(312.768 + 312.768i) q^{8} -0.728696 q^{9} +O(q^{10})$	\(q+(2.77875 - 2.77875i) q^{2} -27.0135i q^{3} +48.5571i q^{4} +(96.7657 + 96.7657i) q^{5} +(-75.0636 - 75.0636i) q^{6} +312.208 q^{7} +(312.768 + 312.768i) q^{8} -0.728696 q^{9} +537.775 q^{10} -1621.10i q^{11} +1311.70 q^{12} +(-1599.67 - 1599.67i) q^{13} +(867.547 - 867.547i) q^{14} +(2613.98 - 2613.98i) q^{15} -1369.45 q^{16} +(1956.65 + 1956.65i) q^{17} +(-2.02486 + 2.02486i) q^{18} +(9305.33 + 9305.33i) q^{19} +(-4698.67 + 4698.67i) q^{20} -8433.83i q^{21} +(-4504.64 - 4504.64i) q^{22} +(3528.74 + 3528.74i) q^{23} +(8448.95 - 8448.95i) q^{24} +3102.22i q^{25} -8890.16 q^{26} -19673.2i q^{27} +15159.9i q^{28} +(6587.87 - 6587.87i) q^{29} -14527.2i q^{30} +(-31435.5 + 31435.5i) q^{31} +(-23822.5 + 23822.5i) q^{32} -43791.7 q^{33} +10874.1 q^{34} +(30211.0 + 30211.0i) q^{35} -35.3834i q^{36} +(-20359.1 - 46381.4i) q^{37} +51714.3 q^{38} +(-43212.7 + 43212.7i) q^{39} +60530.4i q^{40} +1010.89i q^{41} +(-23435.5 - 23435.5i) q^{42} +(-62136.0 - 62136.0i) q^{43} +78716.2 q^{44} +(-70.5128 - 70.5128i) q^{45} +19611.0 q^{46} -95688.6 q^{47} +36993.7i q^{48} -20175.1 q^{49} +(8620.28 + 8620.28i) q^{50} +(52855.9 - 52855.9i) q^{51} +(77675.5 - 77675.5i) q^{52} -116072. q^{53} +(-54666.7 - 54666.7i) q^{54} +(156867. - 156867. i) q^{55} +(97648.6 + 97648.6i) q^{56} +(251369. - 251369. i) q^{57} -36612.0i q^{58} +(167627. + 167627. i) q^{59} +(126927. + 126927. i) q^{60} +(-2678.47 + 2678.47i) q^{61} +174702. i q^{62} -227.505 q^{63} +44748.3i q^{64} -309587. i q^{65} +(-121686. + 121686. i) q^{66} +409672. i q^{67} +(-95009.2 + 95009.2i) q^{68} +(95323.7 - 95323.7i) q^{69} +167898. q^{70} -296668. q^{71} +(-227.913 - 227.913i) q^{72} -540265. i q^{73} +(-185455. - 72309.1i) q^{74} +83801.8 q^{75} +(-451840. + 451840. i) q^{76} -506122. i q^{77} +240154. i q^{78} +(-121002. - 121002. i) q^{79} +(-132516. - 132516. i) q^{80} -531972. q^{81} +(2809.02 + 2809.02i) q^{82} -9274.43 q^{83} +409523. q^{84} +378673. i q^{85} -345321. q^{86} +(-177961. - 177961. i) q^{87} +(507029. - 507029. i) q^{88} +(-737069. + 737069. i) q^{89} -391.875 q^{90} +(-499430. - 499430. i) q^{91} +(-171346. + 171346. i) q^{92} +(849182. + 849182. i) q^{93} +(-265894. + 265894. i) q^{94} +1.80087e6i q^{95} +(643529. + 643529. i) q^{96} +(-86996.9 - 86996.9i) q^{97} +(-56061.6 + 56061.6i) q^{98} +1181.29i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 4 q^{2} - 256 q^{5} + 126 q^{6} - 4 q^{7} + 168 q^{8} - 7140 q^{9}+O(q^{10}) $ 36 * q - 4 * q^2 - 256 * q^5 + 126 * q^6 - 4 * q^7 + 168 * q^8 - 7140 * q^9	\( 36 q - 4 q^{2} - 256 q^{5} + 126 q^{6} - 4 q^{7} + 168 q^{8} - 7140 q^{9} - 1876 q^{10} + 11104 q^{12} - 2904 q^{13} - 7678 q^{14} + 4288 q^{15} - 44824 q^{16} + 2064 q^{17} + 6222 q^{18} - 4954 q^{19} - 43084 q^{20} - 39810 q^{22} + 21966 q^{23} + 79188 q^{24} + 66604 q^{26} + 69500 q^{29} - 32418 q^{31} - 141992 q^{32} + 54752 q^{33} + 256508 q^{34} - 26164 q^{35} + 180242 q^{37} + 329032 q^{38} - 60088 q^{39} - 346014 q^{42} - 144514 q^{43} - 294896 q^{44} + 842152 q^{45} - 522736 q^{46} - 157076 q^{47} + 405652 q^{49} + 46176 q^{50} - 624984 q^{51} - 161884 q^{52} - 512988 q^{53} + 541150 q^{54} + 824640 q^{55} - 608488 q^{56} - 311992 q^{57} + 187582 q^{59} - 1156764 q^{60} - 1321908 q^{61} - 887284 q^{63} + 752126 q^{66} + 1244832 q^{68} + 41960 q^{69} - 1029284 q^{70} + 1316252 q^{71} + 777880 q^{72} + 1117260 q^{74} - 2148904 q^{75} - 814428 q^{76} - 56722 q^{79} + 3750844 q^{80} - 930796 q^{81} + 1462554 q^{82} - 841484 q^{83} + 5065540 q^{84} + 3992612 q^{86} + 2494224 q^{87} - 3796428 q^{88} - 1439724 q^{89} - 5618044 q^{90} - 8644 q^{91} + 7826980 q^{92} - 54064 q^{93} - 2057938 q^{94} - 8819328 q^{96} + 2578548 q^{97} - 6043946 q^{98}+O(q^{100}) \) 36 * q - 4 * q^2 - 256 * q^5 + 126 * q^6 - 4 * q^7 + 168 * q^8 - 7140 * q^9 - 1876 * q^10 + 11104 * q^12 - 2904 * q^13 - 7678 * q^14 + 4288 * q^15 - 44824 * q^16 + 2064 * q^17 + 6222 * q^18 - 4954 * q^19 - 43084 * q^20 - 39810 * q^22 + 21966 * q^23 + 79188 * q^24 + 66604 * q^26 + 69500 * q^29 - 32418 * q^31 - 141992 * q^32 + 54752 * q^33 + 256508 * q^34 - 26164 * q^35 + 180242 * q^37 + 329032 * q^38 - 60088 * q^39 - 346014 * q^42 - 144514 * q^43 - 294896 * q^44 + 842152 * q^45 - 522736 * q^46 - 157076 * q^47 + 405652 * q^49 + 46176 * q^50 - 624984 * q^51 - 161884 * q^52 - 512988 * q^53 + 541150 * q^54 + 824640 * q^55 - 608488 * q^56 - 311992 * q^57 + 187582 * q^59 - 1156764 * q^60 - 1321908 * q^61 - 887284 * q^63 + 752126 * q^66 + 1244832 * q^68 + 41960 * q^69 - 1029284 * q^70 + 1316252 * q^71 + 777880 * q^72 + 1117260 * q^74 - 2148904 * q^75 - 814428 * q^76 - 56722 * q^79 + 3750844 * q^80 - 930796 * q^81 + 1462554 * q^82 - 841484 * q^83 + 5065540 * q^84 + 3992612 * q^86 + 2494224 * q^87 - 3796428 * q^88 - 1439724 * q^89 - 5618044 * q^90 - 8644 * q^91 + 7826980 * q^92 - 54064 * q^93 - 2057938 * q^94 - 8819328 * q^96 + 2578548 * q^97 - 6043946 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	2.77875	−	2.77875i	0.347343	−	0.347343i	−0.511776	−	0.859119i	$-0.671012\pi$
$2$	2.77875	−	2.77875i	0.347343	−	0.347343i	0.859119	+	0.511776i	$0.171012\pi$
$3$		−	27.0135i		−	1.00050i	−0.865881	−	0.500250i	$-0.833241\pi$
$3$		−	27.0135i		−	1.00050i	0.865881	−	0.500250i	$-0.166759\pi$
$4$			48.5571i			0.758705i
$5$	96.7657	+	96.7657i	0.774126	+	0.774126i	0.978825	−	0.204699i	$-0.0656215\pi$
$5$	96.7657	+	96.7657i	0.774126	+	0.774126i	−0.204699	+	0.978825i	$0.565622\pi$
$6$	−75.0636	−	75.0636i	−0.347517	−	0.347517i
$7$	312.208			0.910228			0.455114	−	0.890433i	$-0.349599\pi$
$7$	312.208			0.910228			0.455114	+	0.890433i	$0.349599\pi$
$8$	312.768	+	312.768i	0.610874	+	0.610874i
$9$	−0.728696			−0.000999583
$10$	537.775			0.537775
$11$		−	1621.10i		−	1.21796i	−0.793186	−	0.608980i	$-0.791579\pi$
$11$		−	1621.10i		−	1.21796i	0.793186	−	0.608980i	$-0.208421\pi$
$12$	1311.70			0.759084
$13$	−1599.67	−	1599.67i	−0.728116	−	0.728116i	0.242128	−	0.970244i	$-0.422155\pi$
$13$	−1599.67	−	1599.67i	−0.728116	−	0.728116i	−0.970244	+	0.242128i	$0.922155\pi$
$14$	867.547	−	867.547i	0.316161	−	0.316161i
$15$	2613.98	−	2613.98i	0.774513	−	0.774513i
$16$	−1369.45			−0.334339
$17$	1956.65	+	1956.65i	0.398259	+	0.398259i	0.877619	−	0.479359i	$-0.159131\pi$
$17$	1956.65	+	1956.65i	0.398259	+	0.398259i	−0.479359	+	0.877619i	$0.659131\pi$
$18$	−2.02486	+	2.02486i	−0.000347198	+	0.000347198i
$19$	9305.33	+	9305.33i	1.35666	+	1.35666i	0.878001	+	0.478659i	$0.158877\pi$
$19$	9305.33	+	9305.33i	1.35666	+	1.35666i	0.478659	+	0.878001i	$0.341123\pi$
$20$	−4698.67	+	4698.67i	−0.587334	+	0.587334i
$21$		−	8433.83i		−	0.910682i
$22$	−4504.64	−	4504.64i	−0.423050	−	0.423050i
$23$	3528.74	+	3528.74i	0.290026	+	0.290026i	0.837090	−	0.547065i	$-0.184255\pi$
$23$	3528.74	+	3528.74i	0.290026	+	0.290026i	−0.547065	+	0.837090i	$0.684255\pi$
$24$	8448.95	−	8448.95i	0.611180	−	0.611180i
$25$			3102.22i			0.198542i
$26$	−8890.16			−0.505813
$27$		−	19673.2i		−	0.999500i
$28$			15159.9i			0.690595i
$29$	6587.87	−	6587.87i	0.270116	−	0.270116i	−0.559031	−	0.829147i	$-0.688827\pi$
$29$	6587.87	−	6587.87i	0.270116	−	0.270116i	0.829147	+	0.559031i	$0.188827\pi$
$30$		−	14527.2i		−	0.538044i
$31$	−31435.5	+	31435.5i	−1.05520	+	1.05520i	−0.0568156	+	0.998385i	$0.518095\pi$
$31$	−31435.5	+	31435.5i	−1.05520	+	1.05520i	−0.998385	+	0.0568156i	$0.981905\pi$
$32$	−23822.5	+	23822.5i	−0.727005	+	0.727005i
$33$	−43791.7			−1.21857
$34$	10874.1			0.276665
$35$	30211.0	+	30211.0i	0.704631	+	0.704631i
$36$		−	35.3834i		−	0.000758389i
$37$	−20359.1	−	46381.4i	−0.401934	−	0.915669i
$37$	−20359.1	−	46381.4i	−0.401934	−	0.915669i
$38$	51714.3			0.942453
$39$	−43212.7	+	43212.7i	−0.728480	+	0.728480i
$40$			60530.4i			0.945787i
$41$			1010.89i			0.0146674i	0.999973	+	0.00733371i	$0.00233441\pi$
$41$			1010.89i			0.0146674i	−0.999973	+	0.00733371i	$0.997666\pi$
$42$	−23435.5	−	23435.5i	−0.316319	−	0.316319i
$43$	−62136.0	−	62136.0i	−0.781517	−	0.781517i	0.198570	−	0.980087i	$-0.436370\pi$
$43$	−62136.0	−	62136.0i	−0.781517	−	0.781517i	−0.980087	+	0.198570i	$0.936370\pi$
$44$	78716.2			0.924073
$45$	−70.5128	−	70.5128i	−0.000773803	−	0.000773803i
$46$	19611.0			0.201477
$47$	−95688.6			−0.921651			−0.460826	−	0.887491i	$-0.652447\pi$
$47$	−95688.6			−0.921651			−0.460826	+	0.887491i	$0.652447\pi$
$48$			36993.7i			0.334506i
$49$	−20175.1			−0.171486
$50$	8620.28	+	8620.28i	0.0689623	+	0.0689623i
$51$	52855.9	−	52855.9i	0.398458	−	0.398458i
$52$	77675.5	−	77675.5i	0.552426	−	0.552426i
$53$	−116072.			−0.779648			−0.389824	−	0.920889i	$-0.627464\pi$
$53$	−116072.			−0.779648			−0.389824	+	0.920889i	$0.627464\pi$
$54$	−54666.7	−	54666.7i	−0.347169	−	0.347169i
$55$	156867.	−	156867.i	0.942854	−	0.942854i
$56$	97648.6	+	97648.6i	0.556035	+	0.556035i
