# Properties

 Label 192.7.e.f.65.1 Level $192$ Weight $7$ Character 192.65 Analytic conductor $44.170$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,7,Mod(65,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("192.65");

S:= CuspForms(chi, 7);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$192 = 2^{6} \cdot 3$$ Weight: $$k$$ $$=$$ $$7$$ Character orbit: $$[\chi]$$ $$=$$ 192.e (of order $$2$$, degree $$1$$, not 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: $$44.1703840550$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{-2})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} + 2$$ x^2 + 2 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$2^{2}\cdot 3$$ Twist minimal: no (minimal twist has level 6) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 65.1 Root $$-1.41421i$$ of defining polynomial Character $$\chi$$ $$=$$ 192.65 Dual form 192.7.e.f.65.2

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(21.0000 - 16.9706i) q^{3} -169.706i q^{5} -2.00000 q^{7} +(153.000 - 712.764i) q^{9} +O(q^{10})$$ $$q+(21.0000 - 16.9706i) q^{3} -169.706i q^{5} -2.00000 q^{7} +(153.000 - 712.764i) q^{9} +33.9411i q^{11} +2950.00 q^{13} +(-2880.00 - 3563.82i) q^{15} -4480.23i q^{17} +5258.00 q^{19} +(-42.0000 + 33.9411i) q^{21} -10250.2i q^{23} -13175.0 q^{25} +(-8883.00 - 17564.5i) q^{27} +2206.17i q^{29} -22898.0 q^{31} +(576.000 + 712.764i) q^{33} +339.411i q^{35} -34058.0 q^{37} +(61950.0 - 50063.2i) q^{39} +16766.9i q^{41} -6406.00 q^{43} +(-120960. - 25965.0i) q^{45} +179888. i q^{47} -117645. q^{49} +(-76032.0 - 94084.8i) q^{51} -192548. i q^{53} +5760.00 q^{55} +(110418. - 89231.2i) q^{57} +326819. i q^{59} +62566.0 q^{61} +(-306.000 + 1425.53i) q^{63} -500632. i q^{65} +438698. q^{67} +(-173952. - 215255. i) q^{69} -68221.7i q^{71} -730510. q^{73} +(-276675. + 223587. i) q^{75} -67.8823i q^{77} -340562. q^{79} +(-484623. - 218106. i) q^{81} -496253. i q^{83} -760320. q^{85} +(37440.0 + 46329.6i) q^{87} +386725. i q^{89} -5900.00 q^{91} +(-480858. + 388592. i) q^{93} -892312. i q^{95} -281086. q^{97} +(24192.0 + 5192.99i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 42 q^{3} - 4 q^{7} + 306 q^{9}+O(q^{10})$$ 2 * q + 42 * q^3 - 4 * q^7 + 306 * q^9 $$2 q + 42 q^{3} - 4 q^{7} + 306 q^{9} + 5900 q^{13} - 5760 q^{15} + 10516 q^{19} - 84 q^{21} - 26350 q^{25} - 17766 q^{27} - 45796 q^{31} + 1152 q^{33} - 68116 q^{37} + 123900 q^{39} - 12812 q^{43} - 241920 q^{45} - 235290 q^{49} - 152064 q^{51} + 11520 q^{55} + 220836 q^{57} + 125132 q^{61} - 612 q^{63} + 877396 q^{67} - 347904 q^{69} - 1461020 q^{73} - 553350 q^{75} - 681124 q^{79} - 969246 q^{81} - 1520640 q^{85} + 74880 q^{87} - 11800 q^{91} - 961716 q^{93} - 562172 q^{97} + 48384 q^{99}+O(q^{100})$$ 2 * q + 42 * q^3 - 4 * q^7 + 306 * q^9 + 5900 * q^13 - 5760 * q^15 + 10516 * q^19 - 84 * q^21 - 26350 * q^25 - 17766 * q^27 - 45796 * q^31 + 1152 * q^33 - 68116 * q^37 + 123900 * q^39 - 12812 * q^43 - 241920 * q^45 - 235290 * q^49 - 152064 * q^51 + 11520 * q^55 + 220836 * q^57 + 125132 * q^61 - 612 * q^63 + 877396 * q^67 - 347904 * q^69 - 1461020 * q^73 - 553350 * q^75 - 681124 * q^79 - 969246 * q^81 - 1520640 * q^85 + 74880 * q^87 - 11800 * q^91 - 961716 * q^93 - 562172 * q^97 + 48384 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$$.

 $$n$$ $$65$$ $$127$$ $$133$$ $$\chi(n)$$ $$-1$$ $$1$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 21.0000 16.9706i 0.777778 0.628539i
$$4$$ 0 0
$$5$$ 169.706i 1.35765i −0.734302 0.678823i $$-0.762491\pi$$
0.734302 0.678823i $$-0.237509\pi$$
$$6$$ 0 0
$$7$$ −2.00000 −0.00583090 −0.00291545 0.999996i $$-0.500928\pi$$
−0.00291545 + 0.999996i $$0.500928\pi$$
$$8$$ 0 0
$$9$$ 153.000 712.764i 0.209877 0.977728i
$$10$$ 0 0
$$11$$ 33.9411i 0.0255005i 0.999919 + 0.0127502i $$0.00405864\pi$$
−0.999919 + 0.0127502i $$0.995941\pi$$
$$12$$ 0 0
$$13$$ 2950.00 1.34274 0.671370 0.741122i $$-0.265706\pi$$
0.671370 + 0.741122i $$0.265706\pi$$
$$14$$ 0 0
$$15$$ −2880.00 3563.82i −0.853333 1.05595i
$$16$$ 0 0