$57$	251369.	−	251369.i	1.35734	−	1.35734i
$58$		−	36612.0i		−	0.187646i
$59$	167627.	+	167627.i	0.816185	+	0.816185i	0.985553	−	0.169368i	$-0.0541726\pi$
$59$	167627.	+	167627.i	0.816185	+	0.816185i	−0.169368	+	0.985553i	$0.554173\pi$
$60$	126927.	+	126927.i	0.587627	+	0.587627i
$61$	−2678.47	+	2678.47i	−0.0118004	+	0.0118004i	−0.712982	−	0.701182i	$-0.752656\pi$
$61$	−2678.47	+	2678.47i	−0.0118004	+	0.0118004i	0.701182	+	0.712982i	$0.252656\pi$
$62$			174702.i			0.733033i
$63$	−227.505			−0.000909848
$64$			44748.3i			0.170701i
$65$		−	309587.i		−	1.12731i
$66$	−121686.	+	121686.i	−0.423262	+	0.423262i
$67$			409672.i			1.36211i	0.732232	+	0.681055i	$0.238479\pi$
$67$			409672.i			1.36211i	−0.732232	+	0.681055i	$0.761521\pi$
$68$	−95009.2	+	95009.2i	−0.302161	+	0.302161i
$69$	95323.7	−	95323.7i	0.290171	−	0.290171i
$70$	167898.			0.489497
$71$	−296668.			−0.828887			−0.414443	−	0.910075i	$-0.636024\pi$
$71$	−296668.			−0.828887			−0.414443	+	0.910075i	$0.636024\pi$
$72$	−227.913	−	227.913i	−0.000610620	−	0.000610620i
$73$		−	540265.i		−	1.38880i	−0.719591	−	0.694398i	$-0.755671\pi$
$73$		−	540265.i		−	1.38880i	0.719591	−	0.694398i	$-0.244329\pi$
$74$	−185455.	−	72309.1i	−0.457660	−	0.178442i
$75$	83801.8			0.198641
$76$	−451840.	+	451840.i	−1.02931	+	1.02931i
$77$		−	506122.i		−	1.10862i
$78$			240154.i			0.506065i
$79$	−121002.	−	121002.i	−0.245420	−	0.245420i	0.573668	−	0.819088i	$-0.305520\pi$
$79$	−121002.	−	121002.i	−0.245420	−	0.245420i	−0.819088	+	0.573668i	$0.805520\pi$
$80$	−132516.	−	132516.i	−0.258821	−	0.258821i
$81$	−531972.			−1.00100
$82$	2809.02	+	2809.02i	0.00509463	+	0.00509463i
$83$	−9274.43			−0.0162201			−0.00811004	−	0.999967i	$-0.502582\pi$
$83$	−9274.43			−0.0162201			−0.00811004	+	0.999967i	$0.502582\pi$
$84$	409523.			0.690940
$85$			378673.i			0.616606i
$86$	−345321.			−0.542909
$87$	−177961.	−	177961.i	−0.270251	−	0.270251i
$88$	507029.	−	507029.i	0.744021	−	0.744021i
$89$	−737069.	+	737069.i	−1.04553	+	1.04553i	−0.0466209	+	0.998913i	$0.514845\pi$
$89$	−737069.	+	737069.i	−1.04553	+	1.04553i	−0.998913	+	0.0466209i	$0.985155\pi$
$90$	−391.875			−0.000537551
$91$	−499430.	−	499430.i	−0.662752	−	0.662752i
$92$	−171346.	+	171346.i	−0.220044	+	0.220044i
$93$	849182.	+	849182.i	1.05573	+	1.05573i
$94$	−265894.	+	265894.i	−0.320129	+	0.320129i
$95$			1.80087e6i			2.10045i
$96$	643529.	+	643529.i	0.727368	+	0.727368i
$97$	−86996.9	−	86996.9i	−0.0953209	−	0.0953209i	0.657838	−	0.753159i	$-0.271471\pi$
$97$	−86996.9	−	86996.9i	−0.0953209	−	0.0953209i	−0.753159	+	0.657838i	$0.771471\pi$
$98$	−56061.6	+	56061.6i	−0.0595644	+	0.0595644i
$99$			1181.29i			0.00121745i
$100$	−150635.			−0.150635
$101$		−	1.34686e6i		−	1.30725i	−0.756820	−	0.653623i	$-0.773248\pi$
$101$		−	1.34686e6i		−	1.30725i	0.756820	−	0.653623i	$-0.226752\pi$
$102$		−	293746.i		−	0.276804i
$103$	1.27890e6	−	1.27890e6i	1.17037	−	1.17037i	0.188254	−	0.982120i	$-0.439717\pi$
$103$	1.27890e6	−	1.27890e6i	1.17037	−	1.17037i	0.982120	−	0.188254i	$-0.0602828\pi$
$104$		−	1.00065e6i		−	0.889575i
$105$	816106.	−	816106.i	0.704983	−	0.704983i
$106$	−322534.	+	322534.i	−0.270806	+	0.270806i
$107$	−218651.			−0.178485			−0.0892424	−	0.996010i	$-0.528445\pi$
$107$	−218651.			−0.178485			−0.0892424	+	0.996010i	$0.528445\pi$
$108$	955272.			0.758326
$109$	478923.	+	478923.i	0.369817	+	0.369817i	0.867410	−	0.497594i	$-0.165783\pi$
$109$	478923.	+	478923.i	0.369817	+	0.369817i	−0.497594	+	0.867410i	$0.665783\pi$
$110$		−	871789.i		−	0.654988i
$111$	−1.25292e6	+	549972.i	−0.916126	+	0.402135i
$112$	−427554.			−0.304325
$113$	−580115.	+	580115.i	−0.402049	+	0.402049i	−0.878954	−	0.476906i	$-0.841758\pi$
$113$	−580115.	+	580115.i	−0.402049	+	0.402049i	0.476906	+	0.878954i	$0.341758\pi$
$114$		−	1.39698e6i		−	0.942924i
$115$			682923.i			0.449033i
$116$	319888.	+	319888.i	0.204939	+	0.204939i
$117$	1165.67	+	1165.67i	0.000727813	+	0.000727813i
$118$	931587.			0.566993
$119$	610881.	+	610881.i	0.362507	+	0.362507i
$120$	1.63514e6			0.946260
$121$	−856419.			−0.483426
$122$			14885.6i			0.00819760i
$123$	27307.8			0.0146748
$124$	−1.52642e6	−	1.52642e6i	−0.800586	−	0.800586i
$125$	1.21178e6	−	1.21178e6i	0.620429	−	0.620429i
$126$	−632.178	+	632.178i	−0.000316030	+	0.000316030i
$127$	3.60881e6			1.76178			0.880892	−	0.473317i	$-0.156943\pi$
$127$	3.60881e6			1.76178			0.880892	+	0.473317i	$0.156943\pi$
$128$	−1.40030e6	−	1.40030e6i	−0.667713	−	0.667713i
$129$	−1.67851e6	+	1.67851e6i	−0.781907	+	0.781907i
$130$	−860263.	−	860263.i	−0.391563	−	0.391563i
$131$	−2.14260e6	+	2.14260e6i	−0.953074	+	0.953074i	−0.998947	−	0.0458735i	$-0.985393\pi$
$131$	−2.14260e6	+	2.14260e6i	−0.953074	+	0.953074i	0.0458735	+	0.998947i	$0.485393\pi$
$132$		−	2.12640e6i		−	0.924535i
$133$	2.90520e6	+	2.90520e6i	1.23487	+	1.23487i
$134$	1.13838e6	+	1.13838e6i	0.473120	+	0.473120i
$135$	1.90369e6	−	1.90369e6i	0.773739	−	0.773739i
$136$			1.22395e6i			0.486573i
$137$	−2.05943e6			−0.800914			−0.400457	−	0.916316i	$-0.631149\pi$
$137$	−2.05943e6			−0.800914			−0.400457	+	0.916316i	$0.631149\pi$
$138$		−	529761.i		−	0.201578i
$139$		−	4.44757e6i		−	1.65607i	−0.560676	−	0.828035i	$-0.689459\pi$
$139$		−	4.44757e6i		−	1.65607i	0.560676	−	0.828035i	$-0.310541\pi$
$140$	−1.46696e6	+	1.46696e6i	−0.534607	+	0.534607i
$141$			2.58488e6i			0.922112i
$142$	−824364.	+	824364.i	−0.287908	+	0.287908i
$143$	−2.59324e6	+	2.59324e6i	−0.886817	+	0.886817i
$144$	997.916			0.000334200
$145$	1.27496e6			0.418208
$146$	−1.50126e6	−	1.50126e6i	−0.482389	−	0.482389i
$147$			545001.i			0.171572i
$148$	2.25215e6	−	988582.i	0.694723	−	0.304949i
$149$	2.19421e6			0.663313			0.331656	−	0.943400i	$-0.392393\pi$
$149$	2.19421e6			0.663313			0.331656	+	0.943400i	$0.392393\pi$
$150$	232864.	−	232864.i	0.0689967	−	0.0689967i
$151$			248.395i			7.21460e-5i	1.00000		3.60730e-5i	$1.14824e-5\pi$
$151$			248.395i			7.21460e-5i	−1.00000		3.60730e-5i	$0.999989\pi$
$152$			5.82081e6i			1.65750i
$153$	−1425.80	−	1425.80i	−0.000398093	−	0.000398093i
$154$	−1.40638e6	−	1.40638e6i	−0.385072	−	0.385072i
$155$	−6.08375e6			−1.63372
$156$	−2.09829e6	−	2.09829e6i	−0.552702	−	0.552702i
$157$	3.43503e6			0.887629			0.443814	−	0.896119i	$-0.353625\pi$
$157$	3.43503e6			0.887629			0.443814	+	0.896119i	$0.353625\pi$
$158$	−672466.			−0.170490
$159$			3.13550e6i			0.780038i
$160$	−4.61040e6			−1.12559
$161$	1.10170e6	+	1.10170e6i	0.263990	+	0.263990i
$162$	−1.47821e6	+	1.47821e6i	−0.347690	+	0.347690i
$163$	1.25799e6	−	1.25799e6i	0.290478	−	0.290478i	−0.546791	−	0.837269i	$-0.684151\pi$
$163$	1.25799e6	−	1.25799e6i	0.290478	−	0.290478i	0.837269	+	0.546791i	$0.184151\pi$
$164$	−49086.1			−0.0111283
$165$	−4.23754e6	−	4.23754e6i	−0.943326	−	0.943326i
$166$	−25771.3	+	25771.3i	−0.00563393	+	0.00563393i
$167$	−2.97309e6	−	2.97309e6i	−0.638349	−	0.638349i	0.311799	−	0.950148i	$-0.399068\pi$
$167$	−2.97309e6	−	2.97309e6i	−0.638349	−	0.638349i	−0.950148	+	0.311799i	$0.899068\pi$
$168$	2.63783e6	−	2.63783e6i	0.556313	−	0.556313i
$169$			291089.i			0.0603067i
$170$	1.05224e6	+	1.05224e6i	0.214174	+	0.214174i
$171$	−6780.76	−	6780.76i	−0.00135609	−	0.00135609i
$172$	3.01715e6	−	3.01715e6i	0.592941	−	0.592941i
$173$			1.03507e6i			0.199908i	0.994992	+	0.0999538i	$0.0318695\pi$
$173$			1.03507e6i			0.199908i	−0.994992	+	0.0999538i	$0.968130\pi$
$174$	−989019.			−0.187740
$175$			968538.i			0.180718i
$176$			2.22003e6i			0.407212i
$177$	4.52820e6	−	4.52820e6i	0.816593	−	0.816593i
$178$			4.09625e6i			0.726318i
$179$	−7.36165e6	+	7.36165e6i	−1.28356	+	1.28356i	−0.344932	+	0.938628i	$0.612098\pi$
$179$	−7.36165e6	+	7.36165e6i	−1.28356	+	1.28356i	−0.938628	+	0.344932i	$0.887902\pi$
$180$	3423.90	−	3423.90i	0.000587089	−	0.000587089i
$181$	7.60699e6			1.28285			0.641426	−	0.767185i	$-0.278343\pi$
$181$	7.60699e6			1.28285			0.641426	+	0.767185i	$0.278343\pi$
$182$	−2.77558e6			−0.460404
$183$	72354.9	+	72354.9i	0.0118063	+	0.0118063i
$184$			2.20735e6i			0.354339i
$185$	2.51806e6	−	6.45820e6i	0.397696	−	1.01999i
$186$	4.71932e6			0.733400
$187$	3.17193e6	−	3.17193e6i	0.485064	−	0.485064i
$188$		−	4.64637e6i		−	0.699262i
$189$		−	6.14212e6i		−	0.909772i
$190$	5.00417e6	+	5.00417e6i	0.729578	+	0.729578i
$191$	7.05801e6	+	7.05801e6i	1.01294	+	1.01294i	0.999915	+	0.0130219i	$0.00414510\pi$
$191$	7.05801e6	+	7.05801e6i	1.01294	+	1.01294i	0.0130219	+	0.999915i	$0.495855\pi$
$192$	1.20881e6			0.170786
$193$	1.35373e6	+	1.35373e6i	0.188305	+	0.188305i	0.794963	−	0.606658i	$-0.207490\pi$
$193$	1.35373e6	+	1.35373e6i	0.188305	+	0.188305i	−0.606658	+	0.794963i	$0.707490\pi$
$194$	−483484.			−0.0662182
$195$	−8.36302e6			−1.12787
$196$		−	979647.i		−	0.130107i
$197$	−2.09646e6			−0.274213			−0.137106	−	0.990556i	$-0.543780\pi$
$197$	−2.09646e6			−0.274213			−0.137106	+	0.990556i	$0.543780\pi$
$198$	3282.51	+	3282.51i	0.000422874	+	0.000422874i
$199$	−4.92359e6	+	4.92359e6i	−0.624774	+	0.624774i	−0.946748	−	0.321974i	$-0.895653\pi$
$199$	−4.92359e6	+	4.92359e6i	−0.624774	+	0.624774i	0.321974	+	0.946748i	$0.395653\pi$
$200$	−970274.	+	970274.i	−0.121284	+	0.121284i
$201$	1.10667e7			1.36279
$202$	−3.74258e6	−	3.74258e6i	−0.454063	−	0.454063i
$203$	2.05679e6	−	2.05679e6i	0.245867	−	0.245867i
$204$	2.56653e6	+	2.56653e6i	0.302312	+	0.302312i
$205$	−97819.9	+	97819.9i	−0.0113544	+	0.0113544i
$206$		−	7.10747e6i		−	0.813043i
$207$	−2571.38	−	2571.38i	−0.000289905	−	0.000289905i
$208$	2.19068e6	+	2.19068e6i	0.243438	+	0.243438i
$209$	1.50849e7	−	1.50849e7i	1.65236	−	1.65236i
$210$		−	4.53550e6i		−	0.489742i
$211$	−2.68590e6			−0.285918			−0.142959	−	0.989729i	$-0.545662\pi$
$211$	−2.68590e6			−0.285918			−0.142959	+	0.989729i	$0.545662\pi$
$212$		−	5.63611e6i		−	0.591523i
$213$			8.01403e6i			0.829301i
$214$	−607577.	+	607577.i	−0.0619955	+	0.0619955i
$215$		−	1.20253e7i		−	1.20998i
$216$	6.15313e6	−	6.15313e6i	0.610569	−	0.610569i
$217$	−9.81441e6	+	9.81441e6i	−0.960472	+	0.960472i
$218$	2.66161e6			0.256907
$219$	−1.45945e7			−1.38949
$220$	7.61703e6	+	7.61703e6i	0.715349	+	0.715349i
$221$		−	6.25999e6i		−	0.579958i
$222$	−1.95332e6	+	5.00979e6i	−0.178532	+	0.457889i
$223$	−1.25337e7			−1.13022			−0.565110	−	0.825015i	$-0.691166\pi$
$223$	−1.25337e7			−1.13022			−0.565110	+	0.825015i	$0.691166\pi$
$224$	−7.43757e6	+	7.43757e6i	−0.661740	+	0.661740i
$225$		−	2260.58i		−	0.000198459i
$226$			3.22398e6i			0.279298i
$227$	172677.	+	172677.i	0.0147624	+	0.0147624i	0.714449	−	0.699687i	$-0.246677\pi$
$227$	172677.	+	172677.i	0.0147624	+	0.0147624i	−0.699687	+	0.714449i	$0.746677\pi$
$228$	1.22058e7	+	1.22058e7i	1.02982	+	1.02982i
$229$	−5.67922e6			−0.472914			−0.236457	−	0.971642i	$-0.575986\pi$
$229$	−5.67922e6			−0.472914			−0.236457	+	0.971642i	$0.575986\pi$
$230$	1.89767e6	+	1.89767e6i	0.155969	+	0.155969i
$231$	−1.36721e7			−1.10917
$232$	4.12094e6			0.330014
$233$			1.95636e7i			1.54661i	0.634034	+	0.773305i	$0.281398\pi$
$233$			1.95636e7i			1.54661i	−0.634034	+	0.773305i	$0.718602\pi$
$234$	6478.23			0.000505602
$235$	−9.25938e6	−	9.25938e6i	−0.713474	−	0.713474i
$236$	−8.13950e6	+	8.13950e6i	−0.619244	+	0.619244i
$237$	−3.26868e6	+	3.26868e6i	−0.245543	+	0.245543i
$238$	3.39497e6			0.251828
$239$	1.06868e7	+	1.06868e7i	0.782807	+	0.782807i	0.980304	−	0.197497i	$-0.0632813\pi$
$239$	1.06868e7	+	1.06868e7i	0.782807	+	0.782807i	−0.197497	+	0.980304i	$0.563281\pi$
$240$	−3.57973e6	+	3.57973e6i	−0.258950	+	0.258950i
$241$	−294213.	−	294213.i	−0.0210189	−	0.0210189i	0.696519	−	0.717538i	$-0.254731\pi$
$241$	−294213.	−	294213.i	−0.0210189	−	0.0210189i	−0.717538	+	0.696519i	$0.754731\pi$
$242$	−2.37977e6	+	2.37977e6i	−0.167915	+	0.167915i
$243$			28685.8i			0.00199917i
$244$	−130059.	−	130059.i	−0.00895305	−	0.00895305i
$245$	−1.95226e6	−	1.95226e6i	−0.132752	−	0.132752i
$246$	75881.4	−	75881.4i	0.00509718	−	0.00509718i
$247$		−	2.97709e7i		−	1.97561i
$248$	−1.96640e7			−1.28919
$249$			250535.i			0.0162282i
$250$		−	6.73444e6i		−	0.431004i
$251$	−5.10056e6	+	5.10056e6i	−0.322550	+	0.322550i	−0.849744	−	0.527195i	$-0.823244\pi$
$251$	−5.10056e6	+	5.10056e6i	−0.322550	+	0.322550i	0.527195	+	0.849744i	$0.323244\pi$
$252$		−	11047.0i		−	0.000690307i
$253$	5.72047e6	−	5.72047e6i	0.353240	−	0.353240i
$254$	1.00280e7	−	1.00280e7i	0.611944	−	0.611944i
$255$	1.02293e7			0.616914
$256$	−1.06460e7			−0.634552
$257$	−1.27735e7	−	1.27735e7i	−0.752506	−	0.752506i	0.222440	−	0.974946i	$-0.428598\pi$
$257$	−1.27735e7	−	1.27735e7i	−0.752506	−	0.752506i	−0.974946	+	0.222440i	$0.928598\pi$
$258$			9.32831e6i			0.543180i
$259$	−6.35629e6	−	1.44806e7i	−0.365851	−	0.833467i
$260$	1.50327e7			0.855294
$261$	−4800.56	+	4800.56i	−0.000270004	+	0.000270004i
$262$			1.19075e7i			0.662087i
$263$			2.37210e7i			1.30397i	0.758233	+	0.651984i	$0.226063\pi$
$263$			2.37210e7i			1.30397i	−0.758233	+	0.651984i	$0.773937\pi$
$264$	−1.36966e7	−	1.36966e7i	−0.744392	−	0.744392i
$265$	−1.12318e7	−	1.12318e7i	−0.603546	−	0.603546i
$266$	1.61456e7			0.857847
$267$	1.99108e7	+	1.99108e7i	1.04606	+	1.04606i
$268$	−1.98925e7			−1.03344
$269$	1.91018e7			0.981335			0.490667	−	0.871347i	$-0.336753\pi$
$269$	1.91018e7			0.981335			0.490667	+	0.871347i	$0.336753\pi$
$270$		−	1.05797e7i		−	0.537506i
$271$	7.63706e6			0.383723			0.191862	−	0.981422i	$-0.438547\pi$
$271$	7.63706e6			0.383723			0.191862	+	0.981422i	$0.438547\pi$
$272$	−2.67954e6	−	2.67954e6i	−0.133154	−	0.133154i
$273$	−1.34914e7	+	1.34914e7i	−0.663083	+	0.663083i
$274$	−5.72264e6	+	5.72264e6i	−0.278192	+	0.278192i
$275$	5.02902e6			0.241816
$276$	4.62865e6	+	4.62865e6i	0.220154	+	0.220154i
$277$	2.25266e7	−	2.25266e7i	1.05988	−	1.05988i	0.0617906	−	0.998089i	$-0.480319\pi$
$277$	2.25266e7	−	2.25266e7i	1.05988	−	1.05988i	0.998089	−	0.0617906i	$-0.0196811\pi$
$278$	−1.23587e7	−	1.23587e7i	−0.575225	−	0.575225i
$279$	22906.9	−	22906.9i	0.00105476	−	0.00105476i
$280$			1.88981e7i			0.860882i
$281$	9.53578e6	+	9.53578e6i	0.429771	+	0.429771i	0.888550	−	0.458779i	$-0.151713\pi$
$281$	9.53578e6	+	9.53578e6i	0.429771	+	0.429771i	−0.458779	+	0.888550i	$0.651713\pi$
$282$	7.18273e6	+	7.18273e6i	0.320289	+	0.320289i
$283$	−5.54800e6	+	5.54800e6i	−0.244781	+	0.244781i	−0.818825	−	0.574044i	$-0.805374\pi$
$283$	−5.54800e6	+	5.54800e6i	−0.244781	+	0.244781i	0.574044	+	0.818825i	$0.305374\pi$
$284$		−	1.44053e7i		−	0.628881i
$285$	4.86479e7			2.10150
$286$			1.44119e7i			0.616059i
$287$			315609.i			0.0133507i
$288$	17359.4	−	17359.4i	0.000726702	−	0.000726702i
$289$		−	1.64806e7i		−	0.682779i
$290$	3.54279e6	−	3.54279e6i	0.145262	−	0.145262i
$291$	−2.35009e6	+	2.35009e6i	−0.0953686	+	0.0953686i
$292$	2.62337e7			1.05369
$293$	4.26848e7			1.69695			0.848477	−	0.529232i	$-0.177520\pi$
$293$	4.26848e7			1.69695			0.848477	+	0.529232i	$0.177520\pi$
$294$	1.51442e6	+	1.51442e6i	0.0595942	+	0.0595942i
$295$			3.24411e7i			1.26366i
$296$	8.13891e6	−	2.08743e7i	0.313828	−	0.804890i
$297$	−3.18922e7			−1.21735
$298$	6.09714e6	−	6.09714e6i	0.230397	−	0.230397i
$299$		−	1.12897e7i		−	0.422345i
$300$			4.06918e6i			0.150710i
$301$	−1.93994e7	−	1.93994e7i	−0.711358	−	0.711358i
$302$	690.227	+	690.227i	2.50594e−5	+	2.50594e-5i
$303$	−3.63833e7			−1.30790
$304$	−1.27432e7	−	1.27432e7i	−0.453585	−	0.453585i
$305$	−518369.			−0.0182700
$306$	−7923.88			−0.000276550
$307$			3.12106e7i			1.07867i	0.842092	+	0.539334i	$0.181324\pi$
$307$			3.12106e7i			1.07867i	−0.842092	+	0.539334i	$0.818676\pi$
$308$	2.45758e7			0.841116
$309$	−3.45475e7	−	3.45475e7i	−1.17096	−	1.17096i
$310$	−1.69052e7	+	1.69052e7i	−0.567460	+	0.567460i
$311$	3.74637e7	−	3.74637e7i	1.24546	−	1.24546i	0.287756	−	0.957704i	$-0.407091\pi$
$311$	3.74637e7	−	3.74637e7i	1.24546	−	1.24546i	0.957704	−	0.287756i	$-0.0929091\pi$
$312$	−2.70311e7			−0.890020
$313$	−8.97758e6	−	8.97758e6i	−0.292770	−	0.292770i	0.545404	−	0.838173i	$-0.316376\pi$
$313$	−8.97758e6	−	8.97758e6i	−0.292770	−	0.292770i	−0.838173	+	0.545404i	$0.816376\pi$
$314$	9.54507e6	−	9.54507e6i	0.308312	−	0.308312i
$315$	−22014.7	−	22014.7i	−0.000704337	−	0.000704337i
$316$	5.87550e6	−	5.87550e6i	0.186202	−	0.186202i
$317$		−	1.60622e6i		−	0.0504227i	−0.999682	−	0.0252114i	$-0.991974\pi$
$317$		−	1.60622e6i		−	0.0504227i	0.999682	−	0.0252114i	$-0.00802587\pi$
$318$	8.71276e6	+	8.71276e6i	0.270941	+	0.270941i
$319$	−1.06796e7	−	1.06796e7i	−0.328991	−	0.328991i
$320$	−4.33010e6	+	4.33010e6i	−0.132144	+	0.132144i
$321$			5.90654e6i			0.178574i
$322$	6.12270e6			0.183390
$323$			3.64145e7i			1.08060i
$324$		−	2.58310e7i		−	0.759463i
$325$	4.96253e6	−	4.96253e6i	0.144562	−	0.144562i
$326$		−	6.99126e6i		−	0.201791i
$327$	1.29374e7	−	1.29374e7i	0.370001	−	0.370001i
$328$	−316175.	+	316175.i	−0.00895996	+	0.00895996i
$329$	−2.98748e7			−0.838912
$330$	−2.35501e7			−0.655315
$331$	2.20997e7	+	2.20997e7i	0.609401	+	0.609401i	0.942790	−	0.333388i	$-0.108192\pi$
$331$	2.20997e7	+	2.20997e7i	0.609401	+	0.609401i	−0.333388	+	0.942790i	$0.608192\pi$
$332$		−	450340.i		−	0.0123063i
$333$	14835.6	+	33797.9i	0.000401766	+	0.000915287i
$334$	−1.65229e7			−0.443452
$335$	−3.96422e7	+	3.96422e7i	−1.05444	+	1.05444i
$336$			1.15497e7i			0.304477i
$337$			4.33371e7i			1.13232i	0.824295	+	0.566161i	$0.191572\pi$
$337$			4.33371e7i			1.13232i	−0.824295	+	0.566161i	$0.808428\pi$
$338$	808863.	+	808863.i	0.0209471	+	0.0209471i
$339$	1.56709e7	+	1.56709e7i	0.402250	+	0.402250i
$340$	−1.83873e7			−0.467822
$341$	5.09602e7	+	5.09602e7i	1.28519	+	1.28519i
$342$	−37684.0			−0.000942061
$343$	−4.30298e7			−1.06632
$344$		−	3.88683e7i		−	0.954817i
$345$	1.84481e7			0.449258
$346$	2.87618e6	+	2.87618e6i	0.0694366	+	0.0694366i