$$17$$ 4480.23i 0.911913i −0.890002 0.455956i $$-0.849297\pi$$
0.890002 0.455956i $$-0.150703\pi$$
$$18$$ 0 0
$$19$$ 5258.00 0.766584 0.383292 0.923627i $$-0.374790\pi$$
0.383292 + 0.923627i $$0.374790\pi$$
$$20$$ 0 0
$$21$$ −42.0000 + 33.9411i −0.00453515 + 0.00366495i
$$22$$ 0 0
$$23$$ 10250.2i 0.842461i −0.906954 0.421230i $$-0.861598\pi$$
0.906954 0.421230i $$-0.138402\pi$$
$$24$$ 0 0
$$25$$ −13175.0 −0.843200
$$26$$ 0 0
$$27$$ −8883.00 17564.5i −0.451303 0.892371i
$$28$$ 0 0
$$29$$ 2206.17i 0.0904577i 0.998977 + 0.0452289i $$0.0144017\pi$$
−0.998977 + 0.0452289i $$0.985598\pi$$
$$30$$ 0 0
$$31$$ −22898.0 −0.768621 −0.384311 0.923204i $$-0.625561\pi$$
−0.384311 + 0.923204i $$0.625561\pi$$
$$32$$ 0 0
$$33$$ 576.000 + 712.764i 0.0160280 + 0.0198337i
$$34$$ 0 0
$$35$$ 339.411i 0.00791630i
$$36$$ 0 0
$$37$$ −34058.0 −0.672379 −0.336189 0.941794i $$-0.609138\pi$$
−0.336189 + 0.941794i $$0.609138\pi$$
$$38$$ 0 0
$$39$$ 61950.0 50063.2i 1.04435 0.843965i
$$40$$ 0 0
$$41$$ 16766.9i 0.243277i 0.992574 + 0.121639i $$0.0388149\pi$$
−0.992574 + 0.121639i $$0.961185\pi$$
$$42$$ 0 0
$$43$$ −6406.00 −0.0805715 −0.0402858 0.999188i $$-0.512827\pi$$
−0.0402858 + 0.999188i $$0.512827\pi$$
$$44$$ 0 0
$$45$$ −120960. 25965.0i −1.32741 0.284938i
$$46$$ 0 0
$$47$$ 179888.i 1.73264i 0.499489 + 0.866320i $$0.333521\pi$$
−0.499489 + 0.866320i $$0.666479\pi$$
$$48$$ 0 0
$$49$$ −117645. −0.999966
$$50$$ 0 0
$$51$$ −76032.0 94084.8i −0.573173 0.709266i
$$52$$ 0 0
$$53$$ 192548.i 1.29334i −0.762772 0.646668i $$-0.776162\pi$$
0.762772 0.646668i $$-0.223838\pi$$
$$54$$ 0 0
$$55$$ 5760.00 0.0346206
$$56$$ 0 0
$$57$$ 110418. 89231.2i 0.596232 0.481828i
$$58$$ 0 0
$$59$$ 326819.i 1.59130i 0.605758 + 0.795649i $$0.292870\pi$$
−0.605758 + 0.795649i $$0.707130\pi$$
$$60$$ 0 0
$$61$$ 62566.0 0.275644 0.137822 0.990457i $$-0.455990\pi$$
0.137822 + 0.990457i $$0.455990\pi$$
$$62$$ 0 0
$$63$$ −306.000 + 1425.53i −0.00122377 + 0.00570104i
$$64$$ 0 0
$$65$$ 500632.i 1.82296i
$$66$$ 0 0
$$67$$ 438698. 1.45862 0.729308 0.684185i $$-0.239842\pi$$
0.729308 + 0.684185i $$0.239842\pi$$
$$68$$ 0 0
$$69$$ −173952. 215255.i −0.529520 0.655247i
$$70$$ 0 0
$$71$$ 68221.7i 0.190611i −0.995448 0.0953053i $$-0.969617\pi$$
0.995448 0.0953053i $$-0.0303827\pi$$
$$72$$ 0 0
$$73$$ −730510. −1.87784 −0.938918 0.344141i $$-0.888170\pi$$
−0.938918 + 0.344141i $$0.888170\pi$$
$$74$$ 0 0
$$75$$ −276675. + 223587.i −0.655822 + 0.529984i
$$76$$ 0 0
$$77$$ 67.8823i 0.000148691i
$$78$$ 0 0
$$79$$ −340562. −0.690740 −0.345370 0.938467i $$-0.612247\pi$$
−0.345370 + 0.938467i $$0.612247\pi$$
$$80$$ 0 0
$$81$$ −484623. 218106.i −0.911904 0.410404i
$$82$$ 0 0
$$83$$ 496253.i 0.867899i −0.900937 0.433949i $$-0.857120\pi$$
0.900937 0.433949i $$-0.142880\pi$$
$$84$$ 0 0
$$85$$ −760320. −1.23805
$$86$$ 0 0
$$87$$ 37440.0 + 46329.6i 0.0568562 + 0.0703560i
$$88$$ 0 0
$$89$$ 386725.i 0.548570i 0.961648 + 0.274285i $$0.0884412\pi$$
−0.961648 + 0.274285i $$0.911559\pi$$
$$90$$ 0 0
$$91$$ −5900.00 −0.00782939
$$92$$ 0 0
$$93$$ −480858. + 388592.i −0.597817 + 0.483109i
$$94$$ 0 0
$$95$$ 892312.i 1.04075i
$$96$$ 0 0
$$97$$ −281086. −0.307981 −0.153991 0.988072i $$-0.549213\pi$$
−0.153991 + 0.988072i $$0.549213\pi$$
$$98$$ 0 0
$$99$$ 24192.0 + 5192.99i 0.0249325 + 0.00535195i
$$100$$ 0 0
$$101$$ 945362.i 0.917559i −0.888550 0.458780i $$-0.848287\pi$$
0.888550 0.458780i $$-0.151713\pi$$
$$102$$ 0 0
$$103$$ 865726. 0.792262 0.396131 0.918194i $$-0.370353\pi$$
0.396131 + 0.918194i $$0.370353\pi$$
$$104$$ 0 0
$$105$$ 5760.00 + 7127.64i 0.00497570 + 0.00615712i
$$106$$ 0 0
$$107$$ 1.47410e6i 1.20330i −0.798759 0.601651i $$-0.794510\pi$$
0.798759 0.601651i $$-0.205490\pi$$
$$108$$ 0 0
$$109$$ −650810. −0.502545 −0.251272 0.967916i $$-0.580849\pi$$
−0.251272 + 0.967916i $$0.580849\pi$$
$$110$$ 0 0
$$111$$ −715218. + 577983.i −0.522961 + 0.422616i
$$112$$ 0 0
$$113$$ 1.74417e6i 1.20879i −0.796683 0.604397i $$-0.793414\pi$$
0.796683 0.604397i $$-0.206586\pi$$
$$114$$ 0 0
$$115$$ −1.73952e6 −1.14376