$347$	1.17530e7	−	1.17530e7i	0.281295	−	0.281295i	−0.552330	−	0.833625i	$-0.686261\pi$
$347$	1.17530e7	−	1.17530e7i	0.281295	−	0.281295i	0.833625	+	0.552330i	$0.186261\pi$
$348$	8.64129e6	−	8.64129e6i	0.205041	−	0.205041i
$349$	−3.23257e7			−0.760452			−0.380226	−	0.924894i	$-0.624154\pi$
$349$	−3.23257e7			−0.760452			−0.380226	+	0.924894i	$0.624154\pi$
$350$	2.69132e6	+	2.69132e6i	0.0627713	+	0.0627713i
$351$	−3.14706e7	+	3.14706e7i	−0.727752	+	0.727752i
$352$	3.86188e7	+	3.86188e7i	0.885463	+	0.885463i
$353$	2.28251e7	−	2.28251e7i	0.518906	−	0.518906i	−0.398335	−	0.917240i	$-0.630412\pi$
$353$	2.28251e7	−	2.28251e7i	0.518906	−	0.518906i	0.917240	+	0.398335i	$0.130412\pi$
$354$		−	2.51654e7i		−	0.567276i
$355$	−2.87073e7	−	2.87073e7i	−0.641663	−	0.641663i
$356$	−3.57900e7	−	3.57900e7i	−0.793252	−	0.793252i
$357$	1.65020e7	−	1.65020e7i	0.362688	−	0.362688i
$358$			4.09123e7i			0.891672i
$359$	−4.71855e7			−1.01982			−0.509912	−	0.860227i	$-0.670322\pi$
$359$	−4.71855e7			−1.01982			−0.509912	+	0.860227i	$0.670322\pi$
$360$		−	44108.3i		−	0.000945393i
$361$			1.26132e8i			2.68105i
$362$	2.11379e7	−	2.11379e7i	0.445590	−	0.445590i
$363$			2.31349e7i			0.483668i
$364$	2.42509e7	−	2.42509e7i	0.502833	−	0.502833i
$365$	5.22792e7	−	5.22792e7i	1.07510	−	1.07510i
$366$	402112.			0.00820170
$367$	5.37578e7			1.08753			0.543767	−	0.839236i	$-0.316997\pi$
$367$	5.37578e7			1.08753			0.543767	+	0.839236i	$0.316997\pi$
$368$	−4.83245e6	−	4.83245e6i	−0.0969670	−	0.0969670i
$369$		−	736.635i		−	1.46613e-5i
$370$	−1.09486e7	−	2.49427e7i	−0.216150	−	0.492424i
$371$	−3.62385e7			−0.709657
$372$	−4.12338e7	+	4.12338e7i	−0.800986	+	0.800986i
$373$			3.02093e7i			0.582122i	0.956704	+	0.291061i	$0.0940083\pi$
$373$			3.02093e7i			0.582122i	−0.956704	+	0.291061i	$0.905992\pi$
$374$		−	1.76280e7i		−	0.336967i
$375$	−3.27343e7	−	3.27343e7i	−0.620739	−	0.620739i
$376$	−2.99283e7	−	2.99283e7i	−0.563013	−	0.563013i
$377$	−2.10769e7			−0.393352
$378$	−1.70674e7	−	1.70674e7i	−0.316003	−	0.316003i
$379$	−5.36124e6			−0.0984798			−0.0492399	−	0.998787i	$-0.515680\pi$
$379$	−5.36124e6			−0.0984798			−0.0492399	+	0.998787i	$0.515680\pi$
$380$	−8.74453e7			−1.59362
$381$		−	9.74865e7i		−	1.76266i
$382$	3.92249e7			0.703674
$383$	6.46446e7	+	6.46446e7i	1.15063	+	1.15063i	0.986426	+	0.164205i	$0.0525059\pi$
$383$	6.46446e7	+	6.46446e7i	1.15063	+	1.15063i	0.164205	+	0.986426i	$0.447494\pi$
$384$	−3.78269e7	+	3.78269e7i	−0.668047	+	0.668047i
$385$	4.89753e7	−	4.89753e7i	0.858212	−	0.858212i
$386$	7.52337e6			0.130813
$387$	45278.3	+	45278.3i	0.000781191	+	0.000781191i
$388$	4.22432e6	−	4.22432e6i	0.0723205	−	0.0723205i
$389$	−1.08514e7	−	1.08514e7i	−0.184348	−	0.184348i	0.608900	−	0.793247i	$-0.291611\pi$
$389$	−1.08514e7	−	1.08514e7i	−0.184348	−	0.184348i	−0.793247	+	0.608900i	$0.791611\pi$
$390$	−2.32387e7	+	2.32387e7i	−0.391758	+	0.391758i
$391$			1.38090e7i			0.231011i
$392$	−6.31013e6	−	6.31013e6i	−0.104756	−	0.104756i
$393$	5.78790e7	+	5.78790e7i	0.953550	+	0.953550i
$394$	−5.82553e6	+	5.82553e6i	−0.0952460	+	0.0952460i
$395$		−	2.34176e7i		−	0.379972i
$396$	−57360.2			−0.000923688
$397$		−	9.83200e7i		−	1.57134i	−0.618646	−	0.785670i	$-0.712318\pi$
$397$		−	9.83200e7i		−	1.57134i	0.618646	−	0.785670i	$-0.287682\pi$
$398$			2.73628e7i			0.434022i
$399$	7.84796e7	−	7.84796e7i	1.23549	−	1.23549i
$400$		−	4.24835e6i		−	0.0663804i
$401$	3.55520e6	−	3.55520e6i	0.0551354	−	0.0551354i	−0.679001	−	0.734137i	$-0.737587\pi$
$401$	3.55520e6	−	3.55520e6i	0.0551354	−	0.0551354i	0.734137	+	0.679001i	$0.237587\pi$
$402$	3.07515e7	−	3.07515e7i	0.473356	−	0.473356i
$403$	1.00573e8			1.53662
$404$	6.53996e7			0.991815
$405$	−5.14766e7	−	5.14766e7i	−0.774899	−	0.774899i
$406$		−	1.14306e7i		−	0.170801i
$407$	−7.51891e7	+	3.30043e7i	−1.11525	+	0.489539i
$408$	3.30632e7			0.486816
$409$	1.14150e7	−	1.14150e7i	0.166842	−	0.166842i	−0.618748	−	0.785590i	$-0.712360\pi$
$409$	1.14150e7	−	1.14150e7i	0.166842	−	0.166842i	0.785590	+	0.618748i	$0.212360\pi$
$410$			543633.i			0.00788777i
$411$			5.56324e7i			0.801314i
$412$	6.20997e7	+	6.20997e7i	0.887969	+	0.887969i
$413$	5.23346e7	+	5.23346e7i	0.742914	+	0.742914i
$414$	−14290.4			−0.000201393
$415$	−897447.	−	897447.i	−0.0125564	−	0.0125564i
$416$	7.62163e7			1.05869
$417$	−1.20145e8			−1.65690
$418$		−	8.38343e7i		−	1.14787i
$419$	1.46466e7			0.199110			0.0995551	−	0.995032i	$-0.468258\pi$
$419$	1.46466e7			0.199110			0.0995551	+	0.995032i	$0.468258\pi$
$420$	3.96278e7	+	3.96278e7i	0.534874	+	0.534874i
$421$	−3.82769e7	+	3.82769e7i	−0.512968	+	0.512968i	−0.915435	−	0.402467i	$-0.868153\pi$
$421$	−3.82769e7	+	3.82769e7i	−0.512968	+	0.512968i	0.402467	+	0.915435i	$0.368153\pi$
$422$	−7.46343e6	+	7.46343e6i	−0.0993118	+	0.0993118i
$423$	69727.9			0.000921267
$424$	−3.63035e7	−	3.63035e7i	−0.476267	−	0.476267i
$425$	−6.06995e6	+	6.06995e6i	−0.0790712	+	0.0790712i
$426$	2.22690e7	+	2.22690e7i	0.288052	+	0.288052i
$427$	−836241.	+	836241.i	−0.0107411	+	0.0107411i
$428$		−	1.06171e7i		−	0.135417i
$429$	7.00523e7	+	7.00523e7i	0.887260	+	0.887260i
$430$	−3.34152e7	−	3.34152e7i	−0.420280	−	0.420280i
$431$	−4.68551e7	+	4.68551e7i	−0.585228	+	0.585228i	−0.936335	−	0.351108i	$-0.885805\pi$
$431$	−4.68551e7	+	4.68551e7i	−0.585228	+	0.585228i	0.351108	+	0.936335i	$0.385805\pi$
$432$			2.69415e7i			0.334172i
$433$	6.30773e7			0.776979			0.388489	−	0.921453i	$-0.372997\pi$
$433$	6.30773e7			0.776979			0.388489	+	0.921453i	$0.372997\pi$
$434$			5.45435e7i			0.667227i
$435$		−	3.44411e7i		−	0.418417i
$436$	−2.32551e7	+	2.32551e7i	−0.280582	+	0.280582i
$437$			6.56723e7i			0.786933i
$438$	−4.05543e7	+	4.05543e7i	−0.482630	+	0.482630i
$439$	8.56013e7	−	8.56013e7i	1.01178	−	1.01178i	0.0118524	−	0.999930i	$-0.496227\pi$
$439$	8.56013e7	−	8.56013e7i	1.01178	−	1.01178i	0.999930	−	0.0118524i	$-0.00377282\pi$
$440$	9.81261e7			1.15193
$441$	14701.5			0.000171414
$442$	−1.73949e7	−	1.73949e7i	−0.201445	−	0.201445i
$443$		−	1.87227e7i		−	0.215356i	−0.994186	−	0.107678i	$-0.965658\pi$
$443$		−	1.87227e7i		−	0.215356i	0.994186	−	0.107678i	$-0.0343416\pi$
$444$	−2.67051e7	−	6.08383e7i	−0.305102	−	0.695070i
$445$	−1.42646e8			−1.61875
$446$	−3.48278e7	+	3.48278e7i	−0.392574	+	0.392574i
$447$		−	5.92732e7i		−	0.663644i
$448$			1.39708e7i			0.155377i
$449$	−1.21322e8	−	1.21322e8i	−1.34029	−	1.34029i	−0.895765	−	0.444528i	$-0.853372\pi$
$449$	−1.21322e8	−	1.21322e8i	−1.34029	−	1.34029i	−0.444528	−	0.895765i	$-0.646628\pi$
$450$	−6281.57	−	6281.57i	−6.89335e−5	−	6.89335e-5i
$451$	1.63876e6			0.0178643
$452$	−2.81687e7	−	2.81687e7i	−0.305037	−	0.305037i
$453$	6710.02			7.21821e−5
$454$	959650.			0.0102552
$455$		−	9.66555e7i		−	1.02611i
$456$	1.57240e8			1.65833
$457$	−8.60733e7	−	8.60733e7i	−0.901820	−	0.901820i	0.0937737	−	0.995594i	$-0.470107\pi$
$457$	−8.60733e7	−	8.60733e7i	−0.901820	−	0.901820i	−0.995594	+	0.0937737i	$0.970107\pi$
$458$	−1.57811e7	+	1.57811e7i	−0.164264	+	0.164264i
$459$	3.84934e7	−	3.84934e7i	0.398060	−	0.398060i
$460$	−3.31608e7			−0.340684
$461$	1.26205e7	+	1.26205e7i	0.128817	+	0.128817i	0.768576	−	0.639759i	$-0.220966\pi$
$461$	1.26205e7	+	1.26205e7i	0.128817	+	0.128817i	−0.639759	+	0.768576i	$0.720966\pi$
$462$	−3.79913e7	+	3.79913e7i	−0.385264	+	0.385264i
$463$	−1.27678e8	−	1.27678e8i	−1.28639	−	1.28639i	−0.936961	−	0.349434i	$-0.886374\pi$
$463$	−1.27678e8	−	1.27678e8i	−1.28639	−	1.28639i	−0.349434	−	0.936961i	$-0.613626\pi$
$464$	−9.02178e6	+	9.02178e6i	−0.0903105	+	0.0903105i
$465$			1.64343e8i			1.63453i
$466$	5.43623e7	+	5.43623e7i	0.537205	+	0.537205i
$467$	8.98782e7	+	8.98782e7i	0.882477	+	0.882477i	0.993786	−	0.111308i	$-0.0355042\pi$
$467$	8.98782e7	+	8.98782e7i	0.882477	+	0.882477i	−0.111308	+	0.993786i	$0.535504\pi$
$468$	−56601.8	+	56601.8i	−0.000552196	+	0.000552196i
$469$			1.27903e8i			1.23983i
$470$	−5.14589e7			−0.495641
$471$		−	9.27921e7i		−	0.888072i
$472$			1.04857e8i			0.997173i
$473$	−1.00729e8	+	1.00729e8i	−0.951856	+	0.951856i
$474$			1.81657e7i			0.170575i
$475$	−2.88672e7	+	2.88672e7i	−0.269354	+	0.269354i
$476$	−2.96626e7	+	2.96626e7i	−0.275036	+	0.275036i
$477$	84581.0			0.000779324
$478$	5.93919e7			0.543805
$479$	−1.32583e8	−	1.32583e8i	−1.20637	−	1.20637i	−0.972194	−	0.234178i	$-0.924760\pi$
$479$	−1.32583e8	−	1.32583e8i	−1.20637	−	1.20637i	−0.234178	−	0.972194i	$-0.575240\pi$
$480$			1.24543e8i			1.12615i
$481$	−4.16270e7	+	1.06763e8i	−0.374059	+	0.959368i
$482$	−1.63509e6			−0.0146016
$483$	2.97608e7	−	2.97608e7i	0.264121	−	0.264121i
$484$		−	4.15853e7i		−	0.366778i
$485$		−	1.68366e7i		−	0.147581i
$486$	79710.7	+	79710.7i	0.000694397	+	0.000694397i
$487$	4.17057e6	+	4.17057e6i	0.0361085	+	0.0361085i	0.724930	−	0.688822i	$-0.241872\pi$
$487$	4.17057e6	+	4.17057e6i	0.0361085	+	0.0361085i	−0.688822	+	0.724930i	$0.741872\pi$
$488$	−1.67548e6			−0.0144172
$489$	−3.39827e7	−	3.39827e7i	−0.290624	−	0.290624i
$490$	−1.08497e7			−0.0922208
$491$	−2.01953e8			−1.70611			−0.853053	−	0.521824i	$-0.825252\pi$
$491$	−2.01953e8			−1.70611			−0.853053	+	0.521824i	$0.825252\pi$
$492$			1.32599e6i			0.0111338i
$493$	2.57803e7			0.215153
$494$	−8.27259e7	−	8.27259e7i	−0.686216	−	0.686216i
$495$	−114309.	+	114309.i	−0.000942462	+	0.000942462i
$496$	4.30494e7	−	4.30494e7i	0.352795	−	0.352795i
$497$	−9.26220e7			−0.754476
$498$	696172.	+	696172.i	0.00563675	+	0.00563675i
$499$	1.42856e8	−	1.42856e8i	1.14974	−	1.14974i	0.163132	−	0.986604i	$-0.447840\pi$
$499$	1.42856e8	−	1.42856e8i	1.14974	−	1.14974i	0.986604	−	0.163132i	$-0.0521595\pi$
$500$	5.88404e7	+	5.88404e7i	0.470723	+	0.470723i
$501$	−8.03134e7	+	8.03134e7i	−0.638668	+	0.638668i
$502$			2.83463e7i			0.224071i
$503$	1.63993e8	+	1.63993e8i	1.28861	+	1.28861i	0.935634	+	0.352972i	$0.114829\pi$
$503$	1.63993e8	+	1.63993e8i	1.28861	+	1.28861i	0.352972	+	0.935634i	$0.385171\pi$
$504$	−71156.2	−	71156.2i	−0.000555803	−	0.000555803i
$505$	1.30330e8	−	1.30330e8i	1.01197	−	1.01197i
$506$		−	3.17914e7i		−	0.245391i
$507$	7.86333e6			0.0603369
$508$			1.75233e8i			1.33668i
$509$			2.04090e8i			1.54764i	0.633407	+	0.773819i	$0.281656\pi$
$509$			2.04090e8i			1.54764i	−0.633407	+	0.773819i	$0.718344\pi$
$510$	2.84246e7	−	2.84246e7i	0.214281	−	0.214281i
$511$		−	1.68675e8i		−	1.26412i
$512$	6.00363e7	−	6.00363e7i	0.447306	−	0.447306i
$513$	1.83065e8	−	1.83065e8i	1.35598	−	1.35598i
$514$	−7.09885e7			−0.522756
$515$	2.47507e8			1.81203
$516$	−8.15037e7	−	8.15037e7i	−0.593237	−	0.593237i
$517$			1.55121e8i			1.12253i
$518$	−5.79005e7	−	2.25755e7i	−0.416575	−	0.162423i
$519$	2.79607e7			0.200008
$520$	9.68288e7	−	9.68288e7i	0.688643	−	0.688643i
$521$		−	2.11052e8i		−	1.49237i	−0.665737	−	0.746186i	$-0.731883\pi$
$521$		−	2.11052e8i		−	1.49237i	0.665737	−	0.746186i	$-0.268117\pi$
$522$			26679.0i			0.000187568i
$523$	4.67969e7	+	4.67969e7i	0.327123	+	0.327123i	0.851492	−	0.524368i	$-0.175698\pi$
$523$	4.67969e7	+	4.67969e7i	0.327123	+	0.327123i	−0.524368	+	0.851492i	$0.675698\pi$
$524$	−1.04038e8	−	1.04038e8i	−0.723102	−	0.723102i
$525$	2.61636e7			0.180809
$526$	6.59148e7	+	6.59148e7i	0.452924	+	0.452924i
$527$	−1.23016e8			−0.840487
$528$	5.99707e7			0.407415
$529$		−	1.23132e8i		−	0.831770i
$530$	−6.24204e7			−0.419275
$531$	−122149.	−	122149.i	−0.000815845	−	0.000815845i
$532$	−1.41068e8	+	1.41068e8i	−0.936902	+	0.936902i
$533$	1.61710e6	−	1.61710e6i	0.0106796	−	0.0106796i
$534$	1.10654e8			0.726681
$535$	−2.11580e7	−	2.11580e7i	−0.138170	−	0.138170i
$536$	−1.28132e8	+	1.28132e8i	−0.832078	+	0.832078i
$537$	1.98864e8	+	1.98864e8i	1.28420	+	1.28420i
$538$	5.30790e7	−	5.30790e7i	0.340860	−	0.340860i
$539$			3.27060e7i			0.208863i
$540$	9.24376e7	+	9.24376e7i	0.587040	+	0.587040i
$541$	−2.79693e7	−	2.79693e7i	−0.176640	−	0.176640i	0.613249	−	0.789889i	$-0.289862\pi$
$541$	−2.79693e7	−	2.79693e7i	−0.176640	−	0.176640i	−0.789889	+	0.613249i	$0.789862\pi$
$542$	2.12215e7	−	2.12215e7i	0.133284	−	0.133284i
$543$		−	2.05491e8i		−	1.28349i
$544$	−9.32245e7			−0.579073
$545$			9.26867e7i			0.572569i
$546$			7.49781e7i			0.460635i
$547$	1.02550e8	−	1.02550e8i	0.626574	−	0.626574i	−0.320630	−	0.947204i	$-0.603895\pi$
$547$	1.02550e8	−	1.02550e8i	0.626574	−	0.626574i	0.947204	+	0.320630i	$0.103895\pi$
$548$		−	1.00000e8i		−	0.607657i
$549$	1951.79	−	1951.79i	1.17955e−5	−	1.17955e-5i
$550$	1.39744e7	−	1.39744e7i	0.0839933	−	0.0839933i
$551$	1.22605e8			0.732912
$552$	5.96284e7			0.354516
$553$	−3.77777e7	−	3.77777e7i	−0.223388	−	0.223388i
$554$		−	1.25191e8i		−	0.736284i
$555$	−1.74458e8	−	6.80216e7i	−1.02050	−	0.397894i
$556$	2.15962e8			1.25647
$557$	3.47578e7	−	3.47578e7i	0.201135	−	0.201135i	−0.599351	−	0.800486i	$-0.704575\pi$
$557$	3.47578e7	−	3.47578e7i	0.201135	−	0.201135i	0.800486	+	0.599351i	$0.204575\pi$
$558$		−	127305.i		−	0.000732728i
$559$			1.98795e8i			1.13807i
$560$	−4.13726e7	−	4.13726e7i	−0.235586	−	0.235586i
$561$	−8.56849e7	−	8.56849e7i	−0.485306	−	0.485306i
$562$	5.29950e7			0.298556
$563$	2.47754e8	+	2.47754e8i	1.38834	+	1.38834i	0.828818	+	0.559519i	$0.189014\pi$
$563$	2.47754e8	+	2.47754e8i	1.38834	+	1.38834i	0.559519	+	0.828818i	$0.310986\pi$
$564$	−1.25515e8			−0.699611
$565$	−1.12271e8			−0.622473
$566$			3.08330e7i			0.170046i
$567$	−1.66086e8			−0.911136
$568$	−9.27881e7	−	9.27881e7i	−0.506346	−	0.506346i
$569$	−1.63682e8	+	1.63682e8i	−0.888515	+	0.888515i	−0.994380	−	0.105866i	$-0.966239\pi$
$569$	−1.63682e8	+	1.63682e8i	−0.888515	+	0.888515i	0.105866	+	0.994380i	$0.466239\pi$
$570$	1.35180e8	−	1.35180e8i	0.729942	−	0.729942i
$571$	1.83910e8			0.987866			0.493933	−	0.869500i	$-0.335559\pi$
$571$	1.83910e8			0.987866			0.493933	+	0.869500i	$0.335559\pi$
$572$	−1.25920e8	−	1.25920e8i	−0.672832	−	0.672832i
$573$	1.90662e8	−	1.90662e8i	1.01344	−	1.01344i
$574$	876998.	+	876998.i	0.00463727	+	0.00463727i
$575$	−1.09469e7	+	1.09469e7i	−0.0575824	+	0.0575824i
$576$		−	32607.9i		−	0.000170630i
$577$	−4.57640e7	−	4.57640e7i	−0.238230	−	0.238230i	0.577887	−	0.816117i	$-0.303878\pi$
$577$	−4.57640e7	−	4.57640e7i	−0.238230	−	0.238230i	−0.816117	+	0.577887i	$0.803878\pi$
$578$	−4.57955e7	−	4.57955e7i	−0.237159	−	0.237159i
$579$	3.65691e7	−	3.65691e7i	0.188399	−	0.188399i
$580$			6.19084e7i			0.317297i
$581$	−2.89555e6			−0.0147640
$582$			1.30606e7i			0.0662513i
$583$			1.88164e8i			0.949580i
$584$	1.68978e8	−	1.68978e8i	0.848380	−	0.848380i
$585$			225595.i			0.00112684i
$586$	1.18610e8	−	1.18610e8i	0.589426	−	0.589426i
$587$	−2.16299e8	+	2.16299e8i	−1.06940	+	1.06940i	−0.0719930	+	0.997405i	$0.522936\pi$
$587$	−2.16299e8	+	2.16299e8i	−1.06940	+	1.06940i	−0.997405	+	0.0719930i	$0.977064\pi$
$588$	−2.64637e7			−0.130172
$589$	−5.85035e8			−2.86310
$590$	9.01457e7	+	9.01457e7i	0.438924	+	0.438924i
$591$			5.66327e7i			0.274350i
$592$	2.78809e7	+	6.35171e7i	0.134382	+	0.306144i
$593$	−1.18610e8			−0.568797			−0.284398	−	0.958706i	$-0.591794\pi$
$593$	−1.18610e8			−0.568797			−0.284398	+	0.958706i	$0.591794\pi$
$594$	−8.86204e7	+	8.86204e7i	−0.422838	+	0.422838i
$595$			1.18225e8i			0.561252i
$596$			1.06544e8i			0.503259i
$597$	1.33003e8	+	1.33003e8i	0.625086	+	0.625086i
$598$	−3.13711e7	−	3.13711e7i	−0.146699	−	0.146699i
$599$	3.57437e8			1.66310			0.831551	−	0.555448i	$-0.187453\pi$
$599$	3.57437e8			1.66310			0.831551	+	0.555448i	$0.187453\pi$
$600$	2.62105e7	+	2.62105e7i	0.121345	+	0.121345i
$601$	−2.16744e8			−0.998443			−0.499221	−	0.866474i	$-0.666381\pi$
$601$	−2.16744e8			−0.998443			−0.499221	+	0.866474i	$0.666381\pi$
$602$	−1.07812e8			−0.494171
$603$		−	298527.i		−	0.00136154i
$604$	−12061.4			−5.47376e−5
$605$	−8.28721e7	−	8.28721e7i	−0.374233	−	0.374233i
$606$	−1.01100e8	+	1.01100e8i	−0.454290	+	0.454290i
$607$	1.61996e8	−	1.61996e8i	0.724332	−	0.724332i	−0.245152	−	0.969485i	$-0.578838\pi$
$607$	1.61996e8	−	1.61996e8i	0.724332	−	0.724332i	0.969485	+	0.245152i	$0.0788380\pi$
$608$	−4.43352e8			−1.97260
$609$	−5.55610e7	−	5.55610e7i	−0.245990	−	0.245990i
$610$	−1.44042e6	+	1.44042e6i	−0.00634598	+	0.00634598i
$611$	1.53070e8	+	1.53070e8i	0.671069	+	0.671069i
$612$	69232.9	−	69232.9i	0.000302036	−	0.000302036i
$613$			1.88349e8i			0.817678i	0.912607	+	0.408839i	$0.134066\pi$
$613$			1.88349e8i			0.817678i	−0.912607	+	0.408839i	$0.865934\pi$
$614$	8.67264e7	+	8.67264e7i	0.374668	+	0.374668i
$615$	2.64246e6	+	2.64246e6i	0.0113601	+	0.0113601i
$616$	1.58299e8	−	1.58299e8i	0.677228	−	0.677228i
$617$			1.89641e7i			0.0807376i	0.999185	+	0.0403688i	$0.0128533\pi$
$617$			1.89641e7i			0.0807376i	−0.999185	+	0.0403688i	$0.987147\pi$
$618$	−1.91998e8			−0.813449
$619$			3.44440e8i			1.45225i	0.687561	+	0.726126i	$0.258681\pi$
$619$			3.44440e8i			1.45225i	−0.687561	+	0.726126i	$0.741319\pi$
$620$		−	2.95410e8i		−	1.23951i
$621$	6.94215e7	−	6.94215e7i	0.289881	−	0.289881i
$622$		−	2.08204e8i		−	0.865204i
$623$	−2.30119e8	+	2.30119e8i	−0.951673	+	0.951673i
$624$	5.91778e7	−	5.91778e7i	0.243560	−	0.243560i
$625$	2.82989e8			1.15912
$626$	−4.98928e7			−0.203383
$627$	−4.07496e8	−	4.07496e8i	−1.65318	−	1.65318i
$628$			1.66795e8i			0.673449i
$629$	5.09163e7	−	1.30588e8i	0.204600	−	0.524747i
$630$	−122346.			−0.000489293
$631$	−1.92646e7	+	1.92646e7i	−0.0766781	+	0.0766781i	−0.744406	−	0.667728i	$-0.767267\pi$
$631$	−1.92646e7	+	1.92646e7i	−0.0766781	+	0.0766781i	0.667728	+	0.744406i	$0.267267\pi$
$632$		−	7.56909e7i		−	0.299842i
$633$			7.25555e7i			0.286061i
$634$	−4.46327e6	−	4.46327e6i	−0.0175140	−	0.0175140i
$635$	3.49209e8	+	3.49209e8i	1.36384	+	1.36384i
$636$	−1.52251e8			−0.591819
$637$	3.22736e7	+	3.22736e7i	0.124862	+	0.124862i
$638$	−5.93519e7			−0.228546
$639$	216181.			0.000828542
$640$		−	2.71001e8i		−	1.03379i
$641$	−8.30007e7			−0.315143			−0.157571	−	0.987508i	$-0.550366\pi$