$$116$$ 0 0
$$117$$ 451350. 2.10265e6i 0.281810 1.31283i
$$118$$ 0 0
$$119$$ 8960.46i 0.00531728i
$$120$$ 0 0
$$121$$ 1.77041e6 0.999350
$$122$$ 0 0
$$123$$ 284544. + 352105.i 0.152909 + 0.189216i
$$124$$ 0 0
$$125$$ 415779.i 0.212879i
$$126$$ 0 0
$$127$$ 2.28053e6 1.11333 0.556665 0.830737i $$-0.312081\pi$$
0.556665 + 0.830737i $$0.312081\pi$$
$$128$$ 0 0
$$129$$ −134526. + 108713.i −0.0626667 + 0.0506424i
$$130$$ 0 0
$$131$$ 1.07196e6i 0.476832i 0.971163 + 0.238416i $$0.0766282\pi$$
−0.971163 + 0.238416i $$0.923372\pi$$
$$132$$ 0 0
$$133$$ −10516.0 −0.00446988
$$134$$ 0 0
$$135$$ −2.98080e6 + 1.50750e6i −1.21152 + 0.612709i
$$136$$ 0 0
$$137$$ 2.78338e6i 1.08246i 0.840876 + 0.541228i $$0.182040\pi$$
−0.840876 + 0.541228i $$0.817960\pi$$
$$138$$ 0 0
$$139$$ 4.57395e6 1.70313 0.851563 0.524253i $$-0.175655\pi$$
0.851563 + 0.524253i $$0.175655\pi$$
$$140$$ 0 0
$$141$$ 3.05280e6 + 3.77765e6i 1.08903 + 1.34761i
$$142$$ 0 0
$$143$$ 100126.i 0.0342405i
$$144$$ 0 0
$$145$$ 374400. 0.122809
$$146$$ 0 0
$$147$$ −2.47054e6 + 1.99650e6i −0.777751 + 0.628518i
$$148$$ 0 0
$$149$$ 4.46010e6i 1.34830i 0.738595 + 0.674149i $$0.235489\pi$$
−0.738595 + 0.674149i $$0.764511\pi$$
$$150$$ 0 0
$$151$$ 2.20809e6 0.641338 0.320669 0.947191i $$-0.396092\pi$$
0.320669 + 0.947191i $$0.396092\pi$$
$$152$$ 0 0
$$153$$ −3.19334e6 685475.i −0.891603 0.191389i
$$154$$ 0 0
$$155$$ 3.88592e6i 1.04352i
$$156$$ 0 0
$$157$$ 1.28887e6 0.333051 0.166525 0.986037i $$-0.446745\pi$$
0.166525 + 0.986037i $$0.446745\pi$$
$$158$$ 0 0
$$159$$ −3.26765e6 4.04351e6i −0.812913 1.00593i
$$160$$ 0 0
$$161$$ 20500.4i 0.00491231i
$$162$$ 0 0
$$163$$ 879914. 0.203178 0.101589 0.994826i $$-0.467607\pi$$
0.101589 + 0.994826i $$0.467607\pi$$
$$164$$ 0 0
$$165$$ 120960. 97750.4i 0.0269271 0.0217604i
$$166$$ 0 0
$$167$$ 5.96760e6i 1.28130i 0.767834 + 0.640649i $$0.221335\pi$$
−0.767834 + 0.640649i $$0.778665\pi$$
$$168$$ 0 0
$$169$$ 3.87569e6 0.802951
$$170$$ 0 0
$$171$$ 804474. 3.74771e6i 0.160888 0.749511i
$$172$$ 0 0
$$173$$ 418867.i 0.0808981i 0.999182 + 0.0404490i $$0.0128788\pi$$
−0.999182 + 0.0404490i $$0.987121\pi$$
$$174$$ 0 0
$$175$$ 26350.0 0.00491662
$$176$$ 0 0
$$177$$ 5.54630e6 + 6.86320e6i 1.00019 + 1.23768i
$$178$$ 0 0
$$179$$ 302110.i 0.0526752i −0.999653 0.0263376i $$-0.991616\pi$$
0.999653 0.0263376i $$-0.00838448\pi$$
$$180$$ 0 0
$$181$$ 6.47618e6 1.09215 0.546076 0.837735i $$-0.316121\pi$$
0.546076 + 0.837735i $$0.316121\pi$$
$$182$$ 0 0
$$183$$ 1.31389e6 1.06178e6i 0.214390 0.173253i
$$184$$ 0 0
$$185$$ 5.77983e6i 0.912852i
$$186$$ 0 0
$$187$$ 152064. 0.0232542
$$188$$ 0 0
$$189$$ 17766.0 + 35129.1i 0.00263151 + 0.00520333i
$$190$$ 0 0
$$191$$ 5.02166e6i 0.720687i −0.932820 0.360344i $$-0.882659\pi$$
0.932820 0.360344i $$-0.117341\pi$$
$$192$$ 0 0
$$193$$ 3.50093e6 0.486980 0.243490 0.969903i $$-0.421708\pi$$
0.243490 + 0.969903i $$0.421708\pi$$
$$194$$ 0 0
$$195$$ −8.49600e6 1.05133e7i −1.14580 1.41786i
$$196$$ 0 0
$$197$$ 4.85423e6i 0.634923i 0.948271 + 0.317462i $$0.102830\pi$$
−0.948271 + 0.317462i $$0.897170\pi$$
$$198$$ 0 0
$$199$$ 9.50976e6 1.20673 0.603365 0.797465i $$-0.293826\pi$$
0.603365 + 0.797465i $$0.293826\pi$$
$$200$$ 0 0
$$201$$ 9.21266e6 7.44495e6i 1.13448 0.916798i
$$202$$ 0 0
$$203$$ 4412.35i 0.000527450i
$$204$$ 0 0
$$205$$ 2.84544e6 0.330284
$$206$$ 0 0
$$207$$ −7.30598e6 1.56828e6i −0.823697 0.176813i
$$208$$ 0 0
$$209$$ 178462.i 0.0195483i
$$210$$ 0 0
$$211$$ 7.06414e6 0.751990 0.375995 0.926622i $$-0.377301\pi$$
0.375995 + 0.926622i $$0.377301\pi$$
$$212$$ 0 0
$$213$$ −1.15776e6 1.43265e6i −0.119806 0.148253i
$$214$$ 0 0
$$215$$ 1.08713e6i 0.109388i
$$216$$ 0 0
$$217$$ 45796.0 0.00448176
$$218$$ 0 0
$$219$$ −1.53407e7 + 1.23972e7i −1.46054 + 1.18029i
$$220$$ 0 0
$$221$$ 1.32167e7i 1.22446i
$$222$$ 0 0
$$223$$ −4.66891e6 −0.421019 −0.210509 0.977592i $$-0.567512\pi$$
−0.210509 + 0.977592i $$0.567512\pi$$
$$224$$ 0 0
$$225$$ −2.01578e6 + 9.39066e6i −0.176968 + 0.824420i
$$226$$ 0 0
$$227$$ 1.96525e7i 1.68012i −0.542494 0.840059i $$-0.682520\pi$$