$641$	−8.30007e7			−0.315143			−0.157571	+	0.987508i	$0.550366\pi$
$642$	1.64128e7	+	1.64128e7i	0.0620264	+	0.0620264i
$643$	−3.28002e6	+	3.28002e6i	−0.0123380	+	0.0123380i	−0.713249	−	0.700911i	$-0.752777\pi$
$643$	−3.28002e6	+	3.28002e6i	−0.0123380	+	0.0123380i	0.700911	+	0.713249i	$0.252777\pi$
$644$	−5.34955e7	+	5.34955e7i	−0.200290	+	0.200290i
$645$	−3.24845e8			−1.21059
$646$	1.01187e8	+	1.01187e8i	0.375341	+	0.375341i
$647$	3.02480e8	−	3.02480e8i	1.11682	−	1.11682i	0.124618	−	0.992205i	$-0.460229\pi$
$647$	3.02480e8	−	3.02480e8i	1.11682	−	1.11682i	0.992205	−	0.124618i	$-0.0397706\pi$
$648$	−1.66384e8	−	1.66384e8i	−0.611484	−	0.611484i
$649$	2.71741e8	−	2.71741e8i	0.994080	−	0.994080i
$650$		−	2.75792e7i		−	0.100425i
$651$	2.65121e8	+	2.65121e8i	0.960952	+	0.960952i
$652$	6.10843e7	+	6.10843e7i	0.220388	+	0.220388i
$653$	3.73455e7	−	3.73455e7i	0.134122	−	0.134122i	−0.636859	−	0.770980i	$-0.719767\pi$
$653$	3.73455e7	−	3.73455e7i	0.134122	−	0.134122i	0.770980	+	0.636859i	$0.219767\pi$
$654$		−	7.18994e7i		−	0.257035i
$655$	−4.14660e8			−1.47560
$656$		−	1.38437e6i		−	0.00490390i
$657$			393689.i			0.00138822i
$658$	−8.30143e7	+	8.30143e7i	−0.291391	+	0.291391i
$659$			1.51351e8i			0.528846i	0.964407	+	0.264423i	$0.0851815\pi$
$659$			1.51351e8i			0.528846i	−0.964407	+	0.264423i	$0.914819\pi$
$660$	2.05763e8	−	2.05763e8i	0.715706	−	0.715706i
$661$	1.18555e8	−	1.18555e8i	0.410502	−	0.410502i	−0.471412	−	0.881913i	$-0.656255\pi$
$661$	1.18555e8	−	1.18555e8i	0.410502	−	0.410502i	0.881913	+	0.471412i	$0.156255\pi$
$662$	1.22819e8			0.423343
$663$	−1.69104e8			−0.580248
$664$	−2.90074e6	−	2.90074e6i	−0.00990843	−	0.00990843i
$665$			5.62248e8i			1.91189i
$666$	135140.	+	52691.4i	0.000457470	+	0.000178368i
$667$	4.64938e7			0.156681
$668$	1.44365e8	−	1.44365e8i	0.484319	−	0.484319i
$669$			3.38578e8i			1.13078i
$670$			2.20311e8i			0.732508i
$671$	4.34209e6	+	4.34209e6i	0.0143725	+	0.0143725i
$672$	2.00915e8	+	2.00915e8i	0.662070	+	0.662070i
$673$	3.22503e7			0.105801			0.0529003	−	0.998600i	$-0.483153\pi$
$673$	3.22503e7			0.105801			0.0529003	+	0.998600i	$0.483153\pi$
$674$	1.20423e8	+	1.20423e8i	0.393304	+	0.393304i
$675$	6.10304e7			0.198443
$676$	−1.41345e7			−0.0457551
$677$		−	4.12810e8i		−	1.33041i	−0.746662	−	0.665204i	$-0.768345\pi$
$677$		−	4.12810e8i		−	1.33041i	0.746662	−	0.665204i	$-0.231655\pi$
$678$	8.70911e7			0.279437
$679$	−2.71611e7	−	2.71611e7i	−0.0867637	−	0.0867637i
$680$	−1.18437e8	+	1.18437e8i	−0.376669	+	0.376669i
$681$	4.66460e6	−	4.66460e6i	0.0147698	−	0.0147698i
$682$	2.83211e8			0.892805
$683$	−2.99971e8	−	2.99971e8i	−0.941493	−	0.941493i	0.0568873	−	0.998381i	$-0.481882\pi$
$683$	−2.99971e8	−	2.99971e8i	−0.941493	−	0.941493i	−0.998381	+	0.0568873i	$0.981882\pi$
$684$	329254.	−	329254.i	0.00102888	−	0.00102888i
$685$	−1.99282e8	−	1.99282e8i	−0.620008	−	0.620008i
$686$	−1.19569e8	+	1.19569e8i	−0.370379	+	0.370379i
$687$			1.53416e8i			0.473151i
$688$	8.50924e7	+	8.50924e7i	0.261292	+	0.261292i
$689$	1.85677e8	+	1.85677e8i	0.567675	+	0.567675i
$690$	5.12627e7	−	5.12627e7i	0.156047	−	0.156047i
$691$		−	1.60183e8i		−	0.485491i	−0.970090	−	0.242746i	$-0.921952\pi$
$691$		−	1.60183e8i		−	0.485491i	0.970090	−	0.242746i	$-0.0780481\pi$
$692$	−5.02598e7			−0.151671
$693$			368809.i			0.00110816i
$694$		−	6.53174e7i		−	0.195412i
$695$	4.30373e8	−	4.30373e8i	1.28201	−	1.28201i
$696$		−	1.11321e8i		−	0.330179i
$697$	−1.97796e6	+	1.97796e6i	−0.00584144	+	0.00584144i
$698$	−8.98249e7	+	8.98249e7i	−0.264138	+	0.264138i
$699$	5.28481e8			1.54738
$700$	−4.70294e7			−0.137112
$701$	−4.77668e7	−	4.77668e7i	−0.138667	−	0.138667i	0.634366	−	0.773033i	$-0.281261\pi$
$701$	−4.77668e7	−	4.77668e7i	−0.138667	−	0.138667i	−0.773033	+	0.634366i	$0.781261\pi$
$702$			1.74897e8i			0.505559i
$703$	2.42145e8	−	6.21043e8i	0.696964	−	1.78754i
$704$	7.25416e7			0.207907
$705$	−2.50128e8	+	2.50128e8i	−0.713831	+	0.713831i
$706$		−	1.26850e8i		−	0.360477i
$707$		−	4.20500e8i		−	1.18989i
$708$	2.19876e8	+	2.19876e8i	0.619553	+	0.619553i
$709$	−6.77257e7	−	6.77257e7i	−0.190027	−	0.190027i	0.605681	−	0.795708i	$-0.292901\pi$
$709$	−6.77257e7	−	6.77257e7i	−0.190027	−	0.190027i	−0.795708	+	0.605681i	$0.792901\pi$
$710$	−1.59540e8			−0.445754
$711$	88173.5	+	88173.5i	0.000245318	+	0.000245318i
$712$	−4.61063e8			−1.27738
$713$	−2.21856e8			−0.612071
$714$		−	9.17099e7i		−	0.251954i
$715$	−5.01873e8			−1.37302
$716$	−3.57461e8	−	3.57461e8i	−0.973844	−	0.973844i
$717$	2.88688e8	−	2.88688e8i	0.783198	−	0.783198i
$718$	−1.31117e8	+	1.31117e8i	−0.354229	+	0.354229i
$719$	2.47474e8			0.665798			0.332899	−	0.942963i	$-0.391973\pi$
$719$	2.47474e8			0.665798			0.332899	+	0.942963i	$0.391973\pi$
$720$	96564.1	+	96564.1i	0.000258713	+	0.000258713i
$721$	3.99283e8	−	3.99283e8i	1.06531	−	1.06531i
$722$	3.50490e8	+	3.50490e8i	0.931245	+	0.931245i
$723$	−7.94772e6	+	7.94772e6i	−0.0210294	+	0.0210294i
$724$			3.69373e8i			0.973307i
$725$	2.04370e7	+	2.04370e7i	0.0536295	+	0.0536295i
$726$	6.42859e7	+	6.42859e7i	0.167999	+	0.167999i
$727$	8.46540e7	−	8.46540e7i	0.220315	−	0.220315i	−0.588316	−	0.808631i	$-0.700209\pi$
$727$	8.46540e7	−	8.46540e7i	0.220315	−	0.220315i	0.808631	+	0.588316i	$0.200209\pi$
$728$		−	3.12411e8i		−	0.809716i
$729$	−3.87032e8			−0.998998
$730$		−	2.90541e8i		−	0.746859i
$731$		−	2.43157e8i		−	0.622493i
$732$	−3.51335e6	+	3.51335e6i	−0.00895753	+	0.00895753i
$733$			2.88451e8i			0.732419i	0.930532	+	0.366209i	$0.119345\pi$
$733$			2.88451e8i			0.732419i	−0.930532	+	0.366209i	$0.880655\pi$
$734$	1.49379e8	−	1.49379e8i	0.377748	−	0.377748i
$735$	−5.27374e7	+	5.27374e7i	−0.132818	+	0.132818i
$736$	−1.68127e8			−0.421700
$737$	6.64122e8			1.65900
$738$	−2046.92	−	2046.92i	−5.09251e−6	−	5.09251e-6i
$739$			6.58561e8i			1.63178i	0.578204	+	0.815892i	$0.303754\pi$
$739$			6.58561e8i			1.63178i	−0.578204	+	0.815892i	$0.696246\pi$
$740$	3.13592e8	+	1.22270e8i	0.773872	+	0.301734i
$741$	−8.04217e8			−1.97660
$742$	−1.00698e8	+	1.00698e8i	−0.246495	+	0.246495i
$743$			5.42185e7i			0.132185i	0.997814	+	0.0660923i	$0.0210532\pi$
$743$			5.42185e7i			0.132185i	−0.997814	+	0.0660923i	$0.978947\pi$
$744$			5.31193e8i			1.28983i
$745$	2.12324e8	+	2.12324e8i	0.513488	+	0.513488i
$746$	8.39439e7	+	8.39439e7i	0.202196	+	0.202196i
$747$	6758.24			1.62133e−5
$748$	1.54020e8	+	1.54020e8i	0.368021	+	0.368021i
$749$	−6.82647e7			−0.162462
$750$	−1.81921e8			−0.431219
$751$			5.30131e8i			1.25159i	0.779986	+	0.625797i	$0.215226\pi$
$751$			5.30131e8i			1.25159i	−0.779986	+	0.625797i	$0.784774\pi$
$752$	1.31041e8			0.308144
$753$	1.37784e8	+	1.37784e8i	0.322711	+	0.322711i
$754$	−5.85672e7	+	5.85672e7i	−0.136628	+	0.136628i
$755$	−24036.2	+	24036.2i	−5.58501e−5	+	5.58501e-5i
$756$	2.98244e8			0.690249
$757$	6.99440e7	+	6.99440e7i	0.161236	+	0.161236i	0.783114	−	0.621878i	$-0.213630\pi$
$757$	6.99440e7	+	6.99440e7i	0.161236	+	0.161236i	−0.621878	+	0.783114i	$0.713630\pi$
$758$	−1.48975e7	+	1.48975e7i	−0.0342063	+	0.0342063i
$759$	−1.54530e8	−	1.54530e8i	−0.353416	−	0.353416i
$760$	−5.63255e8	+	5.63255e8i	−1.28311	+	1.28311i
$761$		−	7.24366e8i		−	1.64363i	−0.569755	−	0.821815i	$-0.692962\pi$
$761$		−	7.24366e8i		−	1.64363i	0.569755	−	0.821815i	$-0.307038\pi$
$762$	−2.70890e8	−	2.70890e8i	−0.612250	−	0.612250i
$763$	1.49524e8	+	1.49524e8i	0.336617	+	0.336617i
$764$	−3.42717e8	+	3.42717e8i	−0.768521	+	0.768521i
$765$		−	275938.i		−	0.000616349i
$766$	3.59262e8			0.799328
$767$		−	5.36297e8i		−	1.18856i
$768$			2.87586e8i			0.634869i
$769$	−4.23501e7	+	4.23501e7i	−0.0931270	+	0.0931270i	−0.752135	−	0.659009i	$-0.770976\pi$
$769$	−4.23501e7	+	4.23501e7i	−0.0931270	+	0.0931270i	0.659009	+	0.752135i	$0.270976\pi$
$770$		−	2.72180e8i		−	0.596188i
$771$	−3.45056e8	+	3.45056e8i	−0.752882	+	0.752882i
$772$	−6.57335e7	+	6.57335e7i	−0.142868	+	0.142868i
$773$	−1.79798e8			−0.389267			−0.194633	−	0.980876i	$-0.562352\pi$
$773$	−1.79798e8			−0.389267			−0.194633	+	0.980876i	$0.562352\pi$
$774$	251634.			0.000542683
$775$	−9.75198e7	−	9.75198e7i	−0.209502	−	0.209502i
$776$		−	5.44196e7i		−	0.116458i
$777$	−3.91173e8	+	1.71706e8i	−0.833883	+	0.366034i
$778$	−6.03067e7			−0.128064
$779$	−9.40670e6	+	9.40670e6i	−0.0198987	+	0.0198987i
$780$		−	4.06084e8i		−	0.855722i
$781$			4.80929e8i			1.00955i
$782$	3.83718e7	+	3.83718e7i	0.0802401	+	0.0802401i
$783$	−1.29604e8	−	1.29604e8i	−0.269981	−	0.269981i
$784$	2.76289e7			0.0573345
$785$	3.32393e8	+	3.32393e8i	0.687137	+	0.687137i
$786$	3.21662e8			0.662418
$787$	−6.54412e8			−1.34254			−0.671270	−	0.741213i	$-0.734251\pi$
$787$	−6.54412e8			−1.34254			−0.671270	+	0.741213i	$0.734251\pi$
$788$		−	1.01798e8i		−	0.208047i
$789$	6.40788e8			1.30462
$790$	−6.50717e7	−	6.50717e7i	−0.131981	−	0.131981i
$791$	−1.81117e8	+	1.81117e8i	−0.365956	+	0.365956i