0.542494 0.840059i $$-0.317480\pi$$
$$228$$ 0 0
$$229$$ 4.48178e6 0.373202 0.186601 0.982436i $$-0.440253\pi$$
0.186601 + 0.982436i $$0.440253\pi$$
$$230$$ 0 0
$$231$$ −1152.00 1425.53i −9.34580e−5 0.000115648i
$$232$$ 0 0
$$233$$ 2.29286e6i 0.181263i −0.995884 0.0906316i $$-0.971111\pi$$
0.995884 0.0906316i $$-0.0288886\pi$$
$$234$$ 0 0
$$235$$ 3.05280e7 2.35231
$$236$$ 0 0
$$237$$ −7.15180e6 + 5.77953e6i −0.537243 + 0.434158i
$$238$$ 0 0
$$239$$ 2.64564e6i 0.193793i −0.995294 0.0968964i $$-0.969108\pi$$
0.995294 0.0968964i $$-0.0308915\pi$$
$$240$$ 0 0
$$241$$ −6.99581e6 −0.499789 −0.249894 0.968273i $$-0.580396\pi$$
−0.249894 + 0.968273i $$0.580396\pi$$
$$242$$ 0 0
$$243$$ −1.38785e7 + 3.64411e6i −0.967214 + 0.253964i
$$244$$ 0 0
$$245$$ 1.99650e7i 1.35760i
$$246$$ 0 0
$$247$$ 1.55111e7 1.02932
$$248$$ 0 0
$$249$$ −8.42170e6 1.04213e7i −0.545508 0.675032i
$$250$$ 0 0
$$251$$ 2.84990e7i 1.80223i 0.433585 + 0.901113i $$0.357248\pi$$
−0.433585 + 0.901113i $$0.642752\pi$$
$$252$$ 0 0
$$253$$ 347904. 0.0214831
$$254$$ 0 0
$$255$$ −1.59667e7 + 1.29031e7i −0.962931 + 0.778166i
$$256$$ 0 0
$$257$$ 186812.i 0.0110054i 0.999985 + 0.00550269i $$0.00175157\pi$$
−0.999985 + 0.00550269i $$0.998248\pi$$
$$258$$ 0 0
$$259$$ 68116.0 0.00392058
$$260$$ 0 0
$$261$$ 1.57248e6 + 337544.i 0.0884430 + 0.0189850i
$$262$$ 0 0
$$263$$ 8.61541e6i 0.473597i −0.971559 0.236798i $$-0.923902\pi$$
0.971559 0.236798i $$-0.0760981\pi$$
$$264$$ 0 0
$$265$$ −3.26765e7 −1.75589
$$266$$ 0 0
$$267$$ 6.56294e6 + 8.12123e6i 0.344798 + 0.426666i
$$268$$ 0 0
$$269$$ 7.55132e6i 0.387941i −0.981007 0.193971i $$-0.937863\pi$$
0.981007 0.193971i $$-0.0621367\pi$$
$$270$$ 0 0
$$271$$ −1.39445e7 −0.700642 −0.350321 0.936630i $$-0.613927\pi$$
−0.350321 + 0.936630i $$0.613927\pi$$
$$272$$ 0 0
$$273$$ −123900. + 100126.i −0.00608952 + 0.00492108i
$$274$$ 0 0
$$275$$ 447174.i 0.0215020i
$$276$$ 0 0
$$277$$ −2.81293e7 −1.32349 −0.661744 0.749730i $$-0.730183\pi$$
−0.661744 + 0.749730i $$0.730183\pi$$
$$278$$ 0 0
$$279$$ −3.50339e6 + 1.63209e7i −0.161316 + 0.751503i
$$280$$ 0 0
$$281$$ 2.23430e7i 1.00698i −0.864000 0.503491i $$-0.832049\pi$$
0.864000 0.503491i $$-0.167951\pi$$
$$282$$ 0 0
$$283$$ 1.01418e7 0.447464 0.223732 0.974651i $$-0.428176\pi$$
0.223732 + 0.974651i $$0.428176\pi$$
$$284$$ 0 0
$$285$$ −1.51430e7 1.87386e7i −0.654152 0.809471i
$$286$$ 0 0
$$287$$ 33533.8i 0.00141853i
$$288$$ 0 0
$$289$$ 4.06512e6 0.168415
$$290$$ 0 0
$$291$$ −5.90281e6 + 4.77019e6i −0.239541 + 0.193578i
$$292$$ 0 0
$$293$$ 2.78468e7i 1.10706i −0.832828 0.553532i $$-0.813280\pi$$
0.832828 0.553532i $$-0.186720\pi$$
$$294$$ 0 0
$$295$$ 5.54630e7 2.16042
$$296$$ 0 0
$$297$$ 596160. 301499.i 0.0227559 0.0115084i
$$298$$ 0 0
$$299$$ 3.02381e7i 1.13121i
$$300$$ 0 0
$$301$$ 12812.0 0.000469805
$$302$$ 0 0
$$303$$ −1.60433e7 1.98526e7i −0.576722 0.713657i
$$304$$ 0 0
$$305$$ 1.06178e7i 0.374227i
$$306$$ 0 0
$$307$$ −3.63254e7 −1.25544 −0.627718 0.778440i $$-0.716011\pi$$
−0.627718 + 0.778440i $$0.716011\pi$$
$$308$$ 0 0
$$309$$ 1.81802e7 1.46919e7i 0.616204 0.497968i
$$310$$ 0 0
$$311$$ 3.59921e7i 1.19654i 0.801296 + 0.598268i $$0.204144\pi$$
−0.801296 + 0.598268i $$0.795856\pi$$
$$312$$ 0 0
$$313$$ 4.01099e7 1.30803 0.654016 0.756480i $$-0.273083\pi$$
0.654016 + 0.756480i $$0.273083\pi$$
$$314$$ 0 0
$$315$$ 241920. + 51929.9i 0.00773998 + 0.00166145i
$$316$$ 0 0
$$317$$ 3.94377e7i 1.23804i −0.785377 0.619018i $$-0.787531\pi$$
0.785377 0.619018i $$-0.212469\pi$$
$$318$$ 0 0
$$319$$ −74880.0 −0.00230671
$$320$$ 0 0
$$321$$ −2.50163e7 3.09560e7i −0.756323 0.935902i
$$322$$ 0 0
$$323$$ 2.35570e7i 0.699058i
$$324$$ 0 0
$$325$$ −3.88662e7 −1.13220
$$326$$ 0 0
$$327$$ −1.36670e7 + 1.10446e7i −0.390868 + 0.315869i
$$328$$ 0 0
$$329$$ 359776.i 0.0101029i
$$330$$ 0 0
$$331$$ 2.78363e7 0.767586 0.383793 0.923419i $$-0.374618\pi$$
0.383793 + 0.923419i $$0.374618\pi$$
$$332$$ 0 0
$$333$$ −5.21087e6 + 2.42753e7i −0.141117 + 0.657403i
$$334$$ 0 0
$$335$$ 7.44495e7i 1.98028i
$$336$$ 0 0
$$337$$ −2.37897e7 −0.621582 −0.310791 0.950478i $$-0.600594\pi$$
−0.310791 + 0.950478i $$0.600594\pi$$
$$338$$ 0 0
$$339$$ −2.95995e7 3.66275e7i −0.759775 0.940174i
$$340$$ 0 0
$$341$$ 777184.i 0.0196002i
$$342$$ 0 0
$$343$$ 470588. 0.0116616
$$344$$ 0 0
$$345$$ −3.65299e7 + 2.95206e7i −0.889593 + 0.718900i
$$346$$ 0 0
$$347$$ 5.34078e7i 1.27825i 0.769103 + 0.639125i $$0.220703\pi$$
−0.769103 + 0.639125i $$0.779297\pi$$
$$348$$ 0 0
$$349$$ −4.71677e7 −1.10961 −0.554803 0.831982i $$-0.687206\pi$$
−0.554803 + 0.831982i $$0.687206\pi$$
$$350$$ 0 0
$$351$$ −2.62048e7 5.18154e7i −0.605983 1.19822i
$$352$$ 0 0
$$353$$ 1.75443e7i 0.398852i 0.979913 + 0.199426i $$0.0639078\pi$$
−0.979913 + 0.199426i $$0.936092\pi$$
$$354$$ 0 0
$$355$$ −1.15776e7 −0.258782
$$356$$ 0 0
$$357$$ 152064. + 188170.i 0.00334212 + 0.00413566i
$$358$$ 0 0
$$359$$ 6.18249e7i 1.33623i 0.744059 + 0.668113i $$0.232898\pi$$
−0.744059 + 0.668113i $$0.767102\pi$$
$$360$$ 0 0
$$361$$ −1.93993e7 −0.412349
$$362$$ 0 0
$$363$$ 3.71786e7 3.00448e7i 0.777272 0.628131i
$$364$$ 0 0
$$365$$ 1.23972e8i 2.54943i
$$366$$ 0 0
$$367$$ 3.40461e7 0.688761 0.344381 0.938830i $$-0.388089\pi$$
0.344381 + 0.938830i $$0.388089\pi$$
$$368$$ 0 0
$$369$$ 1.19508e7 + 2.56534e6i 0.237859 + 0.0510582i
$$370$$ 0 0
$$371$$ 385096.i 0.00754132i
$$372$$ 0 0
$$373$$ 5.15781e7 0.993892 0.496946 0.867782i $$-0.334455\pi$$
0.496946 + 0.867782i $$0.334455\pi$$
$$374$$ 0 0
$$375$$ −7.05600e6 8.73135e6i −0.133803 0.165572i
$$376$$ 0 0
$$377$$ 6.50821e6i 0.121461i
$$378$$ 0 0
$$379$$ 4.28828e7 0.787709 0.393855 0.919173i $$-0.371141\pi$$
0.393855 + 0.919173i $$0.371141\pi$$
$$380$$ 0 0
$$381$$ 4.78910e7 3.87018e7i 0.865923 0.699772i
$$382$$ 0 0
$$383$$ 1.51307e7i 0.269316i 0.990892 + 0.134658i $$0.0429936\pi$$
−0.990892 + 0.134658i $$0.957006\pi$$
$$384$$ 0 0
$$385$$ −11520.0 −0.000201869
$$386$$ 0 0
$$387$$ −980118. + 4.56596e6i −0.0169101 + 0.0787770i
$$388$$ 0 0
$$389$$ 6.15319e7i 1.04533i −0.852540 0.522663i $$-0.824939\pi$$
0.852540 0.522663i $$-0.175061\pi$$
$$390$$ 0 0
$$391$$ −4.59233e7 −0.768251
$$392$$ 0 0
$$393$$ 1.81918e7 + 2.25112e7i 0.299708 + 0.370870i
$$394$$ 0 0
$$395$$ 5.77953e7i 0.937780i
$$396$$ 0 0
$$397$$ 8.55816e7 1.36776 0.683878 0.729596i $$-0.260292\pi$$
0.683878 + 0.729596i $$0.260292\pi$$
$$398$$ 0 0
$$399$$ −220836. + 178462.i −0.00347657 + 0.00280949i
$$400$$ 0 0
$$401$$ 4.09739e7i 0.635439i −0.948185 0.317719i $$-0.897083\pi$$
0.948185 0.317719i $$-0.102917\pi$$
$$402$$ 0 0
$$403$$ −6.75491e7 −1.03206
$$404$$ 0 0
$$405$$ −3.70138e7 + 8.22433e7i −0.557183 + 1.23804i
$$406$$ 0 0
$$407$$ 1.15597e6i 0.0171460i
$$408$$ 0 0
$$409$$ 6.10556e7 0.892391 0.446196 0.894935i $$-0.352779\pi$$
0.446196 + 0.894935i $$0.352779\pi$$
$$410$$ 0 0
$$411$$ 4.72355e7 + 5.84509e7i 0.680366 + 0.841910i
$$412$$ 0 0
$$413$$ 653638.i 0.00927870i
$$414$$ 0 0
$$415$$ −8.42170e7 −1.17830
$$416$$ 0 0
$$417$$ 9.60529e7 7.76224e7i 1.32465 1.07048i
$$418$$ 0 0
$$419$$ 3.38860e7i 0.460657i 0.973113 + 0.230329i $$0.0739801\pi$$
−0.973113 + 0.230329i $$0.926020\pi$$
$$420$$ 0 0
$$421$$ 1.96156e7 0.262879 0.131439 0.991324i $$-0.458040\pi$$
0.131439 + 0.991324i $$0.458040\pi$$
$$422$$ 0 0
$$423$$ 1.28218e8 + 2.75229e7i 1.69405 + 0.363641i
$$424$$ 0 0
$$425$$ 5.90270e7i 0.768925i
$$426$$ 0 0
$$427$$ −125132. −0.00160725
$$428$$ 0 0
$$429$$ 1.69920e6 + 2.10265e6i 0.0215215 + 0.0266315i
$$430$$ 0 0
$$431$$ 4.01587e7i 0.501589i 0.968040 + 0.250795i $$0.0806919\pi$$
−0.968040 + 0.250795i $$0.919308\pi$$
$$432$$ 0 0
$$433$$ −845854. −0.0104191 −0.00520957 0.999986i $$-0.501658\pi$$
−0.00520957 + 0.999986i $$0.501658\pi$$
$$434$$ 0 0
$$435$$ 7.86240e6 6.35378e6i 0.0955185 0.0771906i
$$436$$ 0 0
$$437$$ 5.38957e7i 0.645817i
$$438$$ 0 0
$$439$$ 7.48204e7 0.884354 0.442177 0.896928i $$-0.354206\pi$$
0.442177 + 0.896928i $$0.354206\pi$$
$$440$$ 0 0
$$441$$ −1.79997e7 + 8.38531e7i −0.209869 + 0.977695i
$$442$$ 0 0
$$443$$ 1.25246e8i 1.44063i −0.693649 0.720313i $$-0.743998\pi$$
0.693649 0.720313i $$-0.256002\pi$$