$792$	−369470.	+	369470.i	−0.000743711	+	0.000743711i
$793$	8.56936e6			0.0171842
$794$	−2.73206e8	−	2.73206e8i	−0.545794	−	0.545794i
$795$	−3.03409e8	+	3.03409e8i	−0.603848	+	0.603848i
$796$	−2.39076e8	−	2.39076e8i	−0.474019	−	0.474019i
$797$	−9.93044e7	+	9.93044e7i	−0.196152	+	0.196152i	−0.798348	−	0.602196i	$-0.794293\pi$
$797$	−9.93044e7	+	9.93044e7i	−0.196152	+	0.196152i	0.602196	+	0.798348i	$0.294293\pi$
$798$		−	4.36150e8i		−	0.858276i
$799$	−1.87229e8	−	1.87229e8i	−0.367056	−	0.367056i
$800$	−7.39026e7	−	7.39026e7i	−0.144341	−	0.144341i
$801$	537099.	−	537099.i	0.00104510	−	0.00104510i
$802$		−	1.97580e7i		−	0.0383018i
$803$	−8.75827e8			−1.69150
$804$			5.37366e8i			1.03396i
$805$			2.13214e8i			0.408722i
$806$	2.79466e8	−	2.79466e8i	0.533734	−	0.533734i
$807$		−	5.16006e8i		−	0.981825i
$808$	4.21254e8	−	4.21254e8i	0.798564	−	0.798564i
$809$	5.21521e8	−	5.21521e8i	0.984977	−	0.984977i	−0.0149123	−	0.999889i	$-0.504747\pi$
$809$	5.21521e8	−	5.21521e8i	0.984977	−	0.984977i	0.999889	+	0.0149123i	$0.00474690\pi$
$810$	−2.86081e8			−0.538312
$811$	−2.86457e8			−0.537029			−0.268514	−	0.963276i	$-0.586533\pi$
$811$	−2.86457e8			−0.537029			−0.268514	+	0.963276i	$0.586533\pi$
$812$	9.98716e7	+	9.98716e7i	0.186541	+	0.186541i
$813$		−	2.06304e8i		−	0.383915i
$814$	−1.17221e8	+	3.00642e8i	−0.217336	+	0.557412i
$815$	2.43460e8			0.449734
$816$	−7.23837e7	+	7.23837e7i	−0.133220	+	0.133220i
$817$		−	1.15639e9i		−	2.12050i
$818$		−	6.34387e7i		−	0.115903i
$819$	363933.	+	363933.i	0.000662475	+	0.000662475i
$820$	−4.74986e6	−	4.74986e6i	−0.00861467	−	0.00861467i
$821$	−4.76469e8			−0.861005			−0.430502	−	0.902589i	$-0.641664\pi$
$821$	−4.76469e8			−0.861005			−0.430502	+	0.902589i	$0.641664\pi$
$822$	1.54588e8	+	1.54588e8i	0.278331	+	0.278331i
$823$	−3.78454e8			−0.678912			−0.339456	−	0.940622i	$-0.610243\pi$
$823$	−3.78454e8			−0.678912			−0.339456	+	0.940622i	$0.610243\pi$
$824$	7.99997e8			1.42990
$825$		−	1.35851e8i		−	0.241937i
$826$	2.90849e8			0.516092
$827$	3.37054e8	+	3.37054e8i	0.595914	+	0.595914i	0.939223	−	0.343309i	$-0.111548\pi$
$827$	3.37054e8	+	3.37054e8i	0.595914	+	0.595914i	−0.343309	+	0.939223i	$0.611548\pi$
$828$	124859.	−	124859.i	0.000219953	−	0.000219953i
$829$	−1.77566e8	+	1.77566e8i	−0.311670	+	0.311670i	−0.845556	−	0.533886i	$-0.820731\pi$
$829$	−1.77566e8	+	1.77566e8i	−0.311670	+	0.311670i	0.533886	+	0.845556i	$0.320731\pi$
$830$	−4.98755e6			−0.00872275
$831$	−6.08522e8	−	6.08522e8i	−1.06041	−	1.06041i
$832$	7.15825e7	−	7.15825e7i	0.124290	−	0.124290i
$833$	−3.94756e7	−	3.94756e7i	−0.0682958	−	0.0682958i
$834$	−3.33851e8	+	3.33851e8i	−0.575512	+	0.575512i
$835$		−	5.75386e8i		−	0.988325i
$836$	7.32480e8	+	7.32480e8i	1.25365	+	1.25365i
$837$	6.18435e8	+	6.18435e8i	1.05467	+	1.05467i
$838$	4.06991e7	−	4.06991e7i	0.0691596	−	0.0691596i
$839$			1.14796e9i			1.94376i	0.235487	+	0.971878i	$0.424332\pi$
$839$			1.14796e9i			1.94376i	−0.235487	+	0.971878i	$0.575668\pi$
$840$	5.10503e8			0.861312
$841$			5.08023e8i			0.854074i
$842$			2.12723e8i			0.356352i
$843$	2.57595e8	−	2.57595e8i	0.429986	−	0.429986i
$844$		−	1.30420e8i		−	0.216928i
$845$	−2.81675e7	+	2.81675e7i	−0.0466850	+	0.0466850i
$846$	193756.	−	193756.i	0.000319996	−	0.000319996i
$847$	−2.67381e8			−0.440028
$848$	1.58955e8			0.260667
$849$	1.49871e8	+	1.49871e8i	0.244903	+	0.244903i
$850$			3.37337e7i			0.0549297i
$851$	9.18258e7	−	2.35510e8i	0.148996	−	0.382139i
$852$	−3.89138e8			−0.629195
$853$	2.42046e8	−	2.42046e8i	0.389987	−	0.389987i	−0.484695	−	0.874683i	$-0.661070\pi$
$853$	2.42046e8	−	2.42046e8i	0.389987	−	0.389987i	0.874683	+	0.484695i	$0.161070\pi$
$854$			4.64740e6i			0.00746168i
$855$		−	1.31229e6i		−	0.00209958i
$856$	−6.83871e7	−	6.83871e7i	−0.109032	−	0.109032i
$857$	−7.49539e6	−	7.49539e6i	−0.0119084	−	0.0119084i	0.701128	−	0.713036i	$-0.252680\pi$
$857$	−7.49539e6	−	7.49539e6i	−0.0119084	−	0.0119084i	−0.713036	+	0.701128i	$0.752680\pi$
$858$	3.89315e8			0.616367
$859$	4.55655e8	+	4.55655e8i	0.718880	+	0.718880i	0.968376	−	0.249496i	$-0.0802648\pi$
$859$	4.55655e8	+	4.55655e8i	0.718880	+	0.718880i	−0.249496	+	0.968376i	$0.580265\pi$
$860$	5.83913e8			0.918022
$861$	8.52571e6			0.0133574
$862$			2.60397e8i			0.406550i
$863$	4.85694e8			0.755667			0.377833	−	0.925874i	$-0.376669\pi$
$863$	4.85694e8			0.755667			0.377833	+	0.925874i	$0.376669\pi$
$864$	4.68664e8	+	4.68664e8i	0.726641	+	0.726641i
$865$	−1.00159e8	+	1.00159e8i	−0.154754	+	0.154754i
$866$	1.75276e8	−	1.75276e8i	0.269878	−	0.269878i
$867$	−4.45199e8			−0.683120
$868$	−4.76560e8	−	4.76560e8i	−0.728716	−	0.728716i
$869$	−1.96156e8	+	1.96156e8i	−0.298912	+	0.298912i
$870$	−9.57031e7	−	9.57031e7i	−0.145334	−	0.145334i
$871$	6.55341e8	−	6.55341e8i	0.991775	−	0.991775i
$872$			2.99583e8i			0.451823i
$873$	63394.3	+	63394.3i	9.52812e−5	+	9.52812e-5i
$874$	1.82487e8	+	1.82487e8i	0.273336	+	0.273336i
$875$	3.78326e8	−	3.78326e8i	0.564732	−	0.564732i
$876$		−	7.08665e8i		−	1.05421i
$877$	1.20239e9			1.78256			0.891282	−	0.453449i	$-0.149807\pi$
$877$	1.20239e9			1.78256			0.891282	+	0.453449i	$0.149807\pi$
$878$		−	4.75729e8i		−	0.702871i
$879$		−	1.15306e9i		−	1.69780i
$880$	−2.14823e8	+	2.14823e8i	−0.315233	+	0.315233i
$881$			5.38730e8i			0.787850i	0.919143	+	0.393925i	$0.128883\pi$
$881$			5.38730e8i			0.787850i	−0.919143	+	0.393925i	$0.871117\pi$
$882$	40851.9	−	40851.9i	5.95396e−5	−	5.95396e-5i
$883$	4.14609e8	−	4.14609e8i	0.602222	−	0.602222i	−0.338680	−	0.940902i	$-0.609980\pi$
$883$	4.14609e8	−	4.14609e8i	0.602222	−	0.602222i	0.940902	+	0.338680i	$0.109980\pi$
$884$	3.03967e8			0.440017
$885$	8.76349e8			1.26429
$886$	−5.20256e7	−	5.20256e7i	−0.0748025	−	0.0748025i
$887$		−	1.79308e8i		−	0.256938i	−0.991714	−	0.128469i	$-0.958994\pi$
$887$		−	1.79308e8i		−	0.256938i	0.991714	−	0.128469i	$-0.0410063\pi$
$888$	−5.63887e8	−	2.19860e8i	−0.805292	−	0.313984i
$889$	1.12670e9			1.60362
$890$	−3.96377e8	+	3.96377e8i	−0.562262	+	0.562262i
$891$			8.62382e8i			1.21918i
$892$		−	6.08598e8i		−	0.857504i
$893$	−8.90414e8	−	8.90414e8i	−1.25037	−	1.25037i
$894$	−1.64705e8	−	1.64705e8i	−0.230512	−	0.230512i
$895$	−1.42471e9			−1.98727
$896$	−4.37184e8	−	4.37184e8i	−0.607771	−	0.607771i
$897$	−3.04973e8			−0.422556
$898$	−6.74245e8			−0.931083
$899$			4.14186e8i			0.570054i
$900$	109767.			0.000150572
$901$	−2.27111e8	−	2.27111e8i	−0.310502	−	0.310502i
$902$	4.55371e6	−	4.55371e6i	0.00620506	−	0.00620506i
$903$	−5.24045e8	+	5.24045e8i	−0.711713	+	0.711713i
$904$	−3.62882e8			−0.491203
$905$	7.36096e8	+	7.36096e8i	0.993090	+	0.993090i
$906$	18645.4	−	18645.4i	2.50720e−5	−	2.50720e-5i
$907$	6.91792e8	+	6.91792e8i	0.927157	+	0.927157i	0.997521	−	0.0703640i	$-0.0224161\pi$
$907$	6.91792e8	+	6.91792e8i	0.927157	+	0.927157i	−0.0703640	+	0.997521i	$0.522416\pi$
$908$	−8.38469e6	+	8.38469e6i	−0.0112003	+	0.0112003i
$909$			981450.i			0.00130670i
$910$	−2.68581e8	−	2.68581e8i	−0.356411	−	0.356411i
$911$	−4.02074e8	−	4.02074e8i	−0.531803	−	0.531803i	0.389305	−	0.921109i	$-0.372715\pi$
$911$	−4.02074e8	−	4.02074e8i	−0.531803	−	0.531803i	−0.921109	+	0.389305i	$0.872715\pi$
$912$	−3.44239e8	+	3.44239e8i	−0.453811	+	0.453811i
$913$			1.50348e7i			0.0197554i
$914$	−4.78352e8			−0.626482
$915$			1.40030e7i			0.0182792i
$916$		−	2.75767e8i		−	0.358803i
$917$	−6.68936e8	+	6.68936e8i	−0.867514	+	0.867514i
$918$		−	2.13927e8i		−	0.276527i
$919$	−4.89071e8	+	4.89071e8i	−0.630123	+	0.630123i	−0.948099	−	0.317976i	$-0.896997\pi$
$919$	−4.89071e8	+	4.89071e8i	−0.630123	+	0.630123i	0.317976	+	0.948099i	$0.396997\pi$
$920$	−2.13596e8	+	2.13596e8i	−0.274303	+	0.274303i
$921$	8.43108e8			1.07921
$922$	7.01384e7			0.0894877
$923$	4.74571e8	+	4.74571e8i	0.603526	+	0.603526i
$924$		−	6.63879e8i		−	0.841537i
$925$	1.43885e8	−	6.31586e7i	0.181799	−	0.0798008i
$926$	−7.09571e8			−0.893641
$927$	−931929.	+	931929.i	−0.00116989	+	0.00116989i
$928$			3.13879e8i			0.392752i
$929$		−	1.11849e9i		−	1.39503i	−0.716569	−	0.697516i	$-0.754289\pi$
$929$		−	1.11849e9i		−	1.39503i	0.716569	−	0.697516i	$-0.245711\pi$
$930$	4.56669e8	+	4.56669e8i	0.567744	+	0.567744i
$931$	−1.87736e8	−	1.87736e8i	−0.232648	−	0.232648i
$932$	−9.49952e8			−1.17342
$933$	−1.01203e9	−	1.01203e9i	−1.24608	−	1.24608i
$934$	4.99497e8			0.613045
$935$	6.13869e8			0.751001
$936$			729171.i			0.000889205i
$937$	−4.06978e8			−0.494712			−0.247356	−	0.968925i	$-0.579562\pi$
$937$	−4.06978e8			−0.494712			−0.247356	+	0.968925i	$0.579562\pi$
$938$	3.55410e8	+	3.55410e8i	0.430647	+	0.430647i
$939$	−2.42516e8	+	2.42516e8i	−0.292916	+	0.292916i
$940$	4.49609e8	−	4.49609e8i	0.541317	−	0.541317i
$941$	7.61871e8			0.914350			0.457175	−	0.889377i	$-0.348861\pi$
$941$	7.61871e8			0.914350			0.457175	+	0.889377i	$0.348861\pi$
$942$	−2.57846e8	−	2.57846e8i	−0.308466	−	0.308466i