$$444$$ 0 0
$$445$$ 6.56294e7 0.744764
$$446$$ 0 0
$$447$$ 7.56904e7 + 9.36621e7i 0.847458 + 1.04868i
$$448$$ 0 0
$$449$$ 1.12812e8i 1.24628i 0.782109 + 0.623142i $$0.214144\pi$$
−0.782109 + 0.623142i $$0.785856\pi$$
$$450$$ 0 0
$$451$$ −569088. −0.00620369
$$452$$ 0 0
$$453$$ 4.63700e7 3.74726e7i 0.498818 0.403106i
$$454$$ 0 0
$$455$$ 1.00126e6i 0.0106295i
$$456$$ 0 0
$$457$$ 1.57358e8 1.64870 0.824350 0.566081i $$-0.191541\pi$$
0.824350 + 0.566081i $$0.191541\pi$$
$$458$$ 0 0
$$459$$ −7.86931e7 + 3.97979e7i −0.813764 + 0.411549i
$$460$$ 0 0
$$461$$ 1.83107e8i 1.86897i 0.356002 + 0.934485i $$0.384140\pi$$
−0.356002 + 0.934485i $$0.615860\pi$$
$$462$$ 0 0
$$463$$ −1.77978e8 −1.79318 −0.896588 0.442866i $$-0.853962\pi$$
−0.896588 + 0.442866i $$0.853962\pi$$
$$464$$ 0 0
$$465$$ 6.59462e7 + 8.16043e7i 0.655890 + 0.811623i
$$466$$ 0 0
$$467$$ 9.35797e7i 0.918821i −0.888224 0.459410i $$-0.848061\pi$$
0.888224 0.459410i $$-0.151939\pi$$
$$468$$ 0 0
$$469$$ −877396. −0.00850505
$$470$$ 0 0
$$471$$ 2.70663e7 2.18728e7i 0.259039 0.209335i
$$472$$ 0 0
$$473$$ 217427.i 0.00205461i
$$474$$ 0 0
$$475$$ −6.92742e7 −0.646384
$$476$$ 0 0
$$477$$ −1.37241e8 2.94598e7i −1.26453 0.271441i
$$478$$ 0 0
$$479$$ 1.07662e8i 0.979617i −0.871830 0.489808i $$-0.837067\pi$$
0.871830 0.489808i $$-0.162933\pi$$
$$480$$ 0 0
$$481$$ −1.00471e8 −0.902830
$$482$$ 0 0
$$483$$ 347904. + 430509.i 0.00308758 + 0.00382068i
$$484$$ 0 0
$$485$$ 4.77019e7i 0.418129i
$$486$$ 0 0
$$487$$ 4.14432e6 0.0358811 0.0179406 0.999839i $$-0.494289\pi$$
0.0179406 + 0.999839i $$0.494289\pi$$
$$488$$ 0 0
$$489$$ 1.84782e7 1.49326e7i 0.158028 0.127706i
$$490$$ 0 0
$$491$$ 1.19347e8i 1.00824i 0.863633 + 0.504122i $$0.168184\pi$$
−0.863633 + 0.504122i $$0.831816\pi$$
$$492$$ 0 0
$$493$$ 9.88416e6 0.0824896
$$494$$ 0 0
$$495$$ 881280. 4.10552e6i 0.00726605 0.0338495i
$$496$$ 0 0
$$497$$ 136443.i 0.00111143i
$$498$$ 0 0
$$499$$ 1.17436e8 0.945144 0.472572 0.881292i $$-0.343326\pi$$
0.472572 + 0.881292i $$0.343326\pi$$
$$500$$ 0 0
$$501$$ 1.01273e8 + 1.25320e8i 0.805346 + 0.996565i
$$502$$ 0 0
$$503$$ 1.99753e8i 1.56960i −0.619747 0.784802i $$-0.712765\pi$$
0.619747 0.784802i $$-0.287235\pi$$
$$504$$ 0 0
$$505$$ −1.60433e8 −1.24572
$$506$$ 0 0
$$507$$ 8.13895e7 6.57727e7i 0.624517 0.504686i
$$508$$ 0 0
$$509$$ 1.12725e8i 0.854804i −0.904062 0.427402i $$-0.859429\pi$$
0.904062 0.427402i $$-0.140571\pi$$
$$510$$ 0 0
$$511$$ 1.46102e6 0.0109495
$$512$$ 0 0
$$513$$ −4.67068e7 9.23543e7i −0.345962 0.684077i
$$514$$ 0 0
$$515$$ 1.46919e8i 1.07561i
$$516$$ 0 0
$$517$$ −6.10560e6 −0.0441832
$$518$$ 0 0
$$519$$ 7.10842e6 + 8.79622e6i 0.0508476 + 0.0629207i
$$520$$ 0 0
$$521$$ 1.14581e8i 0.810215i −0.914269 0.405108i $$-0.867234\pi$$
0.914269 0.405108i $$-0.132766\pi$$
$$522$$ 0 0
$$523$$ −1.49806e8 −1.04719 −0.523594 0.851968i $$-0.675409\pi$$
−0.523594 + 0.851968i $$0.675409\pi$$
$$524$$ 0 0
$$525$$ 553350. 447174.i 0.00382404 0.00309029i
$$526$$ 0 0
$$527$$ 1.02588e8i 0.700916i
$$528$$ 0 0
$$529$$ 4.29689e7 0.290260
$$530$$ 0 0
$$531$$ 2.32945e8 + 5.00033e7i 1.55586 + 0.333976i
$$532$$ 0 0
$$533$$ 4.94624e7i 0.326658i
$$534$$ 0 0
$$535$$ −2.50163e8 −1.63366
$$536$$ 0 0
$$537$$ −5.12698e6 6.34431e6i −0.0331084 0.0409696i
$$538$$ 0 0
$$539$$ 3.99300e6i 0.0254996i
$$540$$ 0 0
$$541$$ 1.57017e8 0.991644 0.495822 0.868424i $$-0.334867\pi$$
0.495822 + 0.868424i $$0.334867\pi$$
$$542$$ 0 0
$$543$$ 1.36000e8 1.09904e8i 0.849452 0.686461i
$$544$$ 0 0
$$545$$ 1.10446e8i 0.682277i
$$546$$ 0 0
$$547$$ −2.79469e8 −1.70754 −0.853770 0.520650i $$-0.825690\pi$$
−0.853770 + 0.520650i $$0.825690\pi$$
$$548$$ 0 0
$$549$$ 9.57260e6 4.45948e7i 0.0578513 0.269505i
$$550$$ 0 0
$$551$$ 1.16001e7i 0.0693434i
$$552$$ 0 0
$$553$$ 681124. 0.00402764
$$554$$ 0 0
$$555$$ 9.80870e7 + 1.21377e8i 0.573763 + 0.709996i
$$556$$ 0 0
$$557$$ 1.50294e8i 0.869712i −0.900500 0.434856i $$-0.856799\pi$$
0.900500 0.434856i $$-0.143201\pi$$
$$558$$ 0 0
$$559$$ −1.88977e7 −0.108187
$$560$$ 0 0
$$561$$ 3.19334e6 2.58061e6i 0.0180866 0.0146162i
$$562$$ 0 0
$$563$$ 8.27836e7i 0.463894i 0.972728 + 0.231947i $$0.0745097\pi$$
−0.972728 + 0.231947i $$0.925490\pi$$
$$564$$ 0 0
$$565$$ −2.95995e8 −1.64111
$$566$$ 0 0
$$567$$ 969246. + 436211.i 0.00531722 + 0.00239303i
$$568$$ 0 0
$$569$$ 2.57230e8i 1.39632i −0.715942 0.698160i $$-0.754003\pi$$
0.715942 0.698160i $$-0.245997\pi$$
$$570$$ 0 0
$$571$$ 2.84039e7 0.152570 0.0762852 0.997086i $$-0.475694\pi$$
0.0762852 + 0.997086i $$0.475694\pi$$
$$572$$ 0 0
$$573$$ −8.52204e7 1.05455e8i −0.452980 0.560535i
$$574$$ 0 0
$$575$$ 1.35047e8i 0.710363i
$$576$$ 0 0
$$577$$ 6.52476e7 0.339654 0.169827 0.985474i $$-0.445679\pi$$
0.169827 + 0.985474i $$0.445679\pi$$
$$578$$ 0 0
$$579$$ 7.35195e7 5.94128e7i 0.378763 0.306086i
$$580$$ 0 0
$$581$$ 992506.i 0.00506063i
$$582$$ 0 0
$$583$$ 6.53530e6 0.0329807
$$584$$ 0 0
$$585$$ −3.56832e8 7.65966e7i −1.78236 0.382597i
$$586$$ 0 0
$$587$$ 6.66740e7i 0.329642i 0.986324 + 0.164821i $$0.0527046\pi$$
−0.986324 + 0.164821i $$0.947295\pi$$
$$588$$ 0 0
$$589$$ −1.20398e8 −0.589213
$$590$$ 0 0
$$591$$ 8.23789e7 + 1.01939e8i 0.399074 + 0.493829i
$$592$$ 0 0
$$593$$ 1.53324e8i 0.735271i −0.929970 0.367635i $$-0.880167\pi$$
0.929970 0.367635i $$-0.119833\pi$$
$$594$$ 0 0
$$595$$ 1.52064e6 0.00721897
$$596$$ 0 0
$$597$$ 1.99705e8 1.61386e8i 0.938568 0.758478i
$$598$$ 0 0
$$599$$ 2.18294e8i 1.01569i 0.861448 + 0.507846i $$0.169558\pi$$
−0.861448 + 0.507846i $$0.830442\pi$$
$$600$$ 0 0
$$601$$ 1.08478e8 0.499709 0.249854 0.968283i $$-0.419617\pi$$
0.249854 + 0.968283i $$0.419617\pi$$
$$602$$ 0 0
$$603$$ 6.71208e7 3.12688e8i 0.306129 1.42613i
$$604$$ 0 0
$$605$$ 3.00448e8i 1.35676i
$$606$$ 0 0
$$607$$ 3.43321e8 1.53509 0.767547 0.640993i $$-0.221477\pi$$
0.767547 + 0.640993i $$0.221477\pi$$
$$608$$ 0 0
$$609$$ −74880.0 92659.3i −0.000331523 0.000410239i
$$610$$ 0 0
$$611$$ 5.30669e8i 2.32649i
$$612$$ 0 0
$$613$$ −2.96325e8 −1.28643 −0.643216 0.765685i $$-0.722400\pi$$
−0.643216 + 0.765685i $$0.722400\pi$$
$$614$$ 0 0
$$615$$ 5.97542e7 4.82887e7i 0.256888 0.207597i
$$616$$ 0 0
$$617$$ 1.32676e8i 0.564853i 0.959289 + 0.282426i $$0.0911393\pi$$
−0.959289 + 0.282426i $$0.908861\pi$$
$$618$$ 0 0
$$619$$ −4.14773e8 −1.74879 −0.874397 0.485211i $$-0.838743\pi$$
−0.874397 + 0.485211i $$0.838743\pi$$
$$620$$ 0 0
$$621$$ −1.80040e8 + 9.10527e7i −0.751787 + 0.380205i
$$622$$ 0 0
$$623$$ 773450.i 0.00319866i
$$624$$ 0 0
$$625$$ −2.76419e8 −1.13221
$$626$$ 0 0
$$627$$ 3.02861e6 + 3.74771e6i 0.0122868 + 0.0152042i
$$628$$ 0 0
$$629$$ 1.52588e8i 0.613151i
$$630$$ 0 0
$$631$$ −3.03858e8 −1.20944 −0.604718 0.796440i $$-0.706714\pi$$
−0.604718 + 0.796440i $$0.706714\pi$$
$$632$$ 0 0
$$633$$ 1.48347e8 1.19882e8i 0.584881 0.472655i
$$634$$ 0 0
$$635$$ 3.87018e8i 1.51151i
$$636$$ 0 0
$$637$$ −3.47053e8 −1.34269
$$638$$ 0 0
$$639$$ −4.86259e7 1.04379e7i −0.186365 0.0400047i
$$640$$ 0 0
$$641$$ 1.81629e8i 0.689622i 0.938672 + 0.344811i $$0.112057\pi$$
−0.938672 + 0.344811i $$0.887943\pi$$
$$642$$ 0 0
$$643$$ 1.73811e8 0.653798 0.326899 0.945059i $$-0.393996\pi$$
0.326899 + 0.945059i $$0.393996\pi$$
$$644$$ 0 0
$$645$$ 1.84493e7 + 2.28298e7i 0.0687544 + 0.0850792i
$$646$$ 0 0
$$647$$ 2.43137e8i 0.897713i 0.893604 + 0.448856i $$0.148168\pi$$
−0.893604 + 0.448856i $$0.851832\pi$$
$$648$$ 0 0
$$649$$ −1.10926e7 −0.0405788
$$650$$ 0 0
$$651$$ 961716. 777184.i 0.00348581 0.00281696i
$$652$$ 0 0
$$653$$ 4.47562e7i 0.160736i −0.996765 0.0803681i $$-0.974390\pi$$
0.996765 0.0803681i $$-0.0256096\pi$$
$$654$$ 0 0
$$655$$ 1.81918e8 0.647369
$$656$$ 0 0
$$657$$ −1.11768e8 + 5.20681e8i −0.394114 + 1.83601i
$$658$$ 0 0
$$659$$ 1.13574e8i 0.396845i 0.980117 + 0.198423i $$0.0635819\pi$$
−0.980117 + 0.198423i $$0.936418\pi$$
$$660$$ 0 0
$$661$$ 9.93464e7 0.343992 0.171996 0.985098i $$-0.444978\pi$$
0.171996 + 0.985098i $$0.444978\pi$$
$$662$$ 0 0
$$663$$ −2.24294e8 2.77550e8i −0.769623 0.952359i
$$664$$ 0 0
$$665$$ 1.78462e6i 0.00606851i
$$666$$ 0 0
$$667$$ 2.26138e7 0.0762071
$$668$$ 0 0