$943$	−3.56719e6	+	3.56719e6i	−0.00425393	+	0.00425393i
$944$	−2.29558e8	−	2.29558e8i	−0.272883	−	0.272883i
$945$	5.94346e8	−	5.94346e8i	0.704278	−	0.704278i
$946$			5.59801e8i			0.661241i
$947$	7.04599e8	+	7.04599e8i	0.829645	+	0.829645i	0.987467	−	0.157823i	$-0.0504475\pi$
$947$	7.04599e8	+	7.04599e8i	0.829645	+	0.829645i	−0.157823	+	0.987467i	$0.550447\pi$
$948$	−1.58718e8	−	1.58718e8i	−0.186295	−	0.186295i
$949$	−8.64247e8	+	8.64247e8i	−1.01121	+	1.01121i
$950$			1.60429e8i			0.187117i
$951$	−4.33895e7			−0.0504479
$952$			3.82128e8i			0.442892i
$953$			9.45156e8i			1.09201i	0.837783	+	0.546003i	$0.183851\pi$
$953$			9.45156e8i			1.09201i	−0.837783	+	0.546003i	$0.816149\pi$
$954$	235029.	−	235029.i	0.000270693	−	0.000270693i
$955$			1.36595e9i			1.56828i
$956$	−5.18921e8	+	5.18921e8i	−0.593920	+	0.593920i
$957$	−2.88494e8	+	2.88494e8i	−0.329155	+	0.329155i
$958$	−7.36828e8			−0.838050
$959$	−6.42971e8			−0.729014
$960$	1.16971e8	+	1.16971e8i	0.132210	+	0.132210i
$961$		−	1.08887e9i		−	1.22690i
$962$	1.80996e8	+	4.12338e8i	0.203303	+	0.463157i
$963$	159331.			0.000178410
$964$	1.42861e7	−	1.42861e7i	0.0159472	−	0.0159472i
$965$			2.61990e8i			0.291543i
$966$		−	1.65396e8i		−	0.183482i
$967$	−2.91627e8	−	2.91627e8i	−0.322514	−	0.322514i	0.527217	−	0.849731i	$-0.323236\pi$
$967$	−2.91627e8	−	2.91627e8i	−0.322514	−	0.322514i	−0.849731	+	0.527217i	$0.823236\pi$
$968$	−2.67860e8	−	2.67860e8i	−0.295313	−	0.295313i
$969$	9.83683e8			1.08114
$970$	−4.67847e7	−	4.67847e7i	−0.0512612	−	0.0512612i
$971$	−8.23647e8			−0.899671			−0.449835	−	0.893112i	$-0.648517\pi$
$971$	−8.23647e8			−0.899671			−0.449835	+	0.893112i	$0.648517\pi$
$972$	−1.39290e6			−0.00151678
$973$		−	1.38857e9i		−	1.50740i
$974$	2.31779e7			0.0250841
$975$	−1.34055e8	−	1.34055e8i	−0.144634	−	0.144634i
$976$	3.66805e6	−	3.66805e6i	0.00394535	−	0.00394535i
$977$	4.81437e8	−	4.81437e8i	0.516245	−	0.516245i	−0.400188	−	0.916433i	$-0.631055\pi$
$977$	4.81437e8	−	4.81437e8i	0.516245	−	0.516245i	0.916433	+	0.400188i	$0.131055\pi$
$978$	−1.88858e8			−0.201892
$979$	1.19487e9	+	1.19487e9i	1.27342	+	1.27342i
$980$	9.47963e7	−	9.47963e7i	0.100719	−	0.100719i
$981$	−348990.	−	348990.i	−0.000369662	−	0.000369662i
$982$	−5.61176e8	+	5.61176e8i	−0.592605	+	0.592605i
$983$			4.08253e8i			0.429802i	0.976636	+	0.214901i	$0.0689429\pi$
$983$			4.08253e8i			0.429802i	−0.976636	+	0.214901i	$0.931057\pi$
$984$	8.54099e6	+	8.54099e6i	0.00896443	+	0.00896443i
$985$	−2.02865e8	−	2.02865e8i	−0.212275	−	0.212275i
$986$	7.16368e7	−	7.16368e7i	0.0747318	−	0.0747318i
$987$			8.07021e8i			0.839332i
$988$	1.44559e9			1.49891
$989$		−	4.38525e8i		−	0.453320i
$990$			635270.i			0.000654715i
$991$	−1.03761e9	+	1.03761e9i	−1.06614	+	1.06614i	−0.0684853	+	0.997652i	$0.521817\pi$
$991$	−1.03761e9	+	1.03761e9i	−1.06614	+	1.06614i	−0.997652	+	0.0684853i	$0.978183\pi$
$992$		−	1.49774e9i		−	1.53427i
$993$	5.96991e8	−	5.96991e8i	0.609706	−	0.609706i
$994$	−2.57373e8	+	2.57373e8i	−0.262062	+	0.262062i
$995$	−9.52870e8			−0.967307
$996$	−1.21652e7			−0.0123124
$997$	−3.43762e8	−	3.43762e8i	−0.346875	−	0.346875i	0.512069	−	0.858944i	$-0.328879\pi$
$997$	−3.43762e8	−	3.43762e8i	−0.346875	−	0.346875i	−0.858944	+	0.512069i	$0.828879\pi$
$998$		−	7.93923e8i		−	0.798706i
$999$	−9.12468e8	+	4.00529e8i	−0.915211	+	0.401733i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.7.d.a.6.12	✓	36
37.31	odd	4	inner	37.7.d.a.31.12	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.7.d.a.6.12	✓	36	1.1	even	1	trivial
37.7.d.a.31.12	yes	36	37.31	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	37.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.77875 - 2.77875i) q^{2} -27.0135i q^{3} +48.5571i q^{4} +(96.7657 + 96.7657i) q^{5} +(-75.0636 - 75.0636i) q^{6} +312.208 q^{7} +(312.768 + 312.768i) q^{8} -0.728696 q^{9} +O(q^{10})\)	\(q+(2.77875 - 2.77875i) q^{2} -27.0135i q^{3} +48.5571i q^{4} +(96.7657 + 96.7657i) q^{5} +(-75.0636 - 75.0636i) q^{6} +312.208 q^{7} +(312.768 + 312.768i) q^{8} -0.728696 q^{9} +537.775 q^{10} -1621.10i q^{11} +1311.70 q^{12} +(-1599.67 - 1599.67i) q^{13} +(867.547 - 867.547i) q^{14} +(2613.98 - 2613.98i) q^{15} -1369.45 q^{16} +(1956.65 + 1956.65i) q^{17} +(-2.02486 + 2.02486i) q^{18} +(9305.33 + 9305.33i) q^{19} +(-4698.67 + 4698.67i) q^{20} -8433.83i q^{21} +(-4504.64 - 4504.64i) q^{22} +(3528.74 + 3528.74i) q^{23} +(8448.95 - 8448.95i) q^{24} +3102.22i q^{25} -8890.16 q^{26} -19673.2i q^{27} +15159.9i q^{28} +(6587.87 - 6587.87i) q^{29} -14527.2i q^{30} +(-31435.5 + 31435.5i) q^{31} +(-23822.5 + 23822.5i) q^{32} -43791.7 q^{33} +10874.1 q^{34} +(30211.0 + 30211.0i) q^{35} -35.3834i q^{36} +(-20359.1 - 46381.4i) q^{37} +51714.3 q^{38} +(-43212.7 + 43212.7i) q^{39} +60530.4i q^{40} +1010.89i q^{41} +(-23435.5 - 23435.5i) q^{42} +(-62136.0 - 62136.0i) q^{43} +78716.2 q^{44} +(-70.5128 - 70.5128i) q^{45} +19611.0 q^{46} -95688.6 q^{47} +36993.7i q^{48} -20175.1 q^{49} +(8620.28 + 8620.28i) q^{50} +(52855.9 - 52855.9i) q^{51} +(77675.5 - 77675.5i) q^{52} -116072. q^{53} +(-54666.7 - 54666.7i) q^{54} +(156867. - 156867. i) q^{55} +(97648.6 + 97648.6i) q^{56} +(251369. - 251369. i) q^{57} -36612.0i q^{58} +(167627. + 167627. i) q^{59} +(126927. + 126927. i) q^{60} +(-2678.47 + 2678.47i) q^{61} +174702. i q^{62} -227.505 q^{63} +44748.3i q^{64} -309587. i q^{65} +(-121686. + 121686. i) q^{66} +409672. i q^{67} +(-95009.2 + 95009.2i) q^{68} +(95323.7 - 95323.7i) q^{69} +167898. q^{70} -296668. q^{71} +(-227.913 - 227.913i) q^{72} -540265. i q^{73} +(-185455. - 72309.1i) q^{74} +83801.8 q^{75} +(-451840. + 451840. i) q^{76} -506122. i q^{77} +240154. i q^{78} +(-121002. - 121002. i) q^{79} +(-132516. - 132516. i) q^{80} -531972. q^{81} +(2809.02 + 2809.02i) q^{82} -9274.43 q^{83} +409523. q^{84} +378673. i q^{85} -345321. q^{86} +(-177961. - 177961. i) q^{87} +(507029. - 507029. i) q^{88} +(-737069. + 737069. i) q^{89} -391.875 q^{90} +(-499430. - 499430. i) q^{91} +(-171346. + 171346. i) q^{92} +(849182. + 849182. i) q^{93} +(-265894. + 265894. i) q^{94} +1.80087e6i q^{95} +(643529. + 643529. i) q^{96} +(-86996.9 - 86996.9i) q^{97} +(-56061.6 + 56061.6i) q^{98} +1181.29i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 4 q^{2} - 256 q^{5} + 126 q^{6} - 4 q^{7} + 168 q^{8} - 7140 q^{9}+O(q^{10}) \) 36 * q - 4 * q^2 - 256 * q^5 + 126 * q^6 - 4 * q^7 + 168 * q^8 - 7140 * q^9	\( 36 q - 4 q^{2} - 256 q^{5} + 126 q^{6} - 4 q^{7} + 168 q^{8} - 7140 q^{9} - 1876 q^{10} + 11104 q^{12} - 2904 q^{13} - 7678 q^{14} + 4288 q^{15} - 44824 q^{16} + 2064 q^{17} + 6222 q^{18} - 4954 q^{19} - 43084 q^{20} - 39810 q^{22} + 21966 q^{23} + 79188 q^{24} + 66604 q^{26} + 69500 q^{29} - 32418 q^{31} - 141992 q^{32} + 54752 q^{33} + 256508 q^{34} - 26164 q^{35} + 180242 q^{37} + 329032 q^{38} - 60088 q^{39} - 346014 q^{42} - 144514 q^{43} - 294896 q^{44} + 842152 q^{45} - 522736 q^{46} - 157076 q^{47} + 405652 q^{49} + 46176 q^{50} - 624984 q^{51} - 161884 q^{52} - 512988 q^{53} + 541150 q^{54} + 824640 q^{55} - 608488 q^{56} - 311992 q^{57} + 187582 q^{59} - 1156764 q^{60} - 1321908 q^{61} - 887284 q^{63} + 752126 q^{66} + 1244832 q^{68} + 41960 q^{69} - 1029284 q^{70} + 1316252 q^{71} + 777880 q^{72} + 1117260 q^{74} - 2148904 q^{75} - 814428 q^{76} - 56722 q^{79} + 3750844 q^{80} - 930796 q^{81} + 1462554 q^{82} - 841484 q^{83} + 5065540 q^{84} + 3992612 q^{86} + 2494224 q^{87} - 3796428 q^{88} - 1439724 q^{89} - 5618044 q^{90} - 8644 q^{91} + 7826980 q^{92} - 54064 q^{93} - 2057938 q^{94} - 8819328 q^{96} + 2578548 q^{97} - 6043946 q^{98}+O(q^{100}) \) 36 * q - 4 * q^2 - 256 * q^5 + 126 * q^6 - 4 * q^7 + 168 * q^8 - 7140 * q^9 - 1876 * q^10 + 11104 * q^12 - 2904 * q^13 - 7678 * q^14 + 4288 * q^15 - 44824 * q^16 + 2064 * q^17 + 6222 * q^18 - 4954 * q^19 - 43084 * q^20 - 39810 * q^22 + 21966 * q^23 + 79188 * q^24 + 66604 * q^26 + 69500 * q^29 - 32418 * q^31 - 141992 * q^32 + 54752 * q^33 + 256508 * q^34 - 26164 * q^35 + 180242 * q^37 + 329032 * q^38 - 60088 * q^39 - 346014 * q^42 - 144514 * q^43 - 294896 * q^44 + 842152 * q^45 - 522736 * q^46 - 157076 * q^47 + 405652 * q^49 + 46176 * q^50 - 624984 * q^51 - 161884 * q^52 - 512988 * q^53 + 541150 * q^54 + 824640 * q^55 - 608488 * q^56 - 311992 * q^57 + 187582 * q^59 - 1156764 * q^60 - 1321908 * q^61 - 887284 * q^63 + 752126 * q^66 + 1244832 * q^68 + 41960 * q^69 - 1029284 * q^70 + 1316252 * q^71 + 777880 * q^72 + 1117260 * q^74 - 2148904 * q^75 - 814428 * q^76 - 56722 * q^79 + 3750844 * q^80 - 930796 * q^81 + 1462554 * q^82 - 841484 * q^83 + 5065540 * q^84 + 3992612 * q^86 + 2494224 * q^87 - 3796428 * q^88 - 1439724 * q^89 - 5618044 * q^90 - 8644 * q^91 + 7826980 * q^92 - 54064 * q^93 - 2057938 * q^94 - 8819328 * q^96 + 2578548 * q^97 - 6043946 * q^98

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