$$669$$ −9.80472e7 + 7.92341e7i −0.327459 + 0.264627i
$$670$$ 0 0
$$671$$ 2.12356e6i 0.00702906i
$$672$$ 0 0
$$673$$ −2.79412e8 −0.916642 −0.458321 0.888787i $$-0.651549\pi$$
−0.458321 + 0.888787i $$0.651549\pi$$
$$674$$ 0 0
$$675$$ 1.17034e8 + 2.31413e8i 0.380539 + 0.752447i
$$676$$ 0 0
$$677$$ 4.09293e7i 0.131907i 0.997823 + 0.0659536i $$0.0210089\pi$$
−0.997823 + 0.0659536i $$0.978991\pi$$
$$678$$ 0 0
$$679$$ 562172. 0.00179581
$$680$$ 0 0
$$681$$ −3.33514e8 4.12702e8i −1.05602 1.30676i
$$682$$ 0 0
$$683$$ 3.74260e8i 1.17466i −0.809348 0.587329i $$-0.800180\pi$$
0.809348 0.587329i $$-0.199820\pi$$
$$684$$ 0 0
$$685$$ 4.72355e8 1.46959
$$686$$ 0 0
$$687$$ 9.41174e7 7.60584e7i 0.290268 0.234572i
$$688$$ 0 0
$$689$$ 5.68017e8i 1.73661i
$$690$$ 0 0
$$691$$ 1.15164e8 0.349047 0.174524 0.984653i $$-0.444161\pi$$
0.174524 + 0.984653i $$0.444161\pi$$
$$692$$ 0 0
$$693$$ −48384.0 10386.0i −0.000145379 3.12067e-5i
$$694$$ 0 0
$$695$$ 7.76224e8i 2.31224i
$$696$$ 0 0
$$697$$ 7.51196e7 0.221848
$$698$$ 0 0
$$699$$ −3.89111e7 4.81500e7i −0.113931 0.140982i
$$700$$ 0 0
$$701$$ 5.65717e7i 0.164227i 0.996623 + 0.0821137i $$0.0261671\pi$$
−0.996623 + 0.0821137i $$0.973833\pi$$
$$702$$ 0 0
$$703$$ −1.79077e8 −0.515435
$$704$$ 0 0
$$705$$ 6.41088e8 5.18077e8i 1.82958 1.47852i
$$706$$ 0 0
$$707$$ 1.89072e6i 0.00535020i
$$708$$ 0 0
$$709$$ 1.28652e8 0.360975 0.180488 0.983577i $$-0.442232\pi$$
0.180488 + 0.983577i $$0.442232\pi$$
$$710$$ 0 0
$$711$$ −5.21060e7 + 2.42740e8i −0.144970 + 0.675356i
$$712$$ 0 0
$$713$$ 2.34710e8i 0.647533i
$$714$$ 0 0
$$715$$ 1.69920e7 0.0464864
$$716$$ 0 0
$$717$$ −4.48980e7 5.55585e7i −0.121806 0.150728i
$$718$$ 0 0
$$719$$ 2.01053e8i 0.540908i −0.962733 0.270454i $$-0.912826\pi$$
0.962733 0.270454i $$-0.0871738\pi$$
$$720$$ 0 0
$$721$$ −1.73145e6 −0.00461960
$$722$$ 0 0
$$723$$ −1.46912e8 + 1.18723e8i −0.388725 + 0.314137i
$$724$$ 0 0
$$725$$ 2.90663e7i 0.0762739i
$$726$$ 0 0
$$727$$ −5.23208e8 −1.36167 −0.680833 0.732438i $$-0.738382\pi$$
−0.680833 + 0.732438i $$0.738382\pi$$
$$728$$ 0 0
$$729$$ −2.29605e8 + 3.12051e8i −0.592651 + 0.805459i
$$730$$ 0 0
$$731$$ 2.87003e7i 0.0734742i
$$732$$ 0 0
$$733$$ 6.57372e8 1.66917 0.834583 0.550882i $$-0.185709\pi$$
0.834583 + 0.550882i $$0.185709\pi$$
$$734$$ 0 0
$$735$$ 3.38818e8 + 4.19265e8i 0.853304 + 1.05591i
$$736$$ 0 0
$$737$$ 1.48899e7i 0.0371954i
$$738$$ 0 0
$$739$$ 3.50495e8 0.868458 0.434229 0.900803i $$-0.357021\pi$$
0.434229 + 0.900803i $$0.357021\pi$$
$$740$$ 0 0
$$741$$ 3.25733e8 2.63232e8i 0.800585 0.646970i
$$742$$ 0 0
$$743$$ 4.66667e8i 1.13773i −0.822429 0.568867i $$-0.807382\pi$$
0.822429 0.568867i $$-0.192618\pi$$
$$744$$ 0 0
$$745$$ 7.56904e8 1.83051
$$746$$ 0 0
$$747$$ −3.53711e8 7.59267e7i −0.848569 0.182152i
$$748$$ 0 0
$$749$$ 2.94819e6i 0.00701634i
$$750$$ 0 0
$$751$$ 3.36993e7 0.0795612 0.0397806 0.999208i $$-0.487334\pi$$
0.0397806 + 0.999208i $$0.487334\pi$$
$$752$$ 0 0
$$753$$ 4.83645e8 + 5.98480e8i 1.13277 + 1.40173i
$$754$$ 0 0
$$755$$ 3.74726e8i 0.870709i
$$756$$ 0 0
$$757$$ −2.98552e8 −0.688227 −0.344113 0.938928i $$-0.611820\pi$$
−0.344113 + 0.938928i $$0.611820\pi$$
$$758$$ 0 0
$$759$$ 7.30598e6 5.90413e6i 0.0167091 0.0135030i
$$760$$ 0 0
$$761$$ 3.98702e8i 0.904679i 0.891846 + 0.452340i $$0.149410\pi$$
−0.891846 + 0.452340i $$0.850590\pi$$
$$762$$ 0 0
$$763$$ 1.30162e6 0.00293029
$$764$$ 0 0
$$765$$ −1.16329e8 + 5.41928e8i −0.259839 + 1.21048i
$$766$$ 0 0
$$767$$ 9.64116e8i 2.13670i
$$768$$ 0 0
$$769$$ −5.17372e8 −1.13769 −0.568845 0.822444i $$-0.692610\pi$$
−0.568845 + 0.822444i $$0.692610\pi$$
$$770$$ 0 0
$$771$$ 3.17030e6 + 3.92305e6i 0.00691732 + 0.00855974i
$$772$$ 0 0
$$773$$ 1.83241e8i 0.396719i 0.980129 + 0.198360i $$0.0635614\pi$$
−0.980129 + 0.198360i $$0.936439\pi$$
$$774$$ 0 0
$$775$$ 3.01681e8 0.648102
$$776$$ 0 0
$$777$$ 1.43044e6 1.15597e6i 0.00304934 0.00246424i
$$778$$ 0 0
$$779$$ 8.81604e7i 0.186493i
$$780$$ 0 0
$$781$$ 2.31552e6 0.00486066
$$782$$ 0 0
$$783$$ 3.87504e7 1.95974e7i 0.0807218 0.0408239i
$$784$$ 0 0
$$785$$ &